Subgroups — #72240145

Order 2048.

At least 10273 conjugacy classes of subgroups; only the 668 normal subgroups are shown.

The subgroup lattice has 441 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72240144	C₂	1	2	yes	maximal, complemented
2	#72240143	C₂	1	2	yes	maximal, complemented
3	#72240141	C₂	1	2	yes	maximal, complemented
4	#72240139	C₂	1	2	yes	maximal, complemented
5	#72240138	C₂	1	2	yes	maximal, complemented
6	#72240134	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240132	C₂	1	1	yes	maximal, characteristic, complemented
8	#72240130	C₂	1	1	yes	maximal, characteristic, complemented
9	#72236988	C₂	1	1	yes	maximal, characteristic, complemented
10	#72236437	C₂	1	1	yes	maximal, characteristic, complemented
11	#72233581	C₂	1	1	yes	maximal, characteristic, complemented
12	#72233426	C₂	1	2	yes	maximal, complemented
13	#72233420	C₂	1	2	yes	maximal, complemented
14	#72233234	C₂	1	2	yes	maximal, complemented
15	#72233093	C₂	1	2	yes	maximal, complemented
16	#72233000	C₂	1	2	yes	maximal, complemented
17	#72231950	C₂	1	1	yes	maximal, characteristic, complemented
18	#72213293	C₂	1	2	yes	maximal, complemented
19	#72210479	C₂	1	2	yes	maximal, complemented
20	C₂×#62817	C₂²	1	1	yes	characteristic
21	#6470225	C₂²	1	2	yes	—
22	#6437445	C₂²	1	2	yes	—
23	C₂×#21746	C₂²	1	1	yes	characteristic
24	#5486611	C₂²	1	1	yes	characteristic, complemented
25	#5069375	C₂²	1	1	yes	characteristic, complemented
26	#5065220	C₂²	1	1	yes	characteristic, complemented
27	#4894596	C₂²	1	1	yes	characteristic, complemented
28	#4312024	C₂²	1	1	yes	characteristic, complemented
29	#4128936	C₂²	1	1	yes	characteristic, complemented
30	#4117631	C₂²	1	1	yes	characteristic, complemented
31	#4035548	C₂²	1	1	yes	characteristic, complemented
32	#2227686	C₂²	1	1	yes	characteristic, complemented
33	#2108839	C₂²	1	1	yes	characteristic, complemented
34	#616961	C₂²	1	1	yes	characteristic
35	#616960	C₂²	1	1	yes	characteristic
36	#604823	C₂²	1	1	yes	characteristic, complemented
37	#581603	C₂²	1	1	yes	characteristic, complemented
38	#516383	C₂²	1	1	yes	characteristic
39	#496225	C₂²	1	2	yes	complemented
40	#493370	C₂²	1	2	yes	complemented
41	#347048	C₂²	1	2	yes	—
42	#347048	C₂²	1	2	yes	—
43	#347042	C₂²	1	2	yes	—
44	#347042	C₂²	1	2	yes	—
45	#346456	C₂²	1	2	yes	—
46	#346456	C₂²	1	2	yes	—
47	#346446	C₂²	1	2	yes	—
48	#346446	C₂²	1	2	yes	—
49	C₂×#8547	C₂²	1	1	yes	characteristic
50	C₂×#8541	C₂²	1	1	yes	characteristic
51	#187940	C₂²	1	2	yes	—
52	#187940	C₂²	1	2	yes	—
53	#187934	C₂²	1	2	yes	—
54	#187934	C₂²	1	2	yes	—
55	#187928	C₂²	1	2	yes	—
56	#187928	C₂²	1	2	yes	—
57	#187928	C₂²	1	2	yes	—
58	#186835	C₂²	1	2	yes	—
59	#144655	C₂²	1	4	yes	complemented
60	#144654	C₂²	1	4	yes	complemented
61	#144645	C₂²	1	4	yes	complemented
62	#144627	C₂²	1	4	yes	complemented
63	#144415	C₂²	1	4	yes	complemented
64	#144414	C₂²	1	4	yes	complemented
65	#144388	C₂²	1	4	yes	complemented
66	#144386	C₂²	1	4	yes	complemented
67	#139828	C₂²	1	2	yes	complemented
68	#139828	C₂²	1	2	yes	complemented
69	#139816	C₂²	1	4	yes	complemented
70	#139779	C₂²	1	4	yes	complemented
71	#139777	C₂²	1	4	yes	complemented
72	#139773	C₂²	1	4	yes	complemented
73	#139764	C₂²	1	4	yes	complemented
74	#139720	C₂²	1	2	yes	complemented
75	#139720	C₂²	1	2	yes	complemented
76	#139718	C₂²	1	2	yes	complemented
77	#139718	C₂²	1	2	yes	complemented
78	#139716	C₂²	1	2	yes	complemented
79	#139716	C₂²	1	2	yes	complemented
80	#139706	C₂²	1	4	yes	complemented
81	#139706	C₂²	1	4	yes	complemented
82	#139700	C₂²	1	4	yes	complemented
83	#135522	C₂²	1	2	yes	complemented
84	#135522	C₂²	1	2	yes	complemented
85	#135507	C₂²	1	2	yes	complemented
86	#135507	C₂²	1	2	yes	complemented
87	#128073	C₂²	1	2	yes	complemented
88	#128073	C₂²	1	2	yes	complemented
89	#128073	C₂²	1	2	yes	complemented
90	#128009	C₂²	1	2	yes	complemented
91	#62817	C₂³	1	2	yes	—
92	#62817	C₂³	1	2	yes	—
93	C₂×#3484	C₂³	1	2	yes	—
94	C₂²×#535	C₂³	1	1	yes	characteristic
95	C₂²×#534	D₄	1	1	yes	characteristic
96	C₂³×#120	C₂³	1	1	yes	characteristic
97	C₂⁴×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
98	C₂×#2404	D₄	1	1	yes	characteristic, complemented
99	C₂×#2404	D₄	1	1	yes	characteristic, complemented
100	C₂×#2403	D₄	1	1	yes	characteristic
101	C₂×#2403	C₂³	1	1	yes	characteristic
102	C₂²×#379	D₄	1	1	yes	characteristic, complemented
103	#24056	C₂³	1	4	yes	—
104	#23907	C₂³	1	4	yes	—
105	#23906	C₂³	1	4	yes	—
106	#23900	C₂³	1	4	yes	—
107	#21746	C₂³	1	2	yes	—
108	#21746	C₂³	1	2	yes	—
109	C₂×#1783	C₂³	1	2	yes	—
110	C₂×#1781	C₂³	1	2	yes	—
111	C₂×#1781	C₂³	1	2	yes	—
112	#17273	C₂³	1	1	yes	characteristic, complemented
113	#17272	C₂³	1	1	yes	characteristic, complemented
114	#17137	C₂³	1	1	yes	characteristic, complemented
115	#17136	C₂³	1	1	yes	characteristic, complemented
116	#15948	D₄	1	1	yes	characteristic
117	#15948	D₄	1	1	yes	characteristic
118	#15948	C₂³	1	1	yes	characteristic
119	#15948	C₂³	1	1	yes	characteristic
120	#15947	D₄	1	1	yes	characteristic
121	#15947	D₄	1	1	yes	characteristic
122	#15947	C₂³	1	1	yes	characteristic
123	#15947	C₂³	1	1	yes	characteristic
124	#15784	C₂³	1	1	yes	characteristic, complemented
125	#15313	C₂³	1	1	yes	characteristic, complemented
126	#15259	D₄	1	1	yes	characteristic, complemented
127	#15259	D₄	1	1	yes	characteristic, complemented
128	#15259	C₂³	1	1	yes	characteristic
129	#15259	C₂³	1	1	yes	characteristic
130	#15259	C₂³	1	1	yes	characteristic, complemented
131	#15258	D₄	1	1	yes	characteristic, complemented
132	#15258	D₄	1	1	yes	characteristic, complemented
133	#15258	C₂³	1	1	yes	characteristic
134	#15258	C₂³	1	1	yes	characteristic
135	#15258	C₂³	1	1	yes	characteristic, complemented
136	#14666	C₂³	1	1	yes	characteristic, complemented
137	#14662	C₂³	1	1	yes	characteristic, complemented
138	#14516	C₂³	1	1	yes	characteristic, complemented
139	#14419	C₂³	1	1	yes	characteristic, complemented
140	#14419	C₂³	1	1	yes	characteristic, complemented
141	#14358	C₂³	1	1	yes	characteristic, complemented
142	#14335	D₄	1	1	yes	characteristic
143	#14335	C₂³	1	1	yes	characteristic
144	#14255	D₄	1	1	yes	characteristic, complemented
145	#14255	D₄	1	1	yes	characteristic, complemented
146	#14255	C₂³	1	1	yes	characteristic
147	#14255	C₂³	1	1	yes	characteristic
148	#14169	C₂³	1	1	yes	characteristic, complemented
149	#14134	D₄	1	1	yes	characteristic, complemented
150	#14134	D₄	1	1	yes	characteristic, complemented
151	#14134	C₂³	1	1	yes	characteristic
152	#14134	C₂³	1	1	yes	characteristic
153	#14134	C₂³	1	1	yes	characteristic, complemented
154	#13869	D₄	1	1	yes	characteristic, complemented
155	#13869	D₄	1	1	yes	characteristic, complemented
156	#13868	D₄	1	1	yes	characteristic, complemented
157	#13868	D₄	1	1	yes	characteristic, complemented
158	#13867	D₄	1	1	yes	characteristic
159	#13867	C₂³	1	1	yes	characteristic
160	#13867	C₂³	1	1	yes	characteristic
161	#13867	C₂³	1	1	yes	characteristic
162	#12852	C₂³	1	4	yes	complemented
163	#12694	C₂³	1	4	yes	complemented
164	#12693	C₂³	1	4	yes	complemented
165	#12687	C₂³	1	4	yes	complemented
166	#8547	C₂³	1	2	yes	—
167	#8547	C₂³	1	2	yes	—
168	#8541	C₂³	1	2	yes	—
169	#8541	C₂³	1	2	yes	—
170	#8534	C₂³	1	4	yes	—
171	#8534	C₂³	1	4	yes	—
172	#8534	C₂³	1	4	yes	—
173	#8534	C₂³	1	4	yes	—
174	#8534	C₂³	1	4	yes	—
175	#8534	C₂³	1	4	yes	—
176	#8453	C₂³	1	4	yes	—
177	#8453	C₂³	1	4	yes	—
178	#7307	C₂³	1	4	yes	complemented
179	#7307	C₂³	1	4	yes	complemented
180	#7304	C₂³	1	4	yes	complemented
181	#7304	C₂³	1	4	yes	complemented
182	#7304	C₂³	1	4	yes	complemented
183	#7304	C₂³	1	4	yes	complemented
184	#7304	C₂³	1	4	yes	complemented
185	#7304	C₂³	1	4	yes	complemented
186	C₂⁷	C₂×D₄	1	1	yes	characteristic
187	C₂²×H(5,𝔽₂)	#41	1	2	yes	complemented
188	C₂³×#41	C₂×D₄	1	1	yes	characteristic
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
193	#3484	#41	1	4	yes	complemented
194	#3484	C₂⁴	1	4	yes	—
195	C₂²×#127	C₂×D₄	1	1	yes	characteristic
196	C₂²×#127	C₂⁴	1	1	yes	characteristic
197	C₂²×#124	C₂×D₄	1	1	yes	characteristic
198	C₂²×#124	C₂⁴	1	1	yes	characteristic
199	C₂²×#123	C₂×D₄	1	1	yes	characteristic
200	C₂²×#123	C₂×D₄	1	1	yes	characteristic
201	C₂²×#120	C₂×D₄	1	1	yes	characteristic
202	C₂²×#120	C₂×D₄	1	1	yes	characteristic
203	C₂²×#120	C₂×D₄	1	1	yes	characteristic
204	C₂²×#120	C₂×D₄	1	1	yes	characteristic
205	C₂²×#120	C₂×D₄	1	1	yes	characteristic
206	C₂²×#120	C₂×D₄	1	1	yes	characteristic
207	C₂²×#120	C₂×D₄	1	1	yes	characteristic
208	C₂²×#120	C₂×D₄	1	1	yes	characteristic
209	C₂²×#120	C₂×D₄	1	1	yes	characteristic
210	C₂²×#120	C₂×D₄	1	1	yes	characteristic
211	C₂²×#120	C₂×D₄	1	1	yes	characteristic
212	C₂²×#120	C₂⁴	1	1	yes	characteristic
213	C₂²×#120	C₂⁴	1	1	yes	characteristic
214	C₂²×#120	C₂⁴	1	1	yes	characteristic
215	C₂×#518	#41	1	2	yes	complemented
216	C₂²×#117	C₂×D₄	1	1	yes	characteristic
217	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
218	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
219	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
220	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
227	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
228	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
229	C₂×#393	C₂×D₄	1	1	yes	characteristic
230	C₂×#393	C₂×D₄	1	1	yes	characteristic
231	C₂×#393	C₂×D₄	1	1	yes	characteristic
232	C₂×#393	C₂×D₄	1	1	yes	characteristic
233	C₂×#392	C₂×D₄	1	1	yes	characteristic
234	C₂×#392	C₂×D₄	1	1	yes	characteristic
235	C₂×#392	C₂×D₄	1	1	yes	characteristic
236	C₂×#392	C₂×D₄	1	1	yes	characteristic
237	C₂×#386	C₂×D₄	1	1	yes	characteristic
238	C₂×#386	C₂×D₄	1	1	yes	characteristic
239	C₂×#386	C₂×D₄	1	1	yes	characteristic
240	C₂×#386	C₂⁴	1	1	yes	characteristic
241	C₂×#381	C₂×D₄	1	1	yes	characteristic
242	C₂×#381	C₂×D₄	1	1	yes	characteristic
243	C₂×#379	C₂×D₄	1	1	yes	characteristic
244	C₂×#379	C₂×D₄	1	1	yes	characteristic
245	C₂×#379	C₂×D₄	1	1	yes	characteristic
246	C₂×#379	C₂×D₄	1	1	yes	characteristic
247	C₂×#379	C₂×D₄	1	1	yes	characteristic
248	C₂×#379	C₂×D₄	1	1	yes	characteristic
249	#1783	C₂⁴	1	4	yes	—
250	#1781	C₂⁴	1	4	yes	—
251	#1781	C₂⁴	1	4	yes	—
252	#1440	C₂×D₄	1	1	yes	characteristic
253	#1440	C₂×D₄	1	1	yes	characteristic
254	#1440	C₂×D₄	1	1	yes	characteristic
255	#1440	C₂×D₄	1	1	yes	characteristic
256	#1440	C₂×D₄	1	1	yes	characteristic
257	#1440	C₂×D₄	1	1	yes	characteristic
258	#1440	C₂×D₄	1	1	yes	characteristic
259	#1440	C₂×D₄	1	1	yes	characteristic
260	#1438	C₂×D₄	1	1	yes	characteristic
261	#1438	C₂×D₄	1	1	yes	characteristic
262	#1438	C₂×D₄	1	1	yes	characteristic
263	#1438	C₂×D₄	1	1	yes	characteristic
264	#1438	C₂×D₄	1	1	yes	characteristic
265	#1438	C₂×D₄	1	1	yes	characteristic
266	#1438	C₂×D₄	1	1	yes	characteristic
267	#1438	C₂×D₄	1	1	yes	characteristic
268	#1438	C₂×D₄	1	1	yes	characteristic
269	#1438	C₂×D₄	1	1	yes	characteristic
270	#1438	C₂×D₄	1	1	yes	characteristic
271	#1438	C₂×D₄	1	1	yes	characteristic
272	#1438	C₂×D₄	1	1	yes	characteristic
273	#1438	C₂×D₄	1	1	yes	characteristic
274	#1438	C₂×D₄	1	1	yes	characteristic
275	#1438	C₂×D₄	1	1	yes	characteristic
276	#1438	C₂⁴	1	1	yes	characteristic
277	#1438	C₂⁴	1	1	yes	characteristic
278	#1438	C₂⁴	1	1	yes	characteristic
279	#1438	C₂⁴	1	1	yes	characteristic
280	#1438	C₂⁴	1	1	yes	characteristic
281	#1438	C₂⁴	1	1	yes	characteristic
282	#1438	C₂⁴	1	1	yes	characteristic
283	#1438	C₂⁴	1	1	yes	characteristic
284	#1437	C₂×D₄	1	1	yes	characteristic
285	#1437	C₂×D₄	1	1	yes	characteristic
286	#1437	C₂×D₄	1	1	yes	characteristic
287	#1437	C₂×D₄	1	1	yes	characteristic
288	#1437	C₂×D₄	1	1	yes	characteristic
289	#1437	C₂×D₄	1	1	yes	characteristic
290	#1437	C₂×D₄	1	1	yes	characteristic
291	#1437	C₂×D₄	1	1	yes	characteristic
292	C₂⁶	#120	1	1	yes	characteristic
293	C₂⁶	#120	1	1	yes	characteristic
294	C₂⁶	#120	1	1	yes	characteristic
295	C₂⁶	#120	1	1	yes	characteristic
296	C₂⁶	C₂²×D₄	1	1	yes	characteristic
297	C₂⁶	C₂²×D₄	1	1	yes	characteristic
298	C₂⁶	C₂²×D₄	1	1	yes	characteristic
299	C₂⁶	C₂²×D₄	1	1	yes	characteristic
300	C₂⁶	C₂²×D₄	1	1	yes	characteristic
301	C₂×H(5,𝔽₂)	C₂×#41	1	4	yes	—
302	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
303	C₂³×D₄	#120	1	1	yes	characteristic
304	C₂³×D₄	#120	1	1	yes	characteristic
305	C₂³×D₄	#120	1	1	yes	characteristic
306	C₂³×D₄	#120	1	1	yes	characteristic
307	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
308	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
309	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
310	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
311	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
314	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
315	C₂³×D₄	C₂×#41	1	2	yes	—
316	C₂³×D₄	C₂×#41	1	2	yes	—
317	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
318	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
319	C₂³×D₄	C₂⁵	1	1	yes	characteristic
320	C₂⁴×C₄	#120	1	1	yes	characteristic
321	C₂⁴×C₄	#120	1	1	yes	characteristic
322	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
324	#518	C₂×#41	1	4	yes	—
325	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
326	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
327	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
328	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
329	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	#120	1	1	yes	characteristic
331	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
334	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
335	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
338	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
339	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
340	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
341	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
342	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
343	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
344	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
347	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
348	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
349	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
350	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
351	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
352	C₂²×C₄²	C₂²×D₄	1	1	yes	characteristic
353	C₂×#95	C₂²×D₄	1	1	yes	characteristic
354	C₂×#95	C₂²×D₄	1	1	yes	characteristic
355	C₂×#95	C₂²×D₄	1	1	yes	characteristic
356	C₂×#95	C₂²×D₄	1	1	yes	characteristic
357	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
358	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
359	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
360	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
361	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
362	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
363	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
364	C₂⁵	B(4,𝔽₂)	1	1	yes	characteristic
365	C₂⁵	C₂×#120	1	1	yes	characteristic
366	C₂⁵	C₂×#120	1	1	yes	characteristic
367	C₂⁵	C₂×#120	1	1	yes	characteristic
368	C₂⁵	C₂×#120	1	1	yes	characteristic
369	C₂⁵	C₂×#120	1	1	yes	characteristic
370	C₂⁵	C₂×#120	1	1	yes	characteristic
371	C₂⁵	C₂×#120	1	1	yes	characteristic
372	C₂⁵	#525	1	1	yes	characteristic
373	C₂⁵	#525	1	1	yes	characteristic
374	C₂⁵	#535	1	1	yes	characteristic
375	C₂⁵	#535	1	1	yes	characteristic
376	C₂⁵	#546	1	2	yes	—
377	C₂⁵	#546	1	2	yes	—
378	C₂⁵	C₂³×D₄	1	1	yes	characteristic
379	C₂⁵	C₂³×D₄	1	1	yes	characteristic
380	C₂²×D₄	#525	1	2	yes	—
381	C₂²×D₄	#535	1	2	yes	—
382	C₂²×D₄	#546	1	2	yes	—
383	C₂²×D₄	#546	1	2	yes	—
384	C₂²×D₄	#546	1	2	yes	—
385	C₂²×D₄	#546	1	2	yes	—
386	C₂²×D₄	C₂²×#41	1	2	yes	—
387	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
388	C₂³×C₄	C₂×#120	1	1	yes	characteristic
389	C₂³×C₄	C₂×#120	1	1	yes	characteristic
390	C₂³×C₄	C₂×#120	1	1	yes	characteristic
391	C₂³×C₄	C₂×#120	1	1	yes	characteristic
392	C₂³×C₄	C₂×#120	1	1	yes	characteristic
393	C₂³×C₄	#546	1	2	yes	—
394	C₂³×C₄	#546	1	2	yes	—
395	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
396	C₂⁴	#2404	1	1	yes	characteristic
397	C₂⁴	#2404	1	2	yes	—
398	C₂⁴	#2404	1	1	yes	characteristic
399	C₂⁴	#2404	1	1	yes	characteristic
400	C₂⁴	#2404	1	1	yes	characteristic
401	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
402	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
403	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
404	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
405	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
406	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
407	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
408	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
409	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
410	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
411	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
412	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
413	C₂⁴	C₂²×#120	1	1	yes	characteristic
414	C₂⁴	C₂×#525	1	1	yes	characteristic
415	C₂⁴	C₂×#535	1	1	yes	characteristic
416	C₂⁴	C₂×#546	1	2	yes	—
417	C₂²×C₄	#2404	1	2	yes	—
418	C₂²×C₄	C₂×#546	1	2	yes	—
419	C₂³	#23984	1	1	yes	characteristic
420	C₂³	#23984	1	1	yes	characteristic
421	C₂³	#23984	1	1	yes	characteristic
422	C₂³	#23984	1	1	yes	characteristic
423	C₂³	#23996	1	2	yes	—
424	C₂³	#33551	1	2	yes	—
425	C₂³	#33551	1	2	yes	—
426	C₂³	#33552	1	2	yes	—
427	C₂³	C₂×#2404	1	1	yes	characteristic
428	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
429	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
430	C₂²	C₂×#23996	1	1	yes	characteristic
431	C₂²	#6451863	1	1	yes	characteristic
432	C₂²	C₂×#23984	1	1	yes	characteristic
433	C₂²	C₂×#33551	1	1	yes	characteristic
434	C₂²	C₂×#33551	1	1	yes	characteristic
435	C₂²	C₂×#33552	1	1	yes	characteristic
436	C₂²	#7622875	1	1	yes	characteristic
437	C₂	#72238500	1	1	yes	characteristic
438	C₂	#72240104	1	1	yes	characteristic
439	C₂	#72240110	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	C₂×#23984
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. #72240144	C₂	semidirect
2. #72240143	C₂	semidirect
3. #72240141	C₂	semidirect
4. #72240139	C₂	semidirect
5. #72240138	C₂	semidirect
6. #72240134	C₂	semidirect
7. #72240132	C₂	semidirect
8. #72240130	C₂	semidirect
9. #72236988	C₂	semidirect
10. #72236437	C₂	semidirect
11. #72233581	C₂	semidirect
12. #72233426	C₂	semidirect
13. #72233420	C₂	semidirect
14. #72233234	C₂	semidirect
15. #72233093	C₂	semidirect
16. #72233000	C₂	semidirect
17. #72231950	C₂	semidirect
18. #72213293	C₂	semidirect
19. #72210479	C₂	semidirect
24. #5486611	C₂²	semidirect
25. #5069375	C₂²	semidirect
26. #5065220	C₂²	semidirect
27. #4894596	C₂²	semidirect
28. #4312024	C₂²	semidirect
29. #4128936	C₂²	semidirect
30. #4117631	C₂²	semidirect
31. #4035548	C₂²	semidirect
32. #2227686	C₂²	semidirect
33. #2108839	C₂²	semidirect
36. #604823	C₂²	semidirect
37. #581603	C₂²	semidirect
39. #496225	C₂²	semidirect
40. #493370	C₂²	semidirect
59. #144655	C₂²	semidirect
60. #144654	C₂²	semidirect
61. #144645	C₂²	semidirect
62. #144627	C₂²	semidirect
63. #144415	C₂²	semidirect
64. #144414	C₂²	semidirect
65. #144388	C₂²	semidirect
66. #144386	C₂²	semidirect
67. #139828	C₂²	semidirect
68. #139828	C₂²	semidirect
69. #139816	C₂²	semidirect
70. #139779	C₂²	semidirect
71. #139777	C₂²	semidirect
72. #139773	C₂²	semidirect
73. #139764	C₂²	semidirect
74. #139720	C₂²	semidirect
75. #139720	C₂²	semidirect
76. #139718	C₂²	semidirect
77. #139718	C₂²	semidirect
78. #139716	C₂²	semidirect
79. #139716	C₂²	semidirect
80. #139706	C₂²	semidirect
81. #139706	C₂²	semidirect
82. #139700	C₂²	semidirect
83. #135522	C₂²	semidirect
84. #135522	C₂²	semidirect
85. #135507	C₂²	semidirect
86. #135507	C₂²	semidirect
87. #128073	C₂²	semidirect
88. #128073	C₂²	semidirect
89. #128073	C₂²	semidirect
90. #128009	C₂²	semidirect
97. C₂⁴×C₂²⋊C₄	D₄	semidirect
98. C₂×#2404	D₄	semidirect
99. C₂×#2404	D₄	semidirect
102. C₂²×#379	D₄	semidirect
112. #17273	C₂³	semidirect
113. #17272	C₂³	semidirect
114. #17137	C₂³	semidirect
115. #17136	C₂³	semidirect
124. #15784	C₂³	semidirect
125. #15313	C₂³	semidirect
126. #15259	D₄	semidirect
127. #15259	D₄	semidirect
130. #15259	C₂³	semidirect
131. #15258	D₄	semidirect
132. #15258	D₄	semidirect
135. #15258	C₂³	semidirect
136. #14666	C₂³	semidirect
137. #14662	C₂³	semidirect
138. #14516	C₂³	semidirect
139. #14419	C₂³	semidirect
140. #14419	C₂³	semidirect
141. #14358	C₂³	semidirect
144. #14255	D₄	semidirect
145. #14255	D₄	semidirect
148. #14169	C₂³	semidirect
149. #14134	D₄	semidirect
150. #14134	D₄	semidirect
153. #14134	C₂³	semidirect
154. #13869	D₄	semidirect
155. #13869	D₄	semidirect
156. #13868	D₄	semidirect
157. #13868	D₄	semidirect
162. #12852	C₂³	semidirect
163. #12694	C₂³	semidirect
164. #12693	C₂³	semidirect
165. #12687	C₂³	semidirect
178. #7307	C₂³	semidirect
179. #7307	C₂³	semidirect
180. #7304	C₂³	semidirect
181. #7304	C₂³	semidirect
182. #7304	C₂³	semidirect
183. #7304	C₂³	semidirect
184. #7304	C₂³	semidirect
185. #7304	C₂³	semidirect
187. C₂²×H(5,𝔽₂)	#41	semidirect
193. #3484	#41	semidirect
215. C₂×#518	#41	semidirect

Maximal subgroups

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

subgroup	index
#72240144	2
#72240143	2
#72240141	2
#72240139	2
#72240138	2
#72240134	2
#72240132	2
#72240130	2
#72236988	2
#72236437	2
#72233581	2
#72233426	2
#72233420	2
#72233234	2
#72233093	2
#72233000	2
#72231950	2
#72213293	2
#72210479	2