Subgroups — C₇₉⋊#66776 #41001708

Order 26860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×D₈₅	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₇×C₇₉	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇₉⋊#595	—	5	1	no	maximal, Hall
4	D₁₇×C₇₉	—	5	1	no	—
5	C₇₉⋊AGL(1,𝔽₅)	—	17	1	no	maximal, Hall
6	C₁₇×C₇₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
7	D₅×C₇₉	—	17	1	no	—
8	C₅×C₇₉	#595	1	1	yes	characteristic, complemented, Hall
9	#66776	—	79	1	no	maximal, Hall
10	Dic₇₉	—	85	1	no	Hall
11	D₈₅	D₇₉	1	1	yes	characteristic
12	C₂×C₇₉	—	85	1	no	—
13	C₅×C₁₇	Dic₇₉	1	1	yes	characteristic, complemented, Hall
14	C₇₉	#66776	1	1	yes	characteristic, complemented, Sylow
15	#595	—	395	1	no	Hall
16	D₁₇	—	5	1	no	—
17	AGL(1,𝔽₅)	—	1343	1	no	Hall
18	C₁₇	C₇₉⋊AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
19	D₅	—	17	1	no	—
20	C₅	C₇₉⋊#595	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	6715	1	no	Sylow
22	C₂	—	85	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₇×C₇₉	C₄
prime radical, cosocle	C₇₉×D₈₅	C₂
LCS	G ▷ C₅×C₁₇×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.