Subgroups — C₅×C₅⋊(ΓL(1,𝔽₈)⋊D₁₉) #34093030

Order 19950.

80 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)	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×ΓL(1,𝔽₈)⋊D₁₉	—	5	1	no	maximal
5	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×D₉₅	—	7	1	no	maximal, Hall
7	C₅×C₁₉×ΓL(1,𝔽₈)	—	2	2	no	—
8	C₅×C₁₉×ΓL(1,𝔽₈)	D₅	1	1	yes	characteristic, complemented
9	C₅×C₁₉×ΓL(1,𝔽₈)	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×C₅²×C₁₉	—	7	1	no	Hall
11	D₆₆₅	C₃×C₅	1	1	yes	characteristic, complemented
12	C₅×D₁₃₃	—	5	1	no	—
13	C₅×C₅⋊AGL(1,𝔽₇)	—	19	1	no	maximal, Hall
14	C₅×D₉₅	—	7	1	no	Hall
15	ΓL(1,𝔽₈)⋊D₁₉	—	5	1	no	Hall
16	C₅×C₇×C₁₉	—	2	2	no	—
17	C₅×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
18	C₅×C₇×C₁₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	C₃×D₉₅	—	7	1	no	—
20	C₃×C₅×D₁₉	—	35	1	no	—
21	C₅²×ΓL(1,𝔽₈)	D₁₉	1	1	yes	characteristic, complemented, Hall
22	C₅²×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
23	C₁₉×ΓL(1,𝔽₈)	C₅×D₅	1	1	yes	characteristic, complemented, Hall
24	C₅×D₃₅	—	19	1	no	Hall
25	C₃×C₅×C₁₉	—	7	1	no	—
26	C₃×C₅×C₁₉	—	7	1	no	—
27	C₃×C₅×C₁₉	—	14	2	no	—
28	D₁₃₃	—	5	1	no	Hall
29	C₅⋊AGL(1,𝔽₇)	—	19	1	no	—
30	C₅×AGL(1,𝔽₇)	—	95	1	no	—
31	D₉₅	—	21	1	no	—
32	C₅×D₁₉	—	105	1	no	—
33	C₅²×C₇	C₃×D₁₉	1	1	yes	characteristic, complemented, Hall
34	C₃×C₅×D₅	—	133	1	no	Hall
35	C₇×C₁₉	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Hall
36	C₃×D₁₉	—	35	1	no	Hall
37	C₅×ΓL(1,𝔽₈)	—	2	2	no	—
38	C₅×ΓL(1,𝔽₈)	C₅×D₁₉	1	1	yes	characteristic, complemented
39	C₅×ΓL(1,𝔽₈)	D₉₅	1	1	yes	characteristic, complemented
40	C₅×C₁₉	—	2	2	no	—
41	C₅×C₁₉	C₅×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
42	C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
43	C₃×C₅²	—	7	1	no	Hall
44	D₃₅	—	19	1	no	—
45	C₅×D₇	—	95	1	no	—
46	C₃×C₁₉	—	7	1	no	Hall
47	C₅×D₅	—	399	1	no	Hall
48	AGL(1,𝔽₇)	—	95	1	no	Hall
49	D₁₉	—	105	1	no	Hall
50	C₅×C₇	—	2	2	no	—
51	C₅×C₇	C₃×C₅×D₁₉	1	1	yes	characteristic, complemented
52	C₅×C₇	C₃×D₉₅	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅	—	665	1	no	—
54	C₃×D₅	—	133	1	no	—
55	C₅²	ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
56	ΓL(1,𝔽₈)	C₅×D₉₅	1	1	yes	characteristic, complemented, Hall
57	C₁₉	C₅×C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
58	C₃×C₅	—	7	1	no	—
59	C₃×C₅	—	7	1	no	—
60	C₃×C₅	—	14	2	no	—
61	D₇	—	95	1	no	Hall
62	C₂×C₅	—	665	1	no	—
63	D₅	—	133	1	no	—
64	C₇	C₃×C₅×D₉₅	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	665	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₅×ΓL(1,𝔽₈)⋊D₁₉	1	1	yes	characteristic, complemented
68	C₅	C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)	1	1	yes	characteristic, direct product factor
69	C₃	—	7	1	no	Sylow
70	C₂	—	1995	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)
commutator, cosocle, hypocenter	C₅×C₇×C₁₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₁₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₉
UCS	C₁ ◁ C₅

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
3. C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)	C₅	direct (N × H)
5. C₅²×C₇×C₁₉	C₂×C₃	semidirect
8. C₅×C₁₉×ΓL(1,𝔽₈)	D₅	semidirect
9. C₅×C₁₉×ΓL(1,𝔽₈)	C₂×C₅	semidirect
11. D₆₆₅	C₃×C₅	semidirect
17. C₅×C₇×C₁₉	C₃×D₅	semidirect
18. C₅×C₇×C₁₉	C₂×C₃×C₅	semidirect
21. C₅²×ΓL(1,𝔽₈)	D₁₉	semidirect
22. C₅²×C₁₉	AGL(1,𝔽₇)	semidirect
23. C₁₉×ΓL(1,𝔽₈)	C₅×D₅	semidirect
33. C₅²×C₇	C₃×D₁₉	semidirect
35. C₇×C₁₉	C₃×C₅×D₅	semidirect
38. C₅×ΓL(1,𝔽₈)	C₅×D₁₉	semidirect
39. C₅×ΓL(1,𝔽₈)	D₉₅	semidirect
41. C₅×C₁₉	C₅×AGL(1,𝔽₇)	semidirect
42. C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	semidirect
51. C₅×C₇	C₃×C₅×D₁₉	semidirect
52. C₅×C₇	C₃×D₉₅	semidirect
55. C₅²	ΓL(1,𝔽₈)⋊D₁₉	semidirect
56. ΓL(1,𝔽₈)	C₅×D₉₅	semidirect
57. C₁₉	C₅×C₅⋊AGL(1,𝔽₇)	semidirect
64. C₇	C₃×C₅×D₉₅	semidirect
67. C₅	C₅×ΓL(1,𝔽₈)⋊D₁₉	semidirect
68. C₅	C₅⋊(ΓL(1,𝔽₈)⋊D₁₉)	direct (N × H)

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
C₅×ΓL(1,𝔽₈)⋊D₁₉	5
C₃×C₅×D₉₅	7
C₅×C₅⋊AGL(1,𝔽₇)	19

Subgroups — C5×C5⋊(ΓL(1,𝔽8)⋊D19) #34093030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₅⋊(ΓL(1,𝔽₈)⋊D₁₉) #34093030