Subgroups — C₂×C₆₁×#2966 #29563631

Order 15616.

2070 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2966	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₆₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₆₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₆₁×#435	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×D₄×C₆₁	C₂	1	2	yes	maximal, complemented
8	C₂×C₈×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₆₁×#433	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#432	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#405	C₂	1	2	yes	maximal, complemented
12	C₂²×C₄×C₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₆₁	C₂²	1	2	yes	—
17	C₆₁×#529	C₄	1	8	yes	—
18	C₆₁×#529	C₂²	1	8	yes	—
19	C₂×#126×C₆₁	C₄	1	2	yes	—
20	C₂×#125×C₆₁	C₄	1	1	yes	characteristic
21	C₂×#124×C₆₁	C₄	1	1	yes	characteristic
22	C₂×#123×C₆₁	C₄	1	2	yes	—
23	C₂×C₂²⋊Q₈×C₆₁	C₄	1	1	yes	characteristic
24	C₂×#121×C₆₁	C₄	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#117×C₆₁	C₂²	1	2	yes	—
29	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#446	C₂²	1	8	yes	complemented
31	C₈×Q₈×C₆₁	C₂²	1	8	yes	complemented
32	C₆₁×#436	C₂²	1	8	yes	complemented
33	C₆₁×#435	C₂²	1	16	yes	complemented
34	C₈×D₄×C₆₁	C₂²	1	8	yes	complemented
35	C₈×D₄×C₆₁	C₂²	1	16	yes	complemented
36	C₆₁×#433	C₂²	1	16	yes	complemented
37	C₆₁×#432	C₂²	1	8	yes	complemented
38	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
41	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
42	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
43	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
44	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
45	C₆₁×#405	C₂²	1	16	yes	complemented
46	C₂×#97×C₆₁	C₂²	1	2	yes	—
47	C₂×#97×C₆₁	C₂²	1	2	yes	—
48	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
53	C₂×C₄×C₈×C₆₁	C₂²	1	8	yes	complemented
54	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
55	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
56	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
58	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
61	C₂×M₁₆×C₆₁	—	2	8	no	—
62	C₂×M₁₆×C₆₁	C₂³	1	8	yes	—
63	C₂²×C₈×C₆₁	—	2	4	no	—
64	C₂²×C₈×C₆₁	—	2	8	no	—
65	C₂²×C₈×C₆₁	—	2	4	no	—
66	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
69	C₂²×C₈×C₆₁	C₂³	1	4	yes	—
70	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
71	C₂²×C₈×C₆₁	C₂³	1	8	yes	—
72	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
73	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
75	#126×C₆₁	C₂×C₄	1	16	yes	—
76	#125×C₆₁	C₂×C₄	1	8	yes	—
77	#124×C₆₁	C₂×C₄	1	8	yes	—
78	#123×C₆₁	C₂×C₄	1	16	yes	—
79	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	—
80	#121×C₆₁	C₂×C₄	1	8	yes	—
81	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
82	C₄×Q₈×C₆₁	C₂³	1	4	yes	—
83	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
84	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
85	C₄×D₄×C₆₁	C₂³	1	8	yes	—
86	C₄×D₄×C₆₁	C₂³	1	4	yes	—
87	#117×C₆₁	C₂×C₄	1	8	yes	—
88	#117×C₆₁	C₂³	1	8	yes	—
89	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
90	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
93	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
95	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
96	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
97	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
98	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
99	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
100	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄²×C₆₁	C₂×C₄	1	4	yes	—
103	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
106	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
107	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
108	C₄⋊C₈×C₆₁	C₂³	1	4	yes	—
109	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
110	C₄⋊C₈×C₆₁	C₂³	1	8	yes	—
111	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
112	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
113	C₂²⋊C₈×C₆₁	C₂³	1	8	yes	—
114	#97×C₆₁	C₂³	1	8	yes	—
115	#97×C₆₁	C₂³	1	8	yes	—
116	C₄×C₈×C₆₁	C₂³	1	4	yes	—
117	C₄×C₈×C₆₁	C₂³	1	4	yes	—
118	C₄×C₈×C₆₁	C₂³	1	4	yes	—
119	C₄×C₈×C₆₁	C₂³	1	4	yes	—
120	C₄×C₈×C₆₁	C₂³	1	8	yes	—
121	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
122	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
123	C₂×Q₈×C₆₁	—	2	4	no	—
124	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
125	C₂×D₄×C₆₁	—	2	8	no	—
126	C₂×D₄×C₆₁	—	2	4	no	—
127	C₂×D₄×C₆₁	C₂²×C₄	1	8	yes	—
128	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
129	C₂²×C₄×C₆₁	—	2	4	no	—
130	C₂²×C₄×C₆₁	—	2	4	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	4	no	—
134	C₂²×C₄×C₆₁	—	2	4	no	—
135	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
141	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
146	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
150	M₁₆×C₆₁	—	2	16	no	—
151	C₂×C₈×C₆₁	—	2	2	no	—
152	C₂×C₈×C₆₁	—	2	2	no	—
153	C₂×C₈×C₆₁	—	2	4	no	—
154	C₂×C₈×C₆₁	—	2	4	no	—
155	C₂×C₈×C₆₁	—	2	8	no	—
156	C₂×C₈×C₆₁	—	2	16	no	—
157	C₂×C₈×C₆₁	—	2	8	no	—
158	C₂×C₈×C₆₁	#41	1	4	yes	—
159	C₂×C₈×C₆₁	#41	1	4	yes	—
160	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
161	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
162	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
163	C₂×C₈×C₆₁	C₂⁴	1	4	yes	—
164	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
165	C₂×C₈×C₆₁	C₂⁴	1	2	yes	—
166	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
167	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
168	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
169	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
170	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
171	C₄⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
172	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
173	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
174	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
175	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
176	C₂²⋊C₄×C₆₁	C₂²×C₄	1	8	yes	—
177	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
178	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
179	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
180	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
181	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
182	C₄²×C₆₁	C₂⁴	1	2	yes	—
183	C₄²×C₆₁	C₂⁴	1	2	yes	—
184	C₄²×C₆₁	C₂⁴	1	4	yes	—
185	C₂³×C₆₁	—	2	2	no	—
186	C₂³×C₆₁	—	2	2	no	—
187	C₂³×C₆₁	—	2	4	no	—
188	C₂³×C₆₁	—	2	4	no	—
189	C₂³×C₆₁	—	2	4	no	—
190	C₂³×C₆₁	#131	1	4	yes	—
191	C₂³×C₆₁	C₂³×C₄	1	4	yes	—
192	C₂³×C₆₁	C₂³×C₄	1	2	yes	—
193	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
194	Q₈×C₆₁	—	2	8	no	—
195	D₄×C₆₁	—	2	16	no	—
196	D₄×C₆₁	—	2	8	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	4	no	—
199	C₂×C₄×C₆₁	—	2	8	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	4	no	—
205	C₂×C₄×C₆₁	—	2	4	no	—
206	C₂×C₄×C₆₁	—	2	8	no	—
207	C₂×C₄×C₆₁	—	2	8	no	—
208	C₂×C₄×C₆₁	—	2	2	no	—
209	C₂×C₄×C₆₁	—	2	2	no	—
210	C₂×C₄×C₆₁	—	2	4	no	—
211	C₂×C₄×C₆₁	—	2	4	no	—
212	C₂×C₄×C₆₁	#131	1	4	yes	—
213	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
214	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
215	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
216	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
217	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
218	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
219	C₂×C₄×C₆₁	C₂³×C₄	1	4	yes	—
220	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
221	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
222	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
223	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
224	C₂×C₄×C₆₁	C₂⁵	1	1	yes	characteristic
225	C₈×C₆₁	—	2	2	no	—
226	C₈×C₆₁	—	2	2	no	—
227	C₈×C₆₁	—	2	4	no	—
228	C₈×C₆₁	—	2	4	no	—
229	C₈×C₆₁	C₂×#41	1	4	yes	—
230	C₈×C₆₁	C₂×#41	1	4	yes	—
231	C₂×#2966	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₆₁	—	2	2	no	—
233	C₂²×C₆₁	—	2	8	no	—
234	C₂²×C₆₁	—	2	2	no	—
235	C₂²×C₆₁	—	2	4	no	—
236	C₂²×C₆₁	—	2	4	no	—
237	C₂²×C₆₁	—	2	4	no	—
238	C₂²×C₆₁	—	4	8	no	—
239	C₂²×C₆₁	C₄×#41	1	2	yes	—
240	C₂²×C₆₁	C₂×#131	1	4	yes	—
241	C₂²×C₆₁	C₂×#131	1	2	yes	—
242	C₂²×C₆₁	C₂×#131	1	2	yes	—
243	C₂²×C₆₁	C₂⁴×C₄	1	1	yes	characteristic
244	C₄×C₆₁	—	2	2	no	—
245	C₄×C₆₁	—	2	4	no	—
246	C₄×C₆₁	—	2	2	no	—
247	C₄×C₆₁	—	2	2	no	—
248	C₄×C₆₁	—	2	2	no	—
249	C₄×C₆₁	—	2	4	no	—
250	C₄×C₆₁	—	2	4	no	—
251	C₄×C₆₁	C₄×#41	1	2	yes	—
252	C₄×C₆₁	C₂×#131	1	4	yes	—
253	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
254	C₄×C₆₁	C₂²×#41	1	1	yes	characteristic
255	C₂×#529	C₂×C₆₁	1	1	yes	characteristic
256	#2966	C₂×C₆₁	1	16	yes	direct product factor
257	C₂×#446	C₂×C₆₁	1	1	yes	characteristic, complemented
258	C₂×C₈×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
259	C₂×#436	C₂×C₆₁	1	1	yes	characteristic, complemented
260	C₂×#435	C₂×C₆₁	1	2	yes	complemented
261	C₂×C₈×D₄	C₂×C₆₁	1	2	yes	complemented
262	C₂×C₈×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
263	C₂×#433	C₂×C₆₁	1	2	yes	complemented
264	C₂×#432	C₂×C₆₁	1	1	yes	characteristic, complemented
265	C₂×#405	C₂×C₆₁	1	2	yes	complemented
266	C₂²×C₄×C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
267	C₂×C₆₁	—	2	4	no	—
268	C₂×C₆₁	—	4	4	no	—
269	C₂×C₆₁	#2966	1	4	yes	direct product factor
270	C₂×C₆₁	C₂×C₄×#41	1	1	yes	characteristic
271	C₂×C₆₁	C₂²×#131	1	1	yes	characteristic
272	C₂×C₆₁	C₂²×#131	1	1	yes	characteristic
273	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
274	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
275	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
276	C₂³×C₈	C₂²×C₆₁	1	2	yes	—
277	#529	C₄×C₆₁	1	8	yes	—
278	#529	C₂²×C₆₁	1	8	yes	—
279	C₂×#126	C₄×C₆₁	1	2	yes	—
280	C₂×#125	C₄×C₆₁	1	1	yes	characteristic
281	C₂×#124	C₄×C₆₁	1	1	yes	characteristic
282	C₂×#123	C₄×C₆₁	1	2	yes	—
283	C₂×C₂²⋊Q₈	C₄×C₆₁	1	1	yes	characteristic
284	C₂×#121	C₄×C₆₁	1	1	yes	characteristic
285	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
287	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
288	C₂×#117	C₂²×C₆₁	1	2	yes	—
289	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
290	#446	C₂²×C₆₁	1	8	yes	complemented
291	C₈×Q₈	C₂²×C₆₁	1	8	yes	complemented
292	#436	C₂²×C₆₁	1	8	yes	complemented
293	#435	C₂²×C₆₁	1	16	yes	complemented
294	C₈×D₄	C₂²×C₆₁	1	8	yes	complemented
295	C₈×D₄	C₂²×C₆₁	1	16	yes	complemented
296	#433	C₂²×C₆₁	1	16	yes	complemented
297	#432	C₂²×C₆₁	1	8	yes	complemented
298	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
300	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
301	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
302	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
304	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
305	#405	C₂²×C₆₁	1	16	yes	complemented
306	C₂×#97	C₂²×C₆₁	1	2	yes	—
307	C₂×#97	C₂²×C₆₁	1	2	yes	—
308	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
313	C₂×C₄×C₈	C₂²×C₆₁	1	8	yes	complemented
314	C₆₁	C₂×#2966	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
316	C₂²×D₄	C₂×C₄×C₆₁	1	2	yes	—
317	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
318	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
319	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
321	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
322	C₂×M₁₆	—	2	8	no	—
323	C₂×M₁₆	C₂³×C₆₁	1	8	yes	—
324	C₂²×C₈	—	2	4	no	—
325	C₂²×C₈	—	2	8	no	—
326	C₂²×C₈	—	2	4	no	—
327	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
330	C₂²×C₈	C₂³×C₆₁	1	4	yes	—
331	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
332	C₂²×C₈	C₂³×C₆₁	1	8	yes	—
333	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
334	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
335	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
336	#126	C₂×C₄×C₆₁	1	16	yes	—
337	#125	C₂×C₄×C₆₁	1	8	yes	—
338	#124	C₂×C₄×C₆₁	1	8	yes	—
339	#123	C₂×C₄×C₆₁	1	16	yes	—
340	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	—
341	#121	C₂×C₄×C₆₁	1	8	yes	—
342	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
343	C₄×Q₈	C₂³×C₆₁	1	4	yes	—
344	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
345	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
346	C₄×D₄	C₂³×C₆₁	1	8	yes	—
347	C₄×D₄	C₂³×C₆₁	1	4	yes	—
348	#117	C₂×C₄×C₆₁	1	8	yes	—
349	#117	C₂³×C₆₁	1	8	yes	—
350	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
351	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
354	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
359	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
360	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
361	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
362	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
363	C₂×C₄²	C₂×C₄×C₆₁	1	4	yes	—
364	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
366	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
367	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
368	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
369	C₄⋊C₈	C₂³×C₆₁	1	4	yes	—
370	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
371	C₄⋊C₈	C₂³×C₆₁	1	8	yes	—
372	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
373	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
374	C₂²⋊C₈	C₂³×C₆₁	1	8	yes	—
375	#97	C₂³×C₆₁	1	8	yes	—
376	#97	C₂³×C₆₁	1	8	yes	—
377	C₄×C₈	C₂³×C₆₁	1	4	yes	—
378	C₄×C₈	C₂³×C₆₁	1	4	yes	—
379	C₄×C₈	C₂³×C₆₁	1	4	yes	—
380	C₄×C₈	C₂³×C₆₁	1	4	yes	—
381	C₄×C₈	C₂³×C₆₁	1	8	yes	—
382	C₂⁴	C₂²×C₄×C₆₁	1	2	yes	—
383	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
384	C₂×Q₈	—	2	4	no	—
385	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	C₂²×C₄×C₆₁	1	8	yes	—
389	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
397	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
398	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
399	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
400	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
401	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
402	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
403	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
404	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
405	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
406	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
407	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
411	M₁₆	—	2	16	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	—	2	16	no	—
418	C₂×C₈	—	2	8	no	—
419	C₂×C₈	#41×C₆₁	1	4	yes	—
420	C₂×C₈	#41×C₆₁	1	4	yes	—
421	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
422	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
423	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
424	C₂×C₈	C₂⁴×C₆₁	1	4	yes	—
425	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
426	C₂×C₈	C₂⁴×C₆₁	1	2	yes	—
427	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
428	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
429	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
430	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
431	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
432	C₄⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
433	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
434	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
435	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
436	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
437	C₂²⋊C₄	C₂²×C₄×C₆₁	1	8	yes	—
438	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
439	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
440	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
441	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
442	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
443	C₄²	C₂⁴×C₆₁	1	2	yes	—
444	C₄²	C₂⁴×C₆₁	1	2	yes	—
445	C₄²	C₂⁴×C₆₁	1	4	yes	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	4	no	—
449	C₂³	—	2	4	no	—
450	C₂³	—	2	4	no	—
451	C₂³	#131×C₆₁	1	4	yes	—
452	C₂³	C₂³×C₄×C₆₁	1	4	yes	—
453	C₂³	C₂³×C₄×C₆₁	1	2	yes	—
454	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
455	Q₈	—	2	8	no	—
456	D₄	—	2	16	no	—
457	D₄	—	2	8	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	2	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	8	no	—
473	C₂×C₄	#131×C₆₁	1	4	yes	—
474	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
475	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
476	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
477	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
478	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
479	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
480	C₂×C₄	C₂³×C₄×C₆₁	1	4	yes	—
481	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
482	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
484	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
485	C₂×C₄	C₂⁵×C₆₁	1	1	yes	characteristic
486	C₈	—	2	2	no	—
487	C₈	—	2	2	no	—
488	C₈	—	2	4	no	—
489	C₈	—	2	4	no	—
490	C₈	C₂×#41×C₆₁	1	4	yes	—
491	C₈	C₂×#41×C₆₁	1	4	yes	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	8	no	—
495	C₂²	—	2	4	no	—
496	C₂²	—	2	4	no	—
497	C₂²	—	2	4	no	—
498	C₂²	—	4	8	no	—
499	C₂²	C₄×#41×C₆₁	1	2	yes	—
500	C₂²	C₂×#131×C₆₁	1	4	yes	—
501	C₂²	C₂×#131×C₆₁	1	2	yes	—
502	C₂²	C₂×#131×C₆₁	1	2	yes	—
503	C₂²	C₂⁴×C₄×C₆₁	1	1	yes	characteristic
504	C₄	—	2	2	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	2	4	no	—
508	C₄	—	2	4	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	4	no	—
511	C₄	C₄×#41×C₆₁	1	2	yes	—
512	C₄	C₂×#131×C₆₁	1	4	yes	—
513	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
514	C₄	C₂²×#41×C₆₁	1	1	yes	characteristic
515	C₂	—	2	4	no	—
516	C₂	—	4	4	no	—
517	C₂	C₆₁×#2966	1	4	yes	direct product factor
518	C₂	C₂×C₄×#41×C₆₁	1	1	yes	characteristic
519	C₂	C₂²×#131×C₆₁	1	1	yes	characteristic
520	C₂	C₂²×#131×C₆₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₈×C₆₁	C₂³
commutator	C₂²	C₂⁴×C₄×C₆₁
Frattini, cosocle	C₂×C₄	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂³×C₄
prime radical	C₂×#121×C₆₁	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2966	C₂	direct (N × H)
3. C₂×C₆₁×#446	C₂	semidirect
4. C₂×C₈×Q₈×C₆₁	C₂	semidirect
5. C₂×C₆₁×#436	C₂	semidirect
6. C₂×C₆₁×#435	C₂	semidirect
7. C₂×C₈×D₄×C₆₁	C₂	semidirect
8. C₂×C₈×D₄×C₆₁	C₂	semidirect
9. C₂×C₆₁×#433	C₂	semidirect
10. C₂×C₆₁×#432	C₂	semidirect
11. C₂×C₆₁×#405	C₂	semidirect
12. C₂²×C₄×C₈×C₆₁	C₂	semidirect
30. C₆₁×#446	C₂²	semidirect
31. C₈×Q₈×C₆₁	C₂²	semidirect
32. C₆₁×#436	C₂²	semidirect
33. C₆₁×#435	C₂²	semidirect
34. C₈×D₄×C₆₁	C₂²	semidirect
35. C₈×D₄×C₆₁	C₂²	semidirect
36. C₆₁×#433	C₂²	semidirect
37. C₆₁×#432	C₂²	semidirect
45. C₆₁×#405	C₂²	semidirect
53. C₂×C₄×C₈×C₆₁	C₂²	semidirect
231. C₂×#2966	C₆₁	direct (N × H)
256. #2966	C₂×C₆₁	direct (N × H)
257. C₂×#446	C₂×C₆₁	semidirect
258. C₂×C₈×Q₈	C₂×C₆₁	semidirect
259. C₂×#436	C₂×C₆₁	semidirect
260. C₂×#435	C₂×C₆₁	semidirect
261. C₂×C₈×D₄	C₂×C₆₁	semidirect
262. C₂×C₈×D₄	C₂×C₆₁	semidirect
263. C₂×#433	C₂×C₆₁	semidirect
264. C₂×#432	C₂×C₆₁	semidirect
265. C₂×#405	C₂×C₆₁	semidirect
266. C₂²×C₄×C₈	C₂×C₆₁	semidirect
269. C₂×C₆₁	#2966	direct (N × H)
290. #446	C₂²×C₆₁	semidirect
291. C₈×Q₈	C₂²×C₆₁	semidirect
292. #436	C₂²×C₆₁	semidirect
293. #435	C₂²×C₆₁	semidirect
294. C₈×D₄	C₂²×C₆₁	semidirect
295. C₈×D₄	C₂²×C₆₁	semidirect
296. #433	C₂²×C₆₁	semidirect
297. #432	C₂²×C₆₁	semidirect
305. #405	C₂²×C₆₁	semidirect
313. C₂×C₄×C₈	C₂²×C₆₁	semidirect
314. C₆₁	C₂×#2966	direct (N × H)
517. C₂	C₆₁×#2966	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×C₆₁×#529	2
C₆₁×#2966	2
C₂×C₆₁×#446	2
C₂×C₈×Q₈×C₆₁	2
C₂×C₆₁×#436	2
C₂×C₆₁×#435	2
C₂×C₈×D₄×C₆₁	2
C₂×C₆₁×#433	2
C₂×C₆₁×#432	2
C₂×C₆₁×#405	2
C₂²×C₄×C₈×C₆₁	2
C₂×#2966	61

Subgroups — C2×C61×#2966 #29563631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₁×#2966 #29563631