Subgroups — #72315129

Order 4096.

At least 25372 conjugacy classes of subgroups; only the 939 normal subgroups are shown.

The subgroup lattice has 533 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72315113	C₂	1	1	yes	maximal, characteristic, complemented
2	#72315084	C₂	1	1	yes	maximal, characteristic, complemented
3	#72314847	C₂	1	2	yes	maximal, complemented
4	#72314843	C₂	1	2	yes	maximal, complemented
5	#72312643	C₂	1	1	yes	maximal, characteristic, complemented
6	#72312258	C₂	1	1	yes	maximal, characteristic, complemented
7	#72310290	C₂	1	1	yes	maximal, characteristic, complemented
8	#72309848	C₂	1	1	yes	maximal, characteristic, complemented
9	#72271129	C₂	1	1	yes	maximal, characteristic, complemented
10	#72264854	C₂	1	1	yes	maximal, characteristic, complemented
11	#72259011	C₂	1	1	yes	maximal, characteristic, complemented
12	#72256408	C₂	1	2	yes	maximal, complemented
13	#72256350	C₂	1	2	yes	maximal, complemented
14	#72256343	C₂	1	2	yes	maximal, complemented
15	#72256303	C₂	1	2	yes	maximal, complemented
16	#72256292	C₂	1	2	yes	maximal, complemented
17	#72256239	C₂	1	2	yes	maximal, complemented
18	#72256195	C₂²	1	2	yes	complemented
19	#72256193	C₂²	1	2	yes	complemented
20	#72256052	C₂²	1	2	yes	complemented
21	#72256048	C₂²	1	2	yes	complemented
22	#72256043	C₂²	1	2	yes	complemented
23	#72255980	C₂²	1	2	yes	complemented
24	#72255977	C₂²	1	2	yes	complemented
25	#72255971	C₂²	1	2	yes	complemented
26	#72255874	C₂²	1	2	yes	complemented
27	#72255867	C₂²	1	2	yes	complemented
28	#72255849	C₂²	1	2	yes	complemented
29	#72255833	C₂²	1	2	yes	complemented
30	#72255833	C₂²	1	2	yes	complemented
31	#72255830	C₂²	1	2	yes	complemented
32	#72255778	C₂²	1	2	yes	complemented
33	#72255772	C₂²	1	2	yes	complemented
34	#72255764	C₂²	1	2	yes	complemented
35	#72251479	C₂	1	1	yes	maximal, characteristic, complemented
36	#72251476	C₂²	1	2	yes	complemented
37	#72251475	C₂²	1	2	yes	complemented
38	#72251473	C₂²	1	2	yes	complemented
39	#72251471	C₂²	1	2	yes	complemented
40	#72251468	C₂	1	1	yes	maximal, characteristic, complemented
41	#72251463	C₂²	1	2	yes	complemented
42	#72251462	C₂²	1	2	yes	complemented
43	#72251291	C₂	1	1	yes	maximal, characteristic, complemented
44	#72251157	C₂²	1	1	yes	characteristic, complemented
45	#72251143	C₂²	1	1	yes	characteristic, complemented
46	#72251140	C₂²	1	1	yes	characteristic, complemented
47	#72251140	C₂²	1	1	yes	characteristic, complemented
48	#72246299	C₂²	1	2	yes	complemented
49	#72238976	C₂²	1	2	yes	complemented
50	#72238976	C₂²	1	2	yes	complemented
51	#72238974	C₂²	1	2	yes	complemented
52	C₂×#144631	C₂²	1	2	yes	complemented
53	#72238613	C₂²	1	1	yes	characteristic, complemented
54	#72238443	C₂²	1	2	yes	complemented
55	#72238347	C₂	1	1	yes	maximal, characteristic, complemented
56	#72237900	C₂²	1	1	yes	characteristic, complemented
57	#72237899	C₂²	1	1	yes	characteristic, complemented
58	#72237829	C₂²	1	1	yes	characteristic, complemented
59	#72237638	C₂²	1	2	yes	complemented
60	#72237635	C₂²	1	2	yes	complemented
61	#72237634	C₂²	1	2	yes	complemented
62	#72237467	C₂²	1	2	yes	complemented
63	#72237398	C₂²	1	1	yes	characteristic
64	#72237398	C₂²	1	1	yes	characteristic
65	#72237374	C₂²	1	2	yes	complemented
66	#72237033	C₂²	1	2	yes	complemented
67	#72237003	C₂²	1	2	yes	complemented
68	#72236521	C₂²	1	2	yes	complemented
69	#72235242	C₂²	1	2	yes	complemented
70	#72234661	C₂²	1	1	yes	characteristic
71	#72234661	C₂²	1	1	yes	characteristic
72	#72234609	C₂²	1	2	yes	—
73	#72234609	C₂²	1	2	yes	—
74	#72233611	C₂²	1	2	yes	complemented
75	#72233581	C₂²	1	2	yes	—
76	#72233581	C₂²	1	2	yes	—
77	#72233441	C₂²	1	2	yes	complemented
78	#72225784	C₂	1	1	yes	maximal, characteristic, complemented
79	#72225713	C₂²	1	1	yes	characteristic, complemented
80	#72225667	C₂²	1	1	yes	characteristic, complemented
81	#72225650	C₂²	1	1	yes	characteristic, complemented
82	#72225617	C₂²	1	1	yes	characteristic, complemented
83	#72219415	C₂²	1	1	yes	characteristic, complemented
84	#72219414	C₂²	1	1	yes	characteristic, complemented
85	#72219393	C₂²	1	2	yes	—
86	#72219393	C₂²	1	2	yes	—
87	#72219310	C₂²	1	1	yes	characteristic, complemented
88	C₂×#493474	C₂²	1	2	yes	—
89	C₂×#493474	C₂²	1	2	yes	—
90	#72219301	C₂²	1	1	yes	characteristic
91	#72219300	C₂²	1	1	yes	characteristic, complemented
92	#72219299	C₂²	1	1	yes	characteristic
93	#72219254	C₂²	1	1	yes	characteristic
94	C₂²×#8541	C₂²	1	1	yes	characteristic
95	#72219158	C₂²	1	2	yes	complemented
96	#72219120	C₂	1	1	yes	maximal, characteristic, complemented
97	C₂²×#62817	C₂²	1	1	yes	characteristic
98	#72218840	C₂²	1	2	yes	complemented
99	#72218838	C₂²	1	2	yes	complemented
100	#72218498	C₂²	1	1	yes	characteristic, complemented
101	#72218475	C₂²	1	2	yes	—
102	#72218475	C₂²	1	2	yes	—
103	#72218455	C₂²	1	1	yes	characteristic, complemented
104	#72218381	C₂²	1	1	yes	characteristic, complemented
105	#72218313	C₂²	1	1	yes	characteristic, complemented
106	#72218313	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	#72218198	C₂²	1	1	yes	characteristic, complemented
111	#72218198	C₂²	1	1	yes	characteristic, complemented
112	C₂×#139750	C₂²	1	2	yes	complemented
113	#72218069	C₂²	1	1	yes	characteristic, complemented
114	#72215858	C₂²	1	1	yes	characteristic
115	#72215179	C₂²	1	1	yes	characteristic
116	#72215179	C₂²	1	1	yes	characteristic
117	#72215179	C₂²	1	1	yes	characteristic
118	C₂×#511790	C₂²	1	2	yes	—
119	C₂×#511790	C₂²	1	2	yes	—
120	#72213862	C₂²	1	1	yes	characteristic
121	#72210555	C₂²	1	1	yes	characteristic
122	#72210511	C₂²	1	1	yes	characteristic
123	C₂×#62817	C₂³	1	2	yes	—
124	C₂×#62817	C₂³	1	2	yes	—
125	C₂²×#3484	C₂³	1	1	yes	characteristic
126	C₂²×#3484	C₂³	1	1	yes	characteristic
127	C₂⁴×#120	C₂³	1	1	yes	characteristic
128	#7641845	D₄	1	2	yes	complemented
129	#7630939	C₂³	1	1	yes	characteristic
130	C₂×#34980	C₂³	1	1	yes	characteristic
131	C₂×#32873	C₂³	1	1	yes	characteristic, complemented
132	#6440460	D₄	1	2	yes	complemented
133	#6440460	C₂³	1	2	yes	—
134	#6440460	C₂³	1	1	yes	characteristic
135	#6440460	C₂³	1	1	yes	characteristic
136	#6440460	C₂³	1	1	yes	characteristic, complemented
137	C₂×#23895	D₄	1	2	yes	complemented
138	C₂×#23895	C₂³	1	1	yes	characteristic
139	C₂×#23895	C₂³	1	1	yes	characteristic
140	#6437621	D₄	1	2	yes	complemented
141	#6437621	D₄	1	2	yes	complemented
142	#6437621	C₂³	1	1	yes	characteristic
143	#6437621	C₂³	1	2	yes	—
144	#6437621	C₂³	1	1	yes	characteristic
145	#6437621	C₂³	1	1	yes	characteristic, complemented
146	C₂×#23900	C₂³	1	2	yes	—
147	C₂×#23897	C₂³	1	2	yes	—
148	#6374251	C₂³	1	1	yes	characteristic, complemented
149	C₂×#21778	C₂³	1	2	yes	—
150	C₂×#21776	D₄	1	2	yes	complemented
151	C₂×#21776	C₂³	1	1	yes	characteristic
152	C₂×#21776	C₂³	1	1	yes	characteristic
153	C₂×#21776	C₂³	1	1	yes	characteristic, complemented
154	#6374128	C₂³	1	1	yes	characteristic, complemented
155	C₂×#21746	D₄	1	2	yes	complemented
156	#6370693	D₄	1	2	yes	complemented
157	C₂²×#1781	C₂³	1	1	yes	characteristic
158	C₂²×#1781	C₂³	1	1	yes	characteristic
159	#617161	C₂³	1	2	yes	—
160	#616960	C₂³	1	2	yes	—
161	#517411	C₂³	1	1	yes	characteristic
162	#493879	C₂³	1	2	yes	complemented
163	C₂×#12707	C₂³	1	2	yes	—
164	C₂×#12707	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	C₂×#12705	C₂³	1	2	yes	—
169	C₂×#12705	C₂³	1	2	yes	—
170	C₂×#12705	C₂³	1	2	yes	—
171	C₂×#12705	C₂³	1	2	yes	complemented
172	#493357	C₂³	1	2	yes	complemented
173	C₂×#12687	C₂³	1	2	yes	—
174	C₂×#12687	C₂³	1	2	yes	—
175	C₂×#12687	C₂³	1	2	yes	—
176	C₂×#12687	C₂³	1	2	yes	—
177	C₂×#12687	C₂³	1	2	yes	—
178	C₂×#12687	C₂³	1	2	yes	—
179	#392231	D₄	1	2	yes	complemented
180	#392113	C₂³	1	1	yes	characteristic
181	#392113	C₂³	1	1	yes	characteristic
182	#392113	C₂³	1	1	yes	characteristic
183	#392109	C₂³	1	1	yes	characteristic
184	#392109	C₂³	1	1	yes	characteristic
185	#392109	C₂³	1	1	yes	characteristic
186	#392109	C₂³	1	1	yes	characteristic
187	#392030	C₂³	1	1	yes	characteristic, complemented
188	#392030	C₂³	1	1	yes	characteristic, complemented
189	#392030	C₂³	1	1	yes	characteristic, complemented
190	#382707	C₂³	1	1	yes	characteristic, complemented
191	#382707	C₂³	1	1	yes	characteristic, complemented
192	#382544	C₂³	1	1	yes	characteristic, complemented
193	#382436	C₂³	1	2	yes	—
194	#382434	D₄	1	2	yes	complemented
195	#382434	C₂³	1	1	yes	characteristic
196	#382434	C₂³	1	1	yes	characteristic
197	#382434	C₂³	1	1	yes	characteristic, complemented
198	#359811	C₂³	1	1	yes	characteristic, complemented
199	#359558	C₂³	1	2	yes	—
200	#359549	D₄	1	2	yes	complemented
201	#359549	C₂³	1	1	yes	characteristic
202	#359549	C₂³	1	1	yes	characteristic
203	#359501	C₂³	1	2	yes	—
204	#359442	D₄	1	2	yes	complemented
205	#359442	C₂³	1	1	yes	characteristic, complemented
206	#355096	C₂³	1	1	yes	characteristic, complemented
207	#347048	D₄	1	8	yes	complemented
208	#347042	D₄	1	8	yes	complemented
209	#190147	C₂³	1	2	yes	complemented
210	#188109	C₂³	1	2	yes	complemented
211	C₂×#8541	C₂³	1	2	yes	—
212	C₂×#8541	C₂³	1	2	yes	—
213	#187944	C₂³	1	2	yes	—
214	#187944	C₂³	1	2	yes	—
215	#187944	C₂³	1	2	yes	—
216	#187944	C₂³	1	2	yes	—
217	#186835	C₂³	1	2	yes	complemented
218	#146475	C₂³	1	2	yes	complemented
219	#128033	C₂³	1	2	yes	complemented
220	#128033	C₂³	1	2	yes	complemented
221	#128033	C₂³	1	2	yes	complemented
222	#128033	C₂³	1	2	yes	complemented
223	C₂×#7316	C₂³	1	2	yes	complemented
224	C₂×#7316	C₂³	1	2	yes	complemented
225	C₂×#7314	C₂³	1	2	yes	complemented
226	C₂×#7314	C₂³	1	2	yes	complemented
227	C₂×#7314	C₂³	1	2	yes	complemented
228	C₂×#7314	C₂³	1	2	yes	complemented
229	C₂×#7311	C₂³	1	2	yes	complemented
230	C₂×#7311	C₂³	1	2	yes	complemented
231	C₂×#7310	C₂³	1	2	yes	complemented
232	C₂×#7310	C₂³	1	2	yes	complemented
233	#128009	C₂³	1	2	yes	complemented
234	#128009	C₂³	1	2	yes	complemented
235	#108238	C₂³	1	2	yes	complemented
236	C₂⁸	#41	1	1	yes	characteristic, complemented
237	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
238	C₂³×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
239	C₂⁵×D₄	C₂⁴	1	1	yes	characteristic
240	#62817	C₂×D₄	1	8	yes	—
241	C₂×#3484	C₂×D₄	1	2	yes	—
242	C₂×#3484	C₂×D₄	1	2	yes	—
243	C₂×#3484	C₂×D₄	1	1	yes	characteristic
244	C₂×#3484	C₂×D₄	1	1	yes	characteristic
245	C₂×#3484	C₂×D₄	1	1	yes	characteristic
246	C₂×#3484	C₂×D₄	1	1	yes	characteristic
247	C₂×#3484	#41	1	2	yes	complemented
248	C₂×#3484	C₂⁴	1	1	yes	characteristic
249	C₂×#3484	C₂⁴	1	1	yes	characteristic
250	C₂×#3484	C₂⁴	1	1	yes	characteristic
251	C₂×#3484	C₂⁴	1	2	yes	—
252	C₂²×#534	C₂×D₄	1	2	yes	—
253	C₂²×#534	C₂×D₄	1	1	yes	characteristic
254	C₂²×#534	C₂⁴	1	1	yes	characteristic
255	C₂³×#120	C₂×D₄	1	2	yes	—
256	C₂³×#120	C₂×D₄	1	1	yes	characteristic
257	C₂³×#120	#41	1	2	yes	complemented
258	C₂³×#120	C₂⁴	1	2	yes	—
259	C₂²×#518	C₂×D₄	1	1	yes	characteristic
260	C₂²×#518	#41	1	1	yes	characteristic, complemented
261	C₂⁴×C₂²⋊C₄	#41	1	1	yes	characteristic, complemented
262	C₂×#3026	C₂×D₄	1	2	yes	—
263	C₂×#3026	C₂×D₄	1	2	yes	—
264	C₂×#2883	C₂×D₄	1	2	yes	—
265	C₂×#2883	C₂×D₄	1	2	yes	—
266	#34992	C₂×D₄	1	2	yes	—
267	#34992	C₂×D₄	1	2	yes	—
268	#34980	C₂×D₄	1	2	yes	—
269	#34980	C₂×D₄	1	2	yes	—
270	#34171	C₂×D₄	1	1	yes	characteristic
271	#34171	C₂×D₄	1	1	yes	characteristic
272	#34171	C₂⁴	1	1	yes	characteristic
273	C₂×#2308	C₂×D₄	1	1	yes	characteristic
274	C₂×#2308	C₂⁴	1	1	yes	characteristic
275	C₂²×#379	C₂×D₄	1	2	yes	—
276	C₂²×#379	C₂×D₄	1	1	yes	characteristic
277	#23901	C₂×D₄	1	4	yes	—
278	#23901	C₂×D₄	1	4	yes	—
279	#23900	C₂×D₄	1	4	yes	—
280	#23900	C₂×D₄	1	4	yes	—
281	C₂×#1913	C₂×D₄	1	2	yes	—
282	C₂×#1913	C₂×D₄	1	2	yes	—
283	C₂×#1913	C₂×D₄	1	2	yes	—
284	C₂×#1913	C₂×D₄	1	2	yes	—
285	C₂×#1898	C₂×D₄	1	2	yes	—
286	C₂×#1898	C₂×D₄	1	2	yes	—
287	C₂×#1898	C₂×D₄	1	2	yes	—
288	C₂×#1898	C₂×D₄	1	2	yes	—
289	#20960	C₂×D₄	1	2	yes	—
290	#20960	C₂×D₄	1	2	yes	—
291	C₂×#1828	C₂×D₄	1	2	yes	—
292	C₂×#1828	C₂×D₄	1	2	yes	—
293	C₂×#1828	C₂×D₄	1	2	yes	—
294	C₂×#1828	C₂×D₄	1	2	yes	—
295	C₂×#1783	C₂⁴	1	2	yes	—
296	C₂×#1783	C₂⁴	1	2	yes	—
297	C₂×#1783	C₂⁴	1	2	yes	—
298	#20585	C₂×D₄	1	2	yes	—
299	#20585	C₂×D₄	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	C₂⁴	1	2	yes	—
308	C₂×#1781	C₂⁴	1	2	yes	—
309	C₂×#1781	C₂⁴	1	1	yes	characteristic
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	#15948	C₂×D₄	1	4	yes	—
318	#15947	C₂×D₄	1	4	yes	—
319	#14335	C₂⁴	1	2	yes	—
320	#8541	C₂×D₄	1	8	yes	—
321	#8534	C₂×D₄	1	8	yes	—
322	#8534	C₂×D₄	1	8	yes	—
323	C₂⁷	C₂²×D₄	1	1	yes	characteristic
324	C₂⁷	C₂×#41	1	2	yes	—
325	C₂⁷	C₂×#41	1	1	yes	characteristic
326	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
327	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
328	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
329	C₂²×H(5,𝔽₂)	C₂²×D₄	1	1	yes	characteristic
330	C₂²×H(5,𝔽₂)	C₂×#41	1	2	yes	—
331	C₂⁴×D₄	#120	1	2	yes	—
332	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
333	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
334	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
335	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
336	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
337	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
338	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
339	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
340	C₂⁴×D₄	C₂×#41	1	1	yes	characteristic
341	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
342	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
343	C₂⁴×D₄	H(5,𝔽₂)	1	1	yes	characteristic
344	C₂⁴×D₄	C₂⁵	1	1	yes	characteristic
345	C₂⁵×C₄	H(5,𝔽₂)	1	1	yes	characteristic
346	#3484	C₂²×D₄	1	4	yes	—
347	#3484	C₂²×D₄	1	4	yes	—
348	#3484	H(5,𝔽₂)	1	4	yes	—
349	#3484	H(5,𝔽₂)	1	4	yes	—
350	C₂×#534	#120	1	2	yes	—
351	C₂×#534	#120	1	2	yes	—
352	C₂×#534	C₂²×D₄	1	2	yes	—
353	C₂×#534	C₂²×D₄	1	2	yes	—
354	C₂²×#123	C₂²×D₄	1	2	yes	—
355	C₂²×#120	#120	1	2	yes	—
356	C₂²×#120	#120	1	2	yes	—
357	C₂²×#120	C₂²×D₄	1	2	yes	—
358	C₂²×#120	C₂²×D₄	1	2	yes	—
359	C₂²×#120	C₂²×D₄	1	2	yes	—
360	C₂²×#120	C₂²×D₄	1	4	yes	—
361	C₂²×#120	H(5,𝔽₂)	1	4	yes	—
362	C₂×#518	#120	1	2	yes	—
363	C₂×#518	C₂²×D₄	1	1	yes	characteristic
364	C₂×#518	C₂²×D₄	1	1	yes	characteristic
365	C₂×#518	C₂²×D₄	1	1	yes	characteristic
366	C₂×#518	C₂²×D₄	1	1	yes	characteristic
367	C₂×#518	C₂²×D₄	1	1	yes	characteristic
368	C₂×#518	C₂×#41	1	2	yes	—
369	C₂³×C₂²⋊C₄	#120	1	2	yes	—
370	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
371	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
372	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
373	C₂³×C₂²⋊C₄	C₂×#41	1	2	yes	—
374	C₂²×#99	C₂²×D₄	1	2	yes	—
375	C₂²×#99	C₂²×D₄	1	2	yes	—
376	C₂²×#99	C₂²×D₄	1	2	yes	—
377	C₂²×#99	C₂²×D₄	1	2	yes	—
378	C₂²×#99	C₂²×D₄	1	2	yes	—
379	C₂²×#99	C₂²×D₄	1	2	yes	—
380	#2849	#120	1	4	yes	complemented
381	#2846	#120	1	4	yes	complemented
382	C₂×#379	C₂²×D₄	1	2	yes	—
383	C₂×#379	C₂²×D₄	1	2	yes	—
384	#1898	#120	1	8	yes	complemented
385	#1781	C₂²×D₄	1	4	yes	—
386	#1781	C₂²×D₄	1	4	yes	—
387	#1438	C₂²×D₄	1	4	yes	—
388	C₂⁶	B(4,𝔽₂)	1	2	yes	—
389	C₂⁶	C₂×#120	1	1	yes	characteristic
390	C₂⁶	C₂×#120	1	1	yes	characteristic
391	C₂⁶	C₂×#120	1	1	yes	characteristic
392	C₂⁶	#525	1	1	yes	characteristic
393	C₂⁶	#525	1	1	yes	characteristic
394	C₂⁶	#546	1	1	yes	characteristic
395	C₂⁶	#546	1	1	yes	characteristic
396	C₂⁶	#546	1	1	yes	characteristic
397	C₂⁶	#546	1	1	yes	characteristic
398	C₂⁶	#546	1	1	yes	characteristic
399	C₂⁶	#546	1	1	yes	characteristic
400	C₂⁶	#546	1	1	yes	characteristic
401	C₂⁶	#546	1	4	yes	—
402	C₂⁶	C₂³×D₄	1	1	yes	characteristic
403	C₂⁶	C₂²×#41	1	1	yes	characteristic
404	C₂×H(5,𝔽₂)	D₄²	1	4	yes	—
405	C₂×H(5,𝔽₂)	#546	1	4	yes	—
406	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
407	C₂³×D₄	B(4,𝔽₂)	1	2	yes	—
408	C₂³×D₄	C₂×#120	1	1	yes	characteristic
409	C₂³×D₄	C₂×#120	1	1	yes	characteristic
410	C₂³×D₄	C₂×#120	1	2	yes	—
411	C₂³×D₄	C₂×#120	1	2	yes	—
412	C₂³×D₄	#525	1	1	yes	characteristic
413	C₂³×D₄	#525	1	1	yes	characteristic
414	C₂³×D₄	#535	1	1	yes	characteristic
415	C₂³×D₄	#535	1	1	yes	characteristic
416	C₂³×D₄	#546	1	1	yes	characteristic
417	C₂³×D₄	#546	1	1	yes	characteristic
418	C₂³×D₄	#546	1	1	yes	characteristic
419	C₂³×D₄	#546	1	1	yes	characteristic
420	C₂³×D₄	#546	1	1	yes	characteristic
421	C₂³×D₄	#546	1	1	yes	characteristic
422	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
423	C₂³×D₄	C₂³×D₄	1	1	yes	characteristic
424	C₂³×D₄	C₂³×D₄	1	2	yes	—
425	C₂³×D₄	C₂²×#41	1	1	yes	characteristic
426	C₂³×D₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
428	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
429	C₂³×D₄	C₂×H(5,𝔽₂)	1	2	yes	—
430	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	—
431	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
432	C₂⁴×C₄	#535	1	1	yes	characteristic
433	C₂⁴×C₄	#535	1	1	yes	characteristic
434	C₂⁴×C₄	#546	1	1	yes	characteristic
435	C₂⁴×C₄	#546	1	1	yes	characteristic
436	C₂⁴×C₄	#546	1	1	yes	characteristic
437	C₂⁴×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
438	#534	D₄²	1	8	yes	—
439	C₂×#120	B(4,𝔽₂)	1	4	yes	—
440	C₂×#120	B(4,𝔽₂)	1	4	yes	—
441	C₂×#120	C₂×#120	1	4	yes	—
442	C₂×#120	#534	1	4	yes	—
443	#518	D₄²	1	4	yes	—
444	#518	#546	1	4	yes	—
445	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
446	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
447	C₂²×C₂²⋊C₄	C₂×#120	1	2	yes	—
448	C₂²×C₂²⋊C₄	#546	1	4	yes	—
449	#379	C₂×#120	1	4	yes	—
450	C₂⁵	#2404	1	1	yes	characteristic
451	C₂⁵	#2404	1	1	yes	characteristic
452	C₂⁵	#2404	1	1	yes	characteristic
453	C₂⁵	#2404	1	1	yes	characteristic
454	C₂⁵	#2404	1	1	yes	characteristic
455	C₂⁵	#2404	1	1	yes	characteristic
456	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
457	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
458	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
459	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
460	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
461	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
462	C₂⁵	C₂²×#120	1	1	yes	characteristic
463	C₂⁵	C₂²×#120	1	1	yes	characteristic
464	C₂⁵	C₂×#525	1	1	yes	characteristic
465	C₂⁵	C₂×#534	1	1	yes	characteristic
466	C₂⁵	C₂×#546	1	1	yes	characteristic
467	C₂⁵	C₂×#546	1	1	yes	characteristic
468	C₂⁵	C₂×#546	1	1	yes	characteristic
469	C₂⁵	C₂×#546	1	2	yes	—
470	C₂⁵	#3484	1	1	yes	characteristic
471	C₂⁵	#3484	1	1	yes	characteristic
472	C₂⁵	#3490	1	2	yes	—
473	C₂²×D₄	#2403	1	4	yes	—
474	C₂²×D₄	C₂×B(4,𝔽₂)	1	4	yes	—
475	C₂²×D₄	C₂×D₄²	1	2	yes	—
476	C₂²×D₄	C₂×D₄²	1	2	yes	—
477	C₂²×D₄	C₂×#546	1	2	yes	—
478	C₂²×D₄	#3484	1	2	yes	—
479	C₂²×D₄	#3484	1	2	yes	—
480	C₂²×D₄	#3484	1	2	yes	—
481	C₂²×D₄	#3490	1	2	yes	—
482	C₂²×D₄	#3532	1	2	yes	—
483	C₂³×C₄	#2404	1	1	yes	characteristic
484	C₂³×C₄	#2404	1	1	yes	characteristic
485	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
486	C₂³×C₄	C₂×B(4,𝔽₂)	1	2	yes	—
487	C₂³×C₄	C₂×#535	1	1	yes	characteristic
488	C₂³×C₄	C₂×#546	1	1	yes	characteristic
489	C₂³×C₄	#3484	1	2	yes	—
490	C₂³×C₄	#3532	1	2	yes	—
491	C₂×C₂²⋊C₄	#2403	1	4	yes	—
492	C₂×C₂²⋊C₄	C₂×B(4,𝔽₂)	1	4	yes	—
493	C₂⁴	#23900	1	4	yes	—
494	C₂⁴	#23984	1	1	yes	characteristic
495	C₂⁴	#23984	1	1	yes	characteristic
496	C₂⁴	#23984	1	1	yes	characteristic
497	C₂⁴	#23984	1	2	yes	—
498	C₂⁴	#23984	1	2	yes	—
499	C₂⁴	#23984	1	1	yes	characteristic
500	C₂⁴	#23996	1	2	yes	—
501	C₂⁴	C₂×#2403	1	1	yes	characteristic
502	C₂⁴	C₂×#2404	1	1	yes	characteristic
503	C₂⁴	#35346	1	1	yes	characteristic
504	C₂⁴	#36098	1	2	yes	—
505	C₂⁴	#36152	1	1	yes	characteristic
506	C₂⁴	#36152	1	1	yes	characteristic
507	C₂⁴	#37832	1	1	yes	characteristic
508	C₂⁴	#37832	1	1	yes	characteristic
509	C₂⁴	#58991	1	2	yes	—
510	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
511	C₂⁴	C₂²×B(4,𝔽₂)	1	2	yes	—
512	C₂²×C₄	#23900	1	4	yes	—
513	C₂²×C₄	#37645	1	2	yes	—
514	C₂²×C₄	#58991	1	2	yes	—
515	C₂³	#647657	1	1	yes	characteristic
516	C₂³	C₂×#23900	1	2	yes	—
517	C₂³	C₂×#23996	1	1	yes	characteristic
518	C₂³	#6451863	1	1	yes	characteristic
519	C₂³	#6451863	1	1	yes	characteristic
520	C₂³	#6451863	1	1	yes	characteristic
521	C₂³	C₂×#23984	1	1	yes	characteristic
522	C₂³	C₂×#23984	1	1	yes	characteristic
523	C₂³	#6499867	1	2	yes	—
524	C₂²	#72217617	1	1	yes	characteristic
525	C₂²	#72234644	1	1	yes	characteristic
526	C₂²	#72234955	1	1	yes	characteristic
527	C₂²	#72240110	1	1	yes	characteristic
528	C₂²	#72252238	1	1	yes	characteristic
529	C₂²	#72258461	1	1	yes	characteristic
530	C₂²	#72265948	1	1	yes	characteristic
531	C₂	#72266216	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72266216
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. #72315113	C₂	semidirect
2. #72315084	C₂	semidirect
3. #72314847	C₂	semidirect
4. #72314843	C₂	semidirect
5. #72312643	C₂	semidirect
6. #72312258	C₂	semidirect
7. #72310290	C₂	semidirect
8. #72309848	C₂	semidirect
9. #72271129	C₂	semidirect
10. #72264854	C₂	semidirect
11. #72259011	C₂	semidirect
12. #72256408	C₂	semidirect
13. #72256350	C₂	semidirect
14. #72256343	C₂	semidirect
15. #72256303	C₂	semidirect
16. #72256292	C₂	semidirect
17. #72256239	C₂	semidirect
18. #72256195	C₂²	semidirect
19. #72256193	C₂²	semidirect
20. #72256052	C₂²	semidirect
21. #72256048	C₂²	semidirect
22. #72256043	C₂²	semidirect
23. #72255980	C₂²	semidirect
24. #72255977	C₂²	semidirect
25. #72255971	C₂²	semidirect
26. #72255874	C₂²	semidirect
27. #72255867	C₂²	semidirect
28. #72255849	C₂²	semidirect
29. #72255833	C₂²	semidirect
30. #72255833	C₂²	semidirect
31. #72255830	C₂²	semidirect
32. #72255778	C₂²	semidirect
33. #72255772	C₂²	semidirect
34. #72255764	C₂²	semidirect
35. #72251479	C₂	semidirect
36. #72251476	C₂²	semidirect
37. #72251475	C₂²	semidirect
38. #72251473	C₂²	semidirect
39. #72251471	C₂²	semidirect
40. #72251468	C₂	semidirect
41. #72251463	C₂²	semidirect
42. #72251462	C₂²	semidirect
43. #72251291	C₂	semidirect
44. #72251157	C₂²	semidirect
45. #72251143	C₂²	semidirect
46. #72251140	C₂²	semidirect
47. #72251140	C₂²	semidirect
48. #72246299	C₂²	semidirect
49. #72238976	C₂²	semidirect
50. #72238976	C₂²	semidirect
51. #72238974	C₂²	semidirect
52. C₂×#144631	C₂²	semidirect
53. #72238613	C₂²	semidirect
54. #72238443	C₂²	semidirect
55. #72238347	C₂	semidirect
56. #72237900	C₂²	semidirect
57. #72237899	C₂²	semidirect
58. #72237829	C₂²	semidirect
59. #72237638	C₂²	semidirect
60. #72237635	C₂²	semidirect
61. #72237634	C₂²	semidirect
62. #72237467	C₂²	semidirect
65. #72237374	C₂²	semidirect
66. #72237033	C₂²	semidirect
67. #72237003	C₂²	semidirect
68. #72236521	C₂²	semidirect
69. #72235242	C₂²	semidirect
74. #72233611	C₂²	semidirect
77. #72233441	C₂²	semidirect
78. #72225784	C₂	semidirect
79. #72225713	C₂²	semidirect
80. #72225667	C₂²	semidirect
81. #72225650	C₂²	semidirect
82. #72225617	C₂²	semidirect
83. #72219415	C₂²	semidirect
84. #72219414	C₂²	semidirect
87. #72219310	C₂²	semidirect
91. #72219300	C₂²	semidirect
95. #72219158	C₂²	semidirect
96. #72219120	C₂	semidirect
98. #72218840	C₂²	semidirect
99. #72218838	C₂²	semidirect
100. #72218498	C₂²	semidirect
103. #72218455	C₂²	semidirect
104. #72218381	C₂²	semidirect
105. #72218313	C₂²	semidirect
106. #72218313	C₂²	semidirect
110. #72218198	C₂²	semidirect
111. #72218198	C₂²	semidirect
112. C₂×#139750	C₂²	semidirect
113. #72218069	C₂²	semidirect
128. #7641845	D₄	semidirect
131. C₂×#32873	C₂³	semidirect
132. #6440460	D₄	semidirect
136. #6440460	C₂³	semidirect
137. C₂×#23895	D₄	semidirect
140. #6437621	D₄	semidirect
141. #6437621	D₄	semidirect
145. #6437621	C₂³	semidirect
148. #6374251	C₂³	semidirect
150. C₂×#21776	D₄	semidirect
153. C₂×#21776	C₂³	semidirect
154. #6374128	C₂³	semidirect
155. C₂×#21746	D₄	semidirect
156. #6370693	D₄	semidirect
162. #493879	C₂³	semidirect
171. C₂×#12705	C₂³	semidirect
172. #493357	C₂³	semidirect
179. #392231	D₄	semidirect
187. #392030	C₂³	semidirect
188. #392030	C₂³	semidirect
189. #392030	C₂³	semidirect
190. #382707	C₂³	semidirect
191. #382707	C₂³	semidirect
192. #382544	C₂³	semidirect
194. #382434	D₄	semidirect
197. #382434	C₂³	semidirect
198. #359811	C₂³	semidirect
200. #359549	D₄	semidirect
204. #359442	D₄	semidirect
205. #359442	C₂³	semidirect
206. #355096	C₂³	semidirect
207. #347048	D₄	semidirect
208. #347042	D₄	semidirect
209. #190147	C₂³	semidirect
210. #188109	C₂³	semidirect
217. #186835	C₂³	semidirect
218. #146475	C₂³	semidirect
219. #128033	C₂³	semidirect
220. #128033	C₂³	semidirect
221. #128033	C₂³	semidirect
222. #128033	C₂³	semidirect
223. C₂×#7316	C₂³	semidirect
224. C₂×#7316	C₂³	semidirect
225. C₂×#7314	C₂³	semidirect
226. C₂×#7314	C₂³	semidirect
227. C₂×#7314	C₂³	semidirect
228. C₂×#7314	C₂³	semidirect
229. C₂×#7311	C₂³	semidirect
230. C₂×#7311	C₂³	semidirect
231. C₂×#7310	C₂³	semidirect
232. C₂×#7310	C₂³	semidirect
233. #128009	C₂³	semidirect
234. #128009	C₂³	semidirect
235. #108238	C₂³	semidirect
236. C₂⁸	#41	semidirect
238. C₂³×H(5,𝔽₂)	#41	semidirect
247. C₂×#3484	#41	semidirect
257. C₂³×#120	#41	semidirect
260. C₂²×#518	#41	semidirect
261. C₂⁴×C₂²⋊C₄	#41	semidirect
380. #2849	#120	semidirect
381. #2846	#120	semidirect
384. #1898	#120	semidirect

Maximal subgroups

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

subgroup	index
#72315113	2
#72315084	2
#72314847	2
#72314843	2
#72312643	2
#72312258	2
#72310290	2
#72309848	2
#72271129	2
#72264854	2
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