Subgroups — C₆₁×#22417 #29525850

Order 15616.

1490 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#416	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2354	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1892	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1873	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1802	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1788	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₆₁	C₂²	1	2	yes	—
13	C₂³×C₈×C₆₁	C₂²	1	2	yes	—
14	C₆₁×#547	—	2	4	no	—
15	C₆₁×#547	C₄	1	8	yes	complemented
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#123×C₆₁	—	2	2	no	—
18	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	2	yes	—
19	C₂×#121×C₆₁	—	2	1	no	—
20	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#117×C₆₁	C₂²	1	2	yes	—
23	C₂²×C₄⋊C₄×C₆₁	—	2	1	no	—
24	C₈×D₄×C₆₁	—	2	4	no	—
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#416	—	2	8	no	—
27	C₂×#103×C₆₁	C₂²	1	2	yes	—
28	C₂×#103×C₆₁	C₂²	1	2	yes	—
29	C₂×#103×C₆₁	C₂²	1	2	yes	—
30	C₂×#103×C₆₁	C₂²	1	2	yes	—
31	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#102×C₆₁	C₂²	1	2	yes	—
33	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₆₁×#390	—	2	1	no	—
37	C₆₁×#388	—	2	2	no	—
38	C₆₁×#384	C₂²	1	1	yes	characteristic
39	C₆₁×#380	C₂²	1	2	yes	—
40	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
41	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
42	C₆₁×#340	C₂²	1	1	yes	characteristic
43	C₆₁×#340	C₂²	1	1	yes	characteristic
44	C₆₁×#340	C₂²	1	2	yes	—
45	C₂×#41×C₆₁	—	2	4	no	—
46	C₂×#41×C₆₁	—	2	4	no	—
47	C₂×#41×C₆₁	—	2	4	no	—
48	C₂×#41×C₆₁	—	4	2	no	—
49	C₂×#41×C₆₁	—	4	2	no	—
50	C₂×#41×C₆₁	C₂×C₄	1	8	yes	—
51	C₂²×Q₈×C₆₁	C₂³	1	2	yes	—
52	C₂²×D₄×C₆₁	—	2	2	no	—
53	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
54	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₆₁	—	2	2	no	—
56	C₂³×C₄×C₆₁	—	2	1	no	—
57	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
58	C₂²×C₈×C₆₁	—	2	4	no	—
59	C₂²×C₈×C₆₁	—	2	4	no	—
60	C₂²×C₈×C₆₁	—	4	2	no	—
61	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₁	—	2	2	no	—
65	C₄⋊Q₈×C₆₁	C₂×C₄	1	4	yes	—
66	#123×C₆₁	—	2	16	no	—
67	C₂²⋊Q₈×C₆₁	—	2	4	no	—
68	C₂²⋊Q₈×C₆₁	C₂×C₄	1	8	yes	—
69	#121×C₆₁	—	2	8	no	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
72	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
73	C₄×D₄×C₆₁	D₄	1	4	yes	—
74	#117×C₆₁	—	2	4	no	—
75	#117×C₆₁	—	4	2	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	8	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
88	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₆₁	D₄	1	2	yes	—
92	C₂×C₄²×C₆₁	—	2	1	no	—
93	C₂×C₄²×C₆₁	—	2	2	no	—
94	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₆₁	—	2	2	no	—
96	#103×C₆₁	—	2	4	no	—
97	#103×C₆₁	—	2	4	no	—
98	#103×C₆₁	—	4	2	no	—
99	#103×C₆₁	—	4	2	no	—
100	#102×C₆₁	—	2	4	no	—
101	#102×C₆₁	—	2	2	no	—
102	#102×C₆₁	D₄	1	4	yes	complemented
103	C₂²⋊C₈×C₆₁	—	2	4	no	—
104	C₄×C₈×C₆₁	—	2	2	no	—
105	#95×C₆₁	—	2	2	no	—
106	#95×C₆₁	—	2	1	no	—
107	C₂⁴×C₆₁	—	2	1	no	—
108	C₂⁴×C₆₁	C₂×D₄	1	2	yes	—
109	#41×C₆₁	—	2	16	no	—
110	#41×C₆₁	—	4	8	no	—
111	#41×C₆₁	—	4	8	no	—
112	#41×C₆₁	—	4	8	no	—
113	C₂×Q₈×C₆₁	—	2	2	no	—
114	C₂×Q₈×C₆₁	—	2	2	no	—
115	C₂×Q₈×C₆₁	—	2	2	no	—
116	C₂×Q₈×C₆₁	—	2	2	no	—
117	C₂×Q₈×C₆₁	—	2	2	no	—
118	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
119	C₂×D₄×C₆₁	—	2	8	no	—
120	C₂×D₄×C₆₁	—	2	2	no	—
121	C₂×D₄×C₆₁	—	2	2	no	—
122	C₂×D₄×C₆₁	—	2	1	no	—
123	C₂×D₄×C₆₁	—	2	1	no	—
124	C₂×D₄×C₆₁	—	2	1	no	—
125	C₂×D₄×C₆₁	—	4	4	no	—
126	C₂×D₄×C₆₁	—	4	4	no	—
127	C₂×D₄×C₆₁	C₂²⋊C₄	1	4	yes	—
128	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
129	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₆₁	#41	1	2	yes	—
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	2	no	—
135	C₂²×C₄×C₆₁	—	2	1	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	2	2	no	—
138	C₂²×C₄×C₆₁	—	2	4	no	—
139	C₂²×C₄×C₆₁	—	2	8	no	—
140	C₂²×C₄×C₆₁	—	2	1	no	—
141	C₂²×C₄×C₆₁	—	2	2	no	—
142	C₂²×C₄×C₆₁	—	4	4	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	C₂²×C₄	1	4	yes	—
147	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
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	2	no	—
156	C₂×C₈×C₆₁	—	2	2	no	—
157	C₂×C₈×C₆₁	—	2	1	no	—
158	C₂×C₈×C₆₁	—	2	1	no	—
159	C₂×C₈×C₆₁	—	2	2	no	—
160	C₂×C₈×C₆₁	—	4	8	no	—
161	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₆₁	—	2	4	no	—
163	C₄⋊C₄×C₆₁	—	2	8	no	—
164	C₄⋊C₄×C₆₁	—	2	4	no	—
165	C₄⋊C₄×C₆₁	—	2	1	no	—
166	C₄⋊C₄×C₆₁	—	2	1	no	—
167	C₄⋊C₄×C₆₁	—	2	2	no	—
168	C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₄⋊C₄×C₆₁	—	2	1	no	—
170	C₄⋊C₄×C₆₁	—	2	2	no	—
171	C₄⋊C₄×C₆₁	—	4	2	no	—
172	C₄⋊C₄×C₆₁	—	8	1	no	—
173	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	4	yes	—
174	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
175	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
176	C₂²⋊C₄×C₆₁	—	2	8	no	—
177	C₂²⋊C₄×C₆₁	—	2	4	no	—
178	C₂²⋊C₄×C₆₁	—	4	4	no	—
179	C₂²⋊C₄×C₆₁	—	8	2	no	—
180	C₂²⋊C₄×C₆₁	C₂²⋊C₄	1	8	yes	—
181	C₄²×C₆₁	—	4	4	no	—
182	C₄²×C₆₁	—	4	2	no	—
183	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
184	C₄²×C₆₁	C₂×D₄	1	2	yes	—
185	C₂³×C₆₁	—	2	2	no	—
186	C₂³×C₆₁	—	2	2	no	—
187	C₂³×C₆₁	—	2	2	no	—
188	C₂³×C₆₁	—	2	2	no	—
189	C₂³×C₆₁	—	2	2	no	—
190	C₂³×C₆₁	—	2	2	no	—
191	C₂³×C₆₁	—	2	2	no	—
192	C₂³×C₆₁	—	2	2	no	—
193	C₂³×C₆₁	—	2	2	no	—
194	C₂³×C₆₁	—	4	1	no	—
195	C₂³×C₆₁	—	4	1	no	—
196	C₂³×C₆₁	—	4	1	no	—
197	C₂³×C₆₁	—	4	1	no	—
198	C₂³×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
199	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₆₁	—	2	4	no	—
201	Q₈×C₆₁	—	2	4	no	—
202	Q₈×C₆₁	—	4	2	no	—
203	Q₈×C₆₁	—	4	2	no	—
204	D₄×C₆₁	—	2	2	no	—
205	D₄×C₆₁	—	2	2	no	—
206	D₄×C₆₁	—	2	2	no	—
207	D₄×C₆₁	—	2	8	no	—
208	D₄×C₆₁	—	4	16	no	—
209	D₄×C₆₁	C₄×D₄	1	4	yes	—
210	C₂×C₄×C₆₁	—	2	2	no	—
211	C₂×C₄×C₆₁	—	2	2	no	—
212	C₂×C₄×C₆₁	—	2	1	no	—
213	C₂×C₄×C₆₁	—	2	1	no	—
214	C₂×C₄×C₆₁	—	2	4	no	—
215	C₂×C₄×C₆₁	—	2	4	no	—
216	C₂×C₄×C₆₁	—	2	4	no	—
217	C₂×C₄×C₆₁	—	2	4	no	—
218	C₂×C₄×C₆₁	—	2	2	no	—
219	C₂×C₄×C₆₁	—	2	4	no	—
220	C₂×C₄×C₆₁	—	2	2	no	—
221	C₂×C₄×C₆₁	—	4	16	no	—
222	C₂×C₄×C₆₁	—	4	2	no	—
223	C₂×C₄×C₆₁	—	4	2	no	—
224	C₂×C₄×C₆₁	—	4	1	no	—
225	C₂×C₄×C₆₁	—	4	1	no	—
226	C₂×C₄×C₆₁	—	4	1	no	—
227	C₂×C₄×C₆₁	—	4	1	no	—
228	C₂×C₄×C₆₁	—	4	8	no	—
229	C₂×C₄×C₆₁	—	4	2	no	—
230	C₂×C₄×C₆₁	—	4	1	no	—
231	C₂×C₄×C₆₁	—	4	1	no	—
232	C₂×C₄×C₆₁	—	4	2	no	—
233	C₂×C₄×C₆₁	—	4	1	no	—
234	C₂×C₄×C₆₁	—	4	2	no	—
235	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
236	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	4	yes	—
237	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	2	yes	—
238	C₂×C₄×C₆₁	#135	1	2	yes	—
239	C₂×C₄×C₆₁	#135	1	2	yes	—
240	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
241	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
246	C₈×C₆₁	—	2	2	no	—
247	C₈×C₆₁	—	4	2	no	—
248	C₈×C₆₁	—	4	1	no	—
249	#22417	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
250	C₂²×C₆₁	—	2	4	no	—
251	C₂²×C₆₁	—	2	4	no	—
252	C₂²×C₆₁	—	2	4	no	—
253	C₂²×C₆₁	—	2	4	no	—
254	C₂²×C₆₁	—	4	2	no	—
255	C₂²×C₆₁	—	4	2	no	—
256	C₂²×C₆₁	—	4	2	no	—
257	C₂²×C₆₁	—	4	2	no	—
258	C₂²×C₆₁	—	4	2	no	—
259	C₂²×C₆₁	—	4	2	no	—
260	C₂²×C₆₁	—	4	2	no	—
261	C₂²×C₆₁	—	4	2	no	—
262	C₂²×C₆₁	—	4	2	no	—
263	C₂²×C₆₁	—	4	2	no	—
264	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
265	C₂²×C₆₁	D₄²	1	1	yes	characteristic
266	C₂²×C₆₁	#546	1	1	yes	characteristic
267	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
268	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
269	C₂²×C₆₁	#577	1	1	yes	characteristic
270	C₂²×C₆₁	#578	1	1	yes	characteristic
271	C₄×C₆₁	—	2	4	no	—
272	C₄×C₆₁	—	2	2	no	—
273	C₄×C₆₁	—	4	4	no	—
274	C₄×C₆₁	—	4	2	no	—
275	C₄×C₆₁	—	4	2	no	—
276	C₄×C₆₁	—	8	2	no	—
277	C₄×C₆₁	—	8	1	no	—
278	C₄×C₆₁	#416	1	4	yes	complemented
279	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
280	C₄×C₆₁	#518	1	1	yes	characteristic
281	C₄×C₆₁	D₄²	1	1	yes	characteristic
282	C₄×C₆₁	#546	1	1	yes	characteristic
283	C₂×#547	C₂×C₆₁	1	1	yes	characteristic
284	C₂×C₈×D₄	C₂×C₆₁	1	1	yes	characteristic, complemented
285	C₂×#416	C₂×C₆₁	1	2	yes	complemented
286	#2354	C₂×C₆₁	1	1	yes	characteristic, complemented
287	#1981	C₂×C₆₁	1	1	yes	characteristic, complemented
288	#1956	C₂×C₆₁	1	1	yes	characteristic, complemented
289	#1892	C₂×C₆₁	1	2	yes	complemented
290	#1873	C₂×C₆₁	1	2	yes	complemented
291	#1802	C₂×C₆₁	1	1	yes	characteristic, complemented
292	#1788	C₂×C₆₁	1	2	yes	complemented
293	C₄×#102	C₂×C₆₁	1	1	yes	characteristic, complemented
294	C₂×C₆₁	—	4	4	no	—
295	C₂×C₆₁	—	4	4	no	—
296	C₂×C₆₁	D₄×C₂²⋊C₄	1	1	yes	characteristic
297	C₂×C₆₁	C₂×#416	1	1	yes	characteristic
298	C₂×C₆₁	#2898	1	1	yes	characteristic
299	C₂×C₆₁	#3283	1	1	yes	characteristic
300	C₂×C₆₁	#3284	1	1	yes	characteristic
301	C₂×C₆₁	#3302	1	1	yes	characteristic
302	C₂×C₆₁	#3303	1	1	yes	characteristic
303	C₂²×#41	C₂²×C₆₁	1	2	yes	—
304	C₂³×C₈	C₂²×C₆₁	1	2	yes	—
305	#547	—	2	4	no	—
306	#547	C₄×C₆₁	1	8	yes	complemented
307	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
308	C₂×#123	—	2	2	no	—
309	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	2	yes	—
310	C₂×#121	—	2	1	no	—
311	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
313	C₂×#117	C₂²×C₆₁	1	2	yes	—
314	C₂²×C₄⋊C₄	—	2	1	no	—
315	C₈×D₄	—	2	4	no	—
316	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
317	#416	—	2	8	no	—
318	C₂×#103	C₂²×C₆₁	1	2	yes	—
319	C₂×#103	C₂²×C₆₁	1	2	yes	—
320	C₂×#103	C₂²×C₆₁	1	2	yes	—
321	C₂×#103	C₂²×C₆₁	1	2	yes	—
322	C₂×#102	C₂²×C₆₁	1	2	yes	—
323	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
324	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
325	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
326	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
327	#390	—	2	1	no	—
328	#388	—	2	2	no	—
329	#384	C₂²×C₆₁	1	1	yes	characteristic
330	#380	C₂²×C₆₁	1	2	yes	—
331	C₄×C₄⋊C₄	—	2	1	no	—
332	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
333	#340	C₂²×C₆₁	1	2	yes	—
334	#340	C₂²×C₆₁	1	1	yes	characteristic
335	#340	C₂²×C₆₁	1	1	yes	characteristic
336	C₆₁	#22417	1	1	yes	characteristic, direct product factor, Sylow
337	C₂×#41	—	2	4	no	—
338	C₂×#41	—	2	4	no	—
339	C₂×#41	—	2	4	no	—
340	C₂×#41	—	4	2	no	—
341	C₂×#41	—	4	2	no	—
342	C₂×#41	C₂×C₄×C₆₁	1	8	yes	—
343	C₂²×Q₈	C₂³×C₆₁	1	2	yes	—
344	C₂²×D₄	—	2	2	no	—
345	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
346	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
347	C₂³×C₄	—	2	1	no	—
348	C₂³×C₄	—	2	2	no	—
349	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
350	C₂²×C₈	—	2	4	no	—
351	C₂²×C₈	—	2	4	no	—
352	C₂²×C₈	—	4	2	no	—
353	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
354	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
356	C₄⋊Q₈	—	2	2	no	—
357	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	—
358	#123	—	2	16	no	—
359	C₂²⋊Q₈	—	2	4	no	—
360	C₂²⋊Q₈	C₂×C₄×C₆₁	1	8	yes	—
361	#121	—	2	8	no	—
362	C₄×D₄	—	2	2	no	—
363	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
364	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
365	C₄×D₄	D₄×C₆₁	1	4	yes	—
366	#117	—	2	4	no	—
367	#117	—	4	2	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	8	no	—
372	C₂×C₄⋊C₄	—	2	1	no	—
373	C₂×C₄⋊C₄	—	2	1	no	—
374	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
376	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	D₄×C₆₁	1	2	yes	—
384	C₂×C₄²	—	2	2	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
387	C₄⋊C₈	—	2	2	no	—
388	#103	—	2	4	no	—
389	#103	—	2	4	no	—
390	#103	—	4	2	no	—
391	#103	—	4	2	no	—
392	#102	—	2	4	no	—
393	#102	—	2	2	no	—
394	#102	D₄×C₆₁	1	4	yes	complemented
395	C₂²⋊C₈	—	2	4	no	—
396	C₄×C₈	—	2	2	no	—
397	#95	—	2	2	no	—
398	#95	—	2	1	no	—
399	C₂⁴	—	2	1	no	—
400	C₂⁴	C₂×D₄×C₆₁	1	2	yes	—
401	#41	—	2	16	no	—
402	#41	—	4	8	no	—
403	#41	—	4	8	no	—
404	#41	—	4	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
411	C₂×D₄	—	2	8	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	4	4	no	—
418	C₂×D₄	—	4	4	no	—
419	C₂×D₄	C₂²⋊C₄×C₆₁	1	4	yes	—
420	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
421	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
422	C₂×D₄	#41×C₆₁	1	2	yes	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	2	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	4	2	no	—
437	C₂²×C₄	—	4	2	no	—
438	C₂²×C₄	C₂²×C₄×C₆₁	1	4	yes	—
439	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
442	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	—	4	8	no	—
453	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
454	C₄⋊C₄	—	2	4	no	—
455	C₄⋊C₄	—	2	8	no	—
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	4	2	no	—
464	C₄⋊C₄	—	8	1	no	—
465	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	4	yes	—
466	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
467	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
468	C₂²⋊C₄	—	2	8	no	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	4	4	no	—
471	C₂²⋊C₄	—	8	2	no	—
472	C₂²⋊C₄	C₂²⋊C₄×C₆₁	1	8	yes	—
473	C₄²	—	4	4	no	—
474	C₄²	—	4	2	no	—
475	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
476	C₄²	C₂×D₄×C₆₁	1	2	yes	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	4	1	no	—
487	C₂³	—	4	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
491	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
492	Q₈	—	2	4	no	—
493	Q₈	—	2	4	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	4	2	no	—
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	2	8	no	—
499	D₄	—	2	2	no	—
500	D₄	—	4	16	no	—
501	D₄	C₄×D₄×C₆₁	1	4	yes	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	4	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	4	16	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	8	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
528	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	4	yes	—
529	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	2	yes	—
530	C₂×C₄	#135×C₆₁	1	2	yes	—
531	C₂×C₄	#135×C₆₁	1	2	yes	—
532	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
535	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
536	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
537	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	4	2	no	—
540	C₈	—	4	1	no	—
541	C₂²	—	2	4	no	—
542	C₂²	—	2	4	no	—
543	C₂²	—	2	4	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
556	C₂²	D₄²×C₆₁	1	1	yes	characteristic
557	C₂²	C₆₁×#546	1	1	yes	characteristic
558	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
559	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
560	C₂²	C₆₁×#577	1	1	yes	characteristic
561	C₂²	C₆₁×#578	1	1	yes	characteristic
562	C₄	—	2	4	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	2	no	—
569	C₄	C₆₁×#416	1	4	yes	complemented
570	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
571	C₄	C₆₁×#518	1	1	yes	characteristic
572	C₄	D₄²×C₆₁	1	1	yes	characteristic
573	C₄	C₆₁×#546	1	1	yes	characteristic
574	C₂	—	4	4	no	—
575	C₂	—	4	4	no	—
576	C₂	D₄×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
577	C₂	C₂×C₆₁×#416	1	1	yes	characteristic
578	C₂	C₆₁×#2898	1	1	yes	characteristic
579	C₂	C₆₁×#3283	1	1	yes	characteristic
580	C₂	C₆₁×#3284	1	1	yes	characteristic
581	C₂	C₆₁×#3302	1	1	yes	characteristic
582	C₂	C₆₁×#3303	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	C₂×C₆₁×#547	C₂
LCS	G ▷ C₂×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×C₈×D₄×C₆₁	C₂	semidirect
3. C₂×C₆₁×#416	C₂	semidirect
4. C₆₁×#2354	C₂	semidirect
5. C₆₁×#1981	C₂	semidirect
6. C₆₁×#1956	C₂	semidirect
7. C₆₁×#1892	C₂	semidirect
8. C₆₁×#1873	C₂	semidirect
9. C₆₁×#1802	C₂	semidirect
10. C₆₁×#1788	C₂	semidirect
11. C₄×#102×C₆₁	C₂	semidirect
15. C₆₁×#547	C₄	semidirect
102. #102×C₆₁	D₄	semidirect
249. #22417	C₆₁	direct (N × H)
278. C₄×C₆₁	#416	semidirect
284. C₂×C₈×D₄	C₂×C₆₁	semidirect
285. C₂×#416	C₂×C₆₁	semidirect
286. #2354	C₂×C₆₁	semidirect
287. #1981	C₂×C₆₁	semidirect
288. #1956	C₂×C₆₁	semidirect
289. #1892	C₂×C₆₁	semidirect
290. #1873	C₂×C₆₁	semidirect
291. #1802	C₂×C₆₁	semidirect
292. #1788	C₂×C₆₁	semidirect
293. C₄×#102	C₂×C₆₁	semidirect
306. #547	C₄×C₆₁	semidirect
336. C₆₁	#22417	direct (N × H)
394. #102	D₄×C₆₁	semidirect
569. C₄	C₆₁×#416	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#547	2
C₂×C₈×D₄×C₆₁	2
C₂×C₆₁×#416	2
C₆₁×#2354	2
C₆₁×#1981	2
C₆₁×#1956	2
C₆₁×#1892	2
C₆₁×#1873	2
C₆₁×#1802	2
C₆₁×#1788	2
C₄×#102×C₆₁	2
#22417	61

Subgroups — C61×#22417 #29525850

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#22417 #29525850