Subgroups — C₃×C₄×C₇×C₂₅ #14523521

Order 2100.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₇×C₂₅	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₇×C₂₅	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₃×C₄×C₅×C₇	C₅	1	1	yes	maximal, characteristic
5	C₂×C₇×C₂₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₄×C₂₅	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×C₇	C₂×C₅	1	1	yes	characteristic
8	C₇×C₂₅	C₃×C₄	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₃×C₂₅	C₂×C₇	1	1	yes	characteristic
10	C₄×C₅×C₇	C₃×C₅	1	1	yes	characteristic
11	C₃×C₅×C₇	C₄×C₅	1	1	yes	characteristic
12	C₄×C₂₅	C₃×C₇	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₄×C₇	C₂₅	1	1	yes	characteristic, direct product factor, Hall
14	C₃×C₂₅	C₄×C₇	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₅×C₇	C₂×C₃×C₅	1	1	yes	characteristic
16	C₃×C₄×C₅	C₅×C₇	1	1	yes	characteristic
17	C₂×C₂₅	C₂×C₃×C₇	1	1	yes	characteristic
18	C₂×C₃×C₇	C₂×C₂₅	1	1	yes	characteristic
19	C₅×C₇	C₃×C₄×C₅	1	1	yes	characteristic
20	C₂×C₃×C₅	C₂×C₅×C₇	1	1	yes	characteristic
21	C₄×C₇	C₃×C₂₅	1	1	yes	characteristic, direct product factor, Hall
22	C₂₅	C₃×C₄×C₇	1	1	yes	characteristic, direct product factor, Sylow
23	C₃×C₇	C₄×C₂₅	1	1	yes	characteristic, direct product factor, Hall
24	C₄×C₅	C₃×C₅×C₇	1	1	yes	characteristic
25	C₃×C₅	C₄×C₅×C₇	1	1	yes	characteristic
26	C₂×C₇	C₂×C₃×C₂₅	1	1	yes	characteristic
27	C₃×C₄	C₇×C₂₅	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₅	C₂×C₃×C₅×C₇	1	1	yes	characteristic
29	C₇	C₃×C₄×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×C₃	C₂×C₇×C₂₅	1	1	yes	characteristic
31	C₅	C₃×C₄×C₅×C₇	1	1	yes	characteristic
32	C₄	C₃×C₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
33	C₃	C₄×C₇×C₂₅	1	1	yes	characteristic, direct product factor, Sylow
34	C₂	C₂×C₃×C₇×C₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₅	C₂×C₃×C₅×C₇
socle, prime radical	C₂×C₃×C₅×C₇	C₂×C₅
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₂₅	C₃	direct (N × H)
3. C₃×C₇×C₂₅	C₄	direct (N × H)
6. C₃×C₄×C₂₅	C₇	direct (N × H)
8. C₇×C₂₅	C₃×C₄	direct (N × H)
12. C₄×C₂₅	C₃×C₇	direct (N × H)
13. C₃×C₄×C₇	C₂₅	direct (N × H)
14. C₃×C₂₅	C₄×C₇	direct (N × H)
21. C₄×C₇	C₃×C₂₅	direct (N × H)
22. C₂₅	C₃×C₄×C₇	direct (N × H)
23. C₃×C₇	C₄×C₂₅	direct (N × H)
27. C₃×C₄	C₇×C₂₅	direct (N × H)
29. C₇	C₃×C₄×C₂₅	direct (N × H)
32. C₄	C₃×C₇×C₂₅	direct (N × H)
33. C₃	C₄×C₇×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×C₃×C₇×C₂₅	2
C₄×C₇×C₂₅	3
C₃×C₄×C₅×C₇	5
C₃×C₄×C₂₅	7

Subgroups — C3×C4×C7×C25 #14523521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₇×C₂₅ #14523521