Subgroups — C₆₁×#21025 #29524458

Order 15616.

906 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×#424	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#405	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2285	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1917	C₂	1	4	yes	maximal, complemented
5	C₆₁×#1916	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1729	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1729	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1728	C₂	1	1	yes	maximal, characteristic
9	C₂×C₆₁×#336	C₂	1	1	yes	maximal, characteristic
10	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
17	C₆₁×#424	—	2	4	no	—
18	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
20	C₆₁×#405	—	2	4	no	—
21	C₂×#97×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
23	C₆₁×#384	C₄	1	1	yes	characteristic
24	C₆₁×#384	C₄	1	1	yes	characteristic
25	C₆₁×#382	C₄	1	1	yes	characteristic
26	C₆₁×#382	C₄	1	1	yes	characteristic
27	C₆₁×#380	C₄	1	4	yes	—
28	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
29	C₆₁×#336	C₂²	1	2	yes	—
30	C₆₁×#336	C₂²	1	4	yes	—
31	C₆₁×#336	C₂²	1	4	yes	—
32	C₆₁×#336	C₂²	1	4	yes	—
33	C₆₁×#336	C₂²	1	2	yes	—
34	C₂³×C₄×C₆₁	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
36	C₂×M₁₆×C₆₁	—	2	2	no	—
37	C₂×M₁₆×C₆₁	—	2	2	no	—
38	C₂×M₁₆×C₆₁	—	2	2	no	—
39	C₂×M₁₆×C₆₁	—	2	2	no	—
40	C₂×M₁₆×C₆₁	—	2	2	no	—
41	C₂×M₁₆×C₆₁	Q₈	1	4	yes	—
42	C₂²×C₈×C₆₁	—	2	2	no	—
43	C₂²×C₈×C₆₁	—	2	2	no	—
44	C₂²×C₈×C₆₁	—	2	2	no	—
45	C₂²×C₈×C₆₁	—	2	2	no	—
46	C₂²×C₈×C₆₁	—	2	2	no	—
47	C₂²×C₈×C₆₁	D₄	1	4	yes	—
48	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
49	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
53	#117×C₆₁	—	2	2	no	—
54	#117×C₆₁	—	2	2	no	—
55	#117×C₆₁	—	2	2	no	—
56	#117×C₆₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
58	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
64	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₆₁	—	2	2	no	—
66	C₂×C₄²×C₆₁	—	2	2	no	—
67	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
70	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
71	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
72	C₄⋊C₈×C₆₁	—	2	4	no	—
73	C₄⋊C₈×C₆₁	—	2	4	no	—
74	#97×C₆₁	—	2	4	no	—
75	C₄×C₈×C₆₁	—	2	4	no	—
76	#95×C₆₁	C₂×C₄	1	4	yes	—
77	#95×C₆₁	C₂×C₄	1	4	yes	—
78	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₁	—	2	4	no	—
80	C₂²×C₄×C₆₁	—	2	4	no	—
81	C₂²×C₄×C₆₁	—	4	2	no	—
82	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₆₁	#41	1	2	yes	—
92	C₂²×C₄×C₆₁	#41	1	2	yes	—
93	C₂²×C₄×C₆₁	#41	1	2	yes	—
94	C₂²×C₄×C₆₁	#41	1	2	yes	—
95	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
96	M₁₆×C₆₁	—	2	8	no	—
97	M₁₆×C₆₁	—	4	4	no	—
98	C₂×C₈×C₆₁	—	2	8	no	—
99	C₂×C₈×C₆₁	—	2	2	no	—
100	C₂×C₈×C₆₁	—	2	1	no	—
101	C₂×C₈×C₆₁	—	2	1	no	—
102	C₂×C₈×C₆₁	—	2	1	no	—
103	C₂×C₈×C₆₁	—	2	1	no	—
104	C₂×C₈×C₆₁	—	2	2	no	—
105	C₂×C₈×C₆₁	—	2	2	no	—
106	C₂×C₈×C₆₁	—	2	2	no	—
107	C₂×C₈×C₆₁	—	2	2	no	—
108	C₂×C₈×C₆₁	—	2	2	no	—
109	C₂×C₈×C₆₁	—	2	2	no	—
110	C₂×C₈×C₆₁	—	2	2	no	—
111	C₂×C₈×C₆₁	—	4	4	no	—
112	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₆₁	C₂×Q₈	1	4	yes	—
115	C₄⋊C₄×C₆₁	—	2	2	no	—
116	C₄⋊C₄×C₆₁	—	2	2	no	—
117	C₄⋊C₄×C₆₁	—	2	2	no	—
118	C₄⋊C₄×C₆₁	—	2	2	no	—
119	C₄⋊C₄×C₆₁	—	2	8	no	—
120	C₄⋊C₄×C₆₁	—	4	4	no	—
121	C₂²⋊C₄×C₆₁	—	2	4	no	—
122	C₂²⋊C₄×C₆₁	—	2	4	no	—
123	C₄²×C₆₁	—	2	2	no	—
124	C₄²×C₆₁	—	2	2	no	—
125	C₄²×C₆₁	—	2	2	no	—
126	C₄²×C₆₁	—	2	2	no	—
127	C₄²×C₆₁	—	2	2	no	—
128	C₄²×C₆₁	—	2	2	no	—
129	C₄²×C₆₁	—	2	2	no	—
130	C₄²×C₆₁	—	2	2	no	—
131	C₂³×C₆₁	—	2	2	no	—
132	C₂³×C₆₁	—	2	2	no	—
133	C₂³×C₆₁	#117	1	2	yes	—
134	C₂³×C₆₁	C₄×D₄	1	2	yes	—
135	C₂³×C₆₁	C₄×Q₈	1	2	yes	—
136	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₁	—	2	2	no	—
138	C₂×C₄×C₆₁	—	2	2	no	—
139	C₂×C₄×C₆₁	—	2	2	no	—
140	C₂×C₄×C₆₁	—	2	2	no	—
141	C₂×C₄×C₆₁	—	2	2	no	—
142	C₂×C₄×C₆₁	—	2	2	no	—
143	C₂×C₄×C₆₁	—	2	2	no	—
144	C₂×C₄×C₆₁	—	2	4	no	—
145	C₂×C₄×C₆₁	—	2	4	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	4	no	—
148	C₂×C₄×C₆₁	—	2	4	no	—
149	C₂×C₄×C₆₁	—	2	2	no	—
150	C₂×C₄×C₆₁	—	4	8	no	—
151	C₂×C₄×C₆₁	#117	1	2	yes	—
152	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
154	C₂×C₄×C₆₁	C₂²⋊Q₈	1	4	yes	—
155	C₂×C₄×C₆₁	#123	1	4	yes	—
156	C₂×C₄×C₆₁	#125	1	4	yes	—
157	C₂×C₄×C₆₁	#126	1	4	yes	—
158	C₂×C₄×C₆₁	#131	1	4	yes	—
159	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
161	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
165	C₈×C₆₁	—	2	4	no	—
166	C₈×C₆₁	—	2	2	no	—
167	C₈×C₆₁	—	2	2	no	—
168	C₈×C₆₁	—	4	2	no	—
169	C₈×C₆₁	—	4	2	no	—
170	#21025	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₆₁	—	2	4	no	—
172	C₂²×C₆₁	—	2	2	no	—
173	C₂²×C₆₁	—	2	2	no	—
174	C₂²×C₆₁	—	2	4	no	—
175	C₂²×C₆₁	#387	1	4	yes	—
176	C₂²×C₆₁	C₂×#117	1	1	yes	characteristic
177	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂²×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
179	C₂²×C₆₁	C₂×#131	1	2	yes	—
180	C₂²×C₆₁	#568	1	2	yes	—
181	C₄×C₆₁	—	2	4	no	—
182	C₄×C₆₁	—	4	2	no	—
183	C₄×C₆₁	—	4	2	no	—
184	C₄×C₆₁	—	4	2	no	—
185	C₄×C₆₁	—	4	2	no	—
186	C₄×C₆₁	—	4	2	no	—
187	C₄×C₆₁	#387	1	4	yes	—
188	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
189	C₄×C₆₁	C₂×#123	1	1	yes	characteristic
190	C₄×C₆₁	C₂×#125	1	1	yes	characteristic
191	C₄×C₆₁	C₂×#126	1	1	yes	characteristic
192	C₂×#424	C₂×C₆₁	1	1	yes	characteristic
193	C₂×#405	C₂×C₆₁	1	1	yes	characteristic
194	#2285	C₂×C₆₁	1	1	yes	characteristic
195	#1917	C₂×C₆₁	1	4	yes	complemented
196	#1916	C₂×C₆₁	1	4	yes	complemented
197	#1729	C₂×C₆₁	1	1	yes	characteristic
198	#1729	C₂×C₆₁	1	1	yes	characteristic
199	#1728	C₂×C₆₁	1	1	yes	characteristic
200	C₂×#336	C₂×C₆₁	1	1	yes	characteristic
201	C₂×C₆₁	—	2	4	no	—
202	C₂×C₆₁	C₂×#387	1	1	yes	characteristic
203	C₂×C₆₁	#2924	1	2	yes	—
204	C₂×C₆₁	#2931	1	1	yes	characteristic
205	C₂×C₆₁	#2932	1	1	yes	characteristic
206	C₂×C₆₁	#2962	1	2	yes	—
207	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
209	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
210	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
211	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
212	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
213	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
214	#424	—	2	4	no	—
215	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
217	#405	—	2	4	no	—
218	C₂×#97	C₂²×C₆₁	1	2	yes	—
219	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
220	#384	C₄×C₆₁	1	1	yes	characteristic
221	#384	C₄×C₆₁	1	1	yes	characteristic
222	#382	C₄×C₆₁	1	1	yes	characteristic
223	#382	C₄×C₆₁	1	1	yes	characteristic
224	#380	C₄×C₆₁	1	4	yes	—
225	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
226	#336	C₂²×C₆₁	1	2	yes	—
227	#336	C₂²×C₆₁	1	4	yes	—
228	#336	C₂²×C₆₁	1	4	yes	—
229	#336	C₂²×C₆₁	1	4	yes	—
230	#336	C₂²×C₆₁	1	2	yes	—
231	C₆₁	#21025	1	1	yes	characteristic, direct product factor, Sylow
232	C₂³×C₄	C₂×C₄×C₆₁	1	2	yes	—
233	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	Q₈×C₆₁	1	4	yes	—
240	C₂²×C₈	—	2	2	no	—
241	C₂²×C₈	—	2	2	no	—
242	C₂²×C₈	—	2	2	no	—
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	D₄×C₆₁	1	4	yes	—
246	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
247	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
248	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
249	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
260	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	4	yes	—
261	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
262	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
266	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
268	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
269	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
270	C₄⋊C₈	—	2	4	no	—
271	C₄⋊C₈	—	2	4	no	—
272	#97	—	2	4	no	—
273	C₄×C₈	—	2	4	no	—
274	#95	C₂×C₄×C₆₁	1	4	yes	—
275	#95	C₂×C₄×C₆₁	1	4	yes	—
276	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
277	C₂²×C₄	—	2	4	no	—
278	C₂²×C₄	—	2	4	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
281	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
282	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
283	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
284	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
285	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
286	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
288	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
289	C₂²×C₄	#41×C₆₁	1	2	yes	—
290	C₂²×C₄	#41×C₆₁	1	2	yes	—
291	C₂²×C₄	#41×C₆₁	1	2	yes	—
292	C₂²×C₄	#41×C₆₁	1	2	yes	—
293	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
294	M₁₆	—	2	8	no	—
295	M₁₆	—	4	4	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	4	4	no	—
310	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
311	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
312	C₂×C₈	C₂×Q₈×C₆₁	1	4	yes	—
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	8	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	2	4	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	2	no	—
331	C₂³	#117×C₆₁	1	2	yes	—
332	C₂³	C₄×D₄×C₆₁	1	2	yes	—
333	C₂³	C₄×Q₈×C₆₁	1	2	yes	—
334	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	#117×C₆₁	1	2	yes	—
350	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
351	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
352	C₂×C₄	C₂²⋊Q₈×C₆₁	1	4	yes	—
353	C₂×C₄	#123×C₆₁	1	4	yes	—
354	C₂×C₄	#125×C₆₁	1	4	yes	—
355	C₂×C₄	#126×C₆₁	1	4	yes	—
356	C₂×C₄	#131×C₆₁	1	4	yes	—
357	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
358	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
360	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
361	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
362	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
363	C₈	—	2	4	no	—
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	4	2	no	—
367	C₈	—	4	2	no	—
368	C₂²	—	2	4	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	4	no	—
372	C₂²	C₆₁×#387	1	4	yes	—
373	C₂²	C₂×#117×C₆₁	1	1	yes	characteristic
374	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
375	C₂²	C₂×C₄×Q₈×C₆₁	1	1	yes	characteristic
376	C₂²	C₂×#131×C₆₁	1	2	yes	—
377	C₂²	C₆₁×#568	1	2	yes	—
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	C₆₁×#387	1	4	yes	—
385	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
386	C₄	C₂×#123×C₆₁	1	1	yes	characteristic
387	C₄	C₂×#125×C₆₁	1	1	yes	characteristic
388	C₄	C₂×#126×C₆₁	1	1	yes	characteristic
389	C₂	—	2	4	no	—
390	C₂	C₂×C₆₁×#387	1	1	yes	characteristic
391	C₂	C₆₁×#2924	1	2	yes	—
392	C₂	C₆₁×#2931	1	1	yes	characteristic
393	C₂	C₆₁×#2932	1	1	yes	characteristic
394	C₂	C₆₁×#2962	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
4. C₆₁×#1917	C₂	semidirect
5. C₆₁×#1916	C₂	semidirect
170. #21025	C₆₁	direct (N × H)
195. #1917	C₂×C₆₁	semidirect
196. #1916	C₂×C₆₁	semidirect
231. C₆₁	#21025	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×#424	2
C₂×C₆₁×#405	2
C₆₁×#2285	2
C₆₁×#1917	2
C₆₁×#1916	2
C₆₁×#1729	2
C₆₁×#1728	2
C₂×C₆₁×#336	2
#21025	61

Subgroups — C61×#21025 #29524458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21025 #29524458