Subgroups — #28293102

Order 13568.

11770 conjugacy classes of subgroups.

The subgroup lattice has 906 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13133262	C₂	1	2	yes	maximal, complemented
2	#20288476	C₂	1	8	yes	maximal, complemented
3	#20288472	C₂	1	8	yes	maximal, complemented
4	#20288356	C₂	1	8	yes	maximal, complemented
5	#20288353	C₂	1	8	yes	maximal, complemented
6	#20288347	C₂	1	8	yes	maximal, complemented
7	#20288344	C₂	1	8	yes	maximal, complemented
8	#20288041	C₂	1	4	yes	maximal, complemented
9	C₂×#16811185	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#16811182	C₂	1	2	yes	maximal, complemented
11	#534×D₅₃	C₂	1	4	yes	maximal, complemented
12	C₂×#16811096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅₃×#534	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#13133262	—	2	32	no	—
15	C₂×#13133262	C₂²	1	8	yes	complemented
16	C₂×#13133262	C₂²	1	8	yes	complemented
17	C₂×#13133262	C₂²	1	8	yes	complemented
18	C₂×#13133262	C₂²	1	8	yes	complemented
19	C₂²×#11719945	C₂²	1	4	yes	complemented
20	C₂²×#11719947	C₂²	1	4	yes	complemented
21	C₂²×#11719947	C₂²	1	4	yes	complemented
22	C₂³×C₂²⋊D₅₃	C₂²	1	1	yes	characteristic
23	C₂³×C₂²⋊D₅₃	C₂²	1	2	yes	complemented
24	C₂³×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
25	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
26	C₂²×D₄×D₅₃	C₂²	1	4	yes	complemented
27	#16811274	C₂²	1	16	yes	complemented
28	#16811273	C₂²	1	16	yes	complemented
29	#16811271	C₂²	1	32	yes	complemented
30	#16811265	C₂²	1	32	yes	complemented
31	#16811263	C₂²	1	32	yes	complemented
32	#16811262	C₂²	1	32	yes	complemented
33	#16811260	C₂²	1	32	yes	complemented
34	#16811257	C₂²	1	16	yes	complemented
35	D₄×C₂²⋊D₅₃	C₂²	1	16	yes	complemented
36	#16811255	C₂²	1	32	yes	complemented
37	#16811200	C₂²	1	16	yes	complemented
38	#16811195	C₂²	1	16	yes	complemented
39	#16811188	C₂²	1	16	yes	complemented
40	#16811185	C₂²	1	4	yes	complemented
41	#16811185	C₂²	1	8	yes	complemented
42	#16811185	C₂²	1	4	yes	complemented
43	#16811184	C₂²	1	16	yes	complemented
44	#16811183	C₂²	1	16	yes	complemented
45	#16811182	C₂²	1	8	yes	complemented
46	#16811182	C₂²	1	8	yes	complemented
47	#16811182	C₂²	1	8	yes	complemented
48	#16811182	C₂²	1	8	yes	complemented
49	#16811181	C₂²	1	16	yes	complemented
50	#16811168	C₂²	1	16	yes	complemented
51	#16811131	C₂²	1	16	yes	complemented
52	#16811129	C₂²	1	16	yes	complemented
53	C₂×#13133201	C₂²	1	4	yes	complemented
54	C₂×#13133200	C₂²	1	4	yes	complemented
55	C₂×#13133198	C₂²	1	4	yes	complemented
56	#123×D₅₃	C₂²	1	16	yes	complemented
57	C₂×#13133191	C₂²	1	4	yes	complemented
58	C₂×#13133189	C₂²	1	8	yes	complemented
59	#121×D₅₃	C₂²	1	16	yes	complemented
60	C₂×#13133187	C₂²	1	4	yes	complemented
61	C₂×#13133186	C₂²	1	4	yes	complemented
62	C₂×#13133185	C₂²	1	4	yes	complemented
63	#120×D₅₃	C₂²	1	16	yes	complemented
64	#16811096	C₂²	1	8	yes	complemented
65	#16811096	C₂²	1	8	yes	complemented
66	C₂×C₄×C₂²⋊D₅₃	C₂²	1	4	yes	complemented
67	C₂×#13133177	C₂²	1	4	yes	complemented
68	C₂×#13133173	C₂²	1	2	yes	complemented
69	C₂²×C₂²⋊Dic₅₃	C₂²	1	1	yes	characteristic, complemented
70	C₂×C₂²⋊C₄×D₅₃	C₂²	1	2	yes	complemented
71	C₂³×D₄×C₅₃	C₂²	1	2	yes	complemented
72	C₅₃×#534	C₂²	1	4	yes	complemented
73	C₅₃×#534	C₂²	1	8	yes	complemented
74	C₅₃×#534	C₂²	1	4	yes	complemented
75	C₂×#123×C₅₃	C₂²	1	4	yes	complemented
76	C₂×#121×C₅₃	C₂²	1	4	yes	complemented
77	C₂×#120×C₅₃	C₂²	1	4	yes	complemented
78	C₂²×C₂²⋊C₄×C₅₃	C₂²	1	1	yes	characteristic, complemented
79	C₂⁴×D₅₃	C₂³	1	1	yes	characteristic
80	C₂⁴×D₅₃	C₂³	1	4	yes	complemented
81	C₂⁴×D₅₃	C₂³	1	2	yes	complemented
82	#13133262	—	2	64	no	—
83	#13133262	—	2	64	no	—
84	#13133262	—	2	64	no	—
85	#13133262	—	2	64	no	—
86	C₂×#11719945	—	2	32	no	—
87	C₂×#11719945	C₂³	1	16	yes	complemented
88	C₂×#11719945	C₂³	1	16	yes	complemented
89	C₂×#11719947	—	2	32	no	—
90	C₂×#11719947	—	2	32	no	—
91	C₂×#11719947	C₂³	1	16	yes	—
92	C₂×#11719947	C₂³	1	16	yes	complemented
93	C₂×#11719947	C₂³	1	16	yes	complemented
94	C₂×#11719947	C₂³	1	16	yes	complemented
95	C₂²×Dic₁₀₆	C₂³	1	4	yes	complemented
96	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
97	C₂²×D₂₁₂	C₂³	1	4	yes	complemented
98	C₂²×C₂²⋊D₅₃	—	2	16	no	—
99	C₂²×C₂²⋊D₅₃	—	2	32	no	—
100	C₂²×C₂²⋊D₅₃	D₄	1	16	yes	complemented
101	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
102	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
103	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
104	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
105	C₂²×C₂²⋊D₅₃	C₂³	1	2	yes	—
106	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
107	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	—
108	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
109	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
110	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
111	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
112	C₂²×C₂²⋊D₅₃	C₂³	1	4	yes	complemented
113	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
114	C₂²×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
115	C₂²×C₂²⋊D₅₃	C₂³	1	8	yes	complemented
116	C₂×D₄×D₅₃	—	2	32	no	—
117	C₂×D₄×D₅₃	—	2	32	no	—
118	C₂×D₄×D₅₃	C₂³	1	16	yes	—
119	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
120	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
121	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
122	C₂×D₄×D₅₃	C₂³	1	16	yes	complemented
123	C₂³×Dic₅₃	C₂³	1	1	yes	characteristic
124	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
125	C₂³×Dic₅₃	C₂³	1	4	yes	complemented
126	C₂³×Dic₅₃	C₂³	1	2	yes	complemented
127	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
128	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
129	C₂²×C₄×D₅₃	C₂³	1	4	yes	complemented
130	#13133216	C₂³	1	16	yes	complemented
131	#13133213	C₂³	1	16	yes	complemented
132	#13133203	C₂³	1	32	yes	complemented
133	#13133202	C₂³	1	32	yes	complemented
134	#13133201	C₂³	1	16	yes	complemented
135	#13133201	C₂³	1	16	yes	complemented
136	#13133200	C₂³	1	16	yes	complemented
137	#13133200	C₂³	1	16	yes	complemented
138	#13133199	C₂³	1	32	yes	complemented
139	#13133198	C₂³	1	16	yes	complemented
140	#13133198	C₂³	1	16	yes	complemented
141	#13133195	C₂³	1	32	yes	complemented
142	#13133194	C₂³	1	32	yes	complemented
143	#13133192	C₂³	1	16	yes	complemented
144	#13133191	C₂³	1	16	yes	complemented
145	#13133191	C₂³	1	16	yes	complemented
146	#13133190	C₂³	1	32	yes	complemented
147	#13133190	C₂³	1	32	yes	complemented
148	#13133189	C₂³	1	32	yes	complemented
149	#13133189	C₂³	1	32	yes	complemented
150	#13133189	C₂³	1	32	yes	complemented
151	#13133188	C₂³	1	16	yes	complemented
152	#13133187	C₂³	1	16	yes	complemented
153	#13133187	C₂³	1	32	yes	complemented
154	#13133187	C₂³	1	16	yes	complemented
155	#13133186	C₂³	1	16	yes	complemented
156	#13133186	C₂³	1	16	yes	complemented
157	#13133185	C₂³	1	16	yes	complemented
158	#13133185	C₂³	1	32	yes	complemented
159	#13133185	C₂³	1	16	yes	complemented
160	D₄×Dic₅₃	C₂³	1	16	yes	complemented
161	#13133179	C₂³	1	16	yes	complemented
162	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
163	C₄×C₂²⋊D₅₃	C₂³	1	16	yes	complemented
164	#13133177	C₂³	1	32	yes	complemented
165	#13133177	C₂³	1	32	yes	complemented
166	#13133173	C₂³	1	16	yes	complemented
167	C₂×C₄⋊Dic₅₃	C₂³	1	4	yes	complemented
168	C₂×#11719919	C₂³	1	8	yes	complemented
169	C₂×#11719919	C₂³	1	4	yes	complemented
170	C₄⋊C₄×D₅₃	C₂³	1	16	yes	complemented
171	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	—
172	C₂×C₂²⋊Dic₅₃	C₂³	1	2	yes	complemented
173	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
174	C₂×C₂²⋊Dic₅₃	C₂³	1	4	yes	complemented
175	C₂×C₂²⋊Dic₅₃	C₂³	1	8	yes	complemented
176	C₂×#11719921	C₂³	1	8	yes	complemented
177	C₂×#11719921	C₂³	1	4	yes	complemented
178	C₂×#11719921	C₂³	1	8	yes	complemented
179	C₂²⋊C₄×D₅₃	C₂³	1	32	yes	complemented
180	C₂²⋊C₄×D₅₃	C₂³	1	16	yes	complemented
181	C₂×C₄×Dic₅₃	C₂³	1	4	yes	complemented
182	C₂⁵×C₅₃	C₂³	1	1	yes	characteristic
183	C₂⁵×C₅₃	C₂³	1	2	yes	complemented
184	C₂²×D₄×C₅₃	—	2	16	no	—
185	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
186	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
187	C₂²×D₄×C₅₃	C₂³	1	4	yes	—
188	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
189	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
190	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
191	C₂²×D₄×C₅₃	C₂³	1	4	yes	complemented
192	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
193	C₂³×C₄×C₅₃	C₂³	1	2	yes	complemented
194	#123×C₅₃	C₂³	1	16	yes	complemented
195	#123×C₅₃	C₂³	1	16	yes	complemented
196	#121×C₅₃	C₂³	1	16	yes	complemented
197	#121×C₅₃	C₂³	1	16	yes	complemented
198	#120×C₅₃	C₂³	1	16	yes	complemented
199	#120×C₅₃	C₂³	1	16	yes	complemented
200	C₂×C₄⋊C₄×C₅₃	C₂³	1	4	yes	complemented
201	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
203	C₂×C₂²⋊C₄×C₅₃	C₂³	1	2	yes	complemented
204	C₂×C₂²⋊C₄×C₅₃	C₂³	1	4	yes	complemented
205	C₂×C₂²⋊C₄×C₅₃	C₂³	1	8	yes	complemented
206	C₂⁴×C₅₃	—	2	8	no	—
207	C₂⁴×C₅₃	—	8	2	no	—
208	C₂⁴×C₅₃	—	8	4	no	—
209	C₂⁴×C₅₃	C₂×D₄	1	8	yes	complemented
210	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
211	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
212	C₂⁴×C₅₃	C₂⁴	1	4	yes	—
213	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
214	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
215	C₂⁴×C₅₃	C₂⁴	1	2	yes	—
216	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
217	C₂⁴×C₅₃	C₂⁴	1	1	yes	characteristic
218	C₂³×D₅₃	—	2	8	no	—
219	C₂³×D₅₃	—	2	16	no	—
220	C₂³×D₅₃	—	8	2	no	—
221	C₂³×D₅₃	—	8	4	no	—
222	C₂³×D₅₃	—	8	8	no	—
223	C₂³×D₅₃	C₂×D₄	1	8	yes	complemented
224	C₂³×D₅₃	C₂⁴	1	16	yes	—
225	C₂³×D₅₃	C₂⁴	1	4	yes	—
226	C₂³×D₅₃	C₂⁴	1	4	yes	—
227	C₂³×D₅₃	C₂⁴	1	4	yes	—
228	C₂³×D₅₃	C₂⁴	1	4	yes	—
229	C₂³×D₅₃	C₂⁴	1	2	yes	—
230	C₂×D₄×C₅₃	—	2	16	no	—
231	C₂×D₄×C₅₃	—	2	16	no	—
232	C₂×D₄×C₅₃	—	2	16	no	—
233	C₂×D₄×C₅₃	—	2	16	no	—
234	C₂×D₄×C₅₃	—	2	16	no	—
235	C₂×D₄×C₅₃	—	2	16	no	—
236	C₂×D₄×C₅₃	—	8	4	no	—
237	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
238	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
239	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
240	C₂×D₄×C₅₃	C₂⁴	1	8	yes	—
241	C₂×D₄×C₅₃	C₂⁴	1	16	yes	—
242	C₂²×C₄×C₅₃	—	2	8	no	—
243	C₂²×C₄×C₅₃	—	8	2	no	—
244	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
245	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
246	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
249	C₂²×C₄×C₅₃	C₂⁴	1	4	yes	—
250	C₂×C₂²⋊D₅₃	—	2	16	no	—
251	C₂×C₂²⋊D₅₃	—	2	16	no	—
252	C₂×C₂²⋊D₅₃	—	2	16	no	—
253	C₂×C₂²⋊D₅₃	—	2	16	no	—
254	C₂×C₂²⋊D₅₃	—	2	16	no	—
255	C₂×C₂²⋊D₅₃	—	2	16	no	—
256	C₂×C₂²⋊D₅₃	—	2	16	no	—
257	C₂×C₂²⋊D₅₃	—	2	64	no	—
258	C₂×C₂²⋊D₅₃	—	2	64	no	—
259	C₂×C₂²⋊D₅₃	—	2	16	no	—
260	C₂×C₂²⋊D₅₃	—	8	8	no	—
261	C₂×C₂²⋊D₅₃	C₂×D₄	1	32	yes	complemented
262	C₂×C₂²⋊D₅₃	C₂×D₄	1	32	yes	complemented
263	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
264	C₂×C₂²⋊D₅₃	C₂×D₄	1	16	yes	complemented
265	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
266	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
267	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
268	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
269	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
270	C₂×C₂²⋊D₅₃	C₂⁴	1	16	yes	—
271	C₂×C₂²⋊D₅₃	C₂⁴	1	32	yes	—
272	C₂×C₂²⋊D₅₃	C₂⁴	1	8	yes	—
273	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
274	C₂×C₂²⋊D₅₃	C₂⁴	1	4	yes	—
275	C₂²×Dic₅₃	—	2	8	no	—
276	C₂²×Dic₅₃	—	2	16	no	—
277	C₂²×Dic₅₃	—	8	2	no	—
278	C₂²×Dic₅₃	C₂×D₄	1	8	yes	complemented
279	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
280	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
281	C₂²×Dic₅₃	C₂⁴	1	16	yes	—
282	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
283	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
284	C₂²×Dic₅₃	C₂⁴	1	8	yes	—
285	C₂²×Dic₅₃	C₂⁴	1	2	yes	—
286	C₂²×Dic₅₃	C₂⁴	1	4	yes	—
287	#11719947	—	2	64	no	—
288	#11719947	—	2	64	no	—
289	#11719947	—	2	64	no	—
290	#11719947	—	2	64	no	—
291	D₄×D₅₃	—	2	64	no	—
292	D₄×D₅₃	—	2	64	no	—
293	D₄×D₅₃	—	2	64	no	—
294	D₄×D₅₃	—	2	64	no	—
295	D₄×D₅₃	—	8	16	no	—
296	#11719945	—	2	64	no	—
297	#11719945	—	2	64	no	—
298	C₂×D₂₁₂	—	2	16	no	—
299	C₂×D₂₁₂	—	8	4	no	—
300	C₂×D₂₁₂	C₂⁴	1	16	yes	—
301	C₂×D₂₁₂	C₂⁴	1	16	yes	—
302	C₂×C₄×D₅₃	—	2	16	no	—
303	C₂×C₄×D₅₃	—	2	16	no	—
304	C₂×C₄×D₅₃	—	8	4	no	—
305	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
306	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
307	C₂×C₄×D₅₃	C₂⁴	1	16	yes	—
308	C₂×Dic₁₀₆	—	2	16	no	—
309	C₂×Dic₁₀₆	C₂⁴	1	16	yes	—
310	C₄⋊C₄×C₅₃	C₂⁴	1	16	yes	—
311	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
312	C₂²⋊C₄×C₅₃	C₂⁴	1	8	yes	—
313	C₂²⋊C₄×C₅₃	C₂⁴	1	32	yes	—
314	C₂²⋊Dic₅₃	C₂⁴	1	8	yes	—
315	C₂²⋊Dic₅₃	C₂⁴	1	32	yes	—
316	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
317	C₂²⋊Dic₅₃	C₂⁴	1	4	yes	—
318	#11719921	C₂⁴	1	16	yes	—
319	#11719921	C₂⁴	1	32	yes	—
320	#11719921	C₂⁴	1	32	yes	—
321	C₄⋊Dic₅₃	C₂⁴	1	16	yes	—
322	#11719919	C₂⁴	1	32	yes	—
323	#11719919	C₂⁴	1	16	yes	—
324	C₄×Dic₅₃	C₂⁴	1	16	yes	—
325	C₂³×C₅₃	—	2	8	no	—
326	C₂³×C₅₃	—	2	8	no	—
327	C₂³×C₅₃	—	2	8	no	—
328	C₂³×C₅₃	—	4	2	no	—
329	C₂³×C₅₃	—	4	2	no	—
330	C₂³×C₅₃	—	4	2	no	—
331	C₂³×C₅₃	—	4	4	no	—
332	C₂³×C₅₃	—	4	8	no	—
333	C₂³×C₅₃	—	4	4	no	—
334	C₂³×C₅₃	—	4	8	no	—
335	C₂³×C₅₃	—	4	8	no	—
336	C₂³×C₅₃	—	8	8	no	—
337	C₂³×C₅₃	—	8	16	no	—
338	C₂³×C₅₃	C₂²×D₄	1	8	yes	—
339	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
340	C₂³×C₅₃	C₂²×D₄	1	8	yes	—
341	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
342	C₂³×C₅₃	C₂²×D₄	1	4	yes	—
343	C₂³×C₅₃	C₂⁵	1	8	yes	—
344	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
345	C₂³×C₅₃	C₂⁵	1	2	yes	—
346	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
347	C₂³×C₅₃	C₂⁵	1	2	yes	—
348	C₂³×C₅₃	C₂⁵	1	1	yes	characteristic
349	C₂²×D₅₃	—	2	8	no	—
350	C₂²×D₅₃	—	2	8	no	—
351	C₂²×D₅₃	—	2	8	no	—
352	C₂²×D₅₃	—	2	32	no	—
353	C₂²×D₅₃	—	4	4	no	—
354	C₂²×D₅₃	—	4	8	no	—
355	C₂²×D₅₃	—	4	8	no	—
356	C₂²×D₅₃	—	4	8	no	—
357	C₂²×D₅₃	—	4	32	no	—
358	C₂²×D₅₃	—	4	8	no	—
359	C₂²×D₅₃	—	8	8	no	—
360	C₂²×D₅₃	—	8	32	no	—
361	C₂²×D₅₃	—	8	16	no	—
362	C₂²×D₅₃	C₂²×D₄	1	16	yes	—
363	C₂²×D₅₃	C₂²×D₄	1	8	yes	—
364	C₂²×D₅₃	C₂⁵	1	8	yes	—
365	C₂²×D₅₃	C₂⁵	1	4	yes	—
366	D₄×C₅₃	—	2	16	no	—
367	D₄×C₅₃	—	2	16	no	—
368	D₄×C₅₃	—	2	16	no	—
369	D₄×C₅₃	—	2	16	no	—
370	D₄×C₅₃	—	4	16	no	—
371	C₂×C₄×C₅₃	—	2	8	no	—
372	C₂×C₄×C₅₃	—	2	8	no	—
373	C₂×C₄×C₅₃	—	2	8	no	—
374	C₂×C₄×C₅₃	—	4	4	no	—
375	C₂×C₄×C₅₃	—	4	4	no	—
376	C₂×C₄×C₅₃	—	4	4	no	—
377	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
378	C₂×C₄×C₅₃	C₂⁵	1	8	yes	—
379	C₂²⋊D₅₃	—	2	16	no	—
380	C₂²⋊D₅₃	—	2	16	no	—
381	C₂²⋊D₅₃	—	2	16	no	—
382	C₂²⋊D₅₃	—	2	16	no	—
383	C₂²⋊D₅₃	—	2	32	no	—
384	C₂²⋊D₅₃	—	2	32	no	—
385	C₂²⋊D₅₃	—	4	32	no	—
386	C₂²⋊D₅₃	C₂²×D₄	1	16	yes	—
387	C₂²⋊D₅₃	C₂²×D₄	1	32	yes	—
388	C₂²⋊D₅₃	C₂²×D₄	1	16	yes	—
389	C₂×Dic₅₃	—	2	8	no	—
390	C₂×Dic₅₃	—	2	8	no	—
391	C₂×Dic₅₃	—	2	8	no	—
392	C₂×Dic₅₃	—	2	32	no	—
393	C₂×Dic₅₃	—	4	4	no	—
394	C₂×Dic₅₃	—	4	8	no	—
395	C₂×Dic₅₃	C₂²×D₄	1	16	yes	—
396	C₂×Dic₅₃	C₂²×D₄	1	8	yes	—
397	C₂×Dic₅₃	C₂⁵	1	8	yes	—
398	C₂×Dic₅₃	C₂⁵	1	8	yes	—
399	C₂×Dic₅₃	C₂⁵	1	4	yes	—
400	D₂₁₂	—	2	32	no	—
401	D₂₁₂	—	4	16	no	—
402	C₄×D₅₃	—	2	32	no	—
403	C₄×D₅₃	—	2	32	no	—
404	C₄×D₅₃	—	4	16	no	—
405	Dic₁₀₆	—	2	32	no	—
406	#62842	—	53	1	no	maximal, Sylow
407	C₂²×C₅₃	—	2	2	no	—
408	C₂²×C₅₃	—	2	4	no	—
409	C₂²×C₅₃	—	2	2	no	—
410	C₂²×C₅₃	—	2	2	no	—
411	C₂²×C₅₃	—	2	4	no	—
412	C₂²×C₅₃	—	2	8	no	—
413	C₂²×C₅₃	—	2	16	no	—
414	C₂²×C₅₃	—	4	4	no	—
415	C₂²×C₅₃	—	4	8	no	—
416	C₂²×C₅₃	—	4	8	no	—
417	C₂²×C₅₃	—	4	4	no	—
418	C₂²×C₅₃	—	4	4	no	—
419	C₂²×C₅₃	—	4	16	no	—
420	C₂²×C₅₃	—	8	8	no	—
421	C₂²×C₅₃	—	8	8	no	—
422	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
423	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
424	C₂²×C₅₃	C₂³×D₄	1	4	yes	—
425	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
426	C₂²×C₅₃	C₂³×D₄	1	2	yes	—
427	C₂²×C₅₃	C₂⁶	1	1	yes	characteristic
428	C₂×D₅₃	—	2	8	no	—
429	C₂×D₅₃	—	2	8	no	—
430	C₂×D₅₃	—	2	16	no	—
431	C₂×D₅₃	—	4	16	no	—
432	C₂×D₅₃	—	4	8	no	—
433	C₂×D₅₃	—	4	16	no	—
434	C₂×D₅₃	—	8	32	no	—
435	C₂×D₅₃	—	8	8	no	—
436	C₂×D₅₃	—	8	8	no	—
437	C₂×D₅₃	C₂³×D₄	1	8	yes	—
438	C₄×C₅₃	—	2	8	no	—
439	C₄×C₅₃	—	2	8	no	—
440	Dic₅₃	—	2	8	no	—
441	Dic₅₃	—	2	8	no	—
442	Dic₅₃	C₂³×D₄	1	8	yes	—
443	C₂²×H(5,𝔽₂)	—	53	2	no	—
444	#3496	—	53	8	no	—
445	#3496	—	53	8	no	—
446	#3485	—	53	8	no	—
447	#3485	—	53	8	no	—
448	#3484	—	53	8	no	—
449	#3484	—	53	8	no	—
450	#3449	—	53	4	no	—
451	C₂×#534	—	53	2	no	—
452	C₂×#534	—	53	4	no	—
453	C₂×#534	—	53	1	no	—
454	C₂×#534	D₅₃	1	1	yes	characteristic, complemented
455	C₂×#518	—	53	1	no	—
456	C₂×C₅₃	—	2	4	no	—
457	C₂×C₅₃	—	2	2	no	—
458	C₂×C₅₃	—	2	2	no	—
459	C₂×C₅₃	—	2	4	no	—
460	C₂×C₅₃	—	2	2	no	—
461	C₂×C₅₃	—	4	8	no	—
462	C₂×C₅₃	C₂⁴×D₄	1	1	yes	characteristic
463	C₂×C₅₃	H(7,𝔽₂)	1	2	yes	—
464	D₅₃	—	2	8	no	—
465	D₅₃	—	4	8	no	—
466	C₂×H(5,𝔽₂)	—	53	8	no	—
467	C₂×H(5,𝔽₂)	—	53	8	no	—
468	C₂×H(5,𝔽₂)	—	53	8	no	—
469	C₂×H(5,𝔽₂)	—	53	8	no	—
470	C₂×H(5,𝔽₂)	—	106	32	no	—
471	C₂²×#41	—	53	4	no	—
472	C₂²×#41	—	53	4	no	—
473	C₂²×#41	—	53	4	no	—
474	C₂³×D₄	—	53	1	no	—
475	C₂³×D₄	—	53	2	no	—
476	C₂³×D₄	—	53	4	no	—
477	C₂³×D₄	—	53	4	no	—
478	C₂³×D₄	—	53	4	no	—
479	C₂³×D₄	C₂×D₅₃	1	2	yes	complemented
480	#547	—	53	32	no	—
481	#547	—	53	16	no	—
482	#547	—	53	16	no	—
483	#546	—	53	32	no	—
484	#546	—	53	32	no	—
485	#546	—	53	32	no	—
486	#546	—	53	32	no	—
487	D₄²	—	53	16	no	—
488	D₄²	—	53	16	no	—
489	D₄²	—	53	32	no	—
490	#537	—	53	16	no	—
491	#536	—	53	16	no	—
492	#535	—	53	16	no	—
493	#534	—	53	8	no	—
494	#534	—	53	8	no	—
495	#534	—	53	8	no	—
496	#534	—	53	8	no	—
497	#534	—	53	16	no	—
498	#534	—	53	16	no	—
499	#534	—	53	16	no	—
500	#534	—	53	4	no	—
501	#534	—	53	8	no	—
502	#534	—	53	4	no	—
503	#534	C₂×D₅₃	1	4	yes	complemented
504	#534	C₂×D₅₃	1	8	yes	complemented
505	#534	C₂×D₅₃	1	4	yes	complemented
506	#532	—	53	16	no	—
507	#525	—	53	16	no	—
508	#525	—	53	16	no	—
509	C₂×#123	—	53	4	no	—
510	C₂×#123	—	53	4	no	—
511	C₂×#123	—	53	16	no	—
512	C₂×#123	—	53	4	no	—
513	C₂×#123	C₂×D₅₃	1	4	yes	complemented
514	C₂×#121	—	53	8	no	—
515	C₂×#121	—	53	4	no	—
516	C₂×#121	—	53	16	no	—
517	C₂×#121	C₂×D₅₃	1	4	yes	complemented
518	C₂×#120	—	53	4	no	—
519	C₂×#120	—	53	4	no	—
520	C₂×#120	—	53	16	no	—
521	C₂×#120	—	53	4	no	—
522	C₂×#120	C₂×D₅₃	1	4	yes	complemented
523	#518	—	53	8	no	—
524	#518	—	53	8	no	—
525	C₂×C₄×D₄	—	53	4	no	—
526	C₂×C₄×D₄	—	53	4	no	—
527	C₂×#117	—	53	2	no	—
528	C₂²×C₂²⋊C₄	—	53	1	no	—
529	C₂²×C₂²⋊C₄	—	53	2	no	—
530	C₂²×C₂²⋊C₄	C₂×D₅₃	1	1	yes	characteristic, complemented
531	C₅₃	#62842	1	1	yes	characteristic, complemented, Sylow
532	C₂⁵	—	53	1	no	—
533	C₂⁵	—	53	4	no	—
534	C₂⁵	—	53	2	no	—
535	C₂⁵	C₂²×D₅₃	1	1	yes	characteristic
536	C₂⁵	C₂²×D₅₃	1	2	yes	complemented
537	H(5,𝔽₂)	—	106	64	no	—
538	H(5,𝔽₂)	—	106	64	no	—
539	H(5,𝔽₂)	—	106	64	no	—
540	H(5,𝔽₂)	—	106	64	no	—
541	C₂×#41	—	53	16	no	—
542	C₂×#41	—	53	16	no	—
543	C₂×#41	—	53	16	no	—
544	C₂×#41	—	53	16	no	—
545	C₂×#41	—	53	16	no	—
546	C₂×#41	—	53	16	no	—
547	C₂×#41	—	106	32	no	—
548	C₂×#41	—	106	32	no	—
549	C₂×#41	—	106	32	no	—
550	C₂²×Q₈	—	53	4	no	—
551	C₂²×D₄	—	2	16	no	—
552	C₂²×D₄	—	53	16	no	—
553	C₂²×D₄	—	53	2	no	—
554	C₂²×D₄	—	53	2	no	—
555	C₂²×D₄	—	53	4	no	—
556	C₂²×D₄	—	53	4	no	—
557	C₂²×D₄	—	53	4	no	—
558	C₂²×D₄	—	53	4	no	—
559	C₂²×D₄	—	53	4	no	—
560	C₂²×D₄	—	53	4	no	—
561	C₂²×D₄	—	53	4	no	—
562	C₂²×D₄	—	53	4	no	—
563	C₂²×D₄	—	53	4	no	—
564	C₂²×D₄	—	53	4	no	—
565	C₂²×D₄	—	53	16	no	—
566	C₂²×D₄	—	53	16	no	—
567	C₂²×D₄	—	53	8	no	—
568	C₂²×D₄	—	53	16	no	—
569	C₂²×D₄	—	53	16	no	—
570	C₂²×D₄	—	53	16	no	—
571	C₂²×D₄	—	53	16	no	—
572	C₂²×D₄	—	53	16	no	—
573	C₂²×D₄	—	53	4	no	—
574	C₂²×D₄	—	53	4	no	—
575	C₂²×D₄	—	106	32	no	—
576	C₂²×D₄	—	106	32	no	—
577	C₂²×D₄	—	106	32	no	—
578	C₂²×D₄	—	106	16	no	—
579	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
580	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
581	C₂²×D₄	C₂²×D₅₃	1	4	yes	—
582	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
583	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
584	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
585	C₂²×D₄	C₂²×D₅₃	1	4	yes	complemented
586	C₂³×C₄	—	53	1	no	—
587	C₂³×C₄	—	53	2	no	—
588	C₂³×C₄	—	53	4	no	—
589	C₂³×C₄	—	53	2	no	—
590	C₂³×C₄	—	53	4	no	—
591	C₂³×C₄	—	53	4	no	—
592	C₂³×C₄	—	53	4	no	—
593	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
594	C₂³×C₄	C₂²×D₅₃	1	2	yes	complemented
595	C₄⋊Q₈	—	53	16	no	—
596	#127	—	53	16	no	—
597	#124	—	53	32	no	—
598	#123	—	53	16	no	—
599	#123	—	53	16	no	—
600	#123	—	53	16	no	—
601	#123	—	53	16	no	—
602	#123	—	53	32	no	—
603	#123	—	53	16	no	—
604	#123	—	53	32	no	—
605	#123	—	53	16	no	—
606	#123	C₂²×D₅₃	1	16	yes	complemented
607	#123	C₂²×D₅₃	1	16	yes	complemented
608	C₂²⋊Q₈	—	53	32	no	—
609	C₂²⋊Q₈	—	53	32	no	—
610	#121	—	53	32	no	—
611	#121	—	53	16	no	—
612	#121	—	53	32	no	—
613	#121	—	53	32	no	—
614	#121	—	53	16	no	—
615	#121	—	53	16	no	—
616	#121	—	53	16	no	—
617	#121	—	53	32	no	—
618	#121	—	53	32	no	—
619	#121	C₂²×D₅₃	1	16	yes	complemented
620	#121	C₂²×D₅₃	1	16	yes	complemented
621	#120	—	53	16	no	—
622	#120	—	53	16	no	—
623	#120	—	53	16	no	—
624	#120	—	53	16	no	—
625	#120	—	53	32	no	—
626	#120	—	53	16	no	—
627	#120	—	53	32	no	—
628	#120	—	53	16	no	—
629	#120	C₂²×D₅₃	1	16	yes	complemented
630	#120	C₂²×D₅₃	1	16	yes	complemented
631	C₄×D₄	—	53	16	no	—
632	C₄×D₄	—	53	16	no	—
633	C₄×D₄	—	53	16	no	—
634	C₄×D₄	—	53	16	no	—
635	C₄×D₄	—	53	32	no	—
636	C₄×D₄	—	53	32	no	—
637	#117	—	53	16	no	—
638	C₂×C₄⋊C₄	—	53	4	no	—
639	C₂×C₄⋊C₄	—	53	8	no	—
640	C₂×C₄⋊C₄	—	53	4	no	—
641	C₂×C₄⋊C₄	—	53	16	no	—
642	C₂×C₄⋊C₄	C₂²×D₅₃	1	4	yes	complemented
643	C₂×C₂²⋊C₄	—	53	2	no	—
644	C₂×C₂²⋊C₄	—	53	2	no	—
645	C₂×C₂²⋊C₄	—	53	4	no	—
646	C₂×C₂²⋊C₄	—	53	4	no	—
647	C₂×C₂²⋊C₄	—	53	8	no	—
648	C₂×C₂²⋊C₄	—	53	4	no	—
649	C₂×C₂²⋊C₄	—	53	8	no	—
650	C₂×C₂²⋊C₄	—	53	8	no	—
651	C₂×C₂²⋊C₄	—	53	16	no	—
652	C₂×C₂²⋊C₄	—	53	32	no	—
653	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	—
654	C₂×C₂²⋊C₄	C₂²×D₅₃	1	2	yes	complemented
655	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
656	C₂×C₂²⋊C₄	C₂²×D₅₃	1	4	yes	complemented
657	C₂×C₂²⋊C₄	C₂²×D₅₃	1	8	yes	complemented
658	C₂×C₄²	—	53	4	no	—
659	C₂⁴	—	2	8	no	—
660	C₂⁴	—	8	2	no	—
661	C₂⁴	—	8	4	no	—
662	C₂⁴	—	53	8	no	—
663	C₂⁴	—	53	4	no	—
664	C₂⁴	—	53	2	no	—
665	C₂⁴	—	53	16	no	—
666	C₂⁴	—	53	4	no	—
667	C₂⁴	—	53	4	no	—
668	C₂⁴	—	53	4	no	—
669	C₂⁴	—	106	16	no	—
670	C₂⁴	—	106	8	no	—
671	C₂⁴	—	424	4	no	—
672	C₂⁴	—	424	8	no	—
673	C₂⁴	—	424	2	no	—
674	C₂⁴	D₄×D₅₃	1	8	yes	complemented
675	C₂⁴	C₂³×D₅₃	1	4	yes	—
676	C₂⁴	C₂³×D₅₃	1	4	yes	—
677	C₂⁴	C₂³×D₅₃	1	4	yes	—
678	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
679	C₂⁴	C₂³×D₅₃	1	2	yes	—
680	C₂⁴	C₂³×D₅₃	1	2	yes	—
681	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
682	C₂⁴	C₂³×D₅₃	1	1	yes	characteristic
683	#41	—	106	64	no	—
684	#41	—	106	64	no	—
685	#41	—	106	64	no	—
686	#41	—	106	64	no	—
687	#41	—	106	64	no	—
688	#41	—	106	64	no	—
689	C₂×Q₈	—	53	16	no	—
690	C₂×Q₈	—	106	16	no	—
691	C₂×D₄	—	2	16	no	—
692	C₂×D₄	—	2	16	no	—
693	C₂×D₄	—	2	16	no	—
694	C₂×D₄	—	2	16	no	—
695	C₂×D₄	—	2	16	no	—
696	C₂×D₄	—	2	16	no	—
697	C₂×D₄	—	8	4	no	—
698	C₂×D₄	—	53	32	no	—
699	C₂×D₄	—	53	32	no	—
700	C₂×D₄	—	53	16	no	—
701	C₂×D₄	—	53	16	no	—
702	C₂×D₄	—	53	4	no	—
703	C₂×D₄	—	53	4	no	—
704	C₂×D₄	—	53	8	no	—
705	C₂×D₄	—	53	8	no	—
706	C₂×D₄	—	53	16	no	—
707	C₂×D₄	—	53	8	no	—
708	C₂×D₄	—	53	8	no	—
709	C₂×D₄	—	53	8	no	—
710	C₂×D₄	—	53	16	no	—
711	C₂×D₄	—	53	32	no	—
712	C₂×D₄	—	53	16	no	—
713	C₂×D₄	—	53	16	no	—
714	C₂×D₄	—	106	16	no	—
715	C₂×D₄	—	106	16	no	—
716	C₂×D₄	—	106	64	no	—
717	C₂×D₄	—	106	64	no	—
718	C₂×D₄	—	106	64	no	—
719	C₂×D₄	—	106	64	no	—
720	C₂×D₄	—	106	64	no	—
721	C₂×D₄	—	106	64	no	—
722	C₂×D₄	—	106	16	no	—
723	C₂×D₄	—	106	16	no	—
724	C₂×D₄	—	106	16	no	—
725	C₂×D₄	—	106	16	no	—
726	C₂×D₄	—	106	16	no	—
727	C₂×D₄	—	106	16	no	—
728	C₂×D₄	—	106	16	no	—
729	C₂×D₄	—	424	4	no	—
730	C₂×D₄	—	424	16	no	—
731	C₂×D₄	—	424	8	no	—
732	C₂×D₄	C₂³×D₅₃	1	8	yes	—
733	C₂×D₄	C₂³×D₅₃	1	8	yes	—
734	C₂×D₄	C₂³×D₅₃	1	8	yes	—
735	C₂×D₄	C₂³×D₅₃	1	8	yes	—
736	C₂×D₄	C₂³×D₅₃	1	16	yes	—
737	C₂²×C₄	—	2	8	no	—
738	C₂²×C₄	—	8	2	no	—
739	C₂²×C₄	—	53	8	no	—
740	C₂²×C₄	—	53	2	no	—
741	C₂²×C₄	—	53	4	no	—
742	C₂²×C₄	—	53	4	no	—
743	C₂²×C₄	—	53	4	no	—
744	C₂²×C₄	—	53	16	no	—
745	C₂²×C₄	—	53	4	no	—
746	C₂²×C₄	—	53	4	no	—
747	C₂²×C₄	—	53	8	no	—
748	C₂²×C₄	—	53	16	no	—
749	C₂²×C₄	—	53	16	no	—
750	C₂²×C₄	—	53	16	no	—
751	C₂²×C₄	—	106	16	no	—
752	C₂²×C₄	—	106	16	no	—
753	C₂²×C₄	—	106	16	no	—
754	C₂²×C₄	—	106	8	no	—
755	C₂²×C₄	—	424	4	no	—
756	C₂²×C₄	—	424	2	no	—
757	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
758	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
759	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
760	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
761	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
762	C₂²×C₄	C₂³×D₅₃	1	4	yes	—
763	C₄⋊C₄	—	53	32	no	—
764	C₄⋊C₄	—	53	16	no	—
765	C₄⋊C₄	—	53	16	no	—
766	C₄⋊C₄	C₂³×D₅₃	1	16	yes	—
767	C₂²⋊C₄	—	53	8	no	—
768	C₂²⋊C₄	—	53	4	no	—
769	C₂²⋊C₄	—	53	4	no	—
770	C₂²⋊C₄	—	53	32	no	—
771	C₂²⋊C₄	—	53	16	no	—
772	C₂²⋊C₄	—	53	32	no	—
773	C₂²⋊C₄	—	53	32	no	—
774	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
775	C₂²⋊C₄	C₂³×D₅₃	1	32	yes	—
776	C₂²⋊C₄	C₂³×D₅₃	1	8	yes	—
777	C₄²	—	53	16	no	—
778	C₂³	—	2	8	no	—
779	C₂³	—	2	8	no	—
780	C₂³	—	2	8	no	—
781	C₂³	—	4	2	no	—
782	C₂³	—	4	2	no	—
783	C₂³	—	4	4	no	—
784	C₂³	—	4	2	no	—
785	C₂³	—	4	4	no	—
786	C₂³	—	4	8	no	—
787	C₂³	—	4	8	no	—
788	C₂³	—	4	8	no	—
789	C₂³	—	8	8	no	—
790	C₂³	—	8	16	no	—
791	C₂³	—	53	4	no	—
792	C₂³	—	53	16	no	—
793	C₂³	—	53	8	no	—
794	C₂³	—	53	8	no	—
795	C₂³	—	106	32	no	—
796	C₂³	—	106	8	no	—
797	C₂³	—	106	8	no	—
798	C₂³	—	106	8	no	—
799	C₂³	—	424	16	no	—
800	C₂³	—	424	32	no	—
801	C₂³	—	424	8	no	—
802	C₂³	—	212	8	no	—
803	C₂³	—	212	8	no	—
804	C₂³	—	212	32	no	—
805	C₂³	—	212	4	no	—
806	C₂³	—	212	8	no	—
807	C₂³	—	212	8	no	—
808	C₂³	C₂×D₄×D₅₃	1	8	yes	—
809	C₂³	C₂×D₄×D₅₃	1	4	yes	—
810	C₂³	C₂×D₄×D₅₃	1	8	yes	—
811	C₂³	C₂×D₄×D₅₃	1	4	yes	—
812	C₂³	C₂×D₄×D₅₃	1	4	yes	—
813	C₂³	C₂⁴×D₅₃	1	8	yes	—
814	C₂³	C₂⁴×D₅₃	1	2	yes	—
815	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
816	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
817	C₂³	C₂⁴×D₅₃	1	2	yes	—
818	C₂³	C₂⁴×D₅₃	1	1	yes	characteristic
819	Q₈	—	106	32	no	—
820	D₄	—	2	16	no	—
821	D₄	—	2	16	no	—
822	D₄	—	2	16	no	—
823	D₄	—	2	16	no	—
824	D₄	—	4	16	no	—
825	D₄	—	53	16	no	—
826	D₄	—	53	32	no	—
827	D₄	—	53	16	no	—
828	D₄	—	106	32	no	—
829	D₄	—	106	32	no	—
830	D₄	—	106	32	no	—
831	D₄	—	106	16	no	—
832	D₄	—	106	16	no	—
833	D₄	—	106	16	no	—
834	D₄	—	106	16	no	—
835	D₄	—	212	16	no	—
836	D₄	—	212	32	no	—
837	C₂×C₄	—	2	8	no	—
838	C₂×C₄	—	2	8	no	—
839	C₂×C₄	—	2	8	no	—
840	C₂×C₄	—	4	4	no	—
841	C₂×C₄	—	4	4	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	53	16	no	—
844	C₂×C₄	—	53	8	no	—
845	C₂×C₄	—	53	4	no	—
846	C₂×C₄	—	53	8	no	—
847	C₂×C₄	—	53	8	no	—
848	C₂×C₄	—	106	32	no	—
849	C₂×C₄	—	106	32	no	—
850	C₂×C₄	—	106	32	no	—
851	C₂×C₄	—	106	8	no	—
852	C₂×C₄	—	106	8	no	—
853	C₂×C₄	—	106	8	no	—
854	C₂×C₄	—	212	16	no	—
855	C₂×C₄	—	212	4	no	—
856	C₂×C₄	—	212	8	no	—
857	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
858	C₂×C₄	C₂⁴×D₅₃	1	8	yes	—
859	C₂²	—	2	2	no	—
860	C₂²	—	2	2	no	—
861	C₂²	—	2	2	no	—
862	C₂²	—	2	4	no	—
863	C₂²	—	2	4	no	—
864	C₂²	—	2	8	no	—
865	C₂²	—	2	16	no	—
866	C₂²	—	4	8	no	—
867	C₂²	—	4	4	no	—
868	C₂²	—	4	8	no	—
869	C₂²	—	4	4	no	—
870	C₂²	—	4	4	no	—
871	C₂²	—	4	16	no	—
872	C₂²	—	8	8	no	—
873	C₂²	—	8	8	no	—
874	C₂²	—	53	8	no	—
875	C₂²	—	106	8	no	—
876	C₂²	—	106	8	no	—
877	C₂²	—	106	16	no	—
878	C₂²	—	424	8	no	—
879	C₂²	—	424	8	no	—
880	C₂²	—	424	32	no	—
881	C₂²	—	212	16	no	—
882	C₂²	—	212	8	no	—
883	C₂²	—	212	16	no	—
884	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
885	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
886	C₂²	C₂²×D₄×D₅₃	1	4	yes	—
887	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
888	C₂²	C₂²×D₄×D₅₃	1	2	yes	—
889	C₂²	C₂⁵×D₅₃	1	1	yes	characteristic
890	C₄	—	2	8	no	—
891	C₄	—	2	8	no	—
892	C₄	—	53	8	no	—
893	C₄	—	106	8	no	—
894	C₄	—	106	8	no	—
895	C₂	—	2	4	no	—
896	C₂	—	2	2	no	—
897	C₂	—	2	4	no	—
898	C₂	—	2	2	no	—
899	C₂	—	2	2	no	—
900	C₂	—	4	8	no	—
901	C₂	—	106	8	no	—
902	C₂	—	212	8	no	—
903	C₂	C₂³×D₄×D₅₃	1	1	yes	characteristic
904	C₂	#20289525	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁵×D₅₃
commutator, socle, cosocle	C₂²×C₅₃	C₂⁶
Fitting	C₂×C₅₃×#534	C₂
hypercenter	C₂×#534	D₅₃
hypocenter	C₅₃	#62842
LCS	G ▷ C₂²×C₅₃ ▷ C₅₃
UCS	C₁ ◁ C₂² ◁ C₂×#534

Complements

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

N	H ≅ G/N	type
1. C₂²×#13133262	C₂	semidirect
2. #20288476	C₂	semidirect
3. #20288472	C₂	semidirect
4. #20288356	C₂	semidirect
5. #20288353	C₂	semidirect
6. #20288347	C₂	semidirect
7. #20288344	C₂	semidirect
8. #20288041	C₂	semidirect
9. C₂×#16811185	C₂	semidirect
10. C₂×#16811182	C₂	semidirect
11. #534×D₅₃	C₂	semidirect
12. C₂×#16811096	C₂	semidirect
13. C₂×C₅₃×#534	C₂	semidirect
15. C₂×#13133262	C₂²	semidirect
16. C₂×#13133262	C₂²	semidirect
17. C₂×#13133262	C₂²	semidirect
18. C₂×#13133262	C₂²	semidirect
19. C₂²×#11719945	C₂²	semidirect
20. C₂²×#11719947	C₂²	semidirect
21. C₂²×#11719947	C₂²	semidirect
23. C₂³×C₂²⋊D₅₃	C₂²	semidirect
24. C₂³×C₂²⋊D₅₃	C₂²	semidirect
25. C₂²×D₄×D₅₃	C₂²	semidirect
26. C₂²×D₄×D₅₃	C₂²	semidirect
27. #16811274	C₂²	semidirect
28. #16811273	C₂²	semidirect
29. #16811271	C₂²	semidirect
30. #16811265	C₂²	semidirect
31. #16811263	C₂²	semidirect
32. #16811262	C₂²	semidirect
33. #16811260	C₂²	semidirect
34. #16811257	C₂²	semidirect
35. D₄×C₂²⋊D₅₃	C₂²	semidirect
36. #16811255	C₂²	semidirect
37. #16811200	C₂²	semidirect
38. #16811195	C₂²	semidirect
39. #16811188	C₂²	semidirect
40. #16811185	C₂²	semidirect
41. #16811185	C₂²	semidirect
42. #16811185	C₂²	semidirect
43. #16811184	C₂²	semidirect
44. #16811183	C₂²	semidirect
45. #16811182	C₂²	semidirect
46. #16811182	C₂²	semidirect
47. #16811182	C₂²	semidirect
48. #16811182	C₂²	semidirect
49. #16811181	C₂²	semidirect
50. #16811168	C₂²	semidirect
51. #16811131	C₂²	semidirect
52. #16811129	C₂²	semidirect
53. C₂×#13133201	C₂²	semidirect
54. C₂×#13133200	C₂²	semidirect
55. C₂×#13133198	C₂²	semidirect
56. #123×D₅₃	C₂²	semidirect
57. C₂×#13133191	C₂²	semidirect
58. C₂×#13133189	C₂²	semidirect
59. #121×D₅₃	C₂²	semidirect
60. C₂×#13133187	C₂²	semidirect
61. C₂×#13133186	C₂²	semidirect
62. C₂×#13133185	C₂²	semidirect
63. #120×D₅₃	C₂²	semidirect
64. #16811096	C₂²	semidirect
65. #16811096	C₂²	semidirect
66. C₂×C₄×C₂²⋊D₅₃	C₂²	semidirect
67. C₂×#13133177	C₂²	semidirect
68. C₂×#13133173	C₂²	semidirect
69. C₂²×C₂²⋊Dic₅₃	C₂²	semidirect
70. C₂×C₂²⋊C₄×D₅₃	C₂²	semidirect
71. C₂³×D₄×C₅₃	C₂²	semidirect
72. C₅₃×#534	C₂²	semidirect
73. C₅₃×#534	C₂²	semidirect
74. C₅₃×#534	C₂²	semidirect
75. C₂×#123×C₅₃	C₂²	semidirect
76. C₂×#121×C₅₃	C₂²	semidirect
77. C₂×#120×C₅₃	C₂²	semidirect
78. C₂²×C₂²⋊C₄×C₅₃	C₂²	semidirect
80. C₂⁴×D₅₃	C₂³	semidirect
81. C₂⁴×D₅₃	C₂³	semidirect
87. C₂×#11719945	C₂³	semidirect
88. C₂×#11719945	C₂³	semidirect
92. C₂×#11719947	C₂³	semidirect
93. C₂×#11719947	C₂³	semidirect
94. C₂×#11719947	C₂³	semidirect
95. C₂²×Dic₁₀₆	C₂³	semidirect
96. C₂²×D₂₁₂	C₂³	semidirect
97. C₂²×D₂₁₂	C₂³	semidirect
100. C₂²×C₂²⋊D₅₃	D₄	semidirect
108. C₂²×C₂²⋊D₅₃	C₂³	semidirect
109. C₂²×C₂²⋊D₅₃	C₂³	semidirect
110. C₂²×C₂²⋊D₅₃	C₂³	semidirect
111. C₂²×C₂²⋊D₅₃	C₂³	semidirect
112. C₂²×C₂²⋊D₅₃	C₂³	semidirect
113. C₂²×C₂²⋊D₅₃	C₂³	semidirect
114. C₂²×C₂²⋊D₅₃	C₂³	semidirect
115. C₂²×C₂²⋊D₅₃	C₂³	semidirect
119. C₂×D₄×D₅₃	C₂³	semidirect
120. C₂×D₄×D₅₃	C₂³	semidirect
121. C₂×D₄×D₅₃	C₂³	semidirect
122. C₂×D₄×D₅₃	C₂³	semidirect
124. C₂³×Dic₅₃	C₂³	semidirect
125. C₂³×Dic₅₃	C₂³	semidirect
126. C₂³×Dic₅₃	C₂³	semidirect
127. C₂²×C₄×D₅₃	C₂³	semidirect
128. C₂²×C₄×D₅₃	C₂³	semidirect
129. C₂²×C₄×D₅₃	C₂³	semidirect
130. #13133216	C₂³	semidirect
131. #13133213	C₂³	semidirect
132. #13133203	C₂³	semidirect
133. #13133202	C₂³	semidirect
134. #13133201	C₂³	semidirect
135. #13133201	C₂³	semidirect
136. #13133200	C₂³	semidirect
137. #13133200	C₂³	semidirect
138. #13133199	C₂³	semidirect
139. #13133198	C₂³	semidirect
140. #13133198	C₂³	semidirect
141. #13133195	C₂³	semidirect
142. #13133194	C₂³	semidirect
143. #13133192	C₂³	semidirect
144. #13133191	C₂³	semidirect
145. #13133191	C₂³	semidirect
146. #13133190	C₂³	semidirect
147. #13133190	C₂³	semidirect
148. #13133189	C₂³	semidirect
149. #13133189	C₂³	semidirect
150. #13133189	C₂³	semidirect
151. #13133188	C₂³	semidirect
152. #13133187	C₂³	semidirect
153. #13133187	C₂³	semidirect
154. #13133187	C₂³	semidirect
155. #13133186	C₂³	semidirect
156. #13133186	C₂³	semidirect
157. #13133185	C₂³	semidirect
158. #13133185	C₂³	semidirect
159. #13133185	C₂³	semidirect
160. D₄×Dic₅₃	C₂³	semidirect
161. #13133179	C₂³	semidirect
162. C₄×C₂²⋊D₅₃	C₂³	semidirect
163. C₄×C₂²⋊D₅₃	C₂³	semidirect
164. #13133177	C₂³	semidirect
165. #13133177	C₂³	semidirect
166. #13133173	C₂³	semidirect
167. C₂×C₄⋊Dic₅₃	C₂³	semidirect
168. C₂×#11719919	C₂³	semidirect
169. C₂×#11719919	C₂³	semidirect
170. C₄⋊C₄×D₅₃	C₂³	semidirect
172. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
173. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
174. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
175. C₂×C₂²⋊Dic₅₃	C₂³	semidirect
176. C₂×#11719921	C₂³	semidirect
177. C₂×#11719921	C₂³	semidirect
178. C₂×#11719921	C₂³	semidirect
179. C₂²⋊C₄×D₅₃	C₂³	semidirect
180. C₂²⋊C₄×D₅₃	C₂³	semidirect
181. C₂×C₄×Dic₅₃	C₂³	semidirect
183. C₂⁵×C₅₃	C₂³	semidirect
188. C₂²×D₄×C₅₃	C₂³	semidirect
189. C₂²×D₄×C₅₃	C₂³	semidirect
190. C₂²×D₄×C₅₃	C₂³	semidirect
191. C₂²×D₄×C₅₃	C₂³	semidirect
192. C₂³×C₄×C₅₃	C₂³	semidirect
193. C₂³×C₄×C₅₃	C₂³	semidirect
194. #123×C₅₃	C₂³	semidirect
195. #123×C₅₃	C₂³	semidirect
196. #121×C₅₃	C₂³	semidirect
197. #121×C₅₃	C₂³	semidirect
198. #120×C₅₃	C₂³	semidirect
199. #120×C₅₃	C₂³	semidirect
200. C₂×C₄⋊C₄×C₅₃	C₂³	semidirect
202. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
203. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
204. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
205. C₂×C₂²⋊C₄×C₅₃	C₂³	semidirect
209. C₂⁴×C₅₃	C₂×D₄	semidirect
223. C₂³×D₅₃	C₂×D₄	semidirect
261. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
262. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
263. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
264. C₂×C₂²⋊D₅₃	C₂×D₄	semidirect
278. C₂²×Dic₅₃	C₂×D₄	semidirect
454. C₂×#534	D₅₃	semidirect
479. C₂³×D₄	C₂×D₅₃	semidirect
503. #534	C₂×D₅₃	semidirect
504. #534	C₂×D₅₃	semidirect
505. #534	C₂×D₅₃	semidirect
513. C₂×#123	C₂×D₅₃	semidirect
517. C₂×#121	C₂×D₅₃	semidirect
522. C₂×#120	C₂×D₅₃	semidirect
530. C₂²×C₂²⋊C₄	C₂×D₅₃	semidirect
531. C₅₃	#62842	semidirect
536. C₂⁵	C₂²×D₅₃	semidirect
582. C₂²×D₄	C₂²×D₅₃	semidirect
583. C₂²×D₄	C₂²×D₅₃	semidirect
584. C₂²×D₄	C₂²×D₅₃	semidirect
585. C₂²×D₄	C₂²×D₅₃	semidirect
593. C₂³×C₄	C₂²×D₅₃	semidirect
594. C₂³×C₄	C₂²×D₅₃	semidirect
606. #123	C₂²×D₅₃	semidirect
607. #123	C₂²×D₅₃	semidirect
619. #121	C₂²×D₅₃	semidirect
620. #121	C₂²×D₅₃	semidirect
629. #120	C₂²×D₅₃	semidirect
630. #120	C₂²×D₅₃	semidirect
642. C₂×C₄⋊C₄	C₂²×D₅₃	semidirect
654. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
655. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
656. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
657. C₂×C₂²⋊C₄	C₂²×D₅₃	semidirect
674. C₂⁴	D₄×D₅₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13133262	2
#20288476	2
#20288472	2
#20288356	2
#20288353	2
#20288347	2
#20288344	2
#20288041	2
C₂×#16811185	2
C₂×#16811182	2
#534×D₅₃	2
C₂×#16811096	2
C₂×C₅₃×#534	2
#62842	53