Subgroups — C₇₉×#66775 #41001705

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	#595×C₇₉	—	5	1	no	maximal, Hall
4	D₁₇×C₇₉	—	5	1	no	—
5	AGL(1,𝔽₅)×C₇₉	—	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	#66775	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₇₉	—	85	1	no	Hall
11	D₈₅	C₂×C₇₉	1	1	yes	characteristic
12	C₂×C₇₉	—	85	1	no	—
13	C₅×C₁₇	C₄×C₇₉	1	1	yes	characteristic, complemented, Hall
14	C₇₉	#66775	1	1	yes	characteristic, direct product factor, Sylow
15	#595	—	5	1	no	Hall
16	D₁₇	—	5	1	no	—
17	AGL(1,𝔽₅)	—	17	1	no	Hall
18	C₁₇	AGL(1,𝔽₅)×C₇₉	1	1	yes	characteristic, complemented, Sylow
19	D₅	—	17	1	no	—
20	C₅	#595×C₇₉	1	1	yes	characteristic, complemented, Sylow
21	C₄	—	85	1	no	Sylow
22	C₂	—	85	1	no	—

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.