Finite Group Databasebeta

← #14513708

Subgroups — #14513708

Order 1920.

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

normal subgroups only

This group has 510 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
1C5×A4×C4⋊C4C211yesmaximal, characteristic
2C4⋊(A4⋊Dic5)C212yesmaximal
3C4⋊(A4⋊Dic5)C211yesmaximal, characteristic
4#11752130C212yesmaximal
5C4×A4⋊Dic5C211yesmaximal, characteristic
6#10613903—31nomaximal, Hall
7C2×C4×C5×A4C2212yes—
8C2×C4×C5×A4C2211yescharacteristic
9C2×A4⋊Dic5C2211yescharacteristic
10C2×A4⋊Dic5C2211yescharacteristic
11C2×A4⋊Dic5C2212yes—
12#91779—41nomaximal
13#85305—51nomaximal, Hall
14C22×C5×C4⋊C4D311yescharacteristic
15C2×#4036—31no—
16#65501—32no—
17#65501—31no—
18#65499—32no—
19C4×C22⋊Dic5—31no—
20#65275—32no—
21#65274—31no—
22#65273—32no—
23#65266—31no—
24#65262—31no—
25C22×C5×A4C2311yescharacteristic
26C4×C5×A4—22no—
27C4×C5×A4Q812yes—
28A4⋊Dic5—21no—
29A4⋊Dic5—21no—
30A4⋊Dic5—22no—
31C3×C5×C4⋊C4—41no—
32C4⋊Dic15—42no—
33C4⋊Dic15—41no—
34#6712—42no—
35C4×Dic15—41no—
36A4×C4⋊C4D511yescharacteristic
37C4⋊SL(2,ℤ/4)—52no—
38C4⋊SL(2,ℤ/4)—51no—
39SL(2,ℤ/4)⋊C4—52no—
40C4×SL(2,ℤ/4)—51no—
41C23×C4×C5C2×D312yes—
42C23×C4×C5C2×D311yescharacteristic
43C2×C5×C4⋊C4—31no—
44C2×C5×C4⋊C4—31no—
45C2×C5×C4⋊C4—32no—
46C2×C22⋊Dic5—31no—
47C2×C22⋊Dic5—31no—
48C2×C22⋊Dic5—32no—
49C2×C4⋊Dic5—31no—
50C2×C4⋊Dic5—32no—
51C2×C4⋊Dic5—31no—
52C2×C4⋊Dic5—32no—
53C2×#683—32no—
54C2×#683—32no—
55C2×C4×Dic5—31no—
56C2×C4×Dic5—31no—
57#4036—62no—
58#4036—61no—
59#4036—61no—
60#3963—31no—
61#3963—31no—
62#3963—32no—
63#3963—32no—
64#3963—32no—
65#3963—32no—
66#3963—32no—
67#2442—151noSylow
68C2×C5×A4C2×Q811yescharacteristic
69C2×C5×A4#4111yescharacteristic
70C2×C5×A4#4111yescharacteristic
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5—42no—
73C2×Dic15—41no—
74C2×Dic15—41no—
75C2×Dic15—42no—
76C2×C4×A4C2×D512yes—
77C2×C4×A4C2×D511yescharacteristic
78C2×SL(2,ℤ/4)—51no—
79C2×SL(2,ℤ/4)—51no—
80C2×SL(2,ℤ/4)—52no—
81#890—201no—
82C24×C5C22×D311yescharacteristic
83C22×C4×C5—22no—
84C22×C4×C5—31no—
85C22×C4×C5—31no—
86C22×C4×C5—32no—
87C22×C4×C5—32no—
88C22×C4×C5—32no—
89C22×C4×C5—62no—
90C22×C4×C5Dic612yes—
91C22×Dic5—31no—
92C22×Dic5—31no—
93C22×Dic5—31no—
94C22×Dic5—32no—
95C22×Dic5—32no—
96C22×Dic5—31no—
97C5×C4⋊C4—32no—
98C5×C4⋊C4—31no—
99C5×C4⋊C4—61no—
100C5×C4⋊C4S411yescharacteristic
101C22⋊Dic5—61no—
102C22⋊Dic5—62no—
103C22⋊Dic5—61no—
104C22⋊Dic5—61no—
105C22⋊Dic5—61no—
106C22⋊Dic5—62no—
107C4⋊Dic5—62no—
108C4⋊Dic5—61no—
109C4⋊Dic5—62no—
110C4⋊Dic5—62no—
111C4⋊Dic5—61no—
112C4⋊Dic5—122no—
113#683—62no—
114#683—62no—
115#683—122no—
116C4×Dic5—61no—
117C4×Dic5—62no—
118C4×Dic5—61no—
119C2×#125—151no—
120C22×C4⋊C4D1511yescharacteristic
121#400—152no—
122#398—152no—
123#389—151no—
124#389—151no—
125#385—152no—
126#382—151no—
127#380—152no—
128#380—151no—
129C4×C22⋊C4—151no—
130C22×C3×C5—41no—
131C5×A4#12511yescharacteristic, complemented
132C3×C4×C5—42no—
133C3×C4×C5—82no—
134Dic15—81no—
135Dic15—81no—
136Dic15—82no—
137C22×A4C22×D511yescharacteristic
138C4×A4—22no—
139C4×A4Dic1012yes—
140SL(2,ℤ/4)—101no—
141SL(2,ℤ/4)—101no—
142SL(2,ℤ/4)—102no—
143C3×C4⋊C4—41no—
144C4⋊Dic3—202no—
145C4⋊Dic3—201no—
146Dic3⋊C4—202no—
147C4×Dic3—201no—
148C23×C5—31no—
149C23×C5—31no—
150C23×C5—31no—
151C23×C5—31no—
152C23×C5C2×Dic611yescharacteristic
153C23×C5#23711yescharacteristic
154C23×C5#23911yescharacteristic
155C2×C4×C5—31no—
156C2×C4×C5—32no—
157C2×C4×C5—32no—
158C2×C4×C5—32no—
159C2×C4×C5—32no—
160C2×C4×C5—62no—
161C2×C4×C5—62no—
162C2×C4×C5—61no—
163C2×C4×C5—62no—
164C2×C4×C5—62no—
165C2×C4×C5C2×S412yes—
166C2×C4×C5C2×S411yescharacteristic
167C2×Dic5—61no—
168C2×Dic5—61no—
169C2×Dic5—61no—
170C2×Dic5—62no—
171C2×Dic5—62no—
172C2×Dic5—61no—
173C2×Dic5—61no—
174C2×Dic5—61no—
175C2×Dic5—62no—
176C2×Dic5—61no—
177C2×Dic5—61no—
178C2×Dic5—62no—
179C2×Dic5—61no—
180C2×Dic5—61no—
181C2×Dic5—62no—
182C2×Dic5—61no—
183C2×Dic5—61no—
184C2×Dic5—62no—
185C23×C4C2×D1512yes—
186C23×C4C2×D1511yescharacteristic
187#125—302no—
188#125—301no—
189#125—301no—
190C2×C4⋊C4—31no—
191C2×C4⋊C4—31no—
192C2×C4⋊C4—32no—
193C2×C4⋊C4—151no—
194C2×C4⋊C4—152no—
195C2×C4⋊C4—152no—
196C2×C4⋊C4—151no—
197C2×C4⋊C4—152no—
198C2×C4⋊C4—152no—
199C2×C22⋊C4—151no—
200C2×C22⋊C4—151no—
201C2×C22⋊C4—152no—
202C2×C42—151no—
203C2×C42—151no—
204#95—151no—
205#95—151no—
206#95—152no—
207#95—152no—
208#95—152no—
209#95—152no—
210#95—152no—
211C2×C3×C5—41no—
212C2×C3×C5—41no—
213C2×C3×C5—41no—
214C2×A4C2×Dic1011yescharacteristic
215C2×A4#71111yescharacteristic
216C2×A4#71311yescharacteristic
217C2×C3×C4—41no—
218C2×C3×C4—42no—
219C2×Dic3—201no—
220C2×Dic3—201no—
221C2×Dic3—202no—
222C22×C5—31no—
223C22×C5—31no—
224C22×C5—31no—
225C22×C5—31no—
226C22×C5—31no—
227C22×C5—31no—
228C22×C5—31no—
229C22×C5—31no—
230C22×C5—31no—
231C22×C5—61no—
232C22×C5#89011yescharacteristic, complemented
233C22×C5C22×S411yescharacteristic
234C4×C5—22no—
235C4×C5—32no—
236C4×C5—62no—
237C4×C5A4⋊Q812yes—
238Dic5—121no—
239Dic5—122no—
240Dic5—121no—
241Dic5—121no—
242Dic5—121no—
243Dic5—122no—
244C24C22×D1511yescharacteristic
245C22×C4—22no—
246C22×C4—31no—
247C22×C4—31no—
248C22×C4—32no—
249C22×C4—32no—
250C22×C4—32no—
251C22×C4—62no—
252C22×C4—151no—
253C22×C4—151no—
254C22×C4—151no—
255C22×C4—152no—
256C22×C4—152no—
257C22×C4—151no—
258C22×C4Dic3012yes—
259C4⋊C4—32no—
260C4⋊C4—31no—
261C4⋊C4—61no—
262C4⋊C4—302no—
263C4⋊C4—301no—
264C4⋊C4—302no—
265C4⋊C4—302no—
266C4⋊C4—302no—
267C4⋊C4—302no—
268C4⋊C4—301no—
269C4⋊C4—602no—
270C4⋊C4—602no—
271C4⋊C4C5⋊S411yescharacteristic
272C22⋊C4—301no—
273C22⋊C4—302no—
274C22⋊C4—301no—
275C22⋊C4—301no—
276C22⋊C4—301no—
277C22⋊C4—302no—
278C42—301no—
279C42—302no—
280C42—301no—
281C3×C5—41noHall
282C22×C3—41no—
283A4#403611yescharacteristic, complemented
284C3×C4—42no—
285C3×C4—82no—
286Dic3—401no—
287Dic3—401no—
288Dic3—402no—
289C2×C5—31no—
290C2×C5—31no—
291C2×C5—31no—
292C2×C5—31no—
293C2×C5C2×A4⋊Q811yescharacteristic
294C2×C5#591411yescharacteristic
295C2×C5#591911yescharacteristic
296C23—31no—
297C23—31no—
298C23—31no—
299C23—31no—
300C23C2×Dic3011yescharacteristic
301C23#681911yescharacteristic
302C23#682111yescharacteristic
303C2×C4—31no—
304C2×C4—32no—
305C2×C4—32no—
306C2×C4—32no—
307C2×C4—32no—
308C2×C4—62no—
309C2×C4—62no—
310C2×C4—61no—
311C2×C4—62no—
312C2×C4—62no—
313C2×C4—301no—
314C2×C4—301no—
315C2×C4—301no—
316C2×C4—301no—
317C2×C4—302no—
318C2×C4—301no—
319C2×C4—301no—
320C2×C4—302no—
321C2×C4—302no—
322C2×C4—302no—
323C2×C4—301no—
324C2×C4—301no—
325C2×C4—301no—
326C2×C4—301no—
327C2×C4—302no—
328C2×C4—301no—
329C2×C4—301no—
330C2×C4—302no—
331C2×C4C2×C5⋊S412yes—
332C2×C4C2×C5⋊S411yescharacteristic
333C2×C3—41no—
334C2×C3—41no—
335C2×C3—41no—
336C5#8530511yescharacteristic, complemented, Sylow
337C22—31no—
338C22—31no—
339C22—31no—
340C22—31no—
341C22—31no—
342C22—31no—
343C22—31no—
344C22—31no—
345C22—31no—
346C22—61no—
347C22#9177911yescharacteristic, complemented
348C22C22×C5⋊S411yescharacteristic
349C4—22no—
350C4—32no—
351C4—62no—
352C4—601no—
353C4—602no—
354C4—601no—
355C4—601no—
356C4—601no—
357C4—602no—
358C4#9194812yes—
359C3—41noSylow
360C2—31no—
361C2—31no—
362C2—31no—
363C2—31no—
364C2C2×#9194811yescharacteristic
365C2#1175689811yescharacteristic
366C2#1175690311yescharacteristic
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutator, prime radical, cosocleC22×C5×A4C23
FittingC22×C5×C4⋊C4D3
socleC24×C5C22×D3
hypercenterC4⋊C4C5⋊S4
hypocenterC5×A4#125
LCSG ▷ C22×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
131. C5×A4#125semidirect
232. C22×C5#890semidirect
283. A4#4036semidirect
336. C5#85305semidirect
347. C22#91779semidirect

Maximal subgroups

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

subgroupindex
C5×A4×C4⋊C42
C4⋊(A4⋊Dic5)2
#117521302
C4×A4⋊Dic52
#106139033
#917794
#853055