Subgroups — #72315046

Order 4096.

Only the 881 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 480 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72315031	C₂	1	2	yes	maximal, complemented
2	#72315025	C₂	1	2	yes	maximal, complemented
3	#72315022	C₂	1	2	yes	maximal, complemented
4	#72314961	C₂	1	2	yes	maximal, complemented
5	#72314953	C₂	1	2	yes	maximal, complemented
6	#72314855	C₂²	1	2	yes	complemented
7	#72314748	C₂²	1	2	yes	complemented
8	#72314476	C₂	1	1	yes	maximal, characteristic, complemented
9	#72314472	C₂²	1	2	yes	complemented
10	#72313608	C₂	1	1	yes	maximal, characteristic, complemented
11	#72312569	C₂	1	2	yes	maximal, complemented
12	#72312218	C₂²	1	2	yes	complemented
13	#72310363	C₂	1	2	yes	maximal, complemented
14	#72310358	C₂²	1	2	yes	complemented
15	#72310322	C₂²	1	2	yes	complemented
16	#72310205	C₂	1	1	yes	maximal, characteristic, complemented
17	#72309800	C₂²	1	1	yes	characteristic, complemented
18	#72309555	C₂²	1	2	yes	complemented
19	#72300151	C₂	1	1	yes	maximal, characteristic, complemented
20	#72271167	C₂²	1	1	yes	characteristic, complemented
21	#72266864	C₂²	1	1	yes	characteristic, complemented
22	#72266864	C₂²	1	1	yes	characteristic, complemented
23	#72266835	C₂²	1	2	yes	complemented
24	#72266442	C₂	1	1	yes	maximal, characteristic, complemented
25	#72266366	C₂²	1	2	yes	complemented
26	#72265766	C₂²	1	1	yes	characteristic, complemented
27	#72263490	C₂²	1	2	yes	complemented
28	#72260562	C₂²	1	1	yes	characteristic, complemented
29	#72258108	C₂	1	2	yes	maximal, complemented
30	#72258097	C₂²	1	2	yes	complemented
31	#72258094	C₂²	1	2	yes	complemented
32	#72256286	C₂	1	2	yes	maximal, complemented
33	#72256239	C₂	1	2	yes	maximal, complemented
34	#72256119	C₂²	1	1	yes	characteristic, complemented
35	#72256113	C₂²	1	2	yes	complemented
36	#72255971	C₂²	1	2	yes	complemented
37	#72255867	C₂²	1	2	yes	complemented
38	#72255778	C₂²	1	2	yes	complemented
39	#72255777	C₂²	1	2	yes	complemented
40	#72255774	C₂²	1	2	yes	complemented
41	#72255772	C₂²	1	2	yes	complemented
42	#72251583	C₂	1	2	yes	maximal, complemented
43	#72251552	C₂²	1	2	yes	complemented
44	#72251533	C₂²	1	2	yes	complemented
45	#72251530	C₂²	1	2	yes	complemented
46	#72251475	C₂²	1	2	yes	complemented
47	#72240132	C₂²	1	1	yes	characteristic, complemented
48	#72238976	C₂²	1	2	yes	complemented
49	#72238443	C₂²	1	2	yes	complemented
50	#72238343	C₂²	1	2	yes	complemented
51	#72238342	C₂²	1	2	yes	complemented
52	#72237907	C₂	1	1	yes	maximal, characteristic, complemented
53	#72237903	C₂²	1	2	yes	complemented
54	#72237900	C₂²	1	2	yes	complemented
55	#72237899	C₂²	1	2	yes	complemented
56	#72237638	C₂²	1	2	yes	complemented
57	#72237476	C₂²	1	2	yes	complemented
58	#72237472	C₂²	1	2	yes	complemented
59	#72237402	C₂²	1	2	yes	—
60	#72237381	C₂	1	1	yes	maximal, characteristic, complemented
61	#72237374	C₂²	1	2	yes	complemented
62	#72237302	C₂²	1	1	yes	characteristic, complemented
63	#72236678	C₂²	1	2	yes	complemented
64	#72236636	C₂²	1	2	yes	complemented
65	#72236521	C₂²	1	2	yes	complemented
66	#72236508	C₂²	1	2	yes	complemented
67	#72235242	C₂²	1	1	yes	characteristic, complemented
68	#72235130	C₂²	1	2	yes	—
69	#72234953	C₂²	1	2	yes	—
70	#72234625	C₂²	1	1	yes	characteristic, complemented
71	#72234100	C₂²	1	2	yes	complemented
72	#72233581	C₂²	1	2	yes	complemented
73	#72231950	C₂²	1	1	yes	characteristic, complemented
74	#72226366	C₂²	1	2	yes	complemented
75	#72225740	C₂²	1	2	yes	complemented
76	#72225713	C₂²	1	1	yes	characteristic, complemented
77	#72224136	C₂²	1	1	yes	characteristic
78	#72224136	C₂²	1	1	yes	characteristic
79	#72219438	C₂²	1	2	yes	complemented
80	#72219393	C₂²	1	2	yes	complemented
81	#72219314	C₂²	1	1	yes	characteristic, complemented
82	C₂×#139716	C₂²	1	1	yes	characteristic, complemented
83	#72219264	C₂²	1	1	yes	characteristic
84	#72219167	C₂	1	2	yes	maximal, complemented
85	#72219163	C₂²	1	2	yes	complemented
86	#72219162	C₂²	1	2	yes	complemented
87	#72219160	C₂²	1	2	yes	complemented
88	#72219160	C₂²	1	2	yes	complemented
89	#72219159	C₂²	1	2	yes	complemented
90	#72219158	C₂²	1	2	yes	complemented
91	#72219158	C₂²	1	2	yes	complemented
92	#72219157	C₂²	1	2	yes	complemented
93	#72219157	C₂²	1	2	yes	complemented
94	#72219040	C₂²	1	2	yes	—
95	#72218980	C₂²	1	2	yes	complemented
96	#72218838	C₂²	1	2	yes	complemented
97	#72218521	C₂²	1	2	yes	complemented
98	#72218521	C₂²	1	2	yes	complemented
99	#72218475	C₂²	1	2	yes	complemented
100	#72218317	C₂²	1	2	yes	complemented
101	#72218206	C₂²	1	2	yes	complemented
102	C₂×#139731	C₂²	1	2	yes	complemented
103	C₂×#347042	C₂²	1	2	yes	—
104	C₂×#347042	C₂²	1	1	yes	characteristic, complemented
105	C₂×#511790	C₂²	1	2	yes	complemented
106	C₂×#511790	C₂²	1	2	yes	complemented
107	#10586422	C₂³	1	2	yes	—
108	#10586404	C₂³	1	1	yes	characteristic
109	#10586404	C₂³	1	1	yes	characteristic
110	C₂×#62817	C₂³	1	2	yes	—
111	C₂×#62817	C₂³	1	1	yes	characteristic, complemented
112	C₂²×#3532	C₂³	1	1	yes	characteristic
113	#7630939	D₄	1	2	yes	complemented
114	C₂×#34980	C₂³	1	1	yes	characteristic
115	#6499871	D₄	1	2	yes	complemented
116	#6499870	D₄	1	2	yes	complemented
117	#6499869	D₄	1	2	yes	complemented
118	#6499867	D₄	1	2	yes	complemented
119	#6451874	D₄	1	2	yes	complemented
120	C₂×#23984	D₄	1	2	yes	complemented
121	#6451863	D₄	1	4	yes	complemented
122	#6437629	D₄	1	4	yes	complemented
123	C₂×#23895	C₂³	1	2	yes	—
124	C₂×#23895	C₂³	1	2	yes	—
125	#6437621	C₂³	1	2	yes	—
126	#6437621	C₂³	1	2	yes	—
127	#6437621	C₂³	1	2	yes	—
128	#6437621	C₂³	1	2	yes	complemented
129	C₂×#23900	C₂³	1	2	yes	—
130	C₂×#23900	C₂³	1	2	yes	—
131	C₂×#23900	C₂³	1	2	yes	—
132	C₂×#23897	C₂³	1	2	yes	—
133	#6437445	C₂³	1	2	yes	—
134	#6431795	C₂³	1	2	yes	—
135	#6374251	C₂³	1	1	yes	characteristic, complemented
136	#6374210	D₄	1	2	yes	complemented
137	#6374128	C₂³	1	1	yes	characteristic
138	#6374128	C₂³	1	1	yes	characteristic
139	#6374128	C₂³	1	1	yes	characteristic, complemented
140	C₂×#21746	C₂³	1	1	yes	characteristic, complemented
141	#5025789	D₄	1	1	yes	characteristic, complemented
142	#5025782	D₄	1	1	yes	characteristic, complemented
143	#5021140	D₄	1	1	yes	characteristic, complemented
144	#5021138	D₄	1	1	yes	characteristic, complemented
145	#4422949	D₄	1	1	yes	characteristic, complemented
146	#4420586	D₄	1	1	yes	characteristic, complemented
147	#763333	C₂³	1	1	yes	characteristic
148	#686187	D₄	1	1	yes	characteristic, complemented
149	#647656	D₄	1	1	yes	characteristic, complemented
150	#616961	C₂³	1	1	yes	characteristic
151	#616960	C₂³	1	1	yes	characteristic
152	C₂×#15947	C₂³	1	1	yes	characteristic
153	#552670	C₂³	1	1	yes	characteristic
154	C₂×#12707	C₂³	1	2	yes	—
155	C₂×#12707	C₂³	1	2	yes	—
156	C₂×#12707	C₂³	1	2	yes	complemented
157	C₂×#12705	C₂³	1	2	yes	—
158	C₂×#12705	C₂³	1	2	yes	—
159	C₂×#12705	C₂³	1	2	yes	—
160	C₂×#12705	C₂³	1	2	yes	—
161	C₂×#12705	C₂³	1	2	yes	complemented
162	#493370	C₂³	1	2	yes	—
163	#493370	C₂³	1	2	yes	—
164	#493357	C₂³	1	2	yes	—
165	#493357	C₂³	1	2	yes	—
166	#493357	C₂³	1	2	yes	complemented
167	C₂×#12687	C₂³	1	2	yes	—
168	C₂×#12687	C₂³	1	2	yes	—
169	C₂×#12687	C₂³	1	2	yes	complemented
170	#392030	C₂³	1	2	yes	complemented
171	#382544	C₂³	1	2	yes	complemented
172	#382436	C₂³	1	2	yes	—
173	#382434	C₂³	1	2	yes	—
174	#382434	C₂³	1	2	yes	—
175	#382434	C₂³	1	2	yes	complemented
176	#363969	D₄	1	4	yes	complemented
177	#359558	C₂³	1	2	yes	—
178	#359549	C₂³	1	2	yes	—
179	#359549	C₂³	1	2	yes	—
180	#359549	C₂³	1	2	yes	complemented
181	#359528	D₄	1	4	yes	complemented
182	#359509	C₂³	1	2	yes	—
183	#359501	C₂³	1	2	yes	—
184	#359501	C₂³	1	2	yes	complemented
185	#359442	C₂³	1	2	yes	—
186	#188109	C₂³	1	1	yes	characteristic, complemented
187	C₂×#8547	C₂³	1	1	yes	characteristic, complemented
188	#188050	C₂³	1	2	yes	—
189	#188049	C₂³	1	1	yes	characteristic, complemented
190	C₂×#8541	C₂³	1	2	yes	—
191	C₂×#8541	C₂³	1	1	yes	characteristic, complemented
192	#187944	C₂³	1	2	yes	—
193	#187944	C₂³	1	2	yes	—
194	C₂×#8534	C₂³	1	2	yes	—
195	C₂×#8534	C₂³	1	2	yes	—
196	C₂×#8534	C₂³	1	2	yes	complemented
197	#186835	C₂³	1	2	yes	complemented
198	#146479	C₂³	1	2	yes	complemented
199	#146475	C₂³	1	2	yes	complemented
200	#128033	C₂³	1	2	yes	complemented
201	C₂×#7304	C₂³	1	2	yes	complemented
202	C₂×#7316	C₂³	1	2	yes	complemented
203	C₂×#7316	C₂³	1	2	yes	complemented
204	C₂×#7314	C₂³	1	2	yes	complemented
205	C₂×#7314	C₂³	1	2	yes	complemented
206	C₂×#7311	C₂³	1	2	yes	complemented
207	C₂×#7310	C₂³	1	2	yes	complemented
208	C₂×#7310	C₂³	1	2	yes	complemented
209	C₂×#7310	C₂³	1	2	yes	complemented
210	#128009	C₂³	1	2	yes	complemented
211	C₂×#7307	C₂³	1	2	yes	complemented
212	#107130	C₂³	1	2	yes	complemented
213	#107114	C₂³	1	2	yes	complemented
214	C₂⁵×D₄	C₂×D₄	1	1	yes	characteristic
215	#62844	C₂×D₄	1	4	yes	—
216	#62842	C₂×D₄	1	4	yes	—
217	#62842	C₂×D₄	1	2	yes	complemented
218	#62820	C₂×D₄	1	2	yes	—
219	#62817	C₂×D₄	1	2	yes	—
220	C₂×#3490	C₂×D₄	1	2	yes	—
221	C₂×#3484	C₂×D₄	1	2	yes	—
222	C₂×#3484	C₂⁴	1	2	yes	—
223	C₂×#3484	C₂⁴	1	2	yes	—
224	C₂×#3484	C₂⁴	1	2	yes	—
225	C₂²×#551	C₂×D₄	1	1	yes	characteristic
226	C₂²×D₄²	C₂×D₄	1	1	yes	characteristic
227	C₂²×H(3,𝔽₄)	C₂×D₄	1	1	yes	characteristic
228	C₂²×#560	C₂×D₄	1	1	yes	characteristic
229	C₂²×#535	C₂⁴	1	1	yes	characteristic
230	C₂²×#534	C₂⁴	1	1	yes	characteristic
231	C₂²×#534	C₂⁴	1	1	yes	characteristic
232	C₂³×#120	C₂⁴	1	1	yes	characteristic
233	C₂³×#120	C₂⁴	1	1	yes	characteristic
234	C₂×#3026	C₂×D₄	1	4	yes	—
235	C₂×#3026	C₂×D₄	1	4	yes	complemented
236	C₂×#2883	C₂×D₄	1	2	yes	complemented
237	C₂×#2883	C₂×D₄	1	2	yes	complemented
238	C₂×#2849	C₂×D₄	1	1	yes	characteristic
239	C₂×#2849	C₂×D₄	1	1	yes	characteristic
240	C₂×#2846	C₂×D₄	1	1	yes	characteristic
241	C₂×#2846	C₂×D₄	1	1	yes	characteristic
242	C₂×#2846	C₂×D₄	1	4	yes	—
243	#34980	C₂×D₄	1	4	yes	—
244	C₂×#2613	C₂×D₄	1	1	yes	characteristic
245	C₂×#2613	C₂×D₄	1	1	yes	characteristic
246	C₂×#2613	C₂×D₄	1	1	yes	characteristic
247	C₂×#2613	C₂×D₄	1	1	yes	characteristic
248	#34171	C₂×D₄	1	2	yes	—
249	#34171	C₂⁴	1	2	yes	—
250	C₂×#2308	C₂×D₄	1	1	yes	characteristic
251	C₂×#2308	C₂×D₄	1	1	yes	characteristic
252	C₂²×#379	C₂×D₄	1	1	yes	characteristic
253	#23901	C₂×D₄	1	4	yes	—
254	#23900	C₂×D₄	1	4	yes	—
255	#23900	C₂×D₄	1	4	yes	—
256	#23900	C₂×D₄	1	4	yes	—
257	#21747	C₂×D₄	1	2	yes	—
258	#21746	C₂×D₄	1	2	yes	—
259	C₂×#1913	C₂×D₄	1	4	yes	—
260	C₂×#1913	C₂×D₄	1	4	yes	—
261	C₂×#1913	C₂×D₄	1	4	yes	complemented
262	C₂×#1913	C₂×D₄	1	4	yes	complemented
263	C₂×#1898	C₂×D₄	1	4	yes	—
264	C₂×#1898	C₂×D₄	1	4	yes	—
265	#20960	C₂×D₄	1	4	yes	—
266	#20960	C₂×D₄	1	4	yes	complemented
267	C₂×#1828	C₂×D₄	1	4	yes	complemented
268	C₂×#1819	C₂×D₄	1	2	yes	—
269	C₂×#1783	C₂⁴	1	2	yes	—
270	C₂×#1783	C₂⁴	1	2	yes	—
271	#20585	C₂×D₄	1	4	yes	complemented
272	C₂×#1781	C₂⁴	1	2	yes	—
273	C₂×#1781	C₂⁴	1	2	yes	—
274	C₂×#1781	C₂⁴	1	2	yes	—
275	C₂×#1781	C₂⁴	1	2	yes	—
276	C₂×#1781	C₂⁴	1	2	yes	—
277	C₂×#1781	C₂⁴	1	2	yes	—
278	#20354	C₂×D₄	1	2	yes	complemented
279	#15948	C₂×D₄	1	1	yes	characteristic
280	#15948	C₂×D₄	1	1	yes	characteristic
281	#15947	C₂×D₄	1	1	yes	characteristic
282	#15947	C₂×D₄	1	1	yes	characteristic
283	#15947	C₂×D₄	1	1	yes	characteristic
284	#15947	C₂×D₄	1	1	yes	characteristic
285	#15947	C₂×D₄	1	1	yes	characteristic
286	#15947	C₂×D₄	1	1	yes	characteristic
287	#15262	C₂×D₄	1	1	yes	characteristic
288	#15261	C₂×D₄	1	1	yes	characteristic
289	#15259	C₂×D₄	1	1	yes	characteristic
290	#15259	C₂×D₄	1	1	yes	characteristic
291	#15259	C₂×D₄	1	1	yes	characteristic
292	#15258	C₂×D₄	1	1	yes	characteristic
293	#15258	C₂×D₄	1	1	yes	characteristic
294	#15258	C₂×D₄	1	1	yes	characteristic
295	#14658	C₂×D₄	1	1	yes	characteristic
296	#14657	C₂×D₄	1	1	yes	characteristic
297	#14335	C₂⁴	1	1	yes	characteristic
298	#14167	C₂×D₄	1	1	yes	characteristic
299	#14134	C₂×D₄	1	1	yes	characteristic
300	C₂×#1438	C₂⁴	1	1	yes	characteristic
301	C₂⁷	#120	1	1	yes	characteristic, complemented
302	C₂⁷	C₂²×D₄	1	1	yes	characteristic
303	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
304	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
305	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
306	C₂²×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
307	C₂²×H(5,𝔽₂)	H(5,𝔽₂)	1	2	yes	—
308	C₂³×#41	H(5,𝔽₂)	1	1	yes	characteristic
309	C₂⁴×D₄	#120	1	1	yes	characteristic, complemented
310	C₂⁴×D₄	#120	1	1	yes	characteristic, complemented
311	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
312	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
313	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
314	C₂⁵×C₄	#120	1	1	yes	characteristic, complemented
315	#3484	C₂²×D₄	1	4	yes	—
316	#3484	H(5,𝔽₂)	1	4	yes	—
317	C₂×#543	#120	1	2	yes	—
318	C₂×#534	#120	1	4	yes	—
319	C₂×#534	#120	1	2	yes	—
320	C₂×#534	C₂²×D₄	1	4	yes	—
321	C₂×#534	C₂²×D₄	1	4	yes	—
322	C₂×#534	H(5,𝔽₂)	1	4	yes	—
323	C₂²×#127	C₂²×D₄	1	1	yes	characteristic
324	C₂²×#127	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂²×#124	C₂²×D₄	1	1	yes	characteristic
326	C₂²×#124	H(5,𝔽₂)	1	1	yes	characteristic
327	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
328	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
329	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
330	C₂²×#123	C₂²×D₄	1	1	yes	characteristic
331	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
332	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
333	C₂²×#120	C₂²×D₄	1	4	yes	—
334	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
335	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
336	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
337	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
338	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
339	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
340	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
341	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
342	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂²×#120	H(5,𝔽₂)	1	1	yes	characteristic
344	C₂×#518	#120	1	2	yes	—
345	C₂×#518	#120	1	4	yes	—
346	C₂×#518	C₂²×D₄	1	2	yes	—
347	C₂×#518	C₂²×D₄	1	2	yes	—
348	C₂×#518	C₂²×D₄	1	2	yes	—
349	C₂×#518	C₂²×D₄	1	2	yes	—
350	C₂×#518	H(5,𝔽₂)	1	2	yes	—
351	C₂²×#117	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
353	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
354	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
355	C₂³×C₂²⋊C₄	H(5,𝔽₂)	1	1	yes	characteristic
356	C₂²×#99	C₂²×D₄	1	4	yes	—
357	C₂²×#99	C₂²×D₄	1	4	yes	—
358	C₂×#381	#120	1	1	yes	characteristic, complemented
359	C₂×#381	#120	1	1	yes	characteristic, complemented
360	C₂×#381	#120	1	1	yes	characteristic, complemented
361	C₂×#381	#120	1	1	yes	characteristic, complemented
362	C₂×#379	#120	1	1	yes	characteristic, complemented
363	C₂×#379	#120	1	1	yes	characteristic, complemented
364	C₂×#379	#120	1	1	yes	characteristic, complemented
365	C₂×#379	#120	1	1	yes	characteristic, complemented
366	C₂×#379	#120	1	1	yes	characteristic, complemented
367	C₂×#379	#120	1	1	yes	characteristic, complemented
368	C₂×#379	#120	1	1	yes	characteristic, complemented
369	C₂×#379	#120	1	1	yes	characteristic, complemented
370	C₂×#379	C₂²×D₄	1	4	yes	—
371	#1781	C₂²×D₄	1	4	yes	—
372	#1438	C₂²×D₄	1	1	yes	characteristic
373	#1438	C₂²×D₄	1	1	yes	characteristic
374	#1438	C₂²×D₄	1	1	yes	characteristic
375	#1438	C₂²×D₄	1	1	yes	characteristic
376	C₂⁶	C₂×#120	1	1	yes	characteristic
377	C₂⁶	C₂×#120	1	1	yes	characteristic
378	C₂⁶	C₂×#120	1	1	yes	characteristic
379	C₂⁶	C₂×#120	1	1	yes	characteristic
380	C₂⁶	#534	1	1	yes	characteristic
381	C₂⁶	#534	1	1	yes	characteristic
382	C₂⁶	C₂³×D₄	1	1	yes	characteristic
383	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×H(5,𝔽₂)	#534	1	4	yes	—
385	C₂³×Q₈	#534	1	1	yes	characteristic
386	C₂³×D₄	C₂×#120	1	2	yes	—
387	C₂³×D₄	C₂×#120	1	4	yes	—
388	C₂³×D₄	#534	1	2	yes	—
389	C₂³×D₄	#534	1	1	yes	characteristic
390	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
391	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
392	C₂³×D₄	C₂³×D₄	1	2	yes	—
393	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
394	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
395	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
397	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
398	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
399	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
400	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
401	C₂×#123	B(4,𝔽₂)	1	8	yes	complemented
402	C₂×#123	D₄²	1	4	yes	—
403	C₂×#123	D₄²	1	4	yes	—
404	C₂×#120	B(4,𝔽₂)	1	8	yes	complemented
405	C₂×#120	D₄²	1	4	yes	—
406	C₂×#120	D₄²	1	4	yes	—
407	#518	#534	1	4	yes	—
408	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
409	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
410	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
411	C₂²×C₂²⋊C₄	C₂×#120	1	4	yes	—
412	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
413	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
414	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
415	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
416	C₂²×C₂²⋊C₄	#534	1	2	yes	—
417	C₂²×C₂²⋊C₄	#534	1	1	yes	characteristic
418	C₂²×C₂²⋊C₄	#534	1	1	yes	characteristic
419	C₂²×C₄²	#534	1	1	yes	characteristic
420	C₂²×C₄²	#534	1	1	yes	characteristic
421	C₂⁵	#2403	1	2	yes	—
422	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
423	C₂⁵	C₂²×#120	1	1	yes	characteristic
424	C₂⁵	C₂²×#120	1	1	yes	characteristic
425	C₂⁵	C₂×#534	1	1	yes	characteristic
426	C₂⁵	C₂×#534	1	1	yes	characteristic
427	C₂⁵	#3484	1	2	yes	—
428	C₂⁵	#3484	1	1	yes	characteristic
429	C₂⁵	#3484	1	1	yes	characteristic
430	C₂⁵	#3484	1	1	yes	characteristic
431	C₂⁵	#3484	1	1	yes	characteristic
432	C₂⁵	#3484	1	1	yes	characteristic
433	C₂⁵	#3532	1	2	yes	—
434	C₂²×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
435	C₂²×D₄	C₂×#534	1	2	yes	—
436	C₂²×D₄	C₂×D₄²	1	2	yes	—
437	C₂²×D₄	C₂×D₄²	1	2	yes	—
438	C₂²×D₄	#3484	1	2	yes	—
439	C₂²×D₄	#3484	1	2	yes	—
440	C₂²×D₄	#3484	1	2	yes	—
441	C₂²×D₄	#3532	1	2	yes	—
442	C₂²×D₄	#3532	1	2	yes	—
443	C₂³×C₄	#2403	1	2	yes	—
444	C₂³×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
445	C₂³×C₄	C₂×#534	1	1	yes	characteristic
446	C₂³×C₄	#3484	1	2	yes	—
447	C₂³×C₄	#3484	1	1	yes	characteristic
448	C₂³×C₄	#3532	1	2	yes	—
449	C₂×C₂²⋊C₄	#2403	1	2	yes	—
450	C₂×C₂²⋊C₄	#2403	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	8	yes	—
452	C₂⁴	#23900	1	4	yes	—
453	C₂⁴	C₂×#2403	1	1	yes	characteristic
454	C₂⁴	#34980	1	1	yes	characteristic
455	C₂⁴	#34980	1	1	yes	characteristic
456	C₂⁴	#35346	1	1	yes	characteristic
457	C₂⁴	#35346	1	1	yes	characteristic
458	C₂⁴	#36714	1	1	yes	characteristic
459	C₂⁴	#36714	1	1	yes	characteristic
460	C₂⁴	#37644	1	2	yes	—
461	C₂⁴	#37644	1	2	yes	—
462	C₂⁴	C₂²×B(4,𝔽₂)	1	4	yes	—
463	C₂²×C₄	#23900	1	4	yes	—
464	C₂²×C₄	#37644	1	2	yes	—
465	C₂²×C₄	#37644	1	2	yes	—
466	C₂³	#616960	1	1	yes	characteristic
467	C₂³	C₂×#23900	1	2	yes	—
468	C₂³	#6499867	1	2	yes	—
469	C₂³	#6499867	1	2	yes	—
470	C₂³	#6499874	1	1	yes	characteristic
471	C₂³	#6499874	1	1	yes	characteristic
472	C₂³	#6499876	1	2	yes	—
473	C₂²	#72217730	1	1	yes	characteristic
474	C₂²	#72225641	1	1	yes	characteristic
475	C₂²	#72234418	1	2	yes	—
476	C₂²	#72240631	1	2	yes	—
477	C₂²	#72251380	1	1	yes	characteristic
478	C₂	#72266214	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266214
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ 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. #72315031	C₂	semidirect
2. #72315025	C₂	semidirect
3. #72315022	C₂	semidirect
4. #72314961	C₂	semidirect
5. #72314953	C₂	semidirect
6. #72314855	C₂²	semidirect
7. #72314748	C₂²	semidirect
8. #72314476	C₂	semidirect
9. #72314472	C₂²	semidirect
10. #72313608	C₂	semidirect
11. #72312569	C₂	semidirect
12. #72312218	C₂²	semidirect
13. #72310363	C₂	semidirect
14. #72310358	C₂²	semidirect
15. #72310322	C₂²	semidirect
16. #72310205	C₂	semidirect
17. #72309800	C₂²	semidirect
18. #72309555	C₂²	semidirect
19. #72300151	C₂	semidirect
20. #72271167	C₂²	semidirect
21. #72266864	C₂²	semidirect
22. #72266864	C₂²	semidirect
23. #72266835	C₂²	semidirect
24. #72266442	C₂	semidirect
25. #72266366	C₂²	semidirect
26. #72265766	C₂²	semidirect
27. #72263490	C₂²	semidirect
28. #72260562	C₂²	semidirect
29. #72258108	C₂	semidirect
30. #72258097	C₂²	semidirect
31. #72258094	C₂²	semidirect
32. #72256286	C₂	semidirect
33. #72256239	C₂	semidirect
34. #72256119	C₂²	semidirect
35. #72256113	C₂²	semidirect
36. #72255971	C₂²	semidirect
37. #72255867	C₂²	semidirect
38. #72255778	C₂²	semidirect
39. #72255777	C₂²	semidirect
40. #72255774	C₂²	semidirect
41. #72255772	C₂²	semidirect
42. #72251583	C₂	semidirect
43. #72251552	C₂²	semidirect
44. #72251533	C₂²	semidirect
45. #72251530	C₂²	semidirect
46. #72251475	C₂²	semidirect
47. #72240132	C₂²	semidirect
48. #72238976	C₂²	semidirect
49. #72238443	C₂²	semidirect
50. #72238343	C₂²	semidirect
51. #72238342	C₂²	semidirect
52. #72237907	C₂	semidirect
53. #72237903	C₂²	semidirect
54. #72237900	C₂²	semidirect
55. #72237899	C₂²	semidirect
56. #72237638	C₂²	semidirect
57. #72237476	C₂²	semidirect
58. #72237472	C₂²	semidirect
60. #72237381	C₂	semidirect
61. #72237374	C₂²	semidirect
62. #72237302	C₂²	semidirect
63. #72236678	C₂²	semidirect
64. #72236636	C₂²	semidirect
65. #72236521	C₂²	semidirect
66. #72236508	C₂²	semidirect
67. #72235242	C₂²	semidirect
70. #72234625	C₂²	semidirect
71. #72234100	C₂²	semidirect
72. #72233581	C₂²	semidirect
73. #72231950	C₂²	semidirect
74. #72226366	C₂²	semidirect
75. #72225740	C₂²	semidirect
76. #72225713	C₂²	semidirect
79. #72219438	C₂²	semidirect
80. #72219393	C₂²	semidirect
81. #72219314	C₂²	semidirect
82. C₂×#139716	C₂²	semidirect
84. #72219167	C₂	semidirect
85. #72219163	C₂²	semidirect
86. #72219162	C₂²	semidirect
87. #72219160	C₂²	semidirect
88. #72219160	C₂²	semidirect
89. #72219159	C₂²	semidirect
90. #72219158	C₂²	semidirect
91. #72219158	C₂²	semidirect
92. #72219157	C₂²	semidirect
93. #72219157	C₂²	semidirect
95. #72218980	C₂²	semidirect
96. #72218838	C₂²	semidirect
97. #72218521	C₂²	semidirect
98. #72218521	C₂²	semidirect
99. #72218475	C₂²	semidirect
100. #72218317	C₂²	semidirect
101. #72218206	C₂²	semidirect
102. C₂×#139731	C₂²	semidirect
104. C₂×#347042	C₂²	semidirect
105. C₂×#511790	C₂²	semidirect
106. C₂×#511790	C₂²	semidirect
111. C₂×#62817	C₂³	semidirect
113. #7630939	D₄	semidirect
115. #6499871	D₄	semidirect
116. #6499870	D₄	semidirect
117. #6499869	D₄	semidirect
118. #6499867	D₄	semidirect
119. #6451874	D₄	semidirect
120. C₂×#23984	D₄	semidirect
121. #6451863	D₄	semidirect
122. #6437629	D₄	semidirect
128. #6437621	C₂³	semidirect
135. #6374251	C₂³	semidirect
136. #6374210	D₄	semidirect
139. #6374128	C₂³	semidirect
140. C₂×#21746	C₂³	semidirect
141. #5025789	D₄	semidirect
142. #5025782	D₄	semidirect
143. #5021140	D₄	semidirect
144. #5021138	D₄	semidirect
145. #4422949	D₄	semidirect
146. #4420586	D₄	semidirect
148. #686187	D₄	semidirect
149. #647656	D₄	semidirect
156. C₂×#12707	C₂³	semidirect
161. C₂×#12705	C₂³	semidirect
166. #493357	C₂³	semidirect
169. C₂×#12687	C₂³	semidirect
170. #392030	C₂³	semidirect
171. #382544	C₂³	semidirect
175. #382434	C₂³	semidirect
176. #363969	D₄	semidirect
180. #359549	C₂³	semidirect
181. #359528	D₄	semidirect
184. #359501	C₂³	semidirect
186. #188109	C₂³	semidirect
187. C₂×#8547	C₂³	semidirect
189. #188049	C₂³	semidirect
191. C₂×#8541	C₂³	semidirect
196. C₂×#8534	C₂³	semidirect
197. #186835	C₂³	semidirect
198. #146479	C₂³	semidirect
199. #146475	C₂³	semidirect
200. #128033	C₂³	semidirect
201. C₂×#7304	C₂³	semidirect
202. C₂×#7316	C₂³	semidirect
203. C₂×#7316	C₂³	semidirect
204. C₂×#7314	C₂³	semidirect
205. C₂×#7314	C₂³	semidirect
206. C₂×#7311	C₂³	semidirect
207. C₂×#7310	C₂³	semidirect
208. C₂×#7310	C₂³	semidirect
209. C₂×#7310	C₂³	semidirect
210. #128009	C₂³	semidirect
211. C₂×#7307	C₂³	semidirect
212. #107130	C₂³	semidirect
213. #107114	C₂³	semidirect
217. #62842	C₂×D₄	semidirect
235. C₂×#3026	C₂×D₄	semidirect
236. C₂×#2883	C₂×D₄	semidirect
237. C₂×#2883	C₂×D₄	semidirect
261. C₂×#1913	C₂×D₄	semidirect
262. C₂×#1913	C₂×D₄	semidirect
266. #20960	C₂×D₄	semidirect
267. C₂×#1828	C₂×D₄	semidirect
271. #20585	C₂×D₄	semidirect
278. #20354	C₂×D₄	semidirect
301. C₂⁷	#120	semidirect
309. C₂⁴×D₄	#120	semidirect
310. C₂⁴×D₄	#120	semidirect
314. C₂⁵×C₄	#120	semidirect
358. C₂×#381	#120	semidirect
359. C₂×#381	#120	semidirect
360. C₂×#381	#120	semidirect
361. C₂×#381	#120	semidirect
362. C₂×#379	#120	semidirect
363. C₂×#379	#120	semidirect
364. C₂×#379	#120	semidirect
365. C₂×#379	#120	semidirect
366. C₂×#379	#120	semidirect
367. C₂×#379	#120	semidirect
368. C₂×#379	#120	semidirect
369. C₂×#379	#120	semidirect
401. C₂×#123	B(4,𝔽₂)	semidirect
404. C₂×#120	B(4,𝔽₂)	semidirect

Maximal subgroups

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

subgroup	index
#72315031	2
#72315025	2
#72315022	2
#72314961	2
#72314953	2
#72314476	2
#72313608	2
#72312569	2
#72310363	2
#72310205	2
#72300151	2
#72266442	2
#72258108	2
#72256286	2
#72256239	2
#72251583	2
#72237907	2
#72237381	2
#72219167	2