Subgroups — #14271798

Order 1856.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×D₂₉	C₂	1	4	yes	maximal, complemented
2	C₂₉×#127	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745300	C₂	1	4	yes	maximal, complemented
4	#11745299	C₂	1	4	yes	maximal, complemented
5	C₄×D₁₁₆	C₂	1	2	yes	maximal, complemented
6	C₂³×D₂₉	C₂²	1	4	yes	complemented
7	C₂×D₄×C₂₉	C₂²	1	4	yes	complemented
8	C₂×D₄×C₂₉	C₂²	1	2	yes	complemented
9	C₂×C₂²⋊D₂₉	C₂²	1	8	yes	complemented
10	D₄×D₂₉	—	2	16	no	—
11	C₂×D₁₁₆	C₂²	1	2	yes	—
12	C₂×C₄×D₂₉	C₂²	1	4	yes	complemented
13	C₄²×C₂₉	C₂²	1	1	yes	characteristic, complemented
14	C₂²⋊Dic₂₉	C₂²	1	4	yes	complemented
15	#90781	C₂²	1	4	yes	complemented
16	C₄⋊Dic₂₉	C₂²	1	2	yes	complemented
17	C₂³×C₂₉	C₂³	1	4	yes	—
18	C₂²×D₂₉	—	2	16	no	—
19	C₂²×D₂₉	—	4	4	no	—
20	C₂²×D₂₉	C₂³	1	4	yes	—
21	D₄×C₂₉	—	2	8	no	—
22	D₄×C₂₉	—	4	2	no	—
23	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
24	C₂×C₄×C₂₉	C₂³	1	2	yes	—
25	C₂²⋊D₂₉	—	2	16	no	—
26	C₂×Dic₂₉	C₂³	1	4	yes	—
27	D₁₁₆	D₄	1	8	yes	complemented
28	C₄×D₂₉	—	2	8	no	—
29	C₂²×C₂₉	—	2	8	no	—
30	C₂²×C₂₉	—	2	4	no	—
31	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
32	C₂×D₂₉	—	2	4	no	—
33	C₂×D₂₉	—	2	4	no	—
34	C₂×D₂₉	—	4	16	no	—
35	C₂×D₂₉	C₂×D₄	1	8	yes	complemented
36	C₄×C₂₉	—	2	1	no	—
37	C₄×C₂₉	C₂×D₄	1	4	yes	complemented
38	Dic₂₉	—	2	4	no	—
39	D₄²	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	—	4	4	no	—
41	C₂×C₂₉	C₂²×D₄	1	2	yes	—
42	C₂×C₂₉	H(5,𝔽₂)	1	1	yes	characteristic
43	D₂₉	—	2	8	no	—
44	C₂²×D₄	—	29	4	no	—
45	#127	D₂₉	1	1	yes	characteristic, complemented
46	#121	—	29	4	no	—
47	#120	—	29	4	no	—
48	C₄×D₄	—	29	2	no	—
49	C₂₉	D₄²	1	1	yes	characteristic, complemented, Sylow
50	C₂⁴	—	29	4	no	—
51	C₂×D₄	—	29	8	no	—
52	C₂×D₄	—	29	2	no	—
53	C₂×D₄	—	58	16	no	—
54	C₂×D₄	C₂×D₂₉	1	4	yes	complemented
55	C₂×D₄	C₂×D₂₉	1	2	yes	complemented
56	C₂²×C₄	—	29	4	no	—
57	C₄⋊C₄	—	29	2	no	—
58	C₂²⋊C₄	—	29	4	no	—
59	C₂²⋊C₄	—	29	4	no	—
60	C₄²	C₂×D₂₉	1	1	yes	characteristic, complemented
61	C₂³	—	29	4	no	—
62	C₂³	—	58	16	no	—
63	C₂³	—	116	4	no	—
64	C₂³	C₂²×D₂₉	1	4	yes	—
65	D₄	—	2	8	no	—
66	D₄	—	4	2	no	—
67	D₄	—	29	8	no	—
68	D₄	—	58	16	no	—
69	C₂×C₄	—	29	4	no	—
70	C₂×C₄	—	58	8	no	—
71	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
72	C₂×C₄	C₂²×D₂₉	1	2	yes	—
73	C₂²	—	2	8	no	—
74	C₂²	—	2	4	no	—
75	C₂²	—	29	8	no	—
76	C₂²	—	58	4	no	—
77	C₂²	—	58	4	no	—
78	C₂²	—	116	16	no	—
79	C₂²	C₂³×D₂₉	1	1	yes	characteristic
80	C₄	—	2	1	no	—
81	C₄	—	58	4	no	—
82	C₄	D₄×D₂₉	1	4	yes	complemented
83	C₂	—	4	4	no	—
84	C₂	—	58	8	no	—
85	C₂	C₂×D₄×D₂₉	1	2	yes	—
86	C₂	#11745359	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×#127	C₂
hypercenter	#127	D₂₉
hypocenter	C₂₉	D₄²
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #127

Complements

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

N	H ≅ G/N	type
1. C₂×D₄×D₂₉	C₂	semidirect
2. C₂₉×#127	C₂	semidirect
3. #11745300	C₂	semidirect
4. #11745299	C₂	semidirect
5. C₄×D₁₁₆	C₂	semidirect
6. C₂³×D₂₉	C₂²	semidirect
7. C₂×D₄×C₂₉	C₂²	semidirect
8. C₂×D₄×C₂₉	C₂²	semidirect
9. C₂×C₂²⋊D₂₉	C₂²	semidirect
12. C₂×C₄×D₂₉	C₂²	semidirect
13. C₄²×C₂₉	C₂²	semidirect
14. C₂²⋊Dic₂₉	C₂²	semidirect
15. #90781	C₂²	semidirect
16. C₄⋊Dic₂₉	C₂²	semidirect
27. D₁₁₆	D₄	semidirect
35. C₂×D₂₉	C₂×D₄	semidirect
37. C₄×C₂₉	C₂×D₄	semidirect
45. #127	D₂₉	semidirect
49. C₂₉	D₄²	semidirect
54. C₂×D₄	C₂×D₂₉	semidirect
55. C₂×D₄	C₂×D₂₉	semidirect
60. C₄²	C₂×D₂₉	semidirect
82. C₄	D₄×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×D₂₉	2
C₂₉×#127	2
#11745300	2
#11745299	2
C₄×D₁₁₆	2
D₄²	29