Subgroups — C₂×#24902093 #35231323

Order 21088.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₆₅₉	C₂	1	1	yes	maximal, characteristic
2	#24902093	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₆₅₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×C₆₅₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₆₅₉	C₄	1	1	yes	characteristic
6	C₂×Dic₆₅₉	C₄	1	1	yes	characteristic
7	C₄×D₆₅₉	C₄	1	2	yes	—
8	C₄×D₆₅₉	C₂²	1	2	yes	—
9	C₆₅₉⋊C₈	C₂²	1	2	yes	complemented
10	C₂×C₄×C₆₅₉	C₂²	1	1	yes	characteristic
11	C₈×C₆₅₉	C₂²	1	2	yes	complemented
12	C₂²×C₆₅₉	C₂×C₄	1	1	yes	characteristic
13	C₂×D₆₅₉	—	2	2	no	—
14	C₂×D₆₅₉	C₂×C₄	1	2	yes	—
15	C₄×C₆₅₉	C₂×C₄	1	1	yes	characteristic
16	C₄×C₆₅₉	C₂³	1	1	yes	characteristic
17	Dic₆₅₉	C₂×C₄	1	2	yes	—
18	C₂×C₆₅₉	M₁₆	1	2	yes	complemented
19	C₂×C₆₅₉	C₂²×C₄	1	1	yes	characteristic
20	D₆₅₉	—	2	2	no	—
21	C₆₅₉	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₂×M₁₆	—	659	1	no	maximal, Sylow
23	C₂²×C₄	—	659	1	no	—
24	M₁₆	—	659	4	no	—
25	C₂×C₈	—	659	1	no	—
26	C₂×C₈	D₆₅₉	1	1	yes	characteristic, complemented
27	C₂³	—	659	1	no	—
28	C₂×C₄	—	659	1	no	—
29	C₂×C₄	—	659	2	no	—
30	C₂×C₄	—	659	2	no	—
31	C₂×C₄	C₂×D₆₅₉	1	1	yes	characteristic
32	C₈	—	659	2	no	—
33	C₈	C₂×D₆₅₉	1	2	yes	complemented
34	C₂²	—	1318	2	no	—
35	C₂²	—	659	2	no	—
36	C₂²	C₄×D₆₅₉	1	1	yes	characteristic
37	C₄	—	659	2	no	—
38	C₄	C₄×D₆₅₉	1	1	yes	characteristic
39	C₄	C₂²×D₆₅₉	1	1	yes	characteristic
40	C₂	—	1318	2	no	—
41	C₂	#24902093	1	2	yes	direct product factor
42	C₂	C₂×C₄×D₆₅₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₆₅₉
commutator	C₂×C₆₅₉	C₂²×C₄
Frattini	C₄	C₂²×D₆₅₉
Fitting	C₂×C₈×C₆₅₉	C₂
socle	C₂²×C₆₅₉	C₂×C₄
prime radical	C₂²×D₆₅₉	C₄
cosocle	C₄×C₆₅₉	C₂³
hypercenter	C₂×C₈	D₆₅₉
hypocenter	C₆₅₉	C₂×M₁₆
LCS	G ▷ C₂×C₆₅₉ ▷ C₆₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #24902093	C₂	direct (N × H)
3. C₂×C₆₅₉⋊C₈	C₂	semidirect
4. C₂×C₈×C₆₅₉	C₂	semidirect
9. C₆₅₉⋊C₈	C₂²	semidirect
11. C₈×C₆₅₉	C₂²	semidirect
18. C₂×C₆₅₉	M₁₆	semidirect
21. C₆₅₉	C₂×M₁₆	semidirect
26. C₂×C₈	D₆₅₉	semidirect
33. C₈	C₂×D₆₅₉	semidirect
41. C₂	#24902093	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×D₆₅₉	2
#24902093	2
C₂×C₆₅₉⋊C₈	2
C₂×C₈×C₆₅₉	2
C₂×M₁₆	659

Subgroups — C2×#24902093 #35231323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#24902093 #35231323