Finite Group Databasebeta

← #14285235

Subgroups — #14285235

Order 1920.

664 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 664 conjugacy classes of subgroups — too many to draw. Only its 120 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×D5×#127C211yesmaximal, characteristic
2#11746871C212yesmaximal, complemented
3#11746365C211yesmaximal, characteristic, complemented
4C5×#4544C211yesmaximal, characteristic, complemented
5#11745852C212yesmaximal, complemented
6#10599180—31nomaximal, Hall
7C2×C3×D4×D5—22no—
8C2×C3×D4×D5C412yes—
9C3×C5×#127C2211yescharacteristic
10C3×#4086—22no—
11C3×#4086C412yes—
12C3×#4020C2211yescharacteristic
13C3×C42×D5C2211yescharacteristic
14C4⋊(C3⋊#168)C2212yescomplemented
15C5×C4⋊(C3⋊C8)C2212yescomplemented
16#90955—22no—
17#90952—22no—
18#71760—51nomaximal, Hall
19D5×#127D311yescharacteristic
20#65124—32no—
21C5×#331—31no—
22#64764—31no—
23#64705—32no—
24C23×C3×D5—22no—
25C2×C3×C5×D4—22no—
26C2×C3×C5×D4C2×C412yes—
27C2×C3×C22⋊D5—22no—
28C2×C3×C22⋊D5—24no—
29C3×D4×D5—44no—
30C3×D4×D5—44no—
31C3×D4×D5—44no—
32C2×C3×D20—22no—
33C2×C3×D20C2×C412yes—
34C2×C3×C4×D5C2×C411yescharacteristic
35C2×C3×C4×D5D412yes—
36C3×C42×C5C2311yescharacteristic
37C2×C3⋊#168—22no—
38C2×C5×C3⋊C8—22no—
39C3×C4×Dic5C2×C411yescharacteristic
40C3×C4×Dic5D412yes—
41C2×C3×#127—51no—
42#4926—52no—
43#4544—51no—
44#4544—52no—
45#4544D511yescharacteristic, complemented
46C2×D4×D5—22no—
47C2×D4×D5Dic312yes—
48C5×#127C2×D311yescharacteristic
49#4086—22no—
50#4086Dic312yes—
51#4020C2×D311yescharacteristic
52C42×D5C2×D311yescharacteristic
53C5×C4⋊C8—32no—
54#3952—62no—
55#3947—62no—
56C4⋊#168—32no—
57#1555—151noSylow
58C23×C3×C5—22no—
59C22×C3×D5—22no—
60C22×C3×D5—48no—
61C22×C3×D5—44no—
62C22×C3×D5C22⋊C411yescharacteristic
63C3×C5×D4—42no—
64C3×C5×D4—42no—
65C3×C5×D4—42no—
66C2×C3×C4×C5C22×C411yescharacteristic
67C2×C3×C4×C5C2×D412yes—
68C3×C22⋊D5—44no—
69C3×C22⋊D5—48no—
70C2×C3×Dic5C22⋊C412yes—
71C2×C3×Dic5C22⋊C411yescharacteristic
72C3×D20—42no—
73C3×D20—42no—
74C3×D20—42no—
75C3×C4×D5—22no—
76C3×C4×D5—22no—
77C3×C4×D5—22no—
78C3⋊#168—42no—
79C5×C3⋊C8—42no—
80C22×C3×D4—52no—
81C22×C3×D4—102no—
82C3×#127—52no—
83C3×#127—51no—
84C3×#127—102no—
85C3×#127C2×D511yescharacteristic
86C2×C3×C42—51no—
87#830—102no—
88C4⋊(C3⋊C8)—52no—
89C4⋊(C3⋊C8)C2×D512yescomplemented
90#803—102no—
91C23×D5—22no—
92C2×C5×D4—22no—
93C2×C5×D4C2×Dic312yes—
94C2×C22⋊D5—24no—
95C2×C22⋊D5—22no—
96D4×D5—44no—
97D4×D5—44no—
98D4×D5—44no—
99C2×D20—22no—
100C2×D20C2×Dic312yes—
101C2×C4×D5C2×Dic311yescharacteristic
102C2×C4×D5#6712yes—
103C2×C5×C8—62no—
104C42×C5C22×D311yescharacteristic
105C4×Dic5C2×Dic311yescharacteristic
106C4×Dic5#6712yes—
107C2×#168—62no—
108C2×#127—51no—
109#432—152no—
110#331—31no—
111#331—152no—
112#331—151no—
113C22×C3×C5—42no—
114C22×C3×C5—44no—
115C22×C3×C5C2×C22⋊C411yescharacteristic
116C2×C3×D5—22no—
117C2×C3×D5—42no—
118C2×C3×D5—44no—
119C2×C3×D5—88no—
120C2×C3×D5#10012yes—
121C3×C4×C5—21no—
122C3×C4×C5AGL(1,ℤ/8)12yes—
123C3×C4×C5AGL(1,ℤ/8)12yes—
124C3×Dic5—21no—
125C3×Dic5—22no—
126C24×C3—102no—
127C2×C3×D4—22no—
128C2×C3×D4—52no—
129C2×C3×D4—104no—
130C2×C3×D4—102no—
131C2×C3×D4—102no—
132C2×C3×D4—204no—
133C2×C3×D4—204no—
134C2×C3×D4—204no—
135C2×C3×D4C4×D512yes—
136C22×C3×C4—51no—
137C22×C3×C4—52no—
138C3×C42—51no—
139C3×C42—52no—
140C3×C42C22×D511yescharacteristic
141C2×C3⋊C8—22no—
142C2×C3⋊C8—102no—
143C23×C5—22no—
144C22×D5—22no—
145C22×D5—48no—
146C22×D5—44no—
147C22×D5#21711yescharacteristic
148C5×D4—42no—
149C5×D4—42no—
150C5×D4—42no—
151C2×C4×C5C22×Dic311yescharacteristic
152C2×C4×C5C2×#6712yes—
153C22⋊D5—48no—
154C22⋊D5—44no—
155C2×Dic5#21712yes—
156C2×Dic5#21711yescharacteristic
157D20—42no—
158D20—42no—
159D20—42no—
160C4×D5—22no—
161C4×D5—22no—
162C4×D5—22no—
163C5×C8—122no—
164#168—122no—
165C22×D4—52no—
166C22×D4—102no—
167#127—52no—
168#127—51no—
169#127—102no—
170#127D3×D511yescharacteristic
171C2×C42—51no—
172C4⋊C8—32no—
173C4⋊C8—152no—
174C22⋊C8—302no—
175#97—302no—
176C2×C3×C5—82no—
177C2×C3×C5C2×#10011yescharacteristic
178C2×C3×C5#41812yes—
179C3×D5—22no—
180C3×D5—82no—
181C23×C3—22no—
182C23×C3—51no—
183C23×C3—102no—
184C23×C3—204no—
185C23×C3—208no—
186C3×D4—42no—
187C3×D4—42no—
188C3×D4—42no—
189C3×D4—202no—
190C3×D4—204no—
191C3×D4—208no—
192C3×D4—202no—
193C3×D4—202no—
194C2×C3×C4—51no—
195C2×C3×C4—52no—
196C2×C3×C4—102no—
197C2×C3×C4—102no—
198C2×C3×C4—102no—
199C2×C3×C4C2×C4×D511yescharacteristic
200C2×C3×C4D4×D512yes—
201C3⋊C8—42no—
202C3⋊C8—202no—
203C22×C5—44no—
204C22×C5—42no—
205C22×C5C2×#21711yescharacteristic
206C2×D5—22no—
207C2×D5—44no—
208C2×D5—42no—
209C2×D5—88no—
210C2×D5#83312yes—
211C4×C5—21no—
212C4×C5#93212yes—
213C4×C5#93212yes—
214Dic5—22no—
215Dic5—21no—
216C24—102no—
217C2×D4—22no—
218C2×D4—52no—
219C2×D4—104no—
220C2×D4—102no—
221C2×D4—102no—
222C2×D4—204no—
223C2×D4—204no—
224C2×D4—204no—
225C2×D4D5×Dic312yes—
226C22×C4—51no—
227C22×C4—52no—
228C2×C8—62no—
229C2×C8—302no—
230C42—51no—
231C42—52no—
232C42C2×D3×D511yescharacteristic
233C3×C5#155511yescharacteristic, complemented, Hall
234C22×C3—42no—
235C22×C3—44no—
236C22×C3—52no—
237C22×C3—102no—
238C22×C3—202no—
239C22×C3—204no—
240C22×C3—408no—
241C22×C3D5×C22⋊C411yescharacteristic
242C3×C4—21no—
243C3×C4—101no—
244C3×C4—102no—
245C3×C4#405712yes—
246C3×C4#406012yes—
247C2×C5—82no—
248C2×C5#521512yes—
249C2×C5C2×#83311yescharacteristic
250D5—22no—
251D5—82no—
252C23—22no—
253C23—51no—
254C23—102no—
255C23—204no—
256C23—208no—
257D4—42no—
258D4—42no—
259D4—42no—
260D4—202no—
261D4—204no—
262D4—208no—
263D4—202no—
264D4—202no—
265C2×C4—51no—
266C2×C4—52no—
267C2×C4—102no—
268C2×C4—102no—
269C2×C4—102no—
270C2×C4C2×D5×Dic311yescharacteristic
271C2×C4D5×#6712yes—
272C8—122no—
273C8—602no—
274C2×C3—82no—
275C2×C3—102no—
276C2×C3—402no—
277C2×C3D5×#10011yescharacteristic
278C2×C3#6505912yes—
279C5#7176011yescharacteristic, complemented, Sylow
280C22—42no—
281C22—44no—
282C22—52no—
283C22—102no—
284C22—202no—
285C22—204no—
286C22—408no—
287C22D5×#21711yescharacteristic
288C4—21no—
289C4—101no—
290C4—102no—
291C4#9148912yes—
292C4#9149112yes—
293C3#1059918011yescharacteristic, complemented, Sylow
294C2—82no—
295C2—102no—
296C2—402no—
297C2#1174896212yes—
298C2D5×#83311yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×D5×#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. #11746871C2semidirect
3. #11746365C2semidirect
4. C5×#4544C2semidirect
5. #11745852C2semidirect
14. C4⋊(C3⋊#168)C22semidirect
15. C5×C4⋊(C3⋊C8)C22semidirect
45. #4544D5semidirect
89. C4⋊(C3⋊C8)C2×D5semidirect
233. C3×C5#1555semidirect
279. C5#71760semidirect
293. C3#10599180semidirect

Maximal subgroups

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

subgroupindex
C3×D5×#1272
#117468712
#117463652
C5×#45442
#117458522
#105991803
#717605