Subgroups — D₅×D₁₂₂₇ #37589368

Order 24540.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₁₃₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₄₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₄₀₉	—	3	1	no	maximal, Hall
5	C₃×C₅×C₄₀₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×D₁₂₂₇	—	5	1	no	maximal, Hall
7	D₂₀₄₅	—	3	1	no	—
8	C₅×D₄₀₉	—	3	1	no	—
9	D₅×C₄₀₉	D₃	1	1	yes	characteristic, complemented
10	C₂×C₃×C₄₀₉	—	5	1	no	—
11	D₁₂₂₇	—	5	1	no	—
12	D₁₂₂₇	D₅	1	1	yes	characteristic, direct product factor
13	C₅×C₄₀₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
14	C₂×D₄₀₉	—	15	1	no	Hall
15	C₃×C₄₀₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
16	C₂×C₄₀₉	—	5	1	no	—
17	D₄₀₉	—	3	1	no	—
18	D₄₀₉	—	15	1	no	—
19	C₄₀₉	D₃×D₅	1	1	yes	characteristic, complemented, Sylow
20	D₃×D₅	—	409	1	no	maximal, Hall
21	D₁₅	—	409	1	no	—
22	C₃×D₅	D₄₀₉	1	1	yes	characteristic, complemented
23	C₅×D₃	—	409	1	no	—
24	C₂×D₅	—	1227	1	no	Hall
25	C₃×C₅	C₂×D₄₀₉	1	1	yes	characteristic, complemented, Hall
26	C₂×D₃	—	2045	1	no	Hall
27	C₂×C₅	—	1227	1	no	—
28	D₅	—	1227	1	no	—
29	D₅	D₁₂₂₇	1	1	yes	characteristic, direct product factor
30	C₂×C₃	—	5	1	no	—
31	D₃	—	409	1	no	—
32	D₃	—	2045	1	no	—
33	C₅	C₂×D₁₂₂₇	1	1	yes	characteristic, complemented, Sylow
34	C₂²	—	6135	1	no	Sylow
35	C₃	D₅×D₄₀₉	1	1	yes	characteristic, complemented, Sylow
36	C₂	—	5	1	no	—
37	C₂	—	1227	1	no	—
38	C₂	—	6135	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₅×C₄₀₉	C₂²
LCS	G ▷ C₃×C₅×C₄₀₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₁₃₅	C₂	semidirect
2. C₅×D₁₂₂₇	C₂	semidirect
3. C₃×D₅×C₄₀₉	C₂	semidirect
5. C₃×C₅×C₄₀₉	C₂²	semidirect
9. D₅×C₄₀₉	D₃	semidirect
12. D₁₂₂₇	D₅	direct (N × H)
13. C₅×C₄₀₉	C₂×D₃	semidirect
15. C₃×C₄₀₉	C₂×D₅	semidirect
19. C₄₀₉	D₃×D₅	semidirect
22. C₃×D₅	D₄₀₉	semidirect
25. C₃×C₅	C₂×D₄₀₉	semidirect
29. D₅	D₁₂₂₇	direct (N × H)
33. C₅	C₂×D₁₂₂₇	semidirect
35. C₃	D₅×D₄₀₉	semidirect

Maximal subgroups

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

subgroup	index
D₆₁₃₅	2
C₅×D₁₂₂₇	2
C₃×D₅×C₄₀₉	2
D₅×D₄₀₉	3
C₂×D₁₂₂₇	5
D₃×D₅	409

Subgroups — D5×D1227 #37589368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×D₁₂₂₇ #37589368