Subgroups — C₆₁×#26030 #29529463

Order 15616.

706 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#2550	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#2357	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#2067	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2065	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2025	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#2023	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1989	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1987	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1919	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1918	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1835	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1804	C₂	1	1	yes	maximal, characteristic
15	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₆₁×#398	—	2	1	no	—
30	C₆₁×#395	—	2	1	no	—
31	C₆₁×#391	—	2	1	no	—
32	C₆₁×#390	C₂²	1	1	yes	characteristic
33	C₆₁×#390	C₂²	1	1	yes	characteristic
34	C₆₁×#389	—	2	1	no	—
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×#382	C₂²	1	1	yes	characteristic
40	C₆₁×#382	C₂²	1	1	yes	characteristic
41	C₆₁×#381	—	2	1	no	—
42	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
47	C₆₁×#340	C₂²	1	1	yes	characteristic
48	C₆₁×#340	C₂²	1	1	yes	characteristic
49	C₆₁×#340	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×#336	C₂²	1	1	yes	characteristic
58	C₆₁×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₆₁	—	2	1	no	—
60	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₆₁	—	2	1	no	—
62	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₆₁	—	2	2	no	—
67	C₄⋊Q₈×C₆₁	—	4	1	no	—
68	#125×C₆₁	—	2	2	no	—
69	#125×C₆₁	—	4	1	no	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	C₄×D₄×C₆₁	Q₈	1	4	yes	complemented
72	C₂×C₄⋊C₄×C₆₁	—	2	1	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	D₄	1	1	yes	characteristic
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	1	yes	characteristic
81	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₆₁	—	2	1	no	—
87	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
88	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
89	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₄²×C₆₁	—	2	1	no	—
92	C₂×C₄²×C₆₁	—	2	1	no	—
93	C₂×C₄²×C₆₁	—	2	1	no	—
94	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
97	#107×C₆₁	—	2	2	no	—
98	#106×C₆₁	—	2	2	no	—
99	C₄⋊C₈×C₆₁	—	2	2	no	—
100	C₄⋊C₈×C₆₁	—	4	1	no	—
101	C₄⋊C₈×C₆₁	—	4	1	no	—
102	#102×C₆₁	—	2	2	no	—
103	#102×C₆₁	—	2	2	no	—
104	#102×C₆₁	—	4	1	no	—
105	#102×C₆₁	—	4	1	no	—
106	C₄×C₈×C₆₁	—	2	2	no	—
107	#95×C₆₁	—	2	1	no	—
108	#95×C₆₁	—	2	1	no	—
109	#95×C₆₁	—	2	1	no	—
110	#95×C₆₁	—	2	1	no	—
111	#95×C₆₁	—	2	1	no	—
112	#95×C₆₁	—	2	1	no	—
113	#95×C₆₁	—	2	1	no	—
114	#95×C₆₁	—	2	1	no	—
115	#95×C₆₁	—	2	1	no	—
116	#95×C₆₁	D₄	1	1	yes	characteristic
117	#95×C₆₁	D₄	1	1	yes	characteristic
118	C₂⁴×C₆₁	—	2	1	no	—
119	C₂×Q₈×C₆₁	—	4	2	no	—
120	C₂×Q₈×C₆₁	—	4	2	no	—
121	C₂×Q₈×C₆₁	—	8	1	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	—	2	1	no	—
126	C₂×D₄×C₆₁	—	2	1	no	—
127	C₂×D₄×C₆₁	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₆₁	—	2	1	no	—
129	C₂²×C₄×C₆₁	—	2	1	no	—
130	C₂²×C₄×C₆₁	—	2	1	no	—
131	C₂²×C₄×C₆₁	—	2	4	no	—
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	—	8	1	no	—
137	C₂²×C₄×C₆₁	—	8	1	no	—
138	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
145	C₂×C₈×C₆₁	—	2	1	no	—
146	C₂×C₈×C₆₁	—	2	1	no	—
147	C₂×C₈×C₆₁	—	2	1	no	—
148	C₂×C₈×C₆₁	—	2	1	no	—
149	C₂×C₈×C₆₁	—	2	1	no	—
150	C₂×C₈×C₆₁	—	2	1	no	—
151	C₂×C₈×C₆₁	—	2	1	no	—
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	C₄⋊C₄×C₆₁	—	2	2	no	—
158	C₄⋊C₄×C₆₁	—	2	1	no	—
159	C₄⋊C₄×C₆₁	—	2	1	no	—
160	C₄⋊C₄×C₆₁	—	2	1	no	—
161	C₄⋊C₄×C₆₁	—	2	1	no	—
162	C₄⋊C₄×C₆₁	—	2	1	no	—
163	C₄⋊C₄×C₆₁	—	2	1	no	—
164	C₄⋊C₄×C₆₁	—	2	1	no	—
165	C₄⋊C₄×C₆₁	—	2	1	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	—	4	1	no	—
170	C₄⋊C₄×C₆₁	—	4	2	no	—
171	C₄⋊C₄×C₆₁	—	4	2	no	—
172	C₄⋊C₄×C₆₁	—	4	2	no	—
173	C₄⋊C₄×C₆₁	—	4	2	no	—
174	C₄⋊C₄×C₆₁	—	8	1	no	—
175	C₄⋊C₄×C₆₁	C₂×Q₈	1	2	yes	—
176	C₄⋊C₄×C₆₁	#41	1	2	yes	—
177	C₄⋊C₄×C₆₁	#41	1	2	yes	—
178	C₂²⋊C₄×C₆₁	—	2	4	no	—
179	C₂²⋊C₄×C₆₁	—	4	2	no	—
180	C₂²⋊C₄×C₆₁	—	4	2	no	—
181	C₂²⋊C₄×C₆₁	—	8	1	no	—
182	C₂²⋊C₄×C₆₁	—	8	1	no	—
183	C₄²×C₆₁	—	2	1	no	—
184	C₄²×C₆₁	—	2	1	no	—
185	C₄²×C₆₁	—	2	1	no	—
186	C₄²×C₆₁	—	2	1	no	—
187	C₄²×C₆₁	—	8	1	no	—
188	C₄²×C₆₁	—	8	1	no	—
189	C₄²×C₆₁	—	8	1	no	—
190	C₄²×C₆₁	C₂×Q₈	1	2	yes	—
191	C₄²×C₆₁	#41	1	2	yes	—
192	C₂³×C₆₁	—	2	2	no	—
193	C₂³×C₆₁	—	4	1	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	—	4	1	no	—
199	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
200	Q₈×C₆₁	—	8	4	no	—
201	D₄×C₆₁	—	2	2	no	—
202	D₄×C₆₁	—	2	2	no	—
203	D₄×C₆₁	—	4	1	no	—
204	D₄×C₆₁	—	4	1	no	—
205	C₂×C₄×C₆₁	—	2	1	no	—
206	C₂×C₄×C₆₁	—	2	1	no	—
207	C₂×C₄×C₆₁	—	2	1	no	—
208	C₂×C₄×C₆₁	—	2	1	no	—
209	C₂×C₄×C₆₁	—	2	1	no	—
210	C₂×C₄×C₆₁	—	2	1	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	1	no	—
215	C₂×C₄×C₆₁	—	2	2	no	—
216	C₂×C₄×C₆₁	—	2	2	no	—
217	C₂×C₄×C₆₁	—	2	1	no	—
218	C₂×C₄×C₆₁	—	2	1	no	—
219	C₂×C₄×C₆₁	—	2	1	no	—
220	C₂×C₄×C₆₁	—	2	1	no	—
221	C₂×C₄×C₆₁	—	2	1	no	—
222	C₂×C₄×C₆₁	—	2	1	no	—
223	C₂×C₄×C₆₁	—	4	1	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	1	no	—
229	C₂×C₄×C₆₁	—	4	1	no	—
230	C₂×C₄×C₆₁	—	4	1	no	—
231	C₂×C₄×C₆₁	—	4	1	no	—
232	C₂×C₄×C₆₁	—	4	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	—	8	4	no	—
242	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
243	C₂×C₄×C₆₁	C₂²⋊Q₈	1	2	yes	—
244	C₂×C₄×C₆₁	#135	1	2	yes	—
245	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
246	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
247	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
251	C₈×C₆₁	—	4	1	no	—
252	C₈×C₆₁	—	4	1	no	—
253	C₈×C₆₁	—	4	1	no	—
254	C₈×C₆₁	—	4	1	no	—
255	#26030	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₆₁	—	4	2	no	—
257	C₂²×C₆₁	—	4	2	no	—
258	C₂²×C₆₁	—	4	2	no	—
259	C₂²×C₆₁	—	8	1	no	—
260	C₂²×C₆₁	—	8	1	no	—
261	C₂²×C₆₁	—	8	1	no	—
262	C₂²×C₆₁	—	8	1	no	—
263	C₂²×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
264	C₂²×C₆₁	#546	1	1	yes	characteristic
265	C₂²×C₆₁	#548	1	1	yes	characteristic
266	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
267	C₂²×C₆₁	#575	1	1	yes	characteristic
268	C₂²×C₆₁	#576	1	1	yes	characteristic
269	C₂²×C₆₁	#577	1	1	yes	characteristic
270	C₄×C₆₁	—	2	2	no	—
271	C₄×C₆₁	—	2	2	no	—
272	C₄×C₆₁	—	2	2	no	—
273	C₄×C₆₁	—	4	2	no	—
274	C₄×C₆₁	—	4	2	no	—
275	C₄×C₆₁	—	4	1	no	—
276	C₄×C₆₁	—	4	1	no	—
277	C₄×C₆₁	—	4	1	no	—
278	C₄×C₆₁	—	4	2	no	—
279	C₄×C₆₁	—	8	1	no	—
280	C₄×C₆₁	—	8	1	no	—
281	C₄×C₆₁	—	8	1	no	—
282	C₄×C₆₁	—	8	1	no	—
283	C₄×C₆₁	#533	1	1	yes	characteristic
284	C₄×C₆₁	#544	1	1	yes	characteristic
285	C₄×C₆₁	#555	1	1	yes	characteristic
286	C₄×C₆₁	#556	1	1	yes	characteristic
287	#2550	C₂×C₆₁	1	1	yes	characteristic, complemented
288	#2357	C₂×C₆₁	1	1	yes	characteristic
289	#2067	C₂×C₆₁	1	1	yes	characteristic
290	#2065	C₂×C₆₁	1	1	yes	characteristic
291	#2025	C₂×C₆₁	1	1	yes	characteristic
292	#2023	C₂×C₆₁	1	1	yes	characteristic
293	#1989	C₂×C₆₁	1	1	yes	characteristic, complemented
294	#1987	C₂×C₆₁	1	1	yes	characteristic, complemented
295	#1949	C₂×C₆₁	1	1	yes	characteristic, complemented
296	#1939	C₂×C₆₁	1	1	yes	characteristic, complemented
297	#1919	C₂×C₆₁	1	1	yes	characteristic, complemented
298	#1918	C₂×C₆₁	1	1	yes	characteristic, complemented
299	#1835	C₂×C₆₁	1	1	yes	characteristic, complemented
300	#1804	C₂×C₆₁	1	1	yes	characteristic
301	C₄×#102	C₂×C₆₁	1	1	yes	characteristic
302	C₂×C₆₁	—	8	2	no	—
303	C₂×C₆₁	#2439	1	1	yes	characteristic
304	C₂×C₆₁	#3076	1	1	yes	characteristic
305	C₂×C₆₁	#3081	1	1	yes	characteristic
306	C₂×C₆₁	#3301	1	1	yes	characteristic
307	C₂×C₆₁	#3322	1	1	yes	characteristic
308	C₂×C₆₁	#3361	1	1	yes	characteristic
309	C₂×C₆₁	#3371	1	1	yes	characteristic
310	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
311	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
313	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
314	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
316	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
317	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
318	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
319	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
320	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
321	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
322	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
323	#398	—	2	1	no	—
324	#395	—	2	1	no	—
325	#391	—	2	1	no	—
326	#390	C₂²×C₆₁	1	1	yes	characteristic
327	#390	C₂²×C₆₁	1	1	yes	characteristic
328	#389	—	2	1	no	—
329	#389	C₂²×C₆₁	1	1	yes	characteristic
330	#389	C₂²×C₆₁	1	1	yes	characteristic
331	#388	—	2	1	no	—
332	#388	—	2	1	no	—
333	#382	C₂²×C₆₁	1	1	yes	characteristic
334	#382	C₂²×C₆₁	1	1	yes	characteristic
335	#381	—	2	1	no	—
336	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
337	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
338	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
339	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
340	C₄×C₂²⋊C₄	—	2	1	no	—
341	#340	C₂²×C₆₁	1	1	yes	characteristic
342	#340	C₂²×C₆₁	1	1	yes	characteristic
343	#340	C₂²×C₆₁	1	1	yes	characteristic
344	#340	C₂²×C₆₁	1	1	yes	characteristic
345	#340	C₂²×C₆₁	1	1	yes	characteristic
346	#340	C₂²×C₆₁	1	1	yes	characteristic
347	#340	C₂²×C₆₁	1	1	yes	characteristic
348	#340	C₂²×C₆₁	1	1	yes	characteristic
349	#340	C₂²×C₆₁	1	1	yes	characteristic
350	#340	C₂²×C₆₁	1	1	yes	characteristic
351	#336	C₂²×C₆₁	1	1	yes	characteristic
352	#336	C₂²×C₆₁	1	1	yes	characteristic
353	C₆₁	#26030	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²×Q₈	—	2	1	no	—
355	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
356	C₂³×C₄	—	2	1	no	—
357	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
361	C₄⋊Q₈	—	2	2	no	—
362	C₄⋊Q₈	—	4	1	no	—
363	#125	—	2	2	no	—
364	#125	—	4	1	no	—
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	Q₈×C₆₁	1	4	yes	complemented
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
373	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
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×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₂²⋊C₄	—	2	1	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
392	#107	—	2	2	no	—
393	#106	—	2	2	no	—
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	—	4	1	no	—
396	C₄⋊C₈	—	4	1	no	—
397	#102	—	2	2	no	—
398	#102	—	2	2	no	—
399	#102	—	4	1	no	—
400	#102	—	4	1	no	—
401	C₄×C₈	—	2	2	no	—
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	D₄×C₆₁	1	1	yes	characteristic
412	#95	D₄×C₆₁	1	1	yes	characteristic
413	C₂⁴	—	2	1	no	—
414	C₂×Q₈	—	4	2	no	—
415	C₂×Q₈	—	4	2	no	—
416	C₂×Q₈	—	8	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	1	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	C₂×Q₈×C₆₁	1	2	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	8	1	no	—
432	C₂²×C₄	—	8	1	no	—
433	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	2	no	—
466	C₄⋊C₄	—	4	2	no	—
467	C₄⋊C₄	—	4	2	no	—
468	C₄⋊C₄	—	4	2	no	—
469	C₄⋊C₄	—	8	1	no	—
470	C₄⋊C₄	C₂×Q₈×C₆₁	1	2	yes	—
471	C₄⋊C₄	#41×C₆₁	1	2	yes	—
472	C₄⋊C₄	#41×C₆₁	1	2	yes	—
473	C₂²⋊C₄	—	2	4	no	—
474	C₂²⋊C₄	—	4	2	no	—
475	C₂²⋊C₄	—	4	2	no	—
476	C₂²⋊C₄	—	8	1	no	—
477	C₂²⋊C₄	—	8	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	8	1	no	—
483	C₄²	—	8	1	no	—
484	C₄²	—	8	1	no	—
485	C₄²	C₂×Q₈×C₆₁	1	2	yes	—
486	C₄²	#41×C₆₁	1	2	yes	—
487	C₂³	—	2	2	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	4	1	no	—
490	C₂³	—	4	1	no	—
491	C₂³	—	4	1	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
495	Q₈	—	8	4	no	—
496	D₄	—	2	2	no	—
497	D₄	—	2	2	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	8	4	no	—
537	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
538	C₂×C₄	C₂²⋊Q₈×C₆₁	1	2	yes	—
539	C₂×C₄	#135×C₆₁	1	2	yes	—
540	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
541	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
542	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
543	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
544	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
545	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
546	C₈	—	4	1	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	1	no	—
549	C₈	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
558	C₂²	C₆₁×#546	1	1	yes	characteristic
559	C₂²	C₆₁×#548	1	1	yes	characteristic
560	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
561	C₂²	C₆₁×#575	1	1	yes	characteristic
562	C₂²	C₆₁×#576	1	1	yes	characteristic
563	C₂²	C₆₁×#577	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	1	no	—
569	C₄	—	4	1	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	1	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	C₆₁×#533	1	1	yes	characteristic
578	C₄	C₆₁×#544	1	1	yes	characteristic
579	C₄	C₆₁×#555	1	1	yes	characteristic
580	C₄	C₆₁×#556	1	1	yes	characteristic
581	C₂	—	8	2	no	—
582	C₂	C₆₁×#2439	1	1	yes	characteristic
583	C₂	C₆₁×#3076	1	1	yes	characteristic
584	C₂	C₆₁×#3081	1	1	yes	characteristic
585	C₂	C₆₁×#3301	1	1	yes	characteristic
586	C₂	C₆₁×#3322	1	1	yes	characteristic
587	C₂	C₆₁×#3361	1	1	yes	characteristic
588	C₂	C₆₁×#3371	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	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₁ ◁ C₄×C₄⋊C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#2550	C₂	semidirect
7. C₆₁×#1989	C₂	semidirect
8. C₆₁×#1987	C₂	semidirect
9. C₆₁×#1949	C₂	semidirect
10. C₆₁×#1939	C₂	semidirect
11. C₆₁×#1919	C₂	semidirect
12. C₆₁×#1918	C₂	semidirect
13. C₆₁×#1835	C₂	semidirect
71. C₄×D₄×C₆₁	Q₈	semidirect
255. #26030	C₆₁	direct (N × H)
287. #2550	C₂×C₆₁	semidirect
293. #1989	C₂×C₆₁	semidirect
294. #1987	C₂×C₆₁	semidirect
295. #1949	C₂×C₆₁	semidirect
296. #1939	C₂×C₆₁	semidirect
297. #1919	C₂×C₆₁	semidirect
298. #1918	C₂×C₆₁	semidirect
299. #1835	C₂×C₆₁	semidirect
353. C₆₁	#26030	direct (N × H)
366. C₄×D₄	Q₈×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#2550	2
C₆₁×#2357	2
C₆₁×#2067	2
C₆₁×#2065	2
C₆₁×#2025	2
C₆₁×#2023	2
C₆₁×#1989	2
C₆₁×#1987	2
C₆₁×#1949	2
C₆₁×#1939	2
C₆₁×#1919	2
C₆₁×#1918	2
C₆₁×#1835	2
C₆₁×#1804	2
C₄×#102×C₆₁	2
#26030	61

Subgroups — C61×#26030 #29529463

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#26030 #29529463