Subgroups — C₆₁×#24578 #29528011

Order 15616.

896 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#481	C₂	1	1	yes	maximal, characteristic
2	C₂²×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2501	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2345	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2084	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2065	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1948	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1926	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1893	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×#123×C₆₁	—	2	1	no	—
14	C₂×#123×C₆₁	—	2	1	no	—
15	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₆₁×#481	—	2	4	no	—
19	C₂×#106×C₆₁	—	2	4	no	—
20	C₂×#106×C₆₁	C₂²	1	2	yes	—
21	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#106×C₆₁	C₂²	1	2	yes	—
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₆₁	C₂²	1	2	yes	—
27	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#399	—	2	2	no	—
30	C₆₁×#390	C₂²	1	2	yes	—
31	C₆₁×#389	C₂²	1	2	yes	—
32	C₆₁×#387	—	2	2	no	—
33	C₆₁×#384	C₂²	1	2	yes	—
34	C₆₁×#380	—	2	1	no	—
35	C₆₁×#380	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₆₁	—	2	1	no	—
44	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	—	2	1	no	—
46	C₂³×C₄×C₆₁	—	2	1	no	—
47	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₆₁	—	2	2	no	—
49	C₂²×C₈×C₆₁	—	2	4	no	—
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
53	#123×C₆₁	—	4	4	no	—
54	#123×C₆₁	—	4	4	no	—
55	#121×C₆₁	—	2	2	no	—
56	#121×C₆₁	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
58	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
60	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
63	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
65	C₂×C₄⋊C₄×C₆₁	D₄	1	4	yes	—
66	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	—	2	2	no	—
78	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
79	#106×C₆₁	—	2	4	no	—
80	#106×C₆₁	—	2	4	no	—
81	#106×C₆₁	—	2	2	no	—
82	#106×C₆₁	—	2	2	no	—
83	C₄⋊C₈×C₆₁	—	2	4	no	—
84	#102×C₆₁	—	2	4	no	—
85	#102×C₆₁	—	2	2	no	—
86	#102×C₆₁	—	2	2	no	—
87	C₂²⋊C₈×C₆₁	—	2	2	no	—
88	#95×C₆₁	—	2	2	no	—
89	#95×C₆₁	—	2	2	no	—
90	#95×C₆₁	—	2	1	no	—
91	#95×C₆₁	D₄	1	2	yes	—
92	C₂⁴×C₆₁	—	2	1	no	—
93	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₆₁	—	2	1	no	—
95	C₂×D₄×C₆₁	—	2	2	no	—
96	C₂×D₄×C₆₁	—	2	1	no	—
97	C₂×D₄×C₆₁	—	2	2	no	—
98	C₂×D₄×C₆₁	—	4	2	no	—
99	C₂×D₄×C₆₁	—	4	2	no	—
100	C₂×D₄×C₆₁	—	4	2	no	—
101	C₂²×C₄×C₆₁	—	2	2	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	1	no	—
104	C₂²×C₄×C₆₁	—	2	1	no	—
105	C₂²×C₄×C₆₁	—	2	4	no	—
106	C₂²×C₄×C₆₁	—	2	2	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	4	2	no	—
110	C₂²×C₄×C₆₁	—	4	2	no	—
111	C₂²×C₄×C₆₁	—	4	2	no	—
112	C₂²×C₄×C₆₁	—	8	2	no	—
113	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₆₁	#41	1	2	yes	—
118	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
119	C₂×C₈×C₆₁	—	2	8	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	—	2	1	no	—
124	C₂×C₈×C₆₁	—	2	2	no	—
125	C₂×C₈×C₆₁	—	2	2	no	—
126	C₂×C₈×C₆₁	#41	1	4	yes	—
127	C₄⋊C₄×C₆₁	—	2	4	no	—
128	C₄⋊C₄×C₆₁	—	2	1	no	—
129	C₄⋊C₄×C₆₁	—	2	1	no	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	4	4	no	—
137	C₄⋊C₄×C₆₁	—	4	2	no	—
138	C₄⋊C₄×C₆₁	—	4	4	no	—
139	C₄⋊C₄×C₆₁	—	8	2	no	—
140	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
141	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
142	C₂²⋊C₄×C₆₁	—	2	2	no	—
143	C₂²⋊C₄×C₆₁	—	4	4	no	—
144	C₂²⋊C₄×C₆₁	—	4	2	no	—
145	C₂²⋊C₄×C₆₁	—	4	2	no	—
146	C₂²⋊C₄×C₆₁	—	4	4	no	—
147	C₂²⋊C₄×C₆₁	SD₁₆	1	4	yes	—
148	C₄²×C₆₁	—	2	2	no	—
149	C₄²×C₆₁	—	2	2	no	—
150	C₄²×C₆₁	—	8	2	no	—
151	C₂³×C₆₁	—	2	2	no	—
152	C₂³×C₆₁	—	2	2	no	—
153	C₂³×C₆₁	—	4	1	no	—
154	C₂³×C₆₁	—	4	2	no	—
155	C₂³×C₆₁	—	4	1	no	—
156	C₂³×C₆₁	—	4	1	no	—
157	C₂³×C₆₁	—	4	2	no	—
158	C₂³×C₆₁	#121	1	2	yes	—
159	C₂³×C₆₁	C₂×SD₁₆	1	2	yes	—
160	C₂³×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
161	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	D₄×C₆₁	—	4	1	no	—
163	D₄×C₆₁	—	4	1	no	—
164	D₄×C₆₁	—	4	2	no	—
165	D₄×C₆₁	—	8	4	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	2	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	2	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	2	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	2	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	1	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	1	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	1	no	—
187	C₂×C₄×C₆₁	—	4	2	no	—
188	C₂×C₄×C₆₁	—	8	4	no	—
189	C₂×C₄×C₆₁	—	8	4	no	—
190	C₂×C₄×C₆₁	#121	1	2	yes	—
191	C₂×C₄×C₆₁	C₂×SD₁₆	1	4	yes	—
192	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
194	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
196	C₈×C₆₁	—	2	4	no	—
197	C₈×C₆₁	—	4	1	no	—
198	C₈×C₆₁	—	4	1	no	—
199	#24578	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₆₁	—	2	4	no	—
201	C₂²×C₆₁	—	2	4	no	—
202	C₂²×C₆₁	—	2	2	no	—
203	C₂²×C₆₁	—	2	2	no	—
204	C₂²×C₆₁	—	8	2	no	—
205	C₂²×C₆₁	—	8	2	no	—
206	C₂²×C₆₁	—	8	1	no	—
207	C₂²×C₆₁	—	8	1	no	—
208	C₂²×C₆₁	—	8	1	no	—
209	C₂²×C₆₁	#460	1	4	yes	—
210	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
211	C₂²×C₆₁	#547	1	2	yes	—
212	C₂²×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
213	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂²×C₆₁	#577	1	2	yes	—
215	C₄×C₆₁	—	2	4	no	—
216	C₄×C₆₁	—	2	2	no	—
217	C₄×C₆₁	—	4	2	no	—
218	C₄×C₆₁	—	4	2	no	—
219	C₄×C₆₁	—	4	2	no	—
220	C₄×C₆₁	—	8	2	no	—
221	C₄×C₆₁	—	8	2	no	—
222	C₄×C₆₁	—	8	1	no	—
223	C₄×C₆₁	#525	1	1	yes	characteristic
224	C₄×C₆₁	#536	1	1	yes	characteristic
225	C₄×C₆₁	#552	1	2	yes	—
226	C₂×#481	C₂×C₆₁	1	1	yes	characteristic
227	C₂²×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#2501	C₂×C₆₁	1	1	yes	characteristic
229	#2345	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#2084	C₂×C₆₁	1	2	yes	complemented
231	#2065	C₂×C₆₁	1	2	yes	complemented
232	#1948	C₂×C₆₁	1	2	yes	complemented
233	#1926	C₂×C₆₁	1	2	yes	complemented
234	#1893	C₂×C₆₁	1	1	yes	characteristic
235	#1850	C₂×C₆₁	1	1	yes	characteristic, complemented
236	#1823	C₂×C₆₁	1	1	yes	characteristic, complemented
237	C₂×C₆₁	—	2	4	no	—
238	C₂×C₆₁	—	16	1	no	—
239	C₂×C₆₁	#2413	1	1	yes	characteristic
240	C₂×C₆₁	C₂×#460	1	1	yes	characteristic
241	C₂×C₆₁	#3042	1	1	yes	characteristic
242	C₂×C₆₁	#3335	1	2	yes	—
243	C₂×C₆₁	#3345	1	2	yes	—
244	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
245	C₂×#123	—	2	1	no	—
246	C₂×#123	—	2	1	no	—
247	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
249	C₂²×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
250	#481	—	2	4	no	—
251	C₂×#106	—	2	4	no	—
252	C₂×#106	C₂²×C₆₁	1	2	yes	—
253	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×#106	C₂²×C₆₁	1	2	yes	—
256	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
257	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×#102	C₂²×C₆₁	1	2	yes	—
259	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
260	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
261	#399	—	2	2	no	—
262	#390	C₂²×C₆₁	1	2	yes	—
263	#389	C₂²×C₆₁	1	2	yes	—
264	#387	—	2	2	no	—
265	#384	C₂²×C₆₁	1	2	yes	—
266	#380	—	2	1	no	—
267	#380	C₂²×C₆₁	1	1	yes	characteristic
268	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
269	C₄×C₂²⋊C₄	—	2	1	no	—
270	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
271	#340	C₂²×C₆₁	1	2	yes	—
272	#340	C₂²×C₆₁	1	2	yes	—
273	#340	C₂²×C₆₁	1	2	yes	—
274	#336	C₂²×C₆₁	1	2	yes	—
275	C₆₁	#24578	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×D₄	—	2	1	no	—
277	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	1	no	—
280	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	4	no	—
283	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
286	#123	—	4	4	no	—
287	#123	—	4	4	no	—
288	#121	—	2	2	no	—
289	#121	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	D₄×C₆₁	1	4	yes	—
299	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
312	#106	—	2	4	no	—
313	#106	—	2	4	no	—
314	#106	—	2	2	no	—
315	#106	—	2	2	no	—
316	C₄⋊C₈	—	2	4	no	—
317	#102	—	2	4	no	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	C₂²⋊C₈	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	1	no	—
324	#95	D₄×C₆₁	1	2	yes	—
325	C₂⁴	—	2	1	no	—
326	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	8	2	no	—
346	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
350	C₂²×C₄	#41×C₆₁	1	2	yes	—
351	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
352	C₂×C₈	—	2	8	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	#41×C₆₁	1	4	yes	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	4	2	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	—	8	2	no	—
373	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
374	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	4	4	no	—
377	C₂²⋊C₄	—	4	2	no	—
378	C₂²⋊C₄	—	4	2	no	—
379	C₂²⋊C₄	—	4	4	no	—
380	C₂²⋊C₄	SD₁₆×C₆₁	1	4	yes	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	8	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	1	no	—
391	C₂³	#121×C₆₁	1	2	yes	—
392	C₂³	C₂×SD₁₆×C₆₁	1	2	yes	—
393	C₂³	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
394	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
395	D₄	—	4	1	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	1	no	—
398	D₄	—	8	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	8	4	no	—
422	C₂×C₄	—	8	4	no	—
423	C₂×C₄	#121×C₆₁	1	2	yes	—
424	C₂×C₄	C₂×SD₁₆×C₆₁	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
427	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
428	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
429	C₈	—	2	4	no	—
430	C₈	—	4	1	no	—
431	C₈	—	4	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	4	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	2	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	1	no	—
441	C₂²	C₆₁×#460	1	4	yes	—
442	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
443	C₂²	C₆₁×#547	1	2	yes	—
444	C₂²	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
445	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
446	C₂²	C₆₁×#577	1	2	yes	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	4	2	no	—
451	C₄	—	4	2	no	—
452	C₄	—	8	2	no	—
453	C₄	—	8	1	no	—
454	C₄	—	8	2	no	—
455	C₄	C₆₁×#525	1	1	yes	characteristic
456	C₄	C₆₁×#536	1	1	yes	characteristic
457	C₄	C₆₁×#552	1	2	yes	—
458	C₂	—	2	4	no	—
459	C₂	—	16	1	no	—
460	C₂	C₆₁×#2413	1	1	yes	characteristic
461	C₂	C₂×C₆₁×#460	1	1	yes	characteristic
462	C₂	C₆₁×#3042	1	1	yes	characteristic
463	C₂	C₆₁×#3335	1	2	yes	—
464	C₂	C₆₁×#3345	1	2	yes	—

	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
2. C₂²×#106×C₆₁	C₂	semidirect
4. C₆₁×#2345	C₂	semidirect
5. C₆₁×#2084	C₂	semidirect
6. C₆₁×#2065	C₂	semidirect
7. C₆₁×#1948	C₂	semidirect
8. C₆₁×#1926	C₂	semidirect
10. C₆₁×#1850	C₂	semidirect
11. C₆₁×#1823	C₂	semidirect
199. #24578	C₆₁	direct (N × H)
227. C₂²×#106	C₂×C₆₁	semidirect
229. #2345	C₂×C₆₁	semidirect
230. #2084	C₂×C₆₁	semidirect
231. #2065	C₂×C₆₁	semidirect
232. #1948	C₂×C₆₁	semidirect
233. #1926	C₂×C₆₁	semidirect
235. #1850	C₂×C₆₁	semidirect
236. #1823	C₂×C₆₁	semidirect
275. C₆₁	#24578	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×#481	2
C₂²×#106×C₆₁	2
C₆₁×#2501	2
C₆₁×#2345	2
C₆₁×#2084	2
C₆₁×#2065	2
C₆₁×#1948	2
C₆₁×#1926	2
C₆₁×#1893	2
C₆₁×#1850	2
C₆₁×#1823	2
#24578	61

Subgroups — C61×#24578 #29528011

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24578 #29528011