Subgroups — D₁₃₃⋊D₅₉ #44536007

Order 31388.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

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