Subgroups — #14271215

Order 1856.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745168	C₂	1	2	yes	maximal
4	C₈×Dic₂₉	C₂	1	2	yes	maximal, complemented
5	C₄⋊#6597	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×D₂₉	C₄	1	1	yes	characteristic
7	C₂×C₄×D₂₉	C₄	1	1	yes	characteristic
8	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂²	1	2	yes	—
10	C₄²×C₂₉	C₂²	1	1	yes	characteristic
11	C₄×Dic₂₉	C₄	1	1	yes	characteristic
12	C₄×Dic₂₉	C₄	1	1	yes	characteristic
13	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×#6597	C₂²	1	2	yes	—
15	C₂²×D₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
22	C₄×D₂₉	—	2	1	no	—
23	C₄×D₂₉	—	2	1	no	—
24	C₄×D₂₉	—	2	2	no	—
25	C₄×D₂₉	C₈	1	4	yes	complemented
26	C₈×C₂₉	—	2	2	no	—
27	#6597	—	2	2	no	—
28	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
29	C₂×D₂₉	—	2	1	no	—
30	C₂×D₂₉	—	2	1	no	—
31	C₂×D₂₉	C₂×C₈	1	2	yes	—
32	C₄×C₂₉	—	2	1	no	—
33	C₄×C₂₉	C₂×C₈	1	2	yes	—
34	C₄×C₂₉	#41	1	1	yes	characteristic
35	C₄×C₂₉	#41	1	1	yes	characteristic
36	Dic₂₉	—	2	1	no	—
37	Dic₂₉	C₂×C₈	1	2	yes	—
38	Dic₂₉	M₁₆	1	2	yes	—
39	#431	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	#117	1	1	yes	characteristic
41	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
42	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
43	D₂₉	—	2	2	no	—
44	C₂×C₄²	—	29	1	no	—
45	C₄⋊C₈	—	29	1	no	—
46	C₄⋊C₈	D₂₉	1	1	yes	characteristic, complemented
47	C₂²⋊C₈	—	29	2	no	—
48	C₄×C₈	—	29	2	no	—
49	C₂₉	#431	1	1	yes	characteristic, complemented, Sylow
50	C₂²×C₄	—	29	1	no	—
51	C₂²×C₄	—	29	1	no	—
52	C₂²×C₄	—	29	1	no	—
53	C₂×C₈	—	29	2	no	—
54	C₂×C₈	C₂×D₂₉	1	2	yes	—
55	C₄²	—	29	1	no	—
56	C₄²	—	29	1	no	—
57	C₄²	—	29	1	no	—
58	C₄²	C₂×D₂₉	1	1	yes	characteristic
59	C₂³	—	29	1	no	—
60	C₂×C₄	—	29	1	no	—
61	C₂×C₄	—	29	1	no	—
62	C₂×C₄	—	29	4	no	—
63	C₂×C₄	—	29	1	no	—
64	C₂×C₄	—	58	2	no	—
65	C₂×C₄	—	58	1	no	—
66	C₂×C₄	—	58	1	no	—
67	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
68	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
69	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
70	C₈	—	2	2	no	—
71	C₈	—	58	2	no	—
72	C₂²	—	29	2	no	—
73	C₂²	—	58	1	no	—
74	C₂²	—	58	1	no	—
75	C₂²	C₂×C₄×D₂₉	1	1	yes	characteristic
76	C₄	—	2	1	no	—
77	C₄	—	29	2	no	—
78	C₄	—	29	2	no	—
79	C₄	—	58	1	no	—
80	C₄	C₈×D₂₉	1	2	yes	—
81	C₄	#90807	1	1	yes	characteristic
82	C₄	#90809	1	1	yes	characteristic
83	C₂	—	58	2	no	—
84	C₂	#11745254	1	1	yes	characteristic
85	C₂	C₂×C₈×D₂₉	1	1	yes	characteristic
86	C₂	M₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₂²×C₈
Fitting	C₂₉×C₄⋊C₈	C₂
socle	C₂²×C₂₉	C₂²×C₄
prime radical	C₂²×D₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₄⋊C₈	D₂₉
hypocenter	C₂₉	#431
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₂₉×C₄⋊C₈	C₂	semidirect
4. C₈×Dic₂₉	C₂	semidirect
5. C₄⋊#6597	C₂	semidirect
25. C₄×D₂₉	C₈	semidirect
46. C₄⋊C₈	D₂₉	semidirect
49. C₂₉	#431	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄²×D₂₉	2
C₂₉×C₄⋊C₈	2
#11745168	2
C₈×Dic₂₉	2
C₄⋊#6597	2
#431	29