Subgroups — C₃₇×C₅⋊D₄₅ #30659261

Order 16650.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×C₃₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×C₃⋊(C₅⋊D₅)	—	3	1	no	maximal
3	C₃₇×D₄₅	—	5	6	no	maximal
4	C₃×C₅²×C₃₇	D₃	1	1	yes	characteristic
5	C₃₇×C₅⋊D₅	—	9	1	no	Hall
6	C₅×C₉×C₃₇	D₅	1	6	yes	complemented
7	D₁₅×C₃₇	—	15	6	no	—
8	C₅²×C₃₇	D₉	1	1	yes	characteristic, complemented, Hall
9	D₉×C₃₇	—	25	1	no	Hall
10	C₃×C₅×C₃₇	D₁₅	1	6	yes	—
11	C₅⋊D₄₅	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Hall
12	D₅×C₃₇	—	45	6	no	—
13	C₉×C₃₇	C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
14	C₅²×C₉	C₂×C₃₇	1	1	yes	characteristic, complemented, Hall
15	D₃×C₃₇	—	75	1	no	—
16	C₅×C₃₇	D₄₅	1	6	yes	complemented
17	C₃⋊(C₅⋊D₅)	—	3	1	no	—
18	C₃×C₃₇	C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
19	D₄₅	—	5	6	no	—
20	C₃×C₅²	D₃×C₃₇	1	1	yes	characteristic
21	C₂×C₃₇	—	225	1	no	Hall
22	C₅⋊D₅	—	9	1	no	Hall
23	C₅×C₉	D₅×C₃₇	1	6	yes	complemented
24	C₃₇	C₅⋊D₄₅	1	1	yes	characteristic, direct product factor, Sylow
25	D₁₅	—	15	6	no	—
26	C₅²	D₉×C₃₇	1	1	yes	characteristic, complemented, Sylow
27	D₉	—	25	1	no	Hall
28	C₃×C₅	D₁₅×C₃₇	1	6	yes	—
29	D₅	—	45	6	no	—
30	C₉	C₃₇×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
31	D₃	—	75	1	no	—
32	C₅	C₃₇×D₄₅	1	6	yes	complemented
33	C₃	C₃₇×C₃⋊(C₅⋊D₅)	1	1	yes	characteristic
34	C₂	—	225	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃₇	C₅⋊D₄₅
commutator, cosocle, hypocenter	C₅²×C₉	C₂×C₃₇
Frattini	C₃	C₃₇×C₃⋊(C₅⋊D₅)
Fitting	C₅²×C₉×C₃₇	C₂
socle	C₃×C₅²×C₃₇	D₃
LCS	G ▷ C₅²×C₉
UCS	C₁ ◁ 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.