Subgroups — C₆₁×#23012 #29526445

Order 15616.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#461	C₂	1	1	yes	maximal, characteristic
2	C₂×C₆₁×#440	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2365	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2349	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#1960	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1949	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1935	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1877	C₂	1	1	yes	maximal, characteristic
12	C₆₁×#1865	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
17	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#461	C₄	1	8	yes	complemented
25	C₆₁×#440	—	2	4	no	—
26	C₄×SD₁₆×C₆₁	—	2	4	no	—
27	C₂×#107×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×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×#102×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
39	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#391	C₂²	1	1	yes	characteristic
42	C₆₁×#391	C₂²	1	1	yes	characteristic
43	C₆₁×#389	—	2	1	no	—
44	C₆₁×#389	C₂²	1	1	yes	characteristic
45	C₆₁×#389	C₂²	1	1	yes	characteristic
46	C₆₁×#387	—	2	1	no	—
47	C₆₁×#387	—	2	1	no	—
48	C₆₁×#385	—	2	1	no	—
49	C₆₁×#385	—	2	1	no	—
50	C₆₁×#382	C₂²	1	1	yes	characteristic
51	C₆₁×#380	—	2	1	no	—
52	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
53	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
55	C₂×#95×C₆₁	—	2	1	no	—
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×#340	C₂²	1	1	yes	characteristic
60	C₆₁×#336	C₂²	1	1	yes	characteristic
61	C₆₁×#336	C₂²	1	1	yes	characteristic
62	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₆₁	—	2	1	no	—
66	C₂³×C₄×C₆₁	—	2	1	no	—
67	C₂³×C₄×C₆₁	—	2	1	no	—
68	C₂×SD₁₆×C₆₁	—	2	2	no	—
69	C₂×SD₁₆×C₆₁	—	2	2	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×SD₁₆×C₆₁	—	2	2	no	—
72	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	—
73	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	—
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	C₂×C₄	1	4	yes	complemented
80	C₄×Q₈×C₆₁	—	2	2	no	—
81	C₄×Q₈×C₆₁	—	2	2	no	—
82	C₄×Q₈×C₆₁	—	4	1	no	—
83	C₄×Q₈×C₆₁	—	4	1	no	—
84	C₄×D₄×C₆₁	—	2	2	no	—
85	C₄×D₄×C₆₁	—	2	2	no	—
86	C₄×D₄×C₆₁	—	2	2	no	—
87	C₄×D₄×C₆₁	—	4	1	no	—
88	C₄×D₄×C₆₁	—	4	1	no	—
89	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
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	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
106	C₂×C₄²×C₆₁	—	2	1	no	—
107	C₂×C₄²×C₆₁	—	2	1	no	—
108	C₂×C₄²×C₆₁	—	2	1	no	—
109	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
112	#107×C₆₁	—	2	2	no	—
113	#106×C₆₁	—	2	2	no	—
114	C₄⋊C₈×C₆₁	C₂×C₄	1	4	yes	complemented
115	#103×C₆₁	—	2	2	no	—
116	#103×C₆₁	—	2	2	no	—
117	#103×C₆₁	—	4	1	no	—
118	#103×C₆₁	—	4	1	no	—
119	#103×C₆₁	C₂×C₄	1	4	yes	complemented
120	#103×C₆₁	C₂×C₄	1	4	yes	complemented
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	D₄	1	4	yes	—
123	#97×C₆₁	—	2	2	no	—
124	#97×C₆₁	—	2	2	no	—
125	C₄×C₈×C₆₁	—	2	2	no	—
126	#95×C₆₁	—	2	1	no	—
127	#95×C₆₁	—	2	1	no	—
128	#95×C₆₁	—	2	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	D₄	1	1	yes	characteristic
136	#95×C₆₁	D₄	1	1	yes	characteristic
137	C₂⁴×C₆₁	—	2	1	no	—
138	C₂×Q₈×C₆₁	—	2	1	no	—
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	C₂²×C₄	1	2	yes	—
149	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
150	C₂×D₄×C₆₁	—	2	1	no	—
151	C₂×D₄×C₆₁	—	2	1	no	—
152	C₂×D₄×C₆₁	—	2	1	no	—
153	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
154	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
155	C₂×D₄×C₆₁	#41	1	2	yes	—
156	C₂²×C₄×C₆₁	—	2	1	no	—
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	4	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	—	4	2	no	—
165	C₂²×C₄×C₆₁	—	4	2	no	—
166	C₂²×C₄×C₆₁	—	4	2	no	—
167	C₂²×C₄×C₆₁	—	4	2	no	—
168	C₂²×C₄×C₆₁	—	8	1	no	—
169	C₂²×C₄×C₆₁	—	8	1	no	—
170	C₂²×C₄×C₆₁	—	8	1	no	—
171	C₂²×C₄×C₆₁	—	8	1	no	—
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	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
179	SD₁₆×C₆₁	—	2	8	no	—
180	SD₁₆×C₆₁	—	2	8	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	—	2	1	no	—
189	C₂×C₈×C₆₁	—	2	1	no	—
190	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
191	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
192	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
193	C₄⋊C₄×C₆₁	—	2	4	no	—
194	C₄⋊C₄×C₆₁	—	2	4	no	—
195	C₄⋊C₄×C₆₁	—	2	2	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	—	2	1	no	—
202	C₄⋊C₄×C₆₁	—	2	1	no	—
203	C₄⋊C₄×C₆₁	—	2	1	no	—
204	C₄⋊C₄×C₆₁	—	4	1	no	—
205	C₄⋊C₄×C₆₁	—	4	2	no	—
206	C₄⋊C₄×C₆₁	—	4	2	no	—
207	C₄⋊C₄×C₆₁	—	8	1	no	—
208	C₄⋊C₄×C₆₁	—	8	1	no	—
209	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
210	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
211	C₂²⋊C₄×C₆₁	—	2	4	no	—
212	C₂²⋊C₄×C₆₁	—	4	2	no	—
213	C₂²⋊C₄×C₆₁	—	4	2	no	—
214	C₄²×C₆₁	—	2	1	no	—
215	C₄²×C₆₁	—	2	1	no	—
216	C₄²×C₆₁	—	2	1	no	—
217	C₄²×C₆₁	—	2	1	no	—
218	C₄²×C₆₁	—	4	2	no	—
219	C₄²×C₆₁	—	4	2	no	—
220	C₄²×C₆₁	—	4	2	no	—
221	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
222	C₄²×C₆₁	#41	1	2	yes	—
223	C₂³×C₆₁	—	2	2	no	—
224	C₂³×C₆₁	—	2	2	no	—
225	C₂³×C₆₁	—	2	2	no	—
226	C₂³×C₆₁	—	4	1	no	—
227	C₂³×C₆₁	—	4	1	no	—
228	C₂³×C₆₁	—	4	1	no	—
229	C₂³×C₆₁	—	4	1	no	—
230	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₆₁	—	2	2	no	—
232	Q₈×C₆₁	—	2	2	no	—
233	Q₈×C₆₁	—	2	2	no	—
234	Q₈×C₆₁	—	2	2	no	—
235	Q₈×C₆₁	—	4	1	no	—
236	Q₈×C₆₁	—	4	1	no	—
237	Q₈×C₆₁	—	4	1	no	—
238	Q₈×C₆₁	—	4	1	no	—
239	D₄×C₆₁	—	2	2	no	—
240	D₄×C₆₁	—	2	2	no	—
241	D₄×C₆₁	—	2	2	no	—
242	D₄×C₆₁	C₄×D₄	1	4	yes	—
243	C₂×C₄×C₆₁	—	2	1	no	—
244	C₂×C₄×C₆₁	—	2	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	2	no	—
250	C₂×C₄×C₆₁	—	2	2	no	—
251	C₂×C₄×C₆₁	—	2	2	no	—
252	C₂×C₄×C₆₁	—	2	1	no	—
253	C₂×C₄×C₆₁	—	2	1	no	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	2	no	—
256	C₂×C₄×C₆₁	—	2	1	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	—	2	1	no	—
261	C₂×C₄×C₆₁	—	2	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	—	8	4	no	—
280	C₂×C₄×C₆₁	—	8	4	no	—
281	C₂×C₄×C₆₁	—	8	4	no	—
282	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
283	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
284	C₂×C₄×C₆₁	#137	1	2	yes	—
285	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
286	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₆₁	H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₄×C₆₁	2₋¹⁺⁴	1	1	yes	characteristic
291	C₈×C₆₁	—	2	2	no	—
292	C₈×C₆₁	—	2	2	no	—
293	C₈×C₆₁	—	2	2	no	—
294	C₈×C₆₁	—	4	1	no	—
295	#23012	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
296	C₂²×C₆₁	—	2	4	no	—
297	C₂²×C₆₁	—	4	2	no	—
298	C₂²×C₆₁	—	4	2	no	—
299	C₂²×C₆₁	—	4	2	no	—
300	C₂²×C₆₁	—	4	2	no	—
301	C₂²×C₆₁	—	4	2	no	—
302	C₂²×C₆₁	—	4	2	no	—
303	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
304	C₂²×C₆₁	D₄²	1	1	yes	characteristic
305	C₂²×C₆₁	#548	1	1	yes	characteristic
306	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
307	C₂²×C₆₁	#575	1	1	yes	characteristic
308	C₂²×C₆₁	#577	1	1	yes	characteristic
309	C₂²×C₆₁	#577	1	1	yes	characteristic
310	C₄×C₆₁	—	2	2	no	—
311	C₄×C₆₁	—	2	2	no	—
312	C₄×C₆₁	—	2	2	no	—
313	C₄×C₆₁	—	4	2	no	—
314	C₄×C₆₁	—	4	2	no	—
315	C₄×C₆₁	—	4	2	no	—
316	C₄×C₆₁	—	4	1	no	—
317	C₄×C₆₁	—	4	1	no	—
318	C₄×C₆₁	—	4	1	no	—
319	C₄×C₆₁	—	4	2	no	—
320	C₄×C₆₁	—	8	1	no	—
321	C₄×C₆₁	—	8	1	no	—
322	C₄×C₆₁	—	8	1	no	—
323	C₄×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
324	C₄×C₆₁	#520	1	1	yes	characteristic
325	C₄×C₆₁	#547	1	1	yes	characteristic
326	C₄×C₆₁	#553	1	1	yes	characteristic
327	C₂×#461	C₂×C₆₁	1	1	yes	characteristic
328	C₂×#440	C₂×C₆₁	1	1	yes	characteristic
329	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic
330	#2365	C₂×C₆₁	1	1	yes	characteristic, complemented
331	#2349	C₂×C₆₁	1	1	yes	characteristic
332	#1960	C₂×C₆₁	1	1	yes	characteristic, complemented
333	#1949	C₂×C₆₁	1	1	yes	characteristic, complemented
334	#1935	C₂×C₆₁	1	1	yes	characteristic, complemented
335	#1933	C₂×C₆₁	1	1	yes	characteristic, complemented
336	#1877	C₂×C₆₁	1	1	yes	characteristic
337	#1877	C₂×C₆₁	1	1	yes	characteristic
338	#1865	C₂×C₆₁	1	1	yes	characteristic, complemented
339	#1863	C₂×C₆₁	1	1	yes	characteristic, complemented
340	#1771	C₂×C₆₁	1	1	yes	characteristic, complemented
341	#1762	C₂×C₆₁	1	1	yes	characteristic
342	C₂×C₆₁	—	4	4	no	—
343	C₂×C₆₁	#2361	1	1	yes	characteristic
344	C₂×C₆₁	C₄×#137	1	1	yes	characteristic
345	C₂×C₆₁	#2949	1	1	yes	characteristic
346	C₂×C₆₁	#3266	1	1	yes	characteristic
347	C₂×C₆₁	#3267	1	1	yes	characteristic
348	C₂×C₆₁	#3372	1	1	yes	characteristic
349	C₂×C₆₁	#3376	1	1	yes	characteristic
350	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
351	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
352	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
353	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
354	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
358	#461	C₄×C₆₁	1	8	yes	complemented
359	#440	—	2	4	no	—
360	C₄×SD₁₆	—	2	4	no	—
361	C₂×#107	C₂²×C₆₁	1	1	yes	characteristic
362	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
363	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
364	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
365	C₂×#103	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×#102	C₂²×C₆₁	1	1	yes	characteristic
371	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
372	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
373	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
374	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
375	#391	C₂²×C₆₁	1	1	yes	characteristic
376	#391	C₂²×C₆₁	1	1	yes	characteristic
377	#389	—	2	1	no	—
378	#389	C₂²×C₆₁	1	1	yes	characteristic
379	#389	C₂²×C₆₁	1	1	yes	characteristic
380	#387	—	2	1	no	—
381	#387	—	2	1	no	—
382	#385	—	2	1	no	—
383	#385	—	2	1	no	—
384	#382	C₂²×C₆₁	1	1	yes	characteristic
385	#380	—	2	1	no	—
386	C₄×C₄⋊C₄	—	2	1	no	—
387	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
388	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
389	C₂×#95	—	2	1	no	—
390	#340	C₂²×C₆₁	1	1	yes	characteristic
391	#340	C₂²×C₆₁	1	1	yes	characteristic
392	#340	C₂²×C₆₁	1	1	yes	characteristic
393	#340	C₂²×C₆₁	1	1	yes	characteristic
394	#336	C₂²×C₆₁	1	1	yes	characteristic
395	#336	C₂²×C₆₁	1	1	yes	characteristic
396	C₆₁	#23012	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
398	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
400	C₂³×C₄	—	2	1	no	—
401	C₂³×C₄	—	2	1	no	—
402	C₂³×C₄	—	2	1	no	—
403	C₂×SD₁₆	—	2	2	no	—
404	C₂×SD₁₆	—	2	2	no	—
405	C₂×SD₁₆	—	2	2	no	—
406	C₂×SD₁₆	—	2	2	no	—
407	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	—
408	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	—
409	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
410	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
411	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
412	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
413	C₄⋊Q₈	—	2	2	no	—
414	C₄⋊Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
415	C₄×Q₈	—	2	2	no	—
416	C₄×Q₈	—	2	2	no	—
417	C₄×Q₈	—	4	1	no	—
418	C₄×Q₈	—	4	1	no	—
419	C₄×D₄	—	2	2	no	—
420	C₄×D₄	—	2	2	no	—
421	C₄×D₄	—	2	2	no	—
422	C₄×D₄	—	4	1	no	—
423	C₄×D₄	—	4	1	no	—
424	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
425	C₂×C₄⋊C₄	—	2	1	no	—
426	C₂×C₄⋊C₄	—	2	1	no	—
427	C₂×C₄⋊C₄	—	2	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	D₄×C₆₁	1	1	yes	characteristic
432	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	—	2	1	no	—
443	C₂×C₄²	—	2	1	no	—
444	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
445	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
446	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
447	#107	—	2	2	no	—
448	#106	—	2	2	no	—
449	C₄⋊C₈	C₂×C₄×C₆₁	1	4	yes	complemented
450	#103	—	2	2	no	—
451	#103	—	2	2	no	—
452	#103	—	4	1	no	—
453	#103	—	4	1	no	—
454	#103	C₂×C₄×C₆₁	1	4	yes	complemented
455	#103	C₂×C₄×C₆₁	1	4	yes	complemented
456	#102	—	2	2	no	—
457	#102	D₄×C₆₁	1	4	yes	—
458	#97	—	2	2	no	—
459	#97	—	2	2	no	—
460	C₄×C₈	—	2	2	no	—
461	#95	—	2	1	no	—
462	#95	—	2	1	no	—
463	#95	—	2	1	no	—
464	#95	—	2	1	no	—
465	#95	—	2	1	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	D₄×C₆₁	1	1	yes	characteristic
471	#95	D₄×C₆₁	1	1	yes	characteristic
472	C₂⁴	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
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	C₂²×C₄×C₆₁	1	2	yes	—
484	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
489	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
490	C₂×D₄	#41×C₆₁	1	2	yes	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	8	1	no	—
504	C₂²×C₄	—	8	1	no	—
505	C₂²×C₄	—	8	1	no	—
506	C₂²×C₄	—	8	1	no	—
507	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
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	C₂⁴×C₆₁	1	1	yes	characteristic
514	SD₁₆	—	2	8	no	—
515	SD₁₆	—	2	8	no	—
516	C₂×C₈	—	2	1	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	C₂²×C₄×C₆₁	1	2	yes	—
526	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
527	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
528	C₄⋊C₄	—	2	4	no	—
529	C₄⋊C₄	—	2	4	no	—
530	C₄⋊C₄	—	2	2	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	1	no	—
540	C₄⋊C₄	—	4	2	no	—
541	C₄⋊C₄	—	4	2	no	—
542	C₄⋊C₄	—	8	1	no	—
543	C₄⋊C₄	—	8	1	no	—
544	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
545	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	4	2	no	—
554	C₄²	—	4	2	no	—
555	C₄²	—	4	2	no	—
556	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
557	C₄²	#41×C₆₁	1	2	yes	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	2	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	2	2	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	4	1	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	D₄	—	2	2	no	—
575	D₄	—	2	2	no	—
576	D₄	—	2	2	no	—
577	D₄	C₄×D₄×C₆₁	1	4	yes	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	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	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	2	no	—
597	C₂×C₄	—	4	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	—	8	4	no	—
615	C₂×C₄	—	8	4	no	—
616	C₂×C₄	—	8	4	no	—
617	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
618	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
619	C₂×C₄	#137×C₆₁	1	2	yes	—
620	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
621	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
622	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
623	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
624	C₂×C₄	H(5,𝔽₂)×C₆₁	1	1	yes	characteristic
625	C₂×C₄	2₋¹⁺⁴×C₆₁	1	1	yes	characteristic
626	C₈	—	2	2	no	—
627	C₈	—	2	2	no	—
628	C₈	—	2	2	no	—
629	C₈	—	4	1	no	—
630	C₂²	—	2	4	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
638	C₂²	D₄²×C₆₁	1	1	yes	characteristic
639	C₂²	C₆₁×#548	1	1	yes	characteristic
640	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
641	C₂²	C₆₁×#575	1	1	yes	characteristic
642	C₂²	C₆₁×#577	1	1	yes	characteristic
643	C₂²	C₆₁×#577	1	1	yes	characteristic
644	C₄	—	2	2	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	4	2	no	—
648	C₄	—	4	2	no	—
649	C₄	—	4	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	2	no	—
654	C₄	—	8	1	no	—
655	C₄	—	8	1	no	—
656	C₄	—	8	1	no	—
657	C₄	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
658	C₄	C₆₁×#520	1	1	yes	characteristic
659	C₄	C₆₁×#547	1	1	yes	characteristic
660	C₄	C₆₁×#553	1	1	yes	characteristic
661	C₂	—	4	4	no	—
662	C₂	C₆₁×#2361	1	1	yes	characteristic
663	C₂	C₄×#137×C₆₁	1	1	yes	characteristic
664	C₂	C₆₁×#2949	1	1	yes	characteristic
665	C₂	C₆₁×#3266	1	1	yes	characteristic
666	C₂	C₆₁×#3267	1	1	yes	characteristic
667	C₂	C₆₁×#3372	1	1	yes	characteristic
668	C₂	C₆₁×#3376	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	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₂×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
4. C₆₁×#2365	C₂	semidirect
6. C₆₁×#1960	C₂	semidirect
7. C₆₁×#1949	C₂	semidirect
8. C₆₁×#1935	C₂	semidirect
9. C₆₁×#1933	C₂	semidirect
12. C₆₁×#1865	C₂	semidirect
13. C₆₁×#1863	C₂	semidirect
14. C₆₁×#1771	C₂	semidirect
24. C₆₁×#461	C₄	semidirect
79. C₄⋊Q₈×C₆₁	C₂×C₄	semidirect
114. C₄⋊C₈×C₆₁	C₂×C₄	semidirect
119. #103×C₆₁	C₂×C₄	semidirect
120. #103×C₆₁	C₂×C₄	semidirect
295. #23012	C₆₁	direct (N × H)
330. #2365	C₂×C₆₁	semidirect
332. #1960	C₂×C₆₁	semidirect
333. #1949	C₂×C₆₁	semidirect
334. #1935	C₂×C₆₁	semidirect
335. #1933	C₂×C₆₁	semidirect
338. #1865	C₂×C₆₁	semidirect
339. #1863	C₂×C₆₁	semidirect
340. #1771	C₂×C₆₁	semidirect
358. #461	C₄×C₆₁	semidirect
396. C₆₁	#23012	direct (N × H)
414. C₄⋊Q₈	C₂×C₄×C₆₁	semidirect
449. C₄⋊C₈	C₂×C₄×C₆₁	semidirect
454. #103	C₂×C₄×C₆₁	semidirect
455. #103	C₂×C₄×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×#461	2
C₂×C₆₁×#440	2
C₂×C₄×SD₁₆×C₆₁	2
C₆₁×#2365	2
C₆₁×#2349	2
C₆₁×#1960	2
C₆₁×#1949	2
C₆₁×#1935	2
C₆₁×#1933	2
C₆₁×#1877	2
C₆₁×#1865	2
C₆₁×#1863	2
C₆₁×#1771	2
C₆₁×#1762	2
#23012	61

Subgroups — C61×#23012 #29526445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#23012 #29526445