Subgroups — C₅⋊(C₁₇⋊(D₇₃⋊C₃)) #49151925

Order 37230.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₇×C₇₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₆₂₀₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₇⋊(D₇₃⋊C₃)	—	5	1	no	maximal, Hall
4	C₅×C₁₇×C₇₃	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	C₁₇×C₇₃⋊C₃	D₅	1	1	yes	characteristic, complemented, Hall
6	D₁₂₄₁	—	5	1	no	Hall
7	C₅⋊(D₇₃⋊C₃)	—	17	1	no	maximal, Hall
8	C₁₇×C₇₃	C₃×D₅	1	1	yes	characteristic, complemented, Hall
9	C₅×C₇₃⋊C₃	D₁₇	1	1	yes	characteristic, complemented, Hall
10	D₃₆₅	—	17	1	no	Hall
11	C₃×D₈₅	—	73	1	no	maximal, Hall
12	D₇₃⋊C₃	—	85	1	no	Hall
13	C₅×C₇₃	C₃×D₁₇	1	1	yes	characteristic, complemented, Hall
14	C₃×C₅×C₁₇	—	73	1	no	Hall
15	C₇₃⋊C₃	D₈₅	1	1	yes	characteristic, complemented, Hall
16	D₈₅	—	73	1	no	Hall
17	D₇₃	—	85	1	no	Hall
18	C₃×D₁₇	—	365	1	no	Hall
19	C₅×C₁₇	D₇₃⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₇₃	C₃×D₈₅	1	1	yes	characteristic, complemented, Sylow
21	C₃×C₁₇	—	73	1	no	Hall
22	D₁₇	—	365	1	no	Hall
23	C₃×D₅	—	1241	1	no	Hall
24	C₁₇	C₅⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
25	C₃×C₅	—	73	1	no	Hall
26	D₅	—	1241	1	no	Hall
27	C₂×C₃	—	6205	1	no	Hall
28	C₅	C₁₇⋊(D₇₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
29	C₃	—	73	1	no	Sylow
30	C₂	—	6205	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₇×C₇₃	C₂×C₃
LCS	G ▷ C₅×C₁₇×C₇₃
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.