Subgroups — #37548040

Order 23168.

1160 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042026	C₂	1	2	yes	maximal, complemented
2	#26042017	C₂	1	2	yes	maximal, complemented
3	#26041992	C₂	1	1	yes	maximal, characteristic, complemented
4	#26041967	C₂	1	1	yes	maximal, characteristic, complemented
5	#26041954	C₂	1	2	yes	maximal, complemented
6	#26041950	C₂	1	1	yes	maximal, characteristic, complemented
7	#26041930	C₂	1	1	yes	maximal, characteristic, complemented
8	#26041926	C₂	1	1	yes	maximal, characteristic, complemented
9	#26041926	C₂	1	1	yes	maximal, characteristic, complemented
10	#26041925	C₂	1	2	yes	maximal, complemented
11	D₄×D₇₂₄	C₂	1	1	yes	maximal, characteristic, complemented
12	#26041894	C₂	1	1	yes	maximal, characteristic, complemented
13	#26041885	C₂	1	1	yes	maximal, characteristic, complemented
14	#26041880	C₂	1	2	yes	maximal, complemented
15	#26041868	C₂	1	2	yes	maximal, complemented
16	#26041860	C₂	1	1	yes	maximal, characteristic, complemented
17	#26041845	C₂	1	2	yes	maximal, complemented
18	#26041845	C₂	1	1	yes	maximal, characteristic, complemented
19	#26041840	C₂	1	2	yes	maximal, complemented
20	#26041791	C₂	1	1	yes	maximal, characteristic, complemented
21	#26041788	C₂	1	1	yes	maximal, characteristic, complemented
22	#121×D₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
23	#553×C₁₈₁	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
25	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
26	C₂×#15668449	C₂²	1	2	yes	complemented
27	C₂×#15668449	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₇₂₄	C₂²	1	2	yes	—
29	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic
30	C₂×D₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
31	C₂×D₄×D₁₈₁	C₂²	1	2	yes	complemented
32	C₂²×C₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
33	#19153815	C₂²	1	1	yes	characteristic, complemented
34	#19153813	C₂²	1	1	yes	characteristic, complemented
35	#19153812	C₂²	1	2	yes	complemented
36	#19153812	C₂²	1	2	yes	complemented
37	#19153811	C₂²	1	2	yes	complemented
38	#19153809	C₂²	1	2	yes	complemented
39	#19153807	C₂²	1	2	yes	complemented
40	#19153804	C₂²	1	2	yes	complemented
41	#19153803	C₂²	1	1	yes	characteristic, complemented
42	#19153802	C₂²	1	2	yes	complemented
43	#19153802	C₂²	1	2	yes	complemented
44	#19153802	C₂²	1	2	yes	complemented
45	#19153801	C₂²	1	2	yes	—
46	#19153801	C₂²	1	1	yes	characteristic, complemented
47	#19153801	C₂²	1	2	yes	complemented
48	#19153801	C₂²	1	2	yes	complemented
49	#19153801	C₂²	1	2	yes	complemented
50	#19153800	C₂²	1	2	yes	complemented
51	#19153799	C₂²	1	2	yes	complemented
52	#19153799	C₂²	1	2	yes	complemented
53	#19153798	C₂²	1	2	yes	complemented
54	#19153798	C₂²	1	1	yes	characteristic, complemented
55	#19153798	C₂²	1	2	yes	complemented
56	#19153796	C₂²	1	1	yes	characteristic, complemented
57	#19153796	C₂²	1	1	yes	characteristic, complemented
58	#19153796	C₂²	1	2	yes	complemented
59	#19153796	C₂²	1	1	yes	characteristic, complemented
60	#19153795	C₂²	1	2	yes	complemented
61	#19153794	C₂²	1	2	yes	complemented
62	#19153794	C₂²	1	1	yes	characteristic, complemented
63	#19153793	C₂²	1	1	yes	characteristic, complemented
64	#19153791	C₂²	1	1	yes	characteristic
65	#19153791	C₂²	1	2	yes	complemented
66	#19153791	C₂²	1	1	yes	characteristic, complemented
67	#19153791	C₂²	1	1	yes	characteristic, complemented
68	#19153791	C₂²	1	2	yes	complemented
69	#19153791	C₂²	1	2	yes	complemented
70	#19153791	C₂²	1	1	yes	characteristic, complemented
71	#19153790	C₂²	1	2	yes	complemented
72	#19153790	C₂²	1	2	yes	complemented
73	#19153790	C₂²	1	2	yes	complemented
74	#19153790	C₂²	1	1	yes	characteristic, complemented
75	#19153790	C₂²	1	1	yes	characteristic, complemented
76	#19153789	C₂²	1	1	yes	characteristic
77	#19153789	C₂²	1	2	yes	complemented
78	#19153789	C₂²	1	2	yes	complemented
79	#19153789	C₂²	1	2	yes	complemented
80	#19153789	C₂²	1	2	yes	complemented
81	#19153788	C₂²	1	1	yes	characteristic, complemented
82	#19153788	C₂²	1	2	yes	complemented
83	#19153787	C₂²	1	1	yes	characteristic
84	#19153787	C₂²	1	2	yes	complemented
85	#19153787	C₂²	1	2	yes	complemented
86	#19153786	C₂²	1	2	yes	—
87	#19153786	C₂²	1	1	yes	characteristic
88	#19153786	C₂²	1	2	yes	complemented
89	#19153786	C₂²	1	2	yes	complemented
90	#19153786	C₂²	1	2	yes	complemented
91	#19153784	C₂²	1	2	yes	complemented
92	#19153784	C₂²	1	2	yes	complemented
93	#19153784	C₂²	1	2	yes	complemented
94	#19153784	C₂²	1	1	yes	characteristic, complemented
95	C₄×Dic₃₆₂	C₂²	1	1	yes	characteristic, complemented
96	C₄×D₇₂₄	C₂²	1	1	yes	characteristic
97	C₄×D₇₂₄	C₂²	1	2	yes	complemented
98	C₄×D₇₂₄	C₂²	1	2	yes	complemented
99	#19153778	C₂²	1	2	yes	complemented
100	#19153778	C₂²	1	1	yes	characteristic, complemented
101	#19153778	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
103	C₄×C₂²⋊D₁₈₁	C₂²	1	1	yes	characteristic, complemented
104	#19153774	C₂²	1	2	yes	complemented
105	#19153774	C₂²	1	1	yes	characteristic, complemented
106	#19153773	C₂²	1	2	yes	complemented
107	#19153773	C₂²	1	1	yes	characteristic, complemented
108	C₄⋊C₄×D₁₈₁	C₂²	1	1	yes	characteristic, complemented
109	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₈₁	C₂²	1	2	yes	complemented
112	#126×C₁₈₁	C₂²	1	2	yes	complemented
113	#125×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
114	#123×C₁₈₁	C₂²	1	2	yes	complemented
115	#121×C₁₈₁	C₂²	1	1	yes	characteristic
116	#121×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
117	#121×C₁₈₁	C₂²	1	2	yes	complemented
118	C₄×D₄×C₁₈₁	C₂²	1	2	yes	complemented
119	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
121	#117×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₁₈₁	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₈₁	C₂³	1	2	yes	—
124	C₂³×D₁₈₁	C₂³	1	1	yes	characteristic
125	C₂³×D₁₈₁	C₂³	1	2	yes	—
126	#15668449	—	4	2	no	—
127	#15668449	—	4	2	no	—
128	#15668449	—	4	2	no	—
129	#15668449	—	4	4	no	—
130	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
131	C₂×Dic₃₆₂	C₂³	1	1	yes	characteristic
132	C₂×Dic₃₆₂	C₂³	1	2	yes	—
133	C₂×D₇₂₄	—	4	4	no	—
134	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
135	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
136	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
137	C₂×D₇₂₄	C₂³	1	2	yes	—
138	C₂×D₇₂₄	C₂³	1	2	yes	—
139	C₂×D₇₂₄	C₂³	1	2	yes	—
140	C₂×D₇₂₄	C₂³	1	1	yes	characteristic
141	C₂×D₇₂₄	C₂³	1	2	yes	—
142	C₂×D₇₂₄	C₂³	1	2	yes	—
143	C₂×D₇₂₄	C₂³	1	2	yes	—
144	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
146	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
148	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
149	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
150	C₂×C₂²⋊D₁₈₁	C₂³	1	1	yes	characteristic
151	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
152	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
153	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₈₁	C₂³	1	2	yes	—
155	D₄×D₁₈₁	—	4	2	no	—
156	D₄×D₁₈₁	—	4	2	no	—
157	D₄×D₁₈₁	—	4	4	no	—
158	C₂²×Dic₁₈₁	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₈₁	—	4	2	no	—
160	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
161	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
163	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
164	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
165	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
166	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
167	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
168	C₂×C₄×D₁₈₁	C₂³	1	2	yes	—
169	C₂×C₄×D₁₈₁	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
172	C₄⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
174	C₄⋊Dic₁₈₁	C₂³	1	2	yes	—
175	#15668428	C₂³	1	2	yes	—
176	#15668428	C₂³	1	1	yes	characteristic
177	#15668428	C₂³	1	1	yes	characteristic
178	#15668428	C₂³	1	1	yes	characteristic
179	#15668428	C₂³	1	2	yes	—
180	#15668428	C₂³	1	1	yes	characteristic
181	#15668428	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₈₁	C₂³	1	2	yes	—
185	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₁₈₁	C₂³	1	1	yes	characteristic
187	#15668426	C₂³	1	1	yes	characteristic
188	#15668426	C₂³	1	1	yes	characteristic
189	#15668426	C₂³	1	2	yes	—
190	#15668426	C₂³	1	2	yes	—
191	#15668426	C₂³	1	2	yes	—
192	#15668426	C₂³	1	2	yes	—
193	#15668426	C₂³	1	1	yes	characteristic
194	#15668426	C₂³	1	2	yes	—
195	#15668426	C₂³	1	1	yes	characteristic
196	#15668426	C₂³	1	1	yes	characteristic
197	#15668426	C₂³	1	2	yes	—
198	#15668426	C₂³	1	2	yes	—
199	#15668426	C₂³	1	2	yes	—
200	#15668426	C₂³	1	2	yes	—
201	#15668426	C₂³	1	1	yes	characteristic
202	#15668426	C₂³	1	2	yes	—
203	#15668426	C₂³	1	2	yes	—
204	#15668426	C₂³	1	2	yes	—
205	C₄×Dic₁₈₁	C₂³	1	2	yes	—
206	C₄×Dic₁₈₁	C₂³	1	1	yes	characteristic
207	C₄×Dic₁₈₁	C₂³	1	2	yes	—
208	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
209	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
210	C₂×D₄×C₁₈₁	C₂³	1	1	yes	characteristic
211	C₂×D₄×C₁₈₁	C₂³	1	2	yes	—
212	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
213	C₂²×C₄×C₁₈₁	C₂³	1	1	yes	characteristic
214	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
215	C₂²×C₄×C₁₈₁	C₂³	1	2	yes	—
216	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
217	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
218	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
219	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
220	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
221	C₄⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
222	C₄⋊C₄×C₁₈₁	C₂³	1	2	yes	—
223	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
224	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
225	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
226	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
227	C₂²⋊C₄×C₁₈₁	C₂³	1	1	yes	characteristic
228	C₂²⋊C₄×C₁₈₁	C₂³	1	2	yes	—
229	C₄²×C₁₈₁	C₂³	1	2	yes	—
230	C₄²×C₁₈₁	C₂³	1	1	yes	characteristic
231	C₂²×D₁₈₁	—	2	2	no	—
232	C₂²×D₁₈₁	—	2	4	no	—
233	C₂²×D₁₈₁	—	4	1	no	—
234	C₂²×D₁₈₁	—	4	1	no	—
235	C₂²×D₁₈₁	—	4	2	no	—
236	C₂²×D₁₈₁	—	4	2	no	—
237	C₂²×D₁₈₁	—	4	2	no	—
238	C₂²×D₁₈₁	—	4	2	no	—
239	C₂²×D₁₈₁	—	4	2	no	—
240	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
241	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
243	C₂²×D₁₈₁	C₂⁴	1	2	yes	—
244	C₂²×D₁₈₁	C₂⁴	1	1	yes	characteristic
245	Dic₃₆₂	—	2	2	no	—
246	Dic₃₆₂	—	4	1	no	—
247	Dic₃₆₂	—	4	2	no	—
248	D₇₂₄	—	2	2	no	—
249	D₇₂₄	—	2	4	no	—
250	D₇₂₄	—	2	2	no	—
251	D₇₂₄	—	2	2	no	—
252	D₇₂₄	—	4	2	no	—
253	D₇₂₄	—	4	2	no	—
254	D₇₂₄	—	4	2	no	—
255	D₇₂₄	—	4	2	no	—
256	D₇₂₄	—	4	2	no	—
257	D₇₂₄	—	4	1	no	—
258	C₂²⋊D₁₈₁	—	2	2	no	—
259	C₂²⋊D₁₈₁	—	4	2	no	—
260	C₂²⋊D₁₈₁	—	4	2	no	—
261	C₂²⋊D₁₈₁	—	4	2	no	—
262	C₂²⋊D₁₈₁	—	4	2	no	—
263	C₂²⋊D₁₈₁	—	4	1	no	—
264	C₂²⋊D₁₈₁	—	4	1	no	—
265	C₂²⋊D₁₈₁	—	4	1	no	—
266	C₂²⋊D₁₈₁	—	4	2	no	—
267	C₂²⋊D₁₈₁	—	4	2	no	—
268	C₂²⋊D₁₈₁	—	4	2	no	—
269	C₂×Dic₁₈₁	—	4	1	no	—
270	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
271	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₈₁	C₂⁴	1	2	yes	—
275	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
276	C₂×Dic₁₈₁	C₂⁴	1	1	yes	characteristic
277	C₄×D₁₈₁	—	2	4	no	—
278	C₄×D₁₈₁	—	2	2	no	—
279	C₄×D₁₈₁	—	2	2	no	—
280	C₄×D₁₈₁	—	2	2	no	—
281	C₄×D₁₈₁	—	4	1	no	—
282	C₄×D₁₈₁	—	4	1	no	—
283	C₄×D₁₈₁	—	4	2	no	—
284	C₄×D₁₈₁	—	4	2	no	—
285	C₄×D₁₈₁	—	4	2	no	—
286	C₄×D₁₈₁	—	4	2	no	—
287	C₂³×C₁₈₁	C₂⁴	1	2	yes	—
288	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
289	C₂³×C₁₈₁	C₂⁴	1	1	yes	characteristic
290	D₄×C₁₈₁	—	2	2	no	—
291	D₄×C₁₈₁	—	4	2	no	—
292	D₄×C₁₈₁	—	4	1	no	—
293	D₄×C₁₈₁	—	4	2	no	—
294	C₂×C₄×C₁₈₁	—	2	2	no	—
295	C₂×C₄×C₁₈₁	—	2	2	no	—
296	C₂×C₄×C₁₈₁	—	4	2	no	—
297	C₂×C₄×C₁₈₁	—	4	2	no	—
298	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
300	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
301	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
302	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
303	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
304	C₂×C₄×C₁₈₁	C₂⁴	1	2	yes	—
305	C₂×C₄×C₁₈₁	C₂⁴	1	1	yes	characteristic
306	C₂²×C₁₈₁	—	2	1	no	—
307	C₂²×C₁₈₁	—	2	1	no	—
308	C₂²×C₁₈₁	—	2	1	no	—
309	C₂²×C₁₈₁	—	2	2	no	—
310	C₂²×C₁₈₁	—	2	2	no	—
311	C₂²×C₁₈₁	—	2	1	no	—
312	C₂²×C₁₈₁	—	2	1	no	—
313	C₂²×C₁₈₁	—	2	1	no	—
314	C₂²×C₁₈₁	—	2	2	no	—
315	C₂²×C₁₈₁	C₂⁵	1	1	yes	characteristic
316	C₂×D₁₈₁	—	2	1	no	—
317	C₂×D₁₈₁	—	2	1	no	—
318	C₂×D₁₈₁	—	2	1	no	—
319	C₂×D₁₈₁	—	2	1	no	—
320	C₂×D₁₈₁	—	2	2	no	—
321	C₂×D₁₈₁	—	2	2	no	—
322	C₂×D₁₈₁	—	2	2	no	—
323	C₂×D₁₈₁	—	2	1	no	—
324	C₂×D₁₈₁	—	2	2	no	—
325	C₂×D₁₈₁	—	2	1	no	—
326	C₂×D₁₈₁	—	2	2	no	—
327	C₂×D₁₈₁	—	2	1	no	—
328	C₂×D₁₈₁	—	2	1	no	—
329	C₂×D₁₈₁	—	2	2	no	—
330	C₂×D₁₈₁	—	4	4	no	—
331	C₂×D₁₈₁	—	8	4	no	—
332	C₂×D₁₈₁	—	8	4	no	—
333	C₂×D₁₈₁	H(5,𝔽₂)	1	2	yes	—
334	C₄×C₁₈₁	—	2	1	no	—
335	C₄×C₁₈₁	—	2	1	no	—
336	C₄×C₁₈₁	—	2	1	no	—
337	C₄×C₁₈₁	—	2	2	no	—
338	C₄×C₁₈₁	—	2	2	no	—
339	C₄×C₁₈₁	—	2	2	no	—
340	C₄×C₁₈₁	—	2	1	no	—
341	C₄×C₁₈₁	H(5,𝔽₂)	1	2	yes	—
342	Dic₁₈₁	—	2	1	no	—
343	Dic₁₈₁	—	2	1	no	—
344	Dic₁₈₁	—	2	2	no	—
345	Dic₁₈₁	—	2	1	no	—
346	Dic₁₈₁	—	2	1	no	—
347	Dic₁₈₁	—	2	2	no	—
348	Dic₁₈₁	—	2	1	no	—
349	C₂×C₁₈₁	—	4	1	no	—
350	C₂×C₁₈₁	—	4	2	no	—
351	C₂×C₁₈₁	—	4	1	no	—
352	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₁₈₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
354	C₂×C₁₈₁	#585	1	1	yes	characteristic
355	D₁₈₁	—	2	2	no	—
356	D₁₈₁	—	4	1	no	—
357	D₁₈₁	—	4	2	no	—
358	D₁₈₁	—	4	2	no	—
359	D₁₈₁	—	4	1	no	—
360	C₁₈₁	#3542	1	1	yes	characteristic, complemented, Sylow
361	#3542	—	181	1	no	maximal, Sylow
362	#562	—	181	2	no	—
363	#560	—	181	2	no	—
364	#555	—	181	1	no	—
365	#553	D₁₈₁	1	1	yes	characteristic, complemented
366	#552	—	181	1	no	—
367	#551	—	181	2	no	—
368	#550	—	181	1	no	—
369	#547	—	181	1	no	—
370	#546	—	181	1	no	—
371	#546	—	181	1	no	—
372	#546	—	181	2	no	—
373	D₄²	—	181	1	no	—
374	#542	—	181	1	no	—
375	#540	—	181	1	no	—
376	#540	—	181	2	no	—
377	#538	—	181	2	no	—
378	#537	—	181	1	no	—
379	#535	—	181	2	no	—
380	#535	—	181	1	no	—
381	#534	—	181	2	no	—
382	#525	—	181	1	no	—
383	#525	—	181	1	no	—
384	C₂×#121	—	181	1	no	—
385	C₂×#41	—	181	1	no	—
386	C₂×#41	—	181	1	no	—
387	C₂×#41	—	181	2	no	—
388	C₂×#41	—	181	1	no	—
389	C₂²×D₄	—	181	2	no	—
390	C₂²×D₄	—	181	1	no	—
391	C₂²×D₄	—	181	1	no	—
392	C₂²×D₄	—	181	2	no	—
393	C₂³×C₄	—	181	1	no	—
394	C₄⋊Q₈	—	181	1	no	—
395	#127	—	181	2	no	—
396	#127	—	181	2	no	—
397	#127	—	181	1	no	—
398	#126	—	181	2	no	—
399	#126	—	181	2	no	—
400	#126	C₂×D₁₈₁	1	2	yes	complemented
401	#125	—	181	2	no	—
402	#125	C₂×D₁₈₁	1	1	yes	characteristic, complemented
403	#124	—	181	1	no	—
404	#124	—	181	2	no	—
405	#124	—	181	2	no	—
406	#124	—	181	2	no	—
407	#124	—	181	2	no	—
408	#123	—	181	2	no	—
409	#123	—	181	2	no	—
410	#123	—	181	1	no	—
411	#123	—	181	2	no	—
412	#123	—	181	2	no	—
413	#123	—	181	2	no	—
414	#123	—	181	2	no	—
415	#123	—	181	1	no	—
416	#123	—	181	2	no	—
417	#123	—	181	2	no	—
418	#123	—	181	2	no	—
419	#123	C₂×D₁₈₁	1	2	yes	complemented
420	C₂²⋊Q₈	—	181	2	no	—
421	C₂²⋊Q₈	—	181	1	no	—
422	C₂²⋊Q₈	—	181	1	no	—
423	C₂²⋊Q₈	—	181	1	no	—
424	C₂²⋊Q₈	—	181	1	no	—
425	C₂²⋊Q₈	—	181	2	no	—
426	C₂²⋊Q₈	—	181	2	no	—
427	C₂²⋊Q₈	—	181	1	no	—
428	#121	—	181	1	no	—
429	#121	—	181	2	no	—
430	#121	—	181	1	no	—
431	#121	—	181	2	no	—
432	#121	—	181	2	no	—
433	#121	—	181	1	no	—
434	#121	—	181	2	no	—
435	#121	—	181	1	no	—
436	#121	—	181	2	no	—
437	#121	—	181	2	no	—
438	#121	—	181	1	no	—
439	#121	—	181	1	no	—
440	#121	—	181	1	no	—
441	#121	—	181	2	no	—
442	#121	—	181	2	no	—
443	#121	—	181	2	no	—
444	#121	—	181	1	no	—
445	#121	—	181	2	no	—
446	#121	—	181	1	no	—
447	#121	—	181	2	no	—
448	#121	—	181	2	no	—
449	#121	—	181	2	no	—
450	#121	C₂×D₁₈₁	1	1	yes	characteristic
451	#121	C₂×D₁₈₁	1	1	yes	characteristic, complemented
452	#121	C₂×D₁₈₁	1	2	yes	complemented
453	#120	—	181	1	no	—
454	#120	—	181	2	no	—
455	#120	—	181	2	no	—
456	#120	—	181	2	no	—
457	#120	—	181	1	no	—
458	#120	—	181	2	no	—
459	#120	—	181	2	no	—
460	#120	—	181	2	no	—
461	#120	—	181	2	no	—
462	C₄×Q₈	—	181	1	no	—
463	C₄×D₄	—	181	1	no	—
464	C₄×D₄	—	181	1	no	—
465	C₄×D₄	—	181	2	no	—
466	C₄×D₄	—	181	1	no	—
467	C₄×D₄	—	181	1	no	—
468	C₄×D₄	—	181	2	no	—
469	C₄×D₄	—	181	1	no	—
470	C₄×D₄	—	181	2	no	—
471	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
472	C₄×D₄	C₂×D₁₈₁	1	2	yes	complemented
473	C₄×D₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
474	#117	—	181	2	no	—
475	#117	—	181	1	no	—
476	#117	—	181	1	no	—
477	#117	—	181	2	no	—
478	#117	C₂×D₁₈₁	1	1	yes	characteristic, complemented
479	C₂×C₄⋊C₄	—	181	1	no	—
480	C₂×C₄⋊C₄	C₂×D₁₈₁	1	1	yes	characteristic, complemented
481	C₂×C₂²⋊C₄	—	181	2	no	—
482	C₂×C₂²⋊C₄	—	181	2	no	—
483	C₂×C₂²⋊C₄	—	181	2	no	—
484	C₂⁴	—	181	2	no	—
485	C₂⁴	—	181	1	no	—
486	C₂⁴	—	181	2	no	—
487	#41	—	724	2	no	—
488	#41	—	724	2	no	—
489	#41	—	724	2	no	—
490	#41	—	724	4	no	—
491	C₂×Q₈	—	181	1	no	—
492	C₂×Q₈	—	181	1	no	—
493	C₂×Q₈	—	181	2	no	—
494	C₂×D₄	—	181	1	no	—
495	C₂×D₄	—	181	1	no	—
496	C₂×D₄	—	181	1	no	—
497	C₂×D₄	—	181	2	no	—
498	C₂×D₄	—	181	2	no	—
499	C₂×D₄	—	181	2	no	—
500	C₂×D₄	—	181	2	no	—
501	C₂×D₄	—	181	2	no	—
502	C₂×D₄	—	181	1	no	—
503	C₂×D₄	—	181	2	no	—
504	C₂×D₄	—	181	2	no	—
505	C₂×D₄	—	181	2	no	—
506	C₂×D₄	—	181	1	no	—
507	C₂×D₄	—	181	1	no	—
508	C₂×D₄	—	181	1	no	—
509	C₂×D₄	—	181	2	no	—
510	C₂×D₄	—	181	2	no	—
511	C₂×D₄	—	181	1	no	—
512	C₂×D₄	—	181	2	no	—
513	C₂×D₄	—	181	2	no	—
514	C₂×D₄	—	181	2	no	—
515	C₂×D₄	—	724	4	no	—
516	C₂×D₄	—	724	2	no	—
517	C₂×D₄	—	724	2	no	—
518	C₂×D₄	—	724	4	no	—
519	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
520	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
521	C₂×D₄	C₂²×D₁₈₁	1	1	yes	characteristic
522	C₂×D₄	C₂²×D₁₈₁	1	2	yes	—
523	C₂²×C₄	—	181	2	no	—
524	C₂²×C₄	—	181	1	no	—
525	C₂²×C₄	—	181	1	no	—
526	C₂²×C₄	—	181	1	no	—
527	C₂²×C₄	—	181	1	no	—
528	C₂²×C₄	—	181	1	no	—
529	C₂²×C₄	—	181	2	no	—
530	C₂²×C₄	—	181	2	no	—
531	C₂²×C₄	—	181	2	no	—
532	C₂²×C₄	—	181	2	no	—
533	C₂²×C₄	—	181	1	no	—
534	C₂²×C₄	—	724	2	no	—
535	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
536	C₂²×C₄	C₂²×D₁₈₁	1	1	yes	characteristic
537	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
538	C₂²×C₄	C₂²×D₁₈₁	1	2	yes	—
539	C₄⋊C₄	—	181	1	no	—
540	C₄⋊C₄	—	181	2	no	—
541	C₄⋊C₄	—	181	1	no	—
542	C₄⋊C₄	—	181	2	no	—
543	C₄⋊C₄	—	181	1	no	—
544	C₄⋊C₄	—	181	1	no	—
545	C₄⋊C₄	—	181	2	no	—
546	C₄⋊C₄	—	181	1	no	—
547	C₄⋊C₄	—	181	2	no	—
548	C₄⋊C₄	—	181	2	no	—
549	C₄⋊C₄	—	181	1	no	—
550	C₄⋊C₄	—	181	2	no	—
551	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
552	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
553	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
554	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
555	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
556	C₄⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
557	C₄⋊C₄	C₂²×D₁₈₁	1	2	yes	—
558	C₂²⋊C₄	—	181	2	no	—
559	C₂²⋊C₄	—	181	2	no	—
560	C₂²⋊C₄	—	181	2	no	—
561	C₂²⋊C₄	—	181	1	no	—
562	C₂²⋊C₄	—	181	1	no	—
563	C₂²⋊C₄	—	181	1	no	—
564	C₂²⋊C₄	—	181	1	no	—
565	C₂²⋊C₄	—	181	2	no	—
566	C₂²⋊C₄	—	181	2	no	—
567	C₂²⋊C₄	—	181	2	no	—
568	C₂²⋊C₄	—	181	2	no	—
569	C₂²⋊C₄	—	181	1	no	—
570	C₂²⋊C₄	—	181	2	no	—
571	C₂²⋊C₄	—	181	2	no	—
572	C₂²⋊C₄	—	181	1	no	—
573	C₂²⋊C₄	—	181	1	no	—
574	C₂²⋊C₄	—	181	1	no	—
575	C₂²⋊C₄	—	181	2	no	—
576	C₂²⋊C₄	—	181	2	no	—
577	C₂²⋊C₄	—	181	2	no	—
578	C₂²⋊C₄	—	181	2	no	—
579	C₂²⋊C₄	—	181	2	no	—
580	C₂²⋊C₄	—	181	2	no	—
581	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
582	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
583	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
584	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
585	C₂²⋊C₄	C₂²×D₁₈₁	1	2	yes	—
586	C₂²⋊C₄	C₂²×D₁₈₁	1	1	yes	characteristic
587	C₄²	—	181	2	no	—
588	C₄²	—	181	1	no	—
589	C₄²	—	181	2	no	—
590	C₄²	C₂²×D₁₈₁	1	2	yes	—
591	C₄²	C₂²×D₁₈₁	1	1	yes	characteristic
592	C₂³	—	362	4	no	—
593	C₂³	—	362	2	no	—
594	C₂³	—	181	1	no	—
595	C₂³	—	181	2	no	—
596	C₂³	—	181	2	no	—
597	C₂³	—	181	1	no	—
598	C₂³	—	181	1	no	—
599	C₂³	—	724	2	no	—
600	C₂³	—	724	2	no	—
601	C₂³	—	724	2	no	—
602	C₂³	—	724	2	no	—
603	C₂³	—	724	2	no	—
604	C₂³	—	724	1	no	—
605	C₂³	—	724	1	no	—
606	C₂³	C₂³×D₁₈₁	1	2	yes	—
607	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
608	C₂³	C₂³×D₁₈₁	1	1	yes	characteristic
609	Q₈	—	362	2	no	—
610	Q₈	—	724	2	no	—
611	Q₈	—	724	1	no	—
612	D₄	—	2	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	4	2	no	—
615	D₄	—	4	1	no	—
616	D₄	—	362	2	no	—
617	D₄	—	362	4	no	—
618	D₄	—	362	2	no	—
619	D₄	—	362	2	no	—
620	D₄	—	362	2	no	—
621	D₄	—	724	2	no	—
622	D₄	—	724	2	no	—
623	D₄	—	724	2	no	—
624	D₄	—	724	1	no	—
625	D₄	—	724	2	no	—
626	D₄	—	724	2	no	—
627	D₄	—	724	2	no	—
628	D₄	—	724	2	no	—
629	D₄	—	724	2	no	—
630	D₄	—	724	2	no	—
631	D₄	—	724	2	no	—
632	D₄	—	724	1	no	—
633	D₄	—	724	1	no	—
634	D₄	—	724	2	no	—
635	D₄	—	724	2	no	—
636	D₄	—	724	1	no	—
637	C₂×C₄	—	2	2	no	—
638	C₂×C₄	—	2	2	no	—
639	C₂×C₄	—	4	2	no	—
640	C₂×C₄	—	4	2	no	—
641	C₂×C₄	—	362	4	no	—
642	C₂×C₄	—	362	2	no	—
643	C₂×C₄	—	362	2	no	—
644	C₂×C₄	—	362	2	no	—
645	C₂×C₄	—	181	2	no	—
646	C₂×C₄	—	181	1	no	—
647	C₂×C₄	—	181	1	no	—
648	C₂×C₄	—	181	1	no	—
649	C₂×C₄	—	181	2	no	—
650	C₂×C₄	—	181	1	no	—
651	C₂×C₄	—	181	1	no	—
652	C₂×C₄	—	724	1	no	—
653	C₂×C₄	—	724	1	no	—
654	C₂×C₄	—	724	2	no	—
655	C₂×C₄	—	724	2	no	—
656	C₂×C₄	—	724	2	no	—
657	C₂×C₄	—	724	2	no	—
658	C₂×C₄	—	724	1	no	—
659	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
660	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
661	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
662	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
663	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
664	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
665	C₂×C₄	C₂³×D₁₈₁	1	2	yes	—
666	C₂×C₄	C₂³×D₁₈₁	1	1	yes	characteristic
667	C₂²	—	2	1	no	—
668	C₂²	—	2	1	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	1	no	—
671	C₂²	—	2	2	no	—
672	C₂²	—	2	1	no	—
673	C₂²	—	2	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	2	no	—
676	C₂²	—	362	1	no	—
677	C₂²	—	362	1	no	—
678	C₂²	—	362	2	no	—
679	C₂²	—	362	2	no	—
680	C₂²	—	362	1	no	—
681	C₂²	—	362	1	no	—
682	C₂²	—	362	2	no	—
683	C₂²	—	362	1	no	—
684	C₂²	—	362	2	no	—
685	C₂²	—	362	1	no	—
686	C₂²	—	362	1	no	—
687	C₂²	—	362	1	no	—
688	C₂²	—	362	2	no	—
689	C₂²	—	362	2	no	—
690	C₂²	—	1448	4	no	—
691	C₂²	—	1448	4	no	—
692	C₂²	—	181	2	no	—
693	C₂²	—	724	4	no	—
694	C₂²	C₂⁴×D₁₈₁	1	1	yes	characteristic
695	C₄	—	2	2	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	2	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	362	1	no	—
703	C₄	—	362	2	no	—
704	C₄	—	362	1	no	—
705	C₄	—	362	1	no	—
706	C₄	—	362	1	no	—
707	C₄	—	362	1	no	—
708	C₄	—	362	2	no	—
709	C₄	#19153862	1	2	yes	—
710	C₂	—	4	2	no	—
711	C₂	—	4	1	no	—
712	C₂	—	4	1	no	—
713	C₂	—	362	2	no	—
714	C₂	—	724	1	no	—
715	C₂	—	724	2	no	—
716	C₂	—	724	2	no	—
717	C₂	—	724	1	no	—
718	C₂	H(5,𝔽₂)×D₁₈₁	1	1	yes	characteristic
719	C₂	C₂×#19153862	1	1	yes	characteristic
720	C₂	#26042115	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₈₁
commutator, socle, cosocle	C₂²×C₁₈₁	C₂⁵
Fitting	#553×C₁₈₁	C₂
hypercenter	#553	D₁₈₁
hypocenter	C₁₈₁	#3542
LCS	G ▷ C₂²×C₁₈₁ ▷ C₁₈₁
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #26042026	C₂	semidirect
2. #26042017	C₂	semidirect
3. #26041992	C₂	semidirect
4. #26041967	C₂	semidirect
5. #26041954	C₂	semidirect
6. #26041950	C₂	semidirect
7. #26041930	C₂	semidirect
8. #26041926	C₂	semidirect
9. #26041926	C₂	semidirect
10. #26041925	C₂	semidirect
11. D₄×D₇₂₄	C₂	semidirect
12. #26041894	C₂	semidirect
13. #26041885	C₂	semidirect
14. #26041880	C₂	semidirect
15. #26041868	C₂	semidirect
16. #26041860	C₂	semidirect
17. #26041845	C₂	semidirect
18. #26041845	C₂	semidirect
19. #26041840	C₂	semidirect
20. #26041791	C₂	semidirect
21. #26041788	C₂	semidirect
22. #121×D₁₈₁	C₂	semidirect
23. #553×C₁₈₁	C₂	semidirect
24. C₂×#15668449	C₂²	semidirect
25. C₂×#15668449	C₂²	semidirect
26. C₂×#15668449	C₂²	semidirect
27. C₂×#15668449	C₂²	semidirect
30. C₂×D₄×D₁₈₁	C₂²	semidirect
31. C₂×D₄×D₁₈₁	C₂²	semidirect
32. C₂²×C₄×D₁₈₁	C₂²	semidirect
33. #19153815	C₂²	semidirect
34. #19153813	C₂²	semidirect
35. #19153812	C₂²	semidirect
36. #19153812	C₂²	semidirect
37. #19153811	C₂²	semidirect
38. #19153809	C₂²	semidirect
39. #19153807	C₂²	semidirect
40. #19153804	C₂²	semidirect
41. #19153803	C₂²	semidirect
42. #19153802	C₂²	semidirect
43. #19153802	C₂²	semidirect
44. #19153802	C₂²	semidirect
46. #19153801	C₂²	semidirect
47. #19153801	C₂²	semidirect
48. #19153801	C₂²	semidirect
49. #19153801	C₂²	semidirect
50. #19153800	C₂²	semidirect
51. #19153799	C₂²	semidirect
52. #19153799	C₂²	semidirect
53. #19153798	C₂²	semidirect
54. #19153798	C₂²	semidirect
55. #19153798	C₂²	semidirect
56. #19153796	C₂²	semidirect
57. #19153796	C₂²	semidirect
58. #19153796	C₂²	semidirect
59. #19153796	C₂²	semidirect
60. #19153795	C₂²	semidirect
61. #19153794	C₂²	semidirect
62. #19153794	C₂²	semidirect
63. #19153793	C₂²	semidirect
65. #19153791	C₂²	semidirect
66. #19153791	C₂²	semidirect
67. #19153791	C₂²	semidirect
68. #19153791	C₂²	semidirect
69. #19153791	C₂²	semidirect
70. #19153791	C₂²	semidirect
71. #19153790	C₂²	semidirect
72. #19153790	C₂²	semidirect
73. #19153790	C₂²	semidirect
74. #19153790	C₂²	semidirect
75. #19153790	C₂²	semidirect
77. #19153789	C₂²	semidirect
78. #19153789	C₂²	semidirect
79. #19153789	C₂²	semidirect
80. #19153789	C₂²	semidirect
81. #19153788	C₂²	semidirect
82. #19153788	C₂²	semidirect
84. #19153787	C₂²	semidirect
85. #19153787	C₂²	semidirect
88. #19153786	C₂²	semidirect
89. #19153786	C₂²	semidirect
90. #19153786	C₂²	semidirect
91. #19153784	C₂²	semidirect
92. #19153784	C₂²	semidirect
93. #19153784	C₂²	semidirect
94. #19153784	C₂²	semidirect
95. C₄×Dic₃₆₂	C₂²	semidirect
97. C₄×D₇₂₄	C₂²	semidirect
98. C₄×D₇₂₄	C₂²	semidirect
99. #19153778	C₂²	semidirect
100. #19153778	C₂²	semidirect
101. #19153778	C₂²	semidirect
102. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
103. C₄×C₂²⋊D₁₈₁	C₂²	semidirect
104. #19153774	C₂²	semidirect
105. #19153774	C₂²	semidirect
106. #19153773	C₂²	semidirect
107. #19153773	C₂²	semidirect
108. C₄⋊C₄×D₁₈₁	C₂²	semidirect
109. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
110. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
111. C₂²⋊C₄×D₁₈₁	C₂²	semidirect
112. #126×C₁₈₁	C₂²	semidirect
113. #125×C₁₈₁	C₂²	semidirect
114. #123×C₁₈₁	C₂²	semidirect
116. #121×C₁₈₁	C₂²	semidirect
117. #121×C₁₈₁	C₂²	semidirect
118. C₄×D₄×C₁₈₁	C₂²	semidirect
119. C₄×D₄×C₁₈₁	C₂²	semidirect
120. C₄×D₄×C₁₈₁	C₂²	semidirect
121. #117×C₁₈₁	C₂²	semidirect
122. C₂×C₄⋊C₄×C₁₈₁	C₂²	semidirect
360. C₁₈₁	#3542	semidirect
365. #553	D₁₈₁	semidirect
400. #126	C₂×D₁₈₁	semidirect
402. #125	C₂×D₁₈₁	semidirect
419. #123	C₂×D₁₈₁	semidirect
451. #121	C₂×D₁₈₁	semidirect
452. #121	C₂×D₁₈₁	semidirect
471. C₄×D₄	C₂×D₁₈₁	semidirect
472. C₄×D₄	C₂×D₁₈₁	semidirect
473. C₄×D₄	C₂×D₁₈₁	semidirect
478. #117	C₂×D₁₈₁	semidirect
480. C₂×C₄⋊C₄	C₂×D₁₈₁	semidirect

Maximal subgroups

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

subgroup	index
#26042026	2
#26042017	2
#26041992	2
#26041967	2
#26041954	2
#26041950	2
#26041930	2
#26041926	2
#26041925	2
D₄×D₇₂₄	2
#26041894	2
#26041885	2
#26041880	2
#26041868	2
#26041860	2
#26041845	2
#26041840	2
#26041791	2
#26041788	2
#121×D₁₈₁	2
#553×C₁₈₁	2
#3542	181