Subgroups — C₆₁×#25760 #29529193

Order 15616.

1514 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#494	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#462	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₆₁×#451	C₂	1	4	yes	maximal, complemented
5	C₆₁×#2542	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#2001	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1954	C₂	1	1	yes	maximal, characteristic
9	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₆₁	C₂²	1	2	yes	—
11	C₂²×Q₁₆×C₆₁	C₂²	1	2	yes	—
12	C₂²×Q₁₆×C₆₁	C₂²	1	4	yes	—
13	D₄×Q₈×C₆₁	—	2	4	no	—
14	D₄×Q₈×C₆₁	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₆₁	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	4	yes	—
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	—	2	1	no	—
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#494	—	2	4	no	—
25	C₆₁×#462	—	2	4	no	—
26	C₆₁×#451	—	2	16	no	—
27	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#103×C₆₁	C₂²	1	2	yes	—
29	C₂×#103×C₆₁	C₂²	1	4	yes	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₆₁	C₂²	1	4	yes	—
32	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#399	—	2	2	no	—
34	C₆₁×#390	—	2	1	no	—
35	C₆₁×#384	—	2	1	no	—
36	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#340	C₂²	1	2	yes	—
38	C₂²×Q₈×C₆₁	—	2	4	no	—
39	C₂²×Q₈×C₆₁	—	2	4	no	—
40	C₂²×Q₈×C₆₁	—	2	2	no	—
41	C₂²×Q₈×C₆₁	—	2	8	no	—
42	C₂²×Q₈×C₆₁	—	4	4	no	—
43	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
44	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
45	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	—	2	2	no	—
48	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
49	C₂×Q₁₆×C₆₁	—	2	8	no	—
50	C₂×Q₁₆×C₆₁	—	2	4	no	—
51	C₂×Q₁₆×C₆₁	—	2	8	no	—
52	C₂×Q₁₆×C₆₁	—	2	8	no	—
53	C₂×Q₁₆×C₆₁	—	4	4	no	—
54	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₆₁	—	2	8	no	—
57	C₄⋊Q₈×C₆₁	—	2	2	no	—
58	C₄⋊Q₈×C₆₁	—	2	2	no	—
59	C₄⋊Q₈×C₆₁	—	2	2	no	—
60	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
61	C₂²⋊Q₈×C₆₁	—	2	16	no	—
62	C₂²⋊Q₈×C₆₁	—	2	4	no	—
63	C₂²⋊Q₈×C₆₁	—	2	4	no	—
64	C₂²⋊Q₈×C₆₁	—	2	8	no	—
65	C₂²⋊Q₈×C₆₁	—	4	4	no	—
66	C₄×Q₈×C₆₁	—	2	2	no	—
67	C₄×Q₈×C₆₁	D₄	1	4	yes	—
68	C₄×D₄×C₆₁	—	2	8	no	—
69	C₄×D₄×C₆₁	—	2	2	no	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
72	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
78	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
81	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₆₁	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
84	C₂×C₄²×C₆₁	—	2	1	no	—
85	C₂×C₄²×C₆₁	—	2	1	no	—
86	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₆₁	—	2	2	no	—
88	#103×C₆₁	—	2	8	no	—
89	#103×C₆₁	—	2	4	no	—
90	#103×C₆₁	D₄	1	8	yes	complemented
91	C₂²⋊C₈×C₆₁	—	2	8	no	—
92	C₄×C₈×C₆₁	—	2	2	no	—
93	#95×C₆₁	—	2	1	no	—
94	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
95	C₂×Q₈×C₆₁	—	2	8	no	—
96	C₂×Q₈×C₆₁	—	2	1	no	—
97	C₂×Q₈×C₆₁	—	2	2	no	—
98	C₂×Q₈×C₆₁	—	2	2	no	—
99	C₂×Q₈×C₆₁	—	2	4	no	—
100	C₂×Q₈×C₆₁	—	2	2	no	—
101	C₂×Q₈×C₆₁	—	2	4	no	—
102	C₂×Q₈×C₆₁	—	2	2	no	—
103	C₂×Q₈×C₆₁	—	2	4	no	—
104	C₂×Q₈×C₆₁	—	2	4	no	—
105	C₂×Q₈×C₆₁	—	4	8	no	—
106	C₂×Q₈×C₆₁	—	4	16	no	—
107	C₂×Q₈×C₆₁	—	4	8	no	—
108	C₂×Q₈×C₆₁	—	4	8	no	—
109	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
110	C₂×Q₈×C₆₁	C₂×D₄	1	4	yes	—
111	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	2	no	—
114	C₂×D₄×C₆₁	Q₁₆	1	4	yes	complemented
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	8	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	4	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	2	4	no	—
124	C₂²×C₄×C₆₁	—	2	2	no	—
125	C₂²×C₄×C₆₁	—	4	8	no	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
130	Q₁₆×C₆₁	—	4	16	no	—
131	Q₁₆×C₆₁	—	4	8	no	—
132	C₂×C₈×C₆₁	—	2	2	no	—
133	C₂×C₈×C₆₁	—	2	2	no	—
134	C₂×C₈×C₆₁	—	2	4	no	—
135	C₂×C₈×C₆₁	—	2	2	no	—
136	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
137	C₄⋊C₄×C₆₁	—	2	8	no	—
138	C₄⋊C₄×C₆₁	—	2	4	no	—
139	C₄⋊C₄×C₆₁	—	2	4	no	—
140	C₄⋊C₄×C₆₁	—	2	4	no	—
141	C₄⋊C₄×C₆₁	—	2	2	no	—
142	C₄⋊C₄×C₆₁	—	2	1	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	4	8	no	—
145	C₄⋊C₄×C₆₁	—	4	2	no	—
146	C₄⋊C₄×C₆₁	—	4	2	no	—
147	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
148	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₆₁	—	2	8	no	—
150	C₂²⋊C₄×C₆₁	—	2	4	no	—
151	C₂²⋊C₄×C₆₁	—	4	8	no	—
152	C₄²×C₆₁	—	2	4	no	—
153	C₄²×C₆₁	—	4	2	no	—
154	C₄²×C₆₁	C₂×D₄	1	2	yes	—
155	C₄²×C₆₁	C₂×D₄	1	2	yes	—
156	C₂³×C₆₁	—	2	2	no	—
157	C₂³×C₆₁	—	2	4	no	—
158	C₂³×C₆₁	—	2	2	no	—
159	C₂³×C₆₁	—	2	4	no	—
160	C₂³×C₆₁	C₂×Q₁₆	1	4	yes	—
161	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
162	Q₈×C₆₁	—	2	2	no	—
163	Q₈×C₆₁	—	2	4	no	—
164	Q₈×C₆₁	—	2	8	no	—
165	Q₈×C₆₁	—	4	16	no	—
166	Q₈×C₆₁	—	4	2	no	—
167	Q₈×C₆₁	—	4	2	no	—
168	Q₈×C₆₁	—	4	2	no	—
169	Q₈×C₆₁	—	4	2	no	—
170	Q₈×C₆₁	—	4	4	no	—
171	Q₈×C₆₁	#127	1	4	yes	—
172	D₄×C₆₁	—	2	8	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	4	no	—
175	C₂×C₄×C₆₁	—	2	2	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	4	no	—
178	C₂×C₄×C₆₁	—	2	2	no	—
179	C₂×C₄×C₆₁	—	2	4	no	—
180	C₂×C₄×C₆₁	—	2	4	no	—
181	C₂×C₄×C₆₁	—	4	16	no	—
182	C₂×C₄×C₆₁	—	4	4	no	—
183	C₂×C₄×C₆₁	—	4	2	no	—
184	C₂×C₄×C₆₁	—	4	2	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	4	2	no	—
187	C₂×C₄×C₆₁	—	4	2	no	—
188	C₂×C₄×C₆₁	—	4	4	no	—
189	C₂×C₄×C₆₁	—	4	2	no	—
190	C₂×C₄×C₆₁	—	4	4	no	—
191	C₂×C₄×C₆₁	#120	1	2	yes	—
192	C₂×C₄×C₆₁	#120	1	2	yes	—
193	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
194	C₂×C₄×C₆₁	#137	1	2	yes	—
195	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₆₁	H(5,𝔽₂)	1	2	yes	—
199	C₈×C₆₁	—	2	4	no	—
200	C₈×C₆₁	—	4	2	no	—
201	#25760	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₆₁	—	2	4	no	—
203	C₂²×C₆₁	—	2	8	no	—
204	C₂²×C₆₁	—	4	2	no	—
205	C₂²×C₆₁	—	4	2	no	—
206	C₂²×C₆₁	—	4	4	no	—
207	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
208	C₂²×C₆₁	D₄²	1	2	yes	—
209	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
210	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
211	C₂²×C₆₁	#578	1	2	yes	—
212	C₄×C₆₁	—	2	4	no	—
213	C₄×C₆₁	—	2	2	no	—
214	C₄×C₆₁	—	4	2	no	—
215	C₄×C₆₁	—	4	4	no	—
216	C₄×C₆₁	—	4	2	no	—
217	C₄×C₆₁	—	4	4	no	—
218	C₄×C₆₁	—	8	2	no	—
219	C₄×C₆₁	#451	1	4	yes	complemented
220	C₄×C₆₁	C₂×#127	1	1	yes	characteristic
221	C₄×C₆₁	#535	1	1	yes	characteristic
222	C₄×C₆₁	D₄²	1	2	yes	—
223	C₂×D₄×Q₈	C₂×C₆₁	1	1	yes	characteristic
224	C₂×#494	C₂×C₆₁	1	1	yes	characteristic, complemented
225	C₂×#462	C₂×C₆₁	1	1	yes	characteristic, complemented
226	C₂×#451	C₂×C₆₁	1	4	yes	complemented
227	#2542	C₂×C₆₁	1	1	yes	characteristic
228	#2001	C₂×C₆₁	1	4	yes	complemented
229	#1981	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#1954	C₂×C₆₁	1	1	yes	characteristic
231	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
232	C₂×C₆₁	—	4	4	no	—
233	C₂×C₆₁	#2433	1	1	yes	characteristic
234	C₂×C₆₁	C₂×#451	1	1	yes	characteristic
235	C₂×C₆₁	#3011	1	1	yes	characteristic
236	C₂×C₆₁	#3276	1	2	yes	—
237	C₂×C₆₁	D₄×Q₁₆	1	2	yes	—
238	C₂³×Q₈	C₂²×C₆₁	1	2	yes	—
239	C₂²×Q₁₆	C₂²×C₆₁	1	2	yes	—
240	C₂²×Q₁₆	C₂²×C₆₁	1	4	yes	—
241	D₄×Q₈	—	2	4	no	—
242	D₄×Q₈	—	2	4	no	—
243	C₂×C₄⋊Q₈	—	2	1	no	—
244	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
245	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
246	C₂×C₂²⋊Q₈	—	2	2	no	—
247	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
248	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	4	yes	—
249	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
250	C₂×C₄×D₄	—	2	1	no	—
251	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
252	#494	—	2	4	no	—
253	#462	—	2	4	no	—
254	#451	—	2	16	no	—
255	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
256	C₂×#103	C₂²×C₆₁	1	4	yes	—
257	C₂×#103	C₂²×C₆₁	1	2	yes	—
258	C₂×#103	C₂²×C₆₁	1	2	yes	—
259	C₂×C₂²⋊C₈	C₂²×C₆₁	1	4	yes	—
260	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
261	#399	—	2	2	no	—
262	#390	—	2	1	no	—
263	#384	—	2	1	no	—
264	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
265	#340	C₂²×C₆₁	1	2	yes	—
266	C₆₁	#25760	1	1	yes	characteristic, direct product factor, Sylow
267	C₂²×Q₈	—	2	4	no	—
268	C₂²×Q₈	—	2	4	no	—
269	C₂²×Q₈	—	2	2	no	—
270	C₂²×Q₈	—	2	8	no	—
271	C₂²×Q₈	—	4	4	no	—
272	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
273	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
274	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
275	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
276	C₂³×C₄	—	2	2	no	—
277	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
278	C₂×Q₁₆	—	2	8	no	—
279	C₂×Q₁₆	—	2	4	no	—
280	C₂×Q₁₆	—	2	8	no	—
281	C₂×Q₁₆	—	2	8	no	—
282	C₂×Q₁₆	—	4	4	no	—
283	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
284	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
285	C₄⋊Q₈	—	2	8	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
290	C₂²⋊Q₈	—	2	16	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	2	4	no	—
293	C₂²⋊Q₈	—	2	8	no	—
294	C₂²⋊Q₈	—	4	4	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	D₄×C₆₁	1	4	yes	—
297	C₄×D₄	—	2	8	no	—
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	4	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	4	no	—
312	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
316	C₄⋊C₈	—	2	2	no	—
317	#103	—	2	8	no	—
318	#103	—	2	4	no	—
319	#103	D₄×C₆₁	1	8	yes	complemented
320	C₂²⋊C₈	—	2	8	no	—
321	C₄×C₈	—	2	2	no	—
322	#95	—	2	1	no	—
323	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
324	C₂×Q₈	—	2	8	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	4	8	no	—
335	C₂×Q₈	—	4	16	no	—
336	C₂×Q₈	—	4	8	no	—
337	C₂×Q₈	—	4	8	no	—
338	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
339	C₂×Q₈	C₂×D₄×C₆₁	1	4	yes	—
340	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	Q₁₆×C₆₁	1	4	yes	complemented
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	4	8	no	—
355	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
358	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
359	Q₁₆	—	4	16	no	—
360	Q₁₆	—	4	8	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	4	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
366	C₄⋊C₄	—	2	8	no	—
367	C₄⋊C₄	—	2	4	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	2	4	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	8	no	—
374	C₄⋊C₄	—	4	2	no	—
375	C₄⋊C₄	—	4	2	no	—
376	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
377	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
378	C₂²⋊C₄	—	2	8	no	—
379	C₂²⋊C₄	—	2	4	no	—
380	C₂²⋊C₄	—	4	8	no	—
381	C₄²	—	2	4	no	—
382	C₄²	—	4	2	no	—
383	C₄²	C₂×D₄×C₆₁	1	2	yes	—
384	C₄²	C₂×D₄×C₆₁	1	2	yes	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	4	no	—
388	C₂³	—	2	2	no	—
389	C₂³	C₂×Q₁₆×C₆₁	1	4	yes	—
390	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
391	Q₈	—	2	2	no	—
392	Q₈	—	2	4	no	—
393	Q₈	—	2	8	no	—
394	Q₈	—	4	16	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	4	2	no	—
399	Q₈	—	4	4	no	—
400	Q₈	#127×C₆₁	1	4	yes	—
401	D₄	—	2	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	16	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	4	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	#120×C₆₁	1	2	yes	—
421	C₂×C₄	#120×C₆₁	1	2	yes	—
422	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
423	C₂×C₄	#137×C₆₁	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
426	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₆₁	1	2	yes	—
428	C₈	—	2	4	no	—
429	C₈	—	4	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	8	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	4	no	—
435	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
436	C₂²	D₄²×C₆₁	1	2	yes	—
437	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
438	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
439	C₂²	C₆₁×#578	1	2	yes	—
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	4	no	—
446	C₄	—	8	2	no	—
447	C₄	C₆₁×#451	1	4	yes	complemented
448	C₄	C₂×#127×C₆₁	1	1	yes	characteristic
449	C₄	C₆₁×#535	1	1	yes	characteristic
450	C₄	D₄²×C₆₁	1	2	yes	—
451	C₂	—	4	4	no	—
452	C₂	C₆₁×#2433	1	1	yes	characteristic
453	C₂	C₂×C₆₁×#451	1	1	yes	characteristic
454	C₂	C₆₁×#3011	1	1	yes	characteristic
455	C₂	C₆₁×#3276	1	2	yes	—
456	C₂	D₄×Q₁₆×C₆₁	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₆₁×#494	C₂	semidirect
3. C₂×C₆₁×#462	C₂	semidirect
4. C₂×C₆₁×#451	C₂	semidirect
6. C₆₁×#2001	C₂	semidirect
7. C₆₁×#1981	C₂	semidirect
9. C₄×#103×C₆₁	C₂	semidirect
90. #103×C₆₁	D₄	semidirect
114. C₂×D₄×C₆₁	Q₁₆	semidirect
201. #25760	C₆₁	direct (N × H)
219. C₄×C₆₁	#451	semidirect
224. C₂×#494	C₂×C₆₁	semidirect
225. C₂×#462	C₂×C₆₁	semidirect
226. C₂×#451	C₂×C₆₁	semidirect
228. #2001	C₂×C₆₁	semidirect
229. #1981	C₂×C₆₁	semidirect
231. C₄×#103	C₂×C₆₁	semidirect
266. C₆₁	#25760	direct (N × H)
319. #103	D₄×C₆₁	semidirect
343. C₂×D₄	Q₁₆×C₆₁	semidirect
447. C₄	C₆₁×#451	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×D₄×Q₈×C₆₁	2
C₂×C₆₁×#494	2
C₂×C₆₁×#462	2
C₂×C₆₁×#451	2
C₆₁×#2542	2
C₆₁×#2001	2
C₆₁×#1981	2
C₆₁×#1954	2
C₄×#103×C₆₁	2
#25760	61

Subgroups — C61×#25760 #29529193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25760 #29529193