Subgroups — C₁₃²×#157 #20258970

Order 6084.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₃²	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₃²	—	6	2	no	—
4	C₄×C₁₃²	—	9	1	no	maximal, Hall
5	C₃×C₁₃²	—	2	2	no	—
6	C₁₃×#157	C₁₃	1	14	yes	maximal, direct product factor
7	C₂×C₁₃²	—	9	1	no	—
8	C₁₃×C₃⋊D₃	C₂×C₁₃	1	14	yes	—
9	C₁₃²	#157	1	1	yes	characteristic, direct product factor, Sylow
10	C₃²×C₁₃	C₄×C₁₃	1	14	yes	complemented
11	D₃×C₁₃	—	6	28	no	—
12	C₄×C₁₃	—	9	14	no	—
13	C₃×C₁₃	—	2	28	no	—
14	#157	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₃	—	9	14	no	—
16	C₃⋊D₃	C₂×C₁₃²	1	1	yes	characteristic
17	C₁₃	C₁₃×#157	1	14	yes	direct product factor
18	C₃²	C₄×C₁₃²	1	1	yes	characteristic, complemented, Sylow
19	D₃	—	6	2	no	—
20	C₄	—	9	1	no	Sylow
21	C₃	—	2	2	no	—
22	C₂	—	9	1	no	—

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