Subgroups — C₅×#64849 #13100040

Order 1600.

97 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3994	C₂	1	2	yes	maximal
2	C₅×D₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₅×C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
4	C₅×C₈×D₅	C₂²	1	1	yes	characteristic
5	C₅²×C₁₆	C₄	1	1	yes	characteristic, complemented
6	C₅×#672	C₄	1	1	yes	characteristic, complemented
7	#64849	C₅	1	1	yes	maximal, characteristic, direct product factor
8	C₅×#366	—	5	1	no	maximal
9	C₂×C₅×AGL(1,𝔽₅)	—	4	2	no	—
10	C₄×C₅×D₅	D₄	1	1	yes	characteristic
11	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
12	C₅×#168	Q₈	1	1	yes	characteristic
13	#3994	C₂×C₅	1	2	yes	—
14	C₂×C₅×C₁₆	—	5	1	no	—
15	C₅×#107	—	5	2	no	—
16	D₅×C₁₆	C₂×C₅	1	1	yes	characteristic
17	C₂×C₅×D₅	D₈	1	1	yes	characteristic
18	C₅×AGL(1,𝔽₅)	—	8	2	no	—
19	C₄×C₅²	C₄⋊C₄	1	1	yes	characteristic
20	C₅×Dic₅	Q₁₆	1	1	yes	characteristic
21	C₄⋊AGL(1,𝔽₅)	—	2	2	no	—
22	C₂×C₅×C₈	—	5	1	no	—
23	C₅×C₄⋊C₄	—	10	2	no	—
24	C₈×D₅	C₂²×C₅	1	1	yes	characteristic
25	C₅×C₁₆	—	4	1	no	—
26	C₅×C₁₆	—	5	1	no	—
27	C₅×C₁₆	C₄×C₅	1	1	yes	characteristic, complemented
28	C₅×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
29	#672	C₄×C₅	1	1	yes	characteristic, complemented
30	#366	—	5	1	no	Sylow
31	C₂×C₅²	#107	1	1	yes	characteristic
32	C₅×D₅	D₁₆	1	1	yes	characteristic
33	C₅×D₅	Q₃₂	1	1	yes	characteristic
34	C₂×AGL(1,𝔽₅)	—	4	2	no	—
35	C₂×C₄×C₅	—	5	1	no	—
36	C₂×C₄×C₅	—	20	2	no	—
37	C₄×D₅	C₅×D₄	1	1	yes	characteristic
38	C₅×C₈	—	4	1	no	—
39	C₅×C₈	—	5	1	no	—
40	C₅×C₈	C₂×C₄×C₅	1	1	yes	characteristic
41	C₅×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
42	#168	C₅×Q₈	1	1	yes	characteristic
43	C₂×C₁₆	—	5	1	no	—
44	#107	—	5	2	no	—
45	C₅²	#366	1	1	yes	characteristic, complemented, Sylow
46	C₂²×C₅	—	5	1	no	—
47	C₂×D₅	C₅×D₈	1	1	yes	characteristic
48	AGL(1,𝔽₅)	—	8	2	no	—
49	C₄×C₅	—	4	1	no	—
50	C₄×C₅	—	5	1	no	—
51	C₄×C₅	—	40	2	no	—
52	C₄×C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
53	C₄×C₅	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
54	Dic₅	C₅×Q₁₆	1	1	yes	characteristic
55	C₂×C₈	—	5	1	no	—
56	C₄⋊C₄	—	10	2	no	—
57	C₁₆	—	5	1	no	—
58	C₁₆	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
59	C₂×C₅	—	4	1	no	—
60	C₂×C₅	—	5	1	no	—
61	C₂×C₅	—	5	1	no	—
62	C₂×C₅	C₅×#107	1	1	yes	characteristic
63	C₂×C₅	#3994	1	1	yes	characteristic
64	D₅	C₅×D₁₆	1	1	yes	characteristic
65	D₅	C₅×Q₃₂	1	1	yes	characteristic
66	C₂×C₄	—	5	1	no	—
67	C₂×C₄	—	20	2	no	—
68	C₈	—	5	1	no	—
69	C₈	C₂×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
70	C₅	—	4	1	no	—
71	C₅	C₅×#366	1	1	yes	characteristic, complemented
72	C₅	#64849	1	1	yes	characteristic, direct product factor
73	C₂²	—	5	1	no	—
74	C₄	—	5	1	no	—
75	C₄	—	40	2	no	—
76	C₄	C₅×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
77	C₂	—	5	1	no	—
78	C₂	—	5	1	no	—
79	C₂	C₅×#3994	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#3994
commutator	C₅×C₈	C₂×C₄×C₅
Frattini	C₈	C₂×C₅×AGL(1,𝔽₅)
Fitting	C₅²×C₁₆	C₄
socle	C₂×C₅²	#107
prime radical	C₂×C₅×D₅	D₈
cosocle	C₈×D₅	C₂²×C₅
hypercenter	C₅×C₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₅×#366
LCS	G ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₅ ◁ C₄×C₅ ◁ C₅×C₈ ◁ C₅×C₁₆

Complements

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

N	H ≅ G/N	type
5. C₅²×C₁₆	C₄	semidirect
6. C₅×#672	C₄	semidirect
7. #64849	C₅	direct (N × H)
27. C₅×C₁₆	C₄×C₅	semidirect
28. C₅×C₁₆	AGL(1,𝔽₅)	semidirect
29. #672	C₄×C₅	semidirect
45. C₅²	#366	semidirect
58. C₁₆	C₅×AGL(1,𝔽₅)	semidirect
71. C₅	C₅×#366	semidirect
72. C₅	#64849	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×#3994	2
C₅×D₅×C₁₆	2
#64849	5
C₅×#366	5

Subgroups — C5×#64849 #13100040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#64849 #13100040