Subgroups — C₂×#11745179 #14271007

Order 1856.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₂₉	C₂	1	2	yes	maximal
3	#11745179	C₂	1	4	yes	maximal, direct product factor
4	C₂⁴×C₂₉	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₂₉	—	2	4	no	—
6	C₂²×C₄×C₂₉	C₄	1	4	yes	complemented
7	C₂²×C₄×C₂₉	C₂²	1	2	yes	—
8	C₂²×Dic₂₉	—	2	4	no	—
9	C₂²×Dic₂₉	—	2	4	no	—
10	C₂²×Dic₂₉	C₄	1	8	yes	complemented
11	C₂²×Dic₂₉	C₂²	1	4	yes	—
12	C₂³×C₂₉	C₂×C₄	1	4	yes	—
13	C₂³×C₂₉	C₂×C₄	1	2	yes	—
14	C₂³×C₂₉	D₄	1	2	yes	—
15	C₂³×C₂₉	D₄	1	4	yes	—
16	C₂³×C₂₉	Q₈	1	2	yes	—
17	C₂³×C₂₉	C₂³	1	1	yes	characteristic
18	C₂×C₄×C₂₉	—	2	8	no	—
19	C₂×C₄×C₂₉	—	2	4	no	—
20	C₂×C₄×C₂₉	C₂×C₄	1	4	yes	complemented
21	C₂×Dic₂₉	—	2	16	no	—
22	C₂×Dic₂₉	—	2	4	no	—
23	C₂×Dic₂₉	—	2	4	no	—
24	C₂×Dic₂₉	C₂×C₄	1	8	yes	complemented
25	C₂²×C₂₉	C₄²	1	4	yes	—
26	C₂²×C₂₉	C₂²⋊C₄	1	8	yes	—
27	C₂²×C₂₉	C₂²⋊C₄	1	4	yes	—
28	C₂²×C₂₉	C₄⋊C₄	1	8	yes	—
29	C₂²×C₂₉	C₄⋊C₄	1	4	yes	—
30	C₂²×C₂₉	C₂²×C₄	1	2	yes	—
31	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₂₉	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₂₉	C₂×D₄	1	2	yes	—
34	C₂²×C₂₉	C₂×Q₈	1	1	yes	characteristic
35	C₄×C₂₉	—	2	4	no	—
36	Dic₂₉	—	2	8	no	—
37	C₂×#95	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	#95	1	8	yes	complemented
39	C₂×C₂₉	C₂×C₄²	1	1	yes	characteristic
40	C₂×C₂₉	C₂×C₂²⋊C₄	1	2	yes	—
41	C₂×C₂₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₂₉	C₂×C₄⋊C₄	1	2	yes	—
43	C₂×C₂₉	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂³×C₄	—	29	2	no	—
45	C₂³×C₄	D₂₉	1	1	yes	characteristic
46	#95	—	29	4	no	—
47	C₂₉	C₂×#95	1	1	yes	characteristic, complemented, Sylow
48	C₂⁴	C₂×D₂₉	1	1	yes	characteristic
49	C₂²×C₄	—	2	4	no	—
50	C₂²×C₄	—	29	8	no	—
51	C₂²×C₄	—	29	4	no	—
52	C₂²×C₄	—	58	4	no	—
53	C₂²×C₄	—	58	4	no	—
54	C₂²×C₄	Dic₂₉	1	4	yes	complemented
55	C₂²×C₄	C₂×D₂₉	1	2	yes	—
56	C₂³	Dic₅₈	1	2	yes	—
57	C₂³	C₄×D₂₉	1	4	yes	—
58	C₂³	D₁₁₆	1	2	yes	—
59	C₂³	C₂×Dic₂₉	1	2	yes	—
60	C₂³	C₂²⋊D₂₉	1	4	yes	—
61	C₂³	C₂²×D₂₉	1	1	yes	characteristic
62	C₂×C₄	—	2	8	no	—
63	C₂×C₄	—	2	4	no	—
64	C₂×C₄	—	29	8	no	—
65	C₂×C₄	—	58	16	no	—
66	C₂×C₄	—	58	4	no	—
67	C₂×C₄	—	58	4	no	—
68	C₂×C₄	C₂×Dic₂₉	1	4	yes	complemented
69	C₂²	C₄×Dic₂₉	1	4	yes	—
70	C₂²	#90779	1	8	yes	—
71	C₂²	C₄⋊Dic₂₉	1	4	yes	—
72	C₂²	#90781	1	8	yes	—
73	C₂²	C₂²⋊Dic₂₉	1	4	yes	—
74	C₂²	C₂×Dic₅₈	1	1	yes	characteristic
75	C₂²	C₂×C₄×D₂₉	1	2	yes	—
76	C₂²	C₂×D₁₁₆	1	1	yes	characteristic
77	C₂²	C₂²×Dic₂₉	1	1	yes	characteristic
78	C₂²	C₂×C₂²⋊D₂₉	1	2	yes	—
79	C₄	—	2	4	no	—
80	C₄	—	58	8	no	—
81	C₂	#11745179	1	8	yes	direct product factor
82	C₂	C₂×C₄×Dic₂₉	1	1	yes	characteristic
83	C₂	C₂×#90779	1	2	yes	—
84	C₂	C₂×C₄⋊Dic₂₉	1	1	yes	characteristic
85	C₂	C₂×#90781	1	2	yes	—
86	C₂	C₂×C₂²⋊Dic₂₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₂₉
commutator	C₂×C₂₉	C₂×C₄²
Frattini	C₂³	C₂²×D₂₉
Fitting	C₂³×C₄×C₂₉	C₂
socle, prime radical	C₂⁴×C₂₉	C₂²
cosocle	C₂³×C₂₉	C₂³
hypercenter	C₂³×C₄	D₂₉
hypocenter	C₂₉	C₂×#95
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. #11745179	C₂	direct (N × H)
6. C₂²×C₄×C₂₉	C₄	semidirect
10. C₂²×Dic₂₉	C₄	semidirect
20. C₂×C₄×C₂₉	C₂×C₄	semidirect
24. C₂×Dic₂₉	C₂×C₄	semidirect
38. C₂×C₂₉	#95	semidirect
47. C₂₉	C₂×#95	semidirect
54. C₂²×C₄	Dic₂₉	semidirect
68. C₂×C₄	C₂×Dic₂₉	semidirect
81. C₂	#11745179	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₂₉	2
C₂³×Dic₂₉	2
#11745179	2
C₂×#95	29

Subgroups — C2×#11745179 #14271007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11745179 #14271007