Subgroups — D₅₅⋊D₁₀₇ #37555340

Order 23540.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₇×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₅₃₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₁₇₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₁₀₇	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₁₀₇	—	5	1	no	maximal, Hall
6	D₁₁₇₇	D₅	1	1	yes	characteristic, complemented
7	C₁₁×D₁₀₇	—	5	1	no	—
8	D₁₁×C₁₀₇	—	5	1	no	—
9	D₅×D₁₀₇	—	11	1	no	maximal, Hall
10	C₁₁×C₁₀₇	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	D₅₃₅	D₁₁	1	1	yes	characteristic, complemented
12	C₅×D₁₀₇	—	11	1	no	—
13	D₅×C₁₀₇	—	11	1	no	—
14	C₅×C₁₀₇	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×D₁₀₇	—	55	1	no	Hall
16	D₅×D₁₁	—	107	1	no	maximal, Hall
17	C₂×C₁₀₇	—	55	1	no	—
18	D₁₀₇	—	5	1	no	—
19	D₁₀₇	—	11	1	no	—
20	D₅₅	D₁₀₇	1	1	yes	characteristic, complemented
21	C₅×D₁₁	—	107	1	no	—
22	D₅×C₁₁	—	107	1	no	—
23	C₁₀₇	D₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₅×C₁₁	C₂×D₁₀₇	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁	—	535	1	no	Hall
26	C₂×C₁₁	—	535	1	no	—
27	D₁₁	—	5	1	no	—
28	D₁₁	—	107	1	no	—
29	C₂×D₅	—	1177	1	no	Hall
30	C₁₁	D₅×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	1177	1	no	—
32	D₅	—	11	1	no	—
33	D₅	—	107	1	no	—
34	C₅	D₁₁×D₁₀₇	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	5885	1	no	Sylow
36	C₂	—	535	1	no	—
37	C₂	—	55	1	no	—
38	C₂	—	1177	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₁₀₇	C₂²
LCS	G ▷ C₅×C₁₁×C₁₀₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₁₀₇×D₅₅	C₂	semidirect
2. C₁₁×D₅₃₅	C₂	semidirect
3. C₅×D₁₁₇₇	C₂	semidirect
4. C₅×C₁₁×C₁₀₇	C₂²	semidirect
6. D₁₁₇₇	D₅	semidirect
10. C₁₁×C₁₀₇	C₂×D₅	semidirect
11. D₅₃₅	D₁₁	semidirect
14. C₅×C₁₀₇	C₂×D₁₁	semidirect
20. D₅₅	D₁₀₇	semidirect
23. C₁₀₇	D₅×D₁₁	semidirect
24. C₅×C₁₁	C₂×D₁₀₇	semidirect
30. C₁₁	D₅×D₁₀₇	semidirect
34. C₅	D₁₁×D₁₀₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₇×D₅₅	2
C₁₁×D₅₃₅	2
C₅×D₁₁₇₇	2
D₁₁×D₁₀₇	5
D₅×D₁₀₇	11
D₅×D₁₁	107

Subgroups — D55⋊D107 #37555340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₅⋊D₁₀₇ #37555340