Subgroups — C₆₁×#25701 #29529134

Order 15616.

1038 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#477	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2563	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2035	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1954	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1854	C₂	1	4	yes	maximal, complemented
9	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#556	—	2	4	no	—
11	C₆₁×#556	—	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×#126×C₆₁	—	2	2	no	—
15	C₂×#124×C₆₁	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₆₁	C₂²	1	2	yes	—
21	C₆₁×#498	—	2	4	no	—
22	C₆₁×#477	—	2	4	no	—
23	C₂×#107×C₆₁	C₂²	1	2	yes	—
24	C₂×#106×C₆₁	C₂²	1	4	yes	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×#103×C₆₁	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₆₁	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#393	—	2	2	no	—
31	C₆₁×#390	—	2	1	no	—
32	C₆₁×#382	—	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	C₂³	1	2	yes	—
42	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₆₁	—	2	2	no	—
45	C₄⋊Q₈×C₆₁	—	2	2	no	—
46	C₄⋊Q₈×C₆₁	—	2	2	no	—
47	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
48	#126×C₆₁	—	2	16	no	—
49	#124×C₆₁	—	2	8	no	—
50	C₂²⋊Q₈×C₆₁	—	2	4	no	—
51	C₂²⋊Q₈×C₆₁	—	2	4	no	—
52	C₄×Q₈×C₆₁	—	2	8	no	—
53	C₄×Q₈×C₆₁	—	2	2	no	—
54	C₄×Q₈×C₆₁	D₄	1	4	yes	—
55	C₄×D₄×C₆₁	—	2	2	no	—
56	C₄×D₄×C₆₁	—	2	2	no	—
57	#117×C₆₁	—	2	4	no	—
58	#117×C₆₁	—	2	4	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	1	no	—
63	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
71	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
72	C₂×C₄²×C₆₁	—	2	2	no	—
73	C₂×C₄²×C₆₁	—	2	1	no	—
74	C₂×C₄²×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
76	#107×C₆₁	—	2	4	no	—
77	#106×C₆₁	—	2	8	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	#103×C₆₁	—	2	4	no	—
80	#103×C₆₁	—	2	4	no	—
81	C₂²⋊C₈×C₆₁	—	2	8	no	—
82	C₄×C₈×C₆₁	—	2	2	no	—
83	#95×C₆₁	—	2	1	no	—
84	#95×C₆₁	—	2	4	no	—
85	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
86	C₂×Q₈×C₆₁	—	2	4	no	—
87	C₂×Q₈×C₆₁	—	2	1	no	—
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	4	2	no	—
91	C₂×Q₈×C₆₁	—	4	2	no	—
92	C₂×Q₈×C₆₁	—	4	2	no	—
93	C₂×Q₈×C₆₁	—	8	2	no	—
94	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
95	C₂×D₄×C₆₁	—	2	2	no	—
96	C₂×D₄×C₆₁	—	2	2	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	1	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	4	no	—
104	C₂²×C₄×C₆₁	—	2	4	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₆₁	—	2	2	no	—
112	C₂×C₈×C₆₁	—	2	2	no	—
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	4	no	—
115	C₂×C₈×C₆₁	#41	1	4	yes	—
116	C₄⋊C₄×C₆₁	—	2	8	no	—
117	C₄⋊C₄×C₆₁	—	2	4	no	—
118	C₄⋊C₄×C₆₁	—	2	4	no	—
119	C₄⋊C₄×C₆₁	—	2	2	no	—
120	C₄⋊C₄×C₆₁	—	2	1	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	2	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	4	2	no	—
127	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
128	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
129	C₂²⋊C₄×C₆₁	—	2	8	no	—
130	C₂²⋊C₄×C₆₁	—	2	8	no	—
131	C₂²⋊C₄×C₆₁	—	2	4	no	—
132	C₂²⋊C₄×C₆₁	—	8	4	no	—
133	C₄²×C₆₁	—	2	8	no	—
134	C₄²×C₆₁	—	2	4	no	—
135	C₄²×C₆₁	—	4	2	no	—
136	C₄²×C₆₁	C₂×D₄	1	2	yes	—
137	C₄²×C₆₁	C₂×D₄	1	2	yes	—
138	C₂³×C₆₁	—	2	2	no	—
139	C₂³×C₆₁	—	2	4	no	—
140	C₂³×C₆₁	—	2	2	no	—
141	C₂³×C₆₁	—	2	2	no	—
142	C₂³×C₆₁	—	2	4	no	—
143	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₆₁	—	2	2	no	—
145	Q₈×C₆₁	—	2	2	no	—
146	Q₈×C₆₁	—	4	2	no	—
147	Q₈×C₆₁	—	4	8	no	—
148	Q₈×C₆₁	—	8	4	no	—
149	D₄×C₆₁	—	4	4	no	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	2	no	—
154	C₂×C₄×C₆₁	—	2	4	no	—
155	C₂×C₄×C₆₁	—	2	4	no	—
156	C₂×C₄×C₆₁	—	4	2	no	—
157	C₂×C₄×C₆₁	—	4	2	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	2	no	—
160	C₂×C₄×C₆₁	—	4	2	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	4	4	no	—
163	C₂×C₄×C₆₁	—	4	2	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	4	no	—
168	C₂×C₄×C₆₁	#120	1	2	yes	—
169	C₂×C₄×C₆₁	#120	1	2	yes	—
170	C₂×C₄×C₆₁	#135	1	2	yes	—
171	C₂×C₄×C₆₁	#137	1	2	yes	—
172	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
175	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
176	C₈×C₆₁	—	2	4	no	—
177	C₈×C₆₁	—	4	2	no	—
178	#25701	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₆₁	—	4	4	no	—
180	C₂²×C₆₁	—	4	4	no	—
181	C₂²×C₆₁	—	4	2	no	—
182	C₂²×C₆₁	—	4	2	no	—
183	C₂²×C₆₁	—	4	2	no	—
184	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
185	C₂²×C₆₁	#547	1	2	yes	—
186	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
187	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
188	C₂²×C₆₁	#577	1	2	yes	—
189	C₄×C₆₁	—	2	2	no	—
190	C₄×C₆₁	—	4	2	no	—
191	C₄×C₆₁	—	4	2	no	—
192	C₄×C₆₁	—	4	4	no	—
193	C₄×C₆₁	—	4	2	no	—
194	C₄×C₆₁	—	8	2	no	—
195	C₄×C₆₁	—	8	2	no	—
196	C₄×C₆₁	#452	1	4	yes	—
197	C₄×C₆₁	#532	1	1	yes	characteristic
198	C₄×C₆₁	#536	1	1	yes	characteristic
199	C₄×C₆₁	#548	1	2	yes	—
200	C₂×#556	C₂×C₆₁	1	1	yes	characteristic
201	C₂×#498	C₂×C₆₁	1	1	yes	characteristic, complemented
202	C₂×#477	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#2563	C₂×C₆₁	1	1	yes	characteristic
204	#2035	C₂×C₆₁	1	4	yes	complemented
205	#1988	C₂×C₆₁	1	1	yes	characteristic, complemented
206	#1954	C₂×C₆₁	1	1	yes	characteristic
207	#1854	C₂×C₆₁	1	4	yes	complemented
208	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
209	C₂×C₆₁	—	8	2	no	—
210	C₂×C₆₁	#2432	1	1	yes	characteristic
211	C₂×C₆₁	C₂×#452	1	1	yes	characteristic
212	C₂×C₆₁	#3010	1	1	yes	characteristic
213	C₂×C₆₁	#3340	1	2	yes	—
214	C₂×C₆₁	#3356	1	2	yes	—
215	#556	—	2	4	no	—
216	#556	—	2	4	no	—
217	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
218	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
219	C₂×#126	—	2	2	no	—
220	C₂×#124	—	2	1	no	—
221	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
222	C₂×C₄×Q₈	—	2	1	no	—
223	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
224	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
225	C₂×#117	C₂²×C₆₁	1	2	yes	—
226	#498	—	2	4	no	—
227	#477	—	2	4	no	—
228	C₂×#107	C₂²×C₆₁	1	2	yes	—
229	C₂×#106	C₂²×C₆₁	1	4	yes	—
230	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
231	C₂×#103	C₂²×C₆₁	1	2	yes	—
232	C₂×#103	C₂²×C₆₁	1	2	yes	—
233	C₂×C₂²⋊C₈	C₂²×C₆₁	1	4	yes	—
234	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
235	#393	—	2	2	no	—
236	#390	—	2	1	no	—
237	#382	—	2	1	no	—
238	#380	C₂²×C₆₁	1	4	yes	—
239	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
240	#340	C₂²×C₆₁	1	2	yes	—
241	#340	C₂²×C₆₁	1	4	yes	—
242	C₆₁	#25701	1	1	yes	characteristic, direct product factor, Sylow
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	—	2	1	no	—
245	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
246	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
248	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
249	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	—	2	2	no	—
252	C₄⋊Q₈	—	2	2	no	—
253	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
254	#126	—	2	16	no	—
255	#124	—	2	8	no	—
256	C₂²⋊Q₈	—	2	4	no	—
257	C₂²⋊Q₈	—	2	4	no	—
258	C₄×Q₈	—	2	8	no	—
259	C₄×Q₈	—	2	2	no	—
260	C₄×Q₈	D₄×C₆₁	1	4	yes	—
261	C₄×D₄	—	2	2	no	—
262	C₄×D₄	—	2	2	no	—
263	#117	—	2	4	no	—
264	#117	—	2	4	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
273	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	4	no	—
277	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
278	C₂×C₄²	—	2	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	—	2	1	no	—
281	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
282	#107	—	2	4	no	—
283	#106	—	2	8	no	—
284	C₄⋊C₈	—	2	2	no	—
285	#103	—	2	4	no	—
286	#103	—	2	4	no	—
287	C₂²⋊C₈	—	2	8	no	—
288	C₄×C₈	—	2	2	no	—
289	#95	—	2	1	no	—
290	#95	—	2	4	no	—
291	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	8	2	no	—
300	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	4	no	—
321	C₂×C₈	#41×C₆₁	1	4	yes	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
334	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	2	8	no	—
337	C₂²⋊C₄	—	2	4	no	—
338	C₂²⋊C₄	—	8	4	no	—
339	C₄²	—	2	8	no	—
340	C₄²	—	2	4	no	—
341	C₄²	—	4	2	no	—
342	C₄²	C₂×D₄×C₆₁	1	2	yes	—
343	C₄²	C₂×D₄×C₆₁	1	2	yes	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
350	Q₈	—	2	2	no	—
351	Q₈	—	2	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	8	no	—
354	Q₈	—	8	4	no	—
355	D₄	—	4	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	4	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	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	#120×C₆₁	1	2	yes	—
375	C₂×C₄	#120×C₆₁	1	2	yes	—
376	C₂×C₄	#135×C₆₁	1	2	yes	—
377	C₂×C₄	#137×C₆₁	1	2	yes	—
378	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
381	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
382	C₈	—	2	4	no	—
383	C₈	—	4	2	no	—
384	C₂²	—	4	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
390	C₂²	C₆₁×#547	1	2	yes	—
391	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
392	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
393	C₂²	C₆₁×#577	1	2	yes	—
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	2	no	—
399	C₄	—	8	2	no	—
400	C₄	—	8	2	no	—
401	C₄	C₆₁×#452	1	4	yes	—
402	C₄	C₆₁×#532	1	1	yes	characteristic
403	C₄	C₆₁×#536	1	1	yes	characteristic
404	C₄	C₆₁×#548	1	2	yes	—
405	C₂	—	8	2	no	—
406	C₂	C₆₁×#2432	1	1	yes	characteristic
407	C₂	C₂×C₆₁×#452	1	1	yes	characteristic
408	C₂	C₆₁×#3010	1	1	yes	characteristic
409	C₂	C₆₁×#3340	1	2	yes	—
410	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×#477	C₂	semidirect
5. C₆₁×#2035	C₂	semidirect
6. C₆₁×#1988	C₂	semidirect
8. C₆₁×#1854	C₂	semidirect
9. C₄×#103×C₆₁	C₂	semidirect
178. #25701	C₆₁	direct (N × H)
201. C₂×#498	C₂×C₆₁	semidirect
202. C₂×#477	C₂×C₆₁	semidirect
204. #2035	C₂×C₆₁	semidirect
205. #1988	C₂×C₆₁	semidirect
207. #1854	C₂×C₆₁	semidirect
208. C₄×#103	C₂×C₆₁	semidirect
242. C₆₁	#25701	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×#556	2
C₂×C₆₁×#498	2
C₂×C₆₁×#477	2
C₆₁×#2563	2
C₆₁×#2035	2
C₆₁×#1988	2
C₆₁×#1954	2
C₆₁×#1854	2
C₄×#103×C₆₁	2
#25701	61

Subgroups — C61×#25701 #29529134

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25701 #29529134