Subgroups — C₆₁×#19235 #29522668

Order 15616.

640 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×#3246	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3226	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3139	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#2935	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1703	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1699	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1683	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1679	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#131×C₆₁	—	2	1	no	—
13	C₆₁×#533	C₂²	1	1	yes	characteristic
14	C₆₁×#532	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
16	C₆₁×#500	—	2	1	no	—
17	C₆₁×#491	—	2	2	no	—
18	C₆₁×#487	C₂²	1	2	yes	—
19	C₆₁×#487	C₂²	1	2	yes	—
20	C₆₁×#486	—	2	1	no	—
21	C₆₁×#480	—	2	2	no	—
22	C₆₁×#476	C₂²	1	2	yes	—
23	C₆₁×#475	—	2	1	no	—
24	C₆₁×#474	C₂²	1	2	yes	—
25	C₆₁×#474	C₂²	1	2	yes	—
26	C₆₁×#465	—	2	2	no	—
27	C₆₁×#461	C₂²	1	2	yes	—
28	C₆₁×#460	—	2	1	no	—
29	C₆₁×#436	C₂²	1	2	yes	—
30	C₆₁×#435	—	2	2	no	—
31	C₈×D₄×C₆₁	C₂²	1	2	yes	—
32	C₆₁×#431	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
35	C₆₁×#419	—	2	1	no	—
36	C₆₁×#419	—	2	1	no	—
37	C₆₁×#408	—	2	1	no	—
38	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#335	C₂²	1	2	yes	—
40	C₆₁×#334	C₂²	1	2	yes	—
41	C₆₁×#333	C₂²	1	1	yes	characteristic
42	C₆₁×#333	C₂²	1	1	yes	characteristic
43	C₆₁×#332	C₂²	1	2	yes	—
44	C₆₁×#332	C₂²	1	2	yes	—
45	C₆₁×#332	C₂²	1	1	yes	characteristic
46	C₆₁×#332	C₂²	1	1	yes	characteristic
47	C₂×#41×C₆₁	—	2	1	no	—
48	C₂²×Q₈×C₆₁	—	2	1	no	—
49	C₂×SD₁₆×C₆₁	—	2	2	no	—
50	#131×C₆₁	—	4	4	no	—
51	C₂×M₁₆×C₆₁	—	2	2	no	—
52	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
53	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₆₁	—	2	1	no	—
55	C₂²×C₈×C₆₁	—	2	1	no	—
56	C₂²×C₈×C₆₁	—	2	2	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	D₄	1	1	yes	characteristic
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	#127×C₆₁	D₄	1	1	yes	characteristic
65	#125×C₆₁	—	2	1	no	—
66	#124×C₆₁	—	2	1	no	—
67	C₂²⋊Q₈×C₆₁	—	2	1	no	—
68	C₂²⋊Q₈×C₆₁	—	2	1	no	—
69	#121×C₆₁	—	2	1	no	—
70	#121×C₆₁	D₄	1	2	yes	—
71	C₄×Q₈×C₆₁	—	2	1	no	—
72	C₄×Q₈×C₆₁	—	2	1	no	—
73	C₄×D₄×C₆₁	—	2	1	no	—
74	C₄×D₄×C₆₁	C₂³	1	2	yes	—
75	#117×C₆₁	—	2	1	no	—
76	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
77	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
78	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
79	#107×C₆₁	—	2	2	no	—
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	1	yes	characteristic
88	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
89	#103×C₆₁	—	2	2	no	—
90	#103×C₆₁	—	2	2	no	—
91	#103×C₆₁	—	2	2	no	—
92	#103×C₆₁	—	2	2	no	—
93	#103×C₆₁	—	2	2	no	—
94	#102×C₆₁	—	2	2	no	—
95	#102×C₆₁	—	2	2	no	—
96	#102×C₆₁	—	2	2	no	—
97	C₂²⋊C₈×C₆₁	—	2	1	no	—
98	C₂²⋊C₈×C₆₁	—	2	2	no	—
99	C₂²⋊C₈×C₆₁	—	2	2	no	—
100	#97×C₆₁	D₄	1	2	yes	—
101	C₄×C₈×C₆₁	—	2	1	no	—
102	C₄×C₈×C₆₁	C₂³	1	2	yes	—
103	#41×C₆₁	—	4	2	no	—
104	#41×C₆₁	—	4	2	no	—
105	C₂×Q₈×C₆₁	—	2	1	no	—
106	C₂×Q₈×C₆₁	—	2	2	no	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	1	no	—
109	C₂×Q₈×C₆₁	—	4	1	no	—
110	C₂×Q₈×C₆₁	—	4	2	no	—
111	C₂×Q₈×C₆₁	—	4	2	no	—
112	C₂×D₄×C₆₁	—	2	2	no	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	—	2	1	no	—
115	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₁	—	2	2	no	—
117	C₂²×C₄×C₆₁	—	4	1	no	—
118	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
121	SD₁₆×C₆₁	—	8	2	no	—
122	M₁₆×C₆₁	—	2	2	no	—
123	M₁₆×C₆₁	—	2	2	no	—
124	M₁₆×C₆₁	—	4	4	no	—
125	C₂×C₈×C₆₁	—	2	1	no	—
126	C₂×C₈×C₆₁	—	2	1	no	—
127	C₂×C₈×C₆₁	—	2	1	no	—
128	C₂×C₈×C₆₁	—	2	1	no	—
129	C₂×C₈×C₆₁	—	2	2	no	—
130	C₂×C₈×C₆₁	—	4	4	no	—
131	C₂×C₈×C₆₁	—	4	2	no	—
132	C₂×C₈×C₆₁	—	8	1	no	—
133	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
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	1	no	—
139	C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₄⋊C₄×C₆₁	—	2	2	no	—
141	C₄⋊C₄×C₆₁	—	2	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	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₆₁	—	2	2	no	—
148	C₂²⋊C₄×C₆₁	—	2	2	no	—
149	C₂²⋊C₄×C₆₁	—	4	1	no	—
150	C₄²×C₆₁	—	4	1	no	—
151	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₆₁	#41	1	1	yes	characteristic
154	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
155	C₂³×C₆₁	—	2	2	no	—
156	C₂³×C₆₁	#121	1	1	yes	characteristic
157	Q₈×C₆₁	—	4	2	no	—
158	Q₈×C₆₁	—	4	2	no	—
159	Q₈×C₆₁	—	4	2	no	—
160	Q₈×C₆₁	—	4	1	no	—
161	Q₈×C₆₁	—	4	1	no	—
162	Q₈×C₆₁	—	8	1	no	—
163	Q₈×C₆₁	—	8	2	no	—
164	D₄×C₆₁	—	2	2	no	—
165	D₄×C₆₁	—	2	2	no	—
166	D₄×C₆₁	—	4	4	no	—
167	D₄×C₆₁	—	4	2	no	—
168	D₄×C₆₁	—	8	1	no	—
169	C₂×C₄×C₆₁	—	2	1	no	—
170	C₂×C₄×C₆₁	—	2	1	no	—
171	C₂×C₄×C₆₁	—	2	2	no	—
172	C₂×C₄×C₆₁	—	4	1	no	—
173	C₂×C₄×C₆₁	—	4	2	no	—
174	C₂×C₄×C₆₁	—	4	2	no	—
175	C₂×C₄×C₆₁	—	4	1	no	—
176	C₂×C₄×C₆₁	—	4	1	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	8	2	no	—
179	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
181	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
182	C₂×C₄×C₆₁	#135	1	2	yes	—
183	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
184	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
187	C₈×C₆₁	—	2	2	no	—
188	C₈×C₆₁	—	2	2	no	—
189	C₈×C₆₁	—	4	1	no	—
190	C₈×C₆₁	—	4	1	no	—
191	C₈×C₆₁	—	4	1	no	—
192	C₈×C₆₁	—	4	2	no	—
193	C₈×C₆₁	—	4	1	no	—
194	#19235	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₆₁	—	2	1	no	—
196	C₂²×C₆₁	—	2	1	no	—
197	C₂²×C₆₁	—	4	2	no	—
198	C₂²×C₆₁	—	4	2	no	—
199	C₂²×C₆₁	—	4	2	no	—
200	C₂²×C₆₁	#463	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	—	4	2	no	—
206	C₄×C₆₁	—	8	2	no	—
207	C₄×C₆₁	—	8	1	no	—
208	C₄×C₆₁	—	8	1	no	—
209	C₄×C₆₁	#463	1	2	yes	—
210	C₄×C₆₁	C₂×#135	1	1	yes	characteristic
211	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₄×C₆₁	#577	1	1	yes	characteristic
213	C₄×C₆₁	#578	1	1	yes	characteristic
214	#3246	C₂×C₆₁	1	1	yes	characteristic
215	#3226	C₂×C₆₁	1	1	yes	characteristic
216	#3139	C₂×C₆₁	1	1	yes	characteristic, complemented
217	#2935	C₂×C₆₁	1	1	yes	characteristic
218	#1703	C₂×C₆₁	1	2	yes	complemented
219	#1699	C₂×C₆₁	1	2	yes	complemented
220	#1683	C₂×C₆₁	1	2	yes	complemented
221	#1679	C₂×C₆₁	1	2	yes	complemented
222	#1565	C₂×C₆₁	1	1	yes	characteristic, complemented
223	#1542	C₂×C₆₁	1	1	yes	characteristic, complemented
224	C₂×#332	C₂×C₆₁	1	1	yes	characteristic, complemented
225	C₂×C₆₁	—	2	2	no	—
226	C₂×C₆₁	—	8	2	no	—
227	C₂×C₆₁	C₂×#463	1	1	yes	characteristic
228	C₂×C₆₁	#3063	1	1	yes	characteristic
229	C₂×C₆₁	#3069	1	1	yes	characteristic
230	C₂×#131	—	2	1	no	—
231	#533	C₂²×C₆₁	1	1	yes	characteristic
232	#532	C₂²×C₆₁	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
234	#500	—	2	1	no	—
235	#491	—	2	2	no	—
236	#487	C₂²×C₆₁	1	2	yes	—
237	#487	C₂²×C₆₁	1	2	yes	—
238	#486	—	2	1	no	—
239	#480	—	2	2	no	—
240	#476	C₂²×C₆₁	1	2	yes	—
241	#475	—	2	1	no	—
242	#474	C₂²×C₆₁	1	2	yes	—
243	#474	C₂²×C₆₁	1	2	yes	—
244	#465	—	2	2	no	—
245	#461	C₂²×C₆₁	1	2	yes	—
246	#460	—	2	1	no	—
247	#436	C₂²×C₆₁	1	2	yes	—
248	#435	—	2	2	no	—
249	C₈×D₄	C₂²×C₆₁	1	2	yes	—
250	#431	C₂²×C₆₁	1	1	yes	characteristic
251	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
252	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
253	#419	—	2	1	no	—
254	#419	—	2	1	no	—
255	#408	—	2	1	no	—
256	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
257	#335	C₂²×C₆₁	1	2	yes	—
258	#334	C₂²×C₆₁	1	2	yes	—
259	#333	C₂²×C₆₁	1	1	yes	characteristic
260	#333	C₂²×C₆₁	1	1	yes	characteristic
261	#332	C₂²×C₆₁	1	2	yes	—
262	#332	C₂²×C₆₁	1	2	yes	—
263	#332	C₂²×C₆₁	1	1	yes	characteristic
264	#332	C₂²×C₆₁	1	1	yes	characteristic
265	C₆₁	#19235	1	1	yes	characteristic, direct product factor, Sylow
266	C₂×#41	—	2	1	no	—
267	C₂²×Q₈	—	2	1	no	—
268	C₂×SD₁₆	—	2	2	no	—
269	#131	—	4	4	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
272	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
273	C₂²×C₈	—	2	1	no	—
274	C₂²×C₈	—	2	1	no	—
275	C₂²×C₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
281	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
282	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
283	#127	D₄×C₆₁	1	1	yes	characteristic
284	#125	—	2	1	no	—
285	#124	—	2	1	no	—
286	C₂²⋊Q₈	—	2	1	no	—
287	C₂²⋊Q₈	—	2	1	no	—
288	#121	—	2	1	no	—
289	#121	D₄×C₆₁	1	2	yes	—
290	C₄×Q₈	—	2	1	no	—
291	C₄×Q₈	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	C₂³×C₆₁	1	2	yes	—
294	#117	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
298	#107	—	2	2	no	—
299	#107	—	2	2	no	—
300	#106	—	2	2	no	—
301	C₄⋊C₈	—	2	1	no	—
302	C₄⋊C₈	—	2	1	no	—
303	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
304	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
305	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
306	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
307	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
308	#103	—	2	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	2	no	—
311	#103	—	2	2	no	—
312	#103	—	2	2	no	—
313	#102	—	2	2	no	—
314	#102	—	2	2	no	—
315	#102	—	2	2	no	—
316	C₂²⋊C₈	—	2	1	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	#97	D₄×C₆₁	1	2	yes	—
320	C₄×C₈	—	2	1	no	—
321	C₄×C₈	C₂³×C₆₁	1	2	yes	—
322	#41	—	4	2	no	—
323	#41	—	4	2	no	—
324	C₂×Q₈	—	2	1	no	—
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	4	1	no	—
329	C₂×Q₈	—	4	2	no	—
330	C₂×Q₈	—	4	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
339	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
340	SD₁₆	—	8	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	2	2	no	—
343	M₁₆	—	4	4	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	1	no	—
346	C₂×C₈	—	2	1	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	4	4	no	—
350	C₂×C₈	—	4	2	no	—
351	C₂×C₈	—	8	1	no	—
352	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
353	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₄²	—	4	1	no	—
370	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
371	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
372	C₄²	#41×C₆₁	1	1	yes	characteristic
373	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
374	C₂³	—	2	2	no	—
375	C₂³	#121×C₆₁	1	1	yes	characteristic
376	Q₈	—	4	2	no	—
377	Q₈	—	4	2	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	1	no	—
380	Q₈	—	4	1	no	—
381	Q₈	—	8	1	no	—
382	Q₈	—	8	2	no	—
383	D₄	—	2	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	8	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	8	2	no	—
398	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
399	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
400	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
401	C₂×C₄	#135×C₆₁	1	2	yes	—
402	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
403	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	1	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	2	no	—
412	C₈	—	4	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	C₆₁×#463	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	—	4	2	no	—
424	C₄	—	8	2	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	C₆₁×#463	1	2	yes	—
428	C₄	C₂×#135×C₆₁	1	1	yes	characteristic
429	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
430	C₄	C₆₁×#577	1	1	yes	characteristic
431	C₄	C₆₁×#578	1	1	yes	characteristic
432	C₂	—	2	2	no	—
433	C₂	—	8	2	no	—
434	C₂	C₂×C₆₁×#463	1	1	yes	characteristic
435	C₂	C₆₁×#3063	1	1	yes	characteristic
436	C₂	C₆₁×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
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
3. C₆₁×#3139	C₂	semidirect
5. C₆₁×#1703	C₂	semidirect
6. C₆₁×#1699	C₂	semidirect
7. C₆₁×#1683	C₂	semidirect
8. C₆₁×#1679	C₂	semidirect
9. C₆₁×#1565	C₂	semidirect
10. C₆₁×#1542	C₂	semidirect
11. C₂×C₆₁×#332	C₂	semidirect
194. #19235	C₆₁	direct (N × H)
216. #3139	C₂×C₆₁	semidirect
218. #1703	C₂×C₆₁	semidirect
219. #1699	C₂×C₆₁	semidirect
220. #1683	C₂×C₆₁	semidirect
221. #1679	C₂×C₆₁	semidirect
222. #1565	C₂×C₆₁	semidirect
223. #1542	C₂×C₆₁	semidirect
224. C₂×#332	C₂×C₆₁	semidirect
265. C₆₁	#19235	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×#3246	2
C₆₁×#3226	2
C₆₁×#3139	2
C₆₁×#2935	2
C₆₁×#1703	2
C₆₁×#1699	2
C₆₁×#1683	2
C₆₁×#1679	2
C₆₁×#1565	2
C₆₁×#1542	2
C₂×C₆₁×#332	2
#19235	61

Subgroups — C61×#19235 #29522668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19235 #29522668