Subgroups — C₆₁×#25652 #29529085

Order 15616.

1118 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#486	C₂	1	1	yes	maximal, characteristic
3	C₂×C₆₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2042	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1982	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1864	C₂	1	4	yes	maximal, complemented
9	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#559	—	2	4	no	—
11	C₆₁×#559	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₆₁	—	2	1	no	—
16	C₂×#124×C₆₁	C₂²	1	2	yes	—
17	C₂×#123×C₆₁	—	2	2	no	—
18	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	—	2	1	no	—
21	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
22	C₆₁×#486	—	2	4	no	—
23	C₆₁×#475	—	2	4	no	—
24	C₂×#106×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×#103×C₆₁	C₂²	1	2	yes	—
28	C₂×#102×C₆₁	C₂²	1	4	yes	—
29	C₂×#102×C₆₁	C₂²	1	4	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	1	yes	characteristic
40	C₂²×D₄×C₆₁	—	2	1	no	—
41	C₂²×D₄×C₆₁	—	2	1	no	—
42	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₁	—	2	2	no	—
44	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
45	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
46	C₄⋊Q₈×C₆₁	—	2	2	no	—
47	C₄⋊Q₈×C₆₁	—	2	2	no	—
48	C₄⋊Q₈×C₆₁	—	4	4	no	—
49	#127×C₆₁	—	2	2	no	—
50	#127×C₆₁	D₄	1	4	yes	—
51	#124×C₆₁	—	2	8	no	—
52	#124×C₆₁	—	2	4	no	—
53	#124×C₆₁	—	2	4	no	—
54	#123×C₆₁	—	2	16	no	—
55	C₄×Q₈×C₆₁	—	2	2	no	—
56	C₄×Q₈×C₆₁	—	2	2	no	—
57	C₄×Q₈×C₆₁	—	2	2	no	—
58	C₄×Q₈×C₆₁	D₄	1	4	yes	—
59	C₄×D₄×C₆₁	—	2	8	no	—
60	C₄×D₄×C₆₁	—	2	4	no	—
61	C₄×D₄×C₆₁	—	2	4	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	1	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	2	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄²×C₆₁	—	2	1	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	#106×C₆₁	—	2	4	no	—
78	C₄⋊C₈×C₆₁	—	2	2	no	—
79	#103×C₆₁	—	2	4	no	—
80	#103×C₆₁	—	2	4	no	—
81	#102×C₆₁	—	2	8	no	—
82	#102×C₆₁	—	2	8	no	—
83	C₄×C₈×C₆₁	—	2	2	no	—
84	#95×C₆₁	—	2	1	no	—
85	#95×C₆₁	—	2	4	no	—
86	C₂⁴×C₆₁	—	2	2	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	1	no	—
91	C₂×Q₈×C₆₁	—	2	2	no	—
92	C₂×Q₈×C₆₁	—	2	2	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	2	yes	—
97	C₂×D₄×C₆₁	—	2	4	no	—
98	C₂×D₄×C₆₁	—	2	4	no	—
99	C₂×D₄×C₆₁	—	2	2	no	—
100	C₂×D₄×C₆₁	—	2	4	no	—
101	C₂×D₄×C₆₁	—	2	4	no	—
102	C₂×D₄×C₆₁	—	4	2	no	—
103	C₂×D₄×C₆₁	—	4	2	no	—
104	C₂×D₄×C₆₁	—	8	2	no	—
105	C₂×D₄×C₆₁	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	2	1	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	8	no	—
110	C₂²×C₄×C₆₁	—	2	2	no	—
111	C₂²×C₄×C₆₁	—	8	4	no	—
112	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₆₁	—	2	2	no	—
118	C₂×C₈×C₆₁	—	2	2	no	—
119	C₂×C₈×C₆₁	—	2	4	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₄⋊C₄×C₆₁	—	2	4	no	—
123	C₄⋊C₄×C₆₁	—	2	2	no	—
124	C₄⋊C₄×C₆₁	—	2	4	no	—
125	C₄⋊C₄×C₆₁	—	2	1	no	—
126	C₄⋊C₄×C₆₁	—	2	2	no	—
127	C₄⋊C₄×C₆₁	—	2	2	no	—
128	C₄⋊C₄×C₆₁	—	2	2	no	—
129	C₄⋊C₄×C₆₁	—	4	8	no	—
130	C₄⋊C₄×C₆₁	—	4	2	no	—
131	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₄⋊C₄×C₆₁	#41	1	4	yes	—
133	C₂²⋊C₄×C₆₁	—	2	8	no	—
134	C₂²⋊C₄×C₆₁	—	2	8	no	—
135	C₂²⋊C₄×C₆₁	—	2	8	no	—
136	C₄²×C₆₁	—	2	4	no	—
137	C₄²×C₆₁	—	2	2	no	—
138	C₄²×C₆₁	—	2	2	no	—
139	C₄²×C₆₁	—	4	2	no	—
140	C₄²×C₆₁	C₂×D₄	1	2	yes	—
141	C₄²×C₆₁	C₂×D₄	1	2	yes	—
142	C₂³×C₆₁	—	2	4	no	—
143	C₂³×C₆₁	—	4	4	no	—
144	C₂³×C₆₁	—	4	2	no	—
145	C₂³×C₆₁	—	4	2	no	—
146	C₂³×C₆₁	—	4	4	no	—
147	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
148	Q₈×C₆₁	—	2	2	no	—
149	Q₈×C₆₁	—	2	2	no	—
150	Q₈×C₆₁	—	4	2	no	—
151	Q₈×C₆₁	—	4	4	no	—
152	Q₈×C₆₁	—	8	4	no	—
153	D₄×C₆₁	—	2	8	no	—
154	D₄×C₆₁	—	4	2	no	—
155	D₄×C₆₁	—	4	2	no	—
156	D₄×C₆₁	—	4	8	no	—
157	D₄×C₆₁	—	8	4	no	—
158	C₂×C₄×C₆₁	—	2	2	no	—
159	C₂×C₄×C₆₁	—	2	2	no	—
160	C₂×C₄×C₆₁	—	2	2	no	—
161	C₂×C₄×C₆₁	—	2	2	no	—
162	C₂×C₄×C₆₁	—	2	2	no	—
163	C₂×C₄×C₆₁	—	2	4	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	2	no	—
166	C₂×C₄×C₆₁	—	2	4	no	—
167	C₂×C₄×C₆₁	—	4	2	no	—
168	C₂×C₄×C₆₁	—	4	2	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	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	8	8	no	—
175	C₂×C₄×C₆₁	#120	1	2	yes	—
176	C₂×C₄×C₆₁	#120	1	2	yes	—
177	C₂×C₄×C₆₁	#135	1	2	yes	—
178	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
179	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
182	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
183	C₈×C₆₁	—	4	2	no	—
184	C₈×C₆₁	—	4	2	no	—
185	#25652	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₆₁	—	4	4	no	—
187	C₂²×C₆₁	—	4	4	no	—
188	C₂²×C₆₁	—	4	4	no	—
189	C₂²×C₆₁	—	8	4	no	—
190	C₂²×C₆₁	—	8	4	no	—
191	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
192	C₂²×C₆₁	#548	1	2	yes	—
193	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
194	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂²×C₆₁	#577	1	2	yes	—
196	C₄×C₆₁	—	2	2	no	—
197	C₄×C₆₁	—	4	4	no	—
198	C₄×C₆₁	—	4	2	no	—
199	C₄×C₆₁	—	4	2	no	—
200	C₄×C₆₁	—	4	2	no	—
201	C₄×C₆₁	—	4	2	no	—
202	C₄×C₆₁	—	8	2	no	—
203	C₄×C₆₁	#449	1	4	yes	—
204	C₄×C₆₁	#532	1	1	yes	characteristic
205	C₄×C₆₁	#536	1	1	yes	characteristic
206	C₄×C₆₁	#547	1	2	yes	—
207	C₂×#559	C₂×C₆₁	1	1	yes	characteristic
208	C₂×#486	C₂×C₆₁	1	1	yes	characteristic
209	C₂×#475	C₂×C₆₁	1	1	yes	characteristic, complemented
210	#2546	C₂×C₆₁	1	1	yes	characteristic, complemented
211	#2042	C₂×C₆₁	1	4	yes	complemented
212	#1984	C₂×C₆₁	1	1	yes	characteristic, complemented
213	#1982	C₂×C₆₁	1	1	yes	characteristic
214	#1864	C₂×C₆₁	1	4	yes	complemented
215	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
216	C₂×C₆₁	—	8	4	no	—
217	C₂×C₆₁	#2432	1	1	yes	characteristic
218	C₂×C₆₁	C₂×#449	1	1	yes	characteristic
219	C₂×C₆₁	#3009	1	1	yes	characteristic
220	C₂×C₆₁	#3365	1	2	yes	—
221	C₂×C₆₁	#3373	1	2	yes	—
222	#559	—	2	4	no	—
223	#559	—	2	4	no	—
224	C₂×C₄⋊Q₈	—	2	1	no	—
225	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
226	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
227	C₂×#124	—	2	1	no	—
228	C₂×#124	C₂²×C₆₁	1	2	yes	—
229	C₂×#123	—	2	2	no	—
230	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
231	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
232	C₂×C₄×D₄	—	2	1	no	—
233	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
234	#486	—	2	4	no	—
235	#475	—	2	4	no	—
236	C₂×#106	C₂²×C₆₁	1	2	yes	—
237	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
238	C₂×#103	C₂²×C₆₁	1	2	yes	—
239	C₂×#103	C₂²×C₆₁	1	2	yes	—
240	C₂×#102	C₂²×C₆₁	1	4	yes	—
241	C₂×#102	C₂²×C₆₁	1	4	yes	—
242	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
243	#398	—	2	2	no	—
244	#391	—	2	1	no	—
245	#389	C₂²×C₆₁	1	4	yes	—
246	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
247	#340	C₂²×C₆₁	1	2	yes	—
248	#336	C₂²×C₆₁	1	4	yes	—
249	C₆₁	#25652	1	1	yes	characteristic, direct product factor, Sylow
250	C₂²×Q₈	—	2	1	no	—
251	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
252	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	—	2	1	no	—
255	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
256	C₂³×C₄	—	2	2	no	—
257	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
258	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	—	2	2	no	—
261	C₄⋊Q₈	—	4	4	no	—
262	#127	—	2	2	no	—
263	#127	D₄×C₆₁	1	4	yes	—
264	#124	—	2	8	no	—
265	#124	—	2	4	no	—
266	#124	—	2	4	no	—
267	#123	—	2	16	no	—
268	C₄×Q₈	—	2	2	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	2	no	—
271	C₄×Q₈	D₄×C₆₁	1	4	yes	—
272	C₄×D₄	—	2	8	no	—
273	C₄×D₄	—	2	4	no	—
274	C₄×D₄	—	2	4	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
279	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
281	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
289	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
290	#106	—	2	4	no	—
291	C₄⋊C₈	—	2	2	no	—
292	#103	—	2	4	no	—
293	#103	—	2	4	no	—
294	#102	—	2	8	no	—
295	#102	—	2	8	no	—
296	C₄×C₈	—	2	2	no	—
297	#95	—	2	1	no	—
298	#95	—	2	4	no	—
299	C₂⁴	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	—	4	2	no	—
308	C₂×Q₈	—	4	2	no	—
309	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	8	2	no	—
318	C₂×D₄	C₂×D₄×C₆₁	1	4	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	8	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	8	4	no	—
325	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
327	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
329	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	4	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	8	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
345	C₄⋊C₄	#41×C₆₁	1	4	yes	—
346	C₂²⋊C₄	—	2	8	no	—
347	C₂²⋊C₄	—	2	8	no	—
348	C₂²⋊C₄	—	2	8	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	2	no	—
353	C₄²	C₂×D₄×C₆₁	1	2	yes	—
354	C₄²	C₂×D₄×C₆₁	1	2	yes	—
355	C₂³	—	2	4	no	—
356	C₂³	—	4	4	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	4	no	—
360	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
361	Q₈	—	2	2	no	—
362	Q₈	—	2	2	no	—
363	Q₈	—	4	2	no	—
364	Q₈	—	4	4	no	—
365	Q₈	—	8	4	no	—
366	D₄	—	2	8	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	2	no	—
369	D₄	—	4	8	no	—
370	D₄	—	8	4	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	8	8	no	—
388	C₂×C₄	#120×C₆₁	1	2	yes	—
389	C₂×C₄	#120×C₆₁	1	2	yes	—
390	C₂×C₄	#135×C₆₁	1	2	yes	—
391	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
392	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
394	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
395	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
396	C₈	—	4	2	no	—
397	C₈	—	4	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	4	no	—
402	C₂²	—	8	4	no	—
403	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
404	C₂²	C₆₁×#548	1	2	yes	—
405	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
406	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
407	C₂²	C₆₁×#577	1	2	yes	—
408	C₄	—	2	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₆₁×#449	1	4	yes	—
416	C₄	C₆₁×#532	1	1	yes	characteristic
417	C₄	C₆₁×#536	1	1	yes	characteristic
418	C₄	C₆₁×#547	1	2	yes	—
419	C₂	—	8	4	no	—
420	C₂	C₆₁×#2432	1	1	yes	characteristic
421	C₂	C₂×C₆₁×#449	1	1	yes	characteristic
422	C₂	C₆₁×#3009	1	1	yes	characteristic
423	C₂	C₆₁×#3365	1	2	yes	—
424	C₂	C₆₁×#3373	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#127×C₆₁	C₂²
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
3. C₂×C₆₁×#475	C₂	semidirect
4. C₆₁×#2546	C₂	semidirect
5. C₆₁×#2042	C₂	semidirect
6. C₆₁×#1984	C₂	semidirect
8. C₆₁×#1864	C₂	semidirect
9. C₄×#103×C₆₁	C₂	semidirect
185. #25652	C₆₁	direct (N × H)
209. C₂×#475	C₂×C₆₁	semidirect
210. #2546	C₂×C₆₁	semidirect
211. #2042	C₂×C₆₁	semidirect
212. #1984	C₂×C₆₁	semidirect
214. #1864	C₂×C₆₁	semidirect
215. C₄×#103	C₂×C₆₁	semidirect
249. C₆₁	#25652	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×#559	2
C₂×C₆₁×#486	2
C₂×C₆₁×#475	2
C₆₁×#2546	2
C₆₁×#2042	2
C₆₁×#1984	2
C₆₁×#1982	2
C₆₁×#1864	2
C₄×#103×C₆₁	2
#25652	61

Subgroups — C61×#25652 #29529085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25652 #29529085