Subgroups — C₂²×C₁₃×C₂₅×C₂₉ #49179357

Order 37700.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₂₅×C₂₉	C₂	1	3	yes	maximal, direct product factor
2	C₁₃×C₂₅×C₂₉	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₅×C₁₃×C₂₉	C₅	1	1	yes	maximal, characteristic
4	C₂×C₅×C₁₃×C₂₉	C₂×C₅	1	3	yes	—
5	C₂²×C₂₅×C₂₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₃×C₂₉	C₂²×C₅	1	1	yes	characteristic
7	C₂²×C₁₃×C₂₉	C₂₅	1	1	yes	characteristic, direct product factor, Hall
8	C₂×C₂₅×C₂₉	C₂×C₁₃	1	3	yes	direct product factor
9	C₂²×C₁₃×C₂₅	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₁₃×C₂₉	C₂×C₂₅	1	3	yes	direct product factor
11	C₂₅×C₂₉	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₁₃×C₂₅	C₂×C₂₉	1	3	yes	direct product factor
13	C₂²×C₅×C₂₉	C₅×C₁₃	1	1	yes	characteristic
14	C₁₃×C₂₉	C₂²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
15	C₁₃×C₂₅	C₂²×C₂₉	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₅×C₂₉	C₂×C₅×C₁₃	1	3	yes	—
17	C₂²×C₅×C₁₃	C₅×C₂₉	1	1	yes	characteristic
18	C₅×C₂₉	C₂²×C₅×C₁₃	1	1	yes	characteristic
19	C₂×C₅×C₁₃	C₂×C₅×C₂₉	1	3	yes	—
20	C₂²×C₂₉	C₁₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
21	C₂²×C₂₅	C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Hall
22	C₅×C₁₃	C₂²×C₅×C₂₉	1	1	yes	characteristic
23	C₂×C₂₉	C₂×C₁₃×C₂₅	1	3	yes	direct product factor
24	C₂²×C₁₃	C₂₅×C₂₉	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₂₅	C₂×C₁₃×C₂₉	1	3	yes	direct product factor
26	C₂₉	C₂²×C₁₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₃	C₂×C₂₅×C₂₉	1	3	yes	direct product factor
28	C₂₅	C₂²×C₁₃×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
29	C₂²×C₅	C₅×C₁₃×C₂₉	1	1	yes	characteristic
30	C₁₃	C₂²×C₂₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₅	C₂×C₅×C₁₃×C₂₉	1	3	yes	—
32	C₅	C₂²×C₅×C₁₃×C₂₉	1	1	yes	characteristic
33	C₂²	C₁₃×C₂₅×C₂₉	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₁₃×C₂₅×C₂₉	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅×C₁₃×C₂₉
socle, prime radical	C₂²×C₅×C₁₃×C₂₉	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×C₂₅×C₂₉	C₂	direct (N × H)
2. C₁₃×C₂₅×C₂₉	C₂²	direct (N × H)
5. C₂²×C₂₅×C₂₉	C₁₃	direct (N × H)
7. C₂²×C₁₃×C₂₉	C₂₅	direct (N × H)
8. C₂×C₂₅×C₂₉	C₂×C₁₃	direct (N × H)
9. C₂²×C₁₃×C₂₅	C₂₉	direct (N × H)
10. C₂×C₁₃×C₂₉	C₂×C₂₅	direct (N × H)
11. C₂₅×C₂₉	C₂²×C₁₃	direct (N × H)
12. C₂×C₁₃×C₂₅	C₂×C₂₉	direct (N × H)
14. C₁₃×C₂₉	C₂²×C₂₅	direct (N × H)
15. C₁₃×C₂₅	C₂²×C₂₉	direct (N × H)
20. C₂²×C₂₉	C₁₃×C₂₅	direct (N × H)
21. C₂²×C₂₅	C₁₃×C₂₉	direct (N × H)
23. C₂×C₂₉	C₂×C₁₃×C₂₅	direct (N × H)
24. C₂²×C₁₃	C₂₅×C₂₉	direct (N × H)
25. C₂×C₂₅	C₂×C₁₃×C₂₉	direct (N × H)
26. C₂₉	C₂²×C₁₃×C₂₅	direct (N × H)
27. C₂×C₁₃	C₂×C₂₅×C₂₉	direct (N × H)
28. C₂₅	C₂²×C₁₃×C₂₉	direct (N × H)
30. C₁₃	C₂²×C₂₅×C₂₉	direct (N × H)
33. C₂²	C₁₃×C₂₅×C₂₉	direct (N × H)
34. C₂	C₂×C₁₃×C₂₅×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×C₁₃×C₂₅×C₂₉	2
C₂²×C₅×C₁₃×C₂₉	5
C₂²×C₂₅×C₂₉	13
C₂²×C₁₃×C₂₅	29

Subgroups — C22×C13×C25×C29 #49179357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×C₂₅×C₂₉ #49179357