Subgroups — C₂×#88098 #11719085

Order 832.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×#6092	C₂	1	2	yes	maximal, complemented
3	#88098	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₄×D₁₃	C₄	1	1	yes	characteristic
5	C₂×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×#1055	C₂²	1	1	yes	characteristic
7	C₈×D₁₃	C₄	1	2	yes	—
8	C₈×D₁₃	C₂²	1	2	yes	—
9	#6092	C₂²	1	4	yes	complemented
10	C₂²×D₁₃	C₈	1	1	yes	characteristic
11	C₂×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×Dic₁₃	C₈	1	1	yes	characteristic
13	C₄×D₁₃	C₈	1	2	yes	—
14	C₄×D₁₃	C₂×C₄	1	2	yes	—
15	C₈×C₁₃	C₂×C₄	1	2	yes	—
16	#1055	C₂×C₄	1	1	yes	characteristic
17	#1055	C₂³	1	1	yes	characteristic
18	C₂×M₃₂	—	13	1	no	maximal, Sylow
19	C₂²×C₁₃	C₂×C₈	1	1	yes	characteristic
20	C₂×D₁₃	—	2	2	no	—
21	C₂×D₁₃	C₂×C₈	1	2	yes	—
22	C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
23	C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
24	Dic₁₃	C₂×C₈	1	2	yes	—
25	C₂²×C₈	—	13	1	no	—
26	M₃₂	—	13	4	no	—
27	C₂×C₁₆	—	13	2	no	—
28	C₂×C₁₃	M₃₂	1	2	yes	complemented
29	C₂×C₁₃	C₂²×C₈	1	1	yes	characteristic
30	D₁₃	—	2	2	no	—
31	C₂²×C₄	—	13	1	no	—
32	C₂×C₈	—	13	1	no	—
33	C₂×C₈	—	13	2	no	—
34	C₂×C₈	—	13	2	no	—
35	C₂×C₈	#261	1	1	yes	characteristic
36	C₁₆	—	13	4	no	—
37	C₁₃	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
38	C₂³	—	13	1	no	—
39	C₂×C₄	—	13	1	no	—
40	C₂×C₄	—	13	2	no	—
41	C₂×C₄	—	13	2	no	—
42	C₂×C₄	C₂×#261	1	1	yes	characteristic
43	C₈	—	13	1	no	—
44	C₈	—	13	1	no	—
45	C₈	C₂×#261	1	2	yes	—
46	C₂²	—	13	2	no	—
47	C₂²	—	26	2	no	—
48	C₂²	D₁₃⋊C₈	1	1	yes	characteristic
49	C₄	—	13	2	no	—
50	C₄	D₁₃⋊C₈	1	1	yes	characteristic
51	C₄	C₂²×#261	1	1	yes	characteristic
52	C₂	—	26	2	no	—
53	C₂	#88098	1	2	yes	direct product factor
54	C₂	C₂×D₁₃⋊C₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#261
commutator	C₂×C₁₃	C₂²×C₈
Frattini	C₄	C₂²×#261
Fitting	C₂×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₈
prime radical	C₂²×D₁₃	C₈
cosocle	#1055	C₂³
hypercenter	C₂×C₈	#261
hypocenter	C₁₃	C₂×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#6092	C₂	semidirect
3. #88098	C₂	direct (N × H)
9. #6092	C₂²	semidirect
28. C₂×C₁₃	M₃₂	semidirect
37. C₁₃	C₂×M₃₂	semidirect
53. C₂	#88098	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×C₈×D₁₃	2
C₂×#6092	2
#88098	2
C₂×M₃₂	13

Subgroups — C2×#88098 #11719085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#88098 #11719085