Subgroups — C₅⋊(C₅⋊#11716325) #34093044

Order 19950.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×#87704	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₉×C₅⋊D₃₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅⋊#11716325	—	5	1	no	maximal
4	C₅⋊#11716325	—	5	5	no	maximal
5	C₅²×C₇×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₅⋊D₅×C₁₉⋊C₃	—	7	1	no	maximal, Hall
7	C₅×#87704	D₅	1	1	yes	characteristic, complemented
8	C₅×#87704	D₅	1	5	yes	complemented
9	C₅²×C₁₉⋊C₃	—	7	1	no	Hall
10	C₁₉×D₃₅	—	5	1	no	—
11	C₁₉×D₃₅	—	5	5	no	—
12	C₅⋊(C₅⋊AGL(1,𝔽₇))	—	19	1	no	maximal, Hall
13	C₁₉×C₅⋊D₅	—	21	1	no	Hall
14	#11716325	—	25	1	no	Hall
15	C₅×C₇×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
16	C₅×C₇×C₁₉	C₃×D₅	1	5	yes	complemented
17	D₅×C₁₉⋊C₃	—	35	1	no	—
18	D₅×C₁₉⋊C₃	—	35	5	no	—
19	C₅²×ΓL(1,𝔽₈)	—	19	1	no	Hall
20	C₅²×C₁₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
21	#87704	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
22	C₅⋊D₃₅	C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₅×C₁₉⋊C₃	—	7	1	no	—
24	C₅×C₁₉⋊C₃	—	7	5	no	—
25	D₇×C₁₉	—	25	1	no	Hall
26	C₅⋊AGL(1,𝔽₇)	—	95	1	no	—
27	C₅⋊AGL(1,𝔽₇)	—	95	5	no	—
28	D₅×C₁₉	—	105	1	no	—
29	D₅×C₁₉	—	105	5	no	—
30	C₅²×C₇	C₂×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅⋊D₅	—	133	1	no	Hall
32	C₇×C₁₉	C₃×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₁₉⋊C₃	—	175	1	no	Hall
34	C₅×ΓL(1,𝔽₈)	—	19	1	no	—
35	C₅×ΓL(1,𝔽₈)	—	19	5	no	—
36	C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
37	C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	1	5	yes	complemented
38	C₃×C₅²	—	133	1	no	Hall
39	D₃₅	—	5	1	no	—
40	D₃₅	—	5	5	no	—
41	C₁₉⋊C₃	—	7	1	no	Hall
42	C₅⋊D₅	—	21	1	no	Hall
43	AGL(1,𝔽₇)	—	475	1	no	Hall
44	C₂×C₁₉	—	525	1	no	Hall
45	C₅×C₇	D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented
46	C₅×C₇	D₅×C₁₉⋊C₃	1	5	yes	complemented
47	C₃×D₅	—	665	1	no	—
48	C₃×D₅	—	665	5	no	—
49	C₅²	#11716325	1	1	yes	characteristic, complemented, Sylow
50	ΓL(1,𝔽₈)	—	19	1	no	Hall
51	C₁₉	C₅⋊(C₅⋊AGL(1,𝔽₇))	1	1	yes	characteristic, complemented, Sylow
52	C₃×C₅	—	133	1	no	—
53	C₃×C₅	—	133	5	no	—
54	D₇	—	25	1	no	Hall
55	D₅	—	35	1	no	—
56	D₅	—	105	5	no	—
57	C₇	C₅⋊D₅×C₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₃	—	3325	1	no	Hall
59	C₅	C₅⋊#11716325	1	1	yes	characteristic, complemented
60	C₅	C₅⋊#11716325	1	5	yes	complemented
61	C₃	—	133	1	no	Sylow
62	C₂	—	525	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×#87704	C₂	semidirect
2. C₁₉×C₅⋊D₃₅	C₃	semidirect
5. C₅²×C₇×C₁₉	C₂×C₃	semidirect
7. C₅×#87704	D₅	semidirect
8. C₅×#87704	D₅	semidirect
15. C₅×C₇×C₁₉	C₃×D₅	semidirect
16. C₅×C₇×C₁₉	C₃×D₅	semidirect
20. C₅²×C₁₉	AGL(1,𝔽₇)	semidirect
21. #87704	C₅⋊D₅	semidirect
22. C₅⋊D₃₅	C₁₉⋊C₃	semidirect
30. C₅²×C₇	C₂×C₁₉⋊C₃	semidirect
32. C₇×C₁₉	C₃×C₅⋊D₅	semidirect
36. C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	semidirect
37. C₅×C₁₉	C₅⋊AGL(1,𝔽₇)	semidirect
45. C₅×C₇	D₅×C₁₉⋊C₃	semidirect
46. C₅×C₇	D₅×C₁₉⋊C₃	semidirect
49. C₅²	#11716325	semidirect
51. C₁₉	C₅⋊(C₅⋊AGL(1,𝔽₇))	semidirect
57. C₇	C₅⋊D₅×C₁₉⋊C₃	semidirect
59. C₅	C₅⋊#11716325	semidirect
60. C₅	C₅⋊#11716325	semidirect

Maximal subgroups

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

subgroup	index
C₅²×#87704	2
C₁₉×C₅⋊D₃₅	3
C₅⋊#11716325	5
C₅⋊D₅×C₁₉⋊C₃	7
C₅⋊(C₅⋊AGL(1,𝔽₇))	19

Subgroups — C5⋊(C5⋊#11716325) #34093044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅⋊(C₅⋊#11716325) #34093044