Subgroups — C₆₁×#22546 #29525979

Order 15616.

1162 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1983	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1982	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1959	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1957	C₂	1	1	yes	maximal, characteristic
8	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1802	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1762	C₂	1	2	yes	maximal, complemented
11	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#559	—	2	4	no	—
13	C₆₁×#559	C₄	1	8	yes	complemented
14	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₆₁	—	2	1	no	—
16	C₂×#124×C₆₁	C₂²	1	2	yes	—
17	C₂×#123×C₆₁	—	2	2	no	—
18	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	—	2	1	no	—
22	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
23	C₆₁×#446	—	2	4	no	—
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#103×C₆₁	C₂²	1	2	yes	—
29	C₂×#102×C₆₁	C₂²	1	2	yes	—
30	C₂×#102×C₆₁	C₂²	1	2	yes	—
31	C₂×#102×C₆₁	C₂²	1	2	yes	—
32	C₂×#102×C₆₁	C₂²	1	2	yes	—
33	C₂×#97×C₆₁	C₂²	1	2	yes	—
34	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#389	—	2	1	no	—
36	C₆₁×#389	—	2	2	no	—
37	C₆₁×#384	C₂²	1	2	yes	—
38	C₆₁×#384	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	1	yes	characteristic
42	C₆₁×#340	C₂²	1	1	yes	characteristic
43	C₆₁×#340	C₂²	1	2	yes	—
44	C₂²×Q₈×C₆₁	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₆₁	—	2	1	no	—
47	C₂²×D₄×C₆₁	—	2	1	no	—
48	C₂²×D₄×C₆₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₆₁	—	2	2	no	—
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	#127×C₆₁	—	2	2	no	—
54	#127×C₆₁	C₂×C₄	1	4	yes	—
55	#124×C₆₁	—	2	8	no	—
56	#124×C₆₁	—	2	4	no	—
57	#124×C₆₁	C₂×C₄	1	8	yes	—
58	#123×C₆₁	—	2	16	no	—
59	C₄×Q₈×C₆₁	—	2	2	no	—
60	C₄×Q₈×C₆₁	—	4	4	no	—
61	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
62	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	—
63	C₄×Q₈×C₆₁	D₄	1	4	yes	—
64	C₄×D₄×C₆₁	—	2	8	no	—
65	C₄×D₄×C₆₁	—	2	4	no	—
66	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
67	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
70	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
78	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
81	C₂×C₄²×C₆₁	—	2	1	no	—
82	C₂×C₄²×C₆₁	—	2	2	no	—
83	C₂×C₄²×C₆₁	—	2	1	no	—
84	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
86	C₄⋊C₈×C₆₁	—	2	2	no	—
87	C₄⋊C₈×C₆₁	—	2	4	no	—
88	#103×C₆₁	—	2	2	no	—
89	#103×C₆₁	—	2	2	no	—
90	#103×C₆₁	—	4	2	no	—
91	#102×C₆₁	—	2	4	no	—
92	#102×C₆₁	—	2	4	no	—
93	#102×C₆₁	—	4	2	no	—
94	#102×C₆₁	—	4	2	no	—
95	#97×C₆₁	—	2	4	no	—
96	C₄×C₈×C₆₁	—	2	2	no	—
97	#95×C₆₁	—	2	2	no	—
98	#95×C₆₁	—	2	1	no	—
99	C₂⁴×C₆₁	—	2	2	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	2	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	1	no	—
106	C₂×Q₈×C₆₁	—	2	1	no	—
107	C₂×Q₈×C₆₁	C₂²⋊C₄	1	4	yes	—
108	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
109	C₂×D₄×C₆₁	—	2	4	no	—
110	C₂×D₄×C₆₁	—	2	4	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	2	no	—
114	C₂×D₄×C₆₁	—	2	2	no	—
115	C₂×D₄×C₆₁	—	2	2	no	—
116	C₂×D₄×C₆₁	—	4	2	no	—
117	C₂×D₄×C₆₁	—	4	2	no	—
118	C₂×D₄×C₆₁	—	8	1	no	—
119	C₂×D₄×C₆₁	—	8	1	no	—
120	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
121	C₂²×C₄×C₆₁	—	2	1	no	—
122	C₂²×C₄×C₆₁	—	2	1	no	—
123	C₂²×C₄×C₆₁	—	2	1	no	—
124	C₂²×C₄×C₆₁	—	2	8	no	—
125	C₂²×C₄×C₆₁	—	2	2	no	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	8	2	no	—
128	C₂²×C₄×C₆₁	—	8	2	no	—
129	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
134	C₂×C₈×C₆₁	—	2	1	no	—
135	C₂×C₈×C₆₁	—	2	1	no	—
136	C₂×C₈×C₆₁	—	2	1	no	—
137	C₂×C₈×C₆₁	—	2	2	no	—
138	C₂×C₈×C₆₁	—	2	2	no	—
139	C₂×C₈×C₆₁	—	2	1	no	—
140	C₂×C₈×C₆₁	—	2	1	no	—
141	C₂×C₈×C₆₁	—	2	2	no	—
142	C₂×C₈×C₆₁	#41	1	2	yes	—
143	C₄⋊C₄×C₆₁	—	2	4	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	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	1	no	—
149	C₄⋊C₄×C₆₁	—	2	2	no	—
150	C₄⋊C₄×C₆₁	—	4	4	no	—
151	C₄⋊C₄×C₆₁	—	4	2	no	—
152	C₄⋊C₄×C₆₁	—	8	2	no	—
153	C₄⋊C₄×C₆₁	—	8	1	no	—
154	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
155	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	8	yes	—
156	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
157	C₄⋊C₄×C₆₁	#41	1	2	yes	—
158	C₂²⋊C₄×C₆₁	—	2	8	no	—
159	C₂²⋊C₄×C₆₁	—	2	8	no	—
160	C₂²⋊C₄×C₆₁	—	2	8	no	—
161	C₄²×C₆₁	—	2	4	no	—
162	C₄²×C₆₁	—	4	4	no	—
163	C₄²×C₆₁	—	4	2	no	—
164	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
165	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
166	C₄²×C₆₁	C₂×D₄	1	2	yes	—
167	C₄²×C₆₁	C₂×D₄	1	4	yes	—
168	C₂³×C₆₁	—	2	4	no	—
169	C₂³×C₆₁	—	4	2	no	—
170	C₂³×C₆₁	—	4	2	no	—
171	C₂³×C₆₁	—	4	2	no	—
172	C₂³×C₆₁	—	4	2	no	—
173	C₂³×C₆₁	—	4	2	no	—
174	C₂³×C₆₁	—	4	2	no	—
175	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₆₁	—	2	8	no	—
177	Q₈×C₆₁	—	2	2	no	—
178	Q₈×C₆₁	—	2	2	no	—
179	Q₈×C₆₁	—	4	1	no	—
180	Q₈×C₆₁	—	4	1	no	—
181	D₄×C₆₁	—	2	4	no	—
182	D₄×C₆₁	—	2	4	no	—
183	D₄×C₆₁	—	4	2	no	—
184	D₄×C₆₁	—	4	2	no	—
185	D₄×C₆₁	—	4	8	no	—
186	D₄×C₆₁	—	8	4	no	—
187	C₂×C₄×C₆₁	—	2	2	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	2	2	no	—
190	C₂×C₄×C₆₁	—	2	1	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	2	1	no	—
193	C₂×C₄×C₆₁	—	2	2	no	—
194	C₂×C₄×C₆₁	—	2	2	no	—
195	C₂×C₄×C₆₁	—	2	2	no	—
196	C₂×C₄×C₆₁	—	4	1	no	—
197	C₂×C₄×C₆₁	—	4	1	no	—
198	C₂×C₄×C₆₁	—	4	1	no	—
199	C₂×C₄×C₆₁	—	4	1	no	—
200	C₂×C₄×C₆₁	—	4	1	no	—
201	C₂×C₄×C₆₁	—	4	1	no	—
202	C₂×C₄×C₆₁	—	4	2	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	—	4	2	no	—
205	C₂×C₄×C₆₁	—	4	1	no	—
206	C₂×C₄×C₆₁	—	4	1	no	—
207	C₂×C₄×C₆₁	—	4	2	no	—
208	C₂×C₄×C₆₁	—	8	8	no	—
209	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
210	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
211	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
212	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
213	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
214	C₂×C₄×C₆₁	#137	1	2	yes	—
215	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
221	C₈×C₆₁	—	2	2	no	—
222	C₈×C₆₁	—	4	1	no	—
223	C₈×C₆₁	—	4	2	no	—
224	#22546	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₆₁	—	4	4	no	—
226	C₂²×C₆₁	—	4	4	no	—
227	C₂²×C₆₁	—	4	4	no	—
228	C₂²×C₆₁	—	8	2	no	—
229	C₂²×C₆₁	—	8	2	no	—
230	C₂²×C₆₁	—	8	2	no	—
231	C₂²×C₆₁	—	8	2	no	—
232	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
233	C₂²×C₆₁	#548	1	1	yes	characteristic
234	C₂²×C₆₁	#550	1	1	yes	characteristic
235	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
237	C₂²×C₆₁	#576	1	1	yes	characteristic
238	C₂²×C₆₁	#577	1	1	yes	characteristic
239	C₄×C₆₁	—	2	4	no	—
240	C₄×C₆₁	—	2	4	no	—
241	C₄×C₆₁	—	2	2	no	—
242	C₄×C₆₁	—	4	2	no	—
243	C₄×C₆₁	—	4	2	no	—
244	C₄×C₆₁	—	4	2	no	—
245	C₄×C₆₁	—	8	2	no	—
246	C₄×C₆₁	—	8	1	no	—
247	C₄×C₆₁	#417	1	4	yes	—
248	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
249	C₄×C₆₁	#520	1	1	yes	characteristic
250	C₄×C₆₁	#548	1	1	yes	characteristic
251	C₄×C₆₁	#550	1	1	yes	characteristic
252	C₂×#559	C₂×C₆₁	1	1	yes	characteristic
253	C₂×#446	C₂×C₆₁	1	1	yes	characteristic, complemented
254	Q₈×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
255	#1983	C₂×C₆₁	1	2	yes	complemented
256	#1982	C₂×C₆₁	1	1	yes	characteristic
257	#1959	C₂×C₆₁	1	2	yes	complemented
258	#1957	C₂×C₆₁	1	1	yes	characteristic
259	#1803	C₂×C₆₁	1	1	yes	characteristic, complemented
260	#1802	C₂×C₆₁	1	2	yes	complemented
261	#1762	C₂×C₆₁	1	2	yes	complemented
262	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
263	C₂×C₆₁	—	8	4	no	—
264	C₂×C₆₁	#2341	1	1	yes	characteristic
265	C₂×C₆₁	C₂×#417	1	1	yes	characteristic
266	C₂×C₆₁	#2897	1	1	yes	characteristic
267	C₂×C₆₁	#3373	1	1	yes	characteristic
268	C₂×C₆₁	#3375	1	1	yes	characteristic
269	C₂×C₆₁	#3399	1	1	yes	characteristic
270	C₂×C₆₁	#3400	1	1	yes	characteristic
271	#559	—	2	4	no	—
272	#559	C₄×C₆₁	1	8	yes	complemented
273	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
274	C₂×#124	—	2	1	no	—
275	C₂×#124	C₂²×C₆₁	1	2	yes	—
276	C₂×#123	—	2	2	no	—
277	C₂×C₄×Q₈	—	2	1	no	—
278	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
279	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
280	C₂×C₄×D₄	—	2	1	no	—
281	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
282	#446	—	2	4	no	—
283	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
284	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
285	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
286	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
287	C₂×#103	C₂²×C₆₁	1	2	yes	—
288	C₂×#102	C₂²×C₆₁	1	2	yes	—
289	C₂×#102	C₂²×C₆₁	1	2	yes	—
290	C₂×#102	C₂²×C₆₁	1	2	yes	—
291	C₂×#102	C₂²×C₆₁	1	2	yes	—
292	C₂×#97	C₂²×C₆₁	1	2	yes	—
293	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
294	#389	—	2	1	no	—
295	#389	—	2	2	no	—
296	#384	C₂²×C₆₁	1	2	yes	—
297	#384	C₂²×C₆₁	1	1	yes	characteristic
298	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
299	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
300	#340	C₂²×C₆₁	1	1	yes	characteristic
301	#340	C₂²×C₆₁	1	2	yes	—
302	#340	C₂²×C₆₁	1	1	yes	characteristic
303	C₆₁	#22546	1	1	yes	characteristic, direct product factor, Sylow
304	C₂²×Q₈	D₄×C₆₁	1	1	yes	characteristic
305	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	C₂³×C₆₁	1	2	yes	—
309	C₂³×C₄	—	2	2	no	—
310	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
312	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
313	#127	—	2	2	no	—
314	#127	C₂×C₄×C₆₁	1	4	yes	—
315	#124	—	2	8	no	—
316	#124	—	2	4	no	—
317	#124	C₂×C₄×C₆₁	1	8	yes	—
318	#123	—	2	16	no	—
319	C₄×Q₈	—	2	2	no	—
320	C₄×Q₈	—	4	4	no	—
321	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
322	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	—
323	C₄×Q₈	D₄×C₆₁	1	4	yes	—
324	C₄×D₄	—	2	8	no	—
325	C₄×D₄	—	2	4	no	—
326	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
333	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	1	no	—
344	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
345	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
346	C₄⋊C₈	—	2	2	no	—
347	C₄⋊C₈	—	2	4	no	—
348	#103	—	2	2	no	—
349	#103	—	2	2	no	—
350	#103	—	4	2	no	—
351	#102	—	2	4	no	—
352	#102	—	2	4	no	—
353	#102	—	4	2	no	—
354	#102	—	4	2	no	—
355	#97	—	2	4	no	—
356	C₄×C₈	—	2	2	no	—
357	#95	—	2	2	no	—
358	#95	—	2	1	no	—
359	C₂⁴	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	1	no	—
367	C₂×Q₈	C₂²⋊C₄×C₆₁	1	4	yes	—
368	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	8	1	no	—
379	C₂×D₄	—	8	1	no	—
380	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	8	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	8	2	no	—
388	C₂²×C₄	—	8	2	no	—
389	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
393	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	#41×C₆₁	1	2	yes	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	8	2	no	—
413	C₄⋊C₄	—	8	1	no	—
414	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
415	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	8	yes	—
416	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
417	C₄⋊C₄	#41×C₆₁	1	2	yes	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	4	4	no	—
423	C₄²	—	4	2	no	—
424	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
425	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
426	C₄²	C₂×D₄×C₆₁	1	2	yes	—
427	C₄²	C₂×D₄×C₆₁	1	4	yes	—
428	C₂³	—	2	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	2	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	2	no	—
435	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
436	Q₈	—	2	8	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	4	1	no	—
441	D₄	—	2	4	no	—
442	D₄	—	2	4	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	8	no	—
446	D₄	—	8	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	8	8	no	—
469	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
470	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
471	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
472	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
473	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
474	C₂×C₄	#137×C₆₁	1	2	yes	—
475	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
476	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
477	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
478	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
479	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
480	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
481	C₈	—	2	2	no	—
482	C₈	—	4	1	no	—
483	C₈	—	4	2	no	—
484	C₂²	—	4	4	no	—
485	C₂²	—	4	4	no	—
486	C₂²	—	4	4	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	2	no	—
490	C₂²	—	8	2	no	—
491	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
492	C₂²	C₆₁×#548	1	1	yes	characteristic
493	C₂²	C₆₁×#550	1	1	yes	characteristic
494	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
495	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
496	C₂²	C₆₁×#576	1	1	yes	characteristic
497	C₂²	C₆₁×#577	1	1	yes	characteristic
498	C₄	—	2	4	no	—
499	C₄	—	2	4	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	1	no	—
506	C₄	C₆₁×#417	1	4	yes	—
507	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
508	C₄	C₆₁×#520	1	1	yes	characteristic
509	C₄	C₆₁×#548	1	1	yes	characteristic
510	C₄	C₆₁×#550	1	1	yes	characteristic
511	C₂	—	8	4	no	—
512	C₂	C₆₁×#2341	1	1	yes	characteristic
513	C₂	C₂×C₆₁×#417	1	1	yes	characteristic
514	C₂	C₆₁×#2897	1	1	yes	characteristic
515	C₂	C₆₁×#3373	1	1	yes	characteristic
516	C₂	C₆₁×#3375	1	1	yes	characteristic
517	C₂	C₆₁×#3399	1	1	yes	characteristic
518	C₂	C₆₁×#3400	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#127×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₂×C₄×Q₈×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#446	C₂	semidirect
3. Q₈×C₄⋊C₄×C₆₁	C₂	semidirect
4. C₆₁×#1983	C₂	semidirect
6. C₆₁×#1959	C₂	semidirect
8. C₆₁×#1803	C₂	semidirect
9. C₆₁×#1802	C₂	semidirect
10. C₆₁×#1762	C₂	semidirect
11. C₄×#103×C₆₁	C₂	semidirect
13. C₆₁×#559	C₄	semidirect
224. #22546	C₆₁	direct (N × H)
253. C₂×#446	C₂×C₆₁	semidirect
254. Q₈×C₄⋊C₄	C₂×C₆₁	semidirect
255. #1983	C₂×C₆₁	semidirect
257. #1959	C₂×C₆₁	semidirect
259. #1803	C₂×C₆₁	semidirect
260. #1802	C₂×C₆₁	semidirect
261. #1762	C₂×C₆₁	semidirect
262. C₄×#103	C₂×C₆₁	semidirect
272. #559	C₄×C₆₁	semidirect
303. C₆₁	#22546	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×#559	2
C₂×C₆₁×#446	2
Q₈×C₄⋊C₄×C₆₁	2
C₆₁×#1983	2
C₆₁×#1982	2
C₆₁×#1959	2
C₆₁×#1957	2
C₆₁×#1803	2
C₆₁×#1802	2
C₆₁×#1762	2
C₄×#103×C₆₁	2
#22546	61

Subgroups — C61×#22546 #29525979

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22546 #29525979