Subgroups — #11718521

Order 832.

114 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	#88146	C₂	1	2	yes	maximal
3	C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
4	#88057	C₂	1	1	yes	maximal, characteristic, complemented
5	#88047	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
9	#6103	—	2	2	no	—
10	C₄⋊Dic₁₃	C₂²	1	2	yes	—
11	C₄×Dic₁₃	—	2	2	no	—
12	C₂×#1055	C₂²	1	1	yes	characteristic
13	C₈×D₁₃	C₄	1	4	yes	complemented
14	C₂²×D₁₃	D₄	1	1	yes	characteristic
15	C₂×C₄×C₁₃	—	2	2	no	—
16	C₂×C₄×C₁₃	C₂³	1	1	yes	characteristic
17	C₂×Dic₁₃	—	2	2	no	—
18	C₂×Dic₁₃	D₄	1	1	yes	characteristic
19	C₄×D₁₃	C₂×C₄	1	2	yes	—
20	C₄×D₁₃	Q₈	1	2	yes	—
21	C₈×C₁₃	C₂×C₄	1	2	yes	—
22	#1055	C₂×C₄	1	2	yes	—
23	#427	—	13	1	no	maximal, Sylow
24	C₂²×C₁₃	C₂×D₄	1	1	yes	characteristic
25	C₂×D₁₃	—	2	2	no	—
26	C₂×D₁₃	C₄⋊C₄	1	2	yes	—
27	C₄×C₁₃	—	4	2	no	—
28	C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
30	Dic₁₃	—	4	2	no	—
31	Dic₁₃	C₄⋊C₄	1	2	yes	—
32	C₂²×C₈	—	13	1	no	—
33	#117	—	13	2	no	—
34	#107	—	13	2	no	—
35	#106	—	13	1	no	—
36	#106	D₁₃	1	1	yes	characteristic, complemented
37	C₂×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₁₃	#135	1	2	yes	—
39	D₁₃	—	2	2	no	—
40	C₂²×C₄	—	13	1	no	—
41	C₂×C₈	—	13	1	no	—
42	C₂×C₈	—	13	4	no	—
43	C₂×C₈	C₂×D₁₃	1	1	yes	characteristic
44	C₄⋊C₄	—	13	2	no	—
45	C₄⋊C₄	C₂×D₁₃	1	2	yes	—
46	C₂²⋊C₄	—	26	2	no	—
47	C₄²	—	26	2	no	—
48	C₁₃	#427	1	1	yes	characteristic, complemented, Sylow
49	C₂³	—	13	1	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	13	1	no	—
52	C₂×C₄	—	13	2	no	—
53	C₂×C₄	—	13	2	no	—
54	C₂×C₄	—	26	2	no	—
55	C₂×C₄	C₂²×D₁₃	1	1	yes	characteristic
56	C₈	—	13	2	no	—
57	C₈	C₄×D₁₃	1	2	yes	—
58	C₂²	—	13	2	no	—
59	C₂²	—	26	2	no	—
60	C₂²	D₄×D₁₃	1	1	yes	characteristic
61	C₄	—	4	2	no	—
62	C₄	—	13	2	no	—
63	C₄	—	52	2	no	—
64	C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
65	C₄	Q₈×D₁₃	1	1	yes	characteristic
66	C₂	—	26	2	no	—
67	C₂	C₄⋊C₄×D₁₃	1	1	yes	characteristic
68	C₂	#88170	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₃
commutator	C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₁₃
Fitting	C₁₃×#106	C₂
socle	C₂²×C₁₃	C₂×D₄
prime radical	C₂²×D₁₃	D₄
cosocle	C₂×C₄×C₁₃	C₂³
hypercenter	#106	D₁₃
hypocenter	C₁₃	#427
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
3. C₁₃×#106	C₂	semidirect
4. #88057	C₂	semidirect
5. #88047	C₂	semidirect
13. C₈×D₁₃	C₄	semidirect
36. #106	D₁₃	semidirect
48. C₁₃	#427	semidirect

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
#88146	2
C₁₃×#106	2
#88057	2
#88047	2
#427	13