Subgroups — C₅×ΓL(1,𝔽₈₁) #13100038

Order 1600.

89 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3995	C₂	1	1	yes	maximal, characteristic
2	C₅×#3993	C₂	1	1	yes	maximal, characteristic
3	C₅×#3930	C₂	1	1	yes	maximal, characteristic
4	C₅×C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
5	C₅×#700	—	2	1	no	—
6	C₅×C₈×D₅	C₂²	1	1	yes	characteristic
7	C₅²×C₁₆	C₄	1	1	yes	characteristic, complemented
8	C₅×#672	C₄	1	1	yes	characteristic, complemented
9	ΓL(1,𝔽₈₁)	C₅	1	1	yes	maximal, characteristic, direct product factor
10	C₅×#365	—	5	1	no	maximal
11	C₂×C₅×AGL(1,𝔽₅)	—	4	1	no	—
12	C₄×C₅×D₅	D₄	1	1	yes	characteristic
13	C₅×#170	—	4	1	no	—
14	C₅²×C₈	C₂×C₄	1	1	yes	characteristic
15	C₅×#168	Q₈	1	1	yes	characteristic
16	#3995	C₂×C₅	1	1	yes	characteristic
17	#3993	C₂×C₅	1	1	yes	characteristic
18	C₅×M₃₂	—	5	1	no	—
19	C₅×#108	—	5	1	no	—
20	C₅×#106	—	5	1	no	—
21	#3930	C₂×C₅	1	1	yes	characteristic
22	C₂×C₅×D₅	SD₁₆	1	1	yes	characteristic
23	C₅×AGL(1,𝔽₅)	—	8	1	no	—
24	C₄×C₅²	C₄⋊C₄	1	1	yes	characteristic
25	C₅×Dic₅	SD₁₆	1	1	yes	characteristic
26	C₄⋊AGL(1,𝔽₅)	—	2	1	no	—
27	#700	—	2	1	no	—
28	C₅×M₁₆	—	10	1	no	—
29	C₂×C₅×C₈	—	5	1	no	—
30	C₅×C₄⋊C₄	—	10	1	no	—
31	C₈×D₅	C₂²×C₅	1	1	yes	characteristic
32	C₅×C₁₆	—	4	1	no	—
33	C₅×C₁₆	—	5	1	no	—
34	C₅×C₁₆	C₄×C₅	1	1	yes	characteristic, complemented
35	C₅×C₁₆	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
36	#672	C₄×C₅	1	1	yes	characteristic, complemented
37	#365	—	5	1	no	Sylow
38	C₂×C₅²	#106	1	1	yes	characteristic
39	C₅×D₅	—	2	1	no	—
40	C₂×AGL(1,𝔽₅)	—	4	1	no	—
41	C₂×C₄×C₅	—	5	1	no	—
42	C₂×C₄×C₅	—	20	1	no	—
43	C₄×D₅	C₅×D₄	1	1	yes	characteristic
44	#170	—	4	1	no	—
45	C₅×C₈	—	4	1	no	—
46	C₅×C₈	—	5	1	no	—
47	C₅×C₈	—	20	1	no	—
48	C₅×C₈	C₂×C₄×C₅	1	1	yes	characteristic
49	C₅×C₈	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
50	#168	C₅×Q₈	1	1	yes	characteristic
51	M₃₂	—	5	1	no	—
52	#108	—	5	1	no	—
53	#106	—	5	1	no	—
54	C₅²	#365	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₅	—	5	1	no	—
56	C₂×D₅	C₅×SD₁₆	1	1	yes	characteristic
57	AGL(1,𝔽₅)	—	8	1	no	—
58	C₄×C₅	—	4	1	no	—
59	C₄×C₅	—	5	1	no	—
60	C₄×C₅	—	40	1	no	—
61	C₄×C₅	C₅×C₄⋊C₄	1	1	yes	characteristic
62	C₄×C₅	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
63	Dic₅	C₅×SD₁₆	1	1	yes	characteristic
64	M₁₆	—	10	1	no	—
65	C₂×C₈	—	5	1	no	—
66	C₄⋊C₄	—	10	1	no	—
67	C₁₆	—	5	1	no	—
68	C₁₆	C₅×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
69	C₂×C₅	—	4	1	no	—
70	C₂×C₅	—	10	1	no	—
71	C₂×C₅	C₅×#106	1	1	yes	characteristic
72	C₂×C₅	#3993	1	1	yes	characteristic
73	D₅	—	2	1	no	—
74	C₂×C₄	—	5	1	no	—
75	C₂×C₄	—	20	1	no	—
76	C₈	—	5	1	no	—
77	C₈	—	20	1	no	—
78	C₈	C₂×C₅×AGL(1,𝔽₅)	1	1	yes	characteristic
79	C₅	—	4	1	no	—
80	C₅	C₅×#365	1	1	yes	characteristic, complemented
81	C₅	ΓL(1,𝔽₈₁)	1	1	yes	characteristic, direct product factor
82	C₂²	—	5	1	no	—
83	C₄	—	5	1	no	—
84	C₄	—	40	1	no	—
85	C₄	C₅×C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
86	C₂	—	10	1	no	—
87	C₂	C₅×#3993	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₅	#3993
commutator	C₅×C₈	C₂×C₄×C₅
Frattini	C₈	C₂×C₅×AGL(1,𝔽₅)
Fitting	C₅²×C₁₆	C₄
socle	C₂×C₅²	#106
prime radical	C₂×C₅×D₅	SD₁₆
cosocle	C₈×D₅	C₂²×C₅
hypercenter	C₅×C₁₆	AGL(1,𝔽₅)
hypocenter	C₅	C₅×#365
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
7. C₅²×C₁₆	C₄	semidirect
8. C₅×#672	C₄	semidirect
9. ΓL(1,𝔽₈₁)	C₅	direct (N × H)
34. C₅×C₁₆	C₄×C₅	semidirect
35. C₅×C₁₆	AGL(1,𝔽₅)	semidirect
36. #672	C₄×C₅	semidirect
54. C₅²	#365	semidirect
68. C₁₆	C₅×AGL(1,𝔽₅)	semidirect
80. C₅	C₅×#365	semidirect
81. C₅	ΓL(1,𝔽₈₁)	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×#3995	2
C₅×#3993	2
C₅×#3930	2
ΓL(1,𝔽₈₁)	5
C₅×#365	5

Subgroups — C5×ΓL(1,𝔽81) #13100038

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×ΓL(1,𝔽₈₁) #13100038