Subgroups — #35231237

Order 21088.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₃₁₈	C₂	1	1	yes	maximal, characteristic
2	#24902094	C₂	1	1	yes	maximal, characteristic
3	M₁₆×C₆₅₉	C₂	1	1	yes	maximal, characteristic
4	Dic₁₃₁₈	—	2	1	no	—
5	Dic₁₃₁₈	—	2	1	no	—
6	C₂×Dic₆₅₉	C₄	1	2	yes	—
7	C₆₅₉⋊C₈	—	2	1	no	—
8	C₂×C₄×C₆₅₉	C₂²	1	1	yes	characteristic
9	C₈×C₆₅₉	—	2	1	no	—
10	C₂²×C₆₅₉	C₂×C₄	1	1	yes	characteristic
11	C₄×C₆₅₉	D₄	1	1	yes	characteristic
12	C₄×C₆₅₉	D₄	1	1	yes	characteristic
13	Dic₆₅₉	—	2	2	no	—
14	C₂×C₆₅₉	—	2	1	no	—
15	C₂×C₆₅₉	C₂²⋊C₄	1	1	yes	characteristic
16	C₆₅₉	#101	1	1	yes	characteristic, complemented, Sylow
17	#101	—	659	1	no	maximal, Sylow
18	C₂×Q₈	—	659	1	no	—
19	M₁₆	—	659	1	no	—
20	M₁₆	D₆₅₉	1	1	yes	characteristic
21	Q₈	—	1318	1	no	—
22	Q₈	—	1318	1	no	—
23	C₂×C₄	—	659	2	no	—
24	C₂×C₄	C₂×D₆₅₉	1	1	yes	characteristic
25	C₈	—	2	1	no	—
26	C₈	—	1318	1	no	—
27	C₂²	C₄×D₆₅₉	1	1	yes	characteristic
28	C₄	—	1318	2	no	—
29	C₄	C₂²⋊D₆₅₉	1	1	yes	characteristic
30	C₄	D₂₆₃₆	1	1	yes	characteristic
31	C₂	—	2	1	no	—
32	C₂	(C₂×D₆₅₉)⋊C₄	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
16. C₆₅₉	#101	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.