Subgroups — #88112

Order 416.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#1057	C₂	1	2	yes	maximal
2	C₄×Dic₁₃	C₂	1	1	yes	maximal, characteristic
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	#1057	—	2	2	no	—
7	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₃	—	2	1	no	—
9	Dic₁₃	C₈	1	2	yes	complemented
10	Dic₁₃	D₄	1	1	yes	characteristic
11	Dic₁₃	Q₈	1	1	yes	characteristic
12	C₄⋊C₈	—	13	1	no	maximal, Sylow
13	C₂×C₁₃	C₄⋊C₄	1	1	yes	characteristic
14	C₂×C₁₃	C₂×C₈	1	1	yes	characteristic
15	C₂×C₁₃	M₁₆	1	1	yes	characteristic
16	C₂×C₈	—	13	2	no	—
17	C₄²	—	13	1	no	—
18	C₁₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
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	—	13	1	no	—
27	C₄	—	13	1	no	—
28	C₂	D₁₃⋊C₈	1	1	yes	characteristic
29	C₂	C₄⋊#261	1	1	yes	characteristic
30	C₂	#6122	1	1	yes	characteristic

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

N	H ≅ G/N	type
9. Dic₁₃	C₈	semidirect
18. C₁₃	C₄⋊C₈	semidirect

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