Subgroups — #88073

Order 416.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	#6099	C₂	1	2	yes	maximal, complemented
3	C₂³×C₁₃	C₄	1	2	yes	—
4	D₄×C₁₃	—	2	2	no	—
5	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
6	#1055	—	2	2	no	—
7	C₂²×C₁₃	—	2	2	no	—
8	C₂²×C₁₃	—	4	2	no	—
9	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
10	C₄×C₁₃	D₄	1	2	yes	—
11	#100	—	13	1	no	maximal, Sylow
12	C₂×C₁₃	—	2	1	no	—
13	C₂×C₁₃	—	4	2	no	—
14	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
15	C₂×D₄	D₁₃	1	1	yes	characteristic
16	M₁₆	—	13	2	no	—
17	C₁₃	#100	1	1	yes	characteristic, complemented, Sylow
18	C₂³	Dic₁₃	1	2	yes	—
19	D₄	—	2	2	no	—
20	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
21	C₈	—	26	2	no	—
22	C₂²	—	2	2	no	—
23	C₂²	—	4	2	no	—
24	C₂²	C₂×Dic₁₃	1	1	yes	characteristic
25	C₄	C₂²⋊D₁₃	1	2	yes	—
26	C₂	—	2	1	no	—
27	C₂	—	4	2	no	—
28	C₂	C₂²⋊Dic₁₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. #6099	C₂	semidirect
17. C₁₃	#100	semidirect

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