Subgroups — C₂₉×#491 #14270786

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×#103	C₂	1	4	yes	maximal
4	C₂₉×#97	C₂	1	1	yes	maximal, characteristic
5	C₂×Q₈×C₂₉	C₂²	1	2	yes	—
6	C₂×C₈×C₂₉	C₂²	1	2	yes	—
7	C₄⋊C₄×C₂₉	—	2	2	no	—
8	C₄⋊C₄×C₂₉	—	2	2	no	—
9	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	Q₈×C₂₉	—	2	4	no	—
12	C₂×C₄×C₂₉	—	2	2	no	—
13	C₂×C₄×C₂₉	—	2	2	no	—
14	C₂×C₄×C₂₉	D₄	1	2	yes	—
15	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
16	C₈×C₂₉	—	2	2	no	—
17	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
18	C₄×C₂₉	—	2	2	no	—
19	C₄×C₂₉	—	4	2	no	—
20	C₄×C₂₉	—	4	2	no	—
21	C₄×C₂₉	#41	1	2	yes	—
22	#491	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂×C₂₉	#124	1	1	yes	characteristic
24	C₂×C₂₉	#137	1	2	yes	—
25	C₄⋊Q₈	C₂×C₂₉	1	1	yes	characteristic
26	#125	C₂×C₂₉	1	1	yes	characteristic
27	#103	C₂×C₂₉	1	4	yes	—
28	#97	C₂×C₂₉	1	1	yes	characteristic
29	C₂₉	#491	1	1	yes	characteristic, direct product factor, Sylow
30	C₂×Q₈	C₂²×C₂₉	1	2	yes	—
31	C₂×C₈	C₂²×C₂₉	1	2	yes	—
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	2	2	no	—
34	C₄⋊C₄	C₂²×C₂₉	1	2	yes	—
35	C₄²	C₂²×C₂₉	1	1	yes	characteristic
36	Q₈	—	2	4	no	—
37	C₂×C₄	—	2	2	no	—
38	C₂×C₄	—	2	2	no	—
39	C₂×C₄	D₄×C₂₉	1	2	yes	—
40	C₂×C₄	C₂³×C₂₉	1	1	yes	characteristic
41	C₈	—	2	2	no	—
42	C₂²	C₂×D₄×C₂₉	1	1	yes	characteristic
43	C₄	—	2	2	no	—
44	C₄	—	4	2	no	—
45	C₄	—	4	2	no	—
46	C₄	#41×C₂₉	1	2	yes	—
47	C₂	C₂₉×#124	1	1	yes	characteristic
48	C₂	C₂₉×#137	1	2	yes	—

	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. #491	C₂₉	direct (N × H)
29. C₂₉	#491	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×C₄⋊Q₈	2
C₂₉×#125	2
C₂₉×#103	2
C₂₉×#97	2
#491	29

Subgroups — C29×#491 #14270786

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#491 #14270786