Subgroups — C₇₉×#64425 #37551156

Order 23226.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇₉×#3862	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇₉×C₇⋊D₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₇²×C₇₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	AGL(1,𝔽₇)×C₇₉	—	7	2	no	maximal
5	ΓL(1,𝔽₈)×C₇₉	—	7	2	no	—
6	D₇×C₇₉	—	7	2	no	—
7	D₇×C₇₉	—	21	2	no	—
8	C₇×C₇₉	—	3	2	no	—
9	C₇×C₇₉	AGL(1,𝔽₇)	1	2	yes	complemented
10	C₂×C₃×C₇₉	—	49	1	no	Hall
11	#64425	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₃×C₇₉	—	49	1	no	Hall
13	C₂×C₇₉	—	49	1	no	Hall
14	#3862	C₂×C₇₉	1	1	yes	characteristic, complemented, Hall
15	C₇⋊D₇	C₃×C₇₉	1	1	yes	characteristic, complemented, Hall
16	C₇₉	#64425	1	1	yes	characteristic, direct product factor, Sylow
17	C₇²	C₂×C₃×C₇₉	1	1	yes	characteristic, complemented, Sylow
18	AGL(1,𝔽₇)	—	7	2	no	—
19	ΓL(1,𝔽₈)	—	7	2	no	—
20	D₇	—	7	2	no	—
21	D₇	—	21	2	no	—
22	C₇	—	3	2	no	—
23	C₇	AGL(1,𝔽₇)×C₇₉	1	2	yes	complemented
24	C₂×C₃	—	49	1	no	Hall
25	C₃	—	49	1	no	Sylow
26	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇₉	#64425
commutator, cosocle, hypocenter	C₇²	C₂×C₃×C₇₉
Frattini	C₁	G
Fitting, socle	C₇²×C₇₉	C₂×C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₇₉

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.