Finite Group Databasebeta

← C3×D5⋊(D4⋊C8) #14281484

Subgroups — C3×D5⋊(D4⋊C8) #14281484

Order 1920.

688 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×D4×D5C211yesmaximal, characteristic
2C3×D5⋊(C4⋊C8)C211yesmaximal, characteristic, complemented
3C3×C4×D5⋊C8C211yesmaximal, characteristic, complemented
4C3×D4⋊#170C212yesmaximal, complemented
5C3×#64871C212yesmaximal, complemented
6D5⋊(D4⋊C8)C311yesmaximal, characteristic, direct product factor, Hall
7C2×C3×D4×D5C411yescharacteristic
8C22×C3×C4×D5—21no—
9C2×C3×D5⋊C8—21no—
10C2×C3×D5⋊C8—21no—
11C3×C4×C5×D4C411yescharacteristic
12C3×D4×Dic5C2211yescharacteristic
13C3×C4×C22⋊D5—21no—
14C3×#4039C2211yescharacteristic
15C3×D5×C4⋊C4C411yescharacteristic
16C3×#4027—21no—
17C3×D5×C22⋊C4—21no—
18C3×C4×D20C411yescharacteristic
19C3×C42×D5C2211yescharacteristic
20C3×#4004—21no—
21C3×C4⋊#170C2212yescomplemented
22C3×C4×#170—21no—
23C3×C4×#170C2212yescomplemented
24C2×C3×D4⋊C8—51nomaximal, Hall
25C4×D4×D5C2×C311yescharacteristic
26D5⋊(C4⋊C8)C2×C311yescharacteristic, complemented
27C4×D5⋊C8C2×C311yescharacteristic, complemented
28D4⋊#170C2×C312yescomplemented
29#64871C2×C312yescomplemented
30C23×C3×D5—21no—
31C2×C3×C5×D4C2×C411yescharacteristic
32C22×C3×C4×C5—21no—
33C2×C3×C22⋊D5—21no—
34C22×C3×Dic5—21no—
35C3×D4×D5—22no—
36C3×D4×D5C814yescomplemented
37C2×C3×D20C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—42no—
42C2×C3×C4×D5—42no—
43C2×C3×C4×D5C2×C411yescharacteristic
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×#170—22no—
47C2×C3×#170—22no—
48C3×D5⋊C8—24no—
49C3×D5⋊C8—42no—
50C3×C5×C4⋊C4C2×C411yescharacteristic
51C3×C5×C22⋊C4—21no—
52C3×C42×C5C2×C411yescharacteristic
53C3×C22⋊Dic5—21no—
54C3×#685—21no—
55C3×#685—21no—
56C3×C4⋊Dic5C2×C411yescharacteristic
57C3×#683—21no—
58C3×C4×Dic5D411yescharacteristic
59C3×C4×Dic5D411yescharacteristic
60C3×C4×Dic5C2311yescharacteristic
61C2×C3×C4×D4—51no—
62C2×C3×C4⋊C8—51no—
63C2×C3×C4×C8—51no—
64C3×D4⋊C8—52no—
65C3×D4⋊C8—52no—
66C2×D4×D5C3×C411yescharacteristic
67C22×C4×D5—21no—
68C2×D5⋊C8—21no—
69C2×D5⋊C8—21no—
70C4×C5×D4C3×C411yescharacteristic
71D4×Dic5C22×C311yescharacteristic
72C4×C22⋊D5—21no—
73#4039C22×C311yescharacteristic
74D5×C4⋊C4C3×C411yescharacteristic
75#4027—21no—
76D5×C22⋊C4—21no—
77C4×D20C3×C411yescharacteristic
78C42×D5C22×C311yescharacteristic
79#4004—21no—
80C4⋊#170C22×C312yescomplemented
81C4×#170—21no—
82C4×#170C22×C312yescomplemented
83C2×D4⋊C8—51noSylow
84C23×C3×C5—21no—
85C22×C3×D5—21no—
86C22×C3×D5—24no—
87C22×C3×D5—42no—
88C22×C3×D5—42no—
89C22×C3×D5C22⋊C411yescharacteristic
90C3×C5×D4—21no—
91C3×C5×D4C2×C812yescomplemented
92C2×C3×C4×C5—21no—
93C2×C3×C4×C5—42no—
94C2×C3×C4×C5C22⋊C411yescharacteristic
95C2×C3×C4×C5C22⋊C411yescharacteristic
96C2×C3×C4×C5C22×C411yescharacteristic
97C3×C22⋊D5—24no—
98C2×C3×Dic5—21no—
99C2×C3×Dic5—41no—
100C2×C3×Dic5—41no—
101C2×C3×Dic5C22⋊C411yescharacteristic
102C2×C3×Dic5C2×D411yescharacteristic
103C2×C3×Dic5C2×D411yescharacteristic
104C3×D20—21no—
105C3×D20C2×C812yescomplemented
106C3×C4×D5—22no—
107C3×C4×D5—42no—
108C3×C4×D5—42no—
109C3×C4×D5—41no—
110C3×C4×D5—41no—
111C3×C4×D5C2×C812yes—
112C3×C4×D5M1612yes—
113C3×C4×D5D812yes—
114C3×C4×D5SD1612yes—
115C3×#170—24no—
116C3×#170—42no—
117C22×C3×D4—51no—
118C23×C3×C4—101no—
119C22×C3×C8—101no—
120C22×C3×C8—101no—
121C3×C4×D4—51no—
122C3×C4×D4—51no—
123C3×C4×D4—51no—
124C3×C4×D4—101no—
125C3×C4×D4—101no—
126C3×C4×D4AGL(1,𝔽5)11yescharacteristic
127C2×C3×C4⋊C4—51no—
128C2×C3×C22⋊C4—101no—
129C2×C3×C42—51no—
130C3×C4⋊C8—52no—
131C3×C4⋊C8—101no—
132C3×C4×C8—52no—
133C3×C4×C8—101no—
134C23×D5—21no—
135C2×C5×D4C2×C3×C411yescharacteristic
136C22×C4×C5—21no—
137C2×C22⋊D5—21no—
138C22×Dic5—21no—
139D4×D5—22no—
140D4×D5C3×C814yescomplemented
141C2×D20C2×C3×C411yescharacteristic
142C2×C4×D5—21no—
143C2×C4×D5—21no—
144C2×C4×D5—21no—
145C2×C4×D5—42no—
146C2×C4×D5—42no—
147C2×C4×D5C2×C3×C411yescharacteristic
148C2×C4×D5C3×D411yescharacteristic
149C2×C4×D5C3×D411yescharacteristic
150C2×#170—22no—
151C2×#170—22no—
152D5⋊C8—24no—
153D5⋊C8—42no—
154C5×C4⋊C4C2×C3×C411yescharacteristic
155C5×C22⋊C4—21no—
156C42×C5C2×C3×C411yescharacteristic
157C22⋊Dic5—21no—
158#685—21no—
159#685—21no—
160C4⋊Dic5C2×C3×C411yescharacteristic
161#683—21no—
162C4×Dic5C3×D411yescharacteristic
163C4×Dic5C3×D411yescharacteristic
164C4×Dic5C23×C311yescharacteristic
165C2×C4×D4—51no—
166C2×C4⋊C8—51no—
167C2×C4×C8—51no—
168D4⋊C8—52no—
169D4⋊C8—52no—
170C22×C3×C5—22no—
171C22×C3×C5—41no—
172C22×C3×C5—41no—
173C22×C3×C5C2×C22⋊C411yescharacteristic
174C2×C3×D5—22no—
175C2×C3×D5—41no—
176C2×C3×D5—41no—
177C2×C3×D5—48no—
178C2×C3×D5C22⋊C812yes—
179C2×C3×D5#10212yes—
180C2×C3×D5#10412yes—
181C3×C4×C5—21no—
182C3×C4×C5—41no—
183C3×C4×C5#10212yes—
184C3×C4×C5C22×C811yescharacteristic
185C3×C4×C5C2×M1611yescharacteristic
186C3×Dic5—21no—
187C3×Dic5—41no—
188C3×Dic5C22⋊C812yes—
189C3×Dic5C2×D811yescharacteristic
190C3×Dic5C2×SD1611yescharacteristic
191C24×C3—101no—
192C2×C3×D4—54no—
193C2×C3×D4—51no—
194C2×C3×D4—102no—
195C2×C3×D4—101no—
196C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
197C22×C3×C4—21no—
198C22×C3×C4—51no—
199C22×C3×C4—51no—
200C22×C3×C4—51no—
201C22×C3×C4—101no—
202C22×C3×C4—101no—
203C22×C3×C4—101no—
204C22×C3×C4—101no—
205C22×C3×C4—202no—
206C22×C3×C4—202no—
207C2×C3×C8—102no—
208C2×C3×C8—104no—
209C2×C3×C8—102no—
210C2×C3×C8—202no—
211C3×C4⋊C4—51no—
212C3×C4⋊C4—101no—
213C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
214C3×C22⋊C4—21no—
215C3×C22⋊C4—101no—
216C3×C22⋊C4—101no—
217C3×C22⋊C4—101no—
218C3×C42—51no—
219C3×C42—51no—
220C3×C42—51no—
221C3×C42C2×AGL(1,𝔽5)11yescharacteristic
222C23×C5—21no—
223C22×D5—21no—
224C22×D5—24no—
225C22×D5—42no—
226C22×D5—42no—
227C22×D5C3×C22⋊C411yescharacteristic
228C5×D4—21no—
229C5×D4C2×C3×C812yescomplemented
230C2×C4×C5—21no—
231C2×C4×C5—42no—
232C2×C4×C5C3×C22⋊C411yescharacteristic
233C2×C4×C5C3×C22⋊C411yescharacteristic
234C2×C4×C5C22×C3×C411yescharacteristic
235C22⋊D5—24no—
236C2×Dic5—21no—
237C2×Dic5—41no—
238C2×Dic5—41no—
239C2×Dic5C3×C22⋊C411yescharacteristic
240C2×Dic5C2×C3×D411yescharacteristic
241C2×Dic5C2×C3×D411yescharacteristic
242D20—21no—
243D20C2×C3×C812yescomplemented
244C4×D5—22no—
245C4×D5—42no—
246C4×D5—42no—
247C4×D5—41no—
248C4×D5—41no—
249C4×D5C2×C3×C812yes—
250C4×D5C3×M1612yes—
251C4×D5C3×D812yes—
252C4×D5C3×SD1612yes—
253#170—24no—
254#170—42no—
255C22×D4—51no—
256C23×C4—101no—
257C22×C8—101no—
258C22×C8—101no—
259C4×D4—51no—
260C4×D4—51no—
261C4×D4—51no—
262C4×D4—101no—
263C4×D4—101no—
264C4×D4C3×AGL(1,𝔽5)11yescharacteristic
265C2×C4⋊C4—51no—
266C2×C22⋊C4—101no—
267C2×C42—51no—
268C4⋊C8—52no—
269C4⋊C8—101no—
270C4×C8—52no—
271C4×C8—101no—
272C2×C3×C5—42no—
273C2×C3×C5C2×C22⋊C811yescharacteristic
274C2×C3×C5C2×#10211yescharacteristic
275C2×C3×C5C2×#10411yescharacteristic
276C3×D5—42no—
277C3×D5D4⋊C814yescomplemented
278C23×C3—21no—
279C23×C3—51no—
280C23×C3—104no—
281C23×C3—101no—
282C23×C3—202no—
283C23×C3—202no—
284C3×D4—21no—
285C3×D4—52no—
286C3×D4—104no—
287C3×D4—101no—
288C3×D4D5⋊C812yescomplemented
289C2×C3×C4—21no—
290C2×C3×C4—42no—
291C2×C3×C4—51no—
292C2×C3×C4—51no—
293C2×C3×C4—52no—
294C2×C3×C4—52no—
295C2×C3×C4—52no—
296C2×C3×C4—52no—
297C2×C3×C4—51no—
298C2×C3×C4—102no—
299C2×C3×C4—101no—
300C2×C3×C4—201no—
301C2×C3×C4—201no—
302C2×C3×C4—202no—
303C2×C3×C4—201no—
304C2×C3×C4—201no—
305C2×C3×C4—202no—
306C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
307C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
308C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
309C3×C8—104no—
310C3×C8—202no—
311C22×C5—22no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5C2×C3×C22⋊C411yescharacteristic
315C2×D5—22no—
316C2×D5—41no—
317C2×D5—41no—
318C2×D5—48no—
319C2×D5C3×C22⋊C812yes—
320C2×D5C3×#10212yes—
321C2×D5C3×#10412yes—
322C4×C5—21no—
323C4×C5—41no—
324C4×C5C3×#10212yes—
325C4×C5C22×C3×C811yescharacteristic
326C4×C5C2×C3×M1611yescharacteristic
327Dic5—21no—
328Dic5—41no—
329Dic5C3×C22⋊C812yes—
330Dic5C2×C3×D811yescharacteristic
331Dic5C2×C3×SD1611yescharacteristic
332C24—101no—
333C2×D4—54no—
334C2×D4—51no—
335C2×D4—102no—
336C2×D4—101no—
337C2×D4C2×C3×AGL(1,𝔽5)11yescharacteristic
338C22×C4—21no—
339C22×C4—51no—
340C22×C4—51no—
341C22×C4—51no—
342C22×C4—101no—
343C22×C4—101no—
344C22×C4—101no—
345C22×C4—101no—
346C22×C4—202no—
347C22×C4—202no—
348C2×C8—102no—
349C2×C8—104no—
350C2×C8—102no—
351C2×C8—202no—
352C4⋊C4—51no—
353C4⋊C4—101no—
354C4⋊C4C2×C3×AGL(1,𝔽5)11yescharacteristic
355C22⋊C4—21no—
356C22⋊C4—101no—
357C22⋊C4—101no—
358C22⋊C4—101no—
359C42—51no—
360C42—51no—
361C42—51no—
362C42C2×C3×AGL(1,𝔽5)11yescharacteristic
363C3×C5C2×D4⋊C811yescharacteristic, complemented, Hall
364C22×C3—22no—
365C22×C3—41no—
366C22×C3—41no—
367C22×C3—52no—
368C22×C3—52no—
369C22×C3—52no—
370C22×C3—102no—
371C22×C3—208no—
372C22×C3—201no—
373C22×C3—201no—
374C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
375C3×C4—21no—
376C3×C4—41no—
377C3×C4—52no—
378C3×C4—51no—
379C3×C4—51no—
380C3×C4—101no—
381C3×C4—201no—
382C3×C4#400712yes—
383C3×C4C2×D5⋊C811yescharacteristic
384C3×C4D5⋊M1611yescharacteristic
385C2×C5—42no—
386C2×C5C2×C3×C22⋊C811yescharacteristic
387C2×C5C2×C3×#10211yescharacteristic
388C2×C5C2×C3×#10411yescharacteristic
389D5—42no—
390D5C3×D4⋊C814yescomplemented
391C23—21no—
392C23—51no—
393C23—104no—
394C23—101no—
395C23—202no—
396C23—202no—
397D4—21no—
398D4—52no—
399D4—104no—
400D4—101no—
401D4C3×D5⋊C812yescomplemented
402C2×C4—21no—
403C2×C4—42no—
404C2×C4—51no—
405C2×C4—51no—
406C2×C4—52no—
407C2×C4—52no—
408C2×C4—52no—
409C2×C4—52no—
410C2×C4—51no—
411C2×C4—102no—
412C2×C4—101no—
413C2×C4—201no—
414C2×C4—201no—
415C2×C4—202no—
416C2×C4—201no—
417C2×C4—201no—
418C2×C4—202no—
419C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
420C2×C4C3×C22⋊AGL(1,𝔽5)11yescharacteristic
421C2×C4C22×C3×AGL(1,𝔽5)11yescharacteristic
422C8—104no—
423C8—202no—
424C2×C3—42no—
425C2×C3—54no—
426C2×C3—202no—
427C2×C3D5⋊(C22⋊C8)11yescharacteristic
428C2×C3C2×#400711yescharacteristic
429C2×C3D5⋊#10411yescharacteristic
430C5C2×C3×D4⋊C811yescharacteristic, complemented, Sylow
431C22—22no—
432C22—41no—
433C22—41no—
434C22—52no—
435C22—52no—
436C22—52no—
437C22—102no—
438C22—208no—
439C22—201no—
440C22—201no—
441C22C2×C3×C22⋊AGL(1,𝔽5)11yescharacteristic
442C4—21no—
443C4—41no—
444C4—52no—
445C4—51no—
446C4—51no—
447C4—101no—
448C4—201no—
449C4C3×#400712yes—
450C4C2×C3×D5⋊C811yescharacteristic
451C4C3×D5⋊M1611yescharacteristic
452C3D5⋊(D4⋊C8)11yescharacteristic, direct product factor, Sylow
453C2—42no—
454C2—54no—
455C2—202no—
456C2C3×D5⋊(C22⋊C8)11yescharacteristic
457C2C2×C3×#400711yescharacteristic
458C2C3×D5⋊#10411yescharacteristic
subgroupG/H
centerC2×C3×C4C22⋊AGL(1,𝔽5)
commutatorC4×C5C22×C3×C8
FrattiniC2×C4C22×C3×AGL(1,𝔽5)
FittingC3×C4×C5×D4C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D4×D5C4
cosocleC4×Dic5C23×C3
hypercenterC3×C4×D4AGL(1,𝔽5)
hypocenterC5C2×C3×D4⋊C8
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C3×C42 ◁ C3×C4×D4

Complements

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

NH ≅ G/Ntype
2. C3×D5⋊(C4⋊C8)C2semidirect
3. C3×C4×D5⋊C8C2semidirect
4. C3×D4⋊#170C2semidirect
5. C3×#64871C2semidirect
6. D5⋊(D4⋊C8)C3direct (N × H)
21. C3×C4⋊#170C22semidirect
23. C3×C4×#170C22semidirect
26. D5⋊(C4⋊C8)C2×C3semidirect
27. C4×D5⋊C8C2×C3semidirect
28. D4⋊#170C2×C3semidirect
29. #64871C2×C3semidirect
36. C3×D4×D5C8semidirect
80. C4⋊#170C22×C3semidirect
82. C4×#170C22×C3semidirect
91. C3×C5×D4C2×C8semidirect
105. C3×D20C2×C8semidirect
140. D4×D5C3×C8semidirect
229. C5×D4C2×C3×C8semidirect
243. D20C2×C3×C8semidirect
277. C3×D5D4⋊C8semidirect
288. C3×D4D5⋊C8semidirect
363. C3×C5C2×D4⋊C8semidirect
390. D5C3×D4⋊C8semidirect
401. D4C3×D5⋊C8semidirect
430. C5C2×C3×D4⋊C8semidirect
452. C3D5⋊(D4⋊C8)direct (N × H)

Maximal subgroups

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

subgroupindex
C3×C4×D4×D52
C3×D5⋊(C4⋊C8)2
C3×C4×D5⋊C82
C3×D4⋊#1702
C3×#648712
D5⋊(D4⋊C8)3
C2×C3×D4⋊C85