Subgroups — #4294⋊#1043 #30685537

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	#4294⋊AGL(1,𝔽₅)	—	5	5	no	maximal
5	#4294⋊AGL(1,𝔽₅)	—	5	1	no	maximal
6	C₃×C₁₉×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
7	C₁₉⋊#1043	C₉	1	1	yes	characteristic, complemented, Hall
8	D₅×#4294	—	5	5	no	—
9	D₅×#4294	—	5	1	no	—
10	C₃×C₅²×C₁₉	C₃×C₄	1	1	yes	characteristic
11	C₃×C₁₉⋊AGL(1,𝔽₅)	—	5	5	no	—
12	C₃×C₁₉⋊AGL(1,𝔽₅)	—	5	1	no	—
13	C₁₉×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic
14	C₉×#1043	—	19	1	no	maximal, Hall
15	C₅×#4294	AGL(1,𝔽₅)	1	5	yes	complemented
16	C₅×#4294	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
17	#4294⋊C₄	—	25	1	no	Hall
18	C₃×D₅×C₁₉	—	5	5	no	—
19	C₃×D₅×C₁₉	—	5	1	no	—
20	C₅²×C₁₉	C₄×C₉	1	1	yes	characteristic, complemented, Hall
21	C₉×C₅⋊D₅	—	19	1	no	—
22	C₁₉⋊AGL(1,𝔽₅)	—	5	5	no	—
23	C₁₉⋊AGL(1,𝔽₅)	—	5	1	no	—
24	C₂×#4294	—	25	1	no	—
25	C₃×#1043	—	57	1	no	—
26	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	5	yes	—
27	C₃×C₅×C₁₉	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
28	C₃×Dic₁₉	—	25	1	no	—
29	C₅²×C₉	—	19	1	no	Hall
30	D₅×C₁₉	—	5	5	no	—
31	D₅×C₁₉	—	5	1	no	—
32	C₉×AGL(1,𝔽₅)	—	95	5	no	—
33	C₉×AGL(1,𝔽₅)	—	95	1	no	—
34	#4294	#1043	1	1	yes	characteristic, complemented, Hall
35	C₃×C₅⋊D₅	D₁₉⋊C₃	1	1	yes	characteristic
36	C₂×C₃×C₁₉	—	25	1	no	—
37	#1043	—	57	1	no	Hall
38	C₅×C₁₉	C₉×AGL(1,𝔽₅)	1	5	yes	complemented
39	C₅×C₁₉	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
40	C₉×D₅	—	95	5	no	—
41	C₉×D₅	—	95	1	no	—
42	Dic₁₉	—	25	1	no	Hall
43	C₃×C₅²	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic
44	C₃×AGL(1,𝔽₅)	—	285	5	no	—
45	C₃×AGL(1,𝔽₅)	—	95	1	no	—
46	C₃×C₁₉	C₃×#1043	1	1	yes	characteristic
47	C₅⋊D₅	#4294⋊C₂	1	1	yes	characteristic
48	C₅×C₉	—	19	5	no	—
49	C₅×C₉	—	19	1	no	—
50	C₂×C₁₉	—	25	1	no	—
51	C₄×C₉	—	475	1	no	Hall
52	C₃×D₅	—	5	5	no	—
53	C₃×D₅	—	5	1	no	—
54	C₅²	#4294⋊C₄	1	1	yes	characteristic, complemented, Sylow
55	AGL(1,𝔽₅)	—	285	5	no	—
56	AGL(1,𝔽₅)	—	95	1	no	—
57	C₁₉	C₉×#1043	1	1	yes	characteristic, complemented, Sylow
58	C₂×C₉	—	475	1	no	—
59	C₃×C₅	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	1	5	yes	—
60	C₃×C₅	(C₁₉⋊C₃)⋊AGL(1,𝔽₅)	1	1	yes	characteristic
61	C₃×C₄	—	1425	1	no	—
62	D₅	—	5	5	no	—
63	D₅	—	5	1	no	—
64	C₉	—	19	1	no	Sylow
65	C₂×C₃	—	25	1	no	—
66	C₅	#4294⋊AGL(1,𝔽₅)	1	5	yes	complemented
67	C₅	#4294⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
68	C₄	—	1425	1	no	Sylow
69	C₃	(C₁₉⋊C₃)⋊#1043	1	1	yes	characteristic
70	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
7. C₁₉⋊#1043	C₉	semidirect
15. C₅×#4294	AGL(1,𝔽₅)	semidirect
16. C₅×#4294	AGL(1,𝔽₅)	semidirect
20. C₅²×C₁₉	C₄×C₉	semidirect
34. #4294	#1043	semidirect
38. C₅×C₁₉	C₉×AGL(1,𝔽₅)	semidirect
39. C₅×C₁₉	C₉×AGL(1,𝔽₅)	semidirect
54. C₅²	#4294⋊C₄	semidirect
57. C₁₉	C₉×#1043	semidirect
66. C₅	#4294⋊AGL(1,𝔽₅)	semidirect
67. C₅	#4294⋊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
C₅⋊D₅×#4294	2
C₃×C₁₉⋊#1043	3
#4294⋊AGL(1,𝔽₅)	5
C₉×#1043	19