Subgroups — C₁₇²×#157 #23780932

Order 10404.

200 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	C₄×C₁₇²	—	9	1	no	maximal, Hall
5	C₃×C₁₇²	—	2	2	no	—
6	C₁₇×#157	C₁₇	1	18	yes	maximal, direct product factor
7	C₂×C₁₇²	—	9	1	no	—
8	C₁₇×C₃⋊D₃	C₂×C₁₇	1	18	yes	—
9	C₁₇²	#157	1	1	yes	characteristic, direct product factor, Sylow
10	C₃²×C₁₇	C₄×C₁₇	1	18	yes	complemented
11	D₃×C₁₇	—	6	36	no	—
12	C₄×C₁₇	—	9	18	no	—
13	C₃×C₁₇	—	2	36	no	—
14	#157	C₁₇²	1	1	yes	characteristic, direct product factor, Hall
15	C₂×C₁₇	—	9	18	no	—
16	C₃⋊D₃	C₂×C₁₇²	1	1	yes	characteristic
17	C₁₇	C₁₇×#157	1	18	yes	direct product factor
18	C₃²	C₄×C₁₇²	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.