Subgroups — C₁₃×#135 #88229

Order 416.

62 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#41	C₂	1	2	yes	maximal, complemented
2	C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×SD₁₆	C₂	1	2	yes	maximal, complemented
4	C₁₃×D₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	Q₈×C₁₃	C₂²	1	2	yes	—
7	D₄×C₁₃	—	2	2	no	—
8	D₄×C₁₃	C₂²	1	2	yes	—
9	C₂×C₄×C₁₃	—	2	2	no	—
10	C₂×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃	—	2	2	no	—
14	C₂²×C₁₃	D₄	1	1	yes	characteristic
15	C₄×C₁₃	—	2	2	no	—
16	C₄×C₁₃	D₄	1	1	yes	characteristic
17	C₄×C₁₃	C₂³	1	1	yes	characteristic
18	#135	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂×C₁₃	—	2	1	no	—
20	C₂×C₁₃	—	4	2	no	—
21	C₂×C₁₃	C₂×D₄	1	1	yes	characteristic
22	#41	C₂×C₁₃	1	2	yes	complemented
23	Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
24	SD₁₆	C₂×C₁₃	1	2	yes	complemented
25	D₈	C₂×C₁₃	1	1	yes	characteristic, complemented
26	C₂×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
27	C₁₃	#135	1	1	yes	characteristic, direct product factor, Sylow
28	Q₈	C₂²×C₁₃	1	2	yes	—
29	D₄	—	2	2	no	—
30	D₄	C₂²×C₁₃	1	2	yes	—
31	C₂×C₄	—	2	2	no	—
32	C₂×C₄	C₂²×C₁₃	1	1	yes	characteristic
33	C₈	C₂²×C₁₃	1	1	yes	characteristic
34	C₈	C₂²×C₁₃	1	1	yes	characteristic
35	C₂²	—	2	2	no	—
36	C₂²	D₄×C₁₃	1	1	yes	characteristic
37	C₄	—	2	2	no	—
38	C₄	D₄×C₁₃	1	1	yes	characteristic
39	C₄	C₂³×C₁₃	1	1	yes	characteristic
40	C₂	—	2	1	no	—
41	C₂	—	4	2	no	—
42	C₂	C₂×D₄×C₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	D₄
commutator, Frattini, cosocle	C₄	C₂³×C₁₃
socle	C₂×C₁₃	C₂×D₄
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
1. C₁₃×#41	C₂	semidirect
2. C₁₃×Q₁₆	C₂	semidirect
3. C₁₃×SD₁₆	C₂	semidirect
4. C₁₃×D₈	C₂	semidirect
5. C₂×C₈×C₁₃	C₂	semidirect
18. #135	C₁₃	direct (N × H)
22. #41	C₂×C₁₃	semidirect
23. Q₁₆	C₂×C₁₃	semidirect
24. SD₁₆	C₂×C₁₃	semidirect
25. D₈	C₂×C₁₃	semidirect
26. C₂×C₈	C₂×C₁₃	semidirect
27. C₁₃	#135	direct (N × H)

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×Q₁₆	2
C₁₃×SD₁₆	2
C₁₃×D₈	2
C₂×C₈×C₁₃	2
#135	13

Subgroups — C13×#135 #88229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#135 #88229