Subgroups — #30685554

Order 17100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×(C₅⋊D₅)⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉⋊#1043	C₃	1	1	yes	maximal, characteristic
3	C₁₉×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
5	C₁₉⋊#1043	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic
7	C₃×C₁₉⋊AGL(1,𝔽₅)	—	15	2	no	—
8	C₁₉×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic
9	#1043⋊C₉	—	19	1	no	maximal, Hall
10	C₉×Dic₁₉	—	25	1	no	maximal, Hall
11	C₃×D₅×C₁₉	—	15	2	no	—
12	C₅²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
13	(C₅⋊D₅)⋊C₉	D₁₉	1	1	yes	characteristic
14	C₁₉⋊AGL(1,𝔽₅)	—	15	2	no	—
15	C₂×C₉×C₁₉	—	25	1	no	—
16	C₃×#1043	—	19	1	no	—
17	C₃×C₅×C₁₉	—	3	2	no	—
18	C₃×Dic₁₉	—	75	1	no	—
19	C₅²⋊C₉	Dic₁₉	1	1	yes	characteristic, complemented, Hall
20	D₅×C₁₉	—	15	2	no	—
21	C₉×C₁₉	—	25	1	no	Hall
22	C₃×C₅⋊D₅	C₃×D₁₉	1	1	yes	characteristic
23	C₂×C₃×C₁₉	—	75	1	no	—
24	#1043	—	19	1	no	Hall
25	C₅×C₁₉	—	3	2	no	—
26	Dic₁₉	—	75	1	no	Hall
27	C₃×C₅²	C₃×Dic₁₉	1	1	yes	characteristic
28	C₃×AGL(1,𝔽₅)	—	285	2	no	—
29	C₃×C₁₉	#1043⋊C₃	1	1	yes	characteristic
30	C₅⋊D₅	C₉×D₁₉	1	1	yes	characteristic
31	C₂×C₁₉	—	75	1	no	—
32	C₄×C₉	—	475	1	no	Hall
33	C₃×D₅	—	15	2	no	—
34	C₅²	C₉×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
35	AGL(1,𝔽₅)	—	285	2	no	—
36	C₁₉	#1043⋊C₉	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₉	—	25	1	no	—
38	C₃×C₅	—	3	2	no	—
39	C₃×C₄	—	1425	1	no	—
40	D₅	—	15	2	no	—
41	C₉	—	25	1	no	Sylow
42	C₂×C₃	—	75	1	no	—
43	C₅	—	3	2	no	—
44	C₄	—	1425	1	no	Sylow
45	C₃	#19152833	1	1	yes	characteristic
46	C₂	—	75	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#19152833
commutator, hypocenter	C₅²×C₁₉	C₄×C₉
Fitting, socle	C₃×C₅²×C₁₉	C₃×C₄
prime radical, cosocle	C₃×C₁₉×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
3. C₁₉×C₅²⋊C₉	C₄	semidirect
5. C₁₉⋊#1043	C₉	semidirect
12. C₅²×C₁₉	C₄×C₉	semidirect
19. C₅²⋊C₉	Dic₁₉	semidirect
34. C₅²	C₉×Dic₁₉	semidirect
36. C₁₉	#1043⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₉×(C₅⋊D₅)⋊C₉	2
C₃×C₁₉⋊#1043	3
#1043⋊C₉	19
C₉×Dic₁₉	25