Subgroups — C₆₁×#25650 #29529083

Order 15616.

1054 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#474	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2042	C₂	1	4	yes	maximal
6	C₆₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1863	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#556	—	2	4	no	—
11	C₆₁×#556	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#126×C₆₁	—	2	2	no	—
16	C₂×#124×C₆₁	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
18	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	—	2	1	no	—
22	C₆₁×#487	—	2	4	no	—
23	C₆₁×#474	—	2	4	no	—
24	C₂×#107×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₁	C₂²	1	4	yes	—
27	C₂×#103×C₆₁	C₂²	1	4	yes	—
28	C₂×#102×C₆₁	C₂²	1	2	yes	—
29	C₂×#102×C₆₁	C₂²	1	2	yes	—
30	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₆₁×#398	—	2	2	no	—
32	C₆₁×#391	—	2	1	no	—
33	C₆₁×#389	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#340	C₂²	1	2	yes	—
36	C₆₁×#336	C₂²	1	4	yes	—
37	C₂²×Q₈×C₆₁	—	2	1	no	—
38	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
39	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
40	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₆₁	—	2	1	no	—
42	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
43	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₆₁	—	2	2	no	—
45	C₄⋊Q₈×C₆₁	—	2	2	no	—
46	C₄⋊Q₈×C₆₁	—	2	2	no	—
47	C₄⋊Q₈×C₆₁	—	4	4	no	—
48	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
49	#126×C₆₁	—	2	16	no	—
50	#124×C₆₁	—	2	4	no	—
51	#124×C₆₁	—	2	4	no	—
52	C₂²⋊Q₈×C₆₁	—	2	8	no	—
53	C₄×Q₈×C₆₁	—	2	4	no	—
54	C₄×Q₈×C₆₁	—	2	4	no	—
55	C₄×Q₈×C₆₁	—	2	2	no	—
56	C₄×Q₈×C₆₁	—	2	2	no	—
57	C₄×D₄×C₆₁	—	2	2	no	—
58	C₄×D₄×C₆₁	D₄	1	4	yes	—
59	#117×C₆₁	—	2	8	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄²×C₆₁	—	2	2	no	—
74	C₂×C₄²×C₆₁	—	2	1	no	—
75	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
76	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
77	#107×C₆₁	—	2	4	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	#103×C₆₁	—	2	8	no	—
80	#103×C₆₁	—	2	8	no	—
81	#102×C₆₁	—	2	4	no	—
82	#102×C₆₁	—	2	4	no	—
83	C₄×C₈×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	4	no	—
86	C₂⁴×C₆₁	—	2	1	no	—
87	C₂×Q₈×C₆₁	—	2	2	no	—
88	C₂×Q₈×C₆₁	—	2	2	no	—
89	C₂×Q₈×C₆₁	—	2	2	no	—
90	C₂×Q₈×C₆₁	—	2	2	no	—
91	C₂×Q₈×C₆₁	—	2	4	no	—
92	C₂×Q₈×C₆₁	—	2	4	no	—
93	C₂×Q₈×C₆₁	—	4	2	no	—
94	C₂×Q₈×C₆₁	—	4	2	no	—
95	C₂×Q₈×C₆₁	—	4	2	no	—
96	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
97	C₂×D₄×C₆₁	—	2	1	no	—
98	C₂×D₄×C₆₁	—	2	2	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	1	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	4	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	—	4	2	no	—
107	C₂²×C₄×C₆₁	—	4	2	no	—
108	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₆₁	—	2	2	no	—
114	C₂×C₈×C₆₁	—	2	2	no	—
115	C₂×C₈×C₆₁	—	2	2	no	—
116	C₂×C₈×C₆₁	—	2	4	no	—
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₄⋊C₄×C₆₁	—	2	8	no	—
119	C₄⋊C₄×C₆₁	—	2	4	no	—
120	C₄⋊C₄×C₆₁	—	2	4	no	—
121	C₄⋊C₄×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	4	no	—
123	C₄⋊C₄×C₆₁	—	2	1	no	—
124	C₄⋊C₄×C₆₁	—	2	2	no	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	4	8	no	—
128	C₄⋊C₄×C₆₁	—	4	2	no	—
129	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₆₁	#41	1	4	yes	—
131	C₂²⋊C₄×C₆₁	—	2	8	no	—
132	C₂²⋊C₄×C₆₁	—	2	8	no	—
133	C₂²⋊C₄×C₆₁	—	2	4	no	—
134	C₄²×C₆₁	—	2	8	no	—
135	C₄²×C₆₁	—	2	2	no	—
136	C₄²×C₆₁	—	2	2	no	—
137	C₄²×C₆₁	—	4	2	no	—
138	C₄²×C₆₁	C₂×D₄	1	2	yes	—
139	C₄²×C₆₁	C₂×D₄	1	2	yes	—
140	C₂³×C₆₁	—	2	2	no	—
141	C₂³×C₆₁	—	4	2	no	—
142	C₂³×C₆₁	—	4	1	no	—
143	C₂³×C₆₁	—	4	1	no	—
144	C₂³×C₆₁	—	4	2	no	—
145	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₆₁	—	2	8	no	—
147	Q₈×C₆₁	—	4	2	no	—
148	Q₈×C₆₁	—	4	2	no	—
149	Q₈×C₆₁	—	4	4	no	—
150	Q₈×C₆₁	—	8	4	no	—
151	D₄×C₆₁	—	2	2	no	—
152	D₄×C₆₁	—	2	2	no	—
153	D₄×C₆₁	—	4	2	no	—
154	C₂×C₄×C₆₁	—	2	2	no	—
155	C₂×C₄×C₆₁	—	2	2	no	—
156	C₂×C₄×C₆₁	—	2	2	no	—
157	C₂×C₄×C₆₁	—	2	4	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	4	no	—
160	C₂×C₄×C₆₁	—	2	2	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	2	4	no	—
163	C₂×C₄×C₆₁	—	4	4	no	—
164	C₂×C₄×C₆₁	—	4	1	no	—
165	C₂×C₄×C₆₁	—	4	2	no	—
166	C₂×C₄×C₆₁	—	4	1	no	—
167	C₂×C₄×C₆₁	—	4	2	no	—
168	C₂×C₄×C₆₁	—	4	8	no	—
169	C₂×C₄×C₆₁	—	4	2	no	—
170	C₂×C₄×C₆₁	—	4	2	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	#120	1	2	yes	—
173	C₂×C₄×C₆₁	#120	1	2	yes	—
174	C₂×C₄×C₆₁	#135	1	2	yes	—
175	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
176	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
179	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
180	C₈×C₆₁	—	4	2	no	—
181	C₈×C₆₁	—	4	2	no	—
182	#25650	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂²×C₆₁	—	4	2	no	—
184	C₂²×C₆₁	—	4	2	no	—
185	C₂²×C₆₁	—	4	2	no	—
186	C₂²×C₆₁	—	8	2	no	—
187	C₂²×C₆₁	—	8	2	no	—
188	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
189	C₂²×C₆₁	#548	1	2	yes	—
190	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
191	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
192	C₂²×C₆₁	#578	1	2	yes	—
193	C₄×C₆₁	—	2	2	no	—
194	C₄×C₆₁	—	4	4	no	—
195	C₄×C₆₁	—	4	4	no	—
196	C₄×C₆₁	—	4	2	no	—
197	C₄×C₆₁	—	4	2	no	—
198	C₄×C₆₁	—	4	2	no	—
199	C₄×C₆₁	—	8	2	no	—
200	C₄×C₆₁	#449	1	4	yes	—
201	C₄×C₆₁	#532	1	1	yes	characteristic
202	C₄×C₆₁	#536	1	1	yes	characteristic
203	C₄×C₆₁	#547	1	2	yes	—
204	C₂×#556	C₂×C₆₁	1	1	yes	characteristic
205	C₂×#487	C₂×C₆₁	1	1	yes	characteristic, complemented
206	C₂×#474	C₂×C₆₁	1	1	yes	characteristic
207	#2546	C₂×C₆₁	1	1	yes	characteristic, complemented
208	#2042	C₂×C₆₁	1	4	yes	—
209	#1984	C₂×C₆₁	1	1	yes	characteristic, complemented
210	#1981	C₂×C₆₁	1	1	yes	characteristic, complemented
211	#1863	C₂×C₆₁	1	4	yes	complemented
212	C₄×#102	C₂×C₆₁	1	1	yes	characteristic
213	C₂×C₆₁	—	8	2	no	—
214	C₂×C₆₁	#2432	1	1	yes	characteristic
215	C₂×C₆₁	C₂×#449	1	1	yes	characteristic
216	C₂×C₆₁	#3011	1	1	yes	characteristic
217	C₂×C₆₁	#3364	1	2	yes	—
218	C₂×C₆₁	#3367	1	2	yes	—
219	#556	—	2	4	no	—
220	#556	—	2	4	no	—
221	C₂×C₄⋊Q₈	—	2	1	no	—
222	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
224	C₂×#126	—	2	2	no	—
225	C₂×#124	C₂²×C₆₁	1	2	yes	—
226	C₂×C₂²⋊Q₈	—	2	1	no	—
227	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
228	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
229	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
230	C₂×#117	—	2	1	no	—
231	#487	—	2	4	no	—
232	#474	—	2	4	no	—
233	C₂×#107	C₂²×C₆₁	1	2	yes	—
234	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
235	C₂×#103	C₂²×C₆₁	1	4	yes	—
236	C₂×#103	C₂²×C₆₁	1	4	yes	—
237	C₂×#102	C₂²×C₆₁	1	2	yes	—
238	C₂×#102	C₂²×C₆₁	1	2	yes	—
239	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
240	#398	—	2	2	no	—
241	#391	—	2	1	no	—
242	#389	C₂²×C₆₁	1	4	yes	—
243	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
244	#340	C₂²×C₆₁	1	2	yes	—
245	#336	C₂²×C₆₁	1	4	yes	—
246	C₆₁	#25650	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₈	—	2	1	no	—
248	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
249	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
250	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
251	C₂³×C₄	—	2	1	no	—
252	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
253	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
254	C₄⋊Q₈	—	2	2	no	—
255	C₄⋊Q₈	—	2	2	no	—
256	C₄⋊Q₈	—	2	2	no	—
257	C₄⋊Q₈	—	4	4	no	—
258	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
259	#126	—	2	16	no	—
260	#124	—	2	4	no	—
261	#124	—	2	4	no	—
262	C₂²⋊Q₈	—	2	8	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	2	2	no	—
266	C₄×Q₈	—	2	2	no	—
267	C₄×D₄	—	2	2	no	—
268	C₄×D₄	D₄×C₆₁	1	4	yes	—
269	#117	—	2	8	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	4	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
276	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	—	2	1	no	—
285	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
286	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
287	#107	—	2	4	no	—
288	C₄⋊C₈	—	2	2	no	—
289	#103	—	2	8	no	—
290	#103	—	2	8	no	—
291	#102	—	2	4	no	—
292	#102	—	2	4	no	—
293	C₄×C₈	—	2	2	no	—
294	#95	—	2	1	no	—
295	#95	—	2	4	no	—
296	C₂⁴	—	2	1	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	4	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
321	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
322	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	2	4	no	—
327	C₂×C₈	—	2	2	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	8	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
340	C₄⋊C₄	#41×C₆₁	1	4	yes	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₂²⋊C₄	—	2	8	no	—
343	C₂²⋊C₄	—	2	4	no	—
344	C₄²	—	2	8	no	—
345	C₄²	—	2	2	no	—
346	C₄²	—	2	2	no	—
347	C₄²	—	4	2	no	—
348	C₄²	C₂×D₄×C₆₁	1	2	yes	—
349	C₄²	C₂×D₄×C₆₁	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	1	no	—
353	C₂³	—	4	1	no	—
354	C₂³	—	4	2	no	—
355	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
356	Q₈	—	2	8	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	Q₈	—	4	4	no	—
360	Q₈	—	8	4	no	—
361	D₄	—	2	2	no	—
362	D₄	—	2	2	no	—
363	D₄	—	4	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	8	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	#120×C₆₁	1	2	yes	—
383	C₂×C₄	#120×C₆₁	1	2	yes	—
384	C₂×C₄	#135×C₆₁	1	2	yes	—
385	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
386	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
388	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
389	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
390	C₈	—	4	2	no	—
391	C₈	—	4	2	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
398	C₂²	C₆₁×#548	1	2	yes	—
399	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
400	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
401	C₂²	C₆₁×#578	1	2	yes	—
402	C₄	—	2	2	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	8	2	no	—
409	C₄	C₆₁×#449	1	4	yes	—
410	C₄	C₆₁×#532	1	1	yes	characteristic
411	C₄	C₆₁×#536	1	1	yes	characteristic
412	C₄	C₆₁×#547	1	2	yes	—
413	C₂	—	8	2	no	—
414	C₂	C₆₁×#2432	1	1	yes	characteristic
415	C₂	C₂×C₆₁×#449	1	1	yes	characteristic
416	C₂	C₆₁×#3011	1	1	yes	characteristic
417	C₂	C₆₁×#3364	1	2	yes	—
418	C₂	C₆₁×#3367	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#487	C₂	semidirect
4. C₆₁×#2546	C₂	semidirect
6. C₆₁×#1984	C₂	semidirect
7. C₆₁×#1981	C₂	semidirect
8. C₆₁×#1863	C₂	semidirect
182. #25650	C₆₁	direct (N × H)
205. C₂×#487	C₂×C₆₁	semidirect
207. #2546	C₂×C₆₁	semidirect
209. #1984	C₂×C₆₁	semidirect
210. #1981	C₂×C₆₁	semidirect
211. #1863	C₂×C₆₁	semidirect
246. C₆₁	#25650	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×#556	2
C₂×C₆₁×#487	2
C₂×C₆₁×#474	2
C₆₁×#2546	2
C₆₁×#2042	2
C₆₁×#1984	2
C₆₁×#1981	2
C₆₁×#1863	2
C₄×#102×C₆₁	2
#25650	61

Subgroups — C61×#25650 #29529083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25650 #29529083