Subgroups — C₆₁×#19227 #29522660

Order 15616.

628 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3247	C₂	1	2	yes	maximal, complemented
2	C₆₁×#3169	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#2966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1696	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1695	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1687	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1678	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1677	C₂	1	2	yes	maximal, complemented
10	C₂×C₆₁×#334	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1551	C₂	1	2	yes	maximal, complemented
12	C₆₁×#532	C₂²	1	2	yes	—
13	C₆₁×#529	C₂²	1	1	yes	characteristic
14	C₆₁×#500	C₂²	1	1	yes	characteristic
15	C₆₁×#493	C₂²	1	1	yes	characteristic
16	C₆₁×#486	C₂²	1	2	yes	—
17	C₆₁×#478	—	2	2	no	—
18	C₆₁×#477	C₂²	1	2	yes	—
19	C₆₁×#476	C₂²	1	2	yes	—
20	C₆₁×#466	—	2	1	no	—
21	C₆₁×#466	—	2	1	no	—
22	C₆₁×#466	—	2	2	no	—
23	C₆₁×#465	—	2	2	no	—
24	C₆₁×#463	—	2	2	no	—
25	C₆₁×#460	C₂²	1	2	yes	—
26	C₆₁×#459	C₂²	1	2	yes	—
27	C₆₁×#446	C₂²	1	1	yes	characteristic
28	C₈×Q₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₆₁	—	2	1	no	—
30	C₄×D₈×C₆₁	—	2	1	no	—
31	C₆₁×#436	C₂²	1	1	yes	characteristic
32	C₆₁×#435	—	2	1	no	—
33	C₈×D₄×C₆₁	—	2	1	no	—
34	C₈×D₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#433	—	2	1	no	—
36	C₆₁×#432	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₆₁	C₂²	1	2	yes	—
38	C₆₁×#405	—	2	1	no	—
39	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#334	C₂²	1	2	yes	—
41	C₆₁×#334	C₂²	1	1	yes	characteristic
42	C₆₁×#334	C₂²	1	1	yes	characteristic
43	C₆₁×#333	C₂²	1	2	yes	—
44	C₆₁×#333	C₂²	1	2	yes	—
45	C₆₁×#331	C₂²	1	2	yes	—
46	C₆₁×#331	C₂²	1	2	yes	—
47	C₂×#41×C₆₁	—	2	2	no	—
48	C₂×SD₁₆×C₆₁	—	2	2	no	—
49	C₂×D₈×C₆₁	—	2	2	no	—
50	C₂×D₈×C₆₁	—	2	1	no	—
51	C₂×D₈×C₆₁	—	2	1	no	—
52	C₂×M₁₆×C₆₁	—	2	1	no	—
53	C₂²×C₈×C₆₁	—	2	2	no	—
54	C₂²×C₈×C₆₁	—	2	1	no	—
55	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
56	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
57	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
58	#127×C₆₁	C₂³	1	2	yes	—
59	#126×C₆₁	—	2	1	no	—
60	#125×C₆₁	D₄	1	1	yes	characteristic
61	#124×C₆₁	—	2	2	no	—
62	#124×C₆₁	D₄	1	1	yes	characteristic
63	#123×C₆₁	—	2	1	no	—
64	C₂²⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
65	#121×C₆₁	—	2	2	no	—
66	#121×C₆₁	—	2	2	no	—
67	#121×C₆₁	D₄	1	1	yes	characteristic
68	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₆₁	—	2	1	no	—
70	C₄×D₄×C₆₁	—	2	2	no	—
71	C₄×D₄×C₆₁	—	2	2	no	—
72	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
73	#117×C₆₁	—	2	1	no	—
74	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
75	#107×C₆₁	—	2	1	no	—
76	#107×C₆₁	—	2	1	no	—
77	#107×C₆₁	—	2	2	no	—
78	#106×C₆₁	—	2	2	no	—
79	C₄⋊C₈×C₆₁	—	2	1	no	—
80	C₄⋊C₈×C₆₁	—	2	1	no	—
81	C₄⋊C₈×C₆₁	—	2	2	no	—
82	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
85	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
86	#103×C₆₁	—	2	2	no	—
87	#102×C₆₁	—	2	2	no	—
88	#102×C₆₁	—	2	2	no	—
89	#102×C₆₁	—	2	2	no	—
90	#102×C₆₁	—	2	2	no	—
91	#102×C₆₁	—	2	2	no	—
92	C₂²⋊C₈×C₆₁	—	2	1	no	—
93	C₂²⋊C₈×C₆₁	—	2	1	no	—
94	C₂²⋊C₈×C₆₁	—	2	1	no	—
95	#97×C₆₁	—	2	1	no	—
96	#97×C₆₁	—	2	1	no	—
97	C₄×C₈×C₆₁	—	2	1	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	—	8	4	no	—
103	C₂×Q₈×C₆₁	—	2	2	no	—
104	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
105	C₂×D₄×C₆₁	—	2	1	no	—
106	C₂×D₄×C₆₁	—	2	2	no	—
107	C₂×D₄×C₆₁	—	2	2	no	—
108	C₂×D₄×C₆₁	—	2	2	no	—
109	C₂×D₄×C₆₁	—	4	2	no	—
110	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₆₁	—	2	1	no	—
112	C₂²×C₄×C₆₁	—	4	2	no	—
113	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
116	SD₁₆×C₆₁	—	8	2	no	—
117	D₈×C₆₁	—	4	2	no	—
118	D₈×C₆₁	—	4	2	no	—
119	D₈×C₆₁	—	8	2	no	—
120	M₁₆×C₆₁	—	4	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	—	2	1	no	—
123	C₂×C₈×C₆₁	—	2	1	no	—
124	C₂×C₈×C₆₁	—	2	2	no	—
125	C₂×C₈×C₆₁	—	2	2	no	—
126	C₂×C₈×C₆₁	—	4	1	no	—
127	C₂×C₈×C₆₁	—	4	2	no	—
128	C₂×C₈×C₆₁	—	8	2	no	—
129	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₆₁	—	2	1	no	—
134	C₄⋊C₄×C₆₁	—	2	1	no	—
135	C₄⋊C₄×C₆₁	—	2	1	no	—
136	C₄⋊C₄×C₆₁	—	2	1	no	—
137	C₄⋊C₄×C₆₁	—	2	2	no	—
138	C₄⋊C₄×C₆₁	—	2	2	no	—
139	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂²⋊C₄×C₆₁	—	2	1	no	—
142	C₂²⋊C₄×C₆₁	—	2	1	no	—
143	C₂²⋊C₄×C₆₁	—	2	1	no	—
144	C₂²⋊C₄×C₆₁	—	2	1	no	—
145	C₂²⋊C₄×C₆₁	—	2	1	no	—
146	C₂²⋊C₄×C₆₁	—	4	2	no	—
147	C₂²⋊C₄×C₆₁	—	4	2	no	—
148	C₄²×C₆₁	—	2	1	no	—
149	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₆₁	#41	1	1	yes	characteristic
152	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
153	C₂³×C₆₁	—	2	1	no	—
154	C₂³×C₆₁	—	4	2	no	—
155	C₂³×C₆₁	#121	1	1	yes	characteristic
156	Q₈×C₆₁	—	2	2	no	—
157	Q₈×C₆₁	—	8	2	no	—
158	D₄×C₆₁	—	2	2	no	—
159	D₄×C₆₁	—	4	2	no	—
160	D₄×C₆₁	—	4	2	no	—
161	D₄×C₆₁	—	4	2	no	—
162	D₄×C₆₁	—	4	2	no	—
163	D₄×C₆₁	—	4	2	no	—
164	D₄×C₆₁	—	8	2	no	—
165	D₄×C₆₁	—	8	4	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	1	no	—
168	C₂×C₄×C₆₁	—	2	1	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	1	no	—
171	C₂×C₄×C₆₁	—	2	1	no	—
172	C₂×C₄×C₆₁	—	2	1	no	—
173	C₂×C₄×C₆₁	—	4	1	no	—
174	C₂×C₄×C₆₁	—	4	1	no	—
175	C₂×C₄×C₆₁	—	4	2	no	—
176	C₂×C₄×C₆₁	—	8	4	no	—
177	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
179	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
183	C₈×C₆₁	—	2	1	no	—
184	C₈×C₆₁	—	2	1	no	—
185	C₈×C₆₁	—	2	1	no	—
186	C₈×C₆₁	—	4	1	no	—
187	C₈×C₆₁	—	4	1	no	—
188	C₈×C₆₁	—	4	2	no	—
189	C₈×C₆₁	—	4	2	no	—
190	C₈×C₆₁	#135	1	2	yes	—
191	#19227	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₆₁	—	2	1	no	—
193	C₂²×C₆₁	—	2	1	no	—
194	C₂²×C₆₁	—	4	1	no	—
195	C₂²×C₆₁	—	4	1	no	—
196	C₂²×C₆₁	—	4	1	no	—
197	C₂²×C₆₁	—	8	2	no	—
198	C₂²×C₆₁	—	8	2	no	—
199	C₂²×C₆₁	—	8	2	no	—
200	C₂²×C₆₁	#472	1	2	yes	—
201	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
202	C₄×C₆₁	—	2	1	no	—
203	C₄×C₆₁	—	2	1	no	—
204	C₄×C₆₁	—	2	1	no	—
205	C₄×C₆₁	—	2	1	no	—
206	C₄×C₆₁	—	4	1	no	—
207	C₄×C₆₁	—	4	1	no	—
208	C₄×C₆₁	—	4	1	no	—
209	C₄×C₆₁	—	8	2	no	—
210	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
211	C₄×C₆₁	#575	1	1	yes	characteristic
212	C₄×C₆₁	#577	1	2	yes	—
213	#3247	C₂×C₆₁	1	2	yes	complemented
214	#3169	C₂×C₆₁	1	1	yes	characteristic, complemented
215	#2966	C₂×C₆₁	1	1	yes	characteristic, complemented
216	#1696	C₂×C₆₁	1	1	yes	characteristic, complemented
217	#1695	C₂×C₆₁	1	1	yes	characteristic, complemented
218	#1688	C₂×C₆₁	1	1	yes	characteristic, complemented
219	#1687	C₂×C₆₁	1	1	yes	characteristic, complemented
220	#1678	C₂×C₆₁	1	2	yes	complemented
221	#1677	C₂×C₆₁	1	2	yes	complemented
222	C₂×#334	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#1551	C₂×C₆₁	1	2	yes	complemented
224	C₂×C₆₁	—	2	2	no	—
225	C₂×C₆₁	—	8	1	no	—
226	C₂×C₆₁	—	16	2	no	—
227	C₂×C₆₁	#3035	1	1	yes	characteristic
228	C₂×C₆₁	#3060	1	1	yes	characteristic
229	C₂×C₆₁	C₂×#472	1	1	yes	characteristic
230	#532	C₂²×C₆₁	1	2	yes	—
231	#529	C₂²×C₆₁	1	1	yes	characteristic
232	#500	C₂²×C₆₁	1	1	yes	characteristic
233	#493	C₂²×C₆₁	1	1	yes	characteristic
234	#486	C₂²×C₆₁	1	2	yes	—
235	#478	—	2	2	no	—
236	#477	C₂²×C₆₁	1	2	yes	—
237	#476	C₂²×C₆₁	1	2	yes	—
238	#466	—	2	1	no	—
239	#466	—	2	1	no	—
240	#466	—	2	2	no	—
241	#465	—	2	2	no	—
242	#463	—	2	2	no	—
243	#460	C₂²×C₆₁	1	2	yes	—
244	#459	C₂²×C₆₁	1	2	yes	—
245	#446	C₂²×C₆₁	1	1	yes	characteristic
246	C₈×Q₈	C₂²×C₆₁	1	1	yes	characteristic
247	C₄×D₈	—	2	1	no	—
248	C₄×D₈	—	2	1	no	—
249	#436	C₂²×C₆₁	1	1	yes	characteristic
250	#435	—	2	1	no	—
251	C₈×D₄	—	2	1	no	—
252	C₈×D₄	C₂²×C₆₁	1	1	yes	characteristic
253	#433	—	2	1	no	—
254	#432	C₂²×C₆₁	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₆₁	1	2	yes	—
256	#405	—	2	1	no	—
257	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
258	#334	C₂²×C₆₁	1	2	yes	—
259	#334	C₂²×C₆₁	1	1	yes	characteristic
260	#334	C₂²×C₆₁	1	1	yes	characteristic
261	#333	C₂²×C₆₁	1	2	yes	—
262	#333	C₂²×C₆₁	1	2	yes	—
263	#331	C₂²×C₆₁	1	2	yes	—
264	#331	C₂²×C₆₁	1	2	yes	—
265	C₆₁	#19227	1	1	yes	characteristic, direct product factor, Sylow
266	C₂×#41	—	2	2	no	—
267	C₂×SD₁₆	—	2	2	no	—
268	C₂×D₈	—	2	2	no	—
269	C₂×D₈	—	2	1	no	—
270	C₂×D₈	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂²×C₈	—	2	2	no	—
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
275	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
276	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
277	#127	C₂³×C₆₁	1	2	yes	—
278	#126	—	2	1	no	—
279	#125	D₄×C₆₁	1	1	yes	characteristic
280	#124	—	2	2	no	—
281	#124	D₄×C₆₁	1	1	yes	characteristic
282	#123	—	2	1	no	—
283	C₂²⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
284	#121	—	2	2	no	—
285	#121	—	2	2	no	—
286	#121	D₄×C₆₁	1	1	yes	characteristic
287	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
288	C₄×D₄	—	2	1	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
292	#117	—	2	1	no	—
293	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
294	#107	—	2	1	no	—
295	#107	—	2	1	no	—
296	#107	—	2	2	no	—
297	#106	—	2	2	no	—
298	C₄⋊C₈	—	2	1	no	—
299	C₄⋊C₈	—	2	1	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
302	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
303	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
304	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
305	#103	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	#97	—	2	1	no	—
315	#97	—	2	1	no	—
316	C₄×C₈	—	2	1	no	—
317	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
318	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
319	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
320	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
321	#41	—	8	4	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	2	no	—
329	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	4	2	no	—
332	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
334	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
335	SD₁₆	—	8	2	no	—
336	D₈	—	4	2	no	—
337	D₈	—	4	2	no	—
338	D₈	—	8	2	no	—
339	M₁₆	—	4	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	4	1	no	—
346	C₂×C₈	—	4	2	no	—
347	C₂×C₈	—	8	2	no	—
348	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
349	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
351	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
359	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
360	C₂²⋊C₄	—	2	1	no	—
361	C₂²⋊C₄	—	2	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	4	2	no	—
366	C₂²⋊C₄	—	4	2	no	—
367	C₄²	—	2	1	no	—
368	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
370	C₄²	#41×C₆₁	1	1	yes	characteristic
371	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
372	C₂³	—	2	1	no	—
373	C₂³	—	4	2	no	—
374	C₂³	#121×C₆₁	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	8	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	2	no	—
379	D₄	—	4	2	no	—
380	D₄	—	4	2	no	—
381	D₄	—	4	2	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	2	no	—
384	D₄	—	8	4	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	4	no	—
396	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
397	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
398	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
399	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
400	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	4	1	no	—
406	C₈	—	4	1	no	—
407	C₈	—	4	2	no	—
408	C₈	—	4	2	no	—
409	C₈	#135×C₆₁	1	2	yes	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	8	2	no	—
416	C₂²	—	8	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	C₆₁×#472	1	2	yes	—
419	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	1	no	—
425	C₄	—	4	1	no	—
426	C₄	—	4	1	no	—
427	C₄	—	8	2	no	—
428	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
429	C₄	C₆₁×#575	1	1	yes	characteristic
430	C₄	C₆₁×#577	1	2	yes	—
431	C₂	—	2	2	no	—
432	C₂	—	8	1	no	—
433	C₂	—	16	2	no	—
434	C₂	C₆₁×#3035	1	1	yes	characteristic
435	C₂	C₆₁×#3060	1	1	yes	characteristic
436	C₂	C₂×C₆₁×#472	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
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×#3247	C₂	semidirect
2. C₆₁×#3169	C₂	semidirect
3. C₆₁×#2966	C₂	semidirect
4. C₆₁×#1696	C₂	semidirect
5. C₆₁×#1695	C₂	semidirect
6. C₆₁×#1688	C₂	semidirect
7. C₆₁×#1687	C₂	semidirect
8. C₆₁×#1678	C₂	semidirect
9. C₆₁×#1677	C₂	semidirect
10. C₂×C₆₁×#334	C₂	semidirect
11. C₆₁×#1551	C₂	semidirect
191. #19227	C₆₁	direct (N × H)
213. #3247	C₂×C₆₁	semidirect
214. #3169	C₂×C₆₁	semidirect
215. #2966	C₂×C₆₁	semidirect
216. #1696	C₂×C₆₁	semidirect
217. #1695	C₂×C₆₁	semidirect
218. #1688	C₂×C₆₁	semidirect
219. #1687	C₂×C₆₁	semidirect
220. #1678	C₂×C₆₁	semidirect
221. #1677	C₂×C₆₁	semidirect
222. C₂×#334	C₂×C₆₁	semidirect
223. #1551	C₂×C₆₁	semidirect
265. C₆₁	#19227	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×#3247	2
C₆₁×#3169	2
C₆₁×#2966	2
C₆₁×#1696	2
C₆₁×#1695	2
C₆₁×#1688	2
C₆₁×#1687	2
C₆₁×#1678	2
C₆₁×#1677	2
C₂×C₆₁×#334	2
C₆₁×#1551	2
#19227	61

Subgroups — C61×#19227 #29522660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19227 #29522660