Subgroups — #72315156

Order 4096.

Only the 997 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 554 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72315149	C₂	1	1	yes	maximal, characteristic, complemented
2	#72315084	C₂	1	1	yes	maximal, characteristic, complemented
3	#72315053	C₂	1	2	yes	maximal, complemented
4	#72315022	C₂	1	2	yes	maximal, complemented
5	#72314981	C₂	1	2	yes	maximal, complemented
6	#72314872	C₂	1	2	yes	maximal, complemented
7	#72314858	C₂	1	2	yes	maximal, complemented
8	#72314855	C₂²	1	2	yes	complemented
9	#72314742	C₂	1	2	yes	maximal, complemented
10	#72314739	C₂²	1	2	yes	complemented
11	#72314732	C₂	1	2	yes	maximal, complemented
12	#72314729	C₂²	1	2	yes	complemented
13	#72314663	C₂	1	2	yes	maximal, complemented
14	#72314482	C₂	1	1	yes	maximal, characteristic, complemented
15	#72314472	C₂²	1	2	yes	complemented
16	#72314456	C₂²	1	2	yes	complemented
17	#72314452	C₂²	1	2	yes	complemented
18	#72314440	C₂²	1	2	yes	complemented
19	#72312226	C₂	1	1	yes	maximal, characteristic, complemented
20	#72312218	C₂²	1	2	yes	complemented
21	#72312216	C₂²	1	2	yes	complemented
22	#72312214	C₂²	1	2	yes	complemented
23	#72310285	C₂	1	1	yes	maximal, characteristic, complemented
24	#72310283	C₂²	1	2	yes	complemented
25	#72309563	C₂	1	1	yes	maximal, characteristic, complemented
26	#72309555	C₂²	1	2	yes	complemented
27	#72309552	C₂²	1	2	yes	complemented
28	#72266870	C₂	1	1	yes	maximal, characteristic, complemented
29	#72266864	C₂²	1	2	yes	—
30	#72266864	C₂²	1	2	yes	—
31	#72266863	C₂²	1	2	yes	—
32	#72266863	C₂²	1	2	yes	—
33	#72266368	C₂²	1	2	yes	complemented
34	#72266366	C₂²	1	2	yes	complemented
35	#72264799	C₂	1	1	yes	maximal, characteristic, complemented
36	#72264793	C₂	1	1	yes	maximal, characteristic, complemented
37	#72264754	C₂²	1	2	yes	complemented
38	#72262349	C₂	1	1	yes	maximal, characteristic, complemented
39	#72260537	C₂²	1	2	yes	complemented
40	#72259125	C₂²	1	2	yes	complemented
41	C₂×#144639	C₂²	1	2	yes	complemented
42	C₂×#139742	C₂²	1	2	yes	complemented
43	#72256195	C₂²	1	2	yes	complemented
44	#72256043	C₂²	1	2	yes	complemented
45	#72255986	C₂²	1	2	yes	complemented
46	#72255849	C₂²	1	2	yes	complemented
47	#72255841	C₂²	1	2	yes	complemented
48	#72255778	C₂²	1	2	yes	complemented
49	#72255774	C₂²	1	2	yes	complemented
50	#72251523	C₂	1	1	yes	maximal, characteristic, complemented
51	#72251501	C₂²	1	2	yes	complemented
52	#72251499	C₂²	1	2	yes	complemented
53	#72251479	C₂	1	1	yes	maximal, characteristic, complemented
54	#72251476	C₂²	1	2	yes	complemented
55	#72251475	C₂²	1	2	yes	complemented
56	#72251473	C₂²	1	2	yes	complemented
57	#72251471	C₂²	1	2	yes	complemented
58	#72251218	C₂	1	1	yes	maximal, characteristic, complemented
59	#72251171	C₂²	1	1	yes	characteristic, complemented
60	#72246450	C₂²	1	2	yes	complemented
61	#72246288	C₂²	1	2	yes	complemented
62	#72246286	C₂²	1	2	yes	complemented
63	#72238613	C₂²	1	1	yes	characteristic, complemented
64	#72238613	C₂²	1	1	yes	characteristic, complemented
65	#72238612	C₂²	1	1	yes	characteristic, complemented
66	#72238344	C₂	1	1	yes	maximal, characteristic, complemented
67	#72238344	C₂	1	1	yes	maximal, characteristic, complemented
68	#72237900	C₂²	1	1	yes	characteristic, complemented
69	#72237900	C₂²	1	1	yes	characteristic, complemented
70	#72237899	C₂²	1	1	yes	characteristic, complemented
71	#72237829	C₂²	1	1	yes	characteristic, complemented
72	#72237599	C₂²	1	2	yes	complemented
73	#72237472	C₂²	1	2	yes	—
74	#72237472	C₂²	1	2	yes	—
75	#72237472	C₂²	1	2	yes	—
76	#72237472	C₂²	1	2	yes	—
77	#72237398	C₂²	1	1	yes	characteristic
78	#72237398	C₂²	1	1	yes	characteristic
79	#72236928	C₂²	1	2	yes	complemented
80	#72236636	C₂²	1	2	yes	complemented
81	#72236631	C₂²	1	2	yes	complemented
82	#72235130	C₂²	1	2	yes	—
83	#72235130	C₂²	1	2	yes	—
84	#72235130	C₂²	1	2	yes	—
85	#72235130	C₂²	1	2	yes	—
86	#72234663	C₂²	1	1	yes	characteristic
87	#72232884	C₂²	1	1	yes	characteristic
88	#72225667	C₂²	1	1	yes	characteristic, complemented
89	#72225619	C₂²	1	1	yes	characteristic, complemented
90	#72225617	C₂²	1	1	yes	characteristic, complemented
91	#72225617	C₂²	1	1	yes	characteristic, complemented
92	#72219418	C₂²	1	1	yes	characteristic, complemented
93	#72219415	C₂²	1	1	yes	characteristic, complemented
94	#72219414	C₂²	1	1	yes	characteristic, complemented
95	#72219414	C₂²	1	1	yes	characteristic, complemented
96	#72219251	C₂²	1	1	yes	characteristic, complemented
97	#72219248	C₂²	1	1	yes	characteristic, complemented
98	#72219243	C₂²	1	1	yes	characteristic, complemented
99	#72219237	C₂²	1	1	yes	characteristic, complemented
100	#72219225	C₂²	1	1	yes	characteristic
101	C₂²×#8534	C₂²	1	1	yes	characteristic
102	C₂²×#8534	C₂²	1	1	yes	characteristic
103	#72219163	C₂²	1	2	yes	complemented
104	#72219160	C₂²	1	2	yes	complemented
105	#72218498	C₂²	1	1	yes	characteristic, complemented
106	#72218455	C₂²	1	1	yes	characteristic, complemented
107	#72218306	C₂²	1	1	yes	characteristic
108	#72218306	C₂²	1	1	yes	characteristic
109	#72218306	C₂²	1	1	yes	characteristic
110	#72218306	C₂²	1	1	yes	characteristic
111	#72218198	C₂²	1	1	yes	characteristic, complemented
112	#72218180	C₂²	1	1	yes	characteristic, complemented
113	C₂×#144364	C₂²	1	2	yes	complemented
114	C₂×#139743	C₂²	1	2	yes	complemented
115	#72213862	C₂²	1	1	yes	characteristic
116	#72213862	C₂²	1	1	yes	characteristic
117	#72213862	C₂²	1	1	yes	characteristic
118	#72213862	C₂²	1	1	yes	characteristic
119	#72210555	C₂²	1	1	yes	characteristic
120	#72210555	C₂²	1	1	yes	characteristic
121	#72210511	C₂²	1	1	yes	characteristic
122	#72210511	C₂²	1	1	yes	characteristic
123	#10586404	C₂³	1	2	yes	—
124	#10586404	C₂³	1	2	yes	—
125	C₂²×#3484	C₂³	1	1	yes	characteristic
126	C₂²×#3484	C₂³	1	1	yes	characteristic
127	C₂²×#3484	C₂³	1	1	yes	characteristic
128	#7630939	C₂³	1	1	yes	characteristic
129	#7630939	C₂³	1	1	yes	characteristic
130	#7626202	D₄	1	2	yes	complemented
131	C₂×#32873	C₂³	1	1	yes	characteristic, complemented
132	C₂×#23895	D₄	1	2	yes	complemented
133	C₂×#23895	D₄	1	2	yes	complemented
134	C₂×#23895	D₄	1	2	yes	complemented
135	C₂×#23895	D₄	1	2	yes	complemented
136	C₂×#23895	C₂³	1	2	yes	—
137	C₂×#23895	C₂³	1	2	yes	—
138	C₂×#23895	C₂³	1	1	yes	characteristic, complemented
139	#6437621	C₂³	1	1	yes	characteristic
140	#6437621	C₂³	1	1	yes	characteristic
141	#6437621	C₂³	1	1	yes	characteristic
142	#6437621	C₂³	1	1	yes	characteristic
143	C₂×#23897	C₂³	1	2	yes	—
144	C₂×#23897	C₂³	1	2	yes	—
145	#6374251	C₂³	1	1	yes	characteristic
146	#6374251	C₂³	1	1	yes	characteristic
147	C₂×#21776	C₂³	1	1	yes	characteristic, complemented
148	C₂×#21776	C₂³	1	1	yes	characteristic, complemented
149	#6374128	C₂³	1	1	yes	characteristic
150	#6374128	C₂³	1	1	yes	characteristic
151	C₂×#21746	D₄	1	2	yes	complemented
152	#6371007	D₄	1	2	yes	complemented
153	#6370693	D₄	1	2	yes	complemented
154	C₂²×#1781	C₂³	1	1	yes	characteristic
155	C₂²×#1781	C₂³	1	1	yes	characteristic
156	#552677	C₂³	1	2	yes	—
157	#552670	C₂³	1	2	yes	—
158	#517411	C₂³	1	1	yes	characteristic
159	C₂²×#1438	C₂³	1	1	yes	characteristic
160	C₂×#12707	C₂³	1	2	yes	—
161	C₂×#12707	C₂³	1	2	yes	—
162	C₂×#12707	C₂³	1	2	yes	—
163	C₂×#12707	C₂³	1	2	yes	—
164	C₂×#12705	C₂³	1	2	yes	—
165	C₂×#12705	C₂³	1	2	yes	—
166	C₂×#12705	C₂³	1	2	yes	—
167	C₂×#12705	C₂³	1	2	yes	—
168	#493357	C₂³	1	2	yes	—
169	#493357	C₂³	1	2	yes	—
170	#493357	C₂³	1	2	yes	—
171	#493357	C₂³	1	2	yes	—
172	#392113	C₂³	1	1	yes	characteristic
173	#392113	C₂³	1	1	yes	characteristic
174	#392109	C₂³	1	1	yes	characteristic
175	#392109	C₂³	1	1	yes	characteristic
176	#392109	C₂³	1	1	yes	characteristic
177	#392109	C₂³	1	1	yes	characteristic
178	#392030	C₂³	1	1	yes	characteristic, complemented
179	#392030	C₂³	1	1	yes	characteristic, complemented
180	#392030	C₂³	1	1	yes	characteristic, complemented
181	#382544	C₂³	1	1	yes	characteristic, complemented
182	#382544	C₂³	1	1	yes	characteristic, complemented
183	#382434	C₂³	1	1	yes	characteristic, complemented
184	#382434	C₂³	1	1	yes	characteristic, complemented
185	#373637	C₂³	1	1	yes	characteristic, complemented
186	#359558	C₂³	1	2	yes	—
187	#359558	C₂³	1	2	yes	—
188	#359549	D₄	1	2	yes	complemented
189	#359549	D₄	1	2	yes	complemented
190	#359549	D₄	1	2	yes	complemented
191	#359549	D₄	1	2	yes	complemented
192	#359549	C₂³	1	2	yes	—
193	#359549	C₂³	1	2	yes	—
194	#359549	C₂³	1	1	yes	characteristic, complemented
195	#359549	C₂³	1	1	yes	characteristic, complemented
196	#359442	C₂³	1	1	yes	characteristic
197	#359442	C₂³	1	1	yes	characteristic
198	#359442	C₂³	1	1	yes	characteristic
199	#359442	C₂³	1	1	yes	characteristic
200	#355096	C₂³	1	1	yes	characteristic, complemented
201	#355096	C₂³	1	1	yes	characteristic, complemented
202	#187952	D₄	1	4	yes	complemented
203	#187949	D₄	1	4	yes	complemented
204	#187944	C₂³	1	2	yes	—
205	#187944	C₂³	1	2	yes	—
206	#187944	C₂³	1	2	yes	—
207	#187944	C₂³	1	2	yes	—
208	#187944	C₂³	1	2	yes	complemented
209	#187943	D₄	1	4	yes	complemented
210	#187940	D₄	1	4	yes	complemented
211	C₂×#8534	C₂³	1	2	yes	—
212	C₂×#8534	C₂³	1	2	yes	—
213	C₂×#8534	C₂³	1	2	yes	—
214	C₂×#8534	C₂³	1	2	yes	—
215	C₂×#8534	C₂³	1	2	yes	complemented
216	#186835	C₂³	1	2	yes	complemented
217	C₂×#8453	C₂³	1	2	yes	complemented
218	#128033	C₂³	1	2	yes	complemented
219	#128033	C₂³	1	2	yes	complemented
220	C₂×#7304	C₂³	1	2	yes	complemented
221	C₂×#7304	C₂³	1	2	yes	complemented
222	C₂×#7316	C₂³	1	2	yes	complemented
223	C₂×#7316	C₂³	1	2	yes	complemented
224	C₂×#7316	C₂³	1	2	yes	complemented
225	C₂×#7316	C₂³	1	2	yes	complemented
226	C₂×#7311	C₂³	1	2	yes	complemented
227	C₂×#7311	C₂³	1	2	yes	complemented
228	C₂×#7310	C₂³	1	2	yes	complemented
229	C₂×#7310	C₂³	1	2	yes	complemented
230	#128009	C₂³	1	2	yes	complemented
231	#128009	C₂³	1	2	yes	complemented
232	C₂×#7307	C₂³	1	2	yes	complemented
233	C₂×#7307	C₂³	1	2	yes	complemented
234	#108238	C₂³	1	2	yes	complemented
235	#108222	C₂³	1	2	yes	complemented
236	#107130	C₂³	1	2	yes	complemented
237	#107114	C₂³	1	2	yes	complemented
238	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
239	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
240	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
241	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
242	#62863	#41	1	8	yes	complemented
243	#62820	C₂×D₄	1	4	yes	—
244	#62817	C₂×D₄	1	4	yes	—
245	C₂×#3484	C₂×D₄	1	2	yes	—
246	C₂×#3484	C₂×D₄	1	2	yes	—
247	C₂×#3484	C₂×D₄	1	2	yes	—
248	C₂×#3484	C₂×D₄	1	2	yes	—
249	C₂×#3484	C₂×D₄	1	1	yes	characteristic
250	C₂×#3484	C₂×D₄	1	1	yes	characteristic
251	C₂×#3484	C₂×D₄	1	1	yes	characteristic
252	C₂×#3484	C₂×D₄	1	1	yes	characteristic
253	C₂×#3484	#41	1	2	yes	complemented
254	C₂×#3484	#41	1	2	yes	complemented
255	C₂×#3484	C₂⁴	1	1	yes	characteristic
256	C₂×#3484	C₂⁴	1	1	yes	characteristic
257	C₂×#3484	C₂⁴	1	2	yes	—
258	C₂×#3484	C₂⁴	1	2	yes	—
259	C₂²×#534	C₂⁴	1	1	yes	characteristic
260	C₂²×#534	C₂⁴	1	1	yes	characteristic
261	C₂³×#120	C₂×D₄	1	1	yes	characteristic
262	C₂³×#120	C₂×D₄	1	1	yes	characteristic
263	C₂²×#518	C₂×D₄	1	1	yes	characteristic
264	C₂²×#518	#41	1	1	yes	characteristic, complemented
265	C₂²×#518	#41	1	1	yes	characteristic, complemented
266	C₂×#3026	C₂×D₄	1	2	yes	—
267	C₂×#3026	C₂×D₄	1	2	yes	—
268	C₂×#3026	C₂×D₄	1	2	yes	—
269	C₂×#3026	C₂×D₄	1	2	yes	—
270	#34176	C₂×D₄	1	2	yes	—
271	#34176	C₂×D₄	1	2	yes	—
272	#34171	C₂×D₄	1	1	yes	characteristic
273	#34171	C₂×D₄	1	1	yes	characteristic
274	#34171	C₂×D₄	1	1	yes	characteristic
275	#34171	C₂×D₄	1	1	yes	characteristic
276	#34171	C₂×D₄	1	2	yes	—
277	#34171	C₂×D₄	1	2	yes	—
278	#34171	C₂⁴	1	1	yes	characteristic
279	#34171	C₂⁴	1	1	yes	characteristic
280	C₂²×#379	C₂×D₄	1	2	yes	—
281	C₂²×#379	C₂×D₄	1	2	yes	—
282	#21747	C₂×D₄	1	4	yes	—
283	#21746	C₂×D₄	1	4	yes	—
284	C₂×#1913	C₂×D₄	1	2	yes	—
285	C₂×#1913	C₂×D₄	1	2	yes	—
286	C₂×#1913	C₂×D₄	1	2	yes	—
287	C₂×#1913	C₂×D₄	1	2	yes	—
288	C₂×#1913	C₂×D₄	1	2	yes	—
289	C₂×#1913	C₂×D₄	1	2	yes	—
290	C₂×#1913	C₂×D₄	1	2	yes	—
291	C₂×#1913	C₂×D₄	1	2	yes	—
292	#20960	C₂×D₄	1	2	yes	—
293	#20960	C₂×D₄	1	2	yes	—
294	#20960	C₂×D₄	1	2	yes	—
295	#20960	C₂×D₄	1	2	yes	—
296	C₂×#1819	C₂×D₄	1	2	yes	—
297	C₂×#1819	C₂×D₄	1	2	yes	—
298	C₂×#1783	C₂⁴	1	2	yes	—
299	C₂×#1783	C₂⁴	1	2	yes	—
300	C₂×#1781	C₂×D₄	1	2	yes	—
301	C₂×#1781	C₂×D₄	1	2	yes	—
302	C₂×#1781	C₂×D₄	1	2	yes	—
303	C₂×#1781	C₂×D₄	1	2	yes	—
304	C₂×#1781	C₂×D₄	1	2	yes	—
305	C₂×#1781	C₂×D₄	1	2	yes	—
306	C₂×#1781	C₂×D₄	1	2	yes	—
307	C₂×#1781	C₂×D₄	1	2	yes	—
308	C₂×#1781	C₂⁴	1	2	yes	—
309	C₂×#1781	C₂⁴	1	2	yes	—
310	C₂×#1781	C₂⁴	1	1	yes	characteristic
311	C₂×#1781	C₂⁴	1	1	yes	characteristic
312	C₂×#1781	C₂⁴	1	1	yes	characteristic
313	C₂×#1781	C₂⁴	1	1	yes	characteristic
314	C₂×#1781	C₂⁴	1	1	yes	characteristic
315	C₂×#1781	C₂⁴	1	1	yes	characteristic
316	C₂×#1781	C₂⁴	1	1	yes	characteristic
317	C₂×#1781	C₂⁴	1	1	yes	characteristic
318	#14658	C₂×D₄	1	2	yes	—
319	#14657	C₂×D₄	1	2	yes	—
320	#14335	C₂⁴	1	2	yes	—
321	#14167	C₂×D₄	1	2	yes	—
322	#14134	C₂×D₄	1	2	yes	—
323	C₂×#1438	C₂⁴	1	2	yes	—
324	#8534	C₂×D₄	1	4	yes	—
325	#8534	C₂×D₄	1	4	yes	—
326	#8534	C₂×D₄	1	4	yes	—
327	#8534	C₂×D₄	1	4	yes	—
328	#8534	C₂×D₄	1	4	yes	—
329	#8534	C₂×D₄	1	4	yes	—
330	#8534	C₂×D₄	1	4	yes	—
331	#8534	C₂×D₄	1	4	yes	—
332	C₂⁷	C₂²×D₄	1	1	yes	characteristic
333	C₂⁷	H(5,𝔽₂)	1	1	yes	characteristic
334	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
335	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
336	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
337	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
338	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
339	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
340	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
341	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
342	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
343	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
344	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
345	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
346	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
347	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
348	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
349	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
350	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
351	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
352	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
353	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
354	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
355	#3484	C₂²×D₄	1	4	yes	—
356	#3484	C₂²×D₄	1	4	yes	—
357	#3484	C₂×#41	1	4	yes	—
358	#3484	C₂×#41	1	4	yes	—
359	C₂×#534	C₂²×D₄	1	2	yes	—
360	C₂×#534	C₂²×D₄	1	2	yes	—
361	C₂×#534	C₂²×D₄	1	2	yes	—
362	C₂×#534	C₂²×D₄	1	2	yes	—
363	C₂×#534	C₂×#41	1	4	yes	—
364	C₂×#534	H(5,𝔽₂)	1	4	yes	—
365	C₂²×#123	C₂²×D₄	1	2	yes	—
366	C₂²×#123	H(5,𝔽₂)	1	2	yes	—
367	C₂²×#120	#120	1	2	yes	—
368	C₂²×#120	#120	1	2	yes	—
369	C₂²×#120	#120	1	2	yes	—
370	C₂²×#120	#120	1	2	yes	—
371	C₂²×#120	C₂²×D₄	1	2	yes	—
372	C₂²×#120	H(5,𝔽₂)	1	2	yes	—
373	C₂×#518	#120	1	2	yes	—
374	C₂×#518	#120	1	2	yes	—
375	C₂×#518	C₂²×D₄	1	1	yes	characteristic
376	C₂×#518	C₂²×D₄	1	1	yes	characteristic
377	C₂×#518	C₂²×D₄	1	1	yes	characteristic
378	C₂×#518	C₂²×D₄	1	1	yes	characteristic
379	C₂×#518	C₂²×D₄	1	1	yes	characteristic
380	C₂×#518	C₂²×D₄	1	1	yes	characteristic
381	C₂×#518	C₂×#41	1	2	yes	—
382	C₂×#518	C₂×#41	1	2	yes	—
383	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
384	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
385	C₂²×#99	C₂²×D₄	1	2	yes	—
386	C₂²×#99	C₂²×D₄	1	2	yes	—
387	C₂²×#99	C₂²×D₄	1	2	yes	—
388	C₂²×#99	C₂²×D₄	1	2	yes	—
389	#2280	#120	1	4	yes	complemented
390	C₂×#379	#120	1	4	yes	complemented
391	C₂×#379	C₂²×D₄	1	2	yes	—
392	C₂×#379	C₂²×D₄	1	2	yes	—
393	C₂×#379	C₂²×D₄	1	2	yes	—
394	C₂×#379	C₂²×D₄	1	2	yes	—
395	#1819	#120	1	8	yes	complemented
396	#1781	C₂²×D₄	1	4	yes	—
397	#1781	C₂²×D₄	1	4	yes	—
398	#1438	C₂²×D₄	1	2	yes	—
399	#1438	C₂²×D₄	1	2	yes	—
400	#1438	C₂²×D₄	1	2	yes	—
401	#1438	C₂²×D₄	1	2	yes	—
402	C₂⁶	C₂×#120	1	1	yes	characteristic
403	C₂⁶	C₂×#120	1	1	yes	characteristic
404	C₂⁶	C₂×#120	1	1	yes	characteristic
405	C₂⁶	#525	1	1	yes	characteristic
406	C₂⁶	#525	1	1	yes	characteristic
407	C₂⁶	#535	1	1	yes	characteristic
408	C₂⁶	#535	1	1	yes	characteristic
409	C₂⁶	#535	1	1	yes	characteristic
410	C₂⁶	#535	1	1	yes	characteristic
411	C₂⁶	#546	1	1	yes	characteristic
412	C₂⁶	#546	1	1	yes	characteristic
413	C₂⁶	#546	1	1	yes	characteristic
414	C₂⁶	#546	1	1	yes	characteristic
415	C₂⁶	C₂³×D₄	1	1	yes	characteristic
416	C₂⁶	C₂×H(5,𝔽₂)	1	1	yes	characteristic
417	C₂×H(5,𝔽₂)	#525	1	4	yes	—
418	C₂×H(5,𝔽₂)	#525	1	4	yes	—
419	C₂³×D₄	C₂×#120	1	2	yes	—
420	C₂³×D₄	C₂×#120	1	1	yes	characteristic
421	C₂³×D₄	C₂×#120	1	1	yes	characteristic
422	C₂³×D₄	C₂×#120	1	2	yes	—
423	C₂³×D₄	#525	1	1	yes	characteristic
424	C₂³×D₄	#525	1	1	yes	characteristic
425	C₂³×D₄	#525	1	2	yes	—
426	C₂³×D₄	#534	1	2	yes	—
427	C₂³×D₄	#546	1	1	yes	characteristic
428	C₂³×D₄	#546	1	1	yes	characteristic
429	C₂³×D₄	#546	1	1	yes	characteristic
430	C₂³×D₄	#546	1	1	yes	characteristic
431	C₂³×D₄	#546	1	1	yes	characteristic
432	C₂³×D₄	#546	1	1	yes	characteristic
433	C₂³×D₄	#546	1	1	yes	characteristic
434	C₂³×D₄	#546	1	1	yes	characteristic
435	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
436	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
437	C₂³×D₄	C₂³×D₄	1	2	yes	—
438	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
439	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
440	C₂³×D₄	C₂²×#41	1	2	yes	—
441	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
442	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
443	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
444	C₂⁴×C₄	#535	1	1	yes	characteristic
445	C₂⁴×C₄	#535	1	1	yes	characteristic
446	C₂⁴×C₄	#546	1	1	yes	characteristic
447	C₂⁴×C₄	#546	1	1	yes	characteristic
448	C₂⁴×C₄	#546	1	1	yes	characteristic
449	C₂⁴×C₄	#546	1	1	yes	characteristic
450	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
451	C₂×#123	D₄²	1	4	yes	—
452	C₂×#123	D₄²	1	4	yes	—
453	C₂×#123	#546	1	4	yes	—
454	C₂×#123	#546	1	4	yes	—
455	C₂×#120	B(4,𝔽₂)	1	8	yes	—
456	C₂×#120	B(4,𝔽₂)	1	8	yes	—
457	C₂×#120	D₄²	1	4	yes	—
458	C₂×#120	D₄²	1	4	yes	—
459	C₂×#120	#546	1	4	yes	—
460	C₂×#120	#546	1	4	yes	—
461	#518	#525	1	4	yes	—
462	#518	#525	1	4	yes	—
463	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
464	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
465	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
466	C₂²×C₂²⋊C₄	#525	1	2	yes	—
467	C₂²×C₂²⋊C₄	#534	1	2	yes	—
468	C₂²×C₂²⋊C₄	#535	1	2	yes	—
469	#379	C₂×#120	1	4	yes	—
470	#379	C₂×#120	1	4	yes	—
471	C₂⁵	#2403	1	2	yes	—
472	C₂⁵	#2404	1	2	yes	—
473	C₂⁵	#2404	1	1	yes	characteristic
474	C₂⁵	#2404	1	1	yes	characteristic
475	C₂⁵	#2404	1	1	yes	characteristic
476	C₂⁵	#2404	1	1	yes	characteristic
477	C₂⁵	#2404	1	1	yes	characteristic
478	C₂⁵	#2404	1	1	yes	characteristic
479	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
480	C₂⁵	C₂×B(4,𝔽₂)	1	4	yes	—
481	C₂⁵	C₂²×#120	1	1	yes	characteristic
482	C₂⁵	C₂²×#120	1	1	yes	characteristic
483	C₂⁵	C₂×#525	1	1	yes	characteristic
484	C₂⁵	C₂×#525	1	1	yes	characteristic
485	C₂⁵	C₂×#534	1	1	yes	characteristic
486	C₂⁵	C₂×#535	1	1	yes	characteristic
487	C₂⁵	C₂×#535	1	1	yes	characteristic
488	C₂⁵	C₂×#546	1	1	yes	characteristic
489	C₂⁵	C₂×#546	1	1	yes	characteristic
490	C₂⁵	#3484	1	2	yes	—
491	C₂⁵	#3490	1	2	yes	—
492	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
493	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
494	C₂²×D₄	C₂×#525	1	2	yes	—
495	C₂²×D₄	C₂×#525	1	2	yes	—
496	C₂²×D₄	C₂×D₄²	1	2	yes	—
497	C₂²×D₄	C₂×D₄²	1	2	yes	—
498	C₂²×D₄	C₂×#546	1	2	yes	—
499	C₂²×D₄	C₂×#546	1	2	yes	—
500	C₂²×D₄	#3490	1	2	yes	—
501	C₂²×D₄	#3490	1	2	yes	—
502	C₂³×C₄	#2403	1	2	yes	—
503	C₂³×C₄	#2404	1	1	yes	characteristic
504	C₂³×C₄	#2404	1	2	yes	—
505	C₂³×C₄	#2404	1	1	yes	characteristic
506	C₂³×C₄	C₂×#546	1	1	yes	characteristic
507	C₂³×C₄	C₂×#546	1	1	yes	characteristic
508	C₂³×C₄	#3484	1	2	yes	—
509	C₂³×C₄	#3490	1	2	yes	—
510	C₂×C₂²⋊C₄	#2403	1	4	yes	—
511	C₂×C₂²⋊C₄	#2404	1	4	yes	—
512	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
513	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
514	C₂⁴	#23900	1	4	yes	—
515	C₂⁴	#23984	1	2	yes	—
516	C₂⁴	#23984	1	2	yes	—
517	C₂⁴	#23984	1	2	yes	—
518	C₂⁴	#23984	1	2	yes	—
519	C₂⁴	#23996	1	2	yes	—
520	C₂⁴	C₂×#2403	1	1	yes	characteristic
521	C₂⁴	C₂×#2404	1	1	yes	characteristic
522	C₂⁴	C₂×#2404	1	1	yes	characteristic
523	C₂⁴	#35050	1	1	yes	characteristic
524	C₂⁴	#35050	1	1	yes	characteristic
525	C₂⁴	#35222	1	1	yes	characteristic
526	C₂⁴	#36098	1	2	yes	—
527	C₂⁴	#36098	1	2	yes	—
528	C₂⁴	#36614	1	1	yes	characteristic
529	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
530	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
531	C₂²×C₄	#23900	1	4	yes	—
532	C₂²×C₄	#23996	1	2	yes	—
533	C₂²×C₄	#36098	1	2	yes	—
534	C₂²×C₄	#36098	1	2	yes	—
535	C₂²⋊C₄	#23984	1	8	yes	—
536	C₂³	#612425	1	1	yes	characteristic
537	C₂³	C₂×#23900	1	2	yes	—
538	C₂³	C₂×#23996	1	1	yes	characteristic
539	C₂³	C₂×#23996	1	1	yes	characteristic
540	C₂³	#6451863	1	1	yes	characteristic
541	C₂³	#6451863	1	1	yes	characteristic
542	C₂³	C₂×#23984	1	1	yes	characteristic
543	C₂³	C₂×#23984	1	1	yes	characteristic
544	C₂³	C₂×#23984	1	2	yes	—
545	C₂²	#72217576	1	1	yes	characteristic
546	C₂²	#72233156	1	1	yes	characteristic
547	C₂²	#72234587	1	1	yes	characteristic
548	C₂²	#72234587	1	1	yes	characteristic
549	C₂²	#72234955	1	1	yes	characteristic
550	C₂²	#72234955	1	1	yes	characteristic
551	C₂²	#72265948	1	1	yes	characteristic
552	C₂	#72266217	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266217
commutator, Frattini, cosocle	C₂⁴×D₄	C₂⁵
LCS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×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. #72315149	C₂	semidirect
2. #72315084	C₂	semidirect
3. #72315053	C₂	semidirect
4. #72315022	C₂	semidirect
5. #72314981	C₂	semidirect
6. #72314872	C₂	semidirect
7. #72314858	C₂	semidirect
8. #72314855	C₂²	semidirect
9. #72314742	C₂	semidirect
10. #72314739	C₂²	semidirect
11. #72314732	C₂	semidirect
12. #72314729	C₂²	semidirect
13. #72314663	C₂	semidirect
14. #72314482	C₂	semidirect
15. #72314472	C₂²	semidirect
16. #72314456	C₂²	semidirect
17. #72314452	C₂²	semidirect
18. #72314440	C₂²	semidirect
19. #72312226	C₂	semidirect
20. #72312218	C₂²	semidirect
21. #72312216	C₂²	semidirect
22. #72312214	C₂²	semidirect
23. #72310285	C₂	semidirect
24. #72310283	C₂²	semidirect
25. #72309563	C₂	semidirect
26. #72309555	C₂²	semidirect
27. #72309552	C₂²	semidirect
28. #72266870	C₂	semidirect
33. #72266368	C₂²	semidirect
34. #72266366	C₂²	semidirect
35. #72264799	C₂	semidirect
36. #72264793	C₂	semidirect
37. #72264754	C₂²	semidirect
38. #72262349	C₂	semidirect
39. #72260537	C₂²	semidirect
40. #72259125	C₂²	semidirect
41. C₂×#144639	C₂²	semidirect
42. C₂×#139742	C₂²	semidirect
43. #72256195	C₂²	semidirect
44. #72256043	C₂²	semidirect
45. #72255986	C₂²	semidirect
46. #72255849	C₂²	semidirect
47. #72255841	C₂²	semidirect
48. #72255778	C₂²	semidirect
49. #72255774	C₂²	semidirect
50. #72251523	C₂	semidirect
51. #72251501	C₂²	semidirect
52. #72251499	C₂²	semidirect
53. #72251479	C₂	semidirect
54. #72251476	C₂²	semidirect
55. #72251475	C₂²	semidirect
56. #72251473	C₂²	semidirect
57. #72251471	C₂²	semidirect
58. #72251218	C₂	semidirect
59. #72251171	C₂²	semidirect
60. #72246450	C₂²	semidirect
61. #72246288	C₂²	semidirect
62. #72246286	C₂²	semidirect
63. #72238613	C₂²	semidirect
64. #72238613	C₂²	semidirect
65. #72238612	C₂²	semidirect
66. #72238344	C₂	semidirect
67. #72238344	C₂	semidirect
68. #72237900	C₂²	semidirect
69. #72237900	C₂²	semidirect
70. #72237899	C₂²	semidirect
71. #72237829	C₂²	semidirect
72. #72237599	C₂²	semidirect
79. #72236928	C₂²	semidirect
80. #72236636	C₂²	semidirect
81. #72236631	C₂²	semidirect
88. #72225667	C₂²	semidirect
89. #72225619	C₂²	semidirect
90. #72225617	C₂²	semidirect
91. #72225617	C₂²	semidirect
92. #72219418	C₂²	semidirect
93. #72219415	C₂²	semidirect
94. #72219414	C₂²	semidirect
95. #72219414	C₂²	semidirect
96. #72219251	C₂²	semidirect
97. #72219248	C₂²	semidirect
98. #72219243	C₂²	semidirect
99. #72219237	C₂²	semidirect
103. #72219163	C₂²	semidirect
104. #72219160	C₂²	semidirect
105. #72218498	C₂²	semidirect
106. #72218455	C₂²	semidirect
111. #72218198	C₂²	semidirect
112. #72218180	C₂²	semidirect
113. C₂×#144364	C₂²	semidirect
114. C₂×#139743	C₂²	semidirect
130. #7626202	D₄	semidirect
131. C₂×#32873	C₂³	semidirect
132. C₂×#23895	D₄	semidirect
133. C₂×#23895	D₄	semidirect
134. C₂×#23895	D₄	semidirect
135. C₂×#23895	D₄	semidirect
138. C₂×#23895	C₂³	semidirect
147. C₂×#21776	C₂³	semidirect
148. C₂×#21776	C₂³	semidirect
151. C₂×#21746	D₄	semidirect
152. #6371007	D₄	semidirect
153. #6370693	D₄	semidirect
178. #392030	C₂³	semidirect
179. #392030	C₂³	semidirect
180. #392030	C₂³	semidirect
181. #382544	C₂³	semidirect
182. #382544	C₂³	semidirect
183. #382434	C₂³	semidirect
184. #382434	C₂³	semidirect
185. #373637	C₂³	semidirect
188. #359549	D₄	semidirect
189. #359549	D₄	semidirect
190. #359549	D₄	semidirect
191. #359549	D₄	semidirect
194. #359549	C₂³	semidirect
195. #359549	C₂³	semidirect
200. #355096	C₂³	semidirect
201. #355096	C₂³	semidirect
202. #187952	D₄	semidirect
203. #187949	D₄	semidirect
208. #187944	C₂³	semidirect
209. #187943	D₄	semidirect
210. #187940	D₄	semidirect
215. C₂×#8534	C₂³	semidirect
216. #186835	C₂³	semidirect
217. C₂×#8453	C₂³	semidirect
218. #128033	C₂³	semidirect
219. #128033	C₂³	semidirect
220. C₂×#7304	C₂³	semidirect
221. C₂×#7304	C₂³	semidirect
222. C₂×#7316	C₂³	semidirect
223. C₂×#7316	C₂³	semidirect
224. C₂×#7316	C₂³	semidirect
225. C₂×#7316	C₂³	semidirect
226. C₂×#7311	C₂³	semidirect
227. C₂×#7311	C₂³	semidirect
228. C₂×#7310	C₂³	semidirect
229. C₂×#7310	C₂³	semidirect
230. #128009	C₂³	semidirect
231. #128009	C₂³	semidirect
232. C₂×#7307	C₂³	semidirect
233. C₂×#7307	C₂³	semidirect
234. #108238	C₂³	semidirect
235. #108222	C₂³	semidirect
236. #107130	C₂³	semidirect
237. #107114	C₂³	semidirect
239. C₂³×H(5,𝔽₂)	#41	semidirect
240. C₂³×H(5,𝔽₂)	#41	semidirect
242. #62863	#41	semidirect
253. C₂×#3484	#41	semidirect
254. C₂×#3484	#41	semidirect
264. C₂²×#518	#41	semidirect
265. C₂²×#518	#41	semidirect
389. #2280	#120	semidirect
390. C₂×#379	#120	semidirect
395. #1819	#120	semidirect

Maximal subgroups

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

subgroup	index
#72315149	2
#72315084	2
#72315053	2
#72315022	2
#72314981	2
#72314872	2
#72314858	2
#72314742	2
#72314732	2
#72314663	2
#72314482	2
#72312226	2
#72310285	2
#72309563	2
#72266870	2
#72264799	2
#72264793	2
#72262349	2
#72251523	2
#72251479	2
#72251218	2
#72238344	2