Subgroups — D₂₉×#383 #16821880

Order 3712.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×D₂₉	C₂	1	1	yes	maximal, characteristic
2	#14271031	C₂	1	1	yes	maximal, characteristic, complemented
3	#14271030	C₂	1	6	yes	maximal, complemented
4	#95×D₂₉	C₂	1	6	yes	maximal
5	C₂₉×#383	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₄×D₂₉	C₂²	1	4	yes	—
7	C₂²×C₄×D₂₉	C₂²	1	3	yes	—
8	C₂×C₄²×C₂₉	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₂₉	C₂²	1	3	yes	—
10	C₄²×D₂₉	C₄	1	8	yes	complemented
11	C₂₉×#95	C₂²	1	6	yes	—
12	#11745179	C₂²	1	12	yes	—
13	#11745179	C₂²	1	6	yes	—
14	C₂³×D₂₉	C₂³	1	1	yes	characteristic
15	C₂²×C₄×C₂₉	C₂³	1	4	yes	—
16	C₂²×C₄×C₂₉	C₂³	1	3	yes	—
17	C₂²×Dic₂₉	C₂³	1	4	yes	—
18	C₂²×Dic₂₉	C₂³	1	3	yes	—
19	C₂×C₄×D₂₉	—	2	12	no	—
20	C₂×C₄×D₂₉	—	2	24	no	—
21	C₂×C₄×D₂₉	C₂×C₄	1	12	yes	—
22	C₄²×C₂₉	C₂×C₄	1	4	yes	complemented
23	C₄×Dic₂₉	C₂×C₄	1	12	yes	complemented
24	C₂³×C₂₉	C₂⁴	1	1	yes	characteristic
25	C₂²×D₂₉	C₂²×C₄	1	2	yes	—
26	C₂²×D₂₉	#41	1	12	yes	—
27	C₂×C₄×C₂₉	—	2	6	no	—
28	C₂×C₄×C₂₉	—	2	12	no	—
29	C₂×C₄×C₂₉	C₂²×C₄	1	6	yes	—
30	C₂×Dic₂₉	—	2	6	no	—
31	C₂×Dic₂₉	—	2	12	no	—
32	C₂×Dic₂₉	C₂²×C₄	1	6	yes	—
33	C₄×D₂₉	—	2	24	no	—
34	C₄×D₂₉	—	4	16	no	—
35	C₂×#383	—	29	1	no	maximal, Sylow
36	C₂²×C₂₉	C₂³×C₄	1	1	yes	characteristic
37	C₂²×C₂₉	C₂×#41	1	6	yes	—
38	C₂×D₂₉	#117	1	12	yes	—
39	C₂×D₂₉	#126	1	16	yes	—
40	C₄×C₂₉	—	2	6	no	—
41	C₄×C₂₉	—	4	4	no	—
42	Dic₂₉	—	2	6	no	—
43	Dic₂₉	—	4	4	no	—
44	C₂²×C₄²	—	29	1	no	—
45	#383	—	29	1	no	—
46	#383	—	29	6	no	—
47	#383	D₂₉	1	1	yes	characteristic, direct product factor
48	C₂×#95	—	29	6	no	—
49	C₂×C₂₉	C₂×#117	1	3	yes	—
50	C₂×C₂₉	C₂×#126	1	4	yes	—
51	D₂₉	#383	1	8	yes	direct product factor
52	C₂³×C₄	—	29	3	no	—
53	C₂³×C₄	—	29	4	no	—
54	C₂×C₄²	—	29	3	no	—
55	C₂×C₄²	—	29	8	no	—
56	C₂×C₄²	C₂×D₂₉	1	1	yes	characteristic
57	#95	—	29	12	no	—
58	#95	—	29	6	no	—
59	#95	C₂×D₂₉	1	6	yes	—
60	C₂₉	C₂×#383	1	1	yes	characteristic, complemented, Sylow
61	C₂⁴	—	29	1	no	—
62	C₂²×C₄	—	29	3	no	—
63	C₂²×C₄	—	29	12	no	—
64	C₂²×C₄	—	29	4	no	—
65	C₂²×C₄	—	58	12	no	—
66	C₂²×C₄	—	58	24	no	—
67	C₂²×C₄	C₂²×D₂₉	1	4	yes	—
68	C₂²×C₄	C₂²×D₂₉	1	3	yes	—
69	C₄²	—	29	12	no	—
70	C₄²	C₄×D₂₉	1	4	yes	complemented
71	C₂³	—	29	2	no	—
72	C₂³	—	29	12	no	—
73	C₂³	C₂³×D₂₉	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	2	12	no	—
76	C₂×C₄	—	29	6	no	—
77	C₂×C₄	—	58	24	no	—
78	C₂×C₄	—	58	6	no	—
79	C₂×C₄	—	58	12	no	—
80	C₂×C₄	—	116	16	no	—
81	C₂×C₄	C₂×C₄×D₂₉	1	6	yes	—
82	C₂²	—	29	12	no	—
83	C₂²	—	29	16	no	—
84	C₂²	C₂²×C₄×D₂₉	1	1	yes	characteristic
85	C₂²	#41×D₂₉	1	6	yes	—
86	C₄	—	2	6	no	—
87	C₄	—	4	4	no	—
88	C₄	—	58	6	no	—
89	C₄	—	116	4	no	—
90	C₂	—	29	8	no	—
91	C₂	#117×D₂₉	1	3	yes	—
92	C₂	#126×D₂₉	1	4	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₂₉
commutator	C₂²×C₂₉	C₂³×C₄
Fitting	C₂₉×#383	C₂
socle, cosocle	C₂³×C₂₉	C₂⁴
prime radical	C₂³×D₂₉	C₂³
hypercenter	#383	D₂₉
hypocenter	C₂₉	C₂×#383
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂³ ◁ #383

Complements

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

N	H ≅ G/N	type
2. #14271031	C₂	semidirect
3. #14271030	C₂	semidirect
5. C₂₉×#383	C₂	semidirect
10. C₄²×D₂₉	C₄	semidirect
22. C₄²×C₂₉	C₂×C₄	semidirect
23. C₄×Dic₂₉	C₂×C₄	semidirect
47. #383	D₂₉	direct (N × H)
51. D₂₉	#383	direct (N × H)
60. C₂₉	C₂×#383	semidirect
70. C₄²	C₄×D₂₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄²×D₂₉	2
#14271031	2
#14271030	2
#95×D₂₉	2
C₂₉×#383	2
C₂×#383	29

Subgroups — D29×#383 #16821880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₂₉×#383 #16821880