Subgroups — #14271213

Order 1856.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₂₉	C₂	1	1	yes	maximal, characteristic
2	C₂₉×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#6597	C₂	1	1	yes	maximal, characteristic
4	#11745162	C₂	1	2	yes	maximal, complemented
5	C₈×Dic₂₉	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×C₂₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₂₉	C₄	1	1	yes	characteristic
8	C₂²×Dic₂₉	C₄	1	1	yes	characteristic
9	C₂×C₈×C₂₉	C₂²	1	2	yes	—
10	C₄×Dic₂₉	C₄	1	1	yes	characteristic
11	C₄×Dic₂₉	C₄	1	1	yes	characteristic
12	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
13	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
14	C₂×#6597	C₂²	1	2	yes	—
15	C₂³×C₂₉	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₂₉	—	2	2	no	—
17	C₂×C₄×C₂₉	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
19	C₂×Dic₂₉	—	2	2	no	—
20	C₂×Dic₂₉	C₈	1	4	yes	complemented
21	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
22	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
23	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₂₉	C₂×C₄	1	1	yes	characteristic
25	C₈×C₂₉	—	2	2	no	—
26	#6597	—	2	2	no	—
27	C₂²×C₂₉	—	2	1	no	—
28	C₂²×C₂₉	—	2	1	no	—
29	C₂²×C₂₉	C₂×C₈	1	2	yes	—
30	C₂²×C₂₉	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₂₉	—	2	1	no	—
32	C₄×C₂₉	#41	1	2	yes	—
33	Dic₂₉	—	2	1	no	—
34	Dic₂₉	C₂×C₈	1	2	yes	—
35	Dic₂₉	C₂×C₈	1	2	yes	—
36	Dic₂₉	M₁₆	1	2	yes	—
37	#431	—	29	1	no	maximal, Sylow
38	C₂×C₂₉	—	2	2	no	—
39	C₂×C₂₉	#117	1	1	yes	characteristic
40	C₂×C₂₉	C₂²×C₈	1	1	yes	characteristic
41	C₂×C₂₉	C₂×M₁₆	1	1	yes	characteristic
42	C₂×C₄²	—	29	1	no	—
43	C₄⋊C₈	—	29	2	no	—
44	C₂²⋊C₈	—	29	1	no	—
45	C₂²⋊C₈	D₂₉	1	1	yes	characteristic
46	C₄×C₈	—	29	2	no	—
47	C₂₉	#431	1	1	yes	characteristic, complemented, Sylow
48	C₂²×C₄	—	29	1	no	—
49	C₂²×C₄	—	29	1	no	—
50	C₂²×C₄	C₂×D₂₉	1	1	yes	characteristic
51	C₂×C₈	—	29	2	no	—
52	C₂×C₈	C₂×D₂₉	1	2	yes	—
53	C₄²	—	29	1	no	—
54	C₄²	—	29	1	no	—
55	C₄²	—	29	1	no	—
56	C₄²	—	29	1	no	—
57	C₂³	C₄×D₂₉	1	1	yes	characteristic
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	29	4	no	—
60	C₂×C₄	—	29	1	no	—
61	C₂×C₄	—	29	1	no	—
62	C₂×C₄	—	29	1	no	—
63	C₂×C₄	—	29	1	no	—
64	C₂×C₄	—	58	2	no	—
65	C₂×C₄	C₄×D₂₉	1	1	yes	characteristic
66	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
67	C₈	—	2	2	no	—
68	C₈	—	58	2	no	—
69	C₂²	—	2	1	no	—
70	C₂²	—	2	1	no	—
71	C₂²	C₈×D₂₉	1	2	yes	—
72	C₂²	C₂×C₄×D₂₉	1	1	yes	characteristic
73	C₄	—	2	1	no	—
74	C₄	—	29	2	no	—
75	C₄	—	29	2	no	—
76	C₄	—	29	2	no	—
77	C₄	—	58	1	no	—
78	C₄	#90807	1	2	yes	—
79	C₂	—	2	2	no	—
80	C₂	#11745239	1	1	yes	characteristic
81	C₂	C₂×C₈×D₂₉	1	1	yes	characteristic
82	C₂	M₁₆×D₂₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₂₉
commutator	C₂×C₂₉	C₂²×C₈
Fitting	C₂₉×C₂²⋊C₈	C₂
socle	C₂²×C₂₉	C₂²×C₄
prime radical	C₂³×C₂₉	C₂×C₄
cosocle	C₂×C₄×C₂₉	C₂³
hypercenter	C₂²⋊C₈	D₂₉
hypocenter	C₂₉	#431
LCS	G ▷ C₂×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
4. #11745162	C₂	semidirect
5. C₈×Dic₂₉	C₂	semidirect
20. C₂×Dic₂₉	C₈	semidirect
47. C₂₉	#431	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Dic₂₉	2
C₂₉×C₂²⋊C₈	2
C₂²⋊#6597	2
#11745162	2
C₈×Dic₂₉	2
#431	29