Subgroups — C₆₁×#21599 #29525032

Order 15616.

898 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#446	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#97×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1917	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1850	C₂	1	1	yes	maximal, characteristic
9	C₆₁×#1850	C₂	1	1	yes	maximal, characteristic
10	C₆₁×#1797	C₂	1	1	yes	maximal, characteristic
11	C₆₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1770	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1752	C₂	1	1	yes	maximal, characteristic
15	C₈×C₂²⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₂³×C₈×C₆₁	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₆₁	C₄	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#446	—	2	4	no	—
22	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#97×C₆₁	—	2	4	no	—
31	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
32	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
35	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#391	C₄	1	1	yes	characteristic
40	C₆₁×#389	C₄	1	1	yes	characteristic
41	C₆₁×#387	C₄	1	1	yes	characteristic
42	C₆₁×#387	C₄	1	1	yes	characteristic
43	C₆₁×#385	C₄	1	1	yes	characteristic
44	C₆₁×#385	C₄	1	1	yes	characteristic
45	C₆₁×#380	C₄	1	1	yes	characteristic
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	C₄×C₂²⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
51	C₆₁×#336	C₂²	1	1	yes	characteristic
52	C₆₁×#336	C₂²	1	1	yes	characteristic
53	C₆₁×#336	C₂²	1	1	yes	characteristic
54	C₆₁×#336	C₂²	1	1	yes	characteristic
55	C₆₁×#336	C₂²	1	1	yes	characteristic
56	C₆₁×#336	C₂²	1	1	yes	characteristic
57	C₆₁×#336	C₂²	1	1	yes	characteristic
58	C₆₁×#336	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	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₆₁	—	2	2	no	—
66	C₂²×C₈×C₆₁	—	2	2	no	—
67	C₂²×C₈×C₆₁	—	2	2	no	—
68	C₂²×C₈×C₆₁	—	2	2	no	—
69	C₂²×C₈×C₆₁	—	2	2	no	—
70	C₂²×C₈×C₆₁	Q₈	1	4	yes	complemented
71	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
79	C₂²⋊Q₈×C₆₁	—	2	4	no	—
80	C₄×Q₈×C₆₁	—	2	2	no	—
81	C₄×Q₈×C₆₁	—	2	2	no	—
82	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
93	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄²×C₆₁	—	2	2	no	—
96	C₂×C₄²×C₆₁	—	2	2	no	—
97	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₆₁	—	2	2	no	—
106	C₄⋊C₈×C₆₁	—	2	2	no	—
107	C₄⋊C₈×C₆₁	—	2	2	no	—
108	C₄⋊C₈×C₆₁	—	2	2	no	—
109	C₄⋊C₈×C₆₁	—	2	2	no	—
110	C₄⋊C₈×C₆₁	—	2	2	no	—
111	C₂²⋊C₈×C₆₁	—	2	2	no	—
112	C₂²⋊C₈×C₆₁	—	2	2	no	—
113	#97×C₆₁	—	2	2	no	—
114	#97×C₆₁	—	2	2	no	—
115	#97×C₆₁	—	2	2	no	—
116	#97×C₆₁	—	2	2	no	—
117	#97×C₆₁	—	2	2	no	—
118	#97×C₆₁	D₄	1	4	yes	—
119	C₄×C₈×C₆₁	—	2	2	no	—
120	C₄×C₈×C₆₁	—	2	2	no	—
121	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
122	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
123	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
124	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
125	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
126	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
127	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
128	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
129	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
130	#95×C₆₁	C₂×C₄	1	1	yes	characteristic
131	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
132	C₂×Q₈×C₆₁	—	2	2	no	—
133	C₂×Q₈×C₆₁	—	2	2	no	—
134	C₂×Q₈×C₆₁	—	4	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	2	no	—
140	C₂²×C₄×C₆₁	—	2	2	no	—
141	C₂²×C₄×C₆₁	—	2	2	no	—
142	C₂²×C₄×C₆₁	—	2	2	no	—
143	C₂²×C₄×C₆₁	—	4	1	no	—
144	C₂²×C₄×C₆₁	—	4	1	no	—
145	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₆₁	C₂×Q₈	1	2	yes	—
159	C₂²×C₄×C₆₁	#41	1	2	yes	—
160	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
161	C₂×C₈×C₆₁	—	2	8	no	—
162	C₂×C₈×C₆₁	—	2	1	no	—
163	C₂×C₈×C₆₁	—	2	1	no	—
164	C₂×C₈×C₆₁	—	2	1	no	—
165	C₂×C₈×C₆₁	—	2	1	no	—
166	C₂×C₈×C₆₁	—	2	1	no	—
167	C₂×C₈×C₆₁	—	2	1	no	—
168	C₂×C₈×C₆₁	—	2	8	no	—
169	C₂×C₈×C₆₁	—	2	1	no	—
170	C₂×C₈×C₆₁	—	2	1	no	—
171	C₂×C₈×C₆₁	—	2	1	no	—
172	C₂×C₈×C₆₁	—	2	1	no	—
173	C₂×C₈×C₆₁	—	2	1	no	—
174	C₂×C₈×C₆₁	—	2	1	no	—
175	C₂×C₈×C₆₁	—	2	1	no	—
176	C₂×C₈×C₆₁	—	2	1	no	—
177	C₂×C₈×C₆₁	—	2	1	no	—
178	C₂×C₈×C₆₁	—	2	1	no	—
179	C₂×C₈×C₆₁	—	2	1	no	—
180	C₂×C₈×C₆₁	—	2	1	no	—
181	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
182	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
183	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
184	C₂×C₈×C₆₁	C₂×Q₈	1	2	yes	—
185	C₂×C₈×C₆₁	#41	1	2	yes	—
186	C₂×C₈×C₆₁	#41	1	2	yes	—
187	C₄⋊C₄×C₆₁	—	2	2	no	—
188	C₄⋊C₄×C₆₁	—	2	2	no	—
189	C₄⋊C₄×C₆₁	—	2	2	no	—
190	C₄⋊C₄×C₆₁	—	2	2	no	—
191	C₄⋊C₄×C₆₁	—	2	2	no	—
192	C₄⋊C₄×C₆₁	—	2	2	no	—
193	C₄⋊C₄×C₆₁	—	4	1	no	—
194	C₄⋊C₄×C₆₁	—	4	1	no	—
195	C₄⋊C₄×C₆₁	—	4	1	no	—
196	C₂²⋊C₄×C₆₁	—	2	2	no	—
197	C₂²⋊C₄×C₆₁	—	2	2	no	—
198	C₂²⋊C₄×C₆₁	—	2	2	no	—
199	C₂²⋊C₄×C₆₁	M₁₆	1	4	yes	—
200	C₄²×C₆₁	—	2	2	no	—
201	C₄²×C₆₁	—	2	2	no	—
202	C₄²×C₆₁	—	2	1	no	—
203	C₄²×C₆₁	—	2	1	no	—
204	C₄²×C₆₁	—	2	1	no	—
205	C₄²×C₆₁	—	2	1	no	—
206	C₄²×C₆₁	—	2	1	no	—
207	C₄²×C₆₁	—	2	1	no	—
208	C₄²×C₆₁	—	2	1	no	—
209	C₄²×C₆₁	—	2	1	no	—
210	C₄²×C₆₁	—	2	1	no	—
211	C₄²×C₆₁	—	2	1	no	—
212	C₄²×C₆₁	C₂×D₄	1	2	yes	—
213	C₄²×C₆₁	#41	1	2	yes	—
214	C₂³×C₆₁	—	2	1	no	—
215	C₂³×C₆₁	—	2	1	no	—
216	C₂³×C₆₁	—	2	1	no	—
217	C₂³×C₆₁	—	2	1	no	—
218	C₂³×C₆₁	C₄×Q₈	1	2	yes	—
219	C₂³×C₆₁	C₂×M₁₆	1	2	yes	—
220	C₂³×C₆₁	#131	1	2	yes	—
221	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
222	Q₈×C₆₁	—	4	4	no	—
223	C₂×C₄×C₆₁	—	2	1	no	—
224	C₂×C₄×C₆₁	—	2	1	no	—
225	C₂×C₄×C₆₁	—	2	1	no	—
226	C₂×C₄×C₆₁	—	2	1	no	—
227	C₂×C₄×C₆₁	—	2	1	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	—	2	2	no	—
234	C₂×C₄×C₆₁	—	2	2	no	—
235	C₂×C₄×C₆₁	—	2	2	no	—
236	C₂×C₄×C₆₁	—	2	2	no	—
237	C₂×C₄×C₆₁	—	2	1	no	—
238	C₂×C₄×C₆₁	—	2	1	no	—
239	C₂×C₄×C₆₁	—	2	1	no	—
240	C₂×C₄×C₆₁	—	2	1	no	—
241	C₂×C₄×C₆₁	—	2	1	no	—
242	C₂×C₄×C₆₁	—	2	1	no	—
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	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	1	no	—
254	C₂×C₄×C₆₁	—	2	1	no	—
255	C₂×C₄×C₆₁	—	2	1	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	—	4	4	no	—
262	C₂×C₄×C₆₁	—	4	4	no	—
263	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
264	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
265	C₂×C₄×C₆₁	C₄×Q₈	1	2	yes	—
266	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
267	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
268	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₆₁	C₂²×Q₈	1	1	yes	characteristic
270	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
273	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
274	C₈×C₆₁	—	2	2	no	—
275	C₈×C₆₁	—	2	2	no	—
276	C₈×C₆₁	—	2	2	no	—
277	C₈×C₆₁	—	4	1	no	—
278	C₈×C₆₁	—	4	1	no	—
279	C₈×C₆₁	—	4	1	no	—
280	C₈×C₆₁	—	4	1	no	—
281	C₈×C₆₁	C₂²⋊Q₈	1	4	yes	complemented
282	#21599	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
283	C₂²×C₆₁	—	2	2	no	—
284	C₂²×C₆₁	—	2	2	no	—
285	C₂²×C₆₁	—	2	2	no	—
286	C₂²×C₆₁	—	2	2	no	—
287	C₂²×C₆₁	—	2	2	no	—
288	C₂²×C₆₁	—	2	2	no	—
289	C₂²×C₆₁	#446	1	4	yes	complemented
290	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₆₁	C₂×C₄×Q₈	1	1	yes	characteristic
292	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
293	C₂²×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
294	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
295	C₂²×C₆₁	#568	1	1	yes	characteristic
296	C₂²×C₆₁	#568	1	1	yes	characteristic
297	C₄×C₆₁	—	2	2	no	—
298	C₄×C₆₁	—	2	2	no	—
299	C₄×C₆₁	—	2	2	no	—
300	C₄×C₆₁	—	2	2	no	—
301	C₄×C₆₁	—	2	2	no	—
302	C₄×C₆₁	—	4	1	no	—
303	C₄×C₆₁	—	4	1	no	—
304	C₄×C₆₁	—	4	1	no	—
305	C₄×C₆₁	—	4	1	no	—
306	C₄×C₆₁	—	4	1	no	—
307	C₄×C₆₁	—	4	1	no	—
308	C₄×C₆₁	—	4	1	no	—
309	C₄×C₆₁	—	4	1	no	—
310	C₄×C₆₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
311	C₄×C₆₁	#525	1	1	yes	characteristic
312	C₄×C₆₁	#529	1	1	yes	characteristic
313	C₄×C₆₁	#533	1	1	yes	characteristic
314	C₂×#446	C₂×C₆₁	1	1	yes	characteristic, complemented
315	C₂²×#97	C₂×C₆₁	1	1	yes	characteristic
316	C₄×C₂²⋊Q₈	C₂×C₆₁	1	1	yes	characteristic
317	#1985	C₂×C₆₁	1	1	yes	characteristic, complemented
318	#1940	C₂×C₆₁	1	1	yes	characteristic, complemented
319	#1917	C₂×C₆₁	1	1	yes	characteristic, complemented
320	#1917	C₂×C₆₁	1	1	yes	characteristic, complemented
321	#1850	C₂×C₆₁	1	1	yes	characteristic
322	#1850	C₂×C₆₁	1	1	yes	characteristic
323	#1797	C₂×C₆₁	1	1	yes	characteristic
324	#1771	C₂×C₆₁	1	1	yes	characteristic, complemented
325	#1771	C₂×C₆₁	1	1	yes	characteristic, complemented
326	#1770	C₂×C₆₁	1	1	yes	characteristic, complemented
327	#1752	C₂×C₆₁	1	1	yes	characteristic
328	C₈×C₂²⋊C₄	C₂×C₆₁	1	1	yes	characteristic
329	C₂×C₆₁	—	2	4	no	—
330	C₂×C₆₁	C₄×C₂²⋊Q₈	1	1	yes	characteristic
331	C₂×C₆₁	#2933	1	1	yes	characteristic
332	C₂×C₆₁	D₄×M₁₆	1	1	yes	characteristic
333	C₂×C₆₁	C₂×#446	1	1	yes	characteristic
334	C₂×C₆₁	#2961	1	1	yes	characteristic
335	C₂×C₆₁	#2968	1	1	yes	characteristic
336	C₂×C₆₁	#2970	1	1	yes	characteristic
337	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
338	C₂³×C₈	C₂²×C₆₁	1	1	yes	characteristic
339	C₂×C₂²⋊Q₈	C₄×C₆₁	1	1	yes	characteristic
340	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
341	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
342	#446	—	2	4	no	—
343	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
344	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
345	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
346	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
347	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
349	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
350	C₂×C₂²⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
351	C₂×#97	—	2	4	no	—
352	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
353	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
354	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
355	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
356	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
357	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
358	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
359	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
360	#391	C₄×C₆₁	1	1	yes	characteristic
361	#389	C₄×C₆₁	1	1	yes	characteristic
362	#387	C₄×C₆₁	1	1	yes	characteristic
363	#387	C₄×C₆₁	1	1	yes	characteristic
364	#385	C₄×C₆₁	1	1	yes	characteristic
365	#385	C₄×C₆₁	1	1	yes	characteristic
366	#380	C₄×C₆₁	1	1	yes	characteristic
367	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
368	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
369	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
370	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
371	C₄×C₂²⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
372	#336	C₂²×C₆₁	1	1	yes	characteristic
373	#336	C₂²×C₆₁	1	1	yes	characteristic
374	#336	C₂²×C₆₁	1	1	yes	characteristic
375	#336	C₂²×C₆₁	1	1	yes	characteristic
376	#336	C₂²×C₆₁	1	1	yes	characteristic
377	#336	C₂²×C₆₁	1	1	yes	characteristic
378	#336	C₂²×C₆₁	1	1	yes	characteristic
379	#336	C₂²×C₆₁	1	1	yes	characteristic
380	#336	C₂²×C₆₁	1	1	yes	characteristic
381	#336	C₂²×C₆₁	1	1	yes	characteristic
382	C₆₁	#21599	1	1	yes	characteristic, direct product factor, Sylow
383	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
384	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
385	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
387	C₂²×C₈	—	2	2	no	—
388	C₂²×C₈	—	2	2	no	—
389	C₂²×C₈	—	2	2	no	—
390	C₂²×C₈	—	2	2	no	—
391	C₂²×C₈	—	2	2	no	—
392	C₂²×C₈	Q₈×C₆₁	1	4	yes	complemented
393	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
394	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
395	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
396	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
401	C₂²⋊Q₈	—	2	4	no	—
402	C₄×Q₈	—	2	2	no	—
403	C₄×Q₈	—	2	2	no	—
404	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
414	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	2	2	no	—
419	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
420	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
421	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
422	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
425	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
427	C₄⋊C₈	—	2	2	no	—
428	C₄⋊C₈	—	2	2	no	—
429	C₄⋊C₈	—	2	2	no	—
430	C₄⋊C₈	—	2	2	no	—
431	C₄⋊C₈	—	2	2	no	—
432	C₄⋊C₈	—	2	2	no	—
433	C₂²⋊C₈	—	2	2	no	—
434	C₂²⋊C₈	—	2	2	no	—
435	#97	—	2	2	no	—
436	#97	—	2	2	no	—
437	#97	—	2	2	no	—
438	#97	—	2	2	no	—
439	#97	—	2	2	no	—
440	#97	D₄×C₆₁	1	4	yes	—
441	C₄×C₈	—	2	2	no	—
442	C₄×C₈	—	2	2	no	—
443	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
444	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
445	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
446	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
447	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
448	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
449	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
450	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
451	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
452	#95	C₂×C₄×C₆₁	1	1	yes	characteristic
453	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
454	C₂×Q₈	—	2	2	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	4	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	2	2	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
469	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
471	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
472	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
473	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
474	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
477	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
479	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
480	C₂²×C₄	C₂×Q₈×C₆₁	1	2	yes	—
481	C₂²×C₄	#41×C₆₁	1	2	yes	—
482	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
483	C₂×C₈	—	2	8	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	8	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
504	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
505	C₂×C₈	C₂×Q₈×C₆₁	1	2	yes	—
506	C₂×C₈	C₂×Q₈×C₆₁	1	2	yes	—
507	C₂×C₈	#41×C₆₁	1	2	yes	—
508	C₂×C₈	#41×C₆₁	1	2	yes	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	4	1	no	—
516	C₄⋊C₄	—	4	1	no	—
517	C₄⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	M₁₆×C₆₁	1	4	yes	—
522	C₄²	—	2	2	no	—
523	C₄²	—	2	2	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	1	no	—
529	C₄²	—	2	1	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	C₂×D₄×C₆₁	1	2	yes	—
535	C₄²	#41×C₆₁	1	2	yes	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	C₄×Q₈×C₆₁	1	2	yes	—
541	C₂³	C₂×M₁₆×C₆₁	1	2	yes	—
542	C₂³	#131×C₆₁	1	2	yes	—
543	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
544	Q₈	—	4	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
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	—	4	4	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
586	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
587	C₂×C₄	C₄×Q₈×C₆₁	1	2	yes	—
588	C₂×C₄	C₂×M₁₆×C₆₁	1	2	yes	—
589	C₂×C₄	C₂×M₁₆×C₆₁	1	2	yes	—
590	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
591	C₂×C₄	C₂²×Q₈×C₆₁	1	1	yes	characteristic
592	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
593	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
594	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
595	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	—	2	2	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₈	C₂²⋊Q₈×C₆₁	1	4	yes	complemented
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	C₆₁×#446	1	4	yes	complemented
611	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
612	C₂²	C₂×C₄×Q₈×C₆₁	1	1	yes	characteristic
613	C₂²	C₄×#41×C₆₁	1	1	yes	characteristic
614	C₂²	C₂²×M₁₆×C₆₁	1	1	yes	characteristic
615	C₂²	C₂×#131×C₆₁	1	1	yes	characteristic
616	C₂²	C₆₁×#568	1	1	yes	characteristic
617	C₂²	C₆₁×#568	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	C₂×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
632	C₄	C₆₁×#525	1	1	yes	characteristic
633	C₄	C₆₁×#529	1	1	yes	characteristic
634	C₄	C₆₁×#533	1	1	yes	characteristic
635	C₂	—	2	4	no	—
636	C₂	C₄×C₂²⋊Q₈×C₆₁	1	1	yes	characteristic
637	C₂	C₆₁×#2933	1	1	yes	characteristic
638	C₂	D₄×M₁₆×C₆₁	1	1	yes	characteristic
639	C₂	C₂×C₆₁×#446	1	1	yes	characteristic
640	C₂	C₆₁×#2961	1	1	yes	characteristic
641	C₂	C₆₁×#2968	1	1	yes	characteristic
642	C₂	C₆₁×#2970	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂⁴
commutator	C₂³	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂³×C₄
prime radical	C₂⁴×C₆₁	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₆₁×#446	C₂	semidirect
4. C₆₁×#1985	C₂	semidirect
5. C₆₁×#1940	C₂	semidirect
6. C₆₁×#1917	C₂	semidirect
7. C₆₁×#1917	C₂	semidirect
11. C₆₁×#1771	C₂	semidirect
12. C₆₁×#1771	C₂	semidirect
13. C₆₁×#1770	C₂	semidirect
70. C₂²×C₈×C₆₁	Q₈	semidirect
281. C₈×C₆₁	C₂²⋊Q₈	semidirect
282. #21599	C₆₁	direct (N × H)
289. C₂²×C₆₁	#446	semidirect
314. C₂×#446	C₂×C₆₁	semidirect
317. #1985	C₂×C₆₁	semidirect
318. #1940	C₂×C₆₁	semidirect
319. #1917	C₂×C₆₁	semidirect
320. #1917	C₂×C₆₁	semidirect
324. #1771	C₂×C₆₁	semidirect
325. #1771	C₂×C₆₁	semidirect
326. #1770	C₂×C₆₁	semidirect
382. C₆₁	#21599	direct (N × H)
392. C₂²×C₈	Q₈×C₆₁	semidirect
603. C₈	C₂²⋊Q₈×C₆₁	semidirect
610. C₂²	C₆₁×#446	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#446	2
C₂²×#97×C₆₁	2
C₄×C₂²⋊Q₈×C₆₁	2
C₆₁×#1985	2
C₆₁×#1940	2
C₆₁×#1917	2
C₆₁×#1850	2
C₆₁×#1797	2
C₆₁×#1771	2
C₆₁×#1770	2
C₆₁×#1752	2
C₈×C₂²⋊C₄×C₆₁	2
#21599	61

Subgroups — C61×#21599 #29525032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21599 #29525032