Subgroups — C₂×C₃²×C₂₉×C₇₁ #49150430

Order 37062.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₉×C₇₁	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₃×C₂₉×C₇₁	C₃	1	4	yes	maximal, direct product factor
3	C₃×C₂₉×C₇₁	C₂×C₃	1	4	yes	direct product factor
4	C₂×C₂₉×C₇₁	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₂₉×C₇₁	C₂×C₃²	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₃²×C₇₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₃²×C₇₁	C₂×C₂₉	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₃²×C₂₉	C₇₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×C₇₁	C₃×C₂₉	1	4	yes	direct product factor
10	C₃²×C₂₉	C₂×C₇₁	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₇₁	C₂×C₃×C₂₉	1	4	yes	direct product factor
12	C₂×C₃×C₂₉	C₃×C₇₁	1	4	yes	direct product factor
13	C₂×C₇₁	C₃²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₂₉	C₂×C₃×C₇₁	1	4	yes	direct product factor
15	C₇₁	C₂×C₃²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×C₂₉	C₃²×C₇₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂₉	C₂×C₃²×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
18	C₂×C₃²	C₂₉×C₇₁	1	1	yes	characteristic, direct product factor, Hall
19	C₃²	C₂×C₂₉×C₇₁	1	1	yes	characteristic, direct product factor, Sylow
20	C₂×C₃	C₃×C₂₉×C₇₁	1	4	yes	direct product factor
21	C₃	C₂×C₃×C₂₉×C₇₁	1	4	yes	direct product factor
22	C₂	C₃²×C₂₉×C₇₁	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. C₃²×C₂₉×C₇₁	C₂	direct (N × H)
2. C₂×C₃×C₂₉×C₇₁	C₃	direct (N × H)
3. C₃×C₂₉×C₇₁	C₂×C₃	direct (N × H)
4. C₂×C₂₉×C₇₁	C₃²	direct (N × H)
5. C₂₉×C₇₁	C₂×C₃²	direct (N × H)
6. C₂×C₃²×C₇₁	C₂₉	direct (N × H)
7. C₃²×C₇₁	C₂×C₂₉	direct (N × H)
8. C₂×C₃²×C₂₉	C₇₁	direct (N × H)
9. C₂×C₃×C₇₁	C₃×C₂₉	direct (N × H)
10. C₃²×C₂₉	C₂×C₇₁	direct (N × H)
11. C₃×C₇₁	C₂×C₃×C₂₉	direct (N × H)
12. C₂×C₃×C₂₉	C₃×C₇₁	direct (N × H)
13. C₂×C₇₁	C₃²×C₂₉	direct (N × H)
14. C₃×C₂₉	C₂×C₃×C₇₁	direct (N × H)
15. C₇₁	C₂×C₃²×C₂₉	direct (N × H)
16. C₂×C₂₉	C₃²×C₇₁	direct (N × H)
17. C₂₉	C₂×C₃²×C₇₁	direct (N × H)
18. C₂×C₃²	C₂₉×C₇₁	direct (N × H)
19. C₃²	C₂×C₂₉×C₇₁	direct (N × H)
20. C₂×C₃	C₃×C₂₉×C₇₁	direct (N × H)
21. C₃	C₂×C₃×C₂₉×C₇₁	direct (N × H)
22. C₂	C₃²×C₂₉×C₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₂₉×C₇₁	2
C₂×C₃×C₂₉×C₇₁	3
C₂×C₃²×C₇₁	29
C₂×C₃²×C₂₉	71

Subgroups — C2×C32×C29×C71 #49150430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×C₂₉×C₇₁ #49150430