Finite Group Databasebeta

← #14290988

Subgroups — #14290988

Order 1920.

364 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 76 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
1C5×C3⋊#564C211yesmaximal, characteristic, complemented
2C3×#65356C211yesmaximal, characteristic
3#11746897C212yesmaximal
4#11746364C211yesmaximal, characteristic, complemented
5#11745850C212yesmaximal, complemented
6#10602753—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C5×#890—22no—
9C5×#889—22no—
10C5×#889—22no—
11C5×#870C2212yes—
12C3×#4020C2211yescharacteristic
13#91087C2212yes—
14C3×#3941—22no—
15C3×#3935C2211yescharacteristic
16#90964—22no—
17#90964—22no—
18#71250—51nomaximal, Hall
19C5×#564—31no—
20#65356—32no—
21#65356D311yescharacteristic
22#64763—32no—
23#64763—31no—
24C2×C3×D20—22no—
25C2×C3×D20—21no—
26C3×C5×C4⋊C4—22no—
27C3×C5×C4⋊C4D412yes—
28C3×C42×C5C2311yescharacteristic
29C2×C3⋊#168—22no—
30C5×C4⋊Dic3—22no—
31C5×C4⋊Dic3D412yes—
32C5×C4⋊Dic3D412yes—
33C5×Dic3⋊C4—22no—
34C5×Dic3⋊C4—22no—
35C5×Dic3⋊C4—22no—
36C5×Dic3⋊C4—22no—
37C4×C5×Dic3—22no—
38C2×C3×#168—21no—
39C3⋊#564D511yescharacteristic, complemented
40C3×#490—51no—
41#5071—52no—
42#4543—51no—
43#4465—52no—
44C5×#125—32no—
45C5×#125—62no—
46C5×#125—62no—
47C5×#125—62no—
48C5×#125C2×D311yescharacteristic
49#4020C2×D311yescharacteristic
50#3941—22no—
51#3941—62no—
52#3941—62no—
53#3935—32no—
54#3935C2×D311yescharacteristic
55#1658—151noSylow
56C22×C3×D5—41no—
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C2×D412yes—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C5×Dic3—22no—
61C2×C5×Dic3—22no—
62C3×D20—42no—
63C3×D20—44no—
64C3⋊#168—42no—
65C3×#168—41no—
66C3×#127—51no—
67C3×#125C2×D511yescharacteristic
68#890—22no—
69#889—22no—
70#889—22no—
71#870C2×D512yes—
72C3×#102—102no—
73C3×#97—51no—
74#832—102no—
75#832—102no—
76#803—52no—
77C2×D20—22no—
78C2×D20—21no—
79C5×C4⋊C4—22no—
80C5×C4⋊C4—32no—
81C5×C4⋊C4—32no—
82C5×C4⋊C4—62no—
83C5×C4⋊C4—62no—
84C5×C4⋊C4—62no—
85C5×C4⋊C4—62no—
86C5×C4⋊C4—62no—
87C5×C4⋊C4#6712yes—
88C42×C5—62no—
89C42×C5C22×D311yescharacteristic
90C2×#168—21no—
91C2×#168—62no—
92#564—31no—
93#490—51no—
94#490—152no—
95#330—152no—
96#330—151no—
97C22×C3×C5#12011yescharacteristic
98C2×C3×D5—82no—
99C2×C3×D5—81no—
100C3×C4×C5—21no—
101C3×C4×C5—22no—
102C3×C4×C5—42no—
103C5×Dic3—42no—
104C5×Dic3—42no—
105C2×C3×D4—102no—
106C2×C3×D4—101no—
107C2×C3×C8—101no—
108C3×C4⋊C4—22no—
109C3×C4⋊C4C22⋊D512yes—
110C3×C42C22×D511yescharacteristic
111C4⋊Dic3—22no—
112C4⋊Dic3C22⋊D512yes—
113C4⋊Dic3C22⋊D512yes—
114Dic3⋊C4—22no—
115Dic3⋊C4—22no—
116Dic3⋊C4—22no—
117Dic3⋊C4—22no—
118C4×Dic3—22no—
119C2×C3⋊C8—102no—
120C22×D5—41no—
121C2×C4×C5—22no—
122C2×C4×C5—62no—
123C2×C4×C5—62no—
124C2×C4×C5D3×D412yes—
125C2×C4×C5C2×#6711yescharacteristic
126D20—44no—
127D20—42no—
128#168—41no—
129#168—122no—
130#127—51no—
131#125—32no—
132#125—62no—
133#125—62no—
134#125—62no—
135#125D3×D511yescharacteristic
136#102—102no—
137#102—302no—
138#102—302no—
139#97—51no—
140#97—152no—
141C2×C3×C5#45412yes—
142C2×C3×C5#45411yescharacteristic
143C3×D5—161no—
144C23×C3—201no—
145C3×D4—204no—
146C3×D4—202no—
147C2×C3×C4—22no—
148C2×C3×C4C2×C22⋊D511yescharacteristic
149C2×C3×C4C2×C22⋊D512yes—
150C2×Dic3—22no—
151C2×Dic3—22no—
152C3×C8—201no—
153C3⋊C8—202no—
154C22×C5#93711yescharacteristic
155C2×D5—82no—
156C2×D5—81no—
157C4×C5—22no—
158C4×C5—21no—
159C4×C5—42no—
160C4×C5—122no—
161C4×C5—122no—
162C2×D4—101no—
163C2×D4—102no—
164C2×C8—101no—
165C2×C8—302no—
166C4⋊C4—22no—
167C4⋊C4—32no—
168C4⋊C4—32no—
169C4⋊C4—62no—
170C4⋊C4—62no—
171C4⋊C4—62no—
172C4⋊C4—62no—
173C4⋊C4—62no—
174C4⋊C4#120112yes—
175C42—62no—
176C42C2×D3×D511yescharacteristic
177C3×C5#165811yescharacteristic, complemented, Hall
178C22×C3—401no—
179C22×C3—402no—
180C22×C3#409911yescharacteristic
181C3×C4—22no—
182C3×C4—21no—
183C3×C4—42no—
184Dic3—42no—
185Dic3—42no—
186C2×C5#506211yescharacteristic
187C2×C5#520112yes—
188D5—161no—
189C23—201no—
190D4—202no—
191D4—204no—
192C2×C4—22no—
193C2×C4—62no—
194C2×C4—62no—
195C2×C4C2×#120111yescharacteristic
196C2×C4D3×C22⋊D512yes—
197C8—201no—
198C8—602no—
199C2×C3—801no—
200C2×C3#6553411yescharacteristic
201C2×C3#6553412yes—
202C5#7125011yescharacteristic, complemented, Sylow
203C22—401no—
204C22—402no—
205C22#9156811yescharacteristic
206C4—21no—
207C4—22no—
208C4—42no—
209C4—122no—
210C4—122no—
211C3#1060275311yescharacteristic, complemented, Sylow
212C2—801no—
213C2#1174938611yescharacteristic
214C2#1174945812yes—
subgroupG/H
centerC22#91568
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
prime radicalC3×#4020C22
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. C5×C3⋊#564C2semidirect
4. #11746364C2semidirect
5. #11745850C2semidirect
39. C3⋊#564D5semidirect
177. C3×C5#1658semidirect
202. C5#71250semidirect
211. C3#10602753semidirect

Maximal subgroups

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

subgroupindex
C5×C3⋊#5642
C3×#653562
#117468972
#117463642
#117458502
#106027533
#712505