Subgroups — C₂²×C₁₇×C₄₁⋊C₅ #28358289

Order 13940.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×C₄₁⋊C₅	C₂	1	3	yes	maximal, direct product factor
2	C₁₇×C₄₁⋊C₅	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₁₇×C₄₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
4	C₂×C₁₇×C₄₁	C₂×C₅	1	3	yes	complemented
5	C₂²×C₄₁⋊C₅	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₁₇×C₄₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
7	C₂×C₄₁⋊C₅	C₂×C₁₇	1	3	yes	direct product factor
8	C₂²×C₅×C₁₇	—	41	1	no	maximal, Hall
9	C₄₁⋊C₅	C₂²×C₁₇	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₅×C₁₇	—	41	3	no	—
11	C₂²×C₄₁	C₅×C₁₇	1	1	yes	characteristic, complemented, Hall
12	C₅×C₁₇	—	41	1	no	Hall
13	C₂×C₄₁	C₂×C₅×C₁₇	1	3	yes	complemented
14	C₂²×C₁₇	C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
15	C₄₁	C₂²×C₅×C₁₇	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₁₇	C₂×C₄₁⋊C₅	1	3	yes	direct product factor
17	C₂²×C₅	—	41	1	no	Hall
18	C₁₇	C₂²×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
19	C₂×C₅	—	41	3	no	—
20	C₅	—	41	1	no	Sylow
21	C₂²	C₁₇×C₄₁⋊C₅	1	1	yes	characteristic, direct product factor, Sylow
22	C₂	C₂×C₁₇×C₄₁⋊C₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₁₇	C₄₁⋊C₅
commutator, cosocle, hypocenter	C₄₁	C₂²×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₇×C₄₁	C₅
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂²×C₁₇

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.