Subgroups — C₄²×C₅²×C₂₉ #72190039

Order 11600.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅²×C₂₉	C₂	1	3	yes	maximal
2	C₄²×C₅×C₂₉	C₅	1	6	yes	maximal, direct product factor
3	C₂²×C₅²×C₂₉	C₂²	1	1	yes	characteristic
4	C₄×C₅²×C₂₉	C₄	1	6	yes	direct product factor
5	C₂×C₅²×C₂₉	C₂×C₄	1	3	yes	—
6	C₂×C₄×C₅×C₂₉	C₂×C₅	1	18	yes	—
7	C₅²×C₂₉	C₄²	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₅×C₂₉	C₂²×C₅	1	6	yes	—
9	C₄×C₅×C₂₉	C₄×C₅	1	36	yes	direct product factor
10	C₄²×C₂₉	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₄²×C₅²	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂×C₅×C₂₉	C₂×C₄×C₅	1	18	yes	—
13	C₂×C₄×C₂₉	C₂×C₅²	1	3	yes	—
14	C₂×C₄×C₅²	C₂×C₂₉	1	3	yes	—
15	C₅×C₂₉	C₄²×C₅	1	6	yes	direct product factor
16	C₂²×C₂₉	C₂²×C₅²	1	1	yes	characteristic
17	C₄×C₂₉	C₄×C₅²	1	6	yes	direct product factor
18	C₂²×C₅²	C₂²×C₂₉	1	1	yes	characteristic
19	C₄×C₅²	C₄×C₂₉	1	6	yes	direct product factor
20	C₄²×C₅	C₅×C₂₉	1	6	yes	direct product factor
21	C₂×C₂₉	C₂×C₄×C₅²	1	3	yes	—
22	C₂×C₅²	C₂×C₄×C₂₉	1	3	yes	—
23	C₂×C₄×C₅	C₂×C₅×C₂₉	1	18	yes	—
24	C₂₉	C₄²×C₅²	1	1	yes	characteristic, direct product factor, Sylow
25	C₅²	C₄²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
26	C₂²×C₅	C₂²×C₅×C₂₉	1	6	yes	—
27	C₄×C₅	C₄×C₅×C₂₉	1	36	yes	direct product factor
28	C₄²	C₅²×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂×C₅	C₂×C₄×C₅×C₂₉	1	18	yes	—
30	C₂×C₄	C₂×C₅²×C₂₉	1	3	yes	—
31	C₅	C₄²×C₅×C₂₉	1	6	yes	direct product factor
32	C₂²	C₂²×C₅²×C₂₉	1	1	yes	characteristic
33	C₄	C₄×C₅²×C₂₉	1	6	yes	direct product factor
34	C₂	C₂×C₄×C₅²×C₂₉	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂²×C₅²×C₂₉
socle, prime radical	C₂²×C₅²×C₂₉	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄²×C₅×C₂₉	C₅	direct (N × H)
4. C₄×C₅²×C₂₉	C₄	direct (N × H)
7. C₅²×C₂₉	C₄²	direct (N × H)
9. C₄×C₅×C₂₉	C₄×C₅	direct (N × H)
10. C₄²×C₂₉	C₅²	direct (N × H)
11. C₄²×C₅²	C₂₉	direct (N × H)
15. C₅×C₂₉	C₄²×C₅	direct (N × H)
17. C₄×C₂₉	C₄×C₅²	direct (N × H)
19. C₄×C₅²	C₄×C₂₉	direct (N × H)
20. C₄²×C₅	C₅×C₂₉	direct (N × H)
24. C₂₉	C₄²×C₅²	direct (N × H)
25. C₅²	C₄²×C₂₉	direct (N × H)
27. C₄×C₅	C₄×C₅×C₂₉	direct (N × H)
28. C₄²	C₅²×C₂₉	direct (N × H)
31. C₅	C₄²×C₅×C₂₉	direct (N × H)
33. C₄	C₄×C₅²×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×C₄×C₅²×C₂₉	2
C₄²×C₅×C₂₉	5
C₄²×C₅²	29

Subgroups — C42×C52×C29 #72190039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×C₅²×C₂₉ #72190039