Subgroups — #1043×#4294 #30685538

Order 17100.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×#4294	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₉×#1043	C₃	1	1	yes	maximal, characteristic
3	C₅²×#4294	C₄	1	1	yes	characteristic, complemented, Hall
4	AGL(1,𝔽₅)×#4294	—	5	6	no	maximal
5	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	C₁₉×#1043	C₉	1	1	yes	characteristic, complemented, Hall
7	D₅×#4294	—	5	6	no	—
8	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic
9	C₃×C₁₉×AGL(1,𝔽₅)	—	5	6	no	—
10	C₁₉×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic
11	C₉×#1043	—	19	1	no	maximal, Hall
12	C₅×#4294	AGL(1,𝔽₅)	1	6	yes	complemented
13	C₄×#4294	—	25	1	no	Hall
14	C₃×D₅×C₁₉	—	5	6	no	—
15	C₅²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
16	C₉×C₅⋊D₅	—	19	1	no	—
17	C₁₉×AGL(1,𝔽₅)	—	5	6	no	—
18	C₂×#4294	—	25	1	no	—
19	C₃×#1043	C₁₉⋊C₃	1	1	yes	characteristic
20	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	6	yes	—
21	C₃×C₄×C₁₉	—	25	1	no	—
22	C₅²×C₉	—	19	1	no	Hall
23	D₅×C₁₉	—	5	6	no	—
24	C₉×AGL(1,𝔽₅)	—	95	6	no	—
25	#4294	#1043	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅⋊D₅	C₂×C₁₉⋊C₃	1	1	yes	characteristic
27	C₂×C₃×C₁₉	—	25	1	no	—
28	#1043	#4294	1	1	yes	characteristic, direct product factor, Hall
29	C₅×C₁₉	C₉×AGL(1,𝔽₅)	1	6	yes	complemented
30	C₉×D₅	—	95	6	no	—
31	C₄×C₁₉	—	25	1	no	Hall
32	C₃×C₅²	C₄×C₁₉⋊C₃	1	1	yes	characteristic
33	C₃×AGL(1,𝔽₅)	—	5	6	no	—
34	C₃×C₁₉	C₃×#1043	1	1	yes	characteristic
35	C₅⋊D₅	C₂×#4294	1	1	yes	characteristic
36	C₅×C₉	—	19	6	no	—
37	C₂×C₁₉	—	25	1	no	—
38	C₄×C₉	—	475	1	no	Hall
39	C₃×D₅	—	5	6	no	—
40	C₅²	C₄×#4294	1	1	yes	characteristic, complemented, Sylow
41	AGL(1,𝔽₅)	—	5	6	no	—
42	C₁₉	C₉×#1043	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₉	—	475	1	no	—
44	C₃×C₅	AGL(1,𝔽₅)×C₁₉⋊C₃	1	6	yes	—
45	C₃×C₄	—	25	1	no	—
46	D₅	—	5	6	no	—
47	C₉	—	19	1	no	Sylow
48	C₂×C₃	—	25	1	no	—
49	C₅	AGL(1,𝔽₅)×#4294	1	6	yes	complemented
50	C₄	—	25	1	no	Sylow
51	C₃	C₁₉⋊C₃×#1043	1	1	yes	characteristic
52	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	C₁₉⋊C₃×#1043
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. C₅²×#4294	C₄	semidirect
6. C₁₉×#1043	C₉	semidirect
12. C₅×#4294	AGL(1,𝔽₅)	semidirect
15. C₅²×C₁₉	C₄×C₉	semidirect
25. #4294	#1043	direct (N × H)
28. #1043	#4294	direct (N × H)
29. C₅×C₁₉	C₉×AGL(1,𝔽₅)	semidirect
40. C₅²	C₄×#4294	semidirect
42. C₁₉	C₉×#1043	semidirect
49. C₅	AGL(1,𝔽₅)×#4294	semidirect

Maximal subgroups

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

subgroup	index
C₅⋊D₅×#4294	2
C₃×C₁₉×#1043	3
AGL(1,𝔽₅)×#4294	5
C₉×#1043	19