Subgroups — D₁₃₅₂ #72210172

Order 2704.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₇₆	C₂	1	2	yes	maximal, complemented
2	C₈×C₁₆₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₁₆₉	—	2	2	no	—
4	C₄×C₁₆₉	C₂²	1	1	yes	characteristic
5	C₂×C₁₆₉	D₄	1	1	yes	characteristic
6	D₁₆₉	—	4	2	no	—
7	D₁₀₄	—	13	1	no	maximal
8	C₁₆₉	D₈	1	1	yes	characteristic, complemented, Sylow
9	D₅₂	—	13	2	no	—
10	C₈×C₁₃	D₁₃	1	1	yes	characteristic
11	C₂×D₁₃	—	26	2	no	—
12	C₄×C₁₃	C₂×D₁₃	1	1	yes	characteristic
13	C₂×C₁₃	D₅₂	1	1	yes	characteristic
14	D₁₃	—	52	2	no	—
15	D₈	—	169	1	no	Sylow
16	C₁₃	D₁₀₄	1	1	yes	characteristic
17	D₄	—	169	2	no	—
18	C₈	D₁₆₉	1	1	yes	characteristic, complemented
19	C₂²	—	338	2	no	—
20	C₄	C₂×D₁₆₉	1	1	yes	characteristic
21	C₂	—	676	2	no	—
22	C₂	D₆₇₆	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.