Subgroups — #88205

Order 416.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#6107	C₂	1	2	yes	maximal, complemented
4	#6105	C₂	1	2	yes	maximal, complemented
5	#6099	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₃	C₂²	1	1	yes	characteristic
7	D₄×C₁₃	—	2	1	no	—
8	D₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₁₃	—	2	1	no	—
10	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₃	—	2	1	no	—
12	Dic₂₆	—	2	1	no	—
13	Dic₂₆	C₂²	1	2	yes	—
14	#1055	C₂²	1	2	yes	—
15	C₂²×C₁₃	—	2	1	no	—
16	C₂²×C₁₃	D₄	1	1	yes	characteristic
17	C₄×C₁₃	—	2	1	no	—
18	C₄×C₁₃	D₄	1	1	yes	characteristic
19	C₄×C₁₃	C₂³	1	1	yes	characteristic
20	Dic₁₃	—	2	2	no	—
21	#137	—	13	1	no	maximal, Sylow
22	C₂×C₁₃	—	2	1	no	—
23	C₂×C₁₃	—	4	1	no	—
24	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
25	#41	D₁₃	1	1	yes	characteristic
26	C₂×Q₈	—	13	1	no	—
27	Q₁₆	—	13	2	no	—
28	SD₁₆	—	13	2	no	—
29	M₁₆	—	13	1	no	—
30	C₁₃	#137	1	1	yes	characteristic, complemented, Sylow
31	Q₈	—	13	2	no	—
32	Q₈	—	26	1	no	—
33	Q₈	C₂×D₁₃	1	1	yes	characteristic
34	D₄	—	2	1	no	—
35	D₄	C₂×D₁₃	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	26	1	no	—
38	C₂×C₄	C₂×D₁₃	1	1	yes	characteristic
39	C₈	—	13	2	no	—
40	C₂²	—	2	1	no	—
41	C₂²	C₂²⋊D₁₃	1	1	yes	characteristic
42	C₄	—	2	1	no	—
43	C₄	—	26	2	no	—
44	C₄	C₂²⋊D₁₃	1	1	yes	characteristic
45	C₄	C₂²×D₁₃	1	1	yes	characteristic
46	C₂	—	2	1	no	—
47	C₂	—	4	1	no	—
48	C₂	C₂×C₂²⋊D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×C₂²⋊D₁₃
commutator, cosocle	C₄×C₁₃	C₂³
Frattini	C₄	C₂²×D₁₃
Fitting, prime radical	C₁₃×#41	C₂
socle	C₂×C₁₃	C₂×D₄
hypercenter	#41	D₁₃
hypocenter	C₁₃	#137
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #41

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₂₆	C₂	semidirect
3. #6107	C₂	semidirect
4. #6105	C₂	semidirect
5. #6099	C₂	semidirect
30. C₁₃	#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#41	2
C₂×Dic₂₆	2
#6107	2
#6105	2
#6099	2
#137	13