Subgroups — C₂×C₉×D₅×C₁₇₉ #44567340

Order 32220.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₅×C₁₇₉	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₉×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₅×C₁₇₉	C₃	1	1	yes	maximal, characteristic
4	C₅×C₉×C₁₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂²×C₉×C₁₇₉	—	5	1	no	maximal, Hall
6	C₃×D₅×C₁₇₉	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₁₇₉	C₂×C₃	1	1	yes	characteristic
8	C₂×D₅×C₁₇₉	C₉	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₉×C₁₇₉	—	5	2	no	—
10	C₂×C₉×C₁₇₉	D₅	1	1	yes	characteristic, direct product factor
11	C₃×C₅×C₁₇₉	C₂²×C₃	1	1	yes	characteristic
12	C₂²×C₃×C₁₇₉	—	5	1	no	—
13	C₂×C₅×C₁₇₉	C₂×C₉	1	1	yes	characteristic, complemented
14	D₅×C₁₇₉	C₂×C₉	1	2	yes	direct product factor
15	C₉×C₁₇₉	C₂×D₅	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₃×C₁₇₉	—	5	2	no	—
17	C₂×C₃×C₁₇₉	C₃×D₅	1	1	yes	characteristic
18	C₅×C₁₇₉	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₁₇₉	—	5	1	no	Hall
20	C₃×C₁₇₉	C₂×C₃×D₅	1	1	yes	characteristic
21	C₂×C₁₇₉	—	5	2	no	—
22	C₂×C₁₇₉	C₉×D₅	1	1	yes	characteristic, direct product factor
23	C₂×C₉×D₅	C₁₇₉	1	1	yes	maximal, characteristic, direct product factor, Hall
24	C₁₇₉	C₂×C₉×D₅	1	1	yes	characteristic, direct product factor, Sylow
25	C₂×C₅×C₉	C₂×C₁₇₉	1	1	yes	characteristic, complemented
26	C₉×D₅	C₂×C₁₇₉	1	2	yes	direct product factor
27	C₂×C₃×D₅	C₃×C₁₇₉	1	1	yes	characteristic
28	C₅×C₉	C₂²×C₁₇₉	1	1	yes	characteristic, complemented, Hall
29	C₂²×C₉	—	5	1	no	Hall
30	C₂×C₃×C₅	C₂×C₃×C₁₇₉	1	1	yes	characteristic
31	C₃×D₅	C₂×C₃×C₁₇₉	1	2	yes	—
32	C₂×D₅	C₉×C₁₇₉	1	1	yes	characteristic, direct product factor, Hall
33	C₂×C₉	—	5	2	no	—
34	C₂×C₉	D₅×C₁₇₉	1	1	yes	characteristic, direct product factor
35	C₃×C₅	C₂²×C₃×C₁₇₉	1	1	yes	characteristic
36	C₂²×C₃	—	5	1	no	—
37	C₂×C₅	C₂×C₉×C₁₇₉	1	1	yes	characteristic, complemented
38	D₅	C₂×C₉×C₁₇₉	1	2	yes	direct product factor
39	C₉	C₂×D₅×C₁₇₉	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×C₃	—	5	2	no	—
41	C₂×C₃	C₃×D₅×C₁₇₉	1	1	yes	characteristic
42	C₅	C₂²×C₉×C₁₇₉	1	1	yes	characteristic, complemented, Sylow
43	C₂²	—	5	1	no	Sylow
44	C₃	C₂×C₃×D₅×C₁₇₉	1	1	yes	characteristic
45	C₂	—	5	2	no	—
46	C₂	C₉×D₅×C₁₇₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₇₉	D₅
commutator, hypocenter	C₅	C₂²×C₉×C₁₇₉
Frattini	C₃	C₂×C₃×D₅×C₁₇₉
Fitting	C₂×C₅×C₉×C₁₇₉	C₂
socle	C₂×C₃×C₅×C₁₇₉	C₂×C₃
prime radical	C₂×C₃×D₅×C₁₇₉	C₃
cosocle	C₃×C₅	C₂²×C₃×C₁₇₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₉×C₁₇₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₅×C₁₇₉	C₂	direct (N × H)
2. C₂×C₅×C₉×C₁₇₉	C₂	semidirect
4. C₅×C₉×C₁₇₉	C₂²	semidirect
8. C₂×D₅×C₁₇₉	C₉	direct (N × H)
10. C₂×C₉×C₁₇₉	D₅	direct (N × H)
13. C₂×C₅×C₁₇₉	C₂×C₉	semidirect
14. D₅×C₁₇₉	C₂×C₉	direct (N × H)
15. C₉×C₁₇₉	C₂×D₅	direct (N × H)
18. C₅×C₁₇₉	C₂²×C₉	semidirect
22. C₂×C₁₇₉	C₉×D₅	direct (N × H)
23. C₂×C₉×D₅	C₁₇₉	direct (N × H)
24. C₁₇₉	C₂×C₉×D₅	direct (N × H)
25. C₂×C₅×C₉	C₂×C₁₇₉	semidirect
26. C₉×D₅	C₂×C₁₇₉	direct (N × H)
28. C₅×C₉	C₂²×C₁₇₉	semidirect
32. C₂×D₅	C₉×C₁₇₉	direct (N × H)
34. C₂×C₉	D₅×C₁₇₉	direct (N × H)
37. C₂×C₅	C₂×C₉×C₁₇₉	semidirect
38. D₅	C₂×C₉×C₁₇₉	direct (N × H)
39. C₉	C₂×D₅×C₁₇₉	direct (N × H)
42. C₅	C₂²×C₉×C₁₇₉	semidirect
46. C₂	C₉×D₅×C₁₇₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×D₅×C₁₇₉	2
C₂×C₅×C₉×C₁₇₉	2
C₂×C₃×D₅×C₁₇₉	3
C₂²×C₉×C₁₇₉	5
C₂×C₉×D₅	179

Subgroups — C2×C9×D5×C179 #44567340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₅×C₁₇₉ #44567340