Subgroups — C₆₁×#19239 #29522672

Order 15616.

658 conjugacy classes of subgroups.

The subgroup lattice has 446 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×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3152	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1690	C₂	1	2	yes	maximal, complemented
6	C₆₁×#1686	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1670	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
11	C₂×C₆₁×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₆₁	—	2	1	no	—
13	C₂×#137×C₆₁	—	2	1	no	—
14	C₆₁×#533	C₂²	1	1	yes	characteristic
15	C₆₁×#532	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
17	C₆₁×#498	—	2	1	no	—
18	C₆₁×#497	—	2	2	no	—
19	C₆₁×#494	C₂²	1	2	yes	—
20	C₆₁×#492	C₂²	1	2	yes	—
21	C₆₁×#487	—	2	1	no	—
22	C₆₁×#483	—	2	2	no	—
23	C₆₁×#476	—	2	1	no	—
24	C₆₁×#475	C₂²	1	2	yes	—
25	C₆₁×#475	C₂²	1	2	yes	—
26	C₆₁×#475	C₂²	1	2	yes	—
27	C₆₁×#465	—	2	2	no	—
28	C₆₁×#461	—	2	1	no	—
29	C₆₁×#460	C₂²	1	2	yes	—
30	C₆₁×#446	—	2	2	no	—
31	C₆₁×#446	C₂²	1	2	yes	—
32	C₈×Q₈×C₆₁	C₂²	1	2	yes	—
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	—
40	C₆₁×#334	C₂²	1	2	yes	—
41	C₆₁×#332	C₂²	1	2	yes	—
42	C₆₁×#332	C₂²	1	2	yes	—
43	C₆₁×#332	C₂²	1	1	yes	characteristic
44	C₆₁×#332	C₂²	1	1	yes	characteristic
45	C₆₁×#331	C₂²	1	1	yes	characteristic
46	C₆₁×#331	C₂²	1	1	yes	characteristic
47	C₂×#41×C₆₁	—	2	1	no	—
48	C₂²×Q₈×C₆₁	—	2	1	no	—
49	#137×C₆₁	—	4	4	no	—
50	#137×C₆₁	—	4	4	no	—
51	C₂×Q₁₆×C₆₁	—	2	2	no	—
52	C₂×Q₁₆×C₆₁	—	2	2	no	—
53	C₂×SD₁₆×C₆₁	—	2	2	no	—
54	C₂×SD₁₆×C₆₁	—	2	2	no	—
55	C₂×SD₁₆×C₆₁	—	2	2	no	—
56	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
57	C₂×M₁₆×C₆₁	D₄	1	1	yes	characteristic
58	C₂²×C₈×C₆₁	—	2	1	no	—
59	C₂²×C₈×C₆₁	—	2	1	no	—
60	C₄⋊Q₈×C₆₁	—	2	1	no	—
61	C₄⋊Q₈×C₆₁	—	2	1	no	—
62	C₄⋊Q₈×C₆₁	—	2	1	no	—
63	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₆₁	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₆₁	C₂³	1	2	yes	—
66	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
67	#127×C₆₁	C₂³	1	1	yes	characteristic
68	#125×C₆₁	—	2	1	no	—
69	#124×C₆₁	—	2	1	no	—
70	C₂²⋊Q₈×C₆₁	—	2	1	no	—
71	C₂²⋊Q₈×C₆₁	D₄	1	2	yes	—
72	#121×C₆₁	—	2	1	no	—
73	#121×C₆₁	—	2	1	no	—
74	C₄×Q₈×C₆₁	—	2	1	no	—
75	C₄×Q₈×C₆₁	C₂³	1	2	yes	—
76	C₄×D₄×C₆₁	—	2	1	no	—
77	C₄×D₄×C₆₁	—	2	1	no	—
78	#117×C₆₁	—	2	1	no	—
79	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
80	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
81	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
82	#106×C₆₁	—	2	2	no	—
83	#106×C₆₁	—	2	2	no	—
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	1	yes	characteristic
92	C₄⋊C₈×C₆₁	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₆₁	C₂³	1	2	yes	—
94	#103×C₆₁	—	2	2	no	—
95	#103×C₆₁	—	2	2	no	—
96	#103×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	#41×C₆₁	—	4	2	no	—
105	#41×C₆₁	—	4	2	no	—
106	C₂×Q₈×C₆₁	—	2	1	no	—
107	C₂×Q₈×C₆₁	—	2	1	no	—
108	C₂×Q₈×C₆₁	—	2	2	no	—
109	C₂×Q₈×C₆₁	—	4	1	no	—
110	C₂×Q₈×C₆₁	—	4	2	no	—
111	C₂×Q₈×C₆₁	—	4	2	no	—
112	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
113	C₂×D₄×C₆₁	—	2	1	no	—
114	C₂×D₄×C₆₁	—	2	1	no	—
115	C₂×D₄×C₆₁	—	2	1	no	—
116	C₂×D₄×C₆₁	—	4	1	no	—
117	C₂²×C₄×C₆₁	—	4	1	no	—
118	C₂²×C₄×C₆₁	—	4	1	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	4	no	—
123	Q₁₆×C₆₁	—	4	4	no	—
124	SD₁₆×C₆₁	—	4	4	no	—
125	SD₁₆×C₆₁	—	4	4	no	—
126	SD₁₆×C₆₁	—	8	2	no	—
127	M₁₆×C₆₁	—	2	2	no	—
128	M₁₆×C₆₁	SD₁₆	1	4	yes	complemented
129	C₂×C₈×C₆₁	—	2	1	no	—
130	C₂×C₈×C₆₁	—	2	1	no	—
131	C₂×C₈×C₆₁	—	2	1	no	—
132	C₂×C₈×C₆₁	—	2	1	no	—
133	C₂×C₈×C₆₁	—	2	2	no	—
134	C₂×C₈×C₆₁	—	4	2	no	—
135	C₂×C₈×C₆₁	—	8	1	no	—
136	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₆₁	—	2	1	no	—
139	C₄⋊C₄×C₆₁	—	2	1	no	—
140	C₄⋊C₄×C₆₁	—	2	1	no	—
141	C₄⋊C₄×C₆₁	—	2	2	no	—
142	C₄⋊C₄×C₆₁	—	2	2	no	—
143	C₄⋊C₄×C₆₁	—	2	2	no	—
144	C₄⋊C₄×C₆₁	—	2	1	no	—
145	C₄⋊C₄×C₆₁	—	2	2	no	—
146	C₄⋊C₄×C₆₁	—	2	1	no	—
147	C₄⋊C₄×C₆₁	—	4	1	no	—
148	C₄⋊C₄×C₆₁	—	4	1	no	—
149	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₆₁	—	2	2	no	—
151	C₂²⋊C₄×C₆₁	—	4	1	no	—
152	C₂²⋊C₄×C₆₁	—	4	1	no	—
153	C₄²×C₆₁	—	2	2	no	—
154	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₆₁	#41	1	1	yes	characteristic
157	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
158	C₂³×C₆₁	—	4	1	no	—
159	C₂³×C₆₁	#121	1	1	yes	characteristic
160	Q₈×C₆₁	—	2	2	no	—
161	Q₈×C₆₁	—	2	2	no	—
162	Q₈×C₆₁	—	4	2	no	—
163	Q₈×C₆₁	—	4	1	no	—
164	Q₈×C₆₁	—	4	2	no	—
165	Q₈×C₆₁	—	4	1	no	—
166	Q₈×C₆₁	—	8	1	no	—
167	Q₈×C₆₁	—	8	2	no	—
168	D₄×C₆₁	—	4	1	no	—
169	D₄×C₆₁	—	4	1	no	—
170	D₄×C₆₁	—	4	1	no	—
171	D₄×C₆₁	—	4	1	no	—
172	D₄×C₆₁	—	8	1	no	—
173	D₄×C₆₁	—	8	2	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	2	no	—
178	C₂×C₄×C₆₁	—	4	1	no	—
179	C₂×C₄×C₆₁	—	4	1	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	8	2	no	—
182	C₂×C₄×C₆₁	—	8	2	no	—
183	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
184	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
185	C₂×C₄×C₆₁	#121	1	1	yes	characteristic
186	C₂×C₄×C₆₁	C₂×SD₁₆	1	2	yes	—
187	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
188	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
191	C₈×C₆₁	—	2	2	no	—
192	C₈×C₆₁	—	4	1	no	—
193	C₈×C₆₁	—	4	1	no	—
194	C₈×C₆₁	—	4	1	no	—
195	C₈×C₆₁	—	4	2	no	—
196	C₈×C₆₁	—	4	1	no	—
197	C₈×C₆₁	C₂×SD₁₆	1	4	yes	—
198	#19239	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₆₁	—	2	1	no	—
200	C₂²×C₆₁	—	2	1	no	—
201	C₂²×C₆₁	—	8	1	no	—
202	C₂²×C₆₁	—	8	1	no	—
203	C₂²×C₆₁	—	8	1	no	—
204	C₂²×C₆₁	#460	1	2	yes	—
205	C₂²×C₆₁	C₂×#121	1	1	yes	characteristic
206	C₄×C₆₁	—	2	1	no	—
207	C₄×C₆₁	—	2	1	no	—
208	C₄×C₆₁	—	2	1	no	—
209	C₄×C₆₁	—	4	2	no	—
210	C₄×C₆₁	—	4	2	no	—
211	C₄×C₆₁	—	8	1	no	—
212	C₄×C₆₁	—	8	2	no	—
213	C₄×C₆₁	#460	1	2	yes	—
214	C₄×C₆₁	C₂²×SD₁₆	1	1	yes	characteristic
215	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
216	C₄×C₆₁	#577	1	1	yes	characteristic
217	C₄×C₆₁	#578	1	1	yes	characteristic
218	#3246	C₂×C₆₁	1	1	yes	characteristic
219	#3229	C₂×C₆₁	1	1	yes	characteristic, complemented
220	#3152	C₂×C₆₁	1	1	yes	characteristic
221	#2962	C₂×C₆₁	1	1	yes	characteristic, complemented
222	#1690	C₂×C₆₁	1	2	yes	complemented
223	#1686	C₂×C₆₁	1	2	yes	complemented
224	#1670	C₂×C₆₁	1	2	yes	complemented
225	#1666	C₂×C₆₁	1	2	yes	complemented
226	#1565	C₂×C₆₁	1	1	yes	characteristic, complemented
227	#1540	C₂×C₆₁	1	1	yes	characteristic
228	C₂×#332	C₂×C₆₁	1	1	yes	characteristic, complemented
229	C₂×C₆₁	—	2	2	no	—
230	C₂×C₆₁	—	16	1	no	—
231	C₂×C₆₁	C₂×#460	1	1	yes	characteristic
232	C₂×C₆₁	#3063	1	1	yes	characteristic
233	C₂×C₆₁	#3069	1	1	yes	characteristic
234	C₂×#137	—	2	1	no	—
235	C₂×#137	—	2	1	no	—
236	#533	C₂²×C₆₁	1	1	yes	characteristic
237	#532	C₂²×C₆₁	1	1	yes	characteristic
238	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
239	#498	—	2	1	no	—
240	#497	—	2	2	no	—
241	#494	C₂²×C₆₁	1	2	yes	—
242	#492	C₂²×C₆₁	1	2	yes	—
243	#487	—	2	1	no	—
244	#483	—	2	2	no	—
245	#476	—	2	1	no	—
246	#475	C₂²×C₆₁	1	2	yes	—
247	#475	C₂²×C₆₁	1	2	yes	—
248	#475	C₂²×C₆₁	1	2	yes	—
249	#465	—	2	2	no	—
250	#461	—	2	1	no	—
251	#460	C₂²×C₆₁	1	2	yes	—
252	#446	—	2	2	no	—
253	#446	C₂²×C₆₁	1	2	yes	—
254	C₈×Q₈	C₂²×C₆₁	1	2	yes	—
255	#431	C₂²×C₆₁	1	1	yes	characteristic
256	#424	—	2	1	no	—
257	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
258	C₂×C₄⋊C₈	C₂²×C₆₁	1	1	yes	characteristic
259	#405	—	2	1	no	—
260	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
261	#335	C₂²×C₆₁	1	2	yes	—
262	#334	C₂²×C₆₁	1	2	yes	—
263	#332	C₂²×C₆₁	1	2	yes	—
264	#332	C₂²×C₆₁	1	2	yes	—
265	#332	C₂²×C₆₁	1	1	yes	characteristic
266	#332	C₂²×C₆₁	1	1	yes	characteristic
267	#331	C₂²×C₆₁	1	1	yes	characteristic
268	#331	C₂²×C₆₁	1	1	yes	characteristic
269	C₆₁	#19239	1	1	yes	characteristic, direct product factor, Sylow
270	C₂×#41	—	2	1	no	—
271	C₂²×Q₈	—	2	1	no	—
272	#137	—	4	4	no	—
273	#137	—	4	4	no	—
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×SD₁₆	—	2	2	no	—
277	C₂×SD₁₆	—	2	2	no	—
278	C₂×SD₁₆	—	2	2	no	—
279	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
280	C₂×M₁₆	D₄×C₆₁	1	1	yes	characteristic
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	1	no	—
283	C₄⋊Q₈	—	2	1	no	—
284	C₄⋊Q₈	—	2	1	no	—
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
287	C₄⋊Q₈	D₄×C₆₁	1	1	yes	characteristic
288	C₄⋊Q₈	C₂³×C₆₁	1	2	yes	—
289	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
290	#127	C₂³×C₆₁	1	1	yes	characteristic
291	#125	—	2	1	no	—
292	#124	—	2	1	no	—
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	D₄×C₆₁	1	2	yes	—
295	#121	—	2	1	no	—
296	#121	—	2	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	C₂³×C₆₁	1	2	yes	—
299	C₄×D₄	—	2	1	no	—
300	C₄×D₄	—	2	1	no	—
301	#117	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
305	#106	—	2	2	no	—
306	#106	—	2	2	no	—
307	#106	—	2	2	no	—
308	C₄⋊C₈	—	2	2	no	—
309	C₄⋊C₈	—	2	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	2	1	no	—
312	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
313	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
314	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
315	C₄⋊C₈	C₂³×C₆₁	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₆₁	1	2	yes	—
317	#103	—	2	2	no	—
318	#103	—	2	2	no	—
319	#103	—	2	2	no	—
320	#102	—	2	2	no	—
321	C₂²⋊C₈	—	2	1	no	—
322	#97	—	2	2	no	—
323	#97	D₄×C₆₁	1	2	yes	—
324	C₄×C₈	—	2	2	no	—
325	C₄×C₈	—	2	1	no	—
326	C₄×C₈	C₂³×C₆₁	1	2	yes	—
327	#41	—	4	2	no	—
328	#41	—	4	2	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	4	1	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	4	2	no	—
335	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂²×C₄	—	4	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	#41×C₆₁	1	1	yes	characteristic
345	Q₁₆	—	4	4	no	—
346	Q₁₆	—	4	4	no	—
347	SD₁₆	—	4	4	no	—
348	SD₁₆	—	4	4	no	—
349	SD₁₆	—	8	2	no	—
350	M₁₆	—	2	2	no	—
351	M₁₆	SD₁₆×C₆₁	1	4	yes	complemented
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	8	1	no	—
359	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
360	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	1	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	4	1	no	—
372	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₂²⋊C₄	—	4	1	no	—
375	C₂²⋊C₄	—	4	1	no	—
376	C₄²	—	2	2	no	—
377	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
379	C₄²	#41×C₆₁	1	1	yes	characteristic
380	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
381	C₂³	—	4	1	no	—
382	C₂³	#121×C₆₁	1	1	yes	characteristic
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	1	no	—
387	Q₈	—	4	2	no	—
388	Q₈	—	4	1	no	—
389	Q₈	—	8	1	no	—
390	Q₈	—	8	2	no	—
391	D₄	—	4	1	no	—
392	D₄	—	4	1	no	—
393	D₄	—	4	1	no	—
394	D₄	—	4	1	no	—
395	D₄	—	8	1	no	—
396	D₄	—	8	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	8	2	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
407	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
408	C₂×C₄	#121×C₆₁	1	1	yes	characteristic
409	C₂×C₄	C₂×SD₁₆×C₆₁	1	2	yes	—
410	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	4	1	no	—
416	C₈	—	4	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	2	no	—
419	C₈	—	4	1	no	—
420	C₈	C₂×SD₁₆×C₆₁	1	4	yes	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	C₆₁×#460	1	2	yes	—
427	C₂²	C₂×#121×C₆₁	1	1	yes	characteristic
428	C₄	—	2	1	no	—
429	C₄	—	2	1	no	—
430	C₄	—	2	1	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	8	1	no	—
434	C₄	—	8	2	no	—
435	C₄	C₆₁×#460	1	2	yes	—
436	C₄	C₂²×SD₁₆×C₆₁	1	1	yes	characteristic
437	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
438	C₄	C₆₁×#577	1	1	yes	characteristic
439	C₄	C₆₁×#578	1	1	yes	characteristic
440	C₂	—	2	2	no	—
441	C₂	—	16	1	no	—
442	C₂	C₂×C₆₁×#460	1	1	yes	characteristic
443	C₂	C₆₁×#3063	1	1	yes	characteristic
444	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
2. C₆₁×#3229	C₂	semidirect
4. C₆₁×#2962	C₂	semidirect
5. C₆₁×#1690	C₂	semidirect
6. C₆₁×#1686	C₂	semidirect
7. C₆₁×#1670	C₂	semidirect
8. C₆₁×#1666	C₂	semidirect
9. C₆₁×#1565	C₂	semidirect
11. C₂×C₆₁×#332	C₂	semidirect
128. M₁₆×C₆₁	SD₁₆	semidirect
198. #19239	C₆₁	direct (N × H)
219. #3229	C₂×C₆₁	semidirect
221. #2962	C₂×C₆₁	semidirect
222. #1690	C₂×C₆₁	semidirect
223. #1686	C₂×C₆₁	semidirect
224. #1670	C₂×C₆₁	semidirect
225. #1666	C₂×C₆₁	semidirect
226. #1565	C₂×C₆₁	semidirect
228. C₂×#332	C₂×C₆₁	semidirect
269. C₆₁	#19239	direct (N × H)
351. 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×#3229	2
C₆₁×#3152	2
C₆₁×#2962	2
C₆₁×#1690	2
C₆₁×#1686	2
C₆₁×#1670	2
C₆₁×#1666	2
C₆₁×#1565	2
C₆₁×#1540	2
C₂×C₆₁×#332	2
#19239	61

Subgroups — C61×#19239 #29522672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19239 #29522672