Subgroups — C₆₁×#19238 #29522671

Order 15616.

722 conjugacy classes of subgroups.

The subgroup lattice has 478 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, complemented
2	C₆₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3151	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1688	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1686	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1668	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1666	C₂	1	2	yes	maximal, complemented
9	C₆₁×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1540	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₆₁×#331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
13	C₂×AGL(1,ℤ/8)×C₆₁	—	2	1	no	—
14	C₆₁×#533	C₂²	1	1	yes	characteristic
15	C₆₁×#532	C₂²	1	1	yes	characteristic
16	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
17	C₆₁×#496	—	2	2	no	—
18	C₆₁×#493	C₂²	1	2	yes	—
19	C₆₁×#492	—	2	1	no	—
20	C₆₁×#492	C₂²	1	2	yes	—
21	C₆₁×#486	—	2	1	no	—
22	C₆₁×#476	—	2	1	no	—
23	C₆₁×#475	C₂²	1	2	yes	complemented
24	C₆₁×#465	—	2	2	no	—
25	C₆₁×#461	—	2	1	no	—
26	C₆₁×#460	C₂²	1	2	yes	—
27	C₆₁×#460	C₂²	1	2	yes	—
28	C₆₁×#460	C₂²	1	2	yes	complemented
29	C₆₁×#450	—	2	2	no	—
30	C₆₁×#446	—	2	2	no	—
31	C₆₁×#446	C₂²	1	2	yes	complemented
32	C₈×Q₈×C₆₁	C₂²	1	2	yes	complemented
33	C₆₁×#431	C₂²	1	1	yes	characteristic
34	C₆₁×#424	—	2	1	no	—
35	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₆₁	C₂²	1	1	yes	characteristic
37	C₆₁×#405	—	2	1	no	—
38	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
39	C₆₁×#335	C₂²	1	2	yes	complemented
40	C₆₁×#334	C₂²	1	2	yes	complemented
41	C₆₁×#332	C₂²	1	1	yes	characteristic, complemented
42	C₆₁×#332	C₂²	1	1	yes	characteristic, complemented
43	C₆₁×#331	C₂²	1	2	yes	—
44	C₆₁×#331	C₂²	1	2	yes	—
45	C₆₁×#331	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#331	C₂²	1	1	yes	characteristic, complemented
47	C₂×#41×C₆₁	—	2	1	no	—
48	C₂²×D₄×C₆₁	—	2	1	no	—
49	C₂²×D₄×C₆₁	—	2	1	no	—
50	C₂²×D₄×C₆₁	—	2	1	no	—
51	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
52	AGL(1,ℤ/8)×C₆₁	—	4	4	no	—
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×SD₁₆×C₆₁	—	2	2	no	—
55	C₂×SD₁₆×C₆₁	—	2	2	no	—
56	C₂×SD₁₆×C₆₁	—	2	2	no	—
57	C₂×SD₁₆×C₆₁	—	2	2	no	—
58	C₂×D₈×C₆₁	—	2	2	no	—
59	C₂×D₈×C₆₁	—	2	2	no	—
60	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
61	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
62	C₂²×C₈×C₆₁	—	2	1	no	—
63	C₂²×C₈×C₆₁	—	2	1	no	—
64	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	#127×C₆₁	—	2	1	no	—
68	#127×C₆₁	—	2	1	no	—
69	#127×C₆₁	—	2	1	no	—
70	#127×C₆₁	C₂³	1	2	yes	—
71	#127×C₆₁	C₂³	1	1	yes	characteristic
72	#125×C₆₁	—	2	1	no	—
73	#124×C₆₁	—	2	1	no	—
74	C₂²⋊Q₈×C₆₁	—	2	1	no	—
75	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
76	#121×C₆₁	—	2	1	no	—
77	#121×C₆₁	—	2	1	no	—
78	C₄×Q₈×C₆₁	—	2	1	no	—
79	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
80	C₄×D₄×C₆₁	—	2	1	no	—
81	C₄×D₄×C₆₁	—	2	1	no	—
82	#117×C₆₁	—	2	1	no	—
83	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
84	#106×C₆₁	—	2	2	no	—
85	C₄⋊C₈×C₆₁	—	2	2	no	—
86	C₄⋊C₈×C₆₁	—	2	2	no	—
87	C₄⋊C₈×C₆₁	—	2	1	no	—
88	C₄⋊C₈×C₆₁	—	2	1	no	—
89	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
92	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
94	#103×C₆₁	—	2	2	no	—
95	#102×C₆₁	—	2	2	no	—
96	#102×C₆₁	—	2	2	no	—
97	#102×C₆₁	—	2	2	no	—
98	C₂²⋊C₈×C₆₁	—	2	1	no	—
99	#97×C₆₁	—	2	2	no	—
100	#97×C₆₁	D₄	1	2	yes	—
101	C₄×C₈×C₆₁	—	2	2	no	—
102	C₄×C₈×C₆₁	—	2	1	no	—
103	C₄×C₈×C₆₁	C₂³	1	2	yes	—
104	C₂⁴×C₆₁	—	4	1	no	—
105	#41×C₆₁	—	4	2	no	—
106	#41×C₆₁	—	4	2	no	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	1	no	—
109	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
110	C₂×D₄×C₆₁	—	2	1	no	—
111	C₂×D₄×C₆₁	—	2	2	no	—
112	C₂×D₄×C₆₁	—	2	1	no	—
113	C₂×D₄×C₆₁	—	2	2	no	—
114	C₂×D₄×C₆₁	—	2	1	no	—
115	C₂×D₄×C₆₁	—	2	2	no	—
116	C₂×D₄×C₆₁	—	4	1	no	—
117	C₂×D₄×C₆₁	—	4	1	no	—
118	C₂×D₄×C₆₁	—	4	1	no	—
119	C₂×D₄×C₆₁	—	4	1	no	—
120	C₂×D₄×C₆₁	—	4	2	no	—
121	C₂×D₄×C₆₁	—	4	2	no	—
122	C₂×D₄×C₆₁	—	8	1	no	—
123	C₂×D₄×C₆₁	—	8	1	no	—
124	C₂×D₄×C₆₁	—	8	2	no	—
125	C₂²×C₄×C₆₁	—	4	1	no	—
126	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₆₁	#41	1	1	yes	characteristic
129	SD₁₆×C₆₁	—	4	4	no	—
130	SD₁₆×C₆₁	—	4	4	no	—
131	SD₁₆×C₆₁	—	8	2	no	—
132	SD₁₆×C₆₁	—	8	2	no	—
133	SD₁₆×C₆₁	—	8	2	no	—
134	D₈×C₆₁	—	4	4	no	—
135	D₈×C₆₁	—	4	4	no	—
136	M₁₆×C₆₁	—	2	2	no	—
137	M₁₆×C₆₁	SD₁₆	1	4	yes	complemented
138	C₂×C₈×C₆₁	—	2	1	no	—
139	C₂×C₈×C₆₁	—	2	1	no	—
140	C₂×C₈×C₆₁	—	2	1	no	—
141	C₂×C₈×C₆₁	—	2	1	no	—
142	C₂×C₈×C₆₁	—	2	2	no	—
143	C₂×C₈×C₆₁	—	4	2	no	—
144	C₂×C₈×C₆₁	—	8	1	no	—
145	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
147	C₄⋊C₄×C₆₁	—	2	1	no	—
148	C₄⋊C₄×C₆₁	—	2	1	no	—
149	C₄⋊C₄×C₆₁	—	2	1	no	—
150	C₄⋊C₄×C₆₁	—	2	2	no	—
151	C₄⋊C₄×C₆₁	—	2	2	no	—
152	C₄⋊C₄×C₆₁	—	2	1	no	—
153	C₄⋊C₄×C₆₁	—	2	1	no	—
154	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
155	C₂²⋊C₄×C₆₁	—	2	2	no	—
156	C₂²⋊C₄×C₆₁	—	4	1	no	—
157	C₂²⋊C₄×C₆₁	—	4	1	no	—
158	C₄²×C₆₁	—	2	2	no	—
159	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₆₁	#41	1	1	yes	characteristic
162	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
163	C₂³×C₆₁	—	4	1	no	—
164	C₂³×C₆₁	—	4	2	no	—
165	C₂³×C₆₁	—	8	2	no	—
166	C₂³×C₆₁	—	8	2	no	—
167	C₂³×C₆₁	—	8	2	no	—
168	C₂³×C₆₁	#121	1	1	yes	characteristic
169	Q₈×C₆₁	—	2	2	no	—
170	Q₈×C₆₁	—	2	2	no	—
171	Q₈×C₆₁	—	4	1	no	—
172	Q₈×C₆₁	—	4	1	no	—
173	Q₈×C₆₁	—	8	1	no	—
174	D₄×C₆₁	—	4	1	no	—
175	D₄×C₆₁	—	4	2	no	—
176	D₄×C₆₁	—	4	1	no	—
177	D₄×C₆₁	—	4	2	no	—
178	D₄×C₆₁	—	4	1	no	—
179	D₄×C₆₁	—	4	2	no	—
180	D₄×C₆₁	—	4	2	no	—
181	D₄×C₆₁	—	4	1	no	—
182	D₄×C₆₁	—	8	1	no	—
183	D₄×C₆₁	—	8	2	no	—
184	D₄×C₆₁	—	8	2	no	—
185	D₄×C₆₁	—	8	2	no	—
186	D₄×C₆₁	—	8	2	no	—
187	D₄×C₆₁	—	8	2	no	—
188	C₂×C₄×C₆₁	—	2	1	no	—
189	C₂×C₄×C₆₁	—	2	1	no	—
190	C₂×C₄×C₆₁	—	2	2	no	—
191	C₂×C₄×C₆₁	—	2	2	no	—
192	C₂×C₄×C₆₁	—	4	1	no	—
193	C₂×C₄×C₆₁	—	4	1	no	—
194	C₂×C₄×C₆₁	—	8	2	no	—
195	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
196	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
197	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
198	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
199	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
203	C₈×C₆₁	—	2	2	no	—
204	C₈×C₆₁	—	4	1	no	—
205	C₈×C₆₁	—	4	1	no	—
206	C₈×C₆₁	—	4	2	no	—
207	C₈×C₆₁	—	4	1	no	—
208	C₈×C₆₁	—	4	1	no	—
209	C₈×C₆₁	C₂×SD₁₆	1	4	yes	—
210	#19238	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₆₁	—	2	1	no	—
212	C₂²×C₆₁	—	2	1	no	—
213	C₂²×C₆₁	—	8	1	no	—
214	C₂²×C₆₁	—	8	2	no	—
215	C₂²×C₆₁	—	8	2	no	—
216	C₂²×C₆₁	—	8	1	no	—
217	C₂²×C₆₁	—	8	2	no	—
218	C₂²×C₆₁	—	8	1	no	—
219	C₂²×C₆₁	—	16	4	no	—
220	C₂²×C₆₁	#460	1	2	yes	—
221	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
222	C₄×C₆₁	—	2	1	no	—
223	C₄×C₆₁	—	2	1	no	—
224	C₄×C₆₁	—	2	1	no	—
225	C₄×C₆₁	—	4	2	no	—
226	C₄×C₆₁	—	4	2	no	—
227	C₄×C₆₁	—	8	1	no	—
228	C₄×C₆₁	#460	1	2	yes	—
229	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
230	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₆₁	#576	1	1	yes	characteristic
232	C₄×C₆₁	#577	1	1	yes	characteristic
233	#3246	C₂×C₆₁	1	1	yes	characteristic, complemented
234	#3208	C₂×C₆₁	1	1	yes	characteristic, complemented
235	#3151	C₂×C₆₁	1	1	yes	characteristic
236	#2962	C₂×C₆₁	1	1	yes	characteristic, complemented
237	#1688	C₂×C₆₁	1	2	yes	complemented
238	#1686	C₂×C₆₁	1	2	yes	complemented
239	#1668	C₂×C₆₁	1	2	yes	complemented
240	#1666	C₂×C₆₁	1	2	yes	complemented
241	#1565	C₂×C₆₁	1	1	yes	characteristic, complemented
242	#1540	C₂×C₆₁	1	1	yes	characteristic, complemented
243	C₂×#331	C₂×C₆₁	1	1	yes	characteristic, complemented
244	C₂×C₆₁	—	2	2	no	—
245	C₂×C₆₁	—	16	1	no	—
246	C₂×C₆₁	—	16	2	no	—
247	C₂×C₆₁	C₂×#460	1	1	yes	characteristic
248	C₂×C₆₁	#3062	1	1	yes	characteristic
249	C₂×C₆₁	#3068	1	1	yes	characteristic
250	C₂×AGL(1,ℤ/8)	—	2	1	no	—
251	C₂×AGL(1,ℤ/8)	—	2	1	no	—
252	#533	C₂²×C₆₁	1	1	yes	characteristic
253	#532	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
255	#496	—	2	2	no	—
256	#493	C₂²×C₆₁	1	2	yes	—
257	#492	—	2	1	no	—
258	#492	C₂²×C₆₁	1	2	yes	—
259	#486	—	2	1	no	—
260	#476	—	2	1	no	—
261	#475	C₂²×C₆₁	1	2	yes	complemented
262	#465	—	2	2	no	—
263	#461	—	2	1	no	—
264	#460	C₂²×C₆₁	1	2	yes	—
265	#460	C₂²×C₆₁	1	2	yes	—
266	#460	C₂²×C₆₁	1	2	yes	complemented
267	#450	—	2	2	no	—
268	#446	—	2	2	no	—
269	#446	C₂²×C₆₁	1	2	yes	complemented
270	C₈×Q₈	C₂²×C₆₁	1	2	yes	complemented
271	#431	C₂²×C₆₁	1	1	yes	characteristic
272	#424	—	2	1	no	—
273	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
274	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
275	#405	—	2	1	no	—
276	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
277	#335	C₂²×C₆₁	1	2	yes	complemented
278	#334	C₂²×C₆₁	1	2	yes	complemented
279	#332	C₂²×C₆₁	1	1	yes	characteristic, complemented
280	#332	C₂²×C₆₁	1	1	yes	characteristic, complemented
281	#331	C₂²×C₆₁	1	2	yes	—
282	#331	C₂²×C₆₁	1	2	yes	—
283	#331	C₂²×C₆₁	1	1	yes	characteristic, complemented
284	#331	C₂²×C₆₁	1	1	yes	characteristic, complemented
285	C₆₁	#19238	1	1	yes	characteristic, direct product factor, Sylow
286	C₂×#41	—	2	1	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	—	2	1	no	—
289	C₂²×D₄	—	2	1	no	—
290	AGL(1,ℤ/8)	—	4	4	no	—
291	AGL(1,ℤ/8)	—	4	4	no	—
292	C₂×SD₁₆	—	2	2	no	—
293	C₂×SD₁₆	—	2	2	no	—
294	C₂×SD₁₆	—	2	2	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×D₈	—	2	2	no	—
298	C₂×D₈	—	2	2	no	—
299	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
300	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
301	C₂²×C₈	—	2	1	no	—
302	C₂²×C₈	—	2	1	no	—
303	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
304	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
305	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
306	#127	—	2	1	no	—
307	#127	—	2	1	no	—
308	#127	—	2	1	no	—
309	#127	C₂³×C₆₁	1	2	yes	—
310	#127	C₂³×C₆₁	1	1	yes	characteristic
311	#125	—	2	1	no	—
312	#124	—	2	1	no	—
313	C₂²⋊Q₈	—	2	1	no	—
314	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
315	#121	—	2	1	no	—
316	#121	—	2	1	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
319	C₄×D₄	—	2	1	no	—
320	C₄×D₄	—	2	1	no	—
321	#117	—	2	1	no	—
322	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
323	#106	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	C₄⋊C₈	—	2	2	no	—
326	C₄⋊C₈	—	2	1	no	—
327	C₄⋊C₈	—	2	1	no	—
328	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
329	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
330	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
331	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
332	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
333	#103	—	2	2	no	—
334	#102	—	2	2	no	—
335	#102	—	2	2	no	—
336	#102	—	2	2	no	—
337	C₂²⋊C₈	—	2	1	no	—
338	#97	—	2	2	no	—
339	#97	D₄×C₆₁	1	2	yes	—
340	C₄×C₈	—	2	2	no	—
341	C₄×C₈	—	2	1	no	—
342	C₄×C₈	C₂³×C₆₁	1	2	yes	—
343	C₂⁴	—	4	1	no	—
344	#41	—	4	2	no	—
345	#41	—	4	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	1	no	—
356	C₂×D₄	—	4	1	no	—
357	C₂×D₄	—	4	1	no	—
358	C₂×D₄	—	4	1	no	—
359	C₂×D₄	—	4	2	no	—
360	C₂×D₄	—	4	2	no	—
361	C₂×D₄	—	8	1	no	—
362	C₂×D₄	—	8	1	no	—
363	C₂×D₄	—	8	2	no	—
364	C₂²×C₄	—	4	1	no	—
365	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
367	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
368	SD₁₆	—	4	4	no	—
369	SD₁₆	—	4	4	no	—
370	SD₁₆	—	8	2	no	—
371	SD₁₆	—	8	2	no	—
372	SD₁₆	—	8	2	no	—
373	D₈	—	4	4	no	—
374	D₈	—	4	4	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	SD₁₆×C₆₁	1	4	yes	complemented
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	4	2	no	—
383	C₂×C₈	—	8	1	no	—
384	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
385	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	1	no	—
392	C₄⋊C₄	—	2	1	no	—
393	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	4	1	no	—
396	C₂²⋊C₄	—	4	1	no	—
397	C₄²	—	2	2	no	—
398	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
399	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
400	C₄²	#41×C₆₁	1	1	yes	characteristic
401	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
402	C₂³	—	4	1	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	8	2	no	—
405	C₂³	—	8	2	no	—
406	C₂³	—	8	2	no	—
407	C₂³	#121×C₆₁	1	1	yes	characteristic
408	Q₈	—	2	2	no	—
409	Q₈	—	2	2	no	—
410	Q₈	—	4	1	no	—
411	Q₈	—	4	1	no	—
412	Q₈	—	8	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	2	no	—
415	D₄	—	4	1	no	—
416	D₄	—	4	2	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	1	no	—
421	D₄	—	8	1	no	—
422	D₄	—	8	2	no	—
423	D₄	—	8	2	no	—
424	D₄	—	8	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	8	2	no	—
434	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
435	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
436	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
437	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
438	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	4	1	no	—
444	C₈	—	4	1	no	—
445	C₈	—	4	2	no	—
446	C₈	—	4	1	no	—
447	C₈	—	4	1	no	—
448	C₈	C₂×SD₁₆×C₆₁	1	4	yes	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	1	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	16	4	no	—
458	C₂²	C₆₁×#460	1	2	yes	—
459	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	4	2	no	—
465	C₄	—	8	1	no	—
466	C₄	C₆₁×#460	1	2	yes	—
467	C₄	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
468	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
469	C₄	C₆₁×#576	1	1	yes	characteristic
470	C₄	C₆₁×#577	1	1	yes	characteristic
471	C₂	—	2	2	no	—
472	C₂	—	16	2	no	—
473	C₂	—	16	1	no	—
474	C₂	C₂×C₆₁×#460	1	1	yes	characteristic
475	C₂	C₆₁×#3062	1	1	yes	characteristic
476	C₂	C₆₁×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₆₁×#3151	C₂
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×#3246	C₂	semidirect
2. C₆₁×#3208	C₂	semidirect
4. C₆₁×#2962	C₂	semidirect
5. C₆₁×#1688	C₂	semidirect
6. C₆₁×#1686	C₂	semidirect
7. C₆₁×#1668	C₂	semidirect
8. C₆₁×#1666	C₂	semidirect
9. C₆₁×#1565	C₂	semidirect
10. C₆₁×#1540	C₂	semidirect
11. C₂×C₆₁×#331	C₂	semidirect
23. C₆₁×#475	C₂²	semidirect
28. C₆₁×#460	C₂²	semidirect
31. C₆₁×#446	C₂²	semidirect
32. C₈×Q₈×C₆₁	C₂²	semidirect
39. C₆₁×#335	C₂²	semidirect
40. C₆₁×#334	C₂²	semidirect
41. C₆₁×#332	C₂²	semidirect
42. C₆₁×#332	C₂²	semidirect
45. C₆₁×#331	C₂²	semidirect
46. C₆₁×#331	C₂²	semidirect
137. M₁₆×C₆₁	SD₁₆	semidirect
210. #19238	C₆₁	direct (N × H)
233. #3246	C₂×C₆₁	semidirect
234. #3208	C₂×C₆₁	semidirect
236. #2962	C₂×C₆₁	semidirect
237. #1688	C₂×C₆₁	semidirect
238. #1686	C₂×C₆₁	semidirect
239. #1668	C₂×C₆₁	semidirect
240. #1666	C₂×C₆₁	semidirect
241. #1565	C₂×C₆₁	semidirect
242. #1540	C₂×C₆₁	semidirect
243. C₂×#331	C₂×C₆₁	semidirect
261. #475	C₂²×C₆₁	semidirect
266. #460	C₂²×C₆₁	semidirect
269. #446	C₂²×C₆₁	semidirect
270. C₈×Q₈	C₂²×C₆₁	semidirect
277. #335	C₂²×C₆₁	semidirect
278. #334	C₂²×C₆₁	semidirect
279. #332	C₂²×C₆₁	semidirect
280. #332	C₂²×C₆₁	semidirect
283. #331	C₂²×C₆₁	semidirect
284. #331	C₂²×C₆₁	semidirect
285. C₆₁	#19238	direct (N × H)
376. M₁₆	SD₁₆×C₆₁	semidirect

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×#3208	2
C₆₁×#3151	2
C₆₁×#2962	2
C₆₁×#1688	2
C₆₁×#1686	2
C₆₁×#1668	2
C₆₁×#1666	2
C₆₁×#1565	2
C₆₁×#1540	2
C₂×C₆₁×#331	2
#19238	61

Subgroups — C61×#19238 #29522671

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19238 #29522671