Subgroups — C₃×C₁₃×C₁₉×C₃₂ #72201044

Order 23712.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₁₃×C₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₉×C₃₂	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₃×C₈×C₁₃×C₁₉	C₄	1	1	yes	characteristic
4	C₁₃×C₁₆×C₁₉	C₂×C₃	1	1	yes	characteristic
5	C₃×C₄×C₁₃×C₁₉	C₈	1	1	yes	characteristic
6	C₈×C₁₃×C₁₉	C₃×C₄	1	1	yes	characteristic
7	C₃×C₁₉×C₃₂	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₁₃×C₁₉	C₁₆	1	1	yes	characteristic
9	C₃×C₁₃×C₃₂	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₄×C₁₃×C₁₉	C₃×C₈	1	1	yes	characteristic
11	C₃×C₁₆×C₁₉	C₂×C₁₃	1	1	yes	characteristic
12	C₃×C₁₃×C₁₉	C₃₂	1	1	yes	characteristic, direct product factor, Hall
13	C₃×C₁₃×C₁₆	C₂×C₁₉	1	1	yes	characteristic
14	C₁₉×C₃₂	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₃×C₁₉	C₃×C₁₆	1	1	yes	characteristic
16	C₃×C₈×C₁₉	C₄×C₁₃	1	1	yes	characteristic
17	C₁₃×C₃₂	C₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
18	C₃×C₈×C₁₃	C₄×C₁₉	1	1	yes	characteristic
19	C₁₆×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic
20	C₁₃×C₁₉	C₃×C₃₂	1	1	yes	characteristic, direct product factor, Hall
21	C₃×C₄×C₁₉	C₈×C₁₃	1	1	yes	characteristic
22	C₁₃×C₁₆	C₂×C₃×C₁₉	1	1	yes	characteristic
23	C₃×C₄×C₁₃	C₈×C₁₉	1	1	yes	characteristic
24	C₈×C₁₉	C₃×C₄×C₁₃	1	1	yes	characteristic
25	C₂×C₃×C₁₉	C₁₃×C₁₆	1	1	yes	characteristic
26	C₈×C₁₃	C₃×C₄×C₁₉	1	1	yes	characteristic
27	C₃×C₃₂	C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Hall
28	C₂×C₃×C₁₃	C₁₆×C₁₉	1	1	yes	characteristic
29	C₄×C₁₉	C₃×C₈×C₁₃	1	1	yes	characteristic
30	C₃×C₁₉	C₁₃×C₃₂	1	1	yes	characteristic, direct product factor, Hall
31	C₄×C₁₃	C₃×C₈×C₁₉	1	1	yes	characteristic
32	C₃×C₁₆	C₂×C₁₃×C₁₉	1	1	yes	characteristic
33	C₃×C₁₃	C₁₉×C₃₂	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₁₉	C₃×C₁₃×C₁₆	1	1	yes	characteristic
35	C₃₂	C₃×C₁₃×C₁₉	1	1	yes	characteristic, direct product factor, Sylow
36	C₂×C₁₃	C₃×C₁₆×C₁₉	1	1	yes	characteristic
37	C₃×C₈	C₄×C₁₃×C₁₉	1	1	yes	characteristic
38	C₁₉	C₃×C₁₃×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
39	C₁₆	C₂×C₃×C₁₃×C₁₉	1	1	yes	characteristic
40	C₁₃	C₃×C₁₉×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
41	C₃×C₄	C₈×C₁₃×C₁₉	1	1	yes	characteristic
42	C₈	C₃×C₄×C₁₃×C₁₉	1	1	yes	characteristic
43	C₂×C₃	C₁₃×C₁₆×C₁₉	1	1	yes	characteristic
44	C₄	C₃×C₈×C₁₃×C₁₉	1	1	yes	characteristic
45	C₃	C₁₃×C₁₉×C₃₂	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₁₃×C₁₆×C₁₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₁₆	C₂×C₃×C₁₃×C₁₉
socle, prime radical	C₂×C₃×C₁₃×C₁₉	C₁₆
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₁₉×C₃₂	C₃	direct (N × H)
7. C₃×C₁₉×C₃₂	C₁₃	direct (N × H)
9. C₃×C₁₃×C₃₂	C₁₉	direct (N × H)
12. C₃×C₁₃×C₁₉	C₃₂	direct (N × H)
14. C₁₉×C₃₂	C₃×C₁₃	direct (N × H)
17. C₁₃×C₃₂	C₃×C₁₉	direct (N × H)
20. C₁₃×C₁₉	C₃×C₃₂	direct (N × H)
27. C₃×C₃₂	C₁₃×C₁₉	direct (N × H)
30. C₃×C₁₉	C₁₃×C₃₂	direct (N × H)
33. C₃×C₁₃	C₁₉×C₃₂	direct (N × H)
35. C₃₂	C₃×C₁₃×C₁₉	direct (N × H)
38. C₁₉	C₃×C₁₃×C₃₂	direct (N × H)
40. C₁₃	C₃×C₁₉×C₃₂	direct (N × H)
45. C₃	C₁₃×C₁₉×C₃₂	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×C₁₃×C₁₆×C₁₉	2
C₁₃×C₁₉×C₃₂	3
C₃×C₁₉×C₃₂	13
C₃×C₁₃×C₃₂	19

Subgroups — C3×C13×C19×C32 #72201044

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₁₃×C₁₉×C₃₂ #72201044