Subgroups — C₆₁×#19720 #29523153

Order 15616.

656 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#3231	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#3229	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#3209	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#3185	C₂	1	1	yes	maximal, characteristic
6	C₆₁×#3165	C₂	1	1	yes	maximal, characteristic
7	C₆₁×#1723	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1723	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1718	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1718	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1716	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1716	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1707	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1453	C₂	1	1	yes	maximal, characteristic
16	C₆₁×#533	C₂²	1	1	yes	characteristic
17	C₆₁×#533	C₂²	1	1	yes	characteristic
18	C₆₁×#533	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₆₁	C₂²	1	1	yes	characteristic
20	C₆₁×#501	—	2	2	no	—
21	C₆₁×#500	C₂²	1	1	yes	characteristic
22	C₆₁×#500	C₂²	1	1	yes	characteristic
23	C₆₁×#500	C₂²	1	1	yes	characteristic
24	C₆₁×#500	C₂²	1	1	yes	characteristic
25	C₆₁×#498	C₂²	1	1	yes	characteristic
26	C₆₁×#498	C₂²	1	1	yes	characteristic
27	C₆₁×#498	C₂²	1	1	yes	characteristic
28	C₆₁×#498	C₂²	1	1	yes	characteristic
29	C₆₁×#498	C₂²	1	1	yes	characteristic
30	C₆₁×#498	C₂²	1	1	yes	characteristic
31	C₆₁×#498	C₂²	1	1	yes	characteristic
32	C₆₁×#494	C₂²	1	1	yes	characteristic
33	C₆₁×#494	C₂²	1	1	yes	characteristic
34	C₆₁×#494	C₂²	1	1	yes	characteristic
35	C₆₁×#487	C₂²	1	1	yes	characteristic
36	C₆₁×#487	C₂²	1	1	yes	characteristic
37	C₆₁×#487	C₂²	1	1	yes	characteristic
38	C₆₁×#487	C₂²	1	1	yes	characteristic
39	C₆₁×#487	C₂²	1	1	yes	characteristic
40	C₆₁×#487	C₂²	1	1	yes	characteristic
41	C₆₁×#487	C₂²	1	1	yes	characteristic
42	C₆₁×#487	C₂²	1	1	yes	characteristic
43	C₆₁×#487	C₂²	1	1	yes	characteristic
44	C₆₁×#487	C₂²	1	1	yes	characteristic
45	C₆₁×#485	—	2	2	no	—
46	C₆₁×#485	—	2	2	no	—
47	C₆₁×#483	—	2	2	no	—
48	C₆₁×#479	—	2	2	no	—
49	C₆₁×#479	—	2	2	no	—
50	C₆₁×#475	—	2	2	no	—
51	C₆₁×#470	—	2	2	no	—
52	C₆₁×#462	—	2	2	no	—
53	C₆₁×#451	—	2	2	no	—
54	C₆₁×#441	—	2	2	no	—
55	C₆₁×#431	C₂²	1	1	yes	characteristic
56	C₆₁×#431	C₂²	1	1	yes	characteristic
57	C₆₁×#428	—	2	2	no	—
58	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
59	C₆₁×#322	C₂²	1	1	yes	characteristic
60	C₆₁×#322	C₂²	1	1	yes	characteristic
61	C₆₁×#322	C₂²	1	1	yes	characteristic
62	C₈²×C₆₁	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₆₁	—	2	1	no	—
64	C₂×Q₁₆×C₆₁	—	2	2	no	—
65	C₂×Q₁₆×C₆₁	—	2	2	no	—
66	C₂×Q₁₆×C₆₁	—	2	2	no	—
67	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
68	C₄⋊Q₈×C₆₁	—	2	1	no	—
69	C₄⋊Q₈×C₆₁	—	2	1	no	—
70	C₄⋊Q₈×C₆₁	—	2	1	no	—
71	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
72	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
73	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
74	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
75	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
79	#125×C₆₁	—	2	1	no	—
80	#125×C₆₁	—	2	1	no	—
81	#125×C₆₁	—	2	1	no	—
82	C₂²⋊Q₈×C₆₁	—	2	1	no	—
83	C₂²⋊Q₈×C₆₁	—	2	1	no	—
84	C₂²⋊Q₈×C₆₁	—	2	1	no	—
85	C₂²⋊Q₈×C₆₁	—	2	1	no	—
86	C₂²⋊Q₈×C₆₁	—	2	1	no	—
87	C₂²⋊Q₈×C₆₁	—	2	1	no	—
88	C₄×Q₈×C₆₁	—	2	1	no	—
89	C₄×Q₈×C₆₁	—	2	1	no	—
90	C₄×Q₈×C₆₁	—	2	1	no	—
91	C₄×Q₈×C₆₁	—	2	1	no	—
92	C₄×Q₈×C₆₁	—	2	1	no	—
93	C₄×Q₈×C₆₁	—	2	1	no	—
94	#117×C₆₁	—	2	1	no	—
95	#117×C₆₁	—	2	1	no	—
96	#117×C₆₁	—	2	1	no	—
97	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
98	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
99	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
100	#107×C₆₁	—	2	2	no	—
101	#107×C₆₁	—	2	2	no	—
102	#107×C₆₁	—	2	2	no	—
103	#107×C₆₁	—	2	2	no	—
104	#106×C₆₁	—	2	2	no	—
105	#106×C₆₁	—	2	2	no	—
106	#106×C₆₁	—	2	2	no	—
107	#106×C₆₁	—	2	2	no	—
108	#106×C₆₁	—	2	2	no	—
109	#106×C₆₁	—	2	2	no	—
110	#106×C₆₁	—	2	2	no	—
111	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
112	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
113	#103×C₆₁	—	2	2	no	—
114	#103×C₆₁	—	2	2	no	—
115	#103×C₆₁	—	2	2	no	—
116	#103×C₆₁	—	2	2	no	—
117	#103×C₆₁	—	2	2	no	—
118	#103×C₆₁	—	2	2	no	—
119	#103×C₆₁	—	2	2	no	—
120	#103×C₆₁	—	2	2	no	—
121	#103×C₆₁	—	2	2	no	—
122	#103×C₆₁	—	2	2	no	—
123	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
124	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
125	#97×C₆₁	D₄	1	2	yes	—
126	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
127	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
129	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
130	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
131	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₆₁	—	2	1	no	—
133	C₂×Q₈×C₆₁	—	2	1	no	—
134	C₂×Q₈×C₆₁	—	2	1	no	—
135	C₂×Q₈×C₆₁	—	2	1	no	—
136	C₂×Q₈×C₆₁	—	2	1	no	—
137	C₂×Q₈×C₆₁	—	2	1	no	—
138	C₂×Q₈×C₆₁	—	2	1	no	—
139	C₂×Q₈×C₆₁	—	2	1	no	—
140	C₂×Q₈×C₆₁	—	4	1	no	—
141	C₂×Q₈×C₆₁	—	8	2	no	—
142	C₂²×C₄×C₆₁	—	4	1	no	—
143	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
146	Q₁₆×C₆₁	—	4	4	no	—
147	Q₁₆×C₆₁	—	8	2	no	—
148	Q₁₆×C₆₁	—	8	2	no	—
149	M₁₆×C₆₁	—	2	4	no	—
150	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
154	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
156	C₄⋊C₄×C₆₁	—	2	1	no	—
157	C₄⋊C₄×C₆₁	—	2	1	no	—
158	C₄⋊C₄×C₆₁	—	2	1	no	—
159	C₄⋊C₄×C₆₁	—	2	1	no	—
160	C₄⋊C₄×C₆₁	—	2	1	no	—
161	C₄⋊C₄×C₆₁	—	2	1	no	—
162	C₄⋊C₄×C₆₁	—	2	1	no	—
163	C₄⋊C₄×C₆₁	—	2	1	no	—
164	C₄⋊C₄×C₆₁	—	2	1	no	—
165	C₄⋊C₄×C₆₁	—	2	1	no	—
166	C₄⋊C₄×C₆₁	—	2	1	no	—
167	C₄⋊C₄×C₆₁	—	2	1	no	—
168	C₄⋊C₄×C₆₁	—	2	1	no	—
169	C₄⋊C₄×C₆₁	—	2	1	no	—
170	C₄⋊C₄×C₆₁	—	2	1	no	—
171	C₄⋊C₄×C₆₁	—	2	1	no	—
172	C₄⋊C₄×C₆₁	—	4	1	no	—
173	C₄⋊C₄×C₆₁	—	4	1	no	—
174	C₄⋊C₄×C₆₁	—	4	1	no	—
175	C₄⋊C₄×C₆₁	—	4	1	no	—
176	C₄⋊C₄×C₆₁	—	4	1	no	—
177	C₄⋊C₄×C₆₁	—	4	1	no	—
178	C₄⋊C₄×C₆₁	—	4	1	no	—
179	C₄⋊C₄×C₆₁	—	4	1	no	—
180	C₂²⋊C₄×C₆₁	—	4	1	no	—
181	C₂²⋊C₄×C₆₁	—	4	1	no	—
182	C₂²⋊C₄×C₆₁	—	4	1	no	—
183	C₄²×C₆₁	—	4	1	no	—
184	C₄²×C₆₁	—	4	1	no	—
185	C₄²×C₆₁	—	4	1	no	—
186	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
187	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
190	C₂³×C₆₁	#127	1	1	yes	characteristic
191	Q₈×C₆₁	—	4	2	no	—
192	Q₈×C₆₁	—	4	2	no	—
193	Q₈×C₆₁	—	4	2	no	—
194	Q₈×C₆₁	—	4	2	no	—
195	Q₈×C₆₁	—	4	2	no	—
196	Q₈×C₆₁	—	4	2	no	—
197	Q₈×C₆₁	—	4	2	no	—
198	Q₈×C₆₁	—	4	2	no	—
199	Q₈×C₆₁	—	8	2	no	—
200	C₂×C₄×C₆₁	—	2	2	no	—
201	C₂×C₄×C₆₁	—	2	2	no	—
202	C₂×C₄×C₆₁	—	2	2	no	—
203	C₂×C₄×C₆₁	—	4	1	no	—
204	C₂×C₄×C₆₁	—	4	1	no	—
205	C₂×C₄×C₆₁	—	4	1	no	—
206	C₂×C₄×C₆₁	—	4	1	no	—
207	C₂×C₄×C₆₁	—	4	1	no	—
208	C₂×C₄×C₆₁	—	4	1	no	—
209	C₂×C₄×C₆₁	—	4	1	no	—
210	C₂×C₄×C₆₁	—	4	1	no	—
211	C₂×C₄×C₆₁	—	8	2	no	—
212	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
213	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
214	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
215	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
218	C₈×C₆₁	—	2	2	no	—
219	C₈×C₆₁	—	2	2	no	—
220	C₈×C₆₁	—	2	2	no	—
221	C₈×C₆₁	—	2	2	no	—
222	C₈×C₆₁	—	2	2	no	—
223	C₈×C₆₁	#137	1	4	yes	—
224	#19720	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
225	C₂²×C₆₁	—	2	1	no	—
226	C₂²×C₆₁	—	2	1	no	—
227	C₂²×C₆₁	—	2	1	no	—
228	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
229	C₄×C₆₁	—	2	1	no	—
230	C₄×C₆₁	—	2	1	no	—
231	C₄×C₆₁	—	2	1	no	—
232	C₄×C₆₁	—	8	1	no	—
233	C₄×C₆₁	—	8	1	no	—
234	C₄×C₆₁	—	8	1	no	—
235	C₄×C₆₁	—	8	1	no	—
236	C₄×C₆₁	—	8	1	no	—
237	C₄×C₆₁	—	8	1	no	—
238	C₄×C₆₁	—	8	1	no	—
239	C₄×C₆₁	—	8	1	no	—
240	C₄×C₆₁	C₂×#137	1	2	yes	—
241	C₄×C₆₁	#577	1	2	yes	—
242	C₄×C₆₁	#578	1	2	yes	—
243	#3231	C₂×C₆₁	1	1	yes	characteristic
244	#3231	C₂×C₆₁	1	1	yes	characteristic
245	#3229	C₂×C₆₁	1	1	yes	characteristic
246	#3209	C₂×C₆₁	1	1	yes	characteristic
247	#3185	C₂×C₆₁	1	1	yes	characteristic
248	#3165	C₂×C₆₁	1	1	yes	characteristic
249	#1723	C₂×C₆₁	1	1	yes	characteristic, complemented
250	#1723	C₂×C₆₁	1	1	yes	characteristic, complemented
251	#1718	C₂×C₆₁	1	1	yes	characteristic, complemented
252	#1718	C₂×C₆₁	1	1	yes	characteristic, complemented
253	#1716	C₂×C₆₁	1	1	yes	characteristic, complemented
254	#1716	C₂×C₆₁	1	1	yes	characteristic, complemented
255	#1707	C₂×C₆₁	1	1	yes	characteristic, complemented
256	#1707	C₂×C₆₁	1	1	yes	characteristic, complemented
257	#1453	C₂×C₆₁	1	1	yes	characteristic
258	C₂×C₆₁	—	4	1	no	—
259	C₂×C₆₁	#3152	1	1	yes	characteristic
260	C₂×C₆₁	#3154	1	1	yes	characteristic
261	C₂×C₆₁	#3156	1	1	yes	characteristic
262	#533	C₂²×C₆₁	1	1	yes	characteristic
263	#533	C₂²×C₆₁	1	1	yes	characteristic
264	#533	C₂²×C₆₁	1	1	yes	characteristic
265	C₂×C₄⋊Q₈	C₂²×C₆₁	1	1	yes	characteristic
266	#501	—	2	2	no	—
267	#500	C₂²×C₆₁	1	1	yes	characteristic
268	#500	C₂²×C₆₁	1	1	yes	characteristic
269	#500	C₂²×C₆₁	1	1	yes	characteristic
270	#500	C₂²×C₆₁	1	1	yes	characteristic
271	#498	C₂²×C₆₁	1	1	yes	characteristic
272	#498	C₂²×C₆₁	1	1	yes	characteristic
273	#498	C₂²×C₆₁	1	1	yes	characteristic
274	#498	C₂²×C₆₁	1	1	yes	characteristic
275	#498	C₂²×C₆₁	1	1	yes	characteristic
276	#498	C₂²×C₆₁	1	1	yes	characteristic
277	#498	C₂²×C₆₁	1	1	yes	characteristic
278	#494	C₂²×C₆₁	1	1	yes	characteristic
279	#494	C₂²×C₆₁	1	1	yes	characteristic
280	#494	C₂²×C₆₁	1	1	yes	characteristic
281	#487	C₂²×C₆₁	1	1	yes	characteristic
282	#487	C₂²×C₆₁	1	1	yes	characteristic
283	#487	C₂²×C₆₁	1	1	yes	characteristic
284	#487	C₂²×C₆₁	1	1	yes	characteristic
285	#487	C₂²×C₆₁	1	1	yes	characteristic
286	#487	C₂²×C₆₁	1	1	yes	characteristic
287	#487	C₂²×C₆₁	1	1	yes	characteristic
288	#487	C₂²×C₆₁	1	1	yes	characteristic
289	#487	C₂²×C₆₁	1	1	yes	characteristic
290	#487	C₂²×C₆₁	1	1	yes	characteristic
291	#485	—	2	2	no	—
292	#485	—	2	2	no	—
293	#483	—	2	2	no	—
294	#479	—	2	2	no	—
295	#479	—	2	2	no	—
296	#475	—	2	2	no	—
297	#470	—	2	2	no	—
298	#462	—	2	2	no	—
299	#451	—	2	2	no	—
300	#441	—	2	2	no	—
301	#431	C₂²×C₆₁	1	1	yes	characteristic
302	#431	C₂²×C₆₁	1	1	yes	characteristic
303	#428	—	2	2	no	—
304	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
305	#322	C₂²×C₆₁	1	1	yes	characteristic
306	#322	C₂²×C₆₁	1	1	yes	characteristic
307	#322	C₂²×C₆₁	1	1	yes	characteristic
308	C₈²	C₂²×C₆₁	1	1	yes	characteristic
309	C₆₁	#19720	1	1	yes	characteristic, direct product factor, Sylow
310	C₂²×Q₈	—	2	1	no	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×Q₁₆	—	2	2	no	—
314	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	—	2	1	no	—
317	C₄⋊Q₈	—	2	1	no	—
318	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
319	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
320	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
321	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
322	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
324	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
325	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
326	#125	—	2	1	no	—
327	#125	—	2	1	no	—
328	#125	—	2	1	no	—
329	C₂²⋊Q₈	—	2	1	no	—
330	C₂²⋊Q₈	—	2	1	no	—
331	C₂²⋊Q₈	—	2	1	no	—
332	C₂²⋊Q₈	—	2	1	no	—
333	C₂²⋊Q₈	—	2	1	no	—
334	C₂²⋊Q₈	—	2	1	no	—
335	C₄×Q₈	—	2	1	no	—
336	C₄×Q₈	—	2	1	no	—
337	C₄×Q₈	—	2	1	no	—
338	C₄×Q₈	—	2	1	no	—
339	C₄×Q₈	—	2	1	no	—
340	C₄×Q₈	—	2	1	no	—
341	#117	—	2	1	no	—
342	#117	—	2	1	no	—
343	#117	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
347	#107	—	2	2	no	—
348	#107	—	2	2	no	—
349	#107	—	2	2	no	—
350	#107	—	2	2	no	—
351	#106	—	2	2	no	—
352	#106	—	2	2	no	—
353	#106	—	2	2	no	—
354	#106	—	2	2	no	—
355	#106	—	2	2	no	—
356	#106	—	2	2	no	—
357	#106	—	2	2	no	—
358	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
359	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
360	#103	—	2	2	no	—
361	#103	—	2	2	no	—
362	#103	—	2	2	no	—
363	#103	—	2	2	no	—
364	#103	—	2	2	no	—
365	#103	—	2	2	no	—
366	#103	—	2	2	no	—
367	#103	—	2	2	no	—
368	#103	—	2	2	no	—
369	#103	—	2	2	no	—
370	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
371	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
372	#97	D₄×C₆₁	1	2	yes	—
373	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
374	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
375	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
376	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
377	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
378	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	1	no	—
387	C₂×Q₈	—	4	1	no	—
388	C₂×Q₈	—	8	2	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
393	Q₁₆	—	4	4	no	—
394	Q₁₆	—	8	2	no	—
395	Q₁₆	—	8	2	no	—
396	M₁₆	—	2	4	no	—
397	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
399	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
400	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
401	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
402	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	4	1	no	—
420	C₄⋊C₄	—	4	1	no	—
421	C₄⋊C₄	—	4	1	no	—
422	C₄⋊C₄	—	4	1	no	—
423	C₄⋊C₄	—	4	1	no	—
424	C₄⋊C₄	—	4	1	no	—
425	C₄⋊C₄	—	4	1	no	—
426	C₄⋊C₄	—	4	1	no	—
427	C₂²⋊C₄	—	4	1	no	—
428	C₂²⋊C₄	—	4	1	no	—
429	C₂²⋊C₄	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₄²	—	4	1	no	—
432	C₄²	—	4	1	no	—
433	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
434	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
435	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
436	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
437	C₂³	#127×C₆₁	1	1	yes	characteristic
438	Q₈	—	4	2	no	—
439	Q₈	—	4	2	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	2	no	—
446	Q₈	—	8	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
460	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
461	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
465	C₈	—	2	2	no	—
466	C₈	—	2	2	no	—
467	C₈	—	2	2	no	—
468	C₈	—	2	2	no	—
469	C₈	—	2	2	no	—
470	C₈	#137×C₆₁	1	4	yes	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	8	1	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	1	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	8	1	no	—
486	C₄	C₂×#137×C₆₁	1	2	yes	—
487	C₄	C₆₁×#577	1	2	yes	—
488	C₄	C₆₁×#578	1	2	yes	—
489	C₂	—	4	1	no	—
490	C₂	C₆₁×#3152	1	1	yes	characteristic
491	C₂	C₆₁×#3154	1	1	yes	characteristic
492	C₂	C₆₁×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₁
prime radical	C₂³×C₆₁	#127
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
7. C₆₁×#1723	C₂	semidirect
8. C₆₁×#1723	C₂	semidirect
9. C₆₁×#1718	C₂	semidirect
10. C₆₁×#1718	C₂	semidirect
11. C₆₁×#1716	C₂	semidirect
12. C₆₁×#1716	C₂	semidirect
13. C₆₁×#1707	C₂	semidirect
14. C₆₁×#1707	C₂	semidirect
224. #19720	C₆₁	direct (N × H)
249. #1723	C₂×C₆₁	semidirect
250. #1723	C₂×C₆₁	semidirect
251. #1718	C₂×C₆₁	semidirect
252. #1718	C₂×C₆₁	semidirect
253. #1716	C₂×C₆₁	semidirect
254. #1716	C₂×C₆₁	semidirect
255. #1707	C₂×C₆₁	semidirect
256. #1707	C₂×C₆₁	semidirect
309. C₆₁	#19720	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×#3231	2
C₆₁×#3229	2
C₆₁×#3209	2
C₆₁×#3185	2
C₆₁×#3165	2
C₆₁×#1723	2
C₆₁×#1718	2
C₆₁×#1716	2
C₆₁×#1707	2
C₆₁×#1453	2
#19720	61

Subgroups — C61×#19720 #29523153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19720 #29523153