Subgroups — #88100

Order 416.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#261	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#261	C₄	1	2	yes	—
5	C₄×D₁₃	C₂²	1	1	yes	characteristic
6	#1057	C₄	1	2	yes	complemented
7	C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
8	#1055	C₄	1	1	yes	characteristic, complemented
9	C₂×D₁₃	C₂×C₄	1	1	yes	characteristic
10	#261	—	2	2	no	—
11	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	Dic₁₃	C₂×C₄	1	1	yes	characteristic
13	#97	—	13	1	no	maximal, Sylow
14	C₂×C₁₃	C₄²	1	1	yes	characteristic
15	D₁₃	M₁₆	1	2	yes	—
16	C₂×C₈	—	13	1	no	—
17	C₂×C₈	—	13	1	no	—
18	C₄²	—	13	1	no	—
19	C₁₃	#97	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₄	—	13	1	no	—
21	C₂×C₄	—	13	2	no	—
22	C₈	—	13	2	no	—
23	C₈	—	13	1	no	—
24	C₈	#261	1	1	yes	characteristic, complemented
25	C₂²	—	13	1	no	—
26	C₄	—	13	1	no	—
27	C₄	—	26	2	no	—
28	C₄	C₂×#261	1	1	yes	characteristic
29	C₂	—	13	2	no	—
30	C₂	C₄×#261	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.