Subgroups — C₃²×C₇×C₁₁×C₂₅ #31773145

Order 17325.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁×C₂₅	C₃	1	4	yes	maximal, direct product factor
2	C₃²×C₅×C₇×C₁₁	C₅	1	1	yes	maximal, characteristic
3	C₃²×C₁₁×C₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₇×C₁₁×C₂₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
5	C₃²×C₇×C₂₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₃×C₅×C₇×C₁₁	C₃×C₅	1	4	yes	—
7	C₃×C₁₁×C₂₅	C₃×C₇	1	4	yes	direct product factor
8	C₃²×C₇×C₁₁	C₂₅	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₇×C₂₅	C₃×C₁₁	1	4	yes	direct product factor
10	C₃²×C₅×C₁₁	C₅×C₇	1	1	yes	characteristic
11	C₅×C₇×C₁₁	C₃²×C₅	1	1	yes	characteristic
12	C₃²×C₅×C₇	C₅×C₁₁	1	1	yes	characteristic
13	C₁₁×C₂₅	C₃²×C₇	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₇×C₁₁	C₃×C₂₅	1	4	yes	direct product factor
15	C₃²×C₂₅	C₇×C₁₁	1	1	yes	characteristic, direct product factor, Hall
16	C₇×C₂₅	C₃²×C₁₁	1	1	yes	characteristic, direct product factor, Hall
17	C₃×C₅×C₁₁	C₃×C₅×C₇	1	4	yes	—
18	C₃×C₅×C₇	C₃×C₅×C₁₁	1	4	yes	—
19	C₃²×C₁₁	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
20	C₇×C₁₁	C₃²×C₂₅	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₂₅	C₃×C₇×C₁₁	1	4	yes	direct product factor
22	C₃²×C₇	C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Hall
23	C₅×C₁₁	C₃²×C₅×C₇	1	1	yes	characteristic
24	C₃²×C₅	C₅×C₇×C₁₁	1	1	yes	characteristic
25	C₅×C₇	C₃²×C₅×C₁₁	1	1	yes	characteristic
26	C₃×C₁₁	C₃×C₇×C₂₅	1	4	yes	direct product factor
27	C₂₅	C₃²×C₇×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
28	C₃×C₇	C₃×C₁₁×C₂₅	1	4	yes	direct product factor
29	C₃×C₅	C₃×C₅×C₇×C₁₁	1	4	yes	—
30	C₁₁	C₃²×C₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
31	C₃²	C₇×C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
32	C₇	C₃²×C₁₁×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₅	C₃²×C₅×C₇×C₁₁	1	1	yes	characteristic
34	C₃	C₃×C₇×C₁₁×C₂₅	1	4	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₅	C₃²×C₅×C₇×C₁₁
socle, prime radical	C₃²×C₅×C₇×C₁₁	C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₇×C₁₁×C₂₅	C₃	direct (N × H)
3. C₃²×C₁₁×C₂₅	C₇	direct (N × H)
4. C₇×C₁₁×C₂₅	C₃²	direct (N × H)
5. C₃²×C₇×C₂₅	C₁₁	direct (N × H)
7. C₃×C₁₁×C₂₅	C₃×C₇	direct (N × H)
8. C₃²×C₇×C₁₁	C₂₅	direct (N × H)
9. C₃×C₇×C₂₅	C₃×C₁₁	direct (N × H)
13. C₁₁×C₂₅	C₃²×C₇	direct (N × H)
14. C₃×C₇×C₁₁	C₃×C₂₅	direct (N × H)
15. C₃²×C₂₅	C₇×C₁₁	direct (N × H)
16. C₇×C₂₅	C₃²×C₁₁	direct (N × H)
19. C₃²×C₁₁	C₇×C₂₅	direct (N × H)
20. C₇×C₁₁	C₃²×C₂₅	direct (N × H)
21. C₃×C₂₅	C₃×C₇×C₁₁	direct (N × H)
22. C₃²×C₇	C₁₁×C₂₅	direct (N × H)
26. C₃×C₁₁	C₃×C₇×C₂₅	direct (N × H)
27. C₂₅	C₃²×C₇×C₁₁	direct (N × H)
28. C₃×C₇	C₃×C₁₁×C₂₅	direct (N × H)
30. C₁₁	C₃²×C₇×C₂₅	direct (N × H)
31. C₃²	C₇×C₁₁×C₂₅	direct (N × H)
32. C₇	C₃²×C₁₁×C₂₅	direct (N × H)
34. C₃	C₃×C₇×C₁₁×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
C₃×C₇×C₁₁×C₂₅	3
C₃²×C₅×C₇×C₁₁	5
C₃²×C₁₁×C₂₅	7
C₃²×C₇×C₂₅	11

Subgroups — C32×C7×C11×C25 #31773145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₇×C₁₁×C₂₅ #31773145