Subgroups — #28505103

Order 15104.

370 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₅₉⋊C₁₆)	C₂	1	6	yes	maximal
2	C₅₉×#1726	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅₉⋊C₁₆	C₂²	1	4	yes	—
4	C₄⋊(C₅₉⋊C₁₆)	—	2	12	no	—
5	C₂×#97×C₅₉	C₄	1	3	yes	—
6	C₂×C₄×C₈×C₅₉	C₂²	1	3	yes	—
7	C₅₉×#376	C₄	1	1	yes	characteristic
8	C₂×C₅₉⋊C₁₆	—	2	12	no	—
9	C₂²×C₈×C₅₉	C₂×C₄	1	3	yes	—
10	C₂²×C₈×C₅₉	C₂³	1	1	yes	characteristic
11	C₂×C₄²×C₅₉	C₂×C₄	1	3	yes	—
12	#97×C₅₉	—	2	6	no	—
13	C₄×C₈×C₅₉	D₄	1	6	yes	—
14	C₄×C₈×C₅₉	Q₈	1	6	yes	—
15	#95×C₅₉	C₈	1	4	yes	—
16	C₂²×C₄×C₅₉	C₂×C₈	1	6	yes	—
17	C₂²×C₄×C₅₉	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₈×C₅₉	—	2	6	no	—
19	C₂×C₈×C₅₉	C₄⋊C₄	1	6	yes	—
20	C₂×C₈×C₅₉	C₂×D₄	1	3	yes	—
21	C₂×C₈×C₅₉	C₂×Q₈	1	3	yes	—
22	C₄²×C₅₉	C₄⋊C₄	1	6	yes	—
23	C₄²×C₅₉	M₁₆	1	6	yes	—
24	C₅₉⋊C₁₆	—	4	4	no	—
25	C₂³×C₅₉	C₂²×C₈	1	1	yes	characteristic
26	C₂×C₄×C₅₉	—	2	12	no	—
27	C₂×C₄×C₅₉	C₄⋊C₈	1	12	yes	—
28	C₂×C₄×C₅₉	C₂×C₄⋊C₄	1	3	yes	—
29	C₂×C₄×C₅₉	C₂×M₁₆	1	3	yes	—
30	C₈×C₅₉	—	2	6	no	—
31	C₈×C₅₉	#127	1	1	yes	characteristic
32	C₈×C₅₉	C₄⋊Q₈	1	3	yes	—
33	#12899	—	59	1	no	maximal, Sylow
34	C₂²×C₅₉	C₂×C₄⋊C₈	1	3	yes	—
35	C₂²×C₅₉	#504	1	4	yes	—
36	C₄×C₅₉	—	2	12	no	—
37	C₄×C₅₉	#384	1	1	yes	characteristic
38	C₄×C₅₉	#423	1	3	yes	—
39	C₂×C₄⋊C₁₆	—	59	6	no	—
40	#1726	D₅₉	1	1	yes	characteristic
41	C₂×C₅₉	#1842	1	1	yes	characteristic
42	C₂×C₅₉	#2151	1	6	yes	—
43	C₂²×C₁₆	—	59	4	no	—
44	C₂×#97	Dic₅₉	1	3	yes	—
45	C₂×C₄×C₈	C₂×D₅₉	1	3	yes	—
46	#376	Dic₅₉	1	1	yes	characteristic
47	C₄⋊C₁₆	—	118	12	no	—
48	C₅₉	#12899	1	1	yes	characteristic, complemented, Sylow
49	C₂²×C₈	C₂×Dic₅₉	1	3	yes	—
50	C₂²×C₈	C₂²×D₅₉	1	1	yes	characteristic
51	C₂×C₄²	C₂×Dic₅₉	1	3	yes	—
52	C₂×C₁₆	—	118	12	no	—
53	#97	—	2	6	no	—
54	C₄×C₈	Dic₁₁₈	1	6	yes	—
55	C₄×C₈	D₂₃₆	1	6	yes	—
56	#95	C₅₉⋊C₈	1	4	yes	—
57	C₂²×C₄	C₂×C₅₉⋊C₈	1	6	yes	—
58	C₂²×C₄	C₂²×Dic₅₉	1	1	yes	characteristic
59	C₂×C₈	—	2	6	no	—
60	C₂×C₈	C₄⋊Dic₅₉	1	6	yes	—
61	C₂×C₈	C₂×Dic₁₁₈	1	3	yes	—
62	C₂×C₈	C₂×D₂₃₆	1	3	yes	—
63	C₄²	#11745664	1	6	yes	—
64	C₄²	C₄⋊Dic₅₉	1	6	yes	—
65	C₁₆	—	236	4	no	—
66	C₂³	C₂²×C₅₉⋊C₈	1	1	yes	characteristic
67	C₂×C₄	—	2	12	no	—
68	C₂×C₄	C₄⋊(C₅₉⋊C₈)	1	12	yes	—
69	C₂×C₄	C₂×C₄⋊Dic₅₉	1	3	yes	—
70	C₂×C₄	C₂×#11745664	1	3	yes	—
71	C₈	—	2	6	no	—
72	C₈	#14273724	1	1	yes	characteristic
73	C₈	#14273727	1	3	yes	—
74	C₂²	C₂×C₄⋊(C₅₉⋊C₈)	1	3	yes	—
75	C₂²	#16837819	1	4	yes	—
76	C₄	—	2	12	no	—
77	C₄	#16837272	1	1	yes	characteristic
78	C₄	#16837426	1	3	yes	—
79	C₂	#21424248	1	1	yes	characteristic
80	C₂	#21425855	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₈	C₂²×D₅₉
commutator, socle, prime radical	C₂³×C₅₉	C₂²×C₈
Fitting	C₅₉×#1726	C₂
cosocle	C₂²×C₈×C₅₉	C₂³
hypercenter	#1726	D₅₉
hypocenter	C₅₉	#12899
LCS	G ▷ C₂³×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂²×C₈ ◁ #1726

Complements

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

N	H ≅ G/N	type
48. C₅₉	#12899	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₅₉⋊C₁₆)	2
C₅₉×#1726	2
#12899	59