Subgroups — D₅₃×#3496 #28291977

Order 13568.

12378 conjugacy classes of subgroups.

The subgroup lattice has 1316 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	2	yes	maximal, complemented
2	#20288479	C₂	1	1	yes	maximal, characteristic, complemented
3	#20288478	C₂	1	2	yes	maximal, complemented
4	#20288477	C₂	1	2	yes	maximal, complemented
5	#20288476	C₂	1	4	yes	maximal, complemented
6	#20288475	C₂	1	8	yes	maximal, complemented
7	#20288474	C₂	1	2	yes	maximal, complemented
8	#20288473	C₂	1	4	yes	maximal, complemented
9	#20288472	C₂	1	4	yes	maximal, complemented
10	#20288471	C₂	1	4	yes	maximal, complemented
11	#547×D₅₃	C₂	1	4	yes	maximal, complemented
12	#546×D₅₃	C₂	1	8	yes	maximal, complemented
13	D₄²×D₅₃	C₂	1	4	yes	maximal, complemented
14	#537×D₅₃	C₂	1	2	yes	maximal, complemented
15	#534×D₅₃	C₂	1	4	yes	maximal, complemented
16	#532×D₅₃	C₂	1	2	yes	maximal, complemented
17	C₂×#121×D₅₃	C₂	1	4	yes	maximal, complemented
18	C₂×C₄×D₄×D₅₃	C₂	1	1	yes	maximal, characteristic, complemented
19	C₅₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#13133263	C₂²	1	8	yes	complemented
21	C₂×#13133263	C₂²	1	4	yes	complemented
22	C₂×#13133262	C₂²	1	2	yes	complemented
23	C₂×#13133262	C₂²	1	8	yes	complemented
24	C₂×#13133262	C₂²	1	8	yes	complemented
25	H(5,𝔽₂)×D₅₃	—	2	32	no	—
26	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
27	C₂×#41×D₅₃	C₂²	1	8	yes	complemented
28	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
29	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
30	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
31	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
32	C₂³×C₄×D₅₃	C₂²	1	2	yes	complemented
33	#16811278	C₂²	1	4	yes	complemented
34	#16811277	C₂²	1	4	yes	complemented
35	#16811276	C₂²	1	4	yes	complemented
36	#16811275	C₂²	1	8	yes	complemented
37	#16811274	C₂²	1	8	yes	complemented
38	#16811273	C₂²	1	8	yes	complemented
39	#16811272	C₂²	1	8	yes	complemented
40	#16811271	C₂²	1	16	yes	complemented
41	#16811270	C₂²	1	8	yes	complemented
42	#16811269	C₂²	1	8	yes	complemented
43	#16811268	C₂²	1	8	yes	complemented
44	#16811267	C₂²	1	8	yes	complemented
45	#16811266	C₂²	1	8	yes	complemented
46	#16811265	C₂²	1	16	yes	complemented
47	#16811264	C₂²	1	8	yes	complemented
48	#16811263	C₂²	1	16	yes	complemented
49	#16811262	C₂²	1	16	yes	complemented
50	#16811261	C₂²	1	8	yes	complemented
51	#16811260	C₂²	1	16	yes	complemented
52	D₄×D₂₁₂	C₂²	1	4	yes	complemented
53	D₄×D₂₁₂	C₂²	1	4	yes	complemented
54	#16811258	C₂²	1	4	yes	complemented
55	#16811257	C₂²	1	8	yes	complemented
56	#16811257	C₂²	1	8	yes	complemented
57	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
58	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
59	#16811255	C₂²	1	16	yes	complemented
60	#16811204	C₂²	1	2	yes	complemented
61	#16811203	C₂²	1	8	yes	complemented
62	#16811202	C₂²	1	8	yes	complemented
63	#16811201	C₂²	1	4	yes	complemented
64	#16811200	C₂²	1	8	yes	complemented
65	#16811185	C₂²	1	4	yes	complemented
66	#16811184	C₂²	1	16	yes	complemented
67	#16811183	C₂²	1	16	yes	complemented
68	#16811182	C₂²	1	8	yes	complemented
69	#16811181	C₂²	1	8	yes	complemented
70	#16811181	C₂²	1	8	yes	complemented
71	#16811174	C₂²	1	2	yes	complemented
72	#16811173	C₂²	1	2	yes	complemented
73	#16811172	C₂²	1	4	yes	complemented
74	#16811171	C₂²	1	2	yes	complemented
75	#16811170	C₂²	1	4	yes	complemented
76	#16811170	C₂²	1	4	yes	complemented
77	#16811169	C₂²	1	4	yes	complemented
78	#16811168	C₂²	1	4	yes	complemented
79	#16811168	C₂²	1	4	yes	complemented
80	C₄⋊Q₈×D₅₃	C₂²	1	2	yes	complemented
81	#127×D₅₃	C₂²	1	2	yes	complemented
82	#124×D₅₃	C₂²	1	4	yes	complemented
83	#123×D₅₃	C₂²	1	16	yes	complemented
84	C₂²⋊Q₈×D₅₃	C₂²	1	8	yes	complemented
85	C₂×#13133192	C₂²	1	4	yes	complemented
86	C₂×#13133191	C₂²	1	4	yes	complemented
87	C₂×#13133190	C₂²	1	8	yes	complemented
88	C₂×#13133189	C₂²	1	8	yes	complemented
89	C₂×#13133188	C₂²	1	4	yes	complemented
90	#121×D₅₃	C₂²	1	4	yes	complemented
91	#121×D₅₃	C₂²	1	8	yes	complemented
92	#121×D₅₃	C₂²	1	8	yes	complemented
93	#121×D₅₃	C₂²	1	8	yes	complemented
94	#121×D₅₃	C₂²	1	8	yes	complemented
95	#121×D₅₃	C₂²	1	4	yes	complemented
96	#121×D₅₃	C₂²	1	8	yes	complemented
97	#121×D₅₃	C₂²	1	8	yes	complemented
98	#121×D₅₃	C₂²	1	8	yes	complemented
99	#121×D₅₃	C₂²	1	8	yes	complemented
100	#120×D₅₃	C₂²	1	16	yes	complemented
101	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
102	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
103	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
105	C₂×#13133177	C₂²	1	2	yes	complemented
106	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
107	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
108	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
109	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
110	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
111	C₄×D₄×D₅₃	C₂²	1	4	yes	complemented
112	C₂×C₄⋊C₄×D₅₃	C₂²	1	1	yes	characteristic, complemented
113	C₂×C₄⋊C₄×D₅₃	C₂²	1	4	yes	complemented
114	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
115	C₂×C₂²⋊C₄×D₅₃	C₂²	1	8	yes	complemented
116	C₂×C₄²×D₅₃	C₂²	1	1	yes	characteristic, complemented
117	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
118	C₅₃×#547	C₂²	1	4	yes	complemented
119	C₅₃×#546	C₂²	1	8	yes	complemented
120	D₄²×C₅₃	C₂²	1	4	yes	complemented
121	C₅₃×#537	C₂²	1	2	yes	complemented
122	C₅₃×#534	C₂²	1	4	yes	complemented
123	C₅₃×#532	C₂²	1	2	yes	complemented
124	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
125	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
126	C₂⁴×D₅₃	C₂³	1	8	yes	—
127	C₂⁴×D₅₃	C₂³	1	2	yes	—
128	#13133263	—	2	64	no	—
129	#13133263	—	2	32	no	—
130	#13133262	—	2	16	no	—
131	#13133262	—	2	64	no	—
132	#13133262	—	2	64	no	—
133	C₂×#11719949	C₂³	1	8	yes	complemented
134	C₂×#11719949	C₂³	1	4	yes	complemented
135	C₂×#11719945	C₂³	1	16	yes	complemented
136	C₂×#11719945	C₂³	1	8	yes	complemented
137	C₂×#11719945	C₂³	1	4	yes	complemented
138	C₂×#11719945	C₂³	1	8	yes	complemented
139	C₂×#11719947	C₂³	1	8	yes	complemented
140	C₂×#11719947	C₂³	1	16	yes	complemented
141	C₂×#11719947	C₂³	1	8	yes	complemented
142	C₂×#11719947	C₂³	1	4	yes	complemented
143	#41×D₅₃	—	2	64	no	—
144	#41×D₅₃	—	2	32	no	—
145	C₂×Q₈×D₅₃	C₂³	1	4	yes	—
146	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
147	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
148	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
149	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
150	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
151	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
152	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
153	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
154	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
155	C₂×D₄×D₅₃	—	2	64	no	—
156	C₂×D₄×D₅₃	—	2	64	no	—
157	C₂×D₄×D₅₃	—	4	16	no	—
158	C₂×D₄×D₅₃	D₄	1	16	yes	complemented
159	C₂×D₄×D₅₃	C₂³	1	4	yes	—
160	C₂×D₄×D₅₃	C₂³	1	16	yes	—
161	C₂×D₄×D₅₃	C₂³	1	8	yes	—
162	C₂×D₄×D₅₃	C₂³	1	4	yes	—
163	C₂×D₄×D₅₃	C₂³	1	4	yes	—
164	C₂×D₄×D₅₃	C₂³	1	8	yes	—
165	C₂×D₄×D₅₃	C₂³	1	4	yes	—
166	C₂×D₄×D₅₃	C₂³	1	4	yes	—
167	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
168	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
169	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
170	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
171	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
172	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
173	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
174	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
175	C₂²×C₄×D₅₃	—	4	8	no	—
176	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
177	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
178	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
179	C₂²×C₄×D₅₃	C₂³	1	8	yes	—
180	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
181	C₂²×C₄×D₅₃	C₂³	1	4	yes	—
182	C₂²×C₄×D₅₃	C₂³	1	2	yes	—
183	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
184	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
185	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
186	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
187	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
188	#13133217	C₂³	1	2	yes	complemented
189	#13133216	C₂³	1	4	yes	complemented
190	#13133216	C₂³	1	4	yes	complemented
191	#13133215	C₂³	1	4	yes	complemented
192	#13133214	C₂³	1	2	yes	complemented
193	#13133213	C₂³	1	4	yes	complemented
194	#13133213	C₂³	1	4	yes	complemented
195	#13133213	C₂³	1	4	yes	complemented
196	#13133206	C₂³	1	4	yes	complemented
197	#13133205	C₂³	1	4	yes	complemented
198	#13133204	C₂³	1	4	yes	complemented
199	#13133203	C₂³	1	8	yes	complemented
200	#13133203	C₂³	1	8	yes	complemented
201	#13133202	C₂³	1	16	yes	complemented
202	#13133202	C₂³	1	16	yes	complemented
203	#13133201	C₂³	1	16	yes	complemented
204	#13133200	C₂³	1	16	yes	complemented
205	#13133199	C₂³	1	16	yes	complemented
206	#13133199	C₂³	1	16	yes	complemented
207	#13133198	C₂³	1	16	yes	complemented
208	#13133197	C₂³	1	8	yes	complemented
209	#13133196	C₂³	1	8	yes	complemented
210	#13133195	C₂³	1	16	yes	complemented
211	#13133194	C₂³	1	16	yes	complemented
212	#13133193	C₂³	1	8	yes	complemented
213	#13133192	C₂³	1	8	yes	complemented
214	#13133192	C₂³	1	8	yes	complemented
215	#13133192	C₂³	1	8	yes	complemented
216	#13133192	C₂³	1	4	yes	complemented
217	#13133192	C₂³	1	8	yes	complemented
218	#13133192	C₂³	1	4	yes	complemented
219	#13133191	C₂³	1	8	yes	complemented
220	#13133191	C₂³	1	8	yes	complemented
221	#13133191	C₂³	1	8	yes	complemented
222	#13133191	C₂³	1	4	yes	complemented
223	#13133191	C₂³	1	8	yes	complemented
224	#13133191	C₂³	1	4	yes	complemented
225	#13133190	C₂³	1	16	yes	complemented
226	#13133190	C₂³	1	16	yes	complemented
227	#13133190	C₂³	1	16	yes	complemented
228	#13133190	C₂³	1	8	yes	complemented
229	#13133190	C₂³	1	16	yes	complemented
230	#13133190	C₂³	1	8	yes	complemented
231	#13133189	C₂³	1	16	yes	complemented
232	#13133189	C₂³	1	16	yes	complemented
233	#13133189	C₂³	1	8	yes	complemented
234	#13133189	C₂³	1	16	yes	complemented
235	#13133189	C₂³	1	8	yes	complemented
236	#13133189	C₂³	1	16	yes	complemented
237	#13133188	C₂³	1	8	yes	complemented
238	#13133188	C₂³	1	8	yes	complemented
239	#13133188	C₂³	1	8	yes	complemented
240	#13133188	C₂³	1	4	yes	complemented
241	#13133188	C₂³	1	8	yes	complemented
242	#13133188	C₂³	1	4	yes	complemented
243	#13133187	C₂³	1	16	yes	complemented
244	#13133187	C₂³	1	16	yes	complemented
245	#13133187	C₂³	1	16	yes	complemented
246	#13133186	C₂³	1	16	yes	complemented
247	#13133185	C₂³	1	16	yes	complemented
248	#13133185	C₂³	1	16	yes	complemented
249	#13133185	C₂³	1	16	yes	complemented
250	C₄×D₂₁₂	C₂³	1	4	yes	complemented
251	C₄×D₂₁₂	C₂³	1	4	yes	complemented
252	C₄×D₂₁₂	C₂³	1	4	yes	complemented
253	C₄×D₂₁₂	C₂³	1	4	yes	complemented
254	D₄×Dic₅₃	C₂³	1	4	yes	complemented
255	D₄×Dic₅₃	C₂³	1	4	yes	complemented
256	D₄×Dic₅₃	C₂³	1	4	yes	complemented
257	D₄×Dic₅₃	C₂³	1	4	yes	complemented
258	#13133179	C₂³	1	4	yes	complemented
259	#13133179	C₂³	1	4	yes	complemented
260	#13133179	C₂³	1	4	yes	complemented
261	#13133179	C₂³	1	4	yes	complemented
262	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
263	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
264	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
265	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
266	#13133177	C₂³	1	8	yes	complemented
267	#13133177	C₂³	1	8	yes	complemented
268	#13133177	C₂³	1	8	yes	complemented
269	#13133177	C₂³	1	8	yes	complemented
270	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
271	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
272	C₂×#11719919	C₂³	1	8	yes	complemented
273	C₂×#11719919	C₂³	1	2	yes	complemented
274	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
275	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
276	C₄⋊C₄×D₅₃	C₂³	1	8	yes	—
277	C₄⋊C₄×D₅₃	C₂³	1	4	yes	—
278	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
279	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
280	C₄⋊C₄×D₅₃	C₂³	1	4	yes	complemented
281	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
282	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
283	C₂×#11719921	C₂³	1	8	yes	complemented
284	C₂×#11719921	C₂³	1	8	yes	complemented
285	C₂×#11719921	C₂³	1	2	yes	complemented
286	C₂×#11719921	C₂³	1	2	yes	complemented
287	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
288	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
289	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	—
290	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	—
291	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
292	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
293	C₂²⋊C₄×D₅₃	C₂³	1	8	yes	complemented
294	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
295	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
296	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
297	C₄²×D₅₃	C₂³	1	2	yes	—
298	C₄²×D₅₃	C₂³	1	2	yes	—
299	C₄²×D₅₃	C₂³	1	2	yes	complemented
300	C₄²×D₅₃	C₂³	1	2	yes	complemented
301	H(5,𝔽₂)×C₅₃	—	2	16	no	—
302	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
303	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
304	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
305	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
306	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
307	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
308	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
309	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
310	#127×C₅₃	C₂³	1	2	yes	complemented
311	#124×C₅₃	C₂³	1	4	yes	complemented
312	#123×C₅₃	C₂³	1	16	yes	complemented
313	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
314	#121×C₅₃	C₂³	1	8	yes	complemented
315	#121×C₅₃	C₂³	1	8	yes	complemented
316	#121×C₅₃	C₂³	1	4	yes	complemented
317	#121×C₅₃	C₂³	1	8	yes	complemented
318	#121×C₅₃	C₂³	1	8	yes	complemented
319	#121×C₅₃	C₂³	1	4	yes	complemented
320	#120×C₅₃	C₂³	1	16	yes	complemented
321	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
322	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
323	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
324	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
325	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
326	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
327	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
328	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
329	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
330	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
331	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
332	C₂³×D₅₃	—	2	32	no	—
333	C₂³×D₅₃	—	4	4	no	—
334	C₂³×D₅₃	—	4	4	no	—
335	C₂³×D₅₃	—	4	16	no	—
336	C₂³×D₅₃	—	4	16	no	—
337	C₂³×D₅₃	C₂×D₄	1	16	yes	complemented
338	C₂³×D₅₃	C₂⁴	1	8	yes	—
339	C₂³×D₅₃	C₂⁴	1	4	yes	—
340	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
341	C₂³×D₅₃	C₂⁴	1	16	yes	—
342	C₂³×D₅₃	C₂⁴	1	8	yes	—
343	C₂³×D₅₃	C₂⁴	1	4	yes	—
344	C₂³×D₅₃	C₂⁴	1	2	yes	—
345	#41×C₅₃	—	2	32	no	—
346	#41×C₅₃	—	2	16	no	—
347	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
348	C₂×D₄×C₅₃	—	2	32	no	—
349	C₂×D₄×C₅₃	—	2	32	no	—
350	C₂×D₄×C₅₃	—	4	8	no	—
351	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	complemented
352	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
353	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
354	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
355	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
356	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
357	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
358	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
359	C₂²×C₄×C₅₃	—	4	4	no	—
360	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
362	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
363	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
364	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
365	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
366	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
367	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₂²⋊D₅₃	—	2	32	no	—
369	C₂×C₂²⋊D₅₃	—	2	32	no	—
370	C₂×C₂²⋊D₅₃	—	2	64	no	—
371	C₂×C₂²⋊D₅₃	—	4	16	no	—
372	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
373	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
374	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
375	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
376	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
377	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
378	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
379	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
380	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
381	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
382	C₂²×Dic₅₃	—	4	4	no	—
383	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
384	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
385	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
386	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
387	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
388	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
389	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
390	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
391	#11719949	—	2	32	no	—
392	#11719949	—	2	16	no	—
393	Q₈×D₅₃	—	2	16	no	—
394	#11719947	—	2	32	no	—
395	#11719947	—	2	64	no	—
396	#11719947	—	2	32	no	—
397	#11719947	—	2	16	no	—
398	D₄×D₅₃	—	2	64	no	—
399	D₄×D₅₃	—	2	32	no	—
400	D₄×D₅₃	—	2	64	no	—
401	D₄×D₅₃	—	2	64	no	—
402	D₄×D₅₃	—	2	32	no	—
403	D₄×D₅₃	—	2	64	no	—
404	D₄×D₅₃	—	2	32	no	—
405	D₄×D₅₃	—	2	16	no	—
406	D₄×D₅₃	—	2	16	no	—
407	D₄×D₅₃	—	4	16	no	—
408	D₄×D₅₃	—	4	16	no	—
409	D₄×D₅₃	—	4	16	no	—
410	D₄×D₅₃	—	4	8	no	—
411	D₄×D₅₃	C₂×D₄	1	32	yes	complemented
412	D₄×D₅₃	C₂×D₄	1	32	yes	complemented
413	#11719945	—	2	16	no	—
414	#11719945	—	2	64	no	—
415	#11719945	—	2	32	no	—
416	#11719945	—	2	32	no	—
417	C₂×D₂₁₂	—	2	32	no	—
418	C₂×D₂₁₂	—	2	32	no	—
419	C₂×D₂₁₂	—	4	8	no	—
420	C₂×D₂₁₂	C₂×D₄	1	8	yes	complemented
421	C₂×D₂₁₂	C₂⁴	1	4	yes	—
422	C₂×D₂₁₂	C₂⁴	1	16	yes	—
423	C₂×D₂₁₂	C₂⁴	1	8	yes	—
424	C₂×D₂₁₂	C₂⁴	1	4	yes	—
425	C₂×D₂₁₂	C₂⁴	1	4	yes	—
426	C₂×D₂₁₂	C₂⁴	1	8	yes	—
427	C₂×D₂₁₂	C₂⁴	1	4	yes	—
428	C₂×C₄×D₅₃	—	2	32	no	—
429	C₂×C₄×D₅₃	—	2	32	no	—
430	C₂×C₄×D₅₃	—	2	4	no	—
431	C₂×C₄×D₅₃	—	2	16	no	—
432	C₂×C₄×D₅₃	—	4	8	no	—
433	C₂×C₄×D₅₃	—	4	4	no	—
434	C₂×C₄×D₅₃	—	4	8	no	—
435	C₂×C₄×D₅₃	—	4	4	no	—
436	C₂×C₄×D₅₃	—	4	8	no	—
437	C₂×C₄×D₅₃	—	4	4	no	—
438	C₂×C₄×D₅₃	—	4	2	no	—
439	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	complemented
440	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
441	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
442	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
443	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
444	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
445	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
446	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
447	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
448	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
449	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
450	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
451	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
452	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
453	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
454	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
455	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
456	C₂×C₄×D₅₃	C₂⁴	1	2	yes	—
457	C₂×C₄×D₅₃	C₂⁴	1	1	yes	characteristic
458	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
459	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
460	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
461	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
462	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
463	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
464	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
465	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
466	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
467	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
468	C₄²×C₅₃	C₂⁴	1	2	yes	—
469	C₄²×C₅₃	C₂⁴	1	2	yes	—
470	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
471	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
472	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
473	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
474	#11719921	C₂⁴	1	8	yes	—
475	#11719921	C₂⁴	1	8	yes	—
476	#11719921	C₂⁴	1	8	yes	—
477	#11719921	C₂⁴	1	8	yes	—
478	#11719921	C₂⁴	1	16	yes	—
479	#11719921	C₂⁴	1	16	yes	—
480	#11719921	C₂⁴	1	8	yes	—
481	#11719921	C₂⁴	1	8	yes	—
482	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
483	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
484	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
485	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
486	#11719919	C₂⁴	1	8	yes	—
487	#11719919	C₂⁴	1	8	yes	—
488	#11719919	C₂⁴	1	16	yes	—
489	#11719919	C₂⁴	1	8	yes	—
490	C₄×Dic₅₃	C₂⁴	1	2	yes	—
491	C₄×Dic₅₃	C₂⁴	1	2	yes	—
492	C₄×Dic₅₃	C₂⁴	1	2	yes	—
493	C₄×Dic₅₃	C₂⁴	1	2	yes	—
494	C₄×Dic₅₃	C₂⁴	1	2	yes	—
495	C₄×Dic₅₃	C₂⁴	1	2	yes	—
496	C₂³×C₅₃	—	2	16	no	—
497	C₂³×C₅₃	—	4	2	no	—
498	C₂³×C₅₃	—	4	2	no	—
499	C₂³×C₅₃	—	4	8	no	—
500	C₂³×C₅₃	—	4	8	no	—
501	C₂³×C₅₃	C₂²×D₄	1	8	yes	complemented
502	C₂³×C₅₃	C₂⁵	1	8	yes	—
503	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
504	C₂³×C₅₃	C₂⁵	1	4	yes	—
505	C₂²×D₅₃	—	2	2	no	—
506	C₂²×D₅₃	—	2	8	no	—
507	C₂²×D₅₃	—	2	2	no	—
508	C₂²×D₅₃	—	2	8	no	—
509	C₂²×D₅₃	—	2	16	no	—
510	C₂²×D₅₃	—	2	16	no	—
511	C₂²×D₅₃	—	2	16	no	—
512	C₂²×D₅₃	—	2	16	no	—
513	C₂²×D₅₃	—	2	32	no	—
514	C₂²×D₅₃	—	4	32	no	—
515	C₂²×D₅₃	—	4	4	no	—
516	C₂²×D₅₃	—	4	2	no	—
517	C₂²×D₅₃	—	4	4	no	—
518	C₂²×D₅₃	—	4	2	no	—
519	C₂²×D₅₃	—	4	8	no	—
520	C₂²×D₅₃	—	4	16	no	—
521	C₂²×D₅₃	—	4	16	no	—
522	C₂²×D₅₃	—	4	8	no	—
523	C₂²×D₅₃	—	8	64	no	—
524	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
525	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
526	C₂²×D₅₃	C₂²×D₄	1	16	yes	complemented
527	C₂²×D₅₃	C₂²×D₄	1	8	yes	complemented
528	C₂²×D₅₃	C₂⁵	1	8	yes	—
529	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
530	C₂²×D₅₃	C₂⁵	1	4	yes	—
531	C₂²×D₅₃	C₂⁵	1	1	yes	characteristic
532	Q₈×C₅₃	—	2	8	no	—
533	D₄×C₅₃	—	2	32	no	—
534	D₄×C₅₃	—	2	16	no	—
535	D₄×C₅₃	—	2	8	no	—
536	D₄×C₅₃	—	2	8	no	—
537	D₄×C₅₃	—	4	8	no	—
538	D₄×C₅₃	—	4	4	no	—
539	D₄×C₅₃	C₂²×D₄	1	16	yes	complemented
540	C₂×C₄×C₅₃	—	2	16	no	—
541	C₂×C₄×C₅₃	—	2	16	no	—
542	C₂×C₄×C₅₃	—	2	2	no	—
543	C₂×C₄×C₅₃	—	2	8	no	—
544	C₂×C₄×C₅₃	—	4	4	no	—
545	C₂×C₄×C₅₃	—	4	2	no	—
546	C₂×C₄×C₅₃	—	4	1	no	—
547	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	complemented
548	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
549	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
550	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
551	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
552	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
553	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
554	C₂²⋊D₅₃	—	2	32	no	—
555	C₂²⋊D₅₃	—	2	16	no	—
556	C₂²⋊D₅₃	—	2	32	no	—
557	C₂²⋊D₅₃	—	2	16	no	—
558	C₂²⋊D₅₃	—	2	16	no	—
559	C₂²⋊D₅₃	—	2	16	no	—
560	C₂²⋊D₅₃	—	4	16	no	—
561	C₂²⋊D₅₃	—	4	8	no	—
562	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	complemented
563	C₂×Dic₅₃	—	2	16	no	—
564	C₂×Dic₅₃	—	2	16	no	—
565	C₂×Dic₅₃	—	2	2	no	—
566	C₂×Dic₅₃	—	2	8	no	—
567	C₂×Dic₅₃	—	4	4	no	—
568	C₂×Dic₅₃	—	4	2	no	—
569	C₂×Dic₅₃	—	4	1	no	—
570	C₂×Dic₅₃	C₂²×D₄	1	4	yes	complemented
571	C₂×Dic₅₃	C₂⁵	1	8	yes	—
572	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
573	C₂×Dic₅₃	C₂⁵	1	4	yes	—
574	C₂×Dic₅₃	C₂⁵	1	2	yes	—
575	C₂×Dic₅₃	C₂⁵	1	2	yes	—
576	C₂×Dic₅₃	C₂⁵	1	1	yes	characteristic
577	D₂₁₂	—	2	32	no	—
578	D₂₁₂	—	2	16	no	—
579	D₂₁₂	—	2	8	no	—
580	D₂₁₂	—	2	8	no	—
581	D₂₁₂	—	4	8	no	—
582	D₂₁₂	—	4	4	no	—
583	D₂₁₂	C₂²×D₄	1	16	yes	complemented
584	C₄×D₅₃	—	2	16	no	—
585	C₄×D₅₃	—	2	32	no	—
586	C₄×D₅₃	—	2	2	no	—
587	C₄×D₅₃	—	2	8	no	—
588	C₄×D₅₃	—	2	4	no	—
589	C₄×D₅₃	—	2	16	no	—
590	C₄×D₅₃	—	2	2	no	—
591	C₄×D₅₃	—	2	8	no	—
592	C₄×D₅₃	—	2	16	no	—
593	C₄×D₅₃	—	2	2	no	—
594	C₄×D₅₃	—	2	8	no	—
595	C₄×D₅₃	—	4	4	no	—
596	C₄×D₅₃	—	4	4	no	—
597	C₄×D₅₃	—	4	4	no	—
598	C₄×D₅₃	—	4	2	no	—
599	C₄×D₅₃	C₂²×D₄	1	8	yes	—
600	C₄×D₅₃	C₂²×D₄	1	8	yes	complemented
601	C₄×D₅₃	H(5,𝔽₂)	1	4	yes	complemented
602	Dic₁₀₆	—	2	8	no	—
603	Dic₁₀₆	—	2	16	no	—
604	C₂×#3496	—	53	1	no	maximal, Sylow
605	C₂²×C₅₃	—	2	1	no	—
606	C₂²×C₅₃	—	2	4	no	—
607	C₂²×C₅₃	—	2	1	no	—
608	C₂²×C₅₃	—	2	4	no	—
609	C₂²×C₅₃	—	2	8	no	—
610	C₂²×C₅₃	—	2	8	no	—
611	C₂²×C₅₃	—	2	8	no	—
612	C₂²×C₅₃	—	4	8	no	—
613	C₂²×C₅₃	—	8	16	no	—
614	C₂²×C₅₃	C₂³×D₄	1	8	yes	—
615	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
616	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
617	C₂×D₅₃	—	2	1	no	—
618	C₂×D₅₃	—	2	4	no	—
619	C₂×D₅₃	—	2	1	no	—
620	C₂×D₅₃	—	2	4	no	—
621	C₂×D₅₃	—	2	8	no	—
622	C₂×D₅₃	—	2	32	no	—
623	C₂×D₅₃	—	2	8	no	—
624	C₂×D₅₃	—	2	8	no	—
625	C₂×D₅₃	—	2	8	no	—
626	C₂×D₅₃	—	4	16	no	—
627	C₂×D₅₃	—	4	8	no	—
628	C₂×D₅₃	—	4	32	no	—
629	C₂×D₅₃	—	8	32	no	—
630	C₂×D₅₃	—	8	16	no	—
631	C₂×D₅₃	C₂³×D₄	1	8	yes	—
632	C₂×D₅₃	C₂³×D₄	1	2	yes	—
633	C₂×D₅₃	C₂³×D₄	1	2	yes	—
634	C₂×D₅₃	C₂×H(5,𝔽₂)	1	2	yes	—
635	C₂×D₅₃	#585	1	2	yes	—
636	C₄×C₅₃	—	2	8	no	—
637	C₄×C₅₃	—	2	1	no	—
638	C₄×C₅₃	—	2	4	no	—
639	C₄×C₅₃	—	2	2	no	—
640	C₄×C₅₃	C₂³×D₄	1	4	yes	—
641	C₄×C₅₃	C₂×H(5,𝔽₂)	1	2	yes	complemented
642	Dic₅₃	—	2	8	no	—
643	Dic₅₃	—	2	1	no	—
644	Dic₅₃	—	2	4	no	—
645	Dic₅₃	—	2	2	no	—
646	Dic₅₃	C₂³×D₄	1	4	yes	—
647	Dic₅₃	C₂×H(5,𝔽₂)	1	2	yes	complemented
648	C₂²×H(5,𝔽₂)	—	53	2	no	—
649	#3496	—	53	2	no	—
650	#3496	—	53	4	no	—
651	#3496	—	53	8	no	—
652	#3496	—	53	4	no	—
653	#3496	—	53	2	no	—
654	#3496	—	53	4	no	—
655	#3496	—	53	2	no	—
656	#3496	—	53	4	no	—
657	#3496	—	53	1	no	—
658	#3496	D₅₃	1	1	yes	characteristic, direct product factor
659	C₂×#547	—	53	4	no	—
660	C₂×#546	—	53	8	no	—
661	C₂×D₄²	—	53	4	no	—
662	C₂×#537	—	53	2	no	—
663	C₂×#534	—	53	4	no	—
664	C₂×#532	—	53	2	no	—
665	C₂²×#121	—	53	4	no	—
666	C₂²×C₄×D₄	—	53	1	no	—
667	C₂×C₅₃	—	2	2	no	—
668	C₂×C₅₃	—	2	8	no	—
669	C₂×C₅₃	—	4	8	no	—
670	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
671	C₂×C₅₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
672	C₂×C₅₃	C₂×#585	1	1	yes	characteristic
673	D₅₃	—	2	2	no	—
674	D₅₃	—	2	8	no	—
675	D₅₃	—	4	8	no	—
676	D₅₃	#3496	1	4	yes	direct product factor
677	C₂×H(5,𝔽₂)	—	53	8	no	—
678	C₂×H(5,𝔽₂)	—	53	4	no	—
679	C₂×H(5,𝔽₂)	—	53	2	no	—
680	C₂×H(5,𝔽₂)	—	53	8	no	—
681	C₂×H(5,𝔽₂)	—	53	8	no	—
682	C₂×H(5,𝔽₂)	—	106	32	no	—
683	C₂×H(5,𝔽₂)	C₂×D₅₃	1	2	yes	complemented
684	C₂²×#41	—	53	4	no	—
685	C₂²×#41	—	53	8	no	—
686	C₂³×D₄	—	53	1	no	—
687	C₂³×D₄	—	53	8	no	—
688	C₂³×D₄	—	53	8	no	—
689	C₂³×D₄	—	53	4	no	—
690	C₂⁴×C₄	—	53	2	no	—
691	#547	—	53	8	no	—
692	#547	—	53	4	no	—
693	#547	—	53	16	no	—
694	#547	—	53	8	no	—
695	#547	—	53	8	no	—
696	#547	—	53	4	no	—
697	#547	—	53	4	no	—
698	#547	—	53	8	no	—
699	#547	C₂×D₅₃	1	4	yes	complemented
700	#546	—	53	8	no	—
701	#546	—	53	8	no	—
702	#546	—	53	8	no	—
703	#546	—	53	16	no	—
704	#546	—	53	8	no	—
705	#546	—	53	8	no	—
706	#546	—	53	16	no	—
707	#546	—	53	16	no	—
708	#546	—	53	8	no	—
709	#546	—	53	8	no	—
710	#546	—	53	16	no	—
711	#546	C₂×D₅₃	1	8	yes	complemented
712	D₄²	—	53	8	no	—
713	D₄²	—	53	8	no	—
714	D₄²	—	53	4	no	—
715	D₄²	—	53	8	no	—
716	D₄²	—	53	8	no	—
717	D₄²	—	53	16	no	—
718	D₄²	—	53	4	no	—
719	D₄²	—	53	4	no	—
720	D₄²	C₂×D₅₃	1	4	yes	complemented
721	#537	—	53	4	no	—
722	#537	—	53	8	no	—
723	#537	—	53	8	no	—
724	#537	—	53	8	no	—
725	#537	—	53	2	no	—
726	#537	C₂×D₅₃	1	2	yes	complemented
727	#534	—	53	8	no	—
728	#534	—	53	16	no	—
729	#534	—	53	8	no	—
730	#534	—	53	8	no	—
731	#534	—	53	16	no	—
732	#534	—	53	4	no	—
733	#534	C₂×D₅₃	1	4	yes	complemented
734	#532	—	53	4	no	—
735	#532	—	53	2	no	—
736	#532	—	53	2	no	—
737	#532	—	53	4	no	—
738	#532	—	53	4	no	—
739	#532	—	53	4	no	—
740	#532	—	53	4	no	—
741	#532	—	53	4	no	—
742	#532	—	53	2	no	—
743	#532	C₂×D₅₃	1	2	yes	complemented
744	C₂×C₄⋊Q₈	—	53	2	no	—
745	C₂×#127	—	53	2	no	—
746	C₂×#124	—	53	4	no	—
747	C₂×#123	—	53	16	no	—
748	C₂×C₂²⋊Q₈	—	53	8	no	—
749	C₂×#121	—	53	4	no	—
750	C₂×#121	—	53	8	no	—
751	C₂×#121	—	53	4	no	—
752	C₂×#121	—	53	4	no	—
753	C₂×#121	—	53	8	no	—
754	C₂×#121	—	53	8	no	—
755	C₂×#121	—	53	8	no	—
756	C₂×#121	—	53	8	no	—
757	C₂×#121	—	53	8	no	—
758	C₂×#121	—	53	8	no	—
759	C₂×#121	—	53	8	no	—
760	C₂×#121	—	53	4	no	—
761	C₂×#121	—	53	8	no	—
762	C₂×#121	—	53	4	no	—
763	C₂×#121	—	53	8	no	—
764	C₂×#121	C₂×D₅₃	1	4	yes	complemented
765	C₂×#120	—	53	16	no	—
766	C₂×C₄×D₄	—	53	1	no	—
767	C₂×C₄×D₄	—	53	2	no	—
768	C₂×C₄×D₄	—	53	4	no	—
769	C₂×C₄×D₄	—	53	4	no	—
770	C₂×C₄×D₄	—	53	4	no	—
771	C₂×C₄×D₄	—	53	4	no	—
772	C₂×C₄×D₄	—	53	4	no	—
773	C₂×C₄×D₄	—	53	4	no	—
774	C₂×C₄×D₄	—	53	1	no	—
775	C₂×C₄×D₄	—	53	2	no	—
776	C₂×C₄×D₄	—	53	1	no	—
777	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
778	C₂²×C₄⋊C₄	—	53	1	no	—
779	C₂²×C₄⋊C₄	—	53	4	no	—
780	C₂²×C₂²⋊C₄	—	53	2	no	—
781	C₂²×C₂²⋊C₄	—	53	8	no	—
782	C₂²×C₄²	—	53	1	no	—
783	C₅₃	C₂×#3496	1	1	yes	characteristic, complemented, Sylow
784	C₂⁵	—	53	2	no	—
785	C₂⁵	—	53	8	no	—
786	H(5,𝔽₂)	—	2	16	no	—
787	H(5,𝔽₂)	—	106	64	no	—
788	H(5,𝔽₂)	—	106	64	no	—
789	H(5,𝔽₂)	—	106	64	no	—
790	H(5,𝔽₂)	—	106	32	no	—
791	H(5,𝔽₂)	—	106	16	no	—
792	C₂×#41	—	53	4	no	—
793	C₂×#41	—	53	8	no	—
794	C₂×#41	—	53	8	no	—
795	C₂×#41	—	53	4	no	—
796	C₂×#41	—	53	8	no	—
797	C₂×#41	—	53	16	no	—
798	C₂×#41	—	53	8	no	—
799	C₂×#41	—	53	4	no	—
800	C₂×#41	—	53	8	no	—
801	C₂×#41	—	53	16	no	—
802	C₂×#41	—	106	32	no	—
803	C₂×#41	—	106	64	no	—
804	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
805	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
806	C₂²×Q₈	—	53	4	no	—
807	C₂²×D₄	—	53	2	no	—
808	C₂²×D₄	—	53	16	no	—
809	C₂²×D₄	—	53	4	no	—
810	C₂²×D₄	—	53	4	no	—
811	C₂²×D₄	—	53	8	no	—
812	C₂²×D₄	—	53	8	no	—
813	C₂²×D₄	—	53	16	no	—
814	C₂²×D₄	—	53	8	no	—
815	C₂²×D₄	—	53	4	no	—
816	C₂²×D₄	—	53	16	no	—
817	C₂²×D₄	—	53	8	no	—
818	C₂²×D₄	—	53	4	no	—
819	C₂²×D₄	—	53	16	no	—
820	C₂²×D₄	—	53	16	no	—
821	C₂²×D₄	—	53	16	no	—
822	C₂²×D₄	—	53	8	no	—
823	C₂²×D₄	—	53	8	no	—
824	C₂²×D₄	—	53	4	no	—
825	C₂²×D₄	—	53	8	no	—
826	C₂²×D₄	—	53	8	no	—
827	C₂²×D₄	—	53	8	no	—
828	C₂²×D₄	—	53	1	no	—
829	C₂²×D₄	—	53	8	no	—
830	C₂²×D₄	—	53	8	no	—
831	C₂²×D₄	—	53	4	no	—
832	C₂²×D₄	—	106	64	no	—
833	C₂²×D₄	—	106	64	no	—
834	C₂²×D₄	—	212	16	no	—
835	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
836	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
837	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
838	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
839	C₂³×C₄	—	53	1	no	—
840	C₂³×C₄	—	53	2	no	—
841	C₂³×C₄	—	53	8	no	—
842	C₂³×C₄	—	53	4	no	—
843	C₂³×C₄	—	53	8	no	—
844	C₂³×C₄	—	53	1	no	—
845	C₂³×C₄	—	53	4	no	—
846	C₂³×C₄	—	53	1	no	—
847	C₂³×C₄	—	53	2	no	—
848	C₂³×C₄	—	53	2	no	—
849	C₂³×C₄	—	53	4	no	—
850	C₂³×C₄	—	53	4	no	—
851	C₂³×C₄	—	53	2	no	—
852	C₂³×C₄	—	212	8	no	—
853	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
854	C₄⋊Q₈	—	53	4	no	—
855	C₄⋊Q₈	—	53	4	no	—
856	C₄⋊Q₈	—	53	4	no	—
857	C₄⋊Q₈	—	53	2	no	—
858	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
859	#127	—	53	4	no	—
860	#127	—	53	4	no	—
861	#127	—	53	4	no	—
862	#127	—	53	2	no	—
863	#127	C₂²×D₅₃	1	2	yes	complemented
864	#124	—	53	4	no	—
865	#124	—	53	4	no	—
866	#124	—	53	8	no	—
867	#124	—	53	8	no	—
868	#124	—	53	4	no	—
869	#124	C₂²×D₅₃	1	4	yes	complemented
870	#123	—	53	16	no	—
871	#123	—	53	16	no	—
872	#123	—	53	16	no	—
873	#123	—	53	16	no	—
874	#123	—	53	16	no	—
875	#123	—	53	16	no	—
876	#123	—	53	16	no	—
877	#123	C₂²×D₅₃	1	16	yes	complemented
878	C₂²⋊Q₈	—	53	8	no	—
879	C₂²⋊Q₈	—	53	8	no	—
880	C₂²⋊Q₈	—	53	16	no	—
881	C₂²⋊Q₈	—	53	8	no	—
882	C₂²⋊Q₈	—	53	16	no	—
883	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
884	#121	—	53	4	no	—
885	#121	—	53	8	no	—
886	#121	—	53	8	no	—
887	#121	—	53	16	no	—
888	#121	—	53	8	no	—
889	#121	—	53	16	no	—
890	#121	—	53	8	no	—
891	#121	—	53	16	no	—
892	#121	—	53	4	no	—
893	#121	—	53	8	no	—
894	#121	—	53	8	no	—
895	#121	—	53	16	no	—
896	#121	—	53	4	no	—
897	#121	—	53	8	no	—
898	#121	—	53	8	no	—
899	#121	—	53	8	no	—
900	#121	—	53	4	no	—
901	#121	—	53	8	no	—
902	#121	—	53	4	no	—
903	#121	—	53	8	no	—
904	#121	—	53	8	no	—
905	#121	—	53	8	no	—
906	#121	—	53	4	no	—
907	#121	—	53	8	no	—
908	#121	—	53	8	no	—
909	#121	—	53	16	no	—
910	#121	—	53	16	no	—
911	#121	—	53	16	no	—
912	#121	—	53	8	no	—
913	#121	—	53	16	no	—
914	#121	C₂²×D₅₃	1	4	yes	complemented
915	#121	C₂²×D₅₃	1	8	yes	complemented
916	#121	C₂²×D₅₃	1	8	yes	complemented
917	#121	C₂²×D₅₃	1	8	yes	complemented
918	#121	C₂²×D₅₃	1	4	yes	complemented
919	#121	C₂²×D₅₃	1	8	yes	complemented
920	#120	—	53	16	no	—
921	#120	—	53	16	no	—
922	#120	—	53	16	no	—
923	#120	—	53	16	no	—
924	#120	—	53	16	no	—
925	#120	—	53	16	no	—
926	#120	—	53	16	no	—
927	#120	C₂²×D₅₃	1	16	yes	complemented
928	C₄×D₄	—	53	4	no	—
929	C₄×D₄	—	53	4	no	—
930	C₄×D₄	—	53	4	no	—
931	C₄×D₄	—	53	4	no	—
932	C₄×D₄	—	53	8	no	—
933	C₄×D₄	—	53	8	no	—
934	C₄×D₄	—	53	8	no	—
935	C₄×D₄	—	53	8	no	—
936	C₄×D₄	—	53	4	no	—
937	C₄×D₄	—	53	4	no	—
938	C₄×D₄	—	53	4	no	—
939	C₄×D₄	—	53	4	no	—
940	C₄×D₄	—	53	8	no	—
941	C₄×D₄	—	53	8	no	—
942	C₄×D₄	—	53	8	no	—
943	C₄×D₄	—	53	8	no	—
944	C₄×D₄	—	53	4	no	—
945	C₄×D₄	—	53	4	no	—
946	C₄×D₄	—	53	4	no	—
947	C₄×D₄	—	53	4	no	—
948	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
949	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
950	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
951	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
952	C₂×C₄⋊C₄	—	53	2	no	—
953	C₂×C₄⋊C₄	—	53	1	no	—
954	C₂×C₄⋊C₄	—	53	8	no	—
955	C₂×C₄⋊C₄	—	53	4	no	—
956	C₂×C₄⋊C₄	—	53	4	no	—
957	C₂×C₄⋊C₄	—	53	4	no	—
958	C₂×C₄⋊C₄	—	53	4	no	—
959	C₂×C₄⋊C₄	—	53	8	no	—
960	C₂×C₄⋊C₄	—	53	8	no	—
961	C₂×C₄⋊C₄	—	53	8	no	—
962	C₂×C₄⋊C₄	—	53	4	no	—
963	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
964	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
965	C₂×C₂²⋊C₄	—	53	2	no	—
966	C₂×C₂²⋊C₄	—	53	8	no	—
967	C₂×C₂²⋊C₄	—	53	2	no	—
968	C₂×C₂²⋊C₄	—	53	2	no	—
969	C₂×C₂²⋊C₄	—	53	8	no	—
970	C₂×C₂²⋊C₄	—	53	8	no	—
971	C₂×C₂²⋊C₄	—	53	8	no	—
972	C₂×C₂²⋊C₄	—	53	8	no	—
973	C₂×C₂²⋊C₄	—	53	8	no	—
974	C₂×C₂²⋊C₄	—	53	16	no	—
975	C₂×C₂²⋊C₄	—	53	16	no	—
976	C₂×C₂²⋊C₄	—	53	16	no	—
977	C₂×C₂²⋊C₄	—	53	8	no	—
978	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
979	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
980	C₂×C₄²	—	53	1	no	—
981	C₂×C₄²	—	53	1	no	—
982	C₂×C₄²	—	53	1	no	—
983	C₂×C₄²	—	53	2	no	—
984	C₂×C₄²	—	53	2	no	—
985	C₂×C₄²	—	53	2	no	—
986	C₂×C₄²	—	53	2	no	—
987	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
988	C₂⁴	—	53	4	no	—
989	C₂⁴	—	53	1	no	—
990	C₂⁴	—	53	16	no	—
991	C₂⁴	—	53	2	no	—
992	C₂⁴	—	53	4	no	—
993	C₂⁴	—	53	8	no	—
994	C₂⁴	—	53	16	no	—
995	C₂⁴	—	53	8	no	—
996	C₂⁴	—	106	32	no	—
997	C₂⁴	—	212	16	no	—
998	C₂⁴	—	212	16	no	—
999	C₂⁴	—	212	4	no	—
1000	C₂⁴	—	212	4	no	—
1001	C₂⁴	C₂³×D₅₃	1	8	yes	—
1002	C₂⁴	C₂³×D₅₃	1	2	yes	—
1003	#41	—	2	32	no	—
1004	#41	—	2	16	no	—
1005	#41	—	106	32	no	—
1006	#41	—	106	64	no	—
1007	#41	—	106	32	no	—
1008	#41	—	106	32	no	—
1009	#41	—	106	16	no	—
1010	#41	—	106	16	no	—
1011	#41	—	106	64	no	—
1012	#41	—	106	32	no	—
1013	#41	—	106	32	no	—
1014	#41	—	106	16	no	—
1015	C₂×Q₈	—	53	8	no	—
1016	C₂×Q₈	—	53	4	no	—
1017	C₂×Q₈	—	106	16	no	—
1018	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
1019	C₂×D₄	—	2	32	no	—
1020	C₂×D₄	—	2	32	no	—
1021	C₂×D₄	—	4	8	no	—
1022	C₂×D₄	—	53	16	no	—
1023	C₂×D₄	—	53	8	no	—
1024	C₂×D₄	—	53	32	no	—
1025	C₂×D₄	—	53	32	no	—
1026	C₂×D₄	—	53	8	no	—
1027	C₂×D₄	—	53	16	no	—
1028	C₂×D₄	—	53	16	no	—
1029	C₂×D₄	—	53	8	no	—
1030	C₂×D₄	—	53	8	no	—
1031	C₂×D₄	—	53	8	no	—
1032	C₂×D₄	—	53	8	no	—
1033	C₂×D₄	—	53	16	no	—
1034	C₂×D₄	—	53	8	no	—
1035	C₂×D₄	—	53	4	no	—
1036	C₂×D₄	—	53	4	no	—
1037	C₂×D₄	—	53	16	no	—
1038	C₂×D₄	—	53	8	no	—
1039	C₂×D₄	—	53	4	no	—
1040	C₂×D₄	—	53	4	no	—
1041	C₂×D₄	—	53	8	no	—
1042	C₂×D₄	—	106	32	no	—
1043	C₂×D₄	—	106	32	no	—
1044	C₂×D₄	—	106	16	no	—
1045	C₂×D₄	—	106	16	no	—
1046	C₂×D₄	—	106	64	no	—
1047	C₂×D₄	—	106	32	no	—
1048	C₂×D₄	—	106	32	no	—
1049	C₂×D₄	—	106	64	no	—
1050	C₂×D₄	—	106	64	no	—
1051	C₂×D₄	—	106	64	no	—
1052	C₂×D₄	—	106	64	no	—
1053	C₂×D₄	—	106	32	no	—
1054	C₂×D₄	—	106	32	no	—
1055	C₂×D₄	—	106	32	no	—
1056	C₂×D₄	—	212	8	no	—
1057	C₂×D₄	—	212	16	no	—
1058	C₂×D₄	—	212	16	no	—
1059	C₂×D₄	—	212	8	no	—
1060	C₂×D₄	—	212	16	no	—
1061	C₂×D₄	—	212	16	no	—
1062	C₂×D₄	D₄×D₅₃	1	8	yes	complemented
1063	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1064	C₂×D₄	C₂³×D₅₃	1	16	yes	—
1065	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1066	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1067	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1068	C₂×D₄	C₂³×D₅₃	1	8	yes	—
1069	C₂×D₄	C₂³×D₅₃	1	4	yes	—
1070	C₂²×C₄	—	4	4	no	—
1071	C₂²×C₄	—	53	1	no	—
1072	C₂²×C₄	—	53	8	no	—
1073	C₂²×C₄	—	53	1	no	—
1074	C₂²×C₄	—	53	2	no	—
1075	C₂²×C₄	—	53	2	no	—
1076	C₂²×C₄	—	53	1	no	—
1077	C₂²×C₄	—	53	8	no	—
1078	C₂²×C₄	—	53	4	no	—
1079	C₂²×C₄	—	53	8	no	—
1080	C₂²×C₄	—	53	1	no	—
1081	C₂²×C₄	—	53	4	no	—
1082	C₂²×C₄	—	53	2	no	—
1083	C₂²×C₄	—	53	2	no	—
1084	C₂²×C₄	—	53	1	no	—
1085	C₂²×C₄	—	53	1	no	—
1086	C₂²×C₄	—	53	1	no	—
1087	C₂²×C₄	—	53	4	no	—
1088	C₂²×C₄	—	53	8	no	—
1089	C₂²×C₄	—	53	16	no	—
1090	C₂²×C₄	—	53	4	no	—
1091	C₂²×C₄	—	53	4	no	—
1092	C₂²×C₄	—	53	8	no	—
1093	C₂²×C₄	—	53	8	no	—
1094	C₂²×C₄	—	53	2	no	—
1095	C₂²×C₄	—	53	4	no	—
1096	C₂²×C₄	—	53	4	no	—
1097	C₂²×C₄	—	53	4	no	—
1098	C₂²×C₄	—	106	4	no	—
1099	C₂²×C₄	—	106	16	no	—
1100	C₂²×C₄	—	106	32	no	—
1101	C₂²×C₄	—	106	32	no	—
1102	C₂²×C₄	—	212	4	no	—
1103	C₂²×C₄	—	212	8	no	—
1104	C₂²×C₄	—	212	8	no	—
1105	C₂²×C₄	—	212	4	no	—
1106	C₂²×C₄	—	212	2	no	—
1107	C₂²×C₄	—	212	8	no	—
1108	C₂²×C₄	—	212	4	no	—
1109	C₂²×C₄	—	212	4	no	—
1110	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1111	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1112	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1113	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
1114	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1115	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
1116	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
1117	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
1118	C₄⋊C₄	—	53	8	no	—
1119	C₄⋊C₄	—	53	4	no	—
1120	C₄⋊C₄	—	53	8	no	—
1121	C₄⋊C₄	—	53	4	no	—
1122	C₄⋊C₄	—	53	16	no	—
1123	C₄⋊C₄	—	53	8	no	—
1124	C₄⋊C₄	—	53	8	no	—
1125	C₄⋊C₄	—	53	4	no	—
1126	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1127	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1128	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
1129	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1130	C₂²⋊C₄	—	53	8	no	—
1131	C₂²⋊C₄	—	53	8	no	—
1132	C₂²⋊C₄	—	53	16	no	—
1133	C₂²⋊C₄	—	53	8	no	—
1134	C₂²⋊C₄	—	53	8	no	—
1135	C₂²⋊C₄	—	53	8	no	—
1136	C₂²⋊C₄	—	53	8	no	—
1137	C₂²⋊C₄	—	53	8	no	—
1138	C₂²⋊C₄	—	53	16	no	—
1139	C₂²⋊C₄	—	53	16	no	—
1140	C₂²⋊C₄	—	53	8	no	—
1141	C₂²⋊C₄	—	53	8	no	—
1142	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1143	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1144	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1145	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1146	C₄²	—	53	2	no	—
1147	C₄²	—	53	2	no	—
1148	C₄²	—	53	2	no	—
1149	C₄²	—	53	2	no	—
1150	C₄²	—	53	2	no	—
1151	C₄²	—	53	2	no	—
1152	C₄²	C₂³×D₅₃	1	2	yes	—
1153	C₄²	C₂³×D₅₃	1	2	yes	—
1154	C₂³	—	2	16	no	—
1155	C₂³	—	4	2	no	—
1156	C₂³	—	4	2	no	—
1157	C₂³	—	4	8	no	—
1158	C₂³	—	4	8	no	—
1159	C₂³	—	53	1	no	—
1160	C₂³	—	53	4	no	—
1161	C₂³	—	53	16	no	—
1162	C₂³	—	53	4	no	—
1163	C₂³	—	53	1	no	—
1164	C₂³	—	53	16	no	—
1165	C₂³	—	53	8	no	—
1166	C₂³	—	53	8	no	—
1167	C₂³	—	106	2	no	—
1168	C₂³	—	106	8	no	—
1169	C₂³	—	106	2	no	—
1170	C₂³	—	106	8	no	—
1171	C₂³	—	106	32	no	—
1172	C₂³	—	106	16	no	—
1173	C₂³	—	106	16	no	—
1174	C₂³	—	106	16	no	—
1175	C₂³	—	106	16	no	—
1176	C₂³	—	424	64	no	—
1177	C₂³	—	212	8	no	—
1178	C₂³	—	212	16	no	—
1179	C₂³	—	212	8	no	—
1180	C₂³	—	212	16	no	—
1181	C₂³	—	212	2	no	—
1182	C₂³	—	212	4	no	—
1183	C₂³	—	212	2	no	—
1184	C₂³	—	212	4	no	—
1185	C₂³	—	212	32	no	—
1186	C₂³	C₂×D₄×D₅₃	1	8	yes	complemented
1187	C₂³	C₂⁴×D₅₃	1	8	yes	—
1188	C₂³	C₂⁴×D₅₃	1	4	yes	—
1189	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1190	Q₈	—	2	8	no	—
1191	Q₈	—	106	16	no	—
1192	Q₈	—	106	8	no	—
1193	D₄	—	2	32	no	—
1194	D₄	—	2	16	no	—
1195	D₄	—	2	8	no	—
1196	D₄	—	2	8	no	—
1197	D₄	—	4	8	no	—
1198	D₄	—	4	4	no	—
1199	D₄	—	53	32	no	—
1200	D₄	—	53	16	no	—
1201	D₄	—	106	16	no	—
1202	D₄	—	106	32	no	—
1203	D₄	—	106	16	no	—
1204	D₄	—	106	16	no	—
1205	D₄	—	106	16	no	—
1206	D₄	—	106	32	no	—
1207	D₄	—	106	32	no	—
1208	D₄	—	106	16	no	—
1209	D₄	—	106	8	no	—
1210	D₄	—	106	8	no	—
1211	D₄	—	212	4	no	—
1212	D₄	—	212	8	no	—
1213	D₄	—	212	8	no	—
1214	D₄	—	212	16	no	—
1215	D₄	C₂×D₄×D₅₃	1	16	yes	complemented
1216	C₂×C₄	—	2	16	no	—
1217	C₂×C₄	—	2	16	no	—
1218	C₂×C₄	—	2	2	no	—
1219	C₂×C₄	—	2	8	no	—
1220	C₂×C₄	—	4	4	no	—
1221	C₂×C₄	—	4	2	no	—
1222	C₂×C₄	—	4	1	no	—
1223	C₂×C₄	—	53	4	no	—
1224	C₂×C₄	—	53	1	no	—
1225	C₂×C₄	—	53	2	no	—
1226	C₂×C₄	—	53	8	no	—
1227	C₂×C₄	—	53	8	no	—
1228	C₂×C₄	—	53	4	no	—
1229	C₂×C₄	—	53	2	no	—
1230	C₂×C₄	—	53	1	no	—
1231	C₂×C₄	—	53	4	no	—
1232	C₂×C₄	—	53	8	no	—
1233	C₂×C₄	—	106	2	no	—
1234	C₂×C₄	—	106	8	no	—
1235	C₂×C₄	—	106	16	no	—
1236	C₂×C₄	—	106	16	no	—
1237	C₂×C₄	—	106	2	no	—
1238	C₂×C₄	—	106	8	no	—
1239	C₂×C₄	—	106	32	no	—
1240	C₂×C₄	—	106	4	no	—
1241	C₂×C₄	—	106	2	no	—
1242	C₂×C₄	—	106	8	no	—
1243	C₂×C₄	—	106	16	no	—
1244	C₂×C₄	—	106	16	no	—
1245	C₂×C₄	—	106	16	no	—
1246	C₂×C₄	—	106	2	no	—
1247	C₂×C₄	—	106	8	no	—
1248	C₂×C₄	—	212	2	no	—
1249	C₂×C₄	—	212	4	no	—
1250	C₂×C₄	—	212	4	no	—
1251	C₂×C₄	—	212	4	no	—
1252	C₂×C₄	—	212	1	no	—
1253	C₂×C₄	—	212	4	no	—
1254	C₂×C₄	—	212	2	no	—
1255	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	complemented
1256	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1257	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1258	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1259	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1260	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1261	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	4	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	4	no	—
1266	C₂²	—	2	8	no	—
1267	C₂²	—	2	8	no	—
1268	C₂²	—	2	8	no	—
1269	C₂²	—	4	8	no	—
1270	C₂²	—	8	16	no	—
1271	C₂²	—	53	2	no	—
1272	C₂²	—	53	2	no	—
1273	C₂²	—	53	2	no	—
1274	C₂²	—	53	2	no	—
1275	C₂²	—	53	8	no	—
1276	C₂²	—	106	32	no	—
1277	C₂²	—	106	8	no	—
1278	C₂²	—	106	1	no	—
1279	C₂²	—	106	4	no	—
1280	C₂²	—	106	1	no	—
1281	C₂²	—	106	4	no	—
1282	C₂²	—	106	8	no	—
1283	C₂²	—	106	8	no	—
1284	C₂²	—	106	8	no	—
1285	C₂²	—	424	16	no	—
1286	C₂²	—	424	32	no	—
1287	C₂²	—	212	8	no	—
1288	C₂²	—	212	16	no	—
1289	C₂²	—	212	32	no	—
1290	C₂²	C₂²×D₄×D₅₃	1	8	yes	—
1291	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1292	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1293	C₄	—	2	8	no	—
1294	C₄	—	2	1	no	—
1295	C₄	—	2	4	no	—
1296	C₄	—	2	2	no	—
1297	C₄	—	53	4	no	—
1298	C₄	—	53	2	no	—
1299	C₄	—	106	8	no	—
1300	C₄	—	106	1	no	—
1301	C₄	—	106	4	no	—
1302	C₄	—	106	2	no	—
1303	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1304	C₄	H(5,𝔽₂)×D₅₃	1	2	yes	complemented
1305	C₂	—	2	2	no	—
1306	C₂	—	2	8	no	—
1307	C₂	—	4	8	no	—
1308	C₂	—	53	4	no	—
1309	C₂	—	106	8	no	—
1310	C₂	—	106	2	no	—
1311	C₂	—	212	8	no	—
1312	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1313	C₂	C₂×H(5,𝔽₂)×D₅₃	1	1	yes	characteristic
1314	C₂	#585×D₅₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₅₃×#3496	C₂
hypercenter	#3496	D₅₃
hypocenter	C₅₃	C₂×#3496
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ #3496

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. #20288479	C₂	semidirect
3. #20288478	C₂	semidirect
4. #20288477	C₂	semidirect
5. #20288476	C₂	semidirect
6. #20288475	C₂	semidirect
7. #20288474	C₂	semidirect
8. #20288473	C₂	semidirect
9. #20288472	C₂	semidirect
10. #20288471	C₂	semidirect
11. #547×D₅₃	C₂	semidirect
12. #546×D₅₃	C₂	semidirect
13. D₄²×D₅₃	C₂	semidirect
14. #537×D₅₃	C₂	semidirect
15. #534×D₅₃	C₂	semidirect
16. #532×D₅₃	C₂	semidirect
17. C₂×#121×D₅₃	C₂	semidirect
18. C₂×C₄×D₄×D₅₃	C₂	semidirect
19. C₅₃×#3496	C₂	semidirect
20. C₂×#13133263	C₂²	semidirect
21. C₂×#13133263	C₂²	semidirect
22. C₂×#13133262	C₂²	semidirect
23. C₂×#13133262	C₂²	semidirect
24. C₂×#13133262	C₂²	semidirect
26. C₂×#41×D₅₃	C₂²	semidirect
27. C₂×#41×D₅₃	C₂²	semidirect
29. C₂²×D₄×D₅₃	C₂²	semidirect
30. C₂²×D₄×D₅₃	C₂²	semidirect
31. C₂²×D₄×D₅₃	C₂²	semidirect
32. C₂³×C₄×D₅₃	C₂²	semidirect
33. #16811278	C₂²	semidirect
34. #16811277	C₂²	semidirect
35. #16811276	C₂²	semidirect
36. #16811275	C₂²	semidirect
37. #16811274	C₂²	semidirect
38. #16811273	C₂²	semidirect
39. #16811272	C₂²	semidirect
40. #16811271	C₂²	semidirect
41. #16811270	C₂²	semidirect
42. #16811269	C₂²	semidirect
43. #16811268	C₂²	semidirect
44. #16811267	C₂²	semidirect
45. #16811266	C₂²	semidirect
46. #16811265	C₂²	semidirect
47. #16811264	C₂²	semidirect
48. #16811263	C₂²	semidirect
49. #16811262	C₂²	semidirect
50. #16811261	C₂²	semidirect
51. #16811260	C₂²	semidirect
52. D₄×D₂₁₂	C₂²	semidirect
53. D₄×D₂₁₂	C₂²	semidirect
54. #16811258	C₂²	semidirect
55. #16811257	C₂²	semidirect
56. #16811257	C₂²	semidirect
57. D₄×C₂²⋊D₅₃	C₂²	semidirect
58. D₄×C₂²⋊D₅₃	C₂²	semidirect
59. #16811255	C₂²	semidirect
60. #16811204	C₂²	semidirect
61. #16811203	C₂²	semidirect
62. #16811202	C₂²	semidirect
63. #16811201	C₂²	semidirect
64. #16811200	C₂²	semidirect
65. #16811185	C₂²	semidirect
66. #16811184	C₂²	semidirect
67. #16811183	C₂²	semidirect
68. #16811182	C₂²	semidirect
69. #16811181	C₂²	semidirect
70. #16811181	C₂²	semidirect
71. #16811174	C₂²	semidirect
72. #16811173	C₂²	semidirect
73. #16811172	C₂²	semidirect
74. #16811171	C₂²	semidirect
75. #16811170	C₂²	semidirect
76. #16811170	C₂²	semidirect
77. #16811169	C₂²	semidirect
78. #16811168	C₂²	semidirect
79. #16811168	C₂²	semidirect
80. C₄⋊Q₈×D₅₃	C₂²	semidirect
81. #127×D₅₃	C₂²	semidirect
82. #124×D₅₃	C₂²	semidirect
83. #123×D₅₃	C₂²	semidirect
84. C₂²⋊Q₈×D₅₃	C₂²	semidirect
85. C₂×#13133192	C₂²	semidirect
86. C₂×#13133191	C₂²	semidirect
87. C₂×#13133190	C₂²	semidirect
88. C₂×#13133189	C₂²	semidirect
89. C₂×#13133188	C₂²	semidirect
90. #121×D₅₃	C₂²	semidirect
91. #121×D₅₃	C₂²	semidirect
92. #121×D₅₃	C₂²	semidirect
93. #121×D₅₃	C₂²	semidirect
94. #121×D₅₃	C₂²	semidirect
95. #121×D₅₃	C₂²	semidirect
96. #121×D₅₃	C₂²	semidirect
97. #121×D₅₃	C₂²	semidirect
98. #121×D₅₃	C₂²	semidirect
99. #121×D₅₃	C₂²	semidirect
100. #120×D₅₃	C₂²	semidirect
101. C₂×C₄×D₂₁₂	C₂²	semidirect
102. C₂×D₄×Dic₅₃	C₂²	semidirect
103. C₂×#13133179	C₂²	semidirect
104. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
105. C₂×#13133177	C₂²	semidirect
106. C₄×D₄×D₅₃	C₂²	semidirect
107. C₄×D₄×D₅₃	C₂²	semidirect
108. C₄×D₄×D₅₃	C₂²	semidirect
109. C₄×D₄×D₅₃	C₂²	semidirect
110. C₄×D₄×D₅₃	C₂²	semidirect
111. C₄×D₄×D₅₃	C₂²	semidirect
112. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
113. C₂×C₄⋊C₄×D₅₃	C₂²	semidirect
114. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
115. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
116. C₂×C₄²×D₅₃	C₂²	semidirect
117. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
118. C₅₃×#547	C₂²	semidirect
119. C₅₃×#546	C₂²	semidirect
120. D₄²×C₅₃	C₂²	semidirect
121. C₅₃×#537	C₂²	semidirect
122. C₅₃×#534	C₂²	semidirect
123. C₅₃×#532	C₂²	semidirect
124. C₂×#121×C₅₃	C₂²	semidirect
125. C₂×C₄×D₄×C₅₃	C₂²	semidirect
133. C₂×#11719949	C₂³	semidirect
134. C₂×#11719949	C₂³	semidirect
135. C₂×#11719945	C₂³	semidirect
136. C₂×#11719945	C₂³	semidirect
137. C₂×#11719945	C₂³	semidirect
138. C₂×#11719945	C₂³	semidirect
139. C₂×#11719947	C₂³	semidirect
140. C₂×#11719947	C₂³	semidirect
141. C₂×#11719947	C₂³	semidirect
142. C₂×#11719947	C₂³	semidirect
147. C₂²×D₂₁₂	C₂³	semidirect
148. C₂²×D₂₁₂	C₂³	semidirect
149. C₂²×D₂₁₂	C₂³	semidirect
151. C₂²×C₂²⋊D₅₃	C₂³	semidirect
152. C₂²×C₂²⋊D₅₃	C₂³	semidirect
153. C₂²×C₂²⋊D₅₃	C₂³	semidirect
154. C₂²×C₂²⋊D₅₃	C₂³	semidirect
158. C₂×D₄×D₅₃	D₄	semidirect
167. C₂×D₄×D₅₃	C₂³	semidirect
168. C₂×D₄×D₅₃	C₂³	semidirect
169. C₂×D₄×D₅₃	C₂³	semidirect
170. C₂×D₄×D₅₃	C₂³	semidirect
171. C₂×D₄×D₅₃	C₂³	semidirect
172. C₂×D₄×D₅₃	C₂³	semidirect
173. C₂×D₄×D₅₃	C₂³	semidirect
174. C₂³×Dic₅₃	C₂³	semidirect
184. C₂²×C₄×D₅₃	C₂³	semidirect
185. C₂²×C₄×D₅₃	C₂³	semidirect
186. C₂²×C₄×D₅₃	C₂³	semidirect
187. C₂²×C₄×D₅₃	C₂³	semidirect
188. #13133217	C₂³	semidirect
189. #13133216	C₂³	semidirect
190. #13133216	C₂³	semidirect
191. #13133215	C₂³	semidirect
192. #13133214	C₂³	semidirect
193. #13133213	C₂³	semidirect
194. #13133213	C₂³	semidirect
195. #13133213	C₂³	semidirect
196. #13133206	C₂³	semidirect
197. #13133205	C₂³	semidirect
198. #13133204	C₂³	semidirect
199. #13133203	C₂³	semidirect
200. #13133203	C₂³	semidirect
201. #13133202	C₂³	semidirect
202. #13133202	C₂³	semidirect
203. #13133201	C₂³	semidirect
204. #13133200	C₂³	semidirect
205. #13133199	C₂³	semidirect
206. #13133199	C₂³	semidirect
207. #13133198	C₂³	semidirect
208. #13133197	C₂³	semidirect
209. #13133196	C₂³	semidirect
210. #13133195	C₂³	semidirect
211. #13133194	C₂³	semidirect
212. #13133193	C₂³	semidirect
213. #13133192	C₂³	semidirect
214. #13133192	C₂³	semidirect
215. #13133192	C₂³	semidirect
216. #13133192	C₂³	semidirect
217. #13133192	C₂³	semidirect
218. #13133192	C₂³	semidirect
219. #13133191	C₂³	semidirect
220. #13133191	C₂³	semidirect
221. #13133191	C₂³	semidirect
222. #13133191	C₂³	semidirect
223. #13133191	C₂³	semidirect
224. #13133191	C₂³	semidirect
225. #13133190	C₂³	semidirect
226. #13133190	C₂³	semidirect
227. #13133190	C₂³	semidirect
228. #13133190	C₂³	semidirect
229. #13133190	C₂³	semidirect
230. #13133190	C₂³	semidirect
231. #13133189	C₂³	semidirect
232. #13133189	C₂³	semidirect
233. #13133189	C₂³	semidirect
234. #13133189	C₂³	semidirect
235. #13133189	C₂³	semidirect
236. #13133189	C₂³	semidirect
237. #13133188	C₂³	semidirect
238. #13133188	C₂³	semidirect
239. #13133188	C₂³	semidirect
240. #13133188	C₂³	semidirect
241. #13133188	C₂³	semidirect
242. #13133188	C₂³	semidirect
243. #13133187	C₂³	semidirect
244. #13133187	C₂³	semidirect
245. #13133187	C₂³	semidirect
246. #13133186	C₂³	semidirect
247. #13133185	C₂³	semidirect
248. #13133185	C₂³	semidirect
249. #13133185	C₂³	semidirect
250. C₄×D₂₁₂	C₂³	semidirect
251. C₄×D₂₁₂	C₂³	semidirect
252. C₄×D₂₁₂	C₂³	semidirect
253. C₄×D₂₁₂	C₂³	semidirect
254. D₄×Dic₅₃	C₂³	semidirect
255. D₄×Dic₅₃	C₂³	semidirect
256. D₄×Dic₅₃	C₂³	semidirect
257. D₄×Dic₅₃	C₂³	semidirect
258. #13133179	C₂³	semidirect
259. #13133179	C₂³	semidirect
260. #13133179	C₂³	semidirect
261. #13133179	C₂³	semidirect
262. C₄×C₂²⋊D₅₃	C₂³	semidirect
263. C₄×C₂²⋊D₅₃	C₂³	semidirect
264. C₄×C₂²⋊D₅₃	C₂³	semidirect
265. C₄×C₂²⋊D₅₃	C₂³	semidirect
266. #13133177	C₂³	semidirect
267. #13133177	C₂³	semidirect
268. #13133177	C₂³	semidirect
269. #13133177	C₂³	semidirect
270. C₂×C₄⋊Dic₅₃	C₂³	semidirect
271. C₂×C₄⋊Dic₅₃	C₂³	semidirect
272. C₂×#11719919	C₂³	semidirect
273. C₂×#11719919	C₂³	semidirect
278. C₄⋊C₄×D₅₃	C₂³	semidirect
279. C₄⋊C₄×D₅₃	C₂³	semidirect
280. C₄⋊C₄×D₅₃	C₂³	semidirect
281. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
282. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
283. C₂×#11719921	C₂³	semidirect
284. C₂×#11719921	C₂³	semidirect
285. C₂×#11719921	C₂³	semidirect
286. C₂×#11719921	C₂³	semidirect
291. C₂²⋊C₄×D₅₃	C₂³	semidirect
292. C₂²⋊C₄×D₅₃	C₂³	semidirect
293. C₂²⋊C₄×D₅₃	C₂³	semidirect
294. C₂×C₄×Dic₅₃	C₂³	semidirect
295. C₂×C₄×Dic₅₃	C₂³	semidirect
296. C₂×C₄×Dic₅₃	C₂³	semidirect
299. C₄²×D₅₃	C₂³	semidirect
300. C₄²×D₅₃	C₂³	semidirect
302. C₂×#41×C₅₃	C₂³	semidirect
303. C₂×#41×C₅₃	C₂³	semidirect
305. C₂²×D₄×C₅₃	C₂³	semidirect
306. C₂²×D₄×C₅₃	C₂³	semidirect
307. C₂²×D₄×C₅₃	C₂³	semidirect
308. C₂³×C₄×C₅₃	C₂³	semidirect
309. C₄⋊Q₈×C₅₃	C₂³	semidirect
310. #127×C₅₃	C₂³	semidirect
311. #124×C₅₃	C₂³	semidirect
312. #123×C₅₃	C₂³	semidirect
313. C₂²⋊Q₈×C₅₃	C₂³	semidirect
314. #121×C₅₃	C₂³	semidirect
315. #121×C₅₃	C₂³	semidirect
316. #121×C₅₃	C₂³	semidirect
317. #121×C₅₃	C₂³	semidirect
318. #121×C₅₃	C₂³	semidirect
319. #121×C₅₃	C₂³	semidirect
320. #120×C₅₃	C₂³	semidirect
321. C₄×D₄×C₅₃	C₂³	semidirect
322. C₄×D₄×C₅₃	C₂³	semidirect
323. C₄×D₄×C₅₃	C₂³	semidirect
324. C₄×D₄×C₅₃	C₂³	semidirect
325. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
326. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
327. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
328. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
329. C₂×C₄²×C₅₃	C₂³	semidirect
337. C₂³×D₅₃	C₂×D₄	semidirect
351. C₂×D₄×C₅₃	C₂×D₄	semidirect
372. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
411. D₄×D₅₃	C₂×D₄	semidirect
412. D₄×D₅₃	C₂×D₄	semidirect
420. C₂×D₂₁₂	C₂×D₄	semidirect
439. C₂×C₄×D₅₃	C₂×D₄	semidirect
501. C₂³×C₅₃	C₂²×D₄	semidirect
526. C₂²×D₅₃	C₂²×D₄	semidirect
527. C₂²×D₅₃	C₂²×D₄	semidirect
539. D₄×C₅₃	C₂²×D₄	semidirect
547. C₂×C₄×C₅₃	C₂²×D₄	semidirect
562. C₂²⋊D₅₃	C₂²×D₄	semidirect
570. C₂×Dic₅₃	C₂²×D₄	semidirect
583. D₂₁₂	C₂²×D₄	semidirect
600. C₄×D₅₃	C₂²×D₄	semidirect
601. C₄×D₅₃	H(5,𝔽₂)	semidirect
641. C₄×C₅₃	C₂×H(5,𝔽₂)	semidirect
647. Dic₅₃	C₂×H(5,𝔽₂)	semidirect
658. #3496	D₅₃	direct (N × H)
676. D₅₃	#3496	direct (N × H)
683. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
699. #547	C₂×D₅₃	semidirect
711. #546	C₂×D₅₃	semidirect
720. D₄²	C₂×D₅₃	semidirect
726. #537	C₂×D₅₃	semidirect
733. #534	C₂×D₅₃	semidirect
743. #532	C₂×D₅₃	semidirect
764. C₂×#121	C₂×D₅₃	semidirect
777. C₂×C₄×D₄	C₂×D₅₃	semidirect
783. C₅₃	C₂×#3496	semidirect
804. C₂×#41	C₂²×D₅₃	semidirect
805. C₂×#41	C₂²×D₅₃	semidirect
836. C₂²×D₄	C₂²×D₅₃	semidirect
837. C₂²×D₄	C₂²×D₅₃	semidirect
838. C₂²×D₄	C₂²×D₅₃	semidirect
853. C₂³×C₄	C₂²×D₅₃	semidirect
858. C₄⋊Q₈	C₂²×D₅₃	semidirect
863. #127	C₂²×D₅₃	semidirect
869. #124	C₂²×D₅₃	semidirect
877. #123	C₂²×D₅₃	semidirect
883. C₂²⋊Q₈	C₂²×D₅₃	semidirect
914. #121	C₂²×D₅₃	semidirect
915. #121	C₂²×D₅₃	semidirect
916. #121	C₂²×D₅₃	semidirect
917. #121	C₂²×D₅₃	semidirect
918. #121	C₂²×D₅₃	semidirect
919. #121	C₂²×D₅₃	semidirect
927. #120	C₂²×D₅₃	semidirect
948. C₄×D₄	C₂²×D₅₃	semidirect
949. C₄×D₄	C₂²×D₅₃	semidirect
950. C₄×D₄	C₂²×D₅₃	semidirect
951. C₄×D₄	C₂²×D₅₃	semidirect
963. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
964. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
978. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
979. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
987. C₂×C₄²	C₂²×D₅₃	semidirect
1062. C₂×D₄	D₄×D₅₃	semidirect
1186. C₂³	C₂×D₄×D₅₃	semidirect
1215. D₄	C₂×D₄×D₅₃	semidirect
1255. C₂×C₄	C₂×D₄×D₅₃	semidirect
1304. C₄	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
#20288479	2
#20288478	2
#20288477	2
#20288476	2
#20288475	2
#20288474	2
#20288473	2
#20288472	2
#20288471	2
#547×D₅₃	2
#546×D₅₃	2
D₄²×D₅₃	2
#537×D₅₃	2
#534×D₅₃	2
#532×D₅₃	2
C₂×#121×D₅₃	2
C₂×C₄×D₄×D₅₃	2
C₅₃×#3496	2
C₂×#3496	53

Subgroups — D53×#3496 #28291977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₃×#3496 #28291977