Subgroups — C₄×C₆₁×#440 #29523934

Order 15616.

1206 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₁×#440	C₂	1	2	yes	maximal
2	C₂×C₄×SD₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
3	C₄²×Q₈×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄²×D₄×C₆₁	C₂	1	1	yes	maximal, characteristic
5	C₆₁×#1776	C₂	1	2	yes	maximal, complemented
6	C₄×#107×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₁×#1763	C₂	1	2	yes	maximal, complemented
8	C₆₁×#1762	C₂	1	2	yes	maximal
9	C₄×#103×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#102×C₆₁	C₂	1	1	yes	maximal, characteristic
11	C₄×#97×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₆₁	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₆₁	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₆₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₆₁	C₂²	1	2	yes	—
17	C₂²×C₄²×C₆₁	—	2	1	no	—
18	C₆₁×#440	C₄	1	16	yes	direct product factor
19	C₄×SD₁₆×C₆₁	C₄	1	8	yes	complemented
20	C₂×#107×C₆₁	C₂²	1	2	yes	—
21	C₂×#106×C₆₁	C₂²	1	1	yes	characteristic
22	C₂×#103×C₆₁	C₂²	1	2	yes	—
23	C₂×#103×C₆₁	C₂²	1	1	yes	characteristic
24	C₂×#102×C₆₁	C₂²	1	2	yes	—
25	C₂×#102×C₆₁	C₂²	1	1	yes	characteristic
26	C₂×#97×C₆₁	C₂²	1	2	yes	—
27	C₂×#97×C₆₁	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₆₁	—	2	2	no	—
31	C₄×C₄⋊C₄×C₆₁	—	2	1	no	—
32	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₆₁	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₆₁	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₆₁	—	2	2	no	—
37	C₄×C₂²⋊C₄×C₆₁	—	2	1	no	—
38	C₄³×C₆₁	—	2	1	no	—
39	C₄³×C₆₁	C₂²	1	1	yes	characteristic
40	C₆₁×#340	C₂²	1	2	yes	—
41	C₆₁×#340	C₂²	1	2	yes	—
42	C₆₁×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₆₁	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₆₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₆₁	—	2	2	no	—
46	C₂³×C₄×C₆₁	—	2	1	no	—
47	C₂×SD₁₆×C₆₁	C₂×C₄	1	4	yes	—
48	C₂×SD₁₆×C₆₁	C₂×C₄	1	8	yes	—
49	C₂²×C₈×C₆₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₁	C₂³	1	1	yes	characteristic
52	C₄×Q₈×C₆₁	—	2	2	no	—
53	C₄×Q₈×C₆₁	—	2	4	no	—
54	C₄×Q₈×C₆₁	C₂×C₄	1	4	yes	complemented
55	C₄×Q₈×C₆₁	C₂×C₄	1	8	yes	complemented
56	C₄×D₄×C₆₁	—	2	2	no	—
57	C₄×D₄×C₆₁	—	2	4	no	—
58	C₄×D₄×C₆₁	C₂×C₄	1	4	yes	—
59	C₄×D₄×C₆₁	C₂×C₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₆₁	—	2	1	no	—
61	C₂×C₄⋊C₄×C₆₁	—	2	2	no	—
62	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₆₁	C₂³	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₆₁	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₆₁	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₆₁	—	2	2	no	—
68	C₂×C₄²×C₆₁	—	2	2	no	—
69	C₂×C₄²×C₆₁	—	2	1	no	—
70	C₂×C₄²×C₆₁	—	2	2	no	—
71	C₂×C₄²×C₆₁	—	2	2	no	—
72	C₂×C₄²×C₆₁	—	2	1	no	—
73	C₂×C₄²×C₆₁	—	2	1	no	—
74	C₂×C₄²×C₆₁	—	4	4	no	—
75	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₆₁	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₆₁	D₄	1	2	yes	—
78	C₂×C₄²×C₆₁	C₂³	1	2	yes	—
79	C₂×C₄²×C₆₁	C₂³	1	1	yes	characteristic
80	#107×C₆₁	C₂×C₄	1	8	yes	complemented
81	#106×C₆₁	C₂×C₄	1	4	yes	complemented
82	#103×C₆₁	C₂×C₄	1	4	yes	complemented
83	#103×C₆₁	C₂×C₄	1	8	yes	complemented
84	#102×C₆₁	C₂×C₄	1	4	yes	—
85	#102×C₆₁	C₂×C₄	1	8	yes	—
86	#97×C₆₁	—	2	4	no	—
87	#97×C₆₁	C₂×C₄	1	8	yes	complemented
88	C₄×C₈×C₆₁	—	2	2	no	—
89	C₄×C₈×C₆₁	C₂×C₄	1	4	yes	complemented
90	#95×C₆₁	—	2	1	no	—
91	#95×C₆₁	—	2	2	no	—
92	#95×C₆₁	—	2	1	no	—
93	#95×C₆₁	—	2	2	no	—
94	C₂⁴×C₆₁	—	2	1	no	—
95	C₂×Q₈×C₆₁	—	2	1	no	—
96	C₂×Q₈×C₆₁	—	2	2	no	—
97	C₂×Q₈×C₆₁	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₆₁	C₂²×C₄	1	4	yes	—
99	C₂×D₄×C₆₁	—	2	1	no	—
100	C₂×D₄×C₆₁	—	2	2	no	—
101	C₂×D₄×C₆₁	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₆₁	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₆₁	—	2	1	no	—
104	C₂²×C₄×C₆₁	—	2	2	no	—
105	C₂²×C₄×C₆₁	—	2	1	no	—
106	C₂²×C₄×C₆₁	—	2	1	no	—
107	C₂²×C₄×C₆₁	—	2	2	no	—
108	C₂²×C₄×C₆₁	—	2	8	no	—
109	C₂²×C₄×C₆₁	—	2	4	no	—
110	C₂²×C₄×C₆₁	—	4	4	no	—
111	C₂²×C₄×C₆₁	—	4	4	no	—
112	C₂²×C₄×C₆₁	—	4	2	no	—
113	C₂²×C₄×C₆₁	—	4	2	no	—
114	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₆₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₆₁	C₂⁴	1	1	yes	characteristic
119	SD₁₆×C₆₁	C₄²	1	16	yes	complemented
120	C₂×C₈×C₆₁	—	2	2	no	—
121	C₂×C₈×C₆₁	—	2	2	no	—
122	C₂×C₈×C₆₁	—	2	2	no	—
123	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
124	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
125	C₂×C₈×C₆₁	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₆₁	C₂²×C₄	1	4	yes	—
127	C₄⋊C₄×C₆₁	—	2	4	no	—
128	C₄⋊C₄×C₆₁	—	2	8	no	—
129	C₄⋊C₄×C₆₁	—	2	1	no	—
130	C₄⋊C₄×C₆₁	—	2	2	no	—
131	C₄⋊C₄×C₆₁	—	2	1	no	—
132	C₄⋊C₄×C₆₁	—	2	2	no	—
133	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
135	C₄⋊C₄×C₆₁	C₂²×C₄	1	2	yes	—
136	C₄⋊C₄×C₆₁	C₂²×C₄	1	4	yes	—
137	C₂²⋊C₄×C₆₁	—	2	8	no	—
138	C₂²⋊C₄×C₆₁	—	2	4	no	—
139	C₄²×C₆₁	—	2	8	no	—
140	C₄²×C₆₁	—	2	4	no	—
141	C₄²×C₆₁	—	2	2	no	—
142	C₄²×C₆₁	—	2	2	no	—
143	C₄²×C₆₁	—	4	2	no	—
144	C₄²×C₆₁	—	4	4	no	—
145	C₄²×C₆₁	—	4	4	no	—
146	C₄²×C₆₁	—	4	2	no	—
147	C₄²×C₆₁	—	4	2	no	—
148	C₄²×C₆₁	C₂²×C₄	1	2	yes	—
149	C₄²×C₆₁	C₂²×C₄	1	4	yes	—
150	C₄²×C₆₁	#41	1	2	yes	—
151	C₄²×C₆₁	#41	1	4	yes	—
152	C₂³×C₆₁	—	2	2	no	—
153	C₂³×C₆₁	—	2	4	no	—
154	C₂³×C₆₁	—	4	1	no	—
155	C₂³×C₆₁	—	4	1	no	—
156	C₂³×C₆₁	—	4	2	no	—
157	C₂³×C₆₁	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₆₁	—	2	2	no	—
159	Q₈×C₆₁	—	2	4	no	—
160	Q₈×C₆₁	C₂×C₄²	1	4	yes	complemented
161	D₄×C₆₁	—	2	2	no	—
162	D₄×C₆₁	—	2	4	no	—
163	D₄×C₆₁	C₂×C₄²	1	4	yes	—
164	C₂×C₄×C₆₁	—	2	2	no	—
165	C₂×C₄×C₆₁	—	2	4	no	—
166	C₂×C₄×C₆₁	—	2	2	no	—
167	C₂×C₄×C₆₁	—	2	2	no	—
168	C₂×C₄×C₆₁	—	2	2	no	—
169	C₂×C₄×C₆₁	—	2	2	no	—
170	C₂×C₄×C₆₁	—	2	2	no	—
171	C₂×C₄×C₆₁	—	2	2	no	—
172	C₂×C₄×C₆₁	—	2	4	no	—
173	C₂×C₄×C₆₁	—	2	2	no	—
174	C₂×C₄×C₆₁	—	2	4	no	—
175	C₂×C₄×C₆₁	—	4	16	no	—
176	C₂×C₄×C₆₁	—	4	1	no	—
177	C₂×C₄×C₆₁	—	4	2	no	—
178	C₂×C₄×C₆₁	—	4	2	no	—
179	C₂×C₄×C₆₁	—	4	1	no	—
180	C₂×C₄×C₆₁	—	4	2	no	—
181	C₂×C₄×C₆₁	—	4	2	no	—
182	C₂×C₄×C₆₁	—	4	2	no	—
183	C₂×C₄×C₆₁	—	4	8	no	—
184	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
185	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
186	C₂×C₄×C₆₁	C₄×D₄	1	4	yes	—
187	C₂×C₄×C₆₁	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₆₁	AGL(1,ℤ/8)	1	2	yes	—
189	C₂×C₄×C₆₁	#137	1	2	yes	—
190	C₂×C₄×C₆₁	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₆₁	C₂³×C₄	1	2	yes	—
192	C₂×C₄×C₆₁	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₆₁	C₂×#41	1	2	yes	—
194	C₈×C₆₁	—	2	4	no	—
195	C₈×C₆₁	—	2	2	no	—
196	C₈×C₆₁	C₂×C₄²	1	4	yes	complemented
197	C₄×#440	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₆₁	—	2	4	no	—
199	C₂²×C₆₁	—	4	2	no	—
200	C₂²×C₆₁	—	4	2	no	—
201	C₂²×C₆₁	—	4	4	no	—
202	C₂²×C₆₁	—	4	4	no	—
203	C₂²×C₆₁	C₂×C₄×D₄	1	1	yes	characteristic
204	C₂²×C₆₁	C₂×C₄×D₄	1	2	yes	—
205	C₂²×C₆₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
206	C₂²×C₆₁	C₂×#137	1	1	yes	characteristic
207	C₂²×C₆₁	#575	1	2	yes	—
208	C₄×C₆₁	—	2	2	no	—
209	C₄×C₆₁	—	2	4	no	—
210	C₄×C₆₁	—	2	4	no	—
211	C₄×C₆₁	—	2	4	no	—
212	C₄×C₆₁	—	4	2	no	—
213	C₄×C₆₁	—	4	2	no	—
214	C₄×C₆₁	—	4	4	no	—
215	C₄×C₆₁	—	4	4	no	—
216	C₄×C₆₁	#440	1	4	yes	direct product factor
217	C₄×C₆₁	C₂²×C₄²	1	1	yes	characteristic
218	C₄×C₆₁	C₄×#41	1	2	yes	—
219	C₄×C₆₁	C₄×#41	1	1	yes	characteristic
220	C₂×#440	C₂×C₆₁	1	2	yes	—
221	C₂×C₄×SD₁₆	C₂×C₆₁	1	1	yes	characteristic
222	C₄²×Q₈	C₂×C₆₁	1	1	yes	characteristic, complemented
223	C₄²×D₄	C₂×C₆₁	1	1	yes	characteristic
224	#1776	C₂×C₆₁	1	2	yes	complemented
225	C₄×#107	C₂×C₆₁	1	1	yes	characteristic, complemented
226	#1763	C₂×C₆₁	1	2	yes	complemented
227	#1762	C₂×C₆₁	1	2	yes	—
228	C₄×#103	C₂×C₆₁	1	1	yes	characteristic, complemented
229	C₄×#102	C₂×C₆₁	1	1	yes	characteristic
230	C₄×#97	C₂×C₆₁	1	1	yes	characteristic, complemented
231	C₂×C₆₁	—	4	4	no	—
232	C₂×C₆₁	C₄²×D₄	1	1	yes	characteristic
233	C₂×C₆₁	C₂×#440	1	1	yes	characteristic
234	C₂×C₆₁	#2943	1	1	yes	characteristic
235	C₂×C₆₁	C₄×AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₆₁	C₄×#137	1	2	yes	—
237	C₂²×SD₁₆	C₂²×C₆₁	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂²×C₆₁	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂²×C₆₁	1	2	yes	—
240	C₂×C₄×D₄	C₂²×C₆₁	1	1	yes	characteristic
241	C₂×C₄×D₄	C₂²×C₆₁	1	2	yes	—
242	C₂²×C₄²	—	2	1	no	—
243	#440	C₄×C₆₁	1	16	yes	direct product factor
244	C₄×SD₁₆	C₄×C₆₁	1	8	yes	complemented
245	C₂×#107	C₂²×C₆₁	1	2	yes	—
246	C₂×#106	C₂²×C₆₁	1	1	yes	characteristic
247	C₂×#103	C₂²×C₆₁	1	1	yes	characteristic
248	C₂×#103	C₂²×C₆₁	1	2	yes	—
249	C₂×#102	C₂²×C₆₁	1	1	yes	characteristic
250	C₂×#102	C₂²×C₆₁	1	2	yes	—
251	C₂×#97	C₂²×C₆₁	1	2	yes	—
252	C₂×#97	C₂²×C₆₁	1	2	yes	—
253	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
254	C₂×C₄×C₈	C₂²×C₆₁	1	1	yes	characteristic
255	C₄×C₄⋊C₄	—	2	1	no	—
256	C₄×C₄⋊C₄	—	2	2	no	—
257	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
259	C₄×C₄⋊C₄	C₂²×C₆₁	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂²×C₆₁	1	2	yes	—
261	C₄×C₂²⋊C₄	—	2	1	no	—
262	C₄×C₂²⋊C₄	—	2	2	no	—
263	C₄³	—	2	1	no	—
264	C₄³	C₂²×C₆₁	1	1	yes	characteristic
265	#340	C₂²×C₆₁	1	2	yes	—
266	#340	C₂²×C₆₁	1	2	yes	—
267	#340	C₂²×C₆₁	1	2	yes	—
268	C₆₁	C₄×#440	1	1	yes	characteristic, direct product factor, Sylow
269	C₂²×Q₈	C₂³×C₆₁	1	1	yes	characteristic
270	C₂²×D₄	C₂³×C₆₁	1	1	yes	characteristic
271	C₂³×C₄	—	2	2	no	—
272	C₂³×C₄	—	2	1	no	—
273	C₂×SD₁₆	C₂×C₄×C₆₁	1	4	yes	—
274	C₂×SD₁₆	C₂×C₄×C₆₁	1	8	yes	—
275	C₂²×C₈	C₂³×C₆₁	1	2	yes	—
276	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
277	C₂²×C₈	C₂³×C₆₁	1	1	yes	characteristic
278	C₄×Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	4	no	—
280	C₄×Q₈	C₂×C₄×C₆₁	1	4	yes	complemented
281	C₄×Q₈	C₂×C₄×C₆₁	1	8	yes	complemented
282	C₄×D₄	—	2	2	no	—
283	C₄×D₄	—	2	4	no	—
284	C₄×D₄	C₂×C₄×C₆₁	1	4	yes	—
285	C₄×D₄	C₂×C₄×C₆₁	1	8	yes	—
286	C₂×C₄⋊C₄	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³×C₆₁	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³×C₆₁	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₄²	—	2	2	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	2	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	4	4	no	—
301	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
302	C₂×C₄²	D₄×C₆₁	1	1	yes	characteristic
303	C₂×C₄²	D₄×C₆₁	1	2	yes	—
304	C₂×C₄²	C₂³×C₆₁	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₆₁	1	2	yes	—
306	#107	C₂×C₄×C₆₁	1	8	yes	complemented
307	#106	C₂×C₄×C₆₁	1	4	yes	complemented
308	#103	C₂×C₄×C₆₁	1	4	yes	complemented
309	#103	C₂×C₄×C₆₁	1	8	yes	complemented
310	#102	C₂×C₄×C₆₁	1	4	yes	—
311	#102	C₂×C₄×C₆₁	1	8	yes	—
312	#97	—	2	4	no	—
313	#97	C₂×C₄×C₆₁	1	8	yes	complemented
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	C₂×C₄×C₆₁	1	4	yes	complemented
316	#95	—	2	1	no	—
317	#95	—	2	2	no	—
318	#95	—	2	1	no	—
319	#95	—	2	2	no	—
320	C₂⁴	—	2	1	no	—
321	C₂×Q₈	—	2	1	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	C₂²×C₄×C₆₁	1	2	yes	—
324	C₂×Q₈	C₂²×C₄×C₆₁	1	4	yes	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂²×C₄×C₆₁	1	2	yes	—
328	C₂×D₄	C₂²×C₄×C₆₁	1	4	yes	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	—	4	2	no	—
339	C₂²×C₄	—	4	2	no	—
340	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₆₁	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₆₁	1	1	yes	characteristic
344	C₂²×C₄	C₂⁴×C₆₁	1	1	yes	characteristic
345	SD₁₆	C₄²×C₆₁	1	16	yes	complemented
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
350	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
351	C₂×C₈	C₂²×C₄×C₆₁	1	2	yes	—
352	C₂×C₈	C₂²×C₄×C₆₁	1	4	yes	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	8	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
360	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
361	C₄⋊C₄	C₂²×C₄×C₆₁	1	2	yes	—
362	C₄⋊C₄	C₂²×C₄×C₆₁	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₄²	—	2	8	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	2	2	no	—
369	C₄²	—	4	2	no	—
370	C₄²	—	4	4	no	—
371	C₄²	—	4	4	no	—
372	C₄²	—	4	2	no	—
373	C₄²	—	4	2	no	—
374	C₄²	C₂²×C₄×C₆₁	1	2	yes	—
375	C₄²	C₂²×C₄×C₆₁	1	4	yes	—
376	C₄²	#41×C₆₁	1	2	yes	—
377	C₄²	#41×C₆₁	1	4	yes	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂²×D₄×C₆₁	1	1	yes	characteristic
384	Q₈	—	2	2	no	—
385	Q₈	—	2	4	no	—
386	Q₈	C₂×C₄²×C₆₁	1	4	yes	complemented
387	D₄	—	2	2	no	—
388	D₄	—	2	4	no	—
389	D₄	C₂×C₄²×C₆₁	1	4	yes	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	4	16	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
411	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
412	C₂×C₄	C₄×D₄×C₆₁	1	4	yes	—
413	C₂×C₄	C₄×D₄×C₆₁	1	2	yes	—
414	C₂×C₄	AGL(1,ℤ/8)×C₆₁	1	2	yes	—
415	C₂×C₄	#137×C₆₁	1	2	yes	—
416	C₂×C₄	C₂³×C₄×C₆₁	1	1	yes	characteristic
417	C₂×C₄	C₂³×C₄×C₆₁	1	2	yes	—
418	C₂×C₄	C₂×#41×C₆₁	1	1	yes	characteristic
419	C₂×C₄	C₂×#41×C₆₁	1	2	yes	—
420	C₈	—	2	4	no	—
421	C₈	—	2	2	no	—
422	C₈	C₂×C₄²×C₆₁	1	4	yes	complemented
423	C₂²	—	2	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	4	no	—
427	C₂²	—	4	4	no	—
428	C₂²	C₂×C₄×D₄×C₆₁	1	1	yes	characteristic
429	C₂²	C₂×C₄×D₄×C₆₁	1	2	yes	—
430	C₂²	C₂×AGL(1,ℤ/8)×C₆₁	1	1	yes	characteristic
431	C₂²	C₂×#137×C₆₁	1	1	yes	characteristic
432	C₂²	C₆₁×#575	1	2	yes	—
433	C₄	—	2	4	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	4	no	—
441	C₄	C₆₁×#440	1	4	yes	direct product factor
442	C₄	C₂²×C₄²×C₆₁	1	1	yes	characteristic
443	C₄	C₄×#41×C₆₁	1	2	yes	—
444	C₄	C₄×#41×C₆₁	1	1	yes	characteristic
445	C₂	—	4	4	no	—
446	C₂	C₄²×D₄×C₆₁	1	1	yes	characteristic
447	C₂	C₂×C₆₁×#440	1	1	yes	characteristic
448	C₂	C₆₁×#2943	1	1	yes	characteristic
449	C₂	C₄×AGL(1,ℤ/8)×C₆₁	1	2	yes	—
450	C₂	C₄×#137×C₆₁	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₆₁	C₂×D₄
commutator	C₄	C₂²×C₄²×C₆₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₁
socle	C₂³×C₆₁	C₂²×D₄
prime radical	C₂²×D₄×C₆₁	C₂³
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₆₁ ◁ C₄³×C₆₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
3. C₄²×Q₈×C₆₁	C₂	semidirect
5. C₆₁×#1776	C₂	semidirect
6. C₄×#107×C₆₁	C₂	semidirect
7. C₆₁×#1763	C₂	semidirect
9. C₄×#103×C₆₁	C₂	semidirect
11. C₄×#97×C₆₁	C₂	semidirect
18. C₆₁×#440	C₄	direct (N × H)
19. C₄×SD₁₆×C₆₁	C₄	semidirect
54. C₄×Q₈×C₆₁	C₂×C₄	semidirect
55. C₄×Q₈×C₆₁	C₂×C₄	semidirect
80. #107×C₆₁	C₂×C₄	semidirect
81. #106×C₆₁	C₂×C₄	semidirect
82. #103×C₆₁	C₂×C₄	semidirect
83. #103×C₆₁	C₂×C₄	semidirect
87. #97×C₆₁	C₂×C₄	semidirect
89. C₄×C₈×C₆₁	C₂×C₄	semidirect
119. SD₁₆×C₆₁	C₄²	semidirect
160. Q₈×C₆₁	C₂×C₄²	semidirect
196. C₈×C₆₁	C₂×C₄²	semidirect
197. C₄×#440	C₆₁	direct (N × H)
216. C₄×C₆₁	#440	direct (N × H)
222. C₄²×Q₈	C₂×C₆₁	semidirect
224. #1776	C₂×C₆₁	semidirect
225. C₄×#107	C₂×C₆₁	semidirect
226. #1763	C₂×C₆₁	semidirect
228. C₄×#103	C₂×C₆₁	semidirect
230. C₄×#97	C₂×C₆₁	semidirect
243. #440	C₄×C₆₁	direct (N × H)
244. C₄×SD₁₆	C₄×C₆₁	semidirect
268. C₆₁	C₄×#440	direct (N × H)
280. C₄×Q₈	C₂×C₄×C₆₁	semidirect
281. C₄×Q₈	C₂×C₄×C₆₁	semidirect
306. #107	C₂×C₄×C₆₁	semidirect
307. #106	C₂×C₄×C₆₁	semidirect
308. #103	C₂×C₄×C₆₁	semidirect
309. #103	C₂×C₄×C₆₁	semidirect
313. #97	C₂×C₄×C₆₁	semidirect
315. C₄×C₈	C₂×C₄×C₆₁	semidirect
345. SD₁₆	C₄²×C₆₁	semidirect
386. Q₈	C₂×C₄²×C₆₁	semidirect
422. C₈	C₂×C₄²×C₆₁	semidirect
441. C₄	C₆₁×#440	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₆₁×#440	2
C₂×C₄×SD₁₆×C₆₁	2
C₄²×Q₈×C₆₁	2
C₄²×D₄×C₆₁	2
C₆₁×#1776	2
C₄×#107×C₆₁	2
C₆₁×#1763	2
C₆₁×#1762	2
C₄×#103×C₆₁	2
C₄×#102×C₆₁	2
C₄×#97×C₆₁	2
C₄×#440	61

Subgroups — C4×C61×#440 #29523934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₆₁×#440 #29523934