Subgroups — #14272241

Order 1856.

258 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#90807	C₂	1	1	yes	maximal, characteristic
2	C₂×#90800	C₂	1	4	yes	maximal, complemented
3	#11745346	C₂	1	8	yes	maximal, complemented
4	D₂₉⋊M₁₆	C₂	1	2	yes	maximal, complemented
5	C₂×D₄×C₂₉	C₄	1	1	yes	characteristic
6	C₂×C₂²⋊D₂₉	C₄	1	2	yes	—
7	C₂²×Dic₂₉	C₂²	1	2	yes	—
8	#90807	C₄	1	4	yes	—
9	#90807	C₂²	1	4	yes	—
10	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
11	C₂×Dic₅₈	C₄	1	1	yes	characteristic
12	#90800	C₂²	1	4	yes	—
13	#90800	C₂²	1	8	yes	complemented
14	C₂×#6599	C₂²	1	8	yes	complemented
15	#90796	C₂²	1	4	yes	complemented
16	D₂₉⋊C₈	C₂²	1	4	yes	complemented
17	C₂³×C₂₉	C₂×C₄	1	2	yes	—
18	C₂²×D₂₉	C₂×C₄	1	1	yes	characteristic
19	D₄×C₂₉	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
21	C₂²⋊D₂₉	C₂×C₄	1	8	yes	—
22	C₂×Dic₂₉	C₂×C₄	1	2	yes	—
23	C₂×Dic₂₉	C₂×C₄	1	4	yes	—
24	C₂×Dic₂₉	C₂³	1	4	yes	—
25	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
26	C₄×D₂₉	C₂×C₄	1	2	yes	—
27	C₄×D₂₉	C₂³	1	2	yes	—
28	Dic₅₈	C₂×C₄	1	4	yes	—
29	#6599	C₂³	1	8	yes	—
30	C₂²×C₂₉	—	4	2	no	—
31	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
32	C₂²×C₂₉	C₂²×C₄	1	4	yes	—
33	C₂×D₂₉	—	4	1	no	—
34	C₂×D₂₉	C₂²×C₄	1	2	yes	—
35	C₄×C₂₉	C₂²×C₄	1	2	yes	—
36	Dic₂₉	C₂²×C₄	1	4	yes	—
37	Dic₂₉	C₂²×C₄	1	1	yes	characteristic
38	Dic₂₉	C₂⁴	1	1	yes	characteristic
39	#568	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	—	2	1	no	—
41	C₂×C₂₉	—	2	4	no	—
42	C₂×C₂₉	C₂³×C₄	1	1	yes	characteristic
43	D₂₉	—	2	2	no	—
44	C₂×#41	—	29	1	no	—
45	#131	—	29	8	no	—
46	C₂×M₁₆	—	29	2	no	—
47	C₂×M₁₆	—	29	4	no	—
48	C₂₉	#568	1	1	yes	characteristic, complemented, Sylow
49	#41	—	29	4	no	—
50	#41	—	29	4	no	—
51	C₂×Q₈	—	29	1	no	—
52	C₂×D₄	—	29	2	no	—
53	C₂×D₄	#1181	1	1	yes	characteristic
54	C₂²×C₄	—	29	2	no	—
55	C₂²×C₄	—	29	1	no	—
56	M₁₆	—	29	4	no	—
57	M₁₆	—	29	4	no	—
58	M₁₆	—	29	8	no	—
59	C₂×C₈	—	29	4	no	—
60	C₂×C₈	—	29	8	no	—
61	C₂³	—	29	1	no	—
62	C₂³	C₂×#1181	1	2	yes	—
63	Q₈	—	29	4	no	—
64	D₄	—	29	8	no	—
65	D₄	C₂×#1181	1	4	yes	—
66	C₂×C₄	—	29	4	no	—
67	C₂×C₄	—	29	1	no	—
68	C₂×C₄	—	29	2	no	—
69	C₂×C₄	—	29	4	no	—
70	C₂×C₄	—	29	2	no	—
71	C₂×C₄	—	29	2	no	—
72	C₂×C₄	C₂×#1181	1	1	yes	characteristic
73	C₈	—	29	8	no	—
74	C₂²	—	4	2	no	—
75	C₂²	—	29	2	no	—
76	C₂²	—	116	1	no	—
77	C₂²	C₂²×#1181	1	1	yes	characteristic
78	C₂²	C₂²×#1181	1	4	yes	—
79	C₄	—	29	1	no	—
80	C₄	—	29	1	no	—
81	C₄	—	29	4	no	—
82	C₄	C₂²×#1181	1	2	yes	—
83	C₂	—	2	1	no	—
84	C₂	—	2	4	no	—
85	C₂	—	58	2	no	—
86	C₂	C₂³×#1181	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂³×#1181
commutator, socle	C₂×C₂₉	C₂³×C₄
Fitting	C₂×D₄×C₂₉	C₄
prime radical	C₂×#90807	C₂
cosocle	Dic₂₉	C₂⁴
hypercenter	C₂×D₄	#1181
hypocenter	C₂₉	#568
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂ ◁ C₂×D₄

Complements

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

N	H ≅ G/N	type
2. C₂×#90800	C₂	semidirect
3. #11745346	C₂	semidirect
4. D₂₉⋊M₁₆	C₂	semidirect
13. #90800	C₂²	semidirect
14. C₂×#6599	C₂²	semidirect
15. #90796	C₂²	semidirect
16. D₂₉⋊C₈	C₂²	semidirect
48. C₂₉	#568	semidirect

Maximal subgroups

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

subgroup	index
C₂×#90807	2
C₂×#90800	2
#11745346	2
D₂₉⋊M₁₆	2
#568	29