Subgroups — C₃×C₇²×C₈×C₁₃ #72193296

Order 15288.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×C₈×C₁₃	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₇×C₈×C₁₃	C₇	1	8	yes	maximal, direct product factor
3	C₃×C₄×C₇²×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₇²×C₁₃	C₄	1	1	yes	characteristic
5	C₄×C₇²×C₁₃	C₂×C₃	1	1	yes	characteristic
6	C₃×C₇²×C₁₃	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₂×C₇²×C₁₃	C₃×C₄	1	1	yes	characteristic
8	C₃×C₇²×C₈	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₃×C₄×C₇×C₁₃	C₂×C₇	1	8	yes	—
10	C₇×C₈×C₁₃	C₃×C₇	1	8	yes	direct product factor
11	C₇²×C₁₃	C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₄×C₇²	C₂×C₁₃	1	1	yes	characteristic
13	C₂×C₃×C₇×C₁₃	C₄×C₇	1	8	yes	—
14	C₇²×C₈	C₃×C₁₃	1	1	yes	characteristic, direct product factor, Hall
15	C₄×C₇×C₁₃	C₂×C₃×C₇	1	8	yes	—
16	C₃×C₈×C₁₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
17	C₂×C₃×C₇²	C₄×C₁₃	1	1	yes	characteristic
18	C₃×C₇×C₁₃	C₇×C₈	1	8	yes	direct product factor
19	C₄×C₇²	C₂×C₃×C₁₃	1	1	yes	characteristic
20	C₂×C₇×C₁₃	C₃×C₄×C₇	1	8	yes	—
21	C₃×C₇×C₈	C₇×C₁₃	1	8	yes	direct product factor
22	C₃×C₄×C₁₃	C₂×C₇²	1	1	yes	characteristic
23	C₃×C₇²	C₈×C₁₃	1	1	yes	characteristic, direct product factor, Hall
24	C₈×C₁₃	C₃×C₇²	1	1	yes	characteristic, direct product factor, Hall
25	C₂×C₇²	C₃×C₄×C₁₃	1	1	yes	characteristic
26	C₇×C₁₃	C₃×C₇×C₈	1	8	yes	direct product factor
27	C₃×C₄×C₇	C₂×C₇×C₁₃	1	8	yes	—
28	C₂×C₃×C₁₃	C₄×C₇²	1	1	yes	characteristic
29	C₇×C₈	C₃×C₇×C₁₃	1	8	yes	direct product factor
30	C₄×C₁₃	C₂×C₃×C₇²	1	1	yes	characteristic
31	C₇²	C₃×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
32	C₂×C₃×C₇	C₄×C₇×C₁₃	1	8	yes	—
33	C₃×C₁₃	C₇²×C₈	1	1	yes	characteristic, direct product factor, Hall
34	C₄×C₇	C₂×C₃×C₇×C₁₃	1	8	yes	—
35	C₂×C₁₃	C₃×C₄×C₇²	1	1	yes	characteristic
36	C₃×C₈	C₇²×C₁₃	1	1	yes	characteristic, direct product factor, Hall
37	C₃×C₇	C₇×C₈×C₁₃	1	8	yes	direct product factor
38	C₂×C₇	C₃×C₄×C₇×C₁₃	1	8	yes	—
39	C₁₃	C₃×C₇²×C₈	1	1	yes	characteristic, direct product factor, Sylow
40	C₃×C₄	C₂×C₇²×C₁₃	1	1	yes	characteristic
41	C₈	C₃×C₇²×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
42	C₇	C₃×C₇×C₈×C₁₃	1	8	yes	direct product factor
43	C₂×C₃	C₄×C₇²×C₁₃	1	1	yes	characteristic
44	C₄	C₂×C₃×C₇²×C₁₃	1	1	yes	characteristic
45	C₃	C₇²×C₈×C₁₃	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₄×C₇²×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₇²×C₁₃
socle, prime radical	C₂×C₃×C₇²×C₁₃	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇²×C₈×C₁₃	C₃	direct (N × H)
2. C₃×C₇×C₈×C₁₃	C₇	direct (N × H)
6. C₃×C₇²×C₁₃	C₈	direct (N × H)
8. C₃×C₇²×C₈	C₁₃	direct (N × H)
10. C₇×C₈×C₁₃	C₃×C₇	direct (N × H)
11. C₇²×C₁₃	C₃×C₈	direct (N × H)
14. C₇²×C₈	C₃×C₁₃	direct (N × H)
16. C₃×C₈×C₁₃	C₇²	direct (N × H)
18. C₃×C₇×C₁₃	C₇×C₈	direct (N × H)
21. C₃×C₇×C₈	C₇×C₁₃	direct (N × H)
23. C₃×C₇²	C₈×C₁₃	direct (N × H)
24. C₈×C₁₃	C₃×C₇²	direct (N × H)
26. C₇×C₁₃	C₃×C₇×C₈	direct (N × H)
29. C₇×C₈	C₃×C₇×C₁₃	direct (N × H)
31. C₇²	C₃×C₈×C₁₃	direct (N × H)
33. C₃×C₁₃	C₇²×C₈	direct (N × H)
36. C₃×C₈	C₇²×C₁₃	direct (N × H)
37. C₃×C₇	C₇×C₈×C₁₃	direct (N × H)
39. C₁₃	C₃×C₇²×C₈	direct (N × H)
41. C₈	C₃×C₇²×C₁₃	direct (N × H)
42. C₇	C₃×C₇×C₈×C₁₃	direct (N × H)
45. C₃	C₇²×C₈×C₁₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇²×C₈×C₁₃	3
C₃×C₇×C₈×C₁₃	7
C₃×C₄×C₇²×C₁₃	2
C₃×C₇²×C₈	13

Subgroups — C3×C72×C8×C13 #72193296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₇²×C₈×C₁₃ #72193296