Finite Group Databasebeta

← C4⋊C4×C5⋊S4 #14513709

Subgroups — C4⋊C4×C5⋊S4 #14513709

Order 1920.

838 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 838 conjugacy classes of subgroups — too many to draw. Only its 93 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⋊S4C212yesmaximal
2C2×C4×C5⋊S4C211yesmaximal, characteristic
3C5×A4×C4⋊C4C211yesmaximal, characteristic, complemented
4C4⋊(A4⋊Dic5)C211yesmaximal, characteristic, complemented
5#11752130C212yesmaximal, complemented
6C4⋊C4×C22⋊D5—31nomaximal, Hall
7C22×C5⋊S4C2211yescharacteristic
8C2×C4×C5×A4C2212yes—
9C2×C4×C5×A4C2211yescharacteristic
10C2×A4⋊Dic5C2212yes—
11C2×A4⋊Dic5C2211yescharacteristic
12C4×C5⋊S4—24no—
13C4×C5⋊S4C414yescomplemented
14C4⋊C4×D15—41nomaximal
15C4⋊C4×S4—51nomaximal, Hall
16C22×C5×C4⋊C4D311yescharacteristic, complemented
17C2×C4×C22⋊D5—31no—
18C2×C4×C22⋊D5—32no—
19C2×D5×C4⋊C4—31no—
20#65501—31no—
21#65499—32no—
22#65278—32no—
23#65276—31no—
24#65265—31no—
25C4⋊C4×Dic5—31no—
26#65261—32no—
27C22×C5×A4C2311yescharacteristic
28C2×C5⋊S4C2×C412yes—
29C2×C5⋊S4D412yes—
30C2×C5⋊S4Q812yes—
31C2×C4×D15—41no—
32C2×C4×D15—42no—
33C4×C5×A4—22no—
34C4×C5×A4C2×C412yescomplemented
35A4⋊Dic5—22no—
36A4⋊Dic5C2×C412yescomplemented
37C3×C5×C4⋊C4—41no—
38C4⋊Dic15—41no—
39#6712—42no—
40C2×C4×S4—51no—
41C2×C4×S4—52no—
42A4×C4⋊C4D511yescharacteristic, complemented
43C4⋊SL(2,ℤ/4)—51no—
44SL(2,ℤ/4)⋊C4—52no—
45C23×C4×C5C2×D312yes—
46C23×C4×C5C2×D311yescharacteristic
47C22×C22⋊D5—31no—
48C22×C4×D5—31no—
49C22×C4×D5—32no—
50C2×C5×C4⋊C4—31no—
51C2×C5×C4⋊C4—32no—
52C2×C5×C4⋊C4—31no—
53C2×C22⋊Dic5—31no—
54C2×C22⋊Dic5—32no—
55C4×C22⋊D5—34no—
56C4×C22⋊D5—34no—
57C4×C22⋊D5—64no—
58C4×C22⋊D5—64no—
59C2×#685—31no—
60C2×#685—32no—
61C2×C4⋊Dic5—31no—
62C2×C4⋊Dic5—31no—
63C2×#683—31no—
64C2×#683—32no—
65C2×#683—32no—
66C2×#683—32no—
67C2×C4×Dic5—31no—
68C2×C4×Dic5—32no—
69D5×C4⋊C4—61no—
70D5×C4⋊C4—62no—
71D5×C4⋊C4—61no—
72#3963—32no—
73#3963—32no—
74#3963—32no—
75D4×C4⋊C4—151noSylow
76C22×D15—41no—
77C2×C5×A4C22×C411yescharacteristic
78C2×C5×A4C2×D411yescharacteristic
79C2×C5×A4C2×Q811yescharacteristic
80C5⋊S4C4⋊C414yesdirect product factor
81C2×C3×C4×C5—41no—
82C2×C3×C4×C5—42no—
83C2×Dic15—41no—
84C2×Dic15—42no—
85C4×D15—44no—
86C4×D15—84no—
87C22×S4—51no—
88C2×C4×A4C2×D512yes—
89C2×C4×A4C2×D511yescharacteristic
90C2×SL(2,ℤ/4)—51no—
91C2×SL(2,ℤ/4)—52no—
92C4×S4—54no—
93C4×S4—104no—
94D3×C4⋊C4—201no—
95C24×C5C22×D311yescharacteristic
96C23×D5—31no—
97C22×C4×C5—22no—
98C22×C4×C5—31no—
99C22×C4×C5—31no—
100C22×C4×C5—32no—
101C22×C4×C5—32no—
102C22×C4×C5—32no—
103C22×C4×C5—62no—
104C22×C4×C5C4×D312yescomplemented
105C2×C22⋊D5—32no—
106C2×C22⋊D5—32no—
107C2×C22⋊D5—32no—
108C2×C22⋊D5—32no—
109C2×C22⋊D5—32no—
110C2×C22⋊D5—32no—
111C22×Dic5—31no—
112C22×Dic5—31no—
113C22×Dic5—31no—
114C22×Dic5—32no—
115C22×Dic5—32no—
116C2×C4×D5—34no—
117C2×C4×D5—62no—
118C2×C4×D5—61no—
119C2×C4×D5—61no—
120C2×C4×D5—62no—
121C2×C4×D5—64no—
122C2×C4×D5—62no—
123C2×C4×D5—122no—
124C5×C4⋊C4—32no—
125C5×C4⋊C4—31no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4S411yescharacteristic, complemented
128C22⋊Dic5—32no—
129C22⋊Dic5—32no—
130C22⋊Dic5—62no—
131C22⋊Dic5—62no—
132#685—34no—
133#685—64no—
134C4⋊Dic5—61no—
135C4⋊Dic5—62no—
136C4⋊Dic5—61no—
137#683—34no—
138#683—64no—
139#683—62no—
140#683—62no—
141#683—122no—
142C4×Dic5—34no—
143C4×Dic5—64no—
144C2×C4×D4—151no—
145C2×C4×D4—152no—
146C22×C4⋊C4—151no—
147C22×C4⋊C4D1511yescharacteristic, complemented
148#389—152no—
149#385—152no—
150#385—152no—
151#384—151no—
152#380—151no—
153#380—151no—
154C4×C4⋊C4—151no—
155C22×C3×C5—41no—
156C2×D15—42no—
157C2×D15—42no—
158C2×D15—42no—
159C5×A4C2×C4⋊C411yescharacteristic, complemented
160C3×C4×C5—42no—
161C3×C4×C5—82no—
162Dic15—42no—
163Dic15—82no—
164C22×A4C22×D511yescharacteristic
165C2×S4—52no—
166C2×S4—52no—
167C2×S4—52no—
168C2×C4×D3—201no—
169C2×C4×D3—202no—
170C4×A4—22no—
171C4×A4C4×D512yescomplemented
172SL(2,ℤ/4)—52no—
173SL(2,ℤ/4)—102no—
174C3×C4⋊C4—41no—
175C4⋊Dic3—201no—
176Dic3⋊C4—202no—
177C23×C5—31no—
178C23×C5—31no—
179C23×C5—31no—
180C23×C5—31no—
181C23×C5C2×C4×D311yescharacteristic
182C23×C5D3×D411yescharacteristic
183C23×C5D3×Q811yescharacteristic
184C22×D5—32no—
185C22×D5—32no—
186C22×D5—32no—
187C22×D5—61no—
188C22×D5—61no—
189C22×D5—61no—
190C22×D5—61no—
191C2×C4×C5—31no—
192C2×C4×C5—32no—
193C2×C4×C5—32no—
194C2×C4×C5—32no—
195C2×C4×C5—32no—
196C2×C4×C5—62no—
197C2×C4×C5—62no—
198C2×C4×C5—61no—
199C2×C4×C5—62no—
200C2×C4×C5—62no—
201C2×C4×C5C2×S412yes—
202C2×C4×C5C2×S411yescharacteristic
203C22⋊D5—34no—
204C22⋊D5—34no—
205C22⋊D5—34no—
206C22⋊D5—34no—
207C2×Dic5—32no—
208C2×Dic5—32no—
209C2×Dic5—32no—
210C2×Dic5—32no—
211C2×Dic5—32no—
212C2×Dic5—61no—
213C2×Dic5—61no—
214C2×Dic5—61no—
215C2×Dic5—61no—
216C2×Dic5—62no—
217C2×Dic5—62no—
218C2×Dic5—62no—
219C2×Dic5—62no—
220C2×Dic5—62no—
221C2×Dic5—62no—
222C4×D5—64no—
223C4×D5—64no—
224C4×D5—124no—
225C4×D5—124no—
226C22×D4—151no—
227C23×C4—151no—
228C23×C4—152no—
229C23×C4C2×D1512yes—
230C23×C4C2×D1511yescharacteristic
231C4×D4—154no—
232C4×D4—154no—
233C4×D4—304no—
234C4×D4—304no—
235C2×C4⋊C4—31no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—32no—
238C2×C4⋊C4—151no—
239C2×C4⋊C4—151no—
240C2×C4⋊C4—152no—
241C2×C4⋊C4—152no—
242C2×C4⋊C4—151no—
243C2×C4⋊C4—152no—
244C2×C4⋊C4—301no—
245C2×C4⋊C4—302no—
246C2×C4⋊C4—301no—
247C2×C22⋊C4—151no—
248C2×C22⋊C4—151no—
249C2×C22⋊C4—152no—
250C2×C22⋊C4—152no—
251C2×C42—151no—
252C2×C42—152no—
253#95—152no—
254#95—152no—
255#95—152no—
256C2×C3×C5—41no—
257C2×C3×C5—41no—
258C2×C3×C5—41no—
259D15—44no—
260C22×D3—201no—
261C2×A4C2×C4×D511yescharacteristic
262C2×A4D4×D511yescharacteristic
263C2×A4Q8×D511yescharacteristic
264S4—54no—
265C2×C3×C4—41no—
266C2×C3×C4—42no—
267C2×Dic3—201no—
268C2×Dic3—202no—
269C4×D3—204no—
270C4×D3—404no—
271C22×C5—31no—
272C22×C5—31no—
273C22×C5—31no—
274C22×C5—31no—
275C22×C5—31no—
276C22×C5—31no—
277C22×C5—31no—
278C22×C5—31no—
279C22×C5—31no—
280C22×C5—61no—
281C22×C5D3×C4⋊C411yescharacteristic, complemented
282C22×C5C22×S411yescharacteristic
283C2×D5—34no—
284C2×D5—62no—
285C2×D5—62no—
286C2×D5—62no—
287C2×D5—62no—
288C2×D5—62no—
289C2×D5—62no—
290C4×C5—22no—
291C4×C5—32no—
292C4×C5—62no—
293C4×C5C4×S412yescomplemented
294Dic5—34no—
295Dic5—62no—
296Dic5—62no—
297Dic5—122no—
298Dic5—122no—
299C24—151no—
300C24C22×D1511yescharacteristic
301C2×D4—152no—
302C2×D4—152no—
303C2×D4—152no—
304C2×D4—152no—
305C2×D4—152no—
306C2×D4—152no—
307C22×C4—22no—
308C22×C4—31no—
309C22×C4—31no—
310C22×C4—32no—
311C22×C4—32no—
312C22×C4—32no—
313C22×C4—62no—
314C22×C4—154no—
315C22×C4—151no—
316C22×C4—151no—
317C22×C4—151no—
318C22×C4—152no—
319C22×C4—152no—
320C22×C4—301no—
321C22×C4—302no—
322C22×C4—302no—
323C22×C4—304no—
324C22×C4—301no—
325C22×C4—302no—
326C22×C4—602no—
327C22×C4C4×D1512yescomplemented
328C4⋊C4—32no—
329C4⋊C4—31no—
330C4⋊C4—61no—
331C4⋊C4—154no—
332C4⋊C4—302no—
333C4⋊C4—301no—
334C4⋊C4—302no—
335C4⋊C4—304no—
336C4⋊C4—302no—
337C4⋊C4—301no—
338C4⋊C4—602no—
339C4⋊C4C5⋊S411yescharacteristic, direct product factor
340C22⋊C4—154no—
341C22⋊C4—152no—
342C22⋊C4—152no—
343C22⋊C4—304no—
344C22⋊C4—302no—
345C22⋊C4—302no—
346C42—154no—
347C42—304no—
348C3×C5—41noHall
349C22×C3—41no—
350C2×D3—202no—
351C2×D3—202no—
352C2×D3—202no—
353A4D5×C4⋊C411yescharacteristic, complemented
354C3×C4—42no—
355C3×C4—82no—
356Dic3—202no—
357Dic3—402no—
358C2×C5—31no—
359C2×C5—31no—
360C2×C5—31no—
361C2×C5—31no—
362C2×C5C2×C4×S411yescharacteristic
363C2×C5D4×S411yescharacteristic
364C2×C5Q8×S411yescharacteristic
365D5—64no—
366C23—31no—
367C23—31no—
368C23—31no—
369C23—31no—
370C23—152no—
371C23—152no—
372C23—152no—
373C23—301no—
374C23—301no—
375C23—301no—
376C23—301no—
377C23C2×C4×D1511yescharacteristic
378C23D4×D1511yescharacteristic
379C23Q8×D1511yescharacteristic
380D4—154no—
381D4—154no—
382D4—154no—
383D4—154no—
384C2×C4—31no—
385C2×C4—32no—
386C2×C4—32no—
387C2×C4—32no—
388C2×C4—32no—
389C2×C4—62no—
390C2×C4—62no—
391C2×C4—61no—
392C2×C4—62no—
393C2×C4—62no—
394C2×C4—152no—
395C2×C4—152no—
396C2×C4—152no—
397C2×C4—152no—
398C2×C4—152no—
399C2×C4—304no—
400C2×C4—301no—
401C2×C4—301no—
402C2×C4—301no—
403C2×C4—301no—
404C2×C4—304no—
405C2×C4—302no—
406C2×C4—302no—
407C2×C4—302no—
408C2×C4—302no—
409C2×C4—302no—
410C2×C4—302no—
411C2×C4—604no—
412C2×C4—604no—
413C2×C4C2×C5⋊S412yes—
414C2×C4C2×C5⋊S411yescharacteristic
415C2×C3—41no—
416C2×C3—41no—
417C2×C3—41no—
418D3—204no—
419C5C4⋊C4×S411yescharacteristic, complemented, Sylow
420C22—31no—
421C22—31no—
422C22—31no—
423C22—31no—
424C22—31no—
425C22—31no—
426C22—31no—
427C22—31no—
428C22—31no—
429C22—61no—
430C22—154no—
431C22—302no—
432C22—302no—
433C22—302no—
434C22—302no—
435C22—302no—
436C22—302no—
437C22C4⋊C4×D1511yescharacteristic, complemented
438C22C22×C5⋊S411yescharacteristic
439C4—22no—
440C4—32no—
441C4—62no—
442C4—154no—
443C4—302no—
444C4—302no—
445C4—602no—
446C4—602no—
447C4C4×C5⋊S412yescomplemented
448C3—41noSylow
449C2—31no—
450C2—31no—
451C2—31no—
452C2—31no—
453C2—304no—
454C2C2×C4×C5⋊S411yescharacteristic
455C2D4×C5⋊S411yescharacteristic
456C2Q8×C5⋊S411yescharacteristic
subgroupG/H
center, FrattiniC22C22×C5⋊S4
commutatorC2×C5×A4C22×C4
FittingC22×C5×C4⋊C4D3
socleC24×C5C22×D3
prime radicalC22×C5⋊S4C22
cosocleC22×C5×A4C23
hypercenterC4⋊C4C5⋊S4
hypocenterC5×A4C2×C4⋊C4
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C5×A4×C4⋊C4C2semidirect
4. C4⋊(A4⋊Dic5)C2semidirect
5. #11752130C2semidirect
13. C4×C5⋊S4C4semidirect
16. C22×C5×C4⋊C4D3semidirect
34. C4×C5×A4C2×C4semidirect
36. A4⋊Dic5C2×C4semidirect
42. A4×C4⋊C4D5semidirect
80. C5⋊S4C4⋊C4direct (N × H)
104. C22×C4×C5C4×D3semidirect
127. C5×C4⋊C4S4semidirect
147. C22×C4⋊C4D15semidirect
159. C5×A4C2×C4⋊C4semidirect
171. C4×A4C4×D5semidirect
281. C22×C5D3×C4⋊C4semidirect
293. C4×C5C4×S4semidirect
327. C22×C4C4×D15semidirect
339. C4⋊C4C5⋊S4direct (N × H)
353. A4D5×C4⋊C4semidirect
419. C5C4⋊C4×S4semidirect
437. C22C4⋊C4×D15semidirect
447. C4C4×C5⋊S4semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5⋊S42
C5×A4×C4⋊C42
C4⋊(A4⋊Dic5)2
#117521302
C4⋊C4×C22⋊D53
C4⋊C4×D154
C4⋊C4×S45