Subgroups — C₁₃×#90865 #20258972

Order 6084.

112 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	C₁₃×Dic₁₃	—	9	1	no	maximal, Hall
5	C₃×C₁₃²	—	2	2	no	—
6	#90865	C₁₃	1	1	yes	maximal, characteristic, direct product factor
7	C₁₃×#157	—	13	1	no	maximal
8	C₂×C₁₃²	—	9	1	no	—
9	C₁₃×C₃⋊D₃	—	2	6	no	—
10	C₁₃×C₃⋊D₃	D₁₃	1	1	yes	characteristic
11	C₁₃×C₃⋊D₃	C₂×C₁₃	1	1	yes	characteristic
12	C₁₃²	#157	1	1	yes	characteristic, complemented, Sylow
13	C₃²×C₁₃	—	2	6	no	—
14	C₃²×C₁₃	Dic₁₃	1	1	yes	characteristic, complemented
15	C₃²×C₁₃	C₄×C₁₃	1	1	yes	characteristic, complemented
16	D₃×C₁₃	—	6	2	no	—
17	D₃×C₁₃	—	6	2	no	—
18	D₃×C₁₃	—	6	24	no	—
19	C₄×C₁₃	—	117	1	no	—
20	Dic₁₃	—	9	1	no	—
21	C₃×C₁₃	—	2	24	no	—
22	C₃×C₁₃	—	2	2	no	—
23	C₃×C₁₃	—	2	2	no	—
24	#157	—	13	1	no	Hall
25	C₂×C₁₃	—	9	1	no	—
26	C₂×C₁₃	—	9	1	no	—
27	C₂×C₁₃	—	18	6	no	—
28	C₃⋊D₃	C₁₃×D₁₃	1	1	yes	characteristic
29	C₁₃	—	2	6	no	—
30	C₁₃	C₁₃×#157	1	1	yes	characteristic, complemented
31	C₁₃	#90865	1	1	yes	characteristic, direct product factor
32	C₃²	C₁₃×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
33	D₃	—	6	2	no	—
34	C₄	—	117	1	no	Sylow
35	C₃	—	2	2	no	—
36	C₂	—	9	1	no	—

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