Subgroups — C₅×C₈×C₉×C₇₉ #72205403

Order 28440.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×C₈×C₇₉	C₃	1	1	yes	maximal, characteristic
2	C₈×C₉×C₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₅×C₈×C₇₉	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₄×C₅×C₉×C₇₉	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×C₉×C₇₉	C₄	1	1	yes	characteristic
6	C₃×C₄×C₅×C₇₉	C₂×C₃	1	1	yes	characteristic
7	C₅×C₉×C₇₉	C₈	1	1	yes	characteristic, direct product factor, Hall
8	C₄×C₉×C₇₉	C₂×C₅	1	1	yes	characteristic
9	C₂×C₃×C₅×C₇₉	C₃×C₄	1	1	yes	characteristic
10	C₃×C₈×C₇₉	C₃×C₅	1	1	yes	characteristic
11	C₄×C₅×C₇₉	C₂×C₉	1	1	yes	characteristic
12	C₂×C₉×C₇₉	C₄×C₅	1	1	yes	characteristic
13	C₃×C₅×C₇₉	C₃×C₈	1	1	yes	characteristic
14	C₃×C₄×C₇₉	C₂×C₃×C₅	1	1	yes	characteristic
15	C₂×C₅×C₇₉	C₄×C₉	1	1	yes	characteristic
16	C₉×C₇₉	C₅×C₈	1	1	yes	characteristic, direct product factor, Hall
17	C₈×C₇₉	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₇₉	C₃×C₄×C₅	1	1	yes	characteristic
19	C₅×C₇₉	C₈×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₅×C₈×C₉	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₄×C₇₉	C₂×C₅×C₉	1	1	yes	characteristic
22	C₃×C₇₉	C₃×C₅×C₈	1	1	yes	characteristic
23	C₄×C₅×C₉	C₂×C₇₉	1	1	yes	characteristic
24	C₂×C₇₉	C₄×C₅×C₉	1	1	yes	characteristic
25	C₃×C₅×C₈	C₃×C₇₉	1	1	yes	characteristic
26	C₂×C₅×C₉	C₄×C₇₉	1	1	yes	characteristic
27	C₇₉	C₅×C₈×C₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₈×C₉	C₅×C₇₉	1	1	yes	characteristic, direct product factor, Hall
29	C₃×C₄×C₅	C₂×C₃×C₇₉	1	1	yes	characteristic
30	C₅×C₉	C₈×C₇₉	1	1	yes	characteristic, direct product factor, Hall
31	C₅×C₈	C₉×C₇₉	1	1	yes	characteristic, direct product factor, Hall
32	C₄×C₉	C₂×C₅×C₇₉	1	1	yes	characteristic
33	C₂×C₃×C₅	C₃×C₄×C₇₉	1	1	yes	characteristic
34	C₃×C₈	C₃×C₅×C₇₉	1	1	yes	characteristic
35	C₄×C₅	C₂×C₉×C₇₉	1	1	yes	characteristic
36	C₂×C₉	C₄×C₅×C₇₉	1	1	yes	characteristic
37	C₃×C₅	C₃×C₈×C₇₉	1	1	yes	characteristic
38	C₃×C₄	C₂×C₃×C₅×C₇₉	1	1	yes	characteristic
39	C₂×C₅	C₄×C₉×C₇₉	1	1	yes	characteristic
40	C₉	C₅×C₈×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₈	C₅×C₉×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	C₃×C₄×C₅×C₇₉	1	1	yes	characteristic
43	C₅	C₈×C₉×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₄	C₂×C₅×C₉×C₇₉	1	1	yes	characteristic
45	C₃	C₃×C₅×C₈×C₇₉	1	1	yes	characteristic
46	C₂	C₄×C₅×C₉×C₇₉	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃×C₄	C₂×C₃×C₅×C₇₉
socle, prime radical	C₂×C₃×C₅×C₇₉	C₃×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₈×C₉×C₇₉	C₅	direct (N × H)
3. C₅×C₈×C₇₉	C₉	direct (N × H)
7. C₅×C₉×C₇₉	C₈	direct (N × H)
16. C₉×C₇₉	C₅×C₈	direct (N × H)
17. C₈×C₇₉	C₅×C₉	direct (N × H)
19. C₅×C₇₉	C₈×C₉	direct (N × H)
20. C₅×C₈×C₉	C₇₉	direct (N × H)
27. C₇₉	C₅×C₈×C₉	direct (N × H)
28. C₈×C₉	C₅×C₇₉	direct (N × H)
30. C₅×C₉	C₈×C₇₉	direct (N × H)
31. C₅×C₈	C₉×C₇₉	direct (N × H)
40. C₉	C₅×C₈×C₇₉	direct (N × H)
41. C₈	C₅×C₉×C₇₉	direct (N × H)
43. C₅	C₈×C₉×C₇₉	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×C₇₉	3
C₈×C₉×C₇₉	5
C₄×C₅×C₉×C₇₉	2
C₅×C₈×C₉	79

Subgroups — C5×C8×C9×C79 #72205403

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₈×C₉×C₇₉ #72205403