Subgroups — D₁₃₃⋊D₃₁ #30658113

Order 16492.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₁×D₁₃₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×D₂₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×D₅₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×C₁₉×C₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₉×D₃₁	—	7	1	no	maximal, Hall
6	D₅₈₉	D₇	1	1	yes	characteristic, complemented
7	C₁₉×D₃₁	—	7	1	no	—
8	C₃₁×D₁₉	—	7	1	no	—
9	D₇×D₃₁	—	19	1	no	maximal, Hall
10	C₁₉×C₃₁	C₂×D₇	1	1	yes	characteristic, complemented, Hall
11	D₇×D₁₉	—	31	1	no	maximal, Hall
12	D₂₁₇	D₁₉	1	1	yes	characteristic, complemented
13	C₇×D₃₁	—	19	1	no	—
14	D₇×C₃₁	—	19	1	no	—
15	D₁₃₃	D₃₁	1	1	yes	characteristic, complemented
16	C₇×D₁₉	—	31	1	no	—
17	D₇×C₁₉	—	31	1	no	—
18	C₇×C₃₁	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
19	C₇×C₁₉	C₂×D₃₁	1	1	yes	characteristic, complemented, Hall
20	C₂×D₃₁	—	133	1	no	Hall
21	C₂×D₁₉	—	217	1	no	Hall
22	C₂×C₃₁	—	133	1	no	—
23	D₃₁	—	7	1	no	—
24	D₃₁	—	19	1	no	—
25	C₂×C₁₉	—	217	1	no	—
26	D₁₉	—	7	1	no	—
27	D₁₉	—	31	1	no	—
28	C₃₁	D₇×D₁₉	1	1	yes	characteristic, complemented, Sylow
29	C₂×D₇	—	589	1	no	Hall
30	C₁₉	D₇×D₃₁	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₇	—	589	1	no	—
32	D₇	—	19	1	no	—
33	D₇	—	31	1	no	—
34	C₇	D₁₉×D₃₁	1	1	yes	characteristic, complemented, Sylow
35	C₂²	—	4123	1	no	Sylow
36	C₂	—	589	1	no	—
37	C₂	—	133	1	no	—
38	C₂	—	217	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₉×C₃₁	C₂²
LCS	G ▷ C₇×C₁₉×C₃₁
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.