Subgroups — C₆₁×#18652 #29522085

Order 15616.

938 conjugacy classes of subgroups.

The subgroup lattice has 506 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×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₆₁×#498	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3039	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1653	C₂	1	4	yes	maximal, complemented
6	C₆₁×#1651	C₂	1	4	yes	maximal, complemented
7	C₆₁×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1476	C₂	1	1	yes	maximal, characteristic
10	C₂×#137×C₆₁	—	2	1	no	—
11	Q₈²×C₆₁	—	2	1	no	—
12	C₆₁×#557	C₂²	1	2	yes	—
13	C₆₁×#554	—	2	1	no	—
14	C₆₁×#554	—	2	2	no	—
15	D₄×Q₈×C₆₁	—	2	2	no	—
16	D₄×Q₈×C₆₁	C₂²	1	2	yes	—
17	C₆₁×#544	—	2	2	no	—
18	C₆₁×#544	—	2	1	no	—
19	C₆₁×#533	—	2	1	no	—
20	C₆₁×#533	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Q₈×C₆₁	—	2	1	no	—
22	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
24	C₆₁×#520	—	2	1	no	—
25	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#498	—	2	2	no	—
27	C₆₁×#498	—	2	1	no	—
28	C₆₁×#498	C₂²	1	4	yes	—
29	C₆₁×#487	—	2	1	no	—
30	C₆₁×#483	—	2	2	no	—
31	C₆₁×#475	C₂²	1	4	yes	—
32	C₆₁×#462	—	2	1	no	—
33	C₆₁×#462	C₂²	1	2	yes	—
34	C₆₁×#461	—	2	1	no	—
35	C₆₁×#461	C₂²	1	2	yes	—
36	C₆₁×#431	C₂²	1	1	yes	characteristic
37	C₂×#106×C₆₁	—	2	2	no	—
38	C₆₁×#423	C₂²	1	1	yes	characteristic
39	C₆₁×#419	—	2	1	no	—
40	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
41	C₆₁×#332	C₂²	1	4	yes	—
42	C₆₁×Q₈⋊C₈	C₂²	1	4	yes	—
43	C₆₁×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₆₁×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₆₁	—	2	2	no	—
47	C₂²×Q₈×C₆₁	—	2	1	no	—
48	C₂²×Q₈×C₆₁	—	2	1	no	—
49	#137×C₆₁	—	4	4	no	—
50	C₂×Q₁₆×C₆₁	—	2	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	—	2	1	no	—
53	C₂²×C₈×C₆₁	—	2	1	no	—
54	C₄⋊Q₈×C₆₁	—	2	2	no	—
55	C₄⋊Q₈×C₆₁	—	2	2	no	—
56	C₄⋊Q₈×C₆₁	—	2	4	no	—
57	C₄⋊Q₈×C₆₁	—	2	2	no	—
58	C₄⋊Q₈×C₆₁	—	2	2	no	—
59	C₄⋊Q₈×C₆₁	—	2	1	no	—
60	C₄⋊Q₈×C₆₁	—	2	1	no	—
61	C₄⋊Q₈×C₆₁	—	2	1	no	—
62	C₄⋊Q₈×C₆₁	—	2	1	no	—
63	C₄⋊Q₈×C₆₁	—	2	1	no	—
64	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₆₁	D₄	1	2	yes	—
66	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
68	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
69	#125×C₆₁	—	2	2	no	—
70	#125×C₆₁	—	2	4	no	—
71	#125×C₆₁	—	2	2	no	—
72	#125×C₆₁	—	2	1	no	—
73	C₂²⋊Q₈×C₆₁	—	2	2	no	—
74	C₂²⋊Q₈×C₆₁	—	2	4	no	—
75	C₂²⋊Q₈×C₆₁	—	2	4	no	—
76	C₂²⋊Q₈×C₆₁	—	2	1	no	—
77	C₂²⋊Q₈×C₆₁	—	2	2	no	—
78	C₂²⋊Q₈×C₆₁	—	2	4	no	—
79	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
80	C₄×Q₈×C₆₁	—	2	2	no	—
81	C₄×Q₈×C₆₁	—	2	2	no	—
82	C₄×Q₈×C₆₁	—	2	2	no	—
83	C₄×Q₈×C₆₁	—	2	1	no	—
84	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
85	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
86	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
87	C₄×D₄×C₆₁	—	2	4	no	—
88	C₄×D₄×C₆₁	—	2	2	no	—
89	C₄×D₄×C₆₁	—	2	1	no	—
90	C₄×D₄×C₆₁	—	2	1	no	—
91	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
92	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
93	#117×C₆₁	—	2	2	no	—
94	#117×C₆₁	—	2	1	no	—
95	#117×C₆₁	—	2	1	no	—
96	#117×C₆₁	D₄	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
98	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
99	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
100	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
102	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
103	C₂×C₄²×C₆₁	—	2	1	no	—
104	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
105	#106×C₆₁	—	2	8	no	—
106	#106×C₆₁	—	2	4	no	—
107	C₄⋊C₈×C₆₁	—	2	1	no	—
108	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
109	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
110	#103×C₆₁	—	2	4	no	—
111	#103×C₆₁	—	2	2	no	—
112	#103×C₆₁	—	2	2	no	—
113	C₂²⋊C₈×C₆₁	—	2	1	no	—
114	C₄×C₈×C₆₁	—	2	1	no	—
115	C₄×C₈×C₆₁	—	2	1	no	—
116	C₄×C₈×C₆₁	C₂³	1	2	yes	—
117	#41×C₆₁	—	2	2	no	—
118	#41×C₆₁	SD₁₆	1	4	yes	—
119	C₂×Q₈×C₆₁	—	2	4	no	—
120	C₂×Q₈×C₆₁	—	2	1	no	—
121	C₂×Q₈×C₆₁	—	2	2	no	—
122	C₂×Q₈×C₆₁	—	2	2	no	—
123	C₂×Q₈×C₆₁	—	2	2	no	—
124	C₂×Q₈×C₆₁	—	4	1	no	—
125	C₂×Q₈×C₆₁	—	4	2	no	—
126	C₂×Q₈×C₆₁	—	4	2	no	—
127	C₂×Q₈×C₆₁	—	8	2	no	—
128	C₂×Q₈×C₆₁	—	8	4	no	—
129	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
130	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂×D₄×C₆₁	—	2	1	no	—
132	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₆₁	—	2	1	no	—
134	C₂²×C₄×C₆₁	—	2	4	no	—
135	C₂²×C₄×C₆₁	—	2	2	no	—
136	C₂²×C₄×C₆₁	—	2	1	no	—
137	C₂²×C₄×C₆₁	—	2	1	no	—
138	C₂²×C₄×C₆₁	—	4	1	no	—
139	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
142	Q₁₆×C₆₁	—	4	4	no	—
143	SD₁₆×C₆₁	—	4	4	no	—
144	M₁₆×C₆₁	—	4	2	no	—
145	C₂×C₈×C₆₁	—	2	4	no	—
146	C₂×C₈×C₆₁	—	2	2	no	—
147	C₂×C₈×C₆₁	—	2	2	no	—
148	C₂×C₈×C₆₁	—	2	2	no	—
149	C₄⋊C₄×C₆₁	—	2	4	no	—
150	C₄⋊C₄×C₆₁	—	2	4	no	—
151	C₄⋊C₄×C₆₁	—	2	4	no	—
152	C₄⋊C₄×C₆₁	—	2	4	no	—
153	C₄⋊C₄×C₆₁	—	2	1	no	—
154	C₄⋊C₄×C₆₁	—	2	2	no	—
155	C₄⋊C₄×C₆₁	—	2	1	no	—
156	C₄⋊C₄×C₆₁	—	2	2	no	—
157	C₄⋊C₄×C₆₁	—	2	1	no	—
158	C₄⋊C₄×C₆₁	—	2	1	no	—
159	C₄⋊C₄×C₆₁	—	2	2	no	—
160	C₄⋊C₄×C₆₁	—	2	2	no	—
161	C₄⋊C₄×C₆₁	—	2	1	no	—
162	C₄⋊C₄×C₆₁	—	2	2	no	—
163	C₄⋊C₄×C₆₁	—	2	2	no	—
164	C₄⋊C₄×C₆₁	—	2	2	no	—
165	C₄⋊C₄×C₆₁	—	4	1	no	—
166	C₄⋊C₄×C₆₁	—	4	1	no	—
167	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
168	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
169	C₄⋊C₄×C₆₁	C₂×D₄	1	4	yes	—
170	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
171	C₂²⋊C₄×C₆₁	—	2	4	no	—
172	C₂²⋊C₄×C₆₁	—	2	2	no	—
173	C₂²⋊C₄×C₆₁	—	2	1	no	—
174	C₂²⋊C₄×C₆₁	—	2	1	no	—
175	C₂²⋊C₄×C₆₁	—	2	1	no	—
176	C₄²×C₆₁	—	2	4	no	—
177	C₄²×C₆₁	—	2	1	no	—
178	C₄²×C₆₁	—	2	1	no	—
179	C₄²×C₆₁	—	2	1	no	—
180	C₄²×C₆₁	—	2	2	no	—
181	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
185	C₂³×C₆₁	—	2	1	no	—
186	C₂³×C₆₁	#120	1	1	yes	characteristic
187	Q₈×C₆₁	—	2	1	no	—
188	Q₈×C₆₁	—	2	4	no	—
189	Q₈×C₆₁	—	4	4	no	—
190	Q₈×C₆₁	—	4	2	no	—
191	Q₈×C₆₁	—	4	2	no	—
192	Q₈×C₆₁	—	4	2	no	—
193	Q₈×C₆₁	—	8	2	no	—
194	Q₈×C₆₁	—	8	4	no	—
195	Q₈×C₆₁	—	8	2	no	—
196	Q₈×C₆₁	C₂×SD₁₆	1	2	yes	—
197	D₄×C₆₁	—	2	4	no	—
198	D₄×C₆₁	—	2	1	no	—
199	D₄×C₆₁	C₂×SD₁₆	1	2	yes	—
200	C₂×C₄×C₆₁	—	2	1	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	4	no	—
203	C₂×C₄×C₆₁	—	2	2	no	—
204	C₂×C₄×C₆₁	—	2	2	no	—
205	C₂×C₄×C₆₁	—	2	1	no	—
206	C₂×C₄×C₆₁	—	2	1	no	—
207	C₂×C₄×C₆₁	—	2	2	no	—
208	C₂×C₄×C₆₁	—	2	4	no	—
209	C₂×C₄×C₆₁	—	4	2	no	—
210	C₂×C₄×C₆₁	—	4	2	no	—
211	C₂×C₄×C₆₁	—	4	2	no	—
212	C₂×C₄×C₆₁	—	8	2	no	—
213	C₂×C₄×C₆₁	—	8	4	no	—
214	C₂×C₄×C₆₁	—	8	2	no	—
215	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
216	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
217	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
218	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
219	C₂×C₄×C₆₁	#137	1	2	yes	—
220	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
223	C₈×C₆₁	—	2	4	no	—
224	C₈×C₆₁	—	4	2	no	—
225	C₈×C₆₁	—	4	2	no	—
226	#18652	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₆₁	—	2	1	no	—
228	C₂²×C₆₁	—	2	1	no	—
229	C₂²×C₆₁	—	2	2	no	—
230	C₂²×C₆₁	—	4	1	no	—
231	C₂²×C₆₁	—	4	1	no	—
232	C₂²×C₆₁	#448	1	2	yes	—
233	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
234	C₄×C₆₁	—	2	2	no	—
235	C₄×C₆₁	—	2	1	no	—
236	C₄×C₆₁	—	2	1	no	—
237	C₄×C₆₁	—	4	1	no	—
238	C₄×C₆₁	—	4	2	no	—
239	C₄×C₆₁	—	4	4	no	—
240	C₄×C₆₁	—	4	1	no	—
241	C₄×C₆₁	—	4	2	no	—
242	C₄×C₆₁	—	8	2	no	—
243	C₄×C₆₁	#448	1	2	yes	—
244	C₄×C₆₁	#456	1	2	yes	—
245	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
246	C₄×C₆₁	C₂×#137	1	1	yes	characteristic
247	C₄×C₆₁	#577	1	2	yes	—
248	#3503	C₂×C₆₁	1	1	yes	characteristic
249	#3229	C₂×C₆₁	1	1	yes	characteristic, complemented
250	C₂×#498	C₂×C₆₁	1	1	yes	characteristic, complemented
251	#3039	C₂×C₆₁	1	1	yes	characteristic
252	#1653	C₂×C₆₁	1	4	yes	complemented
253	#1651	C₂×C₆₁	1	4	yes	complemented
254	#1549	C₂×C₆₁	1	1	yes	characteristic, complemented
255	#1493	C₂×C₆₁	1	1	yes	characteristic, complemented
256	#1476	C₂×C₆₁	1	1	yes	characteristic
257	C₂×C₆₁	—	2	2	no	—
258	C₂×C₆₁	—	4	2	no	—
259	C₂×C₆₁	C₂×#448	1	1	yes	characteristic
260	C₂×C₆₁	#3009	1	1	yes	characteristic
261	C₂×C₆₁	C₂×#456	1	1	yes	characteristic
262	C₂×#137	—	2	1	no	—
263	Q₈²	—	2	1	no	—
264	#557	C₂²×C₆₁	1	2	yes	—
265	#554	—	2	1	no	—
266	#554	—	2	2	no	—
267	D₄×Q₈	—	2	2	no	—
268	D₄×Q₈	C₂²×C₆₁	1	2	yes	—
269	#544	—	2	2	no	—
270	#544	—	2	1	no	—
271	#533	—	2	1	no	—
272	#533	C₂²×C₆₁	1	1	yes	characteristic
273	C₂×C₄⋊Q₈	—	2	1	no	—
274	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
275	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
276	#520	—	2	1	no	—
277	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
278	#498	—	2	2	no	—
279	#498	—	2	1	no	—
280	#498	C₂²×C₆₁	1	4	yes	—
281	#487	—	2	1	no	—
282	#483	—	2	2	no	—
283	#475	C₂²×C₆₁	1	4	yes	—
284	#462	—	2	1	no	—
285	#462	C₂²×C₆₁	1	2	yes	—
286	#461	—	2	1	no	—
287	#461	C₂²×C₆₁	1	2	yes	—
288	#431	C₂²×C₆₁	1	1	yes	characteristic
289	C₂×#106	—	2	2	no	—
290	#423	C₂²×C₆₁	1	1	yes	characteristic
291	#419	—	2	1	no	—
292	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
293	#332	C₂²×C₆₁	1	4	yes	—
294	Q₈⋊C₈	C₂²×C₆₁	1	4	yes	—
295	Q₈⋊C₈	C₂²×C₆₁	1	2	yes	—
296	D₄⋊C₈	C₂²×C₆₁	1	2	yes	—
297	C₆₁	#18652	1	1	yes	characteristic, direct product factor, Sylow
298	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
299	C₂²×Q₈	—	2	2	no	—
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	—	2	1	no	—
302	#137	—	4	4	no	—
303	C₂×Q₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×M₁₆	—	2	1	no	—
306	C₂²×C₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	—	2	2	no	—
309	C₄⋊Q₈	—	2	4	no	—
310	C₄⋊Q₈	—	2	2	no	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	1	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
318	C₄⋊Q₈	D₄×C₆₁	1	2	yes	—
319	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
321	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
322	#125	—	2	2	no	—
323	#125	—	2	4	no	—
324	#125	—	2	2	no	—
325	#125	—	2	1	no	—
326	C₂²⋊Q₈	—	2	2	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	4	no	—
332	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
333	C₄×Q₈	—	2	2	no	—
334	C₄×Q₈	—	2	2	no	—
335	C₄×Q₈	—	2	2	no	—
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
338	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
339	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
345	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
346	#117	—	2	2	no	—
347	#117	—	2	1	no	—
348	#117	—	2	1	no	—
349	#117	D₄×C₆₁	1	1	yes	characteristic
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	2	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
358	#106	—	2	8	no	—
359	#106	—	2	4	no	—
360	C₄⋊C₈	—	2	1	no	—
361	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
362	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
363	#103	—	2	4	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	C₂²⋊C₈	—	2	1	no	—
367	C₄×C₈	—	2	1	no	—
368	C₄×C₈	—	2	1	no	—
369	C₄×C₈	C₂³×C₆₁	1	2	yes	—
370	#41	—	2	2	no	—
371	#41	SD₁₆×C₆₁	1	4	yes	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	4	1	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	—	4	2	no	—
380	C₂×Q₈	—	8	2	no	—
381	C₂×Q₈	—	8	4	no	—
382	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
383	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	4	1	no	—
392	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
395	Q₁₆	—	4	4	no	—
396	SD₁₆	—	4	4	no	—
397	M₁₆	—	4	2	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₄⋊C₄	—	2	4	no	—
403	C₄⋊C₄	—	2	4	no	—
404	C₄⋊C₄	—	2	4	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	4	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
421	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
422	C₄⋊C₄	C₂×D₄×C₆₁	1	4	yes	—
423	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
424	C₂²⋊C₄	—	2	4	no	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₄²	—	2	4	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	2	no	—
434	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
436	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
437	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
438	C₂³	—	2	1	no	—
439	C₂³	#120×C₆₁	1	1	yes	characteristic
440	Q₈	—	2	1	no	—
441	Q₈	—	2	4	no	—
442	Q₈	—	4	4	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	8	2	no	—
447	Q₈	—	8	4	no	—
448	Q₈	—	8	2	no	—
449	Q₈	C₂×SD₁₆×C₆₁	1	2	yes	—
450	D₄	—	2	4	no	—
451	D₄	—	2	1	no	—
452	D₄	C₂×SD₁₆×C₆₁	1	2	yes	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	8	2	no	—
466	C₂×C₄	—	8	4	no	—
467	C₂×C₄	—	8	2	no	—
468	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
469	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
470	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
471	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
472	C₂×C₄	#137×C₆₁	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
474	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	1	no	—
483	C₂²	—	4	1	no	—
484	C₂²	C₆₁×#448	1	2	yes	—
485	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
486	C₄	—	2	2	no	—
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	4	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	8	2	no	—
495	C₄	C₆₁×#448	1	2	yes	—
496	C₄	C₆₁×#456	1	2	yes	—
497	C₄	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
498	C₄	C₂×#137×C₆₁	1	1	yes	characteristic
499	C₄	C₆₁×#577	1	2	yes	—
500	C₂	—	2	2	no	—
501	C₂	—	4	2	no	—
502	C₂	C₂×C₆₁×#448	1	1	yes	characteristic
503	C₂	C₆₁×#3009	1	1	yes	characteristic
504	C₂	C₂×C₆₁×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×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×#3229	C₂	semidirect
3. C₂×C₆₁×#498	C₂	semidirect
5. C₆₁×#1653	C₂	semidirect
6. C₆₁×#1651	C₂	semidirect
7. C₆₁×#1549	C₂	semidirect
8. C₆₁×#1493	C₂	semidirect
226. #18652	C₆₁	direct (N × H)
249. #3229	C₂×C₆₁	semidirect
250. C₂×#498	C₂×C₆₁	semidirect
252. #1653	C₂×C₆₁	semidirect
253. #1651	C₂×C₆₁	semidirect
254. #1549	C₂×C₆₁	semidirect
255. #1493	C₂×C₆₁	semidirect
297. C₆₁	#18652	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×#3503	2
C₆₁×#3229	2
C₂×C₆₁×#498	2
C₆₁×#3039	2
C₆₁×#1653	2
C₆₁×#1651	2
C₆₁×#1549	2
C₆₁×#1493	2
C₆₁×#1476	2
#18652	61

Subgroups — C61×#18652 #29522085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#18652 #29522085