Subgroups — C₂₉×#501 #14270796

Order 1856.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#125	C₂	1	1	yes	maximal, characteristic
3	C₂₉×#107	C₂	1	2	yes	maximal
4	C₂₉×#106	C₂	1	2	yes	maximal
5	C₂₉×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₂₉	—	2	1	no	—
7	C₂×C₈×C₂₉	C₂²	1	2	yes	—
8	C₄⋊C₄×C₂₉	—	2	1	no	—
9	C₄⋊C₄×C₂₉	—	2	1	no	—
10	C₄⋊C₄×C₂₉	—	2	1	no	—
11	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
12	C₄⋊C₄×C₂₉	C₂²	1	1	yes	characteristic
13	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
14	C₄²×C₂₉	C₂²	1	1	yes	characteristic
15	Q₈×C₂₉	—	4	2	no	—
16	C₂×C₄×C₂₉	—	2	1	no	—
17	C₂×C₄×C₂₉	—	2	1	no	—
18	C₂×C₄×C₂₉	—	2	2	no	—
19	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
22	C₈×C₂₉	Q₈	1	4	yes	complemented
23	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
24	C₄×C₂₉	—	2	1	no	—
25	C₄×C₂₉	—	2	1	no	—
26	C₄×C₂₉	—	4	1	no	—
27	C₄×C₂₉	—	4	2	no	—
28	C₄×C₂₉	—	4	1	no	—
29	C₄×C₂₉	C₂×Q₈	1	2	yes	—
30	#501	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₂₉	C₄⋊Q₈	1	1	yes	characteristic
32	C₂×C₂₉	AGL(1,ℤ/8)	1	1	yes	characteristic
33	C₂×C₂₉	#137	1	1	yes	characteristic
34	C₄⋊Q₈	C₂×C₂₉	1	1	yes	characteristic
35	#125	C₂×C₂₉	1	1	yes	characteristic
36	#107	C₂×C₂₉	1	2	yes	—
37	#106	C₂×C₂₉	1	2	yes	—
38	#97	C₂×C₂₉	1	1	yes	characteristic
39	C₂₉	#501	1	1	yes	characteristic, direct product factor, Sylow
40	C₂×Q₈	—	2	1	no	—
41	C₂×C₈	C₂²×C₂₉	1	2	yes	—
42	C₄⋊C₄	—	2	1	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	2	1	no	—
45	C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
46	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
47	C₄⋊C₄	C₂²×C₂₉	1	1	yes	characteristic
48	C₄²	C₂²×C₂₉	1	1	yes	characteristic
49	Q₈	—	4	2	no	—
50	C₂×C₄	—	2	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	D₄×C₂₉	1	1	yes	characteristic
54	C₂×C₄	D₄×C₂₉	1	1	yes	characteristic
55	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
56	C₈	Q₈×C₂₉	1	4	yes	complemented
57	C₂²	C₂×D₄×C₂₉	1	1	yes	characteristic
58	C₄	—	2	1	no	—
59	C₄	—	2	1	no	—
60	C₄	—	4	2	no	—
61	C₄	—	4	1	no	—
62	C₄	—	4	1	no	—
63	C₄	C₂×Q₈×C₂₉	1	2	yes	—
64	C₂	C₂₉×C₄⋊Q₈	1	1	yes	characteristic
65	C₂	C₂₉×AGL(1,ℤ/8)	1	1	yes	characteristic
66	C₂	C₂₉×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₉	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₂₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ C₄²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
22. C₈×C₂₉	Q₈	semidirect
30. #501	C₂₉	direct (N × H)
39. C₂₉	#501	direct (N × H)
56. C₈	Q₈×C₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×C₄⋊Q₈	2
C₂₉×#125	2
C₂₉×#107	2
C₂₉×#106	2
C₂₉×#97	2
#501	29

Subgroups — C29×#501 #14270796

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#501 #14270796