Subgroups — C₅×D₅×D₂₂₇ #36384191

Order 22700.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×D₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₅×C₂₂₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₁₃₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅²×C₂₂₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₅×D₂₂₇	—	5	1	no	maximal
6	D₅×D₂₂₇	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂×C₅×C₂₂₇	—	5	1	no	—
8	D₁₁₃₅	C₂×C₅	1	1	yes	characteristic, complemented
9	C₅×D₂₂₇	—	2	2	no	—
10	C₅×D₂₂₇	—	5	1	no	—
11	C₅×D₂₂₇	D₅	1	1	yes	characteristic, direct product factor
12	C₅×D₂₂₇	C₂×C₅	1	1	yes	characteristic, complemented
13	D₅×C₂₂₇	C₂×C₅	1	1	yes	characteristic, complemented
14	C₅×C₂₂₇	—	2	2	no	—
15	C₅×C₂₂₇	C₂×D₅	1	1	yes	characteristic, complemented
16	C₅×C₂₂₇	C₂²×C₅	1	1	yes	characteristic, complemented
17	C₂×D₂₂₇	—	5	1	no	Hall
18	C₂×C₂₂₇	—	5	1	no	—
19	D₂₂₇	—	5	1	no	—
20	D₂₂₇	C₅×D₅	1	1	yes	characteristic, direct product factor
21	C₂₂₇	C₂×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
22	C₂×C₅×D₅	—	227	1	no	maximal, Hall
23	C₂×C₅²	—	227	1	no	—
24	C₅×D₅	—	227	1	no	—
25	C₅×D₅	D₂₂₇	1	1	yes	characteristic, direct product factor
26	C₅²	C₂×D₂₂₇	1	1	yes	characteristic, complemented, Sylow
27	C₂²×C₅	—	1135	1	no	—
28	C₂×D₅	—	227	1	no	—
29	C₂×C₅	—	5	1	no	—
30	C₂×C₅	—	1135	1	no	—
31	C₂×C₅	—	454	2	no	—
32	C₂×C₅	—	227	1	no	—
33	C₂×C₅	—	227	1	no	—
34	D₅	—	227	1	no	—
35	D₅	C₅×D₂₂₇	1	1	yes	characteristic, direct product factor
36	C₅	—	2	2	no	—
37	C₅	D₅×D₂₂₇	1	1	yes	characteristic, direct product factor
38	C₅	C₂×C₅×D₂₂₇	1	1	yes	characteristic, complemented
39	C₂²	—	1135	1	no	Sylow
40	C₂	—	5	1	no	—
41	C₂	—	1135	1	no	—
42	C₂	—	227	1	no	—

	subgroup	G/H
center, hypercenter	C₅	D₅×D₂₂₇
commutator, cosocle, hypocenter	C₅×C₂₂₇	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₅²×C₂₂₇	C₂²
LCS	G ▷ C₅×C₂₂₇
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
1. C₅²×D₂₂₇	C₂	semidirect
2. C₅×D₅×C₂₂₇	C₂	semidirect
3. C₅×D₁₁₃₅	C₂	semidirect
4. C₅²×C₂₂₇	C₂²	semidirect
6. D₅×D₂₂₇	C₅	direct (N × H)
8. D₁₁₃₅	C₂×C₅	semidirect
11. C₅×D₂₂₇	D₅	direct (N × H)
12. C₅×D₂₂₇	C₂×C₅	semidirect
13. D₅×C₂₂₇	C₂×C₅	semidirect
15. C₅×C₂₂₇	C₂×D₅	semidirect
16. C₅×C₂₂₇	C₂²×C₅	semidirect
20. D₂₂₇	C₅×D₅	direct (N × H)
21. C₂₂₇	C₂×C₅×D₅	semidirect
25. C₅×D₅	D₂₂₇	direct (N × H)
26. C₅²	C₂×D₂₂₇	semidirect
35. D₅	C₅×D₂₂₇	direct (N × H)
37. C₅	D₅×D₂₂₇	direct (N × H)
38. C₅	C₂×C₅×D₂₂₇	semidirect

Maximal subgroups

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

subgroup	index
C₅²×D₂₂₇	2
C₅×D₅×C₂₂₇	2
C₅×D₁₁₃₅	2
C₂×C₅×D₂₂₇	5
D₅×D₂₂₇	5
C₂×C₅×D₅	227

Subgroups — C5×D5×D227 #36384191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×D₅×D₂₂₇ #36384191