Subgroups — #14270922

Order 1856.

110 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	C₂×C₄×Dic₂₉	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	C₂²×Dic₂₉	—	2	1	no	—
6	C₄⋊C₄×C₂₉	C₄	1	2	yes	complemented
7	C₂²⋊C₄×C₂₉	—	2	1	no	—
8	C₄²×C₂₉	—	2	1	no	—
9	C₄×Dic₂₉	—	2	1	no	—
10	C₄×Dic₂₉	C₄	1	2	yes	complemented
11	#90777	—	2	1	no	—
12	#90777	C₄	1	2	yes	complemented
13	C₂×#6597	—	2	1	no	—
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	4	no	—
23	C₂×Dic₂₉	—	2	2	no	—
24	#6597	—	2	2	no	—
25	C₂²×C₂₉	—	2	2	no	—
26	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
28	C₂²×C₂₉	C₄⋊C₄	1	1	yes	characteristic
29	C₄×C₂₉	—	4	2	no	—
30	C₄×C₂₉	C₄²	1	1	yes	characteristic
31	C₄×C₂₉	C₂²⋊C₄	1	1	yes	characteristic
32	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
33	C₄×C₂₉	C₄⋊C₄	1	1	yes	characteristic
34	Dic₂₉	—	2	4	no	—
35	#339	—	29	1	no	maximal, Sylow
36	C₂×C₂₉	—	2	1	no	—
37	C₂×C₂₉	—	2	1	no	—
38	C₂×C₂₉	#95	1	1	yes	characteristic
39	C₂×C₂₉	#104	1	2	yes	—
40	C₂×M₁₆	—	29	1	no	—
41	#117	D₂₉	1	1	yes	characteristic
42	C₂×C₄²	—	29	1	no	—
43	C₂₉	#339	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	—	58	1	no	—
45	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
46	M₁₆	—	29	2	no	—
47	M₁₆	—	58	1	no	—
48	C₂×C₈	—	58	1	no	—
49	C₄⋊C₄	Dic₂₉	1	2	yes	complemented
50	C₂²⋊C₄	—	2	1	no	—
51	C₄²	—	2	1	no	—
52	C₄²	—	29	2	no	—
53	C₄²	—	58	1	no	—
54	C₂³	C₂²⋊D₂₉	1	1	yes	characteristic
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	58	4	no	—
57	C₂×C₄	—	58	2	no	—
58	C₂×C₄	Dic₅₈	1	1	yes	characteristic
59	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
60	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
61	C₂×C₄	D₁₁₆	1	1	yes	characteristic
62	C₂×C₄	C₂×Dic₂₉	1	1	yes	characteristic
63	C₂×C₄	C₂²⋊D₂₉	1	1	yes	characteristic
64	C₈	—	58	2	no	—
65	C₂²	—	2	2	no	—
66	C₂²	#90779	1	1	yes	characteristic
67	C₂²	#90781	1	1	yes	characteristic
68	C₂²	C₂²⋊Dic₂₉	1	1	yes	characteristic
69	C₄	—	4	2	no	—
70	C₄	—	58	4	no	—
71	C₄	C₄×Dic₂₉	1	1	yes	characteristic
72	C₄	#90779	1	1	yes	characteristic
73	C₄	C₄⋊Dic₂₉	1	1	yes	characteristic
74	C₄	#90781	1	1	yes	characteristic
75	C₂	—	2	1	no	—
76	C₂	—	2	1	no	—
77	C₂	#11745179	1	1	yes	characteristic
78	C₂	#11745185	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊D₂₉
commutator	C₄×C₂₉	C₄²
Frattini	C₂²×C₄	C₂×D₂₉
Fitting	C₂₉×#117	C₂
socle	C₂²×C₂₉	C₂²⋊C₄
prime radical	C₂³×C₂₉	D₄
cosocle	C₂²×C₄×C₂₉	C₂²
hypercenter	#117	D₂₉
hypocenter	C₂₉	#339
LCS	G ▷ C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
6. C₄⋊C₄×C₂₉	C₄	semidirect
10. C₄×Dic₂₉	C₄	semidirect
12. #90777	C₄	semidirect
43. C₂₉	#339	semidirect
49. C₄⋊C₄	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
C₂×C₄×Dic₂₉	2
C₂×#90777	2
#339	29