Subgroups — D₅₃×#3484 #28291967

Order 13568.

14438 conjugacy classes of subgroups.

The subgroup lattice has 1482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×H(5,𝔽₂)×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288351	C₂	1	1	yes	maximal, characteristic, complemented
4	#20288350	C₂	1	1	yes	maximal, characteristic, complemented
5	#20288349	C₂	1	2	yes	maximal, complemented
6	#20288348	C₂	1	2	yes	maximal, complemented
7	#20288347	C₂	1	4	yes	maximal, complemented
8	#20288346	C₂	1	1	yes	maximal, characteristic, complemented
9	#20288345	C₂	1	8	yes	maximal, complemented
10	#20288344	C₂	1	4	yes	maximal, complemented
11	#20288343	C₂	1	8	yes	maximal, complemented
12	#546×D₅₃	C₂	1	8	yes	maximal, complemented
13	D₄²×D₅₃	C₂	1	8	yes	maximal, complemented
14	#535×D₅₃	C₂	1	2	yes	maximal, complemented
15	#534×D₅₃	C₂	1	4	yes	maximal, complemented
16	#525×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₂×#120×D₅₃	C₂	1	4	yes	maximal, complemented
18	#518×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3484	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁵×D₅₃	C₂²	1	2	yes	complemented
21	C₂×#13133263	C₂²	1	4	yes	complemented
22	C₂×#13133263	C₂²	1	2	yes	complemented
23	C₂×#13133262	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13133262	C₂²	1	4	yes	complemented
25	C₂×#13133262	C₂²	1	4	yes	complemented
26	H(5,𝔽₂)×D₅₃	—	2	16	no	—
27	C₂×#41×D₅₃	C₂²	1	2	yes	complemented
28	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
29	C₂³×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
31	C₂²×D₄×D₅₃	—	2	16	no	—
32	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
33	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
34	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
35	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
37	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
38	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
39	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
40	C₂²×D₄×D₅₃	C₂²	1	2	yes	complemented
41	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
42	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
43	C₂³×C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
44	#16811270	C₂²	1	8	yes	complemented
45	#16811269	C₂²	1	8	yes	complemented
46	#16811268	C₂²	1	8	yes	complemented
47	#16811267	C₂²	1	8	yes	complemented
48	#16811266	C₂²	1	8	yes	complemented
49	#16811265	C₂²	1	16	yes	complemented
50	#16811264	C₂²	1	8	yes	complemented
51	#16811263	C₂²	1	16	yes	complemented
52	#16811262	C₂²	1	16	yes	complemented
53	#16811261	C₂²	1	8	yes	complemented
54	#16811260	C₂²	1	16	yes	complemented
55	D₄×D₂₁₂	C₂²	1	8	yes	complemented
56	D₄×D₂₁₂	C₂²	1	8	yes	complemented
57	#16811258	C₂²	1	8	yes	complemented
58	#16811257	C₂²	1	8	yes	complemented
59	#16811257	C₂²	1	16	yes	complemented
60	#16811257	C₂²	1	8	yes	complemented
61	D₄×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
62	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
63	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
64	#16811255	C₂²	1	16	yes	complemented
65	#16811255	C₂²	1	16	yes	complemented
66	#16811192	C₂²	1	2	yes	complemented
67	#16811191	C₂²	1	4	yes	complemented
68	#16811190	C₂²	1	2	yes	complemented
69	#16811189	C₂²	1	8	yes	complemented
70	#16811188	C₂²	1	8	yes	complemented
71	#16811187	C₂²	1	2	yes	complemented
72	#16811186	C₂²	1	4	yes	complemented
73	#16811185	C₂²	1	4	yes	complemented
74	#16811184	C₂²	1	8	yes	complemented
75	#16811184	C₂²	1	8	yes	complemented
76	#16811183	C₂²	1	8	yes	complemented
77	#16811183	C₂²	1	8	yes	complemented
78	#16811182	C₂²	1	4	yes	complemented
79	#16811182	C₂²	1	4	yes	complemented
80	#16811181	C₂²	1	16	yes	complemented
81	#127×D₅₃	C₂²	1	4	yes	complemented
82	#124×D₅₃	C₂²	1	4	yes	complemented
83	#16811136	C₂²	1	4	yes	complemented
84	#16811135	C₂²	1	2	yes	complemented
85	#16811134	C₂²	1	2	yes	complemented
86	#16811133	C₂²	1	4	yes	complemented
87	#16811132	C₂²	1	8	yes	complemented
88	#16811131	C₂²	1	4	yes	complemented
89	#16811130	C₂²	1	2	yes	complemented
90	#16811129	C₂²	1	4	yes	complemented
91	#123×D₅₃	C₂²	1	4	yes	complemented
92	#123×D₅₃	C₂²	1	8	yes	complemented
93	C₂²⋊Q₈×D₅₃	C₂²	1	4	yes	complemented
94	#121×D₅₃	C₂²	1	4	yes	complemented
95	#121×D₅₃	C₂²	1	16	yes	complemented
96	#121×D₅₃	C₂²	1	8	yes	complemented
97	C₂×#13133187	C₂²	1	8	yes	complemented
98	C₂×#13133187	C₂²	1	4	yes	complemented
99	C₂×#13133186	C₂²	1	4	yes	complemented
100	C₂×#13133185	C₂²	1	8	yes	complemented
101	C₂×#13133185	C₂²	1	4	yes	complemented
102	#120×D₅₃	C₂²	1	4	yes	complemented
103	#120×D₅₃	C₂²	1	8	yes	complemented
104	#120×D₅₃	C₂²	1	16	yes	complemented
105	#120×D₅₃	C₂²	1	8	yes	complemented
106	#120×D₅₃	C₂²	1	16	yes	complemented
107	#120×D₅₃	C₂²	1	8	yes	complemented
108	#120×D₅₃	C₂²	1	8	yes	complemented
109	#16811098	C₂²	1	1	yes	characteristic, complemented
110	#16811097	C₂²	1	2	yes	complemented
111	#16811096	C₂²	1	4	yes	complemented
112	#16811095	C₂²	1	8	yes	complemented
113	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
114	C₄×D₄×D₅₃	C₂²	1	8	yes	complemented
115	#117×D₅₃	C₂²	1	2	yes	complemented
116	C₂×C₂²⋊C₄×D₅₃	C₂²	1	4	yes	complemented
117	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
118	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	1	yes	characteristic, complemented
119	C₂³×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
120	C₅₃×#546	C₂²	1	8	yes	complemented
121	D₄²×C₅₃	C₂²	1	8	yes	complemented
122	C₅₃×#535	C₂²	1	2	yes	complemented
123	C₅₃×#534	C₂²	1	4	yes	complemented
124	C₅₃×#525	C₂²	1	2	yes	complemented
125	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
126	C₅₃×#518	C₂²	1	1	yes	characteristic, complemented
127	C₂⁴×D₅₃	—	2	16	no	—
128	C₂⁴×D₅₃	—	4	16	no	—
129	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
130	C₂⁴×D₅₃	C₂³	1	8	yes	—
131	C₂⁴×D₅₃	C₂³	1	2	yes	—
132	C₂⁴×D₅₃	C₂³	1	2	yes	—
133	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
134	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
135	C₂⁴×D₅₃	C₂³	1	8	yes	complemented
136	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
137	C₂⁴×D₅₃	C₂³	1	4	yes	complemented
138	#13133263	—	2	32	no	—
139	#13133263	—	2	16	no	—
140	#13133262	—	2	8	no	—
141	#13133262	—	2	32	no	—
142	#13133262	—	2	32	no	—
143	C₂×#11719949	C₂³	1	2	yes	complemented
144	C₂×#11719949	C₂³	1	4	yes	complemented
145	C₂×#11719945	C₂³	1	4	yes	complemented
146	C₂×#11719945	C₂³	1	4	yes	complemented
147	C₂×#11719945	C₂³	1	2	yes	complemented
148	C₂×#11719945	C₂³	1	8	yes	complemented
149	C₂×#11719947	C₂³	1	2	yes	complemented
150	C₂×#11719947	C₂³	1	4	yes	complemented
151	C₂×#11719947	C₂³	1	8	yes	complemented
152	C₂×#11719947	C₂³	1	4	yes	complemented
153	#41×D₅₃	—	2	32	no	—
154	#41×D₅₃	—	2	16	no	—
155	C₂×Q₈×D₅₃	C₂³	1	2	yes	complemented
156	C₂²×D₂₁₂	—	2	8	no	—
157	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
158	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
159	C₂²×D₂₁₂	C₂³	1	2	yes	complemented
160	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic, complemented
161	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
162	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
163	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
164	C₂²×C₂²⋊D₅₃	—	2	16	no	—
165	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
166	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
167	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
168	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	complemented
169	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
170	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
171	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
172	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
173	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
174	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
175	C₂×D₄×D₅₃	—	2	16	no	—
176	C₂×D₄×D₅₃	—	2	32	no	—
177	C₂×D₄×D₅₃	—	2	8	no	—
178	C₂×D₄×D₅₃	—	2	16	no	—
179	C₂×D₄×D₅₃	—	2	64	no	—
180	C₂×D₄×D₅₃	—	2	64	no	—
181	C₂×D₄×D₅₃	—	2	32	no	—
182	C₂×D₄×D₅₃	—	2	8	no	—
183	C₂×D₄×D₅₃	—	2	8	no	—
184	C₂×D₄×D₅₃	—	4	32	no	—
185	C₂×D₄×D₅₃	D₄	1	16	yes	complemented
186	C₂×D₄×D₅₃	C₂³	1	8	yes	—
187	C₂×D₄×D₅₃	C₂³	1	4	yes	—
188	C₂×D₄×D₅₃	C₂³	1	8	yes	—
189	C₂×D₄×D₅₃	C₂³	1	4	yes	—
190	C₂×D₄×D₅₃	C₂³	1	4	yes	—
191	C₂×D₄×D₅₃	C₂³	1	4	yes	—
192	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
193	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
194	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
195	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
196	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
197	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
198	C₂×D₄×D₅₃	C₂³	1	2	yes	complemented
199	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
200	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
201	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
202	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
203	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
204	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
205	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
206	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
207	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
208	C₂²×C₄×D₅₃	—	2	8	no	—
209	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
210	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
211	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
212	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
213	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic, complemented
214	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
215	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
216	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
217	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
218	#13133214	C₂³	1	4	yes	complemented
219	#13133213	C₂³	1	4	yes	complemented
220	#13133213	C₂³	1	16	yes	complemented
221	#13133213	C₂³	1	4	yes	complemented
222	#13133206	C₂³	1	4	yes	complemented
223	#13133205	C₂³	1	4	yes	complemented
224	#13133204	C₂³	1	4	yes	complemented
225	#13133203	C₂³	1	16	yes	complemented
226	#13133202	C₂³	1	8	yes	complemented
227	#13133202	C₂³	1	16	yes	complemented
228	#13133201	C₂³	1	4	yes	complemented
229	#13133201	C₂³	1	8	yes	complemented
230	#13133200	C₂³	1	4	yes	complemented
231	#13133200	C₂³	1	8	yes	complemented
232	#13133199	C₂³	1	8	yes	complemented
233	#13133199	C₂³	1	16	yes	complemented
234	#13133198	C₂³	1	4	yes	complemented
235	#13133198	C₂³	1	8	yes	complemented
236	#13133197	C₂³	1	4	yes	complemented
237	#13133196	C₂³	1	4	yes	complemented
238	#13133195	C₂³	1	8	yes	complemented
239	#13133194	C₂³	1	8	yes	complemented
240	#13133193	C₂³	1	4	yes	complemented
241	#13133192	C₂³	1	4	yes	complemented
242	#13133192	C₂³	1	16	yes	complemented
243	#13133192	C₂³	1	8	yes	complemented
244	#13133191	C₂³	1	8	yes	complemented
245	#13133191	C₂³	1	4	yes	complemented
246	#13133191	C₂³	1	16	yes	complemented
247	#13133190	C₂³	1	8	yes	complemented
248	#13133190	C₂³	1	16	yes	complemented
249	#13133190	C₂³	1	16	yes	complemented
250	#13133190	C₂³	1	16	yes	complemented
251	#13133189	C₂³	1	8	yes	complemented
252	#13133189	C₂³	1	16	yes	complemented
253	#13133189	C₂³	1	16	yes	complemented
254	#13133189	C₂³	1	16	yes	complemented
255	#13133188	C₂³	1	4	yes	complemented
256	#13133188	C₂³	1	16	yes	complemented
257	#13133188	C₂³	1	8	yes	complemented
258	#13133187	C₂³	1	4	yes	complemented
259	#13133187	C₂³	1	8	yes	complemented
260	#13133187	C₂³	1	16	yes	complemented
261	#13133187	C₂³	1	16	yes	complemented
262	#13133187	C₂³	1	16	yes	complemented
263	#13133187	C₂³	1	16	yes	complemented
264	#13133187	C₂³	1	16	yes	complemented
265	#13133187	C₂³	1	8	yes	complemented
266	#13133187	C₂³	1	8	yes	complemented
267	#13133186	C₂³	1	4	yes	complemented
268	#13133186	C₂³	1	16	yes	complemented
269	#13133186	C₂³	1	8	yes	complemented
270	#13133186	C₂³	1	8	yes	complemented
271	#13133185	C₂³	1	4	yes	complemented
272	#13133185	C₂³	1	8	yes	complemented
273	#13133185	C₂³	1	16	yes	complemented
274	#13133185	C₂³	1	16	yes	complemented
275	#13133185	C₂³	1	16	yes	complemented
276	#13133185	C₂³	1	16	yes	complemented
277	#13133185	C₂³	1	16	yes	complemented
278	#13133185	C₂³	1	8	yes	complemented
279	#13133185	C₂³	1	8	yes	complemented
280	C₄×D₂₁₂	C₂³	1	8	yes	complemented
281	C₄×D₂₁₂	C₂³	1	8	yes	complemented
282	D₄×Dic₅₃	C₂³	1	8	yes	complemented
283	D₄×Dic₅₃	C₂³	1	8	yes	complemented
284	#13133179	C₂³	1	8	yes	complemented
285	#13133179	C₂³	1	8	yes	complemented
286	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
287	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
288	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
289	#13133177	C₂³	1	8	yes	complemented
290	#13133177	C₂³	1	8	yes	complemented
291	#13133177	C₂³	1	16	yes	complemented
292	#13133176	C₂³	1	2	yes	complemented
293	#13133175	C₂³	1	4	yes	complemented
294	#13133174	C₂³	1	4	yes	complemented
295	#13133173	C₂³	1	4	yes	complemented
296	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
297	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
298	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
299	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
300	C₂×#11719921	C₂³	1	8	yes	complemented
301	C₂×#11719921	C₂³	1	8	yes	complemented
302	C₂×#11719921	C₂³	1	8	yes	complemented
303	C₂²⋊C₄×D₅₃	C₂³	1	4	yes	—
304	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
305	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
306	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
307	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
308	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
309	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
310	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
311	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
312	C₄²×D₅₃	C₂³	1	4	yes	complemented
313	C₂⁵×C₅₃	C₂³	1	2	yes	complemented
314	H(5,𝔽₂)×C₅₃	—	2	8	no	—
315	C₂×#41×C₅₃	C₂³	1	2	yes	complemented
316	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
317	C₂²×D₄×C₅₃	—	2	8	no	—
318	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
319	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
320	C₂²×D₄×C₅₃	C₂³	1	2	yes	complemented
321	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
322	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
323	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
324	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
325	C₂³×C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
326	#127×C₅₃	C₂³	1	4	yes	complemented
327	#124×C₅₃	C₂³	1	4	yes	complemented
328	#123×C₅₃	C₂³	1	4	yes	complemented
329	#123×C₅₃	C₂³	1	8	yes	complemented
330	C₂²⋊Q₈×C₅₃	C₂³	1	4	yes	complemented
331	#121×C₅₃	C₂³	1	4	yes	complemented
332	#121×C₅₃	C₂³	1	8	yes	complemented
333	#121×C₅₃	C₂³	1	16	yes	complemented
334	#120×C₅₃	C₂³	1	4	yes	complemented
335	#120×C₅₃	C₂³	1	8	yes	complemented
336	#120×C₅₃	C₂³	1	16	yes	complemented
337	#120×C₅₃	C₂³	1	8	yes	complemented
338	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
339	C₄×D₄×C₅₃	C₂³	1	8	yes	complemented
340	#117×C₅₃	C₂³	1	2	yes	complemented
341	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
342	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
343	C₂⁴×C₅₃	—	2	8	no	—
344	C₂⁴×C₅₃	—	4	8	no	—
345	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
346	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
347	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
348	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
349	C₂⁴×C₅₃	C₂⁴	1	4	yes	complemented
350	C₂³×D₅₃	—	2	4	no	—
351	C₂³×D₅₃	—	2	8	no	—
352	C₂³×D₅₃	—	2	8	no	—
353	C₂³×D₅₃	—	2	32	no	—
354	C₂³×D₅₃	—	2	8	no	—
355	C₂³×D₅₃	—	2	8	no	—
356	C₂³×D₅₃	—	2	32	no	—
357	C₂³×D₅₃	—	2	8	no	—
358	C₂³×D₅₃	—	2	32	no	—
359	C₂³×D₅₃	—	2	16	no	—
360	C₂³×D₅₃	—	4	8	no	—
361	C₂³×D₅₃	—	4	16	no	—
362	C₂³×D₅₃	—	4	8	no	—
363	C₂³×D₅₃	—	4	8	no	—
364	C₂³×D₅₃	—	4	16	no	—
365	C₂³×D₅₃	—	4	8	no	—
366	C₂³×D₅₃	—	4	16	no	—
367	C₂³×D₅₃	—	4	16	no	—
368	C₂³×D₅₃	—	4	8	no	—
369	C₂³×D₅₃	—	4	128	no	—
370	C₂³×D₅₃	C₂×D₄	1	16	yes	complemented
371	C₂³×D₅₃	C₂⁴	1	4	yes	—
372	C₂³×D₅₃	C₂⁴	1	4	yes	—
373	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
374	C₂³×D₅₃	C₂⁴	1	2	yes	—
375	C₂³×D₅₃	C₂⁴	1	8	yes	—
376	C₂³×D₅₃	C₂⁴	1	8	yes	—
377	C₂³×D₅₃	C₂⁴	1	8	yes	—
378	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
379	C₂³×D₅₃	C₂⁴	1	4	yes	—
380	C₂³×D₅₃	C₂⁴	1	2	yes	—
381	C₂³×D₅₃	C₂⁴	1	4	yes	—
382	C₂³×D₅₃	C₂⁴	1	2	yes	—
383	C₂³×D₅₃	C₂⁴	1	2	yes	—
384	C₂³×D₅₃	C₂⁴	1	4	yes	—
385	C₂³×D₅₃	C₂⁴	1	8	yes	complemented
386	C₂³×D₅₃	C₂⁴	1	4	yes	complemented
387	#41×C₅₃	—	2	16	no	—
388	#41×C₅₃	—	2	8	no	—
389	C₂×Q₈×C₅₃	C₂⁴	1	2	yes	complemented
390	C₂×D₄×C₅₃	—	2	8	no	—
391	C₂×D₄×C₅₃	—	2	16	no	—
392	C₂×D₄×C₅₃	—	2	32	no	—
393	C₂×D₄×C₅₃	—	2	16	no	—
394	C₂×D₄×C₅₃	—	2	4	no	—
395	C₂×D₄×C₅₃	—	4	16	no	—
396	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	complemented
397	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
398	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
399	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
400	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
401	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
402	C₂×D₄×C₅₃	C₂⁴	1	8	yes	complemented
403	C₂×D₄×C₅₃	C₂⁴	1	2	yes	complemented
404	C₂×D₄×C₅₃	C₂⁴	1	16	yes	complemented
405	C₂²×C₄×C₅₃	—	2	4	no	—
406	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
407	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
408	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
409	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	complemented
410	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	complemented
411	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	complemented
412	C₂×C₂²⋊D₅₃	—	2	8	no	—
413	C₂×C₂²⋊D₅₃	—	2	16	no	—
414	C₂×C₂²⋊D₅₃	—	2	8	no	—
415	C₂×C₂²⋊D₅₃	—	2	16	no	—
416	C₂×C₂²⋊D₅₃	—	2	64	no	—
417	C₂×C₂²⋊D₅₃	—	2	32	no	—
418	C₂×C₂²⋊D₅₃	—	2	8	no	—
419	C₂×C₂²⋊D₅₃	—	4	16	no	—
420	C₂×C₂²⋊D₅₃	—	4	16	no	—
421	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
422	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
423	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
424	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
425	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
426	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
427	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
428	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
429	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
430	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
431	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	complemented
432	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	complemented
433	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
434	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	complemented
435	C₂²×Dic₅₃	—	2	4	no	—
436	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
437	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
438	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
439	C₂²×Dic₅₃	C₂⁴	1	4	yes	complemented
440	C₂²×Dic₅₃	C₂⁴	1	4	yes	complemented
441	C₂²×Dic₅₃	C₂⁴	1	8	yes	complemented
442	#11719949	—	2	16	no	—
443	#11719949	—	2	8	no	—
444	Q₈×D₅₃	—	2	8	no	—
445	#11719947	—	2	16	no	—
446	#11719947	—	2	32	no	—
447	#11719947	—	2	16	no	—
448	#11719947	—	2	8	no	—
449	D₄×D₅₃	—	2	32	no	—
450	D₄×D₅₃	—	2	16	no	—
451	D₄×D₅₃	—	2	32	no	—
452	D₄×D₅₃	—	2	32	no	—
453	D₄×D₅₃	—	2	32	no	—
454	D₄×D₅₃	—	2	32	no	—
455	D₄×D₅₃	—	2	32	no	—
456	D₄×D₅₃	—	2	32	no	—
457	D₄×D₅₃	—	2	16	no	—
458	D₄×D₅₃	—	2	64	no	—
459	D₄×D₅₃	—	2	32	no	—
460	D₄×D₅₃	—	2	32	no	—
461	D₄×D₅₃	—	2	16	no	—
462	D₄×D₅₃	—	2	16	no	—
463	D₄×D₅₃	—	2	8	no	—
464	D₄×D₅₃	—	2	16	no	—
465	D₄×D₅₃	—	4	32	no	—
466	D₄×D₅₃	—	4	32	no	—
467	D₄×D₅₃	—	4	32	no	—
468	D₄×D₅₃	C₂×D₄	1	32	yes	complemented
469	D₄×D₅₃	C₂×D₄	1	32	yes	complemented
470	#11719945	—	2	8	no	—
471	#11719945	—	2	32	no	—
472	#11719945	—	2	16	no	—
473	#11719945	—	2	16	no	—
474	C₂×D₂₁₂	—	2	8	no	—
475	C₂×D₂₁₂	—	2	16	no	—
476	C₂×D₂₁₂	—	2	4	no	—
477	C₂×D₂₁₂	—	2	32	no	—
478	C₂×D₂₁₂	—	2	16	no	—
479	C₂×D₂₁₂	—	4	16	no	—
480	C₂×D₂₁₂	C₂×D₄	1	8	yes	complemented
481	C₂×D₂₁₂	C₂⁴	1	8	yes	—
482	C₂×D₂₁₂	C₂⁴	1	4	yes	—
483	C₂×D₂₁₂	C₂⁴	1	8	yes	—
484	C₂×D₂₁₂	C₂⁴	1	4	yes	—
485	C₂×D₂₁₂	C₂⁴	1	4	yes	—
486	C₂×D₂₁₂	C₂⁴	1	8	yes	complemented
487	C₂×D₂₁₂	C₂⁴	1	2	yes	complemented
488	C₂×D₂₁₂	C₂⁴	1	16	yes	complemented
489	C₂×C₄×D₅₃	—	2	4	no	—
490	C₂×C₄×D₅₃	—	2	16	no	—
491	C₂×C₄×D₅₃	—	2	4	no	—
492	C₂×C₄×D₅₃	—	2	4	no	—
493	C₂×C₄×D₅₃	—	2	16	no	—
494	C₂×C₄×D₅₃	—	2	16	no	—
495	C₂×C₄×D₅₃	—	2	16	no	—
496	C₂×C₄×D₅₃	—	4	16	no	—
497	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	complemented
498	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
499	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
500	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
501	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
502	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
503	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
504	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
505	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
506	C₂×C₄×D₅₃	C₂⁴	1	8	yes	complemented
507	C₂×C₄×D₅₃	C₂⁴	1	4	yes	complemented
508	C₂×C₄×D₅₃	C₂⁴	1	4	yes	complemented
509	C₂×C₄×D₅₃	C₂⁴	1	16	yes	complemented
510	C₂×Dic₁₀₆	C₂⁴	1	4	yes	complemented
511	C₂×Dic₁₀₆	C₂⁴	1	2	yes	complemented
512	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	complemented
513	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
514	C₂²⋊C₄×C₅₃	C₂⁴	1	4	yes	—
515	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
516	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
517	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	complemented
518	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	complemented
519	C₄²×C₅₃	C₂⁴	1	4	yes	complemented
520	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
521	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
522	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
523	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	complemented
524	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	complemented
525	#11719921	C₂⁴	1	8	yes	—
526	#11719921	C₂⁴	1	8	yes	—
527	#11719921	C₂⁴	1	8	yes	—
528	#11719921	C₂⁴	1	16	yes	complemented
529	#11719921	C₂⁴	1	16	yes	complemented
530	#11719921	C₂⁴	1	16	yes	complemented
531	#11719921	C₂⁴	1	8	yes	complemented
532	#11719921	C₂⁴	1	8	yes	complemented
533	C₄⋊Dic₅₃	C₂⁴	1	4	yes	complemented
534	C₄⋊Dic₅₃	C₂⁴	1	8	yes	complemented
535	#11719919	C₂⁴	1	8	yes	complemented
536	#11719919	C₂⁴	1	8	yes	complemented
537	#11719919	C₂⁴	1	8	yes	complemented
538	C₄×Dic₅₃	C₂⁴	1	8	yes	complemented
539	C₄×Dic₅₃	C₂⁴	1	4	yes	complemented
540	C₂³×C₅₃	—	2	2	no	—
541	C₂³×C₅₃	—	2	4	no	—
542	C₂³×C₅₃	—	2	16	no	—
543	C₂³×C₅₃	—	2	4	no	—
544	C₂³×C₅₃	—	2	16	no	—
545	C₂³×C₅₃	—	2	8	no	—
546	C₂³×C₅₃	—	4	4	no	—
547	C₂³×C₅₃	—	4	8	no	—
548	C₂³×C₅₃	—	4	4	no	—
549	C₂³×C₅₃	—	4	8	no	—
550	C₂³×C₅₃	—	4	32	no	—
551	C₂³×C₅₃	C₂²×D₄	1	8	yes	complemented
552	C₂³×C₅₃	C₂⁵	1	4	yes	—
553	C₂³×C₅₃	C₂⁵	1	4	yes	—
554	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
555	C₂³×C₅₃	C₂⁵	1	4	yes	—
556	C₂³×C₅₃	C₂⁵	1	2	yes	—
557	C₂²×D₅₃	—	2	32	no	—
558	C₂²×D₅₃	—	2	2	no	—
559	C₂²×D₅₃	—	2	4	no	—
560	C₂²×D₅₃	—	2	4	no	—
561	C₂²×D₅₃	—	2	4	no	—
562	C₂²×D₅₃	—	2	16	no	—
563	C₂²×D₅₃	—	2	4	no	—
564	C₂²×D₅₃	—	2	4	no	—
565	C₂²×D₅₃	—	2	4	no	—
566	C₂²×D₅₃	—	2	4	no	—
567	C₂²×D₅₃	—	2	4	no	—
568	C₂²×D₅₃	—	2	16	no	—
569	C₂²×D₅₃	—	2	16	no	—
570	C₂²×D₅₃	—	2	8	no	—
571	C₂²×D₅₃	—	2	8	no	—
572	C₂²×D₅₃	—	2	16	no	—
573	C₂²×D₅₃	—	2	16	no	—
574	C₂²×D₅₃	—	2	8	no	—
575	C₂²×D₅₃	—	2	8	no	—
576	C₂²×D₅₃	—	2	16	no	—
577	C₂²×D₅₃	—	2	16	no	—
578	C₂²×D₅₃	—	2	16	no	—
579	C₂²×D₅₃	—	2	16	no	—
580	C₂²×D₅₃	—	2	16	no	—
581	C₂²×D₅₃	—	4	32	no	—
582	C₂²×D₅₃	—	4	4	no	—
583	C₂²×D₅₃	—	4	8	no	—
584	C₂²×D₅₃	—	4	8	no	—
585	C₂²×D₅₃	—	4	8	no	—
586	C₂²×D₅₃	—	4	8	no	—
587	C₂²×D₅₃	—	4	8	no	—
588	C₂²×D₅₃	—	4	4	no	—
589	C₂²×D₅₃	—	4	128	no	—
590	C₂²×D₅₃	—	4	8	no	—
591	C₂²×D₅₃	—	4	16	no	—
592	C₂²×D₅₃	—	4	32	no	—
593	C₂²×D₅₃	—	4	128	no	—
594	C₂²×D₅₃	—	4	32	no	—
595	C₂²×D₅₃	—	4	32	no	—
596	C₂²×D₅₃	—	4	32	no	—
597	C₂²×D₅₃	—	8	32	no	—
598	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
599	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
600	C₂²×D₅₃	C₂²×D₄	1	8	yes	complemented
601	C₂²×D₅₃	C₂²×D₄	1	16	yes	complemented
602	C₂²×D₅₃	H(5,𝔽₂)	1	8	yes	complemented
603	C₂²×D₅₃	C₂⁵	1	4	yes	—
604	C₂²×D₅₃	C₂⁵	1	4	yes	—
605	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
606	C₂²×D₅₃	C₂⁵	1	4	yes	—
607	C₂²×D₅₃	C₂⁵	1	2	yes	—
608	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
609	Q₈×C₅₃	—	2	4	no	—
610	D₄×C₅₃	—	2	16	no	—
611	D₄×C₅₃	—	2	8	no	—
612	D₄×C₅₃	—	2	16	no	—
613	D₄×C₅₃	—	2	16	no	—
614	D₄×C₅₃	—	2	8	no	—
615	D₄×C₅₃	—	2	4	no	—
616	D₄×C₅₃	—	4	16	no	—
617	D₄×C₅₃	C₂²×D₄	1	16	yes	complemented
618	C₂×C₄×C₅₃	—	2	2	no	—
619	C₂×C₄×C₅₃	—	2	8	no	—
620	C₂×C₄×C₅₃	—	2	8	no	—
621	C₂×C₄×C₅₃	—	2	8	no	—
622	C₂×C₄×C₅₃	—	4	8	no	—
623	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	complemented
624	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
625	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
626	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
627	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
628	C₂²⋊D₅₃	—	2	8	no	—
629	C₂²⋊D₅₃	—	2	16	no	—
630	C₂²⋊D₅₃	—	2	16	no	—
631	C₂²⋊D₅₃	—	2	16	no	—
632	C₂²⋊D₅₃	—	2	8	no	—
633	C₂²⋊D₅₃	—	2	16	no	—
634	C₂²⋊D₅₃	—	2	16	no	—
635	C₂²⋊D₅₃	—	2	16	no	—
636	C₂²⋊D₅₃	—	2	8	no	—
637	C₂²⋊D₅₃	—	2	16	no	—
638	C₂²⋊D₅₃	—	4	16	no	—
639	C₂²⋊D₅₃	—	4	16	no	—
640	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	complemented
641	C₂×Dic₅₃	—	2	2	no	—
642	C₂×Dic₅₃	—	2	8	no	—
643	C₂×Dic₅₃	—	2	8	no	—
644	C₂×Dic₅₃	—	2	8	no	—
645	C₂×Dic₅₃	—	4	8	no	—
646	C₂×Dic₅₃	C₂²×D₄	1	4	yes	complemented
647	C₂×Dic₅₃	C₂⁵	1	4	yes	—
648	C₂×Dic₅₃	C₂⁵	1	2	yes	—
649	C₂×Dic₅₃	C₂⁵	1	8	yes	—
650	C₂×Dic₅₃	C₂⁵	1	2	yes	—
651	D₂₁₂	—	2	16	no	—
652	D₂₁₂	—	2	8	no	—
653	D₂₁₂	—	2	16	no	—
654	D₂₁₂	—	2	16	no	—
655	D₂₁₂	—	2	8	no	—
656	D₂₁₂	—	2	4	no	—
657	D₂₁₂	—	4	16	no	—
658	D₂₁₂	C₂²×D₄	1	16	yes	complemented
659	C₄×D₅₃	—	2	4	no	—
660	C₄×D₅₃	—	2	4	no	—
661	C₄×D₅₃	—	2	8	no	—
662	C₄×D₅₃	—	2	16	no	—
663	C₄×D₅₃	—	2	16	no	—
664	C₄×D₅₃	—	2	8	no	—
665	C₄×D₅₃	—	2	8	no	—
666	C₄×D₅₃	—	2	8	no	—
667	C₄×D₅₃	—	2	8	no	—
668	C₄×D₅₃	—	4	16	no	—
669	C₄×D₅₃	C₂²×D₄	1	8	yes	—
670	C₄×D₅₃	C₂²×D₄	1	8	yes	complemented
671	Dic₁₀₆	—	2	4	no	—
672	Dic₁₀₆	—	2	8	no	—
673	C₂×#3484	—	53	1	no	maximal, Sylow
674	C₂²×C₅₃	—	2	8	no	—
675	C₂²×C₅₃	—	2	2	no	—
676	C₂²×C₅₃	—	2	8	no	—
677	C₂²×C₅₃	—	2	2	no	—
678	C₂²×C₅₃	—	2	2	no	—
679	C₂²×C₅₃	—	2	4	no	—
680	C₂²×C₅₃	—	2	4	no	—
681	C₂²×C₅₃	—	2	8	no	—
682	C₂²×C₅₃	—	2	8	no	—
683	C₂²×C₅₃	—	4	8	no	—
684	C₂²×C₅₃	—	4	32	no	—
685	C₂²×C₅₃	—	4	8	no	—
686	C₂²×C₅₃	—	8	8	no	—
687	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
688	C₂²×C₅₃	C₂³×D₄	1	8	yes	—
689	C₂²×C₅₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
690	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
691	C₂×D₅₃	—	2	16	no	—
692	C₂×D₅₃	—	2	8	no	—
693	C₂×D₅₃	—	2	2	no	—
694	C₂×D₅₃	—	2	8	no	—
695	C₂×D₅₃	—	2	2	no	—
696	C₂×D₅₃	—	2	2	no	—
697	C₂×D₅₃	—	2	8	no	—
698	C₂×D₅₃	—	2	16	no	—
699	C₂×D₅₃	—	2	32	no	—
700	C₂×D₅₃	—	2	4	no	—
701	C₂×D₅₃	—	2	4	no	—
702	C₂×D₅₃	—	2	8	no	—
703	C₂×D₅₃	—	2	8	no	—
704	C₂×D₅₃	—	4	16	no	—
705	C₂×D₅₃	—	4	8	no	—
706	C₂×D₅₃	—	4	32	no	—
707	C₂×D₅₃	—	4	32	no	—
708	C₂×D₅₃	—	4	32	no	—
709	C₂×D₅₃	—	4	16	no	—
710	C₂×D₅₃	—	4	8	no	—
711	C₂×D₅₃	—	4	16	no	—
712	C₂×D₅₃	—	4	16	no	—
713	C₂×D₅₃	—	8	16	no	—
714	C₂×D₅₃	—	8	8	no	—
715	C₂×D₅₃	C₂³×D₄	1	2	yes	—
716	C₂×D₅₃	C₂³×D₄	1	8	yes	—
717	C₂×D₅₃	C₂³×D₄	1	2	yes	—
718	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	—
719	C₂×D₅₃	C₂×H(5,𝔽₂)	1	4	yes	complemented
720	C₄×C₅₃	—	2	4	no	—
721	C₄×C₅₃	—	2	2	no	—
722	C₄×C₅₃	—	2	8	no	—
723	C₄×C₅₃	C₂³×D₄	1	4	yes	—
724	Dic₅₃	—	2	4	no	—
725	Dic₅₃	—	2	2	no	—
726	Dic₅₃	—	2	8	no	—
727	Dic₅₃	C₂³×D₄	1	4	yes	—
728	C₂²×H(5,𝔽₂)	—	53	1	no	—
729	C₂⁴×D₄	—	53	1	no	—
730	#3484	—	53	1	no	—
731	#3484	—	53	1	no	—
732	#3484	—	53	8	no	—
733	#3484	—	53	8	no	—
734	#3484	—	53	2	no	—
735	#3484	—	53	4	no	—
736	#3484	—	53	2	no	—
737	#3484	—	53	4	no	—
738	#3484	—	53	1	no	—
739	#3484	D₅₃	1	1	yes	characteristic, direct product factor
740	C₂×#546	—	53	8	no	—
741	C₂×D₄²	—	53	8	no	—
742	C₂×#535	—	53	2	no	—
743	C₂×#534	—	53	4	no	—
744	C₂×#525	—	53	2	no	—
745	C₂²×#120	—	53	4	no	—
746	C₂×#518	—	53	1	no	—
747	C₂×C₅₃	—	2	2	no	—
748	C₂×C₅₃	—	2	4	no	—
749	C₂×C₅₃	—	2	8	no	—
750	C₂×C₅₃	—	4	4	no	—
751	C₂×C₅₃	—	4	4	no	—
752	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
753	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	2	yes	—
754	D₅₃	—	2	2	no	—
755	D₅₃	—	2	4	no	—
756	D₅₃	—	2	8	no	—
757	D₅₃	—	4	4	no	—
758	D₅₃	—	4	4	no	—
759	D₅₃	#3484	1	4	yes	direct product factor
760	C₂⁶	—	53	2	no	—
761	C₂×H(5,𝔽₂)	—	53	4	no	—
762	C₂×H(5,𝔽₂)	—	53	2	no	—
763	C₂×H(5,𝔽₂)	—	53	1	no	—
764	C₂×H(5,𝔽₂)	—	53	4	no	—
765	C₂×H(5,𝔽₂)	—	53	4	no	—
766	C₂×H(5,𝔽₂)	—	106	16	no	—
767	C₂×H(5,𝔽₂)	C₂×D₅₃	1	1	yes	characteristic, complemented
768	C₂²×#41	—	53	2	no	—
769	C₂²×#41	—	53	4	no	—
770	C₂³×D₄	—	53	1	no	—
771	C₂³×D₄	—	53	2	no	—
772	C₂³×D₄	—	53	1	no	—
773	C₂³×D₄	—	53	2	no	—
774	C₂³×D₄	—	53	1	no	—
775	C₂³×D₄	—	53	8	no	—
776	C₂³×D₄	—	53	2	no	—
777	C₂³×D₄	—	53	8	no	—
778	C₂³×D₄	—	53	1	no	—
779	C₂³×D₄	—	53	4	no	—
780	C₂³×D₄	—	53	4	no	—
781	C₂³×D₄	—	53	8	no	—
782	C₂³×D₄	—	53	1	no	—
783	C₂³×D₄	—	106	16	no	—
784	C₂³×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
785	C₂⁴×C₄	—	53	1	no	—
786	#546	—	53	8	no	—
787	#546	—	53	8	no	—
788	#546	—	53	8	no	—
789	#546	—	53	16	no	—
790	#546	—	53	8	no	—
791	#546	—	53	8	no	—
792	#546	—	53	16	no	—
793	#546	—	53	16	no	—
794	#546	—	53	8	no	—
795	#546	—	53	8	no	—
796	#546	—	53	16	no	—
797	#546	C₂×D₅₃	1	8	yes	complemented
798	D₄²	—	53	8	no	—
799	D₄²	—	53	8	no	—
800	D₄²	—	53	16	no	—
801	D₄²	—	53	8	no	—
802	D₄²	—	53	8	no	—
803	D₄²	—	53	16	no	—
804	D₄²	—	53	8	no	—
805	D₄²	—	53	16	no	—
806	D₄²	—	53	16	no	—
807	D₄²	—	53	8	no	—
808	D₄²	—	53	8	no	—
809	D₄²	C₂×D₅₃	1	8	yes	complemented
810	#535	—	53	2	no	—
811	#535	—	53	2	no	—
812	#535	—	53	4	no	—
813	#535	—	53	4	no	—
814	#535	—	53	8	no	—
815	#535	—	53	8	no	—
816	#535	—	53	2	no	—
817	#535	C₂×D₅₃	1	2	yes	complemented
818	#534	—	53	4	no	—
819	#534	—	53	4	no	—
820	#534	—	53	8	no	—
821	#534	—	53	8	no	—
822	#534	—	53	16	no	—
823	#534	—	53	8	no	—
824	#534	—	53	8	no	—
825	#534	—	53	4	no	—
826	#534	C₂×D₅₃	1	4	yes	complemented
827	C₂×#127	—	53	4	no	—
828	C₂×#124	—	53	4	no	—
829	#525	—	53	2	no	—
830	#525	—	53	2	no	—
831	#525	—	53	4	no	—
832	#525	—	53	4	no	—
833	#525	—	53	4	no	—
834	#525	—	53	4	no	—
835	#525	—	53	8	no	—
836	#525	—	53	2	no	—
837	#525	C₂×D₅₃	1	2	yes	complemented
838	C₂×#123	—	53	4	no	—
839	C₂×#123	—	53	8	no	—
840	C₂×C₂²⋊Q₈	—	53	4	no	—
841	C₂×#121	—	53	4	no	—
842	C₂×#121	—	53	16	no	—
843	C₂×#121	—	53	8	no	—
844	C₂×#120	—	53	4	no	—
845	C₂×#120	—	53	4	no	—
846	C₂×#120	—	53	8	no	—
847	C₂×#120	—	53	4	no	—
848	C₂×#120	—	53	8	no	—
849	C₂×#120	—	53	16	no	—
850	C₂×#120	—	53	8	no	—
851	C₂×#120	—	53	8	no	—
852	C₂×#120	—	53	16	no	—
853	C₂×#120	—	53	8	no	—
854	C₂×#120	—	53	8	no	—
855	C₂×#120	—	53	4	no	—
856	C₂×#120	C₂×D₅₃	1	4	yes	complemented
857	#518	—	53	1	no	—
858	#518	—	53	8	no	—
859	#518	—	53	2	no	—
860	#518	—	53	4	no	—
861	#518	C₂×D₅₃	1	1	yes	characteristic, complemented
862	C₂×C₄×D₄	—	53	8	no	—
863	C₂×C₄×D₄	—	53	8	no	—
864	C₂×#117	—	53	2	no	—
865	C₂²×C₂²⋊C₄	—	53	4	no	—
866	C₂²×C₂²⋊C₄	—	53	8	no	—
867	C₅₃	C₂×#3484	1	1	yes	characteristic, complemented, Sylow
868	C₂⁵	—	53	2	no	—
869	C₂⁵	—	53	1	no	—
870	C₂⁵	—	53	8	no	—
871	C₂⁵	—	53	2	no	—
872	C₂⁵	—	53	2	no	—
873	C₂⁵	—	53	8	no	—
874	C₂⁵	—	53	2	no	—
875	C₂⁵	—	53	2	no	—
876	C₂⁵	—	53	4	no	—
877	C₂⁵	—	106	16	no	—
878	C₂⁵	—	212	16	no	—
879	C₂⁵	C₂²×D₅₃	1	2	yes	complemented
880	H(5,𝔽₂)	—	2	8	no	—
881	H(5,𝔽₂)	—	106	32	no	—
882	H(5,𝔽₂)	—	106	32	no	—
883	H(5,𝔽₂)	—	106	32	no	—
884	H(5,𝔽₂)	—	106	16	no	—
885	H(5,𝔽₂)	—	106	8	no	—
886	C₂×#41	—	53	2	no	—
887	C₂×#41	—	53	4	no	—
888	C₂×#41	—	53	4	no	—
889	C₂×#41	—	53	4	no	—
890	C₂×#41	—	53	2	no	—
891	C₂×#41	—	53	8	no	—
892	C₂×#41	—	53	2	no	—
893	C₂×#41	—	53	4	no	—
894	C₂×#41	—	53	4	no	—
895	C₂×#41	—	53	8	no	—
896	C₂×#41	—	106	16	no	—
897	C₂×#41	—	106	32	no	—
898	C₂×#41	C₂²×D₅₃	1	2	yes	complemented
899	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
900	C₂²×Q₈	—	53	2	no	—
901	C₂²×D₄	—	2	8	no	—
902	C₂²×D₄	—	53	2	no	—
903	C₂²×D₄	—	53	16	no	—
904	C₂²×D₄	—	53	4	no	—
905	C₂²×D₄	—	53	4	no	—
906	C₂²×D₄	—	53	4	no	—
907	C₂²×D₄	—	53	2	no	—
908	C₂²×D₄	—	53	2	no	—
909	C₂²×D₄	—	53	2	no	—
910	C₂²×D₄	—	53	16	no	—
911	C₂²×D₄	—	53	4	no	—
912	C₂²×D₄	—	53	8	no	—
913	C₂²×D₄	—	53	8	no	—
914	C₂²×D₄	—	53	8	no	—
915	C₂²×D₄	—	53	8	no	—
916	C₂²×D₄	—	53	4	no	—
917	C₂²×D₄	—	53	8	no	—
918	C₂²×D₄	—	53	8	no	—
919	C₂²×D₄	—	53	4	no	—
920	C₂²×D₄	—	53	8	no	—
921	C₂²×D₄	—	53	4	no	—
922	C₂²×D₄	—	53	4	no	—
923	C₂²×D₄	—	53	16	no	—
924	C₂²×D₄	—	53	8	no	—
925	C₂²×D₄	—	53	8	no	—
926	C₂²×D₄	—	53	8	no	—
927	C₂²×D₄	—	53	8	no	—
928	C₂²×D₄	—	53	2	no	—
929	C₂²×D₄	—	53	8	no	—
930	C₂²×D₄	—	53	4	no	—
931	C₂²×D₄	—	53	16	no	—
932	C₂²×D₄	—	53	16	no	—
933	C₂²×D₄	—	53	16	no	—
934	C₂²×D₄	—	53	1	no	—
935	C₂²×D₄	—	53	2	no	—
936	C₂²×D₄	—	53	1	no	—
937	C₂²×D₄	—	53	8	no	—
938	C₂²×D₄	—	53	4	no	—
939	C₂²×D₄	—	53	4	no	—
940	C₂²×D₄	—	53	8	no	—
941	C₂²×D₄	—	106	8	no	—
942	C₂²×D₄	—	106	8	no	—
943	C₂²×D₄	—	106	16	no	—
944	C₂²×D₄	—	106	64	no	—
945	C₂²×D₄	—	106	64	no	—
946	C₂²×D₄	—	106	8	no	—
947	C₂²×D₄	—	106	32	no	—
948	C₂²×D₄	—	106	16	no	—
949	C₂²×D₄	—	106	32	no	—
950	C₂²×D₄	—	106	16	no	—
951	C₂²×D₄	—	106	8	no	—
952	C₂²×D₄	—	212	32	no	—
953	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
954	C₂²×D₄	C₂²×D₅₃	1	2	yes	complemented
955	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
956	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
957	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
958	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
959	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
960	C₂³×C₄	—	53	1	no	—
961	C₂³×C₄	—	53	1	no	—
962	C₂³×C₄	—	53	4	no	—
963	C₂³×C₄	—	53	1	no	—
964	C₂³×C₄	—	53	1	no	—
965	C₂³×C₄	—	53	4	no	—
966	C₂³×C₄	—	53	1	no	—
967	C₂³×C₄	—	53	4	no	—
968	C₂³×C₄	—	53	4	no	—
969	C₂³×C₄	—	53	8	no	—
970	C₂³×C₄	—	106	8	no	—
971	C₂³×C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
972	#127	—	53	4	no	—
973	#127	—	53	16	no	—
974	#127	—	53	4	no	—
975	#127	—	53	4	no	—
976	#127	C₂²×D₅₃	1	4	yes	complemented
977	#124	—	53	4	no	—
978	#124	—	53	4	no	—
979	#124	—	53	16	no	—
980	#124	—	53	4	no	—
981	#124	C₂²×D₅₃	1	4	yes	complemented
982	#123	—	53	4	no	—
983	#123	—	53	8	no	—
984	#123	—	53	4	no	—
985	#123	—	53	8	no	—
986	#123	—	53	8	no	—
987	#123	—	53	16	no	—
988	#123	—	53	4	no	—
989	#123	—	53	8	no	—
990	#123	—	53	16	no	—
991	#123	—	53	8	no	—
992	#123	C₂²×D₅₃	1	4	yes	complemented
993	#123	C₂²×D₅₃	1	8	yes	complemented
994	C₂²⋊Q₈	—	53	4	no	—
995	C₂²⋊Q₈	—	53	4	no	—
996	C₂²⋊Q₈	—	53	8	no	—
997	C₂²⋊Q₈	—	53	4	no	—
998	C₂²⋊Q₈	—	53	8	no	—
999	C₂²⋊Q₈	C₂²×D₅₃	1	4	yes	complemented
1000	#121	—	53	8	no	—
1001	#121	—	53	16	no	—
1002	#121	—	53	8	no	—
1003	#121	—	53	4	no	—
1004	#121	—	53	16	no	—
1005	#121	—	53	16	no	—
1006	#121	—	53	16	no	—
1007	#121	—	53	4	no	—
1008	#121	—	53	16	no	—
1009	#121	—	53	8	no	—
1010	#121	—	53	4	no	—
1011	#121	—	53	16	no	—
1012	#121	—	53	8	no	—
1013	#121	—	53	8	no	—
1014	#121	—	53	16	no	—
1015	#121	—	53	16	no	—
1016	#121	—	53	16	no	—
1017	#121	C₂²×D₅₃	1	4	yes	complemented
1018	#121	C₂²×D₅₃	1	16	yes	complemented
1019	#121	C₂²×D₅₃	1	8	yes	complemented
1020	#120	—	53	4	no	—
1021	#120	—	53	8	no	—
1022	#120	—	53	16	no	—
1023	#120	—	53	8	no	—
1024	#120	—	53	4	no	—
1025	#120	—	53	8	no	—
1026	#120	—	53	8	no	—
1027	#120	—	53	16	no	—
1028	#120	—	53	8	no	—
1029	#120	—	53	16	no	—
1030	#120	—	53	16	no	—
1031	#120	—	53	16	no	—
1032	#120	—	53	16	no	—
1033	#120	—	53	8	no	—
1034	#120	—	53	4	no	—
1035	#120	—	53	8	no	—
1036	#120	—	53	16	no	—
1037	#120	—	53	16	no	—
1038	#120	—	53	16	no	—
1039	#120	—	53	16	no	—
1040	#120	—	53	16	no	—
1041	#120	—	53	8	no	—
1042	#120	C₂²×D₅₃	1	4	yes	complemented
1043	#120	C₂²×D₅₃	1	8	yes	complemented
1044	#120	C₂²×D₅₃	1	16	yes	complemented
1045	#120	C₂²×D₅₃	1	8	yes	complemented
1046	C₄×D₄	—	53	8	no	—
1047	C₄×D₄	—	53	8	no	—
1048	C₄×D₄	—	53	8	no	—
1049	C₄×D₄	—	53	16	no	—
1050	C₄×D₄	—	53	8	no	—
1051	C₄×D₄	—	53	8	no	—
1052	C₄×D₄	—	53	8	no	—
1053	C₄×D₄	—	53	8	no	—
1054	C₄×D₄	—	53	16	no	—
1055	C₄×D₄	—	53	8	no	—
1056	C₄×D₄	—	53	8	no	—
1057	C₄×D₄	—	53	8	no	—
1058	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1059	C₄×D₄	C₂²×D₅₃	1	8	yes	complemented
1060	#117	—	53	2	no	—
1061	#117	—	53	4	no	—
1062	#117	—	53	4	no	—
1063	#117	—	53	4	no	—
1064	#117	C₂²×D₅₃	1	2	yes	complemented
1065	C₂×C₄⋊C₄	—	53	4	no	—
1066	C₂×C₄⋊C₄	—	53	8	no	—
1067	C₂×C₂²⋊C₄	—	53	4	no	—
1068	C₂×C₂²⋊C₄	—	53	8	no	—
1069	C₂×C₂²⋊C₄	—	53	8	no	—
1070	C₂×C₂²⋊C₄	—	53	8	no	—
1071	C₂×C₂²⋊C₄	—	53	8	no	—
1072	C₂×C₂²⋊C₄	—	53	4	no	—
1073	C₂×C₂²⋊C₄	—	53	8	no	—
1074	C₂×C₂²⋊C₄	—	53	8	no	—
1075	C₂×C₂²⋊C₄	—	53	16	no	—
1076	C₂×C₂²⋊C₄	—	53	8	no	—
1077	C₂×C₂²⋊C₄	—	53	8	no	—
1078	C₂×C₂²⋊C₄	—	53	16	no	—
1079	C₂×C₂²⋊C₄	—	53	16	no	—
1080	C₂×C₂²⋊C₄	—	53	8	no	—
1081	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
1082	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
1083	C₂×C₄²	—	53	4	no	—
1084	C₂⁴	—	2	8	no	—
1085	C₂⁴	—	4	8	no	—
1086	C₂⁴	—	53	1	no	—
1087	C₂⁴	—	53	2	no	—
1088	C₂⁴	—	53	4	no	—
1089	C₂⁴	—	53	16	no	—
1090	C₂⁴	—	53	4	no	—
1091	C₂⁴	—	53	2	no	—
1092	C₂⁴	—	53	4	no	—
1093	C₂⁴	—	53	4	no	—
1094	C₂⁴	—	53	2	no	—
1095	C₂⁴	—	53	1	no	—
1096	C₂⁴	—	53	8	no	—
1097	C₂⁴	—	53	8	no	—
1098	C₂⁴	—	53	8	no	—
1099	C₂⁴	—	53	4	no	—
1100	C₂⁴	—	53	2	no	—
1101	C₂⁴	—	53	8	no	—
1102	C₂⁴	—	53	4	no	—
1103	C₂⁴	—	106	4	no	—
1104	C₂⁴	—	106	8	no	—
1105	C₂⁴	—	106	16	no	—
1106	C₂⁴	—	106	8	no	—
1107	C₂⁴	—	106	8	no	—
1108	C₂⁴	—	106	32	no	—
1109	C₂⁴	—	106	32	no	—
1110	C₂⁴	—	106	8	no	—
1111	C₂⁴	—	106	32	no	—
1112	C₂⁴	—	106	8	no	—
1113	C₂⁴	—	212	8	no	—
1114	C₂⁴	—	212	16	no	—
1115	C₂⁴	—	212	16	no	—
1116	C₂⁴	—	212	8	no	—
1117	C₂⁴	—	212	16	no	—
1118	C₂⁴	—	212	8	no	—
1119	C₂⁴	—	212	8	no	—
1120	C₂⁴	—	212	16	no	—
1121	C₂⁴	—	212	8	no	—
1122	C₂⁴	—	212	128	no	—
1123	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
1124	C₂⁴	C₂³×D₅₃	1	8	yes	—
1125	C₂⁴	C₂³×D₅₃	1	2	yes	—
1126	C₂⁴	C₂³×D₅₃	1	2	yes	—
1127	C₂⁴	C₂³×D₅₃	1	4	yes	complemented
1128	#41	—	2	16	no	—
1129	#41	—	2	8	no	—
1130	#41	—	106	16	no	—
1131	#41	—	106	32	no	—
1132	#41	—	106	16	no	—
1133	#41	—	106	16	no	—
1134	#41	—	106	8	no	—
1135	#41	—	106	8	no	—
1136	#41	—	106	32	no	—
1137	#41	—	106	16	no	—
1138	#41	—	106	16	no	—
1139	#41	—	106	8	no	—
1140	C₂×Q₈	—	53	4	no	—
1141	C₂×Q₈	—	53	2	no	—
1142	C₂×Q₈	—	106	8	no	—
1143	C₂×Q₈	C₂³×D₅₃	1	2	yes	complemented
1144	C₂×D₄	—	2	8	no	—
1145	C₂×D₄	—	2	16	no	—
1146	C₂×D₄	—	2	32	no	—
1147	C₂×D₄	—	2	16	no	—
1148	C₂×D₄	—	2	4	no	—
1149	C₂×D₄	—	4	16	no	—
1150	C₂×D₄	—	53	16	no	—
1151	C₂×D₄	—	53	8	no	—
1152	C₂×D₄	—	53	32	no	—
1153	C₂×D₄	—	53	32	no	—
1154	C₂×D₄	—	53	8	no	—
1155	C₂×D₄	—	53	8	no	—
1156	C₂×D₄	—	53	4	no	—
1157	C₂×D₄	—	53	4	no	—
1158	C₂×D₄	—	53	8	no	—
1159	C₂×D₄	—	53	8	no	—
1160	C₂×D₄	—	53	8	no	—
1161	C₂×D₄	—	53	8	no	—
1162	C₂×D₄	—	53	8	no	—
1163	C₂×D₄	—	53	4	no	—
1164	C₂×D₄	—	53	16	no	—
1165	C₂×D₄	—	53	16	no	—
1166	C₂×D₄	—	53	8	no	—
1167	C₂×D₄	—	53	4	no	—
1168	C₂×D₄	—	53	8	no	—
1169	C₂×D₄	—	53	4	no	—
1170	C₂×D₄	—	53	8	no	—
1171	C₂×D₄	—	53	4	no	—
1172	C₂×D₄	—	53	8	no	—
1173	C₂×D₄	—	53	2	no	—
1174	C₂×D₄	—	53	16	no	—
1175	C₂×D₄	—	106	32	no	—
1176	C₂×D₄	—	106	16	no	—
1177	C₂×D₄	—	106	8	no	—
1178	C₂×D₄	—	106	16	no	—
1179	C₂×D₄	—	106	16	no	—
1180	C₂×D₄	—	106	16	no	—
1181	C₂×D₄	—	106	8	no	—
1182	C₂×D₄	—	106	8	no	—
1183	C₂×D₄	—	106	64	no	—
1184	C₂×D₄	—	106	32	no	—
1185	C₂×D₄	—	106	32	no	—
1186	C₂×D₄	—	106	16	no	—
1187	C₂×D₄	—	106	32	no	—
1188	C₂×D₄	—	106	32	no	—
1189	C₂×D₄	—	106	16	no	—
1190	C₂×D₄	—	106	32	no	—
1191	C₂×D₄	—	106	32	no	—
1192	C₂×D₄	—	106	32	no	—
1193	C₂×D₄	—	106	32	no	—
1194	C₂×D₄	—	106	64	no	—
1195	C₂×D₄	—	106	32	no	—
1196	C₂×D₄	—	106	8	no	—
1197	C₂×D₄	—	106	16	no	—
1198	C₂×D₄	—	106	8	no	—
1199	C₂×D₄	—	106	16	no	—
1200	C₂×D₄	—	106	32	no	—
1201	C₂×D₄	—	106	16	no	—
1202	C₂×D₄	—	106	4	no	—
1203	C₂×D₄	—	212	16	no	—
1204	C₂×D₄	—	212	32	no	—
1205	C₂×D₄	—	212	32	no	—
1206	C₂×D₄	—	212	32	no	—
1207	C₂×D₄	—	212	16	no	—
1208	C₂×D₄	—	212	16	no	—
1209	C₂×D₄	D₄×D₅₃	1	8	yes	complemented
1210	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1211	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1212	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1213	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1214	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1215	C₂×D₄	C₂³×D₅₃	1	8	yes	complemented
1216	C₂×D₄	C₂³×D₅₃	1	2	yes	complemented
1217	C₂×D₄	C₂³×D₅₃	1	16	yes	complemented
1218	C₂²×C₄	—	2	4	no	—
1219	C₂²×C₄	—	53	1	no	—
1220	C₂²×C₄	—	53	8	no	—
1221	C₂²×C₄	—	53	2	no	—
1222	C₂²×C₄	—	53	2	no	—
1223	C₂²×C₄	—	53	4	no	—
1224	C₂²×C₄	—	53	1	no	—
1225	C₂²×C₄	—	53	4	no	—
1226	C₂²×C₄	—	53	4	no	—
1227	C₂²×C₄	—	53	8	no	—
1228	C₂²×C₄	—	53	8	no	—
1229	C₂²×C₄	—	53	4	no	—
1230	C₂²×C₄	—	53	2	no	—
1231	C₂²×C₄	—	53	4	no	—
1232	C₂²×C₄	—	53	4	no	—
1233	C₂²×C₄	—	53	2	no	—
1234	C₂²×C₄	—	53	8	no	—
1235	C₂²×C₄	—	53	4	no	—
1236	C₂²×C₄	—	53	4	no	—
1237	C₂²×C₄	—	53	16	no	—
1238	C₂²×C₄	—	106	4	no	—
1239	C₂²×C₄	—	106	16	no	—
1240	C₂²×C₄	—	106	16	no	—
1241	C₂²×C₄	—	106	16	no	—
1242	C₂²×C₄	—	106	4	no	—
1243	C₂²×C₄	—	106	16	no	—
1244	C₂²×C₄	—	106	4	no	—
1245	C₂²×C₄	—	106	4	no	—
1246	C₂²×C₄	—	212	16	no	—
1247	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1248	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1249	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1250	C₂²×C₄	C₂³×D₅₃	1	4	yes	complemented
1251	C₂²×C₄	C₂³×D₅₃	1	4	yes	complemented
1252	C₂²×C₄	C₂³×D₅₃	1	8	yes	complemented
1253	C₄⋊C₄	—	53	8	no	—
1254	C₄⋊C₄	—	53	4	no	—
1255	C₄⋊C₄	—	53	8	no	—
1256	C₄⋊C₄	—	53	8	no	—
1257	C₄⋊C₄	—	53	8	no	—
1258	C₄⋊C₄	C₂³×D₅₃	1	4	yes	complemented
1259	C₄⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1260	C₂²⋊C₄	—	53	4	no	—
1261	C₂²⋊C₄	—	53	8	no	—
1262	C₂²⋊C₄	—	53	8	no	—
1263	C₂²⋊C₄	—	53	16	no	—
1264	C₂²⋊C₄	—	53	8	no	—
1265	C₂²⋊C₄	—	53	8	no	—
1266	C₂²⋊C₄	—	53	8	no	—
1267	C₂²⋊C₄	—	53	8	no	—
1268	C₂²⋊C₄	—	53	16	no	—
1269	C₂²⋊C₄	—	53	16	no	—
1270	C₂²⋊C₄	—	53	16	no	—
1271	C₂²⋊C₄	—	53	8	no	—
1272	C₂²⋊C₄	—	53	8	no	—
1273	C₂²⋊C₄	C₂³×D₅₃	1	4	yes	—
1274	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1275	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1276	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	complemented
1277	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	complemented
1278	C₄²	—	53	8	no	—
1279	C₄²	—	53	4	no	—
1280	C₄²	C₂³×D₅₃	1	4	yes	complemented
1281	C₂³	—	2	2	no	—
1282	C₂³	—	2	4	no	—
1283	C₂³	—	2	16	no	—
1284	C₂³	—	2	4	no	—
1285	C₂³	—	2	16	no	—
1286	C₂³	—	2	8	no	—
1287	C₂³	—	4	4	no	—
1288	C₂³	—	4	8	no	—
1289	C₂³	—	4	4	no	—
1290	C₂³	—	4	8	no	—
1291	C₂³	—	4	32	no	—
1292	C₂³	—	53	1	no	—
1293	C₂³	—	53	4	no	—
1294	C₂³	—	53	16	no	—
1295	C₂³	—	53	8	no	—
1296	C₂³	—	53	1	no	—
1297	C₂³	—	53	2	no	—
1298	C₂³	—	53	4	no	—
1299	C₂³	—	53	16	no	—
1300	C₂³	—	53	8	no	—
1301	C₂³	—	53	4	no	—
1302	C₂³	—	53	4	no	—
1303	C₂³	—	106	4	no	—
1304	C₂³	—	106	4	no	—
1305	C₂³	—	106	16	no	—
1306	C₂³	—	106	4	no	—
1307	C₂³	—	106	4	no	—
1308	C₂³	—	106	4	no	—
1309	C₂³	—	106	4	no	—
1310	C₂³	—	106	16	no	—
1311	C₂³	—	106	8	no	—
1312	C₂³	—	106	16	no	—
1313	C₂³	—	106	8	no	—
1314	C₂³	—	106	8	no	—
1315	C₂³	—	106	16	no	—
1316	C₂³	—	106	16	no	—
1317	C₂³	—	106	16	no	—
1318	C₂³	—	106	16	no	—
1319	C₂³	—	106	16	no	—
1320	C₂³	—	106	32	no	—
1321	C₂³	—	106	2	no	—
1322	C₂³	—	106	4	no	—
1323	C₂³	—	106	8	no	—
1324	C₂³	—	106	16	no	—
1325	C₂³	—	106	4	no	—
1326	C₂³	—	106	16	no	—
1327	C₂³	—	424	32	no	—
1328	C₂³	—	212	8	no	—
1329	C₂³	—	212	16	no	—
1330	C₂³	—	212	8	no	—
1331	C₂³	—	212	8	no	—
1332	C₂³	—	212	4	no	—
1333	C₂³	—	212	8	no	—
1334	C₂³	—	212	4	no	—
1335	C₂³	—	212	8	no	—
1336	C₂³	—	212	8	no	—
1337	C₂³	—	212	32	no	—
1338	C₂³	—	212	32	no	—
1339	C₂³	—	212	128	no	—
1340	C₂³	—	212	32	no	—
1341	C₂³	—	212	128	no	—
1342	C₂³	—	212	32	no	—
1343	C₂³	—	212	32	no	—
1344	C₂³	C₂×D₄×D₅₃	1	8	yes	complemented
1345	C₂³	C₂⁴×D₅₃	1	4	yes	—
1346	C₂³	C₂⁴×D₅₃	1	4	yes	—
1347	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1348	C₂³	C₂⁴×D₅₃	1	4	yes	—
1349	C₂³	C₂⁴×D₅₃	1	2	yes	—
1350	Q₈	—	2	4	no	—
1351	Q₈	—	106	8	no	—
1352	Q₈	—	106	4	no	—
1353	D₄	—	2	16	no	—
1354	D₄	—	2	8	no	—
1355	D₄	—	2	16	no	—
1356	D₄	—	2	16	no	—
1357	D₄	—	2	8	no	—
1358	D₄	—	2	4	no	—
1359	D₄	—	4	16	no	—
1360	D₄	—	53	32	no	—
1361	D₄	—	53	16	no	—
1362	D₄	—	106	16	no	—
1363	D₄	—	106	8	no	—
1364	D₄	—	106	16	no	—
1365	D₄	—	106	16	no	—
1366	D₄	—	106	16	no	—
1367	D₄	—	106	8	no	—
1368	D₄	—	106	16	no	—
1369	D₄	—	106	8	no	—
1370	D₄	—	106	16	no	—
1371	D₄	—	106	16	no	—
1372	D₄	—	106	16	no	—
1373	D₄	—	106	8	no	—
1374	D₄	—	106	16	no	—
1375	D₄	—	106	16	no	—
1376	D₄	—	106	8	no	—
1377	D₄	—	106	4	no	—
1378	D₄	—	212	16	no	—
1379	D₄	—	212	16	no	—
1380	D₄	—	212	16	no	—
1381	D₄	C₂×D₄×D₅₃	1	16	yes	complemented
1382	C₂×C₄	—	2	2	no	—
1383	C₂×C₄	—	2	8	no	—
1384	C₂×C₄	—	2	8	no	—
1385	C₂×C₄	—	2	8	no	—
1386	C₂×C₄	—	4	8	no	—
1387	C₂×C₄	—	53	4	no	—
1388	C₂×C₄	—	53	2	no	—
1389	C₂×C₄	—	53	8	no	—
1390	C₂×C₄	—	53	8	no	—
1391	C₂×C₄	—	53	8	no	—
1392	C₂×C₄	—	53	4	no	—
1393	C₂×C₄	—	53	2	no	—
1394	C₂×C₄	—	106	8	no	—
1395	C₂×C₄	—	106	8	no	—
1396	C₂×C₄	—	106	4	no	—
1397	C₂×C₄	—	106	4	no	—
1398	C₂×C₄	—	106	8	no	—
1399	C₂×C₄	—	106	16	no	—
1400	C₂×C₄	—	106	16	no	—
1401	C₂×C₄	—	106	8	no	—
1402	C₂×C₄	—	106	8	no	—
1403	C₂×C₄	—	106	2	no	—
1404	C₂×C₄	—	106	8	no	—
1405	C₂×C₄	—	106	8	no	—
1406	C₂×C₄	—	106	8	no	—
1407	C₂×C₄	—	212	16	no	—
1408	C₂×C₄	—	212	8	no	—
1409	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	complemented
1410	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1411	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1412	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1413	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1414	C₂²	—	2	8	no	—
1415	C₂²	—	2	2	no	—
1416	C₂²	—	2	8	no	—
1417	C₂²	—	2	2	no	—
1418	C₂²	—	2	2	no	—
1419	C₂²	—	2	4	no	—
1420	C₂²	—	2	4	no	—
1421	C₂²	—	2	8	no	—
1422	C₂²	—	2	8	no	—
1423	C₂²	—	4	8	no	—
1424	C₂²	—	4	32	no	—
1425	C₂²	—	4	8	no	—
1426	C₂²	—	8	8	no	—
1427	C₂²	—	53	2	no	—
1428	C₂²	—	53	4	no	—
1429	C₂²	—	53	2	no	—
1430	C₂²	—	53	8	no	—
1431	C₂²	—	53	4	no	—
1432	C₂²	—	106	8	no	—
1433	C₂²	—	106	16	no	—
1434	C₂²	—	106	32	no	—
1435	C₂²	—	106	8	no	—
1436	C₂²	—	106	16	no	—
1437	C₂²	—	106	2	no	—
1438	C₂²	—	106	8	no	—
1439	C₂²	—	106	2	no	—
1440	C₂²	—	106	2	no	—
1441	C₂²	—	106	4	no	—
1442	C₂²	—	106	4	no	—
1443	C₂²	—	106	8	no	—
1444	C₂²	—	106	8	no	—
1445	C₂²	—	424	8	no	—
1446	C₂²	—	424	16	no	—
1447	C₂²	—	212	8	no	—
1448	C₂²	—	212	16	no	—
1449	C₂²	—	212	32	no	—
1450	C₂²	—	212	32	no	—
1451	C₂²	—	212	8	no	—
1452	C₂²	—	212	16	no	—
1453	C₂²	—	212	16	no	—
1454	C₂²	—	212	32	no	—
1455	C₂²	—	212	16	no	—
1456	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1457	C₂²	C₂²×D₄×D₅₃	1	8	yes	—
1458	C₂²	H(5,𝔽₂)×D₅₃	1	4	yes	complemented
1459	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1460	C₄	—	2	2	no	—
1461	C₄	—	2	4	no	—
1462	C₄	—	2	8	no	—
1463	C₄	—	53	4	no	—
1464	C₄	—	106	2	no	—
1465	C₄	—	106	4	no	—
1466	C₄	—	106	8	no	—
1467	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1468	C₂	—	2	2	no	—
1469	C₂	—	2	4	no	—
1470	C₂	—	2	8	no	—
1471	C₂	—	4	4	no	—
1472	C₂	—	4	4	no	—
1473	C₂	—	53	4	no	—
1474	C₂	—	106	2	no	—
1475	C₂	—	106	4	no	—
1476	C₂	—	106	8	no	—
1477	C₂	—	212	4	no	—
1478	C₂	—	212	4	no	—
1479	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1480	C₂	C₂×H(5,𝔽₂)×D₅₃	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3484	C₂
hypercenter	#3484	D₅₃
hypocenter	C₅₃	C₂×#3484
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3484

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×H(5,𝔽₂)×D₅₃	C₂	semidirect
2. C₂³×D₄×D₅₃	C₂	semidirect
3. #20288351	C₂	semidirect
4. #20288350	C₂	semidirect
5. #20288349	C₂	semidirect
6. #20288348	C₂	semidirect
7. #20288347	C₂	semidirect
8. #20288346	C₂	semidirect
9. #20288345	C₂	semidirect
10. #20288344	C₂	semidirect
11. #20288343	C₂	semidirect
12. #546×D₅₃	C₂	semidirect
13. D₄²×D₅₃	C₂	semidirect
14. #535×D₅₃	C₂	semidirect
15. #534×D₅₃	C₂	semidirect
16. #525×D₅₃	C₂	semidirect
17. C₂×#120×D₅₃	C₂	semidirect
18. #518×D₅₃	C₂	semidirect
19. C₅₃×#3484	C₂	semidirect
20. C₂⁵×D₅₃	C₂²	semidirect
21. C₂×#13133263	C₂²	semidirect
22. C₂×#13133263	C₂²	semidirect
23. C₂×#13133262	C₂²	semidirect
24. C₂×#13133262	C₂²	semidirect
25. C₂×#13133262	C₂²	semidirect
27. C₂×#41×D₅₃	C₂²	semidirect
28. C₂×#41×D₅₃	C₂²	semidirect
29. C₂³×D₂₁₂	C₂²	semidirect
30. C₂³×C₂²⋊D₅₃	C₂²	semidirect
33. C₂²×D₄×D₅₃	C₂²	semidirect
34. C₂²×D₄×D₅₃	C₂²	semidirect
35. C₂²×D₄×D₅₃	C₂²	semidirect
36. C₂²×D₄×D₅₃	C₂²	semidirect
37. C₂²×D₄×D₅₃	C₂²	semidirect
38. C₂²×D₄×D₅₃	C₂²	semidirect
39. C₂²×D₄×D₅₃	C₂²	semidirect
40. C₂²×D₄×D₅₃	C₂²	semidirect
41. C₂²×D₄×D₅₃	C₂²	semidirect
42. C₂²×D₄×D₅₃	C₂²	semidirect
43. C₂³×C₄×D₅₃	C₂²	semidirect
44. #16811270	C₂²	semidirect
45. #16811269	C₂²	semidirect
46. #16811268	C₂²	semidirect
47. #16811267	C₂²	semidirect
48. #16811266	C₂²	semidirect
49. #16811265	C₂²	semidirect
50. #16811264	C₂²	semidirect
51. #16811263	C₂²	semidirect
52. #16811262	C₂²	semidirect
53. #16811261	C₂²	semidirect
54. #16811260	C₂²	semidirect
55. D₄×D₂₁₂	C₂²	semidirect
56. D₄×D₂₁₂	C₂²	semidirect
57. #16811258	C₂²	semidirect
58. #16811257	C₂²	semidirect
59. #16811257	C₂²	semidirect
60. #16811257	C₂²	semidirect
61. D₄×C₂²⋊D₅₃	C₂²	semidirect
62. D₄×C₂²⋊D₅₃	C₂²	semidirect
63. D₄×C₂²⋊D₅₃	C₂²	semidirect
64. #16811255	C₂²	semidirect
65. #16811255	C₂²	semidirect
66. #16811192	C₂²	semidirect
67. #16811191	C₂²	semidirect
68. #16811190	C₂²	semidirect
69. #16811189	C₂²	semidirect
70. #16811188	C₂²	semidirect
71. #16811187	C₂²	semidirect
72. #16811186	C₂²	semidirect
73. #16811185	C₂²	semidirect
74. #16811184	C₂²	semidirect
75. #16811184	C₂²	semidirect
76. #16811183	C₂²	semidirect
77. #16811183	C₂²	semidirect
78. #16811182	C₂²	semidirect
79. #16811182	C₂²	semidirect
80. #16811181	C₂²	semidirect
81. #127×D₅₃	C₂²	semidirect
82. #124×D₅₃	C₂²	semidirect
83. #16811136	C₂²	semidirect
84. #16811135	C₂²	semidirect
85. #16811134	C₂²	semidirect
86. #16811133	C₂²	semidirect
87. #16811132	C₂²	semidirect
88. #16811131	C₂²	semidirect
89. #16811130	C₂²	semidirect
90. #16811129	C₂²	semidirect
91. #123×D₅₃	C₂²	semidirect
92. #123×D₅₃	C₂²	semidirect
93. C₂²⋊Q₈×D₅₃	C₂²	semidirect
94. #121×D₅₃	C₂²	semidirect
95. #121×D₅₃	C₂²	semidirect
96. #121×D₅₃	C₂²	semidirect
97. C₂×#13133187	C₂²	semidirect
98. C₂×#13133187	C₂²	semidirect
99. C₂×#13133186	C₂²	semidirect
100. C₂×#13133185	C₂²	semidirect
101. C₂×#13133185	C₂²	semidirect
102. #120×D₅₃	C₂²	semidirect
103. #120×D₅₃	C₂²	semidirect
104. #120×D₅₃	C₂²	semidirect
105. #120×D₅₃	C₂²	semidirect
106. #120×D₅₃	C₂²	semidirect
107. #120×D₅₃	C₂²	semidirect
108. #120×D₅₃	C₂²	semidirect
109. #16811098	C₂²	semidirect
110. #16811097	C₂²	semidirect
111. #16811096	C₂²	semidirect
112. #16811095	C₂²	semidirect
113. C₄×D₄×D₅₃	C₂²	semidirect
114. C₄×D₄×D₅₃	C₂²	semidirect
115. #117×D₅₃	C₂²	semidirect
116. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
117. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
118. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
119. C₂³×D₄×C₅₃	C₂²	semidirect
120. C₅₃×#546	C₂²	semidirect
121. D₄²×C₅₃	C₂²	semidirect
122. C₅₃×#535	C₂²	semidirect
123. C₅₃×#534	C₂²	semidirect
124. C₅₃×#525	C₂²	semidirect
125. C₂×#120×C₅₃	C₂²	semidirect
126. C₅₃×#518	C₂²	semidirect
133. C₂⁴×D₅₃	C₂³	semidirect
134. C₂⁴×D₅₃	C₂³	semidirect
135. C₂⁴×D₅₃	C₂³	semidirect
136. C₂⁴×D₅₃	C₂³	semidirect
137. C₂⁴×D₅₃	C₂³	semidirect
143. C₂×#11719949	C₂³	semidirect
144. C₂×#11719949	C₂³	semidirect
145. C₂×#11719945	C₂³	semidirect
146. C₂×#11719945	C₂³	semidirect
147. C₂×#11719945	C₂³	semidirect
148. C₂×#11719945	C₂³	semidirect
149. C₂×#11719947	C₂³	semidirect
150. C₂×#11719947	C₂³	semidirect
151. C₂×#11719947	C₂³	semidirect
152. C₂×#11719947	C₂³	semidirect
155. C₂×Q₈×D₅₃	C₂³	semidirect
158. C₂²×D₂₁₂	C₂³	semidirect
159. C₂²×D₂₁₂	C₂³	semidirect
160. C₂²×D₂₁₂	C₂³	semidirect
161. C₂²×D₂₁₂	C₂³	semidirect
162. C₂²×D₂₁₂	C₂³	semidirect
163. C₂²×D₂₁₂	C₂³	semidirect
166. C₂²×C₂²⋊D₅₃	C₂³	semidirect
167. C₂²×C₂²⋊D₅₃	C₂³	semidirect
168. C₂²×C₂²⋊D₅₃	C₂³	semidirect
169. C₂²×C₂²⋊D₅₃	C₂³	semidirect
170. C₂²×C₂²⋊D₅₃	C₂³	semidirect
171. C₂²×C₂²⋊D₅₃	C₂³	semidirect
172. C₂²×C₂²⋊D₅₃	C₂³	semidirect
173. C₂²×C₂²⋊D₅₃	C₂³	semidirect
174. C₂²×C₂²⋊D₅₃	C₂³	semidirect
185. C₂×D₄×D₅₃	D₄	semidirect
192. C₂×D₄×D₅₃	C₂³	semidirect
193. C₂×D₄×D₅₃	C₂³	semidirect
194. C₂×D₄×D₅₃	C₂³	semidirect
195. C₂×D₄×D₅₃	C₂³	semidirect
196. C₂×D₄×D₅₃	C₂³	semidirect
197. C₂×D₄×D₅₃	C₂³	semidirect
198. C₂×D₄×D₅₃	C₂³	semidirect
199. C₂×D₄×D₅₃	C₂³	semidirect
200. C₂×D₄×D₅₃	C₂³	semidirect
201. C₂×D₄×D₅₃	C₂³	semidirect
202. C₂×D₄×D₅₃	C₂³	semidirect
203. C₂×D₄×D₅₃	C₂³	semidirect
204. C₂×D₄×D₅₃	C₂³	semidirect
205. C₂×D₄×D₅₃	C₂³	semidirect
206. C₂×D₄×D₅₃	C₂³	semidirect
207. C₂³×Dic₅₃	C₂³	semidirect
212. C₂²×C₄×D₅₃	C₂³	semidirect
213. C₂²×C₄×D₅₃	C₂³	semidirect
214. C₂²×C₄×D₅₃	C₂³	semidirect
215. C₂²×C₄×D₅₃	C₂³	semidirect
216. C₂²×C₄×D₅₃	C₂³	semidirect
217. C₂²×C₄×D₅₃	C₂³	semidirect
218. #13133214	C₂³	semidirect
219. #13133213	C₂³	semidirect
220. #13133213	C₂³	semidirect
221. #13133213	C₂³	semidirect
222. #13133206	C₂³	semidirect
223. #13133205	C₂³	semidirect
224. #13133204	C₂³	semidirect
225. #13133203	C₂³	semidirect
226. #13133202	C₂³	semidirect
227. #13133202	C₂³	semidirect
228. #13133201	C₂³	semidirect
229. #13133201	C₂³	semidirect
230. #13133200	C₂³	semidirect
231. #13133200	C₂³	semidirect
232. #13133199	C₂³	semidirect
233. #13133199	C₂³	semidirect
234. #13133198	C₂³	semidirect
235. #13133198	C₂³	semidirect
236. #13133197	C₂³	semidirect
237. #13133196	C₂³	semidirect
238. #13133195	C₂³	semidirect
239. #13133194	C₂³	semidirect
240. #13133193	C₂³	semidirect
241. #13133192	C₂³	semidirect
242. #13133192	C₂³	semidirect
243. #13133192	C₂³	semidirect
244. #13133191	C₂³	semidirect
245. #13133191	C₂³	semidirect
246. #13133191	C₂³	semidirect
247. #13133190	C₂³	semidirect
248. #13133190	C₂³	semidirect
249. #13133190	C₂³	semidirect
250. #13133190	C₂³	semidirect
251. #13133189	C₂³	semidirect
252. #13133189	C₂³	semidirect
253. #13133189	C₂³	semidirect
254. #13133189	C₂³	semidirect
255. #13133188	C₂³	semidirect
256. #13133188	C₂³	semidirect
257. #13133188	C₂³	semidirect
258. #13133187	C₂³	semidirect
259. #13133187	C₂³	semidirect
260. #13133187	C₂³	semidirect
261. #13133187	C₂³	semidirect
262. #13133187	C₂³	semidirect
263. #13133187	C₂³	semidirect
264. #13133187	C₂³	semidirect
265. #13133187	C₂³	semidirect
266. #13133187	C₂³	semidirect
267. #13133186	C₂³	semidirect
268. #13133186	C₂³	semidirect
269. #13133186	C₂³	semidirect
270. #13133186	C₂³	semidirect
271. #13133185	C₂³	semidirect
272. #13133185	C₂³	semidirect
273. #13133185	C₂³	semidirect
274. #13133185	C₂³	semidirect
275. #13133185	C₂³	semidirect
276. #13133185	C₂³	semidirect
277. #13133185	C₂³	semidirect
278. #13133185	C₂³	semidirect
279. #13133185	C₂³	semidirect
280. C₄×D₂₁₂	C₂³	semidirect
281. C₄×D₂₁₂	C₂³	semidirect
282. D₄×Dic₅₃	C₂³	semidirect
283. D₄×Dic₅₃	C₂³	semidirect
284. #13133179	C₂³	semidirect
285. #13133179	C₂³	semidirect
286. C₄×C₂²⋊D₅₃	C₂³	semidirect
287. C₄×C₂²⋊D₅₃	C₂³	semidirect
288. C₄×C₂²⋊D₅₃	C₂³	semidirect
289. #13133177	C₂³	semidirect
290. #13133177	C₂³	semidirect
291. #13133177	C₂³	semidirect
292. #13133176	C₂³	semidirect
293. #13133175	C₂³	semidirect
294. #13133174	C₂³	semidirect
295. #13133173	C₂³	semidirect
296. C₄⋊C₄×D₅₃	C₂³	semidirect
297. C₄⋊C₄×D₅₃	C₂³	semidirect
298. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
299. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
300. C₂×#11719921	C₂³	semidirect
301. C₂×#11719921	C₂³	semidirect
302. C₂×#11719921	C₂³	semidirect
305. C₂²⋊C₄×D₅₃	C₂³	semidirect
306. C₂²⋊C₄×D₅₃	C₂³	semidirect
307. C₂²⋊C₄×D₅₃	C₂³	semidirect
308. C₂²⋊C₄×D₅₃	C₂³	semidirect
309. C₂²⋊C₄×D₅₃	C₂³	semidirect
310. C₂²⋊C₄×D₅₃	C₂³	semidirect
311. C₂²⋊C₄×D₅₃	C₂³	semidirect
312. C₄²×D₅₃	C₂³	semidirect
313. C₂⁵×C₅₃	C₂³	semidirect
315. C₂×#41×C₅₃	C₂³	semidirect
316. C₂×#41×C₅₃	C₂³	semidirect
319. C₂²×D₄×C₅₃	C₂³	semidirect
320. C₂²×D₄×C₅₃	C₂³	semidirect
321. C₂²×D₄×C₅₃	C₂³	semidirect
322. C₂²×D₄×C₅₃	C₂³	semidirect
323. C₂²×D₄×C₅₃	C₂³	semidirect
324. C₂²×D₄×C₅₃	C₂³	semidirect
325. C₂³×C₄×C₅₃	C₂³	semidirect
326. #127×C₅₃	C₂³	semidirect
327. #124×C₅₃	C₂³	semidirect
328. #123×C₅₃	C₂³	semidirect
329. #123×C₅₃	C₂³	semidirect
330. C₂²⋊Q₈×C₅₃	C₂³	semidirect
331. #121×C₅₃	C₂³	semidirect
332. #121×C₅₃	C₂³	semidirect
333. #121×C₅₃	C₂³	semidirect
334. #120×C₅₃	C₂³	semidirect
335. #120×C₅₃	C₂³	semidirect
336. #120×C₅₃	C₂³	semidirect
337. #120×C₅₃	C₂³	semidirect
338. C₄×D₄×C₅₃	C₂³	semidirect
339. C₄×D₄×C₅₃	C₂³	semidirect
340. #117×C₅₃	C₂³	semidirect
341. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
342. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
349. C₂⁴×C₅₃	C₂⁴	semidirect
370. C₂³×D₅₃	C₂×D₄	semidirect
385. C₂³×D₅₃	C₂⁴	semidirect
386. C₂³×D₅₃	C₂⁴	semidirect
389. C₂×Q₈×C₅₃	C₂⁴	semidirect
396. C₂×D₄×C₅₃	C₂×D₄	semidirect
402. C₂×D₄×C₅₃	C₂⁴	semidirect
403. C₂×D₄×C₅₃	C₂⁴	semidirect
404. C₂×D₄×C₅₃	C₂⁴	semidirect
409. C₂²×C₄×C₅₃	C₂⁴	semidirect
410. C₂²×C₄×C₅₃	C₂⁴	semidirect
411. C₂²×C₄×C₅₃	C₂⁴	semidirect
421. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
430. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
431. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
432. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
433. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
434. C₂×C₂²⋊D₅₃	C₂⁴	semidirect
439. C₂²×Dic₅₃	C₂⁴	semidirect
440. C₂²×Dic₅₃	C₂⁴	semidirect
441. C₂²×Dic₅₃	C₂⁴	semidirect
468. D₄×D₅₃	C₂×D₄	semidirect
469. D₄×D₅₃	C₂×D₄	semidirect
480. C₂×D₂₁₂	C₂×D₄	semidirect
486. C₂×D₂₁₂	C₂⁴	semidirect
487. C₂×D₂₁₂	C₂⁴	semidirect
488. C₂×D₂₁₂	C₂⁴	semidirect
497. C₂×C₄×D₅₃	C₂×D₄	semidirect
506. C₂×C₄×D₅₃	C₂⁴	semidirect
507. C₂×C₄×D₅₃	C₂⁴	semidirect
508. C₂×C₄×D₅₃	C₂⁴	semidirect
509. C₂×C₄×D₅₃	C₂⁴	semidirect
510. C₂×Dic₁₀₆	C₂⁴	semidirect
511. C₂×Dic₁₀₆	C₂⁴	semidirect
512. C₄⋊C₄×C₅₃	C₂⁴	semidirect
513. C₄⋊C₄×C₅₃	C₂⁴	semidirect
516. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
517. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
518. C₂²⋊C₄×C₅₃	C₂⁴	semidirect
519. C₄²×C₅₃	C₂⁴	semidirect
522. C₂²⋊Dic₅₃	C₂⁴	semidirect
523. C₂²⋊Dic₅₃	C₂⁴	semidirect
524. C₂²⋊Dic₅₃	C₂⁴	semidirect
528. #11719921	C₂⁴	semidirect
529. #11719921	C₂⁴	semidirect
530. #11719921	C₂⁴	semidirect
531. #11719921	C₂⁴	semidirect
532. #11719921	C₂⁴	semidirect
533. C₄⋊Dic₅₃	C₂⁴	semidirect
534. C₄⋊Dic₅₃	C₂⁴	semidirect
535. #11719919	C₂⁴	semidirect
536. #11719919	C₂⁴	semidirect
537. #11719919	C₂⁴	semidirect
538. C₄×Dic₅₃	C₂⁴	semidirect
539. C₄×Dic₅₃	C₂⁴	semidirect
551. C₂³×C₅₃	C₂²×D₄	semidirect
600. C₂²×D₅₃	C₂²×D₄	semidirect
601. C₂²×D₅₃	C₂²×D₄	semidirect
602. C₂²×D₅₃	H(5,𝔽₂)	semidirect
617. D₄×C₅₃	C₂²×D₄	semidirect
623. C₂×C₄×C₅₃	C₂²×D₄	semidirect
640. C₂²⋊D₅₃	C₂²×D₄	semidirect
646. C₂×Dic₅₃	C₂²×D₄	semidirect
658. D₂₁₂	C₂²×D₄	semidirect
670. C₄×D₅₃	C₂²×D₄	semidirect
689. C₂²×C₅₃	C₂×H(5,𝔽₂)	semidirect
719. C₂×D₅₃	C₂×H(5,𝔽₂)	semidirect
739. #3484	D₅₃	direct (N × H)
759. D₅₃	#3484	direct (N × H)
767. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
784. C₂³×D₄	C₂×D₅₃	semidirect
797. #546	C₂×D₅₃	semidirect
809. D₄²	C₂×D₅₃	semidirect
817. #535	C₂×D₅₃	semidirect
826. #534	C₂×D₅₃	semidirect
837. #525	C₂×D₅₃	semidirect
856. C₂×#120	C₂×D₅₃	semidirect
861. #518	C₂×D₅₃	semidirect
867. C₅₃	C₂×#3484	semidirect
879. C₂⁵	C₂²×D₅₃	semidirect
898. C₂×#41	C₂²×D₅₃	semidirect
899. C₂×#41	C₂²×D₅₃	semidirect
954. C₂²×D₄	C₂²×D₅₃	semidirect
955. C₂²×D₄	C₂²×D₅₃	semidirect
956. C₂²×D₄	C₂²×D₅₃	semidirect
957. C₂²×D₄	C₂²×D₅₃	semidirect
958. C₂²×D₄	C₂²×D₅₃	semidirect
959. C₂²×D₄	C₂²×D₅₃	semidirect
971. C₂³×C₄	C₂²×D₅₃	semidirect
976. #127	C₂²×D₅₃	semidirect
981. #124	C₂²×D₅₃	semidirect
992. #123	C₂²×D₅₃	semidirect
993. #123	C₂²×D₅₃	semidirect
999. C₂²⋊Q₈	C₂²×D₅₃	semidirect
1017. #121	C₂²×D₅₃	semidirect
1018. #121	C₂²×D₅₃	semidirect
1019. #121	C₂²×D₅₃	semidirect
1042. #120	C₂²×D₅₃	semidirect
1043. #120	C₂²×D₅₃	semidirect
1044. #120	C₂²×D₅₃	semidirect
1045. #120	C₂²×D₅₃	semidirect
1058. C₄×D₄	C₂²×D₅₃	semidirect
1059. C₄×D₄	C₂²×D₅₃	semidirect
1064. #117	C₂²×D₅₃	semidirect
1081. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1082. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
1127. C₂⁴	C₂³×D₅₃	semidirect
1143. C₂×Q₈	C₂³×D₅₃	semidirect
1209. C₂×D₄	D₄×D₅₃	semidirect
1215. C₂×D₄	C₂³×D₅₃	semidirect
1216. C₂×D₄	C₂³×D₅₃	semidirect
1217. C₂×D₄	C₂³×D₅₃	semidirect
1250. C₂²×C₄	C₂³×D₅₃	semidirect
1251. C₂²×C₄	C₂³×D₅₃	semidirect
1252. C₂²×C₄	C₂³×D₅₃	semidirect
1258. C₄⋊C₄	C₂³×D₅₃	semidirect
1259. C₄⋊C₄	C₂³×D₅₃	semidirect
1275. C₂²⋊C₄	C₂³×D₅₃	semidirect
1276. C₂²⋊C₄	C₂³×D₅₃	semidirect
1277. C₂²⋊C₄	C₂³×D₅₃	semidirect
1280. C₄²	C₂³×D₅₃	semidirect
1344. C₂³	C₂×D₄×D₅₃	semidirect
1381. D₄	C₂×D₄×D₅₃	semidirect
1409. C₂×C₄	C₂×D₄×D₅₃	semidirect
1458. C₂²	H(5,𝔽₂)×D₅₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×H(5,𝔽₂)×D₅₃	2
C₂³×D₄×D₅₃	2
#20288351	2
#20288350	2
#20288349	2
#20288348	2
#20288347	2
#20288346	2
#20288345	2
#20288344	2
#20288343	2
#546×D₅₃	2
D₄²×D₅₃	2
#535×D₅₃	2
#534×D₅₃	2
#525×D₅₃	2
C₂×#120×D₅₃	2
#518×D₅₃	2
C₅₃×#3484	2
C₂×#3484	53

Subgroups — D53×#3484 #28291967

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3484 #28291967