Subgroups — C₂₉×#8135 #20303035

Order 7424.

382 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#1744	C₂	1	3	yes	maximal
2	C₂₉×#1273	C₂	1	4	yes	maximal
3	C₂×C₄×C₈×C₂₉	C₂²	1	6	yes	—
4	C₄³×C₂₉	C₂²	1	1	yes	characteristic
5	C₂₉×#336	C₄	1	12	yes	—
6	C₂²×C₈×C₂₉	C₂×C₄	1	12	yes	—
7	C₂×C₄²×C₂₉	C₂×C₄	1	6	yes	—
8	C₂×C₄²×C₂₉	C₂³	1	1	yes	characteristic
9	C₄×C₈×C₂₉	—	2	12	no	—
10	C₂²×C₄×C₂₉	C₄²	1	4	yes	—
11	C₂²×C₄×C₂₉	C₂²×C₄	1	3	yes	—
12	C₂×C₈×C₂₉	—	2	12	no	—
13	C₂×C₈×C₂₉	—	2	24	no	—
14	C₄²×C₂₉	—	2	12	no	—
15	C₄²×C₂₉	#41	1	4	yes	—
16	#8135	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
17	C₂³×C₂₉	C₂×C₄²	1	1	yes	characteristic
18	C₂×C₄×C₂₉	—	2	12	no	—
19	C₂×C₄×C₂₉	#117	1	6	yes	—
20	C₂×C₄×C₂₉	#131	1	12	yes	—
21	C₈×C₂₉	—	4	12	no	—
22	#1744	C₂×C₂₉	1	3	yes	—
23	#1273	C₂×C₂₉	1	4	yes	—
24	C₂²×C₂₉	#376	1	1	yes	characteristic
25	C₂²×C₂₉	#405	1	6	yes	—
26	C₄×C₂₉	—	4	4	no	—
27	C₄×C₂₉	#433	1	12	yes	—
28	C₂×C₄×C₈	C₂²×C₂₉	1	6	yes	—
29	C₄³	C₂²×C₂₉	1	1	yes	characteristic
30	#336	C₄×C₂₉	1	12	yes	—
31	C₂×C₂₉	#1454	1	4	yes	—
32	C₂×C₂₉	#1746	1	3	yes	—
33	C₂²×C₈	C₂×C₄×C₂₉	1	12	yes	—
34	C₂×C₄²	C₂×C₄×C₂₉	1	6	yes	—
35	C₂×C₄²	C₂³×C₂₉	1	1	yes	characteristic
36	C₄×C₈	—	2	12	no	—
37	C₂₉	#8135	1	1	yes	characteristic, direct product factor, Sylow
38	C₂²×C₄	C₄²×C₂₉	1	4	yes	—
39	C₂²×C₄	C₂²×C₄×C₂₉	1	3	yes	—
40	C₂×C₈	—	2	12	no	—
41	C₂×C₈	—	2	24	no	—
42	C₄²	—	2	12	no	—
43	C₄²	#41×C₂₉	1	4	yes	—
44	C₂³	C₂×C₄²×C₂₉	1	1	yes	characteristic
45	C₂×C₄	—	2	12	no	—
46	C₂×C₄	C₂₉×#117	1	6	yes	—
47	C₂×C₄	C₂₉×#131	1	12	yes	—
48	C₈	—	4	12	no	—
49	C₂²	C₂₉×#376	1	1	yes	characteristic
50	C₂²	C₂₉×#405	1	6	yes	—
51	C₄	—	4	4	no	—
52	C₄	C₂₉×#433	1	12	yes	—
53	C₂	C₂₉×#1454	1	4	yes	—
54	C₂	C₂₉×#1746	1	3	yes	—

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

Complements

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

N	H ≅ G/N	type
16. #8135	C₂₉	direct (N × H)
37. C₂₉	#8135	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×#1744	2
C₂₉×#1273	2
#8135	29

Subgroups — C29×#8135 #20303035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#8135 #20303035