Subgroups — #88043

Order 416.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#1055	C₂	1	2	yes	maximal
3	C₂×C₄×C₁₃	C₄	1	2	yes	—
4	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
5	#1055	C₄	1	4	yes	complemented
6	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
7	C₄×C₁₃	—	2	2	no	—
8	C₄×C₁₃	C₂×C₄	1	2	yes	—
9	#97	—	13	1	no	maximal, Sylow
10	C₂×C₁₃	C₄²	1	1	yes	characteristic
11	C₂×C₁₃	M₁₆	1	2	yes	—
12	C₂×C₈	—	13	2	no	—
13	C₄²	D₁₃	1	1	yes	characteristic
14	C₁₃	#97	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₄	Dic₁₃	1	2	yes	—
16	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
17	C₈	—	13	4	no	—
18	C₂²	C₂×Dic₁₃	1	1	yes	characteristic
19	C₄	—	2	2	no	—
20	C₄	C₄×D₁₃	1	2	yes	—
21	C₂	#6099	1	2	yes	—
22	C₂	C₄×Dic₁₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #1055	C₄	semidirect
14. C₁₃	#97	semidirect

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