Subgroups — C₆₁×#20881 #29524314

Order 15616.

1458 conjugacy classes of subgroups.

The subgroup lattice has 508 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	C₂²×#107×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#417	C₂	1	1	yes	maximal, characteristic
4	C₂×C₆₁×#416	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2317	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1863	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1862	C₂	1	4	yes	maximal, complemented
8	C₆₁×#1736	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1729	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₆₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₆₁×#520	—	2	4	no	—
14	C₆₁×#520	—	2	4	no	—
15	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₆₁	—	2	2	no	—
17	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
18	C₂×#117×C₆₁	—	2	1	no	—
19	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#107×C₆₁	—	2	4	no	—
25	C₂×#107×C₆₁	C₂²	1	4	yes	—
26	C₆₁×#417	—	2	4	no	—
27	C₆₁×#416	C₄	1	8	yes	complemented
28	C₂×#103×C₆₁	C₂²	1	2	yes	—
29	C₂×#103×C₆₁	C₂²	1	2	yes	—
30	C₂×#102×C₆₁	C₂²	1	2	yes	—
31	C₂×#102×C₆₁	C₂²	1	2	yes	—
32	C₆₁×#389	C₂²	1	4	yes	—
33	C₆₁×#385	—	2	2	no	—
34	C₆₁×#384	—	2	1	no	—
35	C₆₁×#382	—	2	1	no	—
36	C₆₁×#340	C₂²	1	4	yes	—
37	C₆₁×#336	C₂²	1	4	yes	—
38	C₂×#41×C₆₁	—	2	2	no	—
39	C₂×#41×C₆₁	—	2	2	no	—
40	C₂×#41×C₆₁	—	2	2	no	—
41	C₂×#41×C₆₁	C₂×C₄	1	4	yes	—
42	C₂×#41×C₆₁	D₄	1	4	yes	—
43	C₂×#41×C₆₁	Q₈	1	4	yes	—
44	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₆₁	—	2	1	no	—
46	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	—	2	1	no	—
48	C₂³×C₄×C₆₁	—	2	1	no	—
49	C₂³×C₄×C₆₁	—	2	2	no	—
50	C₂³×C₄×C₆₁	—	2	1	no	—
51	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₆₁	—	2	2	no	—
53	C₂×M₁₆×C₆₁	—	2	2	no	—
54	C₂×M₁₆×C₆₁	—	2	2	no	—
55	C₂²×C₈×C₆₁	—	2	2	no	—
56	C₂²×C₈×C₆₁	—	2	2	no	—
57	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	complemented
58	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
60	C₄×Q₈×C₆₁	—	2	4	no	—
61	C₄×Q₈×C₆₁	—	2	4	no	—
62	C₄×D₄×C₆₁	—	2	16	no	—
63	C₄×D₄×C₆₁	—	2	4	no	—
64	C₄×D₄×C₆₁	—	2	4	no	—
65	#117×C₆₁	—	2	8	no	—
66	#117×C₆₁	—	2	2	no	—
67	#117×C₆₁	—	2	2	no	—
68	#117×C₆₁	—	2	2	no	—
69	#117×C₆₁	C₂×C₄	1	4	yes	complemented
70	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
87	C₂×C₄²×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	—	2	2	no	—
89	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
90	#107×C₆₁	—	2	8	no	—
91	#103×C₆₁	—	2	4	no	—
92	#103×C₆₁	C₂×C₄	1	8	yes	complemented
93	#102×C₆₁	—	2	4	no	—
94	#102×C₆₁	C₂×C₄	1	8	yes	complemented
95	#95×C₆₁	—	2	4	no	—
96	C₂⁴×C₆₁	—	2	1	no	—
97	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
98	#41×C₆₁	—	2	8	no	—
99	#41×C₆₁	—	2	8	no	—
100	#41×C₆₁	—	2	8	no	—
101	#41×C₆₁	C₄⋊C₄	1	16	yes	complemented
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	1	no	—
105	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
106	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
107	C₂×Q₈×C₆₁	C₂×Q₈	1	2	yes	—
108	C₂×D₄×C₆₁	—	2	4	no	—
109	C₂×D₄×C₆₁	—	2	4	no	—
110	C₂×D₄×C₆₁	—	2	4	no	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	—	2	1	no	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	2	4	no	—
119	C₂²×C₄×C₆₁	—	2	4	no	—
120	C₂²×C₄×C₆₁	—	2	4	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	2	8	no	—
124	C₂²×C₄×C₆₁	—	2	4	no	—
125	C₂²×C₄×C₆₁	—	2	2	no	—
126	C₂²×C₄×C₆₁	—	4	2	no	—
127	C₂²×C₄×C₆₁	—	8	4	no	—
128	C₂²×C₄×C₆₁	—	8	2	no	—
129	C₂²×C₄×C₆₁	—	8	2	no	—
130	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
137	C₂²×C₄×C₆₁	#41	1	2	yes	—
138	C₂²×C₄×C₆₁	#41	1	2	yes	—
139	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
140	M₁₆×C₆₁	—	4	4	no	—
141	C₂×C₈×C₆₁	—	2	8	no	—
142	C₂×C₈×C₆₁	—	2	2	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
148	C₄⋊C₄×C₆₁	—	2	8	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	—	2	4	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	2	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	2	no	—
156	C₄⋊C₄×C₆₁	—	4	2	no	—
157	C₄⋊C₄×C₆₁	—	8	4	no	—
158	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
159	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
160	C₂²⋊C₄×C₆₁	—	2	8	no	—
161	C₂²⋊C₄×C₆₁	—	2	4	no	—
162	C₂²⋊C₄×C₆₁	—	2	4	no	—
163	C₄²×C₆₁	—	2	8	no	—
164	C₄²×C₆₁	—	2	4	no	—
165	C₄²×C₆₁	—	2	2	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₂³×C₆₁	—	2	2	no	—
168	C₂³×C₆₁	—	2	2	no	—
169	C₂³×C₆₁	—	2	2	no	—
170	C₂³×C₆₁	—	2	2	no	—
171	C₂³×C₆₁	—	2	2	no	—
172	C₂³×C₆₁	—	4	2	no	—
173	C₂³×C₆₁	—	4	2	no	—
174	C₂³×C₆₁	C₄×D₄	1	2	yes	—
175	C₂³×C₆₁	#120	1	2	yes	—
176	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
177	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₆₁	—	2	2	no	—
179	Q₈×C₆₁	—	2	2	no	—
180	Q₈×C₆₁	—	2	2	no	—
181	Q₈×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
182	D₄×C₆₁	—	2	16	no	—
183	D₄×C₆₁	—	2	2	no	—
184	D₄×C₆₁	—	2	2	no	—
185	D₄×C₆₁	—	2	2	no	—
186	D₄×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	16	no	—
191	C₂×C₄×C₆₁	—	2	4	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	4	no	—
195	C₂×C₄×C₆₁	—	2	4	no	—
196	C₂×C₄×C₆₁	—	2	4	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	—	4	4	no	—
199	C₂×C₄×C₆₁	—	4	2	no	—
200	C₂×C₄×C₆₁	—	4	2	no	—
201	C₂×C₄×C₆₁	—	4	4	no	—
202	C₂×C₄×C₆₁	—	8	4	no	—
203	C₂×C₄×C₆₁	—	8	8	no	—
204	C₂×C₄×C₆₁	—	8	4	no	—
205	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	4	yes	—
206	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
207	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₆₁	#120	1	2	yes	—
209	C₂×C₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
210	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
211	C₂×C₄×C₆₁	#123	1	4	yes	—
212	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
218	C₈×C₆₁	—	2	4	no	—
219	C₈×C₆₁	—	4	2	no	—
220	#20881	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂²×C₆₁	—	2	4	no	—
222	C₂²×C₆₁	—	2	4	no	—
223	C₂²×C₆₁	—	2	2	no	—
224	C₂²×C₆₁	—	2	2	no	—
225	C₂²×C₆₁	—	2	4	no	—
226	C₂²×C₆₁	—	4	4	no	—
227	C₂²×C₆₁	—	4	4	no	—
228	C₂²×C₆₁	—	4	2	no	—
229	C₂²×C₆₁	—	4	2	no	—
230	C₂²×C₆₁	#385	1	4	yes	—
231	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
232	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
233	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
234	C₂²×C₆₁	#576	1	2	yes	—
235	C₂²×C₆₁	#578	1	2	yes	—
236	C₄×C₆₁	—	2	4	no	—
237	C₄×C₆₁	—	4	4	no	—
238	C₄×C₆₁	—	4	2	no	—
239	C₄×C₆₁	—	4	4	no	—
240	C₄×C₆₁	—	4	2	no	—
241	C₄×C₆₁	—	8	2	no	—
242	C₄×C₆₁	#385	1	4	yes	—
243	C₄×C₆₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
244	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
245	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
246	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
247	C₂×#520	C₂×C₆₁	1	1	yes	characteristic
248	C₂²×#107	C₂×C₆₁	1	1	yes	characteristic, complemented
249	C₂×#417	C₂×C₆₁	1	1	yes	characteristic
250	C₂×#416	C₂×C₆₁	1	1	yes	characteristic
251	#2317	C₂×C₆₁	1	1	yes	characteristic, complemented
252	#1863	C₂×C₆₁	1	4	yes	complemented
253	#1862	C₂×C₆₁	1	4	yes	complemented
254	#1736	C₂×C₆₁	1	1	yes	characteristic, complemented
255	#1729	C₂×C₆₁	1	1	yes	characteristic, complemented
256	C₂×C₆₁	—	2	4	no	—
257	C₂×C₆₁	—	4	4	no	—
258	C₂×C₆₁	C₂×#385	1	1	yes	characteristic
259	C₂×C₆₁	#2951	1	2	yes	—
260	C₂×C₆₁	#3008	1	1	yes	characteristic
261	C₂×C₆₁	#3011	1	1	yes	characteristic
262	C₂×C₆₁	#3083	1	2	yes	—
263	C₂²×#41	C₂²×C₆₁	1	1	yes	characteristic
264	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
265	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
266	#520	—	2	4	no	—
267	#520	—	2	4	no	—
268	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
269	C₂×C₄×D₄	—	2	2	no	—
270	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
271	C₂×#117	—	2	1	no	—
272	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
273	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	—	2	1	no	—
275	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
276	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
277	C₂×#107	—	2	4	no	—
278	C₂×#107	C₂²×C₆₁	1	4	yes	—
279	#417	—	2	4	no	—
280	#416	C₄×C₆₁	1	8	yes	complemented
281	C₂×#103	C₂²×C₆₁	1	2	yes	—
282	C₂×#103	C₂²×C₆₁	1	2	yes	—
283	C₂×#102	C₂²×C₆₁	1	2	yes	—
284	C₂×#102	C₂²×C₆₁	1	2	yes	—
285	#389	C₂²×C₆₁	1	4	yes	—
286	#385	—	2	2	no	—
287	#384	—	2	1	no	—
288	#382	—	2	1	no	—
289	#340	C₂²×C₆₁	1	4	yes	—
290	#336	C₂²×C₆₁	1	4	yes	—
291	C₆₁	#20881	1	1	yes	characteristic, direct product factor, Sylow
292	C₂×#41	—	2	2	no	—
293	C₂×#41	—	2	2	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	C₂×C₄×C₆₁	1	4	yes	—
296	C₂×#41	D₄×C₆₁	1	4	yes	—
297	C₂×#41	Q₈×C₆₁	1	4	yes	—
298	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
301	C₂³×C₄	—	2	1	no	—
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	2	no	—
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
306	C₂×M₁₆	—	2	2	no	—
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	2	2	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	complemented
312	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
313	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
314	C₄×Q₈	—	2	4	no	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×D₄	—	2	16	no	—
317	C₄×D₄	—	2	4	no	—
318	C₄×D₄	—	2	4	no	—
319	#117	—	2	8	no	—
320	#117	—	2	2	no	—
321	#117	—	2	2	no	—
322	#117	—	2	2	no	—
323	#117	C₂×C₄×C₆₁	1	4	yes	complemented
324	C₂×C₄⋊C₄	—	2	8	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	4	no	—
332	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
333	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
334	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
336	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
337	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
338	C₂×C₂²⋊C₄	—	2	1	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	1	no	—
343	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
344	#107	—	2	8	no	—
345	#103	—	2	4	no	—
346	#103	C₂×C₄×C₆₁	1	8	yes	complemented
347	#102	—	2	4	no	—
348	#102	C₂×C₄×C₆₁	1	8	yes	complemented
349	#95	—	2	4	no	—
350	C₂⁴	—	2	1	no	—
351	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
352	#41	—	2	8	no	—
353	#41	—	2	8	no	—
354	#41	—	2	8	no	—
355	#41	C₄⋊C₄×C₆₁	1	16	yes	complemented
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
360	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
361	C₂×Q₈	C₂×Q₈×C₆₁	1	2	yes	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
369	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
370	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	8	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	4	2	no	—
381	C₂²×C₄	—	8	4	no	—
382	C₂²×C₄	—	8	2	no	—
383	C₂²×C₄	—	8	2	no	—
384	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
386	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
390	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
391	C₂²×C₄	#41×C₆₁	1	2	yes	—
392	C₂²×C₄	#41×C₆₁	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
394	M₁₆	—	4	4	no	—
395	C₂×C₈	—	2	8	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	2	no	—
411	C₄⋊C₄	—	8	4	no	—
412	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
413	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
414	C₂²⋊C₄	—	2	8	no	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₄²	—	2	8	no	—
418	C₄²	—	2	4	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	2	no	—
425	C₂³	—	2	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	C₄×D₄×C₆₁	1	2	yes	—
429	C₂³	#120×C₆₁	1	2	yes	—
430	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
431	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	2	2	no	—
435	Q₈	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
436	D₄	—	2	16	no	—
437	D₄	—	2	2	no	—
438	D₄	—	2	2	no	—
439	D₄	—	2	2	no	—
440	D₄	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	16	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	—	8	8	no	—
458	C₂×C₄	—	8	4	no	—
459	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	4	yes	—
460	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
461	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
462	C₂×C₄	#120×C₆₁	1	2	yes	—
463	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
464	C₂×C₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
465	C₂×C₄	#123×C₆₁	1	4	yes	—
466	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
467	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
469	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
470	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
472	C₈	—	2	4	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	2	4	no	—
475	C₂²	—	2	4	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	C₆₁×#385	1	4	yes	—
484	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
485	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
486	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
487	C₂²	C₆₁×#576	1	2	yes	—
488	C₂²	C₆₁×#578	1	2	yes	—
489	C₄	—	2	4	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	4	no	—
493	C₄	—	4	2	no	—
494	C₄	—	8	2	no	—
495	C₄	C₆₁×#385	1	4	yes	—
496	C₄	C₂²×C₄⋊C₄×C₆₁	1	1	yes	characteristic
497	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
498	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
499	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
500	C₂	—	2	4	no	—
501	C₂	—	4	4	no	—
502	C₂	C₂×C₆₁×#385	1	1	yes	characteristic
503	C₂	C₆₁×#2951	1	2	yes	—
504	C₂	C₆₁×#3008	1	1	yes	characteristic
505	C₂	C₆₁×#3011	1	1	yes	characteristic
506	C₂	C₆₁×#3083	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	C₂²×#41×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×#117×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#107×C₆₁	C₂	semidirect
5. C₆₁×#2317	C₂	semidirect
6. C₆₁×#1863	C₂	semidirect
7. C₆₁×#1862	C₂	semidirect
8. C₆₁×#1736	C₂	semidirect
9. C₆₁×#1729	C₂	semidirect
27. C₆₁×#416	C₄	semidirect
57. C₂²×C₈×C₆₁	C₂×C₄	semidirect
69. #117×C₆₁	C₂×C₄	semidirect
92. #103×C₆₁	C₂×C₄	semidirect
94. #102×C₆₁	C₂×C₄	semidirect
101. #41×C₆₁	C₄⋊C₄	semidirect
220. #20881	C₆₁	direct (N × H)
248. C₂²×#107	C₂×C₆₁	semidirect
251. #2317	C₂×C₆₁	semidirect
252. #1863	C₂×C₆₁	semidirect
253. #1862	C₂×C₆₁	semidirect
254. #1736	C₂×C₆₁	semidirect
255. #1729	C₂×C₆₁	semidirect
280. #416	C₄×C₆₁	semidirect
291. C₆₁	#20881	direct (N × H)
311. C₂²×C₈	C₂×C₄×C₆₁	semidirect
323. #117	C₂×C₄×C₆₁	semidirect
346. #103	C₂×C₄×C₆₁	semidirect
348. #102	C₂×C₄×C₆₁	semidirect
355. #41	C₄⋊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
C₂²×#107×C₆₁	2
C₂×C₆₁×#417	2
C₂×C₆₁×#416	2
C₆₁×#2317	2
C₆₁×#1863	2
C₆₁×#1862	2
C₆₁×#1736	2
C₆₁×#1729	2
#20881	61

Subgroups — C61×#20881 #29524314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#20881 #29524314