Subgroups — #14272126

Order 1856.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11745345	C₂	1	1	yes	maximal, characteristic
2	D₂₉⋊M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₂₉	C₂	1	1	yes	maximal, characteristic
4	#11745208	C₂	1	2	yes	maximal, complemented
5	C₈×#1181	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
7	C₂²⋊#1181	C₄	1	2	yes	—
8	#90800	C₄	1	2	yes	complemented
9	C₄⋊#1181	C₄	1	2	yes	—
10	C₄×#1181	C₂²	1	2	yes	—
11	#90796	C₄	1	2	yes	complemented
12	D₂₉⋊C₈	C₂²	1	2	yes	—
13	C₂×C₈×C₂₉	C₄	1	1	yes	characteristic, complemented
14	C₂×#6597	C₄	1	1	yes	characteristic, complemented
15	C₈×D₂₉	C₄	1	1	yes	characteristic, complemented
16	C₈×D₂₉	C₄	1	1	yes	characteristic, complemented
17	C₈×D₂₉	C₂²	1	1	yes	characteristic
18	C₈×D₂₉	C₂²	1	1	yes	characteristic
19	C₂²×D₂₉	C₂×C₄	1	1	yes	characteristic
20	C₂×#1181	C₂×C₄	1	4	yes	—
21	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
23	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
24	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
25	C₄×D₂₉	C₂×C₄	1	1	yes	characteristic
26	C₄×D₂₉	C₂³	1	1	yes	characteristic
27	#6599	C₂×C₄	1	4	yes	—
28	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
29	C₈×C₂₉	C₂×C₄	1	1	yes	characteristic
30	#6597	C₂×C₄	1	1	yes	characteristic
31	#6597	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₂₉	C₄²	1	1	yes	characteristic
33	C₂×D₂₉	—	2	2	no	—
34	C₂×D₂₉	C₄²	1	1	yes	characteristic
35	C₂×D₂₉	C₂²×C₄	1	1	yes	characteristic
36	#1181	—	2	4	no	—
37	C₄×C₂₉	C₄²	1	1	yes	characteristic
38	C₄×C₂₉	C₂²×C₄	1	1	yes	characteristic
39	Dic₂₉	C₄²	1	1	yes	characteristic
40	Dic₂₉	C₂²×C₄	1	1	yes	characteristic
41	#405	—	29	1	no	maximal, Sylow
42	C₂×C₂₉	—	2	1	no	—
43	C₂×C₂₉	C₂×C₄²	1	1	yes	characteristic
44	D₂₉	—	2	1	no	—
45	D₂₉	#131	1	2	yes	—
46	C₂×M₁₆	—	29	1	no	—
47	C₂²×C₈	—	29	1	no	—
48	#117	—	29	1	no	—
49	#97	—	29	2	no	—
50	C₄×C₈	—	29	2	no	—
51	C₂₉	#405	1	1	yes	characteristic, complemented, Sylow
52	C₂²×C₄	—	29	1	no	—
53	M₁₆	—	29	2	no	—
54	M₁₆	—	29	2	no	—
55	C₂×C₈	—	29	2	no	—
56	C₂×C₈	—	29	1	no	—
57	C₂×C₈	—	29	1	no	—
58	C₂×C₈	—	29	1	no	—
59	C₂×C₈	—	29	1	no	—
60	C₂×C₈	—	29	1	no	—
61	C₂×C₈	#1181	1	1	yes	characteristic, complemented
62	C₄⋊C₄	—	29	2	no	—
63	C₂²⋊C₄	—	29	2	no	—
64	C₄²	—	29	2	no	—
65	C₂³	—	29	1	no	—
66	C₂×C₄	—	29	1	no	—
67	C₂×C₄	—	29	1	no	—
68	C₂×C₄	—	29	1	no	—
69	C₂×C₄	—	29	1	no	—
70	C₂×C₄	—	29	1	no	—
71	C₂×C₄	—	29	4	no	—
72	C₂×C₄	C₂×#1181	1	1	yes	characteristic
73	C₈	—	29	4	no	—
74	C₈	—	29	1	no	—
75	C₈	—	29	1	no	—
76	C₈	C₂×#1181	1	1	yes	characteristic
77	C₈	C₂×#1181	1	1	yes	characteristic
78	C₂²	—	29	1	no	—
79	C₂²	—	29	1	no	—
80	C₂²	—	58	2	no	—
81	C₂²	C₄×#1181	1	1	yes	characteristic
82	C₄	—	29	1	no	—
83	C₄	—	29	1	no	—
84	C₄	—	58	4	no	—
85	C₄	C₄×#1181	1	1	yes	characteristic
86	C₄	C₂²×#1181	1	1	yes	characteristic
87	C₂	—	2	1	no	—
88	C₂	—	29	2	no	—
89	C₂	—	58	1	no	—
90	C₂	C₂×C₄×#1181	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×#1181
commutator, socle	C₂×C₂₉	C₂×C₄²
Frattini	C₄	C₂²×#1181
Fitting	C₂×C₈×C₂₉	C₄
prime radical	C₂²×D₂₉	C₂×C₄
cosocle	C₄×D₂₉	C₂³
hypercenter	C₂×C₈	#1181
hypocenter	C₂₉	#405
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₈ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
4. #11745208	C₂	semidirect
5. C₈×#1181	C₂	semidirect
8. #90800	C₄	semidirect
11. #90796	C₄	semidirect
13. C₂×C₈×C₂₉	C₄	semidirect
14. C₂×#6597	C₄	semidirect
15. C₈×D₂₉	C₄	semidirect
16. C₈×D₂₉	C₄	semidirect
51. C₂₉	#405	semidirect
61. C₂×C₈	#1181	semidirect

Maximal subgroups

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

subgroup	index
#11745345	2
D₂₉⋊M₁₆	2
C₂×C₈×D₂₉	2
#11745208	2
C₈×#1181	2
#405	29