Subgroups — #88113

Order 416.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₆	C₂	1	1	yes	maximal, characteristic
2	#6122	C₂	1	2	yes	maximal
3	C₂×C₄×C₁₃	C₄	1	1	yes	characteristic
4	C₂×Dic₁₃	C₄	1	1	yes	characteristic
5	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
6	Dic₂₆	—	2	2	no	—
7	#1057	—	2	2	no	—
8	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
9	C₄×C₁₃	—	2	1	no	—
10	Dic₁₃	—	2	1	no	—
11	Dic₁₃	D₄	1	2	yes	—
12	#101	—	13	1	no	maximal, Sylow
13	C₂×C₁₃	—	2	1	no	—
14	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
15	C₂×Q₈	—	13	1	no	—
16	M₁₆	—	13	2	no	—
17	C₁₃	#101	1	1	yes	characteristic, complemented, Sylow
18	Q₈	—	26	2	no	—
19	C₂×C₄	—	13	1	no	—
20	C₂×C₄	—	13	1	no	—
21	C₂×C₄	#261	1	1	yes	characteristic
22	C₈	—	26	2	no	—
23	C₂²	C₂×#261	1	1	yes	characteristic
24	C₄	—	2	1	no	—
25	C₄	—	13	2	no	—
26	C₄	—	26	1	no	—
27	C₂	—	2	1	no	—
28	C₂	C₂²⋊#261	1	1	yes	characteristic

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

N	H ≅ G/N	type
17. C₁₃	#101	semidirect

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