Subgroups — #28293101

Order 13568.

11770 conjugacy classes of subgroups.

The subgroup lattice has 1164 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	#20288474	C₂	1	2	yes	maximal, complemented
7	#20288472	C₂	1	4	yes	maximal, complemented
8	#20288354	C₂	1	8	yes	maximal, complemented
9	#20288352	C₂	1	8	yes	maximal, complemented
10	#20288345	C₂	1	8	yes	maximal, complemented
11	#20288343	C₂	1	8	yes	maximal, complemented
12	#20288043	C₂	1	2	yes	maximal, complemented
13	#20288042	C₂	1	2	yes	maximal, complemented
14	C₂×#16811181	C₂	1	4	yes	maximal, complemented
15	#534×D₅₃	C₂	1	4	yes	maximal, complemented
16	C₂×#16811095	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#13133263	C₂²	1	8	yes	complemented
19	C₂×#13133263	C₂²	1	4	yes	complemented
20	C₂×#13133262	C₂²	1	2	yes	complemented
21	C₂×#13133262	C₂²	1	8	yes	complemented
22	C₂×#13133262	C₂²	1	8	yes	complemented
23	H(5,𝔽₂)×D₅₃	—	2	32	no	—
24	C₂×#41×D₅₃	C₂²	1	4	yes	complemented
25	C₂×#41×D₅₃	C₂²	1	8	yes	complemented
26	C₂²×D₄×D₅₃	C₂²	1	1	yes	characteristic
27	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
28	C₂²×D₄×D₅₃	C₂²	1	8	yes	complemented
29	#16811278	C₂²	1	4	yes	complemented
30	#16811277	C₂²	1	4	yes	complemented
31	#16811276	C₂²	1	4	yes	complemented
32	#16811275	C₂²	1	8	yes	complemented
33	#16811274	C₂²	1	8	yes	complemented
34	#16811273	C₂²	1	8	yes	complemented
35	#16811272	C₂²	1	8	yes	complemented
36	#16811271	C₂²	1	16	yes	complemented
37	#16811270	C₂²	1	8	yes	complemented
38	#16811269	C₂²	1	8	yes	complemented
39	#16811268	C₂²	1	8	yes	complemented
40	#16811267	C₂²	1	8	yes	complemented
41	#16811266	C₂²	1	8	yes	complemented
42	#16811265	C₂²	1	16	yes	complemented
43	#16811264	C₂²	1	8	yes	complemented
44	#16811263	C₂²	1	16	yes	complemented
45	#16811262	C₂²	1	16	yes	complemented
46	#16811261	C₂²	1	8	yes	complemented
47	#16811260	C₂²	1	16	yes	complemented
48	D₄×D₂₁₂	C₂²	1	4	yes	complemented
49	D₄×D₂₁₂	C₂²	1	4	yes	complemented
50	#16811258	C₂²	1	4	yes	complemented
51	#16811257	C₂²	1	8	yes	complemented
52	#16811257	C₂²	1	8	yes	complemented
53	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
54	D₄×C₂²⋊D₅₃	C₂²	1	8	yes	complemented
55	#16811255	C₂²	1	16	yes	complemented
56	#16811204	C₂²	1	2	yes	complemented
57	#16811201	C₂²	1	4	yes	complemented
58	#16811200	C₂²	1	4	yes	complemented
59	#16811200	C₂²	1	4	yes	complemented
60	#16811198	C₂²	1	4	yes	complemented
61	#16811196	C₂²	1	8	yes	complemented
62	#16811193	C₂²	1	4	yes	complemented
63	#16811191	C₂²	1	4	yes	complemented
64	#16811189	C₂²	1	8	yes	complemented
65	#16811186	C₂²	1	4	yes	complemented
66	#16811185	C₂²	1	4	yes	complemented
67	#16811184	C₂²	1	16	yes	complemented
68	#16811183	C₂²	1	16	yes	complemented
69	#16811182	C₂²	1	8	yes	complemented
70	#16811181	C₂²	1	4	yes	complemented
71	#16811181	C₂²	1	8	yes	complemented
72	#16811181	C₂²	1	4	yes	complemented
73	#16811181	C₂²	1	16	yes	complemented
74	#16811181	C₂²	1	16	yes	complemented
75	#16811181	C₂²	1	8	yes	complemented
76	#16811181	C₂²	1	8	yes	complemented
77	#16811173	C₂²	1	2	yes	complemented
78	#16811169	C₂²	1	4	yes	complemented
79	#16811168	C₂²	1	8	yes	complemented
80	#16811136	C₂²	1	8	yes	complemented
81	#16811133	C₂²	1	8	yes	complemented
82	#16811132	C₂²	1	8	yes	complemented
83	#16811132	C₂²	1	8	yes	complemented
84	C₂×#13133202	C₂²	1	8	yes	complemented
85	C₂×#13133199	C₂²	1	8	yes	complemented
86	#123×D₅₃	C₂²	1	16	yes	complemented
87	C₂×#13133191	C₂²	1	4	yes	complemented
88	C₂×#13133189	C₂²	1	8	yes	complemented
89	#121×D₅₃	C₂²	1	8	yes	complemented
90	#121×D₅₃	C₂²	1	8	yes	complemented
91	C₂×#13133187	C₂²	1	8	yes	complemented
92	C₂×#13133185	C₂²	1	8	yes	complemented
93	#120×D₅₃	C₂²	1	16	yes	complemented
94	#16811095	C₂²	1	8	yes	complemented
95	#16811095	C₂²	1	8	yes	complemented
96	C₂×C₄×D₂₁₂	C₂²	1	1	yes	characteristic, complemented
97	C₂×D₄×Dic₅₃	C₂²	1	1	yes	characteristic, complemented
98	C₂×#13133179	C₂²	1	1	yes	characteristic, complemented
99	C₂×C₄×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
100	C₂×#13133177	C₂²	1	2	yes	complemented
101	C₂×#13133175	C₂²	1	1	yes	characteristic, complemented
102	C₂×#13133174	C₂²	1	1	yes	characteristic, complemented
103	C₂²×#11719921	C₂²	1	2	yes	complemented
104	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
105	C₂×H(5,𝔽₂)×C₅₃	C₂²	1	2	yes	complemented
106	C₅₃×#547	C₂²	1	4	yes	complemented
107	C₅₃×#546	C₂²	1	8	yes	complemented
108	D₄²×C₅₃	C₂²	1	4	yes	complemented
109	C₅₃×#537	C₂²	1	2	yes	complemented
110	C₅₃×#534	C₂²	1	4	yes	complemented
111	C₅₃×#532	C₂²	1	2	yes	complemented
112	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
113	C₂×C₄×D₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
114	C₂⁴×D₅₃	C₂³	1	2	yes	—
115	C₂⁴×D₅₃	C₂³	1	8	yes	complemented
116	#13133263	—	2	64	no	—
117	#13133263	—	2	32	no	—
118	#13133262	—	2	16	no	—
119	#13133262	—	2	64	no	—
120	#13133262	—	2	64	no	—
121	C₂×#11719949	C₂³	1	4	yes	—
122	C₂×#11719949	C₂³	1	8	yes	complemented
123	C₂×#11719945	C₂³	1	8	yes	—
124	C₂×#11719945	C₂³	1	16	yes	complemented
125	C₂×#11719945	C₂³	1	8	yes	complemented
126	C₂×#11719945	C₂³	1	4	yes	complemented
127	C₂×#11719947	C₂³	1	4	yes	—
128	C₂×#11719947	C₂³	1	8	yes	complemented
129	C₂×#11719947	C₂³	1	16	yes	complemented
130	C₂×#11719947	C₂³	1	8	yes	complemented
131	#41×D₅₃	—	2	64	no	—
132	#41×D₅₃	—	2	32	no	—
133	C₂×Q₈×D₅₃	C₂³	1	4	yes	complemented
134	C₂²×D₂₁₂	C₂³	1	8	yes	—
135	C₂²×D₂₁₂	C₂³	1	1	yes	characteristic
136	C₂²×D₂₁₂	C₂³	1	8	yes	complemented
137	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
138	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	—
139	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
140	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
141	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
142	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
143	C₂×D₄×D₅₃	—	2	64	no	—
144	C₂×D₄×D₅₃	—	2	64	no	—
145	C₂×D₄×D₅₃	D₄	1	16	yes	complemented
146	C₂×D₄×D₅₃	C₂³	1	16	yes	—
147	C₂×D₄×D₅₃	C₂³	1	8	yes	—
148	C₂×D₄×D₅₃	C₂³	1	8	yes	—
149	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
150	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
151	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
152	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
153	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
154	C₂×D₄×D₅₃	C₂³	1	4	yes	complemented
155	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
156	C₂×D₄×D₅₃	C₂³	1	8	yes	complemented
157	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
158	C₂²×C₄×D₅₃	C₂³	1	1	yes	characteristic
159	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
160	C₂²×C₄×D₅₃	C₂³	1	8	yes	complemented
161	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
162	C₂²×C₄×D₅₃	C₂³	1	2	yes	complemented
163	#13133217	C₂³	1	2	yes	complemented
164	#13133216	C₂³	1	8	yes	complemented
165	#13133215	C₂³	1	4	yes	complemented
166	#13133214	C₂³	1	2	yes	complemented
167	#13133213	C₂³	1	8	yes	complemented
168	#13133213	C₂³	1	4	yes	complemented
169	#13133206	C₂³	1	4	yes	complemented
170	#13133205	C₂³	1	4	yes	complemented
171	#13133204	C₂³	1	4	yes	complemented
172	#13133203	C₂³	1	16	yes	complemented
173	#13133202	C₂³	1	16	yes	complemented
174	#13133202	C₂³	1	16	yes	complemented
175	#13133202	C₂³	1	8	yes	complemented
176	#13133202	C₂³	1	16	yes	complemented
177	#13133202	C₂³	1	8	yes	complemented
178	#13133201	C₂³	1	16	yes	complemented
179	#13133200	C₂³	1	16	yes	complemented
180	#13133199	C₂³	1	16	yes	complemented
181	#13133199	C₂³	1	16	yes	complemented
182	#13133199	C₂³	1	8	yes	complemented
183	#13133199	C₂³	1	16	yes	complemented
184	#13133199	C₂³	1	8	yes	complemented
185	#13133198	C₂³	1	16	yes	complemented
186	#13133197	C₂³	1	8	yes	complemented
187	#13133196	C₂³	1	8	yes	complemented
188	#13133195	C₂³	1	8	yes	complemented
189	#13133195	C₂³	1	8	yes	complemented
190	#13133194	C₂³	1	8	yes	complemented
191	#13133194	C₂³	1	8	yes	complemented
192	#13133193	C₂³	1	8	yes	complemented
193	#13133192	C₂³	1	8	yes	complemented
194	#13133192	C₂³	1	8	yes	complemented
195	#13133192	C₂³	1	8	yes	complemented
196	#13133191	C₂³	1	8	yes	complemented
197	#13133191	C₂³	1	8	yes	complemented
198	#13133191	C₂³	1	8	yes	complemented
199	#13133191	C₂³	1	4	yes	complemented
200	#13133191	C₂³	1	8	yes	complemented
201	#13133191	C₂³	1	4	yes	complemented
202	#13133190	C₂³	1	8	yes	complemented
203	#13133190	C₂³	1	16	yes	complemented
204	#13133190	C₂³	1	16	yes	complemented
205	#13133190	C₂³	1	8	yes	complemented
206	#13133189	C₂³	1	16	yes	complemented
207	#13133189	C₂³	1	16	yes	complemented
208	#13133189	C₂³	1	8	yes	complemented
209	#13133189	C₂³	1	16	yes	complemented
210	#13133189	C₂³	1	8	yes	complemented
211	#13133189	C₂³	1	8	yes	complemented
212	#13133189	C₂³	1	8	yes	complemented
213	#13133188	C₂³	1	8	yes	complemented
214	#13133188	C₂³	1	8	yes	complemented
215	#13133188	C₂³	1	8	yes	complemented
216	#13133187	C₂³	1	16	yes	complemented
217	#13133187	C₂³	1	16	yes	complemented
218	#13133187	C₂³	1	16	yes	complemented
219	#13133187	C₂³	1	8	yes	complemented
220	#13133187	C₂³	1	16	yes	complemented
221	#13133187	C₂³	1	8	yes	complemented
222	#13133186	C₂³	1	16	yes	complemented
223	#13133185	C₂³	1	16	yes	complemented
224	#13133185	C₂³	1	16	yes	complemented
225	#13133185	C₂³	1	8	yes	complemented
226	#13133185	C₂³	1	16	yes	complemented
227	#13133185	C₂³	1	16	yes	complemented
228	#13133185	C₂³	1	8	yes	complemented
229	C₄×D₂₁₂	C₂³	1	4	yes	complemented
230	C₄×D₂₁₂	C₂³	1	4	yes	complemented
231	C₄×D₂₁₂	C₂³	1	4	yes	complemented
232	C₄×D₂₁₂	C₂³	1	4	yes	complemented
233	D₄×Dic₅₃	C₂³	1	8	yes	complemented
234	D₄×Dic₅₃	C₂³	1	8	yes	complemented
235	#13133179	C₂³	1	8	yes	complemented
236	#13133179	C₂³	1	8	yes	complemented
237	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
238	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
239	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
240	C₄×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
241	#13133177	C₂³	1	16	yes	complemented
242	#13133177	C₂³	1	16	yes	complemented
243	#13133175	C₂³	1	8	yes	complemented
244	#13133174	C₂³	1	4	yes	complemented
245	#13133174	C₂³	1	4	yes	complemented
246	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
247	C₂×C₄⋊Dic₅₃	C₂³	1	1	yes	characteristic, complemented
248	C₂×#11719919	C₂³	1	8	yes	complemented
249	C₂×#11719919	C₂³	1	1	yes	characteristic, complemented
250	C₂×#11719919	C₂³	1	1	yes	characteristic, complemented
251	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
252	C₄⋊C₄×D₅₃	C₂³	1	8	yes	complemented
253	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
254	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
255	C₂×#11719921	C₂³	1	1	yes	characteristic
256	C₂×#11719921	C₂³	1	2	yes	—
257	C₂×#11719921	C₂³	1	1	yes	characteristic
258	C₂×#11719921	C₂³	1	8	yes	complemented
259	C₂×#11719921	C₂³	1	8	yes	complemented
260	C₂×#11719921	C₂³	1	2	yes	complemented
261	C₂×#11719921	C₂³	1	2	yes	complemented
262	C₂×#11719921	C₂³	1	8	yes	complemented
263	C₂×#11719921	C₂³	1	8	yes	complemented
264	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
265	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
266	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
267	C₂×C₄×Dic₅₃	C₂³	1	1	yes	characteristic, complemented
268	C₂×C₄×Dic₅₃	C₂³	1	2	yes	complemented
269	H(5,𝔽₂)×C₅₃	—	2	16	no	—
270	C₂×#41×C₅₃	C₂³	1	8	yes	complemented
271	C₂×#41×C₅₃	C₂³	1	4	yes	complemented
272	C₂²×D₄×C₅₃	C₂³	1	1	yes	characteristic
273	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
274	C₂²×D₄×C₅₃	C₂³	1	8	yes	complemented
275	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
276	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
277	C₄⋊Q₈×C₅₃	C₂³	1	2	yes	complemented
278	#127×C₅₃	C₂³	1	2	yes	complemented
279	#124×C₅₃	C₂³	1	4	yes	complemented
280	#123×C₅₃	C₂³	1	16	yes	complemented
281	C₂²⋊Q₈×C₅₃	C₂³	1	8	yes	complemented
282	#121×C₅₃	C₂³	1	8	yes	complemented
283	#121×C₅₃	C₂³	1	8	yes	complemented
284	#121×C₅₃	C₂³	1	4	yes	complemented
285	#121×C₅₃	C₂³	1	8	yes	complemented
286	#121×C₅₃	C₂³	1	8	yes	complemented
287	#121×C₅₃	C₂³	1	4	yes	complemented
288	#120×C₅₃	C₂³	1	16	yes	complemented
289	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
290	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
291	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
292	C₄×D₄×C₅₃	C₂³	1	4	yes	complemented
293	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
294	C₂×C₄⋊C₄×C₅₃	C₂³	1	1	yes	characteristic, complemented
295	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
296	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
297	C₂×C₄²×C₅₃	C₂³	1	1	yes	characteristic, complemented
298	C₂⁴×C₅₃	C₂⁴	1	8	yes	—
299	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
300	C₂³×D₅₃	—	2	32	no	—
301	C₂³×D₅₃	—	8	2	no	—
302	C₂³×D₅₃	—	8	2	no	—
303	C₂³×D₅₃	—	8	8	no	—
304	C₂³×D₅₃	—	8	8	no	—
305	C₂³×D₅₃	C₂×D₄	1	16	yes	complemented
306	C₂³×D₅₃	C₂⁴	1	16	yes	—
307	C₂³×D₅₃	C₂⁴	1	8	yes	—
308	C₂³×D₅₃	C₂⁴	1	8	yes	—
309	C₂³×D₅₃	C₂⁴	1	8	yes	—
310	C₂³×D₅₃	C₂⁴	1	1	yes	characteristic
311	C₂³×D₅₃	C₂⁴	1	2	yes	—
312	#41×C₅₃	—	2	32	no	—
313	#41×C₅₃	—	2	16	no	—
314	C₂×Q₈×C₅₃	C₂⁴	1	4	yes	—
315	C₂×D₄×C₅₃	—	2	32	no	—
316	C₂×D₄×C₅₃	—	2	32	no	—
317	C₂×D₄×C₅₃	—	8	4	no	—
318	C₂×D₄×C₅₃	C₂×D₄	1	8	yes	complemented
319	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
320	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
321	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
322	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
323	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
324	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
325	C₂×D₄×C₅₃	C₂⁴	1	4	yes	—
326	C₂²×C₄×C₅₃	—	8	2	no	—
327	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
328	C₂²×C₄×C₅₃	C₂⁴	1	8	yes	—
329	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
331	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₅₃	C₂⁴	1	2	yes	—
333	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
334	C₂²×C₄×C₅₃	C₂⁴	1	1	yes	characteristic
335	C₂×C₂²⋊D₅₃	—	2	32	no	—
336	C₂×C₂²⋊D₅₃	—	2	32	no	—
337	C₂×C₂²⋊D₅₃	—	2	64	no	—
338	C₂×C₂²⋊D₅₃	—	8	8	no	—
339	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
340	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
341	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
342	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
343	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
344	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
345	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
346	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
347	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
348	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
349	C₂²×Dic₅₃	—	8	2	no	—
350	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
351	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
352	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
353	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
354	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
355	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
356	C₂²×Dic₅₃	C₂⁴	1	1	yes	characteristic
357	#11719949	—	2	32	no	—
358	#11719949	—	2	16	no	—
359	Q₈×D₅₃	—	2	16	no	—
360	#11719947	—	2	32	no	—
361	#11719947	—	2	64	no	—
362	#11719947	—	2	32	no	—
363	#11719947	—	2	16	no	—
364	D₄×D₅₃	—	2	32	no	—
365	D₄×D₅₃	—	2	64	no	—
366	D₄×D₅₃	—	2	64	no	—
367	D₄×D₅₃	—	2	64	no	—
368	D₄×D₅₃	—	2	32	no	—
369	D₄×D₅₃	—	2	64	no	—
370	D₄×D₅₃	—	2	32	no	—
371	D₄×D₅₃	—	2	16	no	—
372	D₄×D₅₃	—	8	8	no	—
373	D₄×D₅₃	—	8	8	no	—
374	D₄×D₅₃	C₂×D₄	1	64	yes	complemented
375	#11719945	—	2	16	no	—
376	#11719945	—	2	64	no	—
377	#11719945	—	2	32	no	—
378	#11719945	—	2	32	no	—
379	C₂×D₂₁₂	—	2	32	no	—
380	C₂×D₂₁₂	—	2	32	no	—
381	C₂×D₂₁₂	—	8	4	no	—
382	C₂×D₂₁₂	C₂×D₄	1	8	yes	complemented
383	C₂×D₂₁₂	C₂⁴	1	8	yes	—
384	C₂×D₂₁₂	C₂⁴	1	16	yes	—
385	C₂×D₂₁₂	C₂⁴	1	4	yes	—
386	C₂×D₂₁₂	C₂⁴	1	8	yes	—
387	C₂×D₂₁₂	C₂⁴	1	4	yes	—
388	C₂×D₂₁₂	C₂⁴	1	4	yes	—
389	C₂×D₂₁₂	C₂⁴	1	4	yes	—
390	C₂×C₄×D₅₃	—	2	32	no	—
391	C₂×C₄×D₅₃	—	2	32	no	—
392	C₂×C₄×D₅₃	—	8	2	no	—
393	C₂×C₄×D₅₃	—	8	2	no	—
394	C₂×C₄×D₅₃	C₂×D₄	1	8	yes	complemented
395	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
396	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
397	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
398	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
399	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
400	C₂×C₄×D₅₃	C₂⁴	1	8	yes	—
401	C₂×C₄×D₅₃	C₂⁴	1	4	yes	—
402	C₂×Dic₁₀₆	C₂⁴	1	8	yes	—
403	C₂×Dic₁₀₆	C₂⁴	1	4	yes	—
404	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
405	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
406	C₄⋊C₄×C₅₃	C₂⁴	1	8	yes	—
407	C₄⋊C₄×C₅₃	C₂⁴	1	4	yes	—
408	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
409	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
410	C₂²⋊C₄×C₅₃	C₂⁴	1	16	yes	—
411	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
412	C₄²×C₅₃	C₂⁴	1	2	yes	—
413	C₄²×C₅₃	C₂⁴	1	2	yes	—
414	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
415	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
416	C₂²⋊Dic₅₃	C₂⁴	1	16	yes	—
417	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
418	#11719921	C₂⁴	1	4	yes	—
419	#11719921	C₂⁴	1	8	yes	—
420	#11719921	C₂⁴	1	8	yes	—
421	#11719921	C₂⁴	1	8	yes	—
422	#11719921	C₂⁴	1	16	yes	—
423	#11719921	C₂⁴	1	16	yes	—
424	#11719921	C₂⁴	1	2	yes	—
425	#11719921	C₂⁴	1	2	yes	—
426	#11719921	C₂⁴	1	8	yes	—
427	#11719921	C₂⁴	1	4	yes	—
428	#11719921	C₂⁴	1	4	yes	—
429	#11719921	C₂⁴	1	8	yes	—
430	#11719921	C₂⁴	1	8	yes	—
431	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
432	C₄⋊Dic₅₃	C₂⁴	1	8	yes	—
433	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
434	C₄⋊Dic₅₃	C₂⁴	1	4	yes	—
435	#11719919	C₂⁴	1	8	yes	—
436	#11719919	C₂⁴	1	16	yes	—
437	#11719919	C₂⁴	1	8	yes	—
438	#11719919	C₂⁴	1	4	yes	—
439	#11719919	C₂⁴	1	2	yes	—
440	#11719919	C₂⁴	1	2	yes	—
441	C₄×Dic₅₃	C₂⁴	1	4	yes	—
442	C₄×Dic₅₃	C₂⁴	1	8	yes	—
443	C₂³×C₅₃	—	2	16	no	—
444	C₂³×C₅₃	—	4	2	no	—
445	C₂³×C₅₃	—	4	2	no	—
446	C₂³×C₅₃	—	4	8	no	—
447	C₂³×C₅₃	—	4	8	no	—
448	C₂³×C₅₃	C₂²×D₄	1	8	yes	—
449	C₂³×C₅₃	C₂⁵	1	8	yes	—
450	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
451	C₂³×C₅₃	C₂⁵	1	4	yes	—
452	C₂²×D₅₃	—	2	16	no	—
453	C₂²×D₅₃	—	2	16	no	—
454	C₂²×D₅₃	—	2	32	no	—
455	C₂²×D₅₃	—	4	2	no	—
456	C₂²×D₅₃	—	4	2	no	—
457	C₂²×D₅₃	—	4	8	no	—
458	C₂²×D₅₃	—	4	8	no	—
459	C₂²×D₅₃	—	4	1	no	—
460	C₂²×D₅₃	—	4	1	no	—
461	C₂²×D₅₃	—	4	8	no	—
462	C₂²×D₅₃	—	4	8	no	—
463	C₂²×D₅₃	—	4	8	no	—
464	C₂²×D₅₃	—	4	16	no	—
465	C₂²×D₅₃	—	4	16	no	—
466	C₂²×D₅₃	—	4	8	no	—
467	C₂²×D₅₃	—	8	16	no	—
468	C₂²×D₅₃	—	8	64	no	—
469	C₂²×D₅₃	C₂²×D₄	1	32	yes	—
470	C₂²×D₅₃	C₂²×D₄	1	4	yes	—
471	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
472	C₂²×D₅₃	C₂⁵	1	8	yes	—
473	C₂²×D₅₃	C₂⁵	1	4	yes	—
474	C₂²×D₅₃	C₂⁵	1	2	yes	—
475	Q₈×C₅₃	—	2	8	no	—
476	D₄×C₅₃	—	2	32	no	—
477	D₄×C₅₃	—	2	16	no	—
478	D₄×C₅₃	—	2	8	no	—
479	D₄×C₅₃	—	4	4	no	—
480	D₄×C₅₃	—	4	8	no	—
481	D₄×C₅₃	—	4	4	no	—
482	D₄×C₅₃	C₂²×D₄	1	16	yes	—
483	C₂×C₄×C₅₃	—	2	16	no	—
484	C₂×C₄×C₅₃	—	2	16	no	—
485	C₂×C₄×C₅₃	—	4	1	no	—
486	C₂×C₄×C₅₃	—	4	2	no	—
487	C₂×C₄×C₅₃	—	4	4	no	—
488	C₂×C₄×C₅₃	—	4	1	no	—
489	C₂×C₄×C₅₃	—	4	4	no	—
490	C₂×C₄×C₅₃	C₂²×D₄	1	4	yes	—
491	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
492	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
493	C₂×C₄×C₅₃	C₂⁵	1	4	yes	—
494	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
495	C₂×C₄×C₅₃	C₂⁵	1	1	yes	characteristic
496	C₂×C₄×C₅₃	C₂⁵	1	2	yes	—
497	C₂²⋊D₅₃	—	2	32	no	—
498	C₂²⋊D₅₃	—	2	16	no	—
499	C₂²⋊D₅₃	—	2	16	no	—
500	C₂²⋊D₅₃	—	2	32	no	—
501	C₂²⋊D₅₃	—	2	16	no	—
502	C₂²⋊D₅₃	—	4	8	no	—
503	C₂²⋊D₅₃	—	4	16	no	—
504	C₂²⋊D₅₃	—	4	8	no	—
505	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	—
506	C₂×Dic₅₃	—	2	16	no	—
507	C₂×Dic₅₃	—	2	16	no	—
508	C₂×Dic₅₃	—	4	1	no	—
509	C₂×Dic₅₃	—	4	2	no	—
510	C₂×Dic₅₃	—	4	1	no	—
511	C₂×Dic₅₃	—	4	8	no	—
512	C₂×Dic₅₃	C₂²×D₄	1	4	yes	—
513	C₂×Dic₅₃	C₂⁵	1	8	yes	—
514	C₂×Dic₅₃	C₂⁵	1	2	yes	—
515	C₂×Dic₅₃	C₂⁵	1	4	yes	—
516	C₂×Dic₅₃	C₂⁵	1	2	yes	—
517	C₂×Dic₅₃	C₂⁵	1	2	yes	—
518	D₂₁₂	—	2	16	no	—
519	D₂₁₂	—	2	32	no	—
520	D₂₁₂	—	2	8	no	—
521	D₂₁₂	—	4	4	no	—
522	D₂₁₂	—	4	8	no	—
523	D₂₁₂	—	4	4	no	—
524	D₂₁₂	C₂²×D₄	1	16	yes	—
525	C₄×D₅₃	—	2	16	no	—
526	C₄×D₅₃	—	2	32	no	—
527	C₄×D₅₃	—	2	16	no	—
528	C₄×D₅₃	—	2	16	no	—
529	C₄×D₅₃	—	4	8	no	—
530	C₄×D₅₃	—	4	8	no	—
531	C₄×D₅₃	C₂²×D₄	1	16	yes	—
532	Dic₁₀₆	—	2	8	no	—
533	Dic₁₀₆	—	2	16	no	—
534	#62842	—	53	1	no	maximal, Sylow
535	C₂²×C₅₃	—	2	1	no	—
536	C₂²×C₅₃	—	2	4	no	—
537	C₂²×C₅₃	—	2	1	no	—
538	C₂²×C₅₃	—	2	4	no	—
539	C₂²×C₅₃	—	2	8	no	—
540	C₂²×C₅₃	—	2	8	no	—
541	C₂²×C₅₃	—	2	8	no	—
542	C₂²×C₅₃	—	4	8	no	—
543	C₂²×C₅₃	—	8	16	no	—
544	C₂²×C₅₃	C₂³×D₄	1	8	yes	—
545	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
546	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
547	C₂×D₅₃	—	2	4	no	—
548	C₂×D₅₃	—	2	4	no	—
549	C₂×D₅₃	—	2	2	no	—
550	C₂×D₅₃	—	2	2	no	—
551	C₂×D₅₃	—	2	8	no	—
552	C₂×D₅₃	—	2	8	no	—
553	C₂×D₅₃	—	2	8	no	—
554	C₂×D₅₃	—	4	4	no	—
555	C₂×D₅₃	—	4	32	no	—
556	C₂×D₅₃	—	4	8	no	—
557	C₂×D₅₃	—	4	32	no	—
558	C₂×D₅₃	—	8	32	no	—
559	C₂×D₅₃	—	8	16	no	—
560	C₂×D₅₃	C₂³×D₄	1	4	yes	—
561	C₂×D₅₃	C₂³×D₄	1	8	yes	—
562	C₄×C₅₃	—	2	8	no	—
563	C₄×C₅₃	—	2	2	no	—
564	C₄×C₅₃	—	2	4	no	—
565	C₄×C₅₃	—	2	1	no	—
566	C₄×C₅₃	—	2	1	no	—
567	C₄×C₅₃	C₂³×D₄	1	4	yes	—
568	Dic₅₃	—	2	8	no	—
569	Dic₅₃	—	2	2	no	—
570	Dic₅₃	—	2	4	no	—
571	Dic₅₃	—	2	2	no	—
572	Dic₅₃	C₂³×D₄	1	4	yes	—
573	C₂²×H(5,𝔽₂)	—	53	2	no	—
574	#3496	—	53	2	no	—
575	#3496	—	53	2	no	—
576	#3496	—	53	4	no	—
577	#3496	—	53	2	no	—
578	#3496	—	53	4	no	—
579	#3496	—	53	1	no	—
580	#3496	D₅₃	1	1	yes	characteristic, complemented
581	#3485	—	53	8	no	—
582	#3485	—	53	8	no	—
583	#3484	—	53	8	no	—
584	#3484	—	53	8	no	—
585	#3449	—	53	2	no	—
586	#3449	—	53	2	no	—
587	C₂×#534	—	53	4	no	—
588	C₂×#534	—	53	4	no	—
589	C₂×#518	—	53	1	no	—
590	C₂×C₅₃	—	2	2	no	—
591	C₂×C₅₃	—	2	8	no	—
592	C₂×C₅₃	—	4	8	no	—
593	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
594	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
595	C₂×C₅₃	H(7,𝔽₂)	1	1	yes	characteristic
596	D₅₃	—	2	4	no	—
597	D₅₃	—	2	8	no	—
598	D₅₃	—	4	8	no	—
599	C₂×H(5,𝔽₂)	—	53	8	no	—
600	C₂×H(5,𝔽₂)	—	53	4	no	—
601	C₂×H(5,𝔽₂)	—	53	2	no	—
602	C₂×H(5,𝔽₂)	—	53	8	no	—
603	C₂×H(5,𝔽₂)	—	53	8	no	—
604	C₂×H(5,𝔽₂)	—	106	32	no	—
605	C₂×H(5,𝔽₂)	C₂×D₅₃	1	2	yes	complemented
606	C₂²×#41	—	53	4	no	—
607	C₂²×#41	—	53	8	no	—
608	C₂³×D₄	—	53	1	no	—
609	C₂³×D₄	—	53	8	no	—
610	C₂³×D₄	—	53	8	no	—
611	#547	—	53	8	no	—
612	#547	—	53	4	no	—
613	#547	—	53	16	no	—
614	#547	—	53	8	no	—
615	#547	—	53	8	no	—
616	#547	—	53	4	no	—
617	#547	—	53	4	no	—
618	#547	—	53	8	no	—
619	#547	C₂×D₅₃	1	4	yes	complemented
620	#546	—	53	8	no	—
621	#546	—	53	8	no	—
622	#546	—	53	8	no	—
623	#546	—	53	16	no	—
624	#546	—	53	8	no	—
625	#546	—	53	8	no	—
626	#546	—	53	16	no	—
627	#546	—	53	16	no	—
628	#546	—	53	8	no	—
629	#546	—	53	8	no	—
630	#546	—	53	16	no	—
631	#546	C₂×D₅₃	1	8	yes	complemented
632	D₄²	—	53	8	no	—
633	D₄²	—	53	8	no	—
634	D₄²	—	53	4	no	—
635	D₄²	—	53	8	no	—
636	D₄²	—	53	8	no	—
637	D₄²	—	53	16	no	—
638	D₄²	—	53	4	no	—
639	D₄²	—	53	4	no	—
640	D₄²	C₂×D₅₃	1	4	yes	complemented
641	#537	—	53	4	no	—
642	#537	—	53	4	no	—
643	#537	—	53	4	no	—
644	#537	—	53	2	no	—
645	#537	C₂×D₅₃	1	2	yes	complemented
646	#536	—	53	4	no	—
647	#536	—	53	4	no	—
648	#536	—	53	8	no	—
649	#535	—	53	4	no	—
650	#535	—	53	4	no	—
651	#535	—	53	8	no	—
652	#534	—	53	8	no	—
653	#534	—	53	16	no	—
654	#534	—	53	4	no	—
655	#534	—	53	8	no	—
656	#534	—	53	4	no	—
657	#534	—	53	16	no	—
658	#534	—	53	16	no	—
659	#534	—	53	8	no	—
660	#534	—	53	8	no	—
661	#534	—	53	16	no	—
662	#534	—	53	4	no	—
663	#534	C₂×D₅₃	1	4	yes	complemented
664	#532	—	53	4	no	—
665	#532	—	53	8	no	—
666	#532	—	53	2	no	—
667	#532	C₂×D₅₃	1	2	yes	complemented
668	#525	—	53	8	no	—
669	#525	—	53	8	no	—
670	#525	—	53	8	no	—
671	#525	—	53	8	no	—
672	C₂×#123	—	53	16	no	—
673	C₂×#123	—	53	8	no	—
674	C₂×#123	—	53	8	no	—
675	C₂×#121	—	53	8	no	—
676	C₂×#121	—	53	4	no	—
677	C₂×#121	—	53	8	no	—
678	C₂×#121	—	53	8	no	—
679	C₂×#121	C₂×D₅₃	1	4	yes	complemented
680	C₂×#120	—	53	8	no	—
681	C₂×#120	—	53	16	no	—
682	C₂×#120	—	53	8	no	—
683	#518	—	53	8	no	—
684	#518	—	53	8	no	—
685	C₂×C₄×D₄	—	53	1	no	—
686	C₂×C₄×D₄	—	53	2	no	—
687	C₂×C₄×D₄	—	53	1	no	—
688	C₂×C₄×D₄	—	53	2	no	—
689	C₂×C₄×D₄	—	53	1	no	—
690	C₂×C₄×D₄	C₂×D₅₃	1	1	yes	characteristic, complemented
691	C₂×#117	—	53	1	no	—
692	C₂×#117	—	53	1	no	—
693	C₂²×C₂²⋊C₄	—	53	2	no	—
694	C₂²×C₂²⋊C₄	—	53	2	no	—
695	C₅₃	#62842	1	1	yes	characteristic, complemented, Sylow
696	C₂⁵	—	53	2	no	—
697	C₂⁵	—	53	8	no	—
698	H(5,𝔽₂)	—	2	16	no	—
699	H(5,𝔽₂)	—	106	64	no	—
700	H(5,𝔽₂)	—	106	64	no	—
701	H(5,𝔽₂)	—	106	64	no	—
702	H(5,𝔽₂)	—	106	32	no	—
703	H(5,𝔽₂)	—	106	16	no	—
704	C₂×#41	—	53	4	no	—
705	C₂×#41	—	53	8	no	—
706	C₂×#41	—	53	4	no	—
707	C₂×#41	—	53	8	no	—
708	C₂×#41	—	53	8	no	—
709	C₂×#41	—	53	16	no	—
710	C₂×#41	—	53	8	no	—
711	C₂×#41	—	53	4	no	—
712	C₂×#41	—	53	8	no	—
713	C₂×#41	—	53	16	no	—
714	C₂×#41	—	106	32	no	—
715	C₂×#41	—	106	64	no	—
716	C₂×#41	C₂²×D₅₃	1	4	yes	complemented
717	C₂×#41	C₂²×D₅₃	1	8	yes	complemented
718	C₂²×Q₈	—	53	4	no	—
719	C₂²×D₄	—	53	2	no	—
720	C₂²×D₄	—	53	16	no	—
721	C₂²×D₄	—	53	8	no	—
722	C₂²×D₄	—	53	8	no	—
723	C₂²×D₄	—	53	8	no	—
724	C₂²×D₄	—	53	16	no	—
725	C₂²×D₄	—	53	8	no	—
726	C₂²×D₄	—	53	16	no	—
727	C₂²×D₄	—	53	16	no	—
728	C₂²×D₄	—	53	8	no	—
729	C₂²×D₄	—	53	16	no	—
730	C₂²×D₄	—	53	4	no	—
731	C₂²×D₄	—	53	16	no	—
732	C₂²×D₄	—	53	8	no	—
733	C₂²×D₄	—	53	8	no	—
734	C₂²×D₄	—	53	8	no	—
735	C₂²×D₄	—	53	8	no	—
736	C₂²×D₄	—	53	1	no	—
737	C₂²×D₄	—	53	8	no	—
738	C₂²×D₄	—	53	8	no	—
739	C₂²×D₄	—	53	4	no	—
740	C₂²×D₄	—	106	64	no	—
741	C₂²×D₄	—	106	64	no	—
742	C₂²×D₄	C₂²×D₅₃	1	1	yes	characteristic
743	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
744	C₂²×D₄	C₂²×D₅₃	1	8	yes	complemented
745	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
746	C₂³×C₄	—	53	1	no	—
747	C₂³×C₄	—	53	2	no	—
748	C₂³×C₄	—	53	8	no	—
749	C₂³×C₄	—	53	8	no	—
750	C₂³×C₄	—	53	2	no	—
751	C₂³×C₄	—	53	2	no	—
752	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
753	C₄⋊Q₈	—	53	4	no	—
754	C₄⋊Q₈	—	53	8	no	—
755	C₄⋊Q₈	—	53	2	no	—
756	C₄⋊Q₈	C₂²×D₅₃	1	2	yes	complemented
757	#127	—	53	8	no	—
758	#127	—	53	4	no	—
759	#127	—	53	2	no	—
760	#127	C₂²×D₅₃	1	2	yes	complemented
761	#124	—	53	4	no	—
762	#124	—	53	4	no	—
763	#124	—	53	16	no	—
764	#124	—	53	4	no	—
765	#124	C₂²×D₅₃	1	4	yes	complemented
766	#123	—	53	16	no	—
767	#123	—	53	16	no	—
768	#123	—	53	8	no	—
769	#123	—	53	16	no	—
770	#123	—	53	8	no	—
771	#123	—	53	16	no	—
772	#123	—	53	16	no	—
773	#123	—	53	8	no	—
774	#123	—	53	16	no	—
775	#123	—	53	8	no	—
776	#123	—	53	16	no	—
777	#123	—	53	16	no	—
778	#123	—	53	16	no	—
779	#123	C₂²×D₅₃	1	16	yes	complemented
780	C₂²⋊Q₈	—	53	8	no	—
781	C₂²⋊Q₈	—	53	8	no	—
782	C₂²⋊Q₈	—	53	8	no	—
783	C₂²⋊Q₈	—	53	8	no	—
784	C₂²⋊Q₈	—	53	8	no	—
785	C₂²⋊Q₈	—	53	8	no	—
786	C₂²⋊Q₈	—	53	8	no	—
787	C₂²⋊Q₈	C₂²×D₅₃	1	8	yes	complemented
788	#121	—	53	8	no	—
789	#121	—	53	16	no	—
790	#121	—	53	8	no	—
791	#121	—	53	8	no	—
792	#121	—	53	8	no	—
793	#121	—	53	16	no	—
794	#121	—	53	16	no	—
795	#121	—	53	8	no	—
796	#121	—	53	8	no	—
797	#121	—	53	8	no	—
798	#121	—	53	8	no	—
799	#121	—	53	4	no	—
800	#121	—	53	4	no	—
801	#121	—	53	8	no	—
802	#121	—	53	8	no	—
803	#121	—	53	8	no	—
804	#121	—	53	8	no	—
805	#121	—	53	8	no	—
806	#121	—	53	8	no	—
807	#121	—	53	16	no	—
808	#121	—	53	16	no	—
809	#121	—	53	8	no	—
810	#121	—	53	8	no	—
811	#121	C₂²×D₅₃	1	4	yes	complemented
812	#121	C₂²×D₅₃	1	8	yes	complemented
813	#121	C₂²×D₅₃	1	4	yes	complemented
814	#121	C₂²×D₅₃	1	8	yes	complemented
815	#121	C₂²×D₅₃	1	8	yes	complemented
816	#121	C₂²×D₅₃	1	8	yes	complemented
817	#120	—	53	16	no	—
818	#120	—	53	16	no	—
819	#120	—	53	8	no	—
820	#120	—	53	8	no	—
821	#120	—	53	16	no	—
822	#120	—	53	16	no	—
823	#120	—	53	16	no	—
824	#120	—	53	8	no	—
825	#120	—	53	16	no	—
826	#120	—	53	8	no	—
827	#120	—	53	16	no	—
828	#120	—	53	16	no	—
829	#120	—	53	16	no	—
830	#120	C₂²×D₅₃	1	16	yes	complemented
831	C₄×D₄	—	53	8	no	—
832	C₄×D₄	—	53	8	no	—
833	C₄×D₄	—	53	8	no	—
834	C₄×D₄	—	53	8	no	—
835	C₄×D₄	—	53	8	no	—
836	C₄×D₄	—	53	8	no	—
837	C₄×D₄	—	53	8	no	—
838	C₄×D₄	—	53	8	no	—
839	C₄×D₄	—	53	16	no	—
840	C₄×D₄	—	53	16	no	—
841	C₄×D₄	—	53	4	no	—
842	C₄×D₄	—	53	4	no	—
843	C₄×D₄	—	53	4	no	—
844	C₄×D₄	—	53	4	no	—
845	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
846	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
847	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
848	C₄×D₄	C₂²×D₅₃	1	4	yes	complemented
849	#117	—	53	8	no	—
850	#117	—	53	4	no	—
851	#117	—	53	4	no	—
852	C₂×C₄⋊C₄	—	53	1	no	—
853	C₂×C₄⋊C₄	—	53	1	no	—
854	C₂×C₄⋊C₄	—	53	1	no	—
855	C₂×C₄⋊C₄	—	53	8	no	—
856	C₂×C₄⋊C₄	—	53	4	no	—
857	C₂×C₄⋊C₄	—	53	8	no	—
858	C₂×C₄⋊C₄	—	53	8	no	—
859	C₂×C₄⋊C₄	C₂²×D₅₃	1	1	yes	characteristic, complemented
860	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
861	C₂×C₂²⋊C₄	—	53	2	no	—
862	C₂×C₂²⋊C₄	—	53	8	no	—
863	C₂×C₂²⋊C₄	—	53	2	no	—
864	C₂×C₂²⋊C₄	—	53	1	no	—
865	C₂×C₂²⋊C₄	—	53	1	no	—
866	C₂×C₂²⋊C₄	—	53	2	no	—
867	C₂×C₂²⋊C₄	—	53	2	no	—
868	C₂×C₂²⋊C₄	—	53	8	no	—
869	C₂×C₂²⋊C₄	—	53	8	no	—
870	C₂×C₂²⋊C₄	—	53	8	no	—
871	C₂×C₂²⋊C₄	—	53	8	no	—
872	C₂×C₂²⋊C₄	—	53	16	no	—
873	C₂×C₂²⋊C₄	—	53	16	no	—
874	C₂×C₂²⋊C₄	—	53	16	no	—
875	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
876	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
877	C₂×C₄²	—	53	2	no	—
878	C₂×C₄²	—	53	1	no	—
879	C₂×C₄²	C₂²×D₅₃	1	1	yes	characteristic, complemented
880	C₂⁴	—	53	16	no	—
881	C₂⁴	—	53	1	no	—
882	C₂⁴	—	53	8	no	—
883	C₂⁴	—	53	2	no	—
884	C₂⁴	—	53	16	no	—
885	C₂⁴	—	53	8	no	—
886	C₂⁴	—	53	8	no	—
887	C₂⁴	—	106	32	no	—
888	C₂⁴	—	424	2	no	—
889	C₂⁴	—	424	2	no	—
890	C₂⁴	—	424	8	no	—
891	C₂⁴	—	424	8	no	—
892	C₂⁴	C₂³×D₅₃	1	8	yes	—
893	C₂⁴	C₂³×D₅₃	1	2	yes	—
894	#41	—	2	32	no	—
895	#41	—	2	16	no	—
896	#41	—	106	32	no	—
897	#41	—	106	64	no	—
898	#41	—	106	32	no	—
899	#41	—	106	32	no	—
900	#41	—	106	16	no	—
901	#41	—	106	16	no	—
902	#41	—	106	64	no	—
903	#41	—	106	32	no	—
904	#41	—	106	32	no	—
905	#41	—	106	16	no	—
906	C₂×Q₈	—	53	8	no	—
907	C₂×Q₈	—	53	4	no	—
908	C₂×Q₈	—	106	16	no	—
909	C₂×Q₈	C₂³×D₅₃	1	4	yes	—
910	C₂×D₄	—	2	32	no	—
911	C₂×D₄	—	2	32	no	—
912	C₂×D₄	—	8	4	no	—
913	C₂×D₄	—	53	16	no	—
914	C₂×D₄	—	53	8	no	—
915	C₂×D₄	—	53	64	no	—
916	C₂×D₄	—	53	8	no	—
917	C₂×D₄	—	53	16	no	—
918	C₂×D₄	—	53	16	no	—
919	C₂×D₄	—	53	8	no	—
920	C₂×D₄	—	53	8	no	—
921	C₂×D₄	—	53	16	no	—
922	C₂×D₄	—	53	8	no	—
923	C₂×D₄	—	53	8	no	—
924	C₂×D₄	—	53	8	no	—
925	C₂×D₄	—	53	4	no	—
926	C₂×D₄	—	53	8	no	—
927	C₂×D₄	—	53	16	no	—
928	C₂×D₄	—	53	4	no	—
929	C₂×D₄	—	53	8	no	—
930	C₂×D₄	—	53	4	no	—
931	C₂×D₄	—	53	4	no	—
932	C₂×D₄	—	106	32	no	—
933	C₂×D₄	—	106	32	no	—
934	C₂×D₄	—	106	16	no	—
935	C₂×D₄	—	106	64	no	—
936	C₂×D₄	—	106	32	no	—
937	C₂×D₄	—	106	32	no	—
938	C₂×D₄	—	106	64	no	—
939	C₂×D₄	—	106	64	no	—
940	C₂×D₄	—	106	64	no	—
941	C₂×D₄	—	106	64	no	—
942	C₂×D₄	—	106	32	no	—
943	C₂×D₄	—	106	32	no	—
944	C₂×D₄	—	106	32	no	—
945	C₂×D₄	—	424	4	no	—
946	C₂×D₄	—	424	8	no	—
947	C₂×D₄	—	424	8	no	—
948	C₂×D₄	—	424	8	no	—
949	C₂×D₄	D₄×D₅₃	1	8	yes	complemented
950	C₂×D₄	C₂³×D₅₃	1	16	yes	—
951	C₂×D₄	C₂³×D₅₃	1	8	yes	—
952	C₂×D₄	C₂³×D₅₃	1	4	yes	—
953	C₂×D₄	C₂³×D₅₃	1	8	yes	—
954	C₂×D₄	C₂³×D₅₃	1	4	yes	—
955	C₂×D₄	C₂³×D₅₃	1	4	yes	—
956	C₂×D₄	C₂³×D₅₃	1	4	yes	—
957	C₂²×C₄	—	8	2	no	—
958	C₂²×C₄	—	53	1	no	—
959	C₂²×C₄	—	53	8	no	—
960	C₂²×C₄	—	53	4	no	—
961	C₂²×C₄	—	53	8	no	—
962	C₂²×C₄	—	53	8	no	—
963	C₂²×C₄	—	53	1	no	—
964	C₂²×C₄	—	53	2	no	—
965	C₂²×C₄	—	53	1	no	—
966	C₂²×C₄	—	53	8	no	—
967	C₂²×C₄	—	53	16	no	—
968	C₂²×C₄	—	53	8	no	—
969	C₂²×C₄	—	53	8	no	—
970	C₂²×C₄	—	53	8	no	—
971	C₂²×C₄	—	53	8	no	—
972	C₂²×C₄	—	53	8	no	—
973	C₂²×C₄	—	106	32	no	—
974	C₂²×C₄	—	106	32	no	—
975	C₂²×C₄	—	424	2	no	—
976	C₂²×C₄	—	424	2	no	—
977	C₂²×C₄	—	424	2	no	—
978	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
979	C₂²×C₄	C₂³×D₅₃	1	8	yes	—
980	C₂²×C₄	C₂³×D₅₃	1	2	yes	—
981	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
982	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
983	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
984	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
985	C₂²×C₄	C₂³×D₅₃	1	1	yes	characteristic
986	C₄⋊C₄	—	53	8	no	—
987	C₄⋊C₄	—	53	16	no	—
988	C₄⋊C₄	—	53	8	no	—
989	C₄⋊C₄	—	53	8	no	—
990	C₄⋊C₄	—	53	4	no	—
991	C₄⋊C₄	—	53	4	no	—
992	C₄⋊C₄	—	53	2	no	—
993	C₄⋊C₄	—	53	2	no	—
994	C₄⋊C₄	—	53	4	no	—
995	C₄⋊C₄	—	53	4	no	—
996	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
997	C₄⋊C₄	C₂³×D₅₃	1	8	yes	—
998	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
999	C₄⋊C₄	C₂³×D₅₃	1	4	yes	—
1000	C₂²⋊C₄	—	53	8	no	—
1001	C₂²⋊C₄	—	53	8	no	—
1002	C₂²⋊C₄	—	53	16	no	—
1003	C₂²⋊C₄	—	53	8	no	—
1004	C₂²⋊C₄	—	53	8	no	—
1005	C₂²⋊C₄	—	53	2	no	—
1006	C₂²⋊C₄	—	53	2	no	—
1007	C₂²⋊C₄	—	53	4	no	—
1008	C₂²⋊C₄	—	53	8	no	—
1009	C₂²⋊C₄	—	53	4	no	—
1010	C₂²⋊C₄	—	53	4	no	—
1011	C₂²⋊C₄	—	53	8	no	—
1012	C₂²⋊C₄	—	53	16	no	—
1013	C₂²⋊C₄	—	53	8	no	—
1014	C₂²⋊C₄	—	53	16	no	—
1015	C₂²⋊C₄	—	53	8	no	—
1016	C₂²⋊C₄	—	53	8	no	—
1017	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1018	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1019	C₂²⋊C₄	C₂³×D₅₃	1	16	yes	—
1020	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
1021	C₄²	—	53	8	no	—
1022	C₄²	—	53	4	no	—
1023	C₄²	C₂³×D₅₃	1	2	yes	—
1024	C₄²	C₂³×D₅₃	1	2	yes	—
1025	C₂³	—	2	16	no	—
1026	C₂³	—	4	2	no	—
1027	C₂³	—	4	2	no	—
1028	C₂³	—	4	8	no	—
1029	C₂³	—	4	8	no	—
1030	C₂³	—	53	2	no	—
1031	C₂³	—	53	4	no	—
1032	C₂³	—	53	4	no	—
1033	C₂³	—	53	32	no	—
1034	C₂³	—	53	8	no	—
1035	C₂³	—	53	8	no	—
1036	C₂³	—	106	32	no	—
1037	C₂³	—	106	16	no	—
1038	C₂³	—	106	16	no	—
1039	C₂³	—	424	16	no	—
1040	C₂³	—	424	64	no	—
1041	C₂³	—	212	8	no	—
1042	C₂³	—	212	8	no	—
1043	C₂³	—	212	16	no	—
1044	C₂³	—	212	16	no	—
1045	C₂³	—	212	2	no	—
1046	C₂³	—	212	2	no	—
1047	C₂³	—	212	1	no	—
1048	C₂³	—	212	8	no	—
1049	C₂³	—	212	1	no	—
1050	C₂³	—	212	8	no	—
1051	C₂³	—	212	8	no	—
1052	C₂³	—	212	8	no	—
1053	C₂³	C₂×D₄×D₅₃	1	8	yes	—
1054	C₂³	C₂⁴×D₅₃	1	8	yes	—
1055	C₂³	C₂⁴×D₅₃	1	4	yes	—
1056	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
1057	Q₈	—	2	8	no	—
1058	Q₈	—	106	16	no	—
1059	Q₈	—	106	8	no	—
1060	D₄	—	2	32	no	—
1061	D₄	—	2	16	no	—
1062	D₄	—	2	8	no	—
1063	D₄	—	4	4	no	—
1064	D₄	—	4	8	no	—
1065	D₄	—	4	4	no	—
1066	D₄	—	53	32	no	—
1067	D₄	—	53	16	no	—
1068	D₄	—	106	16	no	—
1069	D₄	—	106	32	no	—
1070	D₄	—	106	16	no	—
1071	D₄	—	106	16	no	—
1072	D₄	—	106	32	no	—
1073	D₄	—	106	32	no	—
1074	D₄	—	106	16	no	—
1075	D₄	—	106	8	no	—
1076	D₄	—	212	4	no	—
1077	D₄	—	212	8	no	—
1078	D₄	—	212	4	no	—
1079	D₄	—	212	8	no	—
1080	D₄	—	212	16	no	—
1081	D₄	—	212	8	no	—
1082	D₄	C₂×D₄×D₅₃	1	16	yes	—
1083	C₂×C₄	—	2	16	no	—
1084	C₂×C₄	—	2	16	no	—
1085	C₂×C₄	—	4	1	no	—
1086	C₂×C₄	—	4	2	no	—
1087	C₂×C₄	—	4	4	no	—
1088	C₂×C₄	—	4	4	no	—
1089	C₂×C₄	—	4	1	no	—
1090	C₂×C₄	—	53	4	no	—
1091	C₂×C₄	—	53	2	no	—
1092	C₂×C₄	—	53	16	no	—
1093	C₂×C₄	—	53	2	no	—
1094	C₂×C₄	—	53	4	no	—
1095	C₂×C₄	—	53	2	no	—
1096	C₂×C₄	—	53	8	no	—
1097	C₂×C₄	—	106	16	no	—
1098	C₂×C₄	—	106	16	no	—
1099	C₂×C₄	—	106	32	no	—
1100	C₂×C₄	—	106	16	no	—
1101	C₂×C₄	—	106	16	no	—
1102	C₂×C₄	—	106	16	no	—
1103	C₂×C₄	—	212	8	no	—
1104	C₂×C₄	—	212	8	no	—
1105	C₂×C₄	—	212	1	no	—
1106	C₂×C₄	—	212	2	no	—
1107	C₂×C₄	—	212	1	no	—
1108	C₂×C₄	—	212	8	no	—
1109	C₂×C₄	C₂×D₄×D₅₃	1	4	yes	—
1110	C₂×C₄	C₂⁴×D₅₃	1	4	yes	—
1111	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1112	C₂×C₄	C₂⁴×D₅₃	1	1	yes	characteristic
1113	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1114	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
1115	C₂×C₄	C₂⁴×D₅₃	1	2	yes	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	4	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	2	4	no	—
1120	C₂²	—	2	8	no	—
1121	C₂²	—	2	8	no	—
1122	C₂²	—	2	8	no	—
1123	C₂²	—	4	8	no	—
1124	C₂²	—	8	16	no	—
1125	C₂²	—	53	4	no	—
1126	C₂²	—	53	8	no	—
1127	C₂²	—	106	4	no	—
1128	C₂²	—	106	2	no	—
1129	C₂²	—	106	4	no	—
1130	C₂²	—	106	2	no	—
1131	C₂²	—	106	8	no	—
1132	C₂²	—	106	8	no	—
1133	C₂²	—	106	8	no	—
1134	C₂²	—	424	16	no	—
1135	C₂²	—	424	32	no	—
1136	C₂²	—	212	4	no	—
1137	C₂²	—	212	32	no	—
1138	C₂²	—	212	8	no	—
1139	C₂²	—	212	32	no	—
1140	C₂²	C₂²×D₄×D₅₃	1	8	yes	—
1141	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
1142	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
1143	C₄	—	2	8	no	—
1144	C₄	—	2	1	no	—
1145	C₄	—	2	1	no	—
1146	C₄	—	2	4	no	—
1147	C₄	—	2	2	no	—
1148	C₄	—	53	4	no	—
1149	C₄	—	106	8	no	—
1150	C₄	—	106	2	no	—
1151	C₄	—	106	4	no	—
1152	C₄	—	106	2	no	—
1153	C₄	C₂²×D₄×D₅₃	1	4	yes	—
1154	C₂	—	2	2	no	—
1155	C₂	—	2	8	no	—
1156	C₂	—	4	8	no	—
1157	C₂	—	106	8	no	—
1158	C₂	—	106	4	no	—
1159	C₂	—	212	8	no	—
1160	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
1161	C₂	#20289525	1	1	yes	characteristic
1162	C₂	#20289526	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	#62842
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. #20288474	C₂	semidirect
7. #20288472	C₂	semidirect
8. #20288354	C₂	semidirect
9. #20288352	C₂	semidirect
10. #20288345	C₂	semidirect
11. #20288343	C₂	semidirect
12. #20288043	C₂	semidirect
13. #20288042	C₂	semidirect
14. C₂×#16811181	C₂	semidirect
15. #534×D₅₃	C₂	semidirect
16. C₂×#16811095	C₂	semidirect
17. C₅₃×#3496	C₂	semidirect
18. C₂×#13133263	C₂²	semidirect
19. C₂×#13133263	C₂²	semidirect
20. C₂×#13133262	C₂²	semidirect
21. C₂×#13133262	C₂²	semidirect
22. C₂×#13133262	C₂²	semidirect
24. C₂×#41×D₅₃	C₂²	semidirect
25. C₂×#41×D₅₃	C₂²	semidirect
27. C₂²×D₄×D₅₃	C₂²	semidirect
28. C₂²×D₄×D₅₃	C₂²	semidirect
29. #16811278	C₂²	semidirect
30. #16811277	C₂²	semidirect
31. #16811276	C₂²	semidirect
32. #16811275	C₂²	semidirect
33. #16811274	C₂²	semidirect
34. #16811273	C₂²	semidirect
35. #16811272	C₂²	semidirect
36. #16811271	C₂²	semidirect
37. #16811270	C₂²	semidirect
38. #16811269	C₂²	semidirect
39. #16811268	C₂²	semidirect
40. #16811267	C₂²	semidirect
41. #16811266	C₂²	semidirect
42. #16811265	C₂²	semidirect
43. #16811264	C₂²	semidirect
44. #16811263	C₂²	semidirect
45. #16811262	C₂²	semidirect
46. #16811261	C₂²	semidirect
47. #16811260	C₂²	semidirect
48. D₄×D₂₁₂	C₂²	semidirect
49. D₄×D₂₁₂	C₂²	semidirect
50. #16811258	C₂²	semidirect
51. #16811257	C₂²	semidirect
52. #16811257	C₂²	semidirect
53. D₄×C₂²⋊D₅₃	C₂²	semidirect
54. D₄×C₂²⋊D₅₃	C₂²	semidirect
55. #16811255	C₂²	semidirect
56. #16811204	C₂²	semidirect
57. #16811201	C₂²	semidirect
58. #16811200	C₂²	semidirect
59. #16811200	C₂²	semidirect
60. #16811198	C₂²	semidirect
61. #16811196	C₂²	semidirect
62. #16811193	C₂²	semidirect
63. #16811191	C₂²	semidirect
64. #16811189	C₂²	semidirect
65. #16811186	C₂²	semidirect
66. #16811185	C₂²	semidirect
67. #16811184	C₂²	semidirect
68. #16811183	C₂²	semidirect
69. #16811182	C₂²	semidirect
70. #16811181	C₂²	semidirect
71. #16811181	C₂²	semidirect
72. #16811181	C₂²	semidirect
73. #16811181	C₂²	semidirect
74. #16811181	C₂²	semidirect
75. #16811181	C₂²	semidirect
76. #16811181	C₂²	semidirect
77. #16811173	C₂²	semidirect
78. #16811169	C₂²	semidirect
79. #16811168	C₂²	semidirect
80. #16811136	C₂²	semidirect
81. #16811133	C₂²	semidirect
82. #16811132	C₂²	semidirect
83. #16811132	C₂²	semidirect
84. C₂×#13133202	C₂²	semidirect
85. C₂×#13133199	C₂²	semidirect
86. #123×D₅₃	C₂²	semidirect
87. C₂×#13133191	C₂²	semidirect
88. C₂×#13133189	C₂²	semidirect
89. #121×D₅₃	C₂²	semidirect
90. #121×D₅₃	C₂²	semidirect
91. C₂×#13133187	C₂²	semidirect
92. C₂×#13133185	C₂²	semidirect
93. #120×D₅₃	C₂²	semidirect
94. #16811095	C₂²	semidirect
95. #16811095	C₂²	semidirect
96. C₂×C₄×D₂₁₂	C₂²	semidirect
97. C₂×D₄×Dic₅₃	C₂²	semidirect
98. C₂×#13133179	C₂²	semidirect
99. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
100. C₂×#13133177	C₂²	semidirect
101. C₂×#13133175	C₂²	semidirect
102. C₂×#13133174	C₂²	semidirect
103. C₂²×#11719921	C₂²	semidirect
104. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
105. C₂×H(5,𝔽₂)×C₅₃	C₂²	semidirect
106. C₅₃×#547	C₂²	semidirect
107. C₅₃×#546	C₂²	semidirect
108. D₄²×C₅₃	C₂²	semidirect
109. C₅₃×#537	C₂²	semidirect
110. C₅₃×#534	C₂²	semidirect
111. C₅₃×#532	C₂²	semidirect
112. C₂×#121×C₅₃	C₂²	semidirect
113. C₂×C₄×D₄×C₅₃	C₂²	semidirect
115. C₂⁴×D₅₃	C₂³	semidirect
122. C₂×#11719949	C₂³	semidirect
124. C₂×#11719945	C₂³	semidirect
125. C₂×#11719945	C₂³	semidirect
126. C₂×#11719945	C₂³	semidirect
128. C₂×#11719947	C₂³	semidirect
129. C₂×#11719947	C₂³	semidirect
130. C₂×#11719947	C₂³	semidirect
133. C₂×Q₈×D₅₃	C₂³	semidirect
136. C₂²×D₂₁₂	C₂³	semidirect
137. C₂²×D₂₁₂	C₂³	semidirect
140. C₂²×C₂²⋊D₅₃	C₂³	semidirect
141. C₂²×C₂²⋊D₅₃	C₂³	semidirect
142. C₂²×C₂²⋊D₅₃	C₂³	semidirect
145. C₂×D₄×D₅₃	D₄	semidirect
149. C₂×D₄×D₅₃	C₂³	semidirect
150. C₂×D₄×D₅₃	C₂³	semidirect
151. C₂×D₄×D₅₃	C₂³	semidirect
152. C₂×D₄×D₅₃	C₂³	semidirect
153. C₂×D₄×D₅₃	C₂³	semidirect
154. C₂×D₄×D₅₃	C₂³	semidirect
155. C₂×D₄×D₅₃	C₂³	semidirect
156. C₂×D₄×D₅₃	C₂³	semidirect
157. C₂³×Dic₅₃	C₂³	semidirect
159. C₂²×C₄×D₅₃	C₂³	semidirect
160. C₂²×C₄×D₅₃	C₂³	semidirect
161. C₂²×C₄×D₅₃	C₂³	semidirect
162. C₂²×C₄×D₅₃	C₂³	semidirect
163. #13133217	C₂³	semidirect
164. #13133216	C₂³	semidirect
165. #13133215	C₂³	semidirect
166. #13133214	C₂³	semidirect
167. #13133213	C₂³	semidirect
168. #13133213	C₂³	semidirect
169. #13133206	C₂³	semidirect
170. #13133205	C₂³	semidirect
171. #13133204	C₂³	semidirect
172. #13133203	C₂³	semidirect
173. #13133202	C₂³	semidirect
174. #13133202	C₂³	semidirect
175. #13133202	C₂³	semidirect
176. #13133202	C₂³	semidirect
177. #13133202	C₂³	semidirect
178. #13133201	C₂³	semidirect
179. #13133200	C₂³	semidirect
180. #13133199	C₂³	semidirect
181. #13133199	C₂³	semidirect
182. #13133199	C₂³	semidirect
183. #13133199	C₂³	semidirect
184. #13133199	C₂³	semidirect
185. #13133198	C₂³	semidirect
186. #13133197	C₂³	semidirect
187. #13133196	C₂³	semidirect
188. #13133195	C₂³	semidirect
189. #13133195	C₂³	semidirect
190. #13133194	C₂³	semidirect
191. #13133194	C₂³	semidirect
192. #13133193	C₂³	semidirect
193. #13133192	C₂³	semidirect
194. #13133192	C₂³	semidirect
195. #13133192	C₂³	semidirect
196. #13133191	C₂³	semidirect
197. #13133191	C₂³	semidirect
198. #13133191	C₂³	semidirect
199. #13133191	C₂³	semidirect
200. #13133191	C₂³	semidirect
201. #13133191	C₂³	semidirect
202. #13133190	C₂³	semidirect
203. #13133190	C₂³	semidirect
204. #13133190	C₂³	semidirect
205. #13133190	C₂³	semidirect
206. #13133189	C₂³	semidirect
207. #13133189	C₂³	semidirect
208. #13133189	C₂³	semidirect
209. #13133189	C₂³	semidirect
210. #13133189	C₂³	semidirect
211. #13133189	C₂³	semidirect
212. #13133189	C₂³	semidirect
213. #13133188	C₂³	semidirect
214. #13133188	C₂³	semidirect
215. #13133188	C₂³	semidirect
216. #13133187	C₂³	semidirect
217. #13133187	C₂³	semidirect
218. #13133187	C₂³	semidirect
219. #13133187	C₂³	semidirect
220. #13133187	C₂³	semidirect
221. #13133187	C₂³	semidirect
222. #13133186	C₂³	semidirect
223. #13133185	C₂³	semidirect
224. #13133185	C₂³	semidirect
225. #13133185	C₂³	semidirect
226. #13133185	C₂³	semidirect
227. #13133185	C₂³	semidirect
228. #13133185	C₂³	semidirect
229. C₄×D₂₁₂	C₂³	semidirect
230. C₄×D₂₁₂	C₂³	semidirect
231. C₄×D₂₁₂	C₂³	semidirect
232. C₄×D₂₁₂	C₂³	semidirect
233. D₄×Dic₅₃	C₂³	semidirect
234. D₄×Dic₅₃	C₂³	semidirect
235. #13133179	C₂³	semidirect
236. #13133179	C₂³	semidirect
237. C₄×C₂²⋊D₅₃	C₂³	semidirect
238. C₄×C₂²⋊D₅₃	C₂³	semidirect
239. C₄×C₂²⋊D₅₃	C₂³	semidirect
240. C₄×C₂²⋊D₅₃	C₂³	semidirect
241. #13133177	C₂³	semidirect
242. #13133177	C₂³	semidirect
243. #13133175	C₂³	semidirect
244. #13133174	C₂³	semidirect
245. #13133174	C₂³	semidirect
246. C₂×C₄⋊Dic₅₃	C₂³	semidirect
247. C₂×C₄⋊Dic₅₃	C₂³	semidirect
248. C₂×#11719919	C₂³	semidirect
249. C₂×#11719919	C₂³	semidirect
250. C₂×#11719919	C₂³	semidirect
251. C₄⋊C₄×D₅₃	C₂³	semidirect
252. C₄⋊C₄×D₅₃	C₂³	semidirect
253. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
254. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
258. C₂×#11719921	C₂³	semidirect
259. C₂×#11719921	C₂³	semidirect
260. C₂×#11719921	C₂³	semidirect
261. C₂×#11719921	C₂³	semidirect
262. C₂×#11719921	C₂³	semidirect
263. C₂×#11719921	C₂³	semidirect
264. C₂²⋊C₄×D₅₃	C₂³	semidirect
265. C₂²⋊C₄×D₅₃	C₂³	semidirect
266. C₂²⋊C₄×D₅₃	C₂³	semidirect
267. C₂×C₄×Dic₅₃	C₂³	semidirect
268. C₂×C₄×Dic₅₃	C₂³	semidirect
270. C₂×#41×C₅₃	C₂³	semidirect
271. C₂×#41×C₅₃	C₂³	semidirect
273. C₂²×D₄×C₅₃	C₂³	semidirect
274. C₂²×D₄×C₅₃	C₂³	semidirect
275. C₂²×D₄×C₅₃	C₂³	semidirect
276. C₂³×C₄×C₅₃	C₂³	semidirect
277. C₄⋊Q₈×C₅₃	C₂³	semidirect
278. #127×C₅₃	C₂³	semidirect
279. #124×C₅₃	C₂³	semidirect
280. #123×C₅₃	C₂³	semidirect
281. C₂²⋊Q₈×C₅₃	C₂³	semidirect
282. #121×C₅₃	C₂³	semidirect
283. #121×C₅₃	C₂³	semidirect
284. #121×C₅₃	C₂³	semidirect
285. #121×C₅₃	C₂³	semidirect
286. #121×C₅₃	C₂³	semidirect
287. #121×C₅₃	C₂³	semidirect
288. #120×C₅₃	C₂³	semidirect
289. C₄×D₄×C₅₃	C₂³	semidirect
290. C₄×D₄×C₅₃	C₂³	semidirect
291. C₄×D₄×C₅₃	C₂³	semidirect
292. C₄×D₄×C₅₃	C₂³	semidirect
293. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
294. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
295. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
296. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
297. C₂×C₄²×C₅₃	C₂³	semidirect
305. C₂³×D₅₃	C₂×D₄	semidirect
318. C₂×D₄×C₅₃	C₂×D₄	semidirect
339. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
374. D₄×D₅₃	C₂×D₄	semidirect
382. C₂×D₂₁₂	C₂×D₄	semidirect
394. C₂×C₄×D₅₃	C₂×D₄	semidirect
580. #3496	D₅₃	semidirect
605. C₂×H(5,𝔽₂)	C₂×D₅₃	semidirect
619. #547	C₂×D₅₃	semidirect
631. #546	C₂×D₅₃	semidirect
640. D₄²	C₂×D₅₃	semidirect
645. #537	C₂×D₅₃	semidirect
663. #534	C₂×D₅₃	semidirect
667. #532	C₂×D₅₃	semidirect
679. C₂×#121	C₂×D₅₃	semidirect
690. C₂×C₄×D₄	C₂×D₅₃	semidirect
695. C₅₃	#62842	semidirect
716. C₂×#41	C₂²×D₅₃	semidirect
717. C₂×#41	C₂²×D₅₃	semidirect
743. C₂²×D₄	C₂²×D₅₃	semidirect
744. C₂²×D₄	C₂²×D₅₃	semidirect
745. C₂²×D₄	C₂²×D₅₃	semidirect
752. C₂³×C₄	C₂²×D₅₃	semidirect
756. C₄⋊Q₈	C₂²×D₅₃	semidirect
760. #127	C₂²×D₅₃	semidirect
765. #124	C₂²×D₅₃	semidirect
779. #123	C₂²×D₅₃	semidirect
787. C₂²⋊Q₈	C₂²×D₅₃	semidirect
811. #121	C₂²×D₅₃	semidirect
812. #121	C₂²×D₅₃	semidirect
813. #121	C₂²×D₅₃	semidirect
814. #121	C₂²×D₅₃	semidirect
815. #121	C₂²×D₅₃	semidirect
816. #121	C₂²×D₅₃	semidirect
830. #120	C₂²×D₅₃	semidirect
845. C₄×D₄	C₂²×D₅₃	semidirect
846. C₄×D₄	C₂²×D₅₃	semidirect
847. C₄×D₄	C₂²×D₅₃	semidirect
848. C₄×D₄	C₂²×D₅₃	semidirect
859. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
860. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
875. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
876. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
879. C₂×C₄²	C₂²×D₅₃	semidirect
949. C₂×D₄	D₄×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
#20288474	2
#20288472	2
#20288354	2
#20288352	2
#20288345	2
#20288343	2
#20288043	2
#20288042	2
C₂×#16811181	2
#534×D₅₃	2
C₂×#16811095	2
C₅₃×#3496	2
#62842	53