Subgroups — C₆₁×#22919 #29526352

Order 15616.

814 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#485	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2362	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2347	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1942	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1933	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1928	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1919	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1892	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1865	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1854	C₂	1	1	yes	maximal, characteristic
12	C₄×#106×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
15	C₆₁×#1735	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#117×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#485	C₄	1	8	yes	complemented
22	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#106×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	1	yes	characteristic
29	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₆₁×#391	C₂²	1	1	yes	characteristic
34	C₆₁×#389	C₂²	1	1	yes	characteristic
35	C₆₁×#389	C₂²	1	1	yes	characteristic
36	C₆₁×#389	C₂²	1	1	yes	characteristic
37	C₆₁×#388	—	2	1	no	—
38	C₆₁×#388	—	2	1	no	—
39	C₆₁×#388	—	2	1	no	—
40	C₆₁×#388	—	2	1	no	—
41	C₆₁×#387	—	2	1	no	—
42	C₆₁×#383	—	2	1	no	—
43	C₆₁×#380	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
45	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
46	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
47	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
50	C₆₁×#340	C₂²	1	1	yes	characteristic
51	C₆₁×#340	C₂²	1	1	yes	characteristic
52	C₆₁×#340	C₂²	1	1	yes	characteristic
53	C₆₁×#340	C₂²	1	1	yes	characteristic
54	C₆₁×#340	C₂²	1	1	yes	characteristic
55	C₆₁×#340	C₂²	1	1	yes	characteristic
56	C₆₁×#340	C₂²	1	1	yes	characteristic
57	C₆₁×#340	C₂²	1	1	yes	characteristic
58	C₆₁×#336	C₂²	1	1	yes	characteristic
59	C₆₁×#336	C₂²	1	1	yes	characteristic
60	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	—	2	2	no	—
63	C₂²×C₈×C₆₁	—	2	2	no	—
64	C₂²×C₈×C₆₁	—	4	1	no	—
65	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₂²⋊Q₈×C₆₁	—	2	2	no	—
70	C₂²⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
71	C₄×Q₈×C₆₁	—	2	2	no	—
72	C₄×Q₈×C₆₁	—	4	1	no	—
73	#117×C₆₁	—	2	2	no	—
74	#117×C₆₁	—	2	2	no	—
75	#117×C₆₁	—	4	1	no	—
76	#117×C₆₁	C₂×C₄	1	4	yes	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	—	2	1	no	—
96	C₂×C₄²×C₆₁	—	2	1	no	—
97	C₂×C₄²×C₆₁	—	2	1	no	—
98	C₂×C₄²×C₆₁	—	2	1	no	—
99	C₂×C₄²×C₆₁	—	2	1	no	—
100	C₂×C₄²×C₆₁	—	2	1	no	—
101	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
103	#107×C₆₁	—	4	1	no	—
104	#107×C₆₁	C₂×C₄	1	4	yes	—
105	#106×C₆₁	—	2	2	no	—
106	#106×C₆₁	C₂×C₄	1	4	yes	—
107	#103×C₆₁	—	2	2	no	—
108	#103×C₆₁	—	4	1	no	—
109	#103×C₆₁	C₂×C₄	1	4	yes	—
110	#103×C₆₁	C₂×C₄	1	4	yes	—
111	C₂²⋊C₈×C₆₁	C₂×C₄	1	4	yes	—
112	C₄×C₈×C₆₁	—	2	2	no	—
113	C₄×C₈×C₆₁	—	4	1	no	—
114	#95×C₆₁	—	2	1	no	—
115	#95×C₆₁	—	2	1	no	—
116	#95×C₆₁	—	2	1	no	—
117	#95×C₆₁	—	2	1	no	—
118	#95×C₆₁	—	2	1	no	—
119	#95×C₆₁	—	2	1	no	—
120	#95×C₆₁	—	2	1	no	—
121	#95×C₆₁	—	2	1	no	—
122	#95×C₆₁	—	2	1	no	—
123	#95×C₆₁	D₄	1	1	yes	characteristic
124	#95×C₆₁	D₄	1	1	yes	characteristic
125	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
126	C₂×Q₈×C₆₁	—	2	1	no	—
127	C₂×Q₈×C₆₁	—	2	1	no	—
128	C₂×Q₈×C₆₁	—	2	1	no	—
129	C₂×Q₈×C₆₁	—	2	1	no	—
130	C₂×Q₈×C₆₁	—	2	1	no	—
131	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₆₁	—	2	1	no	—
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	—	2	1	no	—
135	C₂²×C₄×C₆₁	—	2	1	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	2	1	no	—
138	C₂²×C₄×C₆₁	—	2	1	no	—
139	C₂²×C₄×C₆₁	—	2	1	no	—
140	C₂²×C₄×C₆₁	—	2	1	no	—
141	C₂²×C₄×C₆₁	—	2	1	no	—
142	C₂²×C₄×C₆₁	—	2	1	no	—
143	C₂²×C₄×C₆₁	—	2	1	no	—
144	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
145	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	#41	1	2	yes	—
151	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
152	C₂×C₈×C₆₁	—	2	1	no	—
153	C₂×C₈×C₆₁	—	2	1	no	—
154	C₂×C₈×C₆₁	—	2	1	no	—
155	C₂×C₈×C₆₁	—	2	1	no	—
156	C₂×C₈×C₆₁	—	2	1	no	—
157	C₂×C₈×C₆₁	—	2	1	no	—
158	C₂×C₈×C₆₁	—	2	1	no	—
159	C₂×C₈×C₆₁	—	2	1	no	—
160	C₂×C₈×C₆₁	—	2	1	no	—
161	C₂×C₈×C₆₁	—	4	4	no	—
162	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
163	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₆₁	#41	1	2	yes	—
165	C₄⋊C₄×C₆₁	—	2	4	no	—
166	C₄⋊C₄×C₆₁	—	2	1	no	—
167	C₄⋊C₄×C₆₁	—	2	1	no	—
168	C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₄⋊C₄×C₆₁	—	2	1	no	—
170	C₄⋊C₄×C₆₁	—	2	1	no	—
171	C₄⋊C₄×C₆₁	—	2	1	no	—
172	C₄⋊C₄×C₆₁	—	2	1	no	—
173	C₄⋊C₄×C₆₁	—	2	1	no	—
174	C₄⋊C₄×C₆₁	—	2	1	no	—
175	C₄⋊C₄×C₆₁	—	2	1	no	—
176	C₄⋊C₄×C₆₁	—	4	2	no	—
177	C₄⋊C₄×C₆₁	—	4	2	no	—
178	C₄⋊C₄×C₆₁	—	4	2	no	—
179	C₄⋊C₄×C₆₁	—	4	2	no	—
180	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
181	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
182	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
183	C₄⋊C₄×C₆₁	#41	1	2	yes	—
184	C₂²⋊C₄×C₆₁	—	2	4	no	—
185	C₂²⋊C₄×C₆₁	—	2	4	no	—
186	C₂²⋊C₄×C₆₁	—	2	2	no	—
187	C₂²⋊C₄×C₆₁	—	2	2	no	—
188	C₂²⋊C₄×C₆₁	—	4	2	no	—
189	C₂²⋊C₄×C₆₁	—	8	1	no	—
190	C₄²×C₆₁	—	2	4	no	—
191	C₄²×C₆₁	—	2	1	no	—
192	C₄²×C₆₁	—	2	1	no	—
193	C₄²×C₆₁	—	2	1	no	—
194	C₄²×C₆₁	—	2	1	no	—
195	C₄²×C₆₁	—	4	2	no	—
196	C₄²×C₆₁	—	4	2	no	—
197	C₄²×C₆₁	—	4	2	no	—
198	C₄²×C₆₁	—	8	1	no	—
199	C₄²×C₆₁	—	8	1	no	—
200	C₂³×C₆₁	—	2	1	no	—
201	C₂³×C₆₁	—	2	1	no	—
202	C₂³×C₆₁	—	2	1	no	—
203	C₂³×C₆₁	—	2	1	no	—
204	C₂³×C₆₁	—	2	1	no	—
205	C₂³×C₆₁	—	2	1	no	—
206	C₂³×C₆₁	C₄×D₄	1	2	yes	—
207	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₆₁	—	2	2	no	—
209	Q₈×C₆₁	—	2	2	no	—
210	Q₈×C₆₁	—	4	1	no	—
211	Q₈×C₆₁	—	4	1	no	—
212	C₂×C₄×C₆₁	—	2	1	no	—
213	C₂×C₄×C₆₁	—	2	1	no	—
214	C₂×C₄×C₆₁	—	2	1	no	—
215	C₂×C₄×C₆₁	—	2	1	no	—
216	C₂×C₄×C₆₁	—	2	1	no	—
217	C₂×C₄×C₆₁	—	2	1	no	—
218	C₂×C₄×C₆₁	—	2	2	no	—
219	C₂×C₄×C₆₁	—	2	2	no	—
220	C₂×C₄×C₆₁	—	2	2	no	—
221	C₂×C₄×C₆₁	—	2	2	no	—
222	C₂×C₄×C₆₁	—	2	2	no	—
223	C₂×C₄×C₆₁	—	2	2	no	—
224	C₂×C₄×C₆₁	—	2	2	no	—
225	C₂×C₄×C₆₁	—	2	2	no	—
226	C₂×C₄×C₆₁	—	2	1	no	—
227	C₂×C₄×C₆₁	—	2	2	no	—
228	C₂×C₄×C₆₁	—	2	1	no	—
229	C₂×C₄×C₆₁	—	2	1	no	—
230	C₂×C₄×C₆₁	—	2	1	no	—
231	C₂×C₄×C₆₁	—	2	1	no	—
232	C₂×C₄×C₆₁	—	2	1	no	—
233	C₂×C₄×C₆₁	—	4	1	no	—
234	C₂×C₄×C₆₁	—	4	1	no	—
235	C₂×C₄×C₆₁	—	4	1	no	—
236	C₂×C₄×C₆₁	—	4	1	no	—
237	C₂×C₄×C₆₁	—	4	1	no	—
238	C₂×C₄×C₆₁	—	4	1	no	—
239	C₂×C₄×C₆₁	—	4	1	no	—
240	C₂×C₄×C₆₁	—	4	1	no	—
241	C₂×C₄×C₆₁	—	4	1	no	—
242	C₂×C₄×C₆₁	—	4	1	no	—
243	C₂×C₄×C₆₁	—	4	1	no	—
244	C₂×C₄×C₆₁	—	4	1	no	—
245	C₂×C₄×C₆₁	—	4	1	no	—
246	C₂×C₄×C₆₁	—	4	1	no	—
247	C₂×C₄×C₆₁	—	4	1	no	—
248	C₂×C₄×C₆₁	—	4	1	no	—
249	C₂×C₄×C₆₁	—	4	1	no	—
250	C₂×C₄×C₆₁	—	4	1	no	—
251	C₂×C₄×C₆₁	—	4	1	no	—
252	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₆₁	#135	1	2	yes	—
254	C₂×C₄×C₆₁	#135	1	2	yes	—
255	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
256	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
260	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
261	C₈×C₆₁	—	2	2	no	—
262	C₈×C₆₁	—	2	2	no	—
263	C₈×C₆₁	—	2	2	no	—
264	C₈×C₆₁	—	4	1	no	—
265	#22919	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
266	C₂²×C₆₁	—	2	2	no	—
267	C₂²×C₆₁	—	2	2	no	—
268	C₂²×C₆₁	—	2	2	no	—
269	C₂²×C₆₁	—	4	1	no	—
270	C₂²×C₆₁	—	4	1	no	—
271	C₂²×C₆₁	—	4	1	no	—
272	C₂²×C₆₁	—	4	1	no	—
273	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
274	C₂²×C₆₁	#546	1	1	yes	characteristic
275	C₂²×C₆₁	#547	1	1	yes	characteristic
276	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
277	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
278	C₂²×C₆₁	#577	1	1	yes	characteristic
279	C₂²×C₆₁	#578	1	1	yes	characteristic
280	C₄×C₆₁	—	2	2	no	—
281	C₄×C₆₁	—	2	2	no	—
282	C₄×C₆₁	—	2	2	no	—
283	C₄×C₆₁	—	4	1	no	—
284	C₄×C₆₁	—	4	2	no	—
285	C₄×C₆₁	—	4	2	no	—
286	C₄×C₆₁	—	4	2	no	—
287	C₄×C₆₁	—	4	2	no	—
288	C₄×C₆₁	—	4	1	no	—
289	C₄×C₆₁	—	4	2	no	—
290	C₄×C₆₁	—	8	1	no	—
291	C₄×C₆₁	—	8	1	no	—
292	C₄×C₆₁	—	8	1	no	—
293	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
294	C₄×C₆₁	#520	1	1	yes	characteristic
295	C₄×C₆₁	#551	1	1	yes	characteristic
296	C₄×C₆₁	#552	1	1	yes	characteristic
297	C₂×#485	C₂×C₆₁	1	1	yes	characteristic
298	#2362	C₂×C₆₁	1	1	yes	characteristic
299	#2347	C₂×C₆₁	1	1	yes	characteristic
300	#1942	C₂×C₆₁	1	1	yes	characteristic, complemented
301	#1933	C₂×C₆₁	1	1	yes	characteristic, complemented
302	#1928	C₂×C₆₁	1	1	yes	characteristic, complemented
303	#1919	C₂×C₆₁	1	1	yes	characteristic, complemented
304	#1918	C₂×C₆₁	1	1	yes	characteristic, complemented
305	#1892	C₂×C₆₁	1	1	yes	characteristic
306	#1865	C₂×C₆₁	1	1	yes	characteristic, complemented
307	#1854	C₂×C₆₁	1	1	yes	characteristic
308	C₄×#106	C₂×C₆₁	1	1	yes	characteristic, complemented
309	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
310	C₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
311	#1735	C₂×C₆₁	1	1	yes	characteristic
312	C₂×C₆₁	—	4	2	no	—
313	C₂×C₆₁	#2359	1	1	yes	characteristic
314	C₂×C₆₁	C₄×#135	1	1	yes	characteristic
315	C₂×C₆₁	#2947	1	1	yes	characteristic
316	C₂×C₆₁	#3301	1	1	yes	characteristic
317	C₂×C₆₁	#3302	1	1	yes	characteristic
318	C₂×C₆₁	#3337	1	1	yes	characteristic
319	C₂×C₆₁	#3342	1	1	yes	characteristic
320	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
321	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
323	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
324	C₂×#117	C₂²×C₆₁	1	1	yes	characteristic
325	#485	C₄×C₆₁	1	8	yes	complemented
326	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
327	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
328	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
329	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
330	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
331	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
332	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
333	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
334	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
335	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
336	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
337	#391	C₂²×C₆₁	1	1	yes	characteristic
338	#389	C₂²×C₆₁	1	1	yes	characteristic
339	#389	C₂²×C₆₁	1	1	yes	characteristic
340	#389	C₂²×C₆₁	1	1	yes	characteristic
341	#388	—	2	1	no	—
342	#388	—	2	1	no	—
343	#388	—	2	1	no	—
344	#388	—	2	1	no	—
345	#387	—	2	1	no	—
346	#383	—	2	1	no	—
347	#380	C₂²×C₆₁	1	1	yes	characteristic
348	C₄×C₄⋊C₄	—	2	1	no	—
349	C₄×C₄⋊C₄	—	2	1	no	—
350	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
351	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
352	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
353	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
354	#340	C₂²×C₆₁	1	1	yes	characteristic
355	#340	C₂²×C₆₁	1	1	yes	characteristic
356	#340	C₂²×C₆₁	1	1	yes	characteristic
357	#340	C₂²×C₆₁	1	1	yes	characteristic
358	#340	C₂²×C₆₁	1	1	yes	characteristic
359	#340	C₂²×C₆₁	1	1	yes	characteristic
360	#340	C₂²×C₆₁	1	1	yes	characteristic
361	#340	C₂²×C₆₁	1	1	yes	characteristic
362	#336	C₂²×C₆₁	1	1	yes	characteristic
363	#336	C₂²×C₆₁	1	1	yes	characteristic
364	C₆₁	#22919	1	1	yes	characteristic, direct product factor, Sylow
365	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
367	C₂²×C₈	—	2	2	no	—
368	C₂²×C₈	—	2	2	no	—
369	C₂²×C₈	—	4	1	no	—
370	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
374	C₂²⋊Q₈	—	2	2	no	—
375	C₂²⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
376	C₄×Q₈	—	2	2	no	—
377	C₄×Q₈	—	4	1	no	—
378	#117	—	2	2	no	—
379	#117	—	2	2	no	—
380	#117	—	4	1	no	—
381	#117	C₂×C₄×C₆₁	1	4	yes	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
390	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
391	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
394	C₂×C₂²⋊C₄	—	2	1	no	—
395	C₂×C₂²⋊C₄	—	2	1	no	—
396	C₂×C₂²⋊C₄	—	2	1	no	—
397	C₂×C₂²⋊C₄	—	2	1	no	—
398	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
399	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
400	C₂×C₄²	—	2	1	no	—
401	C₂×C₄²	—	2	1	no	—
402	C₂×C₄²	—	2	1	no	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
407	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
408	#107	—	4	1	no	—
409	#107	C₂×C₄×C₆₁	1	4	yes	—
410	#106	—	2	2	no	—
411	#106	C₂×C₄×C₆₁	1	4	yes	—
412	#103	—	2	2	no	—
413	#103	—	4	1	no	—
414	#103	C₂×C₄×C₆₁	1	4	yes	—
415	#103	C₂×C₄×C₆₁	1	4	yes	—
416	C₂²⋊C₈	C₂×C₄×C₆₁	1	4	yes	—
417	C₄×C₈	—	2	2	no	—
418	C₄×C₈	—	4	1	no	—
419	#95	—	2	1	no	—
420	#95	—	2	1	no	—
421	#95	—	2	1	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	D₄×C₆₁	1	1	yes	characteristic
429	#95	D₄×C₆₁	1	1	yes	characteristic
430	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
450	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
455	C₂²×C₄	#41×C₆₁	1	2	yes	—
456	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	4	4	no	—
467	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
468	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
469	C₂×C₈	#41×C₆₁	1	2	yes	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	4	2	no	—
482	C₄⋊C₄	—	4	2	no	—
483	C₄⋊C₄	—	4	2	no	—
484	C₄⋊C₄	—	4	2	no	—
485	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
486	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
487	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
488	C₄⋊C₄	#41×C₆₁	1	2	yes	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	4	2	no	—
494	C₂²⋊C₄	—	8	1	no	—
495	C₄²	—	2	4	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	4	2	no	—
501	C₄²	—	4	2	no	—
502	C₄²	—	4	2	no	—
503	C₄²	—	8	1	no	—
504	C₄²	—	8	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	—	2	1	no	—
509	C₂³	—	2	1	no	—
510	C₂³	—	2	1	no	—
511	C₂³	C₄×D₄×C₆₁	1	2	yes	—
512	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
513	Q₈	—	2	2	no	—
514	Q₈	—	2	2	no	—
515	Q₈	—	4	1	no	—
516	Q₈	—	4	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
558	C₂×C₄	#135×C₆₁	1	2	yes	—
559	C₂×C₄	#135×C₆₁	1	2	yes	—
560	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
561	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
562	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
563	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
564	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
565	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
566	C₈	—	2	2	no	—
567	C₈	—	2	2	no	—
568	C₈	—	2	2	no	—
569	C₈	—	4	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	2	2	no	—
572	C₂²	—	2	2	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
578	C₂²	C₆₁×#546	1	1	yes	characteristic
579	C₂²	C₆₁×#547	1	1	yes	characteristic
580	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
581	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
582	C₂²	C₆₁×#577	1	1	yes	characteristic
583	C₂²	C₆₁×#578	1	1	yes	characteristic
584	C₄	—	2	2	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	2	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	2	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	8	1	no	—
595	C₄	—	8	1	no	—
596	C₄	—	8	1	no	—
597	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
598	C₄	C₆₁×#520	1	1	yes	characteristic
599	C₄	C₆₁×#551	1	1	yes	characteristic
600	C₄	C₆₁×#552	1	1	yes	characteristic
601	C₂	—	4	2	no	—
602	C₂	C₆₁×#2359	1	1	yes	characteristic
603	C₂	C₄×#135×C₆₁	1	1	yes	characteristic
604	C₂	C₆₁×#2947	1	1	yes	characteristic
605	C₂	C₆₁×#3301	1	1	yes	characteristic
606	C₂	C₆₁×#3302	1	1	yes	characteristic
607	C₂	C₆₁×#3337	1	1	yes	characteristic
608	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
4. C₆₁×#1942	C₂	semidirect
5. C₆₁×#1933	C₂	semidirect
6. C₆₁×#1928	C₂	semidirect
7. C₆₁×#1919	C₂	semidirect
8. C₆₁×#1918	C₂	semidirect
10. C₆₁×#1865	C₂	semidirect
12. C₄×#106×C₆₁	C₂	semidirect
13. C₄×#103×C₆₁	C₂	semidirect
21. C₆₁×#485	C₄	semidirect
265. #22919	C₆₁	direct (N × H)
300. #1942	C₂×C₆₁	semidirect
301. #1933	C₂×C₆₁	semidirect
302. #1928	C₂×C₆₁	semidirect
303. #1919	C₂×C₆₁	semidirect
304. #1918	C₂×C₆₁	semidirect
306. #1865	C₂×C₆₁	semidirect
308. C₄×#106	C₂×C₆₁	semidirect
309. C₄×#103	C₂×C₆₁	semidirect
325. #485	C₄×C₆₁	semidirect
364. C₆₁	#22919	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×#485	2
C₆₁×#2362	2
C₆₁×#2347	2
C₆₁×#1942	2
C₆₁×#1933	2
C₆₁×#1928	2
C₆₁×#1919	2
C₆₁×#1918	2
C₆₁×#1892	2
C₆₁×#1865	2
C₆₁×#1854	2
C₄×#106×C₆₁	2
C₄×#103×C₆₁	2
C₈×C₂²⋊C₄×C₆₁	2
C₆₁×#1735	2
#22919	61

Subgroups — C61×#22919 #29526352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22919 #29526352