Subgroups — C₂×C₂₉⋊#401 #16822788

Order 3712.

516 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉⋊#401	C₂	1	8	yes	maximal, direct product factor
2	C₂×#11745179	C₂	1	3	yes	maximal
3	C₂×#11745179	C₂	1	3	yes	maximal
4	C₂×C₂₉×#95	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄×C₂₉	C₂²	1	3	yes	—
6	C₂³×Dic₂₉	C₂²	1	1	yes	characteristic
7	C₂³×Dic₂₉	C₂²	1	3	yes	—
8	C₂₉×#95	C₂²	1	4	yes	—
9	#11745179	C₂²	1	12	yes	—
10	#11745179	C₂²	1	12	yes	—
11	C₂⁴×C₂₉	C₂³	1	1	yes	characteristic
12	C₂²×C₄×C₂₉	—	2	6	no	—
13	C₂²×C₄×C₂₉	—	2	12	no	—
14	C₂²×C₄×C₂₉	C₂³	1	6	yes	—
15	C₂²×Dic₂₉	—	2	6	no	—
16	C₂²×Dic₂₉	—	2	6	no	—
17	C₂²×Dic₂₉	—	2	6	no	—
18	C₂²×Dic₂₉	—	2	6	no	—
19	C₂²×Dic₂₉	C₂³	1	2	yes	—
20	C₂²×Dic₂₉	C₂³	1	6	yes	—
21	C₂³×C₂₉	#41	1	6	yes	—
22	C₂³×C₂₉	#41	1	6	yes	—
23	C₂³×C₂₉	#41	1	2	yes	—
24	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
25	C₂×C₄×C₂₉	—	2	6	no	—
26	C₂×C₄×C₂₉	—	2	12	no	—
27	C₂×C₄×C₂₉	—	4	12	no	—
28	C₂×Dic₂₉	—	2	6	no	—
29	C₂×Dic₂₉	—	2	6	no	—
30	C₂×Dic₂₉	—	2	6	no	—
31	C₂×Dic₂₉	—	2	6	no	—
32	C₂×Dic₂₉	—	4	4	no	—
33	C₂×Dic₂₉	—	4	12	no	—
34	C₂×#401	—	29	1	no	maximal, Sylow
35	C₂²×C₂₉	#126	1	4	yes	—
36	C₂²×C₂₉	#126	1	12	yes	—
37	C₂²×C₂₉	#126	1	12	yes	—
38	C₂²×C₂₉	C₂×#41	1	3	yes	—
39	C₂²×C₂₉	C₂×#41	1	3	yes	—
40	C₂²×C₂₉	C₂×#41	1	1	yes	characteristic
41	C₄×C₂₉	—	4	6	no	—
42	Dic₂₉	—	4	2	no	—
43	Dic₂₉	—	4	6	no	—
44	#401	—	29	8	no	—
45	C₂×#95	—	29	3	no	—
46	C₂×#95	—	29	3	no	—
47	C₂×#95	D₂₉	1	1	yes	characteristic
48	C₂×C₂₉	#401	1	8	yes	complemented
49	C₂×C₂₉	C₂×#126	1	3	yes	—
50	C₂×C₂₉	C₂×#126	1	1	yes	characteristic
51	C₂×C₂₉	C₂×#126	1	3	yes	—
52	C₂³×C₄	—	29	1	no	—
53	C₂³×C₄	—	29	3	no	—
54	C₂³×C₄	C₂×D₂₉	1	3	yes	—
55	#95	—	29	12	no	—
56	#95	—	29	12	no	—
57	#95	C₂×D₂₉	1	4	yes	—
58	C₂₉	C₂×#401	1	1	yes	characteristic, complemented, Sylow
59	C₂⁴	C₂²×D₂₉	1	1	yes	characteristic
60	C₂²×C₄	—	2	6	no	—
61	C₂²×C₄	—	2	12	no	—
62	C₂²×C₄	—	29	2	no	—
63	C₂²×C₄	—	29	6	no	—
64	C₂²×C₄	—	58	6	no	—
65	C₂²×C₄	—	58	6	no	—
66	C₂²×C₄	—	58	6	no	—
67	C₂²×C₄	—	58	6	no	—
68	C₂²×C₄	C₂²×D₂₉	1	6	yes	—
69	C₂³	#90805	1	6	yes	—
70	C₂³	#90807	1	6	yes	—
71	C₂³	#90809	1	2	yes	—
72	C₂³	C₂³×D₂₉	1	1	yes	characteristic
73	C₂×C₄	—	2	6	no	—
74	C₂×C₄	—	2	12	no	—
75	C₂×C₄	—	4	12	no	—
76	C₂×C₄	—	58	6	no	—
77	C₂×C₄	—	58	6	no	—
78	C₂×C₄	—	58	6	no	—
79	C₂×C₄	—	58	6	no	—
80	C₂×C₄	—	116	4	no	—
81	C₂×C₄	—	116	12	no	—
82	C₂²	#11745238	1	4	yes	—
83	C₂²	#11745241	1	12	yes	—
84	C₂²	#11745260	1	12	yes	—
85	C₂²	C₂×#90805	1	3	yes	—
86	C₂²	C₂×#90807	1	3	yes	—
87	C₂²	C₂×#90809	1	1	yes	characteristic
88	C₄	—	4	6	no	—
89	C₄	—	116	2	no	—
90	C₄	—	116	6	no	—
91	C₂	C₂₉⋊#401	1	8	yes	direct product factor
92	C₂	C₂×#11745241	1	3	yes	—
93	C₂	C₂×#11745238	1	1	yes	characteristic
94	C₂	C₂×#11745260	1	3	yes	—

	subgroup	G/H
center	C₂⁴	C₂²×D₂₉
commutator, cosocle	C₂³×C₂₉	C₂⁴
Frattini	C₂³	C₂³×D₂₉
Fitting	C₂×C₂₉×#95	C₂
socle, prime radical	C₂⁴×C₂₉	C₂³
hypercenter	C₂×#95	D₂₉
hypocenter	C₂₉	C₂×#401
LCS	G ▷ C₂³×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
1. C₂₉⋊#401	C₂	direct (N × H)
48. C₂×C₂₉	#401	semidirect
58. C₂₉	C₂×#401	semidirect
91. C₂	C₂₉⋊#401	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⋊#401	2
C₂×#11745179	2
C₂×C₂₉×#95	2
C₂×#401	29

Subgroups — C2×C29⋊#401 #16822788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₉⋊#401 #16822788