Subgroups — C₆₁×#24123 #29527556

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2538	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2035	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2001	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1954	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1873	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1854	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₆₁×#556	—	2	4	no	—
14	C₆₁×#556	—	2	4	no	—
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×#126×C₆₁	—	2	2	no	—
17	C₂×#124×C₆₁	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₆₁	—	2	1	no	—
21	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#117×C₆₁	C₂²	1	2	yes	—
25	C₆₁×#475	—	2	4	no	—
26	C₄×Q₁₆×C₆₁	—	2	4	no	—
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₆₁	C₂²	1	2	yes	—
29	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	2	yes	—
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₆₁	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
35	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#396	—	2	2	no	—
38	C₆₁×#390	—	2	1	no	—
39	C₆₁×#389	—	2	1	no	—
40	C₆₁×#384	C₂²	1	1	yes	characteristic
41	C₆₁×#380	C₂²	1	2	yes	—
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₆₁×#340	C₂²	1	2	yes	—
44	C₆₁×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₆₁	—	2	1	no	—
46	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
50	C₂×Q₁₆×C₆₁	—	2	2	no	—
51	C₂×Q₁₆×C₆₁	—	2	2	no	—
52	C₂×Q₁₆×C₆₁	—	2	2	no	—
53	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
55	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₆₁	—	2	2	no	—
57	C₄⋊Q₈×C₆₁	D₄	1	4	yes	—
58	#126×C₆₁	—	2	16	no	—
59	#124×C₆₁	—	2	8	no	—
60	C₂²⋊Q₈×C₆₁	—	2	4	no	—
61	C₂²⋊Q₈×C₆₁	—	2	4	no	—
62	C₂²⋊Q₈×C₆₁	—	2	4	no	—
63	C₂²⋊Q₈×C₆₁	—	4	2	no	—
64	C₄×Q₈×C₆₁	—	2	8	no	—
65	C₄×Q₈×C₆₁	—	2	2	no	—
66	C₄×Q₈×C₆₁	—	2	2	no	—
67	C₄×Q₈×C₆₁	—	2	2	no	—
68	C₄×Q₈×C₆₁	D₄	1	4	yes	—
69	C₄×D₄×C₆₁	—	2	2	no	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	#117×C₆₁	—	2	4	no	—
72	#117×C₆₁	—	2	4	no	—
73	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
75	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
86	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
90	C₂×C₄²×C₆₁	—	2	2	no	—
91	C₂×C₄²×C₆₁	—	2	1	no	—
92	C₂×C₄²×C₆₁	—	2	1	no	—
93	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
94	#107×C₆₁	—	2	2	no	—
95	#106×C₆₁	—	2	4	no	—
96	C₄⋊C₈×C₆₁	—	2	2	no	—
97	#103×C₆₁	—	2	2	no	—
98	#103×C₆₁	—	2	2	no	—
99	#103×C₆₁	—	2	4	no	—
100	#103×C₆₁	—	4	2	no	—
101	C₂²⋊C₈×C₆₁	—	2	4	no	—
102	C₂²⋊C₈×C₆₁	—	4	2	no	—
103	C₄×C₈×C₆₁	—	2	2	no	—
104	#95×C₆₁	—	2	2	no	—
105	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₆₁	—	2	4	no	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	1	no	—
109	C₂×Q₈×C₆₁	—	2	1	no	—
110	C₂×Q₈×C₆₁	—	2	1	no	—
111	C₂×Q₈×C₆₁	—	2	1	no	—
112	C₂×Q₈×C₆₁	—	2	1	no	—
113	C₂×Q₈×C₆₁	—	2	1	no	—
114	C₂×Q₈×C₆₁	—	2	1	no	—
115	C₂×Q₈×C₆₁	—	2	1	no	—
116	C₂×Q₈×C₆₁	—	2	1	no	—
117	C₂×Q₈×C₆₁	—	4	2	no	—
118	C₂×Q₈×C₆₁	—	4	2	no	—
119	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
120	C₂×Q₈×C₆₁	#41	1	2	yes	—
121	C₂×D₄×C₆₁	—	2	2	no	—
122	C₂×D₄×C₆₁	—	2	2	no	—
123	C₂×D₄×C₆₁	—	2	2	no	—
124	C₂²×C₄×C₆₁	—	2	1	no	—
125	C₂²×C₄×C₆₁	—	2	1	no	—
126	C₂²×C₄×C₆₁	—	2	1	no	—
127	C₂²×C₄×C₆₁	—	2	2	no	—
128	C₂²×C₄×C₆₁	—	2	2	no	—
129	C₂²×C₄×C₆₁	—	2	2	no	—
130	C₂²×C₄×C₆₁	—	2	2	no	—
131	C₂²×C₄×C₆₁	—	2	2	no	—
132	C₂²×C₄×C₆₁	—	2	2	no	—
133	C₂²×C₄×C₆₁	—	2	2	no	—
134	C₂²×C₄×C₆₁	—	2	1	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
140	Q₁₆×C₆₁	—	2	8	no	—
141	C₂×C₈×C₆₁	—	2	1	no	—
142	C₂×C₈×C₆₁	—	2	1	no	—
143	C₂×C₈×C₆₁	—	2	1	no	—
144	C₂×C₈×C₆₁	—	2	2	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	—	2	2	no	—
148	C₂×C₈×C₆₁	—	2	1	no	—
149	C₂×C₈×C₆₁	#41	1	2	yes	—
150	C₄⋊C₄×C₆₁	—	2	8	no	—
151	C₄⋊C₄×C₆₁	—	2	4	no	—
152	C₄⋊C₄×C₆₁	—	2	4	no	—
153	C₄⋊C₄×C₆₁	—	2	2	no	—
154	C₄⋊C₄×C₆₁	—	2	1	no	—
155	C₄⋊C₄×C₆₁	—	2	2	no	—
156	C₄⋊C₄×C₆₁	—	2	1	no	—
157	C₄⋊C₄×C₆₁	—	2	1	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	4	4	no	—
161	C₄⋊C₄×C₆₁	—	4	2	no	—
162	C₄⋊C₄×C₆₁	—	4	2	no	—
163	C₄⋊C₄×C₆₁	—	8	1	no	—
164	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
165	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
166	C₂²⋊C₄×C₆₁	—	2	8	no	—
167	C₂²⋊C₄×C₆₁	—	2	8	no	—
168	C₂²⋊C₄×C₆₁	—	2	4	no	—
169	C₂²⋊C₄×C₆₁	—	4	4	no	—
170	C₂²⋊C₄×C₆₁	—	8	2	no	—
171	C₄²×C₆₁	—	2	8	no	—
172	C₄²×C₆₁	—	2	4	no	—
173	C₄²×C₆₁	—	4	2	no	—
174	C₄²×C₆₁	C₂×D₄	1	2	yes	—
175	C₄²×C₆₁	C₂×D₄	1	2	yes	—
176	C₂³×C₆₁	—	2	2	no	—
177	C₂³×C₆₁	—	2	2	no	—
178	C₂³×C₆₁	—	2	2	no	—
179	C₂³×C₆₁	—	2	2	no	—
180	C₂³×C₆₁	—	2	2	no	—
181	C₂³×C₆₁	—	2	2	no	—
182	C₂³×C₆₁	—	2	2	no	—
183	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₆₁	—	2	2	no	—
185	Q₈×C₆₁	—	2	2	no	—
186	Q₈×C₆₁	—	2	2	no	—
187	Q₈×C₆₁	—	2	2	no	—
188	Q₈×C₆₁	—	4	1	no	—
189	Q₈×C₆₁	—	4	1	no	—
190	Q₈×C₆₁	—	4	1	no	—
191	Q₈×C₆₁	—	4	1	no	—
192	Q₈×C₆₁	—	4	8	no	—
193	D₄×C₆₁	—	4	4	no	—
194	C₂×C₄×C₆₁	—	2	1	no	—
195	C₂×C₄×C₆₁	—	2	1	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	4	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	—	4	1	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	—	4	2	no	—
209	C₂×C₄×C₆₁	—	4	1	no	—
210	C₂×C₄×C₆₁	—	4	1	no	—
211	C₂×C₄×C₆₁	—	4	2	no	—
212	C₂×C₄×C₆₁	—	4	2	no	—
213	C₂×C₄×C₆₁	—	4	2	no	—
214	C₂×C₄×C₆₁	—	4	2	no	—
215	C₂×C₄×C₆₁	—	4	1	no	—
216	C₂×C₄×C₆₁	—	4	2	no	—
217	C₂×C₄×C₆₁	—	4	2	no	—
218	C₂×C₄×C₆₁	—	4	1	no	—
219	C₂×C₄×C₆₁	—	4	2	no	—
220	C₂×C₄×C₆₁	—	4	1	no	—
221	C₂×C₄×C₆₁	#120	1	2	yes	—
222	C₂×C₄×C₆₁	#120	1	2	yes	—
223	C₂×C₄×C₆₁	#135	1	2	yes	—
224	C₂×C₄×C₆₁	#137	1	2	yes	—
225	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
231	C₈×C₆₁	—	2	2	no	—
232	C₈×C₆₁	—	4	1	no	—
233	C₈×C₆₁	—	4	2	no	—
234	#24123	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
235	C₂²×C₆₁	—	4	2	no	—
236	C₂²×C₆₁	—	4	2	no	—
237	C₂²×C₆₁	—	4	2	no	—
238	C₂²×C₆₁	—	4	2	no	—
239	C₂²×C₆₁	—	4	2	no	—
240	C₂²×C₆₁	—	4	2	no	—
241	C₂²×C₆₁	—	4	2	no	—
242	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
243	C₂²×C₆₁	#546	1	1	yes	characteristic
244	C₂²×C₆₁	#547	1	1	yes	characteristic
245	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
246	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
247	C₂²×C₆₁	#577	1	1	yes	characteristic
248	C₂²×C₆₁	#578	1	1	yes	characteristic
249	C₄×C₆₁	—	2	2	no	—
250	C₄×C₆₁	—	4	2	no	—
251	C₄×C₆₁	—	4	2	no	—
252	C₄×C₆₁	—	4	2	no	—
253	C₄×C₆₁	—	4	4	no	—
254	C₄×C₆₁	—	4	2	no	—
255	C₄×C₆₁	—	8	1	no	—
256	C₄×C₆₁	—	8	2	no	—
257	C₄×C₆₁	#452	1	4	yes	—
258	C₄×C₆₁	#525	1	1	yes	characteristic
259	C₄×C₆₁	#537	1	1	yes	characteristic
260	C₄×C₆₁	#548	1	1	yes	characteristic
261	C₄×C₆₁	#550	1	1	yes	characteristic
262	C₂×#556	C₂×C₆₁	1	1	yes	characteristic
263	C₂×#475	C₂×C₆₁	1	1	yes	characteristic, complemented
264	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
265	#2538	C₂×C₆₁	1	1	yes	characteristic
266	#2035	C₂×C₆₁	1	2	yes	complemented
267	#2001	C₂×C₆₁	1	2	yes	complemented
268	#1990	C₂×C₆₁	1	1	yes	characteristic, complemented
269	#1954	C₂×C₆₁	1	1	yes	characteristic
270	#1873	C₂×C₆₁	1	2	yes	complemented
271	#1854	C₂×C₆₁	1	2	yes	complemented
272	#1803	C₂×C₆₁	1	1	yes	characteristic, complemented
273	C₂×C₆₁	—	8	2	no	—
274	C₂×C₆₁	#2407	1	1	yes	characteristic
275	C₂×C₆₁	C₂×#452	1	1	yes	characteristic
276	C₂×C₆₁	#3013	1	1	yes	characteristic
277	C₂×C₆₁	#3304	1	1	yes	characteristic
278	C₂×C₆₁	#3328	1	1	yes	characteristic
279	C₂×C₆₁	#3342	1	1	yes	characteristic
280	C₂×C₆₁	#3356	1	1	yes	characteristic
281	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
282	#556	—	2	4	no	—
283	#556	—	2	4	no	—
284	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
285	C₂×#126	—	2	2	no	—
286	C₂×#124	—	2	1	no	—
287	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
288	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
289	C₂×C₄×Q₈	—	2	1	no	—
290	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
291	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
292	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
293	C₂×#117	C₂²×C₆₁	1	2	yes	—
294	#475	—	2	4	no	—
295	C₄×Q₁₆	—	2	4	no	—
296	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
297	C₂×#106	C₂²×C₆₁	1	2	yes	—
298	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
299	C₂×#103	C₂²×C₆₁	1	2	yes	—
300	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
301	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
302	C₂×#103	C₂²×C₆₁	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
304	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
305	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
306	#396	—	2	2	no	—
307	#390	—	2	1	no	—
308	#389	—	2	1	no	—
309	#384	C₂²×C₆₁	1	1	yes	characteristic
310	#380	C₂²×C₆₁	1	2	yes	—
311	#340	C₂²×C₆₁	1	2	yes	—
312	#340	C₂²×C₆₁	1	2	yes	—
313	#340	C₂²×C₆₁	1	2	yes	—
314	C₆₁	#24123	1	1	yes	characteristic, direct product factor, Sylow
315	C₂²×Q₈	—	2	1	no	—
316	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
317	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
318	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
320	C₂×Q₁₆	—	2	2	no	—
321	C₂×Q₁₆	—	2	2	no	—
322	C₂×Q₁₆	—	2	2	no	—
323	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
324	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
325	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
326	C₄⋊Q₈	—	2	2	no	—
327	C₄⋊Q₈	D₄×C₆₁	1	4	yes	—
328	#126	—	2	16	no	—
329	#124	—	2	8	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	—	2	4	no	—
333	C₂²⋊Q₈	—	4	2	no	—
334	C₄×Q₈	—	2	8	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	2	no	—
337	C₄×Q₈	—	2	2	no	—
338	C₄×Q₈	D₄×C₆₁	1	4	yes	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	#117	—	2	4	no	—
342	#117	—	2	4	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
364	#107	—	2	2	no	—
365	#106	—	2	4	no	—
366	C₄⋊C₈	—	2	2	no	—
367	#103	—	2	2	no	—
368	#103	—	2	2	no	—
369	#103	—	2	4	no	—
370	#103	—	4	2	no	—
371	C₂²⋊C₈	—	2	4	no	—
372	C₂²⋊C₈	—	4	2	no	—
373	C₄×C₈	—	2	2	no	—
374	#95	—	2	2	no	—
375	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
376	C₂×Q₈	—	2	4	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	—	4	2	no	—
389	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
390	C₂×Q₈	#41×C₆₁	1	2	yes	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
410	Q₁₆	—	2	8	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	#41×C₆₁	1	2	yes	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	4	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	4	4	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	2	no	—
433	C₄⋊C₄	—	8	1	no	—
434	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
435	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	4	4	no	—
440	C₂²⋊C₄	—	8	2	no	—
441	C₄²	—	2	8	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	4	2	no	—
444	C₄²	C₂×D₄×C₆₁	1	2	yes	—
445	C₄²	C₂×D₄×C₆₁	1	2	yes	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	4	1	no	—
459	Q₈	—	4	1	no	—
460	Q₈	—	4	1	no	—
461	Q₈	—	4	1	no	—
462	Q₈	—	4	8	no	—
463	D₄	—	4	4	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	#120×C₆₁	1	2	yes	—
492	C₂×C₄	#120×C₆₁	1	2	yes	—
493	C₂×C₄	#135×C₆₁	1	2	yes	—
494	C₂×C₄	#137×C₆₁	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
497	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
498	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
499	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
500	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
501	C₈	—	2	2	no	—
502	C₈	—	4	1	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
512	C₂²	C₆₁×#546	1	1	yes	characteristic
513	C₂²	C₆₁×#547	1	1	yes	characteristic
514	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
515	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
516	C₂²	C₆₁×#577	1	1	yes	characteristic
517	C₂²	C₆₁×#578	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	2	no	—
524	C₄	—	8	2	no	—
525	C₄	—	8	1	no	—
526	C₄	C₆₁×#452	1	4	yes	—
527	C₄	C₆₁×#525	1	1	yes	characteristic
528	C₄	C₆₁×#537	1	1	yes	characteristic
529	C₄	C₆₁×#548	1	1	yes	characteristic
530	C₄	C₆₁×#550	1	1	yes	characteristic
531	C₂	—	8	2	no	—
532	C₂	C₆₁×#2407	1	1	yes	characteristic
533	C₂	C₂×C₆₁×#452	1	1	yes	characteristic
534	C₂	C₆₁×#3013	1	1	yes	characteristic
535	C₂	C₆₁×#3304	1	1	yes	characteristic
536	C₂	C₆₁×#3328	1	1	yes	characteristic
537	C₂	C₆₁×#3342	1	1	yes	characteristic
538	C₂	C₆₁×#3356	1	1	yes	characteristic

	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×#475	C₂	semidirect
3. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
5. C₆₁×#2035	C₂	semidirect
6. C₆₁×#2001	C₂	semidirect
7. C₆₁×#1990	C₂	semidirect
9. C₆₁×#1873	C₂	semidirect
10. C₆₁×#1854	C₂	semidirect
11. C₆₁×#1803	C₂	semidirect
234. #24123	C₆₁	direct (N × H)
263. C₂×#475	C₂×C₆₁	semidirect
264. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
266. #2035	C₂×C₆₁	semidirect
267. #2001	C₂×C₆₁	semidirect
268. #1990	C₂×C₆₁	semidirect
270. #1873	C₂×C₆₁	semidirect
271. #1854	C₂×C₆₁	semidirect
272. #1803	C₂×C₆₁	semidirect
314. C₆₁	#24123	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×#556	2
C₂×C₆₁×#475	2
C₂×C₄×Q₁₆×C₆₁	2
C₆₁×#2538	2
C₆₁×#2035	2
C₆₁×#2001	2
C₆₁×#1990	2
C₆₁×#1954	2
C₆₁×#1873	2
C₆₁×#1854	2
C₆₁×#1803	2
#24123	61

Subgroups — C61×#24123 #29527556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#24123 #29527556