Subgroups — #35229666

Order 20896.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₆₅₃	C₂	1	1	yes	maximal, characteristic
2	#23782580	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₆×C₆₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₆₅₃	C₄	1	1	yes	characteristic
5	#19104916	C₄	1	1	yes	characteristic
6	C₈×C₆₅₃	C₂²	1	1	yes	characteristic
7	C₂×D₆₅₃	C₈	1	1	yes	characteristic
8	C₄×C₆₅₃	C₂×C₄	1	1	yes	characteristic
9	Dic₆₅₃	C₈	1	1	yes	characteristic
10	C₂×C₆₅₃	C₂×C₈	1	1	yes	characteristic
11	D₆₅₃	—	2	1	no	—
12	C₆₅₃	M₃₂	1	1	yes	characteristic, complemented, Sylow
13	M₃₂	—	653	1	no	maximal, Sylow
14	C₂×C₈	—	653	1	no	—
15	C₁₆	—	653	1	no	—
16	C₁₆	D₆₅₃	1	1	yes	characteristic, complemented
17	C₂×C₄	—	653	1	no	—
18	C₈	—	653	1	no	—
19	C₈	C₂×D₆₅₃	1	1	yes	characteristic
20	C₂²	—	653	1	no	—
21	C₄	—	653	1	no	—
22	C₄	C₄×D₆₅₃	1	1	yes	characteristic
23	C₂	—	1306	1	no	—
24	C₂	C₈×D₆₅₃	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.