Finite Group Databasebeta

← #14513692

Subgroups — #14513692

Order 1920.

702 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 702 conjugacy classes of subgroups — too many to draw. Only its 77 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
1C2×C4⋊(C5⋊S4)C211yesmaximal, characteristic
2C2×#91948C211yesmaximal, characteristic, complemented
3C42×C5×A4C211yesmaximal, characteristic, complemented
4#11752132C214yesmaximal, complemented
5#10613808—31nomaximal, Hall
6C22×C5⋊S4C2212yes—
7C2×C4×C5×A4C2212yes—
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4⋊Dic5C2212yes—
10C4⋊(C5⋊S4)—22no—
11#91948—22no—
12#91764—41nomaximal
13#85290—51nomaximal, Hall
14C22×C42×C5D311yescharacteristic, complemented
15C2×#4076—31no—
16C2×#4070—31no—
17C2×#4021—31no—
18#65502—34no—
19#65229—34no—
20#65228—31no—
21#65225—31no—
22#65218—31no—
23C22×C5×A4C2311yescharacteristic
24C2×C5⋊S4—22no—
25C2×C5⋊S4—24no—
26C2×D60—41no—
27C2×Dic30—41no—
28C4×C5×A4—22no—
29C4×C5×A4D412yes—
30A4⋊Dic5—22no—
31C3×C42×C5—41no—
32#6714—44no—
33C2×C4⋊S4—51no—
34C2×A4⋊Q8—51no—
35C42×A4D511yescharacteristic, complemented
36(C2×S4)⋊C4—54no—
37C23×C4×C5C2×D312yes—
38C23×C4×C5C2×D311yescharacteristic
39C22×C22⋊D5—32no—
40C22×D20—31no—
41C22×Dic10—31no—
42C2×C42×C5—31no—
43C2×C42×C5—31no—
44C2×C42×C5—32no—
45C2×C22⋊Dic5—32no—
46#4076—62no—
47#4076—62no—
48C2×#685—34no—
49C2×#685—32no—
50C2×#685—34no—
51C2×C4⋊Dic5—31no—
52C2×C4⋊Dic5—31no—
53#4070—62no—
54#4070—62no—
55C2×#683—32no—
56#4021—61no—
57#4021—62no—
58#4021—61no—
59#3963—34no—
60#3963—34no—
61#2850—151noSylow
62C22×D15—42no—
63C2×C5×A4C2×D411yescharacteristic
64C2×C5×A4#4112yes—
65C5⋊S4—42no—
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5—42no—
68C2×Dic15—42no—
69D60—82no—
70Dic30—82no—
71C22×S4—52no—
72C2×C4×A4C2×D512yes—
73C2×C4×A4C2×D511yescharacteristic
74C2×SL(2,ℤ/4)—52no—
75C4⋊S4—102no—
76A4⋊Q8—102no—
77#875—201no—
78C24×C5C22×D311yescharacteristic
79C23×D5—32no—
80C22×C4×C5—22no—
81C22×C4×C5—31no—
82C22×C4×C5—32no—
83C22×C4×C5—31no—
84C22×C4×C5—32no—
85C22×C4×C5—32no—
86C22×C4×C5—62no—
87C22×C4×C5D1212yes—
88C2×C22⋊D5—64no—
89C2×C22⋊D5—62no—
90C2×C22⋊D5—62no—
91C2×C22⋊D5—64no—
92C22×Dic5—32no—
93C22×Dic5—32no—
94C22×Dic5—32no—
95C2×D20—62no—
96C2×D20—61no—
97C2×D20—62no—
98C2×D20—61no—
99C2×Dic10—62no—
100C2×Dic10—61no—
101C2×Dic10—62no—
102C2×Dic10—61no—
103C42×C5—32no—
104C42×C5—31no—
105C42×C5—61no—
106C42×C5S411yescharacteristic, complemented
107C22⋊Dic5—62no—
108C22⋊Dic5—62no—
109#685—64no—
110#685—68no—
111#685—64no—
112#685—64no—
113C4⋊Dic5—62no—
114C4⋊Dic5—62no—
115#683—64no—
116C2×#124—151no—
117C2×C22⋊Q8—151no—
118C2×#121—151no—
119C22×C42D1511yescharacteristic, complemented
120#391—151no—
121#390—151no—
122#388—154no—
123#386—154no—
124#382—151no—
125C22×C3×C5—41no—
126C2×D15—82no—
127C2×D15—84no—
128C5×A4#12411yescharacteristic, complemented
129C3×C4×C5—42no—
130C3×C4×C5—82no—
131Dic15—82no—
132C22×A4C22×D511yescharacteristic
133C2×S4—102no—
134C2×S4—104no—
135C2×D12—201no—
136C2×Dic6—201no—
137C4×A4—22no—
138C4×A4D2012yes—
139SL(2,ℤ/4)—102no—
140C3×C42—41no—
141(C2×D3)⋊C4—204no—
142C23×C5—31no—
143C23×C5—31no—
144C23×C5—32no—
145C23×C5C2×D1211yescharacteristic
146C23×C5#23512yes—
147C22×D5—62no—
148C22×D5—64no—
149C22×D5—62no—
150C22×D5—64no—
151C22×D5—62no—
152C2×C4×C5—31no—
153C2×C4×C5—32no—
154C2×C4×C5—32no—
155C2×C4×C5—32no—
156C2×C4×C5—34no—
157C2×C4×C5—32no—
158C2×C4×C5—62no—
159C2×C4×C5—62no—
160C2×C4×C5—61no—
161C2×C4×C5—62no—
162C2×C4×C5C2×S412yes—
163C2×C4×C5C2×S411yescharacteristic
164C22⋊D5—122no—
165C22⋊D5—124no—
166C22⋊D5—122no—
167C2×Dic5—62no—
168C2×Dic5—62no—
169C2×Dic5—62no—
170C2×Dic5—64no—
171C2×Dic5—62no—
172C2×Dic5—64no—
173C2×Dic5—62no—
174D20—122no—
175D20—122no—
176Dic10—122no—
177Dic10—122no—
178C22×Q8—151no—
179C22×D4—151no—
180C22×D4—152no—
181C23×C4C2×D1512yes—
182C23×C4C2×D1511yescharacteristic
183#124—301no—
184#124—302no—
185#124—301no—
186C22⋊Q8—302no—
187C22⋊Q8—302no—
188#121—302no—
189#121—302no—
190C2×C4⋊C4—151no—
191C2×C4⋊C4—151no—
192C2×C4⋊C4—152no—
193C2×C22⋊C4—152no—
194C2×C22⋊C4—154no—
195C2×C22⋊C4—154no—
196C2×C22⋊C4—152no—
197C2×C42—31no—
198C2×C42—32no—
199C2×C42—31no—
200#95—154no—
201#95—154no—
202C2×C3×C5—41no—
203C2×C3×C5—42no—
204D15—162no—
205C22×D3—202no—
206C2×A4C2×D2011yescharacteristic
207C2×A4#70912yes—
208S4—202no—
209C2×C3×C4—41no—
210C2×C3×C4—42no—
211C2×Dic3—202no—
212D12—402no—
213Dic6—402no—
214C22×C5—31no—
215C22×C5—32no—
216C22×C5—31no—
217C22×C5—31no—
218C22×C5—32no—
219C22×C5—32no—
220C22×C5—61no—
221C22×C5#87511yescharacteristic, complemented
222C22×C5C22×S411yescharacteristic
223C2×D5—122no—
224C2×D5—122no—
225C2×D5—124no—
226C2×D5—122no—
227C2×D5—124no—
228C4×C5—22no—
229C4×C5—32no—
230C4×C5—62no—
231C4×C5C4⋊S412yes—
232Dic5—122no—
233Dic5—122no—
234Dic5—122no—
235C24—152no—
236C24C22×D1511yescharacteristic
237C2×Q8—302no—
238C2×Q8—301no—
239C2×Q8—302no—
240C2×Q8—301no—
241C2×D4—302no—
242C2×D4—301no—
243C2×D4—302no—
244C2×D4—302no—
245C2×D4—304no—
246C2×D4—302no—
247C2×D4—304no—
248C2×D4—301no—
249C22×C4—22no—
250C22×C4—31no—
251C22×C4—32no—
252C22×C4—31no—
253C22×C4—32no—
254C22×C4—32no—
255C22×C4—62no—
256C22×C4—152no—
257C22×C4—152no—
258C22×C4—152no—
259C22×C4D6012yes—
260C4⋊C4—302no—
261C4⋊C4—304no—
262C4⋊C4—302no—
263C22⋊C4—304no—
264C22⋊C4—304no—
265C22⋊C4—308no—
266C22⋊C4—302no—
267C22⋊C4—302no—
268C22⋊C4—304no—
269C42—32no—
270C42—31no—
271C42—61no—
272C42C5⋊S411yescharacteristic, complemented
273C3×C5—41noHall
274C22×C3—41no—
275C2×D3—402no—
276C2×D3—404no—
277A4#402111yescharacteristic, complemented
278C3×C4—42no—
279C3×C4—82no—
280Dic3—402no—
281C2×C5—31no—
282C2×C5—31no—
283C2×C5—32no—
284C2×C5C2×C4⋊S411yescharacteristic
285C2×C5#591212yes—
286D5—242no—
287C23—31no—
288C23—31no—
289C23—32no—
290C23—302no—
291C23—304no—
292C23—302no—
293C23—304no—
294C23—302no—
295C23C2×D6011yescharacteristic
296C23#681712yes—
297Q8—602no—
298Q8—602no—
299D4—602no—
300D4—602no—
301D4—604no—
302D4—602no—
303D4—602no—
304C2×C4—31no—
305C2×C4—32no—
306C2×C4—32no—
307C2×C4—32no—
308C2×C4—34no—
309C2×C4—32no—
310C2×C4—62no—
311C2×C4—62no—
312C2×C4—61no—
313C2×C4—62no—
314C2×C4—302no—
315C2×C4—302no—
316C2×C4—302no—
317C2×C4—304no—
318C2×C4—304no—
319C2×C4—302no—
320C2×C4—302no—
321C2×C4C2×C5⋊S412yes—
322C2×C4C2×C5⋊S411yescharacteristic
323C2×C3—41no—
324C2×C3—42no—
325D3—802no—
326C5#8529011yescharacteristic, complemented, Sylow
327C22—31no—
328C22—32no—
329C22—31no—
330C22—31no—
331C22—32no—
332C22—32no—
333C22—61no—
334C22—602no—
335C22—602no—
336C22—604no—
337C22—602no—
338C22—604no—
339C22#9176411yescharacteristic, complemented
340C22C22×C5⋊S411yescharacteristic
341C4—22no—
342C4—32no—
343C4—62no—
344C4—602no—
345C4—602no—
346C4—602no—
347C4C4⋊(C5⋊S4)12yes—
348C3—41noSylow
349C2—31no—
350C2—31no—
351C2—32no—
352C2—1202no—
353C2C2×C4⋊(C5⋊S4)11yescharacteristic
354C2#1175689612yes—
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, cosocleC22×C5×A4C23
FittingC22×C42×C5D3
socleC24×C5C22×D3
prime radicalC2×C4⋊(C5⋊S4)C2
hypercenterC42C5⋊S4
hypocenterC5×A4#124
LCSG ▷ C22×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C2×#91948C2semidirect
3. C42×C5×A4C2semidirect
4. #11752132C2semidirect
14. C22×C42×C5D3semidirect
35. C42×A4D5semidirect
106. C42×C5S4semidirect
119. C22×C42D15semidirect
128. C5×A4#124semidirect
221. C22×C5#875semidirect
272. C42C5⋊S4semidirect
277. A4#4021semidirect
326. C5#85290semidirect
339. C22#91764semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C5⋊S4)2
C2×#919482
C42×C5×A42
#117521322
#106138083
#917644
#852905