Subgroups — C₂×C₅×C₈×C₈₉ #72186169

Order 7120.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₈×C₈₉	C₂	1	2	yes	maximal, direct product factor
3	C₂²×C₅×C₈₉	C₄	1	1	yes	characteristic
4	C₄×C₅×C₈₉	C₄	1	1	yes	characteristic
5	C₄×C₅×C₈₉	C₂²	1	1	yes	characteristic
6	C₂×C₈×C₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₈₉	C₈	1	2	yes	direct product factor
8	C₂×C₅×C₈₉	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₈₉	C₂×C₅	1	1	yes	characteristic
10	C₈×C₈₉	C₂×C₅	1	2	yes	direct product factor
11	C₅×C₈₉	C₂×C₈	1	1	yes	characteristic, direct product factor, Hall
12	C₂²×C₈₉	C₄×C₅	1	1	yes	characteristic
13	C₄×C₈₉	C₄×C₅	1	1	yes	characteristic
14	C₄×C₈₉	C₂²×C₅	1	1	yes	characteristic
15	C₂×C₈₉	C₅×C₈	1	2	yes	direct product factor
16	C₂×C₈₉	C₂×C₄×C₅	1	1	yes	characteristic
17	C₈₉	C₂×C₅×C₈	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₅×C₈	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₄×C₅	C₂×C₈₉	1	1	yes	characteristic
20	C₅×C₈	C₂×C₈₉	1	2	yes	direct product factor
21	C₂²×C₅	C₄×C₈₉	1	1	yes	characteristic
22	C₄×C₅	C₄×C₈₉	1	1	yes	characteristic
23	C₄×C₅	C₂²×C₈₉	1	1	yes	characteristic
24	C₂×C₈	C₅×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅	C₈×C₈₉	1	2	yes	direct product factor
26	C₂×C₅	C₂×C₄×C₈₉	1	1	yes	characteristic
27	C₂×C₄	C₂×C₅×C₈₉	1	1	yes	characteristic
28	C₈	C₂×C₅×C₈₉	1	2	yes	direct product factor
29	C₅	C₂×C₈×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
30	C₂²	C₄×C₅×C₈₉	1	1	yes	characteristic
31	C₄	C₄×C₅×C₈₉	1	1	yes	characteristic
32	C₄	C₂²×C₅×C₈₉	1	1	yes	characteristic
33	C₂	C₅×C₈×C₈₉	1	2	yes	direct product factor
34	C₂	C₂×C₄×C₅×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂²×C₅×C₈₉
socle, prime radical	C₂²×C₅×C₈₉	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₈×C₈₉	C₂	direct (N × H)
6. C₂×C₈×C₈₉	C₅	direct (N × H)
7. C₂×C₅×C₈₉	C₈	direct (N × H)
10. C₈×C₈₉	C₂×C₅	direct (N × H)
11. C₅×C₈₉	C₂×C₈	direct (N × H)
15. C₂×C₈₉	C₅×C₈	direct (N × H)
17. C₈₉	C₂×C₅×C₈	direct (N × H)
18. C₂×C₅×C₈	C₈₉	direct (N × H)
20. C₅×C₈	C₂×C₈₉	direct (N × H)
24. C₂×C₈	C₅×C₈₉	direct (N × H)
25. C₂×C₅	C₈×C₈₉	direct (N × H)
28. C₈	C₂×C₅×C₈₉	direct (N × H)
29. C₅	C₂×C₈×C₈₉	direct (N × H)
33. C₂	C₅×C₈×C₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×C₈₉	2
C₅×C₈×C₈₉	2
C₂×C₈×C₈₉	5
C₂×C₅×C₈	89

Subgroups — C2×C5×C8×C89 #72186169

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₈×C₈₉ #72186169