Subgroups — #88064

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	C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic
3	#6099	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
5	C₂×Dic₁₃	C₄	1	2	yes	—
6	Dic₂₆	—	2	1	no	—
7	Dic₂₆	—	2	1	no	—
8	C₈×C₁₃	—	2	1	no	—
9	#1055	—	2	1	no	—
10	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
11	C₄×C₁₃	D₄	1	1	yes	characteristic
12	C₄×C₁₃	D₄	1	1	yes	characteristic
13	Dic₁₃	—	2	2	no	—
14	#101	—	13	1	no	maximal, Sylow
15	C₂×C₁₃	—	2	1	no	—
16	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
17	C₂×Q₈	—	13	1	no	—
18	M₁₆	—	13	1	no	—
19	M₁₆	D₁₃	1	1	yes	characteristic
20	C₁₃	#101	1	1	yes	characteristic, complemented, Sylow
21	Q₈	—	26	1	no	—
22	Q₈	—	26	1	no	—
23	C₂×C₄	—	13	2	no	—
24	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
25	C₈	—	2	1	no	—
26	C₈	—	26	1	no	—
27	C₂²	C₄×D₁₃	1	1	yes	characteristic
28	C₄	—	26	2	no	—
29	C₄	D₅₂	1	1	yes	characteristic
30	C₄	C₂²⋊D₁₃	1	1	yes	characteristic
31	C₂	—	2	1	no	—
32	C₂	#6103	1	1	yes	characteristic

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

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

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