Subgroups — Q₈×Dic₁₃ #88199

Order 416.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₁₃	C₂	1	3	yes	maximal
3	C₄×Dic₁₃	C₂	1	3	yes	maximal
4	Q₈×C₁₃	C₄	1	4	yes	complemented
5	C₂×C₄×C₁₃	C₂²	1	3	yes	—
6	C₂×Dic₁₃	C₂²	1	3	yes	—
7	C₂×Dic₁₃	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃	C₂³	1	1	yes	characteristic
9	C₄×C₁₃	C₂×C₄	1	6	yes	—
10	Dic₁₃	—	2	3	no	—
11	Dic₁₃	Q₈	1	2	yes	direct product factor
12	C₄×Q₈	—	13	1	no	maximal, Sylow
13	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
14	C₂×C₁₃	C₂×Q₈	1	1	yes	characteristic
15	C₂×C₁₃	#41	1	1	yes	characteristic
16	C₂×Q₈	D₁₃	1	1	yes	characteristic
17	C₄⋊C₄	—	13	3	no	—
18	C₄²	—	13	3	no	—
19	C₁₃	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
20	Q₈	Dic₁₃	1	4	yes	direct product factor
21	C₂×C₄	—	13	1	no	—
22	C₂×C₄	—	13	3	no	—
23	C₂×C₄	C₂×D₁₃	1	3	yes	—
24	C₂²	C₂²×D₁₃	1	1	yes	characteristic
25	C₄	—	13	2	no	—
26	C₄	—	26	3	no	—
27	C₄	C₂×Dic₁₃	1	6	yes	—
28	C₂	Q₈×D₁₃	1	1	yes	characteristic
29	C₂	#6131	1	1	yes	characteristic
30	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.