Subgroups — C₁₇×#10597479 #23780933

Order 10404.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊D₅₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₇²	C₄	1	1	yes	characteristic, complemented, Hall
3	C₁₇×D₅₁	—	6	2	no	—
4	C₁₇×#595	—	9	1	no	maximal, Hall
5	C₃×C₁₇²	—	2	2	no	—
6	#10597479	C₁₇	1	1	yes	maximal, characteristic, direct product factor
7	C₁₇×#157	—	17	1	no	maximal
8	C₁₇×D₁₇	—	9	1	no	—
9	C₃⋊D₅₁	C₂×C₁₇	1	1	yes	characteristic
10	C₁₇×C₃⋊D₃	—	17	1	no	—
11	C₁₇²	#157	1	1	yes	characteristic, complemented, Sylow
12	C₃²×C₁₇	—	4	4	no	—
13	C₃²×C₁₇	C₄×C₁₇	1	1	yes	characteristic, complemented
14	C₃²×C₁₇	#595	1	1	yes	characteristic, complemented
15	D₅₁	—	6	2	no	—
16	D₃×C₁₇	—	102	2	no	—
17	#595	—	9	1	no	—
18	C₄×C₁₇	—	153	1	no	—
19	C₃×C₁₇	—	2	2	no	—
20	C₃×C₁₇	—	2	2	no	—
21	C₃×C₁₇	—	4	16	no	—
22	#157	—	17	1	no	Hall
23	C₂×C₁₇	—	153	1	no	—
24	D₁₇	—	9	1	no	—
25	C₃⋊D₃	—	17	1	no	—
26	C₁₇	—	4	4	no	—
27	C₁₇	C₁₇×#157	1	1	yes	characteristic, complemented
28	C₁₇	#10597479	1	1	yes	characteristic, direct product factor
29	C₃²	C₁₇×#595	1	1	yes	characteristic, complemented, Sylow
30	D₃	—	102	2	no	—
31	C₄	—	153	1	no	Sylow
32	C₃	—	2	2	no	—
33	C₂	—	153	1	no	—

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