Subgroups — C₂²×A₄×C₂₉ #13063682

Order 1392.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×A₄×C₂₉	C₂	1	3	yes	maximal, direct product factor
2	C₂⁴×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂²×C₃×C₂₉	—	4	1	no	maximal
4	A₄×C₂₉	C₂²	1	1	yes	characteristic, direct product factor
5	C₂³×C₂₉	—	3	3	no	—
6	C₂³×C₂₉	—	3	1	no	—
7	C₂³×C₂₉	C₂×C₃	1	3	yes	complemented
8	C₂×C₃×C₂₉	—	4	3	no	—
9	C₂²×C₂₉	—	3	3	no	—
10	C₂²×C₂₉	—	3	2	no	—
11	C₂²×C₂₉	—	3	3	no	—
12	C₂²×C₂₉	—	3	3	no	—
13	C₂²×C₂₉	A₄	1	1	yes	characteristic, direct product factor
14	C₂²×C₂₉	C₂²×C₃	1	1	yes	characteristic, complemented
15	C₃×C₂₉	—	4	1	no	Hall
16	C₂×C₂₉	—	3	3	no	—
17	C₂×C₂₉	—	3	1	no	—
18	C₂×C₂₉	C₂×A₄	1	3	yes	direct product factor
19	C₂²×A₄	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂₉	C₂²×A₄	1	1	yes	characteristic, direct product factor, Sylow
21	C₂×A₄	C₂×C₂₉	1	3	yes	direct product factor
22	C₂⁴	C₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
23	C₂²×C₃	—	4	1	no	—
24	A₄	C₂²×C₂₉	1	1	yes	characteristic, direct product factor
25	C₂³	—	3	3	no	—
26	C₂³	—	3	1	no	—
27	C₂³	C₂×C₃×C₂₉	1	3	yes	complemented
28	C₂×C₃	—	4	3	no	—
29	C₂²	—	3	3	no	—
30	C₂²	—	3	2	no	—
31	C₂²	—	3	3	no	—
32	C₂²	—	3	3	no	—
33	C₂²	A₄×C₂₉	1	1	yes	characteristic, direct product factor
34	C₂²	C₂²×C₃×C₂₉	1	1	yes	characteristic, complemented
35	C₃	—	4	1	no	Sylow
36	C₂	—	3	1	no	—
37	C₂	—	3	3	no	—
38	C₂	C₂×A₄×C₂₉	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₂₉	A₄
commutator, cosocle, hypocenter	C₂²	C₂²×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂⁴×C₂₉	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₂²×C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂×A₄×C₂₉	C₂	direct (N × H)
2. C₂⁴×C₂₉	C₃	semidirect
4. A₄×C₂₉	C₂²	direct (N × H)
7. C₂³×C₂₉	C₂×C₃	semidirect
13. C₂²×C₂₉	A₄	direct (N × H)
14. C₂²×C₂₉	C₂²×C₃	semidirect
18. C₂×C₂₉	C₂×A₄	direct (N × H)
19. C₂²×A₄	C₂₉	direct (N × H)
20. C₂₉	C₂²×A₄	direct (N × H)
21. C₂×A₄	C₂×C₂₉	direct (N × H)
22. C₂⁴	C₃×C₂₉	semidirect
24. A₄	C₂²×C₂₉	direct (N × H)
27. C₂³	C₂×C₃×C₂₉	semidirect
33. C₂²	A₄×C₂₉	direct (N × H)
34. C₂²	C₂²×C₃×C₂₉	semidirect
38. C₂	C₂×A₄×C₂₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×A₄×C₂₉	2
C₂⁴×C₂₉	3
C₂²×C₃×C₂₉	4
C₂²×A₄	29

Subgroups — C22×A4×C29 #13063682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×A₄×C₂₉ #13063682