Subgroups — C₅⋊(C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)) #34093046

Order 19950.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₁₉×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊D₆₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)	—	5	6	no	maximal
4	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₃×C₅⋊D₉₅	—	7	1	no	maximal, Hall
6	C₅×C₁₉×ΓL(1,𝔽₈)	D₅	1	6	yes	complemented
7	C₃×C₅²×C₁₉	—	7	1	no	Hall
8	D₆₆₅	—	5	6	no	—
9	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	19	1	no	maximal, Hall
10	C₅⋊D₉₅	—	7	1	no	Hall
11	ΓL(1,𝔽₈)⋊D₁₉	—	25	1	no	Hall
12	C₅×C₇×C₁₉	C₃×D₅	1	6	yes	complemented
13	C₃×D₉₅	—	35	6	no	—
14	C₅²×ΓL(1,𝔽₈)	D₁₉	1	1	yes	characteristic, complemented, Hall
15	C₅²×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
16	C₁₉×ΓL(1,𝔽₈)	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
17	C₅⋊D₃₅	—	19	1	no	Hall
18	C₃×C₅×C₁₉	—	7	6	no	—
19	D₁₃₃	—	25	1	no	Hall
20	C₅⋊AGL(1,𝔽₇)	—	95	6	no	—
21	D₉₅	—	35	6	no	—
22	C₅²×C₇	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅⋊D₅	—	133	1	no	Hall
24	C₇×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
25	C₃×D₁₉	—	175	1	no	Hall
26	C₅×ΓL(1,𝔽₈)	D₉₅	1	6	yes	complemented
27	C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	1	6	yes	complemented
28	C₃×C₅²	—	7	1	no	Hall
29	D₃₅	—	95	6	no	—
30	C₃×C₁₉	—	7	1	no	Hall
31	C₅⋊D₅	—	133	1	no	Hall
32	AGL(1,𝔽₇)	—	475	1	no	Hall
33	D₁₉	—	175	1	no	Hall
34	C₅×C₇	C₃×D₉₅	1	6	yes	complemented
35	C₃×D₅	—	665	6	no	—
36	C₅²	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
37	ΓL(1,𝔽₈)	C₅⋊D₉₅	1	1	yes	characteristic, complemented, Hall
38	C₁₉	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	7	6	no	—
40	D₇	—	475	1	no	Hall
41	D₅	—	665	6	no	—
42	C₇	C₃×C₅⋊D₉₅	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	3325	1	no	Hall
44	C₅	C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)	1	6	yes	complemented
45	C₃	—	7	1	no	Sylow
46	C₂	—	3325	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅²×C₇×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₅²×C₁₉×ΓL(1,𝔽₈)	C₂	semidirect
2. C₅⋊D₆₆₅	C₃	semidirect
4. C₅²×C₇×C₁₉	C₂×C₃	semidirect
6. C₅×C₁₉×ΓL(1,𝔽₈)	D₅	semidirect
12. C₅×C₇×C₁₉	C₃×D₅	semidirect
14. C₅²×ΓL(1,𝔽₈)	D₁₉	semidirect
15. C₅²×C₁₉	AGL(1,𝔽₇)	semidirect
16. C₁₉×ΓL(1,𝔽₈)	C₅⋊D₅	semidirect
22. C₅²×C₇	C₃×D₁₉	semidirect
24. C₇×C₁₉	C₃×C₅⋊D₅	semidirect
26. C₅×ΓL(1,𝔽₈)	D₉₅	semidirect
27. C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	semidirect
34. C₅×C₇	C₃×D₉₅	semidirect
36. C₅²	ΓL(1,𝔽₈)⋊D₁₉	semidirect
37. ΓL(1,𝔽₈)	C₅⋊D₉₅	semidirect
38. C₁₉	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
42. C₇	C₃×C₅⋊D₉₅	semidirect
44. C₅	C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅²×C₁₉×ΓL(1,𝔽₈)	2
C₅⋊D₆₆₅	3
C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)	5
C₃×C₅⋊D₉₅	7
C₅⋊(C₅⋊AGL(1,𝔽₇))	19

Subgroups — C5⋊(C5⋊(ΓL(1,𝔽8)⋊D19)) #34093046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊(C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)) #34093046