Subgroups — C₅×#8262 #11930982

Order 1280.

494 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#322	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
5	C₅×#1273	C₂	1	2	yes	maximal
6	C₂×C₅×C₄⋊C₈	C₄	1	4	yes	—
7	C₂×C₅×#97	C₄	1	2	yes	—
8	C₂×C₅×#97	C₄	1	2	yes	—
9	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
10	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
11	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₄³×C₅	C₂²	1	1	yes	characteristic
14	C₅×#336	C₄	1	4	yes	—
15	C₅×#322	—	2	2	no	—
16	C₅×C₈²	—	2	2	no	—
17	#8262	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
19	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
20	C₂²×C₅×C₈	C₂×C₄	1	4	yes	—
21	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
27	C₅×C₄⋊C₈	—	2	8	no	—
28	C₅×#97	—	2	4	no	—
29	C₅×#97	C₈	1	8	yes	complemented
30	C₄×C₅×C₈	—	2	2	no	—
31	C₄×C₅×C₈	—	2	2	no	—
32	C₄×C₅×C₈	—	2	2	no	—
33	C₄×C₅×C₈	—	2	2	no	—
34	C₄×C₅×C₈	—	2	2	no	—
35	C₄×C₅×C₈	D₄	1	2	yes	—
36	C₄×C₅×C₈	Q₈	1	2	yes	—
37	C₄×C₄⋊C₈	C₂×C₅	1	2	yes	—
38	C₄×#97	C₂×C₅	1	1	yes	characteristic
39	C₂×#322	C₂×C₅	1	1	yes	characteristic
40	C₂×C₈²	C₂×C₅	1	1	yes	characteristic
41	#1273	C₂×C₅	1	2	yes	—
42	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
43	C₂²×C₄×C₅	C₄²	1	1	yes	characteristic
44	C₂²×C₄×C₅	C₄²	1	2	yes	—
45	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
47	C₂×C₅×C₈	—	2	2	no	—
48	C₂×C₅×C₈	—	2	4	no	—
49	C₂×C₅×C₈	—	2	2	no	—
50	C₂×C₅×C₈	—	2	4	no	—
51	C₂×C₅×C₈	—	2	4	no	—
52	C₂×C₅×C₈	—	2	4	no	—
53	C₂×C₅×C₈	—	2	4	no	—
54	C₂×C₅×C₈	C₄⋊C₄	1	4	yes	—
55	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
56	C₂×C₅×C₈	C₂×C₈	1	4	yes	—
57	C₂×C₅×C₈	M₁₆	1	8	yes	—
58	C₂×C₅×C₈	M₁₆	1	4	yes	—
59	C₄²×C₅	—	2	2	no	—
60	C₄²×C₅	—	2	4	no	—
61	C₄²×C₅	—	2	4	no	—
62	C₄²×C₅	C₂×C₈	1	4	yes	—
63	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
64	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
65	C₄²×C₅	#41	1	2	yes	—
66	C₂×C₄⋊C₈	C₄×C₅	1	4	yes	—
67	C₂×#97	C₄×C₅	1	2	yes	—
68	C₂×#97	C₄×C₅	1	2	yes	—
69	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
70	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
71	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
73	C₄³	C₂²×C₅	1	1	yes	characteristic
74	#336	C₄×C₅	1	4	yes	—
75	#322	—	2	2	no	—
76	C₈²	—	2	2	no	—
77	C₂³×C₅	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₅	—	2	2	no	—
79	C₂×C₄×C₅	—	2	2	no	—
80	C₂×C₄×C₅	—	2	1	no	—
81	C₂×C₄×C₅	—	2	2	no	—
82	C₂×C₄×C₅	—	2	1	no	—
83	C₂×C₄×C₅	—	2	2	no	—
84	C₂×C₄×C₅	C₄×C₈	1	4	yes	—
85	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
86	C₂×C₄×C₅	#117	1	1	yes	characteristic
87	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
88	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
89	C₂×C₄×C₅	C₂²×C₈	1	2	yes	—
90	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
91	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
92	C₂×C₄×C₅	#131	1	4	yes	—
93	C₅×C₈	—	2	4	no	—
94	C₅×C₈	—	2	8	no	—
95	C₅×C₈	—	4	4	no	—
96	C₅×C₈	C₄⋊C₈	1	8	yes	complemented
97	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
98	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
99	C₂²×C₈	C₂×C₄×C₅	1	4	yes	—
100	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
101	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
102	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
103	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
104	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
105	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
106	C₄⋊C₈	—	2	8	no	—
107	#97	—	2	4	no	—
108	#97	C₅×C₈	1	8	yes	complemented
109	C₄×C₈	—	2	2	no	—
110	C₄×C₈	—	2	2	no	—
111	C₄×C₈	—	2	2	no	—
112	C₄×C₈	—	2	2	no	—
113	C₄×C₈	—	2	2	no	—
114	C₄×C₈	C₅×D₄	1	2	yes	—
115	C₄×C₈	C₅×Q₈	1	2	yes	—
116	C₂²×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
117	C₂²×C₅	C₂×C₄×C₈	1	1	yes	characteristic
118	C₂²×C₅	C₄×M₁₆	1	2	yes	—
119	C₂²×C₅	C₄×M₁₆	1	1	yes	characteristic
120	C₂²×C₅	#405	1	2	yes	—
121	C₄×C₅	—	2	4	no	—
122	C₄×C₅	—	4	1	no	—
123	C₄×C₅	—	4	1	no	—
124	C₄×C₅	C₂×C₄⋊C₈	1	2	yes	—
125	C₄×C₅	#431	1	2	yes	—
126	C₄×C₅	#435	1	4	yes	—
127	C₄×C₅	#446	1	4	yes	—
128	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
129	C₂²×C₄	C₄²×C₅	1	1	yes	characteristic
130	C₂²×C₄	C₄²×C₅	1	2	yes	—
131	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
132	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	2	4	no	—
135	C₂×C₈	—	2	2	no	—
136	C₂×C₈	—	2	4	no	—
137	C₂×C₈	—	2	4	no	—
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	—	2	4	no	—
140	C₂×C₈	C₅×C₄⋊C₄	1	4	yes	—
141	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
142	C₂×C₈	C₂×C₅×C₈	1	4	yes	—
143	C₂×C₈	C₅×M₁₆	1	8	yes	—
144	C₂×C₈	C₅×M₁₆	1	4	yes	—
145	C₄²	—	2	2	no	—
146	C₄²	—	2	4	no	—
147	C₄²	—	2	4	no	—
148	C₄²	C₂×C₅×C₈	1	4	yes	—
149	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
150	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
151	C₄²	C₅×#41	1	2	yes	—
152	C₂×C₅	C₈×M₁₆	1	2	yes	—
153	C₂×C₅	#1453	1	1	yes	characteristic
154	C₂×C₅	#1455	1	1	yes	characteristic
155	C₂×C₅	C₄×C₄⋊C₈	1	1	yes	characteristic
156	C₂×C₅	#1771	1	2	yes	—
157	C₂³	C₂×C₄²×C₅	1	1	yes	characteristic
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	1	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	C₄×C₅×C₈	1	4	yes	—
165	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄	C₅×#117	1	1	yes	characteristic
167	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
168	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
169	C₂×C₄	C₂²×C₅×C₈	1	2	yes	—
170	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
171	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
172	C₂×C₄	C₅×#131	1	4	yes	—
173	C₈	—	2	4	no	—
174	C₈	—	2	8	no	—
175	C₈	—	4	4	no	—
176	C₈	C₅×C₄⋊C₈	1	8	yes	complemented
177	C₅	#8262	1	1	yes	characteristic, direct product factor, Sylow
178	C₂²	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
179	C₂²	C₂×C₄×C₅×C₈	1	1	yes	characteristic
180	C₂²	C₄×C₅×M₁₆	1	1	yes	characteristic
181	C₂²	C₄×C₅×M₁₆	1	2	yes	—
182	C₂²	C₅×#405	1	2	yes	—
183	C₄	—	2	4	no	—
184	C₄	—	4	1	no	—
185	C₄	—	4	1	no	—
186	C₄	C₂×C₅×C₄⋊C₈	1	2	yes	—
187	C₄	C₅×#431	1	2	yes	—
188	C₄	C₅×#435	1	4	yes	—
189	C₄	C₅×#446	1	4	yes	—
190	C₂	C₅×C₈×M₁₆	1	2	yes	—
191	C₂	C₅×#1453	1	1	yes	characteristic
192	C₂	C₅×#1455	1	1	yes	characteristic
193	C₂	C₄×C₅×C₄⋊C₈	1	1	yes	characteristic
194	C₂	C₅×#1771	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₅	C₂³
commutator	C₂²	C₂×C₄×C₅×C₈
Frattini, cosocle	C₂×C₄²	C₂³×C₅
socle, prime radical	C₂³×C₅	C₂×C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
17. #8262	C₅	direct (N × H)
29. C₅×#97	C₈	semidirect
96. C₅×C₈	C₄⋊C₈	semidirect
108. #97	C₅×C₈	semidirect
176. C₈	C₅×C₄⋊C₈	semidirect
177. C₅	#8262	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₄⋊C₈	2
C₄×C₅×#97	2
C₂×C₅×#322	2
C₂×C₅×C₈²	2
C₅×#1273	2
#8262	5

Subgroups — C5×#8262 #11930982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8262 #11930982