Subgroups — C₆₁×#21475 #29524908

Order 15616.

1370 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×2₋¹⁺⁴×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₆₁×#454	C₂	1	1	yes	maximal, characteristic
3	C₄×AGL(1,ℤ/8)×C₆₁	C₂	1	2	yes	maximal, complemented
4	C₆₁×#2326	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₁×#1888	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₁×#1883	C₂	1	2	yes	maximal, complemented
7	C₆₁×#1859	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1857	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₁×#1793	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₁×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×#101×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₆₁	C₂²	1	2	yes	—
14	C₂×#124×C₆₁	C₂²	1	1	yes	characteristic
15	C₆₁×#520	—	2	2	no	—
16	C₆₁×#520	—	2	2	no	—
17	C₆₁×#520	C₂²	1	2	yes	—
18	C₆₁×#519	—	2	2	no	—
19	C₆₁×#519	C₂²	1	1	yes	characteristic
20	C₄×#41×C₆₁	—	2	2	no	—
21	C₄×#41×C₆₁	—	2	2	no	—
22	C₄×#41×C₆₁	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₆₁	—	2	2	no	—
24	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
26	C₆₁×#454	C₄	1	8	yes	complemented
27	C₆₁×#442	—	2	2	no	—
28	C₆₁×#440	—	2	2	no	—
29	C₄×SD₁₆×C₆₁	—	2	2	no	—
30	C₄×D₈×C₆₁	—	2	2	no	—
31	C₆₁×#428	C₂²	1	2	yes	—
32	C₂×#104×C₆₁	C₂²	1	2	yes	—
33	C₂×#104×C₆₁	C₂²	1	2	yes	—
34	C₆₁×#418	C₂²	1	2	yes	—
35	C₆₁×#417	C₂²	1	2	yes	—
36	C₂×#101×C₆₁	C₂²	1	1	yes	characteristic
37	C₂×#101×C₆₁	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₆₁	C₂²	1	2	yes	—
39	C₆₁×#391	C₂²	1	1	yes	characteristic
40	C₆₁×#390	C₂²	1	1	yes	characteristic
41	C₆₁×#388	—	2	2	no	—
42	C₆₁×#385	—	2	2	no	—
43	C₆₁×#384	C₂²	1	1	yes	characteristic
44	C₆₁×#376	C₂²	1	1	yes	characteristic
45	C₆₁×#343	C₂²	1	2	yes	—
46	C₆₁×#339	C₂²	1	2	yes	—
47	C₆₁×#339	C₂²	1	2	yes	—
48	2₋¹⁺⁴×C₆₁	—	2	4	no	—
49	2₋¹⁺⁴×C₆₁	—	2	2	no	—
50	2₋¹⁺⁴×C₆₁	C₂×C₄	1	4	yes	complemented
51	C₂×#41×C₆₁	—	2	2	no	—
52	C₂×#41×C₆₁	—	2	2	no	—
53	C₂×#41×C₆₁	C₂³	1	2	yes	—
54	C₂²×Q₈×C₆₁	—	2	2	no	—
55	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₆₁	—	2	1	no	—
58	AGL(1,ℤ/8)×C₆₁	—	2	4	no	—
59	AGL(1,ℤ/8)×C₆₁	C₂×C₄	1	8	yes	complemented
60	C₂×SD₁₆×C₆₁	—	2	2	no	—
61	C₂×D₈×C₆₁	—	2	2	no	—
62	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
63	C₂×M₁₆×C₆₁	C₂³	1	2	yes	—
64	#124×C₆₁	—	2	2	no	—
65	#124×C₆₁	C₂×C₄	1	4	yes	complemented
66	C₄×Q₈×C₆₁	—	2	2	no	—
67	C₄×Q₈×C₆₁	—	2	4	no	—
68	C₄×Q₈×C₆₁	—	2	2	no	—
69	C₄×Q₈×C₆₁	—	2	2	no	—
70	C₄×Q₈×C₆₁	—	2	2	no	—
71	C₄×Q₈×C₆₁	—	2	2	no	—
72	C₄×Q₈×C₆₁	—	2	2	no	—
73	C₄×Q₈×C₆₁	—	2	2	no	—
74	C₄×Q₈×C₆₁	D₄	1	2	yes	—
75	C₄×Q₈×C₆₁	D₄	1	2	yes	—
76	C₄×D₄×C₆₁	—	2	2	no	—
77	C₄×D₄×C₆₁	—	2	4	no	—
78	C₄×D₄×C₆₁	—	2	2	no	—
79	C₄×D₄×C₆₁	—	2	2	no	—
80	C₄×D₄×C₆₁	—	2	2	no	—
81	C₄×D₄×C₆₁	—	2	4	no	—
82	C₄×D₄×C₆₁	—	2	2	no	—
83	C₄×D₄×C₆₁	—	2	2	no	—
84	C₄×D₄×C₆₁	—	2	2	no	—
85	C₄×D₄×C₆₁	D₄	1	2	yes	—
86	C₄×D₄×C₆₁	D₄	1	2	yes	—
87	#117×C₆₁	—	2	4	no	—
88	#117×C₆₁	—	2	4	no	—
89	#117×C₆₁	—	2	2	no	—
90	#117×C₆₁	—	2	2	no	—
91	#117×C₆₁	—	2	2	no	—
92	#117×C₆₁	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₆₁	—	2	4	no	—
94	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
95	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
96	C₂×C₄⋊C₄×C₆₁	D₄	1	2	yes	—
97	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
102	C₂×C₄²×C₆₁	—	2	4	no	—
103	C₂×C₄²×C₆₁	—	2	2	no	—
104	C₂×C₄²×C₆₁	D₄	1	2	yes	—
105	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
108	#107×C₆₁	—	2	2	no	—
109	#106×C₆₁	—	2	2	no	—
110	#104×C₆₁	—	2	4	no	—
111	#104×C₆₁	C₂×C₄	1	8	yes	complemented
112	#103×C₆₁	—	2	2	no	—
113	#102×C₆₁	—	2	2	no	—
114	#102×C₆₁	—	2	2	no	—
115	#102×C₆₁	—	2	2	no	—
116	#101×C₆₁	—	2	2	no	—
117	#101×C₆₁	C₂×C₄	1	4	yes	complemented
118	#97×C₆₁	—	2	2	no	—
119	C₄×C₈×C₆₁	—	2	2	no	—
120	#95×C₆₁	—	2	1	no	—
121	#95×C₆₁	—	2	1	no	—
122	#95×C₆₁	—	2	2	no	—
123	C₂⁴×C₆₁	—	2	1	no	—
124	#41×C₆₁	—	2	8	no	—
125	#41×C₆₁	—	2	8	no	—
126	#41×C₆₁	—	2	8	no	—
127	#41×C₆₁	—	2	8	no	—
128	#41×C₆₁	—	2	2	no	—
129	#41×C₆₁	—	2	2	no	—
130	#41×C₆₁	C₂²×C₄	1	4	yes	—
131	#41×C₆₁	#41	1	4	yes	—
132	C₂×Q₈×C₆₁	—	2	2	no	—
133	C₂×Q₈×C₆₁	—	2	8	no	—
134	C₂×Q₈×C₆₁	—	2	8	no	—
135	C₂×Q₈×C₆₁	—	2	2	no	—
136	C₂×Q₈×C₆₁	—	2	2	no	—
137	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
138	C₂×Q₈×C₆₁	C₂×D₄	1	2	yes	—
139	C₂×Q₈×C₆₁	#41	1	2	yes	—
140	C₂×D₄×C₆₁	—	2	2	no	—
141	C₂×D₄×C₆₁	—	2	2	no	—
142	C₂×D₄×C₆₁	—	2	2	no	—
143	C₂×D₄×C₆₁	—	2	2	no	—
144	C₂×D₄×C₆₁	—	2	1	no	—
145	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
146	C₂×D₄×C₆₁	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₆₁	—	2	4	no	—
148	C₂²×C₄×C₆₁	—	2	2	no	—
149	C₂²×C₄×C₆₁	—	2	1	no	—
150	C₂²×C₄×C₆₁	—	2	4	no	—
151	C₂²×C₄×C₆₁	—	2	2	no	—
152	C₂²×C₄×C₆₁	—	2	2	no	—
153	C₂²×C₄×C₆₁	—	2	1	no	—
154	C₂²×C₄×C₆₁	—	2	1	no	—
155	C₂²×C₄×C₆₁	—	4	2	no	—
156	C₂²×C₄×C₆₁	—	8	2	no	—
157	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
162	SD₁₆×C₆₁	—	2	8	no	—
163	D₈×C₆₁	—	2	8	no	—
164	M₁₆×C₆₁	—	2	2	no	—
165	M₁₆×C₆₁	—	2	2	no	—
166	M₁₆×C₆₁	—	2	2	no	—
167	M₁₆×C₆₁	C₂²×C₄	1	4	yes	—
168	C₂×C₈×C₆₁	—	2	2	no	—
169	C₂×C₈×C₆₁	—	2	2	no	—
170	C₄⋊C₄×C₆₁	—	2	4	no	—
171	C₄⋊C₄×C₆₁	—	2	2	no	—
172	C₄⋊C₄×C₆₁	—	2	2	no	—
173	C₄⋊C₄×C₆₁	—	2	2	no	—
174	C₄⋊C₄×C₆₁	—	2	4	no	—
175	C₄⋊C₄×C₆₁	—	2	2	no	—
176	C₄⋊C₄×C₆₁	—	2	2	no	—
177	C₄⋊C₄×C₆₁	—	2	2	no	—
178	C₄⋊C₄×C₆₁	—	8	2	no	—
179	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₆₁	C₂×D₄	1	2	yes	—
181	C₂²⋊C₄×C₆₁	—	2	4	no	—
182	C₂²⋊C₄×C₆₁	—	2	2	no	—
183	C₂²⋊C₄×C₆₁	—	2	8	no	—
184	C₂²⋊C₄×C₆₁	—	2	2	no	—
185	C₂²⋊C₄×C₆₁	—	2	2	no	—
186	C₂²⋊C₄×C₆₁	—	4	1	no	—
187	C₂²⋊C₄×C₆₁	—	4	1	no	—
188	C₂²⋊C₄×C₆₁	—	8	2	no	—
189	C₄²×C₆₁	—	2	4	no	—
190	C₄²×C₆₁	—	2	4	no	—
191	C₄²×C₆₁	—	2	2	no	—
192	C₄²×C₆₁	—	2	2	no	—
193	C₄²×C₆₁	—	2	2	no	—
194	C₄²×C₆₁	—	2	2	no	—
195	C₄²×C₆₁	—	2	2	no	—
196	C₄²×C₆₁	—	2	1	no	—
197	C₄²×C₆₁	—	2	2	no	—
198	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
199	C₄²×C₆₁	C₂×D₄	1	2	yes	—
200	C₄²×C₆₁	C₂×D₄	1	2	yes	—
201	C₂³×C₆₁	—	2	2	no	—
202	C₂³×C₆₁	—	2	2	no	—
203	C₂³×C₆₁	—	4	2	no	—
204	C₂³×C₆₁	—	4	2	no	—
205	C₂³×C₆₁	—	4	1	no	—
206	C₂³×C₆₁	—	4	1	no	—
207	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
208	Q₈×C₆₁	—	2	8	no	—
209	Q₈×C₆₁	—	2	4	no	—
210	Q₈×C₆₁	—	2	2	no	—
211	Q₈×C₆₁	—	2	4	no	—
212	Q₈×C₆₁	C₄×D₄	1	4	yes	—
213	D₄×C₆₁	—	2	8	no	—
214	D₄×C₆₁	—	2	4	no	—
215	D₄×C₆₁	—	2	4	no	—
216	D₄×C₆₁	—	2	4	no	—
217	D₄×C₆₁	—	2	2	no	—
218	D₄×C₆₁	—	4	2	no	—
219	D₄×C₆₁	C₄×D₄	1	4	yes	—
220	C₂×C₄×C₆₁	—	2	16	no	—
221	C₂×C₄×C₆₁	—	2	2	no	—
222	C₂×C₄×C₆₁	—	2	2	no	—
223	C₂×C₄×C₆₁	—	2	2	no	—
224	C₂×C₄×C₆₁	—	2	4	no	—
225	C₂×C₄×C₆₁	—	2	4	no	—
226	C₂×C₄×C₆₁	—	2	2	no	—
227	C₂×C₄×C₆₁	—	2	2	no	—
228	C₂×C₄×C₆₁	—	2	2	no	—
229	C₂×C₄×C₆₁	—	2	2	no	—
230	C₂×C₄×C₆₁	—	4	1	no	—
231	C₂×C₄×C₆₁	—	4	1	no	—
232	C₂×C₄×C₆₁	—	4	4	no	—
233	C₂×C₄×C₆₁	—	4	1	no	—
234	C₂×C₄×C₆₁	—	4	1	no	—
235	C₂×C₄×C₆₁	—	4	2	no	—
236	C₂×C₄×C₆₁	—	4	1	no	—
237	C₂×C₄×C₆₁	—	4	2	no	—
238	C₂×C₄×C₆₁	—	4	1	no	—
239	C₂×C₄×C₆₁	—	4	1	no	—
240	C₂×C₄×C₆₁	—	4	1	no	—
241	C₂×C₄×C₆₁	—	8	2	no	—
242	C₂×C₄×C₆₁	—	8	4	no	—
243	C₂×C₄×C₆₁	—	8	4	no	—
244	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
245	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
246	C₂×C₄×C₆₁	#120	1	1	yes	characteristic
247	C₂×C₄×C₆₁	#120	1	2	yes	—
248	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
249	C₂×C₄×C₆₁	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
251	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
252	C₈×C₆₁	—	2	4	no	—
253	C₈×C₆₁	—	4	2	no	—
254	#21475	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
255	C₂²×C₆₁	—	2	1	no	—
256	C₂²×C₆₁	—	2	1	no	—
257	C₂²×C₆₁	—	2	4	no	—
258	C₂²×C₆₁	—	4	4	no	—
259	C₂²×C₆₁	—	4	2	no	—
260	C₂²×C₆₁	—	4	2	no	—
261	C₂²×C₆₁	—	4	2	no	—
262	C₂²×C₆₁	—	8	2	no	—
263	C₂²×C₆₁	—	8	1	no	—
264	C₂²×C₆₁	—	8	1	no	—
265	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
266	C₂²×C₆₁	C₂×#120	1	1	yes	characteristic
267	C₂²×C₆₁	#525	1	1	yes	characteristic
268	C₄×C₆₁	—	2	1	no	—
269	C₄×C₆₁	—	2	1	no	—
270	C₄×C₆₁	—	2	2	no	—
271	C₄×C₆₁	—	2	4	no	—
272	C₄×C₆₁	—	2	4	no	—
273	C₄×C₆₁	—	4	2	no	—
274	C₄×C₆₁	—	4	2	no	—
275	C₄×C₆₁	—	4	2	no	—
276	C₄×C₆₁	—	4	2	no	—
277	C₄×C₆₁	—	8	1	no	—
278	C₄×C₆₁	—	8	1	no	—
279	C₄×C₆₁	C₂×C₄×D₄	1	2	yes	—
280	C₄×C₆₁	#525	1	2	yes	—
281	C₄×2₋¹⁺⁴	C₂×C₆₁	1	1	yes	characteristic, complemented
282	C₂×#454	C₂×C₆₁	1	1	yes	characteristic
283	C₄×AGL(1,ℤ/8)	C₂×C₆₁	1	2	yes	complemented
284	#2326	C₂×C₆₁	1	1	yes	characteristic, complemented
285	#1888	C₂×C₆₁	1	1	yes	characteristic, complemented
286	#1883	C₂×C₆₁	1	2	yes	complemented
287	#1859	C₂×C₆₁	1	2	yes	complemented
288	#1857	C₂×C₆₁	1	1	yes	characteristic, complemented
289	#1793	C₂×C₆₁	1	1	yes	characteristic, complemented
290	#1759	C₂×C₆₁	1	2	yes	complemented
291	C₄×#101	C₂×C₆₁	1	1	yes	characteristic, complemented
292	C₂×C₆₁	—	2	1	no	—
293	C₂×C₆₁	—	2	1	no	—
294	C₂×C₆₁	—	4	4	no	—
295	C₂×C₆₁	—	8	2	no	—
296	C₂×C₆₁	C₄×#120	1	1	yes	characteristic
297	C₂×C₆₁	#3020	1	1	yes	characteristic
298	C₂×C₆₁	#3021	1	1	yes	characteristic
299	C₂×2₋¹⁺⁴	C₂²×C₆₁	1	1	yes	characteristic
300	C₂×AGL(1,ℤ/8)	C₂²×C₆₁	1	2	yes	—
301	C₂×#124	C₂²×C₆₁	1	1	yes	characteristic
302	#520	—	2	2	no	—
303	#520	—	2	2	no	—
304	#520	C₂²×C₆₁	1	2	yes	—
305	#519	—	2	2	no	—
306	#519	C₂²×C₆₁	1	1	yes	characteristic
307	C₄×#41	—	2	2	no	—
308	C₄×#41	—	2	2	no	—
309	C₄×#41	C₂²×C₆₁	1	2	yes	—
310	C₂×C₄×Q₈	—	2	2	no	—
311	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
312	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
313	#454	C₄×C₆₁	1	8	yes	complemented
314	#442	—	2	2	no	—
315	#440	—	2	2	no	—
316	C₄×SD₁₆	—	2	2	no	—
317	C₄×D₈	—	2	2	no	—
318	#428	C₂²×C₆₁	1	2	yes	—
319	C₂×#104	C₂²×C₆₁	1	2	yes	—
320	C₂×#104	C₂²×C₆₁	1	2	yes	—
321	#418	C₂²×C₆₁	1	2	yes	—
322	#417	C₂²×C₆₁	1	2	yes	—
323	C₂×#101	C₂²×C₆₁	1	1	yes	characteristic
324	C₂×#101	C₂²×C₆₁	1	1	yes	characteristic
325	C₄×M₁₆	C₂²×C₆₁	1	2	yes	—
326	#391	C₂²×C₆₁	1	1	yes	characteristic
327	#390	C₂²×C₆₁	1	1	yes	characteristic
328	#388	—	2	2	no	—
329	#385	—	2	2	no	—
330	#384	C₂²×C₆₁	1	1	yes	characteristic
331	#376	C₂²×C₆₁	1	1	yes	characteristic
332	#343	C₂²×C₆₁	1	2	yes	—
333	#339	C₂²×C₆₁	1	2	yes	—
334	#339	C₂²×C₆₁	1	2	yes	—
335	C₆₁	#21475	1	1	yes	characteristic, direct product factor, Sylow
336	2₋¹⁺⁴	—	2	4	no	—
337	2₋¹⁺⁴	—	2	2	no	—
338	2₋¹⁺⁴	C₂×C₄×C₆₁	1	4	yes	complemented
339	C₂×#41	—	2	2	no	—
340	C₂×#41	—	2	2	no	—
341	C₂×#41	C₂³×C₆₁	1	2	yes	—
342	C₂²×Q₈	—	2	2	no	—
343	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
344	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
345	C₂³×C₄	—	2	1	no	—
346	AGL(1,ℤ/8)	—	2	4	no	—
347	AGL(1,ℤ/8)	C₂×C₄×C₆₁	1	8	yes	complemented
348	C₂×SD₁₆	—	2	2	no	—
349	C₂×D₈	—	2	2	no	—
350	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
351	C₂×M₁₆	C₂³×C₆₁	1	2	yes	—
352	#124	—	2	2	no	—
353	#124	C₂×C₄×C₆₁	1	4	yes	complemented
354	C₄×Q₈	—	2	2	no	—
355	C₄×Q₈	—	2	4	no	—
356	C₄×Q₈	—	2	2	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	D₄×C₆₁	1	2	yes	—
363	C₄×Q₈	D₄×C₆₁	1	2	yes	—
364	C₄×D₄	—	2	2	no	—
365	C₄×D₄	—	2	4	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	4	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	D₄×C₆₁	1	2	yes	—
374	C₄×D₄	D₄×C₆₁	1	2	yes	—
375	#117	—	2	4	no	—
376	#117	—	2	4	no	—
377	#117	—	2	2	no	—
378	#117	—	2	2	no	—
379	#117	—	2	2	no	—
380	#117	C₂³×C₆₁	1	2	yes	—
381	C₂×C₄⋊C₄	—	2	4	no	—
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	2	no	—
384	C₂×C₄⋊C₄	D₄×C₆₁	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	2	no	—
388	C₂×C₂²⋊C₄	—	2	1	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₄²	—	2	4	no	—
391	C₂×C₄²	—	2	2	no	—
392	C₂×C₄²	D₄×C₆₁	1	2	yes	—
393	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
395	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
396	#107	—	2	2	no	—
397	#106	—	2	2	no	—
398	#104	—	2	4	no	—
399	#104	C₂×C₄×C₆₁	1	8	yes	complemented
400	#103	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#101	—	2	2	no	—
405	#101	C₂×C₄×C₆₁	1	4	yes	complemented
406	#97	—	2	2	no	—
407	C₄×C₈	—	2	2	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	2	no	—
411	C₂⁴	—	2	1	no	—
412	#41	—	2	8	no	—
413	#41	—	2	8	no	—
414	#41	—	2	8	no	—
415	#41	—	2	8	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	C₂²×C₄×C₆₁	1	4	yes	—
419	#41	#41×C₆₁	1	4	yes	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	8	no	—
422	C₂×Q₈	—	2	8	no	—
423	C₂×Q₈	—	2	2	no	—
424	C₂×Q₈	—	2	2	no	—
425	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
426	C₂×Q₈	C₂×D₄×C₆₁	1	2	yes	—
427	C₂×Q₈	#41×C₆₁	1	2	yes	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
434	C₂×D₄	C₂×D₄×C₆₁	1	2	yes	—
435	C₂²×C₄	—	2	4	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	4	2	no	—
444	C₂²×C₄	—	8	2	no	—
445	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
446	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
447	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
449	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
450	SD₁₆	—	2	8	no	—
451	D₈	—	2	8	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	C₂²×C₄×C₆₁	1	4	yes	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	2	no	—
466	C₄⋊C₄	—	8	2	no	—
467	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
468	C₄⋊C₄	C₂×D₄×C₆₁	1	2	yes	—
469	C₂²⋊C₄	—	2	4	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	8	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	—	8	2	no	—
477	C₄²	—	2	4	no	—
478	C₄²	—	2	4	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	2	no	—
481	C₄²	—	2	2	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	2	no	—
486	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
487	C₄²	C₂×D₄×C₆₁	1	2	yes	—
488	C₄²	C₂×D₄×C₆₁	1	2	yes	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	1	no	—
494	C₂³	—	4	1	no	—
495	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
496	Q₈	—	2	8	no	—
497	Q₈	—	2	4	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	2	4	no	—
500	Q₈	C₄×D₄×C₆₁	1	4	yes	—
501	D₄	—	2	8	no	—
502	D₄	—	2	4	no	—
503	D₄	—	2	4	no	—
504	D₄	—	2	4	no	—
505	D₄	—	2	2	no	—
506	D₄	—	4	2	no	—
507	D₄	C₄×D₄×C₆₁	1	4	yes	—
508	C₂×C₄	—	2	16	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	—	8	4	no	—
531	C₂×C₄	—	8	4	no	—
532	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
533	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
534	C₂×C₄	#120×C₆₁	1	1	yes	characteristic
535	C₂×C₄	#120×C₆₁	1	2	yes	—
536	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₆₁	1	2	yes	—
538	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
539	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
540	C₈	—	2	4	no	—
541	C₈	—	4	2	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	4	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
553	C₂²	C₂×#120×C₆₁	1	1	yes	characteristic
554	C₂²	C₆₁×#525	1	1	yes	characteristic
555	C₄	—	2	4	no	—
556	C₄	—	2	4	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	C₂×C₄×D₄×C₆₁	1	2	yes	—
567	C₄	C₆₁×#525	1	2	yes	—
568	C₂	—	2	1	no	—
569	C₂	—	2	1	no	—
570	C₂	—	4	4	no	—
571	C₂	—	8	2	no	—
572	C₂	C₄×#120×C₆₁	1	1	yes	characteristic
573	C₂	C₆₁×#3020	1	1	yes	characteristic
574	C₂	C₆₁×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₁	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
prime radical	C₂×C₆₁×#454	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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. C₄×2₋¹⁺⁴×C₆₁	C₂	semidirect
3. C₄×AGL(1,ℤ/8)×C₆₁	C₂	semidirect
4. C₆₁×#2326	C₂	semidirect
5. C₆₁×#1888	C₂	semidirect
6. C₆₁×#1883	C₂	semidirect
7. C₆₁×#1859	C₂	semidirect
8. C₆₁×#1857	C₂	semidirect
9. C₆₁×#1793	C₂	semidirect
10. C₆₁×#1759	C₂	semidirect
11. C₄×#101×C₆₁	C₂	semidirect
26. C₆₁×#454	C₄	semidirect
50. 2₋¹⁺⁴×C₆₁	C₂×C₄	semidirect
59. AGL(1,ℤ/8)×C₆₁	C₂×C₄	semidirect
65. #124×C₆₁	C₂×C₄	semidirect
111. #104×C₆₁	C₂×C₄	semidirect
117. #101×C₆₁	C₂×C₄	semidirect
254. #21475	C₆₁	direct (N × H)
281. C₄×2₋¹⁺⁴	C₂×C₆₁	semidirect
283. C₄×AGL(1,ℤ/8)	C₂×C₆₁	semidirect
284. #2326	C₂×C₆₁	semidirect
285. #1888	C₂×C₆₁	semidirect
286. #1883	C₂×C₆₁	semidirect
287. #1859	C₂×C₆₁	semidirect
288. #1857	C₂×C₆₁	semidirect
289. #1793	C₂×C₆₁	semidirect
290. #1759	C₂×C₆₁	semidirect
291. C₄×#101	C₂×C₆₁	semidirect
313. #454	C₄×C₆₁	semidirect
335. C₆₁	#21475	direct (N × H)
338. 2₋¹⁺⁴	C₂×C₄×C₆₁	semidirect
347. AGL(1,ℤ/8)	C₂×C₄×C₆₁	semidirect
353. #124	C₂×C₄×C₆₁	semidirect
399. #104	C₂×C₄×C₆₁	semidirect
405. #101	C₂×C₄×C₆₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×2₋¹⁺⁴×C₆₁	2
C₂×C₆₁×#454	2
C₄×AGL(1,ℤ/8)×C₆₁	2
C₆₁×#2326	2
C₆₁×#1888	2
C₆₁×#1883	2
C₆₁×#1859	2
C₆₁×#1857	2
C₆₁×#1793	2
C₆₁×#1759	2
C₄×#101×C₆₁	2
#21475	61

Subgroups — C61×#21475 #29524908

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₁×#21475 #29524908