Subgroups — C₃⋊(C₅⋊(D₁₁₃⋊C₇)) #37557549

Order 23730.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₁₁₃⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅⋊(D₁₁₃⋊C₇)	—	3	1	no	maximal, Hall
3	C₃⋊(D₁₁₃⋊C₇)	—	5	1	no	maximal, Hall
4	C₅×C₁₁₃⋊C₇	D₃	1	1	yes	characteristic, complemented, Hall
5	D₁₆₉₅	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃×C₁₁₃⋊C₇	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₁₃	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	D₁₁₃⋊C₇	—	15	1	no	Hall
9	D₅₆₅	—	3	1	no	Hall
10	C₁₁₃⋊C₇	D₁₅	1	1	yes	characteristic, complemented, Hall
11	D₃₃₉	—	5	1	no	Hall
12	C₅×C₁₁₃	D₃×C₇	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₁₃	C₇×D₅	1	1	yes	characteristic, complemented, Hall
14	D₁₁₃	—	15	1	no	Hall
15	C₇×D₁₅	—	113	1	no	maximal, Hall
16	C₁₁₃	C₇×D₁₅	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	—	113	1	no	Hall
18	C₇×D₅	—	339	1	no	Hall
19	D₃×C₇	—	565	1	no	Hall
20	C₅×C₇	—	113	1	no	Hall
21	D₁₅	—	791	1	no	Hall
22	C₃×C₇	—	113	1	no	Hall
23	C₃×C₅	D₁₁₃⋊C₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₇	—	1695	1	no	Hall
25	D₅	—	2373	1	no	Hall
26	C₇	—	113	1	no	Sylow
27	D₃	—	3955	1	no	Hall
28	C₅	C₃⋊(D₁₁₃⋊C₇)	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₅⋊(D₁₁₃⋊C₇)	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	1695	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₁₁₃	C₂×C₇
LCS	G ▷ C₃×C₅×C₁₁₃
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.