Finite Group Databasebeta

← C3⋊D3×#4020 #72231588

Subgroups — C3⋊D3×#4020 #72231588

Order 2880.

2988 conjugacy classes of subgroups; only the 364 normal subgroups are shown.

normal subgroups only

This group has 2988 conjugacy classes of subgroups — too many to draw. Only its 364 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
1C2×C3⋊D3×D20C216yesmaximal, complemented
2#13088143C211yesmaximal, characteristic, complemented
3C42×C5×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#4020C211yesmaximal, characteristic, complemented
5#13086928C216yesmaximal, complemented
6D3×#4020—34nomaximal
7C22×D5×C3⋊D3C2214yes—
8C2×C4⋊(C3⋊D15)C2216yescomplemented
9C2×C4×C5×C3⋊D3C2213yes—
10C2×C32×D20C2216yescomplemented
11C2×#67139C22112yescomplemented
12C3⋊D3×D20—224no—
13C32×C42×C5C2211yescharacteristic, complemented
14C4×C5×C3⋊Dic3C2213yescomplemented
15C3⋊D3×#127—51nomaximal, Hall
16C2×D3×D20—324no—
17#91763—34no—
18C42×C5×D3—34no—
19C3×#4020D314yescomplemented
20#91458—324no—
21C22×C3⋊D15C2314yes—
22C22×C5×C3⋊D3C2311yescharacteristic
23C22×C32×D5C2314yes—
24C2×D5×C3⋊D3—224no—
25C2×C32×C4×C5C2313yes—
26C4⋊(C3⋊D15)—212no—
27C2×C5×C3⋊Dic3C2313yes—
28C4×C5×C3⋊D3D4112yescomplemented
29C32×D20—212no—
30#67139—224no—
31C2×#4020—91noHall
32C2×D4×C3⋊D3—56no—
33C32×#127—51no—
34#64149—56no—
35#64083—51no—
36C42×C3⋊D3D511yescharacteristic, complemented
37C22×D3×D5—316no—
38C2×D60—324no—
39C2×C4×C5×D3—312no—
40C2×C3×D20C2×D3124yescomplemented
41C2×#1202—348no—
42D3×D20—696no—
43C3×C42×C5C2×D314yescomplemented
44C4×C5×Dic3—312no—
45D3×#127—154no—
46C22×C32×C5C2411yescharacteristic
47C2×C3⋊D15—212no—
48C2×C5×C3⋊D3C2×D416yes—
49C2×C32×D5—212no—
50D5×C3⋊D3—416no—
51C32×C4×C5C2×D416yescomplemented
52C5×C3⋊Dic3C2×D416yescomplemented
53C22×D20—96no—
54C2×C42×C5—91no—
55#4020—96no—
56#4020—91no—
57#4020C3⋊D311yescharacteristic, direct product factor
58C23×C3⋊D3—54no—
59C2×C32×D4—56no—
60C2×#638—512no—
61D4×C3⋊D3—1024no—
62C2×C4⋊(C3⋊D3)—56no—
63C2×C4×C3⋊D3C2×D513yes—
64C32×C42C2×D511yescharacteristic, complemented
65C4×C3⋊Dic3C2×D513yescomplemented
66C22×D15—316no—
67C22×C5×D3—34no—
68C22×C3×D5C22×D3116yes—
69C2×D3×D5—696no—
70C2×C3×C4×C5C22×D3112yes—
71D60—648no—
72C2×C5×Dic3—312no—
73C4×C5×D3—348no—
74C3×D20—248no—
75#1202—696no—
76C2×D3×D4—1524no—
77C3×#127—54no—
78#940—1524no—
79#874—154no—
80C42×D3—34no—
81C2×C32×C5C22×D413yes—
82C3⋊D15—44no—
83C5×C3⋊D3#12714yescomplemented
84C32×D5—44no—
85C23×D5—94no—
86C22×C4×C5—93no—
87C2×D20—912no—
88C2×D20—96no—
89C2×D20—1824no—
90C2×D20C2×C3⋊D316yescomplemented
91C42×C5—93no—
92C42×C5C2×C3⋊D311yescharacteristic, complemented
93C23×C32—54no—
94C22×C3⋊D3—54no—
95C22×C3⋊D3—1024no—
96C22×C3⋊D3C22×D511yescharacteristic
97C32×D4—1012no—
98C2×C32×C4C22×D513yes—
99#638—1024no—
100C2×C3⋊Dic3C22×D513yes—
101C4⋊(C3⋊D3)—1012no—
102C4×C3⋊D3D20112yescomplemented
103C2×#127—451noSylow
104C22×C3×C5C23×D314yes—
105C2×D15—648no—
106C2×C5×D3—324no—
107C2×C3×D5—248no—
108D3×D5—1264no—
109C3×C4×C5D3×D4124yescomplemented
110C5×Dic3—324no—
111C23×D3—1516no—
112C2×C3×D4—524no—
113C2×#67—1548no—
114D3×D4—3096no—
115C2×D12—1524no—
116C2×C4×D3—312no—
117C3×C42D3×D514yescomplemented
118C4×Dic3—312no—
119C32×C5C2×#12711yescharacteristic, complemented, Hall
120C23×C5—91no—
121C22×D5—94no—
122C22×D5—1824no—
123C22×D5C22×C3⋊D314yes—
124C2×C4×C5—93no—
125C2×C4×C5—912no—
126C2×C4×C5C22×C3⋊D313yes—
127D20—212no—
128D20—1824no—
129D20—1812no—
130C22×C32—1012no—
131C22×C32C23×D511yescharacteristic
132C2×C3⋊D3—1012no—
133C2×C3⋊D3—2016no—
134C2×C3⋊D3C2×D2016yes—
135C32×C4C2×D2016yescomplemented
136C3⋊Dic3C2×D2016yescomplemented
137C22×D4—456no—
138#127—51no—
139#127—456no—
140#127—451no—
141C2×C42—91no—
142C2×C3×C5C2×D3×D4112yes—
143D15—1216no—
144C3×D5—416no—
145C5×D3—316no—
146C23×C3—516no—
147C22×D3—34no—
148C22×D3—1516no—
149C22×D3—3096no—
150C3×D4—1048no—
151C2×C3×C4C2×D3×D5112yes—
152#67—3096no—
153C2×Dic3—312no—
154D12—3048no—
155C4×D3—348no—
156C22×C5—96no—
157C22×C5C23×C3⋊D311yescharacteristic
158C2×D5—212no—
159C2×D5—1812no—
160C2×D5—3616no—
161C4×C5—96no—
162C4×C5D4×C3⋊D316yescomplemented
163C2×C32—204no—
164C2×C32C22×D2013yes—
165C3⋊D3—204no—
166C3⋊D3#402014yesdirect product factor
167C24—454no—
168C2×D4—56no—
169C2×D4—4512no—
170C2×D4—456no—
171C2×D4—9024no—
172C22×C4—93no—
173C42—93no—
174C42D5×C3⋊D311yescharacteristic, complemented
175C3×C5D3×#12714yescomplemented
176C22×C3—1048no—
177C22×C3C22×D3×D514yes—
178C2×D3—324no—
179C2×D3—3048no—
180C2×D3—6064no—
181C3×C4D3×D20124yescomplemented
182Dic3—324no—
183C2×C5—94no—
184C2×C5C2×D4×C3⋊D313yes—
185D5—44no—
186D5—364no—
187C32C2×#402011yescharacteristic, complemented, Sylow
188C23—54no—
189C23—91no—
190C23—454no—
191C23—9024no—
192D4—1012no—
193D4—9024no—
194D4—9012no—
195C2×C4—93no—
196C2×C4—912no—
197C2×C4C2×D5×C3⋊D313yes—
198C2×C3—2016no—
199C2×C3C2×D3×D20112yes—
200D3—316no—
201D3—6016no—
202C5C3⋊D3×#12711yescharacteristic, complemented, Sylow
203C22—96no—
204C22—1012no—
205C22—9012no—
206C22—18016no—
207C22C22×D5×C3⋊D311yescharacteristic
208C4—96no—
209C4C3⋊D3×D2016yescomplemented
210C3D3×#402014yescomplemented
211C2—94no—
212C2—204no—
213C2—1804no—
214C2C2×C3⋊D3×D2013yes—
subgroupG/H
center, FrattiniC22C22×D5×C3⋊D3
commutator, socle, cosocleC22×C32×C5C24
FittingC32×C42×C5C22
hypercenterC42D5×C3⋊D3
hypocenterC32×C5C2×#127
LCSG ▷ C22×C32×C5 ▷ C32×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. C2×C3⋊D3×D20C2semidirect
2. #13088143C2semidirect
3. C42×C5×C3⋊D3C2semidirect
4. C32×#4020C2semidirect
5. #13086928C2semidirect
8. C2×C4⋊(C3⋊D15)C22semidirect
10. C2×C32×D20C22semidirect
11. C2×#67139C22semidirect
13. C32×C42×C5C22semidirect
14. C4×C5×C3⋊Dic3C22semidirect
19. C3×#4020D3semidirect
28. C4×C5×C3⋊D3D4semidirect
36. C42×C3⋊D3D5semidirect
40. C2×C3×D20C2×D3semidirect
43. C3×C42×C5C2×D3semidirect
51. C32×C4×C5C2×D4semidirect
52. C5×C3⋊Dic3C2×D4semidirect
57. #4020C3⋊D3direct (N × H)
64. C32×C42C2×D5semidirect
65. C4×C3⋊Dic3C2×D5semidirect
83. C5×C3⋊D3#127semidirect
90. C2×D20C2×C3⋊D3semidirect
92. C42×C5C2×C3⋊D3semidirect
102. C4×C3⋊D3D20semidirect
109. C3×C4×C5D3×D4semidirect
117. C3×C42D3×D5semidirect
119. C32×C5C2×#127semidirect
135. C32×C4C2×D20semidirect
136. C3⋊Dic3C2×D20semidirect
162. C4×C5D4×C3⋊D3semidirect
166. C3⋊D3#4020direct (N × H)
174. C42D5×C3⋊D3semidirect
175. C3×C5D3×#127semidirect
181. C3×C4D3×D20semidirect
187. C32C2×#4020semidirect
202. C5C3⋊D3×#127semidirect
209. C4C3⋊D3×D20semidirect
210. C3D3×#4020semidirect

Maximal subgroups

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

subgroupindex
C2×C3⋊D3×D202
#130881432
C42×C5×C3⋊D32
C32×#40202
#130869282
D3×#40203
C3⋊D3×#1275