Subgroups — #72262313

Order 2048.

At least 13447 conjugacy classes of subgroups; only the 718 normal subgroups are shown.

The subgroup lattice has 462 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262272	C₂	1	2	yes	maximal, complemented
2	#72262269	C₂	1	2	yes	maximal, complemented
3	#72255642	C₂	1	1	yes	maximal, characteristic, complemented
4	#72249538	C₂	1	1	yes	maximal, characteristic
5	#72249426	C₂	1	2	yes	maximal, complemented
6	#72249424	C₂	1	2	yes	maximal, complemented
7	#72236896	C₂	1	1	yes	maximal, characteristic, complemented
8	#72236837	C₂	1	1	yes	maximal, characteristic, complemented
9	#72236085	C₂	1	1	yes	maximal, characteristic, complemented
10	#72235848	C₂	1	1	yes	maximal, characteristic, complemented
11	#72225994	C₂	1	1	yes	maximal, characteristic, complemented
12	#8126631	C₂²	1	2	yes	—
13	#8125493	C₂²	1	2	yes	—
14	#8108077	C₄	1	2	yes	complemented
15	#8108057	C₄	1	2	yes	complemented
16	#8093660	C₄	1	1	yes	characteristic, complemented
17	#8093623	C₄	1	1	yes	characteristic, complemented
18	#7681968	C₄	1	1	yes	characteristic, complemented
19	#7681927	C₄	1	1	yes	characteristic, complemented
20	#7642273	C₂²	1	1	yes	characteristic
21	#7642244	C₂²	1	1	yes	characteristic
22	C₂×#34980	C₂²	1	1	yes	characteristic
23	#555894	C₂²	1	1	yes	characteristic, complemented
24	#496231	C₂²	1	2	yes	complemented
25	#496231	C₂²	1	2	yes	complemented
26	#496225	C₂²	1	2	yes	complemented
27	#496225	C₂²	1	2	yes	complemented
28	#496194	C₂²	1	2	yes	complemented
29	#496194	C₂²	1	2	yes	complemented
30	#382422	C₂²	1	1	yes	characteristic, complemented
31	#379759	C₂²	1	2	yes	complemented
32	#379733	C₂²	1	2	yes	complemented
33	#201690	C₂²	1	2	yes	complemented
34	C₂×#9497	C₂²	1	1	yes	characteristic, complemented
35	C₂×#9497	C₂²	1	1	yes	characteristic, complemented
36	C₂×#9495	C₂²	1	1	yes	characteristic, complemented
37	C₂×#9495	C₂²	1	1	yes	characteristic, complemented
38	#201322	C₂²	1	2	yes	complemented
39	C₂×#8547	C₂²	1	1	yes	characteristic, complemented
40	C₂×#8541	C₂²	1	1	yes	characteristic, complemented
41	C₂⁵×D₄	D₄	1	1	yes	characteristic
42	C₂×#3490	D₄	1	1	yes	characteristic
43	C₂×#3484	D₄	1	1	yes	characteristic
44	C₂³×#120	C₂³	1	1	yes	characteristic
45	#59193	C₂×C₄	1	2	yes	—
46	#59006	C₂×C₄	1	2	yes	—
47	#58992	C₂×C₄	1	2	yes	—
48	#58990	C₂×C₄	1	2	yes	—
49	#52012	D₄	1	2	yes	—
50	#52004	D₄	1	2	yes	—
51	#51993	D₄	1	2	yes	—
52	#51945	D₄	1	2	yes	—
53	#51940	D₄	1	2	yes	—
54	#51940	D₄	1	2	yes	—
55	#51902	D₄	1	2	yes	—
56	#51895	D₄	1	2	yes	—
57	#50856	D₄	1	2	yes	—
58	#50646	D₄	1	2	yes	—
59	#48922	D₄	1	2	yes	—
60	#48143	D₄	1	2	yes	—
61	#48113	D₄	1	2	yes	—
62	#48088	D₄	1	2	yes	—
63	#47848	D₄	1	2	yes	—
64	#47827	D₄	1	2	yes	—
65	#45568	C₂×C₄	1	2	yes	—
66	#45537	C₂×C₄	1	2	yes	—
67	#45439	C₂×C₄	1	2	yes	—
68	#45438	C₂×C₄	1	2	yes	—
69	#36714	C₂×C₄	1	2	yes	—
70	#36714	D₄	1	2	yes	—
71	#36703	C₂×C₄	1	2	yes	—
72	#36703	D₄	1	2	yes	—
73	C₂×#2849	C₂×C₄	1	1	yes	characteristic
74	C₂×#2849	D₄	1	1	yes	characteristic
75	C₂×#2846	C₂×C₄	1	1	yes	characteristic
76	C₂×#2846	D₄	1	1	yes	characteristic
77	#35390	C₂×C₄	1	1	yes	characteristic
78	#35390	D₄	1	1	yes	characteristic
79	#35367	C₂×C₄	1	1	yes	characteristic
80	#35367	D₄	1	1	yes	characteristic
81	#35350	C₂×C₄	1	1	yes	characteristic
82	#35350	D₄	1	1	yes	characteristic
83	#35346	C₂×C₄	1	1	yes	characteristic
84	#35346	D₄	1	1	yes	characteristic
85	#35222	C₂³	1	2	yes	—
86	#35050	D₄	1	2	yes	—
87	#34980	D₄	1	2	yes	—
88	#34980	C₂³	1	2	yes	—
89	C₂×#2405	D₄	1	1	yes	characteristic
90	C₂×#2405	D₄	1	1	yes	characteristic
91	C₂×#2410	C₂×C₄	1	1	yes	characteristic
92	C₂×#2410	C₂×C₄	1	1	yes	characteristic
93	C₂×#2410	D₄	1	1	yes	characteristic
94	C₂×#2410	D₄	1	1	yes	characteristic
95	C₂×#2403	C₂³	1	1	yes	characteristic
96	C₂×#2403	C₂³	1	1	yes	characteristic
97	#34176	D₄	1	1	yes	characteristic
98	#34171	D₄	1	1	yes	characteristic
99	C₂×#2309	C₂³	1	1	yes	characteristic
100	C₂×#2308	C₂³	1	1	yes	characteristic
101	C₂²×#379	D₄	1	1	yes	characteristic
102	C₂×#1783	C₂³	1	2	yes	—
103	C₂×#1781	C₂³	1	2	yes	—
104	C₂×#1781	C₂³	1	1	yes	characteristic
105	C₂×#1781	C₂³	1	1	yes	characteristic
106	C₂⁷	C₂²⋊C₄	1	1	yes	characteristic
107	C₂⁷	C₂×D₄	1	1	yes	characteristic
108	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
115	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
116	C₂⁵×C₄	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×H(3,𝔽₄)	C₂²⋊C₄	1	2	yes	complemented
118	C₂×#560	C₂²⋊C₄	1	2	yes	complemented
119	C₂×#551	C₂²⋊C₄	1	2	yes	complemented
120	C₂×D₄²	C₂²⋊C₄	1	2	yes	complemented
121	C₂×#543	C₂²⋊C₄	1	1	yes	characteristic
122	C₂×#538	C₂²⋊C₄	1	2	yes	—
123	C₂×#535	C₂×D₄	1	2	yes	—
124	C₂×#535	C₂×D₄	1	2	yes	—
125	C₂×#534	C₂²⋊C₄	1	2	yes	—
126	C₂×#534	C₂²⋊C₄	1	1	yes	characteristic
127	C₂×#534	C₂×D₄	1	2	yes	—
128	C₂×#534	C₂×D₄	1	2	yes	—
129	C₂×#525	C₂×D₄	1	2	yes	—
130	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
131	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
132	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
133	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
134	C₂²×#120	C₂×D₄	1	1	yes	characteristic
135	C₂²×#120	C₂×D₄	1	1	yes	characteristic
136	C₂²×#120	C₂×D₄	1	1	yes	characteristic
137	C₂²×#120	C₂×D₄	1	1	yes	characteristic
138	C₂²×#120	C₂×D₄	1	2	yes	—
139	C₂²×#120	C₂×D₄	1	1	yes	characteristic
140	C₂²×#120	C₂×D₄	1	1	yes	characteristic
141	C₂²×#120	C₂×D₄	1	1	yes	characteristic
142	C₂²×#120	C₂×D₄	1	1	yes	characteristic
143	C₂×#518	C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
148	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
149	#2804	C₂²⋊C₄	1	2	yes	complemented
150	#2748	C₂²⋊C₄	1	2	yes	complemented
151	#2748	C₂²⋊C₄	1	2	yes	complemented
152	#2717	C₂²⋊C₄	1	2	yes	complemented
153	#2709	C₂²⋊C₄	1	2	yes	complemented
154	#2697	C₂²⋊C₄	1	2	yes	complemented
155	#2697	C₂²⋊C₄	1	2	yes	complemented
156	#2684	C₂²⋊C₄	1	2	yes	complemented
157	#2684	C₂²⋊C₄	1	2	yes	complemented
158	#2684	C₂²⋊C₄	1	2	yes	complemented
159	#2683	C₂²⋊C₄	1	2	yes	complemented
160	#2679	C₂²⋊C₄	1	2	yes	complemented
161	#2679	C₂²⋊C₄	1	2	yes	complemented
162	#2669	C₂²⋊C₄	1	2	yes	complemented
163	#2669	C₂²⋊C₄	1	2	yes	complemented
164	#2669	C₂²⋊C₄	1	2	yes	complemented
165	#2561	C₂²⋊C₄	1	2	yes	—
166	#2561	C₂²⋊C₄	1	2	yes	—
167	#2539	C₂²⋊C₄	1	2	yes	—
168	#2539	C₂²⋊C₄	1	2	yes	—
169	#2435	C₂²×C₄	1	2	yes	—
170	#2435	C₂×D₄	1	2	yes	—
171	#2435	C₂×D₄	1	2	yes	—
172	#2435	C₂×D₄	1	2	yes	—
173	#2433	C₂²×C₄	1	2	yes	—
174	#2433	C₂×D₄	1	2	yes	—
175	#2433	C₂×D₄	1	2	yes	—
176	#2433	C₂×D₄	1	2	yes	—
177	#2405	C₂²⋊C₄	1	2	yes	—
178	#2405	C₂²⋊C₄	1	2	yes	—
179	#2405	C₂²×C₄	1	2	yes	—
180	#2405	C₂×D₄	1	2	yes	—
181	#2405	C₂×D₄	1	2	yes	—
182	#2405	C₂×D₄	1	2	yes	—
183	#2403	C₂²⋊C₄	1	2	yes	—
184	#2403	C₂²⋊C₄	1	2	yes	—
185	#2403	C₂²×C₄	1	2	yes	—
186	#2403	C₂×D₄	1	2	yes	—
187	#2403	C₂×D₄	1	2	yes	—
188	#2403	C₂×D₄	1	2	yes	—
189	#2403	C₂×D₄	1	2	yes	—
190	#2403	C₂×D₄	1	2	yes	—
191	#2403	C₂×D₄	1	2	yes	—
192	#2403	C₂×D₄	1	2	yes	—
193	#2403	C₂×D₄	1	2	yes	—
194	#2403	C₂×D₄	1	2	yes	—
195	#2403	C₂×D₄	1	2	yes	—
196	#2403	C₂×D₄	1	2	yes	—
197	#2380	C₂²⋊C₄	1	2	yes	complemented
198	#2379	C₂²⋊C₄	1	2	yes	complemented
199	#2376	C₂²⋊C₄	1	2	yes	complemented
200	#2375	C₂²⋊C₄	1	2	yes	complemented
201	#2375	C₂²⋊C₄	1	2	yes	complemented
202	#2375	C₂²⋊C₄	1	2	yes	complemented
203	#2374	C₂²⋊C₄	1	2	yes	complemented
204	#2372	C₂²⋊C₄	1	2	yes	complemented
205	#2366	C₂²⋊C₄	1	2	yes	complemented
206	#2358	C₂²⋊C₄	1	2	yes	complemented
207	#2358	C₂²⋊C₄	1	2	yes	complemented
208	#2358	C₂²⋊C₄	1	2	yes	complemented
209	#2312	C₂²⋊C₄	1	2	yes	—
210	#2309	C₂²⋊C₄	1	2	yes	—
211	#2309	C₂×D₄	1	2	yes	—
212	#2309	C₂×D₄	1	2	yes	—
213	#2308	C₂²⋊C₄	1	1	yes	characteristic
214	#2308	C₂²⋊C₄	1	1	yes	characteristic
215	#2308	C₂×D₄	1	2	yes	—
216	#2308	C₂×D₄	1	2	yes	—
217	C₂×#386	C₂²×C₄	1	1	yes	characteristic
218	C₂×#386	C₂²×C₄	1	1	yes	characteristic
219	C₂×#386	C₂×D₄	1	1	yes	characteristic
220	C₂×#386	C₂×D₄	1	1	yes	characteristic
221	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
222	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
223	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
224	C₂×#385	C₂²⋊C₄	1	1	yes	characteristic
225	#2280	C₂×D₄	1	2	yes	—
226	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
227	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
228	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
229	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
230	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
231	C₂×#379	C₂²⋊C₄	1	1	yes	characteristic
232	C₂×#379	C₂×D₄	1	1	yes	characteristic
233	C₂×#379	C₂×D₄	1	1	yes	characteristic
234	C₂×#379	C₂×D₄	1	2	yes	—
235	#2273	C₂²⋊C₄	1	1	yes	characteristic
236	#2273	C₂²⋊C₄	1	1	yes	characteristic
237	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂⁶	#120	1	1	yes	characteristic
242	C₂⁶	#120	1	1	yes	characteristic
243	C₂⁶	#120	1	1	yes	characteristic
244	C₂⁶	#120	1	1	yes	characteristic
245	C₂⁶	C₂²×D₄	1	1	yes	characteristic
246	C₂⁶	C₂²×D₄	1	1	yes	characteristic
247	C₂²×#41	#120	1	2	yes	—
248	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
249	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
250	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
251	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
252	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂³×D₄	#120	1	1	yes	characteristic
254	C₂³×D₄	#120	1	1	yes	characteristic
255	C₂³×D₄	#120	1	2	yes	—
256	C₂³×D₄	#120	1	2	yes	—
257	C₂³×D₄	#120	1	2	yes	—
258	C₂³×D₄	#120	1	2	yes	—
259	C₂³×D₄	#120	1	1	yes	characteristic
260	C₂³×D₄	#120	1	2	yes	—
261	C₂³×D₄	#120	1	1	yes	characteristic
262	C₂³×D₄	#120	1	2	yes	—
263	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
264	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
265	C₂³×D₄	C₂²×D₄	1	2	yes	—
266	C₂³×D₄	C₂²×D₄	1	2	yes	—
267	C₂³×D₄	C₂²×D₄	1	2	yes	—
268	C₂³×D₄	C₂²×D₄	1	2	yes	—
269	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
270	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
271	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
273	C₂⁴×C₄	#120	1	1	yes	characteristic
274	C₂⁴×C₄	#120	1	1	yes	characteristic
275	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
276	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
277	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
278	C₂×#127	#120	1	2	yes	—
279	C₂×#127	#120	1	2	yes	—
280	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
281	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
282	C₂×#124	#120	1	2	yes	—
283	C₂×#124	#120	1	2	yes	—
284	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
285	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
286	C₂×#123	#120	1	2	yes	—
287	C₂×#123	#120	1	2	yes	—
288	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×C₂²⋊Q₈	#120	1	2	yes	—
290	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×#121	#120	1	2	yes	—
292	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
295	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
296	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
297	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
298	C₂×#120	#120	1	2	yes	—
299	C₂×#120	#120	1	2	yes	—
300	C₂×#120	#120	1	2	yes	—
301	C₂×#120	#120	1	2	yes	—
302	C₂×#120	#120	1	2	yes	—
303	C₂×#120	#120	1	2	yes	—
304	C₂×#117	#120	1	2	yes	—
305	C₂×#117	#120	1	2	yes	—
306	C₂×#117	#120	1	2	yes	—
307	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
313	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
319	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
320	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
321	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
322	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
323	C₂²×C₂²⋊C₄	#120	1	2	yes	—
324	C₂²×C₂²⋊C₄	#120	1	2	yes	—
325	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	#120	1	2	yes	—
327	C₂²×C₂²⋊C₄	#120	1	2	yes	—
328	#390	C₂×C₂²⋊C₄	1	2	yes	—
329	#390	C₂×C₂²⋊C₄	1	2	yes	—
330	#390	C₂×C₂²⋊C₄	1	2	yes	—
331	#390	C₂×C₂²⋊C₄	1	2	yes	—
332	#390	#120	1	2	yes	—
333	#390	#120	1	2	yes	—
334	#390	#120	1	2	yes	—
335	#390	#120	1	2	yes	—
336	#386	C₂×C₂²⋊C₄	1	2	yes	—
337	#386	C₂×C₂²⋊C₄	1	2	yes	—
338	#386	C₂×C₂²⋊C₄	1	2	yes	—
339	#386	C₂×C₂²⋊C₄	1	2	yes	—
340	#386	C₂×C₂²⋊C₄	1	2	yes	—
341	#386	C₂×C₂²⋊C₄	1	2	yes	—
342	#386	C₂×C₂²⋊C₄	1	2	yes	—
343	#386	C₂×C₂²⋊C₄	1	2	yes	—
344	#386	#120	1	2	yes	—
345	#386	#120	1	2	yes	—
346	#386	#120	1	2	yes	—
347	#386	#120	1	2	yes	—
348	#386	#120	1	2	yes	—
349	#386	#120	1	2	yes	—
350	#386	#120	1	2	yes	—
351	#386	#120	1	2	yes	—
352	#379	C₂×C₂²⋊C₄	1	2	yes	—
353	#379	C₂×C₂²⋊C₄	1	2	yes	—
354	#379	#120	1	2	yes	—
355	#379	#120	1	2	yes	—
356	#379	#120	1	1	yes	characteristic
357	#379	#120	1	1	yes	characteristic
358	#379	#120	1	1	yes	characteristic
359	#379	#120	1	1	yes	characteristic
360	#379	#120	1	1	yes	characteristic
361	#379	#120	1	1	yes	characteristic
362	#379	#120	1	1	yes	characteristic
363	#379	#120	1	1	yes	characteristic
364	C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
365	C₄×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
366	C₄×C₂²⋊C₄	#120	1	2	yes	—
367	C₄×C₂²⋊C₄	#120	1	2	yes	—
368	C₂⁵	#379	1	1	yes	characteristic
369	C₂⁵	#379	1	1	yes	characteristic
370	C₂⁵	#379	1	1	yes	characteristic
371	C₂⁵	#379	1	1	yes	characteristic
372	C₂⁵	#379	1	2	yes	—
373	C₂⁵	#379	1	2	yes	—
374	C₂⁵	#379	1	2	yes	—
375	C₂⁵	B(4,𝔽₂)	1	2	yes	—
376	C₂⁵	#458	1	2	yes	—
377	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
378	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
379	C₂⁵	C₂×#120	1	1	yes	characteristic
380	C₂⁵	C₂×#120	1	1	yes	characteristic
381	C₂⁵	C₂×#120	1	2	yes	—
382	C₂⁵	C₂×#120	1	1	yes	characteristic
383	C₂⁵	C₂×#120	1	1	yes	characteristic
384	C₂⁵	C₂×#120	1	1	yes	characteristic
385	C₂⁵	C₂×#120	1	1	yes	characteristic
386	C₂⁵	C₂×#120	1	2	yes	—
387	C₂⁵	C₂×#120	1	1	yes	characteristic
388	C₂²×Q₈	#379	1	2	yes	—
389	C₂²×D₄	#379	1	2	yes	—
390	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
391	C₂²×D₄	C₂²×C₂²⋊C₄	1	2	yes	—
392	C₂²×D₄	C₂×#120	1	2	yes	—
393	C₂²×D₄	C₂×#120	1	2	yes	—
394	C₂²×D₄	C₂×#120	1	2	yes	—
395	C₂²×D₄	C₂×#120	1	2	yes	—
396	C₂²×D₄	C₂×#120	1	2	yes	—
397	C₂²×D₄	C₂×#120	1	2	yes	—
398	C₂³×C₄	#379	1	1	yes	characteristic
399	C₂³×C₄	#379	1	1	yes	characteristic
400	C₂³×C₄	#379	1	1	yes	characteristic
401	C₂³×C₄	#379	1	1	yes	characteristic
402	C₂³×C₄	#379	1	2	yes	—
403	C₂³×C₄	#379	1	2	yes	—
404	C₂³×C₄	#379	1	2	yes	—
405	C₂³×C₄	#379	1	2	yes	—
406	C₂³×C₄	#379	1	2	yes	—
407	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
408	C₂³×C₄	C₂×#120	1	1	yes	characteristic
409	C₂³×C₄	C₂×#120	1	2	yes	—
410	C₂³×C₄	C₂×#120	1	2	yes	—
411	C₂×C₄⋊C₄	#379	1	2	yes	—
412	C₂×C₄⋊C₄	#379	1	2	yes	—
413	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
419	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	#379	1	1	yes	characteristic
421	C₂×C₂²⋊C₄	#379	1	2	yes	—
422	C₂×C₂²⋊C₄	#379	1	2	yes	—
423	C₂×C₂²⋊C₄	#379	1	2	yes	—
424	C₂×C₂²⋊C₄	#379	1	2	yes	—
425	C₂×C₄²	#379	1	2	yes	—
426	C₂×C₄²	#379	1	2	yes	—
427	C₂×C₄²	#379	1	2	yes	—
428	C₂×C₄²	#379	1	2	yes	—
429	C₂⁴	#1790	1	2	yes	—
430	C₂⁴	#1790	1	2	yes	—
431	C₂⁴	C₂×#379	1	1	yes	characteristic
432	C₂⁴	C₂×#379	1	1	yes	characteristic
433	C₂⁴	C₂×#379	1	1	yes	characteristic
434	C₂⁴	C₂×#379	1	2	yes	—
435	C₂⁴	#2846	1	1	yes	characteristic
436	C₂⁴	#2846	1	1	yes	characteristic
437	C₂⁴	#2846	1	2	yes	—
438	C₂⁴	#2846	1	1	yes	characteristic
439	C₂⁴	#2846	1	1	yes	characteristic
440	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
441	C₂⁴	C₂×#458	1	1	yes	characteristic
442	C₂⁴	#3026	1	1	yes	characteristic
443	C₂⁴	#3026	1	1	yes	characteristic
444	C₂²×C₄	C₂×#379	1	2	yes	—
445	C₂²×C₄	#2846	1	2	yes	—
446	C₂³	#12753	1	4	yes	—
447	C₂³	#14679	1	1	yes	characteristic
448	C₂³	C₂×#1790	1	1	yes	characteristic
449	C₂³	#20609	1	1	yes	characteristic
450	C₂³	#32898	1	1	yes	characteristic
451	C₂³	#32898	1	1	yes	characteristic
452	C₂³	#32900	1	1	yes	characteristic
453	C₂³	#32900	1	1	yes	characteristic
454	C₂²	#392125	1	1	yes	characteristic
455	C₂²	#392135	1	1	yes	characteristic
456	C₂²	#392135	1	1	yes	characteristic
457	C₂²	C₂×#12753	1	2	yes	—
458	C₂	#72218980	1	1	yes	characteristic
459	C₂	#72237472	1	1	yes	characteristic
460	C₂	#72251779	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#392125
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72249538	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72262272	C₂	semidirect
2. #72262269	C₂	semidirect
3. #72255642	C₂	semidirect
5. #72249426	C₂	semidirect
6. #72249424	C₂	semidirect
7. #72236896	C₂	semidirect
8. #72236837	C₂	semidirect
9. #72236085	C₂	semidirect
10. #72235848	C₂	semidirect
11. #72225994	C₂	semidirect
14. #8108077	C₄	semidirect
15. #8108057	C₄	semidirect
16. #8093660	C₄	semidirect
17. #8093623	C₄	semidirect
18. #7681968	C₄	semidirect
19. #7681927	C₄	semidirect
23. #555894	C₂²	semidirect
24. #496231	C₂²	semidirect
25. #496231	C₂²	semidirect
26. #496225	C₂²	semidirect
27. #496225	C₂²	semidirect
28. #496194	C₂²	semidirect
29. #496194	C₂²	semidirect
30. #382422	C₂²	semidirect
31. #379759	C₂²	semidirect
32. #379733	C₂²	semidirect
33. #201690	C₂²	semidirect
34. C₂×#9497	C₂²	semidirect
35. C₂×#9497	C₂²	semidirect
36. C₂×#9495	C₂²	semidirect
37. C₂×#9495	C₂²	semidirect
38. #201322	C₂²	semidirect
39. C₂×#8547	C₂²	semidirect
40. C₂×#8541	C₂²	semidirect
117. C₂×H(3,𝔽₄)	C₂²⋊C₄	semidirect
118. C₂×#560	C₂²⋊C₄	semidirect
119. C₂×#551	C₂²⋊C₄	semidirect
120. C₂×D₄²	C₂²⋊C₄	semidirect
149. #2804	C₂²⋊C₄	semidirect
150. #2748	C₂²⋊C₄	semidirect
151. #2748	C₂²⋊C₄	semidirect
152. #2717	C₂²⋊C₄	semidirect
153. #2709	C₂²⋊C₄	semidirect
154. #2697	C₂²⋊C₄	semidirect
155. #2697	C₂²⋊C₄	semidirect
156. #2684	C₂²⋊C₄	semidirect
157. #2684	C₂²⋊C₄	semidirect
158. #2684	C₂²⋊C₄	semidirect
159. #2683	C₂²⋊C₄	semidirect
160. #2679	C₂²⋊C₄	semidirect
161. #2679	C₂²⋊C₄	semidirect
162. #2669	C₂²⋊C₄	semidirect
163. #2669	C₂²⋊C₄	semidirect
164. #2669	C₂²⋊C₄	semidirect
197. #2380	C₂²⋊C₄	semidirect
198. #2379	C₂²⋊C₄	semidirect
199. #2376	C₂²⋊C₄	semidirect
200. #2375	C₂²⋊C₄	semidirect
201. #2375	C₂²⋊C₄	semidirect
202. #2375	C₂²⋊C₄	semidirect
203. #2374	C₂²⋊C₄	semidirect
204. #2372	C₂²⋊C₄	semidirect
205. #2366	C₂²⋊C₄	semidirect
206. #2358	C₂²⋊C₄	semidirect
207. #2358	C₂²⋊C₄	semidirect
208. #2358	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72262272	2
#72262269	2
#72255642	2
#72249538	2
#72249426	2
#72249424	2
#72236896	2
#72236837	2
#72236085	2
#72235848	2
#72225994	2