Subgroups — C₆₁×#24304 #29527737

Order 15616.

1150 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#478	C₂	1	2	yes	maximal, complemented
3	C₄×#121×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#2023	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1989	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1875	C₂	1	2	yes	maximal
10	C₆₁×#1854	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#533	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#125×C₆₁	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₆₁	—	2	1	no	—
18	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
20	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
21	C₂×C₄×D₄×C₆₁	—	2	1	no	—
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#117×C₆₁	C₂²	1	2	yes	—
24	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#478	—	2	8	no	—
26	C₂×#107×C₆₁	C₂²	1	2	yes	—
27	C₂×#106×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
29	C₂×#102×C₆₁	C₂²	1	2	yes	—
30	C₂×#102×C₆₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
32	C₆₁×#390	C₂²	1	1	yes	characteristic
33	C₆₁×#389	C₂²	1	1	yes	characteristic
34	C₆₁×#388	—	2	1	no	—
35	C₆₁×#386	—	2	1	no	—
36	C₆₁×#380	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#336	C₂²	1	1	yes	characteristic
44	C₆₁×#336	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₆₁	—	2	1	no	—
46	C₂²×Q₈×C₆₁	—	2	1	no	—
47	C₂²×D₄×C₆₁	—	2	1	no	—
48	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	—	2	1	no	—
50	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
54	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
55	C₄⋊Q₈×C₆₁	—	2	4	no	—
56	C₄⋊Q₈×C₆₁	—	2	4	no	—
57	#125×C₆₁	—	2	4	no	—
58	#125×C₆₁	D₄	1	8	yes	complemented
59	C₂²⋊Q₈×C₆₁	—	2	8	no	—
60	C₂²⋊Q₈×C₆₁	—	2	8	no	—
61	#121×C₆₁	—	2	2	no	—
62	#121×C₆₁	Q₈	1	4	yes	complemented
63	C₄×Q₈×C₆₁	—	2	8	no	—
64	C₄×Q₈×C₆₁	—	2	8	no	—
65	C₄×D₄×C₆₁	—	2	4	no	—
66	C₄×D₄×C₆₁	—	4	4	no	—
67	#117×C₆₁	—	2	4	no	—
68	#117×C₆₁	—	2	4	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	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	C₂³	1	1	yes	characteristic
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	2	yes	—
78	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
83	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
85	C₂×C₄²×C₆₁	—	2	2	no	—
86	C₂×C₄²×C₆₁	—	2	4	no	—
87	C₂×C₄²×C₆₁	—	2	1	no	—
88	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
92	#107×C₆₁	—	2	4	no	—
93	#106×C₆₁	—	2	4	no	—
94	C₄⋊C₈×C₆₁	—	2	4	no	—
95	#102×C₆₁	—	2	4	no	—
96	#102×C₆₁	—	2	4	no	—
97	C₂²⋊C₈×C₆₁	—	2	4	no	—
98	#95×C₆₁	—	2	1	no	—
99	#95×C₆₁	—	2	1	no	—
100	#95×C₆₁	—	2	1	no	—
101	C₂⁴×C₆₁	—	2	1	no	—
102	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₆₁	—	2	4	no	—
104	C₂×Q₈×C₆₁	—	2	4	no	—
105	C₂×Q₈×C₆₁	—	4	2	no	—
106	C₂×Q₈×C₆₁	—	4	2	no	—
107	C₂×Q₈×C₆₁	—	4	2	no	—
108	C₂×Q₈×C₆₁	—	4	2	no	—
109	C₂×D₄×C₆₁	—	2	4	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	4	2	no	—
114	C₂×D₄×C₆₁	—	4	2	no	—
115	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	1	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	4	1	no	—
128	C₂²×C₄×C₆₁	—	4	1	no	—
129	C₂²×C₄×C₆₁	—	4	2	no	—
130	C₂²×C₄×C₆₁	—	4	2	no	—
131	C₂²×C₄×C₆₁	—	4	2	no	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
138	C₂²×C₄×C₆₁	#41	1	2	yes	—
139	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
140	C₂×C₈×C₆₁	—	2	2	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₂×C₈×C₆₁	—	2	2	no	—
143	C₂×C₈×C₆₁	—	2	2	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	4	no	—
147	C₄⋊C₄×C₆₁	—	2	4	no	—
148	C₄⋊C₄×C₆₁	—	2	8	no	—
149	C₄⋊C₄×C₆₁	—	2	8	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	4	2	no	—
156	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
157	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
158	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	—
159	C₂²⋊C₄×C₆₁	—	2	8	no	—
160	C₂²⋊C₄×C₆₁	—	2	4	no	—
161	C₂²⋊C₄×C₆₁	—	4	2	no	—
162	C₂²⋊C₄×C₆₁	—	4	2	no	—
163	C₂²⋊C₄×C₆₁	—	4	2	no	—
164	C₂²⋊C₄×C₆₁	—	4	2	no	—
165	C₄²×C₆₁	—	2	8	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	2	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₄²×C₆₁	—	4	2	no	—
170	C₄²×C₆₁	C₂×D₄	1	4	yes	—
171	C₂³×C₆₁	—	2	1	no	—
172	C₂³×C₆₁	—	2	1	no	—
173	C₂³×C₆₁	—	2	1	no	—
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	—	2	1	no	—
176	C₂³×C₆₁	—	2	1	no	—
177	C₂³×C₆₁	—	2	2	no	—
178	C₂³×C₆₁	—	4	1	no	—
179	C₂³×C₆₁	—	4	1	no	—
180	C₂³×C₆₁	—	4	1	no	—
181	C₂³×C₆₁	—	4	1	no	—
182	C₂³×C₆₁	—	4	1	no	—
183	C₂³×C₆₁	—	4	1	no	—
184	C₂³×C₆₁	C₂²⋊Q₈	1	2	yes	—
185	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₆₁	—	4	8	no	—
187	Q₈×C₆₁	—	4	8	no	—
188	D₄×C₆₁	—	2	4	no	—
189	D₄×C₆₁	—	4	8	no	—
190	D₄×C₆₁	—	4	2	no	—
191	C₂×C₄×C₆₁	—	2	1	no	—
192	C₂×C₄×C₆₁	—	2	1	no	—
193	C₂×C₄×C₆₁	—	2	1	no	—
194	C₂×C₄×C₆₁	—	2	1	no	—
195	C₂×C₄×C₆₁	—	2	1	no	—
196	C₂×C₄×C₆₁	—	2	1	no	—
197	C₂×C₄×C₆₁	—	2	1	no	—
198	C₂×C₄×C₆₁	—	2	1	no	—
199	C₂×C₄×C₆₁	—	2	1	no	—
200	C₂×C₄×C₆₁	—	2	1	no	—
201	C₂×C₄×C₆₁	—	2	4	no	—
202	C₂×C₄×C₆₁	—	2	4	no	—
203	C₂×C₄×C₆₁	—	2	4	no	—
204	C₂×C₄×C₆₁	—	2	4	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	4	4	no	—
207	C₂×C₄×C₆₁	—	4	4	no	—
208	C₂×C₄×C₆₁	—	4	2	no	—
209	C₂×C₄×C₆₁	—	4	1	no	—
210	C₂×C₄×C₆₁	—	4	2	no	—
211	C₂×C₄×C₆₁	—	4	1	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	—	4	2	no	—
214	C₂×C₄×C₆₁	—	4	1	no	—
215	C₂×C₄×C₆₁	—	4	1	no	—
216	C₂×C₄×C₆₁	—	4	1	no	—
217	C₂×C₄×C₆₁	—	4	1	no	—
218	C₂×C₄×C₆₁	—	4	1	no	—
219	C₂×C₄×C₆₁	—	4	1	no	—
220	C₂×C₄×C₆₁	—	8	4	no	—
221	C₂×C₄×C₆₁	#120	1	2	yes	—
222	C₂×C₄×C₆₁	#120	1	2	yes	—
223	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
224	C₂×C₄×C₆₁	#135	1	2	yes	—
225	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
228	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
230	C₈×C₆₁	—	4	2	no	—
231	C₈×C₆₁	—	4	2	no	—
232	#24304	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₆₁	—	2	2	no	—
234	C₂²×C₆₁	—	2	2	no	—
235	C₂²×C₆₁	—	2	2	no	—
236	C₂²×C₆₁	—	4	1	no	—
237	C₂²×C₆₁	—	4	1	no	—
238	C₂²×C₆₁	—	4	1	no	—
239	C₂²×C₆₁	—	4	1	no	—
240	C₂²×C₆₁	—	4	2	no	—
241	C₂²×C₆₁	—	4	2	no	—
242	C₂²×C₆₁	—	4	2	no	—
243	C₂²×C₆₁	—	8	1	no	—
244	C₂²×C₆₁	—	8	1	no	—
245	C₂²×C₆₁	—	8	1	no	—
246	C₂²×C₆₁	—	8	1	no	—
247	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
248	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
249	C₂²×C₆₁	#536	1	1	yes	characteristic
250	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
251	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
252	C₂²×C₆₁	#575	1	1	yes	characteristic
253	C₂²×C₆₁	#575	1	1	yes	characteristic
254	C₄×C₆₁	—	2	2	no	—
255	C₄×C₆₁	—	2	2	no	—
256	C₄×C₆₁	—	2	2	no	—
257	C₄×C₆₁	—	2	2	no	—
258	C₄×C₆₁	—	2	2	no	—
259	C₄×C₆₁	—	4	2	no	—
260	C₄×C₆₁	—	4	4	no	—
261	C₄×C₆₁	—	4	4	no	—
262	C₄×C₆₁	—	8	1	no	—
263	C₄×C₆₁	—	8	1	no	—
264	C₄×C₆₁	#548	1	2	yes	—
265	C₄×C₆₁	D₄×Q₈	1	2	yes	—
266	C₂×#533	C₂×C₆₁	1	1	yes	characteristic, complemented
267	C₂×#478	C₂×C₆₁	1	2	yes	complemented
268	C₄×#121	C₂×C₆₁	1	1	yes	characteristic
269	#2058	C₂×C₆₁	1	1	yes	characteristic, complemented
270	#2057	C₂×C₆₁	1	1	yes	characteristic, complemented
271	#2023	C₂×C₆₁	1	1	yes	characteristic, complemented
272	#2023	C₂×C₆₁	1	1	yes	characteristic, complemented
273	#1989	C₂×C₆₁	1	2	yes	complemented
274	#1875	C₂×C₆₁	1	2	yes	—
275	#1854	C₂×C₆₁	1	2	yes	complemented
276	#1797	C₂×C₆₁	1	1	yes	characteristic, complemented
277	C₂×C₆₁	—	4	2	no	—
278	C₂×C₆₁	—	8	2	no	—
279	C₂×C₆₁	#2409	1	1	yes	characteristic
280	C₂×C₆₁	#3002	1	1	yes	characteristic
281	C₂×C₆₁	#3006	1	1	yes	characteristic
282	C₂×C₆₁	#3076	1	1	yes	characteristic
283	C₂×C₆₁	#3077	1	1	yes	characteristic
284	C₂×C₆₁	#3228	1	1	yes	characteristic
285	C₂×C₆₁	#3240	1	1	yes	characteristic
286	#533	—	2	8	no	—
287	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
288	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
289	C₂×#125	C₂²×C₆₁	1	2	yes	—
290	C₂×C₂²⋊Q₈	—	2	1	no	—
291	C₂×C₂²⋊Q₈	—	2	1	no	—
292	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
293	C₂×C₄×Q₈	—	2	1	no	—
294	C₂×C₄×Q₈	—	2	1	no	—
295	C₂×C₄×D₄	—	2	1	no	—
296	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
297	C₂×#117	C₂²×C₆₁	1	2	yes	—
298	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
299	#478	—	2	8	no	—
300	C₂×#107	C₂²×C₆₁	1	2	yes	—
301	C₂×#106	C₂²×C₆₁	1	2	yes	—
302	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
303	C₂×#102	C₂²×C₆₁	1	2	yes	—
304	C₂×#102	C₂²×C₆₁	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
306	#390	C₂²×C₆₁	1	1	yes	characteristic
307	#389	C₂²×C₆₁	1	1	yes	characteristic
308	#388	—	2	1	no	—
309	#386	—	2	1	no	—
310	#380	C₂²×C₆₁	1	1	yes	characteristic
311	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
312	C₄×C₂²⋊C₄	—	2	1	no	—
313	#340	C₂²×C₆₁	1	2	yes	—
314	#340	C₂²×C₆₁	1	2	yes	—
315	#340	C₂²×C₆₁	1	2	yes	—
316	#340	C₂²×C₆₁	1	2	yes	—
317	#336	C₂²×C₆₁	1	1	yes	characteristic
318	#336	C₂²×C₆₁	1	1	yes	characteristic
319	C₆₁	#24304	1	1	yes	characteristic, direct product factor, Sylow
320	C₂²×Q₈	—	2	1	no	—
321	C₂²×Q₈	—	2	1	no	—
322	C₂²×D₄	—	2	1	no	—
323	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
324	C₂³×C₄	—	2	1	no	—
325	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
326	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
327	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
329	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
330	C₄⋊Q₈	—	2	4	no	—
331	C₄⋊Q₈	—	2	4	no	—
332	#125	—	2	4	no	—
333	#125	D₄×C₆₁	1	8	yes	complemented
334	C₂²⋊Q₈	—	2	8	no	—
335	C₂²⋊Q₈	—	2	8	no	—
336	#121	—	2	2	no	—
337	#121	Q₈×C₆₁	1	4	yes	complemented
338	C₄×Q₈	—	2	8	no	—
339	C₄×Q₈	—	2	8	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	4	4	no	—
342	#117	—	2	4	no	—
343	#117	—	2	4	no	—
344	C₂×C₄⋊C₄	—	2	2	no	—
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	4	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
364	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
367	#107	—	2	4	no	—
368	#106	—	2	4	no	—
369	C₄⋊C₈	—	2	4	no	—
370	#102	—	2	4	no	—
371	#102	—	2	4	no	—
372	C₂²⋊C₈	—	2	4	no	—
373	#95	—	2	1	no	—
374	#95	—	2	1	no	—
375	#95	—	2	1	no	—
376	C₂⁴	—	2	1	no	—
377	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	4	2	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	—	4	2	no	—
383	C₂×Q₈	—	4	2	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂×D₄	—	4	2	no	—
390	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	4	1	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	4	2	no	—
406	C₂²×C₄	—	4	2	no	—
407	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
409	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
412	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
413	C₂²×C₄	#41×C₆₁	1	2	yes	—
414	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
432	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
433	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	—
434	C₂²⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	4	2	no	—
437	C₂²⋊C₄	—	4	2	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₂²⋊C₄	—	4	2	no	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	2	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	4	2	no	—
445	C₄²	C₂×D₄×C₆₁	1	4	yes	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	—	4	1	no	—
455	C₂³	—	4	1	no	—
456	C₂³	—	4	1	no	—
457	C₂³	—	4	1	no	—
458	C₂³	—	4	1	no	—
459	C₂³	C₂²⋊Q₈×C₆₁	1	2	yes	—
460	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
461	Q₈	—	4	8	no	—
462	Q₈	—	4	8	no	—
463	D₄	—	2	4	no	—
464	D₄	—	4	8	no	—
465	D₄	—	4	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	4	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	8	4	no	—
496	C₂×C₄	#120×C₆₁	1	2	yes	—
497	C₂×C₄	#120×C₆₁	1	2	yes	—
498	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
499	C₂×C₄	#135×C₆₁	1	2	yes	—
500	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
501	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
502	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
503	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
504	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
505	C₈	—	4	2	no	—
506	C₈	—	4	2	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	1	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	4	2	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	8	1	no	—
518	C₂²	—	8	1	no	—
519	C₂²	—	8	1	no	—
520	C₂²	—	8	1	no	—
521	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
522	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
523	C₂²	C₆₁×#536	1	1	yes	characteristic
524	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
525	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
526	C₂²	C₆₁×#575	1	1	yes	characteristic
527	C₂²	C₆₁×#575	1	1	yes	characteristic
528	C₄	—	2	2	no	—
529	C₄	—	2	2	no	—
530	C₄	—	2	2	no	—
531	C₄	—	2	2	no	—
532	C₄	—	2	2	no	—
533	C₄	—	4	2	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	4	no	—
536	C₄	—	8	1	no	—
537	C₄	—	8	1	no	—
538	C₄	C₆₁×#548	1	2	yes	—
539	C₄	D₄×Q₈×C₆₁	1	2	yes	—
540	C₂	—	4	2	no	—
541	C₂	—	8	2	no	—
542	C₂	C₆₁×#2409	1	1	yes	characteristic
543	C₂	C₆₁×#3002	1	1	yes	characteristic
544	C₂	C₆₁×#3006	1	1	yes	characteristic
545	C₂	C₆₁×#3076	1	1	yes	characteristic
546	C₂	C₆₁×#3077	1	1	yes	characteristic
547	C₂	C₆₁×#3228	1	1	yes	characteristic
548	C₂	C₆₁×#3240	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 ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#533	C₂	semidirect
2. C₂×C₆₁×#478	C₂	semidirect
4. C₆₁×#2058	C₂	semidirect
5. C₆₁×#2057	C₂	semidirect
6. C₆₁×#2023	C₂	semidirect
7. C₆₁×#2023	C₂	semidirect
8. C₆₁×#1989	C₂	semidirect
10. C₆₁×#1854	C₂	semidirect
11. C₆₁×#1797	C₂	semidirect
58. #125×C₆₁	D₄	semidirect
62. #121×C₆₁	Q₈	semidirect
232. #24304	C₆₁	direct (N × H)
266. C₂×#533	C₂×C₆₁	semidirect
267. C₂×#478	C₂×C₆₁	semidirect
269. #2058	C₂×C₆₁	semidirect
270. #2057	C₂×C₆₁	semidirect
271. #2023	C₂×C₆₁	semidirect
272. #2023	C₂×C₆₁	semidirect
273. #1989	C₂×C₆₁	semidirect
275. #1854	C₂×C₆₁	semidirect
276. #1797	C₂×C₆₁	semidirect
319. C₆₁	#24304	direct (N × H)
333. #125	D₄×C₆₁	semidirect
337. #121	Q₈×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×#533	2
C₂×C₆₁×#478	2
C₄×#121×C₆₁	2
C₆₁×#2058	2
C₆₁×#2057	2
C₆₁×#2023	2
C₆₁×#1989	2
C₆₁×#1875	2
C₆₁×#1854	2
C₆₁×#1797	2
#24304	61

Subgroups — C61×#24304 #29527737

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24304 #29527737