Group #28445424 — subgroups

Subgroups — C₅₉×#33315 #28445424

Order 15104.

806 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 382 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	C₂×C₅₉×#499	C₂	1	4	yes	maximal
2	C₅₉×#2859	C₂	1	2	yes	maximal
3	C₅₉×#1847	C₂	1	8	yes	maximal
4	C₄×#97×C₅₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#125×C₅₉	C₂²	1	4	yes	—
6	C₅₉×#499	—	2	16	no	—
7	C₂×#107×C₅₉	C₂²	1	8	yes	—
8	C₂×#106×C₅₉	C₂²	1	8	yes	—
9	C₂×#97×C₅₉	C₂²	1	4	yes	—
10	C₂×C₄×C₈×C₅₉	C₂²	1	2	yes	—
11	C₅₉×#389	—	2	8	no	—
12	C₅₉×#384	C₂²	1	4	yes	—
13	C₅₉×#382	C₂²	1	4	yes	—
14	C₄³×C₅₉	C₂²	1	1	yes	characteristic
15	C₂²×C₈×C₅₉	C₂³	1	4	yes	—
16	#125×C₅₉	—	2	16	no	—
17	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
18	C₂×C₄⋊C₄×C₅₉	—	2	8	no	—
19	C₂×C₄⋊C₄×C₅₉	C₂³	1	8	yes	—
20	C₂×C₄²×C₅₉	D₄	1	4	yes	—
21	C₂×C₄²×C₅₉	C₂³	1	1	yes	characteristic
22	C₂×C₄²×C₅₉	C₂³	1	2	yes	—
23	#107×C₅₉	—	2	16	no	—
24	#106×C₅₉	—	2	16	no	—
25	#97×C₅₉	Q₈	1	16	yes	—
26	C₄×C₈×C₅₉	D₄	1	8	yes	—
27	#95×C₅₉	—	2	8	no	—
28	C₂²×C₄×C₅₉	—	2	8	no	—
29	C₂²×C₄×C₅₉	C₂×D₄	1	2	yes	—
30	C₂²×C₄×C₅₉	C₂×D₄	1	4	yes	—
31	C₂²×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
32	C₂×C₈×C₅₉	C₂×D₄	1	8	yes	—
33	C₂×C₈×C₅₉	C₂×Q₈	1	16	yes	—
34	C₄⋊C₄×C₅₉	—	2	16	no	—
35	C₄⋊C₄×C₅₉	—	4	16	no	—
36	C₄⋊C₄×C₅₉	—	4	16	no	—
37	C₄²×C₅₉	—	4	4	no	—
38	C₄²×C₅₉	C₂×D₄	1	4	yes	—
39	C₄²×C₅₉	C₂×Q₈	1	8	yes	—
40	C₂³×C₅₉	C₂²×D₄	1	1	yes	characteristic
41	C₂×C₄×C₅₉	—	2	8	no	—
42	C₂×C₄×C₅₉	—	2	4	no	—
43	C₂×C₄×C₅₉	—	4	8	no	—
44	C₂×C₄×C₅₉	—	4	16	no	—
45	C₂×C₄×C₅₉	#127	1	4	yes	—
46	C₂×C₄×C₅₉	C₄⋊Q₈	1	8	yes	—
47	C₂×C₄×C₅₉	C₂²×D₄	1	2	yes	—
48	C₂×C₄×C₅₉	C₂²×Q₈	1	4	yes	—
49	C₈×C₅₉	C₄⋊Q₈	1	16	yes	—
50	#33315	C₅₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂²×C₅₉	C₂×#127	1	1	yes	characteristic
52	C₂²×C₅₉	C₂×C₄⋊Q₈	1	2	yes	—
53	C₂²×C₅₉	#575	1	4	yes	—
54	C₄×C₅₉	—	2	4	no	—
55	C₄×C₅₉	—	2	8	no	—
56	C₄×C₅₉	—	8	8	no	—
57	C₄×C₅₉	C₂×C₄⋊Q₈	1	4	yes	—
58	C₂×#499	C₂×C₅₉	1	4	yes	—
59	#2859	C₂×C₅₉	1	2	yes	—
60	#1847	C₂×C₅₉	1	8	yes	—
61	C₄×#97	C₂×C₅₉	1	1	yes	characteristic
62	C₂×C₅₉	#2868	1	1	yes	characteristic
63	C₂×C₅₉	#3150	1	2	yes	—
64	C₂×C₅₉	#3166	1	4	yes	—
65	C₂×#125	C₂²×C₅₉	1	4	yes	—
66	#499	—	2	16	no	—
67	C₂×#107	C₂²×C₅₉	1	8	yes	—
68	C₂×#106	C₂²×C₅₉	1	8	yes	—
69	C₂×#97	C₂²×C₅₉	1	4	yes	—
70	C₂×C₄×C₈	C₂²×C₅₉	1	2	yes	—
71	#389	—	2	8	no	—
72	#384	C₂²×C₅₉	1	4	yes	—
73	#382	C₂²×C₅₉	1	4	yes	—
74	C₄³	C₂²×C₅₉	1	1	yes	characteristic
75	C₅₉	#33315	1	1	yes	characteristic, direct product factor, Sylow
76	C₂²×C₈	C₂³×C₅₉	1	4	yes	—
77	#125	—	2	16	no	—
78	C₂×C₄⋊C₄	—	2	8	no	—
79	C₂×C₄⋊C₄	—	2	8	no	—
80	C₂×C₄⋊C₄	C₂³×C₅₉	1	8	yes	—
81	C₂×C₄²	D₄×C₅₉	1	4	yes	—
82	C₂×C₄²	C₂³×C₅₉	1	1	yes	characteristic
83	C₂×C₄²	C₂³×C₅₉	1	2	yes	—
84	#107	—	2	16	no	—
85	#106	—	2	16	no	—
86	#97	Q₈×C₅₉	1	16	yes	—
87	C₄×C₈	D₄×C₅₉	1	8	yes	—
88	#95	—	2	8	no	—
89	C₂²×C₄	—	2	8	no	—
90	C₂²×C₄	C₂×D₄×C₅₉	1	2	yes	—
91	C₂²×C₄	C₂×D₄×C₅₉	1	4	yes	—
92	C₂²×C₄	C₂⁴×C₅₉	1	1	yes	characteristic
93	C₂×C₈	C₂×D₄×C₅₉	1	8	yes	—
94	C₂×C₈	C₂×Q₈×C₅₉	1	16	yes	—
95	C₄⋊C₄	—	2	16	no	—
96	C₄⋊C₄	—	4	16	no	—
97	C₄⋊C₄	—	4	16	no	—
98	C₄²	—	4	4	no	—
99	C₄²	C₂×D₄×C₅₉	1	4	yes	—
100	C₄²	C₂×Q₈×C₅₉	1	8	yes	—
101	C₂³	C₂²×D₄×C₅₉	1	1	yes	characteristic
102	C₂×C₄	—	2	8	no	—
103	C₂×C₄	—	2	4	no	—
104	C₂×C₄	—	4	8	no	—
105	C₂×C₄	—	4	16	no	—
106	C₂×C₄	#127×C₅₉	1	4	yes	—
107	C₂×C₄	C₄⋊Q₈×C₅₉	1	8	yes	—
108	C₂×C₄	C₂²×D₄×C₅₉	1	2	yes	—
109	C₂×C₄	C₂²×Q₈×C₅₉	1	4	yes	—
110	C₈	C₄⋊Q₈×C₅₉	1	16	yes	—
111	C₂²	C₂×#127×C₅₉	1	1	yes	characteristic
112	C₂²	C₂×C₄⋊Q₈×C₅₉	1	2	yes	—
113	C₂²	C₅₉×#575	1	4	yes	—
114	C₄	—	2	4	no	—
115	C₄	—	2	8	no	—
116	C₄	—	8	8	no	—
117	C₄	C₂×C₄⋊Q₈×C₅₉	1	4	yes	—
118	C₂	C₅₉×#2868	1	1	yes	characteristic
119	C₂	C₅₉×#3150	1	2	yes	—
120	C₂	C₅₉×#3166	1	4	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₅₉×#499

C₂

yes

maximal

C₅₉×#2859

C₂

yes

maximal

C₅₉×#1847

C₂

yes

maximal

C₄×#97×C₅₉

C₂

yes

maximal, characteristic

C₂×#125×C₅₉

C₂²

yes

—

C₅₉×#499

—

C₂×#107×C₅₉

C₂²

yes

—

C₂×#106×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

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

—

#107×C₅₉

—

#106×C₅₉

—

#97×C₅₉

Q₈

yes

—

C₄×C₈×C₅₉

D₄

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×D₄

yes

—

C₂×C₈×C₅₉

C₂×Q₈

yes

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄⋊C₄×C₅₉

—

C₄²×C₅₉

—

C₄²×C₅₉

C₂×D₄

yes

—

C₄²×C₅₉

C₂×Q₈

yes

—

C₂³×C₅₉

C₂²×D₄

yes

characteristic

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

—

C₂×C₄×C₅₉

#127

yes

—

C₂×C₄×C₅₉

C₄⋊Q₈

yes

—

C₂×C₄×C₅₉

C₂²×D₄

yes

—

C₂×C₄×C₅₉

C₂²×Q₈

yes

—

C₈×C₅₉

C₄⋊Q₈

yes

—

#33315

C₅₉

yes

maximal, characteristic, direct product factor, Sylow

C₂²×C₅₉

C₂×#127

yes

characteristic

C₂²×C₅₉

C₂×C₄⋊Q₈

yes

—

C₂²×C₅₉

#575

yes

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

—

C₄×C₅₉

C₂×C₄⋊Q₈

yes

—

C₂×#499

C₂×C₅₉

yes

—

#2859

C₂×C₅₉

yes

—

#1847

C₂×C₅₉

yes

—

C₄×#97

C₂×C₅₉

yes

C₂×C₅₉

yes

C₂×C₅₉

yes

—

C₂×C₅₉

#3166

yes

—

C₂×#125

C₂²×C₅₉

yes

—

#499

—

C₂×#107

C₂²×C₅₉

yes

—

C₂×#106

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

C₅₉

#33315

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

—

#107

—

#106

—

#97

Q₈×C₅₉

yes

—

C₄×C₈

D₄×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×D₄×C₅₉

yes

—

C₂×C₈

C₂×Q₈×C₅₉

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄²

—

C₄²

C₂×D₄×C₅₉

yes

—

100

C₄²

C₂×Q₈×C₅₉

yes

—

101

C₂³

C₂²×D₄×C₅₉

yes

characteristic

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

#127×C₅₉

yes

—

107

C₂×C₄

C₄⋊Q₈×C₅₉

yes

—

108

C₂×C₄

C₂²×D₄×C₅₉

yes

—

109

C₂×C₄

C₂²×Q₈×C₅₉

yes

—

110

C₈

C₄⋊Q₈×C₅₉

yes

—

111

C₂²

C₂×#127×C₅₉

yes

characteristic

112

C₂²

C₂×C₄⋊Q₈×C₅₉

yes

—

113

C₂²

C₅₉×#575

yes

—

114

C₄

—

115

C₄

—

116

C₄

—

117

C₄

C₂×C₄⋊Q₈×C₅₉

yes

—

118

C₂

C₅₉×#2868

yes

characteristic

119

C₂

C₅₉×#3150

yes

—

120

C₂

C₅₉×#3166

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
50. #33315	C₅₉	direct (N × H)
75. C₅₉	#33315	direct (N × H)

H ≅ G/N

type

50. #33315

C₅₉

direct (N × H)

75. C₅₉

#33315

direct (N × H)

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

subgroup	index
C₂×C₅₉×#499	2
C₅₉×#2859	2
C₅₉×#1847	2
C₄×#97×C₅₉	2
#33315	59

subgroup

index

C₂×C₅₉×#499

C₅₉×#2859

C₅₉×#1847

C₄×#97×C₅₉

#33315

Subgroups — C₅₉×#33315 #28445424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C59×#33315 #28445424

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅₉×#33315 #28445424