Subgroups — C₃⋊(C₇⋊(C₅₉⋊AGL(1,𝔽₅))) #37613402

Order 24780.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₅×C₅₉	C₂	1	1	yes	maximal, characteristic
2	C₇⋊(C₅₉⋊AGL(1,𝔽₅))	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇×C₅₉	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₁₂₃₉	—	5	1	no	maximal, Hall
5	C₇×D₅×C₅₉	D₃	1	1	yes	characteristic
6	C₃⋊(C₅₉⋊AGL(1,𝔽₅))	—	7	1	no	maximal, Hall
7	C₂×C₃×C₇×C₅₉	—	5	1	no	—
8	C₅×C₇×C₅₉	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅×C₅₉	D₇	1	1	yes	characteristic
10	Dic₄₁₃	—	15	1	no	Hall
11	C₃×C₇×C₅₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₅₉⋊AGL(1,𝔽₅)	—	21	1	no	Hall
13	C₃×C₅×C₅₉	Dic₇	1	1	yes	characteristic, complemented, Hall
14	C₂×C₇×C₅₉	—	5	1	no	—
15	Dic₁₇₇	—	35	1	no	Hall
16	D₅×C₅₉	D₂₁	1	1	yes	characteristic
17	C₃⋊(C₇⋊AGL(1,𝔽₅))	—	59	1	no	maximal, Hall
18	C₇×C₅₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₅₉	—	5	1	no	—
20	C₅×C₅₉	Dic₂₁	1	1	yes	characteristic, complemented, Hall
21	Dic₅₉	—	105	1	no	Hall
22	C₃×C₇×D₅	D₅₉	1	1	yes	characteristic
23	C₃×C₅₉	C₇⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
24	C₇⋊AGL(1,𝔽₅)	—	177	1	no	Hall
25	C₂×C₅₉	—	5	1	no	—
26	C₃×C₅×C₇	Dic₅₉	1	1	yes	characteristic, complemented, Hall
27	Dic₂₁	—	295	1	no	Hall
28	C₇×D₅	D₁₇₇	1	1	yes	characteristic
29	ΓL(1,𝔽₁₆)	—	413	1	no	Hall
30	C₅₉	C₃⋊(C₇⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃×C₇	—	5	1	no	—
32	C₅×C₇	Dic₁₇₇	1	1	yes	characteristic, complemented, Hall
33	C₃×D₅	D₄₁₃	1	1	yes	characteristic
34	Dic₇	—	885	1	no	Hall
35	C₃×C₇	C₅₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
36	AGL(1,𝔽₅)	—	1239	1	no	Hall
37	C₃×C₅	Dic₄₁₃	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	—	5	1	no	—
39	Dic₃	—	2065	1	no	Hall
40	D₅	D₁₂₃₉	1	1	yes	characteristic
41	C₇	C₃⋊(C₅₉⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₃	—	5	1	no	—
43	C₅	Dic₁₂₃₉	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	6195	1	no	Sylow
45	C₃	C₇⋊(C₅₉⋊AGL(1,𝔽₅))	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₇×C₅₉	C₄
prime radical, cosocle	C₃×C₇×D₅×C₅₉	C₂
LCS	G ▷ C₃×C₅×C₇×C₅₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇×C₅₉	C₄	semidirect
8. C₅×C₇×C₅₉	Dic₃	semidirect
11. C₃×C₇×C₅₉	AGL(1,𝔽₅)	semidirect
13. C₃×C₅×C₅₉	Dic₇	semidirect
18. C₇×C₅₉	ΓL(1,𝔽₁₆)	semidirect
20. C₅×C₅₉	Dic₂₁	semidirect
23. C₃×C₅₉	C₇⋊AGL(1,𝔽₅)	semidirect
26. C₃×C₅×C₇	Dic₅₉	semidirect
30. C₅₉	C₃⋊(C₇⋊AGL(1,𝔽₅))	semidirect
32. C₅×C₇	Dic₁₇₇	semidirect
35. C₃×C₇	C₅₉⋊AGL(1,𝔽₅)	semidirect
37. C₃×C₅	Dic₄₁₃	semidirect
41. C₇	C₃⋊(C₅₉⋊AGL(1,𝔽₅))	semidirect
43. C₅	Dic₁₂₃₉	semidirect
45. C₃	C₇⋊(C₅₉⋊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
C₃×C₇×D₅×C₅₉	2
C₇⋊(C₅₉⋊AGL(1,𝔽₅))	3
Dic₁₂₃₉	5
C₃⋊(C₅₉⋊AGL(1,𝔽₅))	7
C₃⋊(C₇⋊AGL(1,𝔽₅))	59

Subgroups — C3⋊(C7⋊(C59⋊AGL(1,𝔽5))) #37613402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊(C₇⋊(C₅₉⋊AGL(1,𝔽₅))) #37613402