Subgroups — #13062789

Order 1360.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	#10621746	C₂	1	2	yes	maximal, complemented
3	C₂²×C₅×C₁₇	C₄	1	1	yes	characteristic
4	C₅×Dic₁₇	C₄	1	1	yes	characteristic
5	C₅×Dic₁₇	C₂²	1	1	yes	characteristic
6	#63247	—	5	1	no	maximal, Hall
7	C₂×C₅×C₁₇	—	2	1	no	—
8	C₂×C₅×C₁₇	C₂×C₄	1	1	yes	characteristic
9	C₂×Dic₁₇	D₅	1	1	yes	characteristic
10	#3624	—	5	2	no	—
11	C₅×C₁₇	M₁₆	1	1	yes	characteristic, complemented, Hall
12	#681	—	17	1	no	maximal, Hall
13	C₂²×C₁₇	Dic₅	1	1	yes	characteristic
14	Dic₁₇	Dic₅	1	1	yes	characteristic
15	Dic₁₇	C₂×D₅	1	1	yes	characteristic
16	C₂×C₄×C₅	—	17	1	no	—
17	#168	—	17	2	no	—
18	C₂×C₁₇	—	2	1	no	—
19	C₂×C₁₇	C₂×Dic₅	1	1	yes	characteristic
20	C₂²×C₅	#595	1	1	yes	characteristic
21	C₄×C₅	—	17	1	no	—
22	C₄×C₅	—	17	1	no	—
23	C₁₇	#681	1	1	yes	characteristic, complemented, Sylow
24	M₁₆	—	85	1	no	Sylow
25	C₂×C₅	—	2	1	no	—
26	C₂×C₅	C₂×#595	1	1	yes	characteristic
27	C₂×C₄	—	17	1	no	—
28	C₈	—	85	2	no	—
29	C₅	#63247	1	1	yes	characteristic, complemented, Sylow
30	C₂²	#66772	1	1	yes	characteristic
31	C₄	—	17	1	no	—
32	C₄	—	17	1	no	—
33	C₂	—	2	1	no	—
34	C₂	C₂×#66772	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.