Subgroups — C₆₁×#8425 #29511858

Order 15616.

750 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3503	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#1981	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#1806	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1550	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1548	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1503	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1477	C₂	1	1	yes	maximal, characteristic
8	Q₈²×C₆₁	C₄	1	2	yes	complemented
9	C₆₁×#557	—	2	1	no	—
10	C₆₁×#554	—	2	2	no	—
11	C₆₁×#554	C₄	1	2	yes	complemented
12	D₄×Q₈×C₆₁	—	2	2	no	—
13	D₄×Q₈×C₆₁	—	2	1	no	—
14	C₆₁×#544	—	2	2	no	—
15	C₆₁×#544	—	2	1	no	—
16	C₆₁×#533	—	2	1	no	—
17	C₆₁×#533	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
19	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#520	—	2	1	no	—
21	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
22	C₆₁×#431	C₂²	1	1	yes	characteristic
23	C₆₁×#423	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×#104×C₆₁	—	2	1	no	—
26	C₂×#103×C₆₁	—	2	2	no	—
27	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
28	C₆₁×#339	—	2	1	no	—
29	C₆₁×#333	—	2	2	no	—
30	C₆₁×#333	—	2	1	no	—
31	C₆₁×#332	—	2	1	no	—
32	C₆₁×#328	—	2	2	no	—
33	C₆₁×Q₈⋊C₈	—	2	1	no	—
34	C₆₁×D₄⋊C₈	—	2	1	no	—
35	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₆₁	—	2	2	no	—
37	C₂²×Q₈×C₆₁	D₄	1	2	yes	—
38	C₂×M₁₆×C₆₁	—	2	1	no	—
39	C₂²×C₈×C₆₁	—	2	1	no	—
40	C₄⋊Q₈×C₆₁	—	2	2	no	—
41	C₄⋊Q₈×C₆₁	—	2	2	no	—
42	C₄⋊Q₈×C₆₁	—	2	4	no	—
43	C₄⋊Q₈×C₆₁	—	2	2	no	—
44	C₄⋊Q₈×C₆₁	—	2	2	no	—
45	C₄⋊Q₈×C₆₁	—	2	1	no	—
46	C₄⋊Q₈×C₆₁	—	2	1	no	—
47	C₄⋊Q₈×C₆₁	C₂×C₄	1	2	yes	—
48	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
49	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
50	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
51	#125×C₆₁	—	2	2	no	—
52	#125×C₆₁	—	2	4	no	—
53	#125×C₆₁	—	2	2	no	—
54	#125×C₆₁	—	2	1	no	—
55	C₂²⋊Q₈×C₆₁	—	2	2	no	—
56	C₂²⋊Q₈×C₆₁	—	2	4	no	—
57	C₂²⋊Q₈×C₆₁	—	2	4	no	—
58	C₂²⋊Q₈×C₆₁	—	2	2	no	—
59	C₂²⋊Q₈×C₆₁	—	2	4	no	—
60	C₂²⋊Q₈×C₆₁	—	2	1	no	—
61	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×Q₈×C₆₁	—	2	2	no	—
64	C₄×Q₈×C₆₁	—	2	2	no	—
65	C₄×Q₈×C₆₁	—	2	1	no	—
66	C₄×Q₈×C₆₁	C₂×C₄	1	2	yes	—
67	C₄×Q₈×C₆₁	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
69	C₄×D₄×C₆₁	—	2	4	no	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	C₄×D₄×C₆₁	—	2	1	no	—
72	C₄×D₄×C₆₁	—	2	1	no	—
73	C₄×D₄×C₆₁	C₂×C₄	1	1	yes	characteristic
74	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
75	#117×C₆₁	—	2	2	no	—
76	#117×C₆₁	—	2	1	no	—
77	#117×C₆₁	—	2	1	no	—
78	#117×C₆₁	D₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
82	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
83	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
84	C₂×C₄²×C₆₁	—	2	1	no	—
85	C₂×C₄²×C₆₁	—	2	1	no	—
86	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₆₁	—	2	1	no	—
88	C₄⋊C₈×C₆₁	—	2	1	no	—
89	C₄⋊C₈×C₆₁	—	2	1	no	—
90	C₄⋊C₈×C₆₁	—	2	1	no	—
91	C₄⋊C₈×C₆₁	—	2	1	no	—
92	#104×C₆₁	—	4	2	no	—
93	#103×C₆₁	—	4	4	no	—
94	C₂²⋊C₈×C₆₁	—	2	1	no	—
95	C₄×C₈×C₆₁	—	2	1	no	—
96	#95×C₆₁	—	2	1	no	—
97	#41×C₆₁	—	2	1	no	—
98	#41×C₆₁	—	2	1	no	—
99	#41×C₆₁	SD₁₆	1	2	yes	—
100	#41×C₆₁	Q₁₆	1	2	yes	—
101	C₂×Q₈×C₆₁	—	2	4	no	—
102	C₂×Q₈×C₆₁	—	2	2	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	4	2	no	—
105	C₂×Q₈×C₆₁	—	4	2	no	—
106	C₂×Q₈×C₆₁	—	8	2	no	—
107	C₂×Q₈×C₆₁	—	8	2	no	—
108	C₂×Q₈×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×Q₈×C₆₁	C₂²⋊C₄	1	2	yes	—
110	C₂×Q₈×C₆₁	C₂²⋊C₄	1	4	yes	—
111	C₂×D₄×C₆₁	—	2	1	no	—
112	C₂×D₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	—	2	1	no	—
114	C₂²×C₄×C₆₁	—	2	4	no	—
115	C₂²×C₄×C₆₁	—	2	2	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	4	1	no	—
119	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
122	M₁₆×C₆₁	—	4	1	no	—
123	M₁₆×C₆₁	—	4	1	no	—
124	C₂×C₈×C₆₁	—	4	2	no	—
125	C₂×C₈×C₆₁	—	4	1	no	—
126	C₂×C₈×C₆₁	—	4	1	no	—
127	C₂×C₈×C₆₁	—	4	1	no	—
128	C₄⋊C₄×C₆₁	—	2	4	no	—
129	C₄⋊C₄×C₆₁	—	2	4	no	—
130	C₄⋊C₄×C₆₁	—	2	4	no	—
131	C₄⋊C₄×C₆₁	—	2	4	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	2	2	no	—
137	C₄⋊C₄×C₆₁	—	2	1	no	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₄⋊C₄×C₆₁	—	2	1	no	—
141	C₄⋊C₄×C₆₁	—	2	1	no	—
142	C₄⋊C₄×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	4	1	no	—
145	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	2	yes	—
146	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
147	C₄⋊C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₆₁	—	2	4	no	—
149	C₂²⋊C₄×C₆₁	—	2	2	no	—
150	C₂²⋊C₄×C₆₁	—	2	1	no	—
151	C₂²⋊C₄×C₆₁	—	2	1	no	—
152	C₂²⋊C₄×C₆₁	—	2	1	no	—
153	C₄²×C₆₁	—	2	4	no	—
154	C₄²×C₆₁	—	2	1	no	—
155	C₄²×C₆₁	—	2	2	no	—
156	C₄²×C₆₁	—	2	1	no	—
157	C₄²×C₆₁	—	2	1	no	—
158	C₄²×C₆₁	—	4	1	no	—
159	C₄²×C₆₁	—	4	1	no	—
160	C₄²×C₆₁	C₂²×C₄	1	1	yes	characteristic
161	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂³×C₆₁	—	2	1	no	—
165	C₂³×C₆₁	#120	1	1	yes	characteristic
166	Q₈×C₆₁	—	2	1	no	—
167	Q₈×C₆₁	—	4	4	no	—
168	Q₈×C₆₁	—	4	2	no	—
169	Q₈×C₆₁	—	4	2	no	—
170	Q₈×C₆₁	—	4	1	no	—
171	Q₈×C₆₁	—	4	2	no	—
172	Q₈×C₆₁	—	4	1	no	—
173	Q₈×C₆₁	—	8	4	no	—
174	Q₈×C₆₁	#103	1	2	yes	complemented
175	D₄×C₆₁	—	2	2	no	—
176	D₄×C₆₁	—	2	2	no	—
177	D₄×C₆₁	—	2	1	no	—
178	D₄×C₆₁	#103	1	2	yes	complemented
179	C₂×C₄×C₆₁	—	2	1	no	—
180	C₂×C₄×C₆₁	—	2	2	no	—
181	C₂×C₄×C₆₁	—	2	2	no	—
182	C₂×C₄×C₆₁	—	2	1	no	—
183	C₂×C₄×C₆₁	—	2	1	no	—
184	C₂×C₄×C₆₁	—	2	2	no	—
185	C₂×C₄×C₆₁	—	2	1	no	—
186	C₂×C₄×C₆₁	—	2	1	no	—
187	C₂×C₄×C₆₁	—	2	4	no	—
188	C₂×C₄×C₆₁	—	2	2	no	—
189	C₂×C₄×C₆₁	—	4	1	no	—
190	C₂×C₄×C₆₁	—	4	2	no	—
191	C₂×C₄×C₆₁	—	4	1	no	—
192	C₂×C₄×C₆₁	—	4	1	no	—
193	C₂×C₄×C₆₁	—	4	2	no	—
194	C₂×C₄×C₆₁	—	8	2	no	—
195	C₂×C₄×C₆₁	—	8	4	no	—
196	C₂×C₄×C₆₁	—	8	1	no	—
197	C₂×C₄×C₆₁	—	8	1	no	—
198	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₆₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
202	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
203	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
204	C₂×C₄×C₆₁	C₂×SD₁₆	1	1	yes	characteristic
205	C₂×C₄×C₆₁	C₂×Q₁₆	1	1	yes	characteristic
206	C₂×C₄×C₆₁	#137	1	1	yes	characteristic
207	C₂×C₄×C₆₁	#137	1	1	yes	characteristic
208	C₈×C₆₁	—	8	1	no	—
209	C₈×C₆₁	—	8	1	no	—
210	C₈×C₆₁	—	8	1	no	—
211	#8425	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂²×C₆₁	—	2	1	no	—
213	C₂²×C₆₁	—	2	1	no	—
214	C₂²×C₆₁	—	2	2	no	—
215	C₂²×C₆₁	—	4	1	no	—
216	C₂²×C₆₁	—	4	1	no	—
217	C₂²×C₆₁	#379	1	1	yes	characteristic
218	C₂²×C₆₁	#448	1	1	yes	characteristic
219	C₂²×C₆₁	#451	1	1	yes	characteristic
220	C₄×C₆₁	—	2	1	no	—
221	C₄×C₆₁	—	2	1	no	—
222	C₄×C₆₁	—	2	1	no	—
223	C₄×C₆₁	—	2	2	no	—
224	C₄×C₆₁	—	4	1	no	—
225	C₄×C₆₁	—	4	4	no	—
226	C₄×C₆₁	—	4	2	no	—
227	C₄×C₆₁	—	4	1	no	—
228	C₄×C₆₁	—	4	2	no	—
229	C₄×C₆₁	—	8	2	no	—
230	C₄×C₆₁	C₂×#103	1	1	yes	characteristic
231	C₄×C₆₁	#419	1	1	yes	characteristic
232	C₄×C₆₁	#448	1	1	yes	characteristic
233	C₄×C₆₁	#451	1	1	yes	characteristic
234	C₄×C₆₁	#453	1	1	yes	characteristic
235	C₄×C₆₁	#455	1	1	yes	characteristic
236	#3503	C₂×C₆₁	1	1	yes	characteristic
237	#1981	C₂×C₆₁	1	1	yes	characteristic, complemented
238	#1806	C₂×C₆₁	1	1	yes	characteristic
239	#1550	C₂×C₆₁	1	1	yes	characteristic, complemented
240	#1548	C₂×C₆₁	1	1	yes	characteristic, complemented
241	#1503	C₂×C₆₁	1	1	yes	characteristic, complemented
242	#1477	C₂×C₆₁	1	1	yes	characteristic
243	C₂×C₆₁	—	2	1	no	—
244	C₂×C₆₁	—	2	1	no	—
245	C₂×C₆₁	—	4	2	no	—
246	C₂×C₆₁	#1787	1	1	yes	characteristic
247	C₂×C₆₁	#1792	1	1	yes	characteristic
248	C₂×C₆₁	#1796	1	1	yes	characteristic
249	Q₈²	C₄×C₆₁	1	2	yes	complemented
250	#557	—	2	1	no	—
251	#554	—	2	2	no	—
252	#554	C₄×C₆₁	1	2	yes	complemented
253	D₄×Q₈	—	2	2	no	—
254	D₄×Q₈	—	2	1	no	—
255	#544	—	2	2	no	—
256	#544	—	2	1	no	—
257	#533	—	2	1	no	—
258	#533	C₂²×C₆₁	1	1	yes	characteristic
259	C₂×C₄⋊Q₈	—	2	1	no	—
260	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
261	#520	—	2	1	no	—
262	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
263	#431	C₂²×C₆₁	1	1	yes	characteristic
264	#423	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
266	C₂×#104	—	2	1	no	—
267	C₂×#103	—	2	2	no	—
268	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
269	#339	—	2	1	no	—
270	#333	—	2	2	no	—
271	#333	—	2	1	no	—
272	#332	—	2	1	no	—
273	#328	—	2	2	no	—
274	Q₈⋊C₈	—	2	1	no	—
275	D₄⋊C₈	—	2	1	no	—
276	C₆₁	#8425	1	1	yes	characteristic, direct product factor, Sylow
277	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
278	C₂²×Q₈	—	2	2	no	—
279	C₂²×Q₈	D₄×C₆₁	1	2	yes	—
280	C₂×M₁₆	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₄⋊Q₈	—	2	2	no	—
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	—	2	4	no	—
285	C₄⋊Q₈	—	2	2	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	1	no	—
288	C₄⋊Q₈	—	2	1	no	—
289	C₄⋊Q₈	C₂×C₄×C₆₁	1	2	yes	—
290	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
291	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
292	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
293	#125	—	2	2	no	—
294	#125	—	2	4	no	—
295	#125	—	2	2	no	—
296	#125	—	2	1	no	—
297	C₂²⋊Q₈	—	2	2	no	—
298	C₂²⋊Q₈	—	2	4	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	2	4	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×Q₈	C₂×C₄×C₆₁	1	1	yes	characteristic
309	C₄×Q₈	C₂×C₄×C₆₁	1	2	yes	—
310	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	2	no	—
313	C₄×D₄	—	2	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	C₂×C₄×C₆₁	1	1	yes	characteristic
316	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
317	#117	—	2	2	no	—
318	#117	—	2	1	no	—
319	#117	—	2	1	no	—
320	#117	D₄×C₆₁	1	1	yes	characteristic
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	—	2	1	no	—
328	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
329	C₄⋊C₈	—	2	1	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	2	1	no	—
333	C₄⋊C₈	—	2	1	no	—
334	#104	—	4	2	no	—
335	#103	—	4	4	no	—
336	C₂²⋊C₈	—	2	1	no	—
337	C₄×C₈	—	2	1	no	—
338	#95	—	2	1	no	—
339	#41	—	2	1	no	—
340	#41	—	2	1	no	—
341	#41	SD₁₆×C₆₁	1	2	yes	—
342	#41	Q₁₆×C₆₁	1	2	yes	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	—	8	2	no	—
349	C₂×Q₈	—	8	2	no	—
350	C₂×Q₈	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
351	C₂×Q₈	C₂²⋊C₄×C₆₁	1	2	yes	—
352	C₂×Q₈	C₂²⋊C₄×C₆₁	1	4	yes	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
364	M₁₆	—	4	1	no	—
365	M₁₆	—	4	1	no	—
366	C₂×C₈	—	4	2	no	—
367	C₂×C₈	—	4	1	no	—
368	C₂×C₈	—	4	1	no	—
369	C₂×C₈	—	4	1	no	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	2	yes	—
388	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
389	C₄⋊C₄	C₂²⋊C₄×C₆₁	1	1	yes	characteristic
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	2	2	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	2	1	no	—
394	C₂²⋊C₄	—	2	1	no	—
395	C₄²	—	2	4	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	4	1	no	—
401	C₄²	—	4	1	no	—
402	C₄²	C₂²×C₄×C₆₁	1	1	yes	characteristic
403	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
404	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
405	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
406	C₂³	—	2	1	no	—
407	C₂³	#120×C₆₁	1	1	yes	characteristic
408	Q₈	—	2	1	no	—
409	Q₈	—	4	4	no	—
410	Q₈	—	4	2	no	—
411	Q₈	—	4	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	8	4	no	—
416	Q₈	#103×C₆₁	1	2	yes	complemented
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	1	no	—
420	D₄	#103×C₆₁	1	2	yes	complemented
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	8	2	no	—
437	C₂×C₄	—	8	4	no	—
438	C₂×C₄	—	8	1	no	—
439	C₂×C₄	—	8	1	no	—
440	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
441	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
442	C₂×C₄	C₂×C₂²⋊C₄×C₆₁	1	1	yes	characteristic
443	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
444	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
445	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
446	C₂×C₄	C₂×SD₁₆×C₆₁	1	1	yes	characteristic
447	C₂×C₄	C₂×Q₁₆×C₆₁	1	1	yes	characteristic
448	C₂×C₄	#137×C₆₁	1	1	yes	characteristic
449	C₂×C₄	#137×C₆₁	1	1	yes	characteristic
450	C₈	—	8	1	no	—
451	C₈	—	8	1	no	—
452	C₈	—	8	1	no	—
453	C₂²	—	2	1	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	C₆₁×#379	1	1	yes	characteristic
459	C₂²	C₆₁×#448	1	1	yes	characteristic
460	C₂²	C₆₁×#451	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	2	no	—
470	C₄	—	8	2	no	—
471	C₄	C₂×#103×C₆₁	1	1	yes	characteristic
472	C₄	C₆₁×#419	1	1	yes	characteristic
473	C₄	C₆₁×#448	1	1	yes	characteristic
474	C₄	C₆₁×#451	1	1	yes	characteristic
475	C₄	C₆₁×#453	1	1	yes	characteristic
476	C₄	C₆₁×#455	1	1	yes	characteristic
477	C₂	—	2	1	no	—
478	C₂	—	2	1	no	—
479	C₂	—	4	2	no	—
480	C₂	C₆₁×#1787	1	1	yes	characteristic
481	C₂	C₆₁×#1792	1	1	yes	characteristic
482	C₂	C₆₁×#1796	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	#379
commutator	C₄²	C₂²×C₄×C₆₁
Frattini, cosocle	C₂×C₄²	C₂³×C₆₁
prime radical	C₂×#41×C₆₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₁×#1981	C₂	semidirect
4. C₆₁×#1550	C₂	semidirect
5. C₆₁×#1548	C₂	semidirect
6. C₆₁×#1503	C₂	semidirect
8. Q₈²×C₆₁	C₄	semidirect
11. C₆₁×#554	C₄	semidirect
174. Q₈×C₆₁	#103	semidirect
178. D₄×C₆₁	#103	semidirect
211. #8425	C₆₁	direct (N × H)
237. #1981	C₂×C₆₁	semidirect
239. #1550	C₂×C₆₁	semidirect
240. #1548	C₂×C₆₁	semidirect
241. #1503	C₂×C₆₁	semidirect
249. Q₈²	C₄×C₆₁	semidirect
252. #554	C₄×C₆₁	semidirect
276. C₆₁	#8425	direct (N × H)
416. Q₈	#103×C₆₁	semidirect
420. D₄	#103×C₆₁	semidirect

Maximal subgroups

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

subgroup	index
C₆₁×#3503	2
C₆₁×#1981	2
C₆₁×#1806	2
C₆₁×#1550	2
C₆₁×#1548	2
C₆₁×#1503	2
C₆₁×#1477	2
#8425	61

Subgroups — C61×#8425 #29511858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#8425 #29511858