Finite Group Databasebeta

← D5⋊#4467 #14282745

Subgroups — D5⋊#4467 #14282745

Order 1920.

672 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
1D5×#924C211yesmaximal, characteristic
2C2×#91235C211yesmaximal, characteristic
3C3×D5⋊(C22⋊C8)C211yesmaximal, characteristic
4#11746501C212yesmaximal, complemented
5#11746500C212yesmaximal, complemented
6D5⋊#328—31nomaximal, Hall
7C23×ΓL(1,𝔽16)—21no—
8C22×C3×C4×D5C2211yescharacteristic
9C2×D5×Dic6C411yescharacteristic, complemented
10C2×C3×D5⋊C8—21no—
11#91813C411yescharacteristic, complemented
12C5×#924C411yescharacteristic, complemented
13#91574—21no—
14D5×#217—21no—
15D5×C4⋊Dic3C411yescharacteristic, complemented
16D5×Dic3⋊C4—21no—
17#91360C2211yescharacteristic
18#91359C2211yescharacteristic
19#91349—21no—
20#91235—21no—
21#91235C2212yes—
22C3×C22⋊#170—21no—
23C3×#4003C2212yes—
24C2×#4467—51nomaximal, Hall
25D5×C22⋊Q8—31no—
26C2×(C2×AGL(1,𝔽5))⋊C4—31no—
27D5⋊(C22⋊C8)D311yescharacteristic
28#64926—32no—
29#64869—32no—
30C23×C3×D5D411yescharacteristic
31C22×ΓL(1,𝔽16)—24no—
32C22×ΓL(1,𝔽16)—22no—
33C22×ΓL(1,𝔽16)—42no—
34C22×ΓL(1,𝔽16)—42no—
35C22×C3×C4×C5C2×C411yescharacteristic
36C2×Dic30C2×C411yescharacteristic, complemented
37C2×C5×Dic6C2×C411yescharacteristic, complemented
38C22×C3×Dic5D411yescharacteristic
39C2×C3×C4×D5—42no—
40C2×C3×C4×D5C2×C411yescharacteristic
41C2×C3×C4×D5D411yescharacteristic
42C2×C3×C4×D5D411yescharacteristic
43C2×C3×C4×D5C2311yescharacteristic
44C2×#1204—21no—
45C2×D5×Dic3—21no—
46C2×D5×Dic3—21no—
47D5×Dic6—42no—
48C2×C3×#170—22no—
49C3×D5⋊C8—42no—
50#6719—21no—
51C4⋊Dic15C2×C411yescharacteristic, complemented
52#6712—21no—
53C5×#217—21no—
54C5×C4⋊Dic3C2×C411yescharacteristic, complemented
55C5×Dic3⋊C4—21no—
56Dic3⋊Dic5—21no—
57#6669—21no—
58#6668—21no—
59#6665—21no—
60#6665—21no—
61C2×#924—51no—
62C2×C3×C22⋊C8—51no—
63C2×C3⋊#95—51no—
64#4467—52no—
65#4467—52no—
66C23×AGL(1,𝔽5)—61no—
67C2×Q8×D5—31no—
68C22×C4×D5C2×D311yescharacteristic
69C2×D5⋊C8—21no—
70C5×C22⋊Q8—31no—
71#4092—31no—
72#4070—31no—
73#4043—31no—
74#4042—61no—
75D5×C4⋊C4—31no—
76D5×C4⋊C4—61no—
77D5×C22⋊C4—61no—
78#4024—61no—
79C22⋊#170—21no—
80(C2×AGL(1,𝔽5))⋊C4—32no—
81(C2×AGL(1,𝔽5))⋊C4—61no—
82#4003C2×D312yes—
83C2×#328—151noSylow
84C23×C3×C5C22⋊C411yescharacteristic
85C22×C3×D5—22no—
86C22×C3×D5—22no—
87C22×C3×D5C22⋊C411yescharacteristic
88C22×C3×D5SD1612yes—
89C22×C3×D5Q1612yes—
90C22×C3×D5C2×D411yescharacteristic
91C2×ΓL(1,𝔽16)—24no—
92C2×ΓL(1,𝔽16)—42no—
93C2×ΓL(1,𝔽16)—48no—
94C2×ΓL(1,𝔽16)—42no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5C22⋊C411yescharacteristic
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×Dic15—21no—
99C2×Dic15—21no—
100Dic30—41no—
101C2×C5×Dic3—21no—
102C2×C5×Dic3—21no—
103C5×Dic6—41no—
104C2×C3×Dic5—41no—
105C2×C3×Dic5C22⋊C411yescharacteristic
106C2×C3×Dic5C2×D411yescharacteristic
107C3×C4×D5—22no—
108C3×C4×D5—22no—
109C3×C4×D5—41no—
110C3×C4×D5—41no—
111#1204—42no—
112D5×Dic3—42no—
113D5×Dic3—42no—
114C3×#170—42no—
115C23×C3×C4—51no—
116C23×Dic3—101no—
117C22×Dic6—51no—
118C22×C3×C8—101no—
119C2×#217—101no—
120C2×C4⋊Dic3—51no—
121#924—51no—
122#924—51no—
123#924—51no—
124#924—101no—
125#924—101no—
126#924AGL(1,𝔽5)11yescharacteristic, complemented
127C2×Dic3⋊C4—101no—
128C3×C22⋊C8—52no—
129C3×C22⋊C8—101no—
130C3⋊#95—52no—
131C3⋊#95—101no—
132C23×D5D1211yescharacteristic
133C22×AGL(1,𝔽5)—64no—
134C22×AGL(1,𝔽5)—62no—
135C22×AGL(1,𝔽5)—122no—
136C22×AGL(1,𝔽5)—122no—
137C2×C5×Q8—31no—
138C22×C4×C5C4×D311yescharacteristic
139C22×Dic5#6711yescharacteristic
140Q8×D5—122no—
141C2×C4×D5—42no—
142C2×C4×D5—61no—
143C2×C4×D5—61no—
144C2×C4×D5C4×D311yescharacteristic
145C2×C4×D5D1211yescharacteristic
146C2×C4×D5#6711yescharacteristic
147C2×C4×D5C22×D311yescharacteristic
148C2×Dic10—31no—
149C2×Dic10—61no—
150C2×#170—22no—
151D5⋊C8—42no—
152C5×C4⋊C4—31no—
153C5×C4⋊C4—61no—
154C5×C22⋊C4—61no—
155C22⋊Dic5—61no—
156#685—61no—
157#685—61no—
158C4⋊Dic5—31no—
159C4⋊Dic5—61no—
160#683—61no—
161#683—61no—
162#683—61no—
163C2×C22⋊Q8—151no—
164C2×C22⋊C8—51no—
165C2×#95—151no—
166#328—152no—
167#328—152no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5#10312yes—
171C22×C3×C5C2×C22⋊C411yescharacteristic
172C2×C3×D5—21no—
173C2×C3×D5—21no—
174C2×C3×D5—24no—
175C2×C3×D5—24no—
176C2×C3×D5#9912yes—
177C2×C3×D5#10312yes—
178C2×C3×D5#10412yes—
179C2×C3×D5C2×SD1611yescharacteristic
180C2×C3×D5C2×Q1611yescharacteristic
181ΓL(1,𝔽16)—44no—
182C3×C4×C5—21no—
183C3×C4×C5—21no—
184Dic15—41no—
185Dic15—41no—
186C3×Dic5—21no—
187C3×Dic5—21no—
188C5×Dic3—41no—
189C5×Dic3—41no—
190C24×C3—51no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—51no—
194C22×C3×C4—51no—
195C22×C3×C4—51no—
196C22×C3×C4—202no—
197C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
198C22×Dic3—101no—
199C22×Dic3—101no—
200C22×Dic3—102no—
201C22×Dic3—104no—
202C22×Dic3—202no—
203C22×Dic3—202no—
204C2×Dic6—51no—
205C2×Dic6—101no—
206C2×Dic6—202no—
207C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
208C2×C3×C8—102no—
209C2×C3×C8—202no—
210#217—21no—
211#217—101no—
212#217—101no—
213#217—101no—
214C4⋊Dic3—51no—
215C4⋊Dic3—101no—
216C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
217Dic3⋊C4—21no—
218Dic3⋊C4—101no—
219Dic3⋊C4—101no—
220Dic3⋊C4—101no—
221C23×C5(C2×D3)⋊C411yescharacteristic
222C22×D5—22no—
223C22×D5—22no—
224C22×D5#20412yes—
225C22×D5Dic1212yes—
226C22×D5(C2×D3)⋊C411yescharacteristic
227C22×D5C2×D1211yescharacteristic
228C2×AGL(1,𝔽5)—64no—
229C2×AGL(1,𝔽5)—122no—
230C2×AGL(1,𝔽5)—128no—
231C2×AGL(1,𝔽5)—122no—
232C5×Q8—121no—
233C2×C4×C5—41no—
234C2×C4×C5—61no—
235C2×C4×C5—61no—
236C2×C4×C5(C2×D3)⋊C411yescharacteristic
237C2×C4×C5C2×C4×D311yescharacteristic
238C2×Dic5—41no—
239C2×Dic5—61no—
240C2×Dic5—61no—
241C2×Dic5(C2×D3)⋊C411yescharacteristic
242C2×Dic5C2×#6711yescharacteristic
243C4×D5—22no—
244C4×D5—22no—
245C4×D5—41no—
246C4×D5—41no—
247C4×D5—122no—
248C4×D5—122no—
249Dic10—122no—
250Dic10—121no—
251#170—42no—
252C22×Q8—151no—
253C23×C4—51no—
254C23×C4—301no—
255C22×C8—101no—
256C22⋊Q8—31no—
257C22⋊Q8—151no—
258C22⋊Q8—151no—
259C22⋊Q8—151no—
260C22⋊Q8—301no—
261C22⋊Q8—301no—
262C2×C4⋊C4—151no—
263C2×C4⋊C4—301no—
264C2×C22⋊C4—301no—
265C22⋊C8—52no—
266C22⋊C8—101no—
267#95—152no—
268#95—301no—
269C2×C3×C5—22no—
270C2×C3×C5C2×#9911yescharacteristic
271C2×C3×C5C2×#10311yescharacteristic
272C2×C3×C5C2×#10411yescharacteristic
273C3×D5—21no—
274C3×D5—21no—
275C3×D5#32814yescomplemented
276C23×C3—51no—
277C23×C3—51no—
278C23×C3—52no—
279C23×C3—52no—
280C23×C3—102no—
281C23×C3—102no—
282C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
283C2×C3×C4—41no—
284C2×C3×C4—51no—
285C2×C3×C4—51no—
286C2×C3×C4—102no—
287C2×C3×C4—102no—
288C2×C3×C4—201no—
289C2×C3×C4—201no—
290C2×C3×C4—201no—
291C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
292C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
293C2×Dic3—21no—
294C2×Dic3—21no—
295C2×Dic3—104no—
296C2×Dic3—101no—
297C2×Dic3—101no—
298C2×Dic3—202no—
299C2×Dic3—202no—
300C2×Dic3—202no—
301C2×Dic3—208no—
302C2×Dic3—202no—
303Dic6—41no—
304Dic6—202no—
305Dic6—201no—
306C3×C8—202no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5#81612yes—
310C22×C5C2×(C2×D3)⋊C411yescharacteristic
311C2×D5—21no—
312C2×D5—21no—
313C2×D5—24no—
314C2×D5—24no—
315C2×D5#80612yes—
316C2×D5#81612yes—
317C2×D5#82512yes—
318C2×D5C2×#20411yescharacteristic
319C2×D5C2×Dic1211yescharacteristic
320AGL(1,𝔽5)—124no—
321C4×C5—21no—
322C4×C5—21no—
323C4×C5—121no—
324C4×C5—121no—
325Dic5—21no—
326Dic5—21no—
327Dic5—121no—
328Dic5—121no—
329C24—51no—
330C2×Q8—31no—
331C2×Q8—151no—
332C2×Q8—301no—
333C2×Q8—602no—
334C22×C4—51no—
335C22×C4—51no—
336C22×C4—51no—
337C22×C4—51no—
338C22×C4—51no—
339C22×C4—202no—
340C22×C4—301no—
341C22×C4—301no—
342C22×C4—302no—
343C22×C4—304no—
344C22×C4—602no—
345C22×C4—602no—
346C22×C4D3×AGL(1,𝔽5)11yescharacteristic
347C2×C8—102no—
348C2×C8—202no—
349C4⋊C4—31no—
350C4⋊C4—61no—
351C4⋊C4—151no—
352C4⋊C4—301no—
353C4⋊C4—301no—
354C4⋊C4—301no—
355C4⋊C4—301no—
356C22⋊C4—61no—
357C22⋊C4—301no—
358C22⋊C4—301no—
359C22⋊C4—301no—
360C3×C5C2×#32811yescharacteristic, complemented, Hall
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—52no—
364C22×C3—52no—
365C22×C3—52no—
366C22×C3—51no—
367C22×C3—51no—
368C22×C3—104no—
369C22×C3—104no—
370C22×C3—101no—
371C22×C3—101no—
372C22×C3#400912yes—
373C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—101no—
377C3×C4—101no—
378Dic3—41no—
379Dic3—41no—
380Dic3—204no—
381Dic3—201no—
382Dic3—201no—
383C2×C5—22no—
384C2×C5C2×#80611yescharacteristic
385C2×C5C2×#81611yescharacteristic
386C2×C5C2×#82511yescharacteristic
387D5—21no—
388D5—21no—
389D5#446714yescomplemented
390C23—51no—
391C23—52no—
392C23—52no—
393C23—51no—
394C23—102no—
395C23—102no—
396C23(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
397Q8—121no—
398Q8—601no—
399Q8—602no—
400C2×C4—41no—
401C2×C4—51no—
402C2×C4—51no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—102no—
406C2×C4—102no—
407C2×C4—201no—
408C2×C4—201no—
409C2×C4—201no—
410C2×C4—304no—
411C2×C4—301no—
412C2×C4—301no—
413C2×C4—602no—
414C2×C4—602no—
415C2×C4—602no—
416C2×C4—608no—
417C2×C4—602no—
418C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
419C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
420C8—202no—
421C2×C3—22no—
422C2×C3—54no—
423C2×C3—101no—
424C2×C3—101no—
425C2×C3D5⋊#9911yescharacteristic
426C2×C3C2×#400911yescharacteristic
427C2×C3D5⋊#10411yescharacteristic
428C5C2×#446711yescharacteristic, complemented, Sylow
429C22—21no—
430C22—21no—
431C22—52no—
432C22—52no—
433C22—52no—
434C22—51no—
435C22—51no—
436C22—104no—
437C22—104no—
438C22—101no—
439C22—101no—
440C22#9115412yes—
441C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
442C4—21no—
443C4—21no—
444C4—101no—
445C4—101no—
446C4—121no—
447C4—121no—
448C4—604no—
449C4—601no—
450C4—601no—
451C3D5⋊#32811yescharacteristic, complemented, Sylow
452C2—22no—
453C2—54no—
454C2—101no—
455C2—101no—
456C2C2×#9115411yescharacteristic
457C2D5⋊#82511yescharacteristic
458C2D5⋊#80611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#328
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11746501C2semidirect
5. #11746500C2semidirect
9. C2×D5×Dic6C4semidirect
11. #91813C4semidirect
12. C5×#924C4semidirect
15. D5×C4⋊Dic3C4semidirect
36. C2×Dic30C2×C4semidirect
37. C2×C5×Dic6C2×C4semidirect
51. C4⋊Dic15C2×C4semidirect
54. C5×C4⋊Dic3C2×C4semidirect
126. #924AGL(1,𝔽5)semidirect
207. C2×Dic6C2×AGL(1,𝔽5)semidirect
216. C4⋊Dic3C2×AGL(1,𝔽5)semidirect
275. C3×D5#328semidirect
360. C3×C5C2×#328semidirect
389. D5#4467semidirect
428. C5C2×#4467semidirect
451. C3D5⋊#328semidirect

Maximal subgroups

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

subgroupindex
D5×#9242
C2×#912352
C3×D5⋊(C22⋊C8)2
#117465012
#117465002
D5⋊#3283
C2×#44675