Subgroups — C₂³×C₅×C₉×C₇₉ #72205408

Order 28440.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×C₇₉	C₃	1	1	yes	maximal, characteristic
2	C₂³×C₉×C₇₉	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
3	C₂³×C₅×C₇₉	C₉	1	1	yes	characteristic, direct product factor, Hall
4	C₂²×C₅×C₉×C₇₉	C₂	1	7	yes	maximal, direct product factor
5	C₂×C₅×C₉×C₇₉	C₂²	1	7	yes	direct product factor
6	C₂²×C₃×C₅×C₇₉	C₂×C₃	1	7	yes	—
7	C₅×C₉×C₇₉	C₂³	1	1	yes	characteristic, direct product factor, Hall
8	C₂²×C₉×C₇₉	C₂×C₅	1	7	yes	direct product factor
9	C₂×C₃×C₅×C₇₉	C₂²×C₃	1	7	yes	—
10	C₂³×C₃×C₇₉	C₃×C₅	1	1	yes	characteristic
11	C₂²×C₅×C₇₉	C₂×C₉	1	7	yes	direct product factor
12	C₂×C₉×C₇₉	C₂²×C₅	1	7	yes	direct product factor
13	C₃×C₅×C₇₉	C₂³×C₃	1	1	yes	characteristic
14	C₂²×C₃×C₇₉	C₂×C₃×C₅	1	7	yes	—
15	C₂×C₅×C₇₉	C₂²×C₉	1	7	yes	direct product factor
16	C₉×C₇₉	C₂³×C₅	1	1	yes	characteristic, direct product factor, Hall
17	C₂³×C₇₉	C₅×C₉	1	1	yes	characteristic, direct product factor, Hall
18	C₂×C₃×C₇₉	C₂²×C₃×C₅	1	7	yes	—
19	C₅×C₇₉	C₂³×C₉	1	1	yes	characteristic, direct product factor, Hall
20	C₂³×C₅×C₉	C₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₇₉	C₂×C₅×C₉	1	7	yes	direct product factor
22	C₃×C₇₉	C₂³×C₃×C₅	1	1	yes	characteristic
23	C₂²×C₅×C₉	C₂×C₇₉	1	7	yes	direct product factor
24	C₂×C₇₉	C₂²×C₅×C₉	1	7	yes	direct product factor
25	C₂³×C₃×C₅	C₃×C₇₉	1	1	yes	characteristic
26	C₂×C₅×C₉	C₂²×C₇₉	1	7	yes	direct product factor
27	C₇₉	C₂³×C₅×C₉	1	1	yes	characteristic, direct product factor, Sylow
28	C₂³×C₉	C₅×C₇₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂²×C₃×C₅	C₂×C₃×C₇₉	1	7	yes	—
30	C₅×C₉	C₂³×C₇₉	1	1	yes	characteristic, direct product factor, Hall
31	C₂³×C₅	C₉×C₇₉	1	1	yes	characteristic, direct product factor, Hall
32	C₂²×C₉	C₂×C₅×C₇₉	1	7	yes	direct product factor
33	C₂×C₃×C₅	C₂²×C₃×C₇₉	1	7	yes	—
34	C₂³×C₃	C₃×C₅×C₇₉	1	1	yes	characteristic
35	C₂²×C₅	C₂×C₉×C₇₉	1	7	yes	direct product factor
36	C₂×C₉	C₂²×C₅×C₇₉	1	7	yes	direct product factor
37	C₃×C₅	C₂³×C₃×C₇₉	1	1	yes	characteristic
38	C₂²×C₃	C₂×C₃×C₅×C₇₉	1	7	yes	—
39	C₂×C₅	C₂²×C₉×C₇₉	1	7	yes	direct product factor
40	C₉	C₂³×C₅×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
41	C₂³	C₅×C₉×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	C₂²×C₃×C₅×C₇₉	1	7	yes	—
43	C₅	C₂³×C₉×C₇₉	1	1	yes	characteristic, direct product factor, Sylow
44	C₂²	C₂×C₅×C₉×C₇₉	1	7	yes	direct product factor
45	C₃	C₂³×C₃×C₅×C₇₉	1	1	yes	characteristic
46	C₂	C₂²×C₅×C₉×C₇₉	1	7	yes	direct product factor

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₃	C₂³×C₃×C₅×C₇₉
socle, prime radical	C₂³×C₃×C₅×C₇₉	C₃
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₉×C₇₉	C₅	direct (N × H)
3. C₂³×C₅×C₇₉	C₉	direct (N × H)
4. C₂²×C₅×C₉×C₇₉	C₂	direct (N × H)
5. C₂×C₅×C₉×C₇₉	C₂²	direct (N × H)
7. C₅×C₉×C₇₉	C₂³	direct (N × H)
8. C₂²×C₉×C₇₉	C₂×C₅	direct (N × H)
11. C₂²×C₅×C₇₉	C₂×C₉	direct (N × H)
12. C₂×C₉×C₇₉	C₂²×C₅	direct (N × H)
15. C₂×C₅×C₇₉	C₂²×C₉	direct (N × H)
16. C₉×C₇₉	C₂³×C₅	direct (N × H)
17. C₂³×C₇₉	C₅×C₉	direct (N × H)
19. C₅×C₇₉	C₂³×C₉	direct (N × H)
20. C₂³×C₅×C₉	C₇₉	direct (N × H)
21. C₂²×C₇₉	C₂×C₅×C₉	direct (N × H)
23. C₂²×C₅×C₉	C₂×C₇₉	direct (N × H)
24. C₂×C₇₉	C₂²×C₅×C₉	direct (N × H)
26. C₂×C₅×C₉	C₂²×C₇₉	direct (N × H)
27. C₇₉	C₂³×C₅×C₉	direct (N × H)
28. C₂³×C₉	C₅×C₇₉	direct (N × H)
30. C₅×C₉	C₂³×C₇₉	direct (N × H)
31. C₂³×C₅	C₉×C₇₉	direct (N × H)
32. C₂²×C₉	C₂×C₅×C₇₉	direct (N × H)
35. C₂²×C₅	C₂×C₉×C₇₉	direct (N × H)
36. C₂×C₉	C₂²×C₅×C₇₉	direct (N × H)
39. C₂×C₅	C₂²×C₉×C₇₉	direct (N × H)
40. C₉	C₂³×C₅×C₇₉	direct (N × H)
41. C₂³	C₅×C₉×C₇₉	direct (N × H)
43. C₅	C₂³×C₉×C₇₉	direct (N × H)
44. C₂²	C₂×C₅×C₉×C₇₉	direct (N × H)
46. C₂	C₂²×C₅×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
C₂³×C₃×C₅×C₇₉	3
C₂³×C₉×C₇₉	5
C₂²×C₅×C₉×C₇₉	2
C₂³×C₅×C₉	79

Subgroups — C23×C5×C9×C79 #72205408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₅×C₉×C₇₉ #72205408