Subgroups — C₆₁×#17554 #29520987

Order 15616.

1024 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#529	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1512	C₂	1	4	yes	maximal, complemented
5	C₆₁×#1511	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1510	C₂	1	2	yes	maximal
7	C₆₁×#1500	C₂	1	4	yes	maximal, complemented
8	C₆₁×#529	—	2	1	no	—
9	C₆₁×#529	—	2	1	no	—
10	C₆₁×#529	—	2	1	no	—
11	C₆₁×#529	—	2	1	no	—
12	C₆₁×#529	C₄	1	2	yes	complemented
13	C₆₁×#529	C₄	1	2	yes	complemented
14	C₆₁×#529	C₂²	1	2	yes	—
15	C₆₁×#529	C₂²	1	2	yes	—
16	C₂×#126×C₆₁	—	2	1	no	—
17	C₂×#125×C₆₁	C₄	1	1	yes	characteristic, complemented
18	C₂×#124×C₆₁	C₄	1	1	yes	characteristic, complemented
19	C₂×#123×C₆₁	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
21	C₂×#121×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₆₁	C₄	1	1	yes	characteristic, complemented
23	C₂×C₄×D₄×C₆₁	—	2	1	no	—
24	C₂×C₄×D₄×C₆₁	C₄	1	1	yes	characteristic, complemented
25	C₂×#117×C₆₁	—	2	1	no	—
26	C₂²×C₄²×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#432	—	2	1	no	—
28	C₆₁×#432	C₂²	1	2	yes	complemented
29	C₆₁×#431	—	2	1	no	—
30	C₆₁×#431	C₂²	1	2	yes	complemented
31	C₆₁×#423	—	2	1	no	—
32	C₆₁×#407	C₂²	1	2	yes	—
33	C₄×M₁₆×C₆₁	—	2	1	no	—
34	C₆₁×#383	—	2	1	no	—
35	C₆₁×#382	C₂²	1	2	yes	complemented
36	C₆₁×#381	C₂²	1	2	yes	—
37	C₆₁×#380	—	2	1	no	—
38	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
39	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
40	C₆₁×#376	C₂²	1	2	yes	complemented
41	C₆₁×#328	C₂²	1	8	yes	complemented
42	C₆₁×#327	C₂²	1	8	yes	—
43	C₂²×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
44	C₂²×D₄×C₆₁	—	2	1	no	—
45	C₂²×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₆₁	—	2	1	no	—
47	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₆₁	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₆₁	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₆₁	—	2	2	no	—
51	#126×C₆₁	—	2	2	no	—
52	#126×C₆₁	—	2	2	no	—
53	#126×C₆₁	—	2	2	no	—
54	#126×C₆₁	—	2	2	no	—
55	#125×C₆₁	—	2	1	no	—
56	#125×C₆₁	—	2	1	no	—
57	#125×C₆₁	C₂×C₄	1	2	yes	—
58	#125×C₆₁	C₂×C₄	1	2	yes	—
59	#124×C₆₁	—	2	1	no	—
60	#124×C₆₁	—	2	1	no	—
61	#124×C₆₁	C₂×C₄	1	2	yes	—
62	#124×C₆₁	C₂×C₄	1	2	yes	—
63	#123×C₆₁	—	2	2	no	—
64	#123×C₆₁	—	2	2	no	—
65	#123×C₆₁	—	2	2	no	—
66	#123×C₆₁	—	2	2	no	—
67	C₂²⋊Q₈×C₆₁	—	2	1	no	—
68	C₂²⋊Q₈×C₆₁	—	2	1	no	—
69	C₂²⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
70	C₂²⋊Q₈×C₆₁	C₂³	1	2	yes	—
71	#121×C₆₁	—	2	1	no	—
72	#121×C₆₁	—	2	1	no	—
73	#121×C₆₁	C₂×C₄	1	2	yes	—
74	#121×C₆₁	C₂³	1	2	yes	—
75	C₄×Q₈×C₆₁	—	2	1	no	—
76	C₄×Q₈×C₆₁	—	2	1	no	—
77	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
79	C₄×D₄×C₆₁	—	2	2	no	—
80	C₄×D₄×C₆₁	—	2	2	no	—
81	C₄×D₄×C₆₁	—	2	2	no	—
82	C₄×D₄×C₆₁	—	2	2	no	—
83	C₄×D₄×C₆₁	—	2	1	no	—
84	C₄×D₄×C₆₁	—	2	1	no	—
85	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₆₁	C₂×C₄	1	2	yes	—
87	#117×C₆₁	—	2	2	no	—
88	#117×C₆₁	—	2	2	no	—
89	#117×C₆₁	—	2	2	no	—
90	#117×C₆₁	—	2	2	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	2	no	—
96	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
104	C₂×C₄²×C₆₁	—	2	1	no	—
105	C₂×C₄²×C₆₁	—	2	2	no	—
106	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₆₁	—	2	2	no	—
119	C₄⋊C₈×C₆₁	—	2	2	no	—
120	C₂²⋊C₈×C₆₁	—	2	2	no	—
121	C₂²⋊C₈×C₆₁	C₂³	1	4	yes	—
122	#97×C₆₁	—	2	2	no	—
123	C₄×C₈×C₆₁	—	2	2	no	—
124	#95×C₆₁	—	2	2	no	—
125	#95×C₆₁	—	2	2	no	—
126	#95×C₆₁	—	2	2	no	—
127	#95×C₆₁	C₂³	1	4	yes	—
128	C₂⁴×C₆₁	—	2	1	no	—
129	C₂⁴×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂×Q₈×C₆₁	—	2	1	no	—
131	C₂×Q₈×C₆₁	—	4	2	no	—
132	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
133	C₂×D₄×C₆₁	—	2	2	no	—
134	C₂×D₄×C₆₁	—	2	2	no	—
135	C₂×D₄×C₆₁	—	2	1	no	—
136	C₂×D₄×C₆₁	—	4	2	no	—
137	C₂×D₄×C₆₁	—	4	4	no	—
138	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₆₁	—	2	1	no	—
140	C₂²×C₄×C₆₁	—	2	1	no	—
141	C₂²×C₄×C₆₁	—	2	1	no	—
142	C₂²×C₄×C₆₁	—	2	2	no	—
143	C₂²×C₄×C₆₁	—	2	2	no	—
144	C₂²×C₄×C₆₁	—	2	4	no	—
145	C₂²×C₄×C₆₁	—	4	2	no	—
146	C₂²×C₄×C₆₁	—	4	2	no	—
147	C₂²×C₄×C₆₁	—	4	2	no	—
148	C₂²×C₄×C₆₁	—	4	4	no	—
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	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
167	M₁₆×C₆₁	—	4	4	no	—
168	C₂×C₈×C₆₁	—	2	4	no	—
169	C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₄⋊C₄×C₆₁	—	2	2	no	—
171	C₄⋊C₄×C₆₁	—	2	2	no	—
172	C₄⋊C₄×C₆₁	—	2	2	no	—
173	C₄⋊C₄×C₆₁	—	2	2	no	—
174	C₄⋊C₄×C₆₁	—	2	2	no	—
175	C₄⋊C₄×C₆₁	—	2	2	no	—
176	C₄⋊C₄×C₆₁	—	2	1	no	—
177	C₄⋊C₄×C₆₁	—	2	1	no	—
178	C₄⋊C₄×C₆₁	—	2	2	no	—
179	C₄⋊C₄×C₆₁	—	4	4	no	—
180	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
181	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
182	C₂²⋊C₄×C₆₁	—	2	2	no	—
183	C₂²⋊C₄×C₆₁	—	2	2	no	—
184	C₂²⋊C₄×C₆₁	—	2	2	no	—
185	C₂²⋊C₄×C₆₁	—	2	2	no	—
186	C₂²⋊C₄×C₆₁	—	2	2	no	—
187	C₂²⋊C₄×C₆₁	—	2	2	no	—
188	C₂²⋊C₄×C₆₁	—	2	2	no	—
189	C₂²⋊C₄×C₆₁	—	2	2	no	—
190	C₂²⋊C₄×C₆₁	—	2	2	no	—
191	C₂²⋊C₄×C₆₁	—	2	2	no	—
192	C₂²⋊C₄×C₆₁	—	4	4	no	—
193	C₄²×C₆₁	—	2	2	no	—
194	C₄²×C₆₁	—	2	2	no	—
195	C₄²×C₆₁	—	4	4	no	—
196	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
197	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
198	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
199	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
200	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
201	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
202	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
203	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
204	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
205	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
207	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
208	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
212	C₂³×C₆₁	—	2	2	no	—
213	C₂³×C₆₁	—	2	2	no	—
214	C₂³×C₆₁	—	2	2	no	—
215	C₂³×C₆₁	—	4	1	no	—
216	C₂³×C₆₁	—	4	2	no	—
217	C₂³×C₆₁	—	4	2	no	—
218	C₂³×C₆₁	—	4	2	no	—
219	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
220	C₂³×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
222	Q₈×C₆₁	—	4	2	no	—
223	Q₈×C₆₁	—	4	2	no	—
224	D₄×C₆₁	—	4	2	no	—
225	D₄×C₆₁	—	4	2	no	—
226	D₄×C₆₁	—	4	4	no	—
227	D₄×C₆₁	—	4	4	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	2	2	no	—
230	C₂×C₄×C₆₁	—	2	2	no	—
231	C₂×C₄×C₆₁	—	2	2	no	—
232	C₂×C₄×C₆₁	—	2	2	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	2	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	—	4	1	no	—
242	C₂×C₄×C₆₁	—	4	1	no	—
243	C₂×C₄×C₆₁	—	4	1	no	—
244	C₂×C₄×C₆₁	—	4	1	no	—
245	C₂×C₄×C₆₁	—	4	1	no	—
246	C₂×C₄×C₆₁	—	4	1	no	—
247	C₂×C₄×C₆₁	—	4	1	no	—
248	C₂×C₄×C₆₁	—	4	1	no	—
249	C₂×C₄×C₆₁	—	4	4	no	—
250	C₂×C₄×C₆₁	—	4	2	no	—
251	C₂×C₄×C₆₁	—	4	2	no	—
252	C₂×C₄×C₆₁	—	4	2	no	—
253	C₂×C₄×C₆₁	—	4	4	no	—
254	C₂×C₄×C₆₁	—	4	4	no	—
255	C₂×C₄×C₆₁	—	4	4	no	—
256	C₂×C₄×C₆₁	—	4	4	no	—
257	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
260	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
261	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
268	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
269	C₈×C₆₁	—	4	4	no	—
270	#17554	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂²×C₆₁	—	2	1	no	—
272	C₂²×C₆₁	—	2	1	no	—
273	C₂²×C₆₁	—	2	1	no	—
274	C₂²×C₆₁	—	2	1	no	—
275	C₂²×C₆₁	—	2	1	no	—
276	C₂²×C₆₁	—	2	1	no	—
277	C₂²×C₆₁	—	2	1	no	—
278	C₂²×C₆₁	—	4	4	no	—
279	C₂²×C₆₁	—	4	2	no	—
280	C₂²×C₆₁	—	4	2	no	—
281	C₂²×C₆₁	—	4	2	no	—
282	C₂²×C₆₁	—	8	4	no	—
283	C₂²×C₆₁	#410	1	2	yes	—
284	C₂²×C₆₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
285	C₂²×C₆₁	#575	1	2	yes	—
286	C₄×C₆₁	—	2	1	no	—
287	C₄×C₆₁	—	2	1	no	—
288	C₄×C₆₁	—	2	1	no	—
289	C₄×C₆₁	—	2	1	no	—
290	C₄×C₆₁	—	2	1	no	—
291	C₄×C₆₁	—	2	1	no	—
292	C₄×C₆₁	—	2	1	no	—
293	C₄×C₆₁	—	2	1	no	—
294	C₄×C₆₁	—	2	1	no	—
295	C₄×C₆₁	—	2	1	no	—
296	C₄×C₆₁	—	2	1	no	—
297	C₄×C₆₁	—	4	2	no	—
298	C₄×C₆₁	—	4	2	no	—
299	C₄×C₆₁	—	4	2	no	—
300	C₄×C₆₁	—	8	4	no	—
301	C₄×C₆₁	#421	1	2	yes	—
302	C₂×#529	C₂×C₆₁	1	1	yes	characteristic
303	#2920	C₂×C₆₁	1	1	yes	characteristic, complemented
304	#2283	C₂×C₆₁	1	1	yes	characteristic, complemented
305	#1512	C₂×C₆₁	1	4	yes	complemented
306	#1511	C₂×C₆₁	1	2	yes	complemented
307	#1510	C₂×C₆₁	1	2	yes	—
308	#1500	C₂×C₆₁	1	4	yes	complemented
309	C₂×C₆₁	—	2	2	no	—
310	C₂×C₆₁	—	2	2	no	—
311	C₂×C₆₁	—	4	1	no	—
312	C₂×C₆₁	—	8	2	no	—
313	C₂×C₆₁	C₂×#410	1	1	yes	characteristic
314	C₂×C₆₁	#2896	1	1	yes	characteristic
315	C₂×C₆₁	C₂×#421	1	1	yes	characteristic
316	#529	—	2	1	no	—
317	#529	—	2	1	no	—
318	#529	—	2	1	no	—
319	#529	—	2	1	no	—
320	#529	C₄×C₆₁	1	2	yes	complemented
321	#529	C₄×C₆₁	1	2	yes	complemented
322	#529	C₂²×C₆₁	1	2	yes	—
323	#529	C₂²×C₆₁	1	2	yes	—
324	C₂×#126	—	2	1	no	—
325	C₂×#125	C₄×C₆₁	1	1	yes	characteristic, complemented
326	C₂×#124	C₄×C₆₁	1	1	yes	characteristic, complemented
327	C₂×#123	—	2	1	no	—
328	C₂×C₂²⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
329	C₂×#121	C₂²×C₆₁	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₄×C₆₁	1	1	yes	characteristic, complemented
331	C₂×C₄×D₄	—	2	1	no	—
332	C₂×C₄×D₄	C₄×C₆₁	1	1	yes	characteristic, complemented
333	C₂×#117	—	2	1	no	—
334	C₂²×C₄²	C₂²×C₆₁	1	1	yes	characteristic
335	#432	—	2	1	no	—
336	#432	C₂²×C₆₁	1	2	yes	complemented
337	#431	—	2	1	no	—
338	#431	C₂²×C₆₁	1	2	yes	complemented
339	#423	—	2	1	no	—
340	#407	C₂²×C₆₁	1	2	yes	—
341	C₄×M₁₆	—	2	1	no	—
342	#383	—	2	1	no	—
343	#382	C₂²×C₆₁	1	2	yes	complemented
344	#381	C₂²×C₆₁	1	2	yes	—
345	#380	—	2	1	no	—
346	C₄×C₄⋊C₄	—	2	1	no	—
347	C₄×C₂²⋊C₄	—	2	1	no	—
348	#376	C₂²×C₆₁	1	2	yes	complemented
349	#328	C₂²×C₆₁	1	8	yes	complemented
350	#327	C₂²×C₆₁	1	8	yes	—
351	C₆₁	#17554	1	1	yes	characteristic, direct product factor, Sylow
352	C₂²×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
353	C₂²×D₄	—	2	1	no	—
354	C₂²×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
355	C₂³×C₄	—	2	1	no	—
356	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
357	C₂³×C₄	D₄×C₆₁	1	1	yes	characteristic
358	C₂³×C₄	C₂³×C₆₁	1	1	yes	characteristic
359	C₂×M₁₆	—	2	2	no	—
360	#126	—	2	2	no	—
361	#126	—	2	2	no	—
362	#126	—	2	2	no	—
363	#126	—	2	2	no	—
364	#125	—	2	1	no	—
365	#125	—	2	1	no	—
366	#125	C₂×C₄×C₆₁	1	2	yes	—
367	#125	C₂×C₄×C₆₁	1	2	yes	—
368	#124	—	2	1	no	—
369	#124	—	2	1	no	—
370	#124	C₂×C₄×C₆₁	1	2	yes	—
371	#124	C₂×C₄×C₆₁	1	2	yes	—
372	#123	—	2	2	no	—
373	#123	—	2	2	no	—
374	#123	—	2	2	no	—
375	#123	—	2	2	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₂²⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
379	C₂²⋊Q₈	C₂³×C₆₁	1	2	yes	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	C₂×C₄×C₆₁	1	2	yes	—
383	#121	C₂³×C₆₁	1	2	yes	—
384	C₄×Q₈	—	2	1	no	—
385	C₄×Q₈	—	2	1	no	—
386	C₄×Q₈	C₂×C₄×C₆₁	1	2	yes	—
387	C₄×Q₈	C₂×C₄×C₆₁	1	2	yes	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	2	no	—
391	C₄×D₄	—	2	2	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
395	C₄×D₄	C₂×C₄×C₆₁	1	2	yes	—
396	#117	—	2	2	no	—
397	#117	—	2	2	no	—
398	#117	—	2	2	no	—
399	#117	—	2	2	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	2	no	—
405	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂×C₄×C₆₁	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	—	2	1	no	—
408	C₂×C₂²⋊C₄	—	2	1	no	—
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	—	2	2	no	—
413	C₂×C₄²	—	2	1	no	—
414	C₂×C₄²	—	2	2	no	—
415	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
416	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
417	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
418	C₂×C₄²	C₂×C₄×C₆₁	1	1	yes	characteristic
419	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
420	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
421	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
422	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
423	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
424	C₂×C₄²	D₄×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	C₂²⋊C₈	—	2	2	no	—
430	C₂²⋊C₈	C₂³×C₆₁	1	4	yes	—
431	#97	—	2	2	no	—
432	C₄×C₈	—	2	2	no	—
433	#95	—	2	2	no	—
434	#95	—	2	2	no	—
435	#95	—	2	2	no	—
436	#95	C₂³×C₆₁	1	4	yes	—
437	C₂⁴	—	2	1	no	—
438	C₂⁴	C₂×D₄×C₆₁	1	1	yes	characteristic
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	4	2	no	—
446	C₂×D₄	—	4	4	no	—
447	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	4	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	2	no	—
457	C₂²×C₄	—	4	4	no	—
458	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
459	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
460	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
461	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
462	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
463	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
464	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
465	C₂²×C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₄×C₆₁	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
473	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
474	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
475	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
476	M₁₆	—	4	4	no	—
477	C₂×C₈	—	2	4	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	4	4	no	—
489	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
490	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	2	2	no	—
495	C₂²⋊C₄	—	2	2	no	—
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	2	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	2	no	—
501	C₂²⋊C₄	—	4	4	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	4	4	no	—
505	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
506	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
507	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
508	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
509	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
510	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
511	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
512	C₄²	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
513	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
514	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
515	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
516	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
517	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
518	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
519	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
520	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	2	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	2	no	—
528	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
529	C₂³	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
530	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
531	Q₈	—	4	2	no	—
532	Q₈	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	2	no	—
535	D₄	—	4	4	no	—
536	D₄	—	4	4	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	4	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
567	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
568	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
569	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
570	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
571	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
572	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
573	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
574	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
575	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
576	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
577	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
578	C₈	—	4	4	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	8	4	no	—
591	C₂²	C₆₁×#410	1	2	yes	—
592	C₂²	C₂²×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
593	C₂²	C₆₁×#575	1	2	yes	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	2	no	—
608	C₄	—	8	4	no	—
609	C₄	C₆₁×#421	1	2	yes	—
610	C₂	—	2	2	no	—
611	C₂	—	2	2	no	—
612	C₂	—	4	1	no	—
613	C₂	—	8	2	no	—
614	C₂	C₂×C₆₁×#410	1	1	yes	characteristic
615	C₂	C₆₁×#2896	1	1	yes	characteristic
616	C₂	C₂×C₆₁×#421	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂²×C₂²⋊C₄
prime radical	C₂×#121×C₆₁	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂²×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#2920	C₂	semidirect
3. C₆₁×#2283	C₂	semidirect
4. C₆₁×#1512	C₂	semidirect
5. C₆₁×#1511	C₂	semidirect
7. C₆₁×#1500	C₂	semidirect
12. C₆₁×#529	C₄	semidirect
13. C₆₁×#529	C₄	semidirect
17. C₂×#125×C₆₁	C₄	semidirect
18. C₂×#124×C₆₁	C₄	semidirect
22. C₂×C₄×Q₈×C₆₁	C₄	semidirect
24. C₂×C₄×D₄×C₆₁	C₄	semidirect
28. C₆₁×#432	C₂²	semidirect
30. C₆₁×#431	C₂²	semidirect
35. C₆₁×#382	C₂²	semidirect
40. C₆₁×#376	C₂²	semidirect
41. C₆₁×#328	C₂²	semidirect
270. #17554	C₆₁	direct (N × H)
303. #2920	C₂×C₆₁	semidirect
304. #2283	C₂×C₆₁	semidirect
305. #1512	C₂×C₆₁	semidirect
306. #1511	C₂×C₆₁	semidirect
308. #1500	C₂×C₆₁	semidirect
320. #529	C₄×C₆₁	semidirect
321. #529	C₄×C₆₁	semidirect
325. C₂×#125	C₄×C₆₁	semidirect
326. C₂×#124	C₄×C₆₁	semidirect
330. C₂×C₄×Q₈	C₄×C₆₁	semidirect
332. C₂×C₄×D₄	C₄×C₆₁	semidirect
336. #432	C₂²×C₆₁	semidirect
338. #431	C₂²×C₆₁	semidirect
343. #382	C₂²×C₆₁	semidirect
348. #376	C₂²×C₆₁	semidirect
349. #328	C₂²×C₆₁	semidirect
351. C₆₁	#17554	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#529	2
C₆₁×#2920	2
C₆₁×#2283	2
C₆₁×#1512	2
C₆₁×#1511	2
C₆₁×#1510	2
C₆₁×#1500	2
#17554	61

Subgroups — C61×#17554 #29520987

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#17554 #29520987