Subgroups — C₂³×D₈₅ #13062876

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×D₈₅	C₂	1	14	yes	maximal, direct product factor
3	C₂²×C₅×C₁₇	C₂²	1	7	yes	complemented
4	C₂×D₈₅	C₂²	1	28	yes	direct product factor
5	C₂³×D₁₇	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₇	C₂³	1	7	yes	complemented
7	D₈₅	C₂³	1	8	yes	direct product factor
8	C₂³×C₁₇	D₅	1	1	yes	characteristic, complemented
9	C₂²×D₁₇	—	5	14	no	—
10	C₅×C₁₇	C₂⁴	1	1	yes	characteristic, complemented, Hall
11	C₂³×D₅	—	17	1	no	maximal, Hall
12	C₂²×C₁₇	C₂×D₅	1	7	yes	complemented
13	C₂×D₁₇	—	5	28	no	—
14	C₂³×C₅	D₁₇	1	1	yes	characteristic, complemented
15	C₂²×D₅	—	17	14	no	—
16	C₂×C₁₇	C₂²×D₅	1	7	yes	complemented
17	D₁₇	—	5	8	no	—
18	C₂²×C₅	C₂×D₁₇	1	7	yes	complemented
19	C₂×D₅	—	17	28	no	—
20	C₁₇	C₂³×D₅	1	1	yes	characteristic, complemented, Sylow
21	C₂⁴	—	85	1	no	Sylow
22	C₂×C₅	C₂²×D₁₇	1	7	yes	complemented
23	D₅	—	17	8	no	—
24	C₂³	—	85	14	no	—
25	C₂³	D₈₅	1	1	yes	characteristic, direct product factor
26	C₅	C₂³×D₁₇	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	85	28	no	—
28	C₂²	C₂×D₈₅	1	7	yes	direct product factor
29	C₂	—	85	8	no	—
30	C₂	C₂²×D₈₅	1	7	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂³	D₈₅
commutator, cosocle, hypocenter	C₅×C₁₇	C₂⁴
Frattini	C₁	G
Fitting, socle	C₂³×C₅×C₁₇	C₂
LCS	G ▷ C₅×C₁₇
UCS	C₁ ◁ C₂³

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.