Subgroups — C₂³×C₅×D₁₇ #13062874

Order 1360.

268 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×D₁₇	C₂	1	14	yes	maximal, direct product factor
3	C₂²×C₅×C₁₇	C₂²	1	7	yes	complemented
4	C₂×C₅×D₁₇	C₂²	1	28	yes	direct product factor
5	C₂³×D₁₇	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₅×C₁₇	C₂³	1	7	yes	complemented
7	C₅×D₁₇	C₂³	1	8	yes	direct product factor
8	C₂³×C₁₇	C₂×C₅	1	1	yes	characteristic, complemented
9	C₂²×D₁₇	C₂×C₅	1	14	yes	direct product factor
10	C₅×C₁₇	C₂⁴	1	1	yes	characteristic, complemented, Hall
11	C₂⁴×C₅	—	17	1	no	maximal, Hall
12	C₂²×C₁₇	C₂²×C₅	1	7	yes	complemented
13	C₂×D₁₇	C₂²×C₅	1	28	yes	direct product factor
14	C₂³×C₅	—	17	14	no	—
15	C₂³×C₅	D₁₇	1	1	yes	characteristic, direct product factor
16	C₂×C₁₇	C₂³×C₅	1	7	yes	complemented
17	D₁₇	C₂³×C₅	1	8	yes	direct product factor
18	C₂²×C₅	—	17	28	no	—
19	C₂²×C₅	C₂×D₁₇	1	7	yes	direct product factor
20	C₁₇	C₂⁴×C₅	1	1	yes	characteristic, complemented, Sylow
21	C₂⁴	—	17	1	no	Sylow
22	C₂×C₅	—	17	8	no	—
23	C₂×C₅	C₂²×D₁₇	1	7	yes	direct product factor
24	C₂³	—	17	14	no	—
25	C₂³	C₅×D₁₇	1	1	yes	characteristic, direct product factor
26	C₅	C₂³×D₁₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂²	—	17	28	no	—
28	C₂²	C₂×C₅×D₁₇	1	7	yes	direct product factor
29	C₂	—	17	8	no	—
30	C₂	C₂²×C₅×D₁₇	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³×C₅	D₁₇
commutator, cosocle, hypocenter	C₁₇	C₂⁴×C₅
Frattini	C₁	G
Fitting, socle	C₂³×C₅×C₁₇	C₂
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂³×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.