Subgroups — C₂₉×#562 #14270857

Order 1856.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₉×#124	C₂	1	2	yes	maximal, complemented
3	C₂₉×#123	C₂	1	4	yes	maximal, complemented
4	C₂₉×C₂²⋊Q₈	C₂	1	4	yes	maximal, complemented
5	C₂₉×#121	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	4	yes	—
11	C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
12	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
13	C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
14	C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
15	C₂²⋊C₄×C₂₉	C₂²	1	4	yes	—
16	C₄²×C₂₉	C₂²	1	1	yes	characteristic
17	C₂³×C₂₉	C₂³	1	4	yes	—
18	Q₈×C₂₉	—	4	2	no	—
19	D₄×C₂₉	—	4	4	no	—
20	D₄×C₂₉	—	4	2	no	—
21	C₂×C₄×C₂₉	—	4	4	no	—
22	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
23	C₂×C₄×C₂₉	C₂³	1	2	yes	—
24	C₂×C₄×C₂₉	C₂³	1	4	yes	—
25	C₂×C₄×C₂₉	C₂³	1	4	yes	—
26	C₂²×C₂₉	—	2	4	no	—
27	C₂²×C₂₉	—	2	4	no	—
28	C₂²×C₂₉	—	2	4	no	—
29	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
30	C₄×C₂₉	—	2	4	no	—
31	C₄×C₂₉	—	2	4	no	—
32	C₄×C₂₉	—	2	2	no	—
33	C₄×C₂₉	—	2	1	no	—
34	#562	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₂₉	—	4	4	no	—
36	C₂×C₂₉	H(5,𝔽₂)	1	2	yes	—
37	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
38	#125	C₂×C₂₉	1	1	yes	characteristic, complemented
39	#124	C₂×C₂₉	1	2	yes	complemented
40	#123	C₂×C₂₉	1	4	yes	complemented
41	C₂²⋊Q₈	C₂×C₂₉	1	4	yes	complemented
42	#121	C₂×C₂₉	1	4	yes	complemented
43	C₂₉	#562	1	1	yes	characteristic, direct product factor, Sylow
44	C₂×Q₈	C₂²×C₂₉	1	2	yes	—
45	C₂×D₄	C₂²×C₂₉	1	4	yes	—
46	C₂×D₄	C₂²×C₂₉	1	2	yes	—
47	C₂²×C₄	C₂²×C₂₉	1	4	yes	—
48	C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
49	C₄⋊C₄	C₂²×C₂₉	1	4	yes	—
50	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
51	C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
52	C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
53	C₂²⋊C₄	C₂²×C₂₉	1	4	yes	—
54	C₄²	C₂²×C₂₉	1	1	yes	characteristic
55	C₂³	C₂³×C₂₉	1	4	yes	—
56	Q₈	—	4	2	no	—
57	D₄	—	4	4	no	—
58	D₄	—	4	2	no	—
59	C₂×C₄	—	4	4	no	—
60	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
61	C₂×C₄	C₂³×C₂₉	1	2	yes	—
62	C₂×C₄	C₂³×C₂₉	1	4	yes	—
63	C₂×C₄	C₂³×C₂₉	1	4	yes	—
64	C₂²	—	2	4	no	—
65	C₂²	—	2	4	no	—
66	C₂²	—	2	4	no	—
67	C₂²	C₂⁴×C₂₉	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	2	4	no	—
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₂	—	4	4	no	—
73	C₂	C₂₉×H(5,𝔽₂)	1	2	yes	—
74	C₂	C₂₉×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₉	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₂₉
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
1. C₂₉×#125	C₂	semidirect
2. C₂₉×#124	C₂	semidirect
3. C₂₉×#123	C₂	semidirect
4. C₂₉×C₂²⋊Q₈	C₂	semidirect
5. C₂₉×#121	C₂	semidirect
34. #562	C₂₉	direct (N × H)
38. #125	C₂×C₂₉	semidirect
39. #124	C₂×C₂₉	semidirect
40. #123	C₂×C₂₉	semidirect
41. C₂²⋊Q₈	C₂×C₂₉	semidirect
42. #121	C₂×C₂₉	semidirect
43. C₂₉	#562	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×#125	2
C₂₉×#124	2
C₂₉×#123	2
C₂₉×C₂²⋊Q₈	2
C₂₉×#121	2
#562	29

Subgroups — C29×#562 #14270857

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#562 #14270857