Subgroups — #72261578

Order 2048.

At least 9664 conjugacy classes of subgroups; only the 2216 normal subgroups are shown.

The subgroup lattice has 549 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72261548	C₂	1	2	yes	maximal, complemented
2	#72261525	C₂	1	2	yes	maximal, complemented
3	#72261506	C₂	1	1	yes	maximal, characteristic, complemented
4	#72261492	C₂	1	1	yes	maximal, characteristic, complemented
5	#72261466	C₂	1	1	yes	maximal, characteristic, complemented
6	#72261459	C₂	1	4	yes	maximal, complemented
7	#72261451	C₂	1	4	yes	maximal, complemented
8	#72261443	C₂	1	4	yes	maximal, complemented
9	#72261376	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#6437621	C₂	1	2	yes	maximal, complemented
11	C₂³×#3026	C₂	1	1	yes	maximal, characteristic, complemented
12	#72240155	C₂	1	1	yes	maximal, characteristic, complemented
13	#72240127	C₂	1	2	yes	maximal, complemented
14	C₂×#449469	C₂	1	4	yes	maximal, complemented
15	C₂×#6628892	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
17	C₂²×#3484	C₂²	1	1	yes	characteristic, complemented
18	C₂³×#534	C₂²	1	2	yes	—
19	C₂³×#534	C₂²	1	1	yes	characteristic
20	C₂²×#3026	C₂²	1	4	yes	—
21	C₂²×#3026	C₂²	1	4	yes	complemented
22	C₂²×#3026	C₂²	1	4	yes	complemented
23	C₂²×#3026	C₂²	1	4	yes	complemented
24	C₂⁴×#99	C₂²	1	1	yes	characteristic, complemented
25	C₂⁴×#99	C₂²	1	2	yes	complemented
26	C₂×#35347	C₂²	1	2	yes	complemented
27	C₂×#35347	C₂²	1	4	yes	complemented
28	C₂×#34980	C₂²	1	2	yes	—
29	C₂×#34980	C₂²	1	1	yes	characteristic
30	C₂×#34980	C₂²	1	2	yes	—
31	C₂²×#2410	C₂²	1	1	yes	characteristic
32	C₂×#23444	C₂²	1	4	yes	complemented
33	C₂×#23444	C₂²	1	4	yes	complemented
34	C₂²×#1898	C₂²	1	2	yes	complemented
35	C₂²×#1898	C₂²	1	2	yes	complemented
36	C₂×#20960	C₂²	1	4	yes	complemented
37	C₂×#20609	C₂²	1	4	yes	complemented
38	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
39	C₂²×#1781	C₂²	1	2	yes	complemented
40	C₂²×#1781	C₂²	1	2	yes	complemented
41	#5955331	C₂²	1	2	yes	complemented
42	#5955328	C₂²	1	2	yes	complemented
43	#517411	C₂²	1	1	yes	characteristic, complemented
44	#516383	C₂²	1	1	yes	characteristic, complemented
45	#516323	C₂²	1	4	yes	complemented
46	#515529	C₂²	1	2	yes	complemented
47	C₂×#14134	C₂²	1	1	yes	characteristic, complemented
48	C₂×#13867	C₂²	1	2	yes	complemented
49	C₂×#13867	C₂²	1	1	yes	characteristic, complemented
50	C₂×#10995	C₂²	1	8	yes	complemented
51	C₂×#10995	C₂²	1	8	yes	complemented
52	C₂×#10995	C₂²	1	8	yes	complemented
53	C₂×#10980	C₂²	1	4	yes	complemented
54	C₂×#10972	C₂²	1	8	yes	complemented
55	C₂×#10972	C₂²	1	4	yes	complemented
56	C₂×#10972	C₂²	1	4	yes	complemented
57	C₂×#10972	C₂²	1	4	yes	complemented
58	C₂×#10735	C₂²	1	2	yes	complemented
59	C₂×#10725	C₂²	1	2	yes	complemented
60	#153851	C₂²	1	2	yes	complemented
61	#123590	C₂²	1	8	yes	complemented
62	#123581	C₂²	1	4	yes	complemented
63	#123539	C₂²	1	8	yes	complemented
64	#123520	C₂²	1	4	yes	complemented
65	C₂³×H(5,𝔽₂)	C₂³	1	4	yes	—
66	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic, complemented
67	C₂⁵×D₄	C₂³	1	1	yes	characteristic
68	C₂⁵×D₄	C₂³	1	2	yes	—
69	C₂⁵×D₄	C₂³	1	1	yes	characteristic
70	C₂²×#534	D₄	1	16	yes	complemented
71	C₂²×#534	D₄	1	2	yes	complemented
72	C₂²×#534	D₄	1	2	yes	complemented
73	C₂²×#534	C₂³	1	4	yes	—
74	C₂²×#534	C₂³	1	4	yes	—
75	C₂²×#534	C₂³	1	4	yes	—
76	C₂²×#534	C₂³	1	2	yes	—
77	C₂²×#534	C₂³	1	2	yes	—
78	C₂²×#534	C₂³	1	2	yes	—
79	C₂²×#534	C₂³	1	4	yes	—
80	C₂²×#534	C₂³	1	1	yes	characteristic, complemented
81	C₂²×#534	C₂³	1	1	yes	characteristic, complemented
82	C₂³×#123	D₄	1	2	yes	complemented
83	C₂³×#121	C₂³	1	2	yes	—
84	C₂³×#120	D₄	1	2	yes	complemented
85	C₂³×#120	D₄	1	1	yes	characteristic, complemented
86	C₂³×#120	C₂³	1	1	yes	characteristic
87	C₂³×#120	C₂³	1	1	yes	characteristic
88	C₂²×#518	C₂³	1	1	yes	characteristic, complemented
89	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
90	C₂⁴×C₂²⋊C₄	C₂³	1	2	yes	—
91	C₂⁴×C₂²⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×#3026	D₄	1	32	yes	complemented
93	C₂³×#99	C₂³	1	4	yes	—
94	C₂³×#99	C₂³	1	8	yes	—
95	C₂³×#99	C₂³	1	4	yes	—
96	C₂³×#99	C₂³	1	8	yes	—
97	C₂³×#99	C₂³	1	4	yes	complemented
98	C₂³×#99	C₂³	1	4	yes	complemented
99	C₂³×#99	C₂³	1	4	yes	complemented
100	C₂³×#99	C₂³	1	4	yes	complemented
101	C₂×#2849	D₄	1	4	yes	complemented
102	C₂×#2846	D₄	1	4	yes	complemented
103	#34980	D₄	1	16	yes	complemented
104	C₂×#2405	D₄	1	2	yes	complemented
105	C₂×#2405	D₄	1	2	yes	complemented
106	C₂×#2403	D₄	1	2	yes	complemented
107	C₂×#2403	D₄	1	2	yes	complemented
108	C₂×#2613	D₄	1	8	yes	complemented
109	C₂²×#394	D₄	1	2	yes	complemented
110	C₂²×#392	D₄	1	2	yes	complemented
111	C₂×#2308	C₂³	1	4	yes	—
112	C₂×#2308	C₂³	1	2	yes	—
113	C₂×#2308	C₂³	1	4	yes	—
114	C₂×#2308	C₂³	1	4	yes	—
115	C₂×#2308	C₂³	1	2	yes	complemented
116	C₂²×#386	D₄	1	1	yes	characteristic, complemented
117	C₂²×#386	C₂³	1	8	yes	—
118	C₂²×#386	C₂³	1	2	yes	—
119	C₂²×#386	C₂³	1	2	yes	complemented
120	C₂²×#386	C₂³	1	2	yes	complemented
121	C₂²×#386	C₂³	1	2	yes	complemented
122	C₂²×#385	D₄	1	1	yes	characteristic, complemented
123	C₂²×#379	D₄	1	1	yes	characteristic, complemented
124	C₂²×#379	C₂³	1	1	yes	characteristic
125	C₂²×#379	C₂³	1	2	yes	—
126	C₂²×#379	C₂³	1	2	yes	—
127	C₂²×#342	C₂³	1	4	yes	complemented
128	C₂²×#342	C₂³	1	4	yes	complemented
129	C₂²×#342	C₂³	1	8	yes	complemented
130	C₂²×#342	C₂³	1	8	yes	complemented
131	#13794	C₂³	1	2	yes	complemented
132	C₂×C₂²⋊#95	C₂³	1	2	yes	complemented
133	C₂×C₂²⋊#95	C₂³	1	8	yes	complemented
134	C₂⁷	C₂×D₄	1	1	yes	characteristic
135	C₂⁷	C₂×D₄	1	2	yes	—
136	C₂⁷	C₂×D₄	1	1	yes	characteristic
137	C₂⁷	C₂⁴	1	1	yes	characteristic
138	C₂²×H(5,𝔽₂)	C₂×D₄	1	16	yes	complemented
139	C₂⁴×D₄	C₂×D₄	1	2	yes	—
140	C₂⁴×D₄	C₂×D₄	1	2	yes	—
141	C₂⁴×D₄	C₂×D₄	1	2	yes	—
142	C₂⁴×D₄	C₂×D₄	1	2	yes	—
143	C₂⁴×D₄	C₂×D₄	1	8	yes	—
144	C₂⁴×D₄	C₂×D₄	1	8	yes	—
145	C₂⁴×D₄	C₂×D₄	1	8	yes	—
146	C₂⁴×D₄	C₂×D₄	1	2	yes	—
147	C₂⁴×D₄	C₂×D₄	1	4	yes	—
148	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
149	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
150	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
151	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
152	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
153	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
154	C₂⁴×D₄	C₂×D₄	1	2	yes	complemented
155	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
156	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
157	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
158	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
159	C₂⁴×D₄	C₂⁴	1	2	yes	—
160	C₂⁴×D₄	C₂⁴	1	4	yes	—
161	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
162	C₂⁵×C₄	C₂×D₄	1	2	yes	—
163	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
164	C₂⁵×C₄	C₂⁴	1	2	yes	—
165	C₂×#534	C₂×D₄	1	16	yes	—
166	C₂×#534	C₂×D₄	1	32	yes	—
167	C₂×#534	C₂×D₄	1	16	yes	—
168	C₂×#534	C₂×D₄	1	16	yes	—
169	C₂×#534	C₂×D₄	1	16	yes	complemented
170	C₂²×#123	C₂×D₄	1	4	yes	—
171	C₂²×#123	C₂×D₄	1	4	yes	—
172	C₂²×#123	C₂×D₄	1	8	yes	complemented
173	C₂²×#123	C₂×D₄	1	4	yes	complemented
174	C₂²×#120	C₂×D₄	1	4	yes	—
175	C₂²×#120	C₂×D₄	1	4	yes	—
176	C₂²×#120	C₂×D₄	1	4	yes	—
177	C₂²×#120	C₂×D₄	1	4	yes	—
178	C₂²×#120	C₂×D₄	1	8	yes	—
179	C₂²×#120	C₂×D₄	1	8	yes	complemented
180	C₂²×#120	C₂×D₄	1	4	yes	complemented
181	C₂³×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
182	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
184	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
185	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
186	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
187	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
188	C₂³×C₂²⋊C₄	C₂×D₄	1	8	yes	—
189	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
190	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
191	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	—
192	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
193	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
194	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
195	C₂³×C₂²⋊C₄	C₂×D₄	1	2	yes	complemented
196	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
197	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
198	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
199	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
200	C₂³×C₂²⋊C₄	C₂⁴	1	1	yes	characteristic
201	C₂³×C₂²⋊C₄	C₂⁴	1	4	yes	—
202	C₂³×C₂²⋊C₄	C₂⁴	1	2	yes	—
203	C₂²×#99	C₂×D₄	1	16	yes	complemented
204	C₂²×#99	C₂×D₄	1	32	yes	complemented
205	#2308	C₂×D₄	1	16	yes	complemented
206	C₂×#386	C₂×D₄	1	4	yes	complemented
207	C₂×#386	C₂×D₄	1	4	yes	complemented
208	C₂×#381	C₂×D₄	1	8	yes	complemented
209	C₂×#379	C₂×D₄	1	4	yes	—
210	C₂×#379	C₂×D₄	1	4	yes	—
211	C₂×#379	C₂×D₄	1	2	yes	—
212	C₂×#379	C₂×D₄	1	2	yes	—
213	C₂×#379	C₂×D₄	1	8	yes	—
214	C₂×#379	C₂×D₄	1	8	yes	complemented
215	C₂²×#95	C₂×D₄	1	2	yes	complemented
216	C₂²×#95	C₂×D₄	1	2	yes	complemented
217	C₂⁶	#120	1	2	yes	—
218	C₂⁶	#120	1	2	yes	—
219	C₂⁶	#120	1	8	yes	complemented
220	C₂⁶	#120	1	4	yes	complemented
221	C₂⁶	C₂²×D₄	1	1	yes	characteristic
222	C₂⁶	C₂²×D₄	1	1	yes	characteristic
223	C₂⁶	C₂²×D₄	1	1	yes	characteristic
224	C₂⁶	C₂²×D₄	1	1	yes	characteristic
225	C₂⁶	C₂²×D₄	1	2	yes	—
226	C₂⁶	C₂²×D₄	1	4	yes	—
227	C₂⁶	C₂²×D₄	1	1	yes	characteristic
228	C₂⁶	C₂²×D₄	1	1	yes	characteristic
229	C₂⁶	C₂²×D₄	1	2	yes	—
230	C₂⁶	C₂²×D₄	1	1	yes	characteristic
231	C₂⁶	C₂²×D₄	1	1	yes	characteristic
232	C₂⁶	C₂²×D₄	1	1	yes	characteristic
233	C₂⁶	C₂²×D₄	1	2	yes	—
234	C₂⁶	C₂²×D₄	1	1	yes	characteristic
235	C₂⁶	C₂²×D₄	1	4	yes	—
236	C₂⁶	C₂²×D₄	1	4	yes	—
237	C₂⁶	H(5,𝔽₂)	1	2	yes	—
238	C₂⁶	H(5,𝔽₂)	1	2	yes	—
239	C₂⁶	H(5,𝔽₂)	1	4	yes	—
240	C₂⁶	H(5,𝔽₂)	1	4	yes	—
241	C₂⁶	C₂⁵	1	1	yes	characteristic
242	C₂³×D₄	#120	1	4	yes	—
243	C₂³×D₄	#120	1	4	yes	—
244	C₂³×D₄	#120	1	2	yes	—
245	C₂³×D₄	#120	1	2	yes	—
246	C₂³×D₄	#120	1	4	yes	—
247	C₂³×D₄	#120	1	16	yes	complemented
248	C₂³×D₄	#120	1	4	yes	complemented
249	C₂³×D₄	#120	1	4	yes	complemented
250	C₂³×D₄	#120	1	4	yes	complemented
251	C₂³×D₄	#120	1	4	yes	complemented
252	C₂³×D₄	C₂²×D₄	1	4	yes	—
253	C₂³×D₄	C₂²×D₄	1	4	yes	—
254	C₂³×D₄	C₂²×D₄	1	4	yes	—
255	C₂³×D₄	C₂²×D₄	1	8	yes	—
256	C₂³×D₄	C₂²×D₄	1	4	yes	—
257	C₂³×D₄	C₂²×D₄	1	8	yes	—
258	C₂³×D₄	C₂²×D₄	1	4	yes	—
259	C₂³×D₄	C₂²×D₄	1	8	yes	—
260	C₂³×D₄	C₂²×D₄	1	4	yes	—
261	C₂³×D₄	C₂²×D₄	1	8	yes	—
262	C₂³×D₄	C₂²×D₄	1	16	yes	—
263	C₂³×D₄	H(5,𝔽₂)	1	8	yes	—
264	C₂³×D₄	H(5,𝔽₂)	1	16	yes	—
265	C₂⁴×C₄	#120	1	2	yes	—
266	C₂⁴×C₄	#120	1	2	yes	—
267	C₂⁴×C₄	#120	1	8	yes	complemented
268	C₂⁴×C₄	#120	1	4	yes	complemented
269	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
270	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
271	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
272	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
273	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
274	C₂⁴×C₄	C₂²×D₄	1	4	yes	—
275	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
276	C₂⁴×C₄	C₂²×D₄	1	2	yes	—
277	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
278	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
279	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
280	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
281	#534	#120	1	64	yes	complemented
282	C₂×#123	#120	1	16	yes	complemented
283	C₂×#120	#120	1	16	yes	complemented
284	C₂²×C₂²⋊C₄	#120	1	2	yes	—
285	C₂²×C₂²⋊C₄	#120	1	4	yes	—
286	C₂²×C₂²⋊C₄	#120	1	2	yes	—
287	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
288	C₂²×C₂²⋊C₄	#120	1	4	yes	complemented
289	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
290	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
291	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
292	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
293	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
294	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
295	C₂²×C₂²⋊C₄	C₂²×D₄	1	8	yes	—
296	C₂²×C₂²⋊C₄	C₂²×D₄	1	16	yes	—
297	C₂²×C₂²⋊C₄	C₂²×D₄	1	4	yes	—
298	C₂⁵	C₂×#120	1	1	yes	characteristic
299	C₂⁵	C₂×#120	1	1	yes	characteristic
300	C₂⁵	C₂×#120	1	2	yes	—
301	C₂⁵	C₂×#120	1	2	yes	—
302	C₂⁵	C₂×#120	1	2	yes	—
303	C₂⁵	C₂×#120	1	4	yes	—
304	C₂⁵	C₂×#120	1	2	yes	—
305	C₂⁵	C₂×#120	1	4	yes	—
306	C₂⁵	C₂×#120	1	8	yes	—
307	C₂⁵	C₂×#120	1	1	yes	characteristic
308	C₂⁵	C₂×#120	1	1	yes	characteristic
309	C₂⁵	C₂×#120	1	2	yes	—
310	C₂⁵	C₂×#120	1	1	yes	characteristic
311	C₂⁵	C₂×#120	1	1	yes	characteristic
312	C₂⁵	C₂×#120	1	2	yes	—
313	C₂⁵	C₂×#120	1	4	yes	—
314	C₂⁵	C₂×#120	1	2	yes	—
315	C₂⁵	C₂×#120	1	2	yes	—
316	C₂⁵	C₂×#120	1	4	yes	—
317	C₂⁵	C₂×#120	1	2	yes	—
318	C₂⁵	#534	1	1	yes	characteristic
319	C₂⁵	#534	1	1	yes	characteristic
320	C₂⁵	#534	1	2	yes	—
321	C₂⁵	#534	1	4	yes	—
322	C₂⁵	#534	1	2	yes	—
323	C₂⁵	#534	1	2	yes	—
324	C₂⁵	#534	1	4	yes	—
325	C₂⁵	#534	1	4	yes	—
326	C₂⁵	#534	1	4	yes	—
327	C₂⁵	#534	1	2	yes	—
328	C₂⁵	#534	1	4	yes	—
329	C₂⁵	#534	1	2	yes	—
330	C₂⁵	#534	1	4	yes	—
331	C₂⁵	D₄²	1	2	yes	—
332	C₂⁵	D₄²	1	2	yes	—
333	C₂⁵	D₄²	1	8	yes	—
334	C₂⁵	D₄²	1	16	yes	—
335	C₂⁵	D₄²	1	2	yes	—
336	C₂⁵	D₄²	1	2	yes	—
337	C₂⁵	D₄²	1	2	yes	—
338	C₂⁵	D₄²	1	2	yes	—
339	C₂⁵	D₄²	1	2	yes	—
340	C₂⁵	D₄²	1	2	yes	—
341	C₂⁵	D₄²	1	4	yes	—
342	C₂⁵	D₄²	1	4	yes	—
343	C₂⁵	D₄²	1	4	yes	—
344	C₂⁵	D₄²	1	4	yes	—
345	C₂⁵	D₄²	1	4	yes	—
346	C₂⁵	D₄²	1	4	yes	—
347	C₂⁵	D₄²	1	4	yes	—
348	C₂⁵	D₄²	1	4	yes	—
349	C₂⁵	D₄²	1	4	yes	—
350	C₂⁵	D₄²	1	4	yes	—
351	C₂⁵	D₄²	1	4	yes	—
352	C₂⁵	D₄²	1	4	yes	—
353	C₂⁵	D₄²	1	4	yes	—
354	C₂⁵	D₄²	1	4	yes	—
355	C₂⁵	H(3,𝔽₄)	1	4	yes	—
356	C₂⁵	H(3,𝔽₄)	1	4	yes	—
357	C₂⁵	C₂³×D₄	1	1	yes	characteristic
358	C₂⁵	C₂³×D₄	1	1	yes	characteristic
359	C₂⁵	C₂³×D₄	1	2	yes	—
360	C₂⁵	C₂³×D₄	1	1	yes	characteristic
361	C₂⁵	C₂³×D₄	1	2	yes	—
362	C₂⁵	C₂³×D₄	1	4	yes	—
363	C₂⁵	C₂³×D₄	1	2	yes	—
364	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
365	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
366	C₂⁵	C₂×H(5,𝔽₂)	1	2	yes	—
367	C₂⁵	C₂×H(5,𝔽₂)	1	4	yes	—
368	C₂⁵	C₂×H(5,𝔽₂)	1	8	yes	—
369	C₂²×D₄	C₂×#120	1	16	yes	—
370	C₂²×D₄	C₂×#120	1	8	yes	—
371	C₂²×D₄	C₂×#120	1	16	yes	—
372	C₂²×D₄	#534	1	8	yes	—
373	C₂²×D₄	#534	1	16	yes	—
374	C₂²×D₄	D₄²	1	16	yes	—
375	C₂²×D₄	D₄²	1	32	yes	—
376	C₂³×C₄	C₂×#120	1	2	yes	—
377	C₂³×C₄	C₂×#120	1	2	yes	—
378	C₂³×C₄	C₂×#120	1	2	yes	—
379	C₂³×C₄	C₂×#120	1	2	yes	—
380	C₂³×C₄	C₂×#120	1	4	yes	—
381	C₂³×C₄	C₂×#120	1	4	yes	—
382	C₂³×C₄	C₂×#120	1	8	yes	—
383	C₂³×C₄	C₂×#120	1	2	yes	—
384	C₂³×C₄	C₂×#120	1	2	yes	—
385	C₂³×C₄	C₂×#120	1	2	yes	—
386	C₂³×C₄	C₂×#120	1	2	yes	—
387	C₂³×C₄	D₄²	1	8	yes	—
388	C₂³×C₄	D₄²	1	16	yes	—
389	C₂×C₂²⋊C₄	C₂×#120	1	8	yes	—
390	C₂×C₂²⋊C₄	C₂×#120	1	16	yes	—
391	C₂⁴	#2403	1	1	yes	characteristic
392	C₂⁴	#2403	1	1	yes	characteristic
393	C₂⁴	#2403	1	1	yes	characteristic
394	C₂⁴	#2403	1	2	yes	—
395	C₂⁴	#2403	1	2	yes	—
396	C₂⁴	#2403	1	2	yes	—
397	C₂⁴	#2403	1	4	yes	—
398	C₂⁴	#2403	1	4	yes	—
399	C₂⁴	#2403	1	2	yes	—
400	C₂⁴	#2403	1	4	yes	—
401	C₂⁴	#2403	1	1	yes	characteristic
402	C₂⁴	#2403	1	8	yes	—
403	C₂⁴	#2403	1	2	yes	—
404	C₂⁴	#2403	1	2	yes	—
405	C₂⁴	#2403	1	2	yes	—
406	C₂⁴	#2403	1	4	yes	—
407	C₂⁴	#2403	1	4	yes	—
408	C₂⁴	#2403	1	4	yes	—
409	C₂⁴	#2403	1	4	yes	—
410	C₂⁴	#2403	1	4	yes	—
411	C₂⁴	#2403	1	4	yes	—
412	C₂⁴	#2403	1	2	yes	—
413	C₂⁴	#2403	1	2	yes	—
414	C₂⁴	#2403	1	4	yes	—
415	C₂⁴	#2403	1	4	yes	—
416	C₂⁴	#2403	1	2	yes	—
417	C₂⁴	#2403	1	4	yes	—
418	C₂⁴	#2403	1	16	yes	complemented
419	C₂⁴	#2679	1	4	yes	—
420	C₂⁴	#2679	1	4	yes	—
421	C₂⁴	#2679	1	4	yes	—
422	C₂⁴	#2679	1	4	yes	—
423	C₂⁴	#2679	1	4	yes	—
424	C₂⁴	#2679	1	4	yes	—
425	C₂⁴	#2679	1	4	yes	—
426	C₂⁴	#2679	1	4	yes	—
427	C₂⁴	#2679	1	4	yes	—
428	C₂⁴	#2679	1	4	yes	—
429	C₂⁴	#2679	1	4	yes	—
430	C₂⁴	#2679	1	4	yes	—
431	C₂⁴	#2846	1	4	yes	complemented
432	C₂⁴	C₂²×#120	1	1	yes	characteristic
433	C₂⁴	C₂²×#120	1	1	yes	characteristic
434	C₂⁴	C₂²×#120	1	1	yes	characteristic
435	C₂⁴	C₂²×#120	1	2	yes	—
436	C₂⁴	C₂²×#120	1	2	yes	—
437	C₂⁴	C₂²×#120	1	1	yes	characteristic
438	C₂⁴	C₂²×#120	1	4	yes	—
439	C₂⁴	C₂×#534	1	1	yes	characteristic
440	C₂⁴	C₂×#534	1	2	yes	—
441	C₂⁴	C₂×#534	1	1	yes	characteristic
442	C₂⁴	C₂×#534	1	2	yes	—
443	C₂⁴	C₂×#534	1	2	yes	—
444	C₂⁴	C₂×#534	1	1	yes	characteristic
445	C₂⁴	C₂×#534	1	2	yes	—
446	C₂⁴	C₂×#534	1	4	yes	—
447	C₂⁴	C₂×D₄²	1	2	yes	—
448	C₂⁴	C₂×D₄²	1	2	yes	—
449	C₂⁴	C₂×D₄²	1	2	yes	—
450	C₂⁴	C₂×D₄²	1	2	yes	—
451	C₂⁴	C₂×D₄²	1	2	yes	—
452	C₂⁴	C₂×D₄²	1	2	yes	—
453	C₂⁴	C₂×D₄²	1	2	yes	—
454	C₂⁴	C₂×D₄²	1	8	yes	—
455	C₂⁴	C₂×D₄²	1	4	yes	—
456	C₂⁴	C₂×D₄²	1	4	yes	—
457	C₂⁴	C₂×D₄²	1	2	yes	—
458	C₂⁴	C₂×D₄²	1	2	yes	—
459	C₂⁴	C₂×D₄²	1	8	yes	—
460	C₂⁴	#3484	1	4	yes	—
461	C₂⁴	#3484	1	8	yes	—
462	C₂⁴	#3484	1	4	yes	—
463	C₂⁴	#3484	1	4	yes	—
464	C₂⁴	#3484	1	8	yes	—
465	C₂⁴	#3484	1	8	yes	—
466	C₂⁴	#3484	1	4	yes	—
467	C₂⁴	#3484	1	4	yes	—
468	C₂⁴	#3484	1	8	yes	—
469	C₂⁴	#3484	1	8	yes	—
470	C₂⁴	C₂×H(3,𝔽₄)	1	2	yes	—
471	C₂⁴	#3532	1	8	yes	—
472	C₂⁴	#3532	1	8	yes	—
473	C₂⁴	#3532	1	8	yes	—
474	C₂²×C₄	#2403	1	8	yes	—
475	C₂²×C₄	#2403	1	16	yes	complemented
476	C₂²×C₄	#2846	1	4	yes	complemented
477	C₂³	#15947	1	2	yes	—
478	C₂³	#15947	1	2	yes	—
479	C₂³	#15947	1	4	yes	—
480	C₂³	#15947	1	2	yes	—
481	C₂³	#15947	1	4	yes	—
482	C₂³	#15947	1	2	yes	—
483	C₂³	#23895	1	2	yes	—
484	C₂³	#23896	1	2	yes	—
485	C₂³	C₂×#2403	1	2	yes	—
486	C₂³	C₂×#2403	1	1	yes	characteristic
487	C₂³	C₂×#2403	1	2	yes	—
488	C₂³	C₂×#2403	1	2	yes	—
489	C₂³	C₂×#2403	1	2	yes	—
490	C₂³	C₂×#2403	1	1	yes	characteristic
491	C₂³	C₂×#2403	1	4	yes	—
492	C₂³	C₂×#2403	1	1	yes	characteristic
493	C₂³	#34980	1	2	yes	—
494	C₂³	#34980	1	1	yes	characteristic
495	C₂³	#34980	1	2	yes	—
496	C₂³	#34980	1	4	yes	—
497	C₂³	#35346	1	2	yes	—
498	C₂³	#35346	1	4	yes	—
499	C₂³	D₄×#120	1	4	yes	—
500	C₂³	D₄×#120	1	4	yes	—
501	C₂³	D₄×#120	1	4	yes	—
502	C₂³	D₄×#120	1	4	yes	—
503	C₂³	D₄×#120	1	4	yes	—
504	C₂³	D₄×#120	1	4	yes	—
505	C₂³	D₄×#120	1	4	yes	—
506	C₂³	D₄×#120	1	4	yes	—
507	C₂³	C₂×#2846	1	1	yes	characteristic
508	C₂³	#36714	1	2	yes	—
509	C₂³	#36714	1	4	yes	—
510	C₂³	#37644	1	4	yes	—
511	C₂³	#37644	1	4	yes	—
512	C₂³	#37644	1	4	yes	—
513	C₂³	#37644	1	4	yes	—
514	C₂³	#37644	1	4	yes	—
515	C₂³	#37644	1	4	yes	—
516	C₂³	#37644	1	4	yes	—
517	C₂³	#37644	1	8	yes	—
518	C₂³	#37644	1	4	yes	—
519	C₂³	#37644	1	8	yes	—
520	C₂³	#45439	1	8	yes	—
521	C₂³	C₂×#2679	1	2	yes	—
522	C₂³	C₂×#2679	1	2	yes	—
523	C₂³	C₂×#2679	1	2	yes	—
524	C₂³	#58990	1	8	yes	—
525	C₂³	#58990	1	8	yes	—
526	C₂³	#58990	1	8	yes	—
527	C₂²	#449469	1	4	yes	complemented
528	C₂²	C₂×#15947	1	1	yes	characteristic
529	C₂²	#612424	1	1	yes	characteristic
530	C₂²	#612424	1	2	yes	—
531	C₂²	#616960	1	1	yes	characteristic
532	C₂²	#616960	1	2	yes	—
533	C₂²	#647656	1	4	yes	—
534	C₂²	#647656	1	2	yes	—
535	C₂²	#647656	1	4	yes	—
536	C₂²	#647656	1	2	yes	—
537	C₂²	#845297	1	4	yes	—
538	C₂²	#845297	1	4	yes	—
539	C₂²	#845297	1	4	yes	—
540	C₂²	C₂×#23895	1	1	yes	characteristic
541	C₂²	C₂×#23896	1	1	yes	characteristic
542	C₂²	#6437629	1	2	yes	—
543	C₂	#72218795	1	1	yes	characteristic
544	C₂	#72233069	1	2	yes	—
545	C₂	C₂×#449469	1	1	yes	characteristic
546	C₂	#72240604	1	1	yes	characteristic
547	C₂	#72261220	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×#2403
commutator, Frattini, cosocle	C₂⁶	C₂⁵
LCS	G ▷ C₂⁶ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂⁷ ◁ G
LECS	G ▷ C₂⁶ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72261548	C₂	semidirect
2. #72261525	C₂	semidirect
3. #72261506	C₂	semidirect
4. #72261492	C₂	semidirect
5. #72261466	C₂	semidirect
6. #72261459	C₂	semidirect
7. #72261451	C₂	semidirect
8. #72261443	C₂	semidirect
9. #72261376	C₂	semidirect
10. C₂×#6437621	C₂	semidirect
11. C₂³×#3026	C₂	semidirect
12. #72240155	C₂	semidirect
13. #72240127	C₂	semidirect
14. C₂×#449469	C₂	semidirect
15. C₂×#6628892	C₂	semidirect
16. C₂⁴×H(5,𝔽₂)	C₂²	semidirect
17. C₂²×#3484	C₂²	semidirect
21. C₂²×#3026	C₂²	semidirect
22. C₂²×#3026	C₂²	semidirect
23. C₂²×#3026	C₂²	semidirect
24. C₂⁴×#99	C₂²	semidirect
25. C₂⁴×#99	C₂²	semidirect
26. C₂×#35347	C₂²	semidirect
27. C₂×#35347	C₂²	semidirect
32. C₂×#23444	C₂²	semidirect
33. C₂×#23444	C₂²	semidirect
34. C₂²×#1898	C₂²	semidirect
35. C₂²×#1898	C₂²	semidirect
36. C₂×#20960	C₂²	semidirect
37. C₂×#20609	C₂²	semidirect
38. C₂²×#1781	C₂²	semidirect
39. C₂²×#1781	C₂²	semidirect
40. C₂²×#1781	C₂²	semidirect
41. #5955331	C₂²	semidirect
42. #5955328	C₂²	semidirect
43. #517411	C₂²	semidirect
44. #516383	C₂²	semidirect
45. #516323	C₂²	semidirect
46. #515529	C₂²	semidirect
47. C₂×#14134	C₂²	semidirect
48. C₂×#13867	C₂²	semidirect
49. C₂×#13867	C₂²	semidirect
50. C₂×#10995	C₂²	semidirect
51. C₂×#10995	C₂²	semidirect
52. C₂×#10995	C₂²	semidirect
53. C₂×#10980	C₂²	semidirect
54. C₂×#10972	C₂²	semidirect
55. C₂×#10972	C₂²	semidirect
56. C₂×#10972	C₂²	semidirect
57. C₂×#10972	C₂²	semidirect
58. C₂×#10735	C₂²	semidirect
59. C₂×#10725	C₂²	semidirect
60. #153851	C₂²	semidirect
61. #123590	C₂²	semidirect
62. #123581	C₂²	semidirect
63. #123539	C₂²	semidirect
64. #123520	C₂²	semidirect
66. C₂³×H(5,𝔽₂)	C₂³	semidirect
70. C₂²×#534	D₄	semidirect
71. C₂²×#534	D₄	semidirect
72. C₂²×#534	D₄	semidirect
80. C₂²×#534	C₂³	semidirect
81. C₂²×#534	C₂³	semidirect
82. C₂³×#123	D₄	semidirect
84. C₂³×#120	D₄	semidirect
85. C₂³×#120	D₄	semidirect
88. C₂²×#518	C₂³	semidirect
92. C₂×#3026	D₄	semidirect
97. C₂³×#99	C₂³	semidirect
98. C₂³×#99	C₂³	semidirect
99. C₂³×#99	C₂³	semidirect
100. C₂³×#99	C₂³	semidirect
101. C₂×#2849	D₄	semidirect
102. C₂×#2846	D₄	semidirect
103. #34980	D₄	semidirect
104. C₂×#2405	D₄	semidirect
105. C₂×#2405	D₄	semidirect
106. C₂×#2403	D₄	semidirect
107. C₂×#2403	D₄	semidirect
108. C₂×#2613	D₄	semidirect
109. C₂²×#394	D₄	semidirect
110. C₂²×#392	D₄	semidirect
115. C₂×#2308	C₂³	semidirect
116. C₂²×#386	D₄	semidirect
119. C₂²×#386	C₂³	semidirect
120. C₂²×#386	C₂³	semidirect
121. C₂²×#386	C₂³	semidirect
122. C₂²×#385	D₄	semidirect
123. C₂²×#379	D₄	semidirect
127. C₂²×#342	C₂³	semidirect
128. C₂²×#342	C₂³	semidirect
129. C₂²×#342	C₂³	semidirect
130. C₂²×#342	C₂³	semidirect
131. #13794	C₂³	semidirect
132. C₂×C₂²⋊#95	C₂³	semidirect
133. C₂×C₂²⋊#95	C₂³	semidirect
138. C₂²×H(5,𝔽₂)	C₂×D₄	semidirect
154. C₂⁴×D₄	C₂×D₄	semidirect
169. C₂×#534	C₂×D₄	semidirect
172. C₂²×#123	C₂×D₄	semidirect
173. C₂²×#123	C₂×D₄	semidirect
179. C₂²×#120	C₂×D₄	semidirect
180. C₂²×#120	C₂×D₄	semidirect
181. C₂³×C₄⋊C₄	C₂×D₄	semidirect
192. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
193. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
194. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
195. C₂³×C₂²⋊C₄	C₂×D₄	semidirect
203. C₂²×#99	C₂×D₄	semidirect
204. C₂²×#99	C₂×D₄	semidirect
205. #2308	C₂×D₄	semidirect
206. C₂×#386	C₂×D₄	semidirect
207. C₂×#386	C₂×D₄	semidirect
208. C₂×#381	C₂×D₄	semidirect
214. C₂×#379	C₂×D₄	semidirect
215. C₂²×#95	C₂×D₄	semidirect
216. C₂²×#95	C₂×D₄	semidirect
219. C₂⁶	#120	semidirect
220. C₂⁶	#120	semidirect
247. C₂³×D₄	#120	semidirect
248. C₂³×D₄	#120	semidirect
249. C₂³×D₄	#120	semidirect
250. C₂³×D₄	#120	semidirect
251. C₂³×D₄	#120	semidirect
267. C₂⁴×C₄	#120	semidirect
268. C₂⁴×C₄	#120	semidirect
281. #534	#120	semidirect
282. C₂×#123	#120	semidirect
283. C₂×#120	#120	semidirect
287. C₂²×C₂²⋊C₄	#120	semidirect
288. C₂²×C₂²⋊C₄	#120	semidirect
418. C₂⁴	#2403	semidirect
431. C₂⁴	#2846	semidirect
475. C₂²×C₄	#2403	semidirect
476. C₂²×C₄	#2846	semidirect
527. C₂²	#449469	semidirect

Maximal subgroups

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

subgroup	index
#72261548	2
#72261525	2
#72261506	2
#72261492	2
#72261466	2
#72261459	2
#72261451	2
#72261443	2
#72261376	2
C₂×#6437621	2
C₂³×#3026	2
#72240155	2
#72240127	2
C₂×#449469	2
C₂×#6628892	2