Finite Group Databasebeta

← #14290928

Subgroups — #14290928

Order 1920.

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

normal subgroups only

This group has 460 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
1C3×#66034C211yesmaximal, characteristic, complemented
2C5×#5067C211yesmaximal, characteristic, complemented
3#11747042C212yesmaximal, complemented
4#11746364C211yesmaximal, characteristic, complemented
5#11745846C212yesmaximal, complemented
6#10602041—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C5×#874C2211yescharacteristic
9C3×#4042—22no—
10C3×#4041—22no—
11C3×#4040—22no—
12C3×#4021C2212yes—
13C2×#6656—22no—
14C2×#6652—22no—
15#91087C2212yes—
16C5×#809—22no—
17C5×#803C2211yescharacteristic
18#71952—51nomaximal, Hall
19#66034D311yescharacteristic, complemented
20C5×#490—31no—
21#65363—32no—
22#64763—31no—
23#64684—32no—
24C2×C5×D12—22no—
25C2×C5×D12—21no—
26C2×C3×D20—22no—
27C2×C3×D20D412yes—
28C2×C3×C4×D5—22no—
29C2×C3×Dic10D412yes—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4D412yes—
32C3×C42×C5C2311yescharacteristic
33C2×C3⋊#168—22no—
34C2×C5×C3⋊C8—21no—
35C3×#685—22no—
36C3×#685—22no—
37C3×#685—22no—
38C3×#683—22no—
39#6656—44no—
40#6652—44no—
41C3×#562—51no—
42#5067D511yescharacteristic, complemented
43#5058—52no—
44#4543—51no—
45#4540—52no—
46C5×#127—31no—
47C5×#125C2×D311yescharacteristic
48C2×#687—62no—
49C2×#686—62no—
50#4042—22no—
51#4041—22no—
52#4040—22no—
53#4021C2×D312yes—
54C5×#102—62no—
55C5×#97—31no—
56#3935—32no—
57#1656—151noSylow
58C22×C5×D3—41no—
59C22×C3×D5—22no—
60C2×C3×C4×C5—22no—
61C2×C3×C4×C5C2×D412yes—
62C2×C3×C4×C5C2×D411yescharacteristic
63C5×D12—42no—
64C5×D12—42no—
65C5×D12—42no—
66C2×C3×Dic5—22no—
67C3×D20—42no—
68C3×D20—82no—
69C3×C4×D5—82no—
70C3×Dic10—42no—
71C3⋊#168—24no—
72C5×C3⋊C8—41no—
73C3×#125C2×D511yescharacteristic
74C3×#124—52no—
75C3×#123—102no—
76C3×C22⋊Q8—102no—
77C3×#121—102no—
78C2×#215—102no—
79C2×#213—102no—
80#874C2×D511yescharacteristic
81#809—22no—
82#803—52no—
83#803C2×D511yescharacteristic
84C2×C5×D4—61no—
85C2×C5×D4—62no—
86C2×D20—22no—
87C2×D20#6712yes—
88C2×C4×D5—22no—
89C2×Dic10#6712yes—
90C2×C5×C8—61no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4#6712yes—
93C42×C5C22×D311yescharacteristic
94#687—124no—
95#686—124no—
96#685—22no—
97#685—22no—
98#685—22no—
99#683—22no—
100C2×#168—62no—
101#562—51no—
102#496—152no—
103#490—31no—
104#330—151no—
105#329—152no—
106C22×C3×C5#12011yescharacteristic
107C2×C5×D3—82no—
108C2×C5×D3—81no—
109C2×C3×D5—42no—
110C2×C3×D5—42no—
111C2×C3×D5—42no—
112C3×C4×C5—22no—
113C3×C4×C5—21no—
114C3×C4×C5—42no—
115C3×Dic5—42no—
116C2×C3×Q8—52no—
117C2×C3×D4—52no—
118C2×C3×D4—102no—
119C22×C3×C4—102no—
120C2×D12—22no—
121C2×D12—21no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4—102no—
124C3×C4⋊C4C22⋊D512yes—
125C3×C22⋊C4—102no—
126C3×C22⋊C4—102no—
127C3×C22⋊C4—102no—
128C3×C42C22×D511yescharacteristic
129#215—204no—
130#213—204no—
131C2×C3⋊C8—21no—
132C2×C3⋊C8—102no—
133C23×C5—121no—
134C22×D5—22no—
135C5×D4—122no—
136C5×D4—122no—
137C5×D4—122no—
138C2×C4×C5—22no—
139C2×C4×C5C2×#6711yescharacteristic
140C2×C4×C5C2×#6712yes—
141C2×Dic5—22no—
142D20—42no—
143D20—82no—
144C4×D5—82no—
145Dic10—42no—
146C5×C8—121no—
147#168—64no—
148C2×SD16—302no—
149C2×D8—302no—
150#127—31no—
151#125D3×D511yescharacteristic
152#124—52no—
153#123—102no—
154C22⋊Q8—102no—
155#121—102no—
156#102—62no—
157#97—31no—
158#97—152no—
159C2×C3×C5#45312yes—
160C2×C3×C5#45411yescharacteristic
161C3×D5—82no—
162C5×D3—161no—
163C23×C3—102no—
164C22×D3—41no—
165C3×Q8—202no—
166C3×D4—202no—
167C3×D4—402no—
168C2×C3×C4—22no—
169C2×C3×C4—102no—
170C2×C3×C4—402no—
171C2×C3×C4D4×D512yes—
172C2×C3×C4C2×C22⋊D511yescharacteristic
173D12—42no—
174D12—42no—
175D12—42no—
176C3⋊C8—41no—
177C3⋊C8—104no—
178C22×C5—242no—
179C22×C5—241no—
180C22×C5#95311yescharacteristic
181C2×D5—42no—
182C2×D5—42no—
183C2×D5—42no—
184C4×C5—22no—
185C4×C5—21no—
186C4×C5—42no—
187Dic5—42no—
188C2×Q8—52no—
189C2×D4—52no—
190C2×D4—61no—
191C2×D4—62no—
192C2×D4—102no—
193C22×C4—102no—
194SD16—604no—
195D8—604no—
196C2×C8—61no—
197C2×C8—302no—
198C4⋊C4—22no—
199C4⋊C4—102no—
200C4⋊C4#120112yes—
201C22⋊C4—102no—
202C22⋊C4—102no—
203C22⋊C4—102no—
204C42C2×D3×D511yescharacteristic
205C3×C5#165611yescharacteristic, complemented, Hall
206C22×C3—202no—
207C22×C3—202no—
208C22×C3—202no—
209C22×C3#408311yescharacteristic
210C2×D3—81no—
211C2×D3—82no—
212C3×C4—21no—
213C3×C4—22no—
214C3×C4—42no—
215C3×C4—202no—
216C2×C5—481no—
217C2×C5#524112yes—
218C2×C5#524511yescharacteristic
219D5—82no—
220C23—102no—
221C23—121no—
222Q8—202no—
223D4—122no—
224D4—122no—
225D4—122no—
226D4—202no—
227D4—402no—
228C2×C4—22no—
229C2×C4—102no—
230C2×C4—402no—
231C2×C4C2×#120111yescharacteristic
232C2×C4D5×#6712yes—
233C8—121no—
234C8—304no—
235C2×C3—402no—
236C2×C3#6535111yescharacteristic
237C2×C3#6548712yes—
238D3—161no—
239C5#7195211yescharacteristic, complemented, Sylow
240C22—202no—
241C22—202no—
242C22—202no—
243C22—241no—
244C22—242no—
245C22#9156311yescharacteristic
246C4—21no—
247C4—22no—
248C4—42no—
249C4—202no—
250C3#1060204111yescharacteristic, complemented, Sylow
251C2—402no—
252C2—481no—
253C2#1174938311yescharacteristic
254C2#1174941712yes—
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#125C22
socleC22×C3×C5#120
hypercenter#125D3×D5
hypocenterC3×C5#1656
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. C3×#66034C2semidirect
2. C5×#5067C2semidirect
3. #11747042C2semidirect
4. #11746364C2semidirect
5. #11745846C2semidirect
19. #66034D3semidirect
42. #5067D5semidirect
205. C3×C5#1656semidirect
239. C5#71952semidirect
250. C3#10602041semidirect

Maximal subgroups

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

subgroupindex
C3×#660342
C5×#50672
#117470422
#117463642
#117458462
#106020413
#719525