Subgroups — C₅×#2183 #10603691

Order 640.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×C₄⋊C₁₆	C₂	1	2	yes	maximal
4	C₅×#346	C₂	1	2	yes	maximal
5	C₄×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₄×C₅×Q₈	C₄	1	1	yes	characteristic
7	C₂×C₅×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₅×C₁₆	C₂²	1	2	yes	—
9	C₂×C₅×C₁₆	C₂²	1	1	yes	characteristic
10	C₅×C₄⋊C₈	C₄	1	2	yes	—
11	C₅×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₄×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₄×C₅×C₈	C₂²	1	2	yes	—
14	#2183	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
15	C₂×C₅×Q₈	C₈	1	1	yes	characteristic
16	C₂×C₅×C₈	C₂×C₄	1	1	yes	characteristic
17	C₂×C₅×C₈	C₂×C₄	1	2	yes	—
18	C₂×C₅×C₈	C₂³	1	1	yes	characteristic
19	C₅×C₄⋊C₄	C₈	1	2	yes	—
20	C₅×C₄⋊C₄	C₈	1	1	yes	characteristic
21	C₄²×C₅	C₂×C₄	1	2	yes	—
22	C₄²×C₅	C₂×C₄	1	1	yes	characteristic
23	C₅×C₁₆	—	2	1	no	—
24	C₅×C₁₆	—	2	2	no	—
25	C₅×C₁₆	Q₈	1	2	yes	complemented
26	C₈×Q₈	C₂×C₅	1	1	yes	characteristic
27	C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic
28	C₄⋊C₁₆	C₂×C₅	1	2	yes	—
29	#346	C₂×C₅	1	2	yes	—
30	C₄×C₁₆	C₂×C₅	1	1	yes	characteristic
31	C₅×Q₈	—	2	2	no	—
32	C₂×C₄×C₅	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₅	C₂×C₈	1	1	yes	characteristic
34	C₂×C₄×C₅	C₂×C₈	1	2	yes	—
35	C₂×C₄×C₅	C₂×C₈	1	1	yes	characteristic
36	C₂×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
37	C₅×C₈	—	2	1	no	—
38	C₅×C₈	—	2	2	no	—
39	C₅×C₈	C₂×Q₈	1	1	yes	characteristic
40	C₅×C₈	#41	1	1	yes	characteristic
41	C₄×Q₈	C₄×C₅	1	1	yes	characteristic
42	C₂×C₁₆	C₂²×C₅	1	1	yes	characteristic
43	C₂×C₁₆	C₂²×C₅	1	2	yes	—
44	C₂×C₁₆	C₂²×C₅	1	1	yes	characteristic
45	C₄⋊C₈	C₄×C₅	1	2	yes	—
46	C₄⋊C₈	C₄×C₅	1	1	yes	characteristic
47	C₄×C₈	C₂²×C₅	1	1	yes	characteristic
48	C₄×C₈	C₂²×C₅	1	2	yes	—
49	C₂²×C₅	C₂²×C₈	1	1	yes	characteristic
50	C₄×C₅	—	2	2	no	—
51	C₄×C₅	—	2	2	no	—
52	C₄×C₅	—	2	1	no	—
53	C₄×C₅	M₃₂	1	2	yes	—
54	C₄×C₅	C₄×Q₈	1	1	yes	characteristic
55	C₄×C₅	#131	1	1	yes	characteristic
56	C₂×Q₈	C₅×C₈	1	1	yes	characteristic
57	C₂×C₈	C₂×C₄×C₅	1	1	yes	characteristic
58	C₂×C₈	C₂×C₄×C₅	1	2	yes	—
59	C₂×C₈	C₂³×C₅	1	1	yes	characteristic
60	C₄⋊C₄	C₅×C₈	1	2	yes	—
61	C₄⋊C₄	C₅×C₈	1	1	yes	characteristic
62	C₄²	C₂×C₄×C₅	1	2	yes	—
63	C₄²	C₂×C₄×C₅	1	1	yes	characteristic
64	C₁₆	—	2	1	no	—
65	C₁₆	—	2	2	no	—
66	C₁₆	C₅×Q₈	1	2	yes	complemented
67	C₂×C₅	C₈×Q₈	1	1	yes	characteristic
68	C₂×C₅	C₂×M₃₂	1	1	yes	characteristic
69	C₂×C₅	#504	1	1	yes	characteristic
70	Q₈	—	2	2	no	—
71	C₂×C₄	C₂×C₅×C₈	1	2	yes	—
72	C₂×C₄	C₂×C₅×C₈	1	1	yes	characteristic
73	C₂×C₄	C₂×C₅×C₈	1	2	yes	—
74	C₂×C₄	C₂×C₅×C₈	1	1	yes	characteristic
75	C₂×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
76	C₈	—	2	1	no	—
77	C₈	—	2	2	no	—
78	C₈	C₂×C₅×Q₈	1	1	yes	characteristic
79	C₈	C₅×#41	1	1	yes	characteristic
80	C₅	#2183	1	1	yes	characteristic, direct product factor, Sylow
81	C₂²	C₂²×C₅×C₈	1	1	yes	characteristic
82	C₄	—	2	2	no	—
83	C₄	—	2	2	no	—
84	C₄	—	2	1	no	—
85	C₄	C₅×M₃₂	1	2	yes	—
86	C₄	C₄×C₅×Q₈	1	1	yes	characteristic
87	C₄	C₅×#131	1	1	yes	characteristic
88	C₂	C₅×C₈×Q₈	1	1	yes	characteristic
89	C₂	C₂×C₅×M₃₂	1	1	yes	characteristic
90	C₂	C₅×#504	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
14. #2183	C₅	direct (N × H)
25. C₅×C₁₆	Q₈	semidirect
66. C₁₆	C₅×Q₈	semidirect
80. C₅	#2183	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₈×Q₈	2
C₅×C₄⋊C₁₆	2
C₅×#346	2
C₄×C₅×C₁₆	2
#2183	5

Subgroups — C5×#2183 #10603691

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#2183 #10603691