Finite Group Databasebeta

← D5×#4469 #14280780

Subgroups — D5×#4469 #14280780

Order 1920.

656 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×Dic3⋊C4C211yesmaximal, characteristic
2C3×D5×C22⋊C8C211yesmaximal, characteristic
3D5×#830C211yesmaximal, characteristic
4#11746290C211yesmaximal, characteristic, complemented
5C5×#4469C211yesmaximal, characteristic, complemented
6#11745953C211yesmaximal, characteristic, complemented
7#11745952C211yesmaximal, characteristic, complemented
8D5×#324—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×D5×Dic3C411yescharacteristic
11C22×D5×Dic3C411yescharacteristic
12C2×#6712C2211yescharacteristic
13C2×C5×Dic3⋊C4C2211yescharacteristic
14C2×C3×C8×D5—21no—
15C2×Dic3⋊Dic5C411yescharacteristic
16C2×#6669C411yescharacteristic
17D5×Dic3⋊C4—21no—
18D5×Dic3⋊C4—21no—
19D5×Dic3⋊C4—21no—
20D5×Dic3⋊C4—21no—
21C2×D5×C3⋊C8—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3952—21no—
27#90955—21no—
28C2×#4469—51nomaximal, Hall
29C2×D5×C4⋊C4—31no—
30D5×C22⋊C8—31no—
31D5×C22⋊C8D311yescharacteristic
32C5×#324—31no—
33#64748—31no—
34#64689—31no—
35#64689—31no—
36C23×C3×D5C2×C411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15C2×C411yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C22×C5×Dic3C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×C3×C4×D5—42no—
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×D5×Dic3—21no—
49C2×D5×Dic3—21no—
50C2×D5×Dic3—22no—
51C2×D5×Dic3—21no—
52C2×D5×Dic3—21no—
53C2×D5×Dic3—42no—
54C2×D5×Dic3C814yescomplemented
55C2×C3×C5×C8—21no—
56#6712—21no—
57#6712—21no—
58C2×C3⋊#168—21no—
59C5×Dic3⋊C4—21no—
60C5×Dic3⋊C4—21no—
61C2×C5×C3⋊C8—21no—
62C2×C3×#168—21no—
63C3×C8×D5—42no—
64Dic3⋊Dic5—21no—
65Dic3⋊Dic5—21no—
66#6669—21no—
67#6669—21no—
68D5×C3⋊C8—42no—
69C22×Dic3⋊C4—51no—
70C2×C3×C22⋊C8—51no—
71C2×#830—51no—
72#4469—51no—
73#4469—51no—
74#4469—51no—
75#4469D511yescharacteristic, direct product factor
76C22×C4×D5—31no—
77C22×C4×D5—31no—
78C22×C4×D5C2×D311yescharacteristic
79C2×C5×C4⋊C4—31no—
80C2×C4⋊Dic5—31no—
81C2×#683—31no—
82C2×#683—31no—
83C2×C8×D5—21no—
84C2×C8×D5—61no—
85D5×C4⋊C4—61no—
86D5×C4⋊C4—61no—
87D5×C4⋊C4—61no—
88D5×C4⋊C4—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8C2×D311yescharacteristic
91C22⋊#168—31no—
92C22⋊#168C2×D311yescharacteristic
93#3952—21no—
94#3952—61no—
95C2×#324—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×C3×D5—22no—
98C22×C3×D5—22no—
99C22×C3×D5C22⋊C411yescharacteristic
100C22×C3×D5C22⋊C411yescharacteristic
101C22×C3×D5C2×C812yes—
102C22×C3×D5M1612yes—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—21no—
109C2×Dic15—41no—
110C2×Dic15C2×C812yescomplemented
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3C2×C812yescomplemented
116C2×C3×Dic5—41no—
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C22⋊C411yescharacteristic
119C3×C4×D5—22no—
120C3×C4×D5—22no—
121C3×C4×D5—41no—
122C3×C4×D5—41no—
123D5×Dic3—24no—
124D5×Dic3—24no—
125D5×Dic3—42no—
126D5×Dic3—42no—
127C3×C5×C8—41no—
128C3⋊#168—41no—
129C3×#168—41no—
130C5×C3⋊C8—41no—
131C23×C3×C4—51no—
132C23×Dic3—51no—
133C23×Dic3—51no—
134C22×C3×C8—101no—
135C2×Dic3⋊C4—51no—
136C2×Dic3⋊C4—51no—
137C2×Dic3⋊C4—51no—
138C2×Dic3⋊C4—101no—
139C2×Dic3⋊C4—101no—
140C2×Dic3⋊C4—101no—
141C2×Dic3⋊C4—101no—
142C2×Dic3⋊C4C2×D511yescharacteristic
143C22×C3⋊C8—101no—
144C3×C22⋊C8—51no—
145C3×C22⋊C8—101no—
146C3×C22⋊C8C2×D511yescharacteristic
147#830—51no—
148#830—101no—
149#830C2×D511yescharacteristic
150C23×D5C4×D311yescharacteristic
151C22×C4×C5—31no—
152C22×C4×C5—31no—
153C22×C4×C5C22×D311yescharacteristic
154C22×Dic5—31no—
155C22×Dic5—31no—
156C22×Dic5C4×D311yescharacteristic
157C2×C4×D5—34no—
158C2×C4×D5—42no—
159C2×C4×D5—62no—
160C2×C4×D5—61no—
161C2×C4×D5—61no—
162C2×C4×D5—61no—
163C2×C4×D5—61no—
164C2×C4×D5—122no—
165C2×C4×D5D1211yescharacteristic
166C2×C4×D5D1211yescharacteristic
167C2×C4×D5#6711yescharacteristic
168C2×C4×D5#6711yescharacteristic
169C2×C5×C8—21no—
170C2×C5×C8—61no—
171C5×C4⋊C4—61no—
172C5×C4⋊C4—61no—
173C4⋊Dic5—61no—
174C4⋊Dic5—61no—
175#683—61no—
176#683—61no—
177#683—61no—
178#683—61no—
179C2×#168—21no—
180C2×#168—61no—
181C8×D5—42no—
182C8×D5—122no—
183C22×C4⋊C4—151no—
184C2×C22⋊C8—51no—
185C2×C22⋊C8—151no—
186#324—31no—
187#324—151no—
188#324—151no—
189#324—151no—
190C22×C3×C5—21no—
191C22×C3×C5—21no—
192C22×C3×C5C2×C22⋊C411yescharacteristic
193C22×C3×C5C22×C811yescharacteristic
194C22×C3×C5C2×M1611yescharacteristic
195C2×C3×D5—21no—
196C2×C3×D5—21no—
197C2×C3×D5—24no—
198C2×C3×D5—24no—
199C2×C3×D5C22⋊C812yes—
200C2×C3×D5C22⋊C812yes—
201C2×C3×D5#9912yes—
202C2×C3×D5#10112yes—
203C3×C4×C5—21no—
204C3×C4×C5—21no—
205Dic15—22no—
206Dic15—41no—
207C3×Dic5—21no—
208C3×Dic5—21no—
209C5×Dic3—22no—
210C5×Dic3—41no—
211C24×C3—51no—
212C22×C3×C4—51no—
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—51no—
217C22×C3×C4—202no—
218C22×C3×C4C22×D511yescharacteristic
219C22×Dic3—51no—
220C22×Dic3—54no—
221C22×Dic3—51no—
222C22×Dic3—101no—
223C22×Dic3—101no—
224C22×Dic3—102no—
225C22×Dic3—101no—
226C22×Dic3—101no—
227C22×Dic3—202no—
228C22×Dic3C4×D511yescharacteristic
229C22×Dic3C4×D511yescharacteristic
230C2×C3×C8—21no—
231C2×C3×C8—101no—
232C2×C3×C8—202no—
233Dic3⋊C4—21no—
234Dic3⋊C4—21no—
235Dic3⋊C4—101no—
236Dic3⋊C4—101no—
237Dic3⋊C4—101no—
238Dic3⋊C4—101no—
239Dic3⋊C4—101no—
240Dic3⋊C4—101no—
241C2×C3⋊C8—21no—
242C2×C3⋊C8—101no—
243C2×C3⋊C8—202no—
244C23×C5C2×C4×D311yescharacteristic
245C22×D5—22no—
246C22×D5—22no—
247C22×D5D3×C812yes—
248C22×D5ΓL(1,𝔽25)12yes—
249C22×D5(C2×D3)⋊C411yescharacteristic
250C22×D5(C2×D3)⋊C411yescharacteristic
251C2×C4×C5—32no—
252C2×C4×C5—41no—
253C2×C4×C5—61no—
254C2×C4×C5—61no—
255C2×C4×C5—61no—
256C2×C4×C5—121no—
257C2×C4×C5C2×D1211yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C2×Dic5—32no—
260C2×Dic5—41no—
261C2×Dic5—61no—
262C2×Dic5—61no—
263C2×Dic5—61no—
264C2×Dic5—121no—
265C2×Dic5(C2×D3)⋊C411yescharacteristic
266C2×Dic5(C2×D3)⋊C411yescharacteristic
267C4×D5—22no—
268C4×D5—22no—
269C4×D5—41no—
270C4×D5—41no—
271C4×D5—64no—
272C4×D5—64no—
273C4×D5—122no—
274C4×D5—122no—
275C5×C8—41no—
276C5×C8—121no—
277#168—41no—
278#168—121no—
279C23×C4—51no—
280C23×C4—151no—
281C23×C4—151no—
282C22×C8—101no—
283C22×C8—301no—
284C2×C4⋊C4—31no—
285C2×C4⋊C4—151no—
286C2×C4⋊C4—151no—
287C2×C4⋊C4—151no—
288C2×C4⋊C4—301no—
289C2×C4⋊C4—301no—
290C2×C4⋊C4—301no—
291C2×C4⋊C4—301no—
292C22⋊C8—31no—
293C22⋊C8—51no—
294C22⋊C8—101no—
295C22⋊C8—151no—
296C22⋊C8—301no—
297C22⋊C8D3×D511yescharacteristic
298C2×C3×C5—21no—
299C2×C3×C5—21no—
300C2×C3×C5C2×C22⋊C811yescharacteristic
301C2×C3×C5C2×#9911yescharacteristic
302C2×C3×C5C2×#10111yescharacteristic
303C3×D5—22no—
304C3×D5#32414yescomplemented
305C23×C3—51no—
306C23×C3—51no—
307C23×C3—52no—
308C23×C3—52no—
309C23×C3—102no—
310C23×C3—102no—
311C23×C3C2×C4×D511yescharacteristic
312C2×C3×C4—41no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4—102no—
316C2×C3×C4—102no—
317C2×C3×C4—201no—
318C2×C3×C4—201no—
319C2×C3×C4—201no—
320C2×C3×C4D4×D511yescharacteristic
321C2×C3×C4D4×D511yescharacteristic
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—41no—
326C2×Dic3—52no—
327C2×Dic3—104no—
328C2×Dic3—104no—
329C2×Dic3—101no—
330C2×Dic3—101no—
331C2×Dic3—101no—
332C2×Dic3—202no—
333C2×Dic3—202no—
334C2×Dic3—201no—
335C2×Dic3C8×D512yescomplemented
336C3×C8—41no—
337C3×C8—201no—
338C3⋊C8—41no—
339C3⋊C8—201no—
340C22×C5—21no—
341C22×C5—21no—
342C22×C5C2×D3×C811yescharacteristic
343C22×C5C2×ΓL(1,𝔽25)11yescharacteristic
344C22×C5C2×(C2×D3)⋊C411yescharacteristic
345C2×D5—21no—
346C2×D5—21no—
347C2×D5—24no—
348C2×D5—24no—
349C2×D5#80612yes—
350C2×D5(C2×D3)⋊C812yes—
351C2×D5(C2×D3)⋊C812yes—
352C2×D5#82412yes—
353C4×C5—21no—
354C4×C5—21no—
355C4×C5—62no—
356C4×C5—121no—
357Dic5—21no—
358Dic5—21no—
359Dic5—62no—
360Dic5—121no—
361C24—51no—
362C22×C4—31no—
363C22×C4—31no—
364C22×C4—51no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—51no—
368C22×C4—51no—
369C22×C4—154no—
370C22×C4—151no—
371C22×C4—151no—
372C22×C4—202no—
373C22×C4—301no—
374C22×C4—301no—
375C22×C4—302no—
376C22×C4—301no—
377C22×C4—301no—
378C22×C4—602no—
379C22×C4C2×D3×D511yescharacteristic
380C2×C8—21no—
381C2×C8—61no—
382C2×C8—101no—
383C2×C8—202no—
384C2×C8—301no—
385C2×C8—602no—
386C4⋊C4—61no—
387C4⋊C4—61no—
388C4⋊C4—301no—
389C4⋊C4—301no—
390C4⋊C4—301no—
391C4⋊C4—301no—
392C4⋊C4—301no—
393C4⋊C4—301no—
394C3×C5C2×#32411yescharacteristic, complemented, Hall
395C22×C3—21no—
396C22×C3—21no—
397C22×C3—52no—
398C22×C3—52no—
399C22×C3—52no—
400C22×C3—52no—
401C22×C3—104no—
402C22×C3—104no—
403C22×C3—101no—
404C22×C3—101no—
405C22×C3D5×C22⋊C411yescharacteristic
406C22×C3C2×C8×D511yescharacteristic
407C22×C3D5×M1611yescharacteristic
408C3×C4—21no—
409C3×C4—21no—
410C3×C4—101no—
411C3×C4—101no—
412Dic3—22no—
413Dic3—41no—
414Dic3—102no—
415Dic3—201no—
416C2×C5—21no—
417C2×C5—21no—
418C2×C5C2×#80611yescharacteristic
419C2×C5C2×(C2×D3)⋊C811yescharacteristic
420C2×C5C2×#82411yescharacteristic
421D5—22no—
422D5#446914yesdirect product factor
423C23—51no—
424C23—51no—
425C23—52no—
426C23—52no—
427C23—102no—
428C23—102no—
429C23C4×D3×D511yescharacteristic
430C2×C4—32no—
431C2×C4—41no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—61no—
435C2×C4—61no—
436C2×C4—61no—
437C2×C4—102no—
438C2×C4—102no—
439C2×C4—121no—
440C2×C4—152no—
441C2×C4—201no—
442C2×C4—201no—
443C2×C4—201no—
444C2×C4—304no—
445C2×C4—304no—
446C2×C4—301no—
447C2×C4—301no—
448C2×C4—301no—
449C2×C4—602no—
450C2×C4—602no—
451C2×C4—601no—
452C2×C4D5×D1211yescharacteristic
453C2×C4D5×#6711yescharacteristic
454C8—41no—
455C8—121no—
456C8—201no—
457C8—601no—
458C2×C3—21no—
459C2×C3—21no—
460C2×C3—54no—
461C2×C3—102no—
462C2×C3D5×C22⋊C811yescharacteristic
463C2×C3D5×#9911yescharacteristic
464C2×C3D5×#10111yescharacteristic
465C5C2×#446911yescharacteristic, complemented, Sylow
466C22—21no—
467C22—21no—
468C22—52no—
469C22—52no—
470C22—52no—
471C22—52no—
472C22—104no—
473C22—104no—
474C22—101no—
475C22—101no—
476C22D3×C8×D511yescharacteristic
477C22D5×ΓL(1,𝔽25)11yescharacteristic
478C22D5×(C2×D3)⋊C411yescharacteristic
479C4—21no—
480C4—21no—
481C4—62no—
482C4—101no—
483C4—101no—
484C4—121no—
485C4—302no—
486C4—601no—
487C3D5×#32411yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—54no—
491C2—102no—
492C2D5×#80611yescharacteristic
493C2D5×(C2×D3)⋊C811yescharacteristic
494C2D5×#82411yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5C2×#324
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #11746290C2semidirect
5. C5×#4469C2semidirect
6. #11745953C2semidirect
7. #11745952C2semidirect
54. C2×D5×Dic3C8semidirect
75. #4469D5direct (N × H)
110. C2×Dic15C2×C8semidirect
115. C2×C5×Dic3C2×C8semidirect
304. C3×D5#324semidirect
335. C2×Dic3C8×D5semidirect
394. C3×C5C2×#324semidirect
422. D5#4469direct (N × H)
465. C5C2×#4469semidirect
487. C3D5×#324semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic3⋊C42
C3×D5×C22⋊C82
D5×#8302
#117462902
C5×#44692
#117459532
#117459522
D5×#3243
C2×#44695