Subgroups — C₂×C₃³×C₇×C₅₉ #72199745

Order 22302.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₇×C₅₉	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃³×C₅₉	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂×C₃²×C₇×C₅₉	C₃	1	13	yes	maximal, direct product factor
4	C₃²×C₇×C₅₉	C₂×C₃	1	13	yes	direct product factor
5	C₂×C₃×C₇×C₅₉	C₃²	1	13	yes	direct product factor
6	C₃³×C₅₉	C₂×C₇	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₇×C₅₉	C₂×C₃²	1	13	yes	direct product factor
8	C₂×C₃²×C₅₉	C₃×C₇	1	13	yes	direct product factor
9	C₂×C₇×C₅₉	C₃³	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×C₅₉	C₂×C₃×C₇	1	13	yes	direct product factor
11	C₇×C₅₉	C₂×C₃³	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₃³×C₇	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅₉	C₃²×C₇	1	13	yes	direct product factor
14	C₃³×C₇	C₂×C₅₉	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₅₉	C₂×C₃²×C₇	1	13	yes	direct product factor
16	C₂×C₃²×C₇	C₃×C₅₉	1	13	yes	direct product factor
17	C₂×C₅₉	C₃³×C₇	1	1	yes	characteristic, direct product factor, Hall
18	C₃²×C₇	C₂×C₃×C₅₉	1	13	yes	direct product factor
19	C₅₉	C₂×C₃³×C₇	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃³	C₇×C₅₉	1	1	yes	characteristic, direct product factor, Hall
21	C₂×C₃×C₇	C₃²×C₅₉	1	13	yes	direct product factor
22	C₃³	C₂×C₇×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₇	C₂×C₃²×C₅₉	1	13	yes	direct product factor
24	C₂×C₃²	C₃×C₇×C₅₉	1	13	yes	direct product factor
25	C₂×C₇	C₃³×C₅₉	1	1	yes	characteristic, direct product factor, Hall
26	C₃²	C₂×C₃×C₇×C₅₉	1	13	yes	direct product factor
27	C₇	C₂×C₃³×C₅₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₃	C₃²×C₇×C₅₉	1	13	yes	direct product factor
29	C₃	C₂×C₃²×C₇×C₅₉	1	13	yes	direct product factor
30	C₂	C₃³×C₇×C₅₉	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. C₃³×C₇×C₅₉	C₂	direct (N × H)
2. C₂×C₃³×C₅₉	C₇	direct (N × H)
3. C₂×C₃²×C₇×C₅₉	C₃	direct (N × H)
4. C₃²×C₇×C₅₉	C₂×C₃	direct (N × H)
5. C₂×C₃×C₇×C₅₉	C₃²	direct (N × H)
6. C₃³×C₅₉	C₂×C₇	direct (N × H)
7. C₃×C₇×C₅₉	C₂×C₃²	direct (N × H)
8. C₂×C₃²×C₅₉	C₃×C₇	direct (N × H)
9. C₂×C₇×C₅₉	C₃³	direct (N × H)
10. C₃²×C₅₉	C₂×C₃×C₇	direct (N × H)
11. C₇×C₅₉	C₂×C₃³	direct (N × H)
12. C₂×C₃³×C₇	C₅₉	direct (N × H)
13. C₂×C₃×C₅₉	C₃²×C₇	direct (N × H)
14. C₃³×C₇	C₂×C₅₉	direct (N × H)
15. C₃×C₅₉	C₂×C₃²×C₇	direct (N × H)
16. C₂×C₃²×C₇	C₃×C₅₉	direct (N × H)
17. C₂×C₅₉	C₃³×C₇	direct (N × H)
18. C₃²×C₇	C₂×C₃×C₅₉	direct (N × H)
19. C₅₉	C₂×C₃³×C₇	direct (N × H)
20. C₂×C₃³	C₇×C₅₉	direct (N × H)
21. C₂×C₃×C₇	C₃²×C₅₉	direct (N × H)
22. C₃³	C₂×C₇×C₅₉	direct (N × H)
23. C₃×C₇	C₂×C₃²×C₅₉	direct (N × H)
24. C₂×C₃²	C₃×C₇×C₅₉	direct (N × H)
25. C₂×C₇	C₃³×C₅₉	direct (N × H)
26. C₃²	C₂×C₃×C₇×C₅₉	direct (N × H)
27. C₇	C₂×C₃³×C₅₉	direct (N × H)
28. C₂×C₃	C₃²×C₇×C₅₉	direct (N × H)
29. C₃	C₂×C₃²×C₇×C₅₉	direct (N × H)
30. C₂	C₃³×C₇×C₅₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₇×C₅₉	2
C₂×C₃³×C₅₉	7
C₂×C₃²×C₇×C₅₉	3
C₂×C₃³×C₇	59

Subgroups — C2×C33×C7×C59 #72199745

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃³×C₇×C₅₉ #72199745