Subgroups — C₁₇×C₁₉×#1044 #44568113

Order 32300.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₁₉×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₇×C₁₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×C₁₉×AGL(1,𝔽₅)	—	5	2	no	maximal
4	D₅×C₁₇×C₁₉	—	5	2	no	—
5	D₅×C₁₇×C₁₉	—	10	2	no	—
6	C₁₉×#1044	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₁₇×#1044	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₁₇×C₁₉	—	2	2	no	—
9	C₅×C₁₇×C₁₉	AGL(1,𝔽₅)	1	2	yes	complemented
10	C₄×C₁₇×C₁₉	—	25	1	no	Hall
11	C₁₉×C₅⋊D₅	C₂×C₁₇	1	1	yes	characteristic
12	C₁₇×C₅⋊D₅	C₂×C₁₉	1	1	yes	characteristic
13	C₂×C₁₇×C₁₉	—	25	1	no	—
14	C₅²×C₁₉	C₄×C₁₇	1	1	yes	characteristic, complemented, Hall
15	C₅²×C₁₇	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
16	C₁₉×AGL(1,𝔽₅)	—	5	2	no	—
17	C₁₇×AGL(1,𝔽₅)	—	5	2	no	—
18	C₁₇×C₁₉	#1044	1	1	yes	characteristic, direct product factor, Hall
19	D₅×C₁₉	—	5	2	no	—
20	D₅×C₁₉	—	10	2	no	—
21	D₅×C₁₇	—	5	2	no	—
22	D₅×C₁₇	—	10	2	no	—
23	#1044	C₁₇×C₁₉	1	1	yes	characteristic, direct product factor, Hall
24	C₅×C₁₉	—	2	2	no	—
25	C₅×C₁₉	C₁₇×AGL(1,𝔽₅)	1	2	yes	complemented
26	C₅×C₁₇	—	2	2	no	—
27	C₅×C₁₇	C₁₉×AGL(1,𝔽₅)	1	2	yes	complemented
28	C₄×C₁₉	—	25	1	no	Hall
29	C₄×C₁₇	—	25	1	no	Hall
30	C₅⋊D₅	C₂×C₁₇×C₁₉	1	1	yes	characteristic
31	C₂×C₁₉	—	25	1	no	—
32	C₂×C₁₇	—	25	1	no	—
33	C₅²	C₄×C₁₇×C₁₉	1	1	yes	characteristic, complemented, Sylow
34	AGL(1,𝔽₅)	—	5	2	no	—
35	C₁₉	C₁₇×#1044	1	1	yes	characteristic, direct product factor, Sylow
36	C₁₇	C₁₉×#1044	1	1	yes	characteristic, direct product factor, Sylow
37	D₅	—	5	2	no	—
38	D₅	—	10	2	no	—
39	C₅	—	2	2	no	—
40	C₅	C₁₇×C₁₉×AGL(1,𝔽₅)	1	2	yes	complemented
41	C₄	—	25	1	no	Sylow
42	C₂	—	25	1	no	—

	subgroup	G/H
center, hypercenter	C₁₇×C₁₉	#1044
commutator, hypocenter	C₅²	C₄×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₅²×C₁₇×C₁₉	C₄
prime radical	C₁₇×C₁₉×C₅⋊D₅	C₂
cosocle	C₅⋊D₅	C₂×C₁₇×C₁₉
LCS	G ▷ C₅²
UCS	C₁ ◁ C₁₇×C₁₉

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₇×C₁₉	C₄	semidirect
6. C₁₉×#1044	C₁₇	direct (N × H)
7. C₁₇×#1044	C₁₉	direct (N × H)
9. C₅×C₁₇×C₁₉	AGL(1,𝔽₅)	semidirect
14. C₅²×C₁₉	C₄×C₁₇	semidirect
15. C₅²×C₁₇	C₄×C₁₉	semidirect
18. C₁₇×C₁₉	#1044	direct (N × H)
23. #1044	C₁₇×C₁₉	direct (N × H)
25. C₅×C₁₉	C₁₇×AGL(1,𝔽₅)	semidirect
27. C₅×C₁₇	C₁₉×AGL(1,𝔽₅)	semidirect
33. C₅²	C₄×C₁₇×C₁₉	semidirect
35. C₁₉	C₁₇×#1044	direct (N × H)
36. C₁₇	C₁₉×#1044	direct (N × H)
40. C₅	C₁₇×C₁₉×AGL(1,𝔽₅)	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₁₉×C₅⋊D₅	2
C₁₇×C₁₉×AGL(1,𝔽₅)	5
C₁₉×#1044	17
C₁₇×#1044	19

Subgroups — C17×C19×#1044 #44568113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₁₉×#1044 #44568113