Subgroups — C₂²×C₁₁×C₁₃×C₂₅ #28384641

Order 14300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×C₁₃×C₂₅	C₂	1	3	yes	maximal, direct product factor
2	C₁₁×C₁₃×C₂₅	C₂²	1	1	yes	characteristic, direct product factor, Hall
3	C₂²×C₅×C₁₁×C₁₃	C₅	1	1	yes	maximal, characteristic
4	C₂×C₅×C₁₁×C₁₃	C₂×C₅	1	3	yes	—
5	C₂²×C₁₃×C₂₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂²×C₁₁×C₂₅	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₅×C₁₁×C₁₃	C₂²×C₅	1	1	yes	characteristic
8	C₂×C₁₃×C₂₅	C₂×C₁₁	1	3	yes	direct product factor
9	C₂²×C₁₁×C₁₃	C₂₅	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁×C₂₅	C₂×C₁₃	1	3	yes	direct product factor
11	C₁₃×C₂₅	C₂²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
12	C₂×C₁₁×C₁₃	C₂×C₂₅	1	3	yes	direct product factor
13	C₁₁×C₂₅	C₂²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
14	C₂²×C₅×C₁₃	C₅×C₁₁	1	1	yes	characteristic
15	C₂²×C₅×C₁₁	C₅×C₁₃	1	1	yes	characteristic
16	C₁₁×C₁₃	C₂²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₅×C₁₃	C₂×C₅×C₁₁	1	3	yes	—
18	C₂×C₅×C₁₁	C₂×C₅×C₁₃	1	3	yes	—
19	C₂²×C₂₅	C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₁₃	C₂²×C₅×C₁₁	1	1	yes	characteristic
21	C₅×C₁₁	C₂²×C₅×C₁₃	1	1	yes	characteristic
22	C₂²×C₁₃	C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Hall
23	C₂×C₂₅	C₂×C₁₁×C₁₃	1	3	yes	direct product factor
24	C₂²×C₁₁	C₁₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₁₃	C₂×C₁₁×C₂₅	1	3	yes	direct product factor
26	C₂₅	C₂²×C₁₁×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₁₁	C₂×C₁₃×C₂₅	1	3	yes	direct product factor
28	C₂²×C₅	C₅×C₁₁×C₁₃	1	1	yes	characteristic
29	C₁₃	C₂²×C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₁₁	C₂²×C₁₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₅	C₂×C₅×C₁₁×C₁₃	1	3	yes	—
32	C₅	C₂²×C₅×C₁₁×C₁₃	1	1	yes	characteristic
33	C₂²	C₁₁×C₁₃×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₁₁×C₁₃×C₂₅	1	3	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₂²×C₅×C₁₁×C₁₃
socle, prime radical	C₂²×C₅×C₁₁×C₁₃	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×C₁₁×C₁₃×C₂₅	C₂	direct (N × H)
2. C₁₁×C₁₃×C₂₅	C₂²	direct (N × H)
5. C₂²×C₁₃×C₂₅	C₁₁	direct (N × H)
6. C₂²×C₁₁×C₂₅	C₁₃	direct (N × H)
8. C₂×C₁₃×C₂₅	C₂×C₁₁	direct (N × H)
9. C₂²×C₁₁×C₁₃	C₂₅	direct (N × H)
10. C₂×C₁₁×C₂₅	C₂×C₁₃	direct (N × H)
11. C₁₃×C₂₅	C₂²×C₁₁	direct (N × H)
12. C₂×C₁₁×C₁₃	C₂×C₂₅	direct (N × H)
13. C₁₁×C₂₅	C₂²×C₁₃	direct (N × H)
16. C₁₁×C₁₃	C₂²×C₂₅	direct (N × H)
19. C₂²×C₂₅	C₁₁×C₁₃	direct (N × H)
22. C₂²×C₁₃	C₁₁×C₂₅	direct (N × H)
23. C₂×C₂₅	C₂×C₁₁×C₁₃	direct (N × H)
24. C₂²×C₁₁	C₁₃×C₂₅	direct (N × H)
25. C₂×C₁₃	C₂×C₁₁×C₂₅	direct (N × H)
26. C₂₅	C₂²×C₁₁×C₁₃	direct (N × H)
27. C₂×C₁₁	C₂×C₁₃×C₂₅	direct (N × H)
29. C₁₃	C₂²×C₁₁×C₂₅	direct (N × H)
30. C₁₁	C₂²×C₁₃×C₂₅	direct (N × H)
33. C₂²	C₁₁×C₁₃×C₂₅	direct (N × H)
34. C₂	C₂×C₁₁×C₁₃×C₂₅	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×C₁₁×C₁₃×C₂₅	2
C₂²×C₅×C₁₁×C₁₃	5
C₂²×C₁₃×C₂₅	11
C₂²×C₁₁×C₂₅	13

Subgroups — C22×C11×C13×C25 #28384641

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₁×C₁₃×C₂₅ #28384641