Subgroups — C₂×C₄₁×D₁₄₅ #37558112

Order 23780.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×D₁₄₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₂₉×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₂₉×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₄₁×D₂₉	—	5	1	no	maximal, Hall
5	C₂×C₂₉×C₄₁	D₅	1	1	yes	characteristic, complemented
6	C₄₁×D₂₉	—	5	2	no	—
7	C₂₉×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
8	C₂×D₅×C₄₁	—	29	1	no	maximal, Hall
9	C₂×D₁₄₅	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₅×C₄₁	D₂₉	1	1	yes	characteristic, complemented
11	D₅×C₄₁	—	29	2	no	—
12	C₂×C₅×C₂₉	C₂×C₄₁	1	1	yes	characteristic, complemented
13	D₁₄₅	C₂×C₄₁	1	2	yes	direct product factor
14	C₅×C₄₁	C₂×D₂₉	1	1	yes	characteristic, complemented, Hall
15	C₂²×C₄₁	—	145	1	no	Hall
16	C₅×C₂₉	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
17	C₂×D₂₉	—	5	1	no	Hall
18	C₂×C₄₁	—	145	2	no	—
19	C₂×C₄₁	D₁₄₅	1	1	yes	characteristic, direct product factor
20	C₂×C₂₉	D₅×C₄₁	1	1	yes	characteristic, complemented
21	D₂₉	—	5	2	no	—
22	C₄₁	C₂×D₁₄₅	1	1	yes	characteristic, direct product factor, Sylow
23	C₂₉	C₂×D₅×C₄₁	1	1	yes	characteristic, complemented, Sylow
24	C₂×D₅	—	29	1	no	Hall
25	C₂×C₅	C₄₁×D₂₉	1	1	yes	characteristic, complemented
26	D₅	—	29	2	no	—
27	C₅	C₂×C₄₁×D₂₉	1	1	yes	characteristic, complemented, Sylow
28	C₂²	—	145	1	no	Sylow
29	C₂	—	145	2	no	—
30	C₂	C₄₁×D₁₄₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₄₁	D₁₄₅
commutator, cosocle, hypocenter	C₅×C₂₉	C₂²×C₄₁
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₂₉×C₄₁	C₂
LCS	G ▷ C₅×C₂₉
UCS	C₁ ◁ C₂×C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×D₁₄₅	C₂	direct (N × H)
2. C₂×C₅×C₂₉×C₄₁	C₂	semidirect
3. C₅×C₂₉×C₄₁	C₂²	semidirect
5. C₂×C₂₉×C₄₁	D₅	semidirect
7. C₂₉×C₄₁	C₂×D₅	semidirect
9. C₂×D₁₄₅	C₄₁	direct (N × H)
10. C₂×C₅×C₄₁	D₂₉	semidirect
12. C₂×C₅×C₂₉	C₂×C₄₁	semidirect
13. D₁₄₅	C₂×C₄₁	direct (N × H)
14. C₅×C₄₁	C₂×D₂₉	semidirect
16. C₅×C₂₉	C₂²×C₄₁	semidirect
19. C₂×C₄₁	D₁₄₅	direct (N × H)
20. C₂×C₂₉	D₅×C₄₁	semidirect
22. C₄₁	C₂×D₁₄₅	direct (N × H)
23. C₂₉	C₂×D₅×C₄₁	semidirect
25. C₂×C₅	C₄₁×D₂₉	semidirect
27. C₅	C₂×C₄₁×D₂₉	semidirect
30. C₂	C₄₁×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
C₄₁×D₁₄₅	2
C₂×C₅×C₂₉×C₄₁	2
C₂×C₄₁×D₂₉	5
C₂×D₅×C₄₁	29
C₂×D₁₄₅	41

Subgroups — C2×C41×D145 #37558112

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₁×D₁₄₅ #37558112