Subgroups — C₆₁×#25702 #29529135

Order 15616.

1102 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#554	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2547	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2035	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1954	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1853	C₂	1	4	yes	maximal, complemented
9	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#554	—	2	4	no	—
11	C₆₁×#554	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#125×C₆₁	—	2	1	no	—
15	C₂×#124×C₆₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
17	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₁	—	2	1	no	—
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
22	C₆₁×#498	—	2	4	no	—
23	C₆₁×#475	—	2	4	no	—
24	C₂×#106×C₆₁	C₂²	1	4	yes	—
25	C₂×#106×C₆₁	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#103×C₆₁	C₂²	1	2	yes	—
28	C₂×#103×C₆₁	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₆₁	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#397	—	2	2	no	—
32	C₆₁×#391	—	2	1	no	—
33	C₆₁×#380	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#340	C₂²	1	2	yes	—
36	C₆₁×#340	C₂²	1	4	yes	—
37	C₂²×Q₈×C₆₁	—	2	1	no	—
38	C₂²×Q₈×C₆₁	—	2	1	no	—
39	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₆₁	—	2	2	no	—
42	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
45	C₄⋊Q₈×C₆₁	—	2	2	no	—
46	C₄⋊Q₈×C₆₁	—	2	2	no	—
47	C₄⋊Q₈×C₆₁	—	2	2	no	—
48	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
49	#125×C₆₁	—	2	8	no	—
50	#124×C₆₁	—	4	4	no	—
51	C₂²⋊Q₈×C₆₁	—	2	16	no	—
52	C₂²⋊Q₈×C₆₁	—	2	4	no	—
53	C₂²⋊Q₈×C₆₁	—	2	4	no	—
54	C₄×Q₈×C₆₁	—	2	2	no	—
55	C₄×Q₈×C₆₁	D₄	1	4	yes	—
56	C₄×D₄×C₆₁	—	2	8	no	—
57	C₄×D₄×C₆₁	—	2	2	no	—
58	C₄×D₄×C₆₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
65	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
74	C₂×C₄²×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	—	2	1	no	—
76	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
77	#106×C₆₁	—	2	4	no	—
78	#106×C₆₁	—	2	8	no	—
79	C₄⋊C₈×C₆₁	—	2	2	no	—
80	#103×C₆₁	—	2	4	no	—
81	#103×C₆₁	—	2	4	no	—
82	C₂²⋊C₈×C₆₁	—	2	8	no	—
83	C₄×C₈×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	4	no	—
86	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
87	C₂×Q₈×C₆₁	—	2	4	no	—
88	C₂×Q₈×C₆₁	—	2	1	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	—	4	2	no	—
92	C₂×Q₈×C₆₁	—	4	2	no	—
93	C₂×Q₈×C₆₁	—	4	2	no	—
94	C₂×Q₈×C₆₁	—	8	2	no	—
95	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
96	C₂×D₄×C₆₁	—	2	2	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	SD₁₆	1	4	yes	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	8	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	2	4	no	—
106	C₂²×C₄×C₆₁	—	2	4	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	2	no	—
109	C₂²×C₄×C₆₁	—	8	4	no	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
114	C₂×C₈×C₆₁	—	2	2	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₂×C₈×C₆₁	—	2	4	no	—
118	C₂×C₈×C₆₁	#41	1	4	yes	—
119	C₄⋊C₄×C₆₁	—	2	8	no	—
120	C₄⋊C₄×C₆₁	—	2	8	no	—
121	C₄⋊C₄×C₆₁	—	2	4	no	—
122	C₄⋊C₄×C₆₁	—	2	4	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	2	1	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	4	2	no	—
131	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
133	C₂²⋊C₄×C₆₁	—	2	8	no	—
134	C₂²⋊C₄×C₆₁	—	2	4	no	—
135	C₂²⋊C₄×C₆₁	—	4	8	no	—
136	C₄²×C₆₁	—	2	4	no	—
137	C₄²×C₆₁	—	4	2	no	—
138	C₄²×C₆₁	C₂×D₄	1	2	yes	—
139	C₄²×C₆₁	C₂×D₄	1	2	yes	—
140	C₂³×C₆₁	—	2	2	no	—
141	C₂³×C₆₁	—	2	4	no	—
142	C₂³×C₆₁	—	2	2	no	—
143	C₂³×C₆₁	—	2	4	no	—
144	C₂³×C₆₁	C₂×SD₁₆	1	4	yes	—
145	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₆₁	—	2	2	no	—
147	Q₈×C₆₁	—	2	2	no	—
148	Q₈×C₆₁	—	4	2	no	—
149	Q₈×C₆₁	—	8	4	no	—
150	Q₈×C₆₁	—	8	4	no	—
151	D₄×C₆₁	—	2	8	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	2	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	4	no	—
157	C₂×C₄×C₆₁	—	2	4	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	2	no	—
160	C₂×C₄×C₆₁	—	4	4	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	4	2	no	—
163	C₂×C₄×C₆₁	—	4	4	no	—
164	C₂×C₄×C₆₁	—	4	2	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	—	4	2	no	—
168	C₂×C₄×C₆₁	—	4	2	no	—
169	C₂×C₄×C₆₁	—	4	2	no	—
170	C₂×C₄×C₆₁	—	8	8	no	—
171	C₂×C₄×C₆₁	#120	1	2	yes	—
172	C₂×C₄×C₆₁	#120	1	2	yes	—
173	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
174	C₂×C₄×C₆₁	#137	1	2	yes	—
175	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
178	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
179	C₈×C₆₁	—	2	4	no	—
180	C₈×C₆₁	—	4	2	no	—
181	#25702	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂²×C₆₁	—	2	8	no	—
183	C₂²×C₆₁	—	2	4	no	—
184	C₂²×C₆₁	—	4	4	no	—
185	C₂²×C₆₁	—	4	2	no	—
186	C₂²×C₆₁	—	4	2	no	—
187	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
188	C₂²×C₆₁	#547	1	2	yes	—
189	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
190	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
191	C₂²×C₆₁	#577	1	2	yes	—
192	C₄×C₆₁	—	2	2	no	—
193	C₄×C₆₁	—	4	2	no	—
194	C₄×C₆₁	—	4	2	no	—
195	C₄×C₆₁	—	4	2	no	—
196	C₄×C₆₁	—	4	4	no	—
197	C₄×C₆₁	—	8	2	no	—
198	C₄×C₆₁	—	8	2	no	—
199	C₄×C₆₁	#448	1	4	yes	—
200	C₄×C₆₁	#532	1	1	yes	characteristic
201	C₄×C₆₁	#536	1	1	yes	characteristic
202	C₄×C₆₁	#548	1	2	yes	—
203	C₂×#554	C₂×C₆₁	1	1	yes	characteristic
204	C₂×#498	C₂×C₆₁	1	1	yes	characteristic, complemented
205	C₂×#475	C₂×C₆₁	1	1	yes	characteristic, complemented
206	#2547	C₂×C₆₁	1	1	yes	characteristic
207	#2035	C₂×C₆₁	1	4	yes	complemented
208	#1987	C₂×C₆₁	1	1	yes	characteristic, complemented
209	#1954	C₂×C₆₁	1	1	yes	characteristic
210	#1853	C₂×C₆₁	1	4	yes	complemented
211	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
212	C₂×C₆₁	—	4	4	no	—
213	C₂×C₆₁	#2432	1	1	yes	characteristic
214	C₂×C₆₁	C₂×#448	1	1	yes	characteristic
215	C₂×C₆₁	#3009	1	1	yes	characteristic
216	C₂×C₆₁	#3335	1	2	yes	—
217	C₂×C₆₁	#3356	1	2	yes	—
218	#554	—	2	4	no	—
219	#554	—	2	4	no	—
220	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
221	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
222	C₂×#125	—	2	1	no	—
223	C₂×#124	—	2	1	no	—
224	C₂×C₂²⋊Q₈	—	2	2	no	—
225	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
226	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
230	#498	—	2	4	no	—
231	#475	—	2	4	no	—
232	C₂×#106	C₂²×C₆₁	1	2	yes	—
233	C₂×#106	C₂²×C₆₁	1	4	yes	—
234	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
235	C₂×#103	C₂²×C₆₁	1	2	yes	—
236	C₂×#103	C₂²×C₆₁	1	2	yes	—
237	C₂×C₂²⋊C₈	C₂²×C₆₁	1	4	yes	—
238	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
239	#397	—	2	2	no	—
240	#391	—	2	1	no	—
241	#380	C₂²×C₆₁	1	4	yes	—
242	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
243	#340	C₂²×C₆₁	1	2	yes	—
244	#340	C₂²×C₆₁	1	4	yes	—
245	C₆₁	#25702	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×Q₈	—	2	1	no	—
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
249	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
250	C₂³×C₄	—	2	2	no	—
251	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
252	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
253	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
258	#125	—	2	8	no	—
259	#124	—	4	4	no	—
260	C₂²⋊Q₈	—	2	16	no	—
261	C₂²⋊Q₈	—	2	4	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₄×Q₈	—	2	2	no	—
264	C₄×Q₈	D₄×C₆₁	1	4	yes	—
265	C₄×D₄	—	2	8	no	—
266	C₄×D₄	—	2	2	no	—
267	C₄×D₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	4	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	4	no	—
282	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
283	C₂×C₄²	—	2	1	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
286	#106	—	2	4	no	—
287	#106	—	2	8	no	—
288	C₄⋊C₈	—	2	2	no	—
289	#103	—	2	4	no	—
290	#103	—	2	4	no	—
291	C₂²⋊C₈	—	2	8	no	—
292	C₄×C₈	—	2	2	no	—
293	#95	—	2	1	no	—
294	#95	—	2	4	no	—
295	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	1	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×Q₈	—	8	2	no	—
304	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	SD₁₆×C₆₁	1	4	yes	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	8	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	8	4	no	—
319	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	#41×C₆₁	1	4	yes	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
341	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₂²⋊C₄	—	4	8	no	—
345	C₄²	—	2	4	no	—
346	C₄²	—	4	2	no	—
347	C₄²	C₂×D₄×C₆₁	1	2	yes	—
348	C₄²	C₂×D₄×C₆₁	1	2	yes	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	4	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₂×SD₁₆×C₆₁	1	4	yes	—
354	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
355	Q₈	—	2	2	no	—
356	Q₈	—	2	2	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	8	4	no	—
359	Q₈	—	8	4	no	—
360	D₄	—	2	8	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	8	8	no	—
380	C₂×C₄	#120×C₆₁	1	2	yes	—
381	C₂×C₄	#120×C₆₁	1	2	yes	—
382	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
383	C₂×C₄	#137×C₆₁	1	2	yes	—
384	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
385	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
386	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
387	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
388	C₈	—	2	4	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	8	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
396	C₂²	C₆₁×#547	1	2	yes	—
397	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
398	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
399	C₂²	C₆₁×#577	1	2	yes	—
400	C₄	—	2	2	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	4	4	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	2	no	—
407	C₄	C₆₁×#448	1	4	yes	—
408	C₄	C₆₁×#532	1	1	yes	characteristic
409	C₄	C₆₁×#536	1	1	yes	characteristic
410	C₄	C₆₁×#548	1	2	yes	—
411	C₂	—	4	4	no	—
412	C₂	C₆₁×#2432	1	1	yes	characteristic
413	C₂	C₂×C₆₁×#448	1	1	yes	characteristic
414	C₂	C₆₁×#3009	1	1	yes	characteristic
415	C₂	C₆₁×#3335	1	2	yes	—
416	C₂	C₆₁×#3356	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#498	C₂	semidirect
3. C₂×C₆₁×#475	C₂	semidirect
5. C₆₁×#2035	C₂	semidirect
6. C₆₁×#1987	C₂	semidirect
8. C₆₁×#1853	C₂	semidirect
9. C₄×#103×C₆₁	C₂	semidirect
181. #25702	C₆₁	direct (N × H)
204. C₂×#498	C₂×C₆₁	semidirect
205. C₂×#475	C₂×C₆₁	semidirect
207. #2035	C₂×C₆₁	semidirect
208. #1987	C₂×C₆₁	semidirect
210. #1853	C₂×C₆₁	semidirect
211. C₄×#103	C₂×C₆₁	semidirect
245. C₆₁	#25702	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×#554	2
C₂×C₆₁×#498	2
C₂×C₆₁×#475	2
C₆₁×#2547	2
C₆₁×#2035	2
C₆₁×#1987	2
C₆₁×#1954	2
C₆₁×#1853	2
C₄×#103×C₆₁	2
#25702	61

Subgroups — C61×#25702 #29529135

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25702 #29529135