Subgroups — C₆₁×#24273 #29527706

Order 15616.

1384 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	C₂³×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#470	C₂	1	2	yes	maximal, complemented
3	C₂×C₆₁×#435	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2409	C₂	1	2	yes	maximal
5	C₆₁×#2056	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2001	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1971	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1787	C₂	1	2	yes	maximal, complemented
10	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₆₁	—	2	8	no	—
12	C₂²×Q₁₆×C₆₁	—	2	4	no	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#470	—	2	8	no	—
20	C₆₁×#435	—	2	4	no	—
21	C₂×#106×C₆₁	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#103×C₆₁	C₂²	1	4	yes	—
24	C₂×#103×C₆₁	C₂²	1	4	yes	—
25	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#395	—	2	2	no	—
29	C₆₁×#393	—	2	2	no	—
30	C₆₁×#391	C₂²	1	4	yes	—
31	C₆₁×#386	—	2	2	no	—
32	C₆₁×#385	—	2	2	no	—
33	C₆₁×#380	C₂²	1	2	yes	—
34	C₆₁×#340	C₂²	1	2	yes	—
35	C₂²×Q₈×C₆₁	—	2	2	no	—
36	C₂²×Q₈×C₆₁	—	2	8	no	—
37	C₂²×Q₈×C₆₁	—	2	4	no	—
38	C₂²×Q₈×C₆₁	—	2	4	no	—
39	C₂²×Q₈×C₆₁	—	4	4	no	—
40	C₂²×Q₈×C₆₁	C₂³	1	4	yes	—
41	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₁	—	2	2	no	—
43	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂×Q₁₆×C₆₁	—	2	32	no	—
46	C₂×Q₁₆×C₆₁	—	2	8	no	—
47	C₂×Q₁₆×C₆₁	—	2	4	no	—
48	C₂×Q₁₆×C₆₁	—	2	4	no	—
49	C₂×Q₁₆×C₆₁	—	2	4	no	—
50	C₂×Q₁₆×C₆₁	D₄	1	8	yes	complemented
51	C₂×M₁₆×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	—	2	4	no	—
53	C₂²×C₈×C₆₁	—	2	4	no	—
54	C₂²×C₈×C₆₁	D₄	1	4	yes	—
55	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
59	C₂²⋊Q₈×C₆₁	—	2	8	no	—
60	C₂²⋊Q₈×C₆₁	—	4	4	no	—
61	C₄×D₄×C₆₁	—	2	2	no	—
62	C₄×D₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
64	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	4	yes	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
71	#106×C₆₁	—	2	4	no	—
72	C₄⋊C₈×C₆₁	—	2	2	no	—
73	#103×C₆₁	—	2	8	no	—
74	#103×C₆₁	—	4	4	no	—
75	C₂²⋊C₈×C₆₁	—	2	2	no	—
76	C₂²⋊C₈×C₆₁	—	2	2	no	—
77	#97×C₆₁	—	2	2	no	—
78	#95×C₆₁	—	2	2	no	—
79	#95×C₆₁	—	2	4	no	—
80	#95×C₆₁	—	2	4	no	—
81	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
82	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₆₁	—	2	4	no	—
84	C₂×Q₈×C₆₁	—	2	16	no	—
85	C₂×Q₈×C₆₁	—	2	4	no	—
86	C₂×Q₈×C₆₁	—	2	4	no	—
87	C₂×Q₈×C₆₁	—	2	4	no	—
88	C₂×Q₈×C₆₁	—	2	4	no	—
89	C₂×Q₈×C₆₁	—	4	8	no	—
90	C₂×Q₈×C₆₁	—	4	16	no	—
91	C₂×Q₈×C₆₁	—	4	8	no	—
92	C₂×Q₈×C₆₁	—	4	4	no	—
93	C₂×Q₈×C₆₁	C₂×D₄	1	8	yes	—
94	C₂×D₄×C₆₁	—	2	2	no	—
95	C₂×D₄×C₆₁	—	2	4	no	—
96	C₂²×C₄×C₆₁	—	2	2	no	—
97	C₂²×C₄×C₆₁	—	2	2	no	—
98	C₂²×C₄×C₆₁	—	2	4	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	2	no	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	4	no	—
104	C₂²×C₄×C₆₁	—	4	8	no	—
105	C₂²×C₄×C₆₁	—	4	4	no	—
106	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₆₁	#41	1	2	yes	—
112	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₆₁	—	2	16	no	—
114	Q₁₆×C₆₁	—	2	16	no	—
115	M₁₆×C₆₁	—	4	4	no	—
116	C₂×C₈×C₆₁	—	2	2	no	—
117	C₂×C₈×C₆₁	—	2	8	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
124	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
125	C₄⋊C₄×C₆₁	—	2	2	no	—
126	C₄⋊C₄×C₆₁	—	2	4	no	—
127	C₄⋊C₄×C₆₁	—	2	4	no	—
128	C₄⋊C₄×C₆₁	—	4	8	no	—
129	C₂²⋊C₄×C₆₁	—	2	2	no	—
130	C₂²⋊C₄×C₆₁	—	2	2	no	—
131	C₂²⋊C₄×C₆₁	—	4	8	no	—
132	C₂²⋊C₄×C₆₁	—	4	4	no	—
133	C₄²×C₆₁	—	2	1	no	—
134	C₄²×C₆₁	—	2	1	no	—
135	C₂³×C₆₁	—	2	2	no	—
136	C₂³×C₆₁	—	2	2	no	—
137	C₂³×C₆₁	—	2	1	no	—
138	C₂³×C₆₁	—	2	2	no	—
139	C₂³×C₆₁	—	2	2	no	—
140	C₂³×C₆₁	—	2	2	no	—
141	C₂³×C₆₁	#121	1	2	yes	—
142	C₂³×C₆₁	#137	1	4	yes	—
143	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₆₁	—	2	8	no	—
145	Q₈×C₆₁	—	2	8	no	—
146	Q₈×C₆₁	—	4	16	no	—
147	Q₈×C₆₁	—	4	4	no	—
148	Q₈×C₆₁	—	4	4	no	—
149	D₄×C₆₁	—	4	4	no	—
150	C₂×C₄×C₆₁	—	2	2	no	—
151	C₂×C₄×C₆₁	—	2	2	no	—
152	C₂×C₄×C₆₁	—	2	2	no	—
153	C₂×C₄×C₆₁	—	2	4	no	—
154	C₂×C₄×C₆₁	—	2	1	no	—
155	C₂×C₄×C₆₁	—	2	1	no	—
156	C₂×C₄×C₆₁	—	2	1	no	—
157	C₂×C₄×C₆₁	—	2	8	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	—	4	16	no	—
162	C₂×C₄×C₆₁	—	4	4	no	—
163	C₂×C₄×C₆₁	—	4	4	no	—
164	C₂×C₄×C₆₁	—	4	1	no	—
165	C₂×C₄×C₆₁	—	4	1	no	—
166	C₂×C₄×C₆₁	—	4	2	no	—
167	C₂×C₄×C₆₁	—	4	4	no	—
168	C₂×C₄×C₆₁	—	4	4	no	—
169	C₂×C₄×C₆₁	—	4	4	no	—
170	C₂×C₄×C₆₁	#121	1	2	yes	—
171	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
172	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
173	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
175	C₈×C₆₁	—	2	2	no	—
176	C₈×C₆₁	—	4	1	no	—
177	C₈×C₆₁	—	4	1	no	—
178	C₈×C₆₁	#120	1	4	yes	—
179	#24273	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₆₁	—	2	2	no	—
181	C₂²×C₆₁	—	2	8	no	—
182	C₂²×C₆₁	—	2	2	no	—
183	C₂²×C₆₁	—	4	1	no	—
184	C₂²×C₆₁	—	4	4	no	—
185	C₂²×C₆₁	—	4	1	no	—
186	C₂²×C₆₁	—	4	1	no	—
187	C₂²×C₆₁	#470	1	4	yes	complemented
188	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
189	C₂²×C₆₁	D₄²	1	2	yes	—
190	C₂²×C₆₁	C₂×#137	1	2	yes	—
191	C₂²×C₆₁	#578	1	2	yes	—
192	C₄×C₆₁	—	2	2	no	—
193	C₄×C₆₁	—	4	1	no	—
194	C₄×C₆₁	—	4	8	no	—
195	C₄×C₆₁	—	4	1	no	—
196	C₄×C₆₁	—	4	1	no	—
197	C₄×C₆₁	—	8	4	no	—
198	C₄×C₆₁	C₂×#120	1	1	yes	characteristic
199	C₄×C₆₁	#535	1	1	yes	characteristic
200	C₄×C₆₁	#546	1	2	yes	—
201	C₂³×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
202	C₂×#470	C₂×C₆₁	1	2	yes	complemented
203	C₂×#435	C₂×C₆₁	1	1	yes	characteristic
204	#2409	C₂×C₆₁	1	2	yes	—
205	#2056	C₂×C₆₁	1	2	yes	complemented
206	#2001	C₂×C₆₁	1	2	yes	complemented
207	#1971	C₂×C₆₁	1	2	yes	complemented
208	#1807	C₂×C₆₁	1	1	yes	characteristic, complemented
209	#1787	C₂×C₆₁	1	2	yes	complemented
210	C₂×C₆₁	—	2	4	no	—
211	C₂×C₆₁	—	8	1	no	—
212	C₂×C₆₁	#2408	1	1	yes	characteristic
213	C₂×C₆₁	C₂×#470	1	1	yes	characteristic
214	C₂×C₆₁	#3059	1	1	yes	characteristic
215	C₂×C₆₁	#3270	1	4	yes	—
216	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
217	C₂²×Q₁₆	—	2	8	no	—
218	C₂²×Q₁₆	—	2	4	no	—
219	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
220	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
221	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
222	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
223	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
224	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
225	#470	—	2	8	no	—
226	#435	—	2	4	no	—
227	C₂×#106	C₂²×C₆₁	1	2	yes	—
228	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
229	C₂×#103	C₂²×C₆₁	1	4	yes	—
230	C₂×#103	C₂²×C₆₁	1	4	yes	—
231	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
232	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
234	#395	—	2	2	no	—
235	#393	—	2	2	no	—
236	#391	C₂²×C₆₁	1	4	yes	—
237	#386	—	2	2	no	—
238	#385	—	2	2	no	—
239	#380	C₂²×C₆₁	1	2	yes	—
240	#340	C₂²×C₆₁	1	2	yes	—
241	C₆₁	#24273	1	1	yes	characteristic, direct product factor, Sylow
242	C₂²×Q₈	—	2	2	no	—
243	C₂²×Q₈	—	2	8	no	—
244	C₂²×Q₈	—	2	4	no	—
245	C₂²×Q₈	—	2	4	no	—
246	C₂²×Q₈	—	4	4	no	—
247	C₂²×Q₈	C₂³×C₆₁	1	4	yes	—
248	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
251	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
252	C₂×Q₁₆	—	2	32	no	—
253	C₂×Q₁₆	—	2	8	no	—
254	C₂×Q₁₆	—	2	4	no	—
255	C₂×Q₁₆	—	2	4	no	—
256	C₂×Q₁₆	—	2	4	no	—
257	C₂×Q₁₆	D₄×C₆₁	1	8	yes	complemented
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	4	no	—
260	C₂²×C₈	—	2	4	no	—
261	C₂²×C₈	D₄×C₆₁	1	4	yes	—
262	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
264	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
266	C₂²⋊Q₈	—	2	8	no	—
267	C₂²⋊Q₈	—	4	4	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	4	no	—
271	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₆₁	1	4	yes	—
273	C₂×C₂²⋊C₄	—	2	4	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
277	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
278	#106	—	2	4	no	—
279	C₄⋊C₈	—	2	2	no	—
280	#103	—	2	8	no	—
281	#103	—	4	4	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	#97	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	4	no	—
287	#95	—	2	4	no	—
288	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
289	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	16	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	2	4	no	—
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	4	8	no	—
297	C₂×Q₈	—	4	16	no	—
298	C₂×Q₈	—	4	8	no	—
299	C₂×Q₈	—	4	4	no	—
300	C₂×Q₈	C₂×D₄×C₆₁	1	8	yes	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	4	no	—
311	C₂²×C₄	—	4	8	no	—
312	C₂²×C₄	—	4	4	no	—
313	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
317	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
318	C₂²×C₄	#41×C₆₁	1	2	yes	—
319	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
320	Q₁₆	—	2	16	no	—
321	Q₁₆	—	2	16	no	—
322	M₁₆	—	4	4	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	8	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
331	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	4	8	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	4	8	no	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	1	no	—
348	C₂³	#121×C₆₁	1	2	yes	—
349	C₂³	#137×C₆₁	1	4	yes	—
350	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
351	Q₈	—	2	8	no	—
352	Q₈	—	2	8	no	—
353	Q₈	—	4	16	no	—
354	Q₈	—	4	4	no	—
355	Q₈	—	4	4	no	—
356	D₄	—	4	4	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	8	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	16	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	#121×C₆₁	1	2	yes	—
378	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
379	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
380	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
381	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
382	C₈	—	2	2	no	—
383	C₈	—	4	1	no	—
384	C₈	—	4	1	no	—
385	C₈	#120×C₆₁	1	4	yes	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	4	no	—
393	C₂²	C₆₁×#470	1	4	yes	complemented
394	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
395	C₂²	D₄²×C₆₁	1	2	yes	—
396	C₂²	C₂×#137×C₆₁	1	2	yes	—
397	C₂²	C₆₁×#578	1	2	yes	—
398	C₄	—	2	2	no	—
399	C₄	—	4	1	no	—
400	C₄	—	4	1	no	—
401	C₄	—	4	1	no	—
402	C₄	—	4	8	no	—
403	C₄	—	8	4	no	—
404	C₄	C₂×#120×C₆₁	1	1	yes	characteristic
405	C₄	C₆₁×#535	1	1	yes	characteristic
406	C₄	C₆₁×#546	1	2	yes	—
407	C₂	—	2	4	no	—
408	C₂	—	8	1	no	—
409	C₂	C₆₁×#2408	1	1	yes	characteristic
410	C₂	C₂×C₆₁×#470	1	1	yes	characteristic
411	C₂	C₆₁×#3059	1	1	yes	characteristic
412	C₂	C₆₁×#3270	1	4	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂³×Q₁₆×C₆₁	C₂	semidirect
2. C₂×C₆₁×#470	C₂	semidirect
5. C₆₁×#2056	C₂	semidirect
6. C₆₁×#2001	C₂	semidirect
7. C₆₁×#1971	C₂	semidirect
8. C₆₁×#1807	C₂	semidirect
9. C₆₁×#1787	C₂	semidirect
50. C₂×Q₁₆×C₆₁	D₄	semidirect
179. #24273	C₆₁	direct (N × H)
187. C₂²×C₆₁	#470	semidirect
201. C₂³×Q₁₆	C₂×C₆₁	semidirect
202. C₂×#470	C₂×C₆₁	semidirect
205. #2056	C₂×C₆₁	semidirect
206. #2001	C₂×C₆₁	semidirect
207. #1971	C₂×C₆₁	semidirect
208. #1807	C₂×C₆₁	semidirect
209. #1787	C₂×C₆₁	semidirect
241. C₆₁	#24273	direct (N × H)
257. C₂×Q₁₆	D₄×C₆₁	semidirect
393. C₂²	C₆₁×#470	semidirect

Maximal subgroups

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

subgroup	index
C₂³×Q₁₆×C₆₁	2
C₂×C₆₁×#470	2
C₂×C₆₁×#435	2
C₆₁×#2409	2
C₆₁×#2056	2
C₆₁×#2001	2
C₆₁×#1971	2
C₆₁×#1807	2
C₆₁×#1787	2
#24273	61

Subgroups — C61×#24273 #29527706

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24273 #29527706