Subgroups — C₆₁×#21488 #29524921

Order 15616.

1090 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#436	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#121×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1924	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1870	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1797	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₄⋊C₄×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1753	C₂	1	2	yes	maximal, complemented
12	C₂²×M₁₆×C₆₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×#121×C₆₁	C₄	1	1	yes	characteristic
16	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
19	C₆₁×#436	—	2	8	no	—
20	C₆₁×#436	—	2	4	no	—
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	2	yes	—
24	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₆₁	C₂²	1	2	yes	—
28	C₄×M₁₆×C₆₁	—	2	4	no	—
29	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
30	C₂×#97×C₆₁	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₁	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₆₁×#390	C₄	1	1	yes	characteristic
35	C₆₁×#389	C₄	1	1	yes	characteristic
36	C₆₁×#388	C₄	1	2	yes	—
37	C₆₁×#386	C₄	1	2	yes	—
38	C₆₁×#380	C₄	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₆₁	C₂²	1	2	yes	—
41	C₆₁×#336	C₂²	1	2	yes	—
42	C₆₁×#336	C₂²	1	2	yes	—
43	C₆₁×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
45	C₂²×D₄×C₆₁	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	C₂³	1	2	yes	—
49	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₆₁	—	2	2	no	—
51	C₂×M₁₆×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	—	2	2	no	—
53	C₂×M₁₆×C₆₁	—	2	4	no	—
54	C₂×M₁₆×C₆₁	—	2	4	no	—
55	C₂×M₁₆×C₆₁	—	2	2	no	—
56	C₂×M₁₆×C₆₁	—	2	2	no	—
57	C₂×M₁₆×C₆₁	—	2	4	no	—
58	C₂×M₁₆×C₆₁	D₄	1	4	yes	complemented
59	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
60	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
61	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
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	#121×C₆₁	—	2	4	no	—
66	C₄×D₄×C₆₁	—	2	4	no	—
67	C₄×D₄×C₆₁	—	2	4	no	—
68	C₄×D₄×C₆₁	—	2	2	no	—
69	C₄×D₄×C₆₁	—	2	2	no	—
70	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
77	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
78	C₂×C₂²⋊C₄×C₆₁	C₂×C₄	1	2	yes	—
79	C₂×C₄²×C₆₁	—	2	2	no	—
80	C₂×C₄²×C₆₁	—	2	2	no	—
81	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
85	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₆₁	—	2	4	no	—
87	C₄⋊C₈×C₆₁	—	2	2	no	—
88	C₄⋊C₈×C₆₁	—	2	2	no	—
89	C₂²⋊C₈×C₆₁	—	2	4	no	—
90	C₂²⋊C₈×C₆₁	—	2	4	no	—
91	C₂²⋊C₈×C₆₁	—	2	4	no	—
92	C₂²⋊C₈×C₆₁	—	2	4	no	—
93	#97×C₆₁	—	2	2	no	—
94	#97×C₆₁	—	2	2	no	—
95	C₄×C₈×C₆₁	—	2	4	no	—
96	C₄×C₈×C₆₁	—	2	2	no	—
97	C₄×C₈×C₆₁	D₄	1	4	yes	complemented
98	#95×C₆₁	C₂×C₄	1	2	yes	—
99	#95×C₆₁	C₂×C₄	1	2	yes	—
100	#95×C₆₁	C₂×C₄	1	2	yes	—
101	C₂⁴×C₆₁	C₂²×C₄	1	2	yes	—
102	C₂⁴×C₆₁	C₂²×C₄	1	1	yes	characteristic
103	C₂×D₄×C₆₁	—	2	4	no	—
104	C₂×D₄×C₆₁	—	2	2	no	—
105	C₂×D₄×C₆₁	—	2	4	no	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	—	2	2	no	—
108	C₂×D₄×C₆₁	—	4	2	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	2	1	no	—
113	C₂²×C₄×C₆₁	—	2	2	no	—
114	C₂²×C₄×C₆₁	—	2	2	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	2	2	no	—
118	C₂²×C₄×C₆₁	—	2	2	no	—
119	C₂²×C₄×C₆₁	—	2	2	no	—
120	C₂²×C₄×C₆₁	—	2	2	no	—
121	C₂²×C₄×C₆₁	—	2	2	no	—
122	C₂²×C₄×C₆₁	—	2	2	no	—
123	C₂²×C₄×C₆₁	—	4	1	no	—
124	C₂²×C₄×C₆₁	—	4	1	no	—
125	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₆₁	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₆₁	#41	1	2	yes	—
135	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
136	M₁₆×C₆₁	—	2	8	no	—
137	M₁₆×C₆₁	—	2	8	no	—
138	M₁₆×C₆₁	—	4	8	no	—
139	C₂×C₈×C₆₁	—	2	1	no	—
140	C₂×C₈×C₆₁	—	2	1	no	—
141	C₂×C₈×C₆₁	—	2	1	no	—
142	C₂×C₈×C₆₁	—	2	1	no	—
143	C₂×C₈×C₆₁	—	2	1	no	—
144	C₂×C₈×C₆₁	—	2	1	no	—
145	C₂×C₈×C₆₁	—	2	2	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	—	2	2	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₂×C₈×C₆₁	—	2	2	no	—
150	C₂×C₈×C₆₁	—	2	2	no	—
151	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₆₁	#41	1	2	yes	—
156	C₂×C₈×C₆₁	#41	1	2	yes	—
157	C₄⋊C₄×C₆₁	—	2	4	no	—
158	C₄⋊C₄×C₆₁	—	2	2	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	M₁₆	1	4	yes	complemented
161	C₂²⋊C₄×C₆₁	—	2	4	no	—
162	C₂²⋊C₄×C₆₁	—	2	4	no	—
163	C₂²⋊C₄×C₆₁	—	2	4	no	—
164	C₂²⋊C₄×C₆₁	—	2	4	no	—
165	C₂²⋊C₄×C₆₁	—	4	2	no	—
166	C₄²×C₆₁	—	2	2	no	—
167	C₄²×C₆₁	—	2	2	no	—
168	C₄²×C₆₁	—	2	2	no	—
169	C₄²×C₆₁	—	2	1	no	—
170	C₄²×C₆₁	—	2	1	no	—
171	C₄²×C₆₁	—	2	2	no	—
172	C₄²×C₆₁	C₂×D₄	1	2	yes	—
173	C₄²×C₆₁	#41	1	2	yes	—
174	C₂³×C₆₁	—	2	1	no	—
175	C₂³×C₆₁	—	2	1	no	—
176	C₂³×C₆₁	—	2	1	no	—
177	C₂³×C₆₁	—	2	1	no	—
178	C₂³×C₆₁	—	2	1	no	—
179	C₂³×C₆₁	—	2	1	no	—
180	C₂³×C₆₁	—	2	2	no	—
181	C₂³×C₆₁	—	2	2	no	—
182	C₂³×C₆₁	—	2	2	no	—
183	C₂³×C₆₁	—	2	2	no	—
184	C₂³×C₆₁	—	2	2	no	—
185	C₂³×C₆₁	—	2	2	no	—
186	C₂³×C₆₁	—	2	2	no	—
187	C₂³×C₆₁	C₄×D₄	1	2	yes	—
188	C₂³×C₆₁	C₂³×C₄	1	1	yes	characteristic
189	D₄×C₆₁	—	4	8	no	—
190	D₄×C₆₁	—	4	4	no	—
191	C₂×C₄×C₆₁	—	2	1	no	—
192	C₂×C₄×C₆₁	—	2	2	no	—
193	C₂×C₄×C₆₁	—	2	1	no	—
194	C₂×C₄×C₆₁	—	2	1	no	—
195	C₂×C₄×C₆₁	—	2	1	no	—
196	C₂×C₄×C₆₁	—	2	2	no	—
197	C₂×C₄×C₆₁	—	2	2	no	—
198	C₂×C₄×C₆₁	—	2	2	no	—
199	C₂×C₄×C₆₁	—	2	2	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	1	no	—
202	C₂×C₄×C₆₁	—	2	1	no	—
203	C₂×C₄×C₆₁	—	2	2	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	2	no	—
206	C₂×C₄×C₆₁	—	2	2	no	—
207	C₂×C₄×C₆₁	—	2	1	no	—
208	C₂×C₄×C₆₁	—	2	2	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	—	4	4	no	—
214	C₂×C₄×C₆₁	—	4	2	no	—
215	C₂×C₄×C₆₁	—	4	2	no	—
216	C₂×C₄×C₆₁	—	4	2	no	—
217	C₂×C₄×C₆₁	—	4	2	no	—
218	C₂×C₄×C₆₁	—	4	4	no	—
219	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
220	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
221	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
222	C₂×C₄×C₆₁	C₂×M₁₆	1	4	yes	—
223	C₂×C₄×C₆₁	C₂×M₁₆	1	2	yes	—
224	C₂×C₄×C₆₁	#131	1	2	yes	—
225	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
231	C₈×C₆₁	—	2	2	no	—
232	C₈×C₆₁	—	2	2	no	—
233	C₈×C₆₁	—	2	2	no	—
234	C₈×C₆₁	—	4	2	no	—
235	C₈×C₆₁	—	4	2	no	—
236	C₈×C₆₁	#121	1	4	yes	complemented
237	#21488	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂²×C₆₁	—	2	2	no	—
239	C₂²×C₆₁	—	2	2	no	—
240	C₂²×C₆₁	—	2	2	no	—
241	C₂²×C₆₁	—	4	1	no	—
242	C₂²×C₆₁	—	4	1	no	—
243	C₂²×C₆₁	—	4	1	no	—
244	C₂²×C₆₁	—	4	1	no	—
245	C₂²×C₆₁	—	4	2	no	—
246	C₂²×C₆₁	—	4	2	no	—
247	C₂²×C₆₁	—	4	2	no	—
248	C₂²×C₆₁	—	4	2	no	—
249	C₂²×C₆₁	—	4	2	no	—
250	C₂²×C₆₁	—	4	2	no	—
251	C₂²×C₆₁	—	4	2	no	—
252	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
254	C₂²×C₆₁	C₄×#41	1	1	yes	characteristic
255	C₂²×C₆₁	C₂²×M₁₆	1	1	yes	characteristic
256	C₂²×C₆₁	C₂×#131	1	1	yes	characteristic
257	C₂²×C₆₁	#568	1	1	yes	characteristic
258	C₂²×C₆₁	#568	1	1	yes	characteristic
259	C₄×C₆₁	—	2	2	no	—
260	C₄×C₆₁	—	2	4	no	—
261	C₄×C₆₁	—	2	2	no	—
262	C₄×C₆₁	—	4	1	no	—
263	C₄×C₆₁	—	4	1	no	—
264	C₄×C₆₁	—	4	2	no	—
265	C₄×C₆₁	—	4	2	no	—
266	C₄×C₆₁	#436	1	4	yes	complemented
267	C₄×C₆₁	C₂×#121	1	1	yes	characteristic
268	C₄×C₆₁	#525	1	1	yes	characteristic
269	C₄×C₆₁	#529	1	1	yes	characteristic
270	C₄×C₆₁	#532	1	1	yes	characteristic
271	C₂×#436	C₂×C₆₁	1	2	yes	complemented
272	C₂×#436	C₂×C₆₁	1	1	yes	characteristic, complemented
273	C₂×C₄×M₁₆	C₂×C₆₁	1	1	yes	characteristic, complemented
274	C₄×#121	C₂×C₆₁	1	1	yes	characteristic
275	#1954	C₂×C₆₁	1	1	yes	characteristic, complemented
276	#1939	C₂×C₆₁	1	1	yes	characteristic, complemented
277	#1924	C₂×C₆₁	1	2	yes	complemented
278	#1870	C₂×C₆₁	1	2	yes	complemented
279	#1797	C₂×C₆₁	1	1	yes	characteristic, complemented
280	C₈×C₄⋊C₄	C₂×C₆₁	1	1	yes	characteristic, complemented
281	#1753	C₂×C₆₁	1	2	yes	complemented
282	C₂×C₆₁	—	4	2	no	—
283	C₂×C₆₁	—	8	2	no	—
284	C₂×C₆₁	C₄×#121	1	1	yes	characteristic
285	C₂×C₆₁	C₂×#436	1	1	yes	characteristic
286	C₂×C₆₁	#2930	1	1	yes	characteristic
287	C₂×C₆₁	D₄×M₁₆	1	1	yes	characteristic
288	C₂×C₆₁	#2935	1	1	yes	characteristic
289	C₂×C₆₁	#2969	1	1	yes	characteristic
290	C₂×C₆₁	#2971	1	1	yes	characteristic
291	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
292	C₂²×M₁₆	C₂²×C₆₁	1	2	yes	—
293	C₂²×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
294	C₂×#121	C₄×C₆₁	1	1	yes	characteristic
295	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
296	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
297	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
298	#436	—	2	8	no	—
299	#436	—	2	4	no	—
300	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
301	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
304	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
305	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
306	C₂×C₂²⋊C₈	C₂²×C₆₁	1	2	yes	—
307	C₄×M₁₆	—	2	4	no	—
308	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
309	C₂×#97	C₂²×C₆₁	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂²×C₆₁	1	2	yes	—
312	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
313	#390	C₄×C₆₁	1	1	yes	characteristic
314	#389	C₄×C₆₁	1	1	yes	characteristic
315	#388	C₄×C₆₁	1	2	yes	—
316	#386	C₄×C₆₁	1	2	yes	—
317	#380	C₄×C₆₁	1	1	yes	characteristic
318	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
319	C₄×C₂²⋊C₄	C₂²×C₆₁	1	2	yes	—
320	#336	C₂²×C₆₁	1	2	yes	—
321	#336	C₂²×C₆₁	1	2	yes	—
322	#336	C₂²×C₆₁	1	2	yes	—
323	C₆₁	#21488	1	1	yes	characteristic, direct product factor, Sylow
324	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
325	C₂²×D₄	C₂×C₄×C₆₁	1	2	yes	—
326	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
327	C₂³×C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₆₁	1	2	yes	—
329	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	2	4	no	—
334	C₂×M₁₆	—	2	4	no	—
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	4	no	—
338	C₂×M₁₆	D₄×C₆₁	1	4	yes	complemented
339	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
340	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
341	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
342	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
345	#121	—	2	4	no	—
346	C₄×D₄	—	2	4	no	—
347	C₄×D₄	—	2	4	no	—
348	C₄×D₄	—	2	2	no	—
349	C₄×D₄	—	2	2	no	—
350	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
352	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
354	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
355	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
356	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
357	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
358	C₂×C₂²⋊C₄	C₂×C₄×C₆₁	1	2	yes	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	—	2	2	no	—
361	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
362	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
364	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
365	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
366	C₄⋊C₈	—	2	4	no	—
367	C₄⋊C₈	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₂²⋊C₈	—	2	4	no	—
370	C₂²⋊C₈	—	2	4	no	—
371	C₂²⋊C₈	—	2	4	no	—
372	C₂²⋊C₈	—	2	4	no	—
373	#97	—	2	2	no	—
374	#97	—	2	2	no	—
375	C₄×C₈	—	2	4	no	—
376	C₄×C₈	—	2	2	no	—
377	C₄×C₈	D₄×C₆₁	1	4	yes	complemented
378	#95	C₂×C₄×C₆₁	1	2	yes	—
379	#95	C₂×C₄×C₆₁	1	2	yes	—
380	#95	C₂×C₄×C₆₁	1	2	yes	—
381	C₂⁴	C₂²×C₄×C₆₁	1	2	yes	—
382	C₂⁴	C₂²×C₄×C₆₁	1	1	yes	characteristic
383	C₂×D₄	—	2	4	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	4	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	4	1	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
406	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
407	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
408	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
409	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
410	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
411	C₂²×C₄	C₂²×C₄×C₆₁	1	2	yes	—
412	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
414	C₂²×C₄	#41×C₆₁	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
416	M₁₆	—	2	8	no	—
417	M₁₆	—	2	8	no	—
418	M₁₆	—	4	8	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	2	no	—
426	C₂×C₈	—	2	2	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	2	no	—
429	C₂×C₈	—	2	2	no	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
432	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
433	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
434	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
435	C₂×C₈	#41×C₆₁	1	2	yes	—
436	C₂×C₈	#41×C₆₁	1	2	yes	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	M₁₆×C₆₁	1	4	yes	complemented
441	C₂²⋊C₄	—	2	4	no	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	4	no	—
445	C₂²⋊C₄	—	4	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂×D₄×C₆₁	1	2	yes	—
453	C₄²	#41×C₆₁	1	2	yes	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	1	no	—
456	C₂³	—	2	1	no	—
457	C₂³	—	2	1	no	—
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	C₄×D₄×C₆₁	1	2	yes	—
468	C₂³	C₂³×C₄×C₆₁	1	1	yes	characteristic
469	D₄	—	4	8	no	—
470	D₄	—	4	4	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
500	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
501	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
502	C₂×C₄	C₂×M₁₆×C₆₁	1	4	yes	—
503	C₂×C₄	C₂×M₁₆×C₆₁	1	2	yes	—
504	C₂×C₄	#131×C₆₁	1	2	yes	—
505	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
506	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
507	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
508	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
509	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
510	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
511	C₈	—	2	2	no	—
512	C₈	—	2	2	no	—
513	C₈	—	2	2	no	—
514	C₈	—	4	2	no	—
515	C₈	—	4	2	no	—
516	C₈	#121×C₆₁	1	4	yes	complemented
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	—	4	1	no	—
523	C₂²	—	4	1	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
532	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
533	C₂²	C₄×#41×C₆₁	1	1	yes	characteristic
534	C₂²	C₂²×M₁₆×C₆₁	1	1	yes	characteristic
535	C₂²	C₂×#131×C₆₁	1	1	yes	characteristic
536	C₂²	C₆₁×#568	1	1	yes	characteristic
537	C₂²	C₆₁×#568	1	1	yes	characteristic
538	C₄	—	2	2	no	—
539	C₄	—	2	2	no	—
540	C₄	—	2	4	no	—
541	C₄	—	4	2	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	2	no	—
545	C₄	C₆₁×#436	1	4	yes	complemented
546	C₄	C₂×#121×C₆₁	1	1	yes	characteristic
547	C₄	C₆₁×#525	1	1	yes	characteristic
548	C₄	C₆₁×#529	1	1	yes	characteristic
549	C₄	C₆₁×#532	1	1	yes	characteristic
550	C₂	—	4	2	no	—
551	C₂	—	8	2	no	—
552	C₂	C₄×#121×C₆₁	1	1	yes	characteristic
553	C₂	C₂×C₆₁×#436	1	1	yes	characteristic
554	C₂	C₆₁×#2930	1	1	yes	characteristic
555	C₂	D₄×M₁₆×C₆₁	1	1	yes	characteristic
556	C₂	C₆₁×#2935	1	1	yes	characteristic
557	C₂	C₆₁×#2969	1	1	yes	characteristic
558	C₂	C₆₁×#2971	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	C₂×#121×C₆₁	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×#436	C₂	semidirect
2. C₂×C₆₁×#436	C₂	semidirect
3. C₂×C₄×M₁₆×C₆₁	C₂	semidirect
5. C₆₁×#1954	C₂	semidirect
6. C₆₁×#1939	C₂	semidirect
7. C₆₁×#1924	C₂	semidirect
8. C₆₁×#1870	C₂	semidirect
9. C₆₁×#1797	C₂	semidirect
10. C₈×C₄⋊C₄×C₆₁	C₂	semidirect
11. C₆₁×#1753	C₂	semidirect
58. C₂×M₁₆×C₆₁	D₄	semidirect
97. C₄×C₈×C₆₁	D₄	semidirect
160. C₄⋊C₄×C₆₁	M₁₆	semidirect
236. C₈×C₆₁	#121	semidirect
237. #21488	C₆₁	direct (N × H)
266. C₄×C₆₁	#436	semidirect
271. C₂×#436	C₂×C₆₁	semidirect
272. C₂×#436	C₂×C₆₁	semidirect
273. C₂×C₄×M₁₆	C₂×C₆₁	semidirect
275. #1954	C₂×C₆₁	semidirect
276. #1939	C₂×C₆₁	semidirect
277. #1924	C₂×C₆₁	semidirect
278. #1870	C₂×C₆₁	semidirect
279. #1797	C₂×C₆₁	semidirect
280. C₈×C₄⋊C₄	C₂×C₆₁	semidirect
281. #1753	C₂×C₆₁	semidirect
323. C₆₁	#21488	direct (N × H)
338. C₂×M₁₆	D₄×C₆₁	semidirect
377. C₄×C₈	D₄×C₆₁	semidirect
440. C₄⋊C₄	M₁₆×C₆₁	semidirect
516. C₈	#121×C₆₁	semidirect
545. C₄	C₆₁×#436	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#436	2
C₂×C₄×M₁₆×C₆₁	2
C₄×#121×C₆₁	2
C₆₁×#1954	2
C₆₁×#1939	2
C₆₁×#1924	2
C₆₁×#1870	2
C₆₁×#1797	2
C₈×C₄⋊C₄×C₆₁	2
C₆₁×#1753	2
#21488	61

Subgroups — C61×#21488 #29524921

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21488 #29524921