Subgroups — D₁₁×D₃₅₅ #30626839

Order 15620.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₉₀₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₁×D₃₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₁₁×C₇₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×C₁₁×C₇₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₇₁	—	5	1	no	maximal, Hall
6	D₇₈₁	—	5	1	no	—
7	C₁₁×D₇₁	—	5	1	no	—
8	D₁₁×C₇₁	D₅	1	1	yes	characteristic, complemented
9	C₂×D₃₅₅	—	11	1	no	maximal, Hall
10	C₁₁×C₇₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₇₁	—	11	1	no	—
12	D₃₅₅	—	11	1	no	—
13	D₃₅₅	D₁₁	1	1	yes	characteristic, direct product factor
14	C₅×C₇₁	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
15	C₂×D₇₁	—	55	1	no	Hall
16	D₅×D₁₁	—	71	1	no	maximal, Hall
17	C₂×C₇₁	—	11	1	no	—
18	D₇₁	—	5	1	no	—
19	D₇₁	—	55	1	no	—
20	D₅₅	—	71	1	no	—
21	C₅×D₁₁	D₇₁	1	1	yes	characteristic, complemented
22	D₅×C₁₁	—	71	1	no	—
23	C₇₁	D₅×D₁₁	1	1	yes	characteristic, complemented, Sylow
24	C₅×C₁₁	C₂×D₇₁	1	1	yes	characteristic, complemented, Hall
25	C₂×D₁₁	—	355	1	no	Hall
26	C₂×C₁₁	—	355	1	no	—
27	D₁₁	—	355	1	no	—
28	D₁₁	D₃₅₅	1	1	yes	characteristic, direct product factor
29	C₂×D₅	—	781	1	no	Hall
30	C₁₁	C₂×D₃₅₅	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₅	—	11	1	no	—
32	D₅	—	781	1	no	—
33	D₅	—	71	1	no	—
34	C₅	D₁₁×D₇₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	3905	1	no	Sylow
36	C₂	—	11	1	no	—
37	C₂	—	3905	1	no	—
38	C₂	—	355	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅×C₁₁×C₇₁	C₂²
LCS	G ▷ C₅×C₁₁×C₇₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₃₉₀₅	C₂	semidirect
2. C₁₁×D₃₅₅	C₂	semidirect
3. C₅×D₁₁×C₇₁	C₂	semidirect
4. C₅×C₁₁×C₇₁	C₂²	semidirect
8. D₁₁×C₇₁	D₅	semidirect
10. C₁₁×C₇₁	C₂×D₅	semidirect
13. D₃₅₅	D₁₁	direct (N × H)
14. C₅×C₇₁	C₂×D₁₁	semidirect
21. C₅×D₁₁	D₇₁	semidirect
23. C₇₁	D₅×D₁₁	semidirect
24. C₅×C₁₁	C₂×D₇₁	semidirect
28. D₁₁	D₃₅₅	direct (N × H)
30. C₁₁	C₂×D₃₅₅	semidirect
34. C₅	D₁₁×D₇₁	semidirect

Maximal subgroups

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

subgroup	index
D₃₉₀₅	2
C₁₁×D₃₅₅	2
C₅×D₁₁×C₇₁	2
D₁₁×D₇₁	5
C₂×D₃₅₅	11
D₅×D₁₁	71

Subgroups — D11×D355 #30626839

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₁×D₃₅₅ #30626839