Finite Group Databasebeta

← C22×D5×SL(2,ℤ/4) #14514527

Subgroups — C22×D5×SL(2,ℤ/4) #14514527

Order 1920.

3310 conjugacy classes of subgroups; only the 311 normal subgroups are shown.

normal subgroups only

This group has 3310 conjugacy classes of subgroups — too many to draw. Only its 311 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
1C23×D5×A4C211yesmaximal, characteristic
2C22×A4⋊Dic5C211yesmaximal, characteristic, complemented
3C22×C5×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4C2×D5×SL(2,ℤ/4)C2112yesmaximal, direct product factor
5C22×D5×C22⋊C4—31nomaximal, Hall
6C23×C5×A4C2211yescharacteristic
7C22×D5×A4C418yescomplemented
8C22×D5×A4C2216yes—
9C22×D5×Dic3—41nomaximal
10C2×A4⋊Dic5C2216yescomplemented
11C2×C5×SL(2,ℤ/4)C2216yescomplemented
12D5×SL(2,ℤ/4)C22116yesdirect product factor
13C23×SL(2,ℤ/4)—51nomaximal, Hall
14C25×D5D311yescharacteristic
15C23×C4×D5—31no—
16C23×C4×D5—31no—
17C22×C5×C22⋊C4—31no—
18C22×C22⋊Dic5—31no—
19C22×#685—31no—
20C22×#685—31no—
21C2×D5×C22⋊C4—312no—
22C2×D5×C22⋊C4—312no—
23C23×C3×D5—41no—
24C22×C5×A4C2×C414yescomplemented
25C22×C5×A4C2313yes—
26C2×D5×A4C2×C4124yescomplemented
27C2×D5×A4C2314yes—
28C22×Dic15—41no—
29C22×C5×Dic3—41no—
30C2×D5×Dic3—412no—
31A4⋊Dic5C2314yescomplemented
32C5×SL(2,ℤ/4)C2314yescomplemented
33C24×A4—51no—
34C22×SL(2,ℤ/4)—51no—
35C22×SL(2,ℤ/4)—512no—
36C22×SL(2,ℤ/4)D511yescharacteristic, direct product factor
37C25×C5C2×D311yescharacteristic
38C24×D5—31no—
39C24×D5—36no—
40C24×D5—31no—
41C24×D5—38no—
42C24×D5Dic318yescomplemented
43C24×D5C2×D316yes—
44C23×C4×C5—31no—
45C23×C4×C5—31no—
46C23×Dic5—31no—
47C23×Dic5—31no—
48C22×C4×D5—312no—
49C22×C4×D5—312no—
50C22×C4×D5—68no—
51C22×C4×D5—61no—
52C22×C4×D5—66no—
53C22×C4×D5—61no—
54C2×C5×C22⋊C4—36no—
55C2×C5×C22⋊C4—36no—
56C2×C22⋊Dic5—36no—
57C2×C22⋊Dic5—36no—
58C2×#685—312no—
59C2×#685—312no—
60D5×C22⋊C4—348no—
61D5×C22⋊C4—316no—
62C23×C22⋊C4—151noSylow
63C23×C3×C5—41no—
64C22×C3×D5—48no—
65C22×C3×D5—46no—
66C2×C5×A4C22×C416yescomplemented
67C2×C5×A4C2411yescharacteristic
68D5×A4C22×C418yescomplemented
69C2×Dic15—46no—
70C2×C5×Dic3—46no—
71D5×Dic3—416no—
72C23×A4—58no—
73C23×A4—56no—
74C23×A4C2×D511yescharacteristic
75C23×Dic3—201no—
76C2×SL(2,ℤ/4)—56no—
77C2×SL(2,ℤ/4)—516no—
78C2×SL(2,ℤ/4)C2×D516yesdirect product factor
79C24×C5—31no—
80C24×C5—33no—
81C24×C5—34no—
82C24×C5C2×Dic314yescomplemented
83C24×C5C22×D313yes—
84C23×D5—31no—
85C23×D5—38no—
86C23×D5—38no—
87C23×D5—36no—
88C23×D5—36no—
89C23×D5—38no—
90C23×D5—348no—
91C23×D5—324no—
92C23×D5—312no—
93C23×D5—36no—
94C23×D5—624no—
95C23×D5—64no—
96C23×D5—64no—
97C23×D5—63no—
98C23×D5C2×Dic3124yescomplemented
99C23×D5S411yescharacteristic
100C23×D5C22×D314yes—
101C22×C4×C5—36no—
102C22×C4×C5—36no—
103C22×C4×C5—64no—
104C22×C4×C5—63no—
105C22×C4×C5—61no—
106C22×Dic5—36no—
107C22×Dic5—36no—
108C22×Dic5—64no—
109C22×Dic5—63no—
110C22×Dic5—61no—
111C2×C4×D5—316no—
112C2×C4×D5—316no—
113C2×C4×D5—648no—
114C2×C4×D5—612no—
115C2×C4×D5—624no—
116C2×C4×D5—612no—
117C5×C22⋊C4—312no—
118C5×C22⋊C4—34no—
119C22⋊Dic5—312no—
120C22⋊Dic5—34no—
121#685—316no—
122#685—316no—
123C26—51no—
124C24×C4—151no—
125C24×C4—151no—
126C22×C22⋊C4—31no—
127C22×C22⋊C4—1512no—
128C22×C22⋊C4—1512no—
129C22×C22⋊C4—151no—
130C22×C22⋊C4—151no—
131C22×C22⋊C4—151no—
132C22×C3×C5—44no—
133C22×C3×C5—43no—
134C2×C3×D5—424no—
135C2×C3×D5—44no—
136C5×A4C23×C411yescharacteristic, complemented
137Dic15—44no—
138C5×Dic3—44no—
139C24×C3—201no—
140C22×A4—524no—
141C22×A4—54no—
142C22×A4C4×D514yescomplemented
143C22×A4C22×D513yes—
144C22×Dic3—41no—
145C22×Dic3—2012no—
146C22×Dic3—201no—
147SL(2,ℤ/4)—54no—
148SL(2,ℤ/4)C22×D514yesdirect product factor
149C23×C5—34no—
150C23×C5—34no—
151C23×C5—33no—
152C23×C5—33no—
153C23×C5—33no—
154C23×C5—312no—
155C23×C5—36no—
156C23×C5—66no—
157C23×C5—61no—
158C23×C5C22×Dic316yescomplemented
159C23×C5C2×S411yescharacteristic
160C23×C5C23×D311yescharacteristic
161C22×D5—38no—
162C22×D5—36no—
163C22×D5—324no—
164C22×D5—324no—
165C22×D5—348no—
166C22×D5—34no—
167C22×D5—312no—
168C22×D5—34no—
169C22×D5—324no—
170C22×D5—348no—
171C22×D5—38no—
172C22×D5—624no—
173C22×D5—632no—
174C22×D5—612no—
175C22×D5—624no—
176C22×D5—66no—
177C22×D5SL(2,ℤ/4)18yesdirect product factor
178C22×D5C22×Dic318yescomplemented
179C22×D5C2×S416yes—
180C2×C4×C5—34no—
181C2×C4×C5—34no—
182C2×C4×C5—612no—
183C2×C4×C5—66no—
184C2×C4×C5—66no—
185C2×Dic5—34no—
186C2×Dic5—34no—
187C2×Dic5—612no—
188C2×Dic5—66no—
189C2×Dic5—66no—
190C4×D5—632no—
191C4×D5—616no—
192C4×D5—616no—
193C25—58no—
194C25—56no—
195C25—151no—
196C25—151no—
197C25—156no—
198C25—158no—
199C25D3×D511yescharacteristic
200C23×C4—31no—
201C23×C4—31no—
202C23×C4—1512no—
203C23×C4—1512no—
204C23×C4—151no—
205C23×C4—151no—
206C23×C4—301no—
207C23×C4—306no—
208C23×C4—308no—
209C23×C4—301no—
210C2×C22⋊C4—36no—
211C2×C22⋊C4—36no—
212C2×C22⋊C4—1516no—
213C2×C22⋊C4—1548no—
214C2×C22⋊C4—1512no—
215C2×C22⋊C4—1512no—
216C2×C22⋊C4—156no—
217C2×C22⋊C4—156no—
218C2×C3×C5—46no—
219C2×C3×C5—41no—
220C3×D5—48no—
221C23×C3—41no—
222C23×C3—206no—
223C23×C3—208no—
224C2×A4—58no—
225C2×A4C2×C4×D516yescomplemented
226C2×A4C23×D511yescharacteristic
227C2×Dic3—46no—
228C2×Dic3—2016no—
229C2×Dic3—206no—
230C22×C5—36no—
231C22×C5—31no—
232C22×C5—36no—
233C22×C5—36no—
234C22×C5—312no—
235C22×C5—31no—
236C22×C5—33no—
237C22×C5—63no—
238C22×C5—64no—
239C22×C5C2×SL(2,ℤ/4)14yescomplemented
240C22×C5C23×Dic311yescharacteristic, complemented
241C22×C5C22×S413yes—
242C2×D5—324no—
243C2×D5—34no—
244C2×D5—38no—
245C2×D5—38no—
246C2×D5—348no—
247C2×D5—38no—
248C2×D5—64no—
249C2×D5—624no—
250C2×D5C2×SL(2,ℤ/4)124yesdirect product factor
251C2×D5C22×S414yes—
252C4×C5—64no—
253C4×C5—64no—
254Dic5—64no—
255Dic5—64no—
256C24—31no—
257C24—33no—
258C24—34no—
259C24—51no—
260C24—524no—
261C24—54no—
262C24—156no—
263C24—156no—
264C24—158no—
265C24—158no—
266C24—156no—
267C24—1512no—
268C24—158no—
269C24—1548no—
270C24—1524no—
271C24—151no—
272C24—303no—
273C24—304no—
274C24—304no—
275C24—3024no—
276C24D5×Dic314yescomplemented
277C24C2×D3×D513yes—
278C22×C4—36no—
279C22×C4—36no—
280C22×C4—64no—
281C22×C4—63no—
282C22×C4—61no—
283C22×C4—1516no—
284C22×C4—1516no—
285C22×C4—156no—
286C22×C4—156no—
287C22×C4—3012no—
288C22×C4—3024no—
289C22×C4—3048no—
290C22×C4—3012no—
291C22×C4—304no—
292C22×C4—303no—
293C22×C4—301no—
294C22⋊C4—312no—
295C22⋊C4—34no—
296C22⋊C4—1516no—
297C22⋊C4—1516no—
298C22⋊C4—1512no—
299C22⋊C4—154no—
300C3×C5—41noHall
301C22×C3—43no—
302C22×C3—44no—
303C22×C3—204no—
304C22×C3—2024no—
305A4C22×C4×D511yescharacteristic, complemented
306Dic3—44no—
307Dic3—204no—
308C2×C5—31no—
309C2×C5—31no—
310C2×C5—36no—
311C2×C5C22×SL(2,ℤ/4)16yescomplemented
312C2×C5C23×S411yescharacteristic
313D5—38no—
314D5C22×SL(2,ℤ/4)18yesdirect product factor
315C23—33no—
316C23—33no—
317C23—34no—
318C23—34no—
319C23—33no—
320C23—312no—
321C23—36no—
322C23—56no—
323C23—58no—
324C23—58no—
325C23—61no—
326C23—66no—
327C23—154no—
328C23—1512no—
329C23—1524no—
330C23—1524no—
331C23—1548no—
332C23—154no—
333C23—1548no—
334C23—158no—
335C23—1524no—
336C23—156no—
337C23—158no—
338C23—306no—
339C23—3012no—
340C23—3024no—
341C23—3024no—
342C23—3032no—
343C23C2×D5×Dic316yescomplemented
344C23D5×S411yescharacteristic
345C23C22×D3×D511yescharacteristic
346C2×C4—34no—
347C2×C4—34no—
348C2×C4—612no—
349C2×C4—66no—
350C2×C4—66no—
351C2×C4—154no—
352C2×C4—154no—
353C2×C4—3016no—
354C2×C4—3032no—
355C2×C4—3016no—
356C2×C4—3012no—
357C2×C4—306no—
358C2×C4—306no—
359C2×C3—41no—
360C2×C3—46no—
361C2×C3—208no—
362C5C23×SL(2,ℤ/4)11yescharacteristic, complemented, Sylow
363C22—36no—
364C22—31no—
365C22—31no—
366C22—33no—
367C22—36no—
368C22—36no—
369C22—312no—
370C22—54no—
371C22—524no—
372C22—63no—
373C22—64no—
374C22—158no—
375C22—158no—
376C22—1548no—
377C22—158no—
378C22—154no—
379C22—1524no—
380C22—304no—
381C22—3024no—
382C22D5×SL(2,ℤ/4)14yesdirect product factor
383C22C22×D5×Dic311yescharacteristic, complemented
384C22C2×D5×S413yes—
385C4—64no—
386C4—64no—
387C4—304no—
388C4—304no—
389C3—41noSylow
390C2—31no—
391C2—31no—
392C2—36no—
393C2—58no—
394C2—158no—
395C2C2×D5×SL(2,ℤ/4)16yesdirect product factor
396C2C22×D5×S411yescharacteristic
subgroupG/H
center, hypercenterC23D5×S4
commutator, hypocenterC5×A4C23×C4
FrattiniC2C22×D5×S4
Fitting, socleC25×C5C2×D3
prime radicalC23×D5×A4C2
cosocleC2×C5×A4C24
LCSG ▷ C5×A4
UCSC1 ◁ C23

Complements

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

NH ≅ G/Ntype
2. C22×A4⋊Dic5C2semidirect
3. C22×C5×SL(2,ℤ/4)C2semidirect
4. C2×D5×SL(2,ℤ/4)C2direct (N × H)
7. C22×D5×A4C4semidirect
10. C2×A4⋊Dic5C22semidirect
11. C2×C5×SL(2,ℤ/4)C22semidirect
12. D5×SL(2,ℤ/4)C22direct (N × H)
24. C22×C5×A4C2×C4semidirect
26. C2×D5×A4C2×C4semidirect
31. A4⋊Dic5C23semidirect
32. C5×SL(2,ℤ/4)C23semidirect
36. C22×SL(2,ℤ/4)D5direct (N × H)
42. C24×D5Dic3semidirect
66. C2×C5×A4C22×C4semidirect
68. D5×A4C22×C4semidirect
78. C2×SL(2,ℤ/4)C2×D5direct (N × H)
82. C24×C5C2×Dic3semidirect
98. C23×D5C2×Dic3semidirect
136. C5×A4C23×C4semidirect
142. C22×A4C4×D5semidirect
148. SL(2,ℤ/4)C22×D5direct (N × H)
158. C23×C5C22×Dic3semidirect
177. C22×D5SL(2,ℤ/4)direct (N × H)
178. C22×D5C22×Dic3semidirect
225. C2×A4C2×C4×D5semidirect
239. C22×C5C2×SL(2,ℤ/4)semidirect
240. C22×C5C23×Dic3semidirect
250. C2×D5C2×SL(2,ℤ/4)direct (N × H)
276. C24D5×Dic3semidirect
305. A4C22×C4×D5semidirect
311. C2×C5C22×SL(2,ℤ/4)semidirect
314. D5C22×SL(2,ℤ/4)direct (N × H)
343. C23C2×D5×Dic3semidirect
362. C5C23×SL(2,ℤ/4)semidirect
382. C22D5×SL(2,ℤ/4)direct (N × H)
383. C22C22×D5×Dic3semidirect
395. C2C2×D5×SL(2,ℤ/4)direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D5×A42
C22×A4⋊Dic52
C22×C5×SL(2,ℤ/4)2
C2×D5×SL(2,ℤ/4)2
C22×D5×C22⋊C43
C22×D5×Dic34
C23×SL(2,ℤ/4)5