Subgroups — C₃×C₅²×C₈×C₄₇ #72205193

Order 28200.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₈×C₄₇	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₃×C₅×C₈×C₄₇	C₅	1	6	yes	maximal, direct product factor
3	C₃×C₄×C₅²×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅²×C₄₇	C₄	1	1	yes	characteristic
5	C₄×C₅²×C₄₇	C₂×C₃	1	1	yes	characteristic
6	C₃×C₅²×C₄₇	C₈	1	1	yes	characteristic, direct product factor, Hall
7	C₃×C₄×C₅×C₄₇	C₂×C₅	1	6	yes	—
8	C₂×C₅²×C₄₇	C₃×C₄	1	1	yes	characteristic
9	C₅×C₈×C₄₇	C₃×C₅	1	6	yes	direct product factor
10	C₂×C₃×C₅×C₄₇	C₄×C₅	1	6	yes	—
11	C₅²×C₄₇	C₃×C₈	1	1	yes	characteristic, direct product factor, Hall
12	C₃×C₈×C₄₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
13	C₄×C₅×C₄₇	C₂×C₃×C₅	1	6	yes	—
14	C₃×C₅×C₄₇	C₅×C₈	1	6	yes	direct product factor
15	C₃×C₅²×C₈	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₃×C₄×C₄₇	C₂×C₅²	1	1	yes	characteristic
17	C₂×C₅×C₄₇	C₃×C₄×C₅	1	6	yes	—
18	C₈×C₄₇	C₃×C₅²	1	1	yes	characteristic, direct product factor, Hall
19	C₃×C₄×C₅²	C₂×C₄₇	1	1	yes	characteristic
20	C₂×C₃×C₄₇	C₄×C₅²	1	1	yes	characteristic
21	C₅×C₄₇	C₃×C₅×C₈	1	6	yes	direct product factor
22	C₅²×C₈	C₃×C₄₇	1	1	yes	characteristic, direct product factor, Hall
23	C₄×C₄₇	C₂×C₃×C₅²	1	1	yes	characteristic
24	C₂×C₃×C₅²	C₄×C₄₇	1	1	yes	characteristic
25	C₃×C₄₇	C₅²×C₈	1	1	yes	characteristic, direct product factor, Hall
26	C₃×C₅×C₈	C₅×C₄₇	1	6	yes	direct product factor
27	C₄×C₅²	C₂×C₃×C₄₇	1	1	yes	characteristic
28	C₂×C₄₇	C₃×C₄×C₅²	1	1	yes	characteristic
29	C₃×C₅²	C₈×C₄₇	1	1	yes	characteristic, direct product factor, Hall
30	C₃×C₄×C₅	C₂×C₅×C₄₇	1	6	yes	—
31	C₂×C₅²	C₃×C₄×C₄₇	1	1	yes	characteristic
32	C₄₇	C₃×C₅²×C₈	1	1	yes	characteristic, direct product factor, Sylow
33	C₅×C₈	C₃×C₅×C₄₇	1	6	yes	direct product factor
34	C₂×C₃×C₅	C₄×C₅×C₄₇	1	6	yes	—
35	C₅²	C₃×C₈×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
36	C₃×C₈	C₅²×C₄₇	1	1	yes	characteristic, direct product factor, Hall
37	C₄×C₅	C₂×C₃×C₅×C₄₇	1	6	yes	—
38	C₃×C₅	C₅×C₈×C₄₇	1	6	yes	direct product factor
39	C₃×C₄	C₂×C₅²×C₄₇	1	1	yes	characteristic
40	C₂×C₅	C₃×C₄×C₅×C₄₇	1	6	yes	—
41	C₈	C₃×C₅²×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	C₄×C₅²×C₄₇	1	1	yes	characteristic
43	C₅	C₃×C₅×C₈×C₄₇	1	6	yes	direct product factor
44	C₄	C₂×C₃×C₅²×C₄₇	1	1	yes	characteristic
45	C₃	C₅²×C₈×C₄₇	1	1	yes	characteristic, direct product factor, Sylow
46	C₂	C₃×C₄×C₅²×C₄₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄	C₂×C₃×C₅²×C₄₇
socle, prime radical	C₂×C₃×C₅²×C₄₇	C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅²×C₈×C₄₇	C₃	direct (N × H)
2. C₃×C₅×C₈×C₄₇	C₅	direct (N × H)
6. C₃×C₅²×C₄₇	C₈	direct (N × H)
9. C₅×C₈×C₄₇	C₃×C₅	direct (N × H)
11. C₅²×C₄₇	C₃×C₈	direct (N × H)
12. C₃×C₈×C₄₇	C₅²	direct (N × H)
14. C₃×C₅×C₄₇	C₅×C₈	direct (N × H)
15. C₃×C₅²×C₈	C₄₇	direct (N × H)
18. C₈×C₄₇	C₃×C₅²	direct (N × H)
21. C₅×C₄₇	C₃×C₅×C₈	direct (N × H)
22. C₅²×C₈	C₃×C₄₇	direct (N × H)
25. C₃×C₄₇	C₅²×C₈	direct (N × H)
26. C₃×C₅×C₈	C₅×C₄₇	direct (N × H)
29. C₃×C₅²	C₈×C₄₇	direct (N × H)
32. C₄₇	C₃×C₅²×C₈	direct (N × H)
33. C₅×C₈	C₃×C₅×C₄₇	direct (N × H)
35. C₅²	C₃×C₈×C₄₇	direct (N × H)
36. C₃×C₈	C₅²×C₄₇	direct (N × H)
38. C₃×C₅	C₅×C₈×C₄₇	direct (N × H)
41. C₈	C₃×C₅²×C₄₇	direct (N × H)
43. C₅	C₃×C₅×C₈×C₄₇	direct (N × H)
45. C₃	C₅²×C₈×C₄₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₈×C₄₇	3
C₃×C₅×C₈×C₄₇	5
C₃×C₄×C₅²×C₄₇	2
C₃×C₅²×C₈	47

Subgroups — C3×C52×C8×C47 #72205193

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅²×C₈×C₄₇ #72205193