Subgroups — C₆₁×#34954 #29538387

Order 15616.

1948 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2593	C₂	1	4	yes	maximal, complemented
2	C₆₁×#2582	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2571	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2548	C₂	1	2	yes	maximal
5	C₆₁×#2513	C₂	1	4	yes	maximal, complemented
6	C₆₁×#2448	C₂	1	4	yes	maximal, complemented
7	C₆₁×#2395	C₂	1	4	yes	maximal, complemented
8	C₄×#127×C₆₁	C₂	1	1	yes	maximal, characteristic
9	C₄×#124×C₆₁	C₂	1	4	yes	maximal, complemented
10	C₆₁×#2293	C₂	1	4	yes	maximal, complemented
11	C₄²×Q₈×C₆₁	C₂	1	2	yes	maximal, complemented
12	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₆₁	C₂²	1	4	yes	—
14	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₆₁	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
19	C₂×#117×C₆₁	C₂²	1	4	yes	—
20	C₆₁×#400	C₂²	1	4	yes	—
21	C₆₁×#399	C₂²	1	4	yes	—
22	C₆₁×#398	C₂²	1	4	yes	—
23	C₆₁×#397	C₂²	1	8	yes	—
24	C₆₁×#397	C₂²	1	4	yes	—
25	C₆₁×#394	C₂²	1	8	yes	—
26	C₆₁×#391	C₂²	1	4	yes	—
27	C₆₁×#390	C₂²	1	4	yes	—
28	C₆₁×#390	C₂²	1	4	yes	—
29	C₆₁×#390	C₂²	1	4	yes	—
30	C₆₁×#390	C₂²	1	2	yes	—
31	C₆₁×#390	C₂²	1	4	yes	—
32	C₆₁×#389	C₂²	1	4	yes	—
33	C₆₁×#389	C₂²	1	4	yes	—
34	C₆₁×#388	C₂²	1	8	yes	—
35	C₆₁×#388	C₂²	1	8	yes	—
36	C₆₁×#388	C₂²	1	8	yes	—
37	C₆₁×#388	C₂²	1	8	yes	—
38	C₆₁×#384	C₂²	1	1	yes	characteristic
39	C₆₁×#382	C₂²	1	4	yes	—
40	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
41	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
43	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
44	C₄×C₄⋊C₄×C₆₁	C₂²	1	4	yes	—
45	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
46	C₄×C₂²⋊C₄×C₆₁	C₂²	1	8	yes	—
47	C₄×C₂²⋊C₄×C₆₁	C₂²	1	4	yes	—
48	C₄³×C₆₁	C₂²	1	1	yes	characteristic
49	C₄³×C₆₁	C₂²	1	4	yes	—
50	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
51	C₂²×D₄×C₆₁	C₂³	1	4	yes	—
52	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
53	C₂³×C₄×C₆₁	C₂³	1	4	yes	—
54	#127×C₆₁	—	2	4	no	—
55	#124×C₆₁	—	2	16	no	—
56	C₄×Q₈×C₆₁	—	2	8	no	—
57	C₄×Q₈×C₆₁	—	2	8	no	—
58	C₄×Q₈×C₆₁	—	2	8	no	—
59	C₄×D₄×C₆₁	—	2	16	no	—
60	C₄×D₄×C₆₁	—	4	4	no	—
61	#117×C₆₁	—	4	8	no	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
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	4	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₆₁	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₆₁	C₂³	1	4	yes	—
78	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
79	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
80	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
81	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
82	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
83	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
84	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₆₁	C₂³	1	4	yes	—
87	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
89	#95×C₆₁	C₂³	1	4	yes	—
90	#95×C₆₁	C₂³	1	8	yes	—
91	#95×C₆₁	C₂³	1	8	yes	—
92	#95×C₆₁	C₂³	1	4	yes	—
93	#95×C₆₁	C₂³	1	4	yes	—
94	#95×C₆₁	C₂³	1	4	yes	—
95	#95×C₆₁	C₂³	1	4	yes	—
96	C₂⁴×C₆₁	C₂⁴	1	4	yes	—
97	C₂×Q₈×C₆₁	—	2	4	no	—
98	C₂×Q₈×C₆₁	—	2	4	no	—
99	C₂×Q₈×C₆₁	#41	1	8	yes	—
100	C₂×D₄×C₆₁	—	2	8	no	—
101	C₂×D₄×C₆₁	—	2	8	no	—
102	C₂×D₄×C₆₁	—	2	4	no	—
103	C₂×D₄×C₆₁	—	2	8	no	—
104	C₂×D₄×C₆₁	—	4	2	no	—
105	C₂×D₄×C₆₁	—	4	2	no	—
106	C₂²×C₄×C₆₁	—	2	16	no	—
107	C₂²×C₄×C₆₁	—	2	8	no	—
108	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₆₁	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₆₁	—	2	8	no	—
119	C₄⋊C₄×C₆₁	—	2	8	no	—
120	C₄⋊C₄×C₆₁	—	2	8	no	—
121	C₄⋊C₄×C₆₁	—	2	8	no	—
122	C₄⋊C₄×C₆₁	—	2	4	no	—
123	C₄⋊C₄×C₆₁	—	2	4	no	—
124	C₄⋊C₄×C₆₁	—	2	4	no	—
125	C₄⋊C₄×C₆₁	—	4	4	no	—
126	C₄⋊C₄×C₆₁	—	4	4	no	—
127	C₄⋊C₄×C₆₁	—	4	2	no	—
128	C₂²⋊C₄×C₆₁	—	2	16	no	—
129	C₂²⋊C₄×C₆₁	—	2	16	no	—
130	C₂²⋊C₄×C₆₁	—	2	16	no	—
131	C₂²⋊C₄×C₆₁	—	4	8	no	—
132	C₂²⋊C₄×C₆₁	—	4	8	no	—
133	C₂²⋊C₄×C₆₁	—	4	4	no	—
134	C₄²×C₆₁	—	2	8	no	—
135	C₄²×C₆₁	—	2	4	no	—
136	C₄²×C₆₁	—	2	8	no	—
137	C₄²×C₆₁	—	2	8	no	—
138	C₄²×C₆₁	—	2	8	no	—
139	C₄²×C₆₁	—	2	8	no	—
140	C₄²×C₆₁	—	2	2	no	—
141	C₄²×C₆₁	—	4	1	no	—
142	C₄²×C₆₁	—	4	4	no	—
143	C₄²×C₆₁	#41	1	8	yes	—
144	C₄²×C₆₁	#41	1	4	yes	—
145	C₂³×C₆₁	—	2	8	no	—
146	C₂³×C₆₁	—	2	8	no	—
147	C₂³×C₆₁	—	2	4	no	—
148	C₂³×C₆₁	—	2	4	no	—
149	C₂³×C₆₁	—	2	4	no	—
150	C₂³×C₆₁	C₂⁵	1	1	yes	characteristic
151	Q₈×C₆₁	—	2	16	no	—
152	D₄×C₆₁	—	4	8	no	—
153	D₄×C₆₁	—	4	16	no	—
154	C₂×C₄×C₆₁	—	2	2	no	—
155	C₂×C₄×C₆₁	—	2	4	no	—
156	C₂×C₄×C₆₁	—	2	4	no	—
157	C₂×C₄×C₆₁	—	2	1	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	1	no	—
160	C₂×C₄×C₆₁	—	2	4	no	—
161	C₂×C₄×C₆₁	—	2	4	no	—
162	C₂×C₄×C₆₁	—	2	4	no	—
163	C₂×C₄×C₆₁	—	2	4	no	—
164	C₂×C₄×C₆₁	—	2	4	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	2	8	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	4	no	—
169	C₂×C₄×C₆₁	—	2	4	no	—
170	C₂×C₄×C₆₁	—	2	4	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	4	no	—
173	C₂×C₄×C₆₁	—	4	16	no	—
174	C₂×C₄×C₆₁	C₂×#41	1	8	yes	—
175	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
176	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
177	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
178	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
179	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
180	C₂×C₄×C₆₁	C₂×#41	1	4	yes	—
181	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
182	#34954	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₆₁	—	4	8	no	—
184	C₂²×C₆₁	—	4	4	no	—
185	C₂²×C₆₁	—	4	4	no	—
186	C₂²×C₆₁	—	4	8	no	—
187	C₂²×C₆₁	—	4	4	no	—
188	C₂²×C₆₁	C₂²×#41	1	1	yes	characteristic
189	C₂²×C₆₁	C₂²×#41	1	2	yes	—
190	C₂²×C₆₁	C₂²×#41	1	2	yes	—
191	C₂²×C₆₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
192	C₂²×C₆₁	#585	1	1	yes	characteristic
193	C₄×C₆₁	—	2	8	no	—
194	C₄×C₆₁	—	2	2	no	—
195	C₄×C₆₁	—	2	4	no	—
196	C₄×C₆₁	—	4	4	no	—
197	C₄×C₆₁	—	4	4	no	—
198	C₄×C₆₁	—	4	4	no	—
199	C₄×C₆₁	—	4	4	no	—
200	C₄×C₆₁	—	4	1	no	—
201	C₄×C₆₁	#529	1	8	yes	—
202	C₄×C₆₁	#559	1	4	yes	—
203	#2593	C₂×C₆₁	1	4	yes	complemented
204	#2582	C₂×C₆₁	1	1	yes	characteristic, complemented
205	#2571	C₂×C₆₁	1	1	yes	characteristic, complemented
206	#2548	C₂×C₆₁	1	2	yes	—
207	#2513	C₂×C₆₁	1	4	yes	complemented
208	#2448	C₂×C₆₁	1	4	yes	complemented
209	#2395	C₂×C₆₁	1	4	yes	complemented
210	C₄×#127	C₂×C₆₁	1	1	yes	characteristic
211	C₄×#124	C₂×C₆₁	1	4	yes	complemented
212	#2293	C₂×C₆₁	1	4	yes	complemented
213	C₄²×Q₈	C₂×C₆₁	1	2	yes	complemented
214	C₂×C₆₁	—	8	4	no	—
215	C₂×C₆₁	C₂×#529	1	2	yes	—
216	C₂×C₆₁	#3460	1	1	yes	characteristic
217	C₂×C₆₁	C₂×#559	1	1	yes	characteristic
218	C₂×C₆₁	#3480	1	2	yes	—
219	C₂×C₆₁	#3483	1	1	yes	characteristic
220	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
221	C₂×#124	C₂²×C₆₁	1	4	yes	—
222	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
223	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
224	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
225	C₂×C₄×D₄	C₂²×C₆₁	1	4	yes	—
226	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
227	C₂×#117	C₂²×C₆₁	1	4	yes	—
228	#400	C₂²×C₆₁	1	4	yes	—
229	#399	C₂²×C₆₁	1	4	yes	—
230	#398	C₂²×C₆₁	1	4	yes	—
231	#397	C₂²×C₆₁	1	8	yes	—
232	#397	C₂²×C₆₁	1	4	yes	—
233	#394	C₂²×C₆₁	1	8	yes	—
234	#391	C₂²×C₆₁	1	4	yes	—
235	#390	C₂²×C₆₁	1	2	yes	—
236	#390	C₂²×C₆₁	1	4	yes	—
237	#390	C₂²×C₆₁	1	4	yes	—
238	#390	C₂²×C₆₁	1	4	yes	—
239	#390	C₂²×C₆₁	1	4	yes	—
240	#389	C₂²×C₆₁	1	4	yes	—
241	#389	C₂²×C₆₁	1	4	yes	—
242	#388	C₂²×C₆₁	1	8	yes	—
243	#388	C₂²×C₆₁	1	8	yes	—
244	#388	C₂²×C₆₁	1	8	yes	—
245	#388	C₂²×C₆₁	1	8	yes	—
246	#384	C₂²×C₆₁	1	1	yes	characteristic
247	#382	C₂²×C₆₁	1	4	yes	—
248	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
249	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
250	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
251	C₄×C₄⋊C₄	C₂²×C₆₁	1	4	yes	—
252	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
253	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
254	C₄×C₂²⋊C₄	C₂²×C₆₁	1	8	yes	—
255	C₄×C₂²⋊C₄	C₂²×C₆₁	1	4	yes	—
256	C₄³	C₂²×C₆₁	1	1	yes	characteristic
257	C₄³	C₂²×C₆₁	1	4	yes	—
258	C₆₁	#34954	1	1	yes	characteristic, direct product factor, Sylow
259	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
260	C₂²×D₄	C₂³×C₆₁	1	4	yes	—
261	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
262	C₂³×C₄	C₂³×C₆₁	1	4	yes	—
263	#127	—	2	4	no	—
264	#124	—	2	16	no	—
265	C₄×Q₈	—	2	8	no	—
266	C₄×Q₈	—	2	8	no	—
267	C₄×Q₈	—	2	8	no	—
268	C₄×D₄	—	2	16	no	—
269	C₄×D₄	—	4	4	no	—
270	#117	—	4	8	no	—
271	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
272	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
280	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₆₁	1	4	yes	—
286	C₂×C₂²⋊C₄	C₂³×C₆₁	1	8	yes	—
287	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
288	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
289	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
290	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
291	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
292	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
293	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
294	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₆₁	1	4	yes	—
296	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
297	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
298	#95	C₂³×C₆₁	1	4	yes	—
299	#95	C₂³×C₆₁	1	8	yes	—
300	#95	C₂³×C₆₁	1	8	yes	—
301	#95	C₂³×C₆₁	1	4	yes	—
302	#95	C₂³×C₆₁	1	4	yes	—
303	#95	C₂³×C₆₁	1	4	yes	—
304	#95	C₂³×C₆₁	1	4	yes	—
305	C₂⁴	C₂⁴×C₆₁	1	4	yes	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	#41×C₆₁	1	8	yes	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂²×C₄	—	2	16	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
318	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
320	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₆₁	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₆₁	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	2	16	no	—
338	C₂²⋊C₄	—	2	16	no	—
339	C₂²⋊C₄	—	2	16	no	—
340	C₂²⋊C₄	—	4	8	no	—
341	C₂²⋊C₄	—	4	4	no	—
342	C₂²⋊C₄	—	4	8	no	—
343	C₄²	—	2	8	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	8	no	—
346	C₄²	—	2	8	no	—
347	C₄²	—	2	8	no	—
348	C₄²	—	2	8	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	4	no	—
352	C₄²	#41×C₆₁	1	8	yes	—
353	C₄²	#41×C₆₁	1	4	yes	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	C₂⁵×C₆₁	1	1	yes	characteristic
360	Q₈	—	2	16	no	—
361	D₄	—	4	8	no	—
362	D₄	—	4	16	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	4	16	no	—
383	C₂×C₄	C₂×#41×C₆₁	1	8	yes	—
384	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
385	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
386	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
387	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
388	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
389	C₂×C₄	C₂×#41×C₆₁	1	4	yes	—
390	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
391	C₂²	—	4	8	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	8	no	—
395	C₂²	—	4	4	no	—
396	C₂²	C₂²×#41×C₆₁	1	1	yes	characteristic
397	C₂²	C₂²×#41×C₆₁	1	2	yes	—
398	C₂²	C₂²×#41×C₆₁	1	2	yes	—
399	C₂²	C₂×H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
400	C₂²	C₆₁×#585	1	1	yes	characteristic
401	C₄	—	2	8	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	1	no	—
409	C₄	C₆₁×#529	1	8	yes	—
410	C₄	C₆₁×#559	1	4	yes	—
411	C₂	—	8	4	no	—
412	C₂	C₂×C₆₁×#529	1	2	yes	—
413	C₂	C₆₁×#3460	1	1	yes	characteristic
414	C₂	C₂×C₆₁×#559	1	1	yes	characteristic
415	C₂	C₆₁×#3480	1	2	yes	—
416	C₂	C₆₁×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₁
socle	C₂³×C₆₁	C₂⁵
prime radical	C₂×#127×C₆₁	C₂²
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
1. C₆₁×#2593	C₂	semidirect
2. C₆₁×#2582	C₂	semidirect
3. C₆₁×#2571	C₂	semidirect
5. C₆₁×#2513	C₂	semidirect
6. C₆₁×#2448	C₂	semidirect
7. C₆₁×#2395	C₂	semidirect
9. C₄×#124×C₆₁	C₂	semidirect
10. C₆₁×#2293	C₂	semidirect
11. C₄²×Q₈×C₆₁	C₂	semidirect
182. #34954	C₆₁	direct (N × H)
203. #2593	C₂×C₆₁	semidirect
204. #2582	C₂×C₆₁	semidirect
205. #2571	C₂×C₆₁	semidirect
207. #2513	C₂×C₆₁	semidirect
208. #2448	C₂×C₆₁	semidirect
209. #2395	C₂×C₆₁	semidirect
211. C₄×#124	C₂×C₆₁	semidirect
212. #2293	C₂×C₆₁	semidirect
213. C₄²×Q₈	C₂×C₆₁	semidirect
258. C₆₁	#34954	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×#2593	2
C₆₁×#2582	2
C₆₁×#2571	2
C₆₁×#2548	2
C₆₁×#2513	2
C₆₁×#2448	2
C₆₁×#2395	2
C₄×#127×C₆₁	2
C₄×#124×C₆₁	2
C₆₁×#2293	2
C₄²×Q₈×C₆₁	2
#34954	61

Subgroups — C61×#34954 #29538387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#34954 #29538387