Finite Group Databasebeta

← C2×Q8×D5×A4 #14514653

Subgroups — C2×Q8×D5×A4 #14514653

Order 1920.

2608 conjugacy classes of subgroups; only the 291 normal subgroups are shown.

normal subgroups only

This group has 2608 conjugacy classes of subgroups — too many to draw. Only its 291 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×C5×Q8×A4C211yesmaximal, characteristic, complemented
2Q8×D5×A4C218yesmaximal, direct product factor
3C2×C4×D5×A4C213yesmaximal
4C2×A4×Dic10C213yesmaximal, complemented
5C23×Q8×D5C311yesmaximal, characteristic, complemented, Hall
6C22×D5×A4C2211yescharacteristic
7C2×C3×Q8×D5—41nomaximal
8C5×Q8×A4C2214yescomplemented
9C2×C4×C5×A4C2213yes—
10C2×A4×Dic5C2213yes—
11C4×D5×A4C22112yes—
12A4×Dic10C22112yescomplemented
13C22×Q8×A4—51nomaximal, Hall
14C23×C5×Q8C2×C311yescharacteristic, complemented
15C22×Q8×D5—31no—
16C22×Q8×D5—33no—
17C22×Q8×D5—33no—
18C22×Q8×D5—31no—
19C22×Q8×D5—38no—
20C22×Q8×D5C2×C318yescomplemented
21C23×C4×D5C2×C313yes—
22C23×Dic10C2×C313yescomplemented
23C22×C5×A4C2311yescharacteristic
24C2×D5×A4Q814yesdirect product factor
25C2×D5×A4C2312yes—
26C2×C3×C5×Q8—41no—
27C3×Q8×D5—48no—
28C2×C3×C4×D5—43no—
29C2×C3×Dic10—43no—
30C4×C5×A4C2316yes—
31A4×Dic5C2316yes—
32C2×Q8×A4—58no—
33C2×Q8×A4—53no—
34C2×Q8×A4D511yescharacteristic, direct product factor
35C22×C4×A4—53no—
36C24×D5C22×C311yescharacteristic
37C22×C5×Q8—33no—
38C22×C5×Q8—34no—
39C22×C5×Q8—31no—
40C22×C5×Q8C22×C314yescomplemented
41C23×C4×C5C22×C313yes—
42C23×Dic5C22×C313yes—
43C2×Q8×D5—38no—
44C2×Q8×D5—324no—
45C2×Q8×D5—32no—
46C2×Q8×D5—36no—
47C2×Q8×D5—324no—
48C2×Q8×D5—36no—
49C2×Q8×D5—31no—
50C2×Q8×D5—38no—
51C2×Q8×D5—38no—
52C2×Q8×D5—324no—
53C2×Q8×D5—324no—
54C2×Q8×D5—38no—
55C2×Q8×D5—33no—
56C2×Q8×D5—33no—
57C2×Q8×D5A411yescharacteristic, direct product factor
58C22×C4×D5—33no—
59C22×C4×D5—33no—
60C22×C4×D5—33no—
61C22×C4×D5—33no—
62C22×C4×D5—312no—
63C22×C4×D5C22×C3112yes—
64C22×Dic10—33no—
65C22×Dic10—33no—
66C22×Dic10—36no—
67C22×Dic10—312no—
68C22×Dic10C22×C3112yescomplemented
69C24×Q8—51noSylow
70C22×C3×D5—41no—
71C2×C5×A4C2×Q812yescomplemented
72C2×C5×A4C2411yescharacteristic
73D5×A4C2×Q814yesdirect product factor
74C3×C5×Q8—44no—
75C2×C3×C4×C5—43no—
76C2×C3×Dic5—43no—
77C3×C4×D5—412no—
78C3×Dic10—412no—
79C23×A4—51no—
80C22×C3×Q8—201no—
81Q8×A4—512no—
82Q8×A4C2×D514yesdirect product factor
83C2×C4×A4—53no—
84C2×C4×A4—512no—
85C2×C4×A4C2×D513yes—
86C24×C5C23×C311yescharacteristic
87C23×D5—31no—
88C23×D5—31no—
89C23×D5—32no—
90C23×D5—34no—
91C23×D5C3×Q814yescomplemented
92C23×D5C23×C312yes—
93C2×C5×Q8—312no—
94C2×C5×Q8—312no—
95C2×C5×Q8—32no—
96C2×C5×Q8—34no—
97C2×C5×Q8—34no—
98C2×C5×Q8—33no—
99C2×C5×Q8C2×A411yescharacteristic, complemented
100C22×C4×C5—33no—
101C22×C4×C5—33no—
102C22×C4×C5—36no—
103C22×C4×C5C23×C316yes—
104C22×Dic5—33no—
105C22×Dic5—33no—
106C22×Dic5—36no—
107C22×Dic5C23×C316yes—
108Q8×D5—316no—
109Q8×D5—348no—
110Q8×D5—348no—
111Q8×D5—38no—
112Q8×D5—324no—
113Q8×D5—324no—
114Q8×D5C2×A418yesdirect product factor
115C2×C4×D5—36no—
116C2×C4×D5—312no—
117C2×C4×D5—312no—
118C2×C4×D5—312no—
119C2×C4×D5—33no—
120C2×C4×D5—33no—
121C2×C4×D5—33no—
122C2×C4×D5—312no—
123C2×C4×D5—312no—
124C2×C4×D5—312no—
125C2×C4×D5—312no—
126C2×C4×D5—312no—
127C2×C4×D5C2×A413yes—
128C2×Dic10—36no—
129C2×Dic10—312no—
130C2×Dic10—324no—
131C2×Dic10—33no—
132C2×Dic10—36no—
133C2×Dic10—312no—
134C2×Dic10—312no—
135C2×Dic10—312no—
136C2×Dic10—324no—
137C2×Dic10C2×A413yescomplemented
138C23×Q8—58no—
139C23×Q8—53no—
140C23×Q8—151no—
141C23×Q8—153no—
142C23×Q8—153no—
143C23×Q8—158no—
144C23×Q8—151no—
145C23×Q8C3×D511yescharacteristic, complemented
146C24×C4—53no—
147C22×C3×C5—41no—
148C2×C3×D5—44no—
149C2×C3×D5—42no—
150C5×A4C22×Q811yescharacteristic, complemented
151C3×C4×C5—46no—
152C3×Dic5—46no—
153C22×A4—54no—
154C22×A4—52no—
155C22×A4C22×D511yescharacteristic
156C2×C3×Q8—41no—
157C2×C3×Q8—203no—
158C2×C3×Q8—208no—
159C22×C3×C4—203no—
160C4×A4—56no—
161C4×A4C22×D516yes—
162C23×C5—31no—
163C23×C5—32no—
164C23×C5—31no—
165C23×C5C2×C3×Q812yescomplemented
166C23×C5C24×C311yescharacteristic
167C22×D5—32no—
168C22×D5—34no—
169C22×D5—38no—
170C22×D5—31no—
171C22×D5—34no—
172C22×D5—34no—
173C22×D5—32no—
174C22×D5—32no—
175C22×D5—32no—
176C22×D5—34no—
177C22×D5—38no—
178C22×D5—34no—
179C22×D5C2×C3×Q814yescomplemented
180C22×D5C22×A411yescharacteristic
181C5×Q8—38no—
182C5×Q8—312no—
183C5×Q8C22×A414yescomplemented
184C2×C4×C5—36no—
185C2×C4×C5—33no—
186C2×C4×C5—36no—
187C2×C4×C5—36no—
188C2×C4×C5—36no—
189C2×C4×C5C22×A413yes—
190C2×Dic5—36no—
191C2×Dic5—33no—
192C2×Dic5—36no—
193C2×Dic5—36no—
194C2×Dic5—36no—
195C2×Dic5C22×A413yes—
196C4×D5—324no—
197C4×D5—312no—
198C4×D5—312no—
199C4×D5—312no—
200C4×D5C22×A4112yes—
201Dic10—324no—
202Dic10—312no—
203Dic10—324no—
204Dic10C22×A4112yescomplemented
205C25—51no—
206C22×Q8—33no—
207C22×Q8—34no—
208C22×Q8—31no—
209C22×Q8—51no—
210C22×Q8—512no—
211C22×Q8—153no—
212C22×Q8—153no—
213C22×Q8—156no—
214C22×Q8—1512no—
215C22×Q8—153no—
216C22×Q8—158no—
217C22×Q8—158no—
218C22×Q8—153no—
219C22×Q8—1524no—
220C22×Q8—1524no—
221C22×Q8—158no—
222C22×Q8—156no—
223C22×Q8—1524no—
224C22×Q8—152no—
225C22×Q8—1524no—
226C22×Q8—158no—
227C22×Q8—156no—
228C22×Q8—151no—
229C22×Q8C2×C3×D514yescomplemented
230C23×C4—53no—
231C23×C4—512no—
232C23×C4—153no—
233C23×C4—153no—
234C23×C4—1512no—
235C23×C4—153no—
236C23×C4—153no—
237C23×C4C2×C3×D513yes—
238C2×C3×C5—42no—
239C2×C3×C5—41no—
240C3×D5—44no—
241C23×C3—201no—
242C2×A4—54no—
243C2×A4Q8×D512yesdirect product factor
244C2×A4C23×D511yescharacteristic
245C3×Q8—44no—
246C3×Q8—2012no—
247C2×C3×C4—43no—
248C2×C3×C4—2012no—
249C2×C3×C4—203no—
250C22×C5—32no—
251C22×C5—31no—
252C22×C5—32no—
253C22×C5—32no—
254C22×C5—32no—
255C22×C5—31no—
256C22×C5—31no—
257C22×C5C22×C3×Q811yescharacteristic, complemented
258C22×C5C23×A411yescharacteristic
259C2×D5—38no—
260C2×D5—34no—
261C2×D5—34no—
262C2×D5—32no—
263C2×D5—34no—
264C2×D5—38no—
265C2×D5—34no—
266C2×D5—34no—
267C2×D5Q8×A414yesdirect product factor
268C2×D5C23×A412yes—
269C4×C5—36no—
270C4×C5C23×A416yes—
271Dic5—36no—
272Dic5C23×A416yes—
273C24—54no—
274C24—52no—
275C24—151no—
276C24—152no—
277C24—151no—
278C24—154no—
279C24C22×C3×D511yescharacteristic
280C2×Q8—312no—
281C2×Q8—312no—
282C2×Q8—32no—
283C2×Q8—34no—
284C2×Q8—34no—
285C2×Q8—33no—
286C2×Q8—58no—
287C2×Q8—53no—
288C2×Q8—156no—
289C2×Q8—1512no—
290C2×Q8—1512no—
291C2×Q8—1512no—
292C2×Q8—1524no—
293C2×Q8—1524no—
294C2×Q8—156no—
295C2×Q8—1512no—
296C2×Q8—1524no—
297C2×Q8—1524no—
298C2×Q8—1548no—
299C2×Q8—1516no—
300C2×Q8—1548no—
301C2×Q8—158no—
302C2×Q8—153no—
303C2×Q8D5×A411yescharacteristic, direct product factor
304C22×C4—33no—
305C22×C4—33no—
306C22×C4—36no—
307C22×C4—53no—
308C22×C4—56no—
309C22×C4—1512no—
310C22×C4—153no—
311C22×C4—1512no—
312C22×C4—153no—
313C22×C4—1512no—
314C22×C4—1512no—
315C22×C4—156no—
316C22×C4—1512no—
317C22×C4—1512no—
318C22×C4—1512no—
319C22×C4—1512no—
320C22×C4—153no—
321C22×C4—153no—
322C22×C4—156no—
323C22×C4—153no—
324C22×C4C22×C3×D516yes—
325C3×C5—41noHall
326C22×C3—41no—
327C22×C3—202no—
328C22×C3—204no—
329A4C2×Q8×D511yescharacteristic, direct product factor
330C3×C4—46no—
331C3×C4—206no—
332C2×C5—32no—
333C2×C5—31no—
334C2×C5—31no—
335C2×C5C2×Q8×A412yescomplemented
336C2×C5C24×A411yescharacteristic
337D5—34no—
338D5C2×Q8×A414yesdirect product factor
339C23—31no—
340C23—32no—
341C23—31no—
342C23—51no—
343C23—54no—
344C23—152no—
345C23—152no—
346C23—154no—
347C23—154no—
348C23—152no—
349C23—158no—
350C23—154no—
351C23—154no—
352C23—152no—
353C23—158no—
354C23—154no—
355C23—151no—
356C23C3×Q8×D512yescomplemented
357C23C23×C3×D511yescharacteristic
358Q8—38no—
359Q8—312no—
360Q8—512no—
361Q8—1524no—
362Q8—1524no—
363Q8—1512no—
364Q8C2×D5×A414yesdirect product factor
365C2×C4—36no—
366C2×C4—33no—
367C2×C4—36no—
368C2×C4—36no—
369C2×C4—36no—
370C2×C4—53no—
371C2×C4—512no—
372C2×C4—1512no—
373C2×C4—1512no—
374C2×C4—1524no—
375C2×C4—156no—
376C2×C4—156no—
377C2×C4—156no—
378C2×C4—153no—
379C2×C4—1512no—
380C2×C4—156no—
381C2×C4C2×D5×A413yes—
382C2×C3—41no—
383C2×C3—42no—
384C2×C3—204no—
385C5C22×Q8×A411yescharacteristic, complemented, Sylow
386C22—32no—
387C22—31no—
388C22—32no—
389C22—31no—
390C22—31no—
391C22—32no—
392C22—32no—
393C22—52no—
394C22—54no—
395C22—154no—
396C22—154no—
397C22—158no—
398C22—154no—
399C22—154no—
400C22—158no—
401C22—152no—
402C22—154no—
403C22C2×C3×Q8×D511yescharacteristic, complemented
404C22C22×D5×A411yescharacteristic
405C4—36no—
406C4—56no—
407C4—156no—
408C4C22×D5×A416yes—
409C3—41noSylow
410C2—31no—
411C2—32no—
412C2—31no—
413C2—54no—
414C2—154no—
415C2Q8×D5×A412yesdirect product factor
416C2C23×D5×A411yescharacteristic
subgroupG/H
centerC22C22×D5×A4
commutator, cosocleC23×C5C24×C3
FrattiniC2C23×D5×A4
FittingC23×C5×Q8C2×C3
socleC24×C5C23×C3
prime radicalC22×D5×A4C22
hypercenterC2×Q8D5×A4
hypocenterC22×C5C22×C3×Q8
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C5×Q8×A4C2semidirect
2. Q8×D5×A4C2direct (N × H)
4. C2×A4×Dic10C2semidirect
5. C23×Q8×D5C3semidirect
8. C5×Q8×A4C22semidirect
12. A4×Dic10C22semidirect
14. C23×C5×Q8C2×C3semidirect
20. C22×Q8×D5C2×C3semidirect
22. C23×Dic10C2×C3semidirect
24. C2×D5×A4Q8direct (N × H)
34. C2×Q8×A4D5direct (N × H)
40. C22×C5×Q8C22×C3semidirect
57. C2×Q8×D5A4direct (N × H)
68. C22×Dic10C22×C3semidirect
71. C2×C5×A4C2×Q8semidirect
73. D5×A4C2×Q8direct (N × H)
82. Q8×A4C2×D5direct (N × H)
91. C23×D5C3×Q8semidirect
99. C2×C5×Q8C2×A4semidirect
114. Q8×D5C2×A4direct (N × H)
137. C2×Dic10C2×A4semidirect
145. C23×Q8C3×D5semidirect
150. C5×A4C22×Q8semidirect
165. C23×C5C2×C3×Q8semidirect
179. C22×D5C2×C3×Q8semidirect
183. C5×Q8C22×A4semidirect
204. Dic10C22×A4semidirect
229. C22×Q8C2×C3×D5semidirect
243. C2×A4Q8×D5direct (N × H)
257. C22×C5C22×C3×Q8semidirect
267. C2×D5Q8×A4direct (N × H)
303. C2×Q8D5×A4direct (N × H)
329. A4C2×Q8×D5direct (N × H)
335. C2×C5C2×Q8×A4semidirect
338. D5C2×Q8×A4direct (N × H)
356. C23C3×Q8×D5semidirect
364. Q8C2×D5×A4direct (N × H)
385. C5C22×Q8×A4semidirect
403. C22C2×C3×Q8×D5semidirect
415. C2Q8×D5×A4direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×Q8×A42
Q8×D5×A42
C2×C4×D5×A42
C2×A4×Dic102
C23×Q8×D53
C2×C3×Q8×D54
C22×Q8×A45