Subgroups — D₅×C₁₁×C₁₇² #44541121

Order 31790.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₁₁×C₁₇²	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₁₁×C₁₇²	—	5	1	no	maximal, Hall
3	C₁₁×C₁₇²	D₅	1	1	yes	characteristic, direct product factor, Hall
4	D₅×C₁₇²	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
5	D₅×C₁₁×C₁₇	C₁₇	1	18	yes	maximal, direct product factor
6	C₅×C₁₇²	C₂×C₁₁	1	1	yes	characteristic, complemented, Hall
7	C₅×C₁₁×C₁₇	C₂×C₁₇	1	18	yes	complemented
8	C₂×C₁₇²	—	5	1	no	Hall
9	C₂×C₁₁×C₁₇	—	5	18	no	—
10	C₁₇²	D₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
11	C₁₁×C₁₇	D₅×C₁₇	1	18	yes	direct product factor
12	D₅×C₁₇	C₁₁×C₁₇	1	18	yes	direct product factor
13	D₅×C₁₁	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
14	C₅×C₁₇	C₂×C₁₁×C₁₇	1	18	yes	complemented
15	C₅×C₁₁	C₂×C₁₇²	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₇	—	5	18	no	—
17	C₂×C₁₁	—	5	1	no	Hall
18	C₁₇	D₅×C₁₁×C₁₇	1	18	yes	direct product factor
19	C₁₁	D₅×C₁₇²	1	1	yes	characteristic, direct product factor, Sylow
20	D₅	C₁₁×C₁₇²	1	1	yes	characteristic, direct product factor, Hall
21	C₅	C₂×C₁₁×C₁₇²	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	5	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₁×C₁₇²	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₁₁×C₁₇²
Frattini	C₁	G
Fitting, socle	C₅×C₁₁×C₁₇²	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₁×C₁₇²

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.