Subgroups — #72317837

Order 2048.

At least 11354 conjugacy classes of subgroups; only the 772 normal subgroups are shown.

The subgroup lattice has 457 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72317824	C₂	1	1	yes	maximal, characteristic, complemented
2	#72317791	C₂	1	2	yes	maximal, complemented
3	#72317748	C₂	1	2	yes	maximal, complemented
4	#72317643	C₂	1	2	yes	maximal, complemented
5	#72293920	C₂	1	1	yes	maximal, characteristic, complemented
6	#72260517	C₂	1	1	yes	maximal, characteristic, complemented
7	#72240171	C₂	1	2	yes	maximal, complemented
8	#72234687	C₂	1	1	yes	maximal, characteristic, complemented
9	#72234607	C₂	1	1	yes	maximal, characteristic, complemented
10	#72233443	C₂	1	2	yes	maximal, complemented
11	#72233364	C₂	1	2	yes	maximal, complemented
12	#72233019	C₂	1	2	yes	maximal, complemented
13	#72232733	C₂	1	1	yes	maximal, characteristic, complemented
14	#72227862	C₂	1	2	yes	maximal, complemented
15	#72225751	C₂	1	2	yes	maximal, complemented
16	#72218215	C₂	1	2	yes	maximal, complemented
17	#72216616	C₂	1	1	yes	maximal, characteristic, complemented
18	#72210587	C₂	1	2	yes	maximal, complemented
19	#72210575	C₂	1	2	yes	maximal, complemented
20	#10586472	C₂²	1	1	yes	characteristic, complemented
21	C₂×#52004	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×#120	C₂²	1	1	yes	characteristic
23	#6516837	C₂²	1	2	yes	—
24	#6512843	C₂²	1	2	yes	complemented
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	C₂×#23900	C₂²	1	2	yes	complemented
30	#6437445	C₂²	1	2	yes	complemented
31	#6385971	C₂²	1	1	yes	characteristic, complemented
32	#5021210	C₂²	1	1	yes	characteristic, complemented
33	#4941255	C₂²	1	1	yes	characteristic, complemented
34	#4607564	C₂²	1	1	yes	characteristic, complemented
35	#4420586	C₂²	1	1	yes	characteristic
36	#2924786	C₂²	1	1	yes	characteristic, complemented
37	#2039947	C₂²	1	1	yes	characteristic, complemented
38	#2032505	C₂²	1	1	yes	characteristic, complemented
39	#1418363	C₂²	1	1	yes	characteristic, complemented
40	#845297	C₂²	1	1	yes	characteristic, complemented
41	#686207	C₂²	1	1	yes	characteristic
42	#647656	C₂²	1	1	yes	characteristic, complemented
43	#616961	C₂²	1	1	yes	characteristic, complemented
44	#605627	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	#493370	C₂²	1	2	yes	complemented
52	C₂×#12687	C₂²	1	2	yes	complemented
53	#347052	C₂²	1	2	yes	complemented
54	#347048	C₂²	1	2	yes	complemented
55	#347043	C₂²	1	2	yes	complemented
56	#347042	C₂²	1	2	yes	complemented
57	#346459	C₂²	1	2	yes	complemented
58	#346456	C₂²	1	2	yes	complemented
59	#346449	C₂²	1	2	yes	complemented
60	#346446	C₂²	1	2	yes	complemented
61	#188087	C₂²	1	1	yes	characteristic, complemented
62	#188035	C₂²	1	1	yes	characteristic, complemented
63	#187944	C₂²	1	2	yes	complemented
64	#186808	C₂²	1	2	yes	complemented
65	#144412	C₂²	1	4	yes	complemented
66	#144412	C₂²	1	4	yes	complemented
67	#144388	C₂²	1	4	yes	complemented
68	#144388	C₂²	1	4	yes	complemented
69	#144386	C₂²	1	4	yes	complemented
70	#144386	C₂²	1	4	yes	complemented
71	#144366	C₂²	1	4	yes	complemented
72	#144366	C₂²	1	4	yes	complemented
73	#139848	C₂²	1	2	yes	complemented
74	#139828	C₂²	1	2	yes	complemented
75	#139816	C₂²	1	4	yes	complemented
76	#139795	C₂²	1	2	yes	complemented
77	#139794	C₂²	1	2	yes	complemented
78	#139793	C₂²	1	2	yes	complemented
79	#139773	C₂²	1	4	yes	complemented
80	#139764	C₂²	1	4	yes	complemented
81	#139720	C₂²	1	2	yes	complemented
82	#139718	C₂²	1	2	yes	complemented
83	#139716	C₂²	1	2	yes	complemented
84	#139700	C₂²	1	4	yes	complemented
85	#134020	C₂²	1	2	yes	complemented
86	#133893	C₂²	1	2	yes	complemented
87	#133849	C₂²	1	2	yes	complemented
88	#133822	C₂²	1	2	yes	complemented
89	#128058	C₂²	1	2	yes	complemented
90	#128033	C₂²	1	2	yes	complemented
91	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
92	#62818	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
96	C₂²×D₄²	C₂³	1	1	yes	characteristic, complemented
97	C₂²×#535	C₂³	1	1	yes	characteristic
98	C₂³×#120	D₄	1	1	yes	characteristic, complemented
99	C₂³×#120	C₂³	1	1	yes	characteristic
100	C₂×#2684	C₂³	1	1	yes	characteristic, complemented
101	C₂×#2684	C₂³	1	1	yes	characteristic, complemented
102	C₂×#2847	C₂³	1	1	yes	characteristic
103	C₂×#2846	D₄	1	1	yes	characteristic, complemented
104	C₂×#2846	C₂³	1	1	yes	characteristic
105	C₂×#2433	C₂³	1	1	yes	characteristic
106	C₂×#2408	D₄	1	1	yes	characteristic, complemented
107	C₂×#2410	D₄	1	1	yes	characteristic, complemented
108	C₂×#2410	C₂³	1	1	yes	characteristic
109	C₂×#2403	D₄	1	1	yes	characteristic, complemented
110	C₂×#2403	D₄	1	1	yes	characteristic, complemented
111	C₂×#2403	C₂³	1	1	yes	characteristic
112	C₂×#2403	C₂³	1	1	yes	characteristic
113	C₂×#2615	D₄	1	1	yes	characteristic, complemented
114	C₂×#2613	D₄	1	1	yes	characteristic, complemented
115	C₂×#2388	D₄	1	1	yes	characteristic, complemented
116	C₂×#2380	C₂³	1	1	yes	characteristic, complemented
117	C₂×D₄×C₂²⋊C₄	D₄	1	1	yes	characteristic, complemented
118	C₂×C₄×#120	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	#23907	C₂³	1	4	yes	—
125	#23906	C₂³	1	4	yes	—
126	#23900	C₂³	1	4	yes	—
127	#23900	C₂³	1	4	yes	—
128	#23900	C₂³	1	4	yes	—
129	#23900	C₂³	1	4	yes	—
130	#21793	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	#15984	D₄	1	1	yes	characteristic, complemented
136	#15984	C₂³	1	1	yes	characteristic
137	#15948	C₂³	1	1	yes	characteristic
138	#15947	C₂³	1	1	yes	characteristic
139	#15947	C₂³	1	1	yes	characteristic, complemented
140	#15947	C₂³	1	1	yes	characteristic, complemented
141	#15673	D₄	1	1	yes	characteristic, complemented
142	#15673	C₂³	1	1	yes	characteristic
143	#15310	D₄	1	1	yes	characteristic, complemented
144	#15310	C₂³	1	1	yes	characteristic
145	#15266	C₂³	1	1	yes	characteristic, complemented
146	#15266	C₂³	1	1	yes	characteristic, complemented
147	#15261	D₄	1	1	yes	characteristic, complemented
148	#15259	D₄	1	1	yes	characteristic, complemented
149	#15259	C₂³	1	1	yes	characteristic
150	#15259	C₂³	1	1	yes	characteristic, complemented
151	#15259	C₂³	1	1	yes	characteristic, complemented
152	#15258	D₄	1	1	yes	characteristic, complemented
153	#15258	D₄	1	1	yes	characteristic, complemented
154	#15258	C₂³	1	1	yes	characteristic
155	#15258	C₂³	1	1	yes	characteristic, complemented
156	#15258	C₂³	1	1	yes	characteristic, complemented
157	#15257	D₄	1	1	yes	characteristic, complemented
158	#15257	C₂³	1	1	yes	characteristic
159	#14666	C₂³	1	1	yes	characteristic, complemented
160	#14657	D₄	1	1	yes	characteristic, complemented
161	#14516	C₂³	1	1	yes	characteristic, complemented
162	#14358	C₂³	1	1	yes	characteristic, complemented
163	#14335	D₄	1	1	yes	characteristic, complemented
164	#14335	C₂³	1	1	yes	characteristic
165	#14136	D₄	1	1	yes	characteristic, complemented
166	#14134	C₂³	1	1	yes	characteristic, complemented
167	#13902	C₂³	1	1	yes	characteristic
168	#13871	D₄	1	1	yes	characteristic, complemented
169	#12852	C₂³	1	4	yes	complemented
170	#12852	C₂³	1	4	yes	complemented
171	#12694	C₂³	1	4	yes	complemented
172	#12693	C₂³	1	4	yes	complemented
173	#12687	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	#8549	C₂³	1	2	yes	—
178	#8547	C₂³	1	2	yes	—
179	#8542	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
205	C₂²×#127	C₂×D₄	1	1	yes	characteristic, complemented
206	C₂²×#127	C₂⁴	1	1	yes	characteristic
207	C₂²×#124	C₂×D₄	1	1	yes	characteristic, complemented
208	C₂²×#124	C₂⁴	1	1	yes	characteristic
209	C₂²×#123	C₂×D₄	1	1	yes	characteristic, complemented
210	C₂²×#121	C₂×D₄	1	1	yes	characteristic
211	C₂²×#121	C₂×D₄	1	1	yes	characteristic
212	C₂²×#121	C₂×D₄	1	1	yes	characteristic
213	C₂²×#121	C₂⁴	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
221	C₂²×#120	C₂×D₄	1	1	yes	characteristic
222	C₂²×#120	C₂×D₄	1	1	yes	characteristic
223	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
224	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
225	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
226	C₂²×#120	C₂×D₄	1	1	yes	characteristic, complemented
227	C₂²×#120	C₂⁴	1	1	yes	characteristic
228	C₂²×#120	C₂⁴	1	1	yes	characteristic
229	C₂²×#120	C₂⁴	1	1	yes	characteristic
230	C₂²×#120	C₂⁴	1	1	yes	characteristic
231	C₂²×#120	C₂⁴	1	1	yes	characteristic
232	C₂×#518	C₂×D₄	1	2	yes	complemented
233	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
234	C₂²×C₄×D₄	C₂×D₄	1	1	yes	characteristic
235	C₂²×#117	C₂×D₄	1	1	yes	characteristic, complemented
236	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
237	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
238	C₂×B(4,𝔽₂)	C₂×D₄	1	8	yes	—
239	C₂²×#99	C₂×D₄	1	4	yes	complemented
240	#2403	C₂×D₄	1	4	yes	—
241	#2403	C₂×D₄	1	4	yes	—
242	C₂×#395	C₂×D₄	1	1	yes	characteristic, complemented
243	C₂×#394	C₂×D₄	1	1	yes	characteristic, complemented
244	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
245	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
246	C₂×#393	C₂×D₄	1	1	yes	characteristic, complemented
247	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
248	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
249	C₂×#392	C₂×D₄	1	1	yes	characteristic, complemented
250	C₂×#386	C₂×D₄	1	1	yes	characteristic
251	C₂×#386	C₂×D₄	1	1	yes	characteristic
252	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
253	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
254	C₂×#386	C₂×D₄	1	1	yes	characteristic, complemented
255	C₂×#386	C₂⁴	1	1	yes	characteristic
256	C₂×#386	C₂⁴	1	1	yes	characteristic
257	C₂×#385	C₂×D₄	1	1	yes	characteristic
258	C₂×#381	C₂×D₄	1	1	yes	characteristic, complemented
259	C₂×#380	C₂×D₄	1	1	yes	characteristic
260	C₂×#380	C₂×D₄	1	1	yes	characteristic, complemented
261	C₂×#379	C₂×D₄	1	1	yes	characteristic
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, complemented
267	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
268	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
269	C₂×#379	C₂×D₄	1	1	yes	characteristic, complemented
270	C₂×C₄×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
271	C₂×C₄×C₂²⋊C₄	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	#1440	C₂×D₄	1	1	yes	characteristic, complemented
280	#1440	C₂×D₄	1	1	yes	characteristic, complemented
281	#1438	C₂×D₄	1	1	yes	characteristic, complemented
282	#1438	C₂×D₄	1	1	yes	characteristic, complemented
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, complemented
296	#1437	C₂×D₄	1	1	yes	characteristic, complemented
297	#1437	C₂×D₄	1	1	yes	characteristic, complemented
298	#1437	C₂×D₄	1	1	yes	characteristic, complemented
299	#1437	C₂×D₄	1	1	yes	characteristic, complemented
300	#1437	C₂×D₄	1	1	yes	characteristic, complemented
301	#1436	C₂×D₄	1	1	yes	characteristic, complemented
302	#1436	C₂×D₄	1	1	yes	characteristic, complemented
303	C₂⁶	#120	1	1	yes	characteristic
304	C₂⁶	C₂²×D₄	1	1	yes	characteristic
305	C₂⁶	C₂²×D₄	1	1	yes	characteristic
306	C₂⁶	C₂²×D₄	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	C₂×H(5,𝔽₂)	C₂²×D₄	1	4	yes	—
312	C₂³×Q₈	C₂²×D₄	1	1	yes	characteristic
313	C₂³×D₄	#120	1	1	yes	characteristic
314	C₂³×D₄	#120	1	1	yes	characteristic
315	C₂³×D₄	#120	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	4	yes	—
321	C₂³×D₄	#120	1	1	yes	characteristic
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	2	yes	—
342	C₂×#120	#120	1	2	yes	—
343	C₂×#120	C₂²×D₄	1	4	yes	—
344	#518	C₂²×D₄	1	4	yes	—
345	C₂²×C₄⋊C₄	#120	1	1	yes	characteristic
346	C₂²×C₄⋊C₄	C₂²×D₄	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×C₄²	#120	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	2	yes	—
370	#386	#120	1	2	yes	—
371	#386	C₂²×D₄	1	4	yes	—
372	#379	#120	1	4	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	C₂×#120	1	1	yes	characteristic
378	C₂⁵	C₂×#120	1	2	yes	—
379	C₂⁵	C₂×#120	1	1	yes	characteristic
380	C₂⁵	C₂×#120	1	2	yes	—
381	C₂⁵	C₂×#120	1	1	yes	characteristic
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	#534	1	2	yes	—
386	C₂⁵	D₄²	1	2	yes	—
387	C₂⁵	D₄²	1	2	yes	—
388	C₂⁵	C₂³×D₄	1	1	yes	characteristic
389	C₂⁵	C₂³×D₄	1	1	yes	characteristic
390	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
391	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
392	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
393	C₂²×D₄	B(4,𝔽₂)	1	1	yes	characteristic
394	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
395	C₂²×D₄	C₂×#120	1	1	yes	characteristic
396	C₂²×D₄	C₂×#120	1	1	yes	characteristic
397	C₂²×D₄	#534	1	1	yes	characteristic
398	C₂²×D₄	#534	1	1	yes	characteristic
399	C₂²×D₄	D₄²	1	2	yes	—
400	C₂²×D₄	D₄²	1	2	yes	—
401	C₂²×D₄	D₄²	1	2	yes	—
402	C₂²×D₄	D₄²	1	2	yes	—
403	C₂²×D₄	C₂³×D₄	1	2	yes	—
404	C₂²×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
405	C₂³×C₄	C₂×#120	1	1	yes	characteristic
406	C₂³×C₄	C₂×#120	1	1	yes	characteristic
407	C₂³×C₄	C₂×#120	1	1	yes	characteristic
408	C₂³×C₄	C₂×#120	1	1	yes	characteristic
409	C₂³×C₄	C₂×#120	1	1	yes	characteristic
410	C₂³×C₄	C₂×#120	1	1	yes	characteristic
411	C₂³×C₄	C₂×#120	1	2	yes	—
412	C₂³×C₄	D₄²	1	2	yes	—
413	C₂³×C₄	D₄²	1	2	yes	—
414	C₂³×C₄	C₂³×D₄	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
417	C₂⁴	#2403	1	2	yes	—
418	C₂⁴	#2403	1	1	yes	characteristic
419	C₂⁴	#2403	1	1	yes	characteristic
420	C₂⁴	#2403	1	2	yes	—
421	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
422	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
423	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
424	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
425	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
426	C₂⁴	C₂×B(4,𝔽₂)	1	1	yes	characteristic
427	C₂⁴	C₂²×#120	1	1	yes	characteristic
428	C₂⁴	C₂²×#120	1	1	yes	characteristic
429	C₂⁴	C₂×#534	1	1	yes	characteristic
430	C₂⁴	C₂×D₄²	1	2	yes	—
431	C₂²×C₄	#2403	1	1	yes	characteristic
432	C₂²×C₄	#2403	1	1	yes	characteristic
433	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
434	C₂²×C₄	C₂×B(4,𝔽₂)	1	1	yes	characteristic
435	C₂²×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
436	C₂²×C₄	C₂×D₄²	1	2	yes	—
437	C₂³	#23900	1	2	yes	—
438	C₂³	#23900	1	2	yes	—
439	C₂³	#33551	1	2	yes	—
440	C₂³	C₂×#2403	1	1	yes	characteristic
441	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
442	C₂³	C₂²×B(4,𝔽₂)	1	1	yes	characteristic
443	C₂³	#60399	1	2	yes	—
444	C₂×C₄	#23895	1	2	yes	—
445	C₂×C₄	#33551	1	2	yes	—
446	C₂²	C₂×#23900	1	1	yes	characteristic
447	C₂²	C₂×#23895	1	1	yes	characteristic
448	C₂²	#6437632	1	1	yes	characteristic
449	C₂²	C₂×#33551	1	1	yes	characteristic
450	C₂²	C₂×#33551	1	1	yes	characteristic
451	C₂²	#7622880	1	1	yes	characteristic
452	C₂²	#7622886	1	1	yes	characteristic
453	C₂	#72218077	1	1	yes	characteristic
454	C₂	#72233042	1	1	yes	characteristic
455	C₂	#72233051	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 ◁ C₂²×D₄² ◁ 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. #72317824	C₂	semidirect
2. #72317791	C₂	semidirect
3. #72317748	C₂	semidirect
4. #72317643	C₂	semidirect
5. #72293920	C₂	semidirect
6. #72260517	C₂	semidirect
7. #72240171	C₂	semidirect
8. #72234687	C₂	semidirect
9. #72234607	C₂	semidirect
10. #72233443	C₂	semidirect
11. #72233364	C₂	semidirect
12. #72233019	C₂	semidirect
13. #72232733	C₂	semidirect
14. #72227862	C₂	semidirect
15. #72225751	C₂	semidirect
16. #72218215	C₂	semidirect
17. #72216616	C₂	semidirect
18. #72210587	C₂	semidirect
19. #72210575	C₂	semidirect
20. #10586472	C₂²	semidirect
21. C₂×#52004	C₂²	semidirect
24. #6512843	C₂²	semidirect
25. #6500010	C₂²	semidirect
28. #6470225	C₂²	semidirect
29. C₂×#23900	C₂²	semidirect
30. #6437445	C₂²	semidirect
31. #6385971	C₂²	semidirect
32. #5021210	C₂²	semidirect
33. #4941255	C₂²	semidirect
34. #4607564	C₂²	semidirect
36. #2924786	C₂²	semidirect
37. #2039947	C₂²	semidirect
38. #2032505	C₂²	semidirect
39. #1418363	C₂²	semidirect
40. #845297	C₂²	semidirect
42. #647656	C₂²	semidirect
43. #616961	C₂²	semidirect
44. #605627	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. #493370	C₂²	semidirect
52. C₂×#12687	C₂²	semidirect
53. #347052	C₂²	semidirect
54. #347048	C₂²	semidirect
55. #347043	C₂²	semidirect
56. #347042	C₂²	semidirect
57. #346459	C₂²	semidirect
58. #346456	C₂²	semidirect
59. #346449	C₂²	semidirect
60. #346446	C₂²	semidirect
61. #188087	C₂²	semidirect
62. #188035	C₂²	semidirect
63. #187944	C₂²	semidirect
64. #186808	C₂²	semidirect
65. #144412	C₂²	semidirect
66. #144412	C₂²	semidirect
67. #144388	C₂²	semidirect
68. #144388	C₂²	semidirect
69. #144386	C₂²	semidirect
70. #144386	C₂²	semidirect
71. #144366	C₂²	semidirect
72. #144366	C₂²	semidirect
73. #139848	C₂²	semidirect
74. #139828	C₂²	semidirect
75. #139816	C₂²	semidirect
76. #139795	C₂²	semidirect
77. #139794	C₂²	semidirect
78. #139793	C₂²	semidirect
79. #139773	C₂²	semidirect
80. #139764	C₂²	semidirect
81. #139720	C₂²	semidirect
82. #139718	C₂²	semidirect
83. #139716	C₂²	semidirect
84. #139700	C₂²	semidirect
85. #134020	C₂²	semidirect
86. #133893	C₂²	semidirect
87. #133849	C₂²	semidirect
88. #133822	C₂²	semidirect
89. #128058	C₂²	semidirect
90. #128033	C₂²	semidirect
91. C₂⁵×D₄	D₄	semidirect
96. C₂²×D₄²	C₂³	semidirect
98. C₂³×#120	D₄	semidirect
100. C₂×#2684	C₂³	semidirect
101. C₂×#2684	C₂³	semidirect
103. C₂×#2846	D₄	semidirect
106. C₂×#2408	D₄	semidirect
107. C₂×#2410	D₄	semidirect
109. C₂×#2403	D₄	semidirect
110. C₂×#2403	D₄	semidirect
113. C₂×#2615	D₄	semidirect
114. C₂×#2613	D₄	semidirect
115. C₂×#2388	D₄	semidirect
116. C₂×#2380	C₂³	semidirect
117. C₂×D₄×C₂²⋊C₄	D₄	semidirect
118. C₂×C₄×#120	D₄	semidirect
119. #33020	D₄	semidirect
120. #32898	D₄	semidirect
121. #24404	D₄	semidirect
135. #15984	D₄	semidirect
139. #15947	C₂³	semidirect
140. #15947	C₂³	semidirect
141. #15673	D₄	semidirect
143. #15310	D₄	semidirect
145. #15266	C₂³	semidirect
146. #15266	C₂³	semidirect
147. #15261	D₄	semidirect
148. #15259	D₄	semidirect
150. #15259	C₂³	semidirect
151. #15259	C₂³	semidirect
152. #15258	D₄	semidirect
153. #15258	D₄	semidirect
155. #15258	C₂³	semidirect
156. #15258	C₂³	semidirect
157. #15257	D₄	semidirect
159. #14666	C₂³	semidirect
160. #14657	D₄	semidirect
161. #14516	C₂³	semidirect
162. #14358	C₂³	semidirect
163. #14335	D₄	semidirect
165. #14136	D₄	semidirect
166. #14134	C₂³	semidirect
168. #13871	D₄	semidirect
169. #12852	C₂³	semidirect
170. #12852	C₂³	semidirect
171. #12694	C₂³	semidirect
172. #12693	C₂³	semidirect
173. #12687	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
205. C₂²×#127	C₂×D₄	semidirect
207. C₂²×#124	C₂×D₄	semidirect
209. C₂²×#123	C₂×D₄	semidirect
223. C₂²×#120	C₂×D₄	semidirect
224. C₂²×#120	C₂×D₄	semidirect
225. C₂²×#120	C₂×D₄	semidirect
226. C₂²×#120	C₂×D₄	semidirect
232. C₂×#518	C₂×D₄	semidirect
235. C₂²×#117	C₂×D₄	semidirect
239. C₂²×#99	C₂×D₄	semidirect
242. C₂×#395	C₂×D₄	semidirect
243. C₂×#394	C₂×D₄	semidirect
244. C₂×#393	C₂×D₄	semidirect
245. C₂×#393	C₂×D₄	semidirect
246. C₂×#393	C₂×D₄	semidirect
247. C₂×#392	C₂×D₄	semidirect
248. C₂×#392	C₂×D₄	semidirect
249. C₂×#392	C₂×D₄	semidirect
252. C₂×#386	C₂×D₄	semidirect
253. C₂×#386	C₂×D₄	semidirect
254. C₂×#386	C₂×D₄	semidirect
258. C₂×#381	C₂×D₄	semidirect
260. C₂×#380	C₂×D₄	semidirect
266. C₂×#379	C₂×D₄	semidirect
267. C₂×#379	C₂×D₄	semidirect
268. C₂×#379	C₂×D₄	semidirect
269. C₂×#379	C₂×D₄	semidirect
271. C₂×C₄×C₂²⋊C₄	C₂×D₄	semidirect
273. #1867	C₂×D₄	semidirect
274. #1790	C₂×D₄	semidirect
276. #1781	C₂×D₄	semidirect
279. #1440	C₂×D₄	semidirect
280. #1440	C₂×D₄	semidirect
281. #1438	C₂×D₄	semidirect
282. #1438	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
295. #1437	C₂×D₄	semidirect
296. #1437	C₂×D₄	semidirect
297. #1437	C₂×D₄	semidirect
298. #1437	C₂×D₄	semidirect
299. #1437	C₂×D₄	semidirect
300. #1437	C₂×D₄	semidirect
301. #1436	C₂×D₄	semidirect
302. #1436	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72317824	2
#72317791	2
#72317748	2
#72317643	2
#72293920	2
#72260517	2
#72240171	2
#72234687	2
#72234607	2
#72233443	2
#72233364	2
#72233019	2
#72232733	2
#72227862	2
#72225751	2
#72218215	2
#72216616	2
#72210587	2
#72210575	2