Subgroups — #72262333

Order 2048.

At least 13452 conjugacy classes of subgroups; only the 714 normal subgroups are shown.

The subgroup lattice has 460 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262281	C₂	1	2	yes	maximal, complemented
2	#72262280	C₂	1	2	yes	maximal, complemented
3	#72262272	C₂	1	2	yes	maximal, complemented
4	#72262269	C₂	1	2	yes	maximal, complemented
5	#72251570	C₂	1	1	yes	maximal, characteristic, complemented
6	#72249434	C₂	1	1	yes	maximal, characteristic
7	#72236898	C₂	1	1	yes	maximal, characteristic, complemented
8	#72236837	C₂	1	1	yes	maximal, characteristic, complemented
9	#72235932	C₂	1	1	yes	maximal, characteristic, complemented
10	#72235848	C₂	1	1	yes	maximal, characteristic, complemented
11	#72226038	C₂	1	1	yes	maximal, characteristic, complemented
12	#8934496	C₄	1	1	yes	characteristic, complemented
13	#8934400	C₄	1	1	yes	characteristic, complemented
14	#8934400	C₄	1	1	yes	characteristic, complemented
15	#8934377	C₄	1	1	yes	characteristic, complemented
16	#8899018	C₄	1	2	yes	complemented
17	#8898095	C₄	1	2	yes	complemented
18	#8126631	C₂²	1	2	yes	—
19	#8125493	C₂²	1	2	yes	—
20	#7642273	C₂²	1	1	yes	characteristic
21	#7642273	C₂²	1	1	yes	characteristic
22	C₂×#35346	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	#379754	C₂²	1	1	yes	characteristic, complemented
33	#379754	C₂²	1	1	yes	characteristic, complemented
34	#201690	C₂²	1	2	yes	complemented
35	#201687	C₂²	1	2	yes	complemented
36	C₂×#9497	C₂²	1	1	yes	characteristic, complemented
37	C₂×#9497	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	C₂³×H(5,𝔽₂)	D₄	1	1	yes	characteristic
42	C₂×#3490	D₄	1	1	yes	characteristic
43	C₂×#3490	D₄	1	1	yes	characteristic
44	C₂³×#120	C₂³	1	1	yes	characteristic
45	#59193	D₄	1	2	yes	—
46	#59006	D₄	1	2	yes	—
47	#58992	D₄	1	2	yes	—
48	#58990	D₄	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	C₂×C₄	1	2	yes	—
58	#50646	C₂×C₄	1	2	yes	—
59	#48922	C₂×C₄	1	2	yes	—
60	#48143	C₂×C₄	1	2	yes	—
61	#48113	C₂×C₄	1	2	yes	—
62	#48088	C₂×C₄	1	2	yes	—
63	#47848	C₂×C₄	1	2	yes	—
64	#47827	C₂×C₄	1	2	yes	—
65	#45568	D₄	1	2	yes	—
66	#45537	D₄	1	2	yes	—
67	#45439	D₄	1	2	yes	—
68	#45438	D₄	1	2	yes	—
69	#36703	C₂×C₄	1	2	yes	—
70	#36703	D₄	1	2	yes	—
71	C₂×#2846	D₄	1	2	yes	—
72	#35390	C₂×C₄	1	1	yes	characteristic
73	#35390	C₂×C₄	1	1	yes	characteristic
74	#35390	D₄	1	1	yes	characteristic
75	#35390	D₄	1	1	yes	characteristic
76	#35367	C₂×C₄	1	1	yes	characteristic
77	#35367	C₂×C₄	1	1	yes	characteristic
78	#35367	D₄	1	1	yes	characteristic
79	#35367	D₄	1	1	yes	characteristic
80	#35348	C₂×C₄	1	2	yes	—
81	#35348	D₄	1	2	yes	—
82	#35346	C₂×C₄	1	1	yes	characteristic
83	#35346	C₂×C₄	1	1	yes	characteristic
84	#35346	C₂×C₄	1	1	yes	characteristic
85	#35346	C₂×C₄	1	1	yes	characteristic
86	#35346	D₄	1	1	yes	characteristic
87	#35346	D₄	1	1	yes	characteristic
88	#35346	D₄	1	1	yes	characteristic
89	#35346	D₄	1	1	yes	characteristic
90	#35222	C₂³	1	2	yes	—
91	#35050	D₄	1	2	yes	—
92	#34980	C₂³	1	2	yes	—
93	C₂×#2403	D₄	1	1	yes	characteristic
94	C₂×#2403	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	#34176	D₄	1	1	yes	characteristic
99	C₂×#2309	C₂³	1	1	yes	characteristic
100	C₂×#2308	D₄	1	1	yes	characteristic
101	C₂×#2308	C₂³	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	C₂×D₄	1	1	yes	characteristic
107	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
108	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
109	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic
110	C₂²×H(5,𝔽₂)	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	C₂×H(3,𝔽₄)	C₂²⋊C₄	1	2	yes	complemented
117	C₂×#560	C₂²⋊C₄	1	2	yes	complemented
118	C₂×#551	C₂²⋊C₄	1	2	yes	complemented
119	C₂×D₄²	C₂²⋊C₄	1	2	yes	complemented
120	C₂×#543	C₂²⋊C₄	1	1	yes	characteristic, complemented
121	C₂×#543	C₂²⋊C₄	1	1	yes	characteristic, complemented
122	C₂×#538	C₂²⋊C₄	1	2	yes	complemented
123	C₂×#535	C₂×D₄	1	2	yes	—
124	C₂×#535	C₂×D₄	1	2	yes	—
125	C₂×#534	C₂²⋊C₄	1	1	yes	characteristic, complemented
126	C₂×#534	C₂²⋊C₄	1	1	yes	characteristic, complemented
127	C₂×#534	C₂²×C₄	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	2	yes	complemented
131	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
132	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
133	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
134	C₂²×#120	C₂×D₄	1	2	yes	—
135	C₂²×#120	C₂×D₄	1	2	yes	—
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	2	yes	complemented
144	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
145	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
147	#2804	C₂²⋊C₄	1	2	yes	complemented
148	#2748	C₂²⋊C₄	1	2	yes	complemented
149	#2748	C₂²⋊C₄	1	2	yes	complemented
150	#2717	C₂²⋊C₄	1	2	yes	complemented
151	#2709	C₂²⋊C₄	1	2	yes	complemented
152	#2697	C₂²⋊C₄	1	2	yes	complemented
153	#2697	C₂²⋊C₄	1	2	yes	complemented
154	#2684	C₂²⋊C₄	1	2	yes	complemented
155	#2684	C₂²⋊C₄	1	2	yes	complemented
156	#2684	C₂²⋊C₄	1	2	yes	complemented
157	#2683	C₂²⋊C₄	1	2	yes	complemented
158	#2679	C₂²⋊C₄	1	2	yes	complemented
159	#2679	C₂²⋊C₄	1	2	yes	complemented
160	#2669	C₂²⋊C₄	1	2	yes	complemented
161	#2669	C₂²⋊C₄	1	2	yes	complemented
162	#2669	C₂²⋊C₄	1	2	yes	complemented
163	#2561	C₂²⋊C₄	1	2	yes	complemented
164	#2561	C₂²⋊C₄	1	2	yes	complemented
165	#2539	C₂²⋊C₄	1	2	yes	complemented
166	#2539	C₂²⋊C₄	1	2	yes	complemented
167	#2435	C₂²×C₄	1	2	yes	—
168	#2435	C₂×D₄	1	2	yes	—
169	#2435	C₂×D₄	1	2	yes	—
170	#2435	C₂×D₄	1	2	yes	—
171	#2433	C₂²×C₄	1	2	yes	—
172	#2433	C₂×D₄	1	2	yes	—
173	#2433	C₂×D₄	1	2	yes	—
174	#2433	C₂×D₄	1	2	yes	—
175	#2405	C₂×D₄	1	2	yes	—
176	#2405	C₂×D₄	1	2	yes	—
177	#2405	C₂×D₄	1	2	yes	—
178	#2405	C₂×D₄	1	2	yes	—
179	#2403	C₂²⋊C₄	1	1	yes	characteristic
180	#2403	C₂²⋊C₄	1	1	yes	characteristic
181	#2403	C₂²⋊C₄	1	1	yes	characteristic
182	#2403	C₂²⋊C₄	1	1	yes	characteristic
183	#2403	C₂²⋊C₄	1	1	yes	characteristic
184	#2403	C₂²⋊C₄	1	1	yes	characteristic
185	#2403	C₂²⋊C₄	1	1	yes	characteristic
186	#2403	C₂²⋊C₄	1	1	yes	characteristic
187	#2403	C₂²×C₄	1	1	yes	characteristic
188	#2403	C₂²×C₄	1	1	yes	characteristic
189	#2403	C₂²×C₄	1	1	yes	characteristic
190	#2403	C₂²×C₄	1	1	yes	characteristic
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	#2403	C₂×D₄	1	2	yes	—
198	#2403	C₂×D₄	1	2	yes	—
199	#2403	C₂×D₄	1	1	yes	characteristic
200	#2403	C₂×D₄	1	1	yes	characteristic
201	#2403	C₂×D₄	1	1	yes	characteristic
202	#2403	C₂×D₄	1	1	yes	characteristic
203	#2380	C₂²⋊C₄	1	2	yes	complemented
204	#2379	C₂²⋊C₄	1	2	yes	complemented
205	#2376	C₂²⋊C₄	1	2	yes	complemented
206	#2375	C₂²⋊C₄	1	2	yes	complemented
207	#2375	C₂²⋊C₄	1	2	yes	complemented
208	#2375	C₂²⋊C₄	1	2	yes	complemented
209	#2374	C₂²⋊C₄	1	2	yes	complemented
210	#2372	C₂²⋊C₄	1	2	yes	complemented
211	#2366	C₂²⋊C₄	1	2	yes	complemented
212	#2358	C₂²⋊C₄	1	2	yes	complemented
213	#2358	C₂²⋊C₄	1	2	yes	complemented
214	#2358	C₂²⋊C₄	1	2	yes	complemented
215	#2315	C₂²⋊C₄	1	2	yes	complemented
216	#2312	C₂²⋊C₄	1	2	yes	complemented
217	#2309	C₂×D₄	1	2	yes	—
218	#2309	C₂×D₄	1	2	yes	—
219	#2308	C₂²⋊C₄	1	1	yes	characteristic
220	#2308	C₂²⋊C₄	1	1	yes	characteristic
221	#2308	C₂²⋊C₄	1	1	yes	characteristic
222	#2308	C₂²⋊C₄	1	1	yes	characteristic
223	#2308	C₂²×C₄	1	2	yes	—
224	#2308	C₂×D₄	1	2	yes	—
225	C₂×#386	C₂×D₄	1	2	yes	—
226	C₂×#386	C₂×D₄	1	2	yes	—
227	#2280	C₂×D₄	1	2	yes	—
228	C₂×#379	C₂²⋊C₄	1	2	yes	complemented
229	C₂×#379	C₂²⋊C₄	1	2	yes	complemented
230	C₂×#379	C₂×D₄	1	2	yes	—
231	C₂×#379	C₂×D₄	1	1	yes	characteristic
232	C₂×#379	C₂×D₄	1	1	yes	characteristic
233	#2273	C₂²⋊C₄	1	1	yes	characteristic, complemented
234	#2273	C₂²⋊C₄	1	1	yes	characteristic, complemented
235	#2273	C₂²⋊C₄	1	1	yes	characteristic, complemented
236	#2273	C₂²⋊C₄	1	1	yes	characteristic, complemented
237	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂⁶	#120	1	1	yes	characteristic
240	C₂⁶	#120	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	1	yes	characteristic
252	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
253	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
254	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂³×D₄	#120	1	1	yes	characteristic
258	C₂³×D₄	#120	1	1	yes	characteristic
259	C₂³×D₄	#120	1	1	yes	characteristic
260	C₂³×D₄	#120	1	1	yes	characteristic
261	C₂³×D₄	#120	1	1	yes	characteristic
262	C₂³×D₄	#120	1	1	yes	characteristic
263	C₂³×D₄	#120	1	1	yes	characteristic
264	C₂³×D₄	#120	1	2	yes	—
265	C₂³×D₄	#120	1	1	yes	characteristic
266	C₂³×D₄	#120	1	2	yes	—
267	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
268	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
269	C₂³×D₄	C₂²×D₄	1	2	yes	—
270	C₂³×D₄	C₂²×D₄	1	2	yes	—
271	C₂³×D₄	C₂²×D₄	1	2	yes	—
272	C₂³×D₄	C₂²×D₄	1	2	yes	—
273	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
274	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
275	C₂⁴×C₄	#120	1	1	yes	characteristic
276	C₂⁴×C₄	#120	1	1	yes	characteristic
277	C₂⁴×C₄	#120	1	1	yes	characteristic
278	C₂⁴×C₄	#120	1	1	yes	characteristic
279	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
280	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
281	C₂×#127	C₂×C₂²⋊C₄	1	2	yes	—
282	C₂×#127	#120	1	2	yes	—
283	C₂×#127	#120	1	2	yes	—
284	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
285	C₂×#124	C₂×C₂²⋊C₄	1	2	yes	—
286	C₂×#124	#120	1	2	yes	—
287	C₂×#124	#120	1	2	yes	—
288	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
289	C₂×#123	C₂×C₂²⋊C₄	1	2	yes	—
290	C₂×#123	#120	1	2	yes	—
291	C₂×#123	#120	1	2	yes	—
292	C₂×C₂²⋊Q₈	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂×C₂²⋊Q₈	#120	1	2	yes	—
294	C₂×#121	C₂×C₂²⋊C₄	1	2	yes	—
295	C₂×#121	#120	1	2	yes	—
296	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
297	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
298	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
300	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
301	C₂×#120	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂×#120	#120	1	2	yes	—
303	C₂×#120	#120	1	2	yes	—
304	C₂×#120	#120	1	2	yes	—
305	C₂×#120	#120	1	2	yes	—
306	C₂×#120	#120	1	2	yes	—
307	C₂×#120	#120	1	2	yes	—
308	C₂×#117	#120	1	2	yes	—
309	C₂×#117	#120	1	2	yes	—
310	C₂×#117	#120	1	2	yes	—
311	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
318	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
319	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
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	1	yes	characteristic
324	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
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	C₂²×C₂²⋊C₄	#120	1	2	yes	—
329	C₂²×C₂²⋊C₄	#120	1	2	yes	—
330	#390	C₂×C₂²⋊C₄	1	2	yes	—
331	#390	C₂×C₂²⋊C₄	1	2	yes	—
332	#390	C₂×C₂²⋊C₄	1	2	yes	—
333	#390	C₂×C₂²⋊C₄	1	2	yes	—
334	#390	#120	1	2	yes	—
335	#390	#120	1	2	yes	—
336	#390	#120	1	2	yes	—
337	#390	#120	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	C₂×C₂²⋊C₄	1	2	yes	—
345	#386	C₂×C₂²⋊C₄	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	#386	#120	1	2	yes	—
353	#386	#120	1	2	yes	—
354	#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
355	#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
356	#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
357	#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
358	#379	#120	1	2	yes	—
359	#379	#120	1	2	yes	—
360	#379	#120	1	2	yes	—
361	#379	#120	1	2	yes	—
362	#379	#120	1	2	yes	—
363	#379	#120	1	2	yes	—
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	1	yes	characteristic
373	C₂⁵	#379	1	1	yes	characteristic
374	C₂⁵	#379	1	2	yes	—
375	C₂⁵	#379	1	1	yes	characteristic
376	C₂⁵	#379	1	1	yes	characteristic
377	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
378	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
379	C₂⁵	C₂×#120	1	2	yes	—
380	C₂⁵	C₂×#120	1	1	yes	characteristic
381	C₂⁵	C₂×#120	1	1	yes	characteristic
382	C₂⁵	C₂×#120	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
404	C₂³×C₄	#379	1	1	yes	characteristic
405	C₂³×C₄	#379	1	2	yes	—
406	C₂³×C₄	#379	1	2	yes	—
407	C₂³×C₄	#379	1	1	yes	characteristic
408	C₂³×C₄	#379	1	1	yes	characteristic
409	C₂³×C₄	B(4,𝔽₂)	1	2	yes	—
410	C₂³×C₄	#458	1	2	yes	—
411	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
412	C₂³×C₄	C₂×#120	1	1	yes	characteristic
413	C₂³×C₄	C₂×#120	1	2	yes	—
414	C₂³×C₄	C₂×#120	1	2	yes	—
415	C₂×C₄⋊C₄	#379	1	2	yes	—
416	C₂×C₄⋊C₄	#379	1	2	yes	—
417	C₂×C₂²⋊C₄	#379	1	2	yes	—
418	C₂×C₂²⋊C₄	#379	1	2	yes	—
419	C₂×C₂²⋊C₄	#379	1	2	yes	—
420	C₂×C₂²⋊C₄	#379	1	2	yes	—
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	C₂×#379	1	1	yes	characteristic
430	C₂⁴	C₂×#379	1	1	yes	characteristic
431	C₂⁴	C₂×#379	1	2	yes	—
432	C₂⁴	C₂×#379	1	1	yes	characteristic
433	C₂⁴	#2846	1	1	yes	characteristic
434	C₂⁴	#2846	1	2	yes	—
435	C₂⁴	#2846	1	1	yes	characteristic
436	C₂⁴	#2846	1	1	yes	characteristic
437	C₂⁴	#2846	1	1	yes	characteristic
438	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
439	C₂⁴	C₂×#458	1	1	yes	characteristic
440	C₂⁴	#3026	1	1	yes	characteristic
441	C₂⁴	#3026	1	1	yes	characteristic
442	C₂²×C₄	#1790	1	2	yes	—
443	C₂²×C₄	#1790	1	2	yes	—
444	C₂²×C₄	C₂×#379	1	2	yes	—
445	C₂²×C₄	#2846	1	2	yes	—
446	C₂³	#14679	1	1	yes	characteristic
447	C₂³	C₂×#1790	1	1	yes	characteristic
448	C₂³	#20609	1	1	yes	characteristic
449	C₂³	#32898	1	1	yes	characteristic
450	C₂³	#32898	1	1	yes	characteristic
451	C₂³	#32900	1	1	yes	characteristic
452	C₂³	#32900	1	1	yes	characteristic
453	C₂²	#392125	1	1	yes	characteristic
454	C₂²	#392135	1	2	yes	—
455	C₂²	#511790	1	2	yes	—
456	C₂	#72218475	1	1	yes	characteristic
457	C₂	#72238343	1	1	yes	characteristic
458	C₂	#72251662	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#392125
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72249434	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. #72262281	C₂	semidirect
2. #72262280	C₂	semidirect
3. #72262272	C₂	semidirect
4. #72262269	C₂	semidirect
5. #72251570	C₂	semidirect
7. #72236898	C₂	semidirect
8. #72236837	C₂	semidirect
9. #72235932	C₂	semidirect
10. #72235848	C₂	semidirect
11. #72226038	C₂	semidirect
12. #8934496	C₄	semidirect
13. #8934400	C₄	semidirect
14. #8934400	C₄	semidirect
15. #8934377	C₄	semidirect
16. #8899018	C₄	semidirect
17. #8898095	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. #379754	C₂²	semidirect
33. #379754	C₂²	semidirect
34. #201690	C₂²	semidirect
35. #201687	C₂²	semidirect
36. C₂×#9497	C₂²	semidirect
37. C₂×#9497	C₂²	semidirect
38. #201322	C₂²	semidirect
39. C₂×#8547	C₂²	semidirect
40. C₂×#8541	C₂²	semidirect
116. C₂×H(3,𝔽₄)	C₂²⋊C₄	semidirect
117. C₂×#560	C₂²⋊C₄	semidirect
118. C₂×#551	C₂²⋊C₄	semidirect
119. C₂×D₄²	C₂²⋊C₄	semidirect
120. C₂×#543	C₂²⋊C₄	semidirect
121. C₂×#543	C₂²⋊C₄	semidirect
122. C₂×#538	C₂²⋊C₄	semidirect
125. C₂×#534	C₂²⋊C₄	semidirect
126. C₂×#534	C₂²⋊C₄	semidirect
130. C₂²×#120	C₂²⋊C₄	semidirect
131. C₂²×#120	C₂²⋊C₄	semidirect
143. C₂×#518	C₂²⋊C₄	semidirect
147. #2804	C₂²⋊C₄	semidirect
148. #2748	C₂²⋊C₄	semidirect
149. #2748	C₂²⋊C₄	semidirect
150. #2717	C₂²⋊C₄	semidirect
151. #2709	C₂²⋊C₄	semidirect
152. #2697	C₂²⋊C₄	semidirect
153. #2697	C₂²⋊C₄	semidirect
154. #2684	C₂²⋊C₄	semidirect
155. #2684	C₂²⋊C₄	semidirect
156. #2684	C₂²⋊C₄	semidirect
157. #2683	C₂²⋊C₄	semidirect
158. #2679	C₂²⋊C₄	semidirect
159. #2679	C₂²⋊C₄	semidirect
160. #2669	C₂²⋊C₄	semidirect
161. #2669	C₂²⋊C₄	semidirect
162. #2669	C₂²⋊C₄	semidirect
163. #2561	C₂²⋊C₄	semidirect
164. #2561	C₂²⋊C₄	semidirect
165. #2539	C₂²⋊C₄	semidirect
166. #2539	C₂²⋊C₄	semidirect
203. #2380	C₂²⋊C₄	semidirect
204. #2379	C₂²⋊C₄	semidirect
205. #2376	C₂²⋊C₄	semidirect
206. #2375	C₂²⋊C₄	semidirect
207. #2375	C₂²⋊C₄	semidirect
208. #2375	C₂²⋊C₄	semidirect
209. #2374	C₂²⋊C₄	semidirect
210. #2372	C₂²⋊C₄	semidirect
211. #2366	C₂²⋊C₄	semidirect
212. #2358	C₂²⋊C₄	semidirect
213. #2358	C₂²⋊C₄	semidirect
214. #2358	C₂²⋊C₄	semidirect
215. #2315	C₂²⋊C₄	semidirect
216. #2312	C₂²⋊C₄	semidirect
228. C₂×#379	C₂²⋊C₄	semidirect
229. C₂×#379	C₂²⋊C₄	semidirect
233. #2273	C₂²⋊C₄	semidirect
234. #2273	C₂²⋊C₄	semidirect
235. #2273	C₂²⋊C₄	semidirect
236. #2273	C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72262281	2
#72262280	2
#72262272	2
#72262269	2
#72251570	2
#72249434	2
#72236898	2
#72236837	2
#72235932	2
#72235848	2
#72226038	2