Subgroups — C₂₉×#559 #14270854

Order 1856.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#127	C₂	1	1	yes	maximal, characteristic
2	C₂₉×#124	C₂	1	4	yes	maximal, complemented
3	C₂₉×#123	C₂	1	4	yes	maximal, complemented
4	C₄×Q₈×C₂₉	C₂	1	2	yes	maximal, complemented
5	C₄×D₄×C₂₉	C₂	1	4	yes	maximal, complemented
6	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
7	C₂×D₄×C₂₉	C₂²	1	4	yes	—
8	C₂×D₄×C₂₉	C₂²	1	2	yes	—
9	C₂²×C₄×C₂₉	C₂²	1	4	yes	—
10	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
11	C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
12	C₂²⋊C₄×C₂₉	C₂²	1	8	yes	—
13	C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
14	C₄²×C₂₉	C₂²	1	4	yes	—
15	C₄²×C₂₉	C₂²	1	1	yes	characteristic
16	C₂³×C₂₉	C₂³	1	4	yes	—
17	Q₈×C₂₉	—	2	4	no	—
18	D₄×C₂₉	—	2	8	no	—
19	D₄×C₂₉	—	4	2	no	—
20	C₂×C₄×C₂₉	—	4	4	no	—
21	C₂×C₄×C₂₉	C₂³	1	4	yes	—
22	C₂×C₄×C₂₉	C₂³	1	4	yes	—
23	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₂³	1	2	yes	—
25	C₂²×C₂₉	—	2	8	no	—
26	C₂²×C₂₉	—	2	4	no	—
27	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
28	C₄×C₂₉	—	2	4	no	—
29	C₄×C₂₉	—	2	4	no	—
30	C₄×C₂₉	—	2	1	no	—
31	C₄×C₂₉	#41	1	4	yes	—
32	#559	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂×C₂₉	—	4	4	no	—
34	C₂×C₂₉	C₂×#41	1	2	yes	—
35	C₂×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
36	#127	C₂×C₂₉	1	1	yes	characteristic
37	#124	C₂×C₂₉	1	4	yes	complemented
38	#123	C₂×C₂₉	1	4	yes	complemented
39	C₄×Q₈	C₂×C₂₉	1	2	yes	complemented
40	C₄×D₄	C₂×C₂₉	1	4	yes	complemented
41	C₂₉	#559	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×Q₈	C₂²×C₂₉	1	2	yes	—
43	C₂×D₄	C₂²×C₂₉	1	4	yes	—
44	C₂×D₄	C₂²×C₂₉	1	2	yes	—
45	C₂²×C₄	C₂²×C₂₉	1	4	yes	—
46	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
47	C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
48	C₂²⋊C₄	C₂²×C₂₉	1	8	yes	—
49	C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
50	C₄²	C₂²×C₂₉	1	4	yes	—
51	C₄²	C₂²×C₂₉	1	1	yes	characteristic
52	C₂³	C₂³×C₂₉	1	4	yes	—
53	Q₈	—	2	4	no	—
54	D₄	—	2	8	no	—
55	D₄	—	4	2	no	—
56	C₂×C₄	—	4	4	no	—
57	C₂×C₄	C₂³×C₂₉	1	4	yes	—
58	C₂×C₄	C₂³×C₂₉	1	4	yes	—
59	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
60	C₂×C₄	C₂³×C₂₉	1	2	yes	—
61	C₂²	—	2	8	no	—
62	C₂²	—	2	4	no	—
63	C₂²	C₂⁴×C₂₉	1	1	yes	characteristic
64	C₄	—	2	4	no	—
65	C₄	—	2	4	no	—
66	C₄	—	2	1	no	—
67	C₄	#41×C₂₉	1	4	yes	—
68	C₂	—	4	4	no	—
69	C₂	C₂×#41×C₂₉	1	2	yes	—
70	C₂	C₂₉×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₂₉
prime radical	C₂₉×#127	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×#124	C₂	semidirect
3. C₂₉×#123	C₂	semidirect
4. C₄×Q₈×C₂₉	C₂	semidirect
5. C₄×D₄×C₂₉	C₂	semidirect
32. #559	C₂₉	direct (N × H)
37. #124	C₂×C₂₉	semidirect
38. #123	C₂×C₂₉	semidirect
39. C₄×Q₈	C₂×C₂₉	semidirect
40. C₄×D₄	C₂×C₂₉	semidirect
41. C₂₉	#559	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₉×#127	2
C₂₉×#124	2
C₂₉×#123	2
C₄×Q₈×C₂₉	2
C₄×D₄×C₂₉	2
#559	29

Subgroups — C29×#559 #14270854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#559 #14270854