Subgroups — C₆₁×#29931 #29533364

Order 15616.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2620	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2314	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2095	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2093	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2073	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2036	C₂	1	2	yes	maximal, complemented
8	C₆₁×#2033	C₂	1	2	yes	maximal
9	C₆₁×#1983	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1947	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#107×C₆₁	C₂²	1	2	yes	—
17	C₂×#107×C₆₁	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
19	C₂×#103×C₆₁	C₂²	1	2	yes	—
20	C₂×#103×C₆₁	C₂²	1	2	yes	—
21	C₂×#102×C₆₁	C₂²	1	2	yes	—
22	C₂×#102×C₆₁	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
24	C₆₁×#396	—	2	2	no	—
25	C₆₁×#394	—	2	2	no	—
26	C₆₁×#391	C₂²	1	1	yes	characteristic
27	C₆₁×#390	C₂²	1	1	yes	characteristic
28	C₆₁×#388	—	2	2	no	—
29	C₆₁×#387	—	2	2	no	—
30	C₆₁×#384	C₂²	1	1	yes	characteristic
31	C₆₁×#384	C₂²	1	1	yes	characteristic
32	C₆₁×#382	C₂²	1	1	yes	characteristic
33	C₆₁×#380	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
35	C₆₁×#340	C₂²	1	2	yes	—
36	C₆₁×#340	C₂²	1	2	yes	—
37	C₆₁×#336	C₂²	1	1	yes	characteristic
38	C₆₁×#336	C₂²	1	1	yes	characteristic
39	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₆₁	—	2	1	no	—
41	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
43	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
44	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
45	#124×C₆₁	—	2	4	no	—
46	C₂²⋊Q₈×C₆₁	—	4	2	no	—
47	#121×C₆₁	—	4	2	no	—
48	#117×C₆₁	—	2	4	no	—
49	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
50	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
53	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
57	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
60	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
63	C₂×C₄²×C₆₁	—	2	2	no	—
64	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
66	#107×C₆₁	—	4	2	no	—
67	#107×C₆₁	—	4	2	no	—
68	C₄⋊C₈×C₆₁	—	2	4	no	—
69	#103×C₆₁	—	4	2	no	—
70	#103×C₆₁	—	4	2	no	—
71	#102×C₆₁	—	4	2	no	—
72	#102×C₆₁	—	4	2	no	—
73	C₂²⋊C₈×C₆₁	—	4	2	no	—
74	#95×C₆₁	—	2	2	no	—
75	#95×C₆₁	—	2	2	no	—
76	#95×C₆₁	—	2	2	no	—
77	#95×C₆₁	—	2	2	no	—
78	C₂⁴×C₆₁	—	2	1	no	—
79	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
80	C₂×Q₈×C₆₁	—	2	2	no	—
81	C₂×Q₈×C₆₁	—	2	1	no	—
82	C₂×Q₈×C₆₁	—	2	2	no	—
83	C₂×Q₈×C₆₁	—	2	1	no	—
84	C₂×D₄×C₆₁	—	2	2	no	—
85	C₂×D₄×C₆₁	—	2	1	no	—
86	C₂×D₄×C₆₁	—	2	2	no	—
87	C₂×D₄×C₆₁	—	2	1	no	—
88	C₂×D₄×C₆₁	—	4	2	no	—
89	C₂×D₄×C₆₁	—	8	2	no	—
90	C₂²×C₄×C₆₁	—	2	2	no	—
91	C₂²×C₄×C₆₁	—	2	1	no	—
92	C₂²×C₄×C₆₁	—	2	2	no	—
93	C₂²×C₄×C₆₁	—	2	1	no	—
94	C₂²×C₄×C₆₁	—	2	2	no	—
95	C₂²×C₄×C₆₁	—	2	2	no	—
96	C₂²×C₄×C₆₁	—	2	1	no	—
97	C₂²×C₄×C₆₁	—	2	1	no	—
98	C₂²×C₄×C₆₁	—	2	1	no	—
99	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
103	C₂×C₈×C₆₁	—	2	2	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	C₄⋊C₄×C₆₁	—	2	4	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	—	4	2	no	—
117	C₄⋊C₄×C₆₁	—	8	2	no	—
118	C₄⋊C₄×C₆₁	—	8	2	no	—
119	C₂²⋊C₄×C₆₁	—	2	4	no	—
120	C₂²⋊C₄×C₆₁	—	4	2	no	—
121	C₂²⋊C₄×C₆₁	—	4	2	no	—
122	C₂²⋊C₄×C₆₁	—	4	4	no	—
123	C₂²⋊C₄×C₆₁	—	8	2	no	—
124	C₂²⋊C₄×C₆₁	—	8	2	no	—
125	C₄²×C₆₁	—	2	2	no	—
126	C₄²×C₆₁	—	8	2	no	—
127	C₄²×C₆₁	#41	1	4	yes	—
128	C₂³×C₆₁	—	2	1	no	—
129	C₂³×C₆₁	—	2	1	no	—
130	C₂³×C₆₁	—	2	1	no	—
131	C₂³×C₆₁	—	2	2	no	—
132	C₂³×C₆₁	—	2	2	no	—
133	C₂³×C₆₁	—	4	1	no	—
134	C₂³×C₆₁	—	4	1	no	—
135	C₂³×C₆₁	—	4	1	no	—
136	C₂³×C₆₁	—	4	2	no	—
137	C₂³×C₆₁	—	4	2	no	—
138	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
139	Q₈×C₆₁	—	4	2	no	—
140	Q₈×C₆₁	—	4	2	no	—
141	D₄×C₆₁	—	4	2	no	—
142	D₄×C₆₁	—	4	2	no	—
143	D₄×C₆₁	—	8	4	no	—
144	C₂×C₄×C₆₁	—	2	2	no	—
145	C₂×C₄×C₆₁	—	2	2	no	—
146	C₂×C₄×C₆₁	—	2	2	no	—
147	C₂×C₄×C₆₁	—	2	1	no	—
148	C₂×C₄×C₆₁	—	2	1	no	—
149	C₂×C₄×C₆₁	—	2	1	no	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	4	2	no	—
153	C₂×C₄×C₆₁	—	4	2	no	—
154	C₂×C₄×C₆₁	—	4	1	no	—
155	C₂×C₄×C₆₁	—	4	1	no	—
156	C₂×C₄×C₆₁	—	4	1	no	—
157	C₂×C₄×C₆₁	—	4	1	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	2	no	—
160	C₂×C₄×C₆₁	—	4	1	no	—
161	C₂×C₄×C₆₁	—	4	2	no	—
162	C₂×C₄×C₆₁	—	4	2	no	—
163	C₂×C₄×C₆₁	—	4	2	no	—
164	C₂×C₄×C₆₁	—	4	2	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	#123	1	4	yes	—
168	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
169	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
171	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
172	C₈×C₆₁	—	4	2	no	—
173	C₈×C₆₁	—	4	2	no	—
174	#29931	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
175	C₂²×C₆₁	—	4	2	no	—
176	C₂²×C₆₁	—	4	1	no	—
177	C₂²×C₆₁	—	4	1	no	—
178	C₂²×C₆₁	—	4	1	no	—
179	C₂²×C₆₁	—	4	2	no	—
180	C₂²×C₆₁	—	8	2	no	—
181	C₂²×C₆₁	—	8	1	no	—
182	C₂²×C₆₁	—	8	1	no	—
183	C₂²×C₆₁	—	8	1	no	—
184	C₂²×C₆₁	—	8	2	no	—
185	C₂²×C₆₁	C₂×#123	1	1	yes	characteristic
186	C₂²×C₆₁	#535	1	1	yes	characteristic
187	C₂²×C₆₁	#537	1	1	yes	characteristic
188	C₂²×C₆₁	#576	1	2	yes	—
189	C₂²×C₆₁	#578	1	2	yes	—
190	C₄×C₆₁	—	2	4	no	—
191	C₄×C₆₁	—	4	2	no	—
192	C₄×C₆₁	—	4	1	no	—
193	C₄×C₆₁	—	8	1	no	—
194	C₄×C₆₁	—	8	1	no	—
195	C₄×C₆₁	—	8	2	no	—
196	C₄×C₆₁	—	8	1	no	—
197	C₄×C₆₁	—	8	2	no	—
198	C₄×C₆₁	#540	1	2	yes	—
199	C₄×C₆₁	#542	1	2	yes	—
200	#2620	C₂×C₆₁	1	1	yes	characteristic
201	#2314	C₂×C₆₁	1	1	yes	characteristic, complemented
202	#2095	C₂×C₆₁	1	1	yes	characteristic, complemented
203	#2093	C₂×C₆₁	1	1	yes	characteristic, complemented
204	#2074	C₂×C₆₁	1	1	yes	characteristic, complemented
205	#2073	C₂×C₆₁	1	1	yes	characteristic, complemented
206	#2036	C₂×C₆₁	1	2	yes	complemented
207	#2033	C₂×C₆₁	1	2	yes	—
208	#1983	C₂×C₆₁	1	2	yes	complemented
209	#1947	C₂×C₆₁	1	2	yes	complemented
210	#1798	C₂×C₆₁	1	1	yes	characteristic, complemented
211	C₂×C₆₁	—	8	1	no	—
212	C₂×C₆₁	—	16	1	no	—
213	C₂×C₆₁	#2624	1	1	yes	characteristic
214	C₂×C₆₁	#3098	1	2	yes	—
215	C₂×C₆₁	#3220	1	1	yes	characteristic
216	C₂×C₆₁	#3223	1	1	yes	characteristic
217	C₂×C₆₁	#3262	1	2	yes	—
218	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
219	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
220	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
221	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
222	C₂×#107	C₂²×C₆₁	1	2	yes	—
223	C₂×#107	C₂²×C₆₁	1	2	yes	—
224	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
225	C₂×#103	C₂²×C₆₁	1	2	yes	—
226	C₂×#103	C₂²×C₆₁	1	2	yes	—
227	C₂×#102	C₂²×C₆₁	1	2	yes	—
228	C₂×#102	C₂²×C₆₁	1	2	yes	—
229	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
230	#396	—	2	2	no	—
231	#394	—	2	2	no	—
232	#391	C₂²×C₆₁	1	1	yes	characteristic
233	#390	C₂²×C₆₁	1	1	yes	characteristic
234	#388	—	2	2	no	—
235	#387	—	2	2	no	—
236	#384	C₂²×C₆₁	1	1	yes	characteristic
237	#384	C₂²×C₆₁	1	1	yes	characteristic
238	#382	C₂²×C₆₁	1	1	yes	characteristic
239	#380	C₂²×C₆₁	1	2	yes	—
240	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
241	#340	C₂²×C₆₁	1	2	yes	—
242	#340	C₂²×C₆₁	1	2	yes	—
243	#336	C₂²×C₆₁	1	1	yes	characteristic
244	#336	C₂²×C₆₁	1	1	yes	characteristic
245	C₆₁	#29931	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
249	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
250	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
251	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
252	#124	—	2	4	no	—
253	C₂²⋊Q₈	—	4	2	no	—
254	#121	—	4	2	no	—
255	#117	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
260	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
261	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
262	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₂²⋊C₄	—	2	1	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	—	2	2	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
272	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
273	#107	—	4	2	no	—
274	#107	—	4	2	no	—
275	C₄⋊C₈	—	2	4	no	—
276	#103	—	4	2	no	—
277	#103	—	4	2	no	—
278	#102	—	4	2	no	—
279	#102	—	4	2	no	—
280	C₂²⋊C₈	—	4	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	C₂⁴	—	2	1	no	—
286	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	1	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	1	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	—	8	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
309	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	8	2	no	—
325	C₄⋊C₄	—	8	2	no	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	4	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	8	2	no	—
334	C₄²	#41×C₆₁	1	4	yes	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	4	1	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	1	no	—
345	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
346	Q₈	—	4	2	no	—
347	Q₈	—	4	2	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	D₄	—	8	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	#123×C₆₁	1	4	yes	—
375	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
376	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
377	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
378	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₂²	—	4	2	no	—
382	C₂²	—	4	1	no	—
383	C₂²	—	4	1	no	—
384	C₂²	—	4	1	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	1	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	8	2	no	—
391	C₂²	C₂×#123×C₆₁	1	1	yes	characteristic
392	C₂²	C₆₁×#535	1	1	yes	characteristic
393	C₂²	C₆₁×#537	1	1	yes	characteristic
394	C₂²	C₆₁×#576	1	2	yes	—
395	C₂²	C₆₁×#578	1	2	yes	—
396	C₄	—	2	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	4	1	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	1	no	—
401	C₄	—	8	2	no	—
402	C₄	—	8	1	no	—
403	C₄	—	8	2	no	—
404	C₄	C₆₁×#540	1	2	yes	—
405	C₄	C₆₁×#542	1	2	yes	—
406	C₂	—	8	1	no	—
407	C₂	—	16	1	no	—
408	C₂	C₆₁×#2624	1	1	yes	characteristic
409	C₂	C₆₁×#3098	1	2	yes	—
410	C₂	C₆₁×#3220	1	1	yes	characteristic
411	C₂	C₆₁×#3223	1	1	yes	characteristic
412	C₂	C₆₁×#3262	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
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
2. C₆₁×#2314	C₂	semidirect
3. C₆₁×#2095	C₂	semidirect
4. C₆₁×#2093	C₂	semidirect
5. C₆₁×#2074	C₂	semidirect
6. C₆₁×#2073	C₂	semidirect
7. C₆₁×#2036	C₂	semidirect
9. C₆₁×#1983	C₂	semidirect
10. C₆₁×#1947	C₂	semidirect
11. C₆₁×#1798	C₂	semidirect
174. #29931	C₆₁	direct (N × H)
201. #2314	C₂×C₆₁	semidirect
202. #2095	C₂×C₆₁	semidirect
203. #2093	C₂×C₆₁	semidirect
204. #2074	C₂×C₆₁	semidirect
205. #2073	C₂×C₆₁	semidirect
206. #2036	C₂×C₆₁	semidirect
208. #1983	C₂×C₆₁	semidirect
209. #1947	C₂×C₆₁	semidirect
210. #1798	C₂×C₆₁	semidirect
245. C₆₁	#29931	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×#2620	2
C₆₁×#2314	2
C₆₁×#2095	2
C₆₁×#2093	2
C₆₁×#2074	2
C₆₁×#2073	2
C₆₁×#2036	2
C₆₁×#2033	2
C₆₁×#1983	2
C₆₁×#1947	2
C₆₁×#1798	2
#29931	61

Subgroups — C61×#29931 #29533364

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29931 #29533364