Subgroups — #88202

Order 416.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	#6099	C₂	1	3	yes	maximal, complemented
3	C₂×#1055	C₂	1	3	yes	maximal, complemented
4	Q₈×C₁₃	C₄	1	1	yes	characteristic
5	D₄×C₁₃	C₄	1	3	yes	—
6	C₂×C₄×C₁₃	C₂²	1	3	yes	—
7	#1055	C₂²	1	1	yes	characteristic
8	#1055	C₂²	1	3	yes	—
9	C₂²×C₁₃	C₂×C₄	1	3	yes	—
10	C₄×C₁₃	C₂×C₄	1	3	yes	—
11	C₄×C₁₃	C₂³	1	1	yes	characteristic
12	#131	—	13	1	no	maximal, Sylow
13	C₂×C₁₃	—	2	3	no	—
14	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
15	#41	D₁₃	1	1	yes	characteristic
16	M₁₆	—	13	3	no	—
17	C₂×C₈	—	13	3	no	—
18	C₁₃	#131	1	1	yes	characteristic, complemented, Sylow
19	Q₈	Dic₁₃	1	1	yes	characteristic
20	D₄	Dic₁₃	1	3	yes	—
21	C₂×C₄	C₂×D₁₃	1	3	yes	—
22	C₈	—	13	1	no	—
23	C₈	—	13	3	no	—
24	C₂²	C₂×Dic₁₃	1	3	yes	—
25	C₄	C₂×Dic₁₃	1	3	yes	—
26	C₄	C₂²×D₁₃	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂²×Dic₁₃	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.