Subgroups — C₃×C₆₄×C₁₂₅ #72201261

Order 24000.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃₂×C₁₂₅	C₂	1	1	yes	maximal, characteristic
2	C₆₄×C₁₂₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₆×C₁₂₅	C₄	1	1	yes	characteristic
4	C₃×C₂₅×C₆₄	C₅	1	1	yes	maximal, characteristic
5	C₃₂×C₁₂₅	C₂×C₃	1	1	yes	characteristic
6	C₃×C₈×C₁₂₅	C₈	1	1	yes	characteristic
7	C₃×C₂₅×C₃₂	C₂×C₅	1	1	yes	characteristic
8	C₁₆×C₁₂₅	C₃×C₄	1	1	yes	characteristic
9	C₂₅×C₆₄	C₃×C₅	1	1	yes	characteristic
10	C₃×C₄×C₁₂₅	C₁₆	1	1	yes	characteristic
11	C₃×C₁₆×C₂₅	C₄×C₅	1	1	yes	characteristic
12	C₈×C₁₂₅	C₃×C₈	1	1	yes	characteristic
13	C₃×C₅×C₆₄	C₂₅	1	1	yes	characteristic
14	C₂₅×C₃₂	C₂×C₃×C₅	1	1	yes	characteristic
15	C₂×C₃×C₁₂₅	C₃₂	1	1	yes	characteristic
16	C₃×C₈×C₂₅	C₅×C₈	1	1	yes	characteristic
17	C₄×C₁₂₅	C₃×C₁₆	1	1	yes	characteristic
18	C₃×C₅×C₃₂	C₂×C₂₅	1	1	yes	characteristic
19	C₁₆×C₂₅	C₃×C₄×C₅	1	1	yes	characteristic
20	C₃×C₁₂₅	C₆₄	1	1	yes	characteristic, direct product factor, Hall
21	C₅×C₆₄	C₃×C₂₅	1	1	yes	characteristic
22	C₃×C₄×C₂₅	C₅×C₁₆	1	1	yes	characteristic
23	C₂×C₁₂₅	C₃×C₃₂	1	1	yes	characteristic
24	C₃×C₅×C₁₆	C₄×C₂₅	1	1	yes	characteristic
25	C₈×C₂₅	C₃×C₅×C₈	1	1	yes	characteristic
26	C₃×C₆₄	C₁₂₅	1	1	yes	characteristic, direct product factor, Hall
27	C₅×C₃₂	C₂×C₃×C₂₅	1	1	yes	characteristic
28	C₂×C₃×C₂₅	C₅×C₃₂	1	1	yes	characteristic
29	C₁₂₅	C₃×C₆₄	1	1	yes	characteristic, direct product factor, Sylow
30	C₃×C₅×C₈	C₈×C₂₅	1	1	yes	characteristic
31	C₄×C₂₅	C₃×C₅×C₁₆	1	1	yes	characteristic
32	C₃×C₃₂	C₂×C₁₂₅	1	1	yes	characteristic
33	C₅×C₁₆	C₃×C₄×C₂₅	1	1	yes	characteristic
34	C₃×C₂₅	C₅×C₆₄	1	1	yes	characteristic
35	C₆₄	C₃×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₄×C₅	C₁₆×C₂₅	1	1	yes	characteristic
37	C₂×C₂₅	C₃×C₅×C₃₂	1	1	yes	characteristic
38	C₃×C₁₆	C₄×C₁₂₅	1	1	yes	characteristic
39	C₅×C₈	C₃×C₈×C₂₅	1	1	yes	characteristic
40	C₃₂	C₂×C₃×C₁₂₅	1	1	yes	characteristic
41	C₂×C₃×C₅	C₂₅×C₃₂	1	1	yes	characteristic
42	C₂₅	C₃×C₅×C₆₄	1	1	yes	characteristic
43	C₃×C₈	C₈×C₁₂₅	1	1	yes	characteristic
44	C₄×C₅	C₃×C₁₆×C₂₅	1	1	yes	characteristic
45	C₁₆	C₃×C₄×C₁₂₅	1	1	yes	characteristic
46	C₃×C₅	C₂₅×C₆₄	1	1	yes	characteristic
47	C₃×C₄	C₁₆×C₁₂₅	1	1	yes	characteristic
48	C₂×C₅	C₃×C₂₅×C₃₂	1	1	yes	characteristic
49	C₈	C₃×C₈×C₁₂₅	1	1	yes	characteristic
50	C₂×C₃	C₃₂×C₁₂₅	1	1	yes	characteristic
51	C₅	C₃×C₂₅×C₆₄	1	1	yes	characteristic
52	C₄	C₃×C₁₆×C₁₂₅	1	1	yes	characteristic
53	C₃	C₆₄×C₁₂₅	1	1	yes	characteristic, direct product factor, Sylow
54	C₂	C₃×C₃₂×C₁₂₅	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂₅×C₃₂	C₂×C₃×C₅
socle, prime radical	C₂×C₃×C₅	C₂₅×C₃₂
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₆₄×C₁₂₅	C₃	direct (N × H)
20. C₃×C₁₂₅	C₆₄	direct (N × H)
26. C₃×C₆₄	C₁₂₅	direct (N × H)
29. C₁₂₅	C₃×C₆₄	direct (N × H)
35. C₆₄	C₃×C₁₂₅	direct (N × H)
53. C₃	C₆₄×C₁₂₅	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×C₃₂×C₁₂₅	2
C₆₄×C₁₂₅	3
C₃×C₂₅×C₆₄	5

Subgroups — C3×C64×C125 #72201261

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₆₄×C₁₂₅ #72201261