Subgroups — C₅²×D₃×C₂₉⋊C₇ #44478562

Order 30450.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅²×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₂×C₅²×C₂₉⋊C₇	—	3	1	no	maximal, Hall
3	C₅×D₃×C₂₉⋊C₇	C₅	1	6	yes	maximal, direct product factor
4	C₅²×C₂₉⋊C₇	D₃	1	1	yes	characteristic, direct product factor, Hall
5	C₅²×D₃×C₂₉	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₃×C₅×C₂₉⋊C₇	C₂×C₅	1	6	yes	complemented
7	C₃×C₅²×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
8	C₂×C₅×C₂₉⋊C₇	—	3	6	no	—
9	C₂×C₅²×C₂₉	—	3	1	no	Hall
10	D₃×C₂₉⋊C₇	C₅²	1	1	yes	characteristic, direct product factor, Hall
11	C₅²×D₃×C₇	—	29	1	no	maximal, Hall
12	C₅×C₂₉⋊C₇	C₅×D₃	1	6	yes	direct product factor
13	C₅×D₃×C₂₉	C₅×C₇	1	6	yes	complemented
14	C₅²×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented, Hall
15	C₃×C₂₉⋊C₇	C₂×C₅²	1	1	yes	characteristic, complemented, Hall
16	C₃×C₅²×C₇	—	29	1	no	Hall
17	C₃×C₅×C₂₉	C₂×C₅×C₇	1	6	yes	complemented
18	C₂×C₂₉⋊C₇	—	3	1	no	Hall
19	C₂×C₅²×C₇	—	87	1	no	Hall
20	C₂×C₅×C₂₉	—	3	6	no	—
21	C₅×D₃×C₇	—	29	6	no	—
22	C₂₉⋊C₇	C₅²×D₃	1	1	yes	characteristic, direct product factor, Hall
23	C₅²×C₇	—	29	1	no	Hall
24	D₃×C₂₉	C₅²×C₇	1	1	yes	characteristic, complemented, Hall
25	C₅²×D₃	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
26	C₅×C₂₉	C₅×D₃×C₇	1	6	yes	complemented
27	C₃×C₅×C₇	—	29	6	no	—
28	C₃×C₂₉	C₂×C₅²×C₇	1	1	yes	characteristic, complemented, Hall
29	C₃×C₅²	C₂×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
30	C₂×C₅×C₇	—	87	6	no	—
31	C₂×C₂₉	—	3	1	no	Hall
32	C₂×C₅²	—	3	1	no	Hall
33	D₃×C₇	—	29	1	no	Hall
34	C₅×C₇	—	29	6	no	—
35	C₅×D₃	C₅×C₂₉⋊C₇	1	6	yes	direct product factor
36	C₂₉	C₅²×D₃×C₇	1	1	yes	characteristic, complemented, Sylow
37	C₅²	D₃×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Sylow
38	C₃×C₇	—	29	1	no	Hall
39	C₃×C₅	C₂×C₅×C₂₉⋊C₇	1	6	yes	complemented
40	C₂×C₇	—	87	1	no	Hall
41	C₂×C₅	—	3	6	no	—
42	C₇	—	29	1	no	Sylow
43	D₃	C₅²×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
44	C₅	C₅×D₃×C₂₉⋊C₇	1	6	yes	direct product factor
45	C₃	C₂×C₅²×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	3	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅²	D₃×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₃×C₂₉	C₂×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₂×C₇
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₅²

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₂₉⋊C₇	C₂	semidirect
3. C₅×D₃×C₂₉⋊C₇	C₅	direct (N × H)
4. C₅²×C₂₉⋊C₇	D₃	direct (N × H)
5. C₅²×D₃×C₂₉	C₇	semidirect
6. C₃×C₅×C₂₉⋊C₇	C₂×C₅	semidirect
7. C₃×C₅²×C₂₉	C₂×C₇	semidirect
10. D₃×C₂₉⋊C₇	C₅²	direct (N × H)
12. C₅×C₂₉⋊C₇	C₅×D₃	direct (N × H)
13. C₅×D₃×C₂₉	C₅×C₇	semidirect
14. C₅²×C₂₉	D₃×C₇	semidirect
15. C₃×C₂₉⋊C₇	C₂×C₅²	semidirect
17. C₃×C₅×C₂₉	C₂×C₅×C₇	semidirect
22. C₂₉⋊C₇	C₅²×D₃	direct (N × H)
24. D₃×C₂₉	C₅²×C₇	semidirect
25. C₅²×D₃	C₂₉⋊C₇	direct (N × H)
26. C₅×C₂₉	C₅×D₃×C₇	semidirect
28. C₃×C₂₉	C₂×C₅²×C₇	semidirect
29. C₃×C₅²	C₂×C₂₉⋊C₇	semidirect
35. C₅×D₃	C₅×C₂₉⋊C₇	direct (N × H)
36. C₂₉	C₅²×D₃×C₇	semidirect
37. C₅²	D₃×C₂₉⋊C₇	direct (N × H)
39. C₃×C₅	C₂×C₅×C₂₉⋊C₇	semidirect
43. D₃	C₅²×C₂₉⋊C₇	direct (N × H)
44. C₅	C₅×D₃×C₂₉⋊C₇	direct (N × H)
45. C₃	C₂×C₅²×C₂₉⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅²×C₂₉⋊C₇	2
C₂×C₅²×C₂₉⋊C₇	3
C₅×D₃×C₂₉⋊C₇	5
C₅²×D₃×C₂₉	7
C₅²×D₃×C₇	29

Subgroups — C52×D3×C29⋊C7 #44478562

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅²×D₃×C₂₉⋊C₇ #44478562