Finite Group Databasebeta

← C5×Q16×S4 #14511201

Subgroups — C5×Q16×S4 #14511201

Order 1920.

518 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 72 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×Q8×S4C212yesmaximal
2C5×A4×Q16C211yesmaximal, characteristic, complemented
3C5×#5416C212yesmaximal, complemented
4C5×C8×S4C211yesmaximal, characteristic
5C5×#5398C211yesmaximal, characteristic, complemented
6C5×D4×Q16—31nomaximal, Hall
7C5×Q8×A4C2212yes—
8C4×C5×S4—22no—
9C4×C5×S4C2211yescharacteristic
10C5×A4⋊Q8—22no—
11C5×A4⋊Q8C2212yes—
12C5×D3×Q16—41nomaximal
13C5×C8×A4C2211yescharacteristic
14C5×A4⋊C8C2211yescharacteristic
15Q16×S4C511yesmaximal, characteristic, direct product factor, Hall
16C22×C5×Q16—31no—
17C22×C5×Q16D311yescharacteristic, complemented
18C5×D4×Q8—32no—
19C5×#494—31no—
20C5×#467—31no—
21C5×#467—31no—
22C5×#462—32no—
23C5×#451—32no—
24C5×#451—32no—
25C4×C5×Q16—31no—
26C5×C8×D4—31no—
27C2×C5×S4D411yescharacteristic
28C5×D3×Q8—42no—
29C4×C5×A4—22no—
30C4×C5×A4C2311yescharacteristic
31C5×SL(2,ℤ/4)—22no—
32C5×SL(2,ℤ/4)D411yescharacteristic
33C3×C5×Q16—41no—
34C5×#216—42no—
35C5×Dic12—41no—
36C5×D3×C8—41no—
37Q8×S4C2×C512yes—
38A4×Q16C2×C511yescharacteristic, complemented
39#5416C2×C512yescomplemented
40C8×S4C2×C511yescharacteristic
41#5398C2×C511yescharacteristic, complemented
42C22×C5×Q8—32no—
43C22×C5×Q8C2×D312yes—
44C2×C5×Q16—31no—
45C2×C5×Q16—32no—
46C2×C5×Q16—31no—
47C2×C5×Q16—32no—
48C2×C5×Q16—31no—
49C2×C5×Q16—32no—
50C2×C5×Q16—62no—
51C2×C5×Q16—61no—
52C2×C5×Q16—61no—
53C22×C5×C8—31no—
54C22×C5×C8C2×D311yescharacteristic
55C5×C4⋊Q8—32no—
56C5×C4⋊Q8—62no—
57C5×C22⋊Q8—32no—
58C5×C22⋊Q8—32no—
59C5×C22⋊Q8—62no—
60C5×C22⋊Q8—62no—
61C4×C5×Q8—32no—
62C4×C5×D4—31no—
63C4×C5×D4—62no—
64C5×#107—31no—
65C5×C4⋊C8—31no—
66C5×#103—32no—
67C5×#103—32no—
68C5×#103—32no—
69C5×C22⋊C8—31no—
70C5×C22⋊C8—31no—
71C4×C5×C8—31no—
72D4×Q16—31noSylow
73C2×C5×A4C2×D411yescharacteristic
74C5×S4Q1612yesdirect product factor
75C3×C5×Q8—42no—
76C4×C5×D3—41no—
77C4×C5×D3—82no—
78C5×Dic6—42no—
79C5×Dic6—82no—
80C3×C5×C8—41no—
81C5×C3⋊C8—41no—
82Q8×A4C22×C512yes—
83C4×S4—22no—
84C4×S4C22×C511yescharacteristic
85A4⋊Q8—22no—
86A4⋊Q8C22×C512yes—
87D3×Q16—41no—
88C8×A4C22×C511yescharacteristic
89A4⋊C8C22×C511yescharacteristic
90C2×C5×Q8—32no—
91C2×C5×Q8—32no—
92C2×C5×Q8—32no—
93C2×C5×Q8—62no—
94C2×C5×Q8—62no—
95C2×C5×Q8—62no—
96C2×C5×Q8—62no—
97C2×C5×Q8—122no—
98C2×C5×D4—31no—
99C22×C4×C5—22no—
100C22×C4×C5—31no—
101C22×C4×C5—62no—
102C22×C4×C5C22×D311yescharacteristic
103C5×Q16—32no—
104C5×Q16—31no—
105C5×Q16—61no—
106C5×Q16—61no—
107C5×Q16—62no—
108C5×Q16—62no—
109C5×Q16—61no—
110C5×Q16—122no—
111C5×Q16S411yescharacteristic, direct product factor
112C2×C5×C8—31no—
113C2×C5×C8—31no—
114C2×C5×C8—31no—
115C2×C5×C8—31no—
116C2×C5×C8—61no—
117C2×C5×C8—61no—
118C5×C4⋊C4—31no—
119C5×C4⋊C4—32no—
120C5×C4⋊C4—62no—
121C5×C4⋊C4—62no—
122C5×C4⋊C4—62no—
123C5×C4⋊C4—62no—
124C5×C4⋊C4—62no—
125C5×C22⋊C4—31no—
126C5×C22⋊C4—31no—
127C5×C22⋊C4—62no—
128C5×C22⋊C4—62no—
129C42×C5—31no—
130C42×C5—62no—
131C22×Q16—31no—
132C22×Q16C5×D311yescharacteristic, complemented
133D4×Q8—32no—
134#494—31no—
135#467—31no—
136#467—31no—
137#462—32no—
138#451—32no—
139#451—32no—
140C4×Q16—31no—
141C8×D4—31no—
142C2×C5×D3—41no—
143C5×A4C2×Q1611yescharacteristic, complemented
144C3×C4×C5—41no—
145C3×C4×C5—82no—
146C5×Dic3—41no—
147C5×Dic3—82no—
148C2×S4C5×D411yescharacteristic
149D3×Q8—42no—
150C4×A4—22no—
151C4×A4C23×C511yescharacteristic
152SL(2,ℤ/4)—22no—
153SL(2,ℤ/4)C5×D411yescharacteristic
154C3×Q16—41no—
155#216—42no—
156Dic12—41no—
157D3×C8—41no—
158C23×C5—31no—
159C23×C5D3×D411yescharacteristic
160C5×Q8—32no—
161C5×Q8—62no—
162C5×Q8—62no—
163C5×Q8—62no—
164C5×Q8—62no—
165C5×Q8—122no—
166C5×Q8—122no—
167C5×Q8C2×S412yes—
168C5×D4—32no—
169C5×D4—32no—
170C2×C4×C5—31no—
171C2×C4×C5—31no—
172C2×C4×C5—31no—
173C2×C4×C5—31no—
174C2×C4×C5—31no—
175C2×C4×C5—62no—
176C2×C4×C5—61no—
177C2×C4×C5—61no—
178C2×C4×C5—62no—
179C2×C4×C5—62no—
180C2×C4×C5—62no—
181C2×C4×C5—122no—
182C2×C4×C5—122no—
183C5×C8—31no—
184C5×C8—61no—
185C5×C8—61no—
186C5×C8C2×S411yescharacteristic
187C22×Q8—32no—
188C22×Q8C2×C5×D312yes—
189C2×Q16—31no—
190C2×Q16—32no—
191C2×Q16—31no—
192C2×Q16—32no—
193C2×Q16—31no—
194C2×Q16—32no—
195C2×Q16—62no—
196C2×Q16—61no—
197C2×Q16—61no—
198C22×C8—31no—
199C22×C8C2×C5×D311yescharacteristic
200C4⋊Q8—32no—
201C4⋊Q8—62no—
202C22⋊Q8—32no—
203C22⋊Q8—32no—
204C22⋊Q8—62no—
205C22⋊Q8—62no—
206C4×Q8—32no—
207C4×D4—31no—
208C4×D4—62no—
209#107—31no—
210C4⋊C8—31no—
211#103—32no—
212#103—32no—
213#103—32no—
214C22⋊C8—31no—
215C22⋊C8—31no—
216C4×C8—31no—
217C2×C3×C5—41no—
218C5×D3—42no—
219C2×A4C2×C5×D411yescharacteristic
220S4C5×Q1612yesdirect product factor
221C3×Q8—42no—
222C4×D3—41no—
223C4×D3—82no—
224Dic6—42no—
225Dic6—82no—
226C3×C8—41no—
227C3⋊C8—41no—
228C22×C5—31no—
229C22×C5—31no—
230C22×C5—32no—
231C22×C5—61no—
232C22×C5—61no—
233C22×C5D3×Q1611yescharacteristic, complemented
234C4×C5—22no—
235C4×C5—32no—
236C4×C5—31no—
237C4×C5—61no—
238C4×C5—61no—
239C4×C5—62no—
240C4×C5—122no—
241C4×C5—122no—
242C4×C5C22×S411yescharacteristic
243C2×Q8—32no—
244C2×Q8—32no—
245C2×Q8—32no—
246C2×Q8—62no—
247C2×Q8—62no—
248C2×Q8—62no—
249C2×Q8—62no—
250C2×Q8—122no—
251C2×D4—31no—
252C22×C4—22no—
253C22×C4—31no—
254C22×C4—62no—
255C22×C4C22×C5×D311yescharacteristic
256Q16—32no—
257Q16—31no—
258Q16—61no—
259Q16—61no—
260Q16—62no—
261Q16—62no—
262Q16—61no—
263Q16—122no—
264Q16C5×S411yescharacteristic, direct product factor
265C2×C8—31no—
266C2×C8—31no—
267C2×C8—31no—
268C2×C8—31no—
269C2×C8—61no—
270C2×C8—61no—
271C4⋊C4—31no—
272C4⋊C4—32no—
273C4⋊C4—62no—
274C4⋊C4—62no—
275C4⋊C4—62no—
276C4⋊C4—62no—
277C4⋊C4—62no—
278C22⋊C4—31no—
279C22⋊C4—31no—
280C22⋊C4—62no—
281C22⋊C4—62no—
282C42—31no—
283C42—62no—
284C3×C5—41noHall
285C2×D3—41no—
286A4C2×C5×Q1611yescharacteristic, complemented
287C3×C4—41no—
288C3×C4—82no—
289Dic3—41no—
290Dic3—82no—
291C2×C5—31no—
292C2×C5—31no—
293C2×C5—62no—
294C2×C5D4×S411yescharacteristic
295C23—31no—
296C23C5×D3×D411yescharacteristic
297Q8—32no—
298Q8—62no—
299Q8—62no—
300Q8—62no—
301Q8—62no—
302Q8—122no—
303Q8—122no—
304Q8C2×C5×S412yes—
305D4—32no—
306D4—32no—
307C2×C4—31no—
308C2×C4—31no—
309C2×C4—31no—
310C2×C4—31no—
311C2×C4—31no—
312C2×C4—62no—
313C2×C4—61no—
314C2×C4—61no—
315C2×C4—62no—
316C2×C4—62no—
317C2×C4—62no—
318C2×C4—122no—
319C2×C4—122no—
320C8—31no—
321C8—61no—
322C8—61no—
323C8C2×C5×S411yescharacteristic
324C2×C3—41no—
325D3—42no—
326C5Q16×S411yescharacteristic, direct product factor, Sylow
327C22—31no—
328C22—31no—
329C22—32no—
330C22—61no—
331C22—61no—
332C22C5×D3×Q1611yescharacteristic, complemented
333C4—22no—
334C4—32no—
335C4—31no—
336C4—61no—
337C4—61no—
338C4—62no—
339C4—122no—
340C4—122no—
341C4C22×C5×S411yescharacteristic
342C3—41noSylow
343C2—31no—
344C2—31no—
345C2—62no—
346C2C5×D4×S411yescharacteristic
subgroupG/H
centerC2×C5D4×S4
commutator, cosocleC4×A4C23×C5
FrattiniC4C22×C5×S4
FittingC22×C5×Q16D3
socleC23×C5D3×D4
prime radicalC2×C5×S4D4
hypercenterC5×Q16S4
hypocenterA4C2×C5×Q16
LCSG ▷ C4×A4 ▷ C2×A4 ▷ A4
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×Q16

Complements

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

NH ≅ G/Ntype
2. C5×A4×Q16C2semidirect
3. C5×#5416C2semidirect
5. C5×#5398C2semidirect
15. Q16×S4C5direct (N × H)
17. C22×C5×Q16D3semidirect
38. A4×Q16C2×C5semidirect
39. #5416C2×C5semidirect
41. #5398C2×C5semidirect
74. C5×S4Q16direct (N × H)
111. C5×Q16S4direct (N × H)
132. C22×Q16C5×D3semidirect
143. C5×A4C2×Q16semidirect
220. S4C5×Q16direct (N × H)
233. C22×C5D3×Q16semidirect
264. Q16C5×S4direct (N × H)
286. A4C2×C5×Q16semidirect
326. C5Q16×S4direct (N × H)
332. C22C5×D3×Q16semidirect

Maximal subgroups

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

subgroupindex
C5×Q8×S42
C5×A4×Q162
C5×#54162
C5×C8×S42
C5×#53982
C5×D4×Q163
C5×D3×Q164
Q16×S45