Subgroups — C₆₁×#19685 #29523118

Order 15616.

712 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3230	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3206	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3167	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#3165	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3141	C₂	1	1	yes	maximal, characteristic
6	C₂×C₆₁×#487	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1719	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1718	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1718	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1714	C₂	1	2	yes	maximal, complemented
11	C₆₁×#1451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#533	C₂²	1	1	yes	characteristic
13	C₆₁×#532	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#501	—	2	2	no	—
17	C₆₁×#500	C₂²	1	2	yes	—
18	C₆₁×#500	C₂²	1	2	yes	—
19	C₆₁×#498	C₂²	1	2	yes	—
20	C₆₁×#498	C₂²	1	1	yes	characteristic
21	C₆₁×#492	C₂²	1	1	yes	characteristic
22	C₆₁×#492	C₂²	1	2	yes	—
23	C₆₁×#489	—	2	2	no	—
24	C₆₁×#487	—	2	2	no	—
25	C₆₁×#487	C₂²	1	2	yes	—
26	C₆₁×#487	C₂²	1	2	yes	—
27	C₆₁×#487	C₂²	1	2	yes	—
28	C₆₁×#487	C₂²	1	1	yes	characteristic
29	C₆₁×#487	C₂²	1	2	yes	—
30	C₆₁×#487	C₂²	1	2	yes	—
31	C₆₁×#486	C₂²	1	2	yes	—
32	C₆₁×#486	C₂²	1	1	yes	characteristic
33	C₆₁×#484	—	2	2	no	—
34	C₆₁×#477	—	2	2	no	—
35	C₆₁×#465	—	2	2	no	—
36	C₆₁×#461	—	2	2	no	—
37	C₆₁×#448	—	2	2	no	—
38	C₄×SD₁₆×C₆₁	—	2	2	no	—
39	C₆₁×#431	C₂²	1	1	yes	characteristic
40	C₆₁×#428	—	2	2	no	—
41	C₆₁×#417	—	2	2	no	—
42	C₂×#103×C₆₁	—	2	2	no	—
43	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
45	C₆₁×#322	C₂²	1	2	yes	—
46	C₆₁×#322	C₂²	1	2	yes	—
47	C₂×#41×C₆₁	—	2	1	no	—
48	C₂²×Q₈×C₆₁	—	2	1	no	—
49	C₂²×Q₈×C₆₁	—	2	1	no	—
50	C₂×SD₁₆×C₆₁	—	2	2	no	—
51	C₂×SD₁₆×C₆₁	—	2	4	no	—
52	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
53	C₂²×C₈×C₆₁	D₄	1	2	yes	—
54	C₄⋊Q₈×C₆₁	—	2	1	no	—
55	C₄⋊Q₈×C₆₁	—	2	1	no	—
56	C₄⋊Q₈×C₆₁	—	2	1	no	—
57	C₄⋊Q₈×C₆₁	—	2	1	no	—
58	C₄⋊Q₈×C₆₁	—	2	1	no	—
59	C₄⋊Q₈×C₆₁	—	2	1	no	—
60	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
61	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
66	#125×C₆₁	—	2	1	no	—
67	#124×C₆₁	—	2	1	no	—
68	C₂²⋊Q₈×C₆₁	—	2	1	no	—
69	C₂²⋊Q₈×C₆₁	—	2	1	no	—
70	#121×C₆₁	—	2	1	no	—
71	#121×C₆₁	—	2	1	no	—
72	C₄×Q₈×C₆₁	—	2	1	no	—
73	C₄×Q₈×C₆₁	—	2	1	no	—
74	C₄×D₄×C₆₁	—	2	1	no	—
75	C₄×D₄×C₆₁	—	2	1	no	—
76	#117×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
82	#107×C₆₁	—	2	4	no	—
83	#107×C₆₁	—	2	4	no	—
84	#106×C₆₁	—	2	4	no	—
85	#106×C₆₁	—	2	2	no	—
86	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
87	#103×C₆₁	—	2	4	no	—
88	#103×C₆₁	—	2	4	no	—
89	#103×C₆₁	—	2	4	no	—
90	#103×C₆₁	—	2	2	no	—
91	#103×C₆₁	—	2	4	no	—
92	#103×C₆₁	—	2	4	no	—
93	#102×C₆₁	—	2	4	no	—
94	#102×C₆₁	—	2	2	no	—
95	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
96	#97×C₆₁	D₄	1	2	yes	—
97	C₄×C₈×C₆₁	D₄	1	2	yes	—
98	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₆₁	C₂³	1	2	yes	—
101	C₄×C₈×C₆₁	C₂³	1	2	yes	—
102	#41×C₆₁	—	4	4	no	—
103	C₂×Q₈×C₆₁	—	2	1	no	—
104	C₂×Q₈×C₆₁	—	2	1	no	—
105	C₂×Q₈×C₆₁	—	2	2	no	—
106	C₂×Q₈×C₆₁	—	2	1	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	—	4	4	no	—
109	C₂×Q₈×C₆₁	—	4	1	no	—
110	C₂×Q₈×C₆₁	—	4	1	no	—
111	C₂×Q₈×C₆₁	—	8	2	no	—
112	C₂×D₄×C₆₁	—	2	1	no	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	—	2	1	no	—
115	C₂×D₄×C₆₁	—	4	1	no	—
116	C₂²×C₄×C₆₁	—	4	1	no	—
117	C₂²×C₄×C₆₁	—	4	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	SD₁₆×C₆₁	—	4	4	no	—
123	SD₁₆×C₆₁	—	8	4	no	—
124	M₁₆×C₆₁	—	2	4	no	—
125	C₂×C₈×C₆₁	—	4	2	no	—
126	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
129	C₂×C₈×C₆₁	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	1	no	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	2	1	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	2	1	no	—
139	C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₄⋊C₄×C₆₁	—	4	1	no	—
141	C₄⋊C₄×C₆₁	—	4	1	no	—
142	C₄⋊C₄×C₆₁	—	4	1	no	—
143	C₄⋊C₄×C₆₁	—	4	1	no	—
144	C₄⋊C₄×C₆₁	—	4	1	no	—
145	C₄⋊C₄×C₆₁	—	4	1	no	—
146	C₂²⋊C₄×C₆₁	—	4	1	no	—
147	C₂²⋊C₄×C₆₁	—	4	1	no	—
148	C₂²⋊C₄×C₆₁	—	4	1	no	—
149	C₄²×C₆₁	—	4	1	no	—
150	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
154	C₂³×C₆₁	—	4	1	no	—
155	C₂³×C₆₁	#127	1	1	yes	characteristic
156	Q₈×C₆₁	—	4	2	no	—
157	Q₈×C₆₁	—	4	2	no	—
158	Q₈×C₆₁	—	4	4	no	—
159	Q₈×C₆₁	—	4	4	no	—
160	Q₈×C₆₁	—	4	2	no	—
161	Q₈×C₆₁	—	8	2	no	—
162	Q₈×C₆₁	—	8	2	no	—
163	D₄×C₆₁	—	4	2	no	—
164	D₄×C₆₁	—	4	2	no	—
165	D₄×C₆₁	—	4	2	no	—
166	D₄×C₆₁	—	8	2	no	—
167	C₂×C₄×C₆₁	—	2	2	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	4	1	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	1	no	—
172	C₂×C₄×C₆₁	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	8	2	no	—
175	C₂×C₄×C₆₁	—	8	2	no	—
176	C₂×C₄×C₆₁	—	8	2	no	—
177	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
178	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
179	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
180	C₂×C₄×C₆₁	#137	1	4	yes	—
181	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
184	C₈×C₆₁	—	2	4	no	—
185	C₈×C₆₁	—	2	2	no	—
186	C₈×C₆₁	—	2	2	no	—
187	C₈×C₆₁	—	2	4	no	—
188	#19685	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₆₁	—	2	1	no	—
190	C₂²×C₆₁	—	2	1	no	—
191	C₂²×C₆₁	—	8	1	no	—
192	C₂²×C₆₁	—	8	1	no	—
193	C₂²×C₆₁	—	8	1	no	—
194	C₂²×C₆₁	#497	1	2	yes	—
195	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
196	C₄×C₆₁	—	2	1	no	—
197	C₄×C₆₁	—	2	1	no	—
198	C₄×C₆₁	—	8	1	no	—
199	C₄×C₆₁	—	8	2	no	—
200	C₄×C₆₁	—	8	1	no	—
201	C₄×C₆₁	—	8	2	no	—
202	C₄×C₆₁	—	8	1	no	—
203	C₄×C₆₁	#497	1	2	yes	—
204	C₄×C₆₁	C₂×#137	1	2	yes	—
205	C₄×C₆₁	#575	1	2	yes	—
206	C₄×C₆₁	#577	1	2	yes	—
207	#3230	C₂×C₆₁	1	1	yes	characteristic, complemented
208	#3206	C₂×C₆₁	1	1	yes	characteristic
209	#3167	C₂×C₆₁	1	1	yes	characteristic
210	#3165	C₂×C₆₁	1	1	yes	characteristic, complemented
211	#3141	C₂×C₆₁	1	1	yes	characteristic
212	C₂×#487	C₂×C₆₁	1	1	yes	characteristic, complemented
213	#1719	C₂×C₆₁	1	2	yes	complemented
214	#1718	C₂×C₆₁	1	2	yes	complemented
215	#1718	C₂×C₆₁	1	2	yes	complemented
216	#1714	C₂×C₆₁	1	2	yes	complemented
217	#1451	C₂×C₆₁	1	1	yes	characteristic, complemented
218	C₂×C₆₁	—	2	2	no	—
219	C₂×C₆₁	—	16	1	no	—
220	C₂×C₆₁	C₂×#497	1	1	yes	characteristic
221	C₂×C₆₁	#3153	1	1	yes	characteristic
222	C₂×C₆₁	#3154	1	1	yes	characteristic
223	#533	C₂²×C₆₁	1	1	yes	characteristic
224	#532	C₂²×C₆₁	1	1	yes	characteristic
225	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
226	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
227	#501	—	2	2	no	—
228	#500	C₂²×C₆₁	1	2	yes	—
229	#500	C₂²×C₆₁	1	2	yes	—
230	#498	C₂²×C₆₁	1	2	yes	—
231	#498	C₂²×C₆₁	1	1	yes	characteristic
232	#492	C₂²×C₆₁	1	1	yes	characteristic
233	#492	C₂²×C₆₁	1	2	yes	—
234	#489	—	2	2	no	—
235	#487	—	2	2	no	—
236	#487	C₂²×C₆₁	1	2	yes	—
237	#487	C₂²×C₆₁	1	2	yes	—
238	#487	C₂²×C₆₁	1	2	yes	—
239	#487	C₂²×C₆₁	1	1	yes	characteristic
240	#487	C₂²×C₆₁	1	2	yes	—
241	#487	C₂²×C₆₁	1	2	yes	—
242	#486	C₂²×C₆₁	1	2	yes	—
243	#486	C₂²×C₆₁	1	1	yes	characteristic
244	#484	—	2	2	no	—
245	#477	—	2	2	no	—
246	#465	—	2	2	no	—
247	#461	—	2	2	no	—
248	#448	—	2	2	no	—
249	C₄×SD₁₆	—	2	2	no	—
250	#431	C₂²×C₆₁	1	1	yes	characteristic
251	#428	—	2	2	no	—
252	#417	—	2	2	no	—
253	C₂×#103	—	2	2	no	—
254	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
256	#322	C₂²×C₆₁	1	2	yes	—
257	#322	C₂²×C₆₁	1	2	yes	—
258	C₆₁	#19685	1	1	yes	characteristic, direct product factor, Sylow
259	C₂×#41	—	2	1	no	—
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	—	2	1	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×SD₁₆	—	2	4	no	—
264	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
265	C₂²×C₈	D₄×C₆₁	1	2	yes	—
266	C₄⋊Q₈	—	2	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
273	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
274	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
275	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
277	#127	C₂³×C₆₁	1	1	yes	characteristic
278	#125	—	2	1	no	—
279	#124	—	2	1	no	—
280	C₂²⋊Q₈	—	2	1	no	—
281	C₂²⋊Q₈	—	2	1	no	—
282	#121	—	2	1	no	—
283	#121	—	2	1	no	—
284	C₄×Q₈	—	2	1	no	—
285	C₄×Q₈	—	2	1	no	—
286	C₄×D₄	—	2	1	no	—
287	C₄×D₄	—	2	1	no	—
288	#117	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
294	#107	—	2	4	no	—
295	#107	—	2	4	no	—
296	#106	—	2	4	no	—
297	#106	—	2	2	no	—
298	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
299	#103	—	2	4	no	—
300	#103	—	2	4	no	—
301	#103	—	2	4	no	—
302	#103	—	2	2	no	—
303	#103	—	2	4	no	—
304	#103	—	2	4	no	—
305	#102	—	2	4	no	—
306	#102	—	2	2	no	—
307	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
308	#97	D₄×C₆₁	1	2	yes	—
309	C₄×C₈	D₄×C₆₁	1	2	yes	—
310	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
311	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
312	C₄×C₈	C₂³×C₆₁	1	2	yes	—
313	C₄×C₈	C₂³×C₆₁	1	2	yes	—
314	#41	—	4	4	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	4	no	—
321	C₂×Q₈	—	4	1	no	—
322	C₂×Q₈	—	4	1	no	—
323	C₂×Q₈	—	8	2	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
334	SD₁₆	—	4	4	no	—
335	SD₁₆	—	8	4	no	—
336	M₁₆	—	2	4	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
339	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
340	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
341	C₂×C₈	C₂×D₄×C₆₁	1	4	yes	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
363	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
364	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
365	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
366	C₂³	—	4	1	no	—
367	C₂³	#127×C₆₁	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	4	no	—
371	Q₈	—	4	4	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	8	2	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
390	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
391	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
392	C₂×C₄	#137×C₆₁	1	4	yes	—
393	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
395	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
396	C₈	—	2	4	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	4	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	8	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	C₆₁×#497	1	2	yes	—
406	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	1	no	—
414	C₄	C₆₁×#497	1	2	yes	—
415	C₄	C₂×#137×C₆₁	1	2	yes	—
416	C₄	C₆₁×#575	1	2	yes	—
417	C₄	C₆₁×#577	1	2	yes	—
418	C₂	—	2	2	no	—
419	C₂	—	16	1	no	—
420	C₂	C₂×C₆₁×#497	1	1	yes	characteristic
421	C₂	C₆₁×#3153	1	1	yes	characteristic
422	C₂	C₆₁×#3154	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#532	C₂²
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
1. C₆₁×#3230	C₂	semidirect
4. C₆₁×#3165	C₂	semidirect
6. C₂×C₆₁×#487	C₂	semidirect
7. C₆₁×#1719	C₂	semidirect
8. C₆₁×#1718	C₂	semidirect
9. C₆₁×#1718	C₂	semidirect
10. C₆₁×#1714	C₂	semidirect
11. C₆₁×#1451	C₂	semidirect
188. #19685	C₆₁	direct (N × H)
207. #3230	C₂×C₆₁	semidirect
210. #3165	C₂×C₆₁	semidirect
212. C₂×#487	C₂×C₆₁	semidirect
213. #1719	C₂×C₆₁	semidirect
214. #1718	C₂×C₆₁	semidirect
215. #1718	C₂×C₆₁	semidirect
216. #1714	C₂×C₆₁	semidirect
217. #1451	C₂×C₆₁	semidirect
258. C₆₁	#19685	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×#3230	2
C₆₁×#3206	2
C₆₁×#3167	2
C₆₁×#3165	2
C₆₁×#3141	2
C₂×C₆₁×#487	2
C₆₁×#1719	2
C₆₁×#1718	2
C₆₁×#1714	2
C₆₁×#1451	2
#19685	61

Subgroups — C61×#19685 #29523118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19685 #29523118