Subgroups — C₆₁×#29826 #29533259

Order 15616.

890 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#460	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2858	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2065	C₂	1	4	yes	maximal, complemented
6	C₆₁×#2055	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1982	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₆₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#124×C₆₁	—	2	1	no	—
14	C₂×#124×C₆₁	—	2	1	no	—
15	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#475	—	2	4	no	—
17	C₆₁×#460	—	2	4	no	—
18	C₂×#106×C₆₁	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	4	yes	—
22	C₂×#103×C₆₁	C₂²	1	2	yes	—
23	C₂×#102×C₆₁	C₂²	1	2	yes	—
24	C₂×#102×C₆₁	C₂²	1	4	yes	—
25	C₆₁×#391	C₂²	1	2	yes	—
26	C₆₁×#390	—	2	2	no	—
27	C₆₁×#390	C₂²	1	4	yes	—
28	C₆₁×#389	C₂²	1	2	yes	—
29	C₆₁×#387	—	2	2	no	—
30	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
31	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#376	—	2	1	no	—
33	C₄³×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#340	C₂²	1	4	yes	—
35	C₂²×Q₈×C₆₁	—	2	1	no	—
36	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₆₁	—	2	1	no	—
38	C₂²×D₄×C₆₁	—	2	1	no	—
39	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
40	C₂×SD₁₆×C₆₁	—	2	4	no	—
41	C₂×SD₁₆×C₆₁	—	4	4	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	#127×C₆₁	—	2	2	no	—
47	#127×C₆₁	—	2	2	no	—
48	#124×C₆₁	—	4	4	no	—
49	#124×C₆₁	—	4	4	no	—
50	C₄×Q₈×C₆₁	—	2	2	no	—
51	C₄×Q₈×C₆₁	D₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
55	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
58	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
60	C₂×C₄²×C₆₁	—	2	1	no	—
61	C₂×C₄²×C₆₁	—	2	1	no	—
62	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₁	D₄	1	2	yes	—
64	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
66	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
67	#106×C₆₁	—	2	4	no	—
68	C₄⋊C₈×C₆₁	—	2	2	no	—
69	C₄⋊C₈×C₆₁	—	2	2	no	—
70	C₄⋊C₈×C₆₁	—	4	4	no	—
71	#103×C₆₁	—	2	4	no	—
72	#102×C₆₁	—	2	4	no	—
73	#102×C₆₁	—	4	4	no	—
74	#95×C₆₁	—	2	2	no	—
75	#95×C₆₁	—	2	2	no	—
76	#95×C₆₁	—	2	2	no	—
77	#95×C₆₁	—	2	1	no	—
78	C₂⁴×C₆₁	—	2	2	no	—
79	C₂×Q₈×C₆₁	—	2	1	no	—
80	C₂×Q₈×C₆₁	—	2	2	no	—
81	C₂×Q₈×C₆₁	—	2	2	no	—
82	C₂×Q₈×C₆₁	—	4	2	no	—
83	C₂×Q₈×C₆₁	—	4	2	no	—
84	C₂×Q₈×C₆₁	—	4	2	no	—
85	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
86	C₂×D₄×C₆₁	—	2	2	no	—
87	C₂×D₄×C₆₁	—	2	2	no	—
88	C₂×D₄×C₆₁	—	2	4	no	—
89	C₂×D₄×C₆₁	—	2	4	no	—
90	C₂×D₄×C₆₁	—	4	4	no	—
91	C₂×D₄×C₆₁	—	4	2	no	—
92	C₂×D₄×C₆₁	—	4	2	no	—
93	C₂×D₄×C₆₁	—	4	2	no	—
94	C₂×D₄×C₆₁	—	4	2	no	—
95	C₂²×C₄×C₆₁	—	2	1	no	—
96	C₂²×C₄×C₆₁	—	2	1	no	—
97	C₂²×C₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	2	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	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
104	SD₁₆×C₆₁	—	4	8	no	—
105	C₂×C₈×C₆₁	—	2	2	no	—
106	C₂×C₈×C₆₁	—	2	2	no	—
107	C₂×C₈×C₆₁	—	2	4	no	—
108	C₂×C₈×C₆₁	—	2	4	no	—
109	C₄⋊C₄×C₆₁	—	2	4	no	—
110	C₄⋊C₄×C₆₁	—	2	1	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	—	4	4	no	—
116	C₄⋊C₄×C₆₁	—	4	2	no	—
117	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
118	C₂²⋊C₄×C₆₁	—	4	8	no	—
119	C₂²⋊C₄×C₆₁	—	4	8	no	—
120	C₄²×C₆₁	—	2	4	no	—
121	C₄²×C₆₁	—	2	2	no	—
122	C₄²×C₆₁	—	2	2	no	—
123	C₄²×C₆₁	—	2	2	no	—
124	C₄²×C₆₁	—	4	2	no	—
125	C₄²×C₆₁	—	4	2	no	—
126	C₄²×C₆₁	SD₁₆	1	4	yes	complemented
127	C₄²×C₆₁	C₂×D₄	1	2	yes	—
128	C₄²×C₆₁	#41	1	2	yes	—
129	C₂³×C₆₁	—	4	2	no	—
130	C₂³×C₆₁	—	4	4	no	—
131	C₂³×C₆₁	—	4	2	no	—
132	C₂³×C₆₁	—	4	2	no	—
133	C₂³×C₆₁	—	4	4	no	—
134	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₆₁	—	2	2	no	—
136	Q₈×C₆₁	—	2	2	no	—
137	Q₈×C₆₁	—	4	2	no	—
138	Q₈×C₆₁	—	8	4	no	—
139	D₄×C₆₁	—	4	2	no	—
140	D₄×C₆₁	—	4	2	no	—
141	D₄×C₆₁	—	4	4	no	—
142	D₄×C₆₁	—	8	4	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	2	no	—
148	C₂×C₄×C₆₁	—	2	2	no	—
149	C₂×C₄×C₆₁	—	2	2	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	2	no	—
155	C₂×C₄×C₆₁	—	4	2	no	—
156	C₂×C₄×C₆₁	—	4	2	no	—
157	C₂×C₄×C₆₁	—	4	2	no	—
158	C₂×C₄×C₆₁	—	4	2	no	—
159	C₂×C₄×C₆₁	—	4	2	no	—
160	C₂×C₄×C₆₁	#121	1	2	yes	—
161	C₂×C₄×C₆₁	#121	1	2	yes	—
162	C₂×C₄×C₆₁	C₂×SD₁₆	1	4	yes	—
163	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
164	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
168	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
169	C₈×C₆₁	—	4	2	no	—
170	C₈×C₆₁	—	4	2	no	—
171	#29826	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂²×C₆₁	—	8	2	no	—
173	C₂²×C₆₁	—	8	4	no	—
174	C₂²×C₆₁	—	8	4	no	—
175	C₂²×C₆₁	—	8	2	no	—
176	C₂²×C₆₁	—	8	2	no	—
177	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
178	C₂²×C₆₁	#537	1	2	yes	—
179	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
180	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
181	C₂²×C₆₁	#575	1	2	yes	—
182	C₄×C₆₁	—	2	4	no	—
183	C₄×C₆₁	—	2	2	no	—
184	C₄×C₆₁	—	4	2	no	—
185	C₄×C₆₁	—	4	2	no	—
186	C₄×C₆₁	—	4	2	no	—
187	C₄×C₆₁	—	8	2	no	—
188	C₄×C₆₁	—	8	2	no	—
189	C₄×C₆₁	#460	1	4	yes	—
190	C₄×C₆₁	#535	1	1	yes	characteristic
191	C₄×C₆₁	#536	1	1	yes	characteristic
192	C₄×C₆₁	#542	1	2	yes	—
193	C₂×#475	C₂×C₆₁	1	1	yes	characteristic, complemented
194	C₂×#460	C₂×C₆₁	1	1	yes	characteristic
195	#2858	C₂×C₆₁	1	1	yes	characteristic
196	#2295	C₂×C₆₁	1	1	yes	characteristic, complemented
197	#2065	C₂×C₆₁	1	4	yes	complemented
198	#2055	C₂×C₆₁	1	4	yes	complemented
199	#1988	C₂×C₆₁	1	1	yes	characteristic, complemented
200	#1982	C₂×C₆₁	1	1	yes	characteristic
201	#1842	C₂×C₆₁	1	1	yes	characteristic, complemented
202	C₂×C₆₁	—	16	2	no	—
203	C₂×C₆₁	#2620	1	1	yes	characteristic
204	C₂×C₆₁	C₂×#460	1	1	yes	characteristic
205	C₂×C₆₁	#3040	1	1	yes	characteristic
206	C₂×C₆₁	#3246	1	2	yes	—
207	C₂×C₆₁	#3251	1	2	yes	—
208	C₂²×SD₁₆	C₂²×C₆₁	1	2	yes	—
209	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
210	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
211	C₂×#124	—	2	1	no	—
212	C₂×#124	—	2	1	no	—
213	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
214	#475	—	2	4	no	—
215	#460	—	2	4	no	—
216	C₂×#106	C₂²×C₆₁	1	2	yes	—
217	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
218	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂²×C₆₁	1	4	yes	—
220	C₂×#103	C₂²×C₆₁	1	2	yes	—
221	C₂×#102	C₂²×C₆₁	1	2	yes	—
222	C₂×#102	C₂²×C₆₁	1	4	yes	—
223	#391	C₂²×C₆₁	1	2	yes	—
224	#390	—	2	2	no	—
225	#390	C₂²×C₆₁	1	4	yes	—
226	#389	C₂²×C₆₁	1	2	yes	—
227	#387	—	2	2	no	—
228	C₄×C₄⋊C₄	—	2	1	no	—
229	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
230	#376	—	2	1	no	—
231	C₄³	C₂²×C₆₁	1	1	yes	characteristic
232	#340	C₂²×C₆₁	1	4	yes	—
233	C₆₁	#29826	1	1	yes	characteristic, direct product factor, Sylow
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
236	C₂²×D₄	—	2	1	no	—
237	C₂²×D₄	—	2	1	no	—
238	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
239	C₂×SD₁₆	—	2	4	no	—
240	C₂×SD₁₆	—	4	4	no	—
241	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
242	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	—	2	2	no	—
245	#127	—	2	2	no	—
246	#127	—	2	2	no	—
247	#124	—	4	4	no	—
248	#124	—	4	4	no	—
249	C₄×Q₈	—	2	2	no	—
250	C₄×Q₈	D₄×C₆₁	1	4	yes	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
257	C₂×C₂²⋊C₄	—	2	4	no	—
258	C₂×C₂²⋊C₄	—	2	4	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	—	2	1	no	—
261	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
262	C₂×C₄²	D₄×C₆₁	1	2	yes	—
263	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
264	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
265	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
266	#106	—	2	4	no	—
267	C₄⋊C₈	—	2	2	no	—
268	C₄⋊C₈	—	2	2	no	—
269	C₄⋊C₈	—	4	4	no	—
270	#103	—	2	4	no	—
271	#102	—	2	4	no	—
272	#102	—	4	4	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	1	no	—
277	C₂⁴	—	2	2	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	4	2	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
302	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
303	SD₁₆	—	4	8	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	4	no	—
307	C₂×C₈	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	4	4	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
317	C₂²⋊C₄	—	4	8	no	—
318	C₂²⋊C₄	—	4	8	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	4	2	no	—
324	C₄²	—	4	2	no	—
325	C₄²	SD₁₆×C₆₁	1	4	yes	complemented
326	C₄²	C₂×D₄×C₆₁	1	2	yes	—
327	C₄²	#41×C₆₁	1	2	yes	—
328	C₂³	—	4	4	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	4	no	—
332	C₂³	—	4	2	no	—
333	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
334	Q₈	—	2	2	no	—
335	Q₈	—	2	2	no	—
336	Q₈	—	4	2	no	—
337	Q₈	—	8	4	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	4	no	—
341	D₄	—	8	4	no	—
342	D₄	—	8	4	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	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	#121×C₆₁	1	2	yes	—
360	C₂×C₄	#121×C₆₁	1	2	yes	—
361	C₂×C₄	C₂×SD₁₆×C₆₁	1	4	yes	—
362	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
363	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
364	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
365	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
366	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
367	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
368	C₈	—	4	2	no	—
369	C₈	—	4	2	no	—
370	C₂²	—	8	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	4	no	—
374	C₂²	—	8	4	no	—
375	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
376	C₂²	C₆₁×#537	1	2	yes	—
377	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
378	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
379	C₂²	C₆₁×#575	1	2	yes	—
380	C₄	—	2	2	no	—
381	C₄	—	2	4	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	4	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	8	2	no	—
387	C₄	C₆₁×#460	1	4	yes	—
388	C₄	C₆₁×#535	1	1	yes	characteristic
389	C₄	C₆₁×#536	1	1	yes	characteristic
390	C₄	C₆₁×#542	1	2	yes	—
391	C₂	—	16	2	no	—
392	C₂	C₆₁×#2620	1	1	yes	characteristic
393	C₂	C₂×C₆₁×#460	1	1	yes	characteristic
394	C₂	C₆₁×#3040	1	1	yes	characteristic
395	C₂	C₆₁×#3246	1	2	yes	—
396	C₂	C₆₁×#3251	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 ◁ C₄³×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#475	C₂	semidirect
4. C₆₁×#2295	C₂	semidirect
5. C₆₁×#2065	C₂	semidirect
6. C₆₁×#2055	C₂	semidirect
7. C₆₁×#1988	C₂	semidirect
9. C₆₁×#1842	C₂	semidirect
126. C₄²×C₆₁	SD₁₆	semidirect
171. #29826	C₆₁	direct (N × H)
193. C₂×#475	C₂×C₆₁	semidirect
196. #2295	C₂×C₆₁	semidirect
197. #2065	C₂×C₆₁	semidirect
198. #2055	C₂×C₆₁	semidirect
199. #1988	C₂×C₆₁	semidirect
201. #1842	C₂×C₆₁	semidirect
233. C₆₁	#29826	direct (N × H)
325. C₄²	SD₁₆×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₆₁×#475	2
C₂×C₆₁×#460	2
C₆₁×#2858	2
C₆₁×#2295	2
C₆₁×#2065	2
C₆₁×#2055	2
C₆₁×#1988	2
C₆₁×#1982	2
C₆₁×#1842	2
#29826	61

Subgroups — C61×#29826 #29533259

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#29826 #29533259