Subgroups — #88052

Order 416.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	#6090	C₂	1	2	yes	maximal, complemented
3	C₂×C₄×C₁₃	C₄	1	1	yes	characteristic
4	C₈×C₁₃	C₄	1	1	yes	characteristic
5	C₈×C₁₃	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃	C₈	1	1	yes	characteristic
7	C₄×C₁₃	C₈	1	1	yes	characteristic
8	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
9	M₃₂	—	13	1	no	maximal, Sylow
10	C₂×C₁₃	—	2	1	no	—
11	C₂×C₁₃	C₂×C₈	1	1	yes	characteristic
12	C₂×C₈	D₁₃	1	1	yes	characteristic
13	C₁₆	—	13	2	no	—
14	C₁₃	M₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₄	Dic₁₃	1	1	yes	characteristic
16	C₈	Dic₁₃	1	1	yes	characteristic
17	C₈	C₂×D₁₃	1	1	yes	characteristic
18	C₂²	#1055	1	1	yes	characteristic
19	C₄	#1055	1	1	yes	characteristic
20	C₄	C₂×Dic₁₃	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×#1055	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #6090	C₂	semidirect
14. C₁₃	M₃₂	semidirect

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