Subgroups — C₆₁×#24746 #29528179

Order 15616.

900 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#462	C₂	1	2	yes	maximal
3	C₂×C₆₁×#441	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2546	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2351	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#2066	C₂	1	2	yes	maximal
7	C₆₁×#2043	C₂	1	2	yes	maximal
8	C₆₁×#1960	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1940	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1878	C₂	1	2	yes	maximal
11	C₆₁×#1805	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#462	—	2	8	no	—
20	C₆₁×#462	—	2	4	no	—
21	C₆₁×#441	—	2	4	no	—
22	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	2	yes	—
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×#103×C₆₁	C₂²	1	2	yes	—
28	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
32	C₆₁×#398	—	2	1	no	—
33	C₆₁×#398	—	2	1	no	—
34	C₆₁×#391	C₂²	1	2	yes	—
35	C₆₁×#389	—	2	2	no	—
36	C₆₁×#389	—	2	2	no	—
37	C₆₁×#389	C₂²	1	2	yes	—
38	C₆₁×#382	—	2	1	no	—
39	C₆₁×#382	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
41	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
45	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂×Q₁₆×C₆₁	—	2	2	no	—
48	C₂×Q₁₆×C₆₁	—	2	2	no	—
49	C₂×Q₁₆×C₆₁	—	2	4	no	—
50	C₂×Q₁₆×C₆₁	—	2	4	no	—
51	C₂×Q₁₆×C₆₁	—	2	4	no	—
52	C₂×Q₁₆×C₆₁	D₄	1	4	yes	—
53	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₆₁	—	2	4	no	—
57	C₄⋊Q₈×C₆₁	—	2	2	no	—
58	C₄⋊Q₈×C₆₁	—	2	2	no	—
59	C₄⋊Q₈×C₆₁	—	4	2	no	—
60	C₄×Q₈×C₆₁	—	2	2	no	—
61	C₄×Q₈×C₆₁	—	2	4	no	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×Q₈×C₆₁	—	2	2	no	—
64	C₄×Q₈×C₆₁	—	4	2	no	—
65	C₄×Q₈×C₆₁	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	—	2	1	no	—
79	C₂×C₄²×C₆₁	—	2	2	no	—
80	C₂×C₄²×C₆₁	—	2	1	no	—
81	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
83	#106×C₆₁	—	2	2	no	—
84	C₄⋊C₈×C₆₁	—	2	4	no	—
85	C₄⋊C₈×C₆₁	—	2	2	no	—
86	#103×C₆₁	—	2	2	no	—
87	#103×C₆₁	—	2	4	no	—
88	#103×C₆₁	—	2	4	no	—
89	#103×C₆₁	—	2	2	no	—
90	#103×C₆₁	—	2	4	no	—
91	#103×C₆₁	—	4	2	no	—
92	#97×C₆₁	—	2	2	no	—
93	#95×C₆₁	—	2	1	no	—
94	#95×C₆₁	—	2	2	no	—
95	#95×C₆₁	—	2	1	no	—
96	#95×C₆₁	—	2	2	no	—
97	#95×C₆₁	—	2	2	no	—
98	#95×C₆₁	D₄	1	1	yes	characteristic
99	#95×C₆₁	D₄	1	1	yes	characteristic
100	C₂×Q₈×C₆₁	—	2	1	no	—
101	C₂×Q₈×C₆₁	—	2	1	no	—
102	C₂×Q₈×C₆₁	—	2	1	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	1	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	1	no	—
109	C₂×Q₈×C₆₁	—	2	2	no	—
110	C₂×Q₈×C₆₁	—	2	2	no	—
111	C₂×Q₈×C₆₁	—	2	2	no	—
112	C₂×Q₈×C₆₁	—	2	1	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
115	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
116	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
117	C₂×Q₈×C₆₁	#41	1	2	yes	—
118	C₂²×C₄×C₆₁	—	2	1	no	—
119	C₂²×C₄×C₆₁	—	2	1	no	—
120	C₂²×C₄×C₆₁	—	2	1	no	—
121	C₂²×C₄×C₆₁	—	2	1	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
129	Q₁₆×C₆₁	—	2	8	no	—
130	Q₁₆×C₆₁	—	4	8	no	—
131	C₂×C₈×C₆₁	—	2	1	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	1	no	—
134	C₂×C₈×C₆₁	—	2	2	no	—
135	C₂×C₈×C₆₁	—	2	2	no	—
136	C₂×C₈×C₆₁	—	2	2	no	—
137	C₂×C₈×C₆₁	—	2	1	no	—
138	C₂×C₈×C₆₁	—	2	1	no	—
139	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
140	C₄⋊C₄×C₆₁	—	2	4	no	—
141	C₄⋊C₄×C₆₁	—	2	4	no	—
142	C₄⋊C₄×C₆₁	—	2	1	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	1	no	—
145	C₄⋊C₄×C₆₁	—	2	1	no	—
146	C₄⋊C₄×C₆₁	—	2	2	no	—
147	C₄⋊C₄×C₆₁	—	4	4	no	—
148	C₄⋊C₄×C₆₁	—	4	4	no	—
149	C₄⋊C₄×C₆₁	—	4	4	no	—
150	C₄⋊C₄×C₆₁	—	4	2	no	—
151	C₄⋊C₄×C₆₁	—	4	2	no	—
152	C₄⋊C₄×C₆₁	—	4	2	no	—
153	C₄⋊C₄×C₆₁	—	4	4	no	—
154	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
155	C₄²×C₆₁	—	2	4	no	—
156	C₄²×C₆₁	—	2	2	no	—
157	C₄²×C₆₁	—	2	2	no	—
158	C₄²×C₆₁	—	4	4	no	—
159	C₄²×C₆₁	—	4	2	no	—
160	C₄²×C₆₁	C₂×D₄	1	2	yes	—
161	C₄²×C₆₁	#41	1	2	yes	—
162	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₆₁	—	2	2	no	—
164	Q₈×C₆₁	—	2	2	no	—
165	Q₈×C₆₁	—	2	2	no	—
166	Q₈×C₆₁	—	2	2	no	—
167	Q₈×C₆₁	—	2	2	no	—
168	Q₈×C₆₁	—	4	1	no	—
169	Q₈×C₆₁	—	4	1	no	—
170	Q₈×C₆₁	—	4	2	no	—
171	Q₈×C₆₁	—	4	2	no	—
172	Q₈×C₆₁	—	4	2	no	—
173	Q₈×C₆₁	—	4	2	no	—
174	Q₈×C₆₁	#121	1	4	yes	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	2	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	2	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	2	no	—
183	C₂×C₄×C₆₁	—	2	2	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	2	no	—
186	C₂×C₄×C₆₁	—	2	2	no	—
187	C₂×C₄×C₆₁	—	4	1	no	—
188	C₂×C₄×C₆₁	—	4	1	no	—
189	C₂×C₄×C₆₁	—	4	2	no	—
190	C₂×C₄×C₆₁	—	4	1	no	—
191	C₂×C₄×C₆₁	—	4	2	no	—
192	C₂×C₄×C₆₁	—	4	2	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	4	2	no	—
195	C₂×C₄×C₆₁	—	4	2	no	—
196	C₂×C₄×C₆₁	—	4	2	no	—
197	C₂×C₄×C₆₁	—	4	2	no	—
198	C₂×C₄×C₆₁	#121	1	2	yes	—
199	C₂×C₄×C₆₁	#121	1	2	yes	—
200	C₂×C₄×C₆₁	#137	1	4	yes	—
201	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
206	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
207	C₈×C₆₁	—	2	2	no	—
208	C₈×C₆₁	—	4	2	no	—
209	C₈×C₆₁	—	4	1	no	—
210	#24746	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
212	C₂²×C₆₁	D₄²	1	1	yes	characteristic
213	C₂²×C₆₁	#548	1	1	yes	characteristic
214	C₂²×C₆₁	C₂×#137	1	2	yes	—
215	C₂²×C₆₁	#578	1	2	yes	—
216	C₄×C₆₁	—	2	4	no	—
217	C₄×C₆₁	—	2	4	no	—
218	C₄×C₆₁	—	2	2	no	—
219	C₄×C₆₁	—	2	2	no	—
220	C₄×C₆₁	—	4	2	no	—
221	C₄×C₆₁	—	4	2	no	—
222	C₄×C₆₁	—	4	2	no	—
223	C₄×C₆₁	—	8	2	no	—
224	C₄×C₆₁	—	8	2	no	—
225	C₄×C₆₁	—	8	1	no	—
226	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
227	C₄×C₆₁	#537	1	1	yes	characteristic
228	C₄×C₆₁	#547	1	1	yes	characteristic
229	C₄×C₆₁	#553	1	1	yes	characteristic
230	C₂×#462	C₂×C₆₁	1	2	yes	—
231	C₂×#462	C₂×C₆₁	1	1	yes	characteristic
232	C₂×#441	C₂×C₆₁	1	1	yes	characteristic
233	#2546	C₂×C₆₁	1	1	yes	characteristic
234	#2351	C₂×C₆₁	1	1	yes	characteristic
235	#2066	C₂×C₆₁	1	2	yes	—
236	#2043	C₂×C₆₁	1	2	yes	—
237	#1960	C₂×C₆₁	1	1	yes	characteristic
238	#1940	C₂×C₆₁	1	1	yes	characteristic
239	#1878	C₂×C₆₁	1	2	yes	—
240	#1805	C₂×C₆₁	1	1	yes	characteristic
241	C₂×C₆₁	#2416	1	1	yes	characteristic
242	C₂×C₆₁	#3039	1	1	yes	characteristic
243	C₂×C₆₁	#3044	1	1	yes	characteristic
244	C₂×C₆₁	#3270	1	2	yes	—
245	C₂×C₆₁	#3374	1	2	yes	—
246	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
247	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
248	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
249	C₂×C₄⋊Q₈	C₂²×C₆₁	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
252	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
253	#462	—	2	8	no	—
254	#462	—	2	4	no	—
255	#441	—	2	4	no	—
256	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
257	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
259	C₂×#103	C₂²×C₆₁	1	2	yes	—
260	C₂×#103	C₂²×C₆₁	1	2	yes	—
261	C₂×#103	C₂²×C₆₁	1	2	yes	—
262	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
263	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×#103	C₂²×C₆₁	1	2	yes	—
265	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
266	#398	—	2	1	no	—
267	#398	—	2	1	no	—
268	#391	C₂²×C₆₁	1	2	yes	—
269	#389	—	2	2	no	—
270	#389	—	2	2	no	—
271	#389	C₂²×C₆₁	1	2	yes	—
272	#382	—	2	1	no	—
273	#382	C₂²×C₆₁	1	1	yes	characteristic
274	C₄×C₄⋊C₄	—	2	1	no	—
275	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
276	#340	C₂²×C₆₁	1	2	yes	—
277	#336	C₂²×C₆₁	1	2	yes	—
278	C₆₁	#24746	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
280	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×Q₁₆	—	2	4	no	—
285	C₂×Q₁₆	—	2	4	no	—
286	C₂×Q₁₆	—	2	4	no	—
287	C₂×Q₁₆	D₄×C₆₁	1	4	yes	—
288	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
289	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
291	C₄⋊Q₈	—	2	4	no	—
292	C₄⋊Q₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	4	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	4	no	—
297	C₄×Q₈	—	2	2	no	—
298	C₄×Q₈	—	2	2	no	—
299	C₄×Q₈	—	4	2	no	—
300	C₄×Q₈	D₄×C₆₁	1	4	yes	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	2	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
317	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
318	#106	—	2	2	no	—
319	C₄⋊C₈	—	2	4	no	—
320	C₄⋊C₈	—	2	2	no	—
321	#103	—	2	2	no	—
322	#103	—	2	4	no	—
323	#103	—	2	4	no	—
324	#103	—	2	2	no	—
325	#103	—	2	4	no	—
326	#103	—	4	2	no	—
327	#97	—	2	2	no	—
328	#95	—	2	1	no	—
329	#95	—	2	2	no	—
330	#95	—	2	1	no	—
331	#95	—	2	2	no	—
332	#95	—	2	2	no	—
333	#95	D₄×C₆₁	1	1	yes	characteristic
334	#95	D₄×C₆₁	1	1	yes	characteristic
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
350	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
351	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
352	C₂×Q₈	#41×C₆₁	1	2	yes	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
364	Q₁₆	—	2	8	no	—
365	Q₁₆	—	4	8	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	4	2	no	—
386	C₄⋊C₄	—	4	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
390	C₄²	—	2	4	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	4	4	no	—
394	C₄²	—	4	2	no	—
395	C₄²	C₂×D₄×C₆₁	1	2	yes	—
396	C₄²	#41×C₆₁	1	2	yes	—
397	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
398	Q₈	—	2	2	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	Q₈	—	2	2	no	—
402	Q₈	—	2	2	no	—
403	Q₈	—	4	1	no	—
404	Q₈	—	4	1	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	#121×C₆₁	1	4	yes	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	#121×C₆₁	1	2	yes	—
434	C₂×C₄	#121×C₆₁	1	2	yes	—
435	C₂×C₄	#137×C₆₁	1	4	yes	—
436	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
440	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
441	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	2	no	—
445	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
446	C₂²	D₄²×C₆₁	1	1	yes	characteristic
447	C₂²	C₆₁×#548	1	1	yes	characteristic
448	C₂²	C₂×#137×C₆₁	1	2	yes	—
449	C₂²	C₆₁×#578	1	2	yes	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	2	4	no	—
453	C₄	—	2	4	no	—
454	C₄	—	4	2	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	2	no	—
457	C₄	—	8	1	no	—
458	C₄	—	8	2	no	—
459	C₄	—	8	2	no	—
460	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
461	C₄	C₆₁×#537	1	1	yes	characteristic
462	C₄	C₆₁×#547	1	1	yes	characteristic
463	C₄	C₆₁×#553	1	1	yes	characteristic
464	C₂	C₆₁×#2416	1	1	yes	characteristic
465	C₂	C₆₁×#3039	1	1	yes	characteristic
466	C₂	C₆₁×#3044	1	1	yes	characteristic
467	C₂	C₆₁×#3270	1	2	yes	—
468	C₂	C₆₁×#3374	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
210. #24746	C₆₁	direct (N × H)
278. C₆₁	#24746	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×#462	2
C₂×C₆₁×#441	2
C₆₁×#2546	2
C₆₁×#2351	2
C₆₁×#2066	2
C₆₁×#2043	2
C₆₁×#1960	2
C₆₁×#1940	2
C₆₁×#1878	2
C₆₁×#1805	2
#24746	61

Subgroups — C61×#24746 #29528179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24746 #29528179