Subgroups — #14271911

Order 1856.

220 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, complemented
3	#11745257	C₂	1	4	yes	maximal, complemented
4	#11745256	C₂	1	4	yes	maximal, complemented
5	#11745237	C₂	1	2	yes	maximal, complemented
6	C₂×D₁₁₆	C₂²	1	2	yes	—
7	C₂×D₁₁₆	C₂²	1	4	yes	—
8	C₂×C₄×D₂₉	C₂²	1	4	yes	—
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	4	yes	—
14	#90781	C₂²	1	4	yes	—
15	#90781	C₂²	1	4	yes	—
16	#90779	C₂²	1	4	yes	—
17	C₂²×D₂₉	C₂³	1	4	yes	—
18	C₂×C₄×C₂₉	C₂³	1	4	yes	—
19	C₂×C₄×C₂₉	C₂³	1	1	yes	characteristic
20	C₂×C₄×C₂₉	C₂³	1	2	yes	—
21	C₂×Dic₂₉	C₂³	1	4	yes	—
22	D₁₁₆	—	4	2	no	—
23	D₁₁₆	—	4	4	no	—
24	C₄×D₂₉	—	4	4	no	—
25	Dic₅₈	—	4	2	no	—
26	C₂²×C₂₉	C₂⁴	1	1	yes	characteristic
27	C₂×D₂₉	—	2	4	no	—
28	C₂×D₂₉	—	2	4	no	—
29	C₂×D₂₉	—	2	4	no	—
30	C₄×C₂₉	—	2	2	no	—
31	C₄×C₂₉	—	2	4	no	—
32	C₄×C₂₉	—	2	1	no	—
33	Dic₂₉	—	2	4	no	—
34	#562	—	29	1	no	maximal, Sylow
35	C₂×C₂₉	H(5,𝔽₂)	1	2	yes	—
36	C₂×C₂₉	2₋¹⁺⁴	1	1	yes	characteristic
37	D₂₉	—	4	4	no	—
38	#125	D₂₉	1	1	yes	characteristic, complemented
39	#124	—	29	2	no	—
40	#123	—	29	4	no	—
41	C₂²⋊Q₈	—	29	4	no	—
42	#121	—	29	4	no	—
43	C₂₉	#562	1	1	yes	characteristic, complemented, Sylow
44	C₂×Q₈	—	29	2	no	—
45	C₂×D₄	—	29	4	no	—
46	C₂×D₄	—	29	2	no	—
47	C₂²×C₄	—	29	4	no	—
48	C₄⋊C₄	—	29	4	no	—
49	C₄⋊C₄	C₂×D₂₉	1	4	yes	—
50	C₄⋊C₄	C₂×D₂₉	1	2	yes	—
51	C₂²⋊C₄	—	29	4	no	—
52	C₂²⋊C₄	—	29	4	no	—
53	C₂²⋊C₄	—	29	4	no	—
54	C₄²	C₂×D₂₉	1	1	yes	characteristic
55	C₂³	—	29	4	no	—
56	Q₈	—	116	2	no	—
57	D₄	—	116	4	no	—
58	D₄	—	116	2	no	—
59	C₂×C₄	—	29	4	no	—
60	C₂×C₄	—	116	4	no	—
61	C₂×C₄	C₂²×D₂₉	1	1	yes	characteristic
62	C₂×C₄	C₂²×D₂₉	1	2	yes	—
63	C₂×C₄	C₂²×D₂₉	1	4	yes	—
64	C₂²	—	58	4	no	—
65	C₂²	—	58	4	no	—
66	C₂²	—	58	4	no	—
67	C₂²	C₂³×D₂₉	1	1	yes	characteristic
68	C₄	—	2	1	no	—
69	C₄	—	2	4	no	—
70	C₄	—	2	2	no	—
71	C₄	—	58	4	no	—
72	C₂	—	116	4	no	—
73	C₂	#11745362	1	1	yes	characteristic
74	C₂	#11745364	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₂₉
commutator, socle, cosocle	C₂²×C₂₉	C₂⁴
Fitting	C₂₉×#125	C₂
hypercenter	#125	D₂₉
hypocenter	C₂₉	#562
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
2. #11745258	C₂	semidirect
3. #11745257	C₂	semidirect
4. #11745256	C₂	semidirect
5. #11745237	C₂	semidirect
38. #125	D₂₉	semidirect
43. C₂₉	#562	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
#11745257	2
#11745256	2
#11745237	2
#562	29