Subgroups — #14271725

Order 1856.

346 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊D₂₉	C₂	1	2	yes	maximal, complemented
2	C₂×C₂²⋊C₄×C₂₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11745292	C₂	1	4	yes	maximal, complemented
4	#11745248	C₂	1	4	yes	maximal, complemented
5	#11745244	C₂	1	4	yes	maximal, complemented
6	C₂⁴×C₂₉	C₂²	1	1	yes	characteristic
7	C₂³×D₂₉	C₂²	1	2	yes	complemented
8	C₂²×C₄×C₂₉	C₂²	1	2	yes	complemented
9	C₂×C₂²⋊D₂₉	—	2	8	no	—
10	C₂×C₂²⋊D₂₉	C₂²	1	4	yes	—
11	C₂×C₂²⋊D₂₉	C₂²	1	4	yes	complemented
12	C₂²×Dic₂₉	C₂²	1	2	yes	complemented
13	C₂×D₁₁₆	C₂²	1	4	yes	complemented
14	C₂²⋊C₄×C₂₉	C₂²	1	4	yes	complemented
15	#90781	C₂²	1	8	yes	complemented
16	C₄⋊Dic₂₉	C₂²	1	4	yes	complemented
17	C₂³×C₂₉	—	4	2	no	—
18	C₂³×C₂₉	D₄	1	4	yes	complemented
19	C₂³×C₂₉	C₂³	1	2	yes	—
20	C₂³×C₂₉	C₂³	1	1	yes	characteristic
21	C₂²×D₂₉	—	2	4	no	—
22	C₂²×D₂₉	—	4	4	no	—
23	C₂²×D₂₉	C₂³	1	4	yes	—
24	C₂×C₄×C₂₉	—	4	2	no	—
25	C₂×C₄×C₂₉	C₂³	1	4	yes	—
26	C₂²⋊D₂₉	—	2	8	no	—
27	C₂²⋊D₂₉	—	2	8	no	—
28	C₂×Dic₂₉	—	2	4	no	—
29	C₂×Dic₂₉	C₂³	1	4	yes	—
30	D₁₁₆	—	4	4	no	—
31	C₂²×C₂₉	—	2	2	no	—
32	C₂²×C₂₉	—	2	4	no	—
33	C₂²×C₂₉	—	4	4	no	—
34	C₂²×C₂₉	C₂×D₄	1	4	yes	—
35	C₂²×C₂₉	C₂×D₄	1	2	yes	—
36	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
37	C₂×D₂₉	—	2	4	no	—
38	C₂×D₂₉	—	2	8	no	—
39	C₂×D₂₉	—	4	8	no	—
40	C₄×C₂₉	—	2	4	no	—
41	Dic₂₉	—	2	4	no	—
42	#534	—	29	1	no	maximal, Sylow
43	C₂×C₂₉	—	2	4	no	—
44	C₂×C₂₉	—	2	2	no	—
45	C₂×C₂₉	C₂²×D₄	1	1	yes	characteristic
46	C₂×C₂₉	H(5,𝔽₂)	1	2	yes	—
47	D₂₉	—	4	4	no	—
48	C₂²×D₄	—	29	2	no	—
49	#123	—	29	4	no	—
50	#121	—	29	4	no	—
51	#120	—	29	4	no	—
52	C₂×C₂²⋊C₄	D₂₉	1	1	yes	characteristic, complemented
53	C₂₉	#534	1	1	yes	characteristic, complemented, Sylow
54	C₂⁴	—	29	2	no	—
55	C₂⁴	C₂×D₂₉	1	1	yes	characteristic
56	C₂×D₄	—	29	4	no	—
57	C₂×D₄	—	29	4	no	—
58	C₂×D₄	—	29	4	no	—
59	C₂×D₄	—	58	8	no	—
60	C₂²×C₄	—	29	2	no	—
61	C₂²×C₄	C₂×D₂₉	1	2	yes	complemented
62	C₄⋊C₄	—	29	4	no	—
63	C₂²⋊C₄	—	29	8	no	—
64	C₂²⋊C₄	C₂×D₂₉	1	4	yes	complemented
65	C₂³	—	4	2	no	—
66	C₂³	—	29	4	no	—
67	C₂³	—	58	4	no	—
68	C₂³	—	116	4	no	—
69	C₂³	D₁₁₆	1	4	yes	complemented
70	C₂³	C₂²×D₂₉	1	2	yes	—
71	C₂³	C₂²×D₂₉	1	1	yes	characteristic
72	D₄	—	58	8	no	—
73	D₄	—	58	8	no	—
74	D₄	—	116	4	no	—
75	C₂×C₄	—	4	2	no	—
76	C₂×C₄	—	29	4	no	—
77	C₂×C₄	—	58	4	no	—
78	C₂×C₄	C₂²×D₂₉	1	4	yes	—
79	C₂²	—	2	2	no	—
80	C₂²	—	2	4	no	—
81	C₂²	—	4	4	no	—
82	C₂²	—	58	4	no	—
83	C₂²	—	58	8	no	—
84	C₂²	—	116	8	no	—
85	C₂²	C₂×D₁₁₆	1	4	yes	—
86	C₂²	C₂×D₁₁₆	1	2	yes	—
87	C₂²	C₂³×D₂₉	1	1	yes	characteristic
88	C₄	—	2	4	no	—
89	C₄	—	58	4	no	—
90	C₂	—	2	4	no	—
91	C₂	—	2	2	no	—
92	C₂	—	116	4	no	—
93	C₂	C₂²×D₁₁₆	1	1	yes	characteristic
94	C₂	#11745359	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂×C₂²⋊C₄×C₂₉	C₂
hypercenter	C₂×C₂²⋊C₄	D₂₉
hypocenter	C₂₉	#534
LCS	G ▷ C₂²×C₂₉ ▷ C₂₉
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂²⋊D₂₉	C₂	semidirect
2. C₂×C₂²⋊C₄×C₂₉	C₂	semidirect
3. #11745292	C₂	semidirect
4. #11745248	C₂	semidirect
5. #11745244	C₂	semidirect
7. C₂³×D₂₉	C₂²	semidirect
8. C₂²×C₄×C₂₉	C₂²	semidirect
11. C₂×C₂²⋊D₂₉	C₂²	semidirect
12. C₂²×Dic₂₉	C₂²	semidirect
13. C₂×D₁₁₆	C₂²	semidirect
14. C₂²⋊C₄×C₂₉	C₂²	semidirect
15. #90781	C₂²	semidirect
16. C₄⋊Dic₂₉	C₂²	semidirect
18. C₂³×C₂₉	D₄	semidirect
52. C₂×C₂²⋊C₄	D₂₉	semidirect
53. C₂₉	#534	semidirect
61. C₂²×C₄	C₂×D₂₉	semidirect
64. C₂²⋊C₄	C₂×D₂₉	semidirect
69. C₂³	D₁₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊D₂₉	2
C₂×C₂²⋊C₄×C₂₉	2
#11745292	2
#11745248	2
#11745244	2
#534	29