Subgroups — C₂×C₆₁×#2965 #29563630

Order 15616.

2286 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#41×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2965	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#446	C₂	1	2	yes	maximal, complemented
4	C₂×C₆₁×#436	C₂	1	2	yes	maximal, complemented
5	C₂×C₆₁×#435	C₂	1	4	yes	maximal, complemented
6	C₂×C₆₁×#431	C₂	1	2	yes	maximal, complemented
7	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×M₁₆×C₆₁	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₁	C₄	1	1	yes	characteristic
11	C₂²×M₁₆×C₆₁	C₂²	1	4	yes	—
12	C₂³×C₈×C₆₁	C₂²	1	2	yes	—
13	C₄×#41×C₆₁	C₄	1	8	yes	—
14	C₄×#41×C₆₁	C₂²	1	8	yes	—
15	C₂×C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₆₁	C₄	1	2	yes	—
18	C₂×C₄×D₄×C₆₁	C₄	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	C₄	1	2	yes	—
22	C₂×#117×C₆₁	C₄	1	1	yes	characteristic
23	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#446	C₂²	1	16	yes	complemented
26	C₆₁×#436	C₂²	1	16	yes	complemented
27	C₆₁×#435	C₂²	1	32	yes	complemented
28	C₆₁×#431	C₂²	1	16	yes	complemented
29	C₆₁×#431	C₂²	1	8	yes	complemented
30	C₂×C₄⋊C₈×C₆₁	C₂²	1	4	yes	—
31	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
33	C₂×C₂²⋊C₈×C₆₁	C₂²	1	4	yes	—
34	C₄×M₁₆×C₆₁	C₂²	1	16	yes	complemented
35	C₂×#97×C₆₁	C₂²	1	4	yes	—
36	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₆₁	C₂²	1	8	yes	complemented
41	C₂×#41×C₆₁	—	2	8	no	—
42	C₂×#41×C₆₁	C₂×C₄	1	8	yes	—
43	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
45	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
48	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
52	C₂×M₁₆×C₆₁	—	2	16	no	—
53	C₂×M₁₆×C₆₁	C₂³	1	16	yes	—
54	C₂²×C₈×C₆₁	—	2	8	no	—
55	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
56	C₂²×C₈×C₆₁	C₂³	1	8	yes	—
57	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
59	C₄×Q₈×C₆₁	C₂×C₄	1	8	yes	—
60	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
62	C₄×D₄×C₆₁	C₂×C₄	1	16	yes	—
63	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
64	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
65	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
66	C₄×D₄×C₆₁	C₂³	1	8	yes	—
67	C₄×D₄×C₆₁	C₂³	1	4	yes	—
68	#117×C₆₁	C₂×C₄	1	16	yes	—
69	#117×C₆₁	C₂×C₄	1	8	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₆₁	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₆₁	C₂×C₄	1	8	yes	—
82	C₂×C₄²×C₆₁	C₂×C₄	1	4	yes	—
83	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
85	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
86	C₂×C₄²×C₆₁	C₂³	1	8	yes	—
87	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₆₁	C₂³	1	16	yes	—
89	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
90	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
91	C₂²⋊C₈×C₆₁	C₂³	1	16	yes	—
92	#97×C₆₁	C₂³	1	16	yes	—
93	C₄×C₈×C₆₁	C₂³	1	4	yes	—
94	C₄×C₈×C₆₁	C₂³	1	4	yes	—
95	C₄×C₈×C₆₁	C₂³	1	8	yes	—
96	C₄×C₈×C₆₁	C₂³	1	8	yes	—
97	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
98	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
99	#41×C₆₁	—	2	32	no	—
100	C₂×Q₈×C₆₁	—	2	4	no	—
101	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
102	C₂×D₄×C₆₁	—	2	8	no	—
103	C₂×D₄×C₆₁	—	2	4	no	—
104	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
105	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
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	4	no	—
110	C₂²×C₄×C₆₁	—	2	8	no	—
111	C₂²×C₄×C₆₁	M₁₆	1	8	yes	complemented
112	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
115	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
120	C₂²×C₄×C₆₁	C₂²×C₄	1	8	yes	—
121	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
129	M₁₆×C₆₁	—	2	32	no	—
130	C₂×C₈×C₆₁	—	2	4	no	—
131	C₂×C₈×C₆₁	—	2	8	no	—
132	C₂×C₈×C₆₁	—	2	16	no	—
133	C₂×C₈×C₆₁	#41	1	8	yes	complemented
134	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
135	C₂×C₈×C₆₁	C₂⁴	1	8	yes	—
136	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
137	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
138	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
139	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
140	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
141	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
142	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
143	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
144	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
145	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
146	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
147	C₄²×C₆₁	C₂²×C₄	1	8	yes	—
148	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
149	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
150	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
151	C₄²×C₆₁	C₂⁴	1	2	yes	—
152	C₄²×C₆₁	C₂⁴	1	2	yes	—
153	C₄²×C₆₁	C₂⁴	1	4	yes	—
154	C₂³×C₆₁	—	2	2	no	—
155	C₂³×C₆₁	—	2	2	no	—
156	C₂³×C₆₁	—	2	4	no	—
157	C₂³×C₆₁	—	2	4	no	—
158	C₂³×C₆₁	—	2	4	no	—
159	C₂³×C₆₁	C₂×M₁₆	1	4	yes	—
160	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
161	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
162	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
163	Q₈×C₆₁	—	2	8	no	—
164	D₄×C₆₁	—	2	16	no	—
165	D₄×C₆₁	—	2	8	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	4	no	—
168	C₂×C₄×C₆₁	—	2	4	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	4	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	8	no	—
173	C₂×C₄×C₆₁	—	2	16	no	—
174	C₂×C₄×C₆₁	—	2	8	no	—
175	C₂×C₄×C₆₁	—	2	16	no	—
176	C₂×C₄×C₆₁	—	2	4	no	—
177	C₂×C₄×C₆₁	—	2	8	no	—
178	C₂×C₄×C₆₁	C₂×M₁₆	1	4	yes	—
179	C₂×C₄×C₆₁	C₂×M₁₆	1	4	yes	—
180	C₂×C₄×C₆₁	C₂×M₁₆	1	16	yes	complemented
181	C₂×C₄×C₆₁	#131	1	4	yes	—
182	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
183	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
184	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
185	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
186	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
187	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
188	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
189	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
190	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
191	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
192	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
193	C₈×C₆₁	—	2	4	no	—
194	C₈×C₆₁	—	2	8	no	—
195	C₈×C₆₁	C₂×#41	1	8	yes	complemented
196	C₂×#2965	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₆₁	—	2	2	no	—
198	C₂²×C₆₁	—	2	8	no	—
199	C₂²×C₆₁	—	2	2	no	—
200	C₂²×C₆₁	—	2	4	no	—
201	C₂²×C₆₁	—	2	4	no	—
202	C₂²×C₆₁	—	2	4	no	—
203	C₂²×C₆₁	—	4	8	no	—
204	C₂²×C₆₁	C₄×#41	1	2	yes	—
205	C₂²×C₆₁	C₂²×M₁₆	1	4	yes	—
206	C₂²×C₆₁	C₂²×M₁₆	1	2	yes	—
207	C₂²×C₆₁	C₂×#131	1	2	yes	—
208	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
209	C₄×C₆₁	—	2	2	no	—
210	C₄×C₆₁	—	2	4	no	—
211	C₄×C₆₁	—	2	4	no	—
212	C₄×C₆₁	—	2	2	no	—
213	C₄×C₆₁	—	2	4	no	—
214	C₄×C₆₁	C₄×#41	1	2	yes	—
215	C₄×C₆₁	C₂²×M₁₆	1	4	yes	—
216	C₄×C₆₁	C₂²×M₁₆	1	4	yes	—
217	C₄×C₆₁	C₂×#131	1	4	yes	—
218	C₄×C₆₁	C₂²×#41	1	2	yes	—
219	C₂×C₄×#41	C₂×C₆₁	1	1	yes	characteristic
220	#2965	C₂×C₆₁	1	16	yes	direct product factor
221	C₂×#446	C₂×C₆₁	1	2	yes	complemented
222	C₂×#436	C₂×C₆₁	1	2	yes	complemented
223	C₂×#435	C₂×C₆₁	1	4	yes	complemented
224	C₂×#431	C₂×C₆₁	1	2	yes	complemented
225	C₂×#431	C₂×C₆₁	1	1	yes	characteristic, complemented
226	C₂×C₄×M₁₆	C₂×C₆₁	1	2	yes	complemented
227	C₂²×C₄×C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
228	C₂×C₆₁	—	2	4	no	—
229	C₂×C₆₁	—	4	4	no	—
230	C₂×C₆₁	#2965	1	4	yes	direct product factor
231	C₂×C₆₁	C₂×C₄×#41	1	1	yes	characteristic
232	C₂×C₆₁	C₂³×M₁₆	1	1	yes	characteristic
233	C₂×C₆₁	C₂²×#131	1	1	yes	characteristic
234	C₂²×#41	C₄×C₆₁	1	1	yes	characteristic
235	C₂²×M₁₆	C₂²×C₆₁	1	4	yes	—
236	C₂³×C₈	C₂²×C₆₁	1	2	yes	—
237	C₄×#41	C₄×C₆₁	1	8	yes	—
238	C₄×#41	C₂²×C₆₁	1	8	yes	—
239	C₂×C₄×Q₈	C₄×C₆₁	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
241	C₂×C₄×D₄	C₄×C₆₁	1	2	yes	—
242	C₂×C₄×D₄	C₄×C₆₁	1	1	yes	characteristic
243	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
245	C₂×#117	C₄×C₆₁	1	2	yes	—
246	C₂×#117	C₄×C₆₁	1	1	yes	characteristic
247	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
248	C₂²×C₄²	C₂²×C₆₁	1	2	yes	—
249	#446	C₂²×C₆₁	1	16	yes	complemented
250	#436	C₂²×C₆₁	1	16	yes	complemented
251	#435	C₂²×C₆₁	1	32	yes	complemented
252	#431	C₂²×C₆₁	1	16	yes	complemented
253	#431	C₂²×C₆₁	1	8	yes	complemented
254	C₂×C₄⋊C₈	C₂²×C₆₁	1	4	yes	—
255	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
256	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₆₁	1	4	yes	—
258	C₄×M₁₆	C₂²×C₆₁	1	16	yes	complemented
259	C₂×#97	C₂²×C₆₁	1	4	yes	—
260	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
261	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
262	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
263	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
264	C₂×C₄×C₈	C₂²×C₆₁	1	8	yes	complemented
265	C₆₁	C₂×#2965	1	1	yes	characteristic, direct product factor, Sylow
266	C₂×#41	—	2	8	no	—
267	C₂×#41	C₂×C₄×C₆₁	1	8	yes	—
268	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
269	C₂²×D₄	C₂×C₄×C₆₁	1	2	yes	—
270	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
271	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
272	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
273	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
274	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
275	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
277	C₂×M₁₆	—	2	16	no	—
278	C₂×M₁₆	C₂³×C₆₁	1	16	yes	—
279	C₂²×C₈	—	2	8	no	—
280	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
281	C₂²×C₈	C₂³×C₆₁	1	8	yes	—
282	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
283	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
284	C₄×Q₈	C₂×C₄×C₆₁	1	8	yes	—
285	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
286	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
287	C₄×D₄	C₂×C₄×C₆₁	1	16	yes	—
288	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
289	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
290	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
291	C₄×D₄	C₂³×C₆₁	1	8	yes	—
292	C₄×D₄	C₂³×C₆₁	1	4	yes	—
293	#117	C₂×C₄×C₆₁	1	16	yes	—
294	#117	C₂×C₄×C₆₁	1	8	yes	—
295	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
296	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
298	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
300	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
301	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
302	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
303	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
304	C₂×C₄²	C₂×C₄×C₆₁	1	2	yes	—
305	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
306	C₂×C₄²	C₂×C₄×C₆₁	1	8	yes	—
307	C₂×C₄²	C₂×C₄×C₆₁	1	4	yes	—
308	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
309	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
310	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
311	C₂×C₄²	C₂³×C₆₁	1	8	yes	—
312	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₆₁	1	16	yes	—
314	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
315	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
316	C₂²⋊C₈	C₂³×C₆₁	1	16	yes	—
317	#97	C₂³×C₆₁	1	16	yes	—
318	C₄×C₈	C₂³×C₆₁	1	4	yes	—
319	C₄×C₈	C₂³×C₆₁	1	4	yes	—
320	C₄×C₈	C₂³×C₆₁	1	8	yes	—
321	C₄×C₈	C₂³×C₆₁	1	8	yes	—
322	C₂⁴	C₂²×C₄×C₆₁	1	2	yes	—
323	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
324	#41	—	2	32	no	—
325	C₂×Q₈	—	2	4	no	—
326	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
330	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	M₁₆×C₆₁	1	8	yes	complemented
337	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
338	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
339	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
340	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
341	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
342	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
343	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
344	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
345	C₂²×C₄	C₂²×C₄×C₆₁	1	8	yes	—
346	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
347	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
349	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
350	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
352	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
353	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
354	M₁₆	—	2	32	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	2	8	no	—
357	C₂×C₈	—	2	16	no	—
358	C₂×C₈	#41×C₆₁	1	8	yes	complemented
359	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
360	C₂×C₈	C₂⁴×C₆₁	1	8	yes	—
361	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
362	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
363	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
364	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
365	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
366	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
367	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
368	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
369	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
370	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
371	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
372	C₄²	C₂²×C₄×C₆₁	1	8	yes	—
373	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
374	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
375	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
376	C₄²	C₂⁴×C₆₁	1	2	yes	—
377	C₄²	C₂⁴×C₆₁	1	2	yes	—
378	C₄²	C₂⁴×C₆₁	1	4	yes	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	2	4	no	—
384	C₂³	C₂×M₁₆×C₆₁	1	4	yes	—
385	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
386	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
387	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
388	Q₈	—	2	8	no	—
389	D₄	—	2	16	no	—
390	D₄	—	2	8	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	16	no	—
397	C₂×C₄	—	2	8	no	—
398	C₂×C₄	—	2	16	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	8	no	—
403	C₂×C₄	C₂×M₁₆×C₆₁	1	4	yes	—
404	C₂×C₄	C₂×M₁₆×C₆₁	1	4	yes	—
405	C₂×C₄	C₂×M₁₆×C₆₁	1	16	yes	complemented
406	C₂×C₄	#131×C₆₁	1	4	yes	—
407	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
408	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
409	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
410	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
411	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
412	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
413	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
414	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
415	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
416	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
417	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	2	8	no	—
420	C₈	C₂×#41×C₆₁	1	8	yes	complemented
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	4	8	no	—
428	C₂²	C₄×#41×C₆₁	1	2	yes	—
429	C₂²	C₂²×M₁₆×C₆₁	1	4	yes	—
430	C₂²	C₂²×M₁₆×C₆₁	1	2	yes	—
431	C₂²	C₂×#131×C₆₁	1	2	yes	—
432	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	4	no	—
438	C₄	C₄×#41×C₆₁	1	2	yes	—
439	C₄	C₂²×M₁₆×C₆₁	1	4	yes	—
440	C₄	C₂²×M₁₆×C₆₁	1	4	yes	—
441	C₄	C₂×#131×C₆₁	1	4	yes	—
442	C₄	C₂²×#41×C₆₁	1	2	yes	—
443	C₂	—	2	4	no	—
444	C₂	—	4	4	no	—
445	C₂	C₆₁×#2965	1	4	yes	direct product factor
446	C₂	C₂×C₄×#41×C₆₁	1	1	yes	characteristic
447	C₂	C₂³×M₁₆×C₆₁	1	1	yes	characteristic
448	C₂	C₂²×#131×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²×C₆₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂³×C₄
prime radical	C₂²×#41×C₆₁	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2965	C₂	direct (N × H)
3. C₂×C₆₁×#446	C₂	semidirect
4. C₂×C₆₁×#436	C₂	semidirect
5. C₂×C₆₁×#435	C₂	semidirect
6. C₂×C₆₁×#431	C₂	semidirect
7. C₂×C₆₁×#431	C₂	semidirect
8. C₂×C₄×M₁₆×C₆₁	C₂	semidirect
9. C₂²×C₄×C₈×C₆₁	C₂	semidirect
25. C₆₁×#446	C₂²	semidirect
26. C₆₁×#436	C₂²	semidirect
27. C₆₁×#435	C₂²	semidirect
28. C₆₁×#431	C₂²	semidirect
29. C₆₁×#431	C₂²	semidirect
34. C₄×M₁₆×C₆₁	C₂²	semidirect
40. C₂×C₄×C₈×C₆₁	C₂²	semidirect
111. C₂²×C₄×C₆₁	M₁₆	semidirect
133. C₂×C₈×C₆₁	#41	semidirect
180. C₂×C₄×C₆₁	C₂×M₁₆	semidirect
195. C₈×C₆₁	C₂×#41	semidirect
196. C₂×#2965	C₆₁	direct (N × H)
220. #2965	C₂×C₆₁	direct (N × H)
221. C₂×#446	C₂×C₆₁	semidirect
222. C₂×#436	C₂×C₆₁	semidirect
223. C₂×#435	C₂×C₆₁	semidirect
224. C₂×#431	C₂×C₆₁	semidirect
225. C₂×#431	C₂×C₆₁	semidirect
226. C₂×C₄×M₁₆	C₂×C₆₁	semidirect
227. C₂²×C₄×C₈	C₂×C₆₁	semidirect
230. C₂×C₆₁	#2965	direct (N × H)
249. #446	C₂²×C₆₁	semidirect
250. #436	C₂²×C₆₁	semidirect
251. #435	C₂²×C₆₁	semidirect
252. #431	C₂²×C₆₁	semidirect
253. #431	C₂²×C₆₁	semidirect
258. C₄×M₁₆	C₂²×C₆₁	semidirect
264. C₂×C₄×C₈	C₂²×C₆₁	semidirect
265. C₆₁	C₂×#2965	direct (N × H)
336. C₂²×C₄	M₁₆×C₆₁	semidirect
358. C₂×C₈	#41×C₆₁	semidirect
405. C₂×C₄	C₂×M₁₆×C₆₁	semidirect
420. C₈	C₂×#41×C₆₁	semidirect
445. C₂	C₆₁×#2965	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#41×C₆₁	2
C₆₁×#2965	2
C₂×C₆₁×#446	2
C₂×C₆₁×#436	2
C₂×C₆₁×#435	2
C₂×C₆₁×#431	2
C₂×C₄×M₁₆×C₆₁	2
C₂²×C₄×C₈×C₆₁	2
C₂×#2965	61

Subgroups — C2×C61×#2965 #29563630

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#2965 #29563630