Group #28445408 — subgroups

Subgroups — C₅₉×#33299 #28445408

Order 15104.

662 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 286 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅₉×#2859	C₂	1	2	yes	maximal
2	C₅₉×#1992	C₂	1	8	yes	maximal
3	C₅₉×#1835	C₂	1	4	yes	maximal
4	C₄×#97×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#125×C₅₉	C₂²	1	4	yes	—
6	C₂×#97×C₅₉	C₂²	1	4	yes	—
7	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
8	C₅₉×#389	—	2	8	no	—
9	C₅₉×#384	C₂²	1	4	yes	—
10	C₅₉×#382	C₂²	1	4	yes	—
11	C₄³×C₅₉	C₂²	1	1	yes	characteristic
12	C₅₉×#340	C₂²	1	16	yes	—
13	C₂²×C₈×C₅₉	C₂³	1	4	yes	—
14	#125×C₅₉	—	2	16	no	—
15	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
16	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
17	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
18	C₂×C₄²×C₅₉	D₄	1	4	yes	—
19	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
20	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
21	#97×C₅₉	—	2	8	no	—
22	C₄×C₈×C₅₉	Q₈	1	8	yes	—
23	#95×C₅₉	—	2	8	no	—
24	C₂²×C₄×C₅₉	—	2	8	no	—
25	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
26	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
27	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
28	C₂×C₈×C₅₉	—	2	8	no	—
29	C₂×C₈×C₅₉	C₂×Q₈	1	8	yes	—
30	C₄⋊C₄×C₅₉	—	2	16	no	—
31	C₄⋊C₄×C₅₉	—	4	16	no	—
32	C₄⋊C₄×C₅₉	—	4	16	no	—
33	C₄²×C₅₉	—	4	4	no	—
34	C₄²×C₅₉	C₂×Q₈	1	4	yes	—
35	C₄²×C₅₉	#41	1	8	yes	—
36	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
37	C₂×C₄×C₅₉	—	2	8	no	—
38	C₂×C₄×C₅₉	—	2	4	no	—
39	C₂×C₄×C₅₉	—	4	8	no	—
40	C₂×C₄×C₅₉	—	4	16	no	—
41	C₂×C₄×C₅₉	#124	1	8	yes	—
42	C₂×C₄×C₅₉	C₄⋊Q₈	1	4	yes	—
43	C₂×C₄×C₅₉	C₂²×Q₈	1	2	yes	—
44	C₂×C₄×C₅₉	C₂×#41	1	4	yes	—
45	C₈×C₅₉	—	2	8	no	—
46	#33299	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂²×C₅₉	C₂×#124	1	2	yes	—
48	C₂²×C₅₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
49	C₂²×C₅₉	#575	1	4	yes	—
50	C₄×C₅₉	—	2	8	no	—
51	C₄×C₅₉	—	2	4	no	—
52	C₄×C₅₉	—	8	8	no	—
53	C₄×C₅₉	#533	1	4	yes	—
54	#2859	C₂×C₅₉	1	2	yes	—
55	#1992	C₂×C₅₉	1	8	yes	—
56	#1835	C₂×C₅₉	1	4	yes	—
57	C₄×#97	C₂×C₅₉	1	1	yes	characteristic
58	C₂×C₅₉	#2862	1	1	yes	characteristic
59	C₂×C₅₉	#3142	1	4	yes	—
60	C₂×C₅₉	#3162	1	2	yes	—
61	C₂×#125	C₂²×C₅₉	1	4	yes	—
62	C₂×#97	C₂²×C₅₉	1	4	yes	—
63	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	—
64	#389	—	2	8	no	—
65	#384	C₂²×C₅₉	1	4	yes	—
66	#382	C₂²×C₅₉	1	4	yes	—
67	C₄³	C₂²×C₅₉	1	1	yes	characteristic
68	#340	C₂²×C₅₉	1	16	yes	—
69	C₅₉	#33299	1	1	yes	characteristic, direct product factor, Sylow
70	C₂²×C₈	C₂³×C₅₉	1	4	yes	—
71	#125	—	2	16	no	—
72	C₂×C₄⋊C₄	—	2	8	no	—
73	C₂×C₄⋊C₄	—	2	8	no	—
74	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
75	C₂×C₄²	D₄×C₅₉	1	4	yes	—
76	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
77	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
78	#97	—	2	8	no	—
79	C₄×C₈	Q₈×C₅₉	1	8	yes	—
80	#95	—	2	8	no	—
81	C₂²×C₄	—	2	8	no	—
82	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
83	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
84	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
85	C₂×C₈	—	2	8	no	—
86	C₂×C₈	C₂×Q₈×C₅₉	1	8	yes	—
87	C₄⋊C₄	—	2	16	no	—
88	C₄⋊C₄	—	4	16	no	—
89	C₄⋊C₄	—	4	16	no	—
90	C₄²	—	4	4	no	—
91	C₄²	C₂×Q₈×C₅₉	1	4	yes	—
92	C₄²	#41×C₅₉	1	8	yes	—
93	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
94	C₂×C₄	—	2	8	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	4	8	no	—
97	C₂×C₄	—	4	16	no	—
98	C₂×C₄	#124×C₅₉	1	8	yes	—
99	C₂×C₄	C₄⋊Q₈×C₅₉	1	4	yes	—
100	C₂×C₄	C₂²×Q₈×C₅₉	1	2	yes	—
101	C₂×C₄	C₂×#41×C₅₉	1	4	yes	—
102	C₈	—	2	8	no	—
103	C₂²	C₂×#124×C₅₉	1	2	yes	—
104	C₂²	C₂×C₄⋊Q₈×C₅₉	1	1	yes	characteristic
105	C₂²	C₅₉×#575	1	4	yes	—
106	C₄	—	2	8	no	—
107	C₄	—	2	4	no	—
108	C₄	—	8	8	no	—
109	C₄	C₅₉×#533	1	4	yes	—
110	C₂	C₅₉×#2862	1	1	yes	characteristic
111	C₂	C₅₉×#3142	1	4	yes	—
112	C₂	C₅₉×#3162	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₅₉×#2859

C₂

yes

maximal

C₅₉×#1992

C₂

yes

maximal

C₅₉×#1835

C₂

yes

maximal

C₄×#97×C₅₉

C₂

yes

maximal, characteristic

C₂×#125×C₅₉

C₂²

yes

—

C₂×#97×C₅₉

C₂²

yes

—

C₂×C₄×C₈×C₅₉

C₂²

yes

—

C₅₉×#389

—

C₅₉×#384

C₂²

yes

—

C₅₉×#382

C₂²

yes

—

C₄³×C₅₉

C₂²

yes

characteristic

C₅₉×#340

C₂²

yes

—

C₂²×C₈×C₅₉

C₂³

yes

—

#125×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

—

C₂×C₄⋊C₄×C₅₉

C₂³

yes

—

C₂×C₄²×C₅₉

D₄

yes

—

C₂×C₄²×C₅₉

C₂³

yes

characteristic

C₂×C₄²×C₅₉

C₂³

yes

—

#97×C₅₉

—

C₄×C₈×C₅₉

Q₈

yes

—

#95×C₅₉

—

C₂²×C₄×C₅₉

—

C₂²×C₄×C₅₉

C₂×D₄

yes

—

C₂²×C₄×C₅₉

C₂×D₄

yes

—

C₂²×C₄×C₅₉

C₂⁴

yes

characteristic

C₂×C₈×C₅₉

—

C₂×C₈×C₅₉

C₂×Q₈

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂×Q₈

yes

—

C₄²×C₅₉

#41

yes

—

C₂³×C₅₉

C₂²×D₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#124

yes

—

C₂×C₄×C₅₉

C₄⋊Q₈

yes

—

C₂×C₄×C₅₉

C₂²×Q₈

yes

—

C₂×C₄×C₅₉

C₂×#41

yes

—

C₈×C₅₉

—

#33299

C₅₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅₉

C₂×#124

yes

—

C₂²×C₅₉

C₂×C₄⋊Q₈

yes

characteristic

C₂²×C₅₉

#575

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

#533

yes

—

#2859

C₂×C₅₉

yes

—

#1992

C₂×C₅₉

yes

—

#1835

C₂×C₅₉

yes

—

C₄×#97

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#3162

yes

—

C₂×#125

C₂²×C₅₉

yes

—

C₂×#97

C₂²×C₅₉

yes

—

C₂×C₄×C₈

C₂²×C₅₉

yes

—

#389

—

#384

C₂²×C₅₉

yes

—

#382

C₂²×C₅₉

yes

—

C₄³

C₂²×C₅₉

yes

characteristic

#340

C₂²×C₅₉

yes

—

C₅₉

#33299

yes

characteristic, direct product factor, Sylow

C₂²×C₈

C₂³×C₅₉

yes

—

#125

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

C₂³×C₅₉

yes

—

C₂×C₄²

D₄×C₅₉

yes

—

C₂×C₄²

C₂³×C₅₉

yes

characteristic

C₂×C₄²

C₂³×C₅₉

yes

—

#97

—

C₄×C₈

Q₈×C₅₉

yes

—

#95

—

C₂²×C₄

—

C₂²×C₄

C₂×D₄×C₅₉

yes

—

C₂²×C₄

C₂×D₄×C₅₉

yes

—

C₂²×C₄

C₂⁴×C₅₉

yes

characteristic

C₂×C₈

—

C₂×C₈

C₂×Q₈×C₅₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂×Q₈×C₅₉

yes

—

C₄²

#41×C₅₉

yes

—

C₂³

C₂²×D₄×C₅₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#124×C₅₉

yes

—

C₂×C₄

C₄⋊Q₈×C₅₉

yes

—

100

C₂×C₄

C₂²×Q₈×C₅₉

yes

—

101

C₂×C₄

C₂×#41×C₅₉

yes

—

102

C₈

—

103

C₂²

C₂×#124×C₅₉

yes

—

104

C₂²

C₂×C₄⋊Q₈×C₅₉

yes

characteristic

105

C₂²

C₅₉×#575

yes

—

106

C₄

—

107

C₄

—

108

C₄

—

109

C₄

C₅₉×#533

yes

—

110

C₂

C₅₉×#2862

yes

characteristic

111

C₂

C₅₉×#3142

yes

—

112

C₂

C₅₉×#3162

yes

—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₉ ◁ C₄³×C₅₉ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₅₉

C₂²×D₄

commutator, Frattini, cosocle

C₂²×C₄

C₂⁴×C₅₉

LCS

G ▷ C₂²×C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₅₉ ◁ C₄³×C₅₉ ◁ G

N	H ≅ G/N	type
46. #33299	C₅₉	direct (N × H)
69. C₅₉	#33299	direct (N × H)

H ≅ G/N

type

46. #33299

C₅₉

direct (N × H)

69. C₅₉

#33299

direct (N × H)

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

subgroup	index
C₅₉×#2859	2
C₅₉×#1992	2
C₅₉×#1835	2
C₄×#97×C₅₉	2
#33299	59

subgroup

index

C₅₉×#2859

C₅₉×#1992

C₅₉×#1835

C₄×#97×C₅₉

#33299

Subgroups — C₅₉×#33299 #28445408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C59×#33299 #28445408

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33299 #28445408