Subgroups — C₂₉×#1380 #16815094

Order 3712.

152 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×#107	C₂	1	2	yes	maximal
3	C₂²×C₈×C₂₉	C₂²	1	1	yes	characteristic
4	C₂×C₄⋊C₄×C₂₉	—	2	2	no	—
5	C₂×C₁₆×C₂₉	—	2	2	no	—
6	C₂×C₁₆×C₂₉	C₄	1	2	yes	complemented
7	C₂₉×#107	—	2	2	no	—
8	C₂₉×#107	C₄	1	4	yes	complemented
9	C₂²×C₄×C₂₉	—	4	2	no	—
10	C₂²×C₄×C₂₉	D₄	1	1	yes	characteristic
11	C₂×C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₉	C₂×C₄	1	2	yes	—
13	C₂×C₈×C₂₉	D₄	1	2	yes	—
14	C₂×C₈×C₂₉	Q₈	1	1	yes	characteristic
15	C₄⋊C₄×C₂₉	—	2	4	no	—
16	C₄⋊C₄×C₂₉	—	4	2	no	—
17	C₁₆×C₂₉	—	2	2	no	—
18	C₂³×C₂₉	D₈	1	1	yes	characteristic
19	C₂×C₄×C₂₉	—	4	4	no	—
20	C₂×C₄×C₂₉	—	8	2	no	—
21	C₂×C₄×C₂₉	—	8	2	no	—
22	C₂×C₄×C₂₉	C₂²⋊C₄	1	2	yes	—
23	C₂×C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
24	C₂×C₄×C₂₉	SD₁₆	1	2	yes	—
25	C₂×C₄×C₂₉	Q₁₆	1	1	yes	characteristic
26	C₈×C₂₉	C₄²	1	1	yes	characteristic
27	C₈×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₈×C₂₉	C₄⋊C₄	1	2	yes	—
29	#1380	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂²×C₂₉	#102	1	2	yes	—
31	C₂²×C₂₉	#107	1	1	yes	characteristic
32	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
33	C₂²×C₂₉	SD₃₂	1	2	yes	—
34	C₂²×C₂₉	Q₃₂	1	1	yes	characteristic
35	C₄×C₂₉	—	8	4	no	—
36	C₄×C₂₉	#95	1	1	yes	characteristic
37	C₄×C₂₉	#103	1	2	yes	—
38	C₄×C₂₉	#106	1	1	yes	characteristic
39	C₂²×C₁₆	C₂×C₂₉	1	1	yes	characteristic
40	C₂×#107	C₂×C₂₉	1	2	yes	—
41	C₂×C₂₉	#340	1	1	yes	characteristic
42	C₂×C₂₉	#357	1	2	yes	—
43	C₂×C₂₉	#358	1	2	yes	—
44	C₂×C₂₉	#366	1	1	yes	characteristic
45	C₂×C₂₉	#367	1	1	yes	characteristic
46	C₂²×C₈	C₂²×C₂₉	1	1	yes	characteristic
47	C₂×C₄⋊C₄	—	2	2	no	—
48	C₂×C₁₆	—	2	2	no	—
49	C₂×C₁₆	C₄×C₂₉	1	2	yes	complemented
50	#107	—	2	2	no	—
51	#107	C₄×C₂₉	1	4	yes	complemented
52	C₂₉	#1380	1	1	yes	characteristic, direct product factor, Sylow
53	C₂²×C₄	—	4	2	no	—
54	C₂²×C₄	D₄×C₂₉	1	1	yes	characteristic
55	C₂×C₈	C₂×C₄×C₂₉	1	1	yes	characteristic
56	C₂×C₈	C₂×C₄×C₂₉	1	2	yes	—
57	C₂×C₈	D₄×C₂₉	1	2	yes	—
58	C₂×C₈	Q₈×C₂₉	1	1	yes	characteristic
59	C₄⋊C₄	—	2	4	no	—
60	C₄⋊C₄	—	4	2	no	—
61	C₁₆	—	2	2	no	—
62	C₂³	D₈×C₂₉	1	1	yes	characteristic
63	C₂×C₄	—	4	4	no	—
64	C₂×C₄	—	8	2	no	—
65	C₂×C₄	—	8	2	no	—
66	C₂×C₄	C₂²⋊C₄×C₂₉	1	2	yes	—
67	C₂×C₄	C₄⋊C₄×C₂₉	1	1	yes	characteristic
68	C₂×C₄	SD₁₆×C₂₉	1	2	yes	—
69	C₂×C₄	Q₁₆×C₂₉	1	1	yes	characteristic
70	C₈	C₄²×C₂₉	1	1	yes	characteristic
71	C₈	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
72	C₈	C₄⋊C₄×C₂₉	1	2	yes	—
73	C₂²	C₂₉×#102	1	2	yes	—
74	C₂²	C₂₉×#107	1	1	yes	characteristic
75	C₂²	C₂₉×D₁₆	1	1	yes	characteristic
76	C₂²	C₂₉×SD₃₂	1	2	yes	—
77	C₂²	C₂₉×Q₃₂	1	1	yes	characteristic
78	C₄	—	8	4	no	—
79	C₄	C₂₉×#95	1	1	yes	characteristic
80	C₄	C₂₉×#103	1	2	yes	—
81	C₄	C₂₉×#106	1	1	yes	characteristic
82	C₂	C₂₉×#340	1	1	yes	characteristic
83	C₂	C₂₉×#357	1	2	yes	—
84	C₂	C₂₉×#358	1	2	yes	—
85	C₂	C₂₉×#366	1	1	yes	characteristic
86	C₂	C₂₉×#367	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₂×C₁₆×C₂₉	C₄	semidirect
8. C₂₉×#107	C₄	semidirect
29. #1380	C₂₉	direct (N × H)
49. C₂×C₁₆	C₄×C₂₉	semidirect
51. #107	C₄×C₂₉	semidirect
52. C₂₉	#1380	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×#107	2
#1380	29

Subgroups — C29×#1380 #16815094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1380 #16815094