Subgroups — C₆₁×#26965 #29530398

Order 15616.

858 conjugacy classes of subgroups.

The subgroup lattice has 676 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	C₆₁×#2429	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2423	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#2083	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#2036	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#2016	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#2001	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1956	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1933	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1892	C₂	1	1	yes	maximal, characteristic
13	C₆₁×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
16	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×Q₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#467	—	2	4	no	—
26	C₄×Q₁₆×C₆₁	—	2	4	no	—
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#399	—	2	1	no	—
41	C₆₁×#398	—	2	1	no	—
42	C₆₁×#398	—	2	1	no	—
43	C₆₁×#396	—	2	1	no	—
44	C₆₁×#391	C₂²	1	1	yes	characteristic
45	C₆₁×#391	C₂²	1	1	yes	characteristic
46	C₆₁×#389	—	2	1	no	—
47	C₆₁×#389	C₂²	1	1	yes	characteristic
48	C₆₁×#389	C₂²	1	1	yes	characteristic
49	C₆₁×#388	—	2	1	no	—
50	C₆₁×#388	—	2	1	no	—
51	C₆₁×#387	—	2	1	no	—
52	C₆₁×#384	C₂²	1	1	yes	characteristic
53	C₆₁×#380	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₆₁	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×#340	C₂²	1	1	yes	characteristic
59	C₆₁×#336	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×Q₁₆×C₆₁	—	2	2	no	—
66	C₂×Q₁₆×C₆₁	—	2	2	no	—
67	C₂×Q₁₆×C₆₁	—	2	2	no	—
68	C₂×Q₁₆×C₆₁	—	2	2	no	—
69	C₂×Q₁₆×C₆₁	—	2	2	no	—
70	C₂×Q₁₆×C₆₁	—	4	1	no	—
71	C₂²×C₈×C₆₁	—	2	2	no	—
72	C₂²×C₈×C₆₁	—	2	2	no	—
73	C₂²×C₈×C₆₁	—	4	1	no	—
74	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₆₁	—	2	2	no	—
79	C₄⋊Q₈×C₆₁	—	4	1	no	—
80	C₂²⋊Q₈×C₆₁	—	2	2	no	—
81	C₂²⋊Q₈×C₆₁	—	2	2	no	—
82	C₂²⋊Q₈×C₆₁	—	2	2	no	—
83	C₂²⋊Q₈×C₆₁	—	4	1	no	—
84	C₂²⋊Q₈×C₆₁	—	4	1	no	—
85	C₂²⋊Q₈×C₆₁	—	4	1	no	—
86	C₄×Q₈×C₆₁	—	2	2	no	—
87	C₄×Q₈×C₆₁	—	2	2	no	—
88	C₄×Q₈×C₆₁	—	4	1	no	—
89	C₄×Q₈×C₆₁	—	4	1	no	—
90	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
91	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
92	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
93	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
94	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
95	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
96	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
97	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
107	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
109	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₆₁	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	—	2	1	no	—
113	C₂×C₄²×C₆₁	—	2	1	no	—
114	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
116	#107×C₆₁	—	2	2	no	—
117	#107×C₆₁	—	2	2	no	—
118	#103×C₆₁	—	2	2	no	—
119	#103×C₆₁	—	2	2	no	—
120	#103×C₆₁	—	2	2	no	—
121	#103×C₆₁	—	2	2	no	—
122	#103×C₆₁	—	4	1	no	—
123	#103×C₆₁	—	4	1	no	—
124	#103×C₆₁	—	4	1	no	—
125	#103×C₆₁	D₄	1	4	yes	—
126	C₂²⋊C₈×C₆₁	—	2	2	no	—
127	C₄×C₈×C₆₁	—	2	2	no	—
128	C₄×C₈×C₆₁	—	4	1	no	—
129	#95×C₆₁	—	2	1	no	—
130	#95×C₆₁	—	2	1	no	—
131	#95×C₆₁	—	2	1	no	—
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	—	2	1	no	—
134	#95×C₆₁	—	2	1	no	—
135	#95×C₆₁	—	2	1	no	—
136	#95×C₆₁	D₄	1	1	yes	characteristic
137	#95×C₆₁	D₄	1	1	yes	characteristic
138	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₆₁	—	2	1	no	—
140	C₂×Q₈×C₆₁	—	2	1	no	—
141	C₂×Q₈×C₆₁	—	2	1	no	—
142	C₂×Q₈×C₆₁	—	2	1	no	—
143	C₂×Q₈×C₆₁	—	2	1	no	—
144	C₂×Q₈×C₆₁	—	2	1	no	—
145	C₂×Q₈×C₆₁	—	2	1	no	—
146	C₂×Q₈×C₆₁	—	2	1	no	—
147	C₂×Q₈×C₆₁	—	2	1	no	—
148	C₂×Q₈×C₆₁	—	2	1	no	—
149	C₂×Q₈×C₆₁	—	2	1	no	—
150	C₂×Q₈×C₆₁	—	2	1	no	—
151	C₂×Q₈×C₆₁	—	2	1	no	—
152	C₂×Q₈×C₆₁	—	2	1	no	—
153	C₂×Q₈×C₆₁	—	2	1	no	—
154	C₂×Q₈×C₆₁	—	2	1	no	—
155	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
156	C₂×Q₈×C₆₁	#41	1	2	yes	—
157	C₂²×C₄×C₆₁	—	2	1	no	—
158	C₂²×C₄×C₆₁	—	2	1	no	—
159	C₂²×C₄×C₆₁	—	2	1	no	—
160	C₂²×C₄×C₆₁	—	2	1	no	—
161	C₂²×C₄×C₆₁	—	2	1	no	—
162	C₂²×C₄×C₆₁	—	2	1	no	—
163	C₂²×C₄×C₆₁	—	2	1	no	—
164	C₂²×C₄×C₆₁	—	2	1	no	—
165	C₂²×C₄×C₆₁	—	2	1	no	—
166	C₂²×C₄×C₆₁	—	2	1	no	—
167	C₂²×C₄×C₆₁	—	2	1	no	—
168	C₂²×C₄×C₆₁	—	2	1	no	—
169	C₂²×C₄×C₆₁	—	2	1	no	—
170	C₂²×C₄×C₆₁	—	2	1	no	—
171	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
177	Q₁₆×C₆₁	—	2	8	no	—
178	Q₁₆×C₆₁	—	4	4	no	—
179	C₂×C₈×C₆₁	—	2	1	no	—
180	C₂×C₈×C₆₁	—	2	1	no	—
181	C₂×C₈×C₆₁	—	2	1	no	—
182	C₂×C₈×C₆₁	—	2	1	no	—
183	C₂×C₈×C₆₁	—	2	1	no	—
184	C₂×C₈×C₆₁	—	2	1	no	—
185	C₂×C₈×C₆₁	—	2	1	no	—
186	C₂×C₈×C₆₁	—	2	1	no	—
187	C₂×C₈×C₆₁	—	2	1	no	—
188	C₂×C₈×C₆₁	—	4	4	no	—
189	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
190	C₂×C₈×C₆₁	#41	1	2	yes	—
191	C₂×C₈×C₆₁	#41	1	2	yes	—
192	C₄⋊C₄×C₆₁	—	2	1	no	—
193	C₄⋊C₄×C₆₁	—	2	1	no	—
194	C₄⋊C₄×C₆₁	—	2	1	no	—
195	C₄⋊C₄×C₆₁	—	2	1	no	—
196	C₄⋊C₄×C₆₁	—	2	1	no	—
197	C₄⋊C₄×C₆₁	—	2	1	no	—
198	C₄⋊C₄×C₆₁	—	2	1	no	—
199	C₄⋊C₄×C₆₁	—	2	1	no	—
200	C₄⋊C₄×C₆₁	—	2	1	no	—
201	C₄⋊C₄×C₆₁	—	4	2	no	—
202	C₄⋊C₄×C₆₁	—	4	2	no	—
203	C₄⋊C₄×C₆₁	—	4	2	no	—
204	C₄⋊C₄×C₆₁	—	4	2	no	—
205	C₄⋊C₄×C₆₁	—	4	2	no	—
206	C₄⋊C₄×C₆₁	—	4	2	no	—
207	C₄⋊C₄×C₆₁	—	4	2	no	—
208	C₄⋊C₄×C₆₁	—	4	2	no	—
209	C₄⋊C₄×C₆₁	—	4	2	no	—
210	C₄⋊C₄×C₆₁	—	8	1	no	—
211	C₄⋊C₄×C₆₁	—	8	1	no	—
212	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
213	C₂²⋊C₄×C₆₁	—	2	2	no	—
214	C₂²⋊C₄×C₆₁	—	4	2	no	—
215	C₂²⋊C₄×C₆₁	—	4	2	no	—
216	C₂²⋊C₄×C₆₁	—	4	2	no	—
217	C₂²⋊C₄×C₆₁	—	8	1	no	—
218	C₂²⋊C₄×C₆₁	Q₁₆	1	4	yes	complemented
219	C₄²×C₆₁	—	2	1	no	—
220	C₄²×C₆₁	—	2	1	no	—
221	C₄²×C₆₁	—	2	1	no	—
222	C₄²×C₆₁	—	2	1	no	—
223	C₄²×C₆₁	—	4	2	no	—
224	C₄²×C₆₁	—	4	2	no	—
225	C₂³×C₆₁	—	2	1	no	—
226	C₂³×C₆₁	—	2	1	no	—
227	C₂³×C₆₁	—	2	1	no	—
228	C₂³×C₆₁	—	2	1	no	—
229	C₂³×C₆₁	—	2	1	no	—
230	C₂³×C₆₁	—	2	1	no	—
231	C₂³×C₆₁	C₂×Q₁₆	1	2	yes	—
232	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
233	Q₈×C₆₁	—	2	2	no	—
234	Q₈×C₆₁	—	2	2	no	—
235	Q₈×C₆₁	—	2	2	no	—
236	Q₈×C₆₁	—	2	2	no	—
237	Q₈×C₆₁	—	4	1	no	—
238	Q₈×C₆₁	—	4	1	no	—
239	Q₈×C₆₁	—	4	1	no	—
240	Q₈×C₆₁	—	4	1	no	—
241	Q₈×C₆₁	—	4	1	no	—
242	Q₈×C₆₁	—	4	1	no	—
243	Q₈×C₆₁	—	4	1	no	—
244	Q₈×C₆₁	—	4	1	no	—
245	C₂×C₄×C₆₁	—	2	1	no	—
246	C₂×C₄×C₆₁	—	2	1	no	—
247	C₂×C₄×C₆₁	—	2	1	no	—
248	C₂×C₄×C₆₁	—	2	1	no	—
249	C₂×C₄×C₆₁	—	2	1	no	—
250	C₂×C₄×C₆₁	—	2	1	no	—
251	C₂×C₄×C₆₁	—	2	1	no	—
252	C₂×C₄×C₆₁	—	2	1	no	—
253	C₂×C₄×C₆₁	—	2	2	no	—
254	C₂×C₄×C₆₁	—	2	2	no	—
255	C₂×C₄×C₆₁	—	2	1	no	—
256	C₂×C₄×C₆₁	—	2	2	no	—
257	C₂×C₄×C₆₁	—	2	1	no	—
258	C₂×C₄×C₆₁	—	2	1	no	—
259	C₂×C₄×C₆₁	—	2	1	no	—
260	C₂×C₄×C₆₁	—	4	1	no	—
261	C₂×C₄×C₆₁	—	4	1	no	—
262	C₂×C₄×C₆₁	—	4	1	no	—
263	C₂×C₄×C₆₁	—	4	1	no	—
264	C₂×C₄×C₆₁	—	4	1	no	—
265	C₂×C₄×C₆₁	—	4	1	no	—
266	C₂×C₄×C₆₁	—	4	1	no	—
267	C₂×C₄×C₆₁	—	4	1	no	—
268	C₂×C₄×C₆₁	—	4	1	no	—
269	C₂×C₄×C₆₁	—	4	1	no	—
270	C₂×C₄×C₆₁	—	4	1	no	—
271	C₂×C₄×C₆₁	—	4	1	no	—
272	C₂×C₄×C₆₁	—	4	1	no	—
273	C₂×C₄×C₆₁	—	4	1	no	—
274	C₂×C₄×C₆₁	—	4	1	no	—
275	C₂×C₄×C₆₁	—	4	1	no	—
276	C₂×C₄×C₆₁	—	4	1	no	—
277	C₂×C₄×C₆₁	—	4	1	no	—
278	C₂×C₄×C₆₁	—	4	1	no	—
279	C₂×C₄×C₆₁	—	4	1	no	—
280	C₂×C₄×C₆₁	—	4	1	no	—
281	C₂×C₄×C₆₁	—	4	1	no	—
282	C₂×C₄×C₆₁	—	4	1	no	—
283	C₂×C₄×C₆₁	—	4	1	no	—
284	C₂×C₄×C₆₁	—	4	1	no	—
285	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
286	C₂×C₄×C₆₁	C₂×Q₁₆	1	2	yes	—
287	C₂×C₄×C₆₁	#135	1	2	yes	—
288	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
293	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
294	C₈×C₆₁	—	2	2	no	—
295	C₈×C₆₁	—	2	2	no	—
296	C₈×C₆₁	—	2	2	no	—
297	C₈×C₆₁	—	4	1	no	—
298	#26965	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
299	C₂²×C₆₁	—	2	2	no	—
300	C₂²×C₆₁	—	2	2	no	—
301	C₂²×C₆₁	—	2	2	no	—
302	C₂²×C₆₁	—	4	1	no	—
303	C₂²×C₆₁	—	4	1	no	—
304	C₂²×C₆₁	—	4	1	no	—
305	C₂²×C₆₁	—	4	1	no	—
306	C₂²×C₆₁	#532	1	1	yes	characteristic
307	C₂²×C₆₁	D₄²	1	1	yes	characteristic
308	C₂²×C₆₁	#546	1	1	yes	characteristic
309	C₂²×C₆₁	C₂²×Q₁₆	1	1	yes	characteristic
310	C₂²×C₆₁	C₂×#135	1	1	yes	characteristic
311	C₂²×C₆₁	#577	1	1	yes	characteristic
312	C₂²×C₆₁	#578	1	1	yes	characteristic
313	C₄×C₆₁	—	2	2	no	—
314	C₄×C₆₁	—	2	2	no	—
315	C₄×C₆₁	—	2	2	no	—
316	C₄×C₆₁	—	4	1	no	—
317	C₄×C₆₁	—	4	2	no	—
318	C₄×C₆₁	—	4	2	no	—
319	C₄×C₆₁	—	4	1	no	—
320	C₄×C₆₁	—	4	2	no	—
321	C₄×C₆₁	—	8	1	no	—
322	C₄×C₆₁	—	8	1	no	—
323	C₄×C₆₁	—	8	1	no	—
324	C₄×C₆₁	—	8	1	no	—
325	C₄×C₆₁	—	8	1	no	—
326	C₄×C₆₁	#525	1	1	yes	characteristic
327	C₄×C₆₁	#540	1	1	yes	characteristic
328	C₄×C₆₁	#546	1	1	yes	characteristic
329	C₄×C₆₁	#553	1	1	yes	characteristic
330	C₂×#467	C₂×C₆₁	1	1	yes	characteristic
331	C₂×C₄×Q₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
332	#2429	C₂×C₆₁	1	1	yes	characteristic
333	#2423	C₂×C₆₁	1	1	yes	characteristic
334	#2083	C₂×C₆₁	1	1	yes	characteristic, complemented
335	#2036	C₂×C₆₁	1	1	yes	characteristic
336	#2016	C₂×C₆₁	1	1	yes	characteristic, complemented
337	#2001	C₂×C₆₁	1	1	yes	characteristic
338	#1956	C₂×C₆₁	1	1	yes	characteristic, complemented
339	#1933	C₂×C₆₁	1	1	yes	characteristic, complemented
340	#1933	C₂×C₆₁	1	1	yes	characteristic, complemented
341	#1892	C₂×C₆₁	1	1	yes	characteristic
342	#1878	C₂×C₆₁	1	1	yes	characteristic, complemented
343	#1863	C₂×C₆₁	1	1	yes	characteristic, complemented
344	C₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
345	C₂×C₆₁	—	4	2	no	—
346	C₂×C₆₁	#2464	1	1	yes	characteristic
347	C₂×C₆₁	#3170	1	1	yes	characteristic
348	C₂×C₆₁	#3178	1	1	yes	characteristic
349	C₂×C₆₁	#3284	1	1	yes	characteristic
350	C₂×C₆₁	D₄×Q₁₆	1	1	yes	characteristic
351	C₂×C₆₁	#3299	1	1	yes	characteristic
352	C₂×C₆₁	#3300	1	1	yes	characteristic
353	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
354	C₂²×Q₁₆	C₂²×C₆₁	1	1	yes	characteristic
355	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
358	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
359	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
360	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
361	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
362	#467	—	2	4	no	—
363	C₄×Q₁₆	—	2	4	no	—
364	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
366	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
367	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
368	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
369	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
370	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
371	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
372	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
373	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
374	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
375	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
376	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
377	#399	—	2	1	no	—
378	#398	—	2	1	no	—
379	#398	—	2	1	no	—
380	#396	—	2	1	no	—
381	#391	C₂²×C₆₁	1	1	yes	characteristic
382	#391	C₂²×C₆₁	1	1	yes	characteristic
383	#389	—	2	1	no	—
384	#389	C₂²×C₆₁	1	1	yes	characteristic
385	#389	C₂²×C₆₁	1	1	yes	characteristic
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#387	—	2	1	no	—
389	#384	C₂²×C₆₁	1	1	yes	characteristic
390	#380	C₂²×C₆₁	1	1	yes	characteristic
391	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
392	#340	C₂²×C₆₁	1	1	yes	characteristic
393	#340	C₂²×C₆₁	1	1	yes	characteristic
394	#340	C₂²×C₆₁	1	1	yes	characteristic
395	#340	C₂²×C₆₁	1	1	yes	characteristic
396	#336	C₂²×C₆₁	1	1	yes	characteristic
397	#336	C₂²×C₆₁	1	1	yes	characteristic
398	C₆₁	#26965	1	1	yes	characteristic, direct product factor, Sylow
399	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
400	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
401	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
402	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
403	C₂×Q₁₆	—	2	2	no	—
404	C₂×Q₁₆	—	2	2	no	—
405	C₂×Q₁₆	—	2	2	no	—
406	C₂×Q₁₆	—	2	2	no	—
407	C₂×Q₁₆	—	2	2	no	—
408	C₂×Q₁₆	—	4	1	no	—
409	C₂²×C₈	—	2	2	no	—
410	C₂²×C₈	—	2	2	no	—
411	C₂²×C₈	—	4	1	no	—
412	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
415	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
416	C₄⋊Q₈	—	2	2	no	—
417	C₄⋊Q₈	—	4	1	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	2	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	4	1	no	—
422	C₂²⋊Q₈	—	4	1	no	—
423	C₂²⋊Q₈	—	4	1	no	—
424	C₄×Q₈	—	2	2	no	—
425	C₄×Q₈	—	2	2	no	—
426	C₄×Q₈	—	4	1	no	—
427	C₄×Q₈	—	4	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	—	2	1	no	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	—	2	1	no	—
437	C₂×C₄⋊C₄	—	2	1	no	—
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
440	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
442	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
443	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
449	C₂×C₂²⋊C₄	D₄×C₆₁	1	1	yes	characteristic
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	—	2	1	no	—
452	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
454	#107	—	2	2	no	—
455	#107	—	2	2	no	—
456	#103	—	2	2	no	—
457	#103	—	2	2	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#103	—	4	1	no	—
461	#103	—	4	1	no	—
462	#103	—	4	1	no	—
463	#103	D₄×C₆₁	1	4	yes	—
464	C₂²⋊C₈	—	2	2	no	—
465	C₄×C₈	—	2	2	no	—
466	C₄×C₈	—	4	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	—	2	1	no	—
474	#95	D₄×C₆₁	1	1	yes	characteristic
475	#95	D₄×C₆₁	1	1	yes	characteristic
476	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	2	1	no	—
483	C₂×Q₈	—	2	1	no	—
484	C₂×Q₈	—	2	1	no	—
485	C₂×Q₈	—	2	1	no	—
486	C₂×Q₈	—	2	1	no	—
487	C₂×Q₈	—	2	1	no	—
488	C₂×Q₈	—	2	1	no	—
489	C₂×Q₈	—	2	1	no	—
490	C₂×Q₈	—	2	1	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
494	C₂×Q₈	#41×C₆₁	1	2	yes	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
514	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
515	Q₁₆	—	2	8	no	—
516	Q₁₆	—	4	4	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	4	4	no	—
527	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
528	C₂×C₈	#41×C₆₁	1	2	yes	—
529	C₂×C₈	#41×C₆₁	1	2	yes	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	4	2	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	—	4	2	no	—
545	C₄⋊C₄	—	4	2	no	—
546	C₄⋊C₄	—	4	2	no	—
547	C₄⋊C₄	—	4	2	no	—
548	C₄⋊C₄	—	8	1	no	—
549	C₄⋊C₄	—	8	1	no	—
550	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	4	2	no	—
553	C₂²⋊C₄	—	4	2	no	—
554	C₂²⋊C₄	—	4	2	no	—
555	C₂²⋊C₄	—	8	1	no	—
556	C₂²⋊C₄	Q₁₆×C₆₁	1	4	yes	complemented
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	2	1	no	—
560	C₄²	—	2	1	no	—
561	C₄²	—	4	2	no	—
562	C₄²	—	4	2	no	—
563	C₂³	—	2	1	no	—
564	C₂³	—	2	1	no	—
565	C₂³	—	2	1	no	—
566	C₂³	—	2	1	no	—
567	C₂³	—	2	1	no	—
568	C₂³	—	2	1	no	—
569	C₂³	C₂×Q₁₆×C₆₁	1	2	yes	—
570	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
571	Q₈	—	2	2	no	—
572	Q₈	—	2	2	no	—
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	1	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	4	1	no	—
578	Q₈	—	4	1	no	—
579	Q₈	—	4	1	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	1	no	—
582	Q₈	—	4	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	1	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
624	C₂×C₄	C₂×Q₁₆×C₆₁	1	2	yes	—
625	C₂×C₄	#135×C₆₁	1	2	yes	—
626	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
627	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
628	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
629	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
630	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
631	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
632	C₈	—	2	2	no	—
633	C₈	—	2	2	no	—
634	C₈	—	2	2	no	—
635	C₈	—	4	1	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	2	2	no	—
639	C₂²	—	4	1	no	—
640	C₂²	—	4	1	no	—
641	C₂²	—	4	1	no	—
642	C₂²	—	4	1	no	—
643	C₂²	C₆₁×#532	1	1	yes	characteristic
644	C₂²	D₄²×C₆₁	1	1	yes	characteristic
645	C₂²	C₆₁×#546	1	1	yes	characteristic
646	C₂²	C₂²×Q₁₆×C₆₁	1	1	yes	characteristic
647	C₂²	C₂×#135×C₆₁	1	1	yes	characteristic
648	C₂²	C₆₁×#577	1	1	yes	characteristic
649	C₂²	C₆₁×#578	1	1	yes	characteristic
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	4	1	no	—
654	C₄	—	4	2	no	—
655	C₄	—	4	2	no	—
656	C₄	—	4	1	no	—
657	C₄	—	4	2	no	—
658	C₄	—	8	1	no	—
659	C₄	—	8	1	no	—
660	C₄	—	8	1	no	—
661	C₄	—	8	1	no	—
662	C₄	—	8	1	no	—
663	C₄	C₆₁×#525	1	1	yes	characteristic
664	C₄	C₆₁×#540	1	1	yes	characteristic
665	C₄	C₆₁×#546	1	1	yes	characteristic
666	C₄	C₆₁×#553	1	1	yes	characteristic
667	C₂	—	4	2	no	—
668	C₂	C₆₁×#2464	1	1	yes	characteristic
669	C₂	C₆₁×#3170	1	1	yes	characteristic
670	C₂	C₆₁×#3178	1	1	yes	characteristic
671	C₂	C₆₁×#3284	1	1	yes	characteristic
672	C₂	D₄×Q₁₆×C₆₁	1	1	yes	characteristic
673	C₂	C₆₁×#3299	1	1	yes	characteristic
674	C₂	C₆₁×#3300	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₁	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂⁴×C₆₁	C₂×D₄
LCS	G ▷ C₂²×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×#2083	C₂	semidirect
7. C₆₁×#2016	C₂	semidirect
9. C₆₁×#1956	C₂	semidirect
10. C₆₁×#1933	C₂	semidirect
11. C₆₁×#1933	C₂	semidirect
13. C₆₁×#1878	C₂	semidirect
14. C₆₁×#1863	C₂	semidirect
218. C₂²⋊C₄×C₆₁	Q₁₆	semidirect
298. #26965	C₆₁	direct (N × H)
331. C₂×C₄×Q₁₆	C₂×C₆₁	semidirect
334. #2083	C₂×C₆₁	semidirect
336. #2016	C₂×C₆₁	semidirect
338. #1956	C₂×C₆₁	semidirect
339. #1933	C₂×C₆₁	semidirect
340. #1933	C₂×C₆₁	semidirect
342. #1878	C₂×C₆₁	semidirect
343. #1863	C₂×C₆₁	semidirect
398. C₆₁	#26965	direct (N × H)
556. C₂²⋊C₄	Q₁₆×C₆₁	semidirect

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
C₆₁×#2429	2
C₆₁×#2423	2
C₆₁×#2083	2
C₆₁×#2036	2
C₆₁×#2016	2
C₆₁×#2001	2
C₆₁×#1956	2
C₆₁×#1933	2
C₆₁×#1892	2
C₆₁×#1878	2
C₆₁×#1863	2
C₈×C₂²⋊C₄×C₆₁	2
#26965	61

Subgroups — C61×#26965 #29530398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#26965 #29530398