Subgroups — C₅×C₃₇×D₄₉ #31827402

Order 18130.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₃₇×C₄₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×D₄₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×D₇×C₃₇	—	7	1	no	maximal
4	C₃₇×C₄₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
5	C₅×C₇×C₃₇	D₇	1	1	yes	characteristic
6	D₇×C₃₇	—	7	1	no	—
7	C₅×D₄₉	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₅×C₃₇	—	49	1	no	Hall
9	C₇×C₃₇	C₅×D₇	1	1	yes	characteristic
10	C₅×C₄₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
11	C₅×C₃₇	D₄₉	1	1	yes	characteristic, direct product factor, Hall
12	D₄₉	C₅×C₃₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₃₇	—	49	1	no	Hall
14	C₅×D₇	—	7	1	no	—
15	C₄₉	C₂×C₅×C₃₇	1	1	yes	characteristic, complemented, Sylow
16	C₃₇	C₅×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
17	C₅×C₇	D₇×C₃₇	1	1	yes	characteristic
18	D₇	—	7	1	no	—
19	C₂×C₅	—	49	1	no	Hall
20	C₇	C₅×D₇×C₃₇	1	1	yes	characteristic
21	C₅	C₃₇×D₄₉	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅×C₃₇	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂×C₅×C₃₇
Frattini	C₇	C₅×D₇×C₃₇
Fitting	C₅×C₃₇×C₄₉	C₂
socle	C₅×C₇×C₃₇	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₅×C₃₇

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.