Subgroups — C₆₁×#26359 #29529792

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#476	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2440	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2363	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2093	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2087	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2067	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2057	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1919	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1895	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#1874	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1854	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1851	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
19	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₆₁×#476	—	2	4	no	—
24	C₆₁×#428	—	2	4	no	—
25	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×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×#102×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#398	—	2	1	no	—
39	C₆₁×#395	—	2	1	no	—
40	C₆₁×#390	—	2	1	no	—
41	C₆₁×#390	C₂²	1	1	yes	characteristic
42	C₆₁×#389	C₂²	1	1	yes	characteristic
43	C₆₁×#389	C₂²	1	1	yes	characteristic
44	C₆₁×#389	C₂²	1	1	yes	characteristic
45	C₆₁×#388	—	2	1	no	—
46	C₆₁×#386	—	2	1	no	—
47	C₆₁×#385	—	2	1	no	—
48	C₆₁×#384	C₂²	1	1	yes	characteristic
49	C₆₁×#380	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
51	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
52	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
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×Q₈×C₆₁	—	2	1	no	—
62	C₂²×D₄×C₆₁	—	2	1	no	—
63	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₆₁	—	2	1	no	—
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
67	C₂×M₁₆×C₆₁	—	2	2	no	—
68	C₂×M₁₆×C₆₁	—	2	2	no	—
69	C₂×M₁₆×C₆₁	—	2	2	no	—
70	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
74	C₄⋊Q₈×C₆₁	—	2	2	no	—
75	C₄⋊Q₈×C₆₁	—	4	1	no	—
76	C₂²⋊Q₈×C₆₁	—	4	4	no	—
77	#121×C₆₁	—	2	2	no	—
78	#121×C₆₁	Q₈	1	4	yes	complemented
79	C₄×D₄×C₆₁	—	2	2	no	—
80	C₄×D₄×C₆₁	—	4	1	no	—
81	#117×C₆₁	—	2	2	no	—
82	#117×C₆₁	—	4	1	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	2	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	—	2	1	no	—
90	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₄⋊C₄×C₆₁	—	4	1	no	—
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×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₆₁	—	2	1	no	—
108	C₂×C₄²×C₆₁	—	2	1	no	—
109	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
111	#107×C₆₁	—	2	2	no	—
112	#107×C₆₁	—	2	2	no	—
113	#107×C₆₁	—	4	1	no	—
114	#106×C₆₁	—	2	2	no	—
115	#106×C₆₁	—	2	2	no	—
116	#106×C₆₁	D₄	1	4	yes	complemented
117	C₄⋊C₈×C₆₁	—	2	2	no	—
118	C₄⋊C₈×C₆₁	—	2	2	no	—
119	#102×C₆₁	—	2	2	no	—
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	—	4	1	no	—
123	C₂²⋊C₈×C₆₁	—	2	2	no	—
124	#95×C₆₁	—	2	1	no	—
125	#95×C₆₁	—	2	1	no	—
126	#95×C₆₁	—	2	1	no	—
127	#95×C₆₁	—	2	1	no	—
128	#95×C₆₁	—	2	1	no	—
129	#95×C₆₁	D₄	1	1	yes	characteristic
130	#95×C₆₁	D₄	1	1	yes	characteristic
131	C₂⁴×C₆₁	—	2	1	no	—
132	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₆₁	—	4	2	no	—
134	C₂×Q₈×C₆₁	—	4	2	no	—
135	C₂×Q₈×C₆₁	—	8	1	no	—
136	C₂×D₄×C₆₁	—	2	4	no	—
137	C₂×D₄×C₆₁	—	2	1	no	—
138	C₂×D₄×C₆₁	—	2	1	no	—
139	C₂×D₄×C₆₁	—	2	1	no	—
140	C₂×D₄×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	—	2	1	no	—
142	C₂×D₄×C₆₁	—	8	1	no	—
143	C₂×D₄×C₆₁	—	8	1	no	—
144	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
145	C₂²×C₄×C₆₁	—	2	1	no	—
146	C₂²×C₄×C₆₁	—	2	1	no	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	2	1	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	1	no	—
151	C₂²×C₄×C₆₁	—	2	1	no	—
152	C₂²×C₄×C₆₁	—	2	1	no	—
153	C₂²×C₄×C₆₁	—	2	1	no	—
154	C₂²×C₄×C₆₁	—	2	1	no	—
155	C₂²×C₄×C₆₁	—	2	1	no	—
156	C₂²×C₄×C₆₁	—	4	2	no	—
157	C₂²×C₄×C₆₁	—	4	2	no	—
158	C₂²×C₄×C₆₁	—	4	2	no	—
159	C₂²×C₄×C₆₁	—	4	2	no	—
160	C₂²×C₄×C₆₁	—	8	1	no	—
161	C₂²×C₄×C₆₁	—	8	1	no	—
162	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
168	C₂²×C₄×C₆₁	#41	1	2	yes	—
169	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
170	M₁₆×C₆₁	—	2	8	no	—
171	C₂×C₈×C₆₁	—	2	1	no	—
172	C₂×C₈×C₆₁	—	2	1	no	—
173	C₂×C₈×C₆₁	—	2	1	no	—
174	C₂×C₈×C₆₁	—	2	1	no	—
175	C₂×C₈×C₆₁	—	2	1	no	—
176	C₂×C₈×C₆₁	—	2	1	no	—
177	C₂×C₈×C₆₁	—	2	1	no	—
178	C₂×C₈×C₆₁	—	2	1	no	—
179	C₂×C₈×C₆₁	—	2	1	no	—
180	C₂×C₈×C₆₁	—	2	1	no	—
181	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
182	C₂×C₈×C₆₁	#41	1	2	yes	—
183	C₄⋊C₄×C₆₁	—	2	1	no	—
184	C₄⋊C₄×C₆₁	—	2	1	no	—
185	C₄⋊C₄×C₆₁	—	2	1	no	—
186	C₄⋊C₄×C₆₁	—	2	1	no	—
187	C₄⋊C₄×C₆₁	—	2	1	no	—
188	C₄⋊C₄×C₆₁	—	2	1	no	—
189	C₄⋊C₄×C₆₁	—	2	1	no	—
190	C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₄⋊C₄×C₆₁	—	2	1	no	—
192	C₄⋊C₄×C₆₁	—	2	1	no	—
193	C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₄⋊C₄×C₆₁	—	4	2	no	—
195	C₄⋊C₄×C₆₁	—	4	2	no	—
196	C₄⋊C₄×C₆₁	—	4	2	no	—
197	C₄⋊C₄×C₆₁	—	4	2	no	—
198	C₄⋊C₄×C₆₁	—	4	2	no	—
199	C₄⋊C₄×C₆₁	—	8	1	no	—
200	C₄⋊C₄×C₆₁	—	8	1	no	—
201	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
202	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
203	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	—
204	C₂²⋊C₄×C₆₁	—	2	4	no	—
205	C₂²⋊C₄×C₆₁	—	2	2	no	—
206	C₂²⋊C₄×C₆₁	—	2	2	no	—
207	C₂²⋊C₄×C₆₁	—	4	2	no	—
208	C₂²⋊C₄×C₆₁	—	4	2	no	—
209	C₂²⋊C₄×C₆₁	—	4	2	no	—
210	C₂²⋊C₄×C₆₁	—	4	2	no	—
211	C₂²⋊C₄×C₆₁	—	8	1	no	—
212	C₄²×C₆₁	—	2	1	no	—
213	C₄²×C₆₁	—	2	1	no	—
214	C₄²×C₆₁	—	2	1	no	—
215	C₄²×C₆₁	—	2	1	no	—
216	C₄²×C₆₁	—	4	2	no	—
217	C₄²×C₆₁	—	8	1	no	—
218	C₂³×C₆₁	—	2	1	no	—
219	C₂³×C₆₁	—	2	1	no	—
220	C₂³×C₆₁	—	2	1	no	—
221	C₂³×C₆₁	—	2	1	no	—
222	C₂³×C₆₁	—	2	1	no	—
223	C₂³×C₆₁	—	2	1	no	—
224	C₂³×C₆₁	—	2	2	no	—
225	C₂³×C₆₁	—	4	1	no	—
226	C₂³×C₆₁	—	4	1	no	—
227	C₂³×C₆₁	—	4	1	no	—
228	C₂³×C₆₁	—	4	1	no	—
229	C₂³×C₆₁	—	4	1	no	—
230	C₂³×C₆₁	—	4	1	no	—
231	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
232	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₆₁	—	8	4	no	—
234	D₄×C₆₁	—	2	2	no	—
235	D₄×C₆₁	—	2	2	no	—
236	D₄×C₆₁	—	4	1	no	—
237	D₄×C₆₁	—	4	1	no	—
238	D₄×C₆₁	—	8	4	no	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	1	no	—
241	C₂×C₄×C₆₁	—	2	1	no	—
242	C₂×C₄×C₆₁	—	2	1	no	—
243	C₂×C₄×C₆₁	—	2	1	no	—
244	C₂×C₄×C₆₁	—	2	1	no	—
245	C₂×C₄×C₆₁	—	2	2	no	—
246	C₂×C₄×C₆₁	—	2	2	no	—
247	C₂×C₄×C₆₁	—	2	2	no	—
248	C₂×C₄×C₆₁	—	2	2	no	—
249	C₂×C₄×C₆₁	—	2	2	no	—
250	C₂×C₄×C₆₁	—	2	1	no	—
251	C₂×C₄×C₆₁	—	2	2	no	—
252	C₂×C₄×C₆₁	—	2	2	no	—
253	C₂×C₄×C₆₁	—	2	1	no	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	1	no	—
257	C₂×C₄×C₆₁	—	2	1	no	—
258	C₂×C₄×C₆₁	—	4	1	no	—
259	C₂×C₄×C₆₁	—	4	1	no	—
260	C₂×C₄×C₆₁	—	4	1	no	—
261	C₂×C₄×C₆₁	—	4	1	no	—
262	C₂×C₄×C₆₁	—	4	1	no	—
263	C₂×C₄×C₆₁	—	4	1	no	—
264	C₂×C₄×C₆₁	—	4	1	no	—
265	C₂×C₄×C₆₁	—	4	1	no	—
266	C₂×C₄×C₆₁	—	4	1	no	—
267	C₂×C₄×C₆₁	—	4	1	no	—
268	C₂×C₄×C₆₁	—	4	1	no	—
269	C₂×C₄×C₆₁	—	4	1	no	—
270	C₂×C₄×C₆₁	—	4	1	no	—
271	C₂×C₄×C₆₁	—	4	1	no	—
272	C₂×C₄×C₆₁	—	4	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	—	4	1	no	—
275	C₂×C₄×C₆₁	—	4	1	no	—
276	C₂×C₄×C₆₁	—	8	4	no	—
277	C₂×C₄×C₆₁	—	8	4	no	—
278	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
279	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
280	C₂×C₄×C₆₁	#137	1	2	yes	—
281	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
283	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
285	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
286	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
287	C₈×C₆₁	—	2	2	no	—
288	C₈×C₆₁	—	2	2	no	—
289	C₈×C₆₁	—	4	1	no	—
290	C₈×C₆₁	—	4	1	no	—
291	#26359	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂²×C₆₁	—	2	2	no	—
293	C₂²×C₆₁	—	2	2	no	—
294	C₂²×C₆₁	—	2	2	no	—
295	C₂²×C₆₁	—	4	1	no	—
296	C₂²×C₆₁	—	4	1	no	—
297	C₂²×C₆₁	—	4	1	no	—
298	C₂²×C₆₁	—	4	1	no	—
299	C₂²×C₆₁	—	4	2	no	—
300	C₂²×C₆₁	—	4	2	no	—
301	C₂²×C₆₁	—	4	2	no	—
302	C₂²×C₆₁	—	8	1	no	—
303	C₂²×C₆₁	—	8	1	no	—
304	C₂²×C₆₁	—	8	1	no	—
305	C₂²×C₆₁	—	8	1	no	—
306	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
307	C₂²×C₆₁	D₄²	1	1	yes	characteristic
308	C₂²×C₆₁	#547	1	1	yes	characteristic
309	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
310	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
311	C₂²×C₆₁	#576	1	1	yes	characteristic
312	C₂²×C₆₁	#577	1	1	yes	characteristic
313	C₄×C₆₁	—	2	2	no	—
314	C₄×C₆₁	—	2	2	no	—
315	C₄×C₆₁	—	2	2	no	—
316	C₄×C₆₁	—	4	2	no	—
317	C₄×C₆₁	—	4	1	no	—
318	C₄×C₆₁	—	4	2	no	—
319	C₄×C₆₁	—	4	1	no	—
320	C₄×C₆₁	—	4	2	no	—
321	C₄×C₆₁	—	8	1	no	—
322	C₄×C₆₁	—	8	1	no	—
323	C₄×C₆₁	—	8	1	no	—
324	C₄×C₆₁	—	8	1	no	—
325	C₄×C₆₁	#525	1	1	yes	characteristic
326	C₄×C₆₁	#539	1	1	yes	characteristic
327	C₄×C₆₁	D₄×Q₈	1	1	yes	characteristic
328	C₄×C₆₁	#554	1	1	yes	characteristic
329	C₂×#476	C₂×C₆₁	1	1	yes	characteristic, complemented
330	C₂×#428	C₂×C₆₁	1	1	yes	characteristic, complemented
331	#2440	C₂×C₆₁	1	1	yes	characteristic, complemented
332	#2363	C₂×C₆₁	1	1	yes	characteristic
333	#2093	C₂×C₆₁	1	1	yes	characteristic, complemented
334	#2087	C₂×C₆₁	1	1	yes	characteristic, complemented
335	#2067	C₂×C₆₁	1	1	yes	characteristic, complemented
336	#2057	C₂×C₆₁	1	1	yes	characteristic, complemented
337	#1948	C₂×C₆₁	1	1	yes	characteristic, complemented
338	#1919	C₂×C₆₁	1	1	yes	characteristic, complemented
339	#1895	C₂×C₆₁	1	1	yes	characteristic
340	#1874	C₂×C₆₁	1	1	yes	characteristic
341	#1864	C₂×C₆₁	1	1	yes	characteristic, complemented
342	#1854	C₂×C₆₁	1	1	yes	characteristic, complemented
343	#1851	C₂×C₆₁	1	1	yes	characteristic, complemented
344	C₂×C₆₁	—	4	2	no	—
345	C₂×C₆₁	—	8	2	no	—
346	C₂×C₆₁	#2449	1	1	yes	characteristic
347	C₂×C₆₁	#3079	1	1	yes	characteristic
348	C₂×C₆₁	#3081	1	1	yes	characteristic
349	C₂×C₆₁	#3266	1	1	yes	characteristic
350	C₂×C₆₁	#3274	1	1	yes	characteristic
351	C₂×C₆₁	#3345	1	1	yes	characteristic
352	C₂×C₆₁	#3357	1	1	yes	characteristic
353	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
354	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×C₂²⋊Q₈	—	2	1	no	—
356	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
358	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
359	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
360	#476	—	2	4	no	—
361	#428	—	2	4	no	—
362	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
366	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
367	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
368	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
369	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
371	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
372	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
373	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
374	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
375	#398	—	2	1	no	—
376	#395	—	2	1	no	—
377	#390	—	2	1	no	—
378	#390	C₂²×C₆₁	1	1	yes	characteristic
379	#389	C₂²×C₆₁	1	1	yes	characteristic
380	#389	C₂²×C₆₁	1	1	yes	characteristic
381	#389	C₂²×C₆₁	1	1	yes	characteristic
382	#388	—	2	1	no	—
383	#386	—	2	1	no	—
384	#385	—	2	1	no	—
385	#384	C₂²×C₆₁	1	1	yes	characteristic
386	#380	C₂²×C₆₁	1	1	yes	characteristic
387	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
388	C₄×C₂²⋊C₄	—	2	1	no	—
389	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
390	#340	C₂²×C₆₁	1	1	yes	characteristic
391	#340	C₂²×C₆₁	1	1	yes	characteristic
392	#340	C₂²×C₆₁	1	1	yes	characteristic
393	#340	C₂²×C₆₁	1	1	yes	characteristic
394	#340	C₂²×C₆₁	1	1	yes	characteristic
395	#340	C₂²×C₆₁	1	1	yes	characteristic
396	#336	C₂²×C₆₁	1	1	yes	characteristic
397	#336	C₂²×C₆₁	1	1	yes	characteristic
398	C₆₁	#26359	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²×Q₈	—	2	1	no	—
400	C₂²×D₄	—	2	1	no	—
401	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
402	C₂³×C₄	—	2	1	no	—
403	C₂³×C₄	—	2	1	no	—
404	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
405	C₂×M₁₆	—	2	2	no	—
406	C₂×M₁₆	—	2	2	no	—
407	C₂×M₁₆	—	2	2	no	—
408	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
409	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
412	C₄⋊Q₈	—	2	2	no	—
413	C₄⋊Q₈	—	4	1	no	—
414	C₂²⋊Q₈	—	4	4	no	—
415	#121	—	2	2	no	—
416	#121	Q₈×C₆₁	1	4	yes	complemented
417	C₄×D₄	—	2	2	no	—
418	C₄×D₄	—	4	1	no	—
419	#117	—	2	2	no	—
420	#117	—	4	1	no	—
421	C₂×C₄⋊C₄	—	2	2	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	—	2	1	no	—
424	C₂×C₄⋊C₄	—	2	1	no	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	4	1	no	—
430	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
431	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
432	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
445	C₂×C₄²	—	2	1	no	—
446	C₂×C₄²	—	2	1	no	—
447	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
448	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
449	#107	—	2	2	no	—
450	#107	—	2	2	no	—
451	#107	—	4	1	no	—
452	#106	—	2	2	no	—
453	#106	—	2	2	no	—
454	#106	D₄×C₆₁	1	4	yes	complemented
455	C₄⋊C₈	—	2	2	no	—
456	C₄⋊C₈	—	2	2	no	—
457	#102	—	2	2	no	—
458	#102	—	2	2	no	—
459	#102	—	2	2	no	—
460	#102	—	4	1	no	—
461	C₂²⋊C₈	—	2	2	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	D₄×C₆₁	1	1	yes	characteristic
468	#95	D₄×C₆₁	1	1	yes	characteristic
469	C₂⁴	—	2	1	no	—
470	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
471	C₂×Q₈	—	4	2	no	—
472	C₂×Q₈	—	4	2	no	—
473	C₂×Q₈	—	8	1	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	8	1	no	—
481	C₂×D₄	—	8	1	no	—
482	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	2	1	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	1	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	4	2	no	—
495	C₂²×C₄	—	4	2	no	—
496	C₂²×C₄	—	4	2	no	—
497	C₂²×C₄	—	4	2	no	—
498	C₂²×C₄	—	8	1	no	—
499	C₂²×C₄	—	8	1	no	—
500	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
501	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
502	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
503	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
504	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
505	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
506	C₂²×C₄	#41×C₆₁	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
508	M₁₆	—	2	8	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
520	C₂×C₈	#41×C₆₁	1	2	yes	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	4	2	no	—
533	C₄⋊C₄	—	4	2	no	—
534	C₄⋊C₄	—	4	2	no	—
535	C₄⋊C₄	—	4	2	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	8	1	no	—
538	C₄⋊C₄	—	8	1	no	—
539	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
540	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
541	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	—
542	C₂²⋊C₄	—	2	4	no	—
543	C₂²⋊C₄	—	2	2	no	—
544	C₂²⋊C₄	—	2	2	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	8	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	4	2	no	—
555	C₄²	—	8	1	no	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	1	no	—
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	2	1	no	—
561	C₂³	—	2	1	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
570	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
571	Q₈	—	8	4	no	—
572	D₄	—	2	2	no	—
573	D₄	—	2	2	no	—
574	D₄	—	4	1	no	—
575	D₄	—	4	1	no	—
576	D₄	—	8	4	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	8	4	no	—
615	C₂×C₄	—	8	4	no	—
616	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
617	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
618	C₂×C₄	#137×C₆₁	1	2	yes	—
619	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
620	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
621	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
622	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
623	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
624	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
625	C₈	—	2	2	no	—
626	C₈	—	2	2	no	—
627	C₈	—	4	1	no	—
628	C₈	—	4	1	no	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	4	1	no	—
633	C₂²	—	4	1	no	—
634	C₂²	—	4	1	no	—
635	C₂²	—	4	1	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	8	1	no	—
640	C₂²	—	8	1	no	—
641	C₂²	—	8	1	no	—
642	C₂²	—	8	1	no	—
643	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
644	C₂²	D₄²×C₆₁	1	1	yes	characteristic
645	C₂²	C₆₁×#547	1	1	yes	characteristic
646	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
647	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
648	C₂²	C₆₁×#576	1	1	yes	characteristic
649	C₂²	C₆₁×#577	1	1	yes	characteristic
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	4	2	no	—
654	C₄	—	4	1	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	2	no	—
658	C₄	—	8	1	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	C₆₁×#525	1	1	yes	characteristic
663	C₄	C₆₁×#539	1	1	yes	characteristic
664	C₄	D₄×Q₈×C₆₁	1	1	yes	characteristic
665	C₄	C₆₁×#554	1	1	yes	characteristic
666	C₂	—	4	2	no	—
667	C₂	—	8	2	no	—
668	C₂	C₆₁×#2449	1	1	yes	characteristic
669	C₂	C₆₁×#3079	1	1	yes	characteristic
670	C₂	C₆₁×#3081	1	1	yes	characteristic
671	C₂	C₆₁×#3266	1	1	yes	characteristic
672	C₂	C₆₁×#3274	1	1	yes	characteristic
673	C₂	C₆₁×#3345	1	1	yes	characteristic
674	C₂	C₆₁×#3357	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₂²⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#476	C₂	semidirect
2. C₂×C₆₁×#428	C₂	semidirect
3. C₆₁×#2440	C₂	semidirect
5. C₆₁×#2093	C₂	semidirect
6. C₆₁×#2087	C₂	semidirect
7. C₆₁×#2067	C₂	semidirect
8. C₆₁×#2057	C₂	semidirect
9. C₆₁×#1948	C₂	semidirect
10. C₆₁×#1919	C₂	semidirect
13. C₆₁×#1864	C₂	semidirect
14. C₆₁×#1854	C₂	semidirect
15. C₆₁×#1851	C₂	semidirect
78. #121×C₆₁	Q₈	semidirect
116. #106×C₆₁	D₄	semidirect
291. #26359	C₆₁	direct (N × H)
329. C₂×#476	C₂×C₆₁	semidirect
330. C₂×#428	C₂×C₆₁	semidirect
331. #2440	C₂×C₆₁	semidirect
333. #2093	C₂×C₆₁	semidirect
334. #2087	C₂×C₆₁	semidirect
335. #2067	C₂×C₆₁	semidirect
336. #2057	C₂×C₆₁	semidirect
337. #1948	C₂×C₆₁	semidirect
338. #1919	C₂×C₆₁	semidirect
341. #1864	C₂×C₆₁	semidirect
342. #1854	C₂×C₆₁	semidirect
343. #1851	C₂×C₆₁	semidirect
398. C₆₁	#26359	direct (N × H)
416. #121	Q₈×C₆₁	semidirect
454. #106	D₄×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×#476	2
C₂×C₆₁×#428	2
C₆₁×#2440	2
C₆₁×#2363	2
C₆₁×#2093	2
C₆₁×#2087	2
C₆₁×#2067	2
C₆₁×#2057	2
C₆₁×#1948	2
C₆₁×#1919	2
C₆₁×#1895	2
C₆₁×#1874	2
C₆₁×#1864	2
C₆₁×#1854	2
C₆₁×#1851	2
#26359	61

Subgroups — C61×#26359 #29529792

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#26359 #29529792