Finite Group Databasebeta

← D53×#2845 #27590679

Subgroups — D53×#2845 #27590679

Order 13568.

1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.

normal subgroups only

This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20282990C213yesmaximal, complemented
2#20282989C2112yesmaximal, complemented
3#398×D53C2112yesmaximal
4#382×D53C213yesmaximal
5C53×#2845C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×D53C2216yes—
7C2×C4⋊C4×D53C22112yes—
8C2×C42×D53C2211yescharacteristic
9#16810557C22112yes—
10#16810557C22112yes—
11#16810556C22112yes—
12#16810556C22112yes—
13#16810555C22112yes—
14#16810554C22112yes—
15#16810553C22112yes—
16#16810489C2213yes—
17#16810488C2216yes—
18#16810487C22112yes—
19#95×D53C22112yes—
20#95×D53C2214yes—
21C53×#398C22112yes—
22C53×#382C2213yes—
23C22×C4×D53C23112yes—
24C22×C4×D53C2313yes—
25C2×C4⋊Dic53C23112yes—
26C2×C4⋊Dic53C2316yes—
27C2×#11719919C23112yes—
28C2×#11719919C23112yes—
29C2×#11719919C23112yes—
30C4⋊C4×D53—412no—
31C4⋊C4×D53—424no—
32C2×C4×Dic53C2313yes—
33C42×D53Q818yes—
34#13133124C23112yes—
35#13133124C23112yes—
36#13133124C23112yes—
37#13133124C23112yes—
38C2×C4⋊C4×C53C23112yes—
39C2×C4⋊C4×C53C2316yes—
40C2×C42×C53C2311yescharacteristic
41#95×C53C23112yes—
42#95×C53C2314yes—
43C23×D53C2411yescharacteristic
44C22×C4×C53C24112yes—
45C22×C4×C53C2413yes—
46C22×Dic53C24112yes—
47C22×Dic53C2413yes—
48C2×C4×D53—26no—
49C2×C4×D53—26no—
50C2×C4×D53—224no—
51C2×C4×D53—224no—
52C2×C4×D53—224no—
53C2×C4×D53C2×Q8112yes—
54C4⋊C4×C53—46no—
55C4⋊C4×C53—412no—
56C42×C53C2×Q814yes—
57C4⋊Dic53—412no—
58C4⋊Dic53—46no—
59#11719919—412no—
60#11719919—412no—
61#11719919—412no—
62C4×Dic53C2×Q8112yes—
63C23×C53C2511yescharacteristic
64C22×D53C22×Q812yes—
65C22×D53H(5,𝔽2)16yes—
66C22×D532−1+416yes—
67C2×C4×C53—23no—
68C2×C4×C53—23no—
69C2×C4×C53—212no—
70C2×C4×C53—212no—
71C2×C4×C53—212no—
72C2×C4×C53C22×Q816yes—
73C2×Dic53—23no—
74C2×Dic53—23no—
75C2×Dic53—212no—
76C2×Dic53—212no—
77C2×Dic53—212no—
78C2×Dic53C22×Q816yes—
79C4×D53—224no—
80C4×D53—448no—
81C2×#2845—531nomaximal, Sylow
82C22×C53C23×Q811yescharacteristic
83C22×C53C2×H(5,𝔽2)13yes—
84C22×C53C2×2−1+413yes—
85C2×D53#544112yes—
86C2×D53#562112yes—
87C2×D53#56414yes—
88C4×C53—26no—
89C4×C53—412no—
90Dic53—26no—
91Dic53—412no—
92#2845—5312no—
93#2845—533no—
94#2845D5311yescharacteristic, direct product factor
95C2×#398—5312no—
96C2×#382—533no—
97C2×C53C2×#54413yes—
98C2×C53C2×#56213yes—
99C2×C53C2×#56411yescharacteristic
100D53#284518yesdirect product factor
101C22×C4⋊C4—5312no—
102C22×C4⋊C4—536no—
103C22×C42—531no—
104#398—5312no—
105#398—5312no—
106#398—5312no—
107#398—5312no—
108#398—5312no—
109#398—5312no—
110#398—5312no—
111#398C2×D53112yes—
112#382—536no—
113#382—533no—
114#382—5312no—
115#382C2×D5313yes—
116C2×#95—534no—
117C2×#95—5312no—
118C53C2×#284511yescharacteristic, complemented, Sylow
119C23×C4—533no—
120C23×C4—5312no—
121C2×C4⋊C4—5312no—
122C2×C4⋊C4—5312no—
123C2×C4⋊C4—5312no—
124C2×C4⋊C4—536no—
125C2×C4⋊C4—5312no—
126C2×C4⋊C4—21212no—
127C2×C4⋊C4—21224no—
128C2×C4⋊C4C22×D5316yes—
129C2×C4⋊C4C22×D53112yes—
130C2×C42—533no—
131C2×C42—538no—
132C2×C42C22×D5311yescharacteristic
133#95—5312no—
134#95—5312no—
135#95—5312no—
136#95—5312no—
137#95C22×D53112yes—
138#95C22×D5314yes—
139C24—531no—
140C22×C4—533no—
141C22×C4—5312no—
142C22×C4—5312no—
143C22×C4—1066no—
144C22×C4—1066no—
145C22×C4—10624no—
146C22×C4—10624no—
147C22×C4—10624no—
148C22×C4C23×D53112yes—
149C22×C4C23×D5313yes—
150C4⋊C4—46no—
151C4⋊C4—412no—
152C4⋊C4—21212no—
153C4⋊C4—21212no—
154C4⋊C4—21212no—
155C4⋊C4—2126no—
156C4⋊C4—21212no—
157C42—5312no—
158C42Q8×D5314yes—
159C23—532no—
160C23—536no—
161C23—536no—
162C23C24×D5311yescharacteristic
163C2×C4—23no—
164C2×C4—23no—
165C2×C4—212no—
166C2×C4—212no—
167C2×C4—212no—
168C2×C4—536no—
169C2×C4—10624no—
170C2×C4—1063no—
171C2×C4—1063no—
172C2×C4—10612no—
173C2×C4—10612no—
174C2×C4—10612no—
175C2×C4—21248no—
176C2×C4C2×Q8×D5316yes—
177C22—5312no—
178C22—534no—
179C22—5312no—
180C22C22×Q8×D5311yescharacteristic
181C22H(5,𝔽2)×D5313yes—
182C222−1+4×D5313yes—
183C4—26no—
184C4—412no—
185C4—1066no—
186C4—21212no—
187C2—538no—
188C2#544×D5313yes—
189C2#562×D5313yes—
190C2#564×D5311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D53
commutator, socle, cosocleC23×C53C25
FittingC53×#2845C2
prime radicalC23×D53C24
hypercenter#2845D53
hypocenterC53C2×#2845
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #2845

Complements

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

NH ≅ G/Ntype
1. #20282990C2semidirect
2. #20282989C2semidirect
5. C53×#2845C2semidirect
94. #2845D53direct (N × H)
100. D53#2845direct (N × H)
118. C53C2×#2845semidirect

Maximal subgroups

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

subgroupindex
#202829902
#202829892
#398×D532
#382×D532
C53×#28452
C2×#284553