Subgroups — C₃×C₅×C₁₆×C₁₀₃ #72202012

Order 24720.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₈×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	C₅×C₁₆×C₁₀₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₁₆×C₁₀₃	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₈×C₁₀₃	C₂×C₃	1	1	yes	characteristic
5	C₃×C₈×C₁₀₃	C₂×C₅	1	1	yes	characteristic
6	C₃×C₄×C₅×C₁₀₃	C₄	1	1	yes	characteristic
7	C₂×C₃×C₅×C₁₀₃	C₈	1	1	yes	characteristic
8	C₄×C₅×C₁₀₃	C₃×C₄	1	1	yes	characteristic
9	C₁₆×C₁₀₃	C₃×C₅	1	1	yes	characteristic, direct product factor, Hall
10	C₃×C₅×C₁₀₃	C₁₆	1	1	yes	characteristic, direct product factor, Hall
11	C₃×C₄×C₁₀₃	C₄×C₅	1	1	yes	characteristic
12	C₂×C₅×C₁₀₃	C₃×C₈	1	1	yes	characteristic
13	C₈×C₁₀₃	C₂×C₃×C₅	1	1	yes	characteristic
14	C₂×C₃×C₁₀₃	C₅×C₈	1	1	yes	characteristic
15	C₅×C₁₀₃	C₃×C₁₆	1	1	yes	characteristic, direct product factor, Hall
16	C₄×C₁₀₃	C₃×C₄×C₅	1	1	yes	characteristic
17	C₃×C₁₀₃	C₅×C₁₆	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₅×C₁₆	C₁₀₃	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂×C₁₀₃	C₃×C₅×C₈	1	1	yes	characteristic
20	C₃×C₅×C₈	C₂×C₁₀₃	1	1	yes	characteristic
21	C₁₀₃	C₃×C₅×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
22	C₅×C₁₆	C₃×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
23	C₃×C₄×C₅	C₄×C₁₀₃	1	1	yes	characteristic
24	C₃×C₁₆	C₅×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
25	C₅×C₈	C₂×C₃×C₁₀₃	1	1	yes	characteristic
26	C₂×C₃×C₅	C₈×C₁₀₃	1	1	yes	characteristic
27	C₃×C₈	C₂×C₅×C₁₀₃	1	1	yes	characteristic
28	C₄×C₅	C₃×C₄×C₁₀₃	1	1	yes	characteristic
29	C₁₆	C₃×C₅×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
30	C₃×C₅	C₁₆×C₁₀₃	1	1	yes	characteristic, direct product factor, Hall
31	C₃×C₄	C₄×C₅×C₁₀₃	1	1	yes	characteristic
32	C₂×C₅	C₃×C₈×C₁₀₃	1	1	yes	characteristic
33	C₈	C₂×C₃×C₅×C₁₀₃	1	1	yes	characteristic
34	C₂×C₃	C₅×C₈×C₁₀₃	1	1	yes	characteristic
35	C₅	C₃×C₁₆×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
36	C₄	C₃×C₄×C₅×C₁₀₃	1	1	yes	characteristic
37	C₃	C₅×C₁₆×C₁₀₃	1	1	yes	characteristic, direct product factor, Sylow
38	C₂	C₃×C₅×C₈×C₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₈	C₂×C₃×C₅×C₁₀₃
socle, prime radical	C₂×C₃×C₅×C₁₀₃	C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×C₁₆×C₁₀₃	C₃	direct (N × H)
3. C₃×C₁₆×C₁₀₃	C₅	direct (N × H)
9. C₁₆×C₁₀₃	C₃×C₅	direct (N × H)
10. C₃×C₅×C₁₀₃	C₁₆	direct (N × H)
15. C₅×C₁₀₃	C₃×C₁₆	direct (N × H)
17. C₃×C₁₀₃	C₅×C₁₆	direct (N × H)
18. C₃×C₅×C₁₆	C₁₀₃	direct (N × H)
21. C₁₀₃	C₃×C₅×C₁₆	direct (N × H)
22. C₅×C₁₆	C₃×C₁₀₃	direct (N × H)
24. C₃×C₁₆	C₅×C₁₀₃	direct (N × H)
29. C₁₆	C₃×C₅×C₁₀₃	direct (N × H)
30. C₃×C₅	C₁₆×C₁₀₃	direct (N × H)
35. C₅	C₃×C₁₆×C₁₀₃	direct (N × H)
37. C₃	C₅×C₁₆×C₁₀₃	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×C₅×C₈×C₁₀₃	2
C₅×C₁₆×C₁₀₃	3
C₃×C₁₆×C₁₀₃	5
C₃×C₅×C₁₆	103

Subgroups — C3×C5×C16×C103 #72202012

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×C₁₆×C₁₀₃ #72202012