Subgroups — C₆₁×#19161 #29522594

Order 15616.

598 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3170	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3107	C₂	1	2	yes	maximal
3	C₆₁×#2965	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#1700	C₂	1	2	yes	maximal, complemented
5	C₆₁×#1699	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1694	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1693	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1690	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1689	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1564	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1544	C₂	1	2	yes	maximal, complemented
12	C₆₁×#533	C₂²	1	2	yes	—
13	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
14	C₆₁×#500	C₂²	1	1	yes	characteristic
15	C₆₁×#494	C₂²	1	1	yes	characteristic
16	C₆₁×#487	C₂²	1	2	yes	—
17	C₆₁×#485	—	2	2	no	—
18	C₆₁×#475	C₂²	1	2	yes	—
19	C₆₁×#474	C₂²	1	2	yes	—
20	C₆₁×#467	—	2	1	no	—
21	C₆₁×#467	—	2	1	no	—
22	C₆₁×#462	C₂²	1	2	yes	—
23	C₆₁×#461	C₂²	1	2	yes	—
24	C₆₁×#452	—	2	2	no	—
25	C₆₁×#446	C₂²	1	1	yes	characteristic
26	C₆₁×#446	C₂²	1	1	yes	characteristic
27	C₄×Q₁₆×C₆₁	—	2	2	no	—
28	C₄×Q₁₆×C₆₁	—	2	1	no	—
29	C₄×Q₁₆×C₆₁	—	2	1	no	—
30	C₄×SD₁₆×C₆₁	—	2	2	no	—
31	C₆₁×#436	C₂²	1	1	yes	characteristic
32	C₆₁×#436	C₂²	1	1	yes	characteristic
33	C₆₁×#435	—	2	1	no	—
34	C₆₁×#435	—	2	1	no	—
35	C₆₁×#431	—	2	1	no	—
36	C₆₁×#431	C₂²	1	1	yes	characteristic
37	C₆₁×#431	C₂²	1	2	yes	—
38	C₄×M₁₆×C₆₁	—	2	1	no	—
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#335	C₂²	1	2	yes	—
41	C₆₁×#334	C₂²	1	1	yes	characteristic
42	C₆₁×#334	C₂²	1	1	yes	characteristic
43	C₆₁×#332	C₂²	1	2	yes	—
44	C₆₁×#332	C₂²	1	2	yes	—
45	C₆₁×#332	C₂²	1	2	yes	—
46	C₆₁×#332	C₂²	1	2	yes	—
47	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
48	C₂×Q₁₆×C₆₁	—	2	2	no	—
49	C₂×Q₁₆×C₆₁	—	2	1	no	—
50	C₂×Q₁₆×C₆₁	—	2	1	no	—
51	C₂×SD₁₆×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	—	2	1	no	—
53	C₂×M₁₆×C₆₁	—	2	1	no	—
54	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
56	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
58	#125×C₆₁	—	2	2	no	—
59	C₂²⋊Q₈×C₆₁	—	2	2	no	—
60	C₂²⋊Q₈×C₆₁	—	2	2	no	—
61	C₄×Q₈×C₆₁	—	2	2	no	—
62	C₄×Q₈×C₆₁	—	2	2	no	—
63	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
64	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
65	C₄×D₄×C₆₁	—	2	1	no	—
66	C₄×D₄×C₆₁	—	2	1	no	—
67	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
68	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
69	#117×C₆₁	—	2	1	no	—
70	#117×C₆₁	—	2	2	no	—
71	#117×C₆₁	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₆₁	—	2	1	no	—
73	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
74	#107×C₆₁	—	2	1	no	—
75	#107×C₆₁	—	2	1	no	—
76	#107×C₆₁	—	2	2	no	—
77	#106×C₆₁	—	2	2	no	—
78	C₄⋊C₈×C₆₁	—	2	1	no	—
79	C₄⋊C₈×C₆₁	—	2	1	no	—
80	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
83	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
84	#103×C₆₁	—	2	2	no	—
85	#103×C₆₁	—	2	2	no	—
86	#103×C₆₁	—	2	2	no	—
87	#103×C₆₁	—	2	2	no	—
88	#103×C₆₁	—	2	2	no	—
89	#102×C₆₁	—	2	2	no	—
90	C₂²⋊C₈×C₆₁	—	2	1	no	—
91	C₂²⋊C₈×C₆₁	—	2	2	no	—
92	C₂²⋊C₈×C₆₁	—	2	1	no	—
93	C₂²⋊C₈×C₆₁	—	2	1	no	—
94	#97×C₆₁	—	2	1	no	—
95	#97×C₆₁	—	2	1	no	—
96	C₄×C₈×C₆₁	—	2	1	no	—
97	C₄×C₈×C₆₁	—	2	2	no	—
98	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
99	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
102	#41×C₆₁	—	4	2	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	—	2	2	no	—
105	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
106	C₂×D₄×C₆₁	—	2	1	no	—
107	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₆₁	—	2	1	no	—
109	C₂²×C₄×C₆₁	—	2	1	no	—
110	C₂²×C₄×C₆₁	—	2	1	no	—
111	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
114	Q₁₆×C₆₁	—	4	2	no	—
115	Q₁₆×C₆₁	—	4	4	no	—
116	Q₁₆×C₆₁	—	4	2	no	—
117	SD₁₆×C₆₁	—	4	4	no	—
118	M₁₆×C₆₁	—	4	2	no	—
119	M₁₆×C₆₁	—	4	2	no	—
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	1	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	—	2	2	no	—
124	C₂×C₈×C₆₁	—	2	2	no	—
125	C₂×C₈×C₆₁	—	4	1	no	—
126	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₄⋊C₄×C₆₁	—	2	1	no	—
131	C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	—	2	2	no	—
134	C₄⋊C₄×C₆₁	—	2	2	no	—
135	C₄⋊C₄×C₆₁	—	2	2	no	—
136	C₄⋊C₄×C₆₁	—	4	2	no	—
137	C₄⋊C₄×C₆₁	—	4	2	no	—
138	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₆₁	—	2	1	no	—
141	C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₂²⋊C₄×C₆₁	—	2	1	no	—
143	C₂²⋊C₄×C₆₁	—	4	2	no	—
144	C₄²×C₆₁	—	2	1	no	—
145	C₄²×C₆₁	—	2	1	no	—
146	C₄²×C₆₁	—	2	1	no	—
147	C₄²×C₆₁	—	4	2	no	—
148	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₁	#41	1	1	yes	characteristic
151	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
152	C₂³×C₆₁	—	2	1	no	—
153	C₂³×C₆₁	#121	1	1	yes	characteristic
154	Q₈×C₆₁	—	2	2	no	—
155	Q₈×C₆₁	—	4	2	no	—
156	Q₈×C₆₁	—	4	2	no	—
157	Q₈×C₆₁	—	4	2	no	—
158	Q₈×C₆₁	—	4	2	no	—
159	D₄×C₆₁	—	2	2	no	—
160	D₄×C₆₁	—	4	2	no	—
161	C₂×C₄×C₆₁	—	2	1	no	—
162	C₂×C₄×C₆₁	—	2	1	no	—
163	C₂×C₄×C₆₁	—	2	2	no	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	1	no	—
166	C₂×C₄×C₆₁	—	2	1	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	4	2	no	—
169	C₂×C₄×C₆₁	—	4	1	no	—
170	C₂×C₄×C₆₁	—	4	1	no	—
171	C₂×C₄×C₆₁	—	4	2	no	—
172	C₂×C₄×C₆₁	—	4	2	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
175	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
176	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
180	C₈×C₆₁	—	2	1	no	—
181	C₈×C₆₁	—	2	1	no	—
182	C₈×C₆₁	—	2	1	no	—
183	C₈×C₆₁	—	4	1	no	—
184	C₈×C₆₁	—	4	1	no	—
185	C₈×C₆₁	—	4	2	no	—
186	C₈×C₆₁	—	4	2	no	—
187	C₈×C₆₁	#135	1	2	yes	—
188	#19161	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	—	2	1	no	—
192	C₂²×C₆₁	—	4	1	no	—
193	C₂²×C₆₁	—	4	1	no	—
194	C₂²×C₆₁	—	4	1	no	—
195	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
196	C₄×C₆₁	—	2	1	no	—
197	C₄×C₆₁	—	2	1	no	—
198	C₄×C₆₁	—	2	1	no	—
199	C₄×C₆₁	—	4	1	no	—
200	C₄×C₆₁	—	4	1	no	—
201	C₄×C₆₁	—	4	1	no	—
202	C₄×C₆₁	—	8	2	no	—
203	C₄×C₆₁	—	8	2	no	—
204	C₄×C₆₁	#473	1	2	yes	—
205	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
206	C₄×C₆₁	#575	1	1	yes	characteristic
207	C₄×C₆₁	#575	1	2	yes	—
208	#3170	C₂×C₆₁	1	1	yes	characteristic, complemented
209	#3107	C₂×C₆₁	1	2	yes	—
210	#2965	C₂×C₆₁	1	1	yes	characteristic
211	#1700	C₂×C₆₁	1	2	yes	complemented
212	#1699	C₂×C₆₁	1	2	yes	complemented
213	#1694	C₂×C₆₁	1	1	yes	characteristic, complemented
214	#1693	C₂×C₆₁	1	1	yes	characteristic, complemented
215	#1690	C₂×C₆₁	1	1	yes	characteristic, complemented
216	#1689	C₂×C₆₁	1	1	yes	characteristic, complemented
217	#1564	C₂×C₆₁	1	1	yes	characteristic, complemented
218	#1544	C₂×C₆₁	1	2	yes	complemented
219	C₂×C₆₁	—	4	1	no	—
220	C₂×C₆₁	—	8	1	no	—
221	C₂×C₆₁	#3035	1	1	yes	characteristic
222	C₂×C₆₁	#3054	1	1	yes	characteristic
223	C₂×C₆₁	C₂×#473	1	1	yes	characteristic
224	#533	C₂²×C₆₁	1	2	yes	—
225	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
226	#500	C₂²×C₆₁	1	1	yes	characteristic
227	#494	C₂²×C₆₁	1	1	yes	characteristic
228	#487	C₂²×C₆₁	1	2	yes	—
229	#485	—	2	2	no	—
230	#475	C₂²×C₆₁	1	2	yes	—
231	#474	C₂²×C₆₁	1	2	yes	—
232	#467	—	2	1	no	—
233	#467	—	2	1	no	—
234	#462	C₂²×C₆₁	1	2	yes	—
235	#461	C₂²×C₆₁	1	2	yes	—
236	#452	—	2	2	no	—
237	#446	C₂²×C₆₁	1	1	yes	characteristic
238	#446	C₂²×C₆₁	1	1	yes	characteristic
239	C₄×Q₁₆	—	2	2	no	—
240	C₄×Q₁₆	—	2	1	no	—
241	C₄×Q₁₆	—	2	1	no	—
242	C₄×SD₁₆	—	2	2	no	—
243	#436	C₂²×C₆₁	1	1	yes	characteristic
244	#436	C₂²×C₆₁	1	1	yes	characteristic
245	#435	—	2	1	no	—
246	#435	—	2	1	no	—
247	#431	—	2	1	no	—
248	#431	C₂²×C₆₁	1	1	yes	characteristic
249	#431	C₂²×C₆₁	1	2	yes	—
250	C₄×M₁₆	—	2	1	no	—
251	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
252	#335	C₂²×C₆₁	1	2	yes	—
253	#334	C₂²×C₆₁	1	1	yes	characteristic
254	#334	C₂²×C₆₁	1	1	yes	characteristic
255	#332	C₂²×C₆₁	1	2	yes	—
256	#332	C₂²×C₆₁	1	2	yes	—
257	#332	C₂²×C₆₁	1	2	yes	—
258	#332	C₂²×C₆₁	1	2	yes	—
259	C₆₁	#19161	1	1	yes	characteristic, direct product factor, Sylow
260	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
261	C₂×Q₁₆	—	2	2	no	—
262	C₂×Q₁₆	—	2	1	no	—
263	C₂×Q₁₆	—	2	1	no	—
264	C₂×SD₁₆	—	2	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
268	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
269	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
270	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
271	#125	—	2	2	no	—
272	C₂²⋊Q₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
277	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
281	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	—	2	2	no	—
284	#117	D₄×C₆₁	1	1	yes	characteristic
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	2	no	—
290	#106	—	2	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
294	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
295	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
296	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
297	#103	—	2	2	no	—
298	#103	—	2	2	no	—
299	#103	—	2	2	no	—
300	#103	—	2	2	no	—
301	#103	—	2	2	no	—
302	#102	—	2	2	no	—
303	C₂²⋊C₈	—	2	1	no	—
304	C₂²⋊C₈	—	2	2	no	—
305	C₂²⋊C₈	—	2	1	no	—
306	C₂²⋊C₈	—	2	1	no	—
307	#97	—	2	1	no	—
308	#97	—	2	1	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	2	2	no	—
311	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
312	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
313	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
314	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
315	#41	—	4	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
326	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
327	Q₁₆	—	4	2	no	—
328	Q₁₆	—	4	4	no	—
329	Q₁₆	—	4	2	no	—
330	SD₁₆	—	4	4	no	—
331	M₁₆	—	4	2	no	—
332	M₁₆	—	4	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	4	1	no	—
339	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
340	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
342	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
352	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	2	no	—
361	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
363	C₄²	#41×C₆₁	1	1	yes	characteristic
364	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
365	C₂³	—	2	1	no	—
366	C₂³	#121×C₆₁	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	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	—	4	2	no	—
387	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
388	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
389	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
390	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
391	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	4	1	no	—
398	C₈	—	4	2	no	—
399	C₈	—	4	2	no	—
400	C₈	#135×C₆₁	1	2	yes	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	8	2	no	—
415	C₄	—	8	2	no	—
416	C₄	C₆₁×#473	1	2	yes	—
417	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
418	C₄	C₆₁×#575	1	1	yes	characteristic
419	C₄	C₆₁×#575	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	8	1	no	—
422	C₂	C₆₁×#3035	1	1	yes	characteristic
423	C₂	C₆₁×#3054	1	1	yes	characteristic
424	C₂	C₂×C₆₁×#473	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₁	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
socle	C₂²×C₆₁	C₂×#121
prime radical	C₂×#41×C₆₁	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₁ ◁ C₂×C₄²×C₆₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₁×#3170	C₂	semidirect
4. C₆₁×#1700	C₂	semidirect
5. C₆₁×#1699	C₂	semidirect
6. C₆₁×#1694	C₂	semidirect
7. C₆₁×#1693	C₂	semidirect
8. C₆₁×#1690	C₂	semidirect
9. C₆₁×#1689	C₂	semidirect
10. C₆₁×#1564	C₂	semidirect
11. C₆₁×#1544	C₂	semidirect
188. #19161	C₆₁	direct (N × H)
208. #3170	C₂×C₆₁	semidirect
211. #1700	C₂×C₆₁	semidirect
212. #1699	C₂×C₆₁	semidirect
213. #1694	C₂×C₆₁	semidirect
214. #1693	C₂×C₆₁	semidirect
215. #1690	C₂×C₆₁	semidirect
216. #1689	C₂×C₆₁	semidirect
217. #1564	C₂×C₆₁	semidirect
218. #1544	C₂×C₆₁	semidirect
259. C₆₁	#19161	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×#3170	2
C₆₁×#3107	2
C₆₁×#2965	2
C₆₁×#1700	2
C₆₁×#1699	2
C₆₁×#1694	2
C₆₁×#1693	2
C₆₁×#1690	2
C₆₁×#1689	2
C₆₁×#1564	2
C₆₁×#1544	2
#19161	61

Subgroups — C61×#19161 #29522594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19161 #29522594