Subgroups — C₁₃×#131 #88225

Order 416.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₁₃×M₁₆	C₂	1	3	yes	maximal, complemented
3	C₂×C₈×C₁₃	C₂	1	3	yes	maximal, complemented
4	Q₈×C₁₃	C₄	1	1	yes	characteristic
5	D₄×C₁₃	C₄	1	3	yes	—
6	C₂×C₄×C₁₃	C₂²	1	3	yes	—
7	C₈×C₁₃	C₂²	1	3	yes	—
8	C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₁₃	C₂×C₄	1	3	yes	—
10	C₄×C₁₃	C₂×C₄	1	3	yes	—
11	C₄×C₁₃	C₂³	1	1	yes	characteristic
12	#131	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₁₃	—	2	3	no	—
14	C₂×C₁₃	C₂²×C₄	1	1	yes	characteristic
15	#41	C₂×C₁₃	1	1	yes	characteristic
16	M₁₆	C₂×C₁₃	1	3	yes	complemented
17	C₂×C₈	C₂×C₁₃	1	3	yes	complemented
18	C₁₃	#131	1	1	yes	characteristic, direct product factor, Sylow
19	Q₈	C₄×C₁₃	1	1	yes	characteristic
20	D₄	C₄×C₁₃	1	3	yes	—
21	C₂×C₄	C₂²×C₁₃	1	3	yes	—
22	C₈	C₂²×C₁₃	1	3	yes	—
23	C₈	C₂²×C₁₃	1	1	yes	characteristic
24	C₂²	C₂×C₄×C₁₃	1	3	yes	—
25	C₄	C₂×C₄×C₁₃	1	3	yes	—
26	C₄	C₂³×C₁₃	1	1	yes	characteristic
27	C₂	—	2	3	no	—
28	C₂	C₂²×C₄×C₁₃	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.