Subgroups — #13130006

Order 1664.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃×C₃₂	C₂	1	1	yes	maximal, characteristic
2	#11718037	C₂	1	2	yes	maximal, complemented
3	C₁₆×D₁₃	C₄	1	1	yes	characteristic
4	C₁₃×C₃₂	C₄	1	1	yes	characteristic
5	#88034	C₂²	1	1	yes	characteristic
6	C₈×D₁₃	C₈	1	1	yes	characteristic
7	C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
8	#6090	C₈	1	1	yes	characteristic
9	M₁₂₈	—	13	1	no	maximal, Sylow
10	C₄×D₁₃	C₁₆	1	1	yes	characteristic
11	C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
12	#1055	C₁₆	1	1	yes	characteristic
13	C₂×C₃₂	—	13	1	no	—
14	C₆₄	—	13	2	no	—
15	C₂×D₁₃	C₃₂	1	1	yes	characteristic
16	C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
17	Dic₁₃	C₃₂	1	1	yes	characteristic
18	C₂×C₁₆	—	13	1	no	—
19	C₃₂	—	13	1	no	—
20	C₃₂	#261	1	1	yes	characteristic
21	C₂×C₁₃	C₂×C₃₂	1	1	yes	characteristic
22	D₁₃	—	2	1	no	—
23	C₂×C₈	—	13	1	no	—
24	C₁₆	—	13	1	no	—
25	C₁₆	C₂×#261	1	1	yes	characteristic
26	C₁₃	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₄	—	13	1	no	—
28	C₈	—	13	1	no	—
29	C₈	D₁₃⋊C₈	1	1	yes	characteristic
30	C₂²	—	13	1	no	—
31	C₄	—	13	1	no	—
32	C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
33	C₂	—	26	1	no	—
34	C₂	D₁₃⋊C₃₂	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #11718037	C₂	semidirect
26. C₁₃	M₁₂₈	semidirect

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