Subgroups — C₁₃×#102 #88085

Order 416.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₁₃	—	2	1	no	—
5	D₄×C₁₃	—	2	1	no	—
6	D₄×C₁₃	C₄	1	2	yes	complemented
7	C₂×C₄×C₁₃	—	2	1	no	—
8	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₈×C₁₃	—	2	1	no	—
10	C₂²×C₁₃	—	2	2	no	—
11	C₂²×C₁₃	—	4	1	no	—
12	C₂²×C₁₃	—	4	1	no	—
13	C₂²×C₁₃	D₄	1	1	yes	characteristic
14	C₄×C₁₃	—	4	1	no	—
15	C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₄×C₁₃	D₄	1	1	yes	characteristic
17	#102	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
18	C₂×C₁₃	—	4	2	no	—
19	C₂×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
20	C₂×C₁₃	D₈	1	1	yes	characteristic
21	C₂×C₁₃	SD₁₆	1	1	yes	characteristic
22	C₂×D₄	C₂×C₁₃	1	1	yes	characteristic
23	C₂×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
24	C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
25	C₁₃	#102	1	1	yes	characteristic, direct product factor, Sylow
26	C₂³	—	2	1	no	—
27	D₄	—	2	1	no	—
28	D₄	C₄×C₁₃	1	2	yes	complemented
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂²×C₁₃	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₂²	—	2	2	no	—
33	C₂²	—	4	1	no	—
34	C₂²	—	4	1	no	—
35	C₂²	D₄×C₁₃	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
38	C₄	D₄×C₁₃	1	1	yes	characteristic
39	C₂	—	4	2	no	—
40	C₂	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
41	C₂	C₁₃×D₈	1	1	yes	characteristic
42	C₂	C₁₃×SD₁₆	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×C₁₃	C₂	semidirect
3. C₁₃×C₄⋊C₄	C₂	semidirect
6. D₄×C₁₃	C₄	semidirect
17. #102	C₁₃	direct (N × H)
23. C₂×C₈	C₂×C₁₃	semidirect
24. C₄⋊C₄	C₂×C₁₃	semidirect
25. C₁₃	#102	direct (N × H)
28. 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
C₂×D₄×C₁₃	2
C₂×C₈×C₁₃	2
C₁₃×C₄⋊C₄	2
#102	13

Subgroups — C13×#102 #88085

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#102 #88085