Subgroups — C₂₉×#7540 #20302440

Order 7424.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#2262	C₂	1	1	yes	maximal, characteristic
2	C₂₉×M₁₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₉×#1424	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₉×#508	—	2	1	no	—
5	C₂₉×Q₆₄	C₄	1	1	yes	characteristic, complemented
6	C₂₉×SD₆₄	—	2	1	no	—
7	C₂₉×D₃₂	C₄	1	1	yes	characteristic, complemented
8	C₂×C₂₉×C₃₂	C₂²	1	1	yes	characteristic
9	C₂₉×#366	—	2	1	no	—
10	C₂₉×C₆₄	—	2	1	no	—
11	C₂₉×#135	—	4	1	no	—
12	C₂₉×Q₃₂	—	2	1	no	—
13	C₂₉×SD₃₂	—	4	1	no	—
14	C₂₉×D₁₆	—	2	1	no	—
15	C₂×C₁₆×C₂₉	D₄	1	1	yes	characteristic
16	C₂₉×#107	—	4	1	no	—
17	C₂₉×C₃₂	C₂×C₄	1	1	yes	characteristic
18	C₂₉×C₃₂	D₄	1	1	yes	characteristic
19	#41×C₂₉	—	8	1	no	—
20	Q₁₆×C₂₉	—	4	1	no	—
21	SD₁₆×C₂₉	—	8	1	no	—
22	D₈×C₂₉	—	4	1	no	—
23	C₂×C₈×C₂₉	D₈	1	1	yes	characteristic
24	C₄⋊C₄×C₂₉	—	8	1	no	—
25	C₁₆×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₁₆×C₂₉	SD₁₆	1	1	yes	characteristic
27	#7540	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
28	Q₈×C₂₉	—	8	1	no	—
29	D₄×C₂₉	—	8	1	no	—
30	D₄×C₂₉	—	16	1	no	—
31	C₂×C₄×C₂₉	—	16	1	no	—
32	C₂×C₄×C₂₉	—	16	1	no	—
33	C₂×C₄×C₂₉	D₁₆	1	1	yes	characteristic
34	C₈×C₂₉	#102	1	1	yes	characteristic
35	C₈×C₂₉	SD₃₂	1	1	yes	characteristic
36	#2262	C₂×C₂₉	1	1	yes	characteristic
37	M₁₂₈	C₂×C₂₉	1	1	yes	characteristic, complemented
38	#1424	C₂×C₂₉	1	1	yes	characteristic, complemented
39	C₂²×C₂₉	—	16	1	no	—
40	C₂²×C₂₉	D₃₂	1	1	yes	characteristic
41	C₄×C₂₉	—	16	1	no	—
42	C₄×C₂₉	—	32	1	no	—
43	C₄×C₂₉	#357	1	1	yes	characteristic
44	C₄×C₂₉	SD₆₄	1	1	yes	characteristic
45	#508	—	2	1	no	—
46	Q₆₄	C₄×C₂₉	1	1	yes	characteristic, complemented
47	SD₆₄	—	2	1	no	—
48	D₃₂	C₄×C₂₉	1	1	yes	characteristic, complemented
49	C₂×C₃₂	C₂²×C₂₉	1	1	yes	characteristic
50	#366	—	2	1	no	—
51	C₆₄	—	2	1	no	—
52	C₂×C₂₉	—	2	1	no	—
53	C₂×C₂₉	—	32	1	no	—
54	C₂×C₂₉	#1415	1	1	yes	characteristic
55	#135	—	4	1	no	—
56	Q₃₂	—	2	1	no	—
57	SD₃₂	—	4	1	no	—
58	D₁₆	—	2	1	no	—
59	C₂×C₁₆	D₄×C₂₉	1	1	yes	characteristic
60	#107	—	4	1	no	—
61	C₃₂	C₂×C₄×C₂₉	1	1	yes	characteristic
62	C₃₂	D₄×C₂₉	1	1	yes	characteristic
63	C₂₉	#7540	1	1	yes	characteristic, direct product factor, Sylow
64	#41	—	8	1	no	—
65	Q₁₆	—	4	1	no	—
66	SD₁₆	—	8	1	no	—
67	D₈	—	4	1	no	—
68	C₂×C₈	D₈×C₂₉	1	1	yes	characteristic
69	C₄⋊C₄	—	8	1	no	—
70	C₁₆	C₂²⋊C₄×C₂₉	1	1	yes	characteristic
71	C₁₆	SD₁₆×C₂₉	1	1	yes	characteristic
72	Q₈	—	8	1	no	—
73	D₄	—	8	1	no	—
74	D₄	—	16	1	no	—
75	C₂×C₄	—	16	1	no	—
76	C₂×C₄	—	16	1	no	—
77	C₂×C₄	C₂₉×D₁₆	1	1	yes	characteristic
78	C₈	C₂₉×#102	1	1	yes	characteristic
79	C₈	C₂₉×SD₃₂	1	1	yes	characteristic
80	C₂²	—	16	1	no	—
81	C₂²	C₂₉×D₃₂	1	1	yes	characteristic
82	C₄	—	16	1	no	—
83	C₄	—	32	1	no	—
84	C₄	C₂₉×#357	1	1	yes	characteristic
85	C₄	C₂₉×SD₆₄	1	1	yes	characteristic
86	C₂	—	2	1	no	—
87	C₂	—	32	1	no	—
88	C₂	C₂₉×#1415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₉	#1415
commutator	C₃₂	C₂×C₄×C₂₉
Frattini, cosocle	C₂×C₃₂	C₂²×C₂₉
prime radical	C₂₉×#2262	C₂
LCS	G ▷ C₃₂ ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂×C₄×C₂₉ ◁ C₂×C₈×C₂₉ ◁ C₂×C₁₆×C₂₉ ◁ C₂×C₂₉×C₃₂ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂₉×M₁₂₈	C₂	semidirect
3. C₂₉×#1424	C₂	semidirect
5. C₂₉×Q₆₄	C₄	semidirect
7. C₂₉×D₃₂	C₄	semidirect
27. #7540	C₂₉	direct (N × H)
37. M₁₂₈	C₂×C₂₉	semidirect
38. #1424	C₂×C₂₉	semidirect
46. Q₆₄	C₄×C₂₉	semidirect
48. D₃₂	C₄×C₂₉	semidirect
63. C₂₉	#7540	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×#2262	2
C₂₉×M₁₂₈	2
C₂₉×#1424	2
#7540	29

Subgroups — C29×#7540 #20302440

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#7540 #20302440