Subgroups — #14270919

Order 1856.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#117	C₂	1	1	yes	maximal, characteristic
2	#11745288	C₂	1	1	yes	maximal, characteristic
3	C₂×#90777	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
5	C₄⋊C₄×C₂₉	—	2	1	no	—
6	C₂²⋊C₄×C₂₉	—	2	1	no	—
7	C₄²×C₂₉	C₄	1	2	yes	complemented
8	C₂²⋊Dic₂₉	—	2	1	no	—
9	C₄⋊Dic₂₉	—	2	1	no	—
10	C₄×Dic₂₉	C₄	1	2	yes	complemented
11	#90777	—	2	1	no	—
12	#90777	—	2	1	no	—
13	C₂×#6597	C₄	1	2	yes	complemented
14	C₂³×C₂₉	D₄	1	1	yes	characteristic
15	C₂×C₄×C₂₉	—	2	2	no	—
16	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
20	C₂×C₄×C₂₉	D₄	1	1	yes	characteristic
21	C₂×C₄×C₂₉	Q₈	1	1	yes	characteristic
22	C₂×Dic₂₉	—	2	2	no	—
23	#6597	—	2	2	no	—
24	C₂²×C₂₉	—	4	1	no	—
25	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
26	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
28	C₄×C₂₉	—	4	2	no	—
29	C₄×C₂₉	C₄²	1	1	yes	characteristic
30	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
31	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
32	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
33	Dic₂₉	—	4	2	no	—
34	H(3,ℤ/4)	—	29	1	no	maximal, Sylow
35	C₂×C₂₉	—	2	1	no	—
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	—	2	1	no	—
38	C₂×C₂₉	#95	1	1	yes	characteristic
39	C₂×M₁₆	—	29	1	no	—
40	#117	—	29	1	no	—
41	#117	D₂₉	1	1	yes	characteristic
42	C₂₉	H(3,ℤ/4)	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
44	M₁₆	—	58	1	no	—
45	M₁₆	—	58	1	no	—
46	C₂×C₈	—	29	2	no	—
47	C₄⋊C₄	—	2	1	no	—
48	C₄⋊C₄	—	58	1	no	—
49	C₂²⋊C₄	—	2	1	no	—
50	C₂²⋊C₄	—	58	1	no	—
51	C₄²	—	29	2	no	—
52	C₄²	Dic₂₉	1	2	yes	complemented
53	C₂³	C₂²⋊D₂₉	1	1	yes	characteristic
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	58	2	no	—
56	C₂×C₄	Dic₅₈	1	1	yes	characteristic
57	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
58	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
59	C₂×C₄	D₁₁₆	1	1	yes	characteristic
60	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
61	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
62	C₈	—	58	2	no	—
63	C₂²	—	4	1	no	—
64	C₂²	#90779	1	1	yes	characteristic
65	C₂²	#90781	1	1	yes	characteristic
66	C₂²	C₂²⋊Dic₂₉	1	1	yes	characteristic
67	C₄	—	4	2	no	—
68	C₄	—	116	2	no	—
69	C₄	C₄×Dic₂₉	1	1	yes	characteristic
70	C₄	#90779	1	1	yes	characteristic
71	C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
72	C₄	#90781	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	—	2	1	no	—
75	C₂	—	2	1	no	—
76	C₂	#11745179	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₄×Dic₂₉
commutator	C₄×C₂₉	C₄²
Frattini	C₂²×C₄	C₂×D₂₉
Fitting	C₂₉×#117	C₂
socle	C₂×C₂₉	#95
prime radical	C₂³×C₂₉	D₄
cosocle	C₂²×C₄×C₂₉	C₂²
hypercenter	#117	D₂₉
hypocenter	C₂₉	H(3,ℤ/4)
LCS	G ▷ C₄×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
7. C₄²×C₂₉	C₄	semidirect
10. C₄×Dic₂₉	C₄	semidirect
13. C₂×#6597	C₄	semidirect
42. C₂₉	H(3,ℤ/4)	semidirect
52. C₄²	Dic₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#117	2
#11745288	2
C₂×#90777	2
H(3,ℤ/4)	29