Subgroups — #88110

Order 416.

40 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	C₄	1	4	yes	complemented
7	C₂²×C₁₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₁₃	—	2	1	no	—
9	Dic₁₃	—	2	1	no	—
10	Dic₁₃	C₂×C₄	1	2	yes	—
11	#97	—	13	1	no	maximal, Sylow
12	C₂×C₁₃	C₄²	1	1	yes	characteristic
13	C₂×C₁₃	M₁₆	1	1	yes	characteristic
14	C₂×C₁₃	M₁₆	1	1	yes	characteristic
15	C₂×C₈	—	13	2	no	—
16	C₄²	—	13	1	no	—
17	C₁₃	#97	1	1	yes	characteristic, complemented, Sylow
18	C₂×C₄	—	13	1	no	—
19	C₂×C₄	—	13	1	no	—
20	C₂×C₄	#261	1	1	yes	characteristic
21	C₈	—	13	4	no	—
22	C₂²	C₂×#261	1	1	yes	characteristic
23	C₄	—	2	1	no	—
24	C₄	—	13	2	no	—
25	C₄	—	26	1	no	—
26	C₂	#6118	1	1	yes	characteristic
27	C₂	C₄×#261	1	1	yes	characteristic
28	C₂	#6122	1	1	yes	characteristic

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

N	H ≅ G/N	type
6. #1057	C₄	semidirect
17. C₁₃	#97	semidirect

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