Finite Group Databasebeta

← #14290906

Subgroups — #14290906

Order 1920.

460 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 87 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×C5×#562C211yesmaximal, characteristic, complemented
2#11751168C211yesmaximal, characteristic, complemented
3#11751159C212yesmaximal, complemented
4#11746364C211yesmaximal, characteristic, complemented
5#11746361C212yesmaximal, complemented
6#10602745—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C3×C5×#124C2212yes—
9C3×C5×#123—22no—
10C3×C5×C22⋊Q8—22no—
11C3×C5×#121—22no—
12C2×#6717—22no—
13C2×#6715—22no—
14#91763C2211yescharacteristic
15#91093—22no—
16#91087C2211yescharacteristic
17#91087C2212yes—
18#71952—51nomaximal, Hall
19C5×#562D311yescharacteristic, complemented
20#65356—31no—
21#65347—32no—
22#64763—31no—
23#64760—32no—
24C2×C3×C5×Q8D412yes—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4D412yes—
27C22×C3×C4×C5—22no—
28C2×D60—22no—
29C2×D60—21no—
30C3×C5×C4⋊C4—22no—
31C3×C5×C4⋊C4—22no—
32C3×C5×C4⋊C4D412yes—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C42×C5C2311yescharacteristic
37#6717—44no—
38#6715—44no—
39C2×C3⋊#168—22no—
40C2×C3⋊#168—21no—
41C3×#562D511yescharacteristic, complemented
42#5067—51no—
43#5058—52no—
44#4543—51no—
45#4540—52no—
46C5×#125C2×D311yescharacteristic
47C5×#124C2×D312yes—
48C5×#123—22no—
49C5×C22⋊Q8—22no—
50C5×#121—22no—
51C2×#688—62no—
52C2×#686—62no—
53#4020—31no—
54#3941—62no—
55#3935—32no—
56#3935—31no—
57#1656—151noSylow
58C23×C3×C5—22no—
59C22×D15—41no—
60C3×C5×Q8—42no—
61C3×C5×D4—42no—
62C3×C5×D4—82no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—82no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×C3×C4×C5C2×D412yes—
68D60—42no—
69D60—42no—
70D60—42no—
71C3⋊#168—24no—
72C3⋊#168—41no—
73C3×#125C2×D511yescharacteristic
74C3×#124C2×D512yes—
75C3×#123—22no—
76C3×C22⋊Q8—22no—
77C3×#121—22no—
78C2×#215—102no—
79C2×#213—102no—
80#874—51no—
81#809—102no—
82#803—51no—
83#803—52no—
84C2×C5×Q8#6712yes—
85C2×C5×D4—22no—
86C2×C5×D4#6712yes—
87C22×C4×C5—22no—
88C2×D20—61no—
89C2×D20—62no—
90C5×C4⋊C4—22no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4#6712yes—
93C5×C22⋊C4—22no—
94C5×C22⋊C4—22no—
95C5×C22⋊C4—22no—
96C42×C5C22×D311yescharacteristic
97#688—124no—
98#686—124no—
99C2×#168—62no—
100C2×#168—61no—
101#562D1511yescharacteristic, complemented
102#496—152no—
103#490—151no—
104#330—151no—
105#329—152no—
106C22×C3×C5—42no—
107C22×C3×C5—42no—
108C22×C3×C5—42no—
109C22×C3×C5#12011yescharacteristic
110C2×D15—82no—
111C2×D15—81no—
112C3×C4×C5—22no—
113C3×C4×C5—21no—
114C3×C4×C5—42no—
115C3×C4×C5—42no—
116C2×C3×Q8C22⋊D512yes—
117C2×C3×D4—22no—
118C2×C3×D4C22⋊D512yes—
119C22×C3×C4—22no—
120C2×D12—101no—
121C2×D12—102no—
122C3×C4⋊C4—22no—
123C3×C4⋊C4—22no—
124C3×C4⋊C4C22⋊D512yes—
125C3×C22⋊C4—22no—
126C3×C22⋊C4—22no—
127C3×C22⋊C4—22no—
128C3×C42C22×D511yescharacteristic
129#215—204no—
130#213—204no—
131C2×C3⋊C8—102no—
132C2×C3⋊C8—101no—
133C23×C5—22no—
134C22×D5—121no—
135C5×Q8—42no—
136C5×D4—42no—
137C5×D4—82no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—82no—
141C2×C4×C5C2×#6711yescharacteristic
142C2×C4×C5C2×#6712yes—
143D20—122no—
144D20—122no—
145D20—122no—
146#168—64no—
147#168—121no—
148C2×SD16—302no—
149C2×D8—302no—
150#127—151no—
151#125C2×D1511yescharacteristic
152#124C2×D1512yes—
153#123—22no—
154C22⋊Q8—22no—
155#121—22no—
156#102—302no—
157#97—151no—
158#97—152no—
159C2×C3×C5—82no—
160C2×C3×C5#45312yes—
161C2×C3×C5#45411yescharacteristic
162D15—161no—
163C23×C3—22no—
164C22×D3—201no—
165C3×Q8—42no—
166C3×D4—42no—
167C3×D4—82no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—82no—
171C2×C3×C4C2×C22⋊D511yescharacteristic
172C2×C3×C4C2×C22⋊D512yes—
173D12—202no—
174D12—202no—
175D12—202no—
176C3⋊C8—104no—
177C3⋊C8—201no—
178C22×C5—42no—
179C22×C5—42no—
180C22×C5—42no—
181C22×C5#95311yescharacteristic
182C2×D5—242no—
183C2×D5—241no—
184C4×C5—22no—
185C4×C5—21no—
186C4×C5—42no—
187C4×C5—42no—
188C2×Q8#122012yes—
189C2×D4—22no—
190C2×D4—301no—
191C2×D4—302no—
192C2×D4#122012yes—
193C22×C4—22no—
194SD16—604no—
195D8—604no—
196C2×C8—302no—
197C2×C8—301no—
198C4⋊C4—22no—
199C4⋊C4—22no—
200C4⋊C4#122012yes—
201C22⋊C4—22no—
202C22⋊C4—22no—
203C22⋊C4—22no—
204C42C22×D1511yescharacteristic
205C3×C5#165611yescharacteristic, complemented, Hall
206C22×C3—42no—
207C22×C3—42no—
208C22×C3—42no—
209C22×C3#409911yescharacteristic
210C2×D3—402no—
211C2×D3—401no—
212C3×C4—22no—
213C3×C4—21no—
214C3×C4—42no—
215C3×C4—42no—
216C2×C5—82no—
217C2×C5#524112yes—
218C2×C5#524511yescharacteristic
219D5—481no—
220C23—22no—
221C23—601no—
222Q8—42no—
223D4—42no—
224D4—82no—
225D4—602no—
226D4—602no—
227D4—602no—
228C2×C4—22no—
229C2×C4—22no—
230C2×C4—82no—
231C2×C4C2×#122011yescharacteristic
232C2×C4C2×#122012yes—
233C8—304no—
234C8—601no—
235C2×C3—82no—
236C2×C3#6553012yes—
237C2×C3#6553411yescharacteristic
238D3—801no—
239C5#7195211yescharacteristic, complemented, Sylow
240C22—42no—
241C22—42no—
242C22—42no—
243C22—1202no—
244C22—1201no—
245C22#9184211yescharacteristic
246C4—22no—
247C4—21no—
248C4—42no—
249C4—42no—
250C3#1060274511yescharacteristic, complemented, Sylow
251C2—82no—
252C2—2401no—
253C2#1175134212yes—
254C2#1175134611yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#562C2
socleC22×C3×C5#120
hypercenter#562D15
hypocenterC3×C5#1656
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. C3×C5×#562C2semidirect
2. #11751168C2semidirect
3. #11751159C2semidirect
4. #11746364C2semidirect
5. #11746361C2semidirect
19. C5×#562D3semidirect
41. C3×#562D5semidirect
101. #562D15semidirect
205. C3×C5#1656semidirect
239. C5#71952semidirect
250. C3#10602745semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5622
#117511682
#117511592
#117463642
#117463612
#106027453
#719525