Subgroups — D₅₉×D₁₃₃ #44536003

Order 31388.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₇₈₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×D₁₃₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₁₉×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₉×C₅₉	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₉×D₅₉	—	7	1	no	maximal, Hall
6	D₁₁₂₁	—	7	1	no	—
7	C₁₉×D₅₉	D₇	1	1	yes	characteristic, complemented
8	D₁₉×C₅₉	—	7	1	no	—
9	D₇×D₅₉	—	19	1	no	maximal, Hall
10	C₁₉×C₅₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	D₄₁₃	—	19	1	no	—
12	C₇×D₅₉	D₁₉	1	1	yes	characteristic, complemented
13	D₇×C₅₉	—	19	1	no	—
14	C₂×D₁₃₃	—	59	1	no	maximal, Hall
15	C₇×C₅₉	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
16	C₂×C₇×C₁₉	—	59	1	no	—
17	D₁₃₃	—	59	1	no	—
18	D₁₃₃	D₅₉	1	1	yes	characteristic, direct product factor
19	C₂×D₅₉	—	133	1	no	Hall
20	C₇×C₁₉	C₂×D₅₉	1	1	yes	characteristic, complemented, Hall
21	C₂×C₅₉	—	133	1	no	—
22	D₅₉	—	133	1	no	—
23	D₅₉	D₁₃₃	1	1	yes	characteristic, direct product factor
24	C₂×D₁₉	—	413	1	no	Hall
25	C₅₉	C₂×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₁₉	—	59	1	no	—
27	D₁₉	—	7	1	no	—
28	D₁₉	—	413	1	no	—
29	C₂×D₇	—	1121	1	no	Hall
30	C₁₉	D₇×D₅₉	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇	—	59	1	no	—
32	D₇	—	19	1	no	—
33	D₇	—	1121	1	no	—
34	C₇	D₁₉×D₅₉	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	7847	1	no	Sylow
36	C₂	—	59	1	no	—
37	C₂	—	133	1	no	—
38	C₂	—	7847	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₉×C₅₉	C₂²
LCS	G ▷ C₇×C₁₉×C₅₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₇₈₄₇	C₂	semidirect
2. C₅₉×D₁₃₃	C₂	semidirect
3. C₇×C₁₉×D₅₉	C₂	semidirect
4. C₇×C₁₉×C₅₉	C₂²	semidirect
7. C₁₉×D₅₉	D₇	semidirect
10. C₁₉×C₅₉	C₂×D₇	semidirect
12. C₇×D₅₉	D₁₉	semidirect
15. C₇×C₅₉	C₂×D₁₉	semidirect
18. D₁₃₃	D₅₉	direct (N × H)
20. C₇×C₁₉	C₂×D₅₉	semidirect
23. D₅₉	D₁₃₃	direct (N × H)
25. C₅₉	C₂×D₁₃₃	semidirect
30. C₁₉	D₇×D₅₉	semidirect
34. C₇	D₁₉×D₅₉	semidirect

Maximal subgroups

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

subgroup	index
D₇₈₄₇	2
C₅₉×D₁₃₃	2
C₇×C₁₉×D₅₉	2
D₁₉×D₅₉	7
D₇×D₅₉	19
C₂×D₁₃₃	59

Subgroups — D59×D133 #44536003

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅₉×D₁₃₃ #44536003