Subgroups — C₁₇×#10597480 #23780934

Order 10404.

136 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₇²	—	6	2	no	—
4	C₁₇×Dic₁₇	—	9	1	no	maximal, Hall
5	C₃×C₁₇²	—	2	2	no	—
6	#10597480	C₁₇	1	1	yes	maximal, characteristic, direct product factor
7	C₁₇×#157	—	17	1	no	maximal
8	C₂×C₁₇²	—	9	1	no	—
9	C₁₇×C₃⋊D₃	—	2	8	no	—
10	C₁₇×C₃⋊D₃	D₁₇	1	1	yes	characteristic
11	C₁₇×C₃⋊D₃	C₂×C₁₇	1	1	yes	characteristic
12	C₁₇²	#157	1	1	yes	characteristic, complemented, Sylow
13	C₃²×C₁₇	—	2	8	no	—
14	C₃²×C₁₇	Dic₁₇	1	1	yes	characteristic, complemented
15	C₃²×C₁₇	C₄×C₁₇	1	1	yes	characteristic, complemented
16	D₃×C₁₇	—	6	2	no	—
17	D₃×C₁₇	—	6	2	no	—
18	D₃×C₁₇	—	6	32	no	—
19	C₄×C₁₇	—	153	1	no	—
20	Dic₁₇	—	9	1	no	—
21	C₃×C₁₇	—	2	32	no	—
22	C₃×C₁₇	—	2	2	no	—
23	C₃×C₁₇	—	2	2	no	—
24	#157	—	17	1	no	Hall
25	C₂×C₁₇	—	9	1	no	—
26	C₂×C₁₇	—	9	1	no	—
27	C₂×C₁₇	—	18	8	no	—
28	C₃⋊D₃	C₁₇×D₁₇	1	1	yes	characteristic
29	C₁₇	—	2	8	no	—
30	C₁₇	C₁₇×#157	1	1	yes	characteristic, complemented
31	C₁₇	#10597480	1	1	yes	characteristic, direct product factor
32	C₃²	C₁₇×Dic₁₇	1	1	yes	characteristic, complemented, Sylow
33	D₃	—	6	2	no	—
34	C₄	—	153	1	no	Sylow
35	C₃	—	2	2	no	—
36	C₂	—	9	1	no	—

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