Subgroups — C₅×ΓL(1,𝔽₈)×D₁₄₅ #44478592

Order 30450.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×ΓL(1,𝔽₈)×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₅×C₇×D₁₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	ΓL(1,𝔽₈)×D₁₄₅	C₅	1	1	yes	maximal, characteristic, direct product factor
4	C₅×ΓL(1,𝔽₈)×D₂₉	—	5	1	no	maximal
5	C₅²×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×D₁₄₅	—	7	1	no	maximal, Hall
7	C₅×ΓL(1,𝔽₈)×C₂₉	—	2	2	no	—
8	C₅×ΓL(1,𝔽₈)×C₂₉	D₅	1	1	yes	characteristic, complemented
9	C₅×ΓL(1,𝔽₈)×C₂₉	C₂×C₅	1	1	yes	characteristic, complemented
10	C₃×C₅²×C₂₉	—	7	1	no	Hall
11	C₇×D₁₄₅	C₃×C₅	1	1	yes	characteristic, complemented
12	C₅×C₇×D₂₉	—	5	1	no	—
13	C₅×D₁₄₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor, Hall
14	ΓL(1,𝔽₈)×D₂₉	—	5	1	no	Hall
15	C₅×D₅×ΓL(1,𝔽₈)	—	29	1	no	maximal, Hall
16	C₅×C₇×C₂₉	—	2	2	no	—
17	C₅×C₇×C₂₉	C₃×D₅	1	1	yes	characteristic, complemented
18	C₅×C₇×C₂₉	C₂×C₃×C₅	1	1	yes	characteristic, complemented
19	C₃×D₁₄₅	—	7	1	no	—
20	C₃×C₅×D₂₉	—	35	1	no	—
21	C₅²×C₂₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
22	ΓL(1,𝔽₈)×C₂₉	C₅×D₅	1	1	yes	characteristic, complemented, Hall
23	C₅²×ΓL(1,𝔽₈)	D₂₉	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅×C₂₉	—	7	1	no	—
25	C₃×C₅×C₂₉	—	7	1	no	—
26	C₃×C₅×C₂₉	—	14	2	no	—
27	C₇×D₂₉	—	5	1	no	Hall
28	C₅×C₇×D₅	—	29	1	no	Hall
29	D₁₄₅	C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, direct product factor
30	C₅×D₂₉	—	5	1	no	—
31	C₂×C₅×ΓL(1,𝔽₈)	—	145	1	no	—
32	D₅×ΓL(1,𝔽₈)	—	29	1	no	—
33	C₇×C₂₉	C₃×C₅×D₅	1	1	yes	characteristic, complemented, Hall
34	C₅²×C₇	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
35	C₃×D₂₉	—	35	1	no	Hall
36	C₃×C₅×D₅	—	203	1	no	Hall
37	C₅×C₂₉	—	2	2	no	—
38	C₅×C₂₉	D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
39	C₅×C₂₉	C₂×C₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented
40	C₅×ΓL(1,𝔽₈)	—	2	2	no	—
41	C₅×ΓL(1,𝔽₈)	C₅×D₂₉	1	1	yes	characteristic, complemented
42	C₅×ΓL(1,𝔽₈)	D₁₄₅	1	1	yes	characteristic, direct product factor
43	C₃×C₂₉	—	7	1	no	Hall
44	C₃×C₅²	—	7	1	no	Hall
45	C₂×C₅×C₇	—	145	1	no	—
46	C₇×D₅	—	29	1	no	—
47	D₂₉	—	5	1	no	Hall
48	C₅×D₅	—	29	1	no	Hall
49	C₂×ΓL(1,𝔽₈)	—	145	1	no	Hall
50	C₅×C₇	—	2	2	no	—
51	C₅×C₇	C₃×C₅×D₂₉	1	1	yes	characteristic, complemented
52	C₅×C₇	C₃×D₁₄₅	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅	—	1015	1	no	—
54	C₃×D₅	—	203	1	no	—
55	C₂₉	C₅×D₅×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
56	C₅²	ΓL(1,𝔽₈)×D₂₉	1	1	yes	characteristic, complemented, Sylow
57	ΓL(1,𝔽₈)	C₅×D₁₄₅	1	1	yes	characteristic, direct product factor, Hall
58	C₃×C₅	—	7	1	no	—
59	C₃×C₅	—	7	1	no	—
60	C₃×C₅	—	14	2	no	—
61	C₂×C₇	—	145	1	no	Hall
62	C₂×C₅	—	145	1	no	—
63	D₅	—	29	1	no	—
64	C₇	C₃×C₅×D₁₄₅	1	1	yes	characteristic, complemented, Sylow
65	C₂×C₃	—	1015	1	no	Hall
66	C₅	—	2	2	no	—
67	C₅	C₅×ΓL(1,𝔽₈)×D₂₉	1	1	yes	characteristic, complemented
68	C₅	ΓL(1,𝔽₈)×D₁₄₅	1	1	yes	characteristic, direct product factor
69	C₃	—	7	1	no	Sylow
70	C₂	—	145	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₅	ΓL(1,𝔽₈)×D₁₄₅
commutator, cosocle, hypocenter	C₅×C₇×C₂₉	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₅×C₇×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅²×ΓL(1,𝔽₈)×C₂₉	C₂	semidirect
2. C₅×C₇×D₁₄₅	C₃	semidirect
3. ΓL(1,𝔽₈)×D₁₄₅	C₅	direct (N × H)
5. C₅²×C₇×C₂₉	C₂×C₃	semidirect
8. C₅×ΓL(1,𝔽₈)×C₂₉	D₅	semidirect
9. C₅×ΓL(1,𝔽₈)×C₂₉	C₂×C₅	semidirect
11. C₇×D₁₄₅	C₃×C₅	semidirect
13. C₅×D₁₄₅	ΓL(1,𝔽₈)	direct (N × H)
17. C₅×C₇×C₂₉	C₃×D₅	semidirect
18. C₅×C₇×C₂₉	C₂×C₃×C₅	semidirect
21. C₅²×C₂₉	C₂×ΓL(1,𝔽₈)	semidirect
22. ΓL(1,𝔽₈)×C₂₉	C₅×D₅	semidirect
23. C₅²×ΓL(1,𝔽₈)	D₂₉	semidirect
29. D₁₄₅	C₅×ΓL(1,𝔽₈)	direct (N × H)
33. C₇×C₂₉	C₃×C₅×D₅	semidirect
34. C₅²×C₇	C₃×D₂₉	semidirect
38. C₅×C₂₉	D₅×ΓL(1,𝔽₈)	semidirect
39. C₅×C₂₉	C₂×C₅×ΓL(1,𝔽₈)	semidirect
41. C₅×ΓL(1,𝔽₈)	C₅×D₂₉	semidirect
42. C₅×ΓL(1,𝔽₈)	D₁₄₅	direct (N × H)
51. C₅×C₇	C₃×C₅×D₂₉	semidirect
52. C₅×C₇	C₃×D₁₄₅	semidirect
55. C₂₉	C₅×D₅×ΓL(1,𝔽₈)	semidirect
56. C₅²	ΓL(1,𝔽₈)×D₂₉	semidirect
57. ΓL(1,𝔽₈)	C₅×D₁₄₅	direct (N × H)
64. C₇	C₃×C₅×D₁₄₅	semidirect
67. C₅	C₅×ΓL(1,𝔽₈)×D₂₉	semidirect
68. C₅	ΓL(1,𝔽₈)×D₁₄₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×ΓL(1,𝔽₈)×C₂₉	2
C₅×C₇×D₁₄₅	3
ΓL(1,𝔽₈)×D₁₄₅	5
C₅×ΓL(1,𝔽₈)×D₂₉	5
C₃×C₅×D₁₄₅	7
C₅×D₅×ΓL(1,𝔽₈)	29

Subgroups — C5×ΓL(1,𝔽8)×D145 #44478592

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×ΓL(1,𝔽₈)×D₁₄₅ #44478592