Subgroups — C₆₁×#8109 #29511542

Order 15616.

606 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1305	C₂	1	4	yes	maximal
5	C₂×#117×C₆₁	C₄	1	2	yes	—
6	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
7	C₆₁×#432	—	2	1	no	—
8	C₆₁×#432	—	2	1	no	—
9	C₆₁×#432	—	2	1	no	—
10	C₆₁×#432	C₄	1	2	yes	complemented
11	C₆₁×#431	—	2	1	no	—
12	C₆₁×#431	—	2	1	no	—
13	C₆₁×#431	—	2	1	no	—
14	C₆₁×#431	C₄	1	2	yes	complemented
15	C₆₁×#423	—	2	1	no	—
16	C₆₁×#423	C₄	1	2	yes	complemented
17	C₆₁×#407	C₂²	1	2	yes	—
18	C₆₁×#407	C₂²	1	2	yes	—
19	C₄×M₁₆×C₆₁	—	2	1	no	—
20	C₄×M₁₆×C₆₁	C₄	1	2	yes	complemented
21	C₆₁×#384	—	2	1	no	—
22	C₆₁×#382	—	2	1	no	—
23	C₆₁×#380	C₄	1	2	yes	—
24	C₆₁×#380	C₂²	1	2	yes	—
25	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
26	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
27	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
30	C₂×M₁₆×C₆₁	—	2	2	no	—
31	C₂×M₁₆×C₆₁	C₂×C₄	1	4	yes	—
32	#117×C₆₁	—	4	4	no	—
33	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
34	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
35	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
36	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₆₁	—	2	2	no	—
38	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
49	C₂×C₄²×C₆₁	Q₈	1	1	yes	characteristic
50	C₄⋊C₈×C₆₁	—	2	2	no	—
51	C₄⋊C₈×C₆₁	—	2	2	no	—
52	C₄⋊C₈×C₆₁	—	2	2	no	—
53	C₄⋊C₈×C₆₁	—	2	2	no	—
54	C₂²⋊C₈×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	—
58	#97×C₆₁	—	2	2	no	—
59	#97×C₆₁	—	2	2	no	—
60	C₄×C₈×C₆₁	—	2	2	no	—
61	C₄×C₈×C₆₁	—	2	2	no	—
62	#95×C₆₁	—	2	2	no	—
63	#95×C₆₁	—	2	2	no	—
64	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₆₁	—	2	2	no	—
66	C₂²×C₄×C₆₁	—	2	2	no	—
67	C₂²×C₄×C₆₁	—	2	4	no	—
68	C₂²×C₄×C₆₁	—	4	2	no	—
69	C₂²×C₄×C₆₁	—	4	2	no	—
70	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
72	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₆₁	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₁	C₂×Q₈	1	1	yes	characteristic
88	M₁₆×C₆₁	—	4	4	no	—
89	M₁₆×C₆₁	—	4	4	no	—
90	C₂×C₈×C₆₁	—	2	4	no	—
91	C₂×C₈×C₆₁	—	2	4	no	—
92	C₄⋊C₄×C₆₁	—	4	4	no	—
93	C₄⋊C₄×C₆₁	—	4	4	no	—
94	C₄⋊C₄×C₆₁	—	4	4	no	—
95	C₂²⋊C₄×C₆₁	—	4	4	no	—
96	C₄²×C₆₁	—	4	4	no	—
97	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₆₁	C₄⋊C₄	1	1	yes	characteristic
113	C₂³×C₆₁	—	2	1	no	—
114	C₂³×C₆₁	—	2	1	no	—
115	C₂³×C₆₁	—	4	1	no	—
116	C₂³×C₆₁	—	4	1	no	—
117	C₂³×C₆₁	C₂×C₄²	1	1	yes	characteristic
118	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
120	C₂×C₄×C₆₁	—	2	1	no	—
121	C₂×C₄×C₆₁	—	2	1	no	—
122	C₂×C₄×C₆₁	—	2	2	no	—
123	C₂×C₄×C₆₁	—	2	2	no	—
124	C₂×C₄×C₆₁	—	2	2	no	—
125	C₂×C₄×C₆₁	—	2	2	no	—
126	C₂×C₄×C₆₁	—	2	2	no	—
127	C₂×C₄×C₆₁	—	2	2	no	—
128	C₂×C₄×C₆₁	—	2	2	no	—
129	C₂×C₄×C₆₁	—	2	2	no	—
130	C₂×C₄×C₆₁	—	2	2	no	—
131	C₂×C₄×C₆₁	—	2	2	no	—
132	C₂×C₄×C₆₁	—	4	1	no	—
133	C₂×C₄×C₆₁	—	4	1	no	—
134	C₂×C₄×C₆₁	—	4	1	no	—
135	C₂×C₄×C₆₁	—	4	1	no	—
136	C₂×C₄×C₆₁	—	4	1	no	—
137	C₂×C₄×C₆₁	—	4	1	no	—
138	C₂×C₄×C₆₁	—	4	4	no	—
139	C₂×C₄×C₆₁	—	4	4	no	—
140	C₂×C₄×C₆₁	—	4	4	no	—
141	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
144	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
146	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
148	C₂×C₄×C₆₁	#95	1	1	yes	characteristic
149	C₂×C₄×C₆₁	#100	1	2	yes	—
150	C₂×C₄×C₆₁	#101	1	2	yes	—
151	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
153	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
155	C₈×C₆₁	—	4	4	no	—
156	C₈×C₆₁	—	4	4	no	—
157	#8109	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂²×C₆₁	—	2	1	no	—
159	C₂²×C₆₁	—	2	1	no	—
160	C₂²×C₆₁	—	2	1	no	—
161	C₂²×C₆₁	—	2	1	no	—
162	C₂²×C₆₁	—	2	1	no	—
163	C₂²×C₆₁	—	2	1	no	—
164	C₂²×C₆₁	—	2	1	no	—
165	C₂²×C₆₁	—	2	1	no	—
166	C₂²×C₆₁	—	4	2	no	—
167	C₂²×C₆₁	—	4	2	no	—
168	C₂²×C₆₁	C₂×#95	1	1	yes	characteristic
169	C₂²×C₆₁	C₂×#100	1	1	yes	characteristic
170	C₂²×C₆₁	C₂×#101	1	1	yes	characteristic
171	C₄×C₆₁	—	2	1	no	—
172	C₄×C₆₁	—	2	1	no	—
173	C₄×C₆₁	—	2	1	no	—
174	C₄×C₆₁	—	2	1	no	—
175	C₄×C₆₁	—	2	1	no	—
176	C₄×C₆₁	—	2	1	no	—
177	C₄×C₆₁	—	2	1	no	—
178	C₄×C₆₁	—	2	1	no	—
179	C₄×C₆₁	—	8	4	no	—
180	C₄×C₆₁	#343	1	2	yes	—
181	C₄×C₆₁	#343	1	2	yes	—
182	C₄×C₆₁	#344	1	2	yes	—
183	C₄×C₆₁	#410	1	2	yes	—
184	#2920	C₂×C₆₁	1	1	yes	characteristic
185	#2920	C₂×C₆₁	1	1	yes	characteristic
186	#2285	C₂×C₆₁	1	1	yes	characteristic
187	#1305	C₂×C₆₁	1	4	yes	—
188	C₂×C₆₁	—	2	1	no	—
189	C₂×C₆₁	—	2	1	no	—
190	C₂×C₆₁	—	4	1	no	—
191	C₂×C₆₁	—	4	1	no	—
192	C₂×C₆₁	#1740	1	1	yes	characteristic
193	C₂×C₆₁	C₂×#343	1	1	yes	characteristic
194	C₂×C₆₁	C₂×#344	1	1	yes	characteristic
195	C₂×#117	C₄×C₆₁	1	2	yes	—
196	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
197	#432	—	2	1	no	—
198	#432	—	2	1	no	—
199	#432	—	2	1	no	—
200	#432	C₄×C₆₁	1	2	yes	complemented
201	#431	—	2	1	no	—
202	#431	—	2	1	no	—
203	#431	—	2	1	no	—
204	#431	C₄×C₆₁	1	2	yes	complemented
205	#423	—	2	1	no	—
206	#423	C₄×C₆₁	1	2	yes	complemented
207	#407	C₂²×C₆₁	1	2	yes	—
208	#407	C₂²×C₆₁	1	2	yes	—
209	C₄×M₁₆	—	2	1	no	—
210	C₄×M₁₆	C₄×C₆₁	1	2	yes	complemented
211	#384	—	2	1	no	—
212	#382	—	2	1	no	—
213	#380	C₄×C₆₁	1	2	yes	—
214	#380	C₂²×C₆₁	1	2	yes	—
215	C₄×C₄⋊C₄	—	2	1	no	—
216	C₄×C₄⋊C₄	—	2	1	no	—
217	C₆₁	#8109	1	1	yes	characteristic, direct product factor, Sylow
218	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
219	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
220	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
221	C₂×M₁₆	—	2	2	no	—
222	C₂×M₁₆	C₂×C₄×C₆₁	1	4	yes	—
223	#117	—	4	4	no	—
224	C₂×C₄⋊C₄	—	2	2	no	—
225	C₂×C₄⋊C₄	—	2	2	no	—
226	C₂×C₄⋊C₄	—	2	2	no	—
227	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
228	C₂×C₄²	—	2	2	no	—
229	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
230	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
231	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
232	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
233	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
234	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
235	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
236	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
237	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
238	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
239	C₂×C₄²	Q₈×C₆₁	1	1	yes	characteristic
240	C₂×C₄²	Q₈×C₆₁	1	1	yes	characteristic
241	C₄⋊C₈	—	2	2	no	—
242	C₄⋊C₈	—	2	2	no	—
243	C₄⋊C₈	—	2	2	no	—
244	C₄⋊C₈	—	2	2	no	—
245	C₂²⋊C₈	—	2	2	no	—
246	C₂²⋊C₈	—	2	2	no	—
247	C₂²⋊C₈	—	2	2	no	—
248	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	—
249	#97	—	2	2	no	—
250	#97	—	2	2	no	—
251	C₄×C₈	—	2	2	no	—
252	C₄×C₈	—	2	2	no	—
253	#95	—	2	2	no	—
254	#95	—	2	2	no	—
255	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
256	C₂²×C₄	—	2	2	no	—
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	C₄²×C₆₁	1	1	yes	characteristic
262	C₂²×C₄	C₄²×C₆₁	1	1	yes	characteristic
263	C₂²×C₄	C₄²×C₆₁	1	1	yes	characteristic
264	C₂²×C₄	C₄²×C₆₁	1	1	yes	characteristic
265	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
266	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
267	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
268	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
269	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
270	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
271	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
272	C₂²×C₄	C₄⋊C₄×C₆₁	1	1	yes	characteristic
273	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
274	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
276	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
278	C₂²×C₄	C₂×Q₈×C₆₁	1	1	yes	characteristic
279	M₁₆	—	4	4	no	—
280	M₁₆	—	4	4	no	—
281	C₂×C₈	—	2	4	no	—
282	C₂×C₈	—	2	4	no	—
283	C₄⋊C₄	—	4	4	no	—
284	C₄⋊C₄	—	4	4	no	—
285	C₄⋊C₄	—	4	4	no	—
286	C₂²⋊C₄	—	4	4	no	—
287	C₄²	—	4	4	no	—
288	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
289	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
290	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
291	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
292	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
293	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
294	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
295	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
296	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
297	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
298	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
299	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
300	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
301	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
302	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
303	C₄²	C₄⋊C₄×C₆₁	1	1	yes	characteristic
304	C₂³	—	2	1	no	—
305	C₂³	—	2	1	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	C₂×C₄²×C₆₁	1	1	yes	characteristic
309	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
310	C₂³	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	4	1	no	—
324	C₂×C₄	—	4	1	no	—
325	C₂×C₄	—	4	1	no	—
326	C₂×C₄	—	4	1	no	—
327	C₂×C₄	—	4	1	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
333	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
334	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
335	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
336	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
337	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
338	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
339	C₂×C₄	#95×C₆₁	1	1	yes	characteristic
340	C₂×C₄	#100×C₆₁	1	2	yes	—
341	C₂×C₄	#101×C₆₁	1	2	yes	—
342	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
343	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
344	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
345	C₂×C₄	C₂×C₄⋊C₄×C₆₁	1	1	yes	characteristic
346	C₈	—	4	4	no	—
347	C₈	—	4	4	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	1	no	—
352	C₂²	—	2	1	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	C₂×#95×C₆₁	1	1	yes	characteristic
359	C₂²	C₂×#100×C₆₁	1	1	yes	characteristic
360	C₂²	C₂×#101×C₆₁	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	8	4	no	—
370	C₄	C₆₁×#343	1	2	yes	—
371	C₄	C₆₁×#343	1	2	yes	—
372	C₄	C₆₁×#344	1	2	yes	—
373	C₄	C₆₁×#410	1	2	yes	—
374	C₂	—	2	1	no	—
375	C₂	—	2	1	no	—
376	C₂	—	4	1	no	—
377	C₂	—	4	1	no	—
378	C₂	C₆₁×#1740	1	1	yes	characteristic
379	C₂	C₂×C₆₁×#343	1	1	yes	characteristic
380	C₂	C₂×C₆₁×#344	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#95
commutator	C₂³	C₂×C₄²×C₆₁
Frattini, cosocle	C₂³×C₄	C₂³×C₆₁
prime radical	C₂⁴×C₆₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₆₁×#432	C₄	semidirect
14. C₆₁×#431	C₄	semidirect
16. C₆₁×#423	C₄	semidirect
20. C₄×M₁₆×C₆₁	C₄	semidirect
157. #8109	C₆₁	direct (N × H)
200. #432	C₄×C₆₁	semidirect
204. #431	C₄×C₆₁	semidirect
206. #423	C₄×C₆₁	semidirect
210. C₄×M₁₆	C₄×C₆₁	semidirect
217. C₆₁	#8109	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₆₁×#2920	2
C₆₁×#2285	2
C₆₁×#1305	2
#8109	61

Subgroups — C61×#8109 #29511542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#8109 #29511542