Subgroups — C₆₁×#20703 #29524136

Order 15616.

1374 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#520	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#408	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2311	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1825	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1825	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1824	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1823	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1735	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#340	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#520	—	2	4	no	—
16	C₆₁×#520	C₄	1	8	yes	complemented
17	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
18	C₂×C₄×D₄×C₆₁	—	2	2	no	—
19	C₂×C₄×D₄×C₆₁	—	2	1	no	—
20	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₆₁	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
25	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
26	C₆₁×#408	—	2	4	no	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
29	C₆₁×#391	—	2	1	no	—
30	C₆₁×#390	—	2	1	no	—
31	C₆₁×#386	—	2	2	no	—
32	C₆₁×#380	C₂²	1	2	yes	—
33	C₆₁×#380	C₂²	1	2	yes	—
34	C₆₁×#340	C₂²	1	1	yes	characteristic
35	C₆₁×#340	C₂²	1	2	yes	—
36	C₆₁×#340	C₂²	1	2	yes	—
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	1	yes	characteristic
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	1	yes	characteristic
42	C₆₁×#340	C₂²	1	1	yes	characteristic
43	C₆₁×#340	C₂²	1	2	yes	—
44	C₂×#41×C₆₁	—	2	2	no	—
45	C₂×#41×C₆₁	—	2	2	no	—
46	C₂×#41×C₆₁	—	2	2	no	—
47	C₂×#41×C₆₁	—	2	2	no	—
48	C₂×#41×C₆₁	C₂×C₄	1	4	yes	—
49	C₂×#41×C₆₁	D₄	1	4	yes	—
50	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₆₁	D₄	1	2	yes	—
52	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₆₁	—	2	1	no	—
54	C₂³×C₄×C₆₁	—	2	2	no	—
55	C₂³×C₄×C₆₁	—	2	1	no	—
56	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
57	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₆₁	—	2	2	no	—
59	C₂×M₁₆×C₆₁	—	2	2	no	—
60	C₂×M₁₆×C₆₁	—	2	2	no	—
61	C₂²×C₈×C₆₁	—	2	2	no	—
62	C₂²×C₈×C₆₁	—	2	2	no	—
63	C₂²×C₈×C₆₁	—	2	2	no	—
64	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
67	C₄×Q₈×C₆₁	—	2	8	no	—
68	C₄×D₄×C₆₁	—	2	8	no	—
69	C₄×D₄×C₆₁	—	2	16	no	—
70	#117×C₆₁	—	2	2	no	—
71	#117×C₆₁	—	2	4	no	—
72	#117×C₆₁	—	2	2	no	—
73	#117×C₆₁	—	2	2	no	—
74	#117×C₆₁	C₂×C₄	1	4	yes	—
75	#117×C₆₁	C₂×C₄	1	8	yes	complemented
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
84	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	8	yes	complemented
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
96	C₂×C₄²×C₆₁	—	2	1	no	—
97	C₂×C₄²×C₆₁	—	2	2	no	—
98	C₂×C₄²×C₆₁	—	2	1	no	—
99	C₂²⋊C₈×C₆₁	—	2	4	no	—
100	C₂²⋊C₈×C₆₁	—	2	4	no	—
101	#95×C₆₁	—	2	2	no	—
102	#95×C₆₁	—	2	2	no	—
103	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
104	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
105	#41×C₆₁	—	2	8	no	—
106	#41×C₆₁	—	2	8	no	—
107	#41×C₆₁	—	2	8	no	—
108	#41×C₆₁	—	2	8	no	—
109	C₂×Q₈×C₆₁	—	2	2	no	—
110	C₂×Q₈×C₆₁	—	2	2	no	—
111	C₂×Q₈×C₆₁	C₂²⋊C₄	1	4	yes	—
112	C₂×D₄×C₆₁	—	2	4	no	—
113	C₂×D₄×C₆₁	—	2	4	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	2	2	no	—
116	C₂×D₄×C₆₁	C₂²⋊C₄	1	8	yes	—
117	C₂×D₄×C₆₁	C₂²⋊C₄	1	4	yes	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	1	no	—
123	C₂²×C₄×C₆₁	—	2	1	no	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	2	4	no	—
126	C₂²×C₄×C₆₁	—	2	8	no	—
127	C₂²×C₄×C₆₁	—	2	1	no	—
128	C₂²×C₄×C₆₁	—	2	1	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	4	2	no	—
131	C₂²×C₄×C₆₁	—	8	1	no	—
132	C₂²×C₄×C₆₁	—	8	2	no	—
133	C₂²×C₄×C₆₁	—	8	1	no	—
134	C₂²×C₄×C₆₁	—	8	2	no	—
135	C₂²×C₄×C₆₁	—	8	1	no	—
136	C₂²×C₄×C₆₁	—	8	1	no	—
137	C₂²×C₄×C₆₁	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₆₁	#41	1	2	yes	—
144	C₂²×C₄×C₆₁	#41	1	2	yes	—
145	C₂²×C₄×C₆₁	#41	1	2	yes	—
146	C₂²×C₄×C₆₁	#41	1	2	yes	—
147	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
148	M₁₆×C₆₁	—	4	4	no	—
149	C₂×C₈×C₆₁	—	2	1	no	—
150	C₂×C₈×C₆₁	—	2	1	no	—
151	C₂×C₈×C₆₁	—	2	2	no	—
152	C₂×C₈×C₆₁	—	2	1	no	—
153	C₂×C₈×C₆₁	—	2	1	no	—
154	C₂×C₈×C₆₁	—	2	1	no	—
155	C₂×C₈×C₆₁	—	2	1	no	—
156	C₂×C₈×C₆₁	—	2	2	no	—
157	C₂×C₈×C₆₁	—	2	2	no	—
158	C₂×C₈×C₆₁	—	4	4	no	—
159	C₄⋊C₄×C₆₁	—	2	4	no	—
160	C₄⋊C₄×C₆₁	—	2	8	no	—
161	C₄⋊C₄×C₆₁	—	2	1	no	—
162	C₄⋊C₄×C₆₁	—	2	2	no	—
163	C₄⋊C₄×C₆₁	—	2	1	no	—
164	C₄⋊C₄×C₆₁	—	2	2	no	—
165	C₄⋊C₄×C₆₁	—	2	2	no	—
166	C₄⋊C₄×C₆₁	—	2	1	no	—
167	C₄⋊C₄×C₆₁	—	2	1	no	—
168	C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₄⋊C₄×C₆₁	—	2	1	no	—
170	C₄⋊C₄×C₆₁	—	4	2	no	—
171	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
172	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
173	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
174	C₂²⋊C₄×C₆₁	—	2	4	no	—
175	C₂²⋊C₄×C₆₁	—	2	8	no	—
176	C₂²⋊C₄×C₆₁	—	4	2	no	—
177	C₂²⋊C₄×C₆₁	—	8	2	no	—
178	C₂²⋊C₄×C₆₁	—	8	2	no	—
179	C₄²×C₆₁	—	2	4	no	—
180	C₄²×C₆₁	—	2	8	no	—
181	C₄²×C₆₁	—	4	2	no	—
182	C₂³×C₆₁	—	2	1	no	—
183	C₂³×C₆₁	—	2	1	no	—
184	C₂³×C₆₁	—	2	1	no	—
185	C₂³×C₆₁	—	2	1	no	—
186	C₂³×C₆₁	—	2	2	no	—
187	C₂³×C₆₁	—	2	2	no	—
188	C₂³×C₆₁	—	2	2	no	—
189	C₂³×C₆₁	—	2	2	no	—
190	C₂³×C₆₁	—	2	2	no	—
191	C₂³×C₆₁	—	2	2	no	—
192	C₂³×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
193	C₂³×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂³×C₆₁	#123	1	2	yes	—
195	C₂³×C₆₁	#123	1	2	yes	—
196	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₆₁	—	2	8	no	—
198	D₄×C₆₁	—	2	16	no	—
199	D₄×C₆₁	—	2	8	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	4	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	2	no	—
207	C₂×C₄×C₆₁	—	2	2	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	—	4	1	no	—
211	C₂×C₄×C₆₁	—	4	1	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	—	4	1	no	—
214	C₂×C₄×C₆₁	—	4	1	no	—
215	C₂×C₄×C₆₁	—	4	1	no	—
216	C₂×C₄×C₆₁	—	4	1	no	—
217	C₂×C₄×C₆₁	—	4	2	no	—
218	C₂×C₄×C₆₁	—	4	1	no	—
219	C₂×C₄×C₆₁	—	4	2	no	—
220	C₂×C₄×C₆₁	—	4	1	no	—
221	C₂×C₄×C₆₁	—	4	2	no	—
222	C₂×C₄×C₆₁	—	4	1	no	—
223	C₂×C₄×C₆₁	—	4	1	no	—
224	C₂×C₄×C₆₁	—	8	4	no	—
225	C₂×C₄×C₆₁	—	8	8	no	—
226	C₂×C₄×C₆₁	—	8	4	no	—
227	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
228	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂×C₄×C₆₁	#117	1	4	yes	—
230	C₂×C₄×C₆₁	#117	1	4	yes	—
231	C₂×C₄×C₆₁	#123	1	4	yes	—
232	C₂×C₄×C₆₁	#123	1	4	yes	—
233	C₂×C₄×C₆₁	#123	1	2	yes	—
234	C₂×C₄×C₆₁	#123	1	2	yes	—
235	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
239	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
241	C₈×C₆₁	—	4	1	no	—
242	C₈×C₆₁	—	4	1	no	—
243	C₈×C₆₁	—	4	2	no	—
244	#20703	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂²×C₆₁	—	2	2	no	—
246	C₂²×C₆₁	—	2	2	no	—
247	C₂²×C₆₁	—	2	2	no	—
248	C₂²×C₆₁	—	2	2	no	—
249	C₂²×C₆₁	—	2	2	no	—
250	C₂²×C₆₁	—	2	2	no	—
251	C₂²×C₆₁	—	2	4	no	—
252	C₂²×C₆₁	—	2	4	no	—
253	C₂²×C₆₁	—	2	4	no	—
254	C₂²×C₆₁	—	4	2	no	—
255	C₂²×C₆₁	—	4	2	no	—
256	C₂²×C₆₁	—	4	2	no	—
257	C₂²×C₆₁	—	4	2	no	—
258	C₂²×C₆₁	#381	1	4	yes	—
259	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
260	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
261	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
262	C₂²×C₆₁	#576	1	1	yes	characteristic
263	C₂²×C₆₁	#577	1	1	yes	characteristic
264	C₂²×C₆₁	#577	1	1	yes	characteristic
265	C₂²×C₆₁	#578	1	1	yes	characteristic
266	C₄×C₆₁	—	2	4	no	—
267	C₄×C₆₁	—	4	2	no	—
268	C₄×C₆₁	—	4	4	no	—
269	C₄×C₆₁	—	4	2	no	—
270	C₄×C₆₁	—	8	2	no	—
271	C₄×C₆₁	—	8	1	no	—
272	C₄×C₆₁	—	8	1	no	—
273	C₄×C₆₁	#381	1	4	yes	—
274	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
275	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
276	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
277	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
278	C₂×#520	C₂×C₆₁	1	1	yes	characteristic
279	C₂×#408	C₂×C₆₁	1	1	yes	characteristic
280	#2311	C₂×C₆₁	1	1	yes	characteristic
281	#1825	C₂×C₆₁	1	2	yes	complemented
282	#1825	C₂×C₆₁	1	2	yes	complemented
283	#1824	C₂×C₆₁	1	2	yes	complemented
284	#1823	C₂×C₆₁	1	2	yes	complemented
285	#1736	C₂×C₆₁	1	1	yes	characteristic, complemented
286	#1736	C₂×C₆₁	1	1	yes	characteristic, complemented
287	#1735	C₂×C₆₁	1	1	yes	characteristic, complemented
288	C₂×#340	C₂×C₆₁	1	1	yes	characteristic, complemented
289	C₂×C₆₁	—	2	4	no	—
290	C₂×C₆₁	—	4	4	no	—
291	C₂×C₆₁	C₂×#381	1	1	yes	characteristic
292	C₂×C₆₁	#2897	1	1	yes	characteristic
293	C₂×C₆₁	#2898	1	1	yes	characteristic
294	C₂×C₆₁	#3096	1	1	yes	characteristic
295	C₂×C₆₁	#3097	1	1	yes	characteristic
296	C₂×C₆₁	#3098	1	1	yes	characteristic
297	C₂×C₆₁	#3099	1	1	yes	characteristic
298	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
299	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
300	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
301	#520	—	2	4	no	—
302	#520	C₄×C₆₁	1	8	yes	complemented
303	C₂×C₄×Q₈	—	2	1	no	—
304	C₂×C₄×D₄	—	2	2	no	—
305	C₂×C₄×D₄	—	2	1	no	—
306	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
307	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
308	C₂×#117	C₂²×C₆₁	1	2	yes	—
309	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
310	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
311	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
312	#408	—	2	4	no	—
313	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
314	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
315	#391	—	2	1	no	—
316	#390	—	2	1	no	—
317	#386	—	2	2	no	—
318	#380	C₂²×C₆₁	1	2	yes	—
319	#380	C₂²×C₆₁	1	2	yes	—
320	#340	C₂²×C₆₁	1	1	yes	characteristic
321	#340	C₂²×C₆₁	1	2	yes	—
322	#340	C₂²×C₆₁	1	2	yes	—
323	#340	C₂²×C₆₁	1	2	yes	—
324	#340	C₂²×C₆₁	1	1	yes	characteristic
325	#340	C₂²×C₆₁	1	2	yes	—
326	#340	C₂²×C₆₁	1	2	yes	—
327	#340	C₂²×C₆₁	1	1	yes	characteristic
328	#340	C₂²×C₆₁	1	1	yes	characteristic
329	#340	C₂²×C₆₁	1	2	yes	—
330	C₆₁	#20703	1	1	yes	characteristic, direct product factor, Sylow
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	2	no	—
335	C₂×#41	C₂×C₄×C₆₁	1	4	yes	—
336	C₂×#41	D₄×C₆₁	1	4	yes	—
337	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
338	C₂²×D₄	D₄×C₆₁	1	2	yes	—
339	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
340	C₂³×C₄	—	2	1	no	—
341	C₂³×C₄	—	2	2	no	—
342	C₂³×C₄	—	2	1	no	—
343	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
344	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
345	C₂×M₁₆	—	2	2	no	—
346	C₂×M₁₆	—	2	2	no	—
347	C₂×M₁₆	—	2	2	no	—
348	C₂²×C₈	—	2	2	no	—
349	C₂²×C₈	—	2	2	no	—
350	C₂²×C₈	—	2	2	no	—
351	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
354	C₄×Q₈	—	2	8	no	—
355	C₄×D₄	—	2	8	no	—
356	C₄×D₄	—	2	16	no	—
357	#117	—	2	2	no	—
358	#117	—	2	4	no	—
359	#117	—	2	2	no	—
360	#117	—	2	2	no	—
361	#117	C₂×C₄×C₆₁	1	4	yes	—
362	#117	C₂×C₄×C₆₁	1	8	yes	complemented
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	2	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	4	no	—
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
371	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	8	yes	complemented
372	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
373	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂²⋊C₈	—	2	4	no	—
387	C₂²⋊C₈	—	2	4	no	—
388	#95	—	2	2	no	—
389	#95	—	2	2	no	—
390	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
391	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
392	#41	—	2	8	no	—
393	#41	—	2	8	no	—
394	#41	—	2	8	no	—
395	#41	—	2	8	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	2	no	—
398	C₂×Q₈	C₂²⋊C₄×C₆₁	1	4	yes	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	2	no	—
403	C₂×D₄	C₂²⋊C₄×C₆₁	1	8	yes	—
404	C₂×D₄	C₂²⋊C₄×C₆₁	1	4	yes	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	8	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	8	1	no	—
419	C₂²×C₄	—	8	2	no	—
420	C₂²×C₄	—	8	1	no	—
421	C₂²×C₄	—	8	2	no	—
422	C₂²×C₄	—	8	1	no	—
423	C₂²×C₄	—	8	1	no	—
424	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
425	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
428	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
430	C₂²×C₄	#41×C₆₁	1	2	yes	—
431	C₂²×C₄	#41×C₆₁	1	2	yes	—
432	C₂²×C₄	#41×C₆₁	1	2	yes	—
433	C₂²×C₄	#41×C₆₁	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
435	M₁₆	—	4	4	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	2	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	4	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	8	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
459	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
460	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	8	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	8	2	no	—
465	C₂²⋊C₄	—	8	2	no	—
466	C₄²	—	2	4	no	—
467	C₄²	—	2	8	no	—
468	C₄²	—	4	2	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
480	C₂³	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
481	C₂³	#123×C₆₁	1	2	yes	—
482	C₂³	#123×C₆₁	1	2	yes	—
483	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
484	Q₈	—	2	8	no	—
485	D₄	—	2	16	no	—
486	D₄	—	2	8	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	8	4	no	—
512	C₂×C₄	—	8	8	no	—
513	C₂×C₄	—	8	4	no	—
514	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
515	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
516	C₂×C₄	#117×C₆₁	1	4	yes	—
517	C₂×C₄	#117×C₆₁	1	4	yes	—
518	C₂×C₄	#123×C₆₁	1	2	yes	—
519	C₂×C₄	#123×C₆₁	1	2	yes	—
520	C₂×C₄	#123×C₆₁	1	4	yes	—
521	C₂×C₄	#123×C₆₁	1	4	yes	—
522	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
524	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
525	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
526	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
527	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
528	C₈	—	4	1	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	2	2	no	—
534	C₂²	—	2	2	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	2	4	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	4	2	no	—
544	C₂²	C₆₁×#381	1	4	yes	—
545	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
546	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
547	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
548	C₂²	C₆₁×#576	1	1	yes	characteristic
549	C₂²	C₆₁×#577	1	1	yes	characteristic
550	C₂²	C₆₁×#577	1	1	yes	characteristic
551	C₂²	C₆₁×#578	1	1	yes	characteristic
552	C₄	—	2	4	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	4	no	—
555	C₄	—	4	2	no	—
556	C₄	—	8	2	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	C₆₁×#381	1	4	yes	—
560	C₄	C₂×#117×C₆₁	1	1	yes	characteristic
561	C₄	C₂×#117×C₆₁	1	1	yes	characteristic
562	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
563	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
564	C₂	—	2	4	no	—
565	C₂	—	4	4	no	—
566	C₂	C₂×C₆₁×#381	1	1	yes	characteristic
567	C₂	C₆₁×#2897	1	1	yes	characteristic
568	C₂	C₆₁×#2898	1	1	yes	characteristic
569	C₂	C₆₁×#3096	1	1	yes	characteristic
570	C₂	C₆₁×#3097	1	1	yes	characteristic
571	C₂	C₆₁×#3098	1	1	yes	characteristic
572	C₂	C₆₁×#3099	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×#41×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1825	C₂	semidirect
5. C₆₁×#1825	C₂	semidirect
6. C₆₁×#1824	C₂	semidirect
7. C₆₁×#1823	C₂	semidirect
8. C₆₁×#1736	C₂	semidirect
9. C₆₁×#1736	C₂	semidirect
10. C₆₁×#1735	C₂	semidirect
11. C₂×C₆₁×#340	C₂	semidirect
16. C₆₁×#520	C₄	semidirect
75. #117×C₆₁	C₂×C₄	semidirect
84. C₂×C₄⋊C₄×C₆₁	C₂×C₄	semidirect
244. #20703	C₆₁	direct (N × H)
281. #1825	C₂×C₆₁	semidirect
282. #1825	C₂×C₆₁	semidirect
283. #1824	C₂×C₆₁	semidirect
284. #1823	C₂×C₆₁	semidirect
285. #1736	C₂×C₆₁	semidirect
286. #1736	C₂×C₆₁	semidirect
287. #1735	C₂×C₆₁	semidirect
288. C₂×#340	C₂×C₆₁	semidirect
302. #520	C₄×C₆₁	semidirect
330. C₆₁	#20703	direct (N × H)
362. #117	C₂×C₄×C₆₁	semidirect
371. C₂×C₄⋊C₄	C₂×C₄×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#520	2
C₂×C₆₁×#408	2
C₆₁×#2311	2
C₆₁×#1825	2
C₆₁×#1824	2
C₆₁×#1823	2
C₆₁×#1736	2
C₆₁×#1735	2
C₂×C₆₁×#340	2
#20703	61

Subgroups — C61×#20703 #29524136

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#20703 #29524136