Subgroups — C₂×D₃₅×C₈₉ #27159552

Order 12460.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₅×C₈₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₇×C₈₉	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₇×C₈₉	—	5	1	no	maximal, Hall
5	C₂×D₅×C₈₉	—	7	1	no	maximal, Hall
6	C₂×C₇×C₈₉	D₅	1	1	yes	characteristic, complemented
7	D₇×C₈₉	—	5	2	no	—
8	C₂×C₅×C₈₉	D₇	1	1	yes	characteristic, complemented
9	D₅×C₈₉	—	7	2	no	—
10	C₇×C₈₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₅×C₈₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₈₉	—	35	1	no	Hall
13	C₂×C₈₉	—	35	2	no	—
14	C₂×C₈₉	D₃₅	1	1	yes	characteristic, direct product factor
15	C₂×D₃₅	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₈₉	C₂×D₃₅	1	1	yes	characteristic, direct product factor, Sylow
17	C₂×C₅×C₇	C₂×C₈₉	1	1	yes	characteristic, complemented
18	D₃₅	C₂×C₈₉	1	2	yes	direct product factor
19	C₅×C₇	C₂²×C₈₉	1	1	yes	characteristic, complemented, Hall
20	C₂×D₇	—	5	1	no	Hall
21	C₂×D₅	—	7	1	no	Hall
22	C₂×C₇	D₅×C₈₉	1	1	yes	characteristic, complemented
23	D₇	—	5	2	no	—
24	C₂×C₅	D₇×C₈₉	1	1	yes	characteristic, complemented
25	D₅	—	7	2	no	—
26	C₇	C₂×D₅×C₈₉	1	1	yes	characteristic, complemented, Sylow
27	C₅	C₂×D₇×C₈₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	35	1	no	Sylow
29	C₂	—	35	2	no	—
30	C₂	D₃₅×C₈₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₈₉	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂²×C₈₉
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₇×C₈₉	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₂×C₈₉

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.