Subgroups — C₆₁×#20661 #29524094

Order 15616.

1590 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#428	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2280	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×#380	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1809	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1808	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1807	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1736	C₂	1	2	yes	maximal, complemented
9	C₂⁴×C₄×C₆₁	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₆₁	—	2	8	no	—
11	C₂²×M₁₆×C₆₁	C₄	1	8	yes	complemented
12	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₆₁	C₂²	1	2	yes	—
16	C₂×#117×C₆₁	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₆₁	—	2	1	no	—
19	C₆₁×#428	—	2	8	no	—
20	C₂×#107×C₆₁	C₂²	1	4	yes	complemented
21	C₂×#106×C₆₁	C₂²	1	4	yes	complemented
22	C₆₁×#381	—	2	1	no	—
23	C₆₁×#380	—	2	1	no	—
24	C₆₁×#380	—	2	1	no	—
25	C₆₁×#380	C₂²	1	2	yes	—
26	C₆₁×#380	C₂²	1	2	yes	—
27	C₆₁×#380	C₂²	1	1	yes	characteristic
28	C₆₁×#380	C₂²	1	1	yes	characteristic
29	C₆₁×#380	C₂²	1	2	yes	—
30	C₆₁×#379	—	2	1	no	—
31	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
32	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
33	C₂×#95×C₆₁	—	2	1	no	—
34	C₆₁×#340	C₂²	1	4	yes	complemented
35	C₆₁×#340	C₂²	1	4	yes	complemented
36	C₂⁵×C₆₁	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₆₁	—	2	4	no	—
38	C₂³×C₄×C₆₁	—	2	4	no	—
39	C₂³×C₄×C₆₁	—	2	2	no	—
40	C₂³×C₄×C₆₁	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	Q₈	1	4	yes	—
45	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂×M₁₆×C₆₁	—	2	4	no	—
49	C₂×M₁₆×C₆₁	—	2	32	no	—
50	C₂×M₁₆×C₆₁	—	2	8	no	—
51	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	—
52	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	—
53	C₂×M₁₆×C₆₁	C₂×C₄	1	8	yes	complemented
54	C₂×M₁₆×C₆₁	D₄	1	8	yes	—
55	C₂²×C₈×C₆₁	—	2	8	no	—
56	C₂²×C₈×C₆₁	C₂×C₄	1	8	yes	complemented
57	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
59	#117×C₆₁	—	2	4	no	—
60	#117×C₆₁	—	2	4	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	4	4	no	—
74	C₂×C₄²×C₆₁	—	2	2	no	—
75	#107×C₆₁	—	2	8	no	—
76	#106×C₆₁	—	2	8	no	—
77	#95×C₆₁	—	2	2	no	—
78	#95×C₆₁	—	2	2	no	—
79	#95×C₆₁	—	2	1	no	—
80	#95×C₆₁	—	2	1	no	—
81	#95×C₆₁	—	2	2	no	—
82	C₂⁴×C₆₁	—	2	4	no	—
83	C₂⁴×C₆₁	—	2	2	no	—
84	C₂⁴×C₆₁	—	2	2	no	—
85	C₂⁴×C₆₁	—	4	2	no	—
86	C₂⁴×C₆₁	C₄⋊C₄	1	4	yes	—
87	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
88	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
89	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₁	—	2	4	no	—
91	C₂²×C₄×C₆₁	—	2	8	no	—
92	C₂²×C₄×C₆₁	—	2	8	no	—
93	C₂²×C₄×C₆₁	—	2	4	no	—
94	C₂²×C₄×C₆₁	—	2	4	no	—
95	C₂²×C₄×C₆₁	—	2	16	no	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	2	no	—
99	C₂²×C₄×C₆₁	—	2	2	no	—
100	C₂²×C₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	4	no	—
103	C₂²×C₄×C₆₁	—	4	4	no	—
104	C₂²×C₄×C₆₁	—	4	4	no	—
105	C₂²×C₄×C₆₁	—	4	4	no	—
106	C₂²×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
107	C₂²×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
108	C₂²×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
109	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
115	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
118	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
119	C₂²×C₄×C₆₁	#41	1	4	yes	—
120	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
121	M₁₆×C₆₁	—	2	8	no	—
122	M₁₆×C₆₁	—	2	16	no	—
123	M₁₆×C₆₁	C₂²⋊C₄	1	16	yes	complemented
124	C₂×C₈×C₆₁	—	2	4	no	—
125	C₂×C₈×C₆₁	—	2	16	no	—
126	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
128	C₂×C₈×C₆₁	C₂×D₄	1	8	yes	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	4	no	—
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	2	4	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₄⋊C₄×C₆₁	—	4	4	no	—
136	C₂²⋊C₄×C₆₁	—	4	4	no	—
137	C₂²⋊C₄×C₆₁	—	4	4	no	—
138	C₂²⋊C₄×C₆₁	—	4	4	no	—
139	C₂²⋊C₄×C₆₁	—	4	2	no	—
140	C₂²⋊C₄×C₆₁	—	4	4	no	—
141	C₂²⋊C₄×C₆₁	—	4	2	no	—
142	C₄²×C₆₁	—	4	4	no	—
143	C₂³×C₆₁	—	2	2	no	—
144	C₂³×C₆₁	—	2	1	no	—
145	C₂³×C₆₁	—	2	1	no	—
146	C₂³×C₆₁	—	2	2	no	—
147	C₂³×C₆₁	—	2	2	no	—
148	C₂³×C₆₁	—	2	2	no	—
149	C₂³×C₆₁	—	2	1	no	—
150	C₂³×C₆₁	—	2	1	no	—
151	C₂³×C₆₁	—	2	2	no	—
152	C₂³×C₆₁	—	2	8	no	—
153	C₂³×C₆₁	—	2	8	no	—
154	C₂³×C₆₁	—	4	4	no	—
155	C₂³×C₆₁	—	4	8	no	—
156	C₂³×C₆₁	—	4	8	no	—
157	C₂³×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
158	C₂³×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
159	C₂³×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
160	C₂³×C₆₁	#121	1	4	yes	—
161	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
162	C₂³×C₆₁	#137	1	2	yes	—
163	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	2	8	no	—
167	C₂×C₄×C₆₁	—	2	2	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	2	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	4	no	—
173	C₂×C₄×C₆₁	—	2	8	no	—
174	C₂×C₄×C₆₁	—	2	8	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	4	2	no	—
177	C₂×C₄×C₆₁	—	4	4	no	—
178	C₂×C₄×C₆₁	—	4	4	no	—
179	C₂×C₄×C₆₁	—	4	2	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	4	no	—
184	C₂×C₄×C₆₁	—	8	8	no	—
185	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
186	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
187	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
189	C₂×C₄×C₆₁	#117	1	4	yes	—
190	C₂×C₄×C₆₁	#121	1	4	yes	—
191	C₂×C₄×C₆₁	C₂²⋊Q₈	1	8	yes	—
192	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
195	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
196	C₈×C₆₁	—	2	4	no	—
197	C₈×C₆₁	C₂×C₂²⋊C₄	1	8	yes	complemented
198	#20661	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₆₁	—	2	2	no	—
200	C₂²×C₆₁	—	2	2	no	—
201	C₂²×C₆₁	—	2	2	no	—
202	C₂²×C₆₁	—	2	2	no	—
203	C₂²×C₆₁	—	2	4	no	—
204	C₂²×C₆₁	—	2	4	no	—
205	C₂²×C₆₁	—	2	4	no	—
206	C₂²×C₆₁	—	2	4	no	—
207	C₂²×C₆₁	—	2	2	no	—
208	C₂²×C₆₁	—	2	2	no	—
209	C₂²×C₆₁	—	2	2	no	—
210	C₂²×C₆₁	—	4	16	no	—
211	C₂²×C₆₁	—	4	2	no	—
212	C₂²×C₆₁	—	4	2	no	—
213	C₂²×C₆₁	#380	1	4	yes	—
214	C₂²×C₆₁	#428	1	4	yes	complemented
215	C₂²×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
216	C₂²×C₆₁	C₂×#121	1	2	yes	—
217	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
218	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
219	C₂²×C₆₁	#575	1	2	yes	—
220	C₄×C₆₁	—	2	2	no	—
221	C₄×C₆₁	—	2	2	no	—
222	C₄×C₆₁	—	8	2	no	—
223	C₄×C₆₁	—	8	4	no	—
224	C₄×C₆₁	—	8	2	no	—
225	C₄×C₆₁	#380	1	4	yes	—
226	C₄×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
227	C₄×C₆₁	C₂×#117	1	1	yes	characteristic
228	C₄×C₆₁	C₂×C₂²⋊Q₈	1	2	yes	—
229	C₂³×M₁₆	C₂×C₆₁	1	1	yes	characteristic
230	C₂×#428	C₂×C₆₁	1	2	yes	complemented
231	#2280	C₂×C₆₁	1	1	yes	characteristic
232	C₂×#380	C₂×C₆₁	1	1	yes	characteristic
233	#1809	C₂×C₆₁	1	4	yes	complemented
234	#1808	C₂×C₆₁	1	2	yes	complemented
235	#1807	C₂×C₆₁	1	2	yes	complemented
236	#1736	C₂×C₆₁	1	2	yes	complemented
237	C₂×C₆₁	—	2	4	no	—
238	C₂×C₆₁	—	2	4	no	—
239	C₂×C₆₁	—	4	2	no	—
240	C₂×C₆₁	C₂×#380	1	1	yes	characteristic
241	C₂×C₆₁	C₂×#428	1	1	yes	characteristic
242	C₂×C₆₁	#2911	1	1	yes	characteristic
243	C₂×C₆₁	#3055	1	2	yes	—
244	C₂×C₆₁	#3056	1	2	yes	—
245	C₂⁴×C₄	C₂²×C₆₁	1	1	yes	characteristic
246	C₂²×M₁₆	—	2	8	no	—
247	C₂²×M₁₆	C₄×C₆₁	1	8	yes	complemented
248	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
249	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
250	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
251	C₂³×C₈	C₂²×C₆₁	1	2	yes	—
252	C₂×#117	C₂²×C₆₁	1	2	yes	—
253	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
254	C₂²×C₂²⋊C₄	—	2	1	no	—
255	#428	—	2	8	no	—
256	C₂×#107	C₂²×C₆₁	1	4	yes	complemented
257	C₂×#106	C₂²×C₆₁	1	4	yes	complemented
258	#381	—	2	1	no	—
259	#380	—	2	1	no	—
260	#380	—	2	1	no	—
261	#380	C₂²×C₆₁	1	1	yes	characteristic
262	#380	C₂²×C₆₁	1	2	yes	—
263	#380	C₂²×C₆₁	1	1	yes	characteristic
264	#380	C₂²×C₆₁	1	2	yes	—
265	#380	C₂²×C₆₁	1	2	yes	—
266	#379	—	2	1	no	—
267	C₄×C₂²⋊C₄	—	2	1	no	—
268	C₄×C₂²⋊C₄	—	2	1	no	—
269	C₂×#95	—	2	1	no	—
270	#340	C₂²×C₆₁	1	4	yes	complemented
271	#340	C₂²×C₆₁	1	4	yes	complemented
272	C₆₁	#20661	1	1	yes	characteristic, direct product factor, Sylow
273	C₂⁵	D₄×C₆₁	1	1	yes	characteristic
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂×C₄×C₆₁	1	4	yes	—
278	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
279	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
280	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
281	C₂³×C₄	Q₈×C₆₁	1	4	yes	—
282	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
285	C₂×M₁₆	—	2	4	no	—
286	C₂×M₁₆	—	2	32	no	—
287	C₂×M₁₆	—	2	8	no	—
288	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	—
289	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	—
290	C₂×M₁₆	C₂×C₄×C₆₁	1	8	yes	complemented
291	C₂×M₁₆	D₄×C₆₁	1	8	yes	—
292	C₂²×C₈	—	2	8	no	—
293	C₂²×C₈	C₂×C₄×C₆₁	1	8	yes	complemented
294	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
295	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
296	#117	—	2	4	no	—
297	#117	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	1	no	—
309	C₂×C₂²⋊C₄	—	2	1	no	—
310	C₂×C₂²⋊C₄	—	4	4	no	—
311	C₂×C₄²	—	2	2	no	—
312	#107	—	2	8	no	—
313	#106	—	2	8	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	1	no	—
317	#95	—	2	1	no	—
318	#95	—	2	2	no	—
319	C₂⁴	—	2	4	no	—
320	C₂⁴	—	2	2	no	—
321	C₂⁴	—	2	2	no	—
322	C₂⁴	—	4	2	no	—
323	C₂⁴	C₄⋊C₄×C₆₁	1	4	yes	—
324	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
325	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
326	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	16	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	4	4	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	C₄⋊C₄×C₆₁	1	4	yes	—
344	C₂²×C₄	C₄⋊C₄×C₆₁	1	4	yes	—
345	C₂²×C₄	C₄⋊C₄×C₆₁	1	4	yes	—
346	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
347	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
348	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
352	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
353	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
354	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
355	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
356	C₂²×C₄	#41×C₆₁	1	4	yes	—
357	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
358	M₁₆	—	2	8	no	—
359	M₁₆	—	2	16	no	—
360	M₁₆	C₂²⋊C₄×C₆₁	1	16	yes	complemented
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	2	16	no	—
363	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
364	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
365	C₂×C₈	C₂×D₄×C₆₁	1	8	yes	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₄²	—	4	4	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	8	no	—
389	C₂³	—	2	8	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	4	4	no	—
392	C₂³	—	4	8	no	—
393	C₂³	—	4	8	no	—
394	C₂³	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
395	C₂³	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
396	C₂³	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
397	C₂³	#121×C₆₁	1	4	yes	—
398	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
399	C₂³	#137×C₆₁	1	2	yes	—
400	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	8	no	—
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	8	8	no	—
422	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
423	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
424	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
425	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	2	yes	—
426	C₂×C₄	#117×C₆₁	1	4	yes	—
427	C₂×C₄	#121×C₆₁	1	4	yes	—
428	C₂×C₄	C₂²⋊Q₈×C₆₁	1	8	yes	—
429	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
431	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
433	C₈	—	2	4	no	—
434	C₈	C₂×C₂²⋊C₄×C₆₁	1	8	yes	complemented
435	C₂²	—	2	2	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	4	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	4	16	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	2	no	—
449	C₂²	C₆₁×#380	1	4	yes	—
450	C₂²	C₆₁×#428	1	4	yes	complemented
451	C₂²	C₂²×C₄⋊C₄×C₆₁	1	1	yes	characteristic
452	C₂²	C₂×#121×C₆₁	1	2	yes	—
453	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
454	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
455	C₂²	C₆₁×#575	1	2	yes	—
456	C₄	—	2	2	no	—
457	C₄	—	2	2	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	4	no	—
460	C₄	—	8	2	no	—
461	C₄	C₆₁×#380	1	4	yes	—
462	C₄	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
463	C₄	C₂×#117×C₆₁	1	1	yes	characteristic
464	C₄	C₂×C₂²⋊Q₈×C₆₁	1	2	yes	—
465	C₂	—	2	4	no	—
466	C₂	—	2	4	no	—
467	C₂	—	4	2	no	—
468	C₂	C₂×C₆₁×#380	1	1	yes	characteristic
469	C₂	C₂×C₆₁×#428	1	1	yes	characteristic
470	C₂	C₆₁×#2911	1	1	yes	characteristic
471	C₂	C₆₁×#3055	1	2	yes	—
472	C₂	C₆₁×#3056	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁵×C₆₁	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂⁴×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#428	C₂	semidirect
5. C₆₁×#1809	C₂	semidirect
6. C₆₁×#1808	C₂	semidirect
7. C₆₁×#1807	C₂	semidirect
8. C₆₁×#1736	C₂	semidirect
11. C₂²×M₁₆×C₆₁	C₄	semidirect
20. C₂×#107×C₆₁	C₂²	semidirect
21. C₂×#106×C₆₁	C₂²	semidirect
34. C₆₁×#340	C₂²	semidirect
35. C₆₁×#340	C₂²	semidirect
53. C₂×M₁₆×C₆₁	C₂×C₄	semidirect
56. C₂²×C₈×C₆₁	C₂×C₄	semidirect
123. M₁₆×C₆₁	C₂²⋊C₄	semidirect
197. C₈×C₆₁	C₂×C₂²⋊C₄	semidirect
198. #20661	C₆₁	direct (N × H)
214. C₂²×C₆₁	#428	semidirect
230. C₂×#428	C₂×C₆₁	semidirect
233. #1809	C₂×C₆₁	semidirect
234. #1808	C₂×C₆₁	semidirect
235. #1807	C₂×C₆₁	semidirect
236. #1736	C₂×C₆₁	semidirect
247. C₂²×M₁₆	C₄×C₆₁	semidirect
256. C₂×#107	C₂²×C₆₁	semidirect
257. C₂×#106	C₂²×C₆₁	semidirect
270. #340	C₂²×C₆₁	semidirect
271. #340	C₂²×C₆₁	semidirect
272. C₆₁	#20661	direct (N × H)
290. C₂×M₁₆	C₂×C₄×C₆₁	semidirect
293. C₂²×C₈	C₂×C₄×C₆₁	semidirect
360. M₁₆	C₂²⋊C₄×C₆₁	semidirect
434. C₈	C₂×C₂²⋊C₄×C₆₁	semidirect
450. C₂²	C₆₁×#428	semidirect

Maximal subgroups

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

subgroup	index
C₂³×M₁₆×C₆₁	2
C₂×C₆₁×#428	2
C₆₁×#2280	2
C₂×C₆₁×#380	2
C₆₁×#1809	2
C₆₁×#1808	2
C₆₁×#1807	2
C₆₁×#1736	2
#20661	61

Subgroups — C61×#20661 #29524094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#20661 #29524094