Finite Group Databasebeta

← #14289054

Subgroups — #14289054

Order 1920.

480 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 103 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×#555C211yesmaximal, characteristic, complemented
2#11751186C211yesmaximal, characteristic, complemented
3#11751116C212yesmaximal, complemented
4#11746367C211yesmaximal, characteristic, complemented
5D4⋊(C3⋊#168)C212yesmaximal, complemented
6#10602720—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C3×C5×#124—22no—
9C3×C5×#121—22no—
10C3×C4×C5×D4C2212yes—
11C3×C5×#117—22no—
12C2×#6717—22no—
13C2×#6715—22no—
14#91763C2211yescharacteristic
15#91093—22no—
16C4⋊(C3⋊#168)C2212yes—
17C4×C3⋊#168C2211yescharacteristic
18#71927—51nomaximal, Hall
19C5×#555D311yescharacteristic, complemented
20#65374—31no—
21#65304—32no—
22#64766—31no—
23D4⋊#168—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⋊C4D412yes—
32C3×C5×C22⋊C4—24no—
33C3×C5×C22⋊C4—22no—
34C3×C42×C5—22no—
35C3×C42×C5C2311yescharacteristic
36#6717—44no—
37#6715—44no—
38C2×C3⋊#168—21no—
39C2×C3⋊#168—22no—
40C3×#555D511yescharacteristic, complemented
41#5085—51no—
42#5015—52no—
43#4546—51no—
44D4⋊(C3⋊C8)—52no—
45C5×C4⋊Q8C2×D311yescharacteristic
46C5×#124—22no—
47C5×#121—22no—
48C4×C5×D4C2×D312yes—
49C5×#117—22no—
50C2×#688—62no—
51C2×#686—62no—
52#4020—31no—
53#3941—62no—
54C4⋊#168—32no—
55C4×#168—31no—
56#1624—151noSylow
57C23×C3×C5—22no—
58C22×D15—41no—
59C3×C5×Q8—42no—
60C3×C5×D4—22no—
61C3×C5×D4—22no—
62C3×C5×D4—82no—
63C2×C3×C4×C5—22no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—42no—
66C2×C3×C4×C5—42no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×C3×C4×C5C2×D412yes—
69D60—42no—
70D60—42no—
71D60—42no—
72C3⋊#168—22no—
73C3⋊#168—42no—
74C3×C4⋊Q8C2×D511yescharacteristic
75C3×#124—22no—
76C3×#121—22no—
77C3×C4×D4C2×D512yes—
78C3×#117—22no—
79C2×#215—102no—
80C2×#213—102no—
81#874—51no—
82#809—102no—
83C4⋊(C3⋊C8)—52no—
84C4×C3⋊C8—51no—
85C2×C5×Q8#6712yes—
86C2×C5×D4—22no—
87C2×C5×D4#6712yes—
88C22×C4×C5—22no—
89C2×D20—62no—
90C2×D20—61no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4#6712yes—
93C5×C22⋊C4—24no—
94C5×C22⋊C4—22no—
95C42×C5—22no—
96C42×C5C22×D311yescharacteristic
97#688—124no—
98#686—124no—
99C2×#168—61no—
100C2×#168—62no—
101#555D1511yescharacteristic, complemented
102#492—151no—
103#459—152no—
104#333—151no—
105D4⋊C8—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—21no—
113C3×C4×C5—42no—
114C3×C4×C5—42no—
115C3×C4×C5#13512yes—
116C3×C4×C5AGL(1,ℤ/8)12yes—
117C2×C3×Q8C22⋊D512yes—
118C2×C3×D4—22no—
119C2×C3×D4C22⋊D512yes—
120C22×C3×C4—22no—
121C2×D12—102no—
122C2×D12—101no—
123C3×C4⋊C4—22no—
124C3×C4⋊C4C22⋊D512yes—
125C3×C22⋊C4—24no—
126C3×C22⋊C4—22no—
127C3×C42—22no—
128C3×C42C22×D511yescharacteristic
129#215—204no—
130#213—204no—
131C2×C3⋊C8—101no—
132C2×C3⋊C8—102no—
133C23×C5—22no—
134C22×D5—121no—
135C5×Q8—42no—
136C5×D4—22no—
137C5×D4—22no—
138C5×D4—82no—
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5C2×#6711yescharacteristic
144C2×C4×C5C2×#6712yes—
145D20—122no—
146D20—122no—
147D20—122no—
148#168—62no—
149#168—122no—
150C2×SD16—302no—
151C2×D8—302no—
152C4⋊Q8C2×D1511yescharacteristic
153#127—151no—
154#124—22no—
155#121—22no—
156C4×D4C2×D1512yes—
157#117—22no—
158C4⋊C8—152no—
159#102—302no—
160C4×C8—151no—
161C2×C3×C5—82no—
162C2×C3×C5#44912yes—
163C2×C3×C5#45311yescharacteristic
164D15—161no—
165C23×C3—22no—
166C22×D3—201no—
167C3×Q8—42no—
168C3×D4—22no—
169C3×D4—22no—
170C3×D4—82no—
171C2×C3×C4—22no—
172C2×C3×C4—22no—
173C2×C3×C4—42no—
174C2×C3×C4—42no—
175C2×C3×C4C2×C22⋊D511yescharacteristic
176C2×C3×C4C2×C22⋊D512yes—
177D12—202no—
178D12—202no—
179D12—202no—
180C3⋊C8—102no—
181C3⋊C8—202no—
182C22×C5—42no—
183C22×C5—42no—
184C22×C5—42no—
185C22×C5#95311yescharacteristic
186C2×D5—242no—
187C2×D5—241no—
188C4×C5—21no—
189C4×C5—42no—
190C4×C5—42no—
191C4×C5#94912yes—
192C4×C5#95012yes—
193C2×Q8#122012yes—
194C2×D4—22no—
195C2×D4—302no—
196C2×D4—301no—
197C2×D4#122012yes—
198C22×C4—22no—
199SD16—604no—
200D8—604no—
201C2×C8—301no—
202C2×C8—302no—
203C4⋊C4—22no—
204C4⋊C4#122012yes—
205C22⋊C4—24no—
206C22⋊C4—22no—
207C42—22no—
208C42C22×D1511yescharacteristic
209C3×C5#162411yescharacteristic, complemented, Hall
210C22×C3—42no—
211C22×C3—42no—
212C22×C3—42no—
213C22×C3#409911yescharacteristic
214C2×D3—402no—
215C2×D3—401no—
216C3×C4—21no—
217C3×C4—42no—
218C3×C4—42no—
219C3×C4#409512yes—
220C3×C4#409612yes—
221C2×C5—82no—
222C2×C5#523812yes—
223C2×C5#524111yescharacteristic
224D5—481no—
225C23—22no—
226C23—601no—
227Q8—42no—
228D4—22no—
229D4—22no—
230D4—82no—
231D4—602no—
232D4—602no—
233D4—602no—
234C2×C4—22no—
235C2×C4—22no—
236C2×C4—42no—
237C2×C4—42no—
238C2×C4C2×#122011yescharacteristic
239C2×C4C2×#122012yes—
240C8—302no—
241C8—602no—
242C2×C3—82no—
243C2×C3#6552712yes—
244C2×C3#6553011yescharacteristic
245D3—801no—
246C5#7192711yescharacteristic, complemented, Sylow
247C22—42no—
248C22—42no—
249C22—42no—
250C22—1202no—
251C22—1201no—
252C22#9184211yescharacteristic
253C4—21no—
254C4—42no—
255C4—42no—
256C4#9183812yes—
257C4#9183912yes—
258C3#1060272011yescharacteristic, complemented, Sylow
259C2—82no—
260C2—2401no—
261C2#1175133912yes—
262C2#1175134211yescharacteristic
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#555C2
socleC22×C3×C5#120
hypercenter#555D15
hypocenterC3×C5#1624
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #555

Complements

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

NH ≅ G/Ntype
1. C3×C5×#555C2semidirect
2. #11751186C2semidirect
3. #11751116C2semidirect
4. #11746367C2semidirect
5. D4⋊(C3⋊#168)C2semidirect
19. C5×#555D3semidirect
40. C3×#555D5semidirect
101. #555D15semidirect
209. C3×C5#1624semidirect
246. C5#71927semidirect
258. C3#10602720semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5552
#117511862
#117511162
#117463672
D4⋊(C3⋊#168)2
#106027203
#719275