Subgroups — C₂₉×#2263 #16815977

Order 3712.

112 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₉×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×SD₆₄	C₂	1	2	yes	maximal, complemented
4	C₂₉×D₃₂	C₂	1	2	yes	maximal, complemented
5	C₂₉×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂₉×#135	—	2	1	no	—
7	C₂×D₈×C₂₉	—	2	1	no	—
8	C₂₉×Q₃₂	C₂²	1	1	yes	characteristic, complemented
9	C₂₉×SD₃₂	—	2	1	no	—
10	C₂₉×D₁₆	—	2	1	no	—
11	C₂₉×D₁₆	C₂²	1	2	yes	—
12	C₂₉×D₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₆×C₂₉	C₂²	1	1	yes	characteristic
14	C₂₉×C₃₂	C₂²	1	2	yes	complemented
15	#41×C₂₉	—	4	1	no	—
16	C₂×D₄×C₂₉	—	4	1	no	—
17	Q₁₆×C₂₉	—	2	1	no	—
18	SD₁₆×C₂₉	—	4	1	no	—
19	D₈×C₂₉	—	2	2	no	—
20	D₈×C₂₉	—	2	1	no	—
21	D₈×C₂₉	—	4	1	no	—
22	C₂×C₈×C₂₉	D₄	1	1	yes	characteristic
23	C₁₆×C₂₉	D₄	1	1	yes	characteristic
24	C₁₆×C₂₉	C₂³	1	1	yes	characteristic
25	C₂³×C₂₉	—	8	1	no	—
26	Q₈×C₂₉	—	4	1	no	—
27	D₄×C₂₉	—	4	2	no	—
28	D₄×C₂₉	—	4	1	no	—
29	D₄×C₂₉	—	8	1	no	—
30	D₄×C₂₉	—	8	1	no	—
31	C₂×C₄×C₂₉	—	8	1	no	—
32	C₂×C₄×C₂₉	D₈	1	1	yes	characteristic
33	C₈×C₂₉	D₈	1	1	yes	characteristic
34	C₈×C₂₉	C₂×D₄	1	1	yes	characteristic
35	#2263	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₂₉	—	8	1	no	—
37	C₂²×C₂₉	—	8	2	no	—
38	C₂²×C₂₉	—	16	2	no	—
39	C₂²×C₂₉	D₁₆	1	1	yes	characteristic
40	C₄×C₂₉	—	8	1	no	—
41	C₄×C₂₉	D₁₆	1	1	yes	characteristic
42	C₄×C₂₉	C₂×D₈	1	1	yes	characteristic
43	#508	C₂×C₂₉	1	1	yes	characteristic, complemented
44	C₂×D₁₆	C₂×C₂₉	1	1	yes	characteristic, complemented
45	SD₆₄	C₂×C₂₉	1	2	yes	complemented
46	D₃₂	C₂×C₂₉	1	2	yes	complemented
47	M₆₄	C₂×C₂₉	1	1	yes	characteristic, complemented
48	C₂×C₂₉	—	2	1	no	—
49	C₂×C₂₉	—	16	1	no	—
50	C₂×C₂₉	—	16	2	no	—
51	C₂×C₂₉	C₂×D₁₆	1	1	yes	characteristic
52	#135	—	2	1	no	—
53	C₂×D₈	—	2	1	no	—
54	Q₃₂	C₂²×C₂₉	1	1	yes	characteristic, complemented
55	SD₃₂	—	2	1	no	—
56	D₁₆	—	2	1	no	—
57	D₁₆	C₂²×C₂₉	1	2	yes	—
58	D₁₆	C₂²×C₂₉	1	1	yes	characteristic, complemented
59	C₂×C₁₆	C₂²×C₂₉	1	1	yes	characteristic
60	C₃₂	C₂²×C₂₉	1	2	yes	complemented
61	C₂₉	#2263	1	1	yes	characteristic, direct product factor, Sylow
62	#41	—	4	1	no	—
63	C₂×D₄	—	4	1	no	—
64	Q₁₆	—	2	1	no	—
65	SD₁₆	—	4	1	no	—
66	D₈	—	2	2	no	—
67	D₈	—	2	1	no	—
68	D₈	—	4	1	no	—
69	C₂×C₈	D₄×C₂₉	1	1	yes	characteristic
70	C₁₆	D₄×C₂₉	1	1	yes	characteristic
71	C₁₆	C₂³×C₂₉	1	1	yes	characteristic
72	C₂³	—	8	1	no	—
73	Q₈	—	4	1	no	—
74	D₄	—	4	2	no	—
75	D₄	—	4	1	no	—
76	D₄	—	8	1	no	—
77	D₄	—	8	1	no	—
78	C₂×C₄	—	8	1	no	—
79	C₂×C₄	D₈×C₂₉	1	1	yes	characteristic
80	C₈	D₈×C₂₉	1	1	yes	characteristic
81	C₈	C₂×D₄×C₂₉	1	1	yes	characteristic
82	C₂²	—	8	1	no	—
83	C₂²	—	8	2	no	—
84	C₂²	—	16	2	no	—
85	C₂²	C₂₉×D₁₆	1	1	yes	characteristic
86	C₄	—	8	1	no	—
87	C₄	C₂₉×D₁₆	1	1	yes	characteristic
88	C₄	C₂×D₈×C₂₉	1	1	yes	characteristic
89	C₂	—	2	1	no	—
90	C₂	—	16	2	no	—
91	C₂	—	16	1	no	—
92	C₂	C₂×C₂₉×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₉	C₂×D₁₆
commutator, Frattini, cosocle	C₁₆	C₂³×C₂₉
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂×C₈×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₉×#508	C₂	semidirect
2. C₂×C₂₉×D₁₆	C₂	semidirect
3. C₂₉×SD₆₄	C₂	semidirect
4. C₂₉×D₃₂	C₂	semidirect
5. C₂₉×M₆₄	C₂	semidirect
8. C₂₉×Q₃₂	C₂²	semidirect
12. C₂₉×D₁₆	C₂²	semidirect
14. C₂₉×C₃₂	C₂²	semidirect
35. #2263	C₂₉	direct (N × H)
43. #508	C₂×C₂₉	semidirect
44. C₂×D₁₆	C₂×C₂₉	semidirect
45. SD₆₄	C₂×C₂₉	semidirect
46. D₃₂	C₂×C₂₉	semidirect
47. M₆₄	C₂×C₂₉	semidirect
54. Q₃₂	C₂²×C₂₉	semidirect
58. D₁₆	C₂²×C₂₉	semidirect
60. C₃₂	C₂²×C₂₉	semidirect
61. C₂₉	#2263	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×#508	2
C₂×C₂₉×D₁₆	2
C₂₉×SD₆₄	2
C₂₉×D₃₂	2
C₂₉×M₆₄	2
#2263	29

Subgroups — C29×#2263 #16815977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#2263 #16815977