Subgroups — #88128

Order 416.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₂	C₂	1	6	yes	maximal, complemented
2	C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×D₁₃	C₂²	1	4	yes	—
4	C₂×C₄×C₁₃	C₂²	1	3	yes	—
5	D₅₂	—	2	12	no	—
6	C₂²×C₁₃	C₂³	1	1	yes	characteristic
7	C₂×D₁₃	—	2	12	no	—
8	C₄×C₁₃	D₄	1	6	yes	complemented
9	#127	—	13	1	no	maximal, Sylow
10	C₂×C₁₃	C₂×D₄	1	3	yes	—
11	D₁₃	—	4	4	no	—
12	C₂×D₄	—	13	6	no	—
13	C₄²	D₁₃	1	1	yes	characteristic, complemented
14	C₁₃	#127	1	1	yes	characteristic, complemented, Sylow
15	C₂³	—	13	4	no	—
16	D₄	—	26	12	no	—
17	C₂×C₄	C₂×D₁₃	1	3	yes	—
18	C₂²	—	26	12	no	—
19	C₂²	C₂²×D₁₃	1	1	yes	characteristic
20	C₄	D₅₂	1	6	yes	complemented
21	C₂	—	52	4	no	—
22	C₂	C₂×D₅₂	1	3	yes	—

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.