Subgroups — C₂×C₅⋊(ΓL(1,𝔽₈)⋊D₃₇) #29509643

Order 15540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(ΓL(1,𝔽₈)⋊D₃₇)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×ΓL(1,𝔽₈)×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₂₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×ΓL(1,𝔽₈)×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×ΓL(1,𝔽₈)⋊D₃₇	—	5	1	no	maximal, Hall
6	D₁₂₉₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₇×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented
8	C₂×C₃×D₁₈₅	—	7	1	no	maximal, Hall
9	C₂×ΓL(1,𝔽₈)×C₃₇	D₅	1	1	yes	characteristic, complemented
10	ΓL(1,𝔽₈)⋊D₃₇	—	5	2	no	—
11	C₅×C₇×C₃₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₅×C₃₇	—	14	1	no	—
13	C₃×D₁₈₅	—	7	2	no	—
14	C₂×D₂₅₉	—	5	1	no	Hall
15	ΓL(1,𝔽₈)×C₃₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×D₁₈₅	—	7	1	no	Hall
17	C₃×C₅×C₃₇	—	14	1	no	Hall
18	C₂×C₇×C₃₇	C₃×D₅	1	1	yes	characteristic, complemented
19	D₂₅₉	—	5	2	no	—
20	C₂×C₃×D₃₇	—	35	1	no	Hall
21	C₂×C₅⋊AGL(1,𝔽₇)	—	37	1	no	maximal, Hall
22	C₂×C₅×C₃₇	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
23	D₁₈₅	—	7	2	no	—
24	C₇×C₃₇	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃×C₃₇	—	14	1	no	—
26	C₃×D₃₇	—	35	2	no	—
27	C₂×C₅×ΓL(1,𝔽₈)	D₃₇	1	1	yes	characteristic, complemented
28	C₅⋊AGL(1,𝔽₇)	—	37	2	no	—
29	C₅×C₃₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
30	C₂×D₃₇	—	35	1	no	Hall
31	C₂×D₃₅	—	37	1	no	Hall
32	C₃×C₃₇	—	14	1	no	Hall
33	C₅×ΓL(1,𝔽₈)	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
34	C₂×AGL(1,𝔽₇)	—	185	1	no	Hall
35	C₂×C₃₇	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
36	D₃₇	—	35	2	no	—
37	C₂×C₅×C₇	C₃×D₃₇	1	1	yes	characteristic, complemented
38	D₃₅	—	37	2	no	—
39	C₂×C₃×D₅	—	259	1	no	Hall
40	C₂×ΓL(1,𝔽₈)	D₁₈₅	1	1	yes	characteristic, complemented
41	AGL(1,𝔽₇)	—	185	2	no	—
42	C₃₇	C₂×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
43	C₅×C₇	C₂×C₃×D₃₇	1	1	yes	characteristic, complemented, Hall
44	C₂×C₃×C₅	—	14	1	no	—
45	C₃×D₅	—	259	2	no	—
46	C₂×D₇	—	185	1	no	Hall
47	ΓL(1,𝔽₈)	C₂×D₁₈₅	1	1	yes	characteristic, complemented, Hall
48	C₂×D₅	—	259	1	no	Hall
49	C₃×C₅	—	14	1	no	Hall
50	C₂×C₇	C₃×D₁₈₅	1	1	yes	characteristic, complemented
51	D₇	—	185	2	no	—
52	C₂²×C₃	—	1295	1	no	Hall
53	C₂×C₅	ΓL(1,𝔽₈)⋊D₃₇	1	1	yes	characteristic, complemented
54	D₅	—	259	2	no	—
55	C₇	C₂×C₃×D₁₈₅	1	1	yes	characteristic, complemented, Sylow
56	C₂×C₃	—	14	1	no	—
57	C₂×C₃	—	1295	2	no	—
58	C₅	C₂×ΓL(1,𝔽₈)⋊D₃₇	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	1295	1	no	Sylow
60	C₃	—	14	1	no	Sylow
61	C₂	—	1295	2	no	—
62	C₂	C₅⋊(ΓL(1,𝔽₈)⋊D₃₇)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(ΓL(1,𝔽₈)⋊D₃₇)
commutator, cosocle, hypocenter	C₅×C₇×C₃₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₃₇	C₂×C₃
LCS	G ▷ C₅×C₇×C₃₇
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊(ΓL(1,𝔽₈)⋊D₃₇)	C₂	direct (N × H)
2. C₂×C₅×ΓL(1,𝔽₈)×C₃₇	C₂	semidirect
3. C₂×D₁₂₉₅	C₃	semidirect
4. C₅×ΓL(1,𝔽₈)×C₃₇	C₂²	semidirect
6. D₁₂₉₅	C₂×C₃	semidirect
7. C₂×C₅×C₇×C₃₇	C₂×C₃	semidirect
9. C₂×ΓL(1,𝔽₈)×C₃₇	D₅	semidirect
11. C₅×C₇×C₃₇	C₂²×C₃	semidirect
15. ΓL(1,𝔽₈)×C₃₇	C₂×D₅	semidirect
18. C₂×C₇×C₃₇	C₃×D₅	semidirect
22. C₂×C₅×C₃₇	AGL(1,𝔽₇)	semidirect
24. C₇×C₃₇	C₂×C₃×D₅	semidirect
27. C₂×C₅×ΓL(1,𝔽₈)	D₃₇	semidirect
29. C₅×C₃₇	C₂×AGL(1,𝔽₇)	semidirect
33. C₅×ΓL(1,𝔽₈)	C₂×D₃₇	semidirect
35. C₂×C₃₇	C₅⋊AGL(1,𝔽₇)	semidirect
37. C₂×C₅×C₇	C₃×D₃₇	semidirect
40. C₂×ΓL(1,𝔽₈)	D₁₈₅	semidirect
42. C₃₇	C₂×C₅⋊AGL(1,𝔽₇)	semidirect
43. C₅×C₇	C₂×C₃×D₃₇	semidirect
47. ΓL(1,𝔽₈)	C₂×D₁₈₅	semidirect
50. C₂×C₇	C₃×D₁₈₅	semidirect
53. C₂×C₅	ΓL(1,𝔽₈)⋊D₃₇	semidirect
55. C₇	C₂×C₃×D₁₈₅	semidirect
58. C₅	C₂×ΓL(1,𝔽₈)⋊D₃₇	semidirect
62. C₂	C₅⋊(ΓL(1,𝔽₈)⋊D₃₇)	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)⋊D₃₇)	2
C₂×C₅×ΓL(1,𝔽₈)×C₃₇	2
C₂×D₁₂₉₅	3
C₂×ΓL(1,𝔽₈)⋊D₃₇	5
C₂×C₃×D₁₈₅	7
C₂×C₅⋊AGL(1,𝔽₇)	37

Subgroups — C2×C5⋊(ΓL(1,𝔽8)⋊D37) #29509643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊(ΓL(1,𝔽₈)⋊D₃₇) #29509643