Subgroups — C₂×C₇⋊C₉×C₁₅₇ #34089932

Order 19782.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇⋊C₉×C₁₅₇	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₇×C₁₅₇	C₃	1	1	yes	maximal, characteristic
3	C₃×C₇×C₁₅₇	C₂×C₃	1	1	yes	characteristic
4	C₂×C₉×C₁₅₇	—	7	1	no	maximal, Hall
5	C₂×C₇×C₁₅₇	C₉	1	1	yes	characteristic, complemented, Hall
6	C₉×C₁₅₇	—	7	1	no	Hall
7	C₇×C₁₅₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×C₁₅₇	ΓL(1,𝔽₈)	1	1	yes	characteristic
9	C₃×C₁₅₇	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
10	C₂×C₁₅₇	C₇⋊C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₁₅₇	C₂×C₇⋊C₉	1	1	yes	characteristic, direct product factor, Sylow
12	C₂×C₇⋊C₉	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₇⋊C₉	C₂×C₁₅₇	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₃×C₇	C₃×C₁₅₇	1	1	yes	characteristic
15	C₃×C₇	C₂×C₃×C₁₅₇	1	1	yes	characteristic
16	C₂×C₉	—	7	1	no	Hall
17	C₂×C₇	C₉×C₁₅₇	1	1	yes	characteristic, complemented, Hall
18	C₉	—	7	1	no	Sylow
19	C₇	C₂×C₉×C₁₅₇	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	ΓL(1,𝔽₈)×C₁₅₇	1	1	yes	characteristic
21	C₃	C₂×ΓL(1,𝔽₈)×C₁₅₇	1	1	yes	characteristic
22	C₂	C₇⋊C₉×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow

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.