Subgroups — #13113053

Order 1664.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×Q₆₄	C₂	1	1	yes	maximal, characteristic
2	Dic₂₀₈	C₂	1	1	yes	maximal, characteristic
3	#11718035	C₂	1	1	yes	maximal, characteristic
4	C₁₃×Q₃₂	—	2	1	no	—
5	Dic₁₀₄	—	2	1	no	—
6	C₁₃×C₃₂	C₂²	1	1	yes	characteristic
7	C₁₃×Q₁₆	—	4	1	no	—
8	Dic₅₂	—	4	1	no	—
9	C₁₃×C₁₆	D₄	1	1	yes	characteristic
10	Q₁₂₈	—	13	1	no	maximal, Sylow
11	Q₈×C₁₃	—	8	1	no	—
12	Dic₂₆	—	8	1	no	—
13	C₈×C₁₃	D₈	1	1	yes	characteristic
14	Q₆₄	—	13	1	no	—
15	Q₆₄	D₁₃	1	1	yes	characteristic
16	C₆₄	—	13	1	no	—
17	C₄×C₁₃	—	16	1	no	—
18	C₄×C₁₃	D₁₆	1	1	yes	characteristic
19	Dic₁₃	—	16	1	no	—
20	Q₃₂	—	2	1	no	—
21	Q₃₂	—	26	1	no	—
22	C₃₂	C₂×D₁₃	1	1	yes	characteristic
23	C₂×C₁₃	D₃₂	1	1	yes	characteristic
24	Q₁₆	—	4	1	no	—
25	Q₁₆	—	52	1	no	—
26	C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
27	C₁₃	Q₁₂₈	1	1	yes	characteristic, complemented, Sylow
28	Q₈	—	8	1	no	—
29	Q₈	—	104	1	no	—
30	C₈	#6104	1	1	yes	characteristic
31	C₄	—	16	1	no	—
32	C₄	—	208	1	no	—
33	C₄	#88066	1	1	yes	characteristic
34	C₂	#11718111	1	1	yes	characteristic

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

N	H ≅ G/N	type
27. C₁₃	Q₁₂₈	semidirect

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