Finite Group Databasebeta

← D5×#4027 #13105367

Subgroups — D5×#4027 #13105367

Order 1600.

946 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C22⋊D5C211yesmaximal, characteristic
2C22×D5×Dic5C211yesmaximal, characteristic, complemented
3C2×C4×D52C211yesmaximal, characteristic, complemented
4#11717201C211yesmaximal, characteristic, complemented
5C5×#4027C211yesmaximal, characteristic, complemented
6C5×D5×C22⋊C4C211yesmaximal, characteristic, complemented
7#11717091C211yesmaximal, characteristic, complemented
8#11717070C211yesmaximal, characteristic, complemented
9D5×#685C211yesmaximal, characteristic, complemented
10#11717020C211yesmaximal, characteristic, complemented
11#11716999C211yesmaximal, characteristic, complemented
12#11716998C211yesmaximal, characteristic, complemented
13#11716997C211yesmaximal, characteristic, complemented
14D5×#683C211yesmaximal, characteristic, complemented
15C4×D5×Dic5C211yesmaximal, characteristic, complemented
16C23×C5×D5C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C22⋊(C5⋊D5)C2211yescharacteristic
19C22×#1039C2211yescharacteristic, complemented
20C2×C4×C5⋊D5C2211yescharacteristic, complemented
21C2×C5×C22⋊D5C2211yescharacteristic
22C22×C5×Dic5C2211yescharacteristic, complemented
23C2×C4×C5×D5C2211yescharacteristic
24C2×C4×C5×D5C2211yescharacteristic
25C2×C4×C5×D5C2211yescharacteristic, complemented
26D5×C22⋊D5C418yescomplemented
27C2×#6038C2211yescharacteristic
28C2×#6037C2211yescharacteristic
29C2×#6036C2211yescharacteristic, complemented
30C2×D5×Dic5—24no—
31C2×D5×Dic5C2211yescharacteristic
32C2×D5×Dic5C2211yescharacteristic
33C2×D5×Dic5C2211yescharacteristic
34C2×D5×Dic5C2211yescharacteristic, complemented
35C2×D5×Dic5C2211yescharacteristic, complemented
36C2×D5×Dic5C2211yescharacteristic, complemented
37C4×D52—24no—
38C52×C22⋊C4C2211yescharacteristic, complemented
39#87808C2211yescharacteristic, complemented
40#87806C2211yescharacteristic, complemented
41C4×#1039C2211yescharacteristic, complemented
42C5×C22⋊Dic5C2211yescharacteristic, complemented
43C5×#685C2211yescharacteristic, complemented
44C5×#685C2211yescharacteristic, complemented
45C5×#685C2211yescharacteristic, complemented
46C5×#683C2211yescharacteristic, complemented
47C4×C5×Dic5C2211yescharacteristic, complemented
48#87781C2211yescharacteristic, complemented
49#87780C2211yescharacteristic, complemented
50#87779C2211yescharacteristic, complemented
51#87778C2211yescharacteristic, complemented
52Dic52C2211yescharacteristic, complemented
53Dic52C2211yescharacteristic, complemented
54C4×D4×D5—51nomaximal
55C2×#4027—51nomaximal
56C23×C52C2311yescharacteristic
57C22×C5⋊D5C2311yescharacteristic
58C22×C5×D5—22no—
59C22×C5×D5—22no—
60C22×C5×D5C2×C414yescomplemented
61C22×C5×D5C2311yescharacteristic
62C22×C5×D5C2311yescharacteristic
63C22×C5×D5C2311yescharacteristic
64C2×D52—22no—
65C2×D52—22no—
66C2×D52C2×C414yescomplemented
67C2×C4×C52C2311yescharacteristic
68C2×C4×C52C2311yescharacteristic
69C22⋊(C5⋊D5)C2×C414yescomplemented
70C2×#1039—22no—
71C2×#1039C2311yescharacteristic
72C2×#1039C2311yescharacteristic
73C2×#1039C2311yescharacteristic
74C4×C5⋊D5—22no—
75C5×C22⋊D5C2×C414yescomplemented
76C2×C5×Dic5—22no—
77C2×C5×Dic5C2311yescharacteristic
78C2×C5×Dic5C2311yescharacteristic
79C2×C5×Dic5C2311yescharacteristic
80C2×C5×Dic5C2311yescharacteristic
81C2×C5×Dic5C2311yescharacteristic
82C4×C5×D5—22no—
83C4×C5×D5—22no—
84C4×C5×D5—22no—
85#6038C2×C414yescomplemented
86#6037C2×C414yescomplemented
87#6036—22no—
88D5×Dic5—22no—
89D5×Dic5—22no—
90D5×Dic5—22no—
91D5×Dic5—22no—
92D5×Dic5C2×C414yescomplemented
93D5×Dic5D414yescomplemented
94C22×C22⋊D5—51no—
95C23×Dic5—51no—
96C2×D4×D5—51no—
97C22×C4×D5—51no—
98C22×C4×D5—51no—
99C22×C4×D5—51no—
100C4×C5×D4—51no—
101C2×C5×C22⋊C4—51no—
102D4×Dic5—51no—
103C4×C22⋊D5—51no—
104C4×C22⋊D5—51no—
105C2×#685—51no—
106C2×#683—51no—
107C2×C4×Dic5—51no—
108#4039—51no—
109D5×C4⋊C4—51no—
110#4027—51no—
111#4027—51no—
112#4027—51no—
113#4027—51no—
114#4027—51no—
115#4027—51no—
116#4027—51no—
117#4027—51no—
118#4027—51no—
119#4027—102no—
120#4027D511yescharacteristic, direct product factor
121D5×C22⋊C4—51no—
122D5×C22⋊C4D511yescharacteristic, complemented
123C4×D20—51no—
124C42×D5—51no—
125C22×C52—21no—
126C22×C52—21no—
127C22×C52C22×C412yescomplemented
128C22×C52C2411yescharacteristic
129C2×C5⋊D5—21no—
130C2×C5⋊D5—21no—
131C2×C5⋊D5C22×C412yescomplemented
132C2×C5×D5—28no—
133C2×C5×D5—21no—
134C2×C5×D5—21no—
135C2×C5×D5—21no—
136C2×C5×D5—21no—
137C2×C5×D5C22×C412yes—
138C2×C5×D5C22×C412yescomplemented
139C2×C5×D5C22×C412yescomplemented
140C2×C5×D5C2×D412yes—
141C2×C5×D5#4112yes—
142D52—28no—
143C4×C52—21no—
144C4×C52—21no—
145#1039—21no—
146#1039C22×C412yescomplemented
147#1039C2×D412yescomplemented
148C5×Dic5—21no—
149C5×Dic5—21no—
150C5×Dic5—21no—
151C5×Dic5C22×C412yescomplemented
152C5×Dic5C2×D412yescomplemented
153C24×C5—51no—
154C23×D5—51no—
155C23×D5—51no—
156C23×D5C2×D511yescharacteristic
157C2×C5×D4—51no—
158C22×C4×C5—51no—
159C22×C4×C5—51no—
160C22×C4×C5—51no—
161C22×C4×C5—51no—
162C2×C22⋊D5—51no—
163C2×C22⋊D5—51no—
164C2×C22⋊D5—51no—
165C2×C22⋊D5—51no—
166C2×C22⋊D5—58no—
167C2×C22⋊D5—51no—
168C2×C22⋊D5—102no—
169C2×C22⋊D5C2×D511yescharacteristic
170C22×Dic5—51no—
171C22×Dic5—51no—
172C22×Dic5—51no—
173C22×Dic5—51no—
174C22×Dic5—51no—
175C22×Dic5—51no—
176C22×Dic5—51no—
177C22×Dic5—51no—
178C22×Dic5—102no—
179C22×Dic5—104no—
180C22×Dic5C2×D511yescharacteristic, complemented
181D4×D5—58no—
182C2×D20—51no—
183C2×C4×D5—51no—
184C2×C4×D5—51no—
185C2×C4×D5—51no—
186C2×C4×D5—51no—
187C2×C4×D5—51no—
188C2×C4×D5—51no—
189C2×C4×D5—51no—
190C2×C4×D5—51no—
191C2×C4×D5—51no—
192C2×C4×D5—51no—
193C2×C4×D5—102no—
194C2×C4×D5—104no—
195C2×C4×D5—104no—
196C2×C4×D5—104no—
197C2×C4×D5C2×D511yescharacteristic
198C2×C4×D5C2×D511yescharacteristic
199C2×C4×D5C2×D511yescharacteristic, complemented
200C5×C4⋊C4—51no—
201C5×C22⋊C4—22no—
202C5×C22⋊C4—51no—
203C5×C22⋊C4—51no—
204C5×C22⋊C4—51no—
205C5×C22⋊C4—51no—
206C5×C22⋊C4C2×D511yescharacteristic, complemented
207C5×C22⋊C4C2×D511yescharacteristic, complemented
208C42×C5—51no—
209C22⋊Dic5—51no—
210C22⋊Dic5C2×D511yescharacteristic, complemented
211#685—51no—
212#685—51no—
213#685—51no—
214#685—51no—
215#685—51no—
216#685—102no—
217#685C2×D511yescharacteristic, complemented
218#685C2×D511yescharacteristic, complemented
219#685C2×D511yescharacteristic, complemented
220C4⋊Dic5—51no—
221#683—51no—
222#683—51no—
223#683—51no—
224#683—51no—
225#683—51no—
226#683—102no—
227#683C2×D511yescharacteristic, complemented
228C4×Dic5—51no—
229C4×Dic5—51no—
230C4×Dic5—51no—
231C4×Dic5—51no—
232C4×Dic5—51no—
233C4×Dic5—51no—
234C4×Dic5—102no—
235C4×Dic5C2×D511yescharacteristic, complemented
236C2×C4×D4—251noSylow
237C2×C52—22no—
238C2×C52C23×C411yescharacteristic
239C2×C52C22×D411yescharacteristic
240C2×C52C2×#4111yescharacteristic
241C5⋊D5—22no—
242C5×D5—22no—
243C5×D5—22no—
244C5×D5C4×D414yescomplemented
245C23×C5—22no—
246C23×C5—51no—
247C23×C5—54no—
248C23×C5—51no—
249C23×C5—51no—
250C23×C5—102no—
251C23×C5—102no—
252C23×C5C22×D511yescharacteristic
253C23×C5C22×D511yescharacteristic
254C22×D5—22no—
255C22×D5—22no—
256C22×D5—51no—
257C22×D5—51no—
258C22×D5—54no—
259C22×D5—54no—
260C22×D5—102no—
261C22×D5—102no—
262C22×D5—102no—
263C22×D5—102no—
264C22×D5—102no—
265C22×D5C4×D514yescomplemented
266C22×D5C22×D511yescharacteristic
267C22×D5C22×D511yescharacteristic
268C22×D5C22×D511yescharacteristic
269C5×D4—54no—
270C2×C4×C5—22no—
271C2×C4×C5—22no—
272C2×C4×C5—51no—
273C2×C4×C5—51no—
274C2×C4×C5—51no—
275C2×C4×C5—51no—
276C2×C4×C5—51no—
277C2×C4×C5—102no—
278C2×C4×C5—102no—
279C2×C4×C5—102no—
280C2×C4×C5—102no—
281C2×C4×C5C22×D511yescharacteristic
282C2×C4×C5C22×D511yescharacteristic
283C2×C4×C5C22×D511yescharacteristic
284C2×C4×C5C22×D511yescharacteristic
285C22⋊D5—54no—
286C22⋊D5—54no—
287C22⋊D5—54no—
288C22⋊D5—54no—
289C22⋊D5—54no—
290C22⋊D5—108no—
291C22⋊D5C4×D514yescomplemented
292C2×Dic5—22no—
293C2×Dic5—51no—
294C2×Dic5—51no—
295C2×Dic5—51no—
296C2×Dic5—51no—
297C2×Dic5—54no—
298C2×Dic5—54no—
299C2×Dic5—51no—
300C2×Dic5—51no—
301C2×Dic5—102no—
302C2×Dic5—102no—
303C2×Dic5—102no—
304C2×Dic5—102no—
305C2×Dic5—102no—
306C2×Dic5—102no—
307C2×Dic5—102no—
308C2×Dic5—102no—
309C2×Dic5—102no—
310C2×Dic5—204no—
311C2×Dic5C22×D511yescharacteristic
312C2×Dic5C22×D511yescharacteristic
313C2×Dic5C22×D511yescharacteristic
314C2×Dic5C22×D511yescharacteristic
315C2×Dic5C22×D511yescharacteristic
316D20—54no—
317C4×D5—22no—
318C4×D5—22no—
319C4×D5—22no—
320C4×D5—54no—
321C4×D5—54no—
322C4×D5—102no—
323C4×D5—102no—
324C4×D5—102no—
325C4×D5—102no—
326C4×D5—102no—
327C4×D5—102no—
328C4×D5—102no—
329C4×D5—102no—
330C4×D5—204no—
331C22×D4—251no—
332C23×C4—251no—
333C23×C4—251no—
334C4×D4—51no—
335C4×D4—251no—
336C4×D4—251no—
337C4×D4—251no—
338C4×D4—251no—
339C4×D4—251no—
340C4×D4—251no—
341C4×D4—251no—
342C2×C4⋊C4—251no—
343C2×C22⋊C4—51no—
344C2×C22⋊C4—251no—
345C2×C42—251no—
346C52C2×C4×D411yescharacteristic, complemented, Sylow
347C22×C5—21no—
348C22×C5—21no—
349C22×C5—21no—
350C22×C5—21no—
351C22×C5—24no—
352C22×C5—22no—
353C22×C5—42no—
354C22×C5—42no—
355C22×C5—52no—
356C22×C5—52no—
357C22×C5—52no—
358C22×C5—52no—
359C22×C5—52no—
360C22×C5—108no—
361C22×C5—101no—
362C22×C5—101no—
363C22×C5—101no—
364C22×C5—101no—
365C22×C5C2×C4×D512yescomplemented
366C22×C5C2×C4×D512yescomplemented
367C22×C5C23×D511yescharacteristic
368C22×C5C23×D511yescharacteristic
369C2×D5—21no—
370C2×D5—21no—
371C2×D5—21no—
372C2×D5—21no—
373C2×D5—28no—
374C2×D5—52no—
375C2×D5—52no—
376C2×D5—104no—
377C2×D5—108no—
378C2×D5—101no—
379C2×D5—101no—
380C2×D5—101no—
381C2×D5—101no—
382C2×D5—108no—
383C2×D5—202no—
384C2×D5—202no—
385C2×D5C2×C4×D512yes—
386C2×D5C2×C4×D512yescomplemented
387C2×D5C2×C4×D512yescomplemented
388C2×D5D4×D512yes—
389C2×D5#71112yes—
390C4×C5—21no—
391C4×C5—21no—
392C4×C5—21no—
393C4×C5—21no—
394C4×C5—42no—
395C4×C5—42no—
396C4×C5—52no—
397C4×C5—52no—
398C4×C5—101no—
399C4×C5—101no—
400C4×C5—101no—
401Dic5—21no—
402Dic5—21no—
403Dic5—21no—
404Dic5—52no—
405Dic5—52no—
406Dic5—52no—
407Dic5—52no—
408Dic5—104no—
409Dic5—104no—
410Dic5—101no—
411Dic5—101no—
412Dic5—202no—
413Dic5C2×C4×D512yescomplemented
414Dic5D4×D512yescomplemented
415C24—51no—
416C24—251no—
417C2×D4—51no—
418C2×D4—251no—
419C2×D4—258no—
420C2×D4—251no—
421C2×D4—251no—
422C22×C4—51no—
423C22×C4—51no—
424C22×C4—51no—
425C22×C4—51no—
426C22×C4—251no—
427C22×C4—251no—
428C22×C4—251no—
429C22×C4—251no—
430C22×C4—251no—
431C22×C4—251no—
432C22×C4—251no—
433C22×C4—251no—
434C22×C4—251no—
435C22×C4—504no—
436C22×C4—504no—
437C4⋊C4—51no—
438C4⋊C4—251no—
439C4⋊C4—251no—
440C4⋊C4—251no—
441C22⋊C4—51no—
442C22⋊C4—51no—
443C22⋊C4—51no—
444C22⋊C4—51no—
445C22⋊C4—251no—
446C22⋊C4—251no—
447C22⋊C4—251no—
448C22⋊C4D5211yescharacteristic, complemented
449C42—51no—
450C42—251no—
451C42—251no—
452C42—251no—
453C2×C5—22no—
454C2×C5—22no—
455C2×C5—22no—
456C2×C5—22no—
457C2×C5—22no—
458C2×C5—44no—
459C2×C5—54no—
460C2×C5—102no—
461C2×C5—102no—
462C2×C5C22×C4×D511yescharacteristic
463C2×C5C22×C4×D511yescharacteristic
464C2×C5C2×D4×D511yescharacteristic
465C2×C5C2×D4×D511yescharacteristic
466C2×C5C2×#71111yescharacteristic
467C2×C5D5×#4111yescharacteristic
468D5—22no—
469D5—22no—
470D5—102no—
471D5—102no—
472D5—204no—
473D5#402714yesdirect product factor
474C23—51no—
475C23—54no—
476C23—51no—
477C23—51no—
478C23—102no—
479C23—102no—
480C23—254no—
481C23—251no—
482C23—502no—
483C23—502no—
484C23C2×D5211yescharacteristic
485D4—54no—
486D4—254no—
487D4—254no—
488D4—254no—
489C2×C4—51no—
490C2×C4—51no—
491C2×C4—51no—
492C2×C4—51no—
493C2×C4—51no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—102no—
498C2×C4—254no—
499C2×C4—254no—
500C2×C4—251no—
501C2×C4—251no—
502C2×C4—251no—
503C2×C4—502no—
504C2×C4—502no—
505C2×C4—502no—
506C2×C4—502no—
507C2×C4—502no—
508C2×C4—502no—
509C2×C4—502no—
510C2×C4C2×D5211yescharacteristic
511C2×C4C2×D5211yescharacteristic
512C5—22no—
513C5C2×#402711yescharacteristic, complemented
514C5C4×D4×D511yescharacteristic, complemented
515C22—21no—
516C22—21no—
517C22—52no—
518C22—52no—
519C22—52no—
520C22—52no—
521C22—52no—
522C22—108no—
523C22—101no—
524C22—101no—
525C22—101no—
526C22—101no—
527C22—252no—
528C22—508no—
529C22—501no—
530C22—501no—
531C22C4×D5212yescomplemented
532C22C22×D5211yescharacteristic
533C4—21no—
534C4—21no—
535C4—52no—
536C4—52no—
537C4—101no—
538C4—101no—
539C4—101no—
540C4—252no—
541C4—252no—
542C4—501no—
543C2—22no—
544C2—54no—
545C2—102no—
546C2—102no—
547C2—502no—
548C2C2×C4×D5211yescharacteristic
549C2D4×D5211yescharacteristic
550C2D5×#71111yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutatorC2×C52C23×C4
FittingC52×C22⋊C4C22
socle, cosocleC22×C52C24
prime radicalC2×D5×C22⋊D5C2
hypercenterC22⋊C4D52
hypocenterC52C2×C4×D4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×D5×Dic5C2semidirect
3. C2×C4×D52C2semidirect
4. #11717201C2semidirect
5. C5×#4027C2semidirect
6. C5×D5×C22⋊C4C2semidirect
7. #11717091C2semidirect
8. #11717070C2semidirect
9. D5×#685C2semidirect
10. #11717020C2semidirect
11. #11716999C2semidirect
12. #11716998C2semidirect
13. #11716997C2semidirect
14. D5×#683C2semidirect
15. C4×D5×Dic5C2semidirect
19. C22×#1039C22semidirect
20. C2×C4×C5⋊D5C22semidirect
22. C22×C5×Dic5C22semidirect
25. C2×C4×C5×D5C22semidirect
26. D5×C22⋊D5C4semidirect
29. C2×#6036C22semidirect
34. C2×D5×Dic5C22semidirect
35. C2×D5×Dic5C22semidirect
36. C2×D5×Dic5C22semidirect
38. C52×C22⋊C4C22semidirect
39. #87808C22semidirect
40. #87806C22semidirect
41. C4×#1039C22semidirect
42. C5×C22⋊Dic5C22semidirect
43. C5×#685C22semidirect
44. C5×#685C22semidirect
45. C5×#685C22semidirect
46. C5×#683C22semidirect
47. C4×C5×Dic5C22semidirect
48. #87781C22semidirect
49. #87780C22semidirect
50. #87779C22semidirect
51. #87778C22semidirect
52. Dic52C22semidirect
53. Dic52C22semidirect
60. C22×C5×D5C2×C4semidirect
66. C2×D52C2×C4semidirect
69. C22⋊(C5⋊D5)C2×C4semidirect
75. C5×C22⋊D5C2×C4semidirect
85. #6038C2×C4semidirect
86. #6037C2×C4semidirect
92. D5×Dic5C2×C4semidirect
93. D5×Dic5D4semidirect
120. #4027D5direct (N × H)
122. D5×C22⋊C4D5semidirect
127. C22×C52C22×C4semidirect
131. C2×C5⋊D5C22×C4semidirect
138. C2×C5×D5C22×C4semidirect
139. C2×C5×D5C22×C4semidirect
146. #1039C22×C4semidirect
147. #1039C2×D4semidirect
151. C5×Dic5C22×C4semidirect
152. C5×Dic5C2×D4semidirect
180. C22×Dic5C2×D5semidirect
199. C2×C4×D5C2×D5semidirect
206. C5×C22⋊C4C2×D5semidirect
207. C5×C22⋊C4C2×D5semidirect
210. C22⋊Dic5C2×D5semidirect
217. #685C2×D5semidirect
218. #685C2×D5semidirect
219. #685C2×D5semidirect
227. #683C2×D5semidirect
235. C4×Dic5C2×D5semidirect
244. C5×D5C4×D4semidirect
265. C22×D5C4×D5semidirect
291. C22⋊D5C4×D5semidirect
346. C52C2×C4×D4semidirect
365. C22×C5C2×C4×D5semidirect
366. C22×C5C2×C4×D5semidirect
386. C2×D5C2×C4×D5semidirect
387. C2×D5C2×C4×D5semidirect
413. Dic5C2×C4×D5semidirect
414. Dic5D4×D5semidirect
448. C22⋊C4D52semidirect
473. D5#4027direct (N × H)
513. C5C2×#4027semidirect
514. C5C4×D4×D5semidirect
531. C22C4×D52semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊D52
C22×D5×Dic52
C2×C4×D522
#117172012
C5×#40272
C5×D5×C22⋊C42
#117170912
#117170702
D5×#6852
#117170202
#117169992
#117169982
#117169972
D5×#6832
C4×D5×Dic52
C4×D4×D55
C2×#40275