Subgroups — C₆₁×#25832 #29529265

Order 15616.

954 conjugacy classes of subgroups.

The subgroup lattice has 558 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×#3166	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3080	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2660	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#2061	C₂	1	2	yes	maximal, complemented
6	C₆₁×#2060	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1995	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1860	C₂	1	2	yes	maximal
10	C₆₁×#1859	C₂	1	2	yes	maximal
11	C₆₁×#1759	C₂	1	1	yes	maximal, characteristic
12	Q₈²×C₆₁	—	2	1	no	—
13	C₆₁×#557	—	2	1	no	—
14	C₆₁×#554	—	2	1	no	—
15	C₆₁×#554	—	2	2	no	—
16	D₄×Q₈×C₆₁	—	2	2	no	—
17	D₄×Q₈×C₆₁	—	2	1	no	—
18	C₆₁×#544	—	2	2	no	—
19	C₆₁×#544	C₂²	1	2	yes	—
20	C₆₁×#533	—	2	1	no	—
21	C₆₁×#533	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
23	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#125×C₆₁	C₂²	1	1	yes	characteristic
25	C₆₁×#520	C₂²	1	2	yes	—
26	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
27	C₆₁×#501	—	2	1	no	—
28	C₆₁×#501	—	2	1	no	—
29	C₆₁×#499	—	2	2	no	—
30	C₆₁×#479	—	2	1	no	—
31	C₆₁×#479	—	2	1	no	—
32	C₆₁×#478	—	2	1	no	—
33	C₆₁×#478	—	2	1	no	—
34	C₆₁×#428	C₂²	1	1	yes	characteristic
35	C₆₁×#428	C₂²	1	1	yes	characteristic
36	C₆₁×#428	C₂²	1	2	yes	—
37	C₆₁×#428	C₂²	1	2	yes	—
38	C₆₁×#423	C₂²	1	1	yes	characteristic
39	C₂×#104×C₆₁	C₂²	1	2	yes	—
40	C₆₁×#417	C₂²	1	1	yes	characteristic
41	C₆₁×#417	C₂²	1	1	yes	characteristic
42	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#398	—	2	2	no	—
44	C₆₁×#395	—	2	2	no	—
45	C₆₁×#384	C₂²	1	2	yes	—
46	C₆₁×#382	C₂²	1	2	yes	—
47	C₆₁×#376	C₂²	1	1	yes	characteristic
48	C₆₁×#343	C₂²	1	2	yes	—
49	C₆₁×#343	C₂²	1	2	yes	—
50	C₆₁×#339	C₂²	1	2	yes	—
51	C₆₁×#339	C₂²	1	2	yes	—
52	C₆₁×#339	C₂²	1	2	yes	—
53	C₂×#41×C₆₁	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₆₁	—	2	2	no	—
55	C₂²×Q₈×C₆₁	D₄	1	2	yes	—
56	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
57	C₂×M₁₆×C₆₁	C₂³	1	1	yes	characteristic
58	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₆₁	—	2	2	no	—
60	C₄⋊Q₈×C₆₁	—	2	2	no	—
61	C₄⋊Q₈×C₆₁	—	2	4	no	—
62	C₄⋊Q₈×C₆₁	—	2	2	no	—
63	C₄⋊Q₈×C₆₁	—	2	2	no	—
64	C₄⋊Q₈×C₆₁	—	2	1	no	—
65	C₄⋊Q₈×C₆₁	—	2	1	no	—
66	C₄⋊Q₈×C₆₁	—	2	1	no	—
67	C₄⋊Q₈×C₆₁	—	2	1	no	—
68	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
69	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
70	#125×C₆₁	—	2	4	no	—
71	#125×C₆₁	—	2	2	no	—
72	#125×C₆₁	—	2	2	no	—
73	#125×C₆₁	—	2	1	no	—
74	#125×C₆₁	—	2	1	no	—
75	#125×C₆₁	—	2	1	no	—
76	#125×C₆₁	—	2	1	no	—
77	#125×C₆₁	D₄	1	2	yes	—
78	C₂²⋊Q₈×C₆₁	—	2	2	no	—
79	C₂²⋊Q₈×C₆₁	—	2	2	no	—
80	C₂²⋊Q₈×C₆₁	—	2	4	no	—
81	C₂²⋊Q₈×C₆₁	—	2	4	no	—
82	C₂²⋊Q₈×C₆₁	—	2	1	no	—
83	C₂²⋊Q₈×C₆₁	—	2	1	no	—
84	C₂²⋊Q₈×C₆₁	—	2	4	no	—
85	C₄×Q₈×C₆₁	—	2	2	no	—
86	C₄×Q₈×C₆₁	—	2	2	no	—
87	C₄×Q₈×C₆₁	—	2	2	no	—
88	C₄×Q₈×C₆₁	—	2	1	no	—
89	C₄×Q₈×C₆₁	—	2	1	no	—
90	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
91	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
92	C₄×D₄×C₆₁	—	2	2	no	—
93	C₄×D₄×C₆₁	—	2	1	no	—
94	C₄×D₄×C₆₁	—	2	4	no	—
95	C₄×D₄×C₆₁	—	2	1	no	—
96	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
97	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
98	#117×C₆₁	—	2	2	no	—
99	#117×C₆₁	—	2	1	no	—
100	#117×C₆₁	C₂³	1	2	yes	—
101	#117×C₆₁	C₂³	1	1	yes	characteristic
102	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
103	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
104	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
106	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
107	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
108	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
111	C₂×C₄²×C₆₁	—	2	1	no	—
112	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
113	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
114	#107×C₆₁	—	2	1	no	—
115	#107×C₆₁	—	2	1	no	—
116	#107×C₆₁	—	2	2	no	—
117	#107×C₆₁	—	2	2	no	—
118	#106×C₆₁	—	2	1	no	—
119	#106×C₆₁	—	2	1	no	—
120	#106×C₆₁	—	2	2	no	—
121	#106×C₆₁	—	2	2	no	—
122	C₄⋊C₈×C₆₁	—	2	1	no	—
123	C₄⋊C₈×C₆₁	—	2	1	no	—
124	#104×C₆₁	Q₈	1	8	yes	complemented
125	#103×C₆₁	—	2	1	no	—
126	#103×C₆₁	—	2	1	no	—
127	#102×C₆₁	—	2	1	no	—
128	#102×C₆₁	—	2	1	no	—
129	#97×C₆₁	—	2	1	no	—
130	C₄×C₈×C₆₁	—	2	1	no	—
131	#95×C₆₁	—	2	1	no	—
132	#95×C₆₁	—	2	1	no	—
133	#95×C₆₁	—	2	4	no	—
134	#41×C₆₁	—	2	2	no	—
135	#41×C₆₁	C₂×Q₈	1	4	yes	—
136	C₂×Q₈×C₆₁	—	2	4	no	—
137	C₂×Q₈×C₆₁	—	2	1	no	—
138	C₂×Q₈×C₆₁	—	2	2	no	—
139	C₂×Q₈×C₆₁	—	2	1	no	—
140	C₂×Q₈×C₆₁	—	2	2	no	—
141	C₂×Q₈×C₆₁	—	8	2	no	—
142	C₂×Q₈×C₆₁	—	8	4	no	—
143	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₆₁	—	2	1	no	—
145	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₆₁	—	2	1	no	—
147	C₂²×C₄×C₆₁	—	2	2	no	—
148	C₂²×C₄×C₆₁	—	2	4	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	1	no	—
151	C₂²×C₄×C₆₁	—	2	1	no	—
152	C₂²×C₄×C₆₁	—	2	1	no	—
153	C₂²×C₄×C₆₁	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
157	M₁₆×C₆₁	—	2	2	no	—
158	M₁₆×C₆₁	—	2	2	no	—
159	M₁₆×C₆₁	—	2	2	no	—
160	M₁₆×C₆₁	C₂×Q₈	1	4	yes	complemented
161	C₂×C₈×C₆₁	—	2	2	no	—
162	C₂×C₈×C₆₁	—	2	1	no	—
163	C₂×C₈×C₆₁	—	2	1	no	—
164	C₄⋊C₄×C₆₁	—	2	4	no	—
165	C₄⋊C₄×C₆₁	—	2	4	no	—
166	C₄⋊C₄×C₆₁	—	2	4	no	—
167	C₄⋊C₄×C₆₁	—	2	4	no	—
168	C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₄⋊C₄×C₆₁	—	2	2	no	—
171	C₄⋊C₄×C₆₁	—	2	1	no	—
172	C₄⋊C₄×C₆₁	—	2	1	no	—
173	C₄⋊C₄×C₆₁	—	2	1	no	—
174	C₄⋊C₄×C₆₁	—	2	2	no	—
175	C₄⋊C₄×C₆₁	—	2	2	no	—
176	C₄⋊C₄×C₆₁	—	2	2	no	—
177	C₄⋊C₄×C₆₁	—	2	2	no	—
178	C₄⋊C₄×C₆₁	—	2	1	no	—
179	C₄⋊C₄×C₆₁	—	2	1	no	—
180	C₄⋊C₄×C₆₁	—	2	1	no	—
181	C₄⋊C₄×C₆₁	—	2	1	no	—
182	C₄⋊C₄×C₆₁	—	4	1	no	—
183	C₄⋊C₄×C₆₁	—	4	1	no	—
184	C₄⋊C₄×C₆₁	—	4	1	no	—
185	C₄⋊C₄×C₆₁	—	4	1	no	—
186	C₄⋊C₄×C₆₁	—	8	4	no	—
187	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
191	C₂²⋊C₄×C₆₁	—	2	4	no	—
192	C₂²⋊C₄×C₆₁	—	2	2	no	—
193	C₂²⋊C₄×C₆₁	—	2	1	no	—
194	C₂²⋊C₄×C₆₁	—	2	1	no	—
195	C₂²⋊C₄×C₆₁	—	2	1	no	—
196	C₄²×C₆₁	—	2	4	no	—
197	C₄²×C₆₁	—	2	1	no	—
198	C₄²×C₆₁	—	2	1	no	—
199	C₄²×C₆₁	—	2	1	no	—
200	C₄²×C₆₁	—	2	2	no	—
201	C₄²×C₆₁	—	2	2	no	—
202	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₆₁	C₂×Q₈	1	4	yes	complemented
207	C₂³×C₆₁	—	2	1	no	—
208	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
209	Q₈×C₆₁	—	2	1	no	—
210	Q₈×C₆₁	—	4	2	no	—
211	Q₈×C₆₁	—	4	4	no	—
212	Q₈×C₆₁	—	4	2	no	—
213	Q₈×C₆₁	—	8	2	no	—
214	Q₈×C₆₁	—	8	4	no	—
215	Q₈×C₆₁	C₄⋊Q₈	1	2	yes	—
216	D₄×C₆₁	—	2	4	no	—
217	D₄×C₆₁	—	2	1	no	—
218	D₄×C₆₁	C₄⋊Q₈	1	2	yes	—
219	C₂×C₄×C₆₁	—	2	1	no	—
220	C₂×C₄×C₆₁	—	2	4	no	—
221	C₂×C₄×C₆₁	—	2	2	no	—
222	C₂×C₄×C₆₁	—	2	1	no	—
223	C₂×C₄×C₆₁	—	2	1	no	—
224	C₂×C₄×C₆₁	—	2	4	no	—
225	C₂×C₄×C₆₁	—	2	2	no	—
226	C₂×C₄×C₆₁	—	2	4	no	—
227	C₂×C₄×C₆₁	—	4	1	no	—
228	C₂×C₄×C₆₁	—	4	1	no	—
229	C₂×C₄×C₆₁	—	4	2	no	—
230	C₂×C₄×C₆₁	—	4	2	no	—
231	C₂×C₄×C₆₁	—	4	2	no	—
232	C₂×C₄×C₆₁	—	4	2	no	—
233	C₂×C₄×C₆₁	—	4	4	no	—
234	C₂×C₄×C₆₁	—	4	2	no	—
235	C₂×C₄×C₆₁	—	4	2	no	—
236	C₂×C₄×C₆₁	—	4	1	no	—
237	C₂×C₄×C₆₁	—	4	1	no	—
238	C₂×C₄×C₆₁	—	8	4	no	—
239	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
240	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
241	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
242	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
243	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₆₁	C₂²×Q₈	1	2	yes	—
246	C₂×C₄×C₆₁	2₋¹⁺⁴	1	2	yes	—
247	C₈×C₆₁	—	2	4	no	—
248	C₈×C₆₁	—	4	1	no	—
249	C₈×C₆₁	—	4	1	no	—
250	#25832	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂²×C₆₁	—	2	1	no	—
252	C₂²×C₆₁	—	2	1	no	—
253	C₂²×C₆₁	—	2	2	no	—
254	C₂²×C₆₁	—	4	1	no	—
255	C₂²×C₆₁	—	4	1	no	—
256	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
257	C₂²×C₆₁	D₄×Q₈	1	2	yes	—
258	C₄×C₆₁	—	2	2	no	—
259	C₄×C₆₁	—	2	1	no	—
260	C₄×C₆₁	—	2	1	no	—
261	C₄×C₆₁	—	2	1	no	—
262	C₄×C₆₁	—	2	1	no	—
263	C₄×C₆₁	—	4	4	no	—
264	C₄×C₆₁	—	4	1	no	—
265	C₄×C₆₁	—	4	4	no	—
266	C₄×C₆₁	—	4	2	no	—
267	C₄×C₆₁	—	4	1	no	—
268	C₄×C₆₁	—	4	2	no	—
269	C₄×C₆₁	—	8	1	no	—
270	C₄×C₆₁	—	8	1	no	—
271	C₄×C₆₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
272	C₄×C₆₁	#536	1	1	yes	characteristic
273	C₄×C₆₁	D₄×Q₈	1	2	yes	—
274	#3503	C₂×C₆₁	1	1	yes	characteristic
275	#3166	C₂×C₆₁	1	1	yes	characteristic, complemented
276	#3080	C₂×C₆₁	1	1	yes	characteristic
277	#2660	C₂×C₆₁	1	1	yes	characteristic, complemented
278	#2061	C₂×C₆₁	1	2	yes	complemented
279	#2060	C₂×C₆₁	1	2	yes	complemented
280	#1997	C₂×C₆₁	1	1	yes	characteristic, complemented
281	#1995	C₂×C₆₁	1	1	yes	characteristic, complemented
282	#1860	C₂×C₆₁	1	2	yes	—
283	#1859	C₂×C₆₁	1	2	yes	—
284	#1759	C₂×C₆₁	1	1	yes	characteristic
285	C₂×C₆₁	—	2	2	no	—
286	C₂×C₆₁	—	4	2	no	—
287	C₂×C₆₁	#2434	1	1	yes	characteristic
288	C₂×C₆₁	#3019	1	1	yes	characteristic
289	C₂×C₆₁	#3020	1	1	yes	characteristic
290	Q₈²	—	2	1	no	—
291	#557	—	2	1	no	—
292	#554	—	2	1	no	—
293	#554	—	2	2	no	—
294	D₄×Q₈	—	2	2	no	—
295	D₄×Q₈	—	2	1	no	—
296	#544	—	2	2	no	—
297	#544	C₂²×C₆₁	1	2	yes	—
298	#533	—	2	1	no	—
299	#533	C₂²×C₆₁	1	1	yes	characteristic
300	C₂×C₄⋊Q₈	—	2	1	no	—
301	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
302	C₂×#125	C₂²×C₆₁	1	1	yes	characteristic
303	#520	C₂²×C₆₁	1	2	yes	—
304	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
305	#501	—	2	1	no	—
306	#501	—	2	1	no	—
307	#499	—	2	2	no	—
308	#479	—	2	1	no	—
309	#479	—	2	1	no	—
310	#478	—	2	1	no	—
311	#478	—	2	1	no	—
312	#428	C₂²×C₆₁	1	1	yes	characteristic
313	#428	C₂²×C₆₁	1	1	yes	characteristic
314	#428	C₂²×C₆₁	1	2	yes	—
315	#428	C₂²×C₆₁	1	2	yes	—
316	#423	C₂²×C₆₁	1	1	yes	characteristic
317	C₂×#104	C₂²×C₆₁	1	2	yes	—
318	#417	C₂²×C₆₁	1	1	yes	characteristic
319	#417	C₂²×C₆₁	1	1	yes	characteristic
320	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
321	#398	—	2	2	no	—
322	#395	—	2	2	no	—
323	#384	C₂²×C₆₁	1	2	yes	—
324	#382	C₂²×C₆₁	1	2	yes	—
325	#376	C₂²×C₆₁	1	1	yes	characteristic
326	#343	C₂²×C₆₁	1	2	yes	—
327	#343	C₂²×C₆₁	1	2	yes	—
328	#339	C₂²×C₆₁	1	2	yes	—
329	#339	C₂²×C₆₁	1	2	yes	—
330	#339	C₂²×C₆₁	1	2	yes	—
331	C₆₁	#25832	1	1	yes	characteristic, direct product factor, Sylow
332	C₂×#41	C₂³×C₆₁	1	1	yes	characteristic
333	C₂²×Q₈	—	2	2	no	—
334	C₂²×Q₈	D₄×C₆₁	1	2	yes	—
335	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
336	C₂×M₁₆	C₂³×C₆₁	1	1	yes	characteristic
337	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
338	C₄⋊Q₈	—	2	2	no	—
339	C₄⋊Q₈	—	2	2	no	—
340	C₄⋊Q₈	—	2	4	no	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	—	2	2	no	—
343	C₄⋊Q₈	—	2	1	no	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
348	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
349	#125	—	2	4	no	—
350	#125	—	2	2	no	—
351	#125	—	2	2	no	—
352	#125	—	2	1	no	—
353	#125	—	2	1	no	—
354	#125	—	2	1	no	—
355	#125	—	2	1	no	—
356	#125	D₄×C₆₁	1	2	yes	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	4	no	—
360	C₂²⋊Q₈	—	2	4	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	—	2	4	no	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	—	2	1	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
370	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	4	no	—
375	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
376	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
377	#117	—	2	2	no	—
378	#117	—	2	1	no	—
379	#117	C₂³×C₆₁	1	1	yes	characteristic
380	#117	C₂³×C₆₁	1	2	yes	—
381	C₂×C₄⋊C₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	4	no	—
386	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
388	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
389	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
390	C₂×C₄²	—	2	1	no	—
391	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
392	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
393	#107	—	2	1	no	—
394	#107	—	2	1	no	—
395	#107	—	2	2	no	—
396	#107	—	2	2	no	—
397	#106	—	2	1	no	—
398	#106	—	2	1	no	—
399	#106	—	2	2	no	—
400	#106	—	2	2	no	—
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	—	2	1	no	—
403	#104	Q₈×C₆₁	1	8	yes	complemented
404	#103	—	2	1	no	—
405	#103	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#97	—	2	1	no	—
409	C₄×C₈	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	4	no	—
413	#41	—	2	2	no	—
414	#41	C₂×Q₈×C₆₁	1	4	yes	—
415	C₂×Q₈	—	2	4	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	2	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	8	2	no	—
421	C₂×Q₈	—	8	4	no	—
422	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	C₂×D₄×C₆₁	1	4	yes	—
433	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	C₂×Q₈×C₆₁	1	4	yes	complemented
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	4	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	8	4	no	—
466	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
467	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
468	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
469	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	1	no	—
473	C₂²⋊C₄	—	2	1	no	—
474	C₂²⋊C₄	—	2	1	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	2	1	no	—
478	C₄²	—	2	1	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
482	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
484	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
485	C₄²	C₂×Q₈×C₆₁	1	4	yes	complemented
486	C₂³	—	2	1	no	—
487	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
488	Q₈	—	2	1	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	4	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	8	2	no	—
493	Q₈	—	8	4	no	—
494	Q₈	C₄⋊Q₈×C₆₁	1	2	yes	—
495	D₄	—	2	4	no	—
496	D₄	—	2	1	no	—
497	D₄	C₄⋊Q₈×C₆₁	1	2	yes	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	8	4	no	—
518	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
519	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
520	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
521	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
524	C₂×C₄	C₂²×Q₈×C₆₁	1	2	yes	—
525	C₂×C₄	2₋¹⁺⁴×C₆₁	1	2	yes	—
526	C₈	—	2	4	no	—
527	C₈	—	4	1	no	—
528	C₈	—	4	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
535	C₂²	D₄×Q₈×C₆₁	1	2	yes	—
536	C₄	—	2	2	no	—
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	4	4	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	4	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	C₂×C₄⋊Q₈×C₆₁	1	1	yes	characteristic
550	C₄	C₆₁×#536	1	1	yes	characteristic
551	C₄	D₄×Q₈×C₆₁	1	2	yes	—
552	C₂	—	2	2	no	—
553	C₂	—	4	2	no	—
554	C₂	C₆₁×#2434	1	1	yes	characteristic
555	C₂	C₆₁×#3019	1	1	yes	characteristic
556	C₂	C₆₁×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×#41×C₆₁	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ 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×#3166	C₂	semidirect
4. C₆₁×#2660	C₂	semidirect
5. C₆₁×#2061	C₂	semidirect
6. C₆₁×#2060	C₂	semidirect
7. C₆₁×#1997	C₂	semidirect
8. C₆₁×#1995	C₂	semidirect
124. #104×C₆₁	Q₈	semidirect
160. M₁₆×C₆₁	C₂×Q₈	semidirect
206. C₄²×C₆₁	C₂×Q₈	semidirect
250. #25832	C₆₁	direct (N × H)
275. #3166	C₂×C₆₁	semidirect
277. #2660	C₂×C₆₁	semidirect
278. #2061	C₂×C₆₁	semidirect
279. #2060	C₂×C₆₁	semidirect
280. #1997	C₂×C₆₁	semidirect
281. #1995	C₂×C₆₁	semidirect
331. C₆₁	#25832	direct (N × H)
403. #104	Q₈×C₆₁	semidirect
439. M₁₆	C₂×Q₈×C₆₁	semidirect
485. C₄²	C₂×Q₈×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×#3166	2
C₆₁×#3080	2
C₆₁×#2660	2
C₆₁×#2061	2
C₆₁×#2060	2
C₆₁×#1997	2
C₆₁×#1995	2
C₆₁×#1860	2
C₆₁×#1859	2
C₆₁×#1759	2
#25832	61

Subgroups — C61×#25832 #29529265

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#25832 #29529265