Subgroups — C₄×C₅²×C₁₁×C₂₉ #44542012

Order 31900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅²×C₁₁×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₁₁×C₂₉	C₄	1	1	yes	characteristic, direct product factor, Hall
3	C₄×C₅×C₁₁×C₂₉	C₅	1	6	yes	maximal, direct product factor
4	C₂×C₅×C₁₁×C₂₉	C₂×C₅	1	6	yes	—
5	C₄×C₅²×C₂₉	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₁×C₂₉	C₄×C₅	1	6	yes	direct product factor
7	C₂×C₅²×C₂₉	C₂×C₁₁	1	1	yes	characteristic
8	C₄×C₁₁×C₂₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
9	C₄×C₅²×C₁₁	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅²×C₂₉	C₄×C₁₁	1	1	yes	characteristic, direct product factor, Hall
11	C₂×C₁₁×C₂₉	C₂×C₅²	1	1	yes	characteristic
12	C₄×C₅×C₂₉	C₅×C₁₁	1	6	yes	direct product factor
13	C₂×C₅²×C₁₁	C₂×C₂₉	1	1	yes	characteristic
14	C₁₁×C₂₉	C₄×C₅²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅×C₂₉	C₂×C₅×C₁₁	1	6	yes	—
16	C₅²×C₁₁	C₄×C₂₉	1	1	yes	characteristic, direct product factor, Hall
17	C₄×C₅×C₁₁	C₅×C₂₉	1	6	yes	direct product factor
18	C₅×C₂₉	C₄×C₅×C₁₁	1	6	yes	direct product factor
19	C₄×C₂₉	C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₅×C₁₁	C₂×C₅×C₂₉	1	6	yes	—
21	C₄×C₅²	C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Hall
22	C₂×C₂₉	C₂×C₅²×C₁₁	1	1	yes	characteristic
23	C₅×C₁₁	C₄×C₅×C₂₉	1	6	yes	direct product factor
24	C₂×C₅²	C₂×C₁₁×C₂₉	1	1	yes	characteristic
25	C₄×C₁₁	C₅²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
26	C₂₉	C₄×C₅²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
27	C₅²	C₄×C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂×C₁₁	C₂×C₅²×C₂₉	1	1	yes	characteristic
29	C₄×C₅	C₅×C₁₁×C₂₉	1	6	yes	direct product factor
30	C₁₁	C₄×C₅²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₅	C₂×C₅×C₁₁×C₂₉	1	6	yes	—
32	C₅	C₄×C₅×C₁₁×C₂₉	1	6	yes	direct product factor
33	C₄	C₅²×C₁₁×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₅²×C₁₁×C₂₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂	C₂×C₅²×C₁₁×C₂₉
socle, prime radical	C₂×C₅²×C₁₁×C₂₉	C₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅²×C₁₁×C₂₉	C₄	direct (N × H)
3. C₄×C₅×C₁₁×C₂₉	C₅	direct (N × H)
5. C₄×C₅²×C₂₉	C₁₁	direct (N × H)
6. C₅×C₁₁×C₂₉	C₄×C₅	direct (N × H)
8. C₄×C₁₁×C₂₉	C₅²	direct (N × H)
9. C₄×C₅²×C₁₁	C₂₉	direct (N × H)
10. C₅²×C₂₉	C₄×C₁₁	direct (N × H)
12. C₄×C₅×C₂₉	C₅×C₁₁	direct (N × H)
14. C₁₁×C₂₉	C₄×C₅²	direct (N × H)
16. C₅²×C₁₁	C₄×C₂₉	direct (N × H)
17. C₄×C₅×C₁₁	C₅×C₂₉	direct (N × H)
18. C₅×C₂₉	C₄×C₅×C₁₁	direct (N × H)
19. C₄×C₂₉	C₅²×C₁₁	direct (N × H)
21. C₄×C₅²	C₁₁×C₂₉	direct (N × H)
23. C₅×C₁₁	C₄×C₅×C₂₉	direct (N × H)
25. C₄×C₁₁	C₅²×C₂₉	direct (N × H)
26. C₂₉	C₄×C₅²×C₁₁	direct (N × H)
27. C₅²	C₄×C₁₁×C₂₉	direct (N × H)
29. C₄×C₅	C₅×C₁₁×C₂₉	direct (N × H)
30. C₁₁	C₄×C₅²×C₂₉	direct (N × H)
32. C₅	C₄×C₅×C₁₁×C₂₉	direct (N × H)
33. C₄	C₅²×C₁₁×C₂₉	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×C₅²×C₁₁×C₂₉	2
C₄×C₅×C₁₁×C₂₉	5
C₄×C₅²×C₂₉	11
C₄×C₅²×C₁₁	29

Subgroups — C4×C52×C11×C29 #44542012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅²×C₁₁×C₂₉ #44542012