Subgroups — C₅×C₁₆×C₂₈₉ #72200477

Order 23120.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₈×C₂₈₉	C₂	1	1	yes	maximal, characteristic
2	C₁₆×C₂₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₈×C₂₈₉	C₂×C₅	1	1	yes	characteristic
4	C₄×C₅×C₂₈₉	C₄	1	1	yes	characteristic
5	C₂×C₅×C₂₈₉	C₈	1	1	yes	characteristic
6	C₅×C₂₈₉	C₁₆	1	1	yes	characteristic, direct product factor, Hall
7	C₅×C₁₆×C₁₇	C₁₇	1	1	yes	maximal, characteristic
8	C₄×C₂₈₉	C₄×C₅	1	1	yes	characteristic
9	C₅×C₈×C₁₇	C₂×C₁₇	1	1	yes	characteristic
10	C₂×C₂₈₉	C₅×C₈	1	1	yes	characteristic
11	C₄×C₅×C₁₇	C₄×C₁₇	1	1	yes	characteristic
12	C₂₈₉	C₅×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
13	C₁₆×C₁₇	C₅×C₁₇	1	1	yes	characteristic
14	C₂×C₅×C₁₇	C₈×C₁₇	1	1	yes	characteristic
15	C₈×C₁₇	C₂×C₅×C₁₇	1	1	yes	characteristic
16	C₅×C₁₇	C₁₆×C₁₇	1	1	yes	characteristic
17	C₅×C₁₆	C₂₈₉	1	1	yes	characteristic, direct product factor, Hall
18	C₄×C₁₇	C₄×C₅×C₁₇	1	1	yes	characteristic
19	C₅×C₈	C₂×C₂₈₉	1	1	yes	characteristic
20	C₂×C₁₇	C₅×C₈×C₁₇	1	1	yes	characteristic
21	C₄×C₅	C₄×C₂₈₉	1	1	yes	characteristic
22	C₁₇	C₅×C₁₆×C₁₇	1	1	yes	characteristic
23	C₁₆	C₅×C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
24	C₂×C₅	C₈×C₂₈₉	1	1	yes	characteristic
25	C₈	C₂×C₅×C₂₈₉	1	1	yes	characteristic
26	C₅	C₁₆×C₂₈₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₄	C₄×C₅×C₂₈₉	1	1	yes	characteristic
28	C₂	C₅×C₈×C₂₈₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈×C₁₇	C₂×C₅×C₁₇
socle, prime radical	C₂×C₅×C₁₇	C₈×C₁₇
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₆×C₂₈₉	C₅	direct (N × H)
6. C₅×C₂₈₉	C₁₆	direct (N × H)
12. C₂₈₉	C₅×C₁₆	direct (N × H)
17. C₅×C₁₆	C₂₈₉	direct (N × H)
23. C₁₆	C₅×C₂₈₉	direct (N × H)
26. C₅	C₁₆×C₂₈₉	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×C₈×C₂₈₉	2
C₁₆×C₂₈₉	5
C₅×C₁₆×C₁₇	17

Subgroups — C5×C16×C289 #72200477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₁₆×C₂₈₉ #72200477