Finite Group Databasebeta

← D5×#4525 #14280752

Subgroups — D5×#4525 #14280752

Order 1920.

912 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
2D5×#830C212yesmaximal, complemented
3#11746346C211yesmaximal, characteristic, complemented
4C5×#4525C211yesmaximal, characteristic, complemented
5#11745948C212yesmaximal, complemented
6D5×#323—31nomaximal, Hall
7C24×C3×D5C411yescharacteristic
8C22×C3×C4×D5C411yescharacteristic
9C22×C3×C4×D5C2211yescharacteristic
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×C3×C22⋊Dic5C411yescharacteristic
12C2×C3×#685C411yescharacteristic
13C2×C3×#685C2211yescharacteristic
14C3×D5×C22⋊C4—22no—
15C3×D5×C22⋊C4—22no—
16C2×D5×C3⋊C8—22no—
17#91114C2212yescomplemented
18C5×#830C2212yescomplemented
19#90955—22no—
20C2×#4525—51nomaximal, Hall
21C2×D5×C22⋊C4D311yescharacteristic
22D5×C22⋊C8—32no—
23C5×#323—31no—
24#64745—31no—
25#64688—32no—
26C24×C3×C5C2×C411yescharacteristic
27C23×C3×D5—21no—
28C23×C3×D5—21no—
29C23×C3×D5—22no—
30C23×C3×D5—42no—
31C23×C3×D5—42no—
32C23×C3×D5C814yescomplemented
33C23×C3×D5C2×C411yescharacteristic
34C23×C3×D5C2×C411yescharacteristic
35C22×C3×C4×C5C2×C411yescharacteristic
36C22×C3×C4×C5C2311yescharacteristic
37C22×C3×Dic5C2×C411yescharacteristic
38C22×C3×Dic5C2×C411yescharacteristic
39C2×C3×C4×D5—21no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—42no—
42C2×C3×C4×D5—42no—
43C2×C3×C4×D5D412yes—
44C2×C3×C4×D5D412yes—
45C3×C5×C22⋊C4—22no—
46C2×C3⋊#168—22no—
47C2×C5×C3⋊C8—22no—
48C3×C22⋊Dic5—22no—
49C3×#685—22no—
50C3×#685—22no—
51D5×C3⋊C8—44no—
52C22×C3×C22⋊C4—51no—
53C2×#830—52no—
54#4525—51no—
55#4525—52no—
56#4525D511yescharacteristic, direct product factor
57C24×D5Dic311yescharacteristic
58C22×C4×D5Dic311yescharacteristic
59C22×C4×D5C2×D311yescharacteristic
60C2×C5×C22⋊C4C2×D311yescharacteristic
61C2×C22⋊Dic5Dic311yescharacteristic
62C2×#685Dic311yescharacteristic
63C2×#685C2×D311yescharacteristic
64C2×C8×D5—62no—
65D5×C22⋊C4—22no—
66D5×C22⋊C4—22no—
67C5×C22⋊C8—32no—
68C22⋊#168—32no—
69#3952—62no—
70C2×#323—151noSylow
71C23×C3×C5—21no—
72C23×C3×C5—21no—
73C23×C3×C5—41no—
74C23×C3×C5—41no—
75C23×C3×C5C2×C812yescomplemented
76C23×C3×C5C22×C411yescharacteristic
77C22×C3×D5—22no—
78C22×C3×D5—22no—
79C22×C3×D5—21no—
80C22×C3×D5—21no—
81C22×C3×D5—24no—
82C22×C3×D5—24no—
83C22×C3×D5—42no—
84C22×C3×D5—42no—
85C22×C3×D5—48no—
86C22×C3×D5—48no—
87C22×C3×D5—42no—
88C22×C3×D5—42no—
89C22×C3×D5—41no—
90C22×C3×D5—41no—
91C22×C3×D5C22⋊C411yescharacteristic
92C22×C3×D5C22⋊C411yescharacteristic
93C22×C3×D5C2×C812yes—
94C22×C3×D5C2×C812yescomplemented
95C22×C3×D5M1612yes—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C2×D412yes—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—41no—
102C2×C3×Dic5—41no—
103C2×C3×Dic5C22⋊C412yes—
104C3×C4×D5—24no—
105C3×C4×D5—42no—
106C3×C4×D5—42no—
107C3×C4×D5—42no—
108C3⋊#168—42no—
109C5×C3⋊C8—42no—
110C25×C3—51no—
111C23×C3×C4—51no—
112C23×C3×C4—51no—
113C2×C3×C22⋊C4—51no—
114C2×C3×C22⋊C4—51no—
115C2×C3×C22⋊C4—51no—
116C2×C3×C22⋊C4—102no—
117C2×C3×C22⋊C4—102no—
118C2×C3×C22⋊C4C2×D511yescharacteristic
119C22×C3⋊C8—102no—
120#830—52no—
121#830—102no—
122#830C2×D512yescomplemented
123C24×C5C2×Dic311yescharacteristic
124C23×D5—22no—
125C23×D5—21no—
126C23×D5—21no—
127C23×D5—42no—
128C23×D5—42no—
129C23×D5C3⋊C814yescomplemented
130C23×D5C2×Dic311yescharacteristic
131C23×D5C2×Dic311yescharacteristic
132C22×C4×C5C2×Dic311yescharacteristic
133C22×C4×C5C22×D311yescharacteristic
134C22×Dic5C2×Dic311yescharacteristic
135C22×Dic5C2×Dic311yescharacteristic
136C2×C4×D5—21no—
137C2×C4×D5—21no—
138C2×C4×D5—42no—
139C2×C4×D5—42no—
140C2×C4×D5#6712yes—
141C2×C4×D5#6712yes—
142C2×C5×C8—62no—
143C5×C22⋊C4—22no—
144C22⋊Dic5—22no—
145#685—22no—
146#685—22no—
147C2×#168—62no—
148C8×D5—124no—
149C22×C22⋊C4—51no—
150C2×C22⋊C8—152no—
151#323—31no—
152#323—152no—
153#323—151no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—22no—
157C22×C3×C5—42no—
158C22×C3×C5—42no—
159C22×C3×C5—41no—
160C22×C3×C5—41no—
161C22×C3×C5C2×C22⋊C411yescharacteristic
162C22×C3×C5C22×C811yescharacteristic
163C22×C3×C5C2×M1611yescharacteristic
164C2×C3×D5—21no—
165C2×C3×D5—21no—
166C2×C3×D5—24no—
167C2×C3×D5—24no—
168C2×C3×D5—22no—
169C2×C3×D5—48no—
170C2×C3×D5—42no—
171C2×C3×D5—41no—
172C2×C3×D5—41no—
173C2×C3×D5—48no—
174C2×C3×D5—42no—
175C2×C3×D5C22⋊C812yes—
176C2×C3×D5C22⋊C812yes—
177C2×C3×D5#9912yes—
178C2×C3×D5#10012yes—
179C3×C4×C5—22no—
180C3×C4×C5—41no—
181C3×Dic5—22no—
182C3×Dic5—41no—
183C24×C3—51no—
184C24×C3—54no—
185C24×C3—51no—
186C24×C3—101no—
187C24×C3—101no—
188C24×C3—102no—
189C24×C3—202no—
190C24×C3—202no—
191C24×C3C4×D511yescharacteristic
192C22×C3×C4—51no—
193C22×C3×C4—52no—
194C22×C3×C4—52no—
195C22×C3×C4—51no—
196C22×C3×C4—101no—
197C22×C3×C4—101no—
198C22×C3×C4—202no—
199C22×C3×C4—202no—
200C22×C3×C4C4×D511yescharacteristic
201C22×C3×C4C22×D511yescharacteristic
202C3×C22⋊C4—22no—
203C3×C22⋊C4—102no—
204C3×C22⋊C4—102no—
205C3×C22⋊C4—102no—
206C2×C3⋊C8—22no—
207C2×C3⋊C8—102no—
208C2×C3⋊C8—204no—
209C23×C5—21no—
210C23×C5—21no—
211C23×C5—41no—
212C23×C5—41no—
213C23×C5C2×C3⋊C812yescomplemented
214C23×C5C22×Dic311yescharacteristic
215C22×D5—22no—
216C22×D5—22no—
217C22×D5—21no—
218C22×D5—21no—
219C22×D5—24no—
220C22×D5—24no—
221C22×D5—42no—
222C22×D5—42no—
223C22×D5—48no—
224C22×D5—48no—
225C22×D5—42no—
226C22×D5—42no—
227C22×D5—41no—
228C22×D5—41no—
229C22×D5C2×C3⋊C812yes—
230C22×D5C2×C3⋊C812yescomplemented
231C22×D5#20812yes—
232C22×D5#21711yescharacteristic
233C22×D5#21711yescharacteristic
234C2×C4×C5—21no—
235C2×C4×C5—41no—
236C2×C4×C5—41no—
237C2×C4×C5C2×#6712yes—
238C2×Dic5—21no—
239C2×Dic5—41no—
240C2×Dic5—41no—
241C2×Dic5#21712yes—
242C4×D5—24no—
243C4×D5—42no—
244C4×D5—42no—
245C4×D5—42no—
246C5×C8—122no—
247#168—122no—
248C25—51no—
249C23×C4—51no—
250C23×C4—51no—
251C22×C8—302no—
252C2×C22⋊C4—51no—
253C2×C22⋊C4—51no—
254C2×C22⋊C4—51no—
255C2×C22⋊C4—102no—
256C2×C22⋊C4—102no—
257C2×C22⋊C4D3×D511yescharacteristic
258C22⋊C8—32no—
259C22⋊C8—152no—
260C22⋊C8—302no—
261C2×C3×C5—21no—
262C2×C3×C5—21no—
263C2×C3×C5—42no—
264C2×C3×C5C2×C22⋊C811yescharacteristic
265C2×C3×C5C2×#9911yescharacteristic
266C2×C3×C5C2×#10011yescharacteristic
267C3×D5—22no—
268C3×D5—42no—
269C3×D5#32314yescomplemented
270C23×C3—21no—
271C23×C3—21no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3—51no—
275C23×C3—51no—
276C23×C3—52no—
277C23×C3—52no—
278C23×C3—52no—
279C23×C3—102no—
280C23×C3—102no—
281C23×C3—104no—
282C23×C3—104no—
283C23×C3—101no—
284C23×C3—101no—
285C23×C3—201no—
286C23×C3—201no—
287C23×C3—202no—
288C23×C3—202no—
289C23×C3—208no—
290C23×C3—208no—
291C23×C3—202no—
292C23×C3—202no—
293C23×C3C8×D512yescomplemented
294C23×C3C2×C4×D511yescharacteristic
295C2×C3×C4—21no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—52no—
299C2×C3×C4—104no—
300C2×C3×C4—101no—
301C2×C3×C4—202no—
302C2×C3×C4—202no—
303C2×C3×C4—202no—
304C2×C3×C4—201no—
305C2×C3×C4—201no—
306C2×C3×C4D4×D512yes—
307C3⋊C8—42no—
308C3⋊C8—202no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—22no—
312C22×C5—42no—
313C22×C5—42no—
314C22×C5—41no—
315C22×C5—41no—
316C22×C5C22×C3⋊C811yescharacteristic
317C22×C5C2×#20811yescharacteristic
318C22×C5C2×#21711yescharacteristic
319C2×D5—21no—
320C2×D5—21no—
321C2×D5—24no—
322C2×D5—24no—
323C2×D5—22no—
324C2×D5—48no—
325C2×D5—42no—
326C2×D5—41no—
327C2×D5—41no—
328C2×D5—48no—
329C2×D5—42no—
330C2×D5#83012yes—
331C2×D5#83012yes—
332C2×D5#83312yes—
333C2×D5#83412yes—
334C4×C5—22no—
335C4×C5—41no—
336Dic5—22no—
337Dic5—41no—
338C24—51no—
339C24—51no—
340C24—54no—
341C24—101no—
342C24—101no—
343C24—102no—
344C24—202no—
345C24—202no—
346C24D5×Dic311yescharacteristic
347C22×C4—51no—
348C22×C4—52no—
349C22×C4—52no—
350C22×C4—51no—
351C22×C4—101no—
352C22×C4—101no—
353C22×C4—202no—
354C22×C4—202no—
355C22×C4D5×Dic311yescharacteristic
356C22×C4C2×D3×D511yescharacteristic
357C2×C8—62no—
358C2×C8—302no—
359C2×C8—604no—
360C22⋊C4—22no—
361C22⋊C4—102no—
362C22⋊C4—102no—
363C22⋊C4—102no—
364C3×C5C2×#32311yescharacteristic, complemented, Hall
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—22no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—41no—
371C22×C3—41no—
372C22×C3—52no—
373C22×C3—52no—
374C22×C3—52no—
375C22×C3—52no—
376C22×C3—104no—
377C22×C3—104no—
378C22×C3—101no—
379C22×C3—101no—
380C22×C3—102no—
381C22×C3—202no—
382C22×C3—202no—
383C22×C3—208no—
384C22×C3—208no—
385C22×C3—201no—
386C22×C3—201no—
387C22×C3D5×C22⋊C411yescharacteristic
388C22×C3C2×C8×D511yescharacteristic
389C22×C3D5×M1611yescharacteristic
390C3×C4—22no—
391C3×C4—41no—
392C3×C4—102no—
393C3×C4—201no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—42no—
397C2×C5C2×#83011yescharacteristic
398C2×C5C2×#83311yescharacteristic
399C2×C5C2×#83411yescharacteristic
400D5—22no—
401D5—42no—
402D5#452514yesdirect product factor
403C23—21no—
404C23—21no—
405C23—41no—
406C23—41no—
407C23—51no—
408C23—52no—
409C23—52no—
410C23—51no—
411C23—52no—
412C23—102no—
413C23—102no—
414C23—104no—
415C23—104no—
416C23—101no—
417C23—101no—
418C23—201no—
419C23—201no—
420C23—202no—
421C23—202no—
422C23—208no—
423C23—208no—
424C23—202no—
425C23—202no—
426C23D5×C3⋊C812yescomplemented
427C23C2×D5×Dic311yescharacteristic
428C2×C4—21no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—52no—
432C2×C4—104no—
433C2×C4—101no—
434C2×C4—202no—
435C2×C4—202no—
436C2×C4—202no—
437C2×C4—201no—
438C2×C4—201no—
439C2×C4D5×#6712yes—
440C8—122no—
441C8—602no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—42no—
445C2×C3—54no—
446C2×C3—102no—
447C2×C3—202no—
448C2×C3D5×C22⋊C811yescharacteristic
449C2×C3D5×#9911yescharacteristic
450C2×C3D5×#10011yescharacteristic
451C5C2×#452511yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—22no—
455C22—42no—
456C22—42no—
457C22—41no—
458C22—41no—
459C22—52no—
460C22—52no—
461C22—52no—
462C22—52no—
463C22—104no—
464C22—104no—
465C22—101no—
466C22—101no—
467C22—102no—
468C22—202no—
469C22—202no—
470C22—208no—
471C22—208no—
472C22—201no—
473C22—201no—
474C22C2×D5×C3⋊C811yescharacteristic
475C22D5×#20811yescharacteristic
476C22D5×#21711yescharacteristic
477C4—22no—
478C4—41no—
479C4—102no—
480C4—201no—
481C3D5×#32311yescharacteristic, complemented, Sylow
482C2—21no—
483C2—21no—
484C2—42no—
485C2—54no—
486C2—102no—
487C2—202no—
488C2D5×#83011yescharacteristic
489C2D5×#83311yescharacteristic
490C2D5×#83411yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×D5C4
cosocleC22×C3×C4×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#323
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. D5×#830C2semidirect
3. #11746346C2semidirect
4. C5×#4525C2semidirect
5. #11745948C2semidirect
17. #91114C22semidirect
18. C5×#830C22semidirect
32. C23×C3×D5C8semidirect
56. #4525D5direct (N × H)
75. C23×C3×C5C2×C8semidirect
94. C22×C3×D5C2×C8semidirect
122. #830C2×D5semidirect
129. C23×D5C3⋊C8semidirect
213. C23×C5C2×C3⋊C8semidirect
230. C22×D5C2×C3⋊C8semidirect
269. C3×D5#323semidirect
293. C23×C3C8×D5semidirect
364. C3×C5C2×#323semidirect
402. D5#4525direct (N × H)
426. C23D5×C3⋊C8semidirect
451. C5C2×#4525semidirect
481. C3D5×#323semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D5×C22⋊C42
D5×#8302
#117463462
C5×#45252
#117459482
D5×#3233
C2×#45255