Subgroups — #88104

Order 416.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6118	C₂	1	2	yes	maximal
2	C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄×D₁₃	C₂²	1	1	yes	characteristic
4	#1057	—	2	2	no	—
5	C₈×C₁₃	C₄	1	1	yes	characteristic
6	#1055	C₄	1	1	yes	characteristic
7	C₂×D₁₃	Q₈	1	1	yes	characteristic
8	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
9	Dic₁₃	D₄	1	1	yes	characteristic
10	#108	—	13	1	no	maximal, Sylow
11	C₂×C₁₃	C₄⋊C₄	1	1	yes	characteristic
12	D₁₃	—	2	1	no	—
13	M₁₆	—	13	2	no	—
14	C₂×C₈	—	13	1	no	—
15	C₁₃	#108	1	1	yes	characteristic, complemented, Sylow
16	C₂×C₄	—	13	1	no	—
17	C₈	—	13	1	no	—
18	C₈	—	26	2	no	—
19	C₈	#261	1	1	yes	characteristic
20	C₂²	—	13	1	no	—
21	C₄	—	13	1	no	—
22	C₄	C₂×#261	1	1	yes	characteristic
23	C₂	—	26	1	no	—
24	C₂	C₄⋊#261	1	1	yes	characteristic

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

N	H ≅ G/N	type
15. C₁₃	#108	semidirect

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