Subgroups — C₆₁×#26059 #29529492

Order 15616.

820 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#478	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#478	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2552	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2349	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2086	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2059	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2059	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1864	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#1862	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1847	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1802	C₂	1	1	yes	maximal, characteristic
15	C₆₁×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#478	—	2	4	no	—
22	C₆₁×#478	—	2	4	no	—
23	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#398	—	2	1	no	—
38	C₆₁×#398	—	2	1	no	—
39	C₆₁×#389	—	2	1	no	—
40	C₆₁×#389	C₂²	1	1	yes	characteristic
41	C₆₁×#389	C₂²	1	1	yes	characteristic
42	C₆₁×#389	C₂²	1	1	yes	characteristic
43	C₆₁×#389	C₂²	1	1	yes	characteristic
44	C₆₁×#385	—	2	1	no	—
45	C₆₁×#385	—	2	1	no	—
46	C₆₁×#384	—	2	1	no	—
47	C₆₁×#384	C₂²	1	1	yes	characteristic
48	C₆₁×#382	C₂²	1	1	yes	characteristic
49	C₆₁×#380	—	2	1	no	—
50	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
52	C₂×#95×C₆₁	—	2	1	no	—
53	C₆₁×#340	C₂²	1	1	yes	characteristic
54	C₆₁×#340	C₂²	1	1	yes	characteristic
55	C₆₁×#340	C₂²	1	1	yes	characteristic
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#336	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	—	2	1	no	—
63	C₂³×C₄×C₆₁	—	2	1	no	—
64	C₂³×C₄×C₆₁	—	2	1	no	—
65	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
69	#125×C₆₁	—	2	2	no	—
70	#125×C₆₁	—	2	2	no	—
71	#125×C₆₁	—	4	1	no	—
72	#125×C₆₁	—	4	1	no	—
73	C₄×D₄×C₆₁	—	2	2	no	—
74	C₄×D₄×C₆₁	—	2	2	no	—
75	C₄×D₄×C₆₁	—	2	2	no	—
76	C₄×D₄×C₆₁	—	4	1	no	—
77	C₄×D₄×C₆₁	—	4	1	no	—
78	C₄×D₄×C₆₁	Q₈	1	4	yes	—
79	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
86	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
89	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₄²×C₆₁	—	2	1	no	—
102	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	#107×C₆₁	—	2	2	no	—
106	#107×C₆₁	—	2	2	no	—
107	#107×C₆₁	—	4	1	no	—
108	#106×C₆₁	—	2	2	no	—
109	#106×C₆₁	—	2	2	no	—
110	#106×C₆₁	—	4	1	no	—
111	C₄⋊C₈×C₆₁	—	2	2	no	—
112	C₄⋊C₈×C₆₁	—	2	2	no	—
113	C₄⋊C₈×C₆₁	—	2	2	no	—
114	#102×C₆₁	—	2	2	no	—
115	#102×C₆₁	—	2	2	no	—
116	#102×C₆₁	D₄	1	4	yes	—
117	#102×C₆₁	Q₈	1	4	yes	—
118	#97×C₆₁	—	2	2	no	—
119	#95×C₆₁	—	2	1	no	—
120	#95×C₆₁	—	2	1	no	—
121	#95×C₆₁	—	2	1	no	—
122	#95×C₆₁	—	2	1	no	—
123	#95×C₆₁	—	2	1	no	—
124	#95×C₆₁	—	2	1	no	—
125	#95×C₆₁	—	2	1	no	—
126	#95×C₆₁	D₄	1	1	yes	characteristic
127	#95×C₆₁	D₄	1	1	yes	characteristic
128	C₂⁴×C₆₁	—	2	1	no	—
129	C₂×D₄×C₆₁	—	2	1	no	—
130	C₂×D₄×C₆₁	—	2	1	no	—
131	C₂×D₄×C₆₁	—	2	1	no	—
132	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
134	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
135	C₂²×C₄×C₆₁	—	2	1	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	2	1	no	—
138	C₂²×C₄×C₆₁	—	2	4	no	—
139	C₂²×C₄×C₆₁	—	2	1	no	—
140	C₂²×C₄×C₆₁	—	2	1	no	—
141	C₂²×C₄×C₆₁	—	2	1	no	—
142	C₂²×C₄×C₆₁	—	2	1	no	—
143	C₂²×C₄×C₆₁	—	4	2	no	—
144	C₂²×C₄×C₆₁	—	4	2	no	—
145	C₂²×C₄×C₆₁	—	4	2	no	—
146	C₂²×C₄×C₆₁	—	4	2	no	—
147	C₂²×C₄×C₆₁	—	8	1	no	—
148	C₂²×C₄×C₆₁	—	8	1	no	—
149	C₂²×C₄×C₆₁	—	8	1	no	—
150	C₂²×C₄×C₆₁	—	8	1	no	—
151	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
158	C₂×C₈×C₆₁	—	2	1	no	—
159	C₂×C₈×C₆₁	—	2	1	no	—
160	C₂×C₈×C₆₁	—	2	1	no	—
161	C₂×C₈×C₆₁	—	2	1	no	—
162	C₂×C₈×C₆₁	—	2	1	no	—
163	C₂×C₈×C₆₁	—	2	1	no	—
164	C₂×C₈×C₆₁	—	2	1	no	—
165	C₂×C₈×C₆₁	—	2	1	no	—
166	C₂×C₈×C₆₁	—	2	1	no	—
167	C₂×C₈×C₆₁	—	2	1	no	—
168	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
169	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
170	C₄⋊C₄×C₆₁	—	2	1	no	—
171	C₄⋊C₄×C₆₁	—	2	1	no	—
172	C₄⋊C₄×C₆₁	—	2	1	no	—
173	C₄⋊C₄×C₆₁	—	2	1	no	—
174	C₄⋊C₄×C₆₁	—	2	1	no	—
175	C₄⋊C₄×C₆₁	—	2	1	no	—
176	C₄⋊C₄×C₆₁	—	2	1	no	—
177	C₄⋊C₄×C₆₁	—	2	1	no	—
178	C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₄⋊C₄×C₆₁	—	2	1	no	—
181	C₄⋊C₄×C₆₁	—	4	1	no	—
182	C₄⋊C₄×C₆₁	—	4	1	no	—
183	C₄⋊C₄×C₆₁	—	4	2	no	—
184	C₄⋊C₄×C₆₁	—	4	2	no	—
185	C₄⋊C₄×C₆₁	—	4	2	no	—
186	C₄⋊C₄×C₆₁	—	4	2	no	—
187	C₄⋊C₄×C₆₁	—	4	2	no	—
188	C₄⋊C₄×C₆₁	—	8	1	no	—
189	C₄⋊C₄×C₆₁	—	8	1	no	—
190	C₄⋊C₄×C₆₁	—	8	1	no	—
191	C₄⋊C₄×C₆₁	—	8	1	no	—
192	C₄⋊C₄×C₆₁	—	8	1	no	—
193	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	—
195	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	—
196	C₂²⋊C₄×C₆₁	—	2	4	no	—
197	C₂²⋊C₄×C₆₁	—	4	2	no	—
198	C₂²⋊C₄×C₆₁	—	4	2	no	—
199	C₄²×C₆₁	—	2	1	no	—
200	C₄²×C₆₁	—	2	1	no	—
201	C₄²×C₆₁	—	2	1	no	—
202	C₄²×C₆₁	—	2	1	no	—
203	C₄²×C₆₁	—	4	2	no	—
204	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
205	C₄²×C₆₁	#41	1	2	yes	—
206	C₂³×C₆₁	—	2	2	no	—
207	C₂³×C₆₁	—	2	2	no	—
208	C₂³×C₆₁	—	2	2	no	—
209	C₂³×C₆₁	—	4	1	no	—
210	C₂³×C₆₁	—	4	1	no	—
211	C₂³×C₆₁	—	4	1	no	—
212	C₂³×C₆₁	—	4	1	no	—
213	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
214	D₄×C₆₁	—	2	2	no	—
215	D₄×C₆₁	—	2	2	no	—
216	D₄×C₆₁	—	2	2	no	—
217	D₄×C₆₁	C₄⋊Q₈	1	4	yes	—
218	C₂×C₄×C₆₁	—	2	1	no	—
219	C₂×C₄×C₆₁	—	2	1	no	—
220	C₂×C₄×C₆₁	—	2	1	no	—
221	C₂×C₄×C₆₁	—	2	1	no	—
222	C₂×C₄×C₆₁	—	2	2	no	—
223	C₂×C₄×C₆₁	—	2	1	no	—
224	C₂×C₄×C₆₁	—	2	1	no	—
225	C₂×C₄×C₆₁	—	2	1	no	—
226	C₂×C₄×C₆₁	—	2	1	no	—
227	C₂×C₄×C₆₁	—	2	2	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	2	1	no	—
230	C₂×C₄×C₆₁	—	2	1	no	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	2	1	no	—
234	C₂×C₄×C₆₁	—	2	1	no	—
235	C₂×C₄×C₆₁	—	2	1	no	—
236	C₂×C₄×C₆₁	—	2	1	no	—
237	C₂×C₄×C₆₁	—	4	1	no	—
238	C₂×C₄×C₆₁	—	4	1	no	—
239	C₂×C₄×C₆₁	—	4	1	no	—
240	C₂×C₄×C₆₁	—	4	1	no	—
241	C₂×C₄×C₆₁	—	4	1	no	—
242	C₂×C₄×C₆₁	—	4	1	no	—
243	C₂×C₄×C₆₁	—	4	1	no	—
244	C₂×C₄×C₆₁	—	4	1	no	—
245	C₂×C₄×C₆₁	—	4	1	no	—
246	C₂×C₄×C₆₁	—	4	1	no	—
247	C₂×C₄×C₆₁	—	4	1	no	—
248	C₂×C₄×C₆₁	—	4	1	no	—
249	C₂×C₄×C₆₁	—	4	1	no	—
250	C₂×C₄×C₆₁	—	4	1	no	—
251	C₂×C₄×C₆₁	—	4	1	no	—
252	C₂×C₄×C₆₁	—	4	1	no	—
253	C₂×C₄×C₆₁	—	4	1	no	—
254	C₂×C₄×C₆₁	—	4	1	no	—
255	C₂×C₄×C₆₁	—	8	4	no	—
256	C₂×C₄×C₆₁	—	8	4	no	—
257	C₂×C₄×C₆₁	—	8	4	no	—
258	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
259	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
260	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
262	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
263	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
264	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
265	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
266	C₈×C₆₁	—	2	2	no	—
267	C₈×C₆₁	—	2	2	no	—
268	C₈×C₆₁	—	4	1	no	—
269	C₈×C₆₁	—	4	1	no	—
270	#26059	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂²×C₆₁	—	2	4	no	—
272	C₂²×C₆₁	—	4	2	no	—
273	C₂²×C₆₁	—	4	2	no	—
274	C₂²×C₆₁	—	4	2	no	—
275	C₂²×C₆₁	—	4	2	no	—
276	C₂²×C₆₁	—	4	2	no	—
277	C₂²×C₆₁	—	4	2	no	—
278	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
279	C₂²×C₆₁	D₄²	1	1	yes	characteristic
280	C₂²×C₆₁	D₄×Q₈	1	1	yes	characteristic
281	C₂²×C₆₁	#575	1	1	yes	characteristic
282	C₂²×C₆₁	#575	1	1	yes	characteristic
283	C₂²×C₆₁	#576	1	1	yes	characteristic
284	C₂²×C₆₁	#577	1	1	yes	characteristic
285	C₄×C₆₁	—	2	2	no	—
286	C₄×C₆₁	—	2	2	no	—
287	C₄×C₆₁	—	4	2	no	—
288	C₄×C₆₁	—	4	2	no	—
289	C₄×C₆₁	—	4	1	no	—
290	C₄×C₆₁	—	4	1	no	—
291	C₄×C₆₁	—	4	2	no	—
292	C₄×C₆₁	—	4	1	no	—
293	C₄×C₆₁	—	4	1	no	—
294	C₄×C₆₁	—	8	1	no	—
295	C₄×C₆₁	—	8	1	no	—
296	C₄×C₆₁	—	8	1	no	—
297	C₄×C₆₁	—	8	1	no	—
298	C₄×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
299	C₄×C₆₁	#544	1	1	yes	characteristic
300	C₄×C₆₁	#547	1	1	yes	characteristic
301	C₄×C₆₁	#554	1	1	yes	characteristic
302	C₂×#478	C₂×C₆₁	1	1	yes	characteristic
303	C₂×#478	C₂×C₆₁	1	1	yes	characteristic
304	#2552	C₂×C₆₁	1	1	yes	characteristic, complemented
305	#2349	C₂×C₆₁	1	1	yes	characteristic
306	#2088	C₂×C₆₁	1	1	yes	characteristic, complemented
307	#2086	C₂×C₆₁	1	1	yes	characteristic, complemented
308	#2059	C₂×C₆₁	1	1	yes	characteristic, complemented
309	#2059	C₂×C₆₁	1	1	yes	characteristic, complemented
310	#1949	C₂×C₆₁	1	1	yes	characteristic, complemented
311	#1940	C₂×C₆₁	1	1	yes	characteristic, complemented
312	#1864	C₂×C₆₁	1	1	yes	characteristic
313	#1862	C₂×C₆₁	1	1	yes	characteristic
314	#1847	C₂×C₆₁	1	1	yes	characteristic, complemented
315	#1802	C₂×C₆₁	1	1	yes	characteristic
316	#1762	C₂×C₆₁	1	1	yes	characteristic
317	C₂×C₆₁	—	4	4	no	—
318	C₂×C₆₁	#2440	1	1	yes	characteristic
319	C₂×C₆₁	#3080	1	1	yes	characteristic
320	C₂×C₆₁	#3081	1	1	yes	characteristic
321	C₂×C₆₁	#3267	1	1	yes	characteristic
322	C₂×C₆₁	#3268	1	1	yes	characteristic
323	C₂×C₆₁	#3388	1	1	yes	characteristic
324	C₂×C₆₁	#3389	1	1	yes	characteristic
325	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
326	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
327	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
328	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
329	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
330	#478	—	2	4	no	—
331	#478	—	2	4	no	—
332	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
333	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
334	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
335	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
336	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
337	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
338	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
339	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
340	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
341	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
342	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
343	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
344	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
345	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
346	#398	—	2	1	no	—
347	#398	—	2	1	no	—
348	#389	—	2	1	no	—
349	#389	C₂²×C₆₁	1	1	yes	characteristic
350	#389	C₂²×C₆₁	1	1	yes	characteristic
351	#389	C₂²×C₆₁	1	1	yes	characteristic
352	#389	C₂²×C₆₁	1	1	yes	characteristic
353	#385	—	2	1	no	—
354	#385	—	2	1	no	—
355	#384	—	2	1	no	—
356	#384	C₂²×C₆₁	1	1	yes	characteristic
357	#382	C₂²×C₆₁	1	1	yes	characteristic
358	#380	—	2	1	no	—
359	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
360	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×#95	—	2	1	no	—
362	#340	C₂²×C₆₁	1	1	yes	characteristic
363	#340	C₂²×C₆₁	1	1	yes	characteristic
364	#340	C₂²×C₆₁	1	1	yes	characteristic
365	#340	C₂²×C₆₁	1	1	yes	characteristic
366	#340	C₂²×C₆₁	1	1	yes	characteristic
367	#340	C₂²×C₆₁	1	1	yes	characteristic
368	#336	C₂²×C₆₁	1	1	yes	characteristic
369	#336	C₂²×C₆₁	1	1	yes	characteristic
370	C₆₁	#26059	1	1	yes	characteristic, direct product factor, Sylow
371	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
372	C₂³×C₄	—	2	1	no	—
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	—	2	1	no	—
375	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
377	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
378	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
379	#125	—	2	2	no	—
380	#125	—	2	2	no	—
381	#125	—	4	1	no	—
382	#125	—	4	1	no	—
383	C₄×D₄	—	2	2	no	—
384	C₄×D₄	—	2	2	no	—
385	C₄×D₄	—	2	2	no	—
386	C₄×D₄	—	4	1	no	—
387	C₄×D₄	—	4	1	no	—
388	C₄×D₄	Q₈×C₆₁	1	4	yes	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
400	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
401	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₄²	—	2	1	no	—
412	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
413	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
414	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
415	#107	—	2	2	no	—
416	#107	—	2	2	no	—
417	#107	—	4	1	no	—
418	#106	—	2	2	no	—
419	#106	—	2	2	no	—
420	#106	—	4	1	no	—
421	C₄⋊C₈	—	2	2	no	—
422	C₄⋊C₈	—	2	2	no	—
423	C₄⋊C₈	—	2	2	no	—
424	#102	—	2	2	no	—
425	#102	—	2	2	no	—
426	#102	D₄×C₆₁	1	4	yes	—
427	#102	Q₈×C₆₁	1	4	yes	—
428	#97	—	2	2	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	D₄×C₆₁	1	1	yes	characteristic
437	#95	D₄×C₆₁	1	1	yes	characteristic
438	C₂⁴	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
443	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
444	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	4	2	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	8	1	no	—
458	C₂²×C₄	—	8	1	no	—
459	C₂²×C₄	—	8	1	no	—
460	C₂²×C₄	—	8	1	no	—
461	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
462	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
466	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
467	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
479	C₂×C₈	C₂×Q₈×C₆₁	1	2	yes	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	4	1	no	—
492	C₄⋊C₄	—	4	1	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	—	4	2	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	8	1	no	—
499	C₄⋊C₄	—	8	1	no	—
500	C₄⋊C₄	—	8	1	no	—
501	C₄⋊C₄	—	8	1	no	—
502	C₄⋊C₄	—	8	1	no	—
503	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
504	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	—
505	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	4	2	no	—
508	C₂²⋊C₄	—	4	2	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	4	2	no	—
514	C₄²	C₂×Q₈×C₆₁	1	2	yes	—
515	C₄²	#41×C₆₁	1	2	yes	—
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	4	1	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	4	1	no	—
523	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
524	D₄	—	2	2	no	—
525	D₄	—	2	2	no	—
526	D₄	—	2	2	no	—
527	D₄	C₄⋊Q₈×C₆₁	1	4	yes	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	8	4	no	—
566	C₂×C₄	—	8	4	no	—
567	C₂×C₄	—	8	4	no	—
568	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
569	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
571	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
572	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
573	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
574	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
575	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
576	C₈	—	2	2	no	—
577	C₈	—	2	2	no	—
578	C₈	—	4	1	no	—
579	C₈	—	4	1	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	2	no	—
586	C₂²	—	4	2	no	—
587	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
588	C₂²	D₄²×C₆₁	1	1	yes	characteristic
589	C₂²	D₄×Q₈×C₆₁	1	1	yes	characteristic
590	C₂²	C₆₁×#575	1	1	yes	characteristic
591	C₂²	C₆₁×#575	1	1	yes	characteristic
592	C₂²	C₆₁×#576	1	1	yes	characteristic
593	C₂²	C₆₁×#577	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	2	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	1	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	—	8	1	no	—
606	C₄	—	8	1	no	—
607	C₄	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
608	C₄	C₆₁×#544	1	1	yes	characteristic
609	C₄	C₆₁×#547	1	1	yes	characteristic
610	C₄	C₆₁×#554	1	1	yes	characteristic
611	C₂	—	4	4	no	—
612	C₂	C₆₁×#2440	1	1	yes	characteristic
613	C₂	C₆₁×#3080	1	1	yes	characteristic
614	C₂	C₆₁×#3081	1	1	yes	characteristic
615	C₂	C₆₁×#3267	1	1	yes	characteristic
616	C₂	C₆₁×#3268	1	1	yes	characteristic
617	C₂	C₆₁×#3388	1	1	yes	characteristic
618	C₂	C₆₁×#3389	1	1	yes	characteristic

	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 ◁ C₄×C₄⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₆₁×#2552	C₂	semidirect
5. C₆₁×#2088	C₂	semidirect
6. C₆₁×#2086	C₂	semidirect
7. C₆₁×#2059	C₂	semidirect
8. C₆₁×#2059	C₂	semidirect
9. C₆₁×#1949	C₂	semidirect
10. C₆₁×#1940	C₂	semidirect
13. C₆₁×#1847	C₂	semidirect
270. #26059	C₆₁	direct (N × H)
304. #2552	C₂×C₆₁	semidirect
306. #2088	C₂×C₆₁	semidirect
307. #2086	C₂×C₆₁	semidirect
308. #2059	C₂×C₆₁	semidirect
309. #2059	C₂×C₆₁	semidirect
310. #1949	C₂×C₆₁	semidirect
311. #1940	C₂×C₆₁	semidirect
314. #1847	C₂×C₆₁	semidirect
370. C₆₁	#26059	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×#478	2
C₆₁×#2552	2
C₆₁×#2349	2
C₆₁×#2088	2
C₆₁×#2086	2
C₆₁×#2059	2
C₆₁×#1949	2
C₆₁×#1940	2
C₆₁×#1864	2
C₆₁×#1862	2
C₆₁×#1847	2
C₆₁×#1802	2
C₆₁×#1762	2
#26059	61

Subgroups — C61×#26059 #29529492

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#26059 #29529492