Subgroups — C₂×C₅×C₇×C₁₇×C₂₃ #41032837

Order 27370.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₇×C₁₇×C₂₃	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₇×C₁₇×C₂₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₅×C₁₇×C₂₃	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₇×C₂₃	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
5	C₅×C₁₇×C₂₃	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₅×C₇×C₂₃	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₅×C₇×C₁₇	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₅×C₇×C₂₃	C₂×C₁₇	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₇×C₂₃	C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
10	C₅×C₇×C₁₇	C₂×C₂₃	1	1	yes	characteristic, direct product factor, Hall
11	C₁₇×C₂₃	C₂×C₅×C₇	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₇×C₂₃	C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
13	C₂×C₇×C₁₇	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂×C₅×C₂₃	C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅×C₁₇	C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₂₃	C₂×C₅×C₁₇	1	1	yes	characteristic, direct product factor, Hall
17	C₇×C₁₇	C₂×C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
18	C₅×C₂₃	C₂×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
19	C₅×C₁₇	C₂×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₇	C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₂₃	C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Hall
22	C₅×C₇	C₂×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₁₇	C₅×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
24	C₂₃	C₂×C₅×C₇×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
25	C₁₇	C₂×C₅×C₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
26	C₂×C₇	C₅×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₅	C₇×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Hall
28	C₇	C₂×C₅×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
29	C₅	C₂×C₇×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₂	C₅×C₇×C₁₇×C₂₃	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center	G	C₁
commutator, Frattini	C₁	G
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×C₇×C₁₇×C₂₃	C₂	direct (N × H)
2. C₂×C₇×C₁₇×C₂₃	C₅	direct (N × H)
3. C₂×C₅×C₁₇×C₂₃	C₇	direct (N × H)
4. C₇×C₁₇×C₂₃	C₂×C₅	direct (N × H)
5. C₅×C₁₇×C₂₃	C₂×C₇	direct (N × H)
6. C₂×C₅×C₇×C₂₃	C₁₇	direct (N × H)
7. C₂×C₅×C₇×C₁₇	C₂₃	direct (N × H)
8. C₅×C₇×C₂₃	C₂×C₁₇	direct (N × H)
9. C₂×C₁₇×C₂₃	C₅×C₇	direct (N × H)
10. C₅×C₇×C₁₇	C₂×C₂₃	direct (N × H)
11. C₁₇×C₂₃	C₂×C₅×C₇	direct (N × H)
12. C₂×C₇×C₂₃	C₅×C₁₇	direct (N × H)
13. C₂×C₇×C₁₇	C₅×C₂₃	direct (N × H)
14. C₂×C₅×C₂₃	C₇×C₁₇	direct (N × H)
15. C₂×C₅×C₁₇	C₇×C₂₃	direct (N × H)
16. C₇×C₂₃	C₂×C₅×C₁₇	direct (N × H)
17. C₇×C₁₇	C₂×C₅×C₂₃	direct (N × H)
18. C₅×C₂₃	C₂×C₇×C₁₇	direct (N × H)
19. C₅×C₁₇	C₂×C₇×C₂₃	direct (N × H)
20. C₂×C₅×C₇	C₁₇×C₂₃	direct (N × H)
21. C₂×C₂₃	C₅×C₇×C₁₇	direct (N × H)
22. C₅×C₇	C₂×C₁₇×C₂₃	direct (N × H)
23. C₂×C₁₇	C₅×C₇×C₂₃	direct (N × H)
24. C₂₃	C₂×C₅×C₇×C₁₇	direct (N × H)
25. C₁₇	C₂×C₅×C₇×C₂₃	direct (N × H)
26. C₂×C₇	C₅×C₁₇×C₂₃	direct (N × H)
27. C₂×C₅	C₇×C₁₇×C₂₃	direct (N × H)
28. C₇	C₂×C₅×C₁₇×C₂₃	direct (N × H)
29. C₅	C₂×C₇×C₁₇×C₂₃	direct (N × H)
30. C₂	C₅×C₇×C₁₇×C₂₃	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×C₇×C₁₇×C₂₃	2
C₂×C₇×C₁₇×C₂₃	5
C₂×C₅×C₁₇×C₂₃	7
C₂×C₅×C₇×C₂₃	17
C₂×C₅×C₇×C₁₇	23

Subgroups — C2×C5×C7×C17×C23 #41032837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₇×C₁₇×C₂₃ #41032837