Subgroups — D₂₇₃₅₂ #72290664

Order 54704.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃₆₇₆	C₂	1	2	yes	maximal, complemented
2	C₈×C₁₃×C₂₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₃₄₁₉	—	2	2	no	—
4	C₄×C₁₃×C₂₆₃	C₂²	1	1	yes	characteristic
5	C₂×C₁₃×C₂₆₃	D₄	1	1	yes	characteristic
6	D₃₄₁₉	—	4	2	no	—
7	D₂₁₀₄	—	13	1	no	maximal, Hall
8	C₁₃×C₂₆₃	D₈	1	1	yes	characteristic, complemented, Hall
9	D₁₀₅₂	—	13	2	no	—
10	C₈×C₂₆₃	D₁₃	1	1	yes	characteristic, complemented
11	C₂×D₂₆₃	—	26	2	no	—
12	C₄×C₂₆₃	C₂×D₁₃	1	1	yes	characteristic
13	C₂×C₂₆₃	D₅₂	1	1	yes	characteristic
14	D₂₆₃	—	52	2	no	—
15	C₂₆₃	D₁₀₄	1	1	yes	characteristic, complemented, Sylow
16	D₁₀₄	—	263	1	no	maximal, Hall
17	D₅₂	—	263	2	no	—
18	C₈×C₁₃	D₂₆₃	1	1	yes	characteristic, complemented
19	C₂×D₁₃	—	526	2	no	—
20	C₄×C₁₃	C₂×D₂₆₃	1	1	yes	characteristic
21	C₂×C₁₃	D₁₀₅₂	1	1	yes	characteristic
22	D₁₃	—	1052	2	no	—
23	D₈	—	3419	1	no	Sylow
24	C₁₃	D₂₁₀₄	1	1	yes	characteristic, complemented, Sylow
25	D₄	—	3419	2	no	—
26	C₈	D₃₄₁₉	1	1	yes	characteristic, complemented
27	C₂²	—	6838	2	no	—
28	C₄	C₂×D₃₄₁₉	1	1	yes	characteristic
29	C₂	—	13676	2	no	—
30	C₂	D₁₃₆₇₆	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.