Subgroups — C₄×C₉×C₂₉×C₃₁ #44569015

Order 32364.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₂₉×C₃₁	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×C₂₉×C₃₁	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₉×C₃₁	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₃×C₂₉×C₃₁	C₂×C₃	1	1	yes	characteristic
5	C₄×C₂₉×C₃₁	C₉	1	1	yes	characteristic, direct product factor, Hall
6	C₃×C₂₉×C₃₁	C₃×C₄	1	1	yes	characteristic
7	C₂×C₂₉×C₃₁	C₂×C₉	1	1	yes	characteristic
8	C₄×C₉×C₃₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₄×C₉×C₂₉	C₃₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂₉×C₃₁	C₄×C₉	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₉×C₃₁	C₂×C₂₉	1	1	yes	characteristic
12	C₂×C₉×C₂₉	C₂×C₃₁	1	1	yes	characteristic
13	C₃×C₄×C₃₁	C₃×C₂₉	1	1	yes	characteristic
14	C₃×C₄×C₂₉	C₃×C₃₁	1	1	yes	characteristic
15	C₉×C₃₁	C₄×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₉×C₂₉	C₄×C₃₁	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₃₁	C₂×C₃×C₂₉	1	1	yes	characteristic
18	C₂×C₃×C₂₉	C₂×C₃×C₃₁	1	1	yes	characteristic
19	C₄×C₃₁	C₉×C₂₉	1	1	yes	characteristic, direct product factor, Hall
20	C₄×C₂₉	C₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₃₁	C₃×C₄×C₂₉	1	1	yes	characteristic
22	C₃×C₂₉	C₃×C₄×C₃₁	1	1	yes	characteristic
23	C₂×C₃₁	C₂×C₉×C₂₉	1	1	yes	characteristic
24	C₂×C₂₉	C₂×C₉×C₃₁	1	1	yes	characteristic
25	C₄×C₉	C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Hall
26	C₃₁	C₄×C₉×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
27	C₂₉	C₄×C₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₉	C₂×C₂₉×C₃₁	1	1	yes	characteristic
29	C₃×C₄	C₃×C₂₉×C₃₁	1	1	yes	characteristic
30	C₉	C₄×C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₃	C₂×C₃×C₂₉×C₃₁	1	1	yes	characteristic
32	C₄	C₉×C₂₉×C₃₁	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₃×C₄×C₂₉×C₃₁	1	1	yes	characteristic
34	C₂	C₂×C₉×C₂₉×C₃₁	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₃	C₂×C₃×C₂₉×C₃₁
socle, prime radical	C₂×C₃×C₂₉×C₃₁	C₂×C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×C₂₉×C₃₁	C₄	direct (N × H)
5. C₄×C₂₉×C₃₁	C₉	direct (N × H)
8. C₄×C₉×C₃₁	C₂₉	direct (N × H)
9. C₄×C₉×C₂₉	C₃₁	direct (N × H)
10. C₂₉×C₃₁	C₄×C₉	direct (N × H)
15. C₉×C₃₁	C₄×C₂₉	direct (N × H)
16. C₉×C₂₉	C₄×C₃₁	direct (N × H)
19. C₄×C₃₁	C₉×C₂₉	direct (N × H)
20. C₄×C₂₉	C₉×C₃₁	direct (N × H)
25. C₄×C₉	C₂₉×C₃₁	direct (N × H)
26. C₃₁	C₄×C₉×C₂₉	direct (N × H)
27. C₂₉	C₄×C₉×C₃₁	direct (N × H)
30. C₉	C₄×C₂₉×C₃₁	direct (N × H)
32. C₄	C₉×C₂₉×C₃₁	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×C₉×C₂₉×C₃₁	2
C₃×C₄×C₂₉×C₃₁	3
C₄×C₉×C₃₁	29
C₄×C₉×C₂₉	31

Subgroups — C4×C9×C29×C31 #44569015

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₉×C₂₉×C₃₁ #44569015