Subgroups — C₅×#478 #65641

Order 320.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
3	C₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#102	C₂	1	1	yes	maximal, characteristic
7	C₅×#102	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂²×C₄×C₅	—	2	1	no	—
10	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₅×C₄⋊C₄	—	2	1	no	—
13	C₅×C₄⋊C₄	—	2	1	no	—
14	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₅×C₂²⋊C₄	—	2	1	no	—
18	C₄²×C₅	C₂²	1	1	yes	characteristic
19	#478	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂³×C₅	—	2	1	no	—
21	C₅×D₄	—	2	1	no	—
22	C₅×D₄	Q₈	1	2	yes	—
23	C₂×C₄×C₅	—	2	1	no	—
24	C₂×C₄×C₅	—	2	1	no	—
25	C₂×C₄×C₅	—	2	1	no	—
26	C₂×C₄×C₅	—	4	2	no	—
27	C₂×C₄×C₅	D₄	1	1	yes	characteristic
28	C₂×C₄×C₅	D₄	1	1	yes	characteristic
29	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
30	C₅×C₈	—	2	1	no	—
31	C₅×C₈	—	2	1	no	—
32	#125	C₂×C₅	1	1	yes	characteristic, complemented
33	C₄×D₄	C₂×C₅	1	1	yes	characteristic
34	#107	C₂×C₅	1	1	yes	characteristic, complemented
35	#106	C₂×C₅	1	1	yes	characteristic, complemented
36	C₄⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
37	#102	C₂×C₅	1	1	yes	characteristic
38	#102	C₂×C₅	1	1	yes	characteristic
39	C₂²×C₅	—	2	2	no	—
40	C₂²×C₅	—	4	1	no	—
41	C₂²×C₅	—	4	1	no	—
42	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
43	C₄×C₅	—	2	1	no	—
44	C₄×C₅	—	2	1	no	—
45	C₄×C₅	—	4	1	no	—
46	C₄×C₅	—	4	1	no	—
47	C₄×C₅	—	4	1	no	—
48	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
49	C₄×C₅	#41	1	1	yes	characteristic
50	C₂×D₄	C₂²×C₅	1	1	yes	characteristic
51	C₂²×C₄	—	2	1	no	—
52	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
53	C₂×C₈	C₂²×C₅	1	1	yes	characteristic
54	C₄⋊C₄	—	2	1	no	—
55	C₄⋊C₄	—	2	1	no	—
56	C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
57	C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
58	C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
59	C₂²⋊C₄	—	2	1	no	—
60	C₄²	C₂²×C₅	1	1	yes	characteristic
61	C₂×C₅	—	4	2	no	—
62	C₂×C₅	C₂²⋊Q₈	1	1	yes	characteristic
63	C₂×C₅	#135	1	1	yes	characteristic
64	C₂×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
65	C₂³	—	2	1	no	—
66	D₄	—	2	1	no	—
67	D₄	C₅×Q₈	1	2	yes	—
68	C₂×C₄	—	2	1	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	—	2	1	no	—
71	C₂×C₄	—	4	2	no	—
72	C₂×C₄	C₅×D₄	1	1	yes	characteristic
73	C₂×C₄	C₅×D₄	1	1	yes	characteristic
74	C₂×C₄	C₂³×C₅	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	2	1	no	—
77	C₅	#478	1	1	yes	characteristic, direct product factor, Sylow
78	C₂²	—	2	2	no	—
79	C₂²	—	4	1	no	—
80	C₂²	—	4	1	no	—
81	C₂²	C₂×C₅×D₄	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	4	1	no	—
86	C₄	—	4	1	no	—
87	C₄	C₂×C₅×Q₈	1	1	yes	characteristic
88	C₄	C₅×#41	1	1	yes	characteristic
89	C₂	—	4	2	no	—
90	C₂	C₅×C₂²⋊Q₈	1	1	yes	characteristic
91	C₂	C₅×#135	1	1	yes	characteristic
92	C₂	C₅×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₅
prime radical	C₂×C₅×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#125	C₂	semidirect
3. C₅×#107	C₂	semidirect
4. C₅×#106	C₂	semidirect
5. C₅×C₄⋊C₈	C₂	semidirect
19. #478	C₅	direct (N × H)
32. #125	C₂×C₅	semidirect
34. #107	C₂×C₅	semidirect
35. #106	C₂×C₅	semidirect
36. C₄⋊C₈	C₂×C₅	semidirect
77. C₅	#478	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×#125	2
C₄×C₅×D₄	2
C₅×#107	2
C₅×#106	2
C₅×C₄⋊C₈	2
C₅×#102	2
#478	5

Subgroups — C5×#478 #65641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#478 #65641