Subgroups — #14271776

Order 1856.

192 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	#11745260	C₂	1	4	yes	maximal
3	#11745259	C₂	1	2	yes	maximal
4	#11745252	C₂	1	4	yes	maximal, complemented
5	#11745249	C₂	1	2	yes	maximal, complemented
6	#11745234	C₂	1	1	yes	maximal, characteristic
7	#11745231	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
9	C₂×Dic₅₈	C₂²	1	2	yes	—
10	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
11	C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
12	C₄²×C₂₉	C₂²	1	1	yes	characteristic
13	#90781	C₂²	1	2	yes	—
14	#90781	C₂²	1	4	yes	—
15	C₄⋊Dic₂₉	C₂²	1	4	yes	—
16	C₄⋊Dic₂₉	C₂²	1	4	yes	—
17	#90779	C₂²	1	2	yes	—
18	#90779	C₂²	1	4	yes	—
19	C₄×Dic₂₉	C₂²	1	1	yes	characteristic
20	C₄×Dic₂₉	C₂²	1	4	yes	—
21	C₂²×D₂₉	C₂³	1	1	yes	characteristic
22	C₂×C₄×C₂₉	C₂³	1	4	yes	—
23	C₂×C₄×C₂₉	C₂³	1	2	yes	—
24	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
25	C₂×Dic₂₉	C₂³	1	2	yes	—
26	C₂×Dic₂₉	C₂³	1	4	yes	—
27	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
28	C₄×D₂₉	—	2	2	no	—
29	Dic₅₈	—	2	4	no	—
30	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
31	C₂×D₂₉	—	2	1	no	—
32	C₂×D₂₉	—	2	2	no	—
33	C₄×C₂₉	—	2	4	no	—
34	C₄×C₂₉	—	2	2	no	—
35	C₄×C₂₉	#41	1	2	yes	—
36	Dic₂₉	—	2	4	no	—
37	Dic₂₉	—	2	1	no	—
38	Dic₂₉	—	2	2	no	—
39	#541	—	29	1	no	maximal, Sylow
40	C₂×C₂₉	C₂×#41	1	1	yes	characteristic
41	C₂×C₂₉	2₋¹⁺⁴	1	2	yes	—
42	D₂₉	—	4	1	no	—
43	C₄⋊Q₈	—	29	1	no	—
44	#126	—	29	4	no	—
45	#125	—	29	4	no	—
46	#125	D₂₉	1	1	yes	characteristic, complemented
47	C₂²⋊Q₈	—	29	2	no	—
48	C₄×Q₈	—	29	2	no	—
49	#117	—	29	1	no	—
50	C₂₉	#541	1	1	yes	characteristic, complemented, Sylow
51	C₂×Q₈	—	29	2	no	—
52	C₂²×C₄	—	29	1	no	—
53	C₄⋊C₄	—	29	2	no	—
54	C₄⋊C₄	—	29	4	no	—
55	C₄⋊C₄	—	29	4	no	—
56	C₄⋊C₄	—	29	4	no	—
57	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
58	C₄⋊C₄	C₂×D₂₉	1	4	yes	—
59	C₂²⋊C₄	—	29	2	no	—
60	C₂²⋊C₄	—	29	4	no	—
61	C₄²	—	29	1	no	—
62	C₄²	—	29	4	no	—
63	C₄²	C₂×D₂₉	1	1	yes	characteristic
64	C₂³	—	29	1	no	—
65	Q₈	—	58	4	no	—
66	C₂×C₄	—	29	2	no	—
67	C₂×C₄	—	29	4	no	—
68	C₂×C₄	—	29	1	no	—
69	C₂×C₄	—	58	2	no	—
70	C₂×C₄	C₂²×D₂₉	1	4	yes	—
71	C₂×C₄	C₂²×D₂₉	1	2	yes	—
72	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
73	C₂²	—	58	1	no	—
74	C₂²	—	58	2	no	—
75	C₂²	C₂³×D₂₉	1	1	yes	characteristic
76	C₄	—	2	4	no	—
77	C₄	—	2	2	no	—
78	C₄	—	58	1	no	—
79	C₄	—	58	4	no	—
80	C₄	—	58	2	no	—
81	C₄	#90809	1	2	yes	—
82	C₂	—	116	1	no	—
83	C₂	C₂×#90809	1	1	yes	characteristic
84	C₂	#11745365	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×#125	C₂
prime radical	C₂²×D₂₉	C₂³
hypercenter	#125	D₂₉
hypocenter	C₂₉	#541
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ #125

Complements

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

N	H ≅ G/N	type
1. C₂₉×#125	C₂	semidirect
4. #11745252	C₂	semidirect
5. #11745249	C₂	semidirect
7. #11745231	C₂	semidirect
46. #125	D₂₉	semidirect
50. C₂₉	#541	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
#11745260	2
#11745259	2
#11745252	2
#11745249	2
#11745234	2
#11745231	2
#541	29