Subgroups — C₆₁×#19294 #29522727

Order 15616.

694 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3115	C₂	1	2	yes	maximal, complemented
3	C₆₁×#2965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#1690	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1689	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×#1686	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1685	C₂	1	2	yes	maximal, complemented
10	C₆₁×#1568	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1553	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₆₁	—	2	1	no	—
13	C₂×#135×C₆₁	—	2	1	no	—
14	C₆₁×#532	C₂²	1	2	yes	—
15	C₄×#41×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#495	—	2	1	no	—
17	C₆₁×#495	—	2	1	no	—
18	C₆₁×#494	C₂²	1	1	yes	characteristic
19	C₆₁×#493	C₂²	1	1	yes	characteristic
20	C₆₁×#492	C₂²	1	2	yes	—
21	C₆₁×#482	—	2	2	no	—
22	C₆₁×#475	C₂²	1	2	yes	—
23	C₆₁×#474	C₂²	1	2	yes	—
24	C₆₁×#460	C₂²	1	2	yes	—
25	C₆₁×#459	C₂²	1	2	yes	—
26	C₆₁×#449	—	2	2	no	—
27	C₆₁×#446	C₂²	1	1	yes	characteristic
28	C₆₁×#446	C₂²	1	1	yes	characteristic
29	C₆₁×#442	—	2	2	no	—
30	C₆₁×#440	—	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×#432	C₂²	1	2	yes	—
36	C₆₁×#431	—	2	1	no	—
37	C₆₁×#431	C₂²	1	1	yes	characteristic
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×#331	C₂²	1	2	yes	—
46	C₆₁×#331	C₂²	1	2	yes	—
47	C₂×#41×C₆₁	—	2	2	no	—
48	C₂×#41×C₆₁	D₄	1	1	yes	characteristic
49	#135×C₆₁	—	4	4	no	—
50	#135×C₆₁	—	4	4	no	—
51	C₂×Q₁₆×C₆₁	—	2	1	no	—
52	C₂×Q₁₆×C₆₁	—	2	1	no	—
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×SD₁₆×C₆₁	—	2	2	no	—
55	C₂×SD₁₆×C₆₁	—	2	2	no	—
56	C₂×D₈×C₆₁	—	2	2	no	—
57	C₂×D₈×C₆₁	—	2	1	no	—
58	C₂×D₈×C₆₁	—	2	1	no	—
59	C₂×M₁₆×C₆₁	—	2	1	no	—
60	C₂×M₁₆×C₆₁	—	2	1	no	—
61	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
64	#127×C₆₁	C₂³	1	2	yes	—
65	#124×C₆₁	—	2	2	no	—
66	#121×C₆₁	—	2	2	no	—
67	#121×C₆₁	—	2	2	no	—
68	C₄×Q₈×C₆₁	D₄	1	1	yes	characteristic
69	C₄×Q₈×C₆₁	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₆₁	—	2	1	no	—
71	C₄×D₄×C₆₁	—	2	1	no	—
72	C₄×D₄×C₆₁	—	2	2	no	—
73	C₄×D₄×C₆₁	—	2	2	no	—
74	C₄×D₄×C₆₁	D₄	1	1	yes	characteristic
75	C₄×D₄×C₆₁	C₂³	1	1	yes	characteristic
76	#117×C₆₁	—	2	1	no	—
77	#117×C₆₁	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₆₁	—	2	1	no	—
79	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
80	#107×C₆₁	—	2	2	no	—
81	#106×C₆₁	—	2	2	no	—
82	C₄⋊C₈×C₆₁	—	2	1	no	—
83	C₄⋊C₈×C₆₁	—	2	1	no	—
84	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
85	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
87	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
88	#103×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	2	no	—
94	C₂²⋊C₈×C₆₁	—	2	1	no	—
95	C₂²⋊C₈×C₆₁	—	2	1	no	—
96	#97×C₆₁	—	2	1	no	—
97	#97×C₆₁	—	2	1	no	—
98	#97×C₆₁	—	2	2	no	—
99	C₄×C₈×C₆₁	—	2	1	no	—
100	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
101	C₄×C₈×C₆₁	D₄	1	1	yes	characteristic
102	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
104	#41×C₆₁	—	4	2	no	—
105	#41×C₆₁	—	4	4	no	—
106	#41×C₆₁	—	4	4	no	—
107	C₂×Q₈×C₆₁	—	2	2	no	—
108	C₂×Q₈×C₆₁	C₂×D₄	1	1	yes	characteristic
109	C₂×D₄×C₆₁	—	2	1	no	—
110	C₂×D₄×C₆₁	—	2	2	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	4	2	no	—
114	C₂×D₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	—	2	1	no	—
116	C₂²×C₄×C₆₁	—	2	1	no	—
117	C₂²×C₄×C₆₁	—	2	1	no	—
118	C₂²×C₄×C₆₁	—	4	2	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	#41	1	1	yes	characteristic
122	Q₁₆×C₆₁	—	4	2	no	—
123	Q₁₆×C₆₁	—	4	2	no	—
124	SD₁₆×C₆₁	—	4	4	no	—
125	SD₁₆×C₆₁	—	4	4	no	—
126	SD₁₆×C₆₁	—	4	4	no	—
127	D₈×C₆₁	—	4	2	no	—
128	D₈×C₆₁	—	4	4	no	—
129	D₈×C₆₁	—	4	2	no	—
130	M₁₆×C₆₁	—	4	2	no	—
131	M₁₆×C₆₁	—	4	2	no	—
132	C₂×C₈×C₆₁	—	2	2	no	—
133	C₂×C₈×C₆₁	—	2	2	no	—
134	C₂×C₈×C₆₁	—	2	1	no	—
135	C₂×C₈×C₆₁	—	2	1	no	—
136	C₂×C₈×C₆₁	—	2	2	no	—
137	C₂×C₈×C₆₁	—	2	2	no	—
138	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₁	C₂×D₄	1	1	yes	characteristic
142	C₄⋊C₄×C₆₁	—	2	1	no	—
143	C₄⋊C₄×C₆₁	—	2	1	no	—
144	C₄⋊C₄×C₆₁	—	2	2	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
147	C₄⋊C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
148	C₂²⋊C₄×C₆₁	—	2	1	no	—
149	C₂²⋊C₄×C₆₁	—	2	1	no	—
150	C₂²⋊C₄×C₆₁	—	2	1	no	—
151	C₂²⋊C₄×C₆₁	—	4	2	no	—
152	C₂²⋊C₄×C₆₁	—	4	2	no	—
153	C₄²×C₆₁	—	2	1	no	—
154	C₄²×C₆₁	—	2	1	no	—
155	C₄²×C₆₁	—	2	1	no	—
156	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₆₁	#41	1	1	yes	characteristic
159	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
160	C₂³×C₆₁	—	2	1	no	—
161	C₂³×C₆₁	—	4	2	no	—
162	C₂³×C₆₁	#121	1	1	yes	characteristic
163	Q₈×C₆₁	—	2	2	no	—
164	Q₈×C₆₁	—	4	2	no	—
165	Q₈×C₆₁	—	4	2	no	—
166	D₄×C₆₁	—	2	2	no	—
167	D₄×C₆₁	—	4	2	no	—
168	D₄×C₆₁	—	4	2	no	—
169	D₄×C₆₁	—	4	2	no	—
170	D₄×C₆₁	—	4	2	no	—
171	D₄×C₆₁	—	4	2	no	—
172	D₄×C₆₁	—	8	2	no	—
173	D₄×C₆₁	—	8	4	no	—
174	C₂×C₄×C₆₁	—	2	1	no	—
175	C₂×C₄×C₆₁	—	2	1	no	—
176	C₂×C₄×C₆₁	—	2	2	no	—
177	C₂×C₄×C₆₁	—	2	1	no	—
178	C₂×C₄×C₆₁	—	2	1	no	—
179	C₂×C₄×C₆₁	—	2	1	no	—
180	C₂×C₄×C₆₁	—	4	1	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	1	no	—
184	C₂×C₄×C₆₁	—	4	1	no	—
185	C₂×C₄×C₆₁	—	4	2	no	—
186	C₂×C₄×C₆₁	—	8	4	no	—
187	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
188	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
189	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
193	C₈×C₆₁	—	2	1	no	—
194	C₈×C₆₁	—	2	1	no	—
195	C₈×C₆₁	—	4	1	no	—
196	C₈×C₆₁	—	4	1	no	—
197	C₈×C₆₁	—	4	2	no	—
198	C₈×C₆₁	—	4	2	no	—
199	C₈×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
200	C₈×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
201	#19294	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
202	C₂²×C₆₁	—	2	1	no	—
203	C₂²×C₆₁	—	2	1	no	—
204	C₂²×C₆₁	—	2	1	no	—
205	C₂²×C₆₁	—	4	1	no	—
206	C₂²×C₆₁	—	4	1	no	—
207	C₂²×C₆₁	—	4	1	no	—
208	C₂²×C₆₁	—	8	2	no	—
209	C₂²×C₆₁	—	8	2	no	—
210	C₂²×C₆₁	—	8	2	no	—
211	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
212	C₄×C₆₁	—	2	1	no	—
213	C₄×C₆₁	—	2	1	no	—
214	C₄×C₆₁	—	2	1	no	—
215	C₄×C₆₁	—	2	1	no	—
216	C₄×C₆₁	—	4	1	no	—
217	C₄×C₆₁	—	4	1	no	—
218	C₄×C₆₁	—	4	1	no	—
219	C₄×C₆₁	—	8	2	no	—
220	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
222	C₄×C₆₁	#575	1	2	yes	—
223	#3147	C₂×C₆₁	1	1	yes	characteristic, complemented
224	#3115	C₂×C₆₁	1	2	yes	complemented
225	#2965	C₂×C₆₁	1	1	yes	characteristic, complemented
226	#1690	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#1689	C₂×C₆₁	1	1	yes	characteristic, complemented
228	#1688	C₂×C₆₁	1	1	yes	characteristic, complemented
229	#1687	C₂×C₆₁	1	1	yes	characteristic, complemented
230	#1686	C₂×C₆₁	1	2	yes	complemented
231	#1685	C₂×C₆₁	1	2	yes	complemented
232	#1568	C₂×C₆₁	1	1	yes	characteristic, complemented
233	#1553	C₂×C₆₁	1	2	yes	complemented
234	C₂×C₆₁	—	4	1	no	—
235	C₂×C₆₁	—	8	1	no	—
236	C₂×C₆₁	—	16	2	no	—
237	C₂×C₆₁	#3038	1	1	yes	characteristic
238	C₂×C₆₁	#3054	1	1	yes	characteristic
239	C₂×C₆₁	#3067	1	1	yes	characteristic
240	C₂×#135	—	2	1	no	—
241	C₂×#135	—	2	1	no	—
242	#532	C₂²×C₆₁	1	2	yes	—
243	C₄×#41	C₂²×C₆₁	1	1	yes	characteristic
244	#495	—	2	1	no	—
245	#495	—	2	1	no	—
246	#494	C₂²×C₆₁	1	1	yes	characteristic
247	#493	C₂²×C₆₁	1	1	yes	characteristic
248	#492	C₂²×C₆₁	1	2	yes	—
249	#482	—	2	2	no	—
250	#475	C₂²×C₆₁	1	2	yes	—
251	#474	C₂²×C₆₁	1	2	yes	—
252	#460	C₂²×C₆₁	1	2	yes	—
253	#459	C₂²×C₆₁	1	2	yes	—
254	#449	—	2	2	no	—
255	#446	C₂²×C₆₁	1	1	yes	characteristic
256	#446	C₂²×C₆₁	1	1	yes	characteristic
257	#442	—	2	2	no	—
258	#440	—	2	2	no	—
259	#436	C₂²×C₆₁	1	1	yes	characteristic
260	#436	C₂²×C₆₁	1	1	yes	characteristic
261	#435	—	2	1	no	—
262	#435	—	2	1	no	—
263	#432	C₂²×C₆₁	1	2	yes	—
264	#431	—	2	1	no	—
265	#431	C₂²×C₆₁	1	1	yes	characteristic
266	C₄×M₁₆	—	2	1	no	—
267	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
268	#335	C₂²×C₆₁	1	2	yes	—
269	#334	C₂²×C₆₁	1	1	yes	characteristic
270	#334	C₂²×C₆₁	1	1	yes	characteristic
271	#332	C₂²×C₆₁	1	2	yes	—
272	#332	C₂²×C₆₁	1	2	yes	—
273	#331	C₂²×C₆₁	1	2	yes	—
274	#331	C₂²×C₆₁	1	2	yes	—
275	C₆₁	#19294	1	1	yes	characteristic, direct product factor, Sylow
276	C₂×#41	—	2	2	no	—
277	C₂×#41	D₄×C₆₁	1	1	yes	characteristic
278	#135	—	4	4	no	—
279	#135	—	4	4	no	—
280	C₂×Q₁₆	—	2	1	no	—
281	C₂×Q₁₆	—	2	1	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	—	2	1	no	—
287	C₂×D₈	—	2	1	no	—
288	C₂×M₁₆	—	2	1	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
291	C₂²×C₈	D₄×C₆₁	1	1	yes	characteristic
292	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
293	#127	C₂³×C₆₁	1	2	yes	—
294	#124	—	2	2	no	—
295	#121	—	2	2	no	—
296	#121	—	2	2	no	—
297	C₄×Q₈	D₄×C₆₁	1	1	yes	characteristic
298	C₄×Q₈	C₂³×C₆₁	1	1	yes	characteristic
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	2	no	—
302	C₄×D₄	—	2	2	no	—
303	C₄×D₄	D₄×C₆₁	1	1	yes	characteristic
304	C₄×D₄	C₂³×C₆₁	1	1	yes	characteristic
305	#117	—	2	1	no	—
306	#117	D₄×C₆₁	1	1	yes	characteristic
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
309	#107	—	2	2	no	—
310	#106	—	2	2	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	—	2	1	no	—
313	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
314	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
316	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
317	#103	—	2	2	no	—
318	#102	—	2	2	no	—
319	#102	—	2	2	no	—
320	#102	—	2	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	C₂²⋊C₈	—	2	2	no	—
323	C₂²⋊C₈	—	2	1	no	—
324	C₂²⋊C₈	—	2	1	no	—
325	#97	—	2	1	no	—
326	#97	—	2	1	no	—
327	#97	—	2	2	no	—
328	C₄×C₈	—	2	1	no	—
329	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
330	C₄×C₈	D₄×C₆₁	1	1	yes	characteristic
331	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
332	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
333	#41	—	4	2	no	—
334	#41	—	4	4	no	—
335	#41	—	4	4	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	C₂×D₄×C₆₁	1	1	yes	characteristic
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	—	4	2	no	—
343	C₂×D₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
350	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
351	Q₁₆	—	4	2	no	—
352	Q₁₆	—	4	2	no	—
353	SD₁₆	—	4	4	no	—
354	SD₁₆	—	4	4	no	—
355	SD₁₆	—	4	4	no	—
356	D₈	—	4	2	no	—
357	D₈	—	4	4	no	—
358	D₈	—	4	2	no	—
359	M₁₆	—	4	2	no	—
360	M₁₆	—	4	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	2	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
368	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
369	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
370	C₂×C₈	C₂×D₄×C₆₁	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
376	C₄⋊C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
377	C₂²⋊C₄	—	2	1	no	—
378	C₂²⋊C₄	—	2	1	no	—
379	C₂²⋊C₄	—	2	1	no	—
380	C₂²⋊C₄	—	4	2	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₄²	—	2	1	no	—
383	C₄²	—	2	1	no	—
384	C₄²	—	2	1	no	—
385	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
386	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
387	C₄²	#41×C₆₁	1	1	yes	characteristic
388	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
389	C₂³	—	2	1	no	—
390	C₂³	—	4	2	no	—
391	C₂³	#121×C₆₁	1	1	yes	characteristic
392	Q₈	—	2	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	D₄	—	2	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	8	2	no	—
402	D₄	—	8	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	4	1	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
417	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
418	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
420	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
421	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	4	1	no	—
426	C₈	—	4	2	no	—
427	C₈	—	4	2	no	—
428	C₈	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
429	C₈	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	2	no	—
438	C₂²	—	8	2	no	—
439	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	1	no	—
446	C₄	—	4	1	no	—
447	C₄	—	8	2	no	—
448	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
449	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
450	C₄	C₆₁×#575	1	2	yes	—
451	C₂	—	4	1	no	—
452	C₂	—	8	1	no	—
453	C₂	—	16	2	no	—
454	C₂	C₆₁×#3038	1	1	yes	characteristic
455	C₂	C₆₁×#3054	1	1	yes	characteristic
456	C₂	C₆₁×#3067	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×#3147	C₂	semidirect
2. C₆₁×#3115	C₂	semidirect
3. C₆₁×#2965	C₂	semidirect
4. C₆₁×#1690	C₂	semidirect
5. C₆₁×#1689	C₂	semidirect
6. C₆₁×#1688	C₂	semidirect
7. C₆₁×#1687	C₂	semidirect
8. C₆₁×#1686	C₂	semidirect
9. C₆₁×#1685	C₂	semidirect
10. C₆₁×#1568	C₂	semidirect
11. C₆₁×#1553	C₂	semidirect
201. #19294	C₆₁	direct (N × H)
223. #3147	C₂×C₆₁	semidirect
224. #3115	C₂×C₆₁	semidirect
225. #2965	C₂×C₆₁	semidirect
226. #1690	C₂×C₆₁	semidirect
227. #1689	C₂×C₆₁	semidirect
228. #1688	C₂×C₆₁	semidirect
229. #1687	C₂×C₆₁	semidirect
230. #1686	C₂×C₆₁	semidirect
231. #1685	C₂×C₆₁	semidirect
232. #1568	C₂×C₆₁	semidirect
233. #1553	C₂×C₆₁	semidirect
275. C₆₁	#19294	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×#3147	2
C₆₁×#3115	2
C₆₁×#2965	2
C₆₁×#1690	2
C₆₁×#1689	2
C₆₁×#1688	2
C₆₁×#1687	2
C₆₁×#1686	2
C₆₁×#1685	2
C₆₁×#1568	2
C₆₁×#1553	2
#19294	61

Subgroups — C61×#19294 #29522727

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19294 #29522727