Subgroups — #14271529

Order 1856.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	#11745236	C₂	1	1	yes	maximal, characteristic
3	#11745157	C₂	1	4	yes	maximal, complemented
4	#11745151	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₁₁₆	—	2	2	no	—
6	C₂×D₁₁₆	C₂²	1	2	yes	—
7	C₄⋊C₄×C₂₉	—	2	2	no	—
8	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
9	C₄²×C₂₉	C₂²	1	1	yes	characteristic
10	C₂×#6597	C₂²	1	2	yes	—
11	C₂²×D₂₉	—	2	2	no	—
12	C₂×C₄×C₂₉	—	2	2	no	—
13	C₂×C₄×C₂₉	D₄	1	2	yes	—
14	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
15	D₁₁₆	—	2	4	no	—
16	D₁₁₆	—	4	4	no	—
17	#6597	—	2	2	no	—
18	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
19	C₂×D₂₉	—	4	2	no	—
20	C₂×D₂₉	—	4	4	no	—
21	C₄×C₂₉	—	2	2	no	—
22	C₄×C₂₉	—	4	2	no	—
23	C₄×C₂₉	#41	1	2	yes	—
24	#490	—	29	1	no	maximal, Sylow
25	C₂×C₂₉	#124	1	1	yes	characteristic
26	C₂×C₂₉	AGL(1,ℤ/8)	1	2	yes	—
27	D₂₉	—	8	2	no	—
28	#127	—	29	1	no	—
29	#125	D₂₉	1	1	yes	characteristic, complemented
30	#102	—	29	4	no	—
31	#97	—	29	1	no	—
32	C₂₉	#490	1	1	yes	characteristic, complemented, Sylow
33	C₂×D₄	—	29	2	no	—
34	C₂×D₄	—	58	2	no	—
35	C₂×C₈	—	29	2	no	—
36	C₄⋊C₄	—	2	2	no	—
37	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
38	C₄²	C₂×D₂₉	1	1	yes	characteristic
39	C₂³	—	58	2	no	—
40	D₄	—	58	4	no	—
41	D₄	—	116	4	no	—
42	C₂×C₄	—	2	2	no	—
43	C₂×C₄	C₂²⋊D₂₉	1	2	yes	—
44	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
45	C₈	—	58	2	no	—
46	C₂²	—	116	2	no	—
47	C₂²	—	116	4	no	—
48	C₂²	C₂×C₂²⋊D₂₉	1	1	yes	characteristic
49	C₄	—	2	2	no	—
50	C₄	—	4	2	no	—
51	C₄	#90809	1	2	yes	—
52	C₂	—	232	2	no	—
53	C₂	#11745309	1	1	yes	characteristic
54	C₂	#11745311	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊D₂₉
commutator, cosocle	C₂×C₄×C₂₉	C₂³
Frattini	C₂×C₄	C₂²×D₂₉
Fitting	C₂₉×#125	C₂
socle	C₂²×C₂₉	C₂×D₄
prime radical	#11745236	C₂
hypercenter	#125	D₂₉
hypocenter	C₂₉	#490
LCS	G ▷ C₂×C₄×C₂₉ ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
1. C₂₉×#125	C₂	semidirect
3. #11745157	C₂	semidirect
4. #11745151	C₂	semidirect
29. #125	D₂₉	semidirect
32. C₂₉	#490	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×#125	2
#11745236	2
#11745157	2
#11745151	2
#490	29