Subgroups — #72240176

Order 2048.

At least 12340 conjugacy classes of subgroups; only the 772 normal subgroups are shown.

The subgroup lattice has 465 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72240175	C₂	1	2	yes	maximal, complemented
2	#72240171	C₂	1	2	yes	maximal, complemented
3	#72240170	C₂	1	2	yes	maximal, complemented
4	#72240169	C₂	1	2	yes	maximal, complemented
5	#72240151	C₂	1	1	yes	maximal, characteristic, complemented
6	#72240134	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240132	C₂	1	1	yes	maximal, characteristic, complemented
8	#72236483	C₂	1	1	yes	maximal, characteristic, complemented
9	#72233581	C₂	1	1	yes	maximal, characteristic, complemented
10	#72233364	C₂	1	2	yes	maximal, complemented
11	#72233093	C₂	1	2	yes	maximal, complemented
12	#72233037	C₂	1	2	yes	maximal, complemented
13	#72231950	C₂	1	1	yes	maximal, characteristic, complemented
14	#72227862	C₂	1	2	yes	maximal, complemented
15	#72225994	C₂	1	1	yes	maximal, characteristic, complemented
16	#72213719	C₂	1	2	yes	maximal, complemented
17	#72213293	C₂	1	2	yes	maximal, complemented
18	#72210587	C₂	1	2	yes	maximal, complemented
19	#72210575	C₂	1	2	yes	maximal, complemented
20	C₂×#62817	C₂²	1	1	yes	characteristic, complemented
21	C₂×#52004	C₂²	1	1	yes	characteristic, complemented
22	C₂×#34980	C₂²	1	1	yes	characteristic
23	#6508692	C₂²	1	2	yes	complemented
24	#6500010	C₂²	1	2	yes	—
25	#6500010	C₂²	1	2	yes	complemented
26	#6499867	C₂²	1	2	yes	—
27	#6470225	C₂²	1	2	yes	—
28	#6470225	C₂²	1	2	yes	complemented
29	#6470225	C₂²	1	2	yes	complemented
30	#6437445	C₂²	1	2	yes	complemented
31	C₂×#21746	C₂²	1	1	yes	characteristic, complemented
32	#5021162	C₂²	1	1	yes	characteristic, complemented
33	#4941255	C₂²	1	1	yes	characteristic, complemented
34	#4867137	C₂²	1	1	yes	characteristic, complemented
35	#4607564	C₂²	1	1	yes	characteristic, complemented
36	#4312024	C₂²	1	1	yes	characteristic, complemented
37	#2924619	C₂²	1	1	yes	characteristic, complemented
38	#2039305	C₂²	1	1	yes	characteristic, complemented
39	#2032505	C₂²	1	1	yes	characteristic, complemented
40	#1418393	C₂²	1	1	yes	characteristic, complemented
41	#647656	C₂²	1	1	yes	characteristic, complemented
42	#616961	C₂²	1	1	yes	characteristic
43	#616960	C₂²	1	1	yes	characteristic
44	#604823	C₂²	1	1	yes	characteristic, complemented
45	#512119	C₂²	1	4	yes	complemented
46	#511771	C₂²	1	4	yes	complemented
47	#508087	C₂²	1	4	yes	complemented
48	#508087	C₂²	1	4	yes	complemented
49	#496225	C₂²	1	2	yes	complemented
50	#496225	C₂²	1	2	yes	complemented
51	#496225	C₂²	1	2	yes	complemented
52	#493370	C₂²	1	2	yes	complemented
53	#347048	C₂²	1	2	yes	complemented
54	#347048	C₂²	1	2	yes	complemented
55	#347042	C₂²	1	2	yes	—
56	#347042	C₂²	1	2	yes	complemented
57	#346456	C₂²	1	2	yes	complemented
58	#346456	C₂²	1	2	yes	complemented
59	#346446	C₂²	1	2	yes	—
60	#346446	C₂²	1	2	yes	complemented
61	C₂×#8547	C₂²	1	1	yes	characteristic, complemented
62	C₂×#8541	C₂²	1	1	yes	characteristic, complemented
63	#187928	C₂²	1	2	yes	complemented
64	#186835	C₂²	1	2	yes	complemented
65	#144421	C₂²	1	4	yes	complemented
66	#144415	C₂²	1	4	yes	complemented
67	#144414	C₂²	1	4	yes	complemented
68	#144412	C₂²	1	4	yes	complemented
69	#144412	C₂²	1	4	yes	complemented
70	#144388	C₂²	1	4	yes	complemented
71	#144386	C₂²	1	4	yes	complemented
72	#144366	C₂²	1	4	yes	complemented
73	#139828	C₂²	1	2	yes	complemented
74	#139828	C₂²	1	2	yes	complemented
75	#139816	C₂²	1	4	yes	complemented
76	#139773	C₂²	1	4	yes	complemented
77	#139764	C₂²	1	4	yes	complemented
78	#139720	C₂²	1	2	yes	complemented
79	#139720	C₂²	1	2	yes	complemented
80	#139718	C₂²	1	2	yes	complemented
81	#139718	C₂²	1	2	yes	complemented
82	#139716	C₂²	1	2	yes	complemented
83	#139716	C₂²	1	2	yes	complemented
84	#139700	C₂²	1	4	yes	complemented
85	#133925	C₂²	1	2	yes	complemented
86	#133893	C₂²	1	2	yes	complemented
87	#133893	C₂²	1	2	yes	complemented
88	#133822	C₂²	1	2	yes	complemented
89	#128073	C₂²	1	2	yes	complemented
90	#128009	C₂²	1	2	yes	complemented
91	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
92	#62817	C₂³	1	2	yes	—
93	#62817	C₂³	1	2	yes	—
94	C₂×#3484	C₂³	1	2	yes	—
95	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
96	C₂²×#535	C₂³	1	1	yes	characteristic
97	C₂²×#534	D₄	1	1	yes	characteristic, complemented
98	C₂³×#120	C₂³	1	1	yes	characteristic
99	C₂×#2684	C₂³	1	1	yes	characteristic, complemented
100	C₂×#2684	C₂³	1	1	yes	characteristic, complemented
101	C₂×#2849	D₄	1	1	yes	characteristic, complemented
102	C₂×#2849	C₂³	1	1	yes	characteristic
103	C₂×#2846	D₄	1	1	yes	characteristic, complemented
104	C₂×#2846	C₂³	1	1	yes	characteristic
105	C₂×#2404	D₄	1	1	yes	characteristic, complemented
106	C₂×#2404	D₄	1	1	yes	characteristic, complemented
107	C₂×#2405	D₄	1	1	yes	characteristic, complemented
108	C₂×#2405	D₄	1	1	yes	characteristic, complemented
109	C₂×#2410	D₄	1	1	yes	characteristic, complemented
110	C₂×#2410	D₄	1	1	yes	characteristic, complemented
111	C₂×#2410	C₂³	1	1	yes	characteristic
112	C₂×#2410	C₂³	1	1	yes	characteristic
113	C₂×#2403	D₄	1	1	yes	characteristic, complemented
114	C₂×#2403	C₂³	1	1	yes	characteristic
115	C₂×#2403	C₂³	1	1	yes	characteristic
116	C₂×#2403	C₂³	1	1	yes	characteristic
117	C₂×#2380	C₂³	1	1	yes	characteristic, complemented
118	C₂²×#379	D₄	1	1	yes	characteristic, complemented
119	#33020	D₄	1	4	yes	complemented
120	#32898	D₄	1	4	yes	complemented
121	#24404	D₄	1	8	yes	complemented
122	#24056	C₂³	1	4	yes	—
123	#24056	C₂³	1	4	yes	—
124	#24056	C₂³	1	4	yes	—
125	#23907	C₂³	1	4	yes	—
126	#23906	C₂³	1	4	yes	—
127	#23900	C₂³	1	4	yes	—
128	#23900	C₂³	1	4	yes	—
129	#23900	C₂³	1	4	yes	—
130	#21746	C₂³	1	2	yes	—
131	#21746	C₂³	1	2	yes	—
132	C₂×#1783	C₂³	1	2	yes	—
133	C₂×#1781	C₂³	1	2	yes	—
134	C₂×#1781	C₂³	1	2	yes	—
135	#16014	C₂³	1	1	yes	characteristic, complemented
136	#15948	D₄	1	1	yes	characteristic, complemented
137	#15948	D₄	1	1	yes	characteristic, complemented
138	#15948	C₂³	1	1	yes	characteristic
139	#15948	C₂³	1	1	yes	characteristic
140	#15947	D₄	1	1	yes	characteristic, complemented
141	#15947	D₄	1	1	yes	characteristic, complemented
142	#15947	C₂³	1	1	yes	characteristic
143	#15947	C₂³	1	1	yes	characteristic
144	#15947	C₂³	1	1	yes	characteristic, complemented
145	#15784	C₂³	1	1	yes	characteristic, complemented
146	#15313	C₂³	1	1	yes	characteristic, complemented
147	#15266	C₂³	1	1	yes	characteristic, complemented
148	#15266	C₂³	1	1	yes	characteristic, complemented
149	#15259	D₄	1	1	yes	characteristic, complemented
150	#15259	D₄	1	1	yes	characteristic, complemented
151	#15259	C₂³	1	1	yes	characteristic
152	#15259	C₂³	1	1	yes	characteristic
153	#15259	C₂³	1	1	yes	characteristic, complemented
154	#15258	D₄	1	1	yes	characteristic, complemented
155	#15258	D₄	1	1	yes	characteristic, complemented
156	#15258	C₂³	1	1	yes	characteristic
157	#15258	C₂³	1	1	yes	characteristic
158	#15258	C₂³	1	1	yes	characteristic, complemented
159	#14666	C₂³	1	1	yes	characteristic, complemented
160	#14516	C₂³	1	1	yes	characteristic, complemented
161	#14358	C₂³	1	1	yes	characteristic, complemented
162	#14335	D₄	1	1	yes	characteristic, complemented
163	#14335	C₂³	1	1	yes	characteristic
164	#14134	C₂³	1	1	yes	characteristic, complemented
165	#13868	D₄	1	1	yes	characteristic, complemented
166	#13868	D₄	1	1	yes	characteristic, complemented
167	#13867	D₄	1	1	yes	characteristic, complemented
168	#13867	C₂³	1	1	yes	characteristic
169	#12852	C₂³	1	4	yes	complemented
170	#12852	C₂³	1	4	yes	complemented
171	#12852	C₂³	1	4	yes	complemented
172	#12694	C₂³	1	4	yes	complemented
173	#12693	C₂³	1	4	yes	complemented
174	#12687	C₂³	1	4	yes	complemented
175	#12687	C₂³	1	4	yes	complemented
176	#12687	C₂³	1	4	yes	complemented
177	#8547	C₂³	1	2	yes	—
178	#8547	C₂³	1	2	yes	—
179	#8541	C₂³	1	2	yes	—
180	#8541	C₂³	1	2	yes	—
181	#8534	C₂³	1	4	yes	—
182	#8534	C₂³	1	4	yes	—
183	#8453	C₂³	1	4	yes	—
184	#8453	C₂³	1	4	yes	—
185	#7307	C₂³	1	4	yes	complemented
186	#7307	C₂³	1	4	yes	complemented
187	#7304	C₂³	1	4	yes	complemented
188	#7304	C₂³	1	4	yes	complemented
189	C₂⁷	C₂×D₄	1	1	yes	characteristic
190	C₂⁷	C₂×D₄	1	1	yes	characteristic
191	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	complemented
192	C₂³×#41	C₂×D₄	1	1	yes	characteristic, complemented
193	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
194	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
195	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
196	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
197	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
198	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
199	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic, complemented
200	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
201	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
202	#3484	C₂×D₄	1	4	yes	complemented
203	#3484	C₂⁴	1	4	yes	—
204	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
205	C₂²×#127	C₂⁴	1	1	yes	characteristic
206	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
207	C₂²×#124	C₂⁴	1	1	yes	characteristic
208	C₂²×#123	C₂×D₄	1	1	yes	characteristic
209	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂²×#120	C₂×D₄	1	1	yes	characteristic
211	C₂²×#120	C₂×D₄	1	1	yes	characteristic
212	C₂²×#120	C₂×D₄	1	1	yes	characteristic
213	C₂²×#120	C₂×D₄	1	1	yes	characteristic
214	C₂²×#120	C₂×D₄	1	1	yes	characteristic
215	C₂²×#120	C₂×D₄	1	1	yes	characteristic
216	C₂²×#120	C₂×D₄	1	1	yes	characteristic
217	C₂²×#120	C₂×D₄	1	1	yes	characteristic
218	C₂²×#120	C₂×D₄	1	1	yes	characteristic
219	C₂²×#120	C₂×D₄	1	1	yes	characteristic
220	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
221	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
222	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
223	C₂²×#120	C₂⁴	1	1	yes	characteristic
224	C₂²×#120	C₂⁴	1	1	yes	characteristic
225	C₂²×#120	C₂⁴	1	1	yes	characteristic
226	C₂²×#120	C₂⁴	1	1	yes	characteristic
227	C₂²×#120	C₂⁴	1	1	yes	characteristic
228	C₂×#518	C₂×D₄	1	2	yes	complemented
229	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
230	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
231	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
232	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
233	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
235	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	—
237	C₂²×#99	C₂×D₄	1	4	yes	complemented
238	#2403	C₂×D₄	1	4	yes	—
239	#2403	C₂×D₄	1	4	yes	—
240	C₂×#393	C₂×D₄	1	1	yes	characteristic
241	C₂×#393	C₂×D₄	1	1	yes	characteristic
242	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
243	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
244	C₂×#392	C₂×D₄	1	1	yes	characteristic
245	C₂×#392	C₂×D₄	1	1	yes	characteristic
246	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
247	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
248	C₂×#386	C₂×D₄	1	1	yes	characteristic
249	C₂×#386	C₂×D₄	1	1	yes	characteristic
250	C₂×#386	C₂×D₄	1	1	yes	characteristic
251	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
252	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
253	C₂×#386	C₂⁴	1	1	yes	characteristic
254	C₂×#386	C₂⁴	1	1	yes	characteristic
255	C₂×#386	C₂⁴	1	1	yes	characteristic
256	C₂×#385	C₂×D₄	1	1	yes	characteristic
257	C₂×#385	C₂×D₄	1	1	yes	characteristic
258	C₂×#385	C₂×D₄	1	1	yes	characteristic
259	C₂×#385	C₂×D₄	1	1	yes	characteristic
260	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
261	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
262	C₂×#379	C₂×D₄	1	1	yes	characteristic
263	C₂×#379	C₂×D₄	1	1	yes	characteristic
264	C₂×#379	C₂×D₄	1	1	yes	characteristic
265	C₂×#379	C₂×D₄	1	1	yes	characteristic
266	C₂×#379	C₂×D₄	1	1	yes	characteristic
267	C₂×#379	C₂×D₄	1	1	yes	characteristic
268	C₂×#379	C₂×D₄	1	1	yes	characteristic
269	C₂×#379	C₂×D₄	1	1	yes	characteristic
270	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
271	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
272	#1889	C₂×D₄	1	8	yes	—
273	#1867	C₂×D₄	1	8	yes	complemented
274	#1790	C₂×D₄	1	8	yes	complemented
275	#1783	C₂⁴	1	4	yes	—
276	#1781	C₂×D₄	1	4	yes	complemented
277	#1781	C₂⁴	1	4	yes	—
278	#1781	C₂⁴	1	4	yes	—
279	#1438	C₂×D₄	1	1	yes	characteristic
280	#1438	C₂×D₄	1	1	yes	characteristic
281	#1438	C₂×D₄	1	1	yes	characteristic
282	#1438	C₂×D₄	1	1	yes	characteristic
283	#1438	C₂×D₄	1	1	yes	characteristic, complemented
284	#1438	C₂×D₄	1	1	yes	characteristic, complemented
285	#1438	C₂×D₄	1	1	yes	characteristic, complemented
286	#1438	C₂×D₄	1	1	yes	characteristic, complemented
287	#1438	C₂×D₄	1	1	yes	characteristic, complemented
288	#1438	C₂×D₄	1	1	yes	characteristic, complemented
289	#1438	C₂×D₄	1	1	yes	characteristic, complemented
290	#1438	C₂×D₄	1	1	yes	characteristic, complemented
291	#1438	C₂⁴	1	1	yes	characteristic
292	#1438	C₂⁴	1	1	yes	characteristic
293	#1438	C₂⁴	1	1	yes	characteristic
294	#1438	C₂⁴	1	1	yes	characteristic
295	#1437	C₂×D₄	1	1	yes	characteristic
296	#1437	C₂×D₄	1	1	yes	characteristic
297	#1437	C₂×D₄	1	1	yes	characteristic
298	#1437	C₂×D₄	1	1	yes	characteristic
299	#1437	C₂×D₄	1	1	yes	characteristic, complemented
300	#1437	C₂×D₄	1	1	yes	characteristic, complemented
301	#1437	C₂×D₄	1	1	yes	characteristic, complemented
302	#1437	C₂×D₄	1	1	yes	characteristic, complemented
303	C₂⁶	#120	1	1	yes	characteristic
304	C₂⁶	#120	1	1	yes	characteristic
305	C₂⁶	#120	1	1	yes	characteristic
306	C₂⁶	#120	1	1	yes	characteristic
307	C₂⁶	C₂²×D₄	1	1	yes	characteristic
308	C₂⁶	C₂²×D₄	1	1	yes	characteristic
309	C₂⁶	C₂²×D₄	1	1	yes	characteristic
310	C₂⁶	C₂²×D₄	1	1	yes	characteristic
311	C₂⁶	C₂²×D₄	1	1	yes	characteristic
312	C₂⁶	C₂²×D₄	1	1	yes	characteristic
313	C₂⁶	C₂²×D₄	1	1	yes	characteristic
314	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
315	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
316	C₂³×D₄	#120	1	1	yes	characteristic
317	C₂³×D₄	#120	1	1	yes	characteristic
318	C₂³×D₄	#120	1	1	yes	characteristic
319	C₂³×D₄	#120	1	1	yes	characteristic
320	C₂³×D₄	#120	1	2	yes	—
321	C₂³×D₄	#120	1	2	yes	—
322	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
323	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
324	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
325	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
326	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
327	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
328	C₂³×D₄	C₂²×D₄	1	2	yes	—
329	C₂³×D₄	C₂²×D₄	1	2	yes	—
330	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
331	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
332	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
333	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
334	C₂³×D₄	C₂⁵	1	1	yes	characteristic
335	C₂⁴×C₄	#120	1	1	yes	characteristic
336	C₂⁴×C₄	#120	1	1	yes	characteristic
337	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
341	C₂×#120	#120	1	4	yes	—
342	C₂×#120	C₂²×D₄	1	4	yes	—
343	#518	C₂²×D₄	1	4	yes	—
344	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
350	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
351	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
352	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
353	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
354	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
355	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
356	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
357	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
358	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
359	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
360	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
361	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
362	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
363	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
364	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
365	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
366	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
367	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
368	C₂×#99	C₂²×D₄	1	8	yes	—
369	#386	#120	1	4	yes	—
370	#386	C₂²×D₄	1	4	yes	—
371	#379	#120	1	2	yes	—
372	#379	#120	1	2	yes	—
373	C₂×#95	C₂²×D₄	1	1	yes	characteristic
374	C₂×#95	C₂²×D₄	1	1	yes	characteristic
375	C₂×#95	C₂²×D₄	1	1	yes	characteristic
376	C₂×#95	C₂²×D₄	1	1	yes	characteristic
377	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
378	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
379	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
380	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
381	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
382	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
383	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
384	C₂⁵	B(4,𝔽₂)	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	C₂⁵	C₂×#120	1	1	yes	characteristic
389	C₂⁵	C₂×#120	1	1	yes	characteristic
390	C₂⁵	C₂×#120	1	2	yes	—
391	C₂⁵	C₂×#120	1	1	yes	characteristic
392	C₂⁵	C₂×#120	1	1	yes	characteristic
393	C₂⁵	C₂×#120	1	1	yes	characteristic
394	C₂⁵	C₂×#120	1	1	yes	characteristic
395	C₂⁵	#534	1	1	yes	characteristic
396	C₂⁵	#534	1	1	yes	characteristic
397	C₂⁵	D₄²	1	2	yes	—
398	C₂⁵	D₄²	1	2	yes	—
399	C₂⁵	C₂³×D₄	1	1	yes	characteristic
400	C₂⁵	C₂³×D₄	1	1	yes	characteristic
401	C₂²×D₄	C₂×#120	1	2	yes	—
402	C₂²×D₄	#534	1	2	yes	—
403	C₂²×D₄	D₄²	1	2	yes	—
404	C₂²×D₄	D₄²	1	2	yes	—
405	C₂²×D₄	D₄²	1	2	yes	—
406	C₂²×D₄	D₄²	1	2	yes	—
407	C₂²×D₄	C₂³×D₄	1	2	yes	—
408	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
409	C₂³×C₄	C₂×#120	1	1	yes	characteristic
410	C₂³×C₄	C₂×#120	1	1	yes	characteristic
411	C₂³×C₄	C₂×#120	1	1	yes	characteristic
412	C₂³×C₄	C₂×#120	1	1	yes	characteristic
413	C₂³×C₄	C₂×#120	1	1	yes	characteristic
414	C₂³×C₄	C₂×#120	1	2	yes	—
415	C₂³×C₄	D₄²	1	2	yes	—
416	C₂³×C₄	D₄²	1	2	yes	—
417	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
418	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
420	C₂⁴	#2403	1	1	yes	characteristic
421	C₂⁴	#2403	1	1	yes	characteristic
422	C₂⁴	#2403	1	2	yes	—
423	C₂⁴	#2403	1	1	yes	characteristic
424	C₂⁴	#2403	1	1	yes	characteristic
425	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
426	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
427	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
428	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
429	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
430	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
431	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
432	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
433	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
434	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
435	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
436	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
437	C₂⁴	C₂²×#120	1	1	yes	characteristic
438	C₂⁴	C₂²×#120	1	1	yes	characteristic
439	C₂⁴	C₂×#534	1	1	yes	characteristic
440	C₂⁴	C₂×D₄²	1	2	yes	—
441	C₂²×C₄	#2403	1	2	yes	—
442	C₂²×C₄	C₂×D₄²	1	2	yes	—
443	C₂³	#23900	1	1	yes	characteristic
444	C₂³	#23900	1	1	yes	characteristic
445	C₂³	#23900	1	1	yes	characteristic
446	C₂³	#23900	1	1	yes	characteristic
447	C₂³	#33551	1	2	yes	—
448	C₂³	#33551	1	2	yes	—
449	C₂³	#33551	1	2	yes	—
450	C₂³	C₂×#2403	1	1	yes	characteristic
451	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
452	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
453	C₂³	#60399	1	2	yes	—
454	C₂²	C₂×#23900	1	1	yes	characteristic
455	C₂²	#6437629	1	1	yes	characteristic
456	C₂²	#6437632	1	1	yes	characteristic
457	C₂²	C₂×#33551	1	1	yes	characteristic
458	C₂²	C₂×#33551	1	1	yes	characteristic
459	C₂²	C₂×#33551	1	1	yes	characteristic
460	C₂²	#7622875	1	1	yes	characteristic
461	C₂	#72218077	1	1	yes	characteristic
462	C₂	#72233116	1	1	yes	characteristic
463	C₂	#72237496	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23900
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72240175	C₂	semidirect
2. #72240171	C₂	semidirect
3. #72240170	C₂	semidirect
4. #72240169	C₂	semidirect
5. #72240151	C₂	semidirect
6. #72240134	C₂	semidirect
7. #72240132	C₂	semidirect
8. #72236483	C₂	semidirect
9. #72233581	C₂	semidirect
10. #72233364	C₂	semidirect
11. #72233093	C₂	semidirect
12. #72233037	C₂	semidirect
13. #72231950	C₂	semidirect
14. #72227862	C₂	semidirect
15. #72225994	C₂	semidirect
16. #72213719	C₂	semidirect
17. #72213293	C₂	semidirect
18. #72210587	C₂	semidirect
19. #72210575	C₂	semidirect
20. C₂×#62817	C₂²	semidirect
21. C₂×#52004	C₂²	semidirect
23. #6508692	C₂²	semidirect
25. #6500010	C₂²	semidirect
28. #6470225	C₂²	semidirect
29. #6470225	C₂²	semidirect
30. #6437445	C₂²	semidirect
31. C₂×#21746	C₂²	semidirect
32. #5021162	C₂²	semidirect
33. #4941255	C₂²	semidirect
34. #4867137	C₂²	semidirect
35. #4607564	C₂²	semidirect
36. #4312024	C₂²	semidirect
37. #2924619	C₂²	semidirect
38. #2039305	C₂²	semidirect
39. #2032505	C₂²	semidirect
40. #1418393	C₂²	semidirect
41. #647656	C₂²	semidirect
44. #604823	C₂²	semidirect
45. #512119	C₂²	semidirect
46. #511771	C₂²	semidirect
47. #508087	C₂²	semidirect
48. #508087	C₂²	semidirect
49. #496225	C₂²	semidirect
50. #496225	C₂²	semidirect
51. #496225	C₂²	semidirect
52. #493370	C₂²	semidirect
53. #347048	C₂²	semidirect
54. #347048	C₂²	semidirect
56. #347042	C₂²	semidirect
57. #346456	C₂²	semidirect
58. #346456	C₂²	semidirect
60. #346446	C₂²	semidirect
61. C₂×#8547	C₂²	semidirect
62. C₂×#8541	C₂²	semidirect
63. #187928	C₂²	semidirect
64. #186835	C₂²	semidirect
65. #144421	C₂²	semidirect
66. #144415	C₂²	semidirect
67. #144414	C₂²	semidirect
68. #144412	C₂²	semidirect
69. #144412	C₂²	semidirect
70. #144388	C₂²	semidirect
71. #144386	C₂²	semidirect
72. #144366	C₂²	semidirect
73. #139828	C₂²	semidirect
74. #139828	C₂²	semidirect
75. #139816	C₂²	semidirect
76. #139773	C₂²	semidirect
77. #139764	C₂²	semidirect
78. #139720	C₂²	semidirect
79. #139720	C₂²	semidirect
80. #139718	C₂²	semidirect
81. #139718	C₂²	semidirect
82. #139716	C₂²	semidirect
83. #139716	C₂²	semidirect
84. #139700	C₂²	semidirect
85. #133925	C₂²	semidirect
86. #133893	C₂²	semidirect
87. #133893	C₂²	semidirect
88. #133822	C₂²	semidirect
89. #128073	C₂²	semidirect
90. #128009	C₂²	semidirect
91. C₂⁵×D₄	D₄	semidirect
95. C₂²×D₄²	C₂³	semidirect
97. C₂²×#534	D₄	semidirect
99. C₂×#2684	C₂³	semidirect
100. C₂×#2684	C₂³	semidirect
101. C₂×#2849	D₄	semidirect
103. C₂×#2846	D₄	semidirect
105. C₂×#2404	D₄	semidirect
106. C₂×#2404	D₄	semidirect
107. C₂×#2405	D₄	semidirect
108. C₂×#2405	D₄	semidirect
109. C₂×#2410	D₄	semidirect
110. C₂×#2410	D₄	semidirect
113. C₂×#2403	D₄	semidirect
117. C₂×#2380	C₂³	semidirect
118. C₂²×#379	D₄	semidirect
119. #33020	D₄	semidirect
120. #32898	D₄	semidirect
121. #24404	D₄	semidirect
135. #16014	C₂³	semidirect
136. #15948	D₄	semidirect
137. #15948	D₄	semidirect
140. #15947	D₄	semidirect
141. #15947	D₄	semidirect
144. #15947	C₂³	semidirect
145. #15784	C₂³	semidirect
146. #15313	C₂³	semidirect
147. #15266	C₂³	semidirect
148. #15266	C₂³	semidirect
149. #15259	D₄	semidirect
150. #15259	D₄	semidirect
153. #15259	C₂³	semidirect
154. #15258	D₄	semidirect
155. #15258	D₄	semidirect
158. #15258	C₂³	semidirect
159. #14666	C₂³	semidirect
160. #14516	C₂³	semidirect
161. #14358	C₂³	semidirect
162. #14335	D₄	semidirect
164. #14134	C₂³	semidirect
165. #13868	D₄	semidirect
166. #13868	D₄	semidirect
167. #13867	D₄	semidirect
169. #12852	C₂³	semidirect
170. #12852	C₂³	semidirect
171. #12852	C₂³	semidirect
172. #12694	C₂³	semidirect
173. #12693	C₂³	semidirect
174. #12687	C₂³	semidirect
175. #12687	C₂³	semidirect
176. #12687	C₂³	semidirect
185. #7307	C₂³	semidirect
186. #7307	C₂³	semidirect
187. #7304	C₂³	semidirect
188. #7304	C₂³	semidirect
191. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
192. C₂³×#41	C₂×D₄	semidirect
199. C₂⁴×D₄	C₂×D₄	semidirect
202. #3484	C₂×D₄	semidirect
204. C₂²×#127	C₂×D₄	semidirect
206. C₂²×#124	C₂×D₄	semidirect
209. C₂²×#123	C₂×D₄	semidirect
220. C₂²×#120	C₂×D₄	semidirect
221. C₂²×#120	C₂×D₄	semidirect
222. C₂²×#120	C₂×D₄	semidirect
228. C₂×#518	C₂×D₄	semidirect
229. C₂²×#117	C₂×D₄	semidirect
235. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
237. C₂²×#99	C₂×D₄	semidirect
242. C₂×#393	C₂×D₄	semidirect
243. C₂×#393	C₂×D₄	semidirect
246. C₂×#392	C₂×D₄	semidirect
247. C₂×#392	C₂×D₄	semidirect
251. C₂×#386	C₂×D₄	semidirect
252. C₂×#386	C₂×D₄	semidirect
260. C₂×#381	C₂×D₄	semidirect
261. C₂×#381	C₂×D₄	semidirect
270. C₂×#379	C₂×D₄	semidirect
271. C₂×#379	C₂×D₄	semidirect
273. #1867	C₂×D₄	semidirect
274. #1790	C₂×D₄	semidirect
276. #1781	C₂×D₄	semidirect
283. #1438	C₂×D₄	semidirect
284. #1438	C₂×D₄	semidirect
285. #1438	C₂×D₄	semidirect
286. #1438	C₂×D₄	semidirect
287. #1438	C₂×D₄	semidirect
288. #1438	C₂×D₄	semidirect
289. #1438	C₂×D₄	semidirect
290. #1438	C₂×D₄	semidirect
299. #1437	C₂×D₄	semidirect
300. #1437	C₂×D₄	semidirect
301. #1437	C₂×D₄	semidirect
302. #1437	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72240175	2
#72240171	2
#72240170	2
#72240169	2
#72240151	2
#72240134	2
#72240132	2
#72236483	2
#72233581	2
#72233364	2
#72233093	2
#72233037	2
#72231950	2
#72227862	2
#72225994	2
#72213719	2
#72213293	2
#72210587	2
#72210575	2