Subgroups — #72262866

Order 2048.

At least 9048 conjugacy classes of subgroups; only the 1244 normal subgroups are shown.

The subgroup lattice has 476 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72262798	C₂	1	1	yes	maximal, characteristic, complemented
2	#72262662	C₂	1	2	yes	maximal, complemented
3	#72262634	C₂	1	1	yes	maximal, characteristic, complemented
4	#72262429	C₂	1	2	yes	maximal, complemented
5	#72262342	C₂	1	2	yes	maximal, complemented
6	#72256422	C₂	1	2	yes	maximal, complemented
7	#72237612	C₂	1	2	yes	maximal, complemented
8	#72237461	C₂	1	1	yes	maximal, characteristic, complemented
9	#72235932	C₂	1	2	yes	maximal, complemented
10	#72235924	C₂	1	2	yes	maximal, complemented
11	#72235861	C₂	1	1	yes	maximal, characteristic, complemented
12	#72235768	C₂	1	1	yes	maximal, characteristic, complemented
13	#72234806	C₂	1	1	yes	maximal, characteristic, complemented
14	#72233891	C₂	1	2	yes	maximal, complemented
15	#72233891	C₂	1	2	yes	maximal, complemented
16	#72219377	C₂	1	1	yes	maximal, characteristic, complemented
17	#72219038	C₂	1	2	yes	maximal, complemented
18	#72210600	C₂	1	2	yes	maximal, complemented
19	#72210600	C₂	1	2	yes	maximal, complemented
20	C₂×#62818	C₂²	1	1	yes	characteristic
21	C₂³×D₄²	C₂²	1	1	yes	characteristic
22	#7643002	C₂²	1	2	yes	—
23	#7642350	C₂²	1	2	yes	—
24	#7642273	C₂²	1	2	yes	—
25	#7642244	C₂²	1	2	yes	—
26	C₂×#37232	C₂²	1	1	yes	characteristic, complemented
27	C₂×#36714	C₂²	1	1	yes	characteristic, complemented
28	#7630939	C₂²	1	2	yes	—
29	#7630939	C₂²	1	2	yes	—
30	C₂×#35348	C₂²	1	1	yes	characteristic, complemented
31	#7626203	C₂²	1	1	yes	characteristic
32	#6470226	C₂²	1	2	yes	complemented
33	#6470226	C₂²	1	2	yes	complemented
34	#6470225	C₂²	1	2	yes	complemented
35	#6470225	C₂²	1	2	yes	complemented
36	#6453039	C₂²	1	2	yes	complemented
37	#6451874	C₂²	1	2	yes	complemented
38	#6432949	C₂²	1	4	yes	complemented
39	#618455	C₂²	1	1	yes	characteristic
40	#618455	C₂²	1	1	yes	characteristic, complemented
41	#618316	C₂²	1	1	yes	characteristic
42	#618316	C₂²	1	1	yes	characteristic, complemented
43	#612617	C₂²	1	1	yes	characteristic, complemented
44	#612617	C₂²	1	1	yes	characteristic, complemented
45	#612424	C₂²	1	1	yes	characteristic, complemented
46	#612424	C₂²	1	1	yes	characteristic, complemented
47	#555894	C₂²	1	1	yes	characteristic, complemented
48	#515363	C₂²	1	1	yes	characteristic, complemented
49	#515285	C₂²	1	1	yes	characteristic, complemented
50	#405156	C₂²	1	4	yes	complemented
51	#394058	C₂²	1	4	yes	complemented
52	#392699	C₂²	1	4	yes	complemented
53	#392109	C₂²	1	2	yes	complemented
54	#392109	C₂²	1	2	yes	complemented
55	#382422	C₂²	1	2	yes	complemented
56	#359921	C₂²	1	2	yes	complemented
57	#359705	C₂²	1	2	yes	complemented
58	#233542	C₂²	1	4	yes	complemented
59	#233542	C₂²	1	4	yes	complemented
60	#233541	C₂²	1	4	yes	complemented
61	#233541	C₂²	1	4	yes	complemented
62	#201690	C₂²	1	4	yes	complemented
63	#201687	C₂²	1	4	yes	complemented
64	#201668	C₂²	1	2	yes	complemented
65	#201668	C₂²	1	2	yes	complemented
66	#201664	C₂²	1	2	yes	complemented
67	#201664	C₂²	1	2	yes	complemented
68	C₂×#8546	C₂²	1	2	yes	complemented
69	C₂×#8542	C₂²	1	1	yes	characteristic
70	C₂×#8542	C₂²	1	1	yes	characteristic
71	C₂×#8542	C₂²	1	2	yes	complemented
72	C₂×#8541	C₂²	1	2	yes	complemented
73	#187945	C₂²	1	2	yes	complemented
74	#187945	C₂²	1	2	yes	complemented
75	#187928	C₂²	1	2	yes	complemented
76	#187928	C₂²	1	2	yes	complemented
77	#187928	C₂²	1	2	yes	complemented
78	#187928	C₂²	1	2	yes	complemented
79	#115690	C₂²	1	4	yes	complemented
80	#115690	C₂²	1	4	yes	complemented
81	#115204	C₂²	1	4	yes	complemented
82	#115204	C₂²	1	4	yes	complemented
83	#115204	C₂²	1	4	yes	complemented
84	#115204	C₂²	1	4	yes	complemented
85	#107115	C₂²	1	2	yes	complemented
86	#107115	C₂²	1	2	yes	complemented
87	#106766	C₂²	1	2	yes	complemented
88	#106766	C₂²	1	2	yes	complemented
89	#106766	C₂²	1	2	yes	complemented
90	#106766	C₂²	1	2	yes	complemented
91	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
92	C₂⁵×D₄	D₄	1	1	yes	characteristic, complemented
93	C₂⁵×D₄	C₂³	1	1	yes	characteristic
94	C₂⁵×D₄	C₂³	1	1	yes	characteristic
95	C₂×#3490	C₂³	1	2	yes	—
96	C₂×#3484	C₂³	1	2	yes	—
97	C₂×#3484	C₂³	1	2	yes	—
98	C₂²×#534	C₂³	1	1	yes	characteristic
99	C₂³×#127	C₂³	1	1	yes	characteristic
100	C₂³×#121	D₄	1	1	yes	characteristic, complemented
101	C₂³×#121	D₄	1	1	yes	characteristic, complemented
102	C₂³×#121	C₂³	1	1	yes	characteristic
103	C₂³×#121	C₂³	1	1	yes	characteristic
104	C₂³×#120	D₄	1	1	yes	characteristic, complemented
105	C₂³×#120	D₄	1	1	yes	characteristic, complemented
106	C₂³×#120	C₂³	1	1	yes	characteristic
107	C₂³×#120	C₂³	1	1	yes	characteristic
108	C₂³×#120	C₂³	1	1	yes	characteristic
109	C₂²×#518	C₂³	1	1	yes	characteristic
110	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
111	C₂³×C₄×D₄	D₄	1	1	yes	characteristic, complemented
112	#37232	D₄	1	8	yes	complemented
113	#36714	D₄	1	8	yes	complemented
114	C₂×#2846	C₂³	1	4	yes	—
115	#35554	D₄	1	4	yes	complemented
116	#35527	D₄	1	4	yes	complemented
117	#35390	D₄	1	4	yes	complemented
118	#35367	D₄	1	4	yes	complemented
119	#35350	D₄	1	4	yes	complemented
120	#35348	D₄	1	8	yes	complemented
121	#35346	D₄	1	4	yes	complemented
122	#34992	C₂³	1	4	yes	—
123	#34980	C₂³	1	4	yes	—
124	#34980	C₂³	1	4	yes	—
125	#34980	C₂³	1	4	yes	—
126	#34980	C₂³	1	4	yes	—
127	C₂×#2405	C₂³	1	1	yes	characteristic
128	C₂×#2405	C₂³	1	1	yes	characteristic
129	C₂×#2405	C₂³	1	1	yes	characteristic
130	C₂×#2405	C₂³	1	1	yes	characteristic
131	C₂×#2403	C₂³	1	1	yes	characteristic
132	C₂×#2403	C₂³	1	1	yes	characteristic
133	C₂×#2403	C₂³	1	1	yes	characteristic
134	C₂×#2403	C₂³	1	1	yes	characteristic
135	#34176	C₂³	1	2	yes	—
136	#34171	C₂³	1	2	yes	—
137	#34171	C₂³	1	2	yes	—
138	C₂×#2315	C₂³	1	1	yes	characteristic
139	C₂×#2309	C₂³	1	1	yes	characteristic
140	C₂×#2308	C₂³	1	1	yes	characteristic
141	C₂×#2308	C₂³	1	1	yes	characteristic
142	C₂²×#379	C₂³	1	1	yes	characteristic
143	#21746	C₂³	1	4	yes	—
144	#21746	C₂³	1	4	yes	—
145	#21746	C₂³	1	4	yes	—
146	#21746	C₂³	1	4	yes	—
147	C₂×#1898	C₂³	1	4	yes	—
148	C₂×#1898	C₂³	1	4	yes	—
149	C₂×#1819	C₂³	1	2	yes	—
150	C₂×#1819	C₂³	1	2	yes	—
151	C₂×#1819	C₂³	1	4	yes	—
152	C₂×#1781	C₂³	1	2	yes	—
153	C₂×#1781	C₂³	1	2	yes	—
154	C₂×#1781	C₂³	1	2	yes	—
155	C₂×#1781	C₂³	1	2	yes	—
156	C₂×#1781	C₂³	1	4	yes	—
157	C₂×#1781	C₂³	1	4	yes	—
158	C₂×#1781	C₂³	1	4	yes	—
159	C₂×#1781	C₂³	1	4	yes	—
160	#15984	D₄	1	4	yes	complemented
161	#15950	D₄	1	4	yes	complemented
162	#15260	D₄	1	4	yes	complemented
163	#15257	D₄	1	4	yes	complemented
164	#14679	C₂³	1	1	yes	characteristic
165	#14679	C₂³	1	1	yes	characteristic
166	#14679	C₂³	1	4	yes	—
167	#14341	C₂³	1	1	yes	characteristic
168	#14341	C₂³	1	1	yes	characteristic
169	#13867	C₂³	1	1	yes	characteristic
170	#13867	C₂³	1	1	yes	characteristic
171	#13867	C₂³	1	1	yes	characteristic
172	#13867	C₂³	1	1	yes	characteristic
173	#13867	C₂³	1	1	yes	characteristic
174	#13867	C₂³	1	1	yes	characteristic
175	#13867	C₂³	1	1	yes	characteristic
176	#13867	C₂³	1	1	yes	characteristic
177	#10735	C₂³	1	4	yes	—
178	#10735	C₂³	1	4	yes	—
179	#8101	C₂³	1	4	yes	—
180	#8101	C₂³	1	4	yes	—
181	#8101	C₂³	1	4	yes	—
182	#8101	C₂³	1	4	yes	—
183	C₂⁷	C₂×D₄	1	1	yes	characteristic
184	C₂⁷	C₂×D₄	1	1	yes	characteristic
185	C₂⁷	C₂×D₄	1	1	yes	characteristic
186	C₂⁷	C₂⁴	1	1	yes	characteristic
187	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
188	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
189	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
191	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
192	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
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
200	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
201	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
202	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
203	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
204	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
205	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
206	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
207	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
208	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
209	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
210	C₂×#543	C₂×D₄	1	2	yes	—
211	C₂×#534	C₂×D₄	1	4	yes	—
212	C₂×#534	C₂×D₄	1	2	yes	—
213	C₂×#534	C₂×D₄	1	4	yes	—
214	C₂×#534	C₂×D₄	1	8	yes	—
215	C₂²×#127	C₂×D₄	1	4	yes	—
216	C₂²×#127	C₂×D₄	1	4	yes	—
217	C₂²×#123	C₂×D₄	1	2	yes	complemented
218	C₂²×#123	C₂×D₄	1	2	yes	complemented
219	C₂²×#121	C₂×D₄	1	4	yes	—
220	C₂²×#121	C₂×D₄	1	4	yes	—
221	C₂²×#120	C₂×D₄	1	8	yes	—
222	C₂²×#120	C₂×D₄	1	4	yes	—
223	C₂²×#120	C₂×D₄	1	4	yes	—
224	C₂²×#120	C₂×D₄	1	4	yes	—
225	C₂²×#120	C₂×D₄	1	4	yes	—
226	C₂²×#120	C₂×D₄	1	2	yes	complemented
227	C₂²×#120	C₂×D₄	1	2	yes	complemented
228	C₂²×#120	C₂⁴	1	4	yes	—
229	C₂×#518	C₂×D₄	1	4	yes	—
230	C₂×#518	C₂×D₄	1	2	yes	—
231	C₂×#518	C₂×D₄	1	2	yes	—
232	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
233	C₂³×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
234	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
235	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
236	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
237	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
238	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
239	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
240	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
241	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
242	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
243	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
244	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
245	C₂³×C₄²	C₂×D₄	1	1	yes	characteristic
246	#2405	C₂×D₄	1	8	yes	—
247	#2405	C₂×D₄	1	8	yes	—
248	#2405	C₂×D₄	1	8	yes	—
249	#2405	C₂×D₄	1	8	yes	—
250	#2403	C₂×D₄	1	8	yes	—
251	#2403	C₂×D₄	1	8	yes	—
252	#2403	C₂×D₄	1	8	yes	—
253	#2403	C₂×D₄	1	8	yes	—
254	#2315	C₂×D₄	1	4	yes	—
255	#2309	C₂×D₄	1	4	yes	—
256	#2309	C₂×D₄	1	4	yes	—
257	#2308	C₂×D₄	1	4	yes	—
258	#2308	C₂×D₄	1	4	yes	—
259	#2308	C₂×D₄	1	8	yes	—
260	C₂×#386	C₂×D₄	1	2	yes	complemented
261	C₂×#386	C₂×D₄	1	2	yes	complemented
262	C₂×#386	C₂×D₄	1	2	yes	complemented
263	C₂×#386	C₂×D₄	1	2	yes	complemented
264	C₂×#385	C₂×D₄	1	2	yes	complemented
265	C₂×#385	C₂×D₄	1	2	yes	complemented
266	C₂×#381	C₂×D₄	1	2	yes	complemented
267	C₂×#379	C₂×D₄	1	8	yes	—
268	C₂×#379	C₂×D₄	1	2	yes	complemented
269	C₂×#379	C₂⁴	1	4	yes	—
270	C₂×#379	C₂⁴	1	4	yes	—
271	C₂×#379	C₂⁴	1	1	yes	characteristic
272	C₂×#379	C₂⁴	1	1	yes	characteristic
273	C₂×#379	C₂⁴	1	1	yes	characteristic
274	C₂×#379	C₂⁴	1	1	yes	characteristic
275	C₂×#379	C₂⁴	1	4	yes	—
276	#2273	C₂×D₄	1	4	yes	—
277	#1440	C₂×D₄	1	4	yes	complemented
278	#1440	C₂×D₄	1	4	yes	complemented
279	#1438	C₂×D₄	1	4	yes	complemented
280	#1438	C₂×D₄	1	4	yes	complemented
281	#1438	C₂×D₄	1	4	yes	complemented
282	#1438	C₂×D₄	1	4	yes	complemented
283	C₂⁶	#120	1	2	yes	—
284	C₂⁶	#120	1	2	yes	—
285	C₂⁶	C₂²×D₄	1	1	yes	characteristic
286	C₂⁶	C₂²×D₄	1	1	yes	characteristic
287	C₂⁶	C₂²×D₄	1	1	yes	characteristic
288	C₂⁶	C₂²×D₄	1	1	yes	characteristic
289	C₂⁶	C₂²×D₄	1	4	yes	—
290	C₂⁶	C₂²×D₄	1	1	yes	characteristic
291	C₂⁶	C₂²×D₄	1	1	yes	characteristic
292	C₂⁶	C₂²×D₄	1	1	yes	characteristic
293	C₂⁶	C₂²×D₄	1	1	yes	characteristic
294	C₂⁶	C₂⁵	1	1	yes	characteristic
295	C₂³×D₄	#120	1	4	yes	—
296	C₂³×D₄	#120	1	2	yes	—
297	C₂³×D₄	#120	1	2	yes	—
298	C₂³×D₄	#120	1	4	yes	—
299	C₂³×D₄	#120	1	2	yes	—
300	C₂³×D₄	#120	1	4	yes	—
301	C₂³×D₄	#120	1	2	yes	—
302	C₂³×D₄	#120	1	4	yes	—
303	C₂³×D₄	C₂²×D₄	1	4	yes	—
304	C₂³×D₄	C₂²×D₄	1	4	yes	—
305	C₂³×D₄	C₂²×D₄	1	4	yes	—
306	C₂³×D₄	C₂²×D₄	1	4	yes	—
307	C₂³×D₄	C₂²×D₄	1	4	yes	—
308	C₂³×D₄	C₂²×D₄	1	4	yes	—
309	C₂³×D₄	C₂²×D₄	1	2	yes	—
310	C₂³×D₄	C₂²×D₄	1	2	yes	—
311	C₂³×D₄	C₂²×D₄	1	2	yes	—
312	C₂³×D₄	C₂²×D₄	1	2	yes	—
313	C₂³×D₄	C₂²×D₄	1	2	yes	—
314	C₂³×D₄	C₂²×D₄	1	2	yes	—
315	C₂³×D₄	C₂²×D₄	1	4	yes	—
316	C₂³×D₄	C₂²×D₄	1	4	yes	—
317	C₂³×D₄	C₂²×D₄	1	2	yes	—
318	C₂³×D₄	C₂²×D₄	1	2	yes	—
319	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
320	C₂³×D₄	H(5,𝔽₂)	1	4	yes	—
321	C₂⁴×C₄	#120	1	4	yes	—
322	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
323	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
324	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
325	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
326	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
327	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
328	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
329	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
330	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
331	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
332	C₂×#123	#120	1	16	yes	complemented
333	C₂×#120	#120	1	16	yes	complemented
334	C₂²×C₄⋊C₄	#120	1	4	yes	—
335	C₂²×C₂²⋊C₄	#120	1	4	yes	—
336	C₂²×C₂²⋊C₄	#120	1	2	yes	—
337	C₂²×C₂²⋊C₄	#120	1	4	yes	—
338	C₂²×C₂²⋊C₄	#120	1	2	yes	—
339	C₂²×C₂²⋊C₄	#120	1	2	yes	—
340	C₂²×C₂²⋊C₄	#120	1	4	yes	—
341	C₂²×C₂²⋊C₄	#120	1	4	yes	—
342	C₂²×C₂²⋊C₄	#120	1	2	yes	—
343	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
344	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
345	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
346	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
347	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
348	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
349	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
350	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
351	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
352	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
353	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
354	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
355	C₂²×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
356	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
357	C₂²×C₂²⋊C₄	H(5,𝔽₂)	1	4	yes	—
358	C₂²×C₄²	#120	1	2	yes	—
359	C₂²×C₄²	#120	1	2	yes	—
360	#386	#120	1	16	yes	complemented
361	#386	#120	1	16	yes	complemented
362	#379	C₂²×D₄	1	8	yes	—
363	#379	C₂²×D₄	1	8	yes	—
364	C₂⁵	C₂×#120	1	2	yes	—
365	C₂⁵	C₂×#120	1	2	yes	—
366	C₂⁵	C₂×#120	1	1	yes	characteristic
367	C₂⁵	C₂×#120	1	2	yes	—
368	C₂⁵	C₂×#120	1	2	yes	—
369	C₂⁵	C₂×#120	1	2	yes	—
370	C₂⁵	C₂×#120	1	2	yes	—
371	C₂⁵	C₂×#120	1	4	yes	—
372	C₂⁵	C₂×#120	1	2	yes	—
373	C₂⁵	C₂×#120	1	2	yes	—
374	C₂⁵	C₂×#120	1	2	yes	—
375	C₂⁵	C₂×#120	1	2	yes	—
376	C₂⁵	C₂×#120	1	1	yes	characteristic
377	C₂⁵	#534	1	2	yes	—
378	C₂⁵	#534	1	2	yes	—
379	C₂⁵	C₂³×D₄	1	1	yes	characteristic
380	C₂⁵	C₂³×D₄	1	2	yes	—
381	C₂⁵	C₂³×D₄	1	1	yes	characteristic
382	C₂⁵	C₂³×D₄	1	1	yes	characteristic
383	C₂⁵	C₂³×D₄	1	2	yes	—
384	C₂⁵	C₂³×D₄	1	2	yes	—
385	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
386	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
387	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
388	C₂²×D₄	C₂×#120	1	16	yes	—
389	C₂²×D₄	D₄²	1	4	yes	—
390	C₂²×D₄	D₄²	1	4	yes	—
391	C₂²×D₄	D₄²	1	4	yes	—
392	C₂²×D₄	D₄²	1	4	yes	—
393	C₂²×D₄	D₄²	1	4	yes	—
394	C₂²×D₄	D₄²	1	4	yes	—
395	C₂²×D₄	D₄²	1	4	yes	—
396	C₂²×D₄	D₄²	1	4	yes	—
397	C₂³×C₄	C₂×#120	1	2	yes	—
398	C₂³×C₄	C₂×#120	1	1	yes	characteristic
399	C₂³×C₄	C₂×#120	1	2	yes	—
400	C₂³×C₄	C₂×#120	1	4	yes	—
401	C₂³×C₄	C₂×#120	1	2	yes	—
402	C₂³×C₄	C₂×#120	1	4	yes	—
403	C₂³×C₄	C₂×#120	1	4	yes	—
404	C₂³×C₄	C₂×#120	1	2	yes	—
405	C₂³×C₄	C₂×#120	1	2	yes	—
406	C₂³×C₄	C₂×#120	1	2	yes	—
407	C₂³×C₄	C₂×#120	1	2	yes	—
408	C₂³×C₄	C₂×#120	1	2	yes	—
409	C₂³×C₄	C₂×#120	1	2	yes	—
410	C₂³×C₄	C₂×#120	1	2	yes	—
411	C₂³×C₄	C₂×#120	1	1	yes	characteristic
412	C₂³×C₄	C₂×#120	1	1	yes	characteristic
413	C₂³×C₄	C₂×#120	1	2	yes	—
414	C₂³×C₄	C₂×#120	1	1	yes	characteristic
415	C₂³×C₄	#534	1	2	yes	—
416	C₂³×C₄	#534	1	2	yes	—
417	C₂³×C₄	#534	1	2	yes	—
418	C₂³×C₄	#534	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
420	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
421	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
422	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
423	C₂×C₂²⋊C₄	D₄²	1	4	yes	—
424	C₂⁴	#2403	1	4	yes	—
425	C₂⁴	#2403	1	2	yes	—
426	C₂⁴	#2403	1	2	yes	—
427	C₂⁴	#2846	1	4	yes	—
428	C₂⁴	C₂²×#120	1	1	yes	characteristic
429	C₂⁴	C₂²×#120	1	1	yes	characteristic
430	C₂⁴	C₂²×#120	1	1	yes	characteristic
431	C₂⁴	C₂²×#120	1	4	yes	—
432	C₂⁴	C₂²×#120	1	1	yes	characteristic
433	C₂⁴	C₂×#534	1	1	yes	characteristic
434	C₂⁴	C₂×#534	1	1	yes	characteristic
435	C₂⁴	C₂×#534	1	1	yes	characteristic
436	C₂⁴	C₂×D₄²	1	2	yes	—
437	C₂⁴	C₂×D₄²	1	2	yes	—
438	C₂⁴	C₂×D₄²	1	2	yes	—
439	C₂⁴	C₂×D₄²	1	2	yes	—
440	C₂⁴	C₂×D₄²	1	2	yes	—
441	C₂⁴	C₂×D₄²	1	2	yes	—
442	C₂⁴	#3484	1	4	yes	—
443	C₂⁴	#3484	1	4	yes	—
444	C₂⁴	#3484	1	4	yes	—
445	C₂²×C₄	#2403	1	2	yes	—
446	C₂²×C₄	#2403	1	4	yes	—
447	C₂²×C₄	#2403	1	2	yes	—
448	C₂²×C₄	#2403	1	2	yes	—
449	C₂²×C₄	#2403	1	2	yes	—
450	C₂²×C₄	#2403	1	4	yes	—
451	C₂²×C₄	#2846	1	4	yes	—
452	C₂³	#23895	1	4	yes	—
453	C₂³	C₂×#2403	1	1	yes	characteristic
454	C₂³	C₂×#2403	1	1	yes	characteristic
455	C₂³	C₂×#2403	1	1	yes	characteristic
456	C₂³	#34980	1	1	yes	characteristic
457	C₂³	#34980	1	1	yes	characteristic
458	C₂³	#34980	1	1	yes	characteristic
459	C₂³	D₄×#120	1	4	yes	—
460	C₂³	D₄×#120	1	4	yes	—
461	C₂³	C₂×#2846	1	1	yes	characteristic
462	C₂³	#60399	1	2	yes	—
463	C₂³	#60401	1	2	yes	—
464	C₂×C₄	#23895	1	4	yes	—
465	C₂²	#612424	1	1	yes	characteristic
466	C₂²	C₂×#23895	1	2	yes	—
467	C₂²	C₂×#23895	1	2	yes	—
468	C₂²	#6437633	1	1	yes	characteristic
469	C₂²	#6437636	1	1	yes	characteristic
470	C₂²	#6470246	1	2	yes	—
471	C₂²	#6628900	1	2	yes	—
472	C₂	#72213862	1	1	yes	characteristic
473	C₂	#72213862	1	1	yes	characteristic
474	C₂	#72251698	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#612424
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁶ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂² ▷ C₁

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72262798	C₂	semidirect
2. #72262662	C₂	semidirect
3. #72262634	C₂	semidirect
4. #72262429	C₂	semidirect
5. #72262342	C₂	semidirect
6. #72256422	C₂	semidirect
7. #72237612	C₂	semidirect
8. #72237461	C₂	semidirect
9. #72235932	C₂	semidirect
10. #72235924	C₂	semidirect
11. #72235861	C₂	semidirect
12. #72235768	C₂	semidirect
13. #72234806	C₂	semidirect
14. #72233891	C₂	semidirect
15. #72233891	C₂	semidirect
16. #72219377	C₂	semidirect
17. #72219038	C₂	semidirect
18. #72210600	C₂	semidirect
19. #72210600	C₂	semidirect
26. C₂×#37232	C₂²	semidirect
27. C₂×#36714	C₂²	semidirect
30. C₂×#35348	C₂²	semidirect
32. #6470226	C₂²	semidirect
33. #6470226	C₂²	semidirect
34. #6470225	C₂²	semidirect
35. #6470225	C₂²	semidirect
36. #6453039	C₂²	semidirect
37. #6451874	C₂²	semidirect
38. #6432949	C₂²	semidirect
40. #618455	C₂²	semidirect
42. #618316	C₂²	semidirect
43. #612617	C₂²	semidirect
44. #612617	C₂²	semidirect
45. #612424	C₂²	semidirect
46. #612424	C₂²	semidirect
47. #555894	C₂²	semidirect
48. #515363	C₂²	semidirect
49. #515285	C₂²	semidirect
50. #405156	C₂²	semidirect
51. #394058	C₂²	semidirect
52. #392699	C₂²	semidirect
53. #392109	C₂²	semidirect
54. #392109	C₂²	semidirect
55. #382422	C₂²	semidirect
56. #359921	C₂²	semidirect
57. #359705	C₂²	semidirect
58. #233542	C₂²	semidirect
59. #233542	C₂²	semidirect
60. #233541	C₂²	semidirect
61. #233541	C₂²	semidirect
62. #201690	C₂²	semidirect
63. #201687	C₂²	semidirect
64. #201668	C₂²	semidirect
65. #201668	C₂²	semidirect
66. #201664	C₂²	semidirect
67. #201664	C₂²	semidirect
68. C₂×#8546	C₂²	semidirect
71. C₂×#8542	C₂²	semidirect
72. C₂×#8541	C₂²	semidirect
73. #187945	C₂²	semidirect
74. #187945	C₂²	semidirect
75. #187928	C₂²	semidirect
76. #187928	C₂²	semidirect
77. #187928	C₂²	semidirect
78. #187928	C₂²	semidirect
79. #115690	C₂²	semidirect
80. #115690	C₂²	semidirect
81. #115204	C₂²	semidirect
82. #115204	C₂²	semidirect
83. #115204	C₂²	semidirect
84. #115204	C₂²	semidirect
85. #107115	C₂²	semidirect
86. #107115	C₂²	semidirect
87. #106766	C₂²	semidirect
88. #106766	C₂²	semidirect
89. #106766	C₂²	semidirect
90. #106766	C₂²	semidirect
91. C₂⁵×D₄	D₄	semidirect
92. C₂⁵×D₄	D₄	semidirect
100. C₂³×#121	D₄	semidirect
101. C₂³×#121	D₄	semidirect
104. C₂³×#120	D₄	semidirect
105. C₂³×#120	D₄	semidirect
110. C₂³×C₄×D₄	D₄	semidirect
111. C₂³×C₄×D₄	D₄	semidirect
112. #37232	D₄	semidirect
113. #36714	D₄	semidirect
115. #35554	D₄	semidirect
116. #35527	D₄	semidirect
117. #35390	D₄	semidirect
118. #35367	D₄	semidirect
119. #35350	D₄	semidirect
120. #35348	D₄	semidirect
121. #35346	D₄	semidirect
160. #15984	D₄	semidirect
161. #15950	D₄	semidirect
162. #15260	D₄	semidirect
163. #15257	D₄	semidirect
217. C₂²×#123	C₂×D₄	semidirect
218. C₂²×#123	C₂×D₄	semidirect
226. C₂²×#120	C₂×D₄	semidirect
227. C₂²×#120	C₂×D₄	semidirect
260. C₂×#386	C₂×D₄	semidirect
261. C₂×#386	C₂×D₄	semidirect
262. C₂×#386	C₂×D₄	semidirect
263. C₂×#386	C₂×D₄	semidirect
264. C₂×#385	C₂×D₄	semidirect
265. C₂×#385	C₂×D₄	semidirect
266. C₂×#381	C₂×D₄	semidirect
268. C₂×#379	C₂×D₄	semidirect
277. #1440	C₂×D₄	semidirect
278. #1440	C₂×D₄	semidirect
279. #1438	C₂×D₄	semidirect
280. #1438	C₂×D₄	semidirect
281. #1438	C₂×D₄	semidirect
282. #1438	C₂×D₄	semidirect
332. C₂×#123	#120	semidirect
333. C₂×#120	#120	semidirect
360. #386	#120	semidirect
361. #386	#120	semidirect

Maximal subgroups

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

subgroup	index
#72262798	2
#72262662	2
#72262634	2
#72262429	2
#72262342	2
#72256422	2
#72237612	2
#72237461	2
#72235932	2
#72235924	2
#72235861	2
#72235768	2
#72234806	2
#72233891	2
#72219377	2
#72219038	2
#72210600	2