Subgroups — C₂×C₁₇⋊(D₄₁⋊C₅) #28358287

Order 13940.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇⋊(D₄₁⋊C₅)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₇×C₄₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×C₄₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₆₉₇	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₁₇×C₄₁	C₂×C₅	1	1	yes	characteristic, complemented
6	D₆₉₇	C₂×C₅	1	2	yes	complemented
7	C₂×D₄₁⋊C₅	—	17	1	no	maximal, Hall
8	C₁₇×C₄₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
9	C₂×C₄₁⋊C₅	D₁₇	1	1	yes	characteristic, complemented
10	D₄₁⋊C₅	—	17	2	no	—
11	C₂×C₅×D₁₇	—	41	1	no	maximal, Hall
12	C₄₁⋊C₅	C₂×D₁₇	1	1	yes	characteristic, complemented, Hall
13	C₂×C₅×C₁₇	—	41	1	no	—
14	C₅×D₁₇	—	41	2	no	—
15	C₂×D₄₁	—	17	1	no	Hall
16	C₅×C₁₇	—	41	1	no	Hall
17	C₂×C₄₁	C₅×D₁₇	1	1	yes	characteristic, complemented
18	D₄₁	—	17	2	no	—
19	C₂×D₁₇	—	205	1	no	Hall
20	C₄₁	C₂×C₅×D₁₇	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₇	D₄₁⋊C₅	1	1	yes	characteristic, complemented
22	D₁₇	—	205	2	no	—
23	C₂²×C₅	—	697	1	no	Hall
24	C₁₇	C₂×D₄₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₅	—	41	1	no	—
26	C₂×C₅	—	697	2	no	—
27	C₅	—	41	1	no	Sylow
28	C₂²	—	3485	1	no	Sylow
29	C₂	—	3485	2	no	—
30	C₂	C₁₇⋊(D₄₁⋊C₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₁₇⋊(D₄₁⋊C₅)
commutator, cosocle, hypocenter	C₁₇×C₄₁	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₁₇×C₄₁	C₂×C₅
LCS	G ▷ C₁₇×C₄₁
UCS	C₁ ◁ C₂

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.