Subgroups — C₆₁×#18679 #29522112

Order 15616.

946 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3506	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3249	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3167	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3077	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1652	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1641	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1638	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1631	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1493	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#559	—	2	2	no	—
13	C₆₁×#556	C₂²	1	2	yes	—
14	C₆₁×#555	—	2	1	no	—
15	C₆₁×#553	—	2	2	no	—
16	C₆₁×#550	C₂²	1	2	yes	—
17	C₆₁×#547	—	2	1	no	—
18	C₆₁×#538	—	2	2	no	—
19	C₆₁×#535	—	2	1	no	—
20	C₆₁×#533	C₂²	1	1	yes	characteristic
21	C₆₁×#533	C₂²	1	1	yes	characteristic
22	C₆₁×#532	C₂²	1	1	yes	characteristic
23	C₆₁×#525	—	2	2	no	—
24	C₆₁×#520	—	2	1	no	—
25	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
27	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
28	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
29	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#478	—	2	2	no	—
31	C₆₁×#477	—	2	1	no	—
32	C₆₁×#477	C₂²	1	2	yes	complemented
33	C₆₁×#476	C₂²	1	2	yes	—
34	C₆₁×#474	C₂²	1	2	yes	—
35	C₆₁×#467	—	2	2	no	—
36	C₆₁×#465	—	2	2	no	—
37	C₆₁×#462	—	2	1	no	—
38	C₆₁×#462	C₂²	1	2	yes	complemented
39	C₄×SD₁₆×C₆₁	—	2	2	no	—
40	C₆₁×#428	—	2	1	no	—
41	C₆₁×#423	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
43	C₆₁×#418	—	2	1	no	—
44	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#332	C₂²	1	2	yes	complemented
46	C₆₁×#331	C₂²	1	2	yes	complemented
47	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
48	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	complemented
49	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
50	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×#41×C₆₁	—	2	2	no	—
52	C₂×#41×C₆₁	—	2	1	no	—
53	C₂²×D₄×C₆₁	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₆₁	—	2	1	no	—
55	C₂×Q₁₆×C₆₁	—	2	2	no	—
56	C₂×SD₁₆×C₆₁	—	2	2	no	—
57	C₂×M₁₆×C₆₁	—	2	1	no	—
58	C₂²×C₈×C₆₁	—	2	1	no	—
59	C₂²×C₈×C₆₁	—	2	1	no	—
60	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
61	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
65	#127×C₆₁	—	2	2	no	—
66	#127×C₆₁	C₂³	1	1	yes	characteristic
67	#126×C₆₁	—	2	4	no	—
68	#125×C₆₁	—	2	1	no	—
69	#125×C₆₁	—	2	1	no	—
70	#124×C₆₁	—	2	4	no	—
71	#124×C₆₁	—	2	2	no	—
72	#124×C₆₁	—	2	1	no	—
73	#123×C₆₁	—	2	4	no	—
74	#123×C₆₁	—	2	4	no	—
75	C₂²⋊Q₈×C₆₁	—	2	2	no	—
76	C₂²⋊Q₈×C₆₁	—	2	1	no	—
77	C₂²⋊Q₈×C₆₁	—	2	1	no	—
78	C₂²⋊Q₈×C₆₁	—	2	1	no	—
79	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
80	#121×C₆₁	—	2	2	no	—
81	#121×C₆₁	—	2	2	no	—
82	#121×C₆₁	—	2	4	no	—
83	#121×C₆₁	—	2	1	no	—
84	#121×C₆₁	—	2	2	no	—
85	#121×C₆₁	D₄	1	2	yes	—
86	#120×C₆₁	—	2	4	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	—	2	1	no	—
91	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
92	C₄×D₄×C₆₁	—	2	4	no	—
93	C₄×D₄×C₆₁	—	2	4	no	—
94	C₄×D₄×C₆₁	—	2	2	no	—
95	C₄×D₄×C₆₁	—	2	1	no	—
96	C₄×D₄×C₆₁	—	2	1	no	—
97	C₄×D₄×C₆₁	—	2	1	no	—
98	C₄×D₄×C₆₁	D₄	1	2	yes	—
99	C₄×D₄×C₆₁	D₄	1	2	yes	—
100	C₄×D₄×C₆₁	C₂³	1	2	yes	—
101	#117×C₆₁	—	2	2	no	—
102	#117×C₆₁	—	2	1	no	—
103	#117×C₆₁	—	2	2	no	—
104	#117×C₆₁	—	2	1	no	—
105	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
106	C₂×C₄⋊C₄×C₆₁	D₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
108	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
109	#107×C₆₁	—	2	2	no	—
110	#107×C₆₁	—	2	2	no	—
111	#106×C₆₁	—	2	2	no	—
112	#106×C₆₁	—	2	2	no	—
113	C₄⋊C₈×C₆₁	—	2	1	no	—
114	C₄⋊C₈×C₆₁	—	2	1	no	—
115	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
116	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
117	#103×C₆₁	—	2	2	no	—
118	#103×C₆₁	—	2	2	no	—
119	#103×C₆₁	—	2	2	no	—
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	—	2	2	no	—
123	C₄×C₈×C₆₁	—	2	1	no	—
124	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
126	C₂⁴×C₆₁	—	2	1	no	—
127	#41×C₆₁	—	4	2	no	—
128	#41×C₆₁	—	4	2	no	—
129	#41×C₆₁	—	8	2	no	—
130	#41×C₆₁	—	8	2	no	—
131	C₂×Q₈×C₆₁	—	2	1	no	—
132	C₂×Q₈×C₆₁	—	2	1	no	—
133	C₂×Q₈×C₆₁	—	2	1	no	—
134	C₂×Q₈×C₆₁	—	2	1	no	—
135	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₆₁	—	2	2	no	—
137	C₂×D₄×C₆₁	—	2	4	no	—
138	C₂×D₄×C₆₁	—	2	4	no	—
139	C₂×D₄×C₆₁	—	2	1	no	—
140	C₂×D₄×C₆₁	—	2	2	no	—
141	C₂×D₄×C₆₁	—	2	2	no	—
142	C₂×D₄×C₆₁	—	2	1	no	—
143	C₂×D₄×C₆₁	—	2	1	no	—
144	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
145	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
146	C₂²×C₄×C₆₁	—	2	4	no	—
147	C₂²×C₄×C₆₁	—	2	1	no	—
148	C₂²×C₄×C₆₁	—	2	2	no	—
149	C₂²×C₄×C₆₁	—	2	2	no	—
150	C₂²×C₄×C₆₁	—	2	2	no	—
151	C₂²×C₄×C₆₁	—	8	1	no	—
152	C₂²×C₄×C₆₁	—	8	1	no	—
153	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
156	Q₁₆×C₆₁	—	8	2	no	—
157	SD₁₆×C₆₁	—	4	4	no	—
158	M₁₆×C₆₁	—	4	2	no	—
159	C₂×C₈×C₆₁	—	2	1	no	—
160	C₂×C₈×C₆₁	—	2	1	no	—
161	C₂×C₈×C₆₁	—	2	2	no	—
162	C₂×C₈×C₆₁	—	2	2	no	—
163	C₂×C₈×C₆₁	—	4	2	no	—
164	C₂×C₈×C₆₁	—	8	1	no	—
165	C₄⋊C₄×C₆₁	—	2	4	no	—
166	C₄⋊C₄×C₆₁	—	2	1	no	—
167	C₄⋊C₄×C₆₁	—	2	1	no	—
168	C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₄⋊C₄×C₆₁	—	2	2	no	—
170	C₄⋊C₄×C₆₁	—	2	1	no	—
171	C₄⋊C₄×C₆₁	—	2	1	no	—
172	C₄⋊C₄×C₆₁	—	2	2	no	—
173	C₄⋊C₄×C₆₁	—	2	1	no	—
174	C₄⋊C₄×C₆₁	—	2	1	no	—
175	C₄⋊C₄×C₆₁	—	2	1	no	—
176	C₄⋊C₄×C₆₁	—	2	1	no	—
177	C₄⋊C₄×C₆₁	—	4	1	no	—
178	C₄⋊C₄×C₆₁	—	4	1	no	—
179	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
182	C₂²⋊C₄×C₆₁	—	2	4	no	—
183	C₂²⋊C₄×C₆₁	—	2	4	no	—
184	C₂²⋊C₄×C₆₁	—	2	4	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	—	4	1	no	—
191	C₄²×C₆₁	—	2	4	no	—
192	C₄²×C₆₁	—	2	2	no	—
193	C₄²×C₆₁	—	4	1	no	—
194	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
197	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
198	C₂³×C₆₁	—	2	2	no	—
199	C₂³×C₆₁	—	2	2	no	—
200	C₂³×C₆₁	—	4	2	no	—
201	C₂³×C₆₁	—	8	1	no	—
202	C₂³×C₆₁	—	8	1	no	—
203	C₂³×C₆₁	#120	1	1	yes	characteristic
204	Q₈×C₆₁	—	2	2	no	—
205	Q₈×C₆₁	—	2	2	no	—
206	Q₈×C₆₁	—	4	2	no	—
207	Q₈×C₆₁	—	4	1	no	—
208	Q₈×C₆₁	—	4	1	no	—
209	Q₈×C₆₁	—	4	1	no	—
210	Q₈×C₆₁	—	4	1	no	—
211	Q₈×C₆₁	—	8	1	no	—
212	D₄×C₆₁	—	2	2	no	—
213	D₄×C₆₁	—	2	2	no	—
214	D₄×C₆₁	—	4	2	no	—
215	D₄×C₆₁	—	4	4	no	—
216	D₄×C₆₁	—	4	1	no	—
217	D₄×C₆₁	—	4	1	no	—
218	D₄×C₆₁	—	4	1	no	—
219	D₄×C₆₁	—	4	1	no	—
220	D₄×C₆₁	—	4	2	no	—
221	D₄×C₆₁	—	8	4	no	—
222	D₄×C₆₁	—	8	4	no	—
223	C₂×C₄×C₆₁	—	2	1	no	—
224	C₂×C₄×C₆₁	—	2	1	no	—
225	C₂×C₄×C₆₁	—	2	2	no	—
226	C₂×C₄×C₆₁	—	2	2	no	—
227	C₂×C₄×C₆₁	—	2	2	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	4	1	no	—
230	C₂×C₄×C₆₁	—	4	2	no	—
231	C₂×C₄×C₆₁	—	4	2	no	—
232	C₂×C₄×C₆₁	—	4	4	no	—
233	C₂×C₄×C₆₁	—	4	1	no	—
234	C₂×C₄×C₆₁	—	4	1	no	—
235	C₂×C₄×C₆₁	—	8	2	no	—
236	C₂×C₄×C₆₁	—	8	1	no	—
237	C₂×C₄×C₆₁	—	8	4	no	—
238	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
239	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
240	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
241	C₂×C₄×C₆₁	#135	1	2	yes	—
242	C₂×C₄×C₆₁	#137	1	2	yes	—
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×D₄	1	1	yes	characteristic
246	C₈×C₆₁	—	2	2	no	—
247	C₈×C₆₁	—	4	1	no	—
248	C₈×C₆₁	—	4	2	no	—
249	C₈×C₆₁	—	4	2	no	—
250	#18679	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	—	4	2	no	—
254	C₂²×C₆₁	—	4	2	no	—
255	C₂²×C₆₁	—	4	2	no	—
256	C₂²×C₆₁	—	4	2	no	—
257	C₂²×C₆₁	—	4	2	no	—
258	C₂²×C₆₁	—	4	2	no	—
259	C₂²×C₆₁	—	8	4	no	—
260	C₂²×C₆₁	#452	1	2	yes	—
261	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
262	C₄×C₆₁	—	2	1	no	—
263	C₄×C₆₁	—	2	1	no	—
264	C₄×C₆₁	—	2	1	no	—
265	C₄×C₆₁	—	4	2	no	—
266	C₄×C₆₁	—	4	2	no	—
267	C₄×C₆₁	—	4	2	no	—
268	C₄×C₆₁	—	4	2	no	—
269	C₄×C₆₁	—	8	1	no	—
270	C₄×C₆₁	—	8	1	no	—
271	C₄×C₆₁	#452	1	2	yes	—
272	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
273	C₄×C₆₁	C₂×#137	1	1	yes	characteristic
274	C₄×C₆₁	#576	1	1	yes	characteristic
275	C₄×C₆₁	#577	1	1	yes	characteristic
276	#3506	C₂×C₆₁	1	1	yes	characteristic
277	#3249	C₂×C₆₁	1	1	yes	characteristic, complemented
278	#3167	C₂×C₆₁	1	1	yes	characteristic, complemented
279	#3077	C₂×C₆₁	1	1	yes	characteristic, complemented
280	#1652	C₂×C₆₁	1	2	yes	complemented
281	#1641	C₂×C₆₁	1	2	yes	complemented
282	#1638	C₂×C₆₁	1	2	yes	complemented
283	#1631	C₂×C₆₁	1	2	yes	complemented
284	#1547	C₂×C₆₁	1	1	yes	characteristic, complemented
285	#1493	C₂×C₆₁	1	1	yes	characteristic, complemented
286	C₂×D₄⋊C₈	C₂×C₆₁	1	1	yes	characteristic, complemented
287	C₂×C₆₁	—	2	2	no	—
288	C₂×C₆₁	—	8	2	no	—
289	C₂×C₆₁	—	8	2	no	—
290	C₂×C₆₁	C₂×#452	1	1	yes	characteristic
291	C₂×C₆₁	#3012	1	1	yes	characteristic
292	C₂×C₆₁	#3018	1	1	yes	characteristic
293	#559	—	2	2	no	—
294	#556	C₂²×C₆₁	1	2	yes	—
295	#555	—	2	1	no	—
296	#553	—	2	2	no	—
297	#550	C₂²×C₆₁	1	2	yes	—
298	#547	—	2	1	no	—
299	#538	—	2	2	no	—
300	#535	—	2	1	no	—
301	#533	C₂²×C₆₁	1	1	yes	characteristic
302	#533	C₂²×C₆₁	1	1	yes	characteristic
303	#532	C₂²×C₆₁	1	1	yes	characteristic
304	#525	—	2	2	no	—
305	#520	—	2	1	no	—
306	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
307	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
308	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
309	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
310	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
311	#478	—	2	2	no	—
312	#477	—	2	1	no	—
313	#477	C₂²×C₆₁	1	2	yes	complemented
314	#476	C₂²×C₆₁	1	2	yes	—
315	#474	C₂²×C₆₁	1	2	yes	—
316	#467	—	2	2	no	—
317	#465	—	2	2	no	—
318	#462	—	2	1	no	—
319	#462	C₂²×C₆₁	1	2	yes	complemented
320	C₄×SD₁₆	—	2	2	no	—
321	#428	—	2	1	no	—
322	#423	C₂²×C₆₁	1	1	yes	characteristic
323	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
324	#418	—	2	1	no	—
325	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
326	#332	C₂²×C₆₁	1	2	yes	complemented
327	#331	C₂²×C₆₁	1	2	yes	complemented
328	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	complemented
329	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	complemented
330	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
331	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
332	C₆₁	#18679	1	1	yes	characteristic, direct product factor, Sylow
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	2	1	no	—
335	C₂²×D₄	D₄×C₆₁	1	1	yes	characteristic
336	C₂³×C₄	—	2	1	no	—
337	C₂×Q₁₆	—	2	2	no	—
338	C₂×SD₁₆	—	2	2	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂²×C₈	—	2	1	no	—
341	C₂²×C₈	—	2	1	no	—
342	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
343	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
344	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
345	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
346	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
347	#127	—	2	2	no	—
348	#127	C₂³×C₆₁	1	1	yes	characteristic
349	#126	—	2	4	no	—
350	#125	—	2	1	no	—
351	#125	—	2	1	no	—
352	#124	—	2	4	no	—
353	#124	—	2	2	no	—
354	#124	—	2	1	no	—
355	#123	—	2	4	no	—
356	#123	—	2	4	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	1	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
362	#121	—	2	2	no	—
363	#121	—	2	2	no	—
364	#121	—	2	4	no	—
365	#121	—	2	1	no	—
366	#121	—	2	2	no	—
367	#121	D₄×C₆₁	1	2	yes	—
368	#120	—	2	4	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
374	C₄×D₄	—	2	4	no	—
375	C₄×D₄	—	2	4	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	D₄×C₆₁	1	2	yes	—
381	C₄×D₄	D₄×C₆₁	1	2	yes	—
382	C₄×D₄	C₂³×C₆₁	1	2	yes	—
383	#117	—	2	2	no	—
384	#117	—	2	1	no	—
385	#117	—	2	2	no	—
386	#117	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	D₄×C₆₁	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
391	#107	—	2	2	no	—
392	#107	—	2	2	no	—
393	#106	—	2	2	no	—
394	#106	—	2	2	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
398	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
399	#103	—	2	2	no	—
400	#103	—	2	2	no	—
401	#103	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	2	2	no	—
405	C₄×C₈	—	2	1	no	—
406	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
407	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
408	C₂⁴	—	2	1	no	—
409	#41	—	4	2	no	—
410	#41	—	4	2	no	—
411	#41	—	8	2	no	—
412	#41	—	8	2	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	1	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
427	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	8	1	no	—
434	C₂²×C₄	—	8	1	no	—
435	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
438	Q₁₆	—	8	2	no	—
439	SD₁₆	—	4	4	no	—
440	M₁₆	—	4	2	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	4	2	no	—
446	C₂×C₈	—	8	1	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
462	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₄²	—	2	4	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	4	1	no	—
476	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
477	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
479	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	8	1	no	—
484	C₂³	—	8	1	no	—
485	C₂³	#120×C₆₁	1	1	yes	characteristic
486	Q₈	—	2	2	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	4	2	no	—
489	Q₈	—	4	1	no	—
490	Q₈	—	4	1	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	8	1	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	4	2	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	1	no	—
499	D₄	—	4	1	no	—
500	D₄	—	4	1	no	—
501	D₄	—	4	1	no	—
502	D₄	—	4	2	no	—
503	D₄	—	8	4	no	—
504	D₄	—	8	4	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	4	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	8	2	no	—
518	C₂×C₄	—	8	1	no	—
519	C₂×C₄	—	8	4	no	—
520	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
521	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
522	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
523	C₂×C₄	#135×C₆₁	1	2	yes	—
524	C₂×C₄	#137×C₆₁	1	2	yes	—
525	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
526	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	4	1	no	—
530	C₈	—	4	2	no	—
531	C₈	—	4	2	no	—
532	C₂²	—	2	1	no	—
533	C₂²	—	2	1	no	—
534	C₂²	—	4	2	no	—
535	C₂²	—	4	2	no	—
536	C₂²	—	4	2	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	8	4	no	—
541	C₂²	C₆₁×#452	1	2	yes	—
542	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	1	no	—
552	C₄	C₆₁×#452	1	2	yes	—
553	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
554	C₄	C₂×#137×C₆₁	1	1	yes	characteristic
555	C₄	C₆₁×#576	1	1	yes	characteristic
556	C₄	C₆₁×#577	1	1	yes	characteristic
557	C₂	—	2	2	no	—
558	C₂	—	8	2	no	—
559	C₂	—	8	2	no	—
560	C₂	C₂×C₆₁×#452	1	1	yes	characteristic
561	C₂	C₆₁×#3012	1	1	yes	characteristic
562	C₂	C₆₁×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3506	C₂
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×#3249	C₂	semidirect
3. C₆₁×#3167	C₂	semidirect
4. C₆₁×#3077	C₂	semidirect
5. C₆₁×#1652	C₂	semidirect
6. C₆₁×#1641	C₂	semidirect
7. C₆₁×#1638	C₂	semidirect
8. C₆₁×#1631	C₂	semidirect
9. C₆₁×#1547	C₂	semidirect
10. C₆₁×#1493	C₂	semidirect
11. C₂×C₆₁×D₄⋊C₈	C₂	semidirect
26. C₆₁×#498	C₂²	semidirect
27. C₆₁×#492	C₂²	semidirect
28. C₆₁×#487	C₂²	semidirect
29. C₆₁×#486	C₂²	semidirect
32. C₆₁×#477	C₂²	semidirect
38. C₆₁×#462	C₂²	semidirect
45. C₆₁×#332	C₂²	semidirect
46. C₆₁×#331	C₂²	semidirect
47. C₆₁×Q₈⋊C₈	C₂²	semidirect
48. C₆₁×Q₈⋊C₈	C₂²	semidirect
250. #18679	C₆₁	direct (N × H)
277. #3249	C₂×C₆₁	semidirect
278. #3167	C₂×C₆₁	semidirect
279. #3077	C₂×C₆₁	semidirect
280. #1652	C₂×C₆₁	semidirect
281. #1641	C₂×C₆₁	semidirect
282. #1638	C₂×C₆₁	semidirect
283. #1631	C₂×C₆₁	semidirect
284. #1547	C₂×C₆₁	semidirect
285. #1493	C₂×C₆₁	semidirect
286. C₂×D₄⋊C₈	C₂×C₆₁	semidirect
307. #498	C₂²×C₆₁	semidirect
308. #492	C₂²×C₆₁	semidirect
309. #487	C₂²×C₆₁	semidirect
310. #486	C₂²×C₆₁	semidirect
313. #477	C₂²×C₆₁	semidirect
319. #462	C₂²×C₆₁	semidirect
326. #332	C₂²×C₆₁	semidirect
327. #331	C₂²×C₆₁	semidirect
328. Q₈⋊C₈	C₂²×C₆₁	semidirect
329. Q₈⋊C₈	C₂²×C₆₁	semidirect
332. C₆₁	#18679	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₁×#3506	2
C₆₁×#3249	2
C₆₁×#3167	2
C₆₁×#3077	2
C₆₁×#1652	2
C₆₁×#1641	2
C₆₁×#1638	2
C₆₁×#1631	2
C₆₁×#1547	2
C₆₁×#1493	2
C₂×C₆₁×D₄⋊C₈	2
#18679	61

Subgroups — C61×#18679 #29522112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#18679 #29522112