Subgroups — C₆₁×#29879 #29533312

Order 15616.

730 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#431	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2851	C₂	1	2	yes	maximal
4	C₆₁×#2088	C₂	1	2	yes	maximal, complemented
5	C₆₁×#2087	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2086	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2077	C₂	1	2	yes	maximal
8	C₆₁×#2076	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#2075	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1991	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1835	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₆₁	C₂²	1	2	yes	—
13	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#499	—	2	4	no	—
15	C₆₁×#431	—	2	4	no	—
16	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×#106×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#389	C₂²	1	2	yes	—
26	C₆₁×#389	C₂²	1	2	yes	—
27	C₆₁×#387	—	2	2	no	—
28	C₆₁×#387	—	2	2	no	—
29	C₆₁×#385	—	2	2	no	—
30	C₆₁×#385	—	2	2	no	—
31	C₆₁×#382	C₂²	1	2	yes	—
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	1	yes	characteristic
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
48	#125×C₆₁	—	2	4	no	—
49	#125×C₆₁	—	2	4	no	—
50	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
54	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄²×C₆₁	—	2	2	no	—
61	C₂×C₄²×C₆₁	—	2	2	no	—
62	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
66	#107×C₆₁	—	2	2	no	—
67	#107×C₆₁	—	2	2	no	—
68	#106×C₆₁	—	2	4	no	—
69	C₄⋊C₈×C₆₁	—	2	2	no	—
70	C₄⋊C₈×C₆₁	—	2	2	no	—
71	C₂²⋊C₈×C₆₁	—	2	2	no	—
72	C₂²⋊C₈×C₆₁	—	2	2	no	—
73	C₄×C₈×C₆₁	—	2	2	no	—
74	C₄×C₈×C₆₁	D₄	1	4	yes	—
75	#95×C₆₁	—	2	2	no	—
76	#95×C₆₁	—	2	2	no	—
77	#95×C₆₁	—	2	2	no	—
78	#95×C₆₁	—	2	2	no	—
79	#95×C₆₁	—	2	2	no	—
80	#95×C₆₁	—	2	2	no	—
81	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	—	2	2	no	—
83	C₂²×C₄×C₆₁	—	2	2	no	—
84	C₂²×C₄×C₆₁	—	2	2	no	—
85	C₂²×C₄×C₆₁	—	2	2	no	—
86	C₂²×C₄×C₆₁	—	2	1	no	—
87	C₂²×C₄×C₆₁	—	2	1	no	—
88	C₂²×C₄×C₆₁	—	2	2	no	—
89	C₂²×C₄×C₆₁	—	2	2	no	—
90	C₂²×C₄×C₆₁	—	2	2	no	—
91	C₂²×C₄×C₆₁	—	2	2	no	—
92	C₂²×C₄×C₆₁	—	2	2	no	—
93	C₂²×C₄×C₆₁	—	2	2	no	—
94	C₂²×C₄×C₆₁	—	4	2	no	—
95	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₆₁	—	2	2	no	—
102	C₂×C₈×C₆₁	—	2	2	no	—
103	C₂×C₈×C₆₁	—	2	1	no	—
104	C₂×C₈×C₆₁	—	2	1	no	—
105	C₂×C₈×C₆₁	—	2	2	no	—
106	C₂×C₈×C₆₁	—	2	2	no	—
107	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
109	C₄⋊C₄×C₆₁	—	2	2	no	—
110	C₄⋊C₄×C₆₁	—	2	2	no	—
111	C₄⋊C₄×C₆₁	—	2	2	no	—
112	C₄⋊C₄×C₆₁	—	2	2	no	—
113	C₄⋊C₄×C₆₁	—	2	2	no	—
114	C₄⋊C₄×C₆₁	—	2	2	no	—
115	C₄⋊C₄×C₆₁	—	2	2	no	—
116	C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₄⋊C₄×C₆₁	—	4	4	no	—
118	C₄⋊C₄×C₆₁	—	4	4	no	—
119	C₄⋊C₄×C₆₁	—	4	4	no	—
120	C₄⋊C₄×C₆₁	—	4	4	no	—
121	C₂²⋊C₄×C₆₁	—	4	4	no	—
122	C₂²⋊C₄×C₆₁	—	4	4	no	—
123	C₄²×C₆₁	—	2	2	no	—
124	C₄²×C₆₁	—	2	2	no	—
125	C₄²×C₆₁	—	2	1	no	—
126	C₄²×C₆₁	—	2	1	no	—
127	C₄²×C₆₁	C₂×D₄	1	2	yes	—
128	C₄²×C₆₁	#41	1	2	yes	—
129	C₂³×C₆₁	—	2	1	no	—
130	C₂³×C₆₁	—	2	2	no	—
131	C₂³×C₆₁	—	2	1	no	—
132	C₂³×C₆₁	—	2	2	no	—
133	C₂³×C₆₁	#135	1	2	yes	—
134	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
135	C₂×C₄×C₆₁	—	2	8	no	—
136	C₂×C₄×C₆₁	—	2	1	no	—
137	C₂×C₄×C₆₁	—	2	1	no	—
138	C₂×C₄×C₆₁	—	2	1	no	—
139	C₂×C₄×C₆₁	—	2	1	no	—
140	C₂×C₄×C₆₁	—	2	2	no	—
141	C₂×C₄×C₆₁	—	2	1	no	—
142	C₂×C₄×C₆₁	—	2	1	no	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	4	4	no	—
146	C₂×C₄×C₆₁	—	4	1	no	—
147	C₂×C₄×C₆₁	—	4	1	no	—
148	C₂×C₄×C₆₁	—	4	2	no	—
149	C₂×C₄×C₆₁	—	4	2	no	—
150	C₂×C₄×C₆₁	—	4	2	no	—
151	C₂×C₄×C₆₁	—	4	2	no	—
152	C₂×C₄×C₆₁	—	4	2	no	—
153	C₂×C₄×C₆₁	—	4	2	no	—
154	C₂×C₄×C₆₁	—	4	2	no	—
155	C₂×C₄×C₆₁	—	4	2	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	#121	1	2	yes	—
162	C₂×C₄×C₆₁	#121	1	2	yes	—
163	C₂×C₄×C₆₁	#135	1	2	yes	—
164	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
167	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
168	C₈×C₆₁	—	2	2	no	—
169	C₈×C₆₁	—	2	2	no	—
170	C₈×C₆₁	—	4	1	no	—
171	C₈×C₆₁	—	4	1	no	—
172	#29879	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₆₁	—	2	4	no	—
174	C₂²×C₆₁	—	2	2	no	—
175	C₂²×C₆₁	—	4	1	no	—
176	C₂²×C₆₁	—	4	2	no	—
177	C₂²×C₆₁	—	4	1	no	—
178	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
179	C₂²×C₆₁	#536	1	2	yes	—
180	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
181	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
182	C₂²×C₆₁	#575	1	2	yes	—
183	C₄×C₆₁	—	2	2	no	—
184	C₄×C₆₁	—	2	2	no	—
185	C₄×C₆₁	—	2	2	no	—
186	C₄×C₆₁	—	4	1	no	—
187	C₄×C₆₁	—	4	1	no	—
188	C₄×C₆₁	—	8	2	no	—
189	C₄×C₆₁	—	8	2	no	—
190	C₄×C₆₁	—	8	2	no	—
191	C₄×C₆₁	—	8	2	no	—
192	C₄×C₆₁	#536	1	1	yes	characteristic
193	C₄×C₆₁	#536	1	1	yes	characteristic
194	C₄×C₆₁	#541	1	2	yes	—
195	C₂×#499	C₂×C₆₁	1	1	yes	characteristic, complemented
196	C₂×#431	C₂×C₆₁	1	1	yes	characteristic
197	#2851	C₂×C₆₁	1	2	yes	—
198	#2088	C₂×C₆₁	1	2	yes	complemented
199	#2087	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#2086	C₂×C₆₁	1	1	yes	characteristic, complemented
201	#2077	C₂×C₆₁	1	2	yes	—
202	#2076	C₂×C₆₁	1	1	yes	characteristic
203	#2075	C₂×C₆₁	1	1	yes	characteristic
204	#1991	C₂×C₆₁	1	2	yes	complemented
205	#1835	C₂×C₆₁	1	1	yes	characteristic, complemented
206	C₂×C₆₁	—	4	2	no	—
207	C₂×C₆₁	#2621	1	1	yes	characteristic
208	C₂×C₆₁	#3050	1	1	yes	characteristic
209	C₂×C₆₁	#3054	1	1	yes	characteristic
210	C₂×C₆₁	#3232	1	2	yes	—
211	C₂×C₆₁	#3233	1	2	yes	—
212	C₂×#125	C₂²×C₆₁	1	2	yes	—
213	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
214	#499	—	2	4	no	—
215	#431	—	2	4	no	—
216	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
217	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
218	C₂×#106	C₂²×C₆₁	1	2	yes	—
219	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
221	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
222	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
223	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
225	#389	C₂²×C₆₁	1	2	yes	—
226	#389	C₂²×C₆₁	1	2	yes	—
227	#387	—	2	2	no	—
228	#387	—	2	2	no	—
229	#385	—	2	2	no	—
230	#385	—	2	2	no	—
231	#382	C₂²×C₆₁	1	2	yes	—
232	#380	C₂²×C₆₁	1	2	yes	—
233	#380	C₂²×C₆₁	1	2	yes	—
234	#340	C₂²×C₆₁	1	1	yes	characteristic
235	#340	C₂²×C₆₁	1	2	yes	—
236	#340	C₂²×C₆₁	1	1	yes	characteristic
237	#340	C₂²×C₆₁	1	2	yes	—
238	#340	C₂²×C₆₁	1	2	yes	—
239	#340	C₂²×C₆₁	1	2	yes	—
240	#340	C₂²×C₆₁	1	2	yes	—
241	C₆₁	#29879	1	1	yes	characteristic, direct product factor, Sylow
242	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
243	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
244	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
245	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
249	#125	—	2	4	no	—
250	#125	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
257	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
258	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
264	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
267	#107	—	2	2	no	—
268	#107	—	2	2	no	—
269	#106	—	2	4	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₄⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	2	2	no	—
274	C₄×C₈	—	2	2	no	—
275	C₄×C₈	D₄×C₆₁	1	4	yes	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
297	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
309	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₂²⋊C₄	—	4	4	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	C₂×D₄×C₆₁	1	2	yes	—
329	C₄²	#41×C₆₁	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	1	no	—
334	C₂³	#135×C₆₁	1	2	yes	—
335	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	#121×C₆₁	1	2	yes	—
363	C₂×C₄	#121×C₆₁	1	2	yes	—
364	C₂×C₄	#135×C₆₁	1	2	yes	—
365	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
366	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
367	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
368	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
369	C₈	—	2	2	no	—
370	C₈	—	2	2	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	2	no	—
378	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
379	C₂²	C₆₁×#536	1	2	yes	—
380	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
381	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
382	C₂²	C₆₁×#575	1	2	yes	—
383	C₄	—	2	2	no	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	8	2	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	C₆₁×#536	1	1	yes	characteristic
393	C₄	C₆₁×#536	1	1	yes	characteristic
394	C₄	C₆₁×#541	1	2	yes	—
395	C₂	—	4	2	no	—
396	C₂	C₆₁×#2621	1	1	yes	characteristic
397	C₂	C₆₁×#3050	1	1	yes	characteristic
398	C₂	C₆₁×#3054	1	1	yes	characteristic
399	C₂	C₆₁×#3232	1	2	yes	—
400	C₂	C₆₁×#3233	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#499	C₂	semidirect
4. C₆₁×#2088	C₂	semidirect
5. C₆₁×#2087	C₂	semidirect
6. C₆₁×#2086	C₂	semidirect
10. C₆₁×#1991	C₂	semidirect
11. C₆₁×#1835	C₂	semidirect
172. #29879	C₆₁	direct (N × H)
195. C₂×#499	C₂×C₆₁	semidirect
198. #2088	C₂×C₆₁	semidirect
199. #2087	C₂×C₆₁	semidirect
200. #2086	C₂×C₆₁	semidirect
204. #1991	C₂×C₆₁	semidirect
205. #1835	C₂×C₆₁	semidirect
241. C₆₁	#29879	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×#499	2
C₂×C₆₁×#431	2
C₆₁×#2851	2
C₆₁×#2088	2
C₆₁×#2087	2
C₆₁×#2086	2
C₆₁×#2077	2
C₆₁×#2076	2
C₆₁×#2075	2
C₆₁×#1991	2
C₆₁×#1835	2
#29879	61

Subgroups — C61×#29879 #29533312

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29879 #29533312