Subgroups — C₂×C₆₁×#2623 #29538012

Order 15616.

3002 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#123×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2623	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₆₁×#400	C₂	1	2	yes	maximal, complemented
5	C₂×C₆₁×#399	C₂	1	2	yes	maximal, complemented
6	C₂×C₆₁×#398	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#397	C₂	1	2	yes	maximal, complemented
8	C₂×C₆₁×#386	C₂	1	2	yes	maximal
9	C₂×C₆₁×#385	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#381	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₆₁	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₆₁	C₂²	1	2	yes	—
14	C₂×#123×C₆₁	—	2	8	no	—
15	C₂×#123×C₆₁	C₂²	1	8	yes	—
16	C₂²×C₄⋊C₄×C₆₁	—	2	8	no	—
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
20	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	8	yes	complemented
23	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
27	C₂²×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
28	C₆₁×#400	C₂²	1	16	yes	complemented
29	C₆₁×#399	C₂²	1	16	yes	complemented
30	C₆₁×#398	C₂²	1	16	yes	complemented
31	C₆₁×#397	C₂²	1	16	yes	complemented
32	C₆₁×#386	C₂²	1	16	yes	—
33	C₆₁×#385	C₂²	1	16	yes	complemented
34	C₆₁×#381	C₂²	1	8	yes	complemented
35	C₂×#95×C₆₁	C₂²	1	2	yes	—
36	C₂×#95×C₆₁	C₂²	1	2	yes	—
37	C₂×#95×C₆₁	C₂²	1	4	yes	—
38	C₂×#95×C₆₁	C₂²	1	4	yes	—
39	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
40	C₂⁵×C₆₁	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₆₁	—	2	4	no	—
42	C₂²×D₄×C₆₁	—	2	8	no	—
43	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
44	C₂³×C₄×C₆₁	—	2	8	no	—
45	C₂³×C₄×C₆₁	—	2	8	no	—
46	C₂³×C₄×C₆₁	—	4	8	no	—
47	C₂³×C₄×C₆₁	D₄	1	8	yes	—
48	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
49	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
52	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
54	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₆₁	C₂³	1	8	yes	—
57	#123×C₆₁	—	2	32	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	32	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₆₁	—	4	8	no	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	16	yes	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	8	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	4	8	no	—
74	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₆₁	C₂³	1	16	yes	—
79	#95×C₆₁	C₂³	1	8	yes	—
80	#95×C₆₁	C₂³	1	8	yes	—
81	#95×C₆₁	C₂³	1	16	yes	—
82	#95×C₆₁	C₂³	1	16	yes	—
83	C₂⁴×C₆₁	—	2	4	no	—
84	C₂⁴×C₆₁	—	2	4	no	—
85	C₂⁴×C₆₁	—	2	2	no	—
86	C₂⁴×C₆₁	—	2	4	no	—
87	C₂⁴×C₆₁	—	2	4	no	—
88	C₂⁴×C₆₁	—	2	4	no	—
89	C₂⁴×C₆₁	C₂×D₄	1	4	yes	—
90	C₂⁴×C₆₁	#41	1	8	yes	—
91	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
92	C₂⁴×C₆₁	C₂⁴	1	2	yes	—
93	C₂⁴×C₆₁	C₂⁴	1	1	yes	characteristic
94	C₂×D₄×C₆₁	—	2	8	no	—
95	C₂×D₄×C₆₁	—	2	16	no	—
96	C₂×D₄×C₆₁	—	4	16	no	—
97	C₂²×C₄×C₆₁	—	2	32	no	—
98	C₂²×C₄×C₆₁	—	2	16	no	—
99	C₂²×C₄×C₆₁	—	2	4	no	—
100	C₂²×C₄×C₆₁	—	2	4	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	16	no	—
104	C₂²×C₄×C₆₁	—	2	8	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	2	8	no	—
107	C₂²×C₄×C₆₁	—	2	4	no	—
108	C₂²×C₄×C₆₁	—	2	8	no	—
109	C₂²×C₄×C₆₁	—	2	8	no	—
110	C₂²×C₄×C₆₁	—	2	4	no	—
111	C₂²×C₄×C₆₁	—	2	8	no	—
112	C₂²×C₄×C₆₁	—	2	4	no	—
113	C₂²×C₄×C₆₁	—	2	8	no	—
114	C₂²×C₄×C₆₁	—	4	16	no	—
115	C₂²×C₄×C₆₁	—	4	32	no	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₆₁	C₂×D₄	1	16	yes	—
119	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
120	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
121	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
122	C₂²×C₄×C₆₁	C₂⁴	1	8	yes	—
123	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
124	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
126	C₄⋊C₄×C₆₁	—	2	16	no	—
127	C₄⋊C₄×C₆₁	—	2	16	no	—
128	C₄⋊C₄×C₆₁	—	2	8	no	—
129	C₄⋊C₄×C₆₁	—	2	8	no	—
130	C₄⋊C₄×C₆₁	—	4	16	no	—
131	C₂²⋊C₄×C₆₁	—	2	8	no	—
132	C₂²⋊C₄×C₆₁	—	2	16	no	—
133	C₂²⋊C₄×C₆₁	—	2	8	no	—
134	C₂²⋊C₄×C₆₁	—	2	8	no	—
135	C₂²⋊C₄×C₆₁	—	4	16	no	—
136	C₂³×C₆₁	—	2	8	no	—
137	C₂³×C₆₁	—	2	8	no	—
138	C₂³×C₆₁	—	2	32	no	—
139	C₂³×C₆₁	—	2	4	no	—
140	C₂³×C₆₁	—	2	4	no	—
141	C₂³×C₆₁	—	2	2	no	—
142	C₂³×C₆₁	—	2	4	no	—
143	C₂³×C₆₁	—	2	4	no	—
144	C₂³×C₆₁	—	2	4	no	—
145	C₂³×C₆₁	—	4	4	no	—
146	C₂³×C₆₁	—	4	4	no	—
147	C₂³×C₆₁	—	4	4	no	—
148	C₂³×C₆₁	—	4	16	no	—
149	C₂³×C₆₁	#123	1	16	yes	—
150	C₂³×C₆₁	C₂²×D₄	1	4	yes	—
151	C₂³×C₆₁	C₂²×D₄	1	2	yes	—
152	C₂³×C₆₁	C₂×#41	1	8	yes	—
153	C₂³×C₆₁	C₂×#41	1	4	yes	—
154	C₂³×C₆₁	H(5,𝔽₂)	1	4	yes	—
155	C₂³×C₆₁	2₋¹⁺⁴	1	4	yes	—
156	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
157	D₄×C₆₁	—	4	16	no	—
158	C₂×C₄×C₆₁	—	2	32	no	—
159	C₂×C₄×C₆₁	—	2	8	no	—
160	C₂×C₄×C₆₁	—	2	8	no	—
161	C₂×C₄×C₆₁	—	2	4	no	—
162	C₂×C₄×C₆₁	—	2	4	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	8	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	8	no	—
168	C₂×C₄×C₆₁	—	2	4	no	—
169	C₂×C₄×C₆₁	—	2	8	no	—
170	C₂×C₄×C₆₁	—	2	8	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	8	no	—
173	C₂×C₄×C₆₁	—	2	4	no	—
174	C₂×C₄×C₆₁	—	2	8	no	—
175	C₂×C₄×C₆₁	—	4	32	no	—
176	C₂×C₄×C₆₁	—	4	4	no	—
177	C₂×C₄×C₆₁	—	4	4	no	—
178	C₂×C₄×C₆₁	—	4	16	no	—
179	C₂×C₄×C₆₁	—	4	4	no	—
180	C₂×C₄×C₆₁	—	4	16	no	—
181	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
182	C₂×C₄×C₆₁	C₂²×D₄	1	4	yes	—
183	C₂×#2623	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₆₁	—	2	32	no	—
185	C₂²×C₆₁	—	2	4	no	—
186	C₂²×C₆₁	—	2	4	no	—
187	C₂²×C₆₁	—	2	16	no	—
188	C₂²×C₆₁	—	4	2	no	—
189	C₂²×C₆₁	—	4	2	no	—
190	C₂²×C₆₁	—	4	2	no	—
191	C₂²×C₆₁	—	4	8	no	—
192	C₂²×C₆₁	—	8	8	no	—
193	C₂²×C₆₁	C₂×#123	1	8	yes	—
194	C₂²×C₆₁	C₂×#123	1	4	yes	—
195	C₂²×C₆₁	#535	1	4	yes	—
196	C₂²×C₆₁	#536	1	4	yes	—
197	C₂²×C₆₁	#539	1	16	yes	—
198	C₂²×C₆₁	C₂³×D₄	1	1	yes	characteristic
199	C₂²×C₆₁	C₂²×#41	1	2	yes	—
200	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	2	yes	—
201	C₂²×C₆₁	C₂×2₋¹⁺⁴	1	2	yes	—
202	C₄×C₆₁	—	2	4	no	—
203	C₄×C₆₁	—	2	4	no	—
204	C₄×C₆₁	—	4	2	no	—
205	C₄×C₆₁	—	4	2	no	—
206	C₄×C₆₁	—	4	8	no	—
207	C₄×C₆₁	—	4	2	no	—
208	C₄×C₆₁	—	4	8	no	—
209	C₂²×#123	C₂×C₆₁	1	1	yes	characteristic
210	C₂³×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
211	#2623	C₂×C₆₁	1	16	yes	direct product factor
212	C₂×#400	C₂×C₆₁	1	2	yes	complemented
213	C₂×#399	C₂×C₆₁	1	2	yes	complemented
214	C₂×#398	C₂×C₆₁	1	2	yes	complemented
215	C₂×#397	C₂×C₆₁	1	2	yes	complemented
216	C₂×#386	C₂×C₆₁	1	2	yes	—
217	C₂×#385	C₂×C₆₁	1	2	yes	complemented
218	C₂×#381	C₂×C₆₁	1	1	yes	characteristic, complemented
219	C₂×C₆₁	—	2	8	no	—
220	C₂×C₆₁	—	8	2	no	—
221	C₂×C₆₁	#2623	1	8	yes	direct product factor
222	C₂×C₆₁	C₂²×#123	1	1	yes	characteristic
223	C₂×C₆₁	C₂×#535	1	1	yes	characteristic
224	C₂×C₆₁	C₂×#536	1	1	yes	characteristic
225	C₂×C₆₁	C₂×#539	1	4	yes	—
226	C₂³×D₄	C₂²×C₆₁	1	1	yes	characteristic
227	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
228	C₂⁴×C₄	C₂²×C₆₁	1	2	yes	—
229	C₂×#123	—	2	8	no	—
230	C₂×#123	C₂²×C₆₁	1	8	yes	—
231	C₂²×C₄⋊C₄	—	2	8	no	—
232	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
233	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
234	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
235	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
237	C₂²×C₄⋊C₄	C₂²×C₆₁	1	8	yes	complemented
238	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
239	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
240	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
241	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
243	#400	C₂²×C₆₁	1	16	yes	complemented
244	#399	C₂²×C₆₁	1	16	yes	complemented
245	#398	C₂²×C₆₁	1	16	yes	complemented
246	#397	C₂²×C₆₁	1	16	yes	complemented
247	#386	C₂²×C₆₁	1	16	yes	—
248	#385	C₂²×C₆₁	1	16	yes	complemented
249	#381	C₂²×C₆₁	1	8	yes	complemented
250	C₂×#95	C₂²×C₆₁	1	2	yes	—
251	C₂×#95	C₂²×C₆₁	1	4	yes	—
252	C₂×#95	C₂²×C₆₁	1	4	yes	—
253	C₂×#95	C₂²×C₆₁	1	2	yes	—
254	C₆₁	C₂×#2623	1	1	yes	characteristic, direct product factor, Sylow
255	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
256	C₂⁵	C₂³×C₆₁	1	1	yes	characteristic
257	C₂²×D₄	—	2	4	no	—
258	C₂²×D₄	—	2	8	no	—
259	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
260	C₂³×C₄	—	2	8	no	—
261	C₂³×C₄	—	2	8	no	—
262	C₂³×C₄	—	4	8	no	—
263	C₂³×C₄	D₄×C₆₁	1	8	yes	—
264	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
265	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
267	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
268	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
269	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
270	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
271	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
272	C₂³×C₄	C₂³×C₆₁	1	8	yes	—
273	#123	—	2	32	no	—
274	C₂×C₄⋊C₄	—	2	8	no	—
275	C₂×C₄⋊C₄	—	2	8	no	—
276	C₂×C₄⋊C₄	—	2	32	no	—
277	C₂×C₄⋊C₄	—	2	4	no	—
278	C₂×C₄⋊C₄	—	2	4	no	—
279	C₂×C₄⋊C₄	—	4	8	no	—
280	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
281	C₂×C₄⋊C₄	C₂³×C₆₁	1	8	yes	—
282	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
283	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
284	C₂×C₄⋊C₄	C₂³×C₆₁	1	16	yes	—
285	C₂×C₂²⋊C₄	—	2	4	no	—
286	C₂×C₂²⋊C₄	—	2	8	no	—
287	C₂×C₂²⋊C₄	—	2	4	no	—
288	C₂×C₂²⋊C₄	—	2	4	no	—
289	C₂×C₂²⋊C₄	—	4	8	no	—
290	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
291	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
292	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
293	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
294	C₂×C₂²⋊C₄	C₂³×C₆₁	1	16	yes	—
295	#95	C₂³×C₆₁	1	8	yes	—
296	#95	C₂³×C₆₁	1	8	yes	—
297	#95	C₂³×C₆₁	1	16	yes	—
298	#95	C₂³×C₆₁	1	16	yes	—
299	C₂⁴	—	2	4	no	—
300	C₂⁴	—	2	4	no	—
301	C₂⁴	—	2	2	no	—
302	C₂⁴	—	2	4	no	—
303	C₂⁴	—	2	4	no	—
304	C₂⁴	—	2	4	no	—
305	C₂⁴	C₂×D₄×C₆₁	1	4	yes	—
306	C₂⁴	#41×C₆₁	1	8	yes	—
307	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
308	C₂⁴	C₂⁴×C₆₁	1	2	yes	—
309	C₂⁴	C₂⁴×C₆₁	1	1	yes	characteristic
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	16	no	—
312	C₂×D₄	—	4	16	no	—
313	C₂²×C₄	—	2	32	no	—
314	C₂²×C₄	—	2	16	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	16	no	—
320	C₂²×C₄	—	2	8	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	8	no	—
325	C₂²×C₄	—	2	8	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	8	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	4	16	no	—
331	C₂²×C₄	—	4	32	no	—
332	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
333	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
334	C₂²×C₄	C₂×D₄×C₆₁	1	16	yes	—
335	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
336	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
337	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₆₁	1	8	yes	—
339	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
341	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
342	C₄⋊C₄	—	2	16	no	—
343	C₄⋊C₄	—	2	16	no	—
344	C₄⋊C₄	—	2	8	no	—
345	C₄⋊C₄	—	2	8	no	—
346	C₄⋊C₄	—	4	16	no	—
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	—	2	16	no	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	8	no	—
351	C₂²⋊C₄	—	4	16	no	—
352	C₂³	—	2	8	no	—
353	C₂³	—	2	8	no	—
354	C₂³	—	2	32	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	2	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	2	4	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	4	4	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	16	no	—
364	C₂³	—	4	4	no	—
365	C₂³	#123×C₆₁	1	16	yes	—
366	C₂³	C₂²×D₄×C₆₁	1	4	yes	—
367	C₂³	C₂²×D₄×C₆₁	1	2	yes	—
368	C₂³	C₂×#41×C₆₁	1	8	yes	—
369	C₂³	C₂×#41×C₆₁	1	4	yes	—
370	C₂³	H(5,𝔽₂)×C₆₁	1	4	yes	—
371	C₂³	2₋¹⁺⁴×C₆₁	1	4	yes	—
372	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
373	D₄	—	4	16	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	32	no	—
377	C₂×C₄	—	2	8	no	—
378	C₂×C₄	—	2	8	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	8	no	—
391	C₂×C₄	—	4	32	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	16	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	16	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
398	C₂×C₄	C₂²×D₄×C₆₁	1	4	yes	—
399	C₂²	—	2	32	no	—
400	C₂²	—	2	4	no	—
401	C₂²	—	2	4	no	—
402	C₂²	—	2	16	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	2	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	8	no	—
407	C₂²	—	8	8	no	—
408	C₂²	C₂×#123×C₆₁	1	8	yes	—
409	C₂²	C₂×#123×C₆₁	1	4	yes	—
410	C₂²	C₆₁×#535	1	4	yes	—
411	C₂²	C₆₁×#536	1	4	yes	—
412	C₂²	C₆₁×#539	1	16	yes	—
413	C₂²	C₂³×D₄×C₆₁	1	1	yes	characteristic
414	C₂²	C₂²×#41×C₆₁	1	2	yes	—
415	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	2	yes	—
416	C₂²	C₂×2₋¹⁺⁴×C₆₁	1	2	yes	—
417	C₄	—	2	4	no	—
418	C₄	—	2	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	8	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	8	no	—
424	C₂	—	2	8	no	—
425	C₂	—	8	2	no	—
426	C₂	C₆₁×#2623	1	8	yes	direct product factor
427	C₂	C₂²×#123×C₆₁	1	1	yes	characteristic
428	C₂	C₂×C₆₁×#535	1	1	yes	characteristic
429	C₂	C₂×C₆₁×#536	1	1	yes	characteristic
430	C₂	C₂×C₆₁×#539	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
prime radical	C₂³×D₄×C₆₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄⋊C₄×C₆₁	C₂	semidirect
3. C₆₁×#2623	C₂	direct (N × H)
4. C₂×C₆₁×#400	C₂	semidirect
5. C₂×C₆₁×#399	C₂	semidirect
6. C₂×C₆₁×#398	C₂	semidirect
7. C₂×C₆₁×#397	C₂	semidirect
9. C₂×C₆₁×#385	C₂	semidirect
10. C₂×C₆₁×#381	C₂	semidirect
22. C₂²×C₄⋊C₄×C₆₁	C₂²	semidirect
28. C₆₁×#400	C₂²	semidirect
29. C₆₁×#399	C₂²	semidirect
30. C₆₁×#398	C₂²	semidirect
31. C₆₁×#397	C₂²	semidirect
33. C₆₁×#385	C₂²	semidirect
34. C₆₁×#381	C₂²	semidirect
183. C₂×#2623	C₆₁	direct (N × H)
210. C₂³×C₄⋊C₄	C₂×C₆₁	semidirect
211. #2623	C₂×C₆₁	direct (N × H)
212. C₂×#400	C₂×C₆₁	semidirect
213. C₂×#399	C₂×C₆₁	semidirect
214. C₂×#398	C₂×C₆₁	semidirect
215. C₂×#397	C₂×C₆₁	semidirect
217. C₂×#385	C₂×C₆₁	semidirect
218. C₂×#381	C₂×C₆₁	semidirect
221. C₂×C₆₁	#2623	direct (N × H)
237. C₂²×C₄⋊C₄	C₂²×C₆₁	semidirect
243. #400	C₂²×C₆₁	semidirect
244. #399	C₂²×C₆₁	semidirect
245. #398	C₂²×C₆₁	semidirect
246. #397	C₂²×C₆₁	semidirect
248. #385	C₂²×C₆₁	semidirect
249. #381	C₂²×C₆₁	semidirect
254. C₆₁	C₂×#2623	direct (N × H)
426. C₂	C₆₁×#2623	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#123×C₆₁	2
C₂³×C₄⋊C₄×C₆₁	2
C₆₁×#2623	2
C₂×C₆₁×#400	2
C₂×C₆₁×#399	2
C₂×C₆₁×#398	2
C₂×C₆₁×#397	2
C₂×C₆₁×#386	2
C₂×C₆₁×#385	2
C₂×C₆₁×#381	2
C₂×#2623	61

Subgroups — C2×C61×#2623 #29538012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#2623 #29538012