Subgroups — C₃⋊(C₇₉⋊#1043) #37557261

Order 23700.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅⋊D₅×C₇₉	C₂	1	1	yes	maximal, characteristic
2	C₇₉⋊#1043	—	3	1	no	maximal, Hall
3	C₃×C₅²×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃⋊(C₇₉⋊AGL(1,𝔽₅))	—	5	6	no	maximal
5	C₅⋊D₅×C₇₉	D₃	1	1	yes	characteristic
6	C₃×D₅×C₇₉	—	5	6	no	—
7	C₅²×C₇₉	Dic₃	1	1	yes	characteristic, complemented, Hall
8	C₇₉⋊AGL(1,𝔽₅)	—	15	6	no	—
9	C₃×C₅×C₇₉	AGL(1,𝔽₅)	1	6	yes	complemented
10	Dic₂₃₇	—	25	1	no	Hall
11	D₅×C₇₉	—	5	6	no	—
12	C₂×C₃×C₇₉	—	25	1	no	—
13	C₅×C₇₉	ΓL(1,𝔽₁₆)	1	6	yes	complemented
14	Dic₇₉	—	75	1	no	Hall
15	C₃⋊#1043	—	79	1	no	maximal, Hall
16	C₃×C₇₉	#1043	1	1	yes	characteristic, complemented, Hall
17	C₂×C₇₉	—	25	1	no	—
18	C₃×C₅⋊D₅	D₇₉	1	1	yes	characteristic
19	#1043	—	237	1	no	Hall
20	C₇₉	C₃⋊#1043	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₅²	Dic₇₉	1	1	yes	characteristic, complemented, Hall
22	ΓL(1,𝔽₁₆)	—	395	6	no	—
23	C₅⋊D₅	D₂₃₇	1	1	yes	characteristic
24	C₃×D₅	—	5	6	no	—
25	C₅²	Dic₂₃₇	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	1185	6	no	—
27	C₃×C₅	C₇₉⋊AGL(1,𝔽₅)	1	6	yes	complemented
28	Dic₃	—	1975	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	25	1	no	—
31	C₅	C₃⋊(C₇₉⋊AGL(1,𝔽₅))	1	6	yes	complemented
32	C₄	—	5925	1	no	Sylow
33	C₃	C₇₉⋊#1043	1	1	yes	characteristic, complemented, Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅²×C₇₉	C₄
prime radical, cosocle	C₃×C₅⋊D₅×C₇₉	C₂
LCS	G ▷ C₃×C₅²×C₇₉
UCS	C₁

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

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