Subgroups — C₂²×C₁₃×Dic₇ #13089900

Order 1456.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₇×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×Dic₇	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₇×C₁₃	C₄	1	4	yes	complemented
4	C₂²×C₇×C₁₃	C₂²	1	3	yes	—
5	C₁₃×Dic₇	C₂²	1	4	yes	direct product factor
6	C₂²×C₄×C₁₃	—	7	1	no	maximal, Hall
7	C₂×C₇×C₁₃	C₂×C₄	1	6	yes	complemented
8	C₂×C₇×C₁₃	C₂³	1	1	yes	characteristic
9	C₂²×Dic₇	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₁₃	D₇	1	1	yes	characteristic
11	C₂×C₄×C₁₃	—	7	6	no	—
12	C₇×C₁₃	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
13	C₂³×C₇	C₂×C₁₃	1	1	yes	characteristic
14	C₂×Dic₇	C₂×C₁₃	1	6	yes	direct product factor
15	C₂²×C₁₃	Dic₇	1	4	yes	direct product factor
16	C₂²×C₁₃	C₂×D₇	1	3	yes	—
17	C₄×C₁₃	—	7	4	no	—
18	C₂²×C₇	C₄×C₁₃	1	4	yes	complemented
19	C₂²×C₇	C₂²×C₁₃	1	3	yes	—
20	Dic₇	C₂²×C₁₃	1	4	yes	direct product factor
21	C₂×C₁₃	C₂×Dic₇	1	6	yes	direct product factor
22	C₂×C₁₃	C₂²×D₇	1	1	yes	characteristic
23	C₂²×C₄	—	7	1	no	Sylow
24	C₂×C₇	C₂×C₄×C₁₃	1	6	yes	complemented
25	C₂×C₇	C₂³×C₁₃	1	1	yes	characteristic
26	C₁₃	C₂²×Dic₇	1	1	yes	characteristic, direct product factor, Sylow
27	C₂³	C₁₃×D₇	1	1	yes	characteristic
28	C₂×C₄	—	7	6	no	—
29	C₇	C₂²×C₄×C₁₃	1	1	yes	characteristic, complemented, Sylow
30	C₂²	C₁₃×Dic₇	1	4	yes	direct product factor
31	C₂²	C₂×C₁₃×D₇	1	3	yes	—
32	C₄	—	7	4	no	—
33	C₂	C₂×C₁₃×Dic₇	1	6	yes	direct product factor
34	C₂	C₂²×C₁₃×D₇	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₁₃	D₇
commutator, hypocenter	C₇	C₂²×C₄×C₁₃
Frattini	C₂	C₂²×C₁₃×D₇
Fitting, socle, prime radical	C₂³×C₇×C₁₃	C₂
cosocle	C₂×C₇	C₂³×C₁₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₂³×C₁₃

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×Dic₇	C₂	direct (N × H)
3. C₂²×C₇×C₁₃	C₄	semidirect
5. C₁₃×Dic₇	C₂²	direct (N × H)
7. C₂×C₇×C₁₃	C₂×C₄	semidirect
9. C₂²×Dic₇	C₁₃	direct (N × H)
12. C₇×C₁₃	C₂²×C₄	semidirect
14. C₂×Dic₇	C₂×C₁₃	direct (N × H)
15. C₂²×C₁₃	Dic₇	direct (N × H)
18. C₂²×C₇	C₄×C₁₃	semidirect
20. Dic₇	C₂²×C₁₃	direct (N × H)
21. C₂×C₁₃	C₂×Dic₇	direct (N × H)
24. C₂×C₇	C₂×C₄×C₁₃	semidirect
26. C₁₃	C₂²×Dic₇	direct (N × H)
29. C₇	C₂²×C₄×C₁₃	semidirect
30. C₂²	C₁₃×Dic₇	direct (N × H)
33. C₂	C₂×C₁₃×Dic₇	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₇×C₁₃	2
C₂×C₁₃×Dic₇	2
C₂²×C₄×C₁₃	7
C₂²×Dic₇	13

Subgroups — C22×C13×Dic7 #13089900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₁₃×Dic₇ #13089900