Subgroups — C₆₁×#29882 #29533315

Order 15616.

672 conjugacy classes of subgroups.

The subgroup lattice has 396 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×#433	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2629	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×#1992	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1834	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₆₁	C₂²	1	2	yes	—
13	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#499	—	2	4	no	—
15	C₆₁×#433	—	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×#97×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#398	—	2	2	no	—
26	C₆₁×#398	—	2	2	no	—
27	C₆₁×#396	—	2	2	no	—
28	C₆₁×#396	—	2	2	no	—
29	C₆₁×#389	C₂²	1	2	yes	—
30	C₆₁×#389	C₂²	1	2	yes	—
31	C₆₁×#384	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	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×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	#125×C₆₁	—	2	4	no	—
47	#125×C₆₁	—	2	4	no	—
48	#117×C₆₁	—	2	2	no	—
49	#117×C₆₁	—	2	2	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	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
59	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
68	#107×C₆₁	—	2	2	no	—
69	#107×C₆₁	—	2	2	no	—
70	#106×C₆₁	—	2	4	no	—
71	C₄⋊C₈×C₆₁	—	2	2	no	—
72	C₄⋊C₈×C₆₁	—	2	2	no	—
73	C₂²⋊C₈×C₆₁	—	2	2	no	—
74	C₂²⋊C₈×C₆₁	—	2	2	no	—
75	#97×C₆₁	—	2	2	no	—
76	C₄×C₈×C₆₁	D₄	1	4	yes	—
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	1	no	—
83	C₂²×C₄×C₆₁	—	2	1	no	—
84	C₂²×C₄×C₆₁	—	2	2	no	—
85	C₂²×C₄×C₆₁	—	2	2	no	—
86	C₂²×C₄×C₆₁	—	2	2	no	—
87	C₂²×C₄×C₆₁	—	2	2	no	—
88	C₂²×C₄×C₆₁	—	2	2	no	—
89	C₂²×C₄×C₆₁	—	2	2	no	—
90	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₆₁	—	2	2	no	—
97	C₂×C₈×C₆₁	—	2	2	no	—
98	C₂×C₈×C₆₁	—	2	1	no	—
99	C₂×C₈×C₆₁	—	2	1	no	—
100	C₂×C₈×C₆₁	—	2	2	no	—
101	C₂×C₈×C₆₁	—	2	2	no	—
102	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
103	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
104	C₄⋊C₄×C₆₁	—	2	2	no	—
105	C₄⋊C₄×C₆₁	—	2	2	no	—
106	C₄⋊C₄×C₆₁	—	2	2	no	—
107	C₄⋊C₄×C₆₁	—	2	2	no	—
108	C₄⋊C₄×C₆₁	—	2	2	no	—
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	—	4	4	no	—
115	C₄⋊C₄×C₆₁	—	4	4	no	—
116	C₄⋊C₄×C₆₁	—	8	2	no	—
117	C₄⋊C₄×C₆₁	—	8	2	no	—
118	C₄⋊C₄×C₆₁	—	8	2	no	—
119	C₄⋊C₄×C₆₁	—	8	2	no	—
120	C₂²⋊C₄×C₆₁	—	2	2	no	—
121	C₂²⋊C₄×C₆₁	—	2	2	no	—
122	C₂²⋊C₄×C₆₁	—	8	2	no	—
123	C₂²⋊C₄×C₆₁	—	8	2	no	—
124	C₄²×C₆₁	—	2	1	no	—
125	C₄²×C₆₁	—	2	1	no	—
126	C₄²×C₆₁	C₂×D₄	1	2	yes	—
127	C₄²×C₆₁	#41	1	2	yes	—
128	C₂³×C₆₁	—	2	1	no	—
129	C₂³×C₆₁	—	2	2	no	—
130	C₂³×C₆₁	—	2	1	no	—
131	C₂³×C₆₁	—	2	2	no	—
132	C₂³×C₆₁	—	2	1	no	—
133	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
134	C₂×C₄×C₆₁	—	2	1	no	—
135	C₂×C₄×C₆₁	—	2	2	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	2	no	—
143	C₂×C₄×C₆₁	—	2	1	no	—
144	C₂×C₄×C₆₁	—	4	1	no	—
145	C₂×C₄×C₆₁	—	4	1	no	—
146	C₂×C₄×C₆₁	—	4	2	no	—
147	C₂×C₄×C₆₁	—	4	2	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	#121	1	2	yes	—
160	C₂×C₄×C₆₁	#121	1	2	yes	—
161	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
164	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
165	C₈×C₆₁	—	2	2	no	—
166	C₈×C₆₁	—	2	2	no	—
167	C₈×C₆₁	—	4	1	no	—
168	C₈×C₆₁	—	4	1	no	—
169	#29882	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₆₁	—	4	1	no	—
171	C₂²×C₆₁	—	4	2	no	—
172	C₂²×C₆₁	—	4	2	no	—
173	C₂²×C₆₁	—	4	1	no	—
174	C₂²×C₆₁	—	4	1	no	—
175	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
176	C₂²×C₆₁	#536	1	2	yes	—
177	C₂²×C₆₁	#576	1	1	yes	characteristic
178	C₂²×C₆₁	#577	1	2	yes	—
179	C₂²×C₆₁	#578	1	1	yes	characteristic
180	C₄×C₆₁	—	2	2	no	—
181	C₄×C₆₁	—	2	2	no	—
182	C₄×C₆₁	—	4	1	no	—
183	C₄×C₆₁	—	4	1	no	—
184	C₄×C₆₁	—	4	1	no	—
185	C₄×C₆₁	—	8	2	no	—
186	C₄×C₆₁	—	8	2	no	—
187	C₄×C₆₁	—	8	2	no	—
188	C₄×C₆₁	—	8	2	no	—
189	C₄×C₆₁	#536	1	1	yes	characteristic
190	C₄×C₆₁	#536	1	1	yes	characteristic
191	C₄×C₆₁	#541	1	2	yes	—
192	C₂×#499	C₂×C₆₁	1	1	yes	characteristic, complemented
193	C₂×#433	C₂×C₆₁	1	1	yes	characteristic
194	#2629	C₂×C₆₁	1	2	yes	—
195	#2088	C₂×C₆₁	1	2	yes	complemented
196	#2087	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#2086	C₂×C₆₁	1	1	yes	characteristic, complemented
198	#2077	C₂×C₆₁	1	2	yes	—
199	#2076	C₂×C₆₁	1	1	yes	characteristic
200	#2075	C₂×C₆₁	1	1	yes	characteristic
201	#1992	C₂×C₆₁	1	2	yes	complemented
202	#1834	C₂×C₆₁	1	1	yes	characteristic, complemented
203	C₂×C₆₁	—	8	1	no	—
204	C₂×C₆₁	#2621	1	1	yes	characteristic
205	C₂×C₆₁	#3060	1	1	yes	characteristic
206	C₂×C₆₁	#3061	1	1	yes	characteristic
207	C₂×C₆₁	#3241	1	2	yes	—
208	C₂×C₆₁	#3242	1	2	yes	—
209	C₂×#125	C₂²×C₆₁	1	2	yes	—
210	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
211	#499	—	2	4	no	—
212	#433	—	2	4	no	—
213	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
214	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
215	C₂×#106	C₂²×C₆₁	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
218	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
220	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
222	#398	—	2	2	no	—
223	#398	—	2	2	no	—
224	#396	—	2	2	no	—
225	#396	—	2	2	no	—
226	#389	C₂²×C₆₁	1	2	yes	—
227	#389	C₂²×C₆₁	1	2	yes	—
228	#384	C₂²×C₆₁	1	2	yes	—
229	#380	C₂²×C₆₁	1	2	yes	—
230	#380	C₂²×C₆₁	1	2	yes	—
231	#340	C₂²×C₆₁	1	1	yes	characteristic
232	#340	C₂²×C₆₁	1	2	yes	—
233	#340	C₂²×C₆₁	1	1	yes	characteristic
234	#340	C₂²×C₆₁	1	2	yes	—
235	#340	C₂²×C₆₁	1	2	yes	—
236	#340	C₂²×C₆₁	1	2	yes	—
237	#340	C₂²×C₆₁	1	2	yes	—
238	C₆₁	#29882	1	1	yes	characteristic, direct product factor, Sylow
239	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
240	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
244	#125	—	2	4	no	—
245	#125	—	2	4	no	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	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	D₄×C₆₁	1	1	yes	characteristic
255	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
265	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
266	#107	—	2	2	no	—
267	#107	—	2	2	no	—
268	#106	—	2	4	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	2	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	#97	—	2	2	no	—
274	C₄×C₈	D₄×C₆₁	1	4	yes	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	#95	—	2	2	no	—
279	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
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	2	no	—
288	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
293	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	1	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
301	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	4	4	no	—
313	C₄⋊C₄	—	4	4	no	—
314	C₄⋊C₄	—	8	2	no	—
315	C₄⋊C₄	—	8	2	no	—
316	C₄⋊C₄	—	8	2	no	—
317	C₄⋊C₄	—	8	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₂²⋊C₄	—	8	2	no	—
322	C₄²	—	2	1	no	—
323	C₄²	—	2	1	no	—
324	C₄²	C₂×D₄×C₆₁	1	2	yes	—
325	C₄²	#41×C₆₁	1	2	yes	—
326	C₂³	—	2	2	no	—
327	C₂³	—	2	1	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	1	no	—
330	C₂³	—	2	1	no	—
331	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	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	#121×C₆₁	1	2	yes	—
358	C₂×C₄	#121×C₆₁	1	2	yes	—
359	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
360	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
361	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
362	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	—	4	1	no	—
366	C₈	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
373	C₂²	C₆₁×#536	1	2	yes	—
374	C₂²	C₆₁×#576	1	1	yes	characteristic
375	C₂²	C₆₁×#577	1	2	yes	—
376	C₂²	C₆₁×#578	1	1	yes	characteristic
377	C₄	—	2	2	no	—
378	C₄	—	2	2	no	—
379	C₄	—	4	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	8	2	no	—
383	C₄	—	8	2	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	C₆₁×#536	1	1	yes	characteristic
387	C₄	C₆₁×#536	1	1	yes	characteristic
388	C₄	C₆₁×#541	1	2	yes	—
389	C₂	—	8	1	no	—
390	C₂	C₆₁×#2621	1	1	yes	characteristic
391	C₂	C₆₁×#3060	1	1	yes	characteristic
392	C₂	C₆₁×#3061	1	1	yes	characteristic
393	C₂	C₆₁×#3241	1	2	yes	—
394	C₂	C₆₁×#3242	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 ◁ C₂×#117×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×#1992	C₂	semidirect
11. C₆₁×#1834	C₂	semidirect
169. #29882	C₆₁	direct (N × H)
192. C₂×#499	C₂×C₆₁	semidirect
195. #2088	C₂×C₆₁	semidirect
196. #2087	C₂×C₆₁	semidirect
197. #2086	C₂×C₆₁	semidirect
201. #1992	C₂×C₆₁	semidirect
202. #1834	C₂×C₆₁	semidirect
238. C₆₁	#29882	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×#433	2
C₆₁×#2629	2
C₆₁×#2088	2
C₆₁×#2087	2
C₆₁×#2086	2
C₆₁×#2077	2
C₆₁×#2076	2
C₆₁×#2075	2
C₆₁×#1992	2
C₆₁×#1834	2
#29882	61

Subgroups — C61×#29882 #29533315

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29882 #29533315