Subgroups — C₂×C₅⋊(ΓL(1,𝔽₈)⋊D₈₉) #49153155

Order 37380.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(ΓL(1,𝔽₈)⋊D₈₉)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×ΓL(1,𝔽₈)×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₁₁₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×ΓL(1,𝔽₈)×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×ΓL(1,𝔽₈)⋊D₈₉	—	5	1	no	maximal, Hall
6	D₃₁₁₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₇×C₈₉	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×D₄₄₅	—	7	1	no	maximal, Hall
9	ΓL(1,𝔽₈)⋊D₈₉	—	5	2	no	—
10	C₂×ΓL(1,𝔽₈)×C₈₉	D₅	1	1	yes	characteristic, complemented
11	C₅×C₇×C₈₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₃×D₄₄₅	—	7	2	no	—
13	C₂×C₃×C₅×C₈₉	—	7	1	no	—
14	C₂×D₆₂₃	—	5	1	no	Hall
15	ΓL(1,𝔽₈)×C₈₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₄₄₅	—	7	1	no	Hall
17	C₃×C₅×C₈₉	—	7	1	no	Hall
18	C₂×C₇×C₈₉	C₃×D₅	1	1	yes	characteristic, complemented
19	D₆₂₃	—	5	2	no	—
20	C₂×C₃×D₈₉	—	35	1	no	Hall
21	C₂×C₅×C₈₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
22	D₄₄₅	—	7	2	no	—
23	C₇×C₈₉	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₈₉	—	7	1	no	—
25	C₃×D₈₉	—	35	2	no	—
26	C₅×C₈₉	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
27	C₂×C₅⋊AGL(1,𝔽₇)	—	89	1	no	maximal, Hall
28	C₂×D₈₉	—	35	1	no	Hall
29	C₃×C₈₉	—	7	1	no	Hall
30	C₂×C₅×ΓL(1,𝔽₈)	D₈₉	1	1	yes	characteristic, complemented
31	C₅⋊AGL(1,𝔽₇)	—	89	2	no	—
32	C₂×C₈₉	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
33	D₈₉	—	35	2	no	—
34	C₂×D₃₅	—	89	1	no	Hall
35	C₅×ΓL(1,𝔽₈)	C₂×D₈₉	1	1	yes	characteristic, complemented, Hall
36	C₈₉	C₂×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
37	C₂×AGL(1,𝔽₇)	—	445	1	no	Hall
38	C₂×C₅×C₇	C₃×D₈₉	1	1	yes	characteristic, complemented
39	D₃₅	—	89	2	no	—
40	C₂×C₃×D₅	—	623	1	no	Hall
41	C₂×ΓL(1,𝔽₈)	D₄₄₅	1	1	yes	characteristic, complemented
42	AGL(1,𝔽₇)	—	445	2	no	—
43	C₅×C₇	C₂×C₃×D₈₉	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅	—	7	1	no	—
45	C₃×D₅	—	623	2	no	—
46	C₂×D₇	—	445	1	no	Hall
47	ΓL(1,𝔽₈)	C₂×D₄₄₅	1	1	yes	characteristic, complemented, Hall
48	C₂×D₅	—	623	1	no	Hall
49	C₃×C₅	—	7	1	no	Hall
50	C₂×C₇	C₃×D₄₄₅	1	1	yes	characteristic, complemented
51	D₇	—	445	2	no	—
52	C₂²×C₃	—	3115	1	no	Hall
53	C₂×C₅	ΓL(1,𝔽₈)⋊D₈₉	1	1	yes	characteristic, complemented
54	D₅	—	623	2	no	—
55	C₇	C₂×C₃×D₄₄₅	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	7	1	no	—
57	C₂×C₃	—	3115	2	no	—
58	C₅	C₂×ΓL(1,𝔽₈)⋊D₈₉	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	3115	1	no	Sylow
60	C₃	—	7	1	no	Sylow
61	C₂	—	3115	2	no	—
62	C₂	C₅⋊(ΓL(1,𝔽₈)⋊D₈₉)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(ΓL(1,𝔽₈)⋊D₈₉)
commutator, cosocle, hypocenter	C₅×C₇×C₈₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₈₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₈₉
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊(ΓL(1,𝔽₈)⋊D₈₉)	C₂	direct (N × H)
2. C₂×C₅×ΓL(1,𝔽₈)×C₈₉	C₂	semidirect
3. C₂×D₃₁₁₅	C₃	semidirect
4. C₅×ΓL(1,𝔽₈)×C₈₉	C₂²	semidirect
6. D₃₁₁₅	C₂×C₃	semidirect
7. C₂×C₅×C₇×C₈₉	C₂×C₃	semidirect
10. C₂×ΓL(1,𝔽₈)×C₈₉	D₅	semidirect
11. C₅×C₇×C₈₉	C₂²×C₃	semidirect
15. ΓL(1,𝔽₈)×C₈₉	C₂×D₅	semidirect
18. C₂×C₇×C₈₉	C₃×D₅	semidirect
21. C₂×C₅×C₈₉	AGL(1,𝔽₇)	semidirect
23. C₇×C₈₉	C₂×C₃×D₅	semidirect
26. C₅×C₈₉	C₂×AGL(1,𝔽₇)	semidirect
30. C₂×C₅×ΓL(1,𝔽₈)	D₈₉	semidirect
32. C₂×C₈₉	C₅⋊AGL(1,𝔽₇)	semidirect
35. C₅×ΓL(1,𝔽₈)	C₂×D₈₉	semidirect
36. C₈₉	C₂×C₅⋊AGL(1,𝔽₇)	semidirect
38. C₂×C₅×C₇	C₃×D₈₉	semidirect
41. C₂×ΓL(1,𝔽₈)	D₄₄₅	semidirect
43. C₅×C₇	C₂×C₃×D₈₉	semidirect
47. ΓL(1,𝔽₈)	C₂×D₄₄₅	semidirect
50. C₂×C₇	C₃×D₄₄₅	semidirect
53. C₂×C₅	ΓL(1,𝔽₈)⋊D₈₉	semidirect
55. C₇	C₂×C₃×D₄₄₅	semidirect
58. C₅	C₂×ΓL(1,𝔽₈)⋊D₈₉	semidirect
62. C₂	C₅⋊(ΓL(1,𝔽₈)⋊D₈₉)	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⋊(ΓL(1,𝔽₈)⋊D₈₉)	2
C₂×C₅×ΓL(1,𝔽₈)×C₈₉	2
C₂×D₃₁₁₅	3
C₂×ΓL(1,𝔽₈)⋊D₈₉	5
C₂×C₃×D₄₄₅	7
C₂×C₅⋊AGL(1,𝔽₇)	89

Subgroups — C2×C5⋊(ΓL(1,𝔽8)⋊D89) #49153155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊(ΓL(1,𝔽₈)⋊D₈₉) #49153155