Subgroups — C₆₁×#19719 #29523152

Order 15616.

840 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×#3228	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₁×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×#3207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₁×#3205	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#3182	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#3151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1721	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₁×#1721	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1719	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1717	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₁×#1715	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₁×#1714	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₁×#1706	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₁×#1453	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×AGL(1,ℤ/8)×C₆₁	—	2	2	no	—
17	C₆₁×#533	C₂²	1	1	yes	characteristic
18	C₆₁×#532	C₂²	1	1	yes	characteristic
19	C₆₁×#532	C₂²	1	1	yes	characteristic
20	C₂×#127×C₆₁	C₂²	1	1	yes	characteristic
21	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
22	C₆₁×#500	C₂²	1	1	yes	characteristic, complemented
23	C₆₁×#498	C₂²	1	1	yes	characteristic, complemented
24	C₆₁×#496	—	2	2	no	—
25	C₆₁×#493	C₂²	1	1	yes	characteristic
26	C₆₁×#493	C₂²	1	1	yes	characteristic
27	C₆₁×#493	C₂²	1	1	yes	characteristic
28	C₆₁×#493	C₂²	1	1	yes	characteristic
29	C₆₁×#493	C₂²	1	1	yes	characteristic, complemented
30	C₆₁×#492	C₂²	1	1	yes	characteristic
31	C₆₁×#492	C₂²	1	1	yes	characteristic
32	C₆₁×#492	C₂²	1	1	yes	characteristic
33	C₆₁×#492	C₂²	1	1	yes	characteristic
34	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
35	C₆₁×#492	C₂²	1	1	yes	characteristic, complemented
36	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
37	C₆₁×#487	C₂²	1	1	yes	characteristic, complemented
38	C₆₁×#486	C₂²	1	1	yes	characteristic
39	C₆₁×#486	C₂²	1	1	yes	characteristic
40	C₆₁×#486	C₂²	1	1	yes	characteristic
41	C₆₁×#486	C₂²	1	1	yes	characteristic
42	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
43	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
44	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
45	C₆₁×#486	C₂²	1	1	yes	characteristic, complemented
46	C₆₁×#482	—	2	2	no	—
47	C₆₁×#478	—	2	2	no	—
48	C₆₁×#468	—	2	2	no	—
49	C₆₁×#463	—	2	2	no	—
50	C₆₁×#460	—	2	2	no	—
51	C₆₁×#459	—	2	2	no	—
52	C₆₁×#450	—	2	2	no	—
53	C₆₁×#449	—	2	2	no	—
54	C₆₁×#447	—	2	2	no	—
55	C₆₁×#440	—	2	2	no	—
56	C₆₁×#431	C₂²	1	1	yes	characteristic
57	C₆₁×#431	C₂²	1	1	yes	characteristic
58	C₄×M₁₆×C₆₁	C₂²	1	1	yes	characteristic
59	C₆₁×#322	C₂²	1	1	yes	characteristic, complemented
60	C₆₁×#322	C₂²	1	1	yes	characteristic, complemented
61	C₆₁×#322	C₂²	1	1	yes	characteristic, complemented
62	C₈²×C₆₁	C₂²	1	1	yes	characteristic, complemented
63	C₂×#41×C₆₁	—	2	1	no	—
64	C₂×#41×C₆₁	—	2	1	no	—
65	C₂²×D₄×C₆₁	—	2	1	no	—
66	C₂²×D₄×C₆₁	—	2	1	no	—
67	C₂²×D₄×C₆₁	—	2	1	no	—
68	AGL(1,ℤ/8)×C₆₁	—	4	8	no	—
69	C₂×SD₁₆×C₆₁	—	2	2	no	—
70	C₂×SD₁₆×C₆₁	—	2	2	no	—
71	C₂×SD₁₆×C₆₁	—	2	2	no	—
72	C₂×SD₁₆×C₆₁	—	2	2	no	—
73	C₂×SD₁₆×C₆₁	—	2	2	no	—
74	C₂×SD₁₆×C₆₁	—	2	2	no	—
75	C₂×D₈×C₆₁	—	2	2	no	—
76	C₂×D₈×C₆₁	—	2	2	no	—
77	C₂×D₈×C₆₁	—	2	2	no	—
78	C₂×D₈×C₆₁	—	2	2	no	—
79	C₂×D₈×C₆₁	—	2	2	no	—
80	C₂×M₁₆×C₆₁	D₄	1	2	yes	—
81	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₆₁	C₂³	1	1	yes	characteristic
85	#127×C₆₁	—	2	1	no	—
86	#127×C₆₁	—	2	1	no	—
87	#127×C₆₁	—	2	1	no	—
88	#127×C₆₁	C₂³	1	1	yes	characteristic
89	#127×C₆₁	C₂³	1	1	yes	characteristic
90	#127×C₆₁	C₂³	1	1	yes	characteristic
91	#127×C₆₁	C₂³	1	1	yes	characteristic
92	#125×C₆₁	—	2	1	no	—
93	#124×C₆₁	—	2	1	no	—
94	#124×C₆₁	—	2	1	no	—
95	C₂²⋊Q₈×C₆₁	—	2	1	no	—
96	C₂²⋊Q₈×C₆₁	—	2	1	no	—
97	#121×C₆₁	—	2	1	no	—
98	#121×C₆₁	—	2	1	no	—
99	#121×C₆₁	—	2	1	no	—
100	#121×C₆₁	—	2	1	no	—
101	C₄×Q₈×C₆₁	—	2	1	no	—
102	C₄×Q₈×C₆₁	—	2	1	no	—
103	C₄×D₄×C₆₁	—	2	1	no	—
104	C₄×D₄×C₆₁	—	2	1	no	—
105	C₄×D₄×C₆₁	—	2	1	no	—
106	C₄×D₄×C₆₁	—	2	1	no	—
107	#117×C₆₁	—	2	1	no	—
108	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
109	#107×C₆₁	—	2	2	no	—
110	#107×C₆₁	—	2	2	no	—
111	#106×C₆₁	—	2	2	no	—
112	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
113	C₄⋊C₈×C₆₁	D₄	1	2	yes	—
114	#103×C₆₁	—	2	2	no	—
115	#103×C₆₁	—	2	2	no	—
116	#102×C₆₁	—	2	2	no	—
117	#102×C₆₁	—	2	2	no	—
118	#102×C₆₁	—	2	2	no	—
119	#102×C₆₁	—	2	2	no	—
120	#102×C₆₁	—	2	2	no	—
121	#102×C₆₁	—	2	2	no	—
122	#102×C₆₁	—	2	2	no	—
123	#102×C₆₁	—	2	2	no	—
124	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
125	C₂²⋊C₈×C₆₁	D₄	1	2	yes	—
126	#97×C₆₁	D₄	1	2	yes	—
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	C₄×C₈×C₆₁	C₂³	1	1	yes	characteristic
133	C₂⁴×C₆₁	—	4	1	no	—
134	#41×C₆₁	—	4	4	no	—
135	#41×C₆₁	—	8	2	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×D₄×C₆₁	—	2	1	no	—
141	C₂×D₄×C₆₁	—	2	1	no	—
142	C₂×D₄×C₆₁	—	2	1	no	—
143	C₂×D₄×C₆₁	—	2	1	no	—
144	C₂×D₄×C₆₁	—	2	1	no	—
145	C₂×D₄×C₆₁	—	2	1	no	—
146	C₂×D₄×C₆₁	—	2	1	no	—
147	C₂×D₄×C₆₁	—	2	1	no	—
148	C₂×D₄×C₆₁	—	2	1	no	—
149	C₂×D₄×C₆₁	—	2	1	no	—
150	C₂×D₄×C₆₁	—	2	1	no	—
151	C₂×D₄×C₆₁	—	2	1	no	—
152	C₂×D₄×C₆₁	—	4	4	no	—
153	C₂×D₄×C₆₁	—	4	1	no	—
154	C₂×D₄×C₆₁	—	4	1	no	—
155	C₂×D₄×C₆₁	—	4	1	no	—
156	C₂×D₄×C₆₁	—	4	1	no	—
157	C₂×D₄×C₆₁	—	4	1	no	—
158	C₂×D₄×C₆₁	—	8	2	no	—
159	C₂×D₄×C₆₁	—	8	2	no	—
160	C₂²×C₄×C₆₁	—	4	1	no	—
161	C₂²×C₄×C₆₁	—	4	1	no	—
162	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
165	SD₁₆×C₆₁	—	4	4	no	—
166	SD₁₆×C₆₁	—	4	4	no	—
167	SD₁₆×C₆₁	—	4	4	no	—
168	SD₁₆×C₆₁	—	8	2	no	—
169	SD₁₆×C₆₁	—	8	2	no	—
170	SD₁₆×C₆₁	—	8	2	no	—
171	D₈×C₆₁	—	4	4	no	—
172	D₈×C₆₁	—	4	4	no	—
173	D₈×C₆₁	—	8	2	no	—
174	D₈×C₆₁	—	8	2	no	—
175	D₈×C₆₁	—	8	2	no	—
176	M₁₆×C₆₁	—	2	4	no	—
177	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
178	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
179	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
180	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
181	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
182	C₂×C₈×C₆₁	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₆₁	—	2	1	no	—
184	C₄⋊C₄×C₆₁	—	2	1	no	—
185	C₄⋊C₄×C₆₁	—	2	1	no	—
186	C₄⋊C₄×C₆₁	—	2	1	no	—
187	C₄⋊C₄×C₆₁	—	2	1	no	—
188	C₄⋊C₄×C₆₁	—	2	1	no	—
189	C₄⋊C₄×C₆₁	—	2	1	no	—
190	C₄⋊C₄×C₆₁	—	2	1	no	—
191	C₄⋊C₄×C₆₁	—	4	1	no	—
192	C₄⋊C₄×C₆₁	—	4	1	no	—
193	C₂²⋊C₄×C₆₁	—	4	1	no	—
194	C₂²⋊C₄×C₆₁	—	4	1	no	—
195	C₂²⋊C₄×C₆₁	—	4	1	no	—
196	C₂²⋊C₄×C₆₁	—	4	1	no	—
197	C₂²⋊C₄×C₆₁	—	4	1	no	—
198	C₄²×C₆₁	—	4	1	no	—
199	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₆₁	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₆₁	C₂⁴	1	1	yes	characteristic
203	C₂³×C₆₁	—	4	1	no	—
204	C₂³×C₆₁	—	4	1	no	—
205	C₂³×C₆₁	—	4	1	no	—
206	C₂³×C₆₁	—	4	1	no	—
207	C₂³×C₆₁	—	8	2	no	—
208	C₂³×C₆₁	—	8	2	no	—
209	C₂³×C₆₁	—	8	2	no	—
210	C₂³×C₆₁	#127	1	1	yes	characteristic
211	Q₈×C₆₁	—	4	2	no	—
212	Q₈×C₆₁	—	4	2	no	—
213	Q₈×C₆₁	—	4	2	no	—
214	Q₈×C₆₁	—	4	2	no	—
215	D₄×C₆₁	—	4	2	no	—
216	D₄×C₆₁	—	4	2	no	—
217	D₄×C₆₁	—	4	2	no	—
218	D₄×C₆₁	—	4	2	no	—
219	D₄×C₆₁	—	4	2	no	—
220	D₄×C₆₁	—	4	2	no	—
221	D₄×C₆₁	—	4	2	no	—
222	D₄×C₆₁	—	4	2	no	—
223	D₄×C₆₁	—	4	2	no	—
224	D₄×C₆₁	—	4	2	no	—
225	D₄×C₆₁	—	4	2	no	—
226	D₄×C₆₁	—	4	2	no	—
227	D₄×C₆₁	—	8	2	no	—
228	D₄×C₆₁	—	8	2	no	—
229	D₄×C₆₁	—	8	2	no	—
230	D₄×C₆₁	—	8	2	no	—
231	D₄×C₆₁	—	8	2	no	—
232	C₂×C₄×C₆₁	—	2	2	no	—
233	C₂×C₄×C₆₁	—	2	2	no	—
234	C₂×C₄×C₆₁	—	2	2	no	—
235	C₂×C₄×C₆₁	—	4	1	no	—
236	C₂×C₄×C₆₁	—	4	1	no	—
237	C₂×C₄×C₆₁	—	4	1	no	—
238	C₂×C₄×C₆₁	—	4	1	no	—
239	C₂×C₄×C₆₁	—	8	2	no	—
240	C₂×C₄×C₆₁	—	8	2	no	—
241	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
242	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
243	C₂×C₄×C₆₁	#127	1	1	yes	characteristic
244	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₆₁	C₂²×D₄	1	1	yes	characteristic
247	C₈×C₆₁	—	2	2	no	—
248	C₈×C₆₁	—	2	2	no	—
249	C₈×C₆₁	—	2	2	no	—
250	C₈×C₆₁	—	2	2	no	—
251	C₈×C₆₁	—	2	2	no	—
252	C₈×C₆₁	AGL(1,ℤ/8)	1	4	yes	—
253	#19719	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂²×C₆₁	—	2	1	no	—
255	C₂²×C₆₁	—	2	1	no	—
256	C₂²×C₆₁	—	2	1	no	—
257	C₂²×C₆₁	—	8	1	no	—
258	C₂²×C₆₁	—	8	1	no	—
259	C₂²×C₆₁	—	8	1	no	—
260	C₂²×C₆₁	—	8	1	no	—
261	C₂²×C₆₁	—	8	1	no	—
262	C₂²×C₆₁	—	8	1	no	—
263	C₂²×C₆₁	—	8	1	no	—
264	C₂²×C₆₁	—	8	1	no	—
265	C₂²×C₆₁	—	8	1	no	—
266	C₂²×C₆₁	—	8	1	no	—
267	C₂²×C₆₁	—	8	1	no	—
268	C₂²×C₆₁	—	8	1	no	—
269	C₂²×C₆₁	—	16	4	no	—
270	C₂²×C₆₁	C₂×#127	1	1	yes	characteristic
271	C₄×C₆₁	—	2	1	no	—
272	C₄×C₆₁	—	2	1	no	—
273	C₄×C₆₁	—	2	1	no	—
274	C₄×C₆₁	—	8	1	no	—
275	C₄×C₆₁	—	8	1	no	—
276	C₄×C₆₁	—	8	1	no	—
277	C₄×C₆₁	—	8	1	no	—
278	C₄×C₆₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
279	C₄×C₆₁	#576	1	2	yes	—
280	C₄×C₆₁	#577	1	2	yes	—
281	#3228	C₂×C₆₁	1	1	yes	characteristic, complemented
282	#3208	C₂×C₆₁	1	1	yes	characteristic, complemented
283	#3207	C₂×C₆₁	1	1	yes	characteristic, complemented
284	#3205	C₂×C₆₁	1	1	yes	characteristic, complemented
285	#3182	C₂×C₆₁	1	1	yes	characteristic, complemented
286	#3151	C₂×C₆₁	1	1	yes	characteristic, complemented
287	#1721	C₂×C₆₁	1	1	yes	characteristic, complemented
288	#1721	C₂×C₆₁	1	1	yes	characteristic, complemented
289	#1719	C₂×C₆₁	1	1	yes	characteristic, complemented
290	#1717	C₂×C₆₁	1	1	yes	characteristic, complemented
291	#1715	C₂×C₆₁	1	1	yes	characteristic, complemented
292	#1714	C₂×C₆₁	1	1	yes	characteristic, complemented
293	#1706	C₂×C₆₁	1	1	yes	characteristic, complemented
294	#1706	C₂×C₆₁	1	1	yes	characteristic, complemented
295	#1453	C₂×C₆₁	1	1	yes	characteristic, complemented
296	C₂×C₆₁	—	4	1	no	—
297	C₂×C₆₁	—	16	1	no	—
298	C₂×C₆₁	—	16	1	no	—
299	C₂×C₆₁	—	16	1	no	—
300	C₂×C₆₁	—	16	1	no	—
301	C₂×C₆₁	#3151	1	1	yes	characteristic
302	C₂×C₆₁	#3154	1	1	yes	characteristic
303	C₂×C₆₁	#3155	1	1	yes	characteristic
304	C₂×AGL(1,ℤ/8)	—	2	2	no	—
305	#533	C₂²×C₆₁	1	1	yes	characteristic
306	#532	C₂²×C₆₁	1	1	yes	characteristic
307	#532	C₂²×C₆₁	1	1	yes	characteristic
308	C₂×#127	C₂²×C₆₁	1	1	yes	characteristic
309	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
310	#500	C₂²×C₆₁	1	1	yes	characteristic, complemented
311	#498	C₂²×C₆₁	1	1	yes	characteristic, complemented
312	#496	—	2	2	no	—
313	#493	C₂²×C₆₁	1	1	yes	characteristic
314	#493	C₂²×C₆₁	1	1	yes	characteristic
315	#493	C₂²×C₆₁	1	1	yes	characteristic
316	#493	C₂²×C₆₁	1	1	yes	characteristic
317	#493	C₂²×C₆₁	1	1	yes	characteristic, complemented
318	#492	C₂²×C₆₁	1	1	yes	characteristic
319	#492	C₂²×C₆₁	1	1	yes	characteristic
320	#492	C₂²×C₆₁	1	1	yes	characteristic
321	#492	C₂²×C₆₁	1	1	yes	characteristic
322	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
323	#492	C₂²×C₆₁	1	1	yes	characteristic, complemented
324	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
325	#487	C₂²×C₆₁	1	1	yes	characteristic, complemented
326	#486	C₂²×C₆₁	1	1	yes	characteristic
327	#486	C₂²×C₆₁	1	1	yes	characteristic
328	#486	C₂²×C₆₁	1	1	yes	characteristic
329	#486	C₂²×C₆₁	1	1	yes	characteristic
330	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
331	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
332	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
333	#486	C₂²×C₆₁	1	1	yes	characteristic, complemented
334	#482	—	2	2	no	—
335	#478	—	2	2	no	—
336	#468	—	2	2	no	—
337	#463	—	2	2	no	—
338	#460	—	2	2	no	—
339	#459	—	2	2	no	—
340	#450	—	2	2	no	—
341	#449	—	2	2	no	—
342	#447	—	2	2	no	—
343	#440	—	2	2	no	—
344	#431	C₂²×C₆₁	1	1	yes	characteristic
345	#431	C₂²×C₆₁	1	1	yes	characteristic
346	C₄×M₁₆	C₂²×C₆₁	1	1	yes	characteristic
347	#322	C₂²×C₆₁	1	1	yes	characteristic, complemented
348	#322	C₂²×C₆₁	1	1	yes	characteristic, complemented
349	#322	C₂²×C₆₁	1	1	yes	characteristic, complemented
350	C₈²	C₂²×C₆₁	1	1	yes	characteristic, complemented
351	C₆₁	#19719	1	1	yes	characteristic, direct product factor, Sylow
352	C₂×#41	—	2	1	no	—
353	C₂×#41	—	2	1	no	—
354	C₂²×D₄	—	2	1	no	—
355	C₂²×D₄	—	2	1	no	—
356	C₂²×D₄	—	2	1	no	—
357	AGL(1,ℤ/8)	—	4	8	no	—
358	C₂×SD₁₆	—	2	2	no	—
359	C₂×SD₁₆	—	2	2	no	—
360	C₂×SD₁₆	—	2	2	no	—
361	C₂×SD₁₆	—	2	2	no	—
362	C₂×SD₁₆	—	2	2	no	—
363	C₂×SD₁₆	—	2	2	no	—
364	C₂×D₈	—	2	2	no	—
365	C₂×D₈	—	2	2	no	—
366	C₂×D₈	—	2	2	no	—
367	C₂×D₈	—	2	2	no	—
368	C₂×D₈	—	2	2	no	—
369	C₂×M₁₆	D₄×C₆₁	1	2	yes	—
370	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
371	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
372	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
373	C₄⋊Q₈	C₂³×C₆₁	1	1	yes	characteristic
374	#127	—	2	1	no	—
375	#127	—	2	1	no	—
376	#127	—	2	1	no	—
377	#127	C₂³×C₆₁	1	1	yes	characteristic
378	#127	C₂³×C₆₁	1	1	yes	characteristic
379	#127	C₂³×C₆₁	1	1	yes	characteristic
380	#127	C₂³×C₆₁	1	1	yes	characteristic
381	#125	—	2	1	no	—
382	#124	—	2	1	no	—
383	#124	—	2	1	no	—
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	#121	—	2	1	no	—
387	#121	—	2	1	no	—
388	#121	—	2	1	no	—
389	#121	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	—	2	1	no	—
396	#117	—	2	1	no	—
397	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
398	#107	—	2	2	no	—
399	#107	—	2	2	no	—
400	#106	—	2	2	no	—
401	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
402	C₄⋊C₈	D₄×C₆₁	1	2	yes	—
403	#103	—	2	2	no	—
404	#103	—	2	2	no	—
405	#102	—	2	2	no	—
406	#102	—	2	2	no	—
407	#102	—	2	2	no	—
408	#102	—	2	2	no	—
409	#102	—	2	2	no	—
410	#102	—	2	2	no	—
411	#102	—	2	2	no	—
412	#102	—	2	2	no	—
413	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
414	C₂²⋊C₈	D₄×C₆₁	1	2	yes	—
415	#97	D₄×C₆₁	1	2	yes	—
416	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
417	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
418	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
419	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
420	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
421	C₄×C₈	C₂³×C₆₁	1	1	yes	characteristic
422	C₂⁴	—	4	1	no	—
423	#41	—	4	4	no	—
424	#41	—	8	2	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	4	4	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	—	8	2	no	—
448	C₂×D₄	—	8	2	no	—
449	C₂²×C₄	—	4	1	no	—
450	C₂²×C₄	—	4	1	no	—
451	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
452	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
454	SD₁₆	—	4	4	no	—
455	SD₁₆	—	4	4	no	—
456	SD₁₆	—	4	4	no	—
457	SD₁₆	—	8	2	no	—
458	SD₁₆	—	8	2	no	—
459	SD₁₆	—	8	2	no	—
460	D₈	—	4	4	no	—
461	D₈	—	4	4	no	—
462	D₈	—	8	2	no	—
463	D₈	—	8	2	no	—
464	D₈	—	8	2	no	—
465	M₁₆	—	2	4	no	—
466	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
467	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
468	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
469	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
470	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
471	C₂×C₈	C₂×D₄×C₆₁	1	2	yes	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	4	1	no	—
481	C₄⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₂²⋊C₄	—	4	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₄²	—	4	1	no	—
488	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
489	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
490	C₄²	C₂×D₄×C₆₁	1	1	yes	characteristic
491	C₄²	C₂⁴×C₆₁	1	1	yes	characteristic
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	—	8	2	no	—
497	C₂³	—	8	2	no	—
498	C₂³	—	8	2	no	—
499	C₂³	#127×C₆₁	1	1	yes	characteristic
500	Q₈	—	4	2	no	—
501	Q₈	—	4	2	no	—
502	Q₈	—	4	2	no	—
503	Q₈	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	8	2	no	—
517	D₄	—	8	2	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	2	no	—
520	D₄	—	8	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
531	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
532	C₂×C₄	#127×C₆₁	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
534	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
535	C₂×C₄	C₂²×D₄×C₆₁	1	1	yes	characteristic
536	C₈	—	2	2	no	—
537	C₈	—	2	2	no	—
538	C₈	—	2	2	no	—
539	C₈	—	2	2	no	—
540	C₈	—	2	2	no	—
541	C₈	AGL(1,ℤ/8)×C₆₁	1	4	yes	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	—	8	1	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	16	4	no	—
558	C₂²	C₂×#127×C₆₁	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	C₂×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
567	C₄	C₆₁×#576	1	2	yes	—
568	C₄	C₆₁×#577	1	2	yes	—
569	C₂	—	4	1	no	—
570	C₂	—	16	1	no	—
571	C₂	—	16	1	no	—
572	C₂	—	16	1	no	—
573	C₂	—	16	1	no	—
574	C₂	C₆₁×#3151	1	1	yes	characteristic
575	C₂	C₆₁×#3154	1	1	yes	characteristic
576	C₂	C₆₁×#3155	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#127
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×#3228	C₂	semidirect
2. C₆₁×#3208	C₂	semidirect
3. C₆₁×#3207	C₂	semidirect
4. C₆₁×#3205	C₂	semidirect
5. C₆₁×#3182	C₂	semidirect
6. C₆₁×#3151	C₂	semidirect
7. C₆₁×#1721	C₂	semidirect
8. C₆₁×#1721	C₂	semidirect
9. C₆₁×#1719	C₂	semidirect
10. C₆₁×#1717	C₂	semidirect
11. C₆₁×#1715	C₂	semidirect
12. C₆₁×#1714	C₂	semidirect
13. C₆₁×#1706	C₂	semidirect
14. C₆₁×#1706	C₂	semidirect
15. C₆₁×#1453	C₂	semidirect
21. C₆₁×#500	C₂²	semidirect
22. C₆₁×#500	C₂²	semidirect
23. C₆₁×#498	C₂²	semidirect
29. C₆₁×#493	C₂²	semidirect
34. C₆₁×#492	C₂²	semidirect
35. C₆₁×#492	C₂²	semidirect
36. C₆₁×#487	C₂²	semidirect
37. C₆₁×#487	C₂²	semidirect
42. C₆₁×#486	C₂²	semidirect
43. C₆₁×#486	C₂²	semidirect
44. C₆₁×#486	C₂²	semidirect
45. C₆₁×#486	C₂²	semidirect
59. C₆₁×#322	C₂²	semidirect
60. C₆₁×#322	C₂²	semidirect
61. C₆₁×#322	C₂²	semidirect
62. C₈²×C₆₁	C₂²	semidirect
253. #19719	C₆₁	direct (N × H)
281. #3228	C₂×C₆₁	semidirect
282. #3208	C₂×C₆₁	semidirect
283. #3207	C₂×C₆₁	semidirect
284. #3205	C₂×C₆₁	semidirect
285. #3182	C₂×C₆₁	semidirect
286. #3151	C₂×C₆₁	semidirect
287. #1721	C₂×C₆₁	semidirect
288. #1721	C₂×C₆₁	semidirect
289. #1719	C₂×C₆₁	semidirect
290. #1717	C₂×C₆₁	semidirect
291. #1715	C₂×C₆₁	semidirect
292. #1714	C₂×C₆₁	semidirect
293. #1706	C₂×C₆₁	semidirect
294. #1706	C₂×C₆₁	semidirect
295. #1453	C₂×C₆₁	semidirect
309. #500	C₂²×C₆₁	semidirect
310. #500	C₂²×C₆₁	semidirect
311. #498	C₂²×C₆₁	semidirect
317. #493	C₂²×C₆₁	semidirect
322. #492	C₂²×C₆₁	semidirect
323. #492	C₂²×C₆₁	semidirect
324. #487	C₂²×C₆₁	semidirect
325. #487	C₂²×C₆₁	semidirect
330. #486	C₂²×C₆₁	semidirect
331. #486	C₂²×C₆₁	semidirect
332. #486	C₂²×C₆₁	semidirect
333. #486	C₂²×C₆₁	semidirect
347. #322	C₂²×C₆₁	semidirect
348. #322	C₂²×C₆₁	semidirect
349. #322	C₂²×C₆₁	semidirect
350. C₈²	C₂²×C₆₁	semidirect
351. C₆₁	#19719	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×#3228	2
C₆₁×#3208	2
C₆₁×#3207	2
C₆₁×#3205	2
C₆₁×#3182	2
C₆₁×#3151	2
C₆₁×#1721	2
C₆₁×#1719	2
C₆₁×#1717	2
C₆₁×#1715	2
C₆₁×#1714	2
C₆₁×#1706	2
C₆₁×#1453	2
#19719	61

Subgroups — C61×#19719 #29523152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#19719 #29523152