Subgroups — C₂₉×#1381 #16815095

Order 3712.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#108	C₂	1	2	yes	maximal
3	C₂×M₁₆×C₂₉	—	2	2	no	—
4	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₂₉	—	2	2	no	—
6	C₂×C₁₆×C₂₉	C₄	1	2	yes	—
7	C₂₉×#108	—	2	2	no	—
8	C₂₉×#108	C₄	1	4	yes	—
9	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
10	M₁₆×C₂₉	—	2	4	no	—
11	M₁₆×C₂₉	—	4	2	no	—
12	C₂×C₈×C₂₉	—	4	2	no	—
13	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₂₉	D₄	1	2	yes	—
16	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
17	C₁₆×C₂₉	—	2	2	no	—
18	C₂³×C₂₉	Q₁₆	1	1	yes	characteristic
19	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
20	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
22	C₂×C₄×C₂₉	SD₁₆	1	2	yes	—
23	C₈×C₂₉	—	4	4	no	—
24	C₈×C₂₉	C₄²	1	1	yes	characteristic
25	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
27	#1381	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	C₂²×C₂₉	—	2	2	no	—
29	C₂²×C₂₉	#103	1	2	yes	—
30	C₂²×C₂₉	#107	1	1	yes	characteristic
31	C₄×C₂₉	#95	1	1	yes	characteristic
32	C₄×C₂₉	#102	1	2	yes	—
33	C₄×C₂₉	#106	1	1	yes	characteristic
34	C₂²×C₁₆	C₂×C₂₉	1	1	yes	characteristic
35	C₂×#108	C₂×C₂₉	1	2	yes	—
36	C₂×C₂₉	—	2	2	no	—
37	C₂×C₂₉	#340	1	1	yes	characteristic
38	C₂×C₂₉	#368	1	2	yes	—
39	C₂×M₁₆	—	2	2	no	—
40	C₂²×C₈	C₂²×C₂₉	1	1	yes	characteristic
41	C₂×C₁₆	—	2	2	no	—
42	C₂×C₁₆	C₄×C₂₉	1	2	yes	—
43	#108	—	2	2	no	—
44	#108	C₄×C₂₉	1	4	yes	—
45	C₂₉	#1381	1	1	yes	characteristic, direct product factor, Sylow
46	C₂²×C₄	D₄×C₂₉	1	1	yes	characteristic
47	M₁₆	—	2	4	no	—
48	M₁₆	—	4	2	no	—
49	C₂×C₈	—	4	2	no	—
50	C₂×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
51	C₂×C₈	C₂×C₄×C₂₉	1	2	yes	—
52	C₂×C₈	D₄×C₂₉	1	2	yes	—
53	C₂×C₈	Q₈×C₂₉	1	1	yes	characteristic
54	C₁₆	—	2	2	no	—
55	C₂³	Q₁₆×C₂₉	1	1	yes	characteristic
56	C₂×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
57	C₂×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
58	C₂×C₄	D₈×C₂₉	1	1	yes	characteristic
59	C₂×C₄	SD₁₆×C₂₉	1	2	yes	—
60	C₈	—	4	4	no	—
61	C₈	C₄²×C₂₉	1	1	yes	characteristic
62	C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
63	C₈	C₄⋊C₄×C₂₉	1	2	yes	—
64	C₂²	—	2	2	no	—
65	C₂²	C₂₉×#103	1	2	yes	—
66	C₂²	C₂₉×#107	1	1	yes	characteristic
67	C₄	C₂₉×#95	1	1	yes	characteristic
68	C₄	C₂₉×#102	1	2	yes	—
69	C₄	C₂₉×#106	1	1	yes	characteristic
70	C₂	—	2	2	no	—
71	C₂	C₂₉×#340	1	1	yes	characteristic
72	C₂	C₂₉×#368	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₉	D₈
commutator	C₈	C₄²×C₂₉
Frattini, cosocle	C₂²×C₈	C₂²×C₂₉
socle	C₂²×C₂₉	#107
prime radical	C₂³×C₂₉	Q₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ C₂²×C₈×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
27. #1381	C₂₉	direct (N × H)
45. C₂₉	#1381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₆×C₂₉	2
C₂×C₂₉×#108	2
#1381	29

Subgroups — C29×#1381 #16815095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1381 #16815095