Subgroups — C₆₁×#23026 #29526459

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#467	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#427	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2362	C₂	1	2	yes	maximal
5	C₆₁×#1969	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1927	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1873	C₂	1	2	yes	maximal
9	C₆₁×#1865	C₂	1	2	yes	maximal, complemented
10	C₄×#107×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
16	C₂×#117×C₆₁	C₂²	1	2	yes	—
17	C₆₁×#467	C₄	1	8	yes	complemented
18	C₄×Q₁₆×C₆₁	—	2	4	no	—
19	C₆₁×#427	—	2	4	no	—
20	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#106×C₆₁	C₂²	1	2	yes	—
24	C₂×#103×C₆₁	C₂²	1	2	yes	—
25	C₂×#103×C₆₁	C₂²	1	2	yes	—
26	C₂×#103×C₆₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₆₁×#391	C₂²	1	2	yes	—
31	C₆₁×#389	C₂²	1	2	yes	—
32	C₆₁×#388	—	2	2	no	—
33	C₆₁×#388	—	2	2	no	—
34	C₆₁×#387	—	2	2	no	—
35	C₄×C₄⋊C₄×C₆₁	—	2	2	no	—
36	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
38	C₆₁×#340	C₂²	1	2	yes	—
39	C₆₁×#340	C₂²	1	2	yes	—
40	C₆₁×#336	C₂²	1	1	yes	characteristic
41	C₆₁×#336	C₂²	1	1	yes	characteristic
42	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
43	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₆₁	—	2	2	no	—
45	C₂×Q₁₆×C₆₁	—	2	2	no	—
46	C₂×Q₁₆×C₆₁	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₆₁	—	2	2	no	—
48	C₂²×C₈×C₆₁	—	2	2	no	—
49	C₂²×C₈×C₆₁	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²⋊Q₈×C₆₁	—	2	4	no	—
55	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	—
56	C₄×Q₈×C₆₁	—	2	4	no	—
57	C₄×Q₈×C₆₁	—	4	2	no	—
58	#117×C₆₁	—	2	4	no	—
59	#117×C₆₁	—	4	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	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₆₁	—	2	2	no	—
71	C₂×C₄²×C₆₁	—	2	2	no	—
72	C₂×C₄²×C₆₁	—	2	2	no	—
73	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	#107×C₆₁	—	2	2	no	—
76	#107×C₆₁	C₂×C₄	1	4	yes	—
77	#107×C₆₁	D₄	1	4	yes	—
78	#106×C₆₁	—	2	4	no	—
79	#103×C₆₁	—	2	4	no	—
80	#103×C₆₁	—	4	2	no	—
81	#103×C₆₁	C₂×C₄	1	8	yes	—
82	C₂²⋊C₈×C₆₁	—	2	2	no	—
83	C₄×C₈×C₆₁	—	2	2	no	—
84	C₄×C₈×C₆₁	—	2	2	no	—
85	#95×C₆₁	—	2	2	no	—
86	#95×C₆₁	—	2	2	no	—
87	#95×C₆₁	—	2	2	no	—
88	#95×C₆₁	—	2	2	no	—
89	#95×C₆₁	D₄	1	1	yes	characteristic
90	#95×C₆₁	D₄	1	1	yes	characteristic
91	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
92	C₂×Q₈×C₆₁	—	2	2	no	—
93	C₂×Q₈×C₆₁	—	2	2	no	—
94	C₂×Q₈×C₆₁	—	2	2	no	—
95	C₂×Q₈×C₆₁	—	2	2	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₆₁	—	2	1	no	—
99	C₂²×C₄×C₆₁	—	2	1	no	—
100	C₂²×C₄×C₆₁	—	2	1	no	—
101	C₂²×C₄×C₆₁	—	2	1	no	—
102	C₂²×C₄×C₆₁	—	2	2	no	—
103	C₂²×C₄×C₆₁	—	2	2	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	2	2	no	—
106	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	#41	1	2	yes	—
113	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
114	Q₁₆×C₆₁	—	2	8	no	—
115	C₂×C₈×C₆₁	—	2	1	no	—
116	C₂×C₈×C₆₁	—	2	1	no	—
117	C₂×C₈×C₆₁	—	2	8	no	—
118	C₂×C₈×C₆₁	—	2	1	no	—
119	C₂×C₈×C₆₁	—	2	1	no	—
120	C₂×C₈×C₆₁	—	2	1	no	—
121	C₂×C₈×C₆₁	—	2	1	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	—	2	1	no	—
124	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₆₁	#41	1	2	yes	—
128	C₄⋊C₄×C₆₁	—	2	8	no	—
129	C₄⋊C₄×C₆₁	—	2	2	no	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	2	2	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	4	4	no	—
134	C₄⋊C₄×C₆₁	—	4	4	no	—
135	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
136	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
137	C₂²⋊C₄×C₆₁	—	2	8	no	—
138	C₂²⋊C₄×C₆₁	—	2	2	no	—
139	C₂²⋊C₄×C₆₁	—	2	2	no	—
140	C₂²⋊C₄×C₆₁	—	4	4	no	—
141	C₄²×C₆₁	—	2	1	no	—
142	C₄²×C₆₁	—	2	1	no	—
143	C₄²×C₆₁	—	2	1	no	—
144	C₄²×C₆₁	—	2	1	no	—
145	C₄²×C₆₁	—	4	4	no	—
146	C₄²×C₆₁	—	4	4	no	—
147	C₄²×C₆₁	—	4	4	no	—
148	C₂³×C₆₁	—	2	1	no	—
149	C₂³×C₆₁	—	2	1	no	—
150	C₂³×C₆₁	—	2	1	no	—
151	C₂³×C₆₁	—	2	1	no	—
152	C₂³×C₆₁	—	2	1	no	—
153	C₂³×C₆₁	—	2	1	no	—
154	C₂³×C₆₁	C₄×D₄	1	2	yes	—
155	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
156	Q₈×C₆₁	—	2	4	no	—
157	Q₈×C₆₁	—	2	4	no	—
158	Q₈×C₆₁	—	4	2	no	—
159	Q₈×C₆₁	—	4	2	no	—
160	C₂×C₄×C₆₁	—	2	1	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	1	no	—
164	C₂×C₄×C₆₁	—	2	1	no	—
165	C₂×C₄×C₆₁	—	2	1	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	4	no	—
171	C₂×C₄×C₆₁	—	2	4	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	2	4	no	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	2	1	no	—
176	C₂×C₄×C₆₁	—	2	1	no	—
177	C₂×C₄×C₆₁	—	2	1	no	—
178	C₂×C₄×C₆₁	—	2	1	no	—
179	C₂×C₄×C₆₁	—	4	2	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	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	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₆₁	#135	1	2	yes	—
190	C₂×C₄×C₆₁	#135	1	2	yes	—
191	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
192	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
196	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
197	C₈×C₆₁	—	2	2	no	—
198	C₈×C₆₁	—	4	1	no	—
199	C₈×C₆₁	—	4	1	no	—
200	C₈×C₆₁	C₄×D₄	1	4	yes	—
201	#23026	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₆₁	—	2	2	no	—
203	C₂²×C₆₁	—	2	2	no	—
204	C₂²×C₆₁	—	2	2	no	—
205	C₂²×C₆₁	—	4	1	no	—
206	C₂²×C₆₁	—	4	1	no	—
207	C₂²×C₆₁	—	4	1	no	—
208	C₂²×C₆₁	—	4	1	no	—
209	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
210	C₂²×C₆₁	D₄²	1	1	yes	characteristic
211	C₂²×C₆₁	#547	1	1	yes	characteristic
212	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
213	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
214	C₂²×C₆₁	#578	1	1	yes	characteristic
215	C₂²×C₆₁	#578	1	1	yes	characteristic
216	C₄×C₆₁	—	2	2	no	—
217	C₄×C₆₁	—	2	2	no	—
218	C₄×C₆₁	—	2	2	no	—
219	C₄×C₆₁	—	4	1	no	—
220	C₄×C₆₁	—	4	4	no	—
221	C₄×C₆₁	—	4	4	no	—
222	C₄×C₆₁	—	4	1	no	—
223	C₄×C₆₁	—	4	4	no	—
224	C₄×C₆₁	—	8	2	no	—
225	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
226	C₄×C₆₁	#520	1	1	yes	characteristic
227	C₄×C₆₁	#548	1	1	yes	characteristic
228	C₄×C₆₁	#553	1	1	yes	characteristic
229	C₂×#467	C₂×C₆₁	1	1	yes	characteristic
230	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
231	C₂×#427	C₂×C₆₁	1	1	yes	characteristic
232	#2362	C₂×C₆₁	1	2	yes	—
233	#1969	C₂×C₆₁	1	1	yes	characteristic, complemented
234	#1942	C₂×C₆₁	1	1	yes	characteristic, complemented
235	#1927	C₂×C₆₁	1	2	yes	complemented
236	#1873	C₂×C₆₁	1	2	yes	—
237	#1865	C₂×C₆₁	1	2	yes	complemented
238	C₄×#107	C₂×C₆₁	1	1	yes	characteristic, complemented
239	C₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
240	C₂×C₆₁	—	4	2	no	—
241	C₂×C₆₁	#2361	1	1	yes	characteristic
242	C₂×C₆₁	C₄×#135	1	1	yes	characteristic
243	C₂×C₆₁	#2950	1	1	yes	characteristic
244	C₂×C₆₁	#3283	1	1	yes	characteristic
245	C₂×C₆₁	#3285	1	1	yes	characteristic
246	C₂×C₆₁	#3336	1	1	yes	characteristic
247	C₂×C₆₁	#3342	1	1	yes	characteristic
248	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
249	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
250	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
252	C₂×#117	C₂²×C₆₁	1	2	yes	—
253	#467	C₄×C₆₁	1	8	yes	complemented
254	C₄×Q₁₆	—	2	4	no	—
255	#427	—	2	4	no	—
256	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
257	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×#106	C₂²×C₆₁	1	2	yes	—
260	C₂×#103	C₂²×C₆₁	1	2	yes	—
261	C₂×#103	C₂²×C₆₁	1	2	yes	—
262	C₂×#103	C₂²×C₆₁	1	2	yes	—
263	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
264	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
266	#391	C₂²×C₆₁	1	2	yes	—
267	#389	C₂²×C₆₁	1	2	yes	—
268	#388	—	2	2	no	—
269	#388	—	2	2	no	—
270	#387	—	2	2	no	—
271	C₄×C₄⋊C₄	—	2	2	no	—
272	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
273	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
274	#340	C₂²×C₆₁	1	2	yes	—
275	#340	C₂²×C₆₁	1	2	yes	—
276	#336	C₂²×C₆₁	1	1	yes	characteristic
277	#336	C₂²×C₆₁	1	1	yes	characteristic
278	C₆₁	#23026	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
280	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×Q₁₆	C₂×C₄×C₆₁	1	4	yes	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	C₂×C₄×C₆₁	1	4	yes	—
287	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	—
293	C₄×Q₈	—	2	4	no	—
294	C₄×Q₈	—	4	2	no	—
295	#117	—	2	4	no	—
296	#117	—	4	2	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
302	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
306	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
307	C₂×C₄²	—	2	2	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
312	#107	—	2	2	no	—
313	#107	C₂×C₄×C₆₁	1	4	yes	—
314	#107	D₄×C₆₁	1	4	yes	—
315	#106	—	2	4	no	—
316	#103	—	2	4	no	—
317	#103	—	4	2	no	—
318	#103	C₂×C₄×C₆₁	1	8	yes	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₄×C₈	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	D₄×C₆₁	1	1	yes	characteristic
327	#95	D₄×C₆₁	1	1	yes	characteristic
328	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
344	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
349	C₂²×C₄	#41×C₆₁	1	2	yes	—
350	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
351	Q₁₆	—	2	8	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	8	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
362	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
364	C₂×C₈	#41×C₆₁	1	2	yes	—
365	C₄⋊C₄	—	2	8	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	4	no	—
372	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
373	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
374	C₂²⋊C₄	—	2	8	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	4	4	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	2	1	no	—
380	C₄²	—	2	1	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	4	4	no	—
383	C₄²	—	4	4	no	—
384	C₄²	—	4	4	no	—
385	C₂³	—	2	1	no	—
386	C₂³	—	2	1	no	—
387	C₂³	—	2	1	no	—
388	C₂³	—	2	1	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	1	no	—
391	C₂³	C₄×D₄×C₆₁	1	2	yes	—
392	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
393	Q₈	—	2	4	no	—
394	Q₈	—	2	4	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
426	C₂×C₄	#135×C₆₁	1	2	yes	—
427	C₂×C₄	#135×C₆₁	1	2	yes	—
428	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
430	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
432	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
433	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	1	no	—
437	C₈	C₄×D₄×C₆₁	1	4	yes	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
446	C₂²	D₄²×C₆₁	1	1	yes	characteristic
447	C₂²	C₆₁×#547	1	1	yes	characteristic
448	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
449	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
450	C₂²	C₆₁×#578	1	1	yes	characteristic
451	C₂²	C₆₁×#578	1	1	yes	characteristic
452	C₄	—	2	2	no	—
453	C₄	—	2	2	no	—
454	C₄	—	2	2	no	—
455	C₄	—	4	1	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	4	no	—
458	C₄	—	4	1	no	—
459	C₄	—	4	4	no	—
460	C₄	—	8	2	no	—
461	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
462	C₄	C₆₁×#520	1	1	yes	characteristic
463	C₄	C₆₁×#548	1	1	yes	characteristic
464	C₄	C₆₁×#553	1	1	yes	characteristic
465	C₂	—	4	2	no	—
466	C₂	C₆₁×#2361	1	1	yes	characteristic
467	C₂	C₄×#135×C₆₁	1	1	yes	characteristic
468	C₂	C₆₁×#2950	1	1	yes	characteristic
469	C₂	C₆₁×#3283	1	1	yes	characteristic
470	C₂	C₆₁×#3285	1	1	yes	characteristic
471	C₂	C₆₁×#3336	1	1	yes	characteristic
472	C₂	C₆₁×#3342	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	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂×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. C₂×C₄×Q₁₆×C₆₁	C₂	semidirect
5. C₆₁×#1969	C₂	semidirect
6. C₆₁×#1942	C₂	semidirect
7. C₆₁×#1927	C₂	semidirect
9. C₆₁×#1865	C₂	semidirect
10. C₄×#107×C₆₁	C₂	semidirect
17. C₆₁×#467	C₄	semidirect
201. #23026	C₆₁	direct (N × H)
230. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
233. #1969	C₂×C₆₁	semidirect
234. #1942	C₂×C₆₁	semidirect
235. #1927	C₂×C₆₁	semidirect
237. #1865	C₂×C₆₁	semidirect
238. C₄×#107	C₂×C₆₁	semidirect
253. #467	C₄×C₆₁	semidirect
278. C₆₁	#23026	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×#467	2
C₂×C₄×Q₁₆×C₆₁	2
C₂×C₆₁×#427	2
C₆₁×#2362	2
C₆₁×#1969	2
C₆₁×#1942	2
C₆₁×#1927	2
C₆₁×#1873	2
C₆₁×#1865	2
C₄×#107×C₆₁	2
C₈×C₂²⋊C₄×C₆₁	2
#23026	61

Subgroups — C61×#23026 #29526459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23026 #29526459