Subgroups — C₁₃×#104 #88087

Order 416.

44 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	C₁₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×C₁₃	C₄	1	1	yes	characteristic, complemented
5	D₄×C₁₃	—	2	1	no	—
6	D₄×C₁₃	C₄	1	1	yes	characteristic, complemented
7	C₂×C₄×C₁₃	—	2	1	no	—
8	C₂×C₄×C₁₃	—	2	1	no	—
9	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₈×C₁₃	—	2	1	no	—
11	C₂²×C₁₃	—	2	1	no	—
12	C₂²×C₁₃	D₄	1	1	yes	characteristic
13	C₄×C₁₃	—	2	2	no	—
14	C₄×C₁₃	—	2	1	no	—
15	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₃	D₄	1	1	yes	characteristic
17	#104	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₁₃	—	2	1	no	—
19	C₂×C₁₃	—	4	1	no	—
20	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
21	#41	C₂×C₁₃	1	1	yes	characteristic
22	M₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
23	C₄²	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₁₃	#104	1	1	yes	characteristic, direct product factor, Sylow
25	Q₈	C₄×C₁₃	1	1	yes	characteristic, complemented
26	D₄	—	2	1	no	—
27	D₄	C₄×C₁₃	1	1	yes	characteristic, complemented
28	C₂×C₄	—	2	1	no	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂²×C₁₃	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₂²	—	2	1	no	—
33	C₂²	D₄×C₁₃	1	1	yes	characteristic
34	C₄	—	2	2	no	—
35	C₄	—	2	1	no	—
36	C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
37	C₄	D₄×C₁₃	1	1	yes	characteristic
38	C₂	—	2	1	no	—
39	C₂	—	4	1	no	—
40	C₂	C₁₃×C₂²⋊C₄	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×M₁₆	C₂	semidirect
3. C₄²×C₁₃	C₂	semidirect
4. Q₈×C₁₃	C₄	semidirect
6. D₄×C₁₃	C₄	semidirect
17. #104	C₁₃	direct (N × H)
22. M₁₆	C₂×C₁₃	semidirect
23. C₄²	C₂×C₁₃	semidirect
24. C₁₃	#104	direct (N × H)
25. Q₈	C₄×C₁₃	semidirect
27. D₄	C₄×C₁₃	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
C₁₃×M₁₆	2
C₄²×C₁₃	2
#104	13

Subgroups — C13×#104 #88087

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#104 #88087