Subgroups — C₂×C₄×C₅×C₇×C₈₉ #72202155

Order 24920.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₇×C₈₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₄×C₅×C₈₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂²×C₅×C₇×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×C₇×C₈₉	C₂	1	2	yes	maximal, direct product factor
5	C₂×C₅×C₇×C₈₉	C₄	1	2	yes	direct product factor
6	C₂×C₅×C₇×C₈₉	C₂²	1	1	yes	characteristic
7	C₅×C₇×C₈₉	C₂×C₄	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₇×C₈₉	C₂×C₅	1	1	yes	characteristic
9	C₄×C₇×C₈₉	C₂×C₅	1	2	yes	direct product factor
10	C₂²×C₅×C₈₉	C₂×C₇	1	1	yes	characteristic
11	C₄×C₅×C₈₉	C₂×C₇	1	2	yes	direct product factor
12	C₂×C₇×C₈₉	C₄×C₅	1	2	yes	direct product factor
13	C₂×C₇×C₈₉	C₂²×C₅	1	1	yes	characteristic
14	C₂×C₅×C₈₉	C₄×C₇	1	2	yes	direct product factor
15	C₂×C₅×C₈₉	C₂²×C₇	1	1	yes	characteristic
16	C₂×C₄×C₈₉	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
17	C₇×C₈₉	C₂×C₄×C₅	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₈₉	C₂×C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
19	C₂²×C₈₉	C₂×C₅×C₇	1	1	yes	characteristic
20	C₄×C₈₉	C₂×C₅×C₇	1	2	yes	direct product factor
21	C₂×C₄×C₅×C₇	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₈₉	C₄×C₅×C₇	1	2	yes	direct product factor
23	C₂×C₈₉	C₂²×C₅×C₇	1	1	yes	characteristic
24	C₂²×C₅×C₇	C₂×C₈₉	1	1	yes	characteristic
25	C₄×C₅×C₇	C₂×C₈₉	1	2	yes	direct product factor
26	C₈₉	C₂×C₄×C₅×C₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₅×C₇	C₄×C₈₉	1	2	yes	direct product factor
28	C₂×C₅×C₇	C₂²×C₈₉	1	1	yes	characteristic
29	C₂×C₄×C₇	C₅×C₈₉	1	1	yes	characteristic, direct product factor, Hall
30	C₂×C₄×C₅	C₇×C₈₉	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₇	C₂×C₄×C₈₉	1	1	yes	characteristic, direct product factor, Hall
32	C₂²×C₇	C₂×C₅×C₈₉	1	1	yes	characteristic
33	C₄×C₇	C₂×C₅×C₈₉	1	2	yes	direct product factor
34	C₂²×C₅	C₂×C₇×C₈₉	1	1	yes	characteristic
35	C₄×C₅	C₂×C₇×C₈₉	1	2	yes	direct product factor
36	C₂×C₇	C₄×C₅×C₈₉	1	2	yes	direct product factor
37	C₂×C₇	C₂²×C₅×C₈₉	1	1	yes	characteristic
38	C₂×C₅	C₄×C₇×C₈₉	1	2	yes	direct product factor
39	C₂×C₅	C₂²×C₇×C₈₉	1	1	yes	characteristic
40	C₂×C₄	C₅×C₇×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₇	C₂×C₄×C₅×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₅	C₂×C₄×C₇×C₈₉	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²	C₂×C₅×C₇×C₈₉	1	1	yes	characteristic
44	C₄	C₂×C₅×C₇×C₈₉	1	2	yes	direct product factor
45	C₂	C₄×C₅×C₇×C₈₉	1	2	yes	direct product factor
46	C₂	C₂²×C₅×C₇×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂²×C₅×C₇×C₈₉
socle, prime radical	C₂²×C₅×C₇×C₈₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄×C₇×C₈₉	C₅	direct (N × H)
2. C₂×C₄×C₅×C₈₉	C₇	direct (N × H)
4. C₄×C₅×C₇×C₈₉	C₂	direct (N × H)
5. C₂×C₅×C₇×C₈₉	C₄	direct (N × H)
7. C₅×C₇×C₈₉	C₂×C₄	direct (N × H)
9. C₄×C₇×C₈₉	C₂×C₅	direct (N × H)
11. C₄×C₅×C₈₉	C₂×C₇	direct (N × H)
12. C₂×C₇×C₈₉	C₄×C₅	direct (N × H)
14. C₂×C₅×C₈₉	C₄×C₇	direct (N × H)
16. C₂×C₄×C₈₉	C₅×C₇	direct (N × H)
17. C₇×C₈₉	C₂×C₄×C₅	direct (N × H)
18. C₅×C₈₉	C₂×C₄×C₇	direct (N × H)
20. C₄×C₈₉	C₂×C₅×C₇	direct (N × H)
21. C₂×C₄×C₅×C₇	C₈₉	direct (N × H)
22. C₂×C₈₉	C₄×C₅×C₇	direct (N × H)
25. C₄×C₅×C₇	C₂×C₈₉	direct (N × H)
26. C₈₉	C₂×C₄×C₅×C₇	direct (N × H)
27. C₂×C₅×C₇	C₄×C₈₉	direct (N × H)
29. C₂×C₄×C₇	C₅×C₈₉	direct (N × H)
30. C₂×C₄×C₅	C₇×C₈₉	direct (N × H)
31. C₅×C₇	C₂×C₄×C₈₉	direct (N × H)
33. C₄×C₇	C₂×C₅×C₈₉	direct (N × H)
35. C₄×C₅	C₂×C₇×C₈₉	direct (N × H)
36. C₂×C₇	C₄×C₅×C₈₉	direct (N × H)
38. C₂×C₅	C₄×C₇×C₈₉	direct (N × H)
40. C₂×C₄	C₅×C₇×C₈₉	direct (N × H)
41. C₇	C₂×C₄×C₅×C₈₉	direct (N × H)
42. C₅	C₂×C₄×C₇×C₈₉	direct (N × H)
44. C₄	C₂×C₅×C₇×C₈₉	direct (N × H)
45. C₂	C₄×C₅×C₇×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×C₇×C₈₉	5
C₂×C₄×C₅×C₈₉	7
C₂²×C₅×C₇×C₈₉	2
C₄×C₅×C₇×C₈₉	2
C₂×C₄×C₅×C₇	89

Subgroups — C2×C4×C5×C7×C89 #72202155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₅×C₇×C₈₉ #72202155