Finite Group Databasebeta

← #14285236

Subgroups — #14285236

Order 1920.

664 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 102 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
1D15×#127C211yesmaximal, characteristic
2#11746867C212yesmaximal, complemented
3C5×#4544C211yesmaximal, characteristic, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5#11745854C212yesmaximal, complemented
6#10599180—31nomaximal, Hall
7C2×D4×D15—22no—
8C2×D4×D15C412yes—
9C3×C5×#127C2211yescharacteristic
10#91829—22no—
11#91829C412yes—
12#91763C2211yescharacteristic
13C42×D15C2211yescharacteristic
14C5×C4⋊(C3⋊C8)C2212yescomplemented
15C3×C4⋊#168C2212yescomplemented
16#90957—22no—
17#90954—22no—
18#68387—51nomaximal, Hall
19D5×#127—31no—
20#65124—32no—
21C5×#331—31no—
22#64764D311yescharacteristic, complemented
23#64705—32no—
24C23×D15—22no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4C2×C412yes—
27C2×#1220—22no—
28C2×#1220—24no—
29D4×D15—44no—
30D4×D15—44no—
31D4×D15—44no—
32C2×D60—22no—
33C2×D60C2×C412yes—
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D412yes—
36C3×C42×C5C2311yescharacteristic
37C4×Dic15C2×C411yescharacteristic
38C4×Dic15D412yes—
39C2×C5×C3⋊C8—22no—
40C2×C3×#168—22no—
41D3×#127—51no—
42#4835—52no—
43C3×#331—51no—
44#4544D511yescharacteristic, complemented
45#4485—52no—
46C2×D4×D5—32no—
47C2×D4×D5—62no—
48C5×#127C2×D311yescharacteristic
49#4086—32no—
50#4086—62no—
51#4020—31no—
52C42×D5—31no—
53C5×C4⋊C8—32no—
54#3952—62no—
55#3947—62no—
56C4⋊#168C2×D312yescomplemented
57#1555—151noSylow
58C23×C3×C5—22no—
59C22×D15—22no—
60C22×D15—48no—
61C22×D15—44no—
62C22×D15C22⋊C411yescharacteristic
63C3×C5×D4—42no—
64C3×C5×D4—42no—
65C3×C5×D4—42no—
66C2×C3×C4×C5C22×C411yescharacteristic
67C2×C3×C4×C5C2×D412yes—
68#1220—44no—
69#1220—48no—
70C2×Dic15C22⋊C412yes—
71C2×Dic15C22⋊C411yescharacteristic
72D60—42no—
73D60—42no—
74D60—42no—
75C4×D15—22no—
76C4×D15—22no—
77C4×D15—22no—
78C3×#168—42no—
79C5×C3⋊C8—42no—
80C2×D3×D4—52no—
81C2×D3×D4—102no—
82C3×#127C2×D511yescharacteristic
83#940—52no—
84#940—102no—
85#874—51no—
86C42×D3—51no—
87C3×C4⋊C8—52no—
88(C2×D3)⋊C8—102no—
89#815—102no—
90C4⋊(C3⋊C8)C2×D512yescomplemented
91C23×D5—62no—
92C2×C5×D4—22no—
93C2×C5×D4C4×D312yes—
94C2×C22⋊D5—62no—
95C2×C22⋊D5—64no—
96D4×D5—124no—
97D4×D5—124no—
98D4×D5—124no—
99C2×D20—32no—
100C2×D20—62no—
101C2×C4×D5—31no—
102C2×C4×D5—32no—
103C2×C5×C8—62no—
104C42×C5C22×D311yescharacteristic
105C4×Dic5—31no—
106C4×Dic5—32no—
107C2×#168—22no—
108C2×#127—151no—
109#432—152no—
110#331—31no—
111#331—51no—
112#331—152no—
113C22×C3×C5—42no—
114C22×C3×C5—44no—
115C22×C3×C5C2×C22⋊C411yescharacteristic
116C2×D15—22no—
117C2×D15—42no—
118C2×D15—44no—
119C2×D15—88no—
120C2×D15#10012yes—
121C3×C4×C5—21no—
122C3×C4×C5AGL(1,ℤ/8)12yes—
123C3×C4×C5AGL(1,ℤ/8)12yes—
124Dic15—21no—
125Dic15—22no—
126C23×D3—102no—
127C2×C3×D4—22no—
128C2×C3×D4C4×D512yes—
129C2×#67—104no—
130C2×#67—102no—
131D3×D4—204no—
132D3×D4—204no—
133D3×D4—204no—
134C2×D12—52no—
135C2×D12—102no—
136C2×C4×D3—51no—
137C2×C4×D3—52no—
138C2×C3×C8—102no—
139C3×C42C22×D511yescharacteristic
140C4×Dic3—51no—
141C4×Dic3—52no—
142C2×C3⋊C8—22no—
143C23×C5—22no—
144C22×D5—31no—
145C22×D5—62no—
146C22×D5—124no—
147C22×D5—128no—
148C5×D4—42no—
149C5×D4—42no—
150C5×D4—42no—
151C2×C4×C5C2×C4×D311yescharacteristic
152C2×C4×C5D3×D412yes—
153C22⋊D5—124no—
154C22⋊D5—128no—
155C2×Dic5—31no—
156C2×Dic5—32no—
157D20—122no—
158D20—122no—
159D20—122no—
160C4×D5—62no—
161C4×D5—62no—
162C4×D5—62no—
163C5×C8—122no—
164#168—42no—
165C22×D4—152no—
166C22×D4—302no—
167#127—152no—
168#127—151no—
169#127—302no—
170#127D3×D511yescharacteristic
171C2×C42—151no—
172C4⋊C8—32no—
173C4⋊C8—52no—
174C22⋊C8—302no—
175#97—302no—
176C2×C3×C5—82no—
177C2×C3×C5C2×#10011yescharacteristic
178C2×C3×C5#41812yes—
179D15—22no—
180D15—82no—
181C23×C3—22no—
182C22×D3—51no—
183C22×D3—102no—
184C22×D3—204no—
185C22×D3—208no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—42no—
189C2×C3×C4C2×C4×D511yescharacteristic
190C2×C3×C4D4×D512yes—
191#67—204no—
192#67—208no—
193C2×Dic3—51no—
194C2×Dic3—52no—
195D12—202no—
196D12—202no—
197D12—202no—
198C4×D3—102no—
199C4×D3—102no—
200C4×D3—102no—
201C3×C8—202no—
202C3⋊C8—42no—
203C22×C5—42no—
204C22×C5—44no—
205C22×C5D3×C22⋊C411yescharacteristic
206C2×D5—32no—
207C2×D5—62no—
208C2×D5—122no—
209C2×D5—124no—
210C2×D5—248no—
211C4×C5—21no—
212C4×C5#91112yes—
213C4×C5#91412yes—
214Dic5—61no—
215Dic5—62no—
216C24—302no—
217C2×D4—22no—
218C2×D4—152no—
219C2×D4—304no—
220C2×D4—302no—
221C2×D4—302no—
222C2×D4—604no—
223C2×D4—604no—
224C2×D4—604no—
225C2×D4#120012yes—
226C22×C4—151no—
227C22×C4—152no—
228C2×C8—62no—
229C2×C8—102no—
230C42—151no—
231C42—152no—
232C42C2×D3×D511yescharacteristic
233C3×C5#155511yescharacteristic, complemented, Hall
234C22×C3—42no—
235C22×C3—44no—
236C22×C3D5×C22⋊C411yescharacteristic
237C2×D3—52no—
238C2×D3—102no—
239C2×D3—202no—
240C2×D3—204no—
241C2×D3—408no—
242C3×C4—21no—
243C3×C4#405712yes—
244C3×C4#406012yes—
245Dic3—101no—
246Dic3—102no—
247C2×C5—82no—
248C2×C5D3×#10011yescharacteristic
249C2×C5#477012yes—
250D5—62no—
251D5—242no—
252C23—22no—
253C23—151no—
254C23—302no—
255C23—604no—
256C23—608no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—602no—
261D4—604no—
262D4—608no—
263D4—602no—
264D4—602no—
265C2×C4—151no—
266C2×C4—152no—
267C2×C4—302no—
268C2×C4—302no—
269C2×C4—302no—
270C2×C4C2×#120011yescharacteristic
271C2×C4#679012yes—
272C8—122no—
273C8—202no—
274C2×C3—82no—
275C2×C3D5×#10011yescharacteristic
276C2×C3#6505912yes—
277D3—102no—
278D3—402no—
279C5#6838711yescharacteristic, complemented, Sylow
280C22—42no—
281C22—44no—
282C22—152no—
283C22—302no—
284C22—602no—
285C22—604no—
286C22—1208no—
287C22#9156111yescharacteristic
288C4—21no—
289C4—301no—
290C4—302no—
291C4#9149812yes—
292C4#9150012yes—
293C3#1059918011yescharacteristic, complemented, Sylow
294C2—82no—
295C2—302no—
296C2—1202no—
297C2#1174897212yes—
298C2#1174912711yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C2×C22⋊C4
prime radicalD15×#127C2
cosocleC3×C42×C5C23
hypercenter#127D3×D5
hypocenterC3×C5#1555
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11746867C2semidirect
3. C5×#4544C2semidirect
4. C3×#64764C2semidirect
5. #11745854C2semidirect
14. C5×C4⋊(C3⋊C8)C22semidirect
15. C3×C4⋊#168C22semidirect
22. #64764D3semidirect
44. #4544D5semidirect
56. C4⋊#168C2×D3semidirect
90. C4⋊(C3⋊C8)C2×D5semidirect
233. C3×C5#1555semidirect
279. C5#68387semidirect
293. C3#10599180semidirect

Maximal subgroups

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

subgroupindex
D15×#1272
#117468672
C5×#45442
C3×#647642
#117458542
#105991803
#683875