Subgroups — C₂₉×#1829 #16815543

Order 3712.

272 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#518	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂₉×#100	C₂	1	2	yes	maximal
3	C₂₉×#344	C₂	1	4	yes	maximal, complemented
4	C₂²×D₄×C₂₉	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₂₉	C₂²	1	4	yes	—
6	C₄×D₄×C₂₉	—	2	4	no	—
7	C₂₉×#117	C₂²	1	2	yes	—
8	C₂×C₂²⋊C₄×C₂₉	C₄	1	4	yes	—
9	C₂₉×#100	—	2	4	no	—
10	C₂⁴×C₂₉	C₂×C₄	1	2	yes	—
11	C₂×D₄×C₂₉	—	2	4	no	—
12	C₂×D₄×C₂₉	D₄	1	4	yes	—
13	C₂²×C₄×C₂₉	—	2	4	no	—
14	C₂²×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	M₁₆×C₂₉	—	2	4	no	—
16	M₁₆×C₂₉	—	2	4	no	—
17	C₂×C₈×C₂₉	—	2	4	no	—
18	C₄⋊C₄×C₂₉	—	2	2	no	—
19	C₂²⋊C₄×C₂₉	—	2	4	no	—
20	C₂²⋊C₄×C₂₉	C₂×C₄	1	4	yes	—
21	C₄²×C₂₉	—	2	2	no	—
22	C₂³×C₂₉	—	2	4	no	—
23	C₂³×C₂₉	—	8	2	no	—
24	C₂³×C₂₉	C₂²⋊C₄	1	4	yes	—
25	C₂³×C₂₉	C₂²×C₄	1	1	yes	characteristic
26	D₄×C₂₉	—	2	8	no	—
27	C₂×C₄×C₂₉	—	2	4	no	—
28	C₂×C₄×C₂₉	—	8	4	no	—
29	C₂×C₄×C₂₉	C₂×D₄	1	2	yes	—
30	C₂×C₄×C₂₉	#41	1	4	yes	—
31	C₈×C₂₉	—	4	4	no	—
32	#1829	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
33	C₂²×C₂₉	—	2	4	no	—
34	C₂²×C₂₉	—	4	1	no	—
35	C₂²×C₂₉	—	4	4	no	—
36	C₂²×C₂₉	—	8	4	no	—
37	C₂²×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂²×C₂₉	#117	1	2	yes	—
39	C₄×C₂₉	—	4	4	no	—
40	C₄×C₂₉	#123	1	4	yes	—
41	#518	C₂×C₂₉	1	1	yes	characteristic
42	C₂×#100	C₂×C₂₉	1	2	yes	—
43	#344	C₂×C₂₉	1	4	yes	complemented
44	C₂×C₂₉	—	2	1	no	—
45	C₂×C₂₉	—	2	2	no	—
46	C₂×C₂₉	—	4	4	no	—
47	C₂×C₂₉	#381	1	1	yes	characteristic
48	C₂²×D₄	C₂²×C₂₉	1	1	yes	characteristic
49	C₂×M₁₆	C₂²×C₂₉	1	4	yes	—
50	C₄×D₄	—	2	4	no	—
51	#117	C₂²×C₂₉	1	2	yes	—
52	C₂×C₂²⋊C₄	C₄×C₂₉	1	4	yes	—
53	#100	—	2	4	no	—
54	C₂₉	#1829	1	1	yes	characteristic, direct product factor, Sylow
55	C₂⁴	C₂×C₄×C₂₉	1	2	yes	—
56	C₂×D₄	—	2	4	no	—
57	C₂×D₄	D₄×C₂₉	1	4	yes	—
58	C₂²×C₄	—	2	4	no	—
59	C₂²×C₄	C₂³×C₂₉	1	1	yes	characteristic
60	M₁₆	—	2	4	no	—
61	M₁₆	—	2	4	no	—
62	C₂×C₈	—	2	4	no	—
63	C₄⋊C₄	—	2	2	no	—
64	C₂²⋊C₄	—	2	4	no	—
65	C₂²⋊C₄	C₂×C₄×C₂₉	1	4	yes	—
66	C₄²	—	2	2	no	—
67	C₂³	—	2	4	no	—
68	C₂³	—	8	2	no	—
69	C₂³	C₂²⋊C₄×C₂₉	1	4	yes	—
70	C₂³	C₂²×C₄×C₂₉	1	1	yes	characteristic
71	D₄	—	2	8	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	8	4	no	—
74	C₂×C₄	C₂×D₄×C₂₉	1	2	yes	—
75	C₂×C₄	#41×C₂₉	1	4	yes	—
76	C₈	—	4	4	no	—
77	C₂²	—	2	4	no	—
78	C₂²	—	4	1	no	—
79	C₂²	—	4	4	no	—
80	C₂²	—	8	4	no	—
81	C₂²	C₂×C₂²⋊C₄×C₂₉	1	1	yes	characteristic
82	C₂²	C₂₉×#117	1	2	yes	—
83	C₄	—	4	4	no	—
84	C₄	C₂₉×#123	1	4	yes	—
85	C₂	—	2	1	no	—
86	C₂	—	2	2	no	—
87	C₂	—	4	4	no	—
88	C₂	C₂₉×#381	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₉	#381
commutator	C₂³	C₂²×C₄×C₂₉
Frattini, cosocle	C₂²×C₄	C₂³×C₂₉
prime radical	C₂²×D₄×C₂₉	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₉ ◁ C₂²×C₄×C₂₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂₉×#344	C₂	semidirect
32. #1829	C₂₉	direct (N × H)
43. #344	C₂×C₂₉	semidirect
54. C₂₉	#1829	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×#518	2
C₂×C₂₉×#100	2
C₂₉×#344	2
#1829	29

Subgroups — C29×#1829 #16815543

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#1829 #16815543