Subgroups — C₁₉×#11744621 #30685515

Order 17100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×C₃⋊D₇₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₉×C₂₅	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₉×#4380	—	5	1	no	maximal
4	C₁₉×D₇₅	—	6	2	no	—
5	C₁₉×#1035	—	9	1	no	maximal, Hall
6	C₁₉×C₃⋊D₁₅	—	5	1	no	—
7	C₃×C₁₉×C₂₅	—	2	2	no	—
8	C₁₉×D₂₅	—	9	1	no	—
9	#11744621	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₃²×C₅×C₁₉	AGL(1,𝔽₅)	1	1	yes	characteristic
11	C₁₉×#157	—	25	1	no	Hall
12	C₁₉×D₁₅	—	30	2	no	—
13	C₁₉×C₂₅	#157	1	1	yes	characteristic, complemented, Hall
14	C₃⋊D₇₅	C₂×C₁₉	1	1	yes	characteristic
15	C₁₉×AGL(1,𝔽₅)	—	45	1	no	—
16	C₃⋊D₃×C₁₉	—	25	1	no	—
17	C₃×C₅×C₁₉	—	2	2	no	—
18	C₃²×C₂₅	C₄×C₁₉	1	1	yes	characteristic, complemented, Hall
19	D₅×C₁₉	—	45	1	no	—
20	#4380	—	5	1	no	—
21	C₃²×C₁₉	#1035	1	1	yes	characteristic, complemented, Hall
22	D₇₅	—	6	2	no	—
23	D₃×C₁₉	—	150	2	no	—
24	#1035	—	9	1	no	Hall
25	C₅×C₁₉	#4380	1	1	yes	characteristic
26	C₃⋊D₁₅	—	5	1	no	—
27	C₄×C₁₉	—	225	1	no	Hall
28	C₃×C₂₅	—	2	2	no	—
29	C₃×C₁₉	—	2	2	no	—
30	D₂₅	—	9	1	no	—
31	C₃²×C₅	C₁₉×AGL(1,𝔽₅)	1	1	yes	characteristic
32	C₂×C₁₉	—	225	1	no	—
33	#157	—	25	1	no	Hall
34	D₁₅	—	30	2	no	—
35	C₂₅	C₁₉×#157	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	45	1	no	—
37	C₁₉	#11744621	1	1	yes	characteristic, direct product factor, Sylow
38	C₃⋊D₃	—	25	1	no	—
39	C₃×C₅	—	2	2	no	—
40	D₅	—	45	1	no	—
41	C₃²	C₁₉×#1035	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	150	2	no	—
43	C₅	C₁₉×#4380	1	1	yes	characteristic
44	C₄	—	225	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₁₉	#11744621
commutator, hypocenter	C₃²×C₂₅	C₄×C₁₉
Frattini	C₅	C₁₉×#4380
Fitting	C₃²×C₁₉×C₂₅	C₄
socle	C₃²×C₅×C₁₉	AGL(1,𝔽₅)
prime radical	C₁₉×C₃⋊D₇₅	C₂
cosocle	C₃⋊D₇₅	C₂×C₁₉
LCS	G ▷ C₃²×C₂₅
UCS	C₁ ◁ C₁₉

Complements

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

N	H ≅ G/N	type
2. C₃²×C₁₉×C₂₅	C₄	semidirect
9. #11744621	C₁₉	direct (N × H)
13. C₁₉×C₂₅	#157	semidirect
18. C₃²×C₂₅	C₄×C₁₉	semidirect
21. C₃²×C₁₉	#1035	semidirect
35. C₂₅	C₁₉×#157	semidirect
37. C₁₉	#11744621	direct (N × H)
41. C₃²	C₁₉×#1035	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×C₃⋊D₇₅	2
C₁₉×#4380	5
C₁₉×#1035	9
#11744621	19

Subgroups — C19×#11744621 #30685515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11744621 #30685515