Subgroups — C₅×D₁₅×C₂₉⋊C₇ #44478564

Order 30450.

80 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	C₅×D₅×C₂₉⋊C₇	—	3	1	no	maximal, Hall
3	D₁₅×C₂₉⋊C₇	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×D₃×C₂₉⋊C₇	—	5	1	no	maximal
5	C₅²×C₂₉⋊C₇	D₃	1	1	yes	characteristic, complemented, Hall
6	C₅×C₂₉×D₁₅	C₇	1	1	yes	maximal, characteristic, complemented, Hall
7	C₃×C₅×C₂₉⋊C₇	—	2	2	no	—
8	C₃×C₅×C₂₉⋊C₇	D₅	1	1	yes	characteristic, complemented
9	C₃×C₅×C₂₉⋊C₇	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×C₅²×C₂₉	C₂×C₇	1	1	yes	characteristic, complemented, Hall
11	D₅×C₂₉⋊C₇	—	3	1	no	—
12	C₂×C₅×C₂₉⋊C₇	—	15	1	no	—
13	C₅×D₅×C₂₉	—	3	1	no	Hall
14	D₃×C₂₉⋊C₇	—	5	1	no	Hall
15	C₅×C₇×D₁₅	—	29	1	no	maximal, Hall
16	C₅×C₂₉⋊C₇	—	2	2	no	—
17	C₅×C₂₉⋊C₇	C₅×D₃	1	1	yes	characteristic, complemented
18	C₅×C₂₉⋊C₇	D₁₅	1	1	yes	characteristic, direct product factor
19	C₂₉×D₁₅	C₅×C₇	1	1	yes	characteristic, complemented
20	C₅×D₃×C₂₉	—	5	1	no	—
21	C₅²×C₂₉	D₃×C₇	1	1	yes	characteristic, complemented, Hall
22	C₃×C₂₉⋊C₇	C₅×D₅	1	1	yes	characteristic, complemented, Hall
23	C₃×C₅²×C₇	—	29	1	no	Hall
24	C₃×C₅×C₂₉	—	2	2	no	—
25	C₃×C₅×C₂₉	C₇×D₅	1	1	yes	characteristic, complemented
26	C₃×C₅×C₂₉	C₂×C₅×C₇	1	1	yes	characteristic, complemented
27	C₂×C₂₉⋊C₇	—	15	1	no	Hall
28	C₅×C₇×D₅	—	87	1	no	Hall
29	C₂×C₅×C₂₉	—	15	1	no	—
30	D₅×C₂₉	—	3	1	no	—
31	C₇×D₁₅	—	29	1	no	—
32	C₅×D₃×C₇	—	145	1	no	—
33	C₂₉⋊C₇	C₅×D₁₅	1	1	yes	characteristic, direct product factor, Hall
34	C₅²×C₇	—	29	1	no	Hall
35	D₃×C₂₉	—	5	1	no	Hall
36	C₅×D₁₅	C₂₉⋊C₇	1	1	yes	characteristic, direct product factor, Hall
37	C₅×C₂₉	—	2	2	no	—
38	C₅×C₂₉	C₅×D₃×C₇	1	1	yes	characteristic, complemented
39	C₅×C₂₉	C₇×D₁₅	1	1	yes	characteristic, complemented
40	C₃×C₅×C₇	—	29	1	no	—
41	C₃×C₅×C₇	—	29	1	no	—
42	C₃×C₅×C₇	—	58	2	no	—
43	C₃×C₂₉	C₅×C₇×D₅	1	1	yes	characteristic, complemented, Hall
44	C₃×C₅²	C₂×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
45	C₂×C₅×C₇	—	435	1	no	—
46	C₇×D₅	—	87	1	no	—
47	C₂×C₂₉	—	15	1	no	Hall
48	C₅×D₅	—	3	1	no	Hall
49	D₃×C₇	—	145	1	no	Hall
50	C₅×C₇	—	29	1	no	—
51	C₅×C₇	—	29	1	no	—
52	C₅×C₇	—	58	2	no	—
53	D₁₅	C₅×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
54	C₅×D₃	—	5	1	no	—
55	C₂₉	C₅×C₇×D₁₅	1	1	yes	characteristic, complemented, Sylow
56	C₅²	D₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
57	C₃×C₇	—	29	1	no	Hall
58	C₃×C₅	—	2	2	no	—
59	C₃×C₅	C₂×C₅×C₂₉⋊C₇	1	1	yes	characteristic, complemented
60	C₃×C₅	D₅×C₂₉⋊C₇	1	1	yes	characteristic, complemented
61	C₂×C₇	—	435	1	no	Hall
62	C₂×C₅	—	15	1	no	—
63	D₅	—	3	1	no	—
64	C₇	—	29	1	no	Sylow
65	D₃	—	5	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₅×D₃×C₂₉⋊C₇	1	1	yes	characteristic, complemented
68	C₅	D₁₅×C₂₉⋊C₇	1	1	yes	characteristic, direct product factor
69	C₃	C₅×D₅×C₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
70	C₂	—	15	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	D₁₅×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₃×C₅×C₂₉	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₂×C₇
LCS	G ▷ C₃×C₅×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₃×C₅²×C₂₉⋊C₇	C₂	semidirect
3. D₁₅×C₂₉⋊C₇	C₅	direct (N × H)
5. C₅²×C₂₉⋊C₇	D₃	semidirect
6. C₅×C₂₉×D₁₅	C₇	semidirect
8. C₃×C₅×C₂₉⋊C₇	D₅	semidirect
9. C₃×C₅×C₂₉⋊C₇	C₂×C₅	semidirect
10. C₃×C₅²×C₂₉	C₂×C₇	semidirect
17. C₅×C₂₉⋊C₇	C₅×D₃	semidirect
18. C₅×C₂₉⋊C₇	D₁₅	direct (N × H)
19. C₂₉×D₁₅	C₅×C₇	semidirect
21. C₅²×C₂₉	D₃×C₇	semidirect
22. C₃×C₂₉⋊C₇	C₅×D₅	semidirect
25. C₃×C₅×C₂₉	C₇×D₅	semidirect
26. C₃×C₅×C₂₉	C₂×C₅×C₇	semidirect
33. C₂₉⋊C₇	C₅×D₁₅	direct (N × H)
36. C₅×D₁₅	C₂₉⋊C₇	direct (N × H)
38. C₅×C₂₉	C₅×D₃×C₇	semidirect
39. C₅×C₂₉	C₇×D₁₅	semidirect
43. C₃×C₂₉	C₅×C₇×D₅	semidirect
44. C₃×C₅²	C₂×C₂₉⋊C₇	semidirect
53. D₁₅	C₅×C₂₉⋊C₇	direct (N × H)
55. C₂₉	C₅×C₇×D₁₅	semidirect
56. C₅²	D₃×C₂₉⋊C₇	semidirect
59. C₃×C₅	C₂×C₅×C₂₉⋊C₇	semidirect
60. C₃×C₅	D₅×C₂₉⋊C₇	semidirect
67. C₅	C₅×D₃×C₂₉⋊C₇	semidirect
68. C₅	D₁₅×C₂₉⋊C₇	direct (N × H)
69. C₃	C₅×D₅×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
C₅×D₅×C₂₉⋊C₇	3
D₁₅×C₂₉⋊C₇	5
C₅×D₃×C₂₉⋊C₇	5
C₅×C₂₉×D₁₅	7
C₅×C₇×D₁₅	29

Subgroups — C5×D15×C29⋊C7 #44478564

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₁₅×C₂₉⋊C₇ #44478564