Finite Group Databasebeta

← #14290987

Subgroups — #14290987

Order 1920.

364 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 72 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#11756445C211yesmaximal, characteristic, complemented
2C5×#5067C211yesmaximal, characteristic
3#11746908C212yesmaximal
4C3×#64763C211yesmaximal, characteristic, complemented
5#11745851C212yesmaximal, complemented
6#10602043—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91779—22no—
9#91778—22no—
10#91778—22no—
11#91759C2212yes—
12C5×#874C2211yescharacteristic
13C5×#809—22no—
14C5×#803C2211yescharacteristic
15C3×#3935C2212yes—
16#90967—22no—
17#90967—22no—
18#68375—51nomaximal, Hall
19C5⋊#564—31no—
20C5×#490—31no—
21#65360—32no—
22#64763D311yescharacteristic, complemented
23#64685—32no—
24C2×C5×D12—22no—
25C2×C5×D12—21no—
26C3×C5×C4⋊C4—22no—
27C3×C5×C4⋊C4D412yes—
28C3×C42×C5C2311yescharacteristic
29C4⋊Dic15—22no—
30C4⋊Dic15D412yes—
31C4⋊Dic15D412yes—
32#6712—22no—
33#6712—22no—
34#6712—22no—
35#6712—22no—
36C4×Dic15—22no—
37C2×C5×C3⋊C8—21no—
38C2×C3×#168—22no—
39C3⋊#564—51no—
40#5067D511yescharacteristic
41#4713—52no—
42C3×#330—51no—
43#4465—52no—
44C5×#127—31no—
45C5×#125C2×D311yescharacteristic
46#4036—62no—
47#4035—62no—
48#4035—62no—
49#4016—32no—
50C5×#102—62no—
51C5×#97—31no—
52#3964—62no—
53#3964—62no—
54#3935C2×D312yes—
55#1658—151noSylow
56C22×C5×D3—41no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D412yes—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×Dic15—22no—
61C2×Dic15—22no—
62C5×D12—42no—
63C5×D12—44no—
64C3×#168—42no—
65C5×C3⋊C8—41no—
66C3×#125C2×D511yescharacteristic
67#890—102no—
68#889—102no—
69#889—102no—
70#874C2×D511yescharacteristic
71#870—52no—
72C3×#97—52no—
73#821—102no—
74#821—102no—
75#809—22no—
76#803C2×D511yescharacteristic
77C2×C5×D4—61no—
78C2×C5×D4—62no—
79C2×C5×C8—61no—
80C5×C4⋊C4—22no—
81C5×C4⋊C4D1212yes—
82C42×C5C22×D311yescharacteristic
83C4⋊Dic5—32no—
84C4⋊Dic5—32no—
85C4⋊Dic5—62no—
86#683—62no—
87#683—62no—
88#683—62no—
89#683—62no—
90C4×Dic5—62no—
91C2×#168—22no—
92#564—151no—
93#490—31no—
94#490—152no—
95#330—51no—
96#330—152no—
97C22×C3×C5#12011yescharacteristic
98C2×C5×D3—81no—
99C2×C5×D3—82no—
100C3×C4×C5—21no—
101C3×C4×C5—22no—
102C3×C4×C5—42no—
103Dic15—42no—
104Dic15—42no—
105C2×D12—22no—
106C2×D12—21no—
107C2×C3×C8—102no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4C22⋊D512yes—
110C3×C42C22×D511yescharacteristic
111C4⋊Dic3—52no—
112C4⋊Dic3—52no—
113C4⋊Dic3—102no—
114Dic3⋊C4—102no—
115Dic3⋊C4—102no—
116Dic3⋊C4—102no—
117Dic3⋊C4—102no—
118C4×Dic3—102no—
119C2×C3⋊C8—21no—
120C23×C5—121no—
121C5×D4—122no—
122C5×D4—124no—
123C2×C4×C5—22no—
124C2×C4×C5C2×D1211yescharacteristic
125C2×C4×C5D3×D412yes—
126C2×Dic5—62no—
127C2×Dic5—62no—
128C5×C8—121no—
129#168—42no—
130#127—31no—
131#125—152no—
132#125—302no—
133#125—302no—
134#125—302no—
135#125D3×D511yescharacteristic
136#102—62no—
137#102—302no—
138#102—302no—
139#97—31no—
140#97—52no—
141C2×C3×C5#45411yescharacteristic
142C2×C3×C5#45412yes—
143C5×D3—161no—
144C22×D3—41no—
145C2×C3×C4—22no—
146C2×C3×C4D4×D512yes—
147C2×C3×C4C2×C22⋊D511yescharacteristic
148C2×Dic3—102no—
149C2×Dic3—102no—
150D12—42no—
151D12—44no—
152C3×C8—202no—
153C3⋊C8—41no—
154C22×C5—241no—
155C22×C5—242no—
156C22×C5#88211yescharacteristic
157C4×C5—21no—
158C4×C5—22no—
159C4×C5—42no—
160Dic5—122no—
161Dic5—122no—
162C2×D4—61no—
163C2×D4—62no—
164C2×C8—61no—
165C2×C8—102no—
166C4⋊C4—22no—
167C4⋊C4—152no—
168C4⋊C4—152no—
169C4⋊C4—302no—
170C4⋊C4—302no—
171C4⋊C4—302no—
172C4⋊C4—302no—
173C4⋊C4—302no—
174C4⋊C4#120312yes—
175C42—302no—
176C42C2×D3×D511yescharacteristic
177C3×C5#165811yescharacteristic, complemented, Hall
178C22×C3#408311yescharacteristic
179C2×D3—81no—
180C2×D3—82no—
181C3×C4—21no—
182C3×C4—22no—
183C3×C4—42no—
184Dic3—202no—
185Dic3—202no—
186C2×C5—481no—
187C2×C5#475311yescharacteristic
188C2×C5#482712yes—
189C23—121no—
190D4—122no—
191D4—124no—
192C2×C4—22no—
193C2×C4—302no—
194C2×C4—302no—
195C2×C4C2×#120311yescharacteristic
196C2×C4#679012yes—
197C8—121no—
198C8—202no—
199C2×C3#6535111yescharacteristic
200C2×C3#6549012yes—
201D3—161no—
202C5#6837511yescharacteristic, complemented, Sylow
203C22—241no—
204C22—242no—
205C22#9157311yescharacteristic
206C4—21no—
207C4—22no—
208C4—42no—
209C4—602no—
210C4—602no—
211C3#1060204311yescharacteristic, complemented, Sylow
212C2—481no—
213C2#1174938911yescharacteristic
214C2#1174946112yes—
subgroupG/H
centerC22#91573
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC5×#874C22
hypercenter#125D3×D5
hypocenterC3×C5#1658
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
1. #11756445C2semidirect
4. C3×#64763C2semidirect
5. #11745851C2semidirect
22. #64763D3semidirect
177. C3×C5#1658semidirect
202. C5#68375semidirect
211. C3#10602043semidirect

Maximal subgroups

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

subgroupindex
#117564452
C5×#50672
#117469082
C3×#647632
#117458512
#106020433
#683755