Subgroups — C₅×D₂₂₈₉ #37504331

Order 22890.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₇×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×D₇₆₃	—	3	1	no	maximal, Hall
3	D₂₂₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₇×C₁₀₉	D₃	1	1	yes	characteristic, complemented, Hall
5	C₅×D₃₂₇	—	7	1	no	maximal, Hall
6	C₃×C₇×C₁₀₉	C₂×C₅	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅×C₁₀₉	D₇	1	1	yes	characteristic, complemented, Hall
8	D₇₆₃	—	3	1	no	Hall
9	C₅×D₁₀₉	—	21	1	no	Hall
10	C₇×C₁₀₉	C₅×D₃	1	1	yes	characteristic, complemented, Hall
11	D₃₂₇	—	7	1	no	Hall
12	C₅×C₁₀₉	D₂₁	1	1	yes	characteristic, complemented, Hall
13	C₃×C₁₀₉	C₅×D₇	1	1	yes	characteristic, complemented, Hall
14	D₁₀₉	—	21	1	no	Hall
15	C₅×D₂₁	—	109	1	no	maximal, Hall
16	C₁₀₉	C₅×D₂₁	1	1	yes	characteristic, complemented, Sylow
17	C₃×C₅×C₇	D₁₀₉	1	1	yes	characteristic, complemented, Hall
18	C₅×D₇	—	327	1	no	Hall
19	D₂₁	—	109	1	no	Hall
20	C₅×C₇	D₃₂₇	1	1	yes	characteristic, complemented, Hall
21	C₅×D₃	—	763	1	no	Hall
22	C₃×C₇	C₅×D₁₀₉	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅	D₇₆₃	1	1	yes	characteristic, complemented, Hall
24	D₇	—	327	1	no	Hall
25	C₂×C₅	—	2289	1	no	Hall
26	C₇	C₅×D₃₂₇	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	763	1	no	Hall
28	C₅	D₂₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	C₅×D₇₆₃	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	2289	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₂₂₈₉
commutator, cosocle, hypocenter	C₃×C₇×C₁₀₉	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₀₉	C₂
LCS	G ▷ C₃×C₇×C₁₀₉
UCS	C₁ ◁ C₅

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.