Subgroups — #14271719

Order 1856.

222 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	#11745258	C₂	1	4	yes	maximal
3	#11745254	C₂	1	2	yes	maximal
4	#11745250	C₂	1	2	yes	maximal, complemented
5	#11745249	C₂	1	4	yes	maximal, complemented
6	C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
7	#11745232	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₉	C₂²	1	2	yes	—
9	C₂×C₄×D₂₉	C₂²	1	1	yes	characteristic
10	C₂×Dic₅₈	C₂²	1	4	yes	—
11	C₄⋊C₄×C₂₉	C₂²	1	4	yes	—
12	C₄⋊C₄×C₂₉	C₂²	1	2	yes	—
13	C₄²×C₂₉	C₂²	1	1	yes	characteristic
14	#90781	C₂²	1	4	yes	—
15	C₄⋊Dic₂₉	C₂²	1	2	yes	—
16	#90779	C₂²	1	4	yes	—
17	#90779	C₂²	1	4	yes	—
18	C₄×Dic₂₉	C₂²	1	2	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	2	yes	—
23	C₂×C₄×C₂₉	C₂³	1	4	yes	—
24	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
25	C₂×Dic₂₉	C₂³	1	4	yes	—
26	C₂×Dic₂₉	C₂³	1	1	yes	characteristic
27	C₂×Dic₂₉	C₂³	1	2	yes	—
28	C₄×D₂₉	—	2	4	no	—
29	C₄×D₂₉	Q₈	1	4	yes	complemented
30	Dic₅₈	—	2	8	no	—
31	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
32	C₂×D₂₉	—	2	2	no	—
33	C₂×D₂₉	C₂×Q₈	1	2	yes	—
34	C₄×C₂₉	—	2	4	no	—
35	C₄×C₂₉	—	2	2	no	—
36	C₄×C₂₉	C₂×Q₈	1	2	yes	—
37	Dic₂₉	—	2	4	no	—
38	Dic₂₉	C₂×Q₈	1	2	yes	—
39	Dic₂₉	#41	1	4	yes	—
40	#533	—	29	1	no	maximal, Sylow
41	C₂×C₂₉	C₂²×Q₈	1	1	yes	characteristic
42	C₂×C₂₉	C₂×#41	1	2	yes	—
43	D₂₉	—	2	2	no	—
44	C₄⋊Q₈	—	29	2	no	—
45	#125	—	29	1	no	—
46	#125	D₂₉	1	1	yes	characteristic, complemented
47	C₂²⋊Q₈	—	29	4	no	—
48	C₄×Q₈	—	29	4	no	—
49	#117	—	29	2	no	—
50	C₂×C₄²	—	29	1	no	—
51	C₂₉	#533	1	1	yes	characteristic, complemented, Sylow
52	C₂×Q₈	—	29	4	no	—
53	C₂²×C₄	—	29	1	no	—
54	C₂²×C₄	—	29	2	no	—
55	C₄⋊C₄	—	29	2	no	—
56	C₄⋊C₄	—	29	4	no	—
57	C₄⋊C₄	—	29	4	no	—
58	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
59	C₄⋊C₄	C₂×D₂₉	1	4	yes	—
60	C₂²⋊C₄	—	29	4	no	—
61	C₄²	—	29	2	no	—
62	C₄²	—	29	1	no	—
63	C₄²	—	29	4	no	—
64	C₄²	C₂×D₂₉	1	1	yes	characteristic
65	C₂³	—	29	1	no	—
66	Q₈	—	58	8	no	—
67	C₂×C₄	—	29	1	no	—
68	C₂×C₄	—	29	2	no	—
69	C₂×C₄	—	29	4	no	—
70	C₂×C₄	—	29	4	no	—
71	C₂×C₄	—	58	4	no	—
72	C₂×C₄	C₂²×D₂₉	1	2	yes	—
73	C₂×C₄	C₂²×D₂₉	1	4	yes	—
74	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
75	C₂²	—	29	2	no	—
76	C₂²	—	58	2	no	—
77	C₂²	C₂³×D₂₉	1	1	yes	characteristic
78	C₄	—	2	2	no	—
79	C₄	—	2	4	no	—
80	C₄	—	29	2	no	—
81	C₄	—	29	4	no	—
82	C₄	—	58	4	no	—
83	C₄	Q₈×D₂₉	1	2	yes	—
84	C₂	—	58	2	no	—
85	C₂	C₂×Q₈×D₂₉	1	1	yes	characteristic
86	C₂	#41×D₂₉	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	#533
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. #11745250	C₂	semidirect
5. #11745249	C₂	semidirect
7. #11745232	C₂	semidirect
29. C₄×D₂₉	Q₈	semidirect
46. #125	D₂₉	semidirect
51. C₂₉	#533	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
#11745258	2
#11745254	2
#11745250	2
#11745249	2
C₄²×D₂₉	2
#11745232	2
#533	29