Finite Group Databasebeta

← #14290984

Subgroups — #14290984

Order 1920.

364 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 75 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
2#11751168C211yesmaximal, characteristic
3#11750814C212yesmaximal
4C3×C5×#330C211yesmaximal, characteristic, complemented
5#11746286C212yesmaximal, complemented
6#10599168—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8#91779—22no—
9#91778—22no—
10#91778—22no—
11#91763C2211yescharacteristic
12#91759C2212yes—
13C3×C5×#97C2212yes—
14#91105—22no—
15#91105—22no—
16#91093—22no—
17#91087C2211yescharacteristic
18#68375—51nomaximal, Hall
19C5⋊#564—31no—
20#65356—31no—
21#65002—32no—
22C5×#330D311yescharacteristic, complemented
23#64685—32no—
24C2×D60—21no—
25C2×D60—22no—
26C2×C3×C5×C8—22no—
27C3×C5×C4⋊C4—22no—
28C3×C5×C4⋊C4D412yes—
29C3×C42×C5C2311yescharacteristic
30C4⋊Dic15—22no—
31C4⋊Dic15D412yes—
32C4⋊Dic15D412yes—
33#6712—22no—
34#6712—22no—
35#6712—22no—
36#6712—22no—
37C4×Dic15—22no—
38C2×C3⋊#168—21no—
39C3⋊#564—51no—
40#5067—51no—
41#4713—52no—
42C3×#330D511yescharacteristic, complemented
43#4465—52no—
44C5×#125C2×D311yescharacteristic
45#4036—62no—
46#4035—62no—
47#4035—62no—
48#4020—31no—
49#4016—32no—
50C5×#97C2×D312yes—
51#3953—62no—
52#3953—62no—
53#3941—62no—
54#3935—31no—
55#1658—151noSylow
56C22×D15—41no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×Dic15—22no—
61C2×Dic15—22no—
62D60—42no—
63D60—44no—
64C3×C5×C8—42no—
65C3⋊#168—41no—
66C3×#125C2×D511yescharacteristic
67#890—102no—
68#889—102no—
69#889—102no—
70#874—51no—
71#870—52no—
72C3×#97C2×D512yes—
73#821—102no—
74#821—102no—
75#809—102no—
76#803—51no—
77C2×D20—61no—
78C2×D20—62no—
79C2×C5×C8—22no—
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—61no—
92#564—151no—
93#490—151no—
94#490—152no—
95#330—152no—
96#330D1511yescharacteristic, complemented
97C22×C3×C5#12011yescharacteristic
98C2×D15—81no—
99C2×D15—82no—
100C3×C4×C5—21no—
101C3×C4×C5—22no—
102C3×C4×C5—42no—
103Dic15—42no—
104Dic15—42no—
105C2×D12—101no—
106C2×D12—102no—
107C2×C3×C8—22no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4D2012yes—
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—101no—
120C22×D5—121no—
121C2×C4×C5—22no—
122C2×C4×C5C2×D1211yescharacteristic
123C2×C4×C5D3×D412yes—
124C2×Dic5—62no—
125C2×Dic5—62no—
126D20—122no—
127D20—124no—
128C5×C8—42no—
129#168—121no—
130#127—151no—
131#125—152no—
132#125—302no—
133#125—302no—
134#125—302no—
135#125C2×D1511yescharacteristic
136#102—302no—
137#102—302no—
138#102—302no—
139#97—151no—
140#97C2×D1512yes—
141C2×C3×C5#45411yescharacteristic
142C2×C3×C5#45412yes—
143D15—161no—
144C22×D3—201no—
145C2×C3×C4—22no—
146C2×C3×C4C2×D2011yescharacteristic
147C2×C3×C4D4×D512yes—
148C2×Dic3—102no—
149C2×Dic3—102no—
150D12—202no—
151D12—204no—
152C3×C8—42no—
153C3⋊C8—201no—
154C22×C5#88211yescharacteristic
155C2×D5—241no—
156C2×D5—242no—
157C4×C5—21no—
158C4×C5—22no—
159C4×C5—42no—
160Dic5—122no—
161Dic5—122no—
162C2×D4—301no—
163C2×D4—302no—
164C2×C8—22no—
165C2×C8—301no—
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⋊C4D6012yes—
175C42—302no—
176C42C22×D1511yescharacteristic
177C3×C5#165811yescharacteristic, complemented, Hall
178C22×C3#402811yescharacteristic
179C2×D3—401no—
180C2×D3—402no—
181C3×C4—21no—
182C3×C4—22no—
183C3×C4—42no—
184Dic3—202no—
185Dic3—202no—
186C2×C5#475311yescharacteristic
187C2×C5#482712yes—
188D5—481no—
189C23—601no—
190D4—604no—
191D4—602no—
192C2×C4—22no—
193C2×C4—302no—
194C2×C4—302no—
195C2×C4C2×D6011yescharacteristic
196C2×C4D4×D1512yes—
197C8—42no—
198C8—601no—
199C2×C3#6504211yescharacteristic
200C2×C3#6511612yes—
201D3—801no—
202C5#6837511yescharacteristic, complemented, Sylow
203C22—1202no—
204C22—1201no—
205C22#9177111yescharacteristic
206C4—22no—
207C4—21no—
208C4—42no—
209C4—602no—
210C4—602no—
211C3#1059916811yescharacteristic, complemented, Sylow
212C2—2401no—
213C2#1175085411yescharacteristic
214C2#1175092812yes—
subgroupG/H
centerC22#91771
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#330C2
socleC22×C3×C5#120
prime radical#91763C22
hypercenter#330D15
hypocenterC3×C5#1658
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #11756445C2semidirect
4. C3×C5×#330C2semidirect
5. #11746286C2semidirect
22. C5×#330D3semidirect
42. C3×#330D5semidirect
96. #330D15semidirect
177. C3×C5#1658semidirect
202. C5#68375semidirect
211. C3#10599168semidirect

Maximal subgroups

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

subgroupindex
#117564452
#117511682
#117508142
C3×C5×#3302
#117462862
#105991683
#683755