Finite Group Databasebeta

← C2×D5×A4⋊C8 #14512997

Subgroups — C2×D5×A4⋊C8 #14512997

Order 1920.

806 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 119 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×D5×A4C211yesmaximal, characteristic
2C2×A4⋊#168C211yesmaximal, characteristic, complemented
3C2×C5×A4⋊C8C211yesmaximal, characteristic, complemented
4D5×A4⋊C8C214yesmaximal, direct product factor
5C2×D5×C22⋊C8—31nomaximal, Hall
6C22×D5×A4C411yescharacteristic
7C2×C4×C5×A4C2211yescharacteristic
8C2×A4×Dic5C411yescharacteristic
9C4×D5×A4C412yes—
10C4×D5×A4C2212yes—
11C2×D5×C3⋊C8—41nomaximal
12A4⋊#168C2212yescomplemented
13C5×A4⋊C8C2212yescomplemented
14C22×A4⋊C8—51nomaximal, Hall
15C23×C4×D5D311yescharacteristic
16C22×C8×D5—31no—
17C22×C8×D5—31no—
18C2×C5×C22⋊C8—31no—
19C2×C22⋊#168—31no—
20C2×#3952—31no—
21C2×#3952—31no—
22D5×C22⋊C8—34no—
23D5×C22⋊C8—34no—
24C22×C5×A4C2×C411yescharacteristic
25C2×D5×A4C814yescomplemented
26C2×D5×A4C2×C412yes—
27C2×C3×C4×D5—41no—
28C4×C5×A4C2×C411yescharacteristic
29C4×C5×A4C2311yescharacteristic
30A4×Dic5C2×C412yes—
31C2×C3⋊#168—41no—
32C2×C5×C3⋊C8—41no—
33D5×C3⋊C8—44no—
34C22×C4×A4—51no—
35C2×A4⋊C8—51no—
36C2×A4⋊C8—54no—
37C2×A4⋊C8D511yescharacteristic, direct product factor
38C24×D5Dic311yescharacteristic
39C23×C4×C5C2×D311yescharacteristic
40C23×Dic5Dic311yescharacteristic
41C22×C4×D5—31no—
42C22×C4×D5—31no—
43C22×C4×D5—31no—
44C22×C4×D5—31no—
45C22×C4×D5—32no—
46C22×C4×D5—32no—
47C22×C4×D5Dic312yes—
48C22×C4×D5C2×D312yes—
49C22×C5×C8—31no—
50C22×C5×C8—31no—
51C22×#168—31no—
52C22×#168—31no—
53C2×C8×D5—34no—
54C2×C8×D5—34no—
55C2×C8×D5—61no—
56C2×C8×D5—61no—
57C2×C8×D5—62no—
58C2×C8×D5—61no—
59C2×C8×D5—62no—
60C2×C8×D5—61no—
61C5×C22⋊C8—32no—
62C5×C22⋊C8—32no—
63C22⋊#168—32no—
64C22⋊#168—32no—
65#3952—34no—
66#3952—34no—
67C22×C22⋊C8—151noSylow
68C22×C3×D5—41no—
69C2×C5×A4C2×C812yescomplemented
70C2×C5×A4C22×C411yescharacteristic
71D5×A4C2×C814yescomplemented
72C2×C3×C4×C5—41no—
73C2×C3×Dic5—41no—
74C3×C4×D5—42no—
75C3×C4×D5—42no—
76C3⋊#168—42no—
77C5×C3⋊C8—42no—
78C23×A4—51no—
79C2×C4×A4—51no—
80C2×C4×A4—52no—
81C2×C4×A4—52no—
82C2×C4×A4C2×D511yescharacteristic
83C22×C3⋊C8—201no—
84A4⋊C8—52no—
85A4⋊C8C2×D512yesdirect product factor
86C24×C5C2×Dic311yescharacteristic
87C23×D5—31no—
88C23×D5—31no—
89C23×D5—32no—
90C23×D5—34no—
91C23×D5C3⋊C814yescomplemented
92C23×D5C2×Dic312yes—
93C22×C4×C5—31no—
94C22×C4×C5—31no—
95C22×C4×C5—31no—
96C22×C4×C5—31no—
97C22×C4×C5C2×Dic311yescharacteristic
98C22×C4×C5C22×D311yescharacteristic
99C22×Dic5—31no—
100C22×Dic5—31no—
101C22×Dic5—32no—
102C22×Dic5C2×Dic312yes—
103C2×C4×D5—31no—
104C2×C4×D5—31no—
105C2×C4×D5—31no—
106C2×C4×D5—32no—
107C2×C4×D5—32no—
108C2×C4×D5—32no—
109C2×C4×D5—32no—
110C2×C4×D5—32no—
111C2×C4×D5—32no—
112C2×C4×D5—32no—
113C2×C4×D5—32no—
114C2×C4×D5—32no—
115C2×C4×D5—32no—
116C2×C4×D5—62no—
117C2×C4×D5—61no—
118C2×C4×D5—61no—
119C2×C4×D5—62no—
120C2×C4×D5—61no—
121C2×C4×D5S411yescharacteristic
122C2×C5×C8—32no—
123C2×C5×C8—32no—
124C2×C5×C8—61no—
125C2×C5×C8—61no—
126C2×C5×C8—61no—
127C2×C5×C8—61no—
128C2×#168—32no—
129C2×#168—32no—
130C2×#168—61no—
131C2×#168—61no—
132C2×#168—61no—
133C2×#168—61no—
134C8×D5—64no—
135C8×D5—64no—
136C8×D5—64no—
137C8×D5—64no—
138C24×C4—51no—
139C23×C8—151no—
140C23×C8—151no—
141C2×C22⋊C8—31no—
142C2×C22⋊C8—154no—
143C2×C22⋊C8—154no—
144C2×C22⋊C8—151no—
145C2×C22⋊C8—151no—
146C2×C22⋊C8—151no—
147C22×C3×C5—41no—
148C2×C3×D5—44no—
149C2×C3×D5—42no—
150C5×A4C22×C811yescharacteristic, complemented
151C3×C4×C5—41no—
152C3×C4×C5—41no—
153C3×Dic5—42no—
154C22×A4—54no—
155C22×A4—52no—
156C22×A4C4×D511yescharacteristic
157C22×C3×C4—201no—
158C4×A4—52no—
159C4×A4C4×D511yescharacteristic
160C4×A4C22×D511yescharacteristic
161C2×C3⋊C8—41no—
162C2×C3⋊C8—204no—
163C2×C3⋊C8—201no—
164C23×C5—31no—
165C23×C5—31no—
166C23×C5—32no—
167C23×C5C2×C3⋊C812yescomplemented
168C23×C5C22×Dic311yescharacteristic
169C22×D5—31no—
170C22×D5—34no—
171C22×D5—34no—
172C22×D5—32no—
173C22×D5—32no—
174C22×D5—32no—
175C22×D5—34no—
176C22×D5—38no—
177C22×D5—34no—
178C22×D5—64no—
179C22×D5—61no—
180C22×D5—62no—
181C22×D5C2×C3⋊C814yescomplemented
182C22×D5SL(2,ℤ/4)11yescharacteristic
183C2×C4×C5—31no—
184C2×C4×C5—31no—
185C2×C4×C5—31no—
186C2×C4×C5—31no—
187C2×C4×C5—31no—
188C2×C4×C5—31no—
189C2×C4×C5—31no—
190C2×C4×C5—61no—
191C2×C4×C5C2×S411yescharacteristic
192C2×Dic5—31no—
193C2×Dic5—32no—
194C2×Dic5—32no—
195C2×Dic5—32no—
196C2×Dic5—61no—
197C2×Dic5SL(2,ℤ/4)11yescharacteristic
198C4×D5—32no—
199C4×D5—32no—
200C4×D5—32no—
201C4×D5—32no—
202C4×D5—32no—
203C4×D5—32no—
204C4×D5—62no—
205C4×D5—62no—
206C4×D5SL(2,ℤ/4)12yes—
207C4×D5C2×S412yes—
208C5×C8—62no—
209C5×C8—62no—
210#168—62no—
211#168—62no—
212C25—51no—
213C23×C4—51no—
214C23×C4—52no—
215C23×C4—52no—
216C23×C4—151no—
217C23×C4—152no—
218C23×C4—151no—
219C23×C4—151no—
220C23×C4—151no—
221C23×C4—152no—
222C23×C4D3×D511yescharacteristic
223C22×C8—31no—
224C22×C8—31no—
225C22×C8—154no—
226C22×C8—154no—
227C22×C8—151no—
228C22×C8—151no—
229C22×C8—301no—
230C22×C8—302no—
231C22×C8—301no—
232C22×C8—302no—
233C22×C8—301no—
234C22×C8—301no—
235C22⋊C8—32no—
236C22⋊C8—32no—
237C22⋊C8—154no—
238C22⋊C8—154no—
239C22⋊C8—152no—
240C22⋊C8—152no—
241C2×C3×C5—42no—
242C2×C3×C5—41no—
243C3×D5—44no—
244C23×C3—201no—
245C2×A4—54no—
246C2×A4C8×D512yescomplemented
247C2×A4C2×C4×D511yescharacteristic
248C2×C3×C4—41no—
249C2×C3×C4—202no—
250C2×C3×C4—202no—
251C2×C3×C4—201no—
252C3⋊C8—42no—
253C3⋊C8—202no—
254C22×C5—32no—
255C22×C5—31no—
256C22×C5—32no—
257C22×C5—32no—
258C22×C5—31no—
259C22×C5—31no—
260C22×C5—61no—
261C22×C5C22×C3⋊C811yescharacteristic, complemented
262C22×C5C2×SL(2,ℤ/4)11yescharacteristic
263C2×D5—34no—
264C2×D5—32no—
265C2×D5—34no—
266C2×D5—34no—
267C2×D5—38no—
268C2×D5—34no—
269C2×D5—62no—
270C2×D5—64no—
271C2×D5A4⋊C814yesdirect product factor
272C2×D5C2×SL(2,ℤ/4)12yes—
273C4×C5—31no—
274C4×C5—31no—
275C4×C5C2×SL(2,ℤ/4)11yescharacteristic
276C4×C5C22×S411yescharacteristic
277Dic5—32no—
278Dic5C2×SL(2,ℤ/4)12yes—
279C24—52no—
280C24—54no—
281C24—151no—
282C24—151no—
283C24—152no—
284C24—154no—
285C24D5×Dic311yescharacteristic
286C22×C4—31no—
287C22×C4—31no—
288C22×C4—31no—
289C22×C4—31no—
290C22×C4—51no—
291C22×C4—52no—
292C22×C4—152no—
293C22×C4—151no—
294C22×C4—152no—
295C22×C4—152no—
296C22×C4—152no—
297C22×C4—151no—
298C22×C4—152no—
299C22×C4—152no—
300C22×C4—152no—
301C22×C4—152no—
302C22×C4—152no—
303C22×C4—152no—
304C22×C4—151no—
305C22×C4—151no—
306C22×C4—152no—
307C22×C4—151no—
308C22×C4—301no—
309C22×C4—301no—
310C22×C4—301no—
311C22×C4—302no—
312C22×C4—302no—
313C22×C4D5×Dic311yescharacteristic
314C22×C4C2×D3×D511yescharacteristic
315C2×C8—32no—
316C2×C8—32no—
317C2×C8—61no—
318C2×C8—61no—
319C2×C8—61no—
320C2×C8—61no—
321C2×C8—152no—
322C2×C8—152no—
323C2×C8—304no—
324C2×C8—304no—
325C2×C8—304no—
326C2×C8—304no—
327C2×C8—301no—
328C2×C8—301no—
329C2×C8—301no—
330C2×C8—301no—
331C3×C5—41noHall
332C22×C3—41no—
333C22×C3—202no—
334C22×C3—204no—
335A4C2×C8×D511yescharacteristic, complemented
336C3×C4—41no—
337C3×C4—41no—
338C3×C4—202no—
339C2×C5—31no—
340C2×C5—32no—
341C2×C5—31no—
342C2×C5C2×A4⋊C812yescomplemented
343C2×C5C22×SL(2,ℤ/4)11yescharacteristic
344D5—34no—
345D5C2×A4⋊C814yesdirect product factor
346C23—31no—
347C23—31no—
348C23—32no—
349C23—51no—
350C23—54no—
351C23—152no—
352C23—152no—
353C23—154no—
354C23—154no—
355C23—152no—
356C23—154no—
357C23—158no—
358C23—154no—
359C23—151no—
360C23—301no—
361C23—302no—
362C23—304no—
363C23D5×C3⋊C812yescomplemented
364C23C2×D5×Dic311yescharacteristic
365C2×C4—31no—
366C2×C4—31no—
367C2×C4—31no—
368C2×C4—31no—
369C2×C4—31no—
370C2×C4—31no—
371C2×C4—31no—
372C2×C4—51no—
373C2×C4—52no—
374C2×C4—52no—
375C2×C4—61no—
376C2×C4—152no—
377C2×C4—152no—
378C2×C4—152no—
379C2×C4—152no—
380C2×C4—152no—
381C2×C4—152no—
382C2×C4—151no—
383C2×C4—152no—
384C2×C4—152no—
385C2×C4—152no—
386C2×C4—302no—
387C2×C4—302no—
388C2×C4—301no—
389C2×C4D5×S411yescharacteristic
390C8—62no—
391C8—62no—
392C8—302no—
393C8—302no—
394C2×C3—42no—
395C2×C3—41no—
396C2×C3—204no—
397C5C22×A4⋊C811yescharacteristic, complemented, Sylow
398C22—31no—
399C22—32no—
400C22—32no—
401C22—32no—
402C22—31no—
403C22—31no—
404C22—54no—
405C22—52no—
406C22—61no—
407C22—154no—
408C22—154no—
409C22—158no—
410C22—154no—
411C22—154no—
412C22—152no—
413C22—302no—
414C22—304no—
415C22C2×D5×C3⋊C811yescharacteristic, complemented
416C22D5×SL(2,ℤ/4)11yescharacteristic
417C4—31no—
418C4—31no—
419C4—52no—
420C4—152no—
421C4D5×SL(2,ℤ/4)11yescharacteristic
422C4C2×D5×S411yescharacteristic
423C3—41noSylow
424C2—31no—
425C2—31no—
426C2—32no—
427C2—54no—
428C2—154no—
429C2D5×A4⋊C812yesdirect product factor
430C2C2×D5×SL(2,ℤ/4)11yescharacteristic
subgroupG/H
center, hypercenterC2×C4D5×S4
commutator, hypocenterC5×A4C22×C8
FrattiniC4C2×D5×S4
FittingC23×C4×C5C2×D3
socleC24×C5C2×Dic3
prime radicalC22×D5×A4C4
cosocleC4×C5×A4C23
LCSG ▷ C5×A4
UCSC1 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
2. C2×A4⋊#168C2semidirect
3. C2×C5×A4⋊C8C2semidirect
4. D5×A4⋊C8C2direct (N × H)
12. A4⋊#168C22semidirect
13. C5×A4⋊C8C22semidirect
25. C2×D5×A4C8semidirect
37. C2×A4⋊C8D5direct (N × H)
69. C2×C5×A4C2×C8semidirect
71. D5×A4C2×C8semidirect
85. A4⋊C8C2×D5direct (N × H)
91. C23×D5C3⋊C8semidirect
150. C5×A4C22×C8semidirect
167. C23×C5C2×C3⋊C8semidirect
181. C22×D5C2×C3⋊C8semidirect
246. C2×A4C8×D5semidirect
261. C22×C5C22×C3⋊C8semidirect
271. C2×D5A4⋊C8direct (N × H)
335. A4C2×C8×D5semidirect
342. C2×C5C2×A4⋊C8semidirect
345. D5C2×A4⋊C8direct (N × H)
363. C23D5×C3⋊C8semidirect
397. C5C22×A4⋊C8semidirect
415. C22C2×D5×C3⋊C8semidirect
429. C2D5×A4⋊C8direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D5×A42
C2×A4⋊#1682
C2×C5×A4⋊C82
D5×A4⋊C82
C2×D5×C22⋊C83
C2×D5×C3⋊C84
C22×A4⋊C85