Finite Group Databasebeta

← C2×Q8×C5⋊S4 #14514599

Subgroups — C2×Q8×C5⋊S4 #14514599

Order 1920.

1622 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 1622 conjugacy classes of subgroups — too many to draw. Only its 173 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×C5⋊S4C218yesmaximal, direct product factor
3C2×C4×C5⋊S4C213yesmaximal
4C2×#91948C213yesmaximal, complemented
5C2×Q8×C22⋊D5—31nomaximal, Hall
6C22×C5⋊S4C2211yescharacteristic
7C2×Q8×D15—41nomaximal
8C5×Q8×A4C2214yescomplemented
9C2×C4×C5×A4C2213yes—
10C2×A4⋊Dic5C2213yes—
11C4×C5⋊S4C22112yes—
12#91948C22112yescomplemented
13C2×Q8×S4—51nomaximal, Hall
14C23×C5×Q8D311yescharacteristic, complemented
15C22×Q8×D5—31no—
16Q8×C22⋊D5—38no—
17Q8×C22⋊D5—38no—
18C2×#4092—33no—
19C2×Q8×Dic5—31no—
20C2×#4090—33no—
21C2×C4×C22⋊D5—33no—
22C2×#4070—33no—
23C22×C5×A4C2311yescharacteristic
24C2×C5⋊S4Q814yesdirect product factor
25C2×C5⋊S4C2312yes—
26C2×C3×C5×Q8—41no—
27Q8×D15—48no—
28C2×C4×D15—43no—
29C2×Dic30—43no—
30C4×C5×A4C2316yes—
31A4⋊Dic5C2316yes—
32C2×Q8×A4D511yescharacteristic, complemented
33Q8×S4—58no—
34C2×C4×S4—53no—
35C2×A4⋊Q8—53no—
36C22×C5×Q8—31no—
37C22×C5×Q8—33no—
38C22×C5×Q8—34no—
39C22×C5×Q8C2×D314yescomplemented
40C23×C4×C5C2×D313yes—
41C22×C22⋊D5—31no—
42C2×Q8×D5—38no—
43C2×Q8×D5—64no—
44C2×Q8×D5—63no—
45C2×Q8×D5—61no—
46C22×C4×D5—33no—
47C22×Dic10—33no—
48C2×C22⋊Dic5—33no—
49#4092—324no—
50Q8×Dic5—38no—
51#4090—324no—
52C4×C22⋊D5—312no—
53C4×C22⋊D5—312no—
54C2×#685—33no—
55C2×C4⋊Dic5—33no—
56#4070—312no—
57#4070—312no—
58C2×#683—36no—
59C2×#683—33no—
60C2×C4×Dic5—33no—
61C2×D4×Q8—151noSylow
62C22×D15—41no—
63C2×C5×A4C2×Q812yescomplemented
64C2×C5×A4C2411yescharacteristic
65C5⋊S4C2×Q814yesdirect product factor
66C3×C5×Q8—44no—
67C2×C3×C4×C5—43no—
68C2×Dic15—43no—
69C4×D15—412no—
70Dic30—412no—
71C22×S4—51no—
72C2×D3×Q8—201no—
73Q8×A4C2×D514yescomplemented
74C2×C4×A4C2×D513yes—
75C2×SL(2,ℤ/4)—53no—
76C4×S4—512no—
77A4⋊Q8—512no—
78C24×C5C22×D311yescharacteristic
79C23×D5—31no—
80C2×C5×Q8—34no—
81C2×C5×Q8—34no—
82C2×C5×Q8—312no—
83C2×C5×Q8—33no—
84C2×C5×Q8—61no—
85C2×C5×Q8—66no—
86C2×C5×Q8S411yescharacteristic, complemented
87C22×C4×C5—33no—
88C22×C4×C5—33no—
89C22×C4×C5—36no—
90C22×C4×C5C22×D316yes—
91C2×C22⋊D5—34no—
92C2×C22⋊D5—32no—
93C2×C22⋊D5—34no—
94C2×C22⋊D5—32no—
95C22×Dic5—31no—
96C22×Dic5—33no—
97C22×Dic5—33no—
98Q8×D5—624no—
99Q8×D5—68no—
100C2×C4×D5—312no—
101C2×C4×D5—63no—
102C2×C4×D5—66no—
103C2×C4×D5—63no—
104C2×Dic10—312no—
105C2×Dic10—63no—
106C2×Dic10—66no—
107C2×Dic10—63no—
108C22⋊Dic5—36no—
109C22⋊Dic5—36no—
110#685—312no—
111C4⋊Dic5—312no—
112#683—324no—
113#683—312no—
114C4×Dic5—312no—
115C23×Q8—151no—
116C23×Q8D1511yescharacteristic, complemented
117D4×Q8—158no—
118D4×Q8—158no—
119C2×C4⋊Q8—153no—
120C2×C22⋊Q8—153no—
121C2×C22⋊Q8—153no—
122C2×C4×Q8—151no—
123C2×C4×D4—153no—
124C22×C3×C5—41no—
125C2×D15—44no—
126C2×D15—42no—
127C5×A4C22×Q811yescharacteristic, complemented
128C3×C4×C5—46no—
129Dic15—46no—
130C22×A4C22×D511yescharacteristic
131C2×S4—54no—
132C2×S4—52no—
133C2×C3×Q8—41no—
134D3×Q8—208no—
135C2×C4×D3—203no—
136C2×Dic6—203no—
137C4×A4C22×D516yes—
138SL(2,ℤ/4)—56no—
139C23×C5—31no—
140C23×C5—31no—
141C23×C5—32no—
142C23×C5D3×Q812yescomplemented
143C23×C5C23×D311yescharacteristic
144C22×D5—32no—
145C22×D5—34no—
146C22×D5—61no—
147C22×D5—62no—
148C22×D5—61no—
149C5×Q8—312no—
150C5×Q8—64no—
151C5×Q8C2×S414yescomplemented
152C2×C4×C5—33no—
153C2×C4×C5—36no—
154C2×C4×C5—36no—
155C2×C4×C5—36no—
156C2×C4×C5—63no—
157C2×C4×C5C2×S413yes—
158C22⋊D5—38no—
159C22⋊D5—34no—
160C22⋊D5—34no—
161C2×Dic5—32no—
162C2×Dic5—34no—
163C2×Dic5—36no—
164C2×Dic5—36no—
165C2×Dic5—63no—
166C2×Dic5—66no—
167C2×Dic5—63no—
168C4×D5—612no—
169C4×D5—612no—
170Dic10—612no—
171Dic10—612no—
172C22×Q8—31no—
173C22×Q8—33no—
174C22×Q8—34no—
175C22×Q8—153no—
176C22×Q8—158no—
177C22×Q8—304no—
178C22×Q8—303no—
179C22×Q8—301no—
180C22×Q8C2×D1514yescomplemented
181C22×D4—151no—
182C23×C4—153no—
183C23×C4C2×D1513yes—
184C4⋊Q8—1524no—
185C22⋊Q8—1512no—
186C22⋊Q8—1524no—
187C22⋊Q8—1512no—
188C4×Q8—158no—
189C4×D4—1512no—
190C4×D4—1512no—
191C2×C4⋊C4—153no—
192C2×C4⋊C4—153no—
193C2×C4⋊C4—156no—
194C2×C22⋊C4—153no—
195C2×C22⋊C4—153no—
196C2×C42—153no—
197C2×C3×C5—42no—
198C2×C3×C5—41no—
199D15—44no—
200C22×D3—201no—
201C2×A4Q8×D512yescomplemented
202C2×A4C23×D511yescharacteristic
203S4—54no—
204C3×Q8—44no—
205C2×C3×C4—43no—
206C2×Dic3—203no—
207C4×D3—2012no—
208Dic6—2012no—
209C22×C5—32no—
210C22×C5—31no—
211C22×C5—32no—
212C22×C5—32no—
213C22×C5—31no—
214C22×C5—31no—
215C22×C5—61no—
216C22×C5C2×D3×Q811yescharacteristic, complemented
217C22×C5C22×S411yescharacteristic
218C2×D5—34no—
219C2×D5—62no—
220C2×D5—64no—
221C2×D5—64no—
222C2×D5—62no—
223C4×C5—36no—
224C4×C5C22×S416yes—
225Dic5—34no—
226Dic5—66no—
227Dic5—66no—
228C24—151no—
229C24C22×D1511yescharacteristic
230C2×Q8—34no—
231C2×Q8—34no—
232C2×Q8—312no—
233C2×Q8—33no—
234C2×Q8—61no—
235C2×Q8—66no—
236C2×Q8—1512no—
237C2×Q8—303no—
238C2×Q8—306no—
239C2×Q8—3024no—
240C2×Q8—308no—
241C2×Q8—303no—
242C2×Q8C5⋊S411yescharacteristic, direct product factor
243C2×D4—152no—
244C2×D4—154no—
245C2×D4—154no—
246C2×D4—152no—
247C22×C4—33no—
248C22×C4—33no—
249C22×C4—36no—
250C22×C4—1512no—
251C22×C4—151no—
252C22×C4—153no—
253C22×C4—153no—
254C22×C4—303no—
255C22×C4—306no—
256C22×C4—303no—
257C22×C4C22×D1516yes—
258C4⋊C4—1512no—
259C4⋊C4—1512no—
260C4⋊C4—1524no—
261C22⋊C4—1512no—
262C22⋊C4—156no—
263C22⋊C4—156no—
264C42—1512no—
265C3×C5—41noHall
266C22×C3—41no—
267C2×D3—202no—
268C2×D3—204no—
269A4C2×Q8×D511yescharacteristic, complemented
270C3×C4—46no—
271Dic3—206no—
272C2×C5—31no—
273C2×C5—31no—
274C2×C5—32no—
275C2×C5Q8×S412yescomplemented
276C2×C5C23×S411yescharacteristic
277D5—64no—
278C23—31no—
279C23—31no—
280C23—32no—
281C23—152no—
282C23—154no—
283C23—301no—
284C23—302no—
285C23—301no—
286C23Q8×D1512yescomplemented
287C23C23×D1511yescharacteristic
288Q8—312no—
289Q8—64no—
290Q8—3012no—
291Q8—3012no—
292Q8C2×C5⋊S414yesdirect product factor
293D4—158no—
294D4—154no—
295D4—154no—
296C2×C4—33no—
297C2×C4—36no—
298C2×C4—36no—
299C2×C4—36no—
300C2×C4—63no—
301C2×C4—152no—
302C2×C4—154no—
303C2×C4—156no—
304C2×C4—156no—
305C2×C4—3012no—
306C2×C4—303no—
307C2×C4—306no—
308C2×C4—303no—
309C2×C4—3012no—
310C2×C4C2×C5⋊S413yes—
311C2×C3—42no—
312C2×C3—41no—
313D3—204no—
314C5C2×Q8×S411yescharacteristic, complemented, Sylow
315C22—32no—
316C22—31no—
317C22—32no—
318C22—32no—
319C22—31no—
320C22—31no—
321C22—61no—
322C22—154no—
323C22—302no—
324C22—304no—
325C22—304no—
326C22—302no—
327C22C2×Q8×D1511yescharacteristic, complemented
328C22C22×C5⋊S411yescharacteristic
329C4—36no—
330C4—154no—
331C4—306no—
332C4—306no—
333C4C22×C5⋊S416yes—
334C3—41noSylow
335C2—31no—
336C2—31no—
337C2—32no—
338C2—304no—
339C2Q8×C5⋊S412yesdirect product factor
340C2C23×C5⋊S411yescharacteristic
subgroupG/H
centerC22C22×C5⋊S4
commutator, cosocleC2×C5×A4C24
FrattiniC2C23×C5⋊S4
FittingC23×C5×Q8D3
socleC24×C5C22×D3
prime radicalC22×C5⋊S4C22
hypercenterC2×Q8C5⋊S4
hypocenterC5×A4C22×Q8
LCSG ▷ C2×C5×A4 ▷ C5×A4
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×C5⋊S4C2direct (N × H)
4. C2×#91948C2semidirect
8. C5×Q8×A4C22semidirect
12. #91948C22semidirect
14. C23×C5×Q8D3semidirect
24. C2×C5⋊S4Q8direct (N × H)
32. C2×Q8×A4D5semidirect
39. C22×C5×Q8C2×D3semidirect
63. C2×C5×A4C2×Q8semidirect
65. C5⋊S4C2×Q8direct (N × H)
73. Q8×A4C2×D5semidirect
86. C2×C5×Q8S4semidirect
116. C23×Q8D15semidirect
127. C5×A4C22×Q8semidirect
142. C23×C5D3×Q8semidirect
151. C5×Q8C2×S4semidirect
180. C22×Q8C2×D15semidirect
201. C2×A4Q8×D5semidirect
216. C22×C5C2×D3×Q8semidirect
242. C2×Q8C5⋊S4direct (N × H)
269. A4C2×Q8×D5semidirect
275. C2×C5Q8×S4semidirect
286. C23Q8×D15semidirect
292. Q8C2×C5⋊S4direct (N × H)
314. C5C2×Q8×S4semidirect
327. C22C2×Q8×D15semidirect
339. C2Q8×C5⋊S4direct (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×C5⋊S42
C2×C4×C5⋊S42
C2×#919482
C2×Q8×C22⋊D53
C2×Q8×D154
C2×Q8×S45