Finite Group Databasebeta

← #14513622

Subgroups — #14513622

Order 1920.

742 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 742 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C22×C5×SL(2,ℤ/4)C211yesmaximal, characteristic
2A4×C22⋊Dic5C211yesmaximal, characteristic
3#11752151C211yesmaximal, characteristic
4SL(2,ℤ/4)⋊Dic5C212yesmaximal, complemented
5Dic5×SL(2,ℤ/4)C212yesmaximal, complemented
6#10613828—31nomaximal, Hall
7C23×C5×A4C2211yescharacteristic
8C2×A4×Dic5C2212yes—
9C2×A4⋊Dic5C2212yes—
10C2×C5×SL(2,ℤ/4)C414yescomplemented
11C2×C5×SL(2,ℤ/4)C2211yescharacteristic
12C2×C5×SL(2,ℤ/4)C2211yescharacteristic
13#91529—41nomaximal
14#85292—51nomaximal, Hall
15C22×C5×C22⋊C4—31no—
16C22×C22⋊Dic5D311yescharacteristic
17C2×#4072—31no—
18#65536—31no—
19#65501—31no—
20#65500—31no—
21C4×C22⋊Dic5—31no—
22#65240—32no—
23#65240—32no—
24#65239—32no—
25C22⋊C4×Dic5—32no—
26C22×C5×A4—22no—
27C22×C5×A4C2×C412yes—
28C22×C5×A4C2311yescharacteristic
29C22×C5×Dic3—41no—
30A4×Dic5—22no—
31A4⋊Dic5—22no—
32C5×SL(2,ℤ/4)C2×C412yes—
33C5×SL(2,ℤ/4)C2×C412yes—
34#6719—41no—
35C3×C22⋊Dic5—41no—
36Dic3⋊Dic5—42no—
37Dic3×Dic5—42no—
38C22×SL(2,ℤ/4)D511yescharacteristic
39A4×C22⋊C4—51no—
40#5432—51no—
41SL(2,ℤ/4)⋊C4—52no—
42C4×SL(2,ℤ/4)—52no—
43C25×C5C2×D311yescharacteristic
44C23×C4×C5—31no—
45C23×C4×C5—31no—
46C23×Dic5C2×D312yes—
47C2×C5×C22⋊C4—34no—
48C2×C5×C22⋊C4—31no—
49C2×C5×C22⋊C4—31no—
50C2×C5×C22⋊C4—34no—
51C2×C5×C22⋊C4—31no—
52C2×C5×C22⋊C4—31no—
53C2×C22⋊Dic5—31no—
54C2×C22⋊Dic5—32no—
55C2×C22⋊Dic5—31no—
56C2×C22⋊Dic5—31no—
57C2×C22⋊Dic5—31no—
58C2×C22⋊Dic5—32no—
59C2×C22⋊Dic5—32no—
60#4072—61no—
61#4072—62no—
62#4072—61no—
63C2×C4⋊Dic5—32no—
64C2×C4⋊Dic5—32no—
65C2×C4×Dic5—32no—
66C2×C4×Dic5—32no—
67#3963—32no—
68#3963—32no—
69#3963—32no—
70#3963—32no—
71#2342—151noSylow
72C23×C3×C5—41no—
73C2×C5×A4—22no—
74C2×C5×A4C22×C411yescharacteristic
75C2×C5×A4#4112yes—
76C2×Dic15—42no—
77C2×C5×Dic3—41no—
78C2×C5×Dic3—41no—
79C2×C5×Dic3—44no—
80C2×C3×Dic5—42no—
81C23×A4C2×D511yescharacteristic
82C2×C4×A4—52no—
83C2×SL(2,ℤ/4)—52no—
84C2×SL(2,ℤ/4)Dic514yescomplemented
85C2×SL(2,ℤ/4)C2×D511yescharacteristic
86C2×SL(2,ℤ/4)C2×D511yescharacteristic
87#877—201no—
88C24×C5—22no—
89C24×C5—31no—
90C24×C5—31no—
91C24×C5—32no—
92C24×C5—62no—
93C24×C5C4×D312yes—
94C24×C5C22×D311yescharacteristic
95C22×C4×C5—34no—
96C22×C4×C5—31no—
97C22×C4×C5—31no—
98C22×C4×C5—31no—
99C22×C4×C5—31no—
100C22×C4×C5—34no—
101C22×C4×C5—62no—
102C22×C4×C5—61no—
103C22×C4×C5—61no—
104C22×C4×C5—122no—
105C22×Dic5—22no—
106C22×Dic5—32no—
107C22×Dic5—32no—
108C22×Dic5—32no—
109C22×Dic5—32no—
110C22×Dic5—62no—
111C5×C22⋊C4—32no—
112C5×C22⋊C4—32no—
113C5×C22⋊C4—34no—
114C5×C22⋊C4—34no—
115C5×C22⋊C4—32no—
116C5×C22⋊C4—32no—
117C22⋊Dic5—31no—
118C22⋊Dic5—32no—
119C22⋊Dic5—61no—
120C22⋊Dic5—62no—
121C22⋊Dic5—62no—
122C22⋊Dic5—61no—
123C22⋊Dic5—62no—
124C22⋊Dic5—61no—
125C22⋊Dic5—122no—
126C22⋊Dic5S411yescharacteristic
127C4⋊Dic5—62no—
128C4⋊Dic5—62no—
129C4⋊Dic5—122no—
130C4×Dic5—62no—
131C4×Dic5—62no—
132C4×Dic5—122no—
133C2×#117—151no—
134C22×C22⋊C4—31no—
135C22×C22⋊C4—51no—
136#388—152no—
137#388—152no—
138#385—152no—
139#381—151no—
140#380—151no—
141#379—151no—
142C4×C22⋊C4—152no—
143C4×C22⋊C4—151no—
144C22×C3×C5—42no—
145C22×C3×C5—41no—
146C22×C3×C5—82no—
147C5×A4#11711yescharacteristic, complemented
148Dic15—82no—
149C3×Dic5—82no—
150C5×Dic3—42no—
151C5×Dic3—42no—
152C22×A4—22no—
153C22×A4C2×Dic512yes—
154C22×A4C22×D511yescharacteristic
155C22×Dic3—41no—
156C4×A4—102no—
157SL(2,ℤ/4)—102no—
158SL(2,ℤ/4)C2×Dic512yes—
159SL(2,ℤ/4)C2×Dic512yes—
160C3×C22⋊C4—201no—
161#217—201no—
162Dic3⋊C4—202no—
163C4×Dic3—202no—
164C23×C5—22no—
165C23×C5—31no—
166C23×C5—32no—
167C23×C5—31no—
168C23×C5—32no—
169C23×C5—32no—
170C23×C5—32no—
171C23×C5—31no—
172C23×C5—62no—
173C23×C5—62no—
174C23×C5—61no—
175C23×C5—62no—
176C23×C5—62no—
177C23×C5—64no—
178C23×C5—62no—
179C23×C5—122no—
180C23×C5C2×C4×D311yescharacteristic
181C23×C5#23712yes—
182C23×C5C2×S411yescharacteristic
183C2×C4×C5—32no—
184C2×C4×C5—32no—
185C2×C4×C5—32no—
186C2×C4×C5—32no—
187C2×C4×C5—62no—
188C2×C4×C5—62no—
189C2×C4×C5—61no—
190C2×C4×C5—61no—
191C2×C4×C5—64no—
192C2×C4×C5—64no—
193C2×C4×C5—61no—
194C2×C4×C5—61no—
195C2×C4×C5—124no—
196C2×Dic5—32no—
197C2×Dic5—62no—
198C2×Dic5—62no—
199C2×Dic5—62no—
200C2×Dic5—62no—
201C2×Dic5—62no—
202C2×Dic5—62no—
203C2×Dic5—62no—
204C2×Dic5—62no—
205C2×Dic5—62no—
206C2×Dic5—62no—
207C2×Dic5C2×S412yes—
208C25D3×D511yescharacteristic
209C23×C4—31no—
210C23×C4—31no—
211C23×C4—52no—
212#117—301no—
213#117—302no—
214#117—301no—
215C2×C4⋊C4—152no—
216C2×C4⋊C4—152no—
217C2×C22⋊C4—34no—
218C2×C22⋊C4—31no—
219C2×C22⋊C4—31no—
220C2×C22⋊C4—34no—
221C2×C22⋊C4—31no—
222C2×C22⋊C4—31no—
223C2×C22⋊C4—151no—
224C2×C22⋊C4—151no—
225C2×C22⋊C4—152no—
226C2×C22⋊C4—151no—
227C2×C22⋊C4—151no—
228C2×C22⋊C4—152no—
229C2×C22⋊C4—152no—
230C2×C42—152no—
231C2×C42—152no—
232#95—152no—
233#95—152no—
234#95—152no—
235#95—152no—
236C2×C3×C5—41no—
237C2×C3×C5—42no—
238C2×C3×C5—82no—
239C23×C3—41no—
240C2×A4—22no—
241C2×A4#70912yes—
242C2×A4C22×Dic511yescharacteristic
243C2×C3×C4—202no—
244C2×Dic3—41no—
245C2×Dic3—41no—
246C2×Dic3—44no—
247C2×Dic3—202no—
248C22×C5—22no—
249C22×C5—31no—
250C22×C5—32no—
251C22×C5—31no—
252C22×C5—31no—
253C22×C5—32no—
254C22×C5—32no—
255C22×C5—32no—
256C22×C5—62no—
257C22×C5—62no—
258C22×C5—64no—
259C22×C5—61no—
260C22×C5—62no—
261C22×C5—62no—
262C22×C5—62no—
263C22×C5—122no—
264C22×C5#87711yescharacteristic, complemented
265C22×C5C4×S412yes—
266C22×C5C22×S411yescharacteristic
267C4×C5—62no—
268C4×C5—62no—
269C4×C5—62no—
270C4×C5—62no—
271Dic5—22no—
272Dic5—62no—
273Dic5—122no—
274Dic5—122no—
275C24—22no—
276C24—31no—
277C24—31no—
278C24—32no—
279C24—62no—
280C24D3×Dic512yes—
281C24C2×D3×D511yescharacteristic
282C22×C4—31no—
283C22×C4—31no—
284C22×C4—31no—
285C22×C4—31no—
286C22×C4—34no—
287C22×C4—34no—
288C22×C4—61no—
289C22×C4—62no—
290C22×C4—61no—
291C22×C4—102no—
292C22×C4—122no—
293C22×C4—152no—
294C22×C4—152no—
295C22×C4—152no—
296C22×C4—152no—
297C22×C4—302no—
298C4⋊C4—302no—
299C4⋊C4—302no—
300C4⋊C4—602no—
301C22⋊C4—32no—
302C22⋊C4—32no—
303C22⋊C4—34no—
304C22⋊C4—34no—
305C22⋊C4—32no—
306C22⋊C4—32no—
307C22⋊C4—51no—
308C22⋊C4—152no—
309C22⋊C4—151no—
310C22⋊C4—301no—
311C22⋊C4—301no—
312C22⋊C4—302no—
313C22⋊C4—302no—
314C22⋊C4—302no—
315C22⋊C4—301no—
316C22⋊C4—602no—
317C42—302no—
318C42—302no—
319C42—602no—
320C3×C5—41noHall
321C22×C3—41no—
322C22×C3—42no—
323C22×C3—82no—
324A4#407211yescharacteristic, complemented
325C3×C4—402no—
326Dic3—42no—
327Dic3—42no—
328Dic3—402no—
329C2×C5—22no—
330C2×C5—32no—
331C2×C5—31no—
332C2×C5—31no—
333C2×C5—62no—
334C2×C5C2×C4×S411yescharacteristic
335C2×C5#591412yes—
336C23—22no—
337C23—31no—
338C23—31no—
339C23—32no—
340C23—32no—
341C23—31no—
342C23—32no—
343C23—32no—
344C23—62no—
345C23—62no—
346C23—61no—
347C23—62no—
348C23—62no—
349C23—64no—
350C23—62no—
351C23—122no—
352C23#677912yes—
353C23C2×D3×Dic511yescharacteristic
354C23D5×S411yescharacteristic
355C2×C4—32no—
356C2×C4—32no—
357C2×C4—32no—
358C2×C4—32no—
359C2×C4—52no—
360C2×C4—62no—
361C2×C4—62no—
362C2×C4—61no—
363C2×C4—61no—
364C2×C4—64no—
365C2×C4—61no—
366C2×C4—61no—
367C2×C4—64no—
368C2×C4—124no—
369C2×C4—152no—
370C2×C4—302no—
371C2×C4—302no—
372C2×C4—302no—
373C2×C4—302no—
374C2×C4—302no—
375C2×C4—302no—
376C2×C4—302no—
377C2×C4—302no—
378C2×C4—302no—
379C2×C4—302no—
380C2×C3—41no—
381C2×C3—42no—
382C2×C3—82no—
383C5#8529211yescharacteristic, complemented, Sylow
384C22—22no—
385C22—32no—
386C22—31no—
387C22—31no—
388C22—31no—
389C22—32no—
390C22—32no—
391C22—32no—
392C22—62no—
393C22—62no—
394C22—64no—
395C22—61no—
396C22—62no—
397C22—62no—
398C22—62no—
399C22—122no—
400C22#9152911yescharacteristic, complemented
401C22Dic5×S412yes—
402C22C2×D5×S411yescharacteristic
403C4—62no—
404C4—62no—
405C4—62no—
406C4—62no—
407C4—102no—
408C4—302no—
409C4—602no—
410C4—602no—
411C3—41noSylow
412C2—22no—
413C2—31no—
414C2—32no—
415C2—31no—
416C2—62no—
417C2C2×Dic5×S411yescharacteristic
418C2#1175679312yes—
subgroupG/H
center, FrattiniC22C2×D5×S4
commutatorC2×C5×A4C22×C4
FittingC25×C5C2×D3
socleC24×C5C22×D3
prime radicalC23×C5×A4C22
cosocleC22×C5×A4C23
hypercenterC23D5×S4
hypocenterC5×A4#117
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
4. SL(2,ℤ/4)⋊Dic5C2semidirect
5. Dic5×SL(2,ℤ/4)C2semidirect
10. C2×C5×SL(2,ℤ/4)C4semidirect
84. C2×SL(2,ℤ/4)Dic5semidirect
147. C5×A4#117semidirect
264. C22×C5#877semidirect
324. A4#4072semidirect
383. C5#85292semidirect
400. C22#91529semidirect

Maximal subgroups

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

subgroupindex
C22×C5×SL(2,ℤ/4)2
A4×C22⋊Dic52
#117521512
SL(2,ℤ/4)⋊Dic52
Dic5×SL(2,ℤ/4)2
#106138283
#915294
#852925