Finite Group Databasebeta

← #13106395

Subgroups — #13106395

Order 1600.

762 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#711C211yesmaximal, characteristic, complemented
2C2×D5×C22⋊D5C211yesmaximal, characteristic, complemented
3#11717259C211yesmaximal, characteristic, complemented
4C5×#4083C211yesmaximal, characteristic, complemented
5#11717101C211yesmaximal, characteristic, complemented
6#11717096C211yesmaximal, characteristic, complemented
7#11717091C211yesmaximal, characteristic, complemented
8Dic5×C22⋊D5C211yesmaximal, characteristic, complemented
9#11717088C211yesmaximal, characteristic, complemented
10#11717084C211yesmaximal, characteristic, complemented
11C2×#87778C211yesmaximal, characteristic, complemented
12D5×#685C211yesmaximal, characteristic, complemented
13#11717025C211yesmaximal, characteristic, complemented
14#11717023C211yesmaximal, characteristic, complemented
15#11717006C211yesmaximal, characteristic, complemented
16C23×C5×D5C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C52×D4C2211yescharacteristic, complemented
19C2×C22⋊(C5⋊D5)C2211yescharacteristic
20C2×C22⋊(C5⋊D5)C2211yescharacteristic, complemented
21C22×#1039C2211yescharacteristic, complemented
22C2×C5×C22⋊D5C2211yescharacteristic
23C2×C5×C22⋊D5C2211yescharacteristic
24C2×C5×C22⋊D5C2211yescharacteristic, complemented
25C2×C5×C22⋊D5C2211yescharacteristic, complemented
26C22×C5×Dic5C2211yescharacteristic, complemented
27C22×C5×Dic5C2211yescharacteristic, complemented
28C5×#711—24no—
29C2×C4×C5×D5C2211yescharacteristic, complemented
30C2×C5×Dic10C2211yescharacteristic, complemented
31D5×C22⋊D5—24no—
32C2×#6038C2211yescharacteristic
33C2×#6037C2211yescharacteristic
34C2×D5×Dic5C2211yescharacteristic
35C2×D5×Dic5C2211yescharacteristic, complemented
36C22⋊#1039C2211yescharacteristic, complemented
37#87808C2211yescharacteristic, complemented
38#87806C2211yescharacteristic, complemented
39C5×C22⋊Dic5C2211yescharacteristic, complemented
40C5×#685C2211yescharacteristic
41C5×#685C2211yescharacteristic, complemented
42#87780C2211yescharacteristic, complemented
43#87780C2211yescharacteristic, complemented
44#87780C2211yescharacteristic, complemented
45#87779C2211yescharacteristic, complemented
46#87779C2211yescharacteristic, complemented
47#87778C2211yescharacteristic
48#87778C2211yescharacteristic
49#87778C2211yescharacteristic, complemented
50#87778C2211yescharacteristic, complemented
51#87778C2211yescharacteristic, complemented
52Dic52C2211yescharacteristic, complemented
53#66163—51nomaximal
54#65925—51nomaximal
55C23×C52C2311yescharacteristic
56C23×C52C2311yescharacteristic
57C22×C5⋊D5C2311yescharacteristic
58C22×C5×D5—22no—
59C22×C5×D5—22no—
60C22×C5×D5—41no—
61C22×C5×D5C2311yescharacteristic
62C22×C5×D5C2311yescharacteristic
63C22×C5×D5C2311yescharacteristic
64C2×D52—22no—
65C2×D52—22no—
66C2×D52—41no—
67C52×D4—22no—
68C2×C4×C52C2311yescharacteristic
69C22⋊(C5⋊D5)—22no—
70C22⋊(C5⋊D5)—41no—
71C2×#1039—41no—
72C2×#1039C2311yescharacteristic
73C2×#1039C2311yescharacteristic
74C2×#1039C2311yescharacteristic
75C5×C22⋊D5—22no—
76C5×C22⋊D5—22no—
77C5×C22⋊D5—41no—
78C5×C22⋊D5D414yescomplemented
79C2×C5×Dic5—22no—
80C2×C5×Dic5—22no—
81C2×C5×Dic5C2311yescharacteristic
82C2×C5×Dic5C2311yescharacteristic
83C2×C5×Dic5C2311yescharacteristic
84C2×C5×Dic5C2311yescharacteristic
85C2×C5×Dic5C2311yescharacteristic
86C4×C5×D5—22no—
87C5×Dic10—22no—
88#6038—22no—
89#6037—22no—
90D5×Dic5—22no—
91D5×Dic5—41no—
92C2×C5×#41—51no—
93C22×C22⋊D5—51no—
94C2×#711D511yescharacteristic, complemented
95C2×D4×D5—51no—
96C5×#120—51no—
97C2×C22⋊Dic5—51no—
98#4093—51no—
99#4092—51no—
100#4085—51no—
101#4085—51no—
102#4085—51no—
103#4085—51no—
104#4085—102no—
105#4084—51no—
106#4083—51no—
107#4083—51no—
108#4083D511yescharacteristic, complemented
109D4×Dic5—51no—
110D4×Dic5—51no—
111#4076—51no—
112#4075—51no—
113#4075—51no—
114C4×C22⋊D5—51no—
115C2×#685—51no—
116C2×#685—51no—
117#4032—51no—
118#4031—51no—
119#4029—51no—
120#4027—51no—
121D5×C22⋊C4—51no—
122#4024—51no—
123C22×C52—21no—
124C22×C52—21no—
125C22×C52—21no—
126C22×C52—21no—
127C22×C52—21no—
128C22×C52C2×D412yes—
129C22×C52C2411yescharacteristic
130C2×C5⋊D5—21no—
131C2×C5⋊D5—21no—
132C2×C5⋊D5—21no—
133C2×C5×D5—21no—
134C2×C5×D5—21no—
135C2×C5×D5—21no—
136C2×C5×D5—21no—
137C2×C5×D5—21no—
138C2×C5×D5—21no—
139C2×C5×D5—21no—
140C2×C5×D5—44no—
141C2×C5×D5C2×D412yes—
142C2×C5×D5#4112yescomplemented
143D52—44no—
144C4×C52—21no—
145#1039—21no—
146#1039—21no—
147#1039—21no—
148C5×Dic5—21no—
149C5×Dic5—21no—
150C5×Dic5—21no—
151C5×Dic5—21no—
152C5×Dic5C2×D412yes—
153C24×C5—51no—
154C23×D5—51no—
155C23×D5—51no—
156C23×D5C2×D511yescharacteristic
157C5×#41—104no—
158C2×C5×Q8—51no—
159C2×C5×D4—22no—
160C2×C5×D4—51no—
161C2×C5×D4—51no—
162C2×C5×D4—51no—
163C2×C5×D4—51no—
164C2×C5×D4C2×D511yescharacteristic, complemented
165C2×C5×D4C2×D511yescharacteristic, complemented
166C22×C4×C5—51no—
167C22×C4×C5—51no—
168C22×C4×C5—51no—
169C2×C22⋊D5—51no—
170C2×C22⋊D5—51no—
171C2×C22⋊D5—51no—
172C2×C22⋊D5—51no—
173C2×C22⋊D5—51no—
174C2×C22⋊D5—51no—
175C2×C22⋊D5—51no—
176C2×C22⋊D5—102no—
177C2×C22⋊D5—102no—
178C2×C22⋊D5—104no—
179C2×C22⋊D5C2×D511yescharacteristic
180C2×C22⋊D5C2×D511yescharacteristic
181C2×C22⋊D5C2×D511yescharacteristic, complemented
182C2×C22⋊D5C2×D511yescharacteristic, complemented
183C22×Dic5—51no—
184C22×Dic5—51no—
185C22×Dic5—51no—
186C22×Dic5—51no—
187C22×Dic5—102no—
188C22×Dic5C2×D511yescharacteristic, complemented
189C22×Dic5C2×D511yescharacteristic, complemented
190#711—24no—
191D4×D5—104no—
192C2×D20—51no—
193C2×C4×D5—51no—
194C2×C4×D5—51no—
195C2×C4×D5C2×D511yescharacteristic, complemented
196C2×Dic10C2×D511yescharacteristic, complemented
197C5×C22⋊C4—51no—
198C5×C22⋊C4—51no—
199C5×C22⋊C4—51no—
200C22⋊Dic5—51no—
201C22⋊Dic5—51no—
202C22⋊Dic5—51no—
203C22⋊Dic5—51no—
204C22⋊Dic5—51no—
205C22⋊Dic5—51no—
206C22⋊Dic5—51no—
207C22⋊Dic5—102no—
208C22⋊Dic5C2×D511yescharacteristic, complemented
209#685—51no—
210#685—51no—
211#685—51no—
212#685—51no—
213#685—51no—
214#685—51no—
215#685—51no—
216#685—51no—
217#685—51no—
218#685—51no—
219#685—51no—
220#685—102no—
221#685C2×D511yescharacteristic
222#685C2×D511yescharacteristic, complemented
223C4⋊Dic5—51no—
224C4⋊Dic5—51no—
225C4⋊Dic5—51no—
226#683—51no—
227#683—51no—
228#683—51no—
229#683—51no—
230#683—51no—
231#683—102no—
232C4×Dic5—51no—
233C4×Dic5—51no—
234#546—251noSylow
235C2×C52—22no—
236C2×C52—41no—
237C2×C52C22×D411yescharacteristic
238C2×C52C2×#4111yescharacteristic
239C2×C52H(5,𝔽2)11yescharacteristic
240C5⋊D5—41no—
241C5×D5—22no—
242C5×D5—22no—
243C5×D5—41no—
244C23×C5—22no—
245C23×C5—22no—
246C23×C5—51no—
247C23×C5—51no—
248C23×C5—51no—
249C23×C5—102no—
250C23×C5—102no—
251C23×C5—201no—
252C23×C5C22×D511yescharacteristic
253C23×C5C22×D511yescharacteristic
254C23×C5C22×D511yescharacteristic
255C23×C5C22×D511yescharacteristic
256C22×D5—22no—
257C22×D5—22no—
258C22×D5—41no—
259C22×D5—51no—
260C22×D5—51no—
261C22×D5—102no—
262C22×D5—102no—
263C22×D5—102no—
264C22×D5—102no—
265C22×D5—102no—
266C22×D5—201no—
267C22×D5—201no—
268C22×D5C22×D511yescharacteristic
269C22×D5C22×D511yescharacteristic
270C22×D5C22×D511yescharacteristic
271C5×Q8—102no—
272C5×D4—22no—
273C5×D4—22no—
274C5×D4—44no—
275C5×D4—54no—
276C5×D4—102no—
277C5×D4—102no—
278C5×D4—201no—
279C2×C4×C5—22no—
280C2×C4×C5—51no—
281C2×C4×C5—51no—
282C2×C4×C5—51no—
283C2×C4×C5—51no—
284C2×C4×C5—51no—
285C2×C4×C5—102no—
286C2×C4×C5—102no—
287C2×C4×C5—102no—
288C2×C4×C5C22×D511yescharacteristic
289C2×C4×C5C22×D511yescharacteristic
290C22⋊D5—22no—
291C22⋊D5—22no—
292C22⋊D5—41no—
293C22⋊D5—102no—
294C22⋊D5—102no—
295C22⋊D5—102no—
296C22⋊D5—102no—
297C22⋊D5—102no—
298C22⋊D5—204no—
299C22⋊D5—201no—
300C22⋊D5—201no—
301C22⋊D5—204no—
302C22⋊D5C22⋊D514yescomplemented
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—51no—
306C2×Dic5—51no—
307C2×Dic5—51no—
308C2×Dic5—51no—
309C2×Dic5—51no—
310C2×Dic5—51no—
311C2×Dic5—102no—
312C2×Dic5—102no—
313C2×Dic5—102no—
314C2×Dic5—102no—
315C2×Dic5—201no—
316C2×Dic5—201no—
317C2×Dic5—201no—
318C2×Dic5—204no—
319C2×Dic5C22×D511yescharacteristic
320C2×Dic5C22×D511yescharacteristic
321C2×Dic5C22×D511yescharacteristic
322C2×Dic5C22×D511yescharacteristic
323C2×Dic5C22×D511yescharacteristic
324D20—102no—
325C4×D5—22no—
326C4×D5—102no—
327C4×D5—201no—
328Dic10—22no—
329C2×#41—51no—
330C22×D4—251no—
331#124—251no—
332#123—251no—
333#123—251no—
334C22⋊Q8—251no—
335#121—251no—
336#121—251no—
337#121—251no—
338#120—51no—
339#120—251no—
340C4×D4—251no—
341C4×D4—251no—
342C2×C22⋊C4—251no—
343C2×C22⋊C4—251no—
344C52#54611yescharacteristic, complemented, Sylow
345C22×C5—21no—
346C22×C5—21no—
347C22×C5—21no—
348C22×C5—21no—
349C22×C5—21no—
350C22×C5—21no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—21no—
355C22×C5—24no—
356C22×C5—22no—
357C22×C5—42no—
358C22×C5—42no—
359C22×C5—42no—
360C22×C5—42no—
361C22×C5—42no—
362C22×C5—52no—
363C22×C5—52no—
364C22×C5—101no—
365C22×C5—101no—
366C22×C5—101no—
367C22×C5—101no—
368C22×C5—101no—
369C22×C5—101no—
370C22×C5—101no—
371C22×C5—204no—
372C22×C5D4×D512yes—
373C22×C5C2×C22⋊D512yes—
374C22×C5C23×D511yescharacteristic
375C22×C5C23×D511yescharacteristic
376C2×D5—21no—
377C2×D5—21no—
378C2×D5—21no—
379C2×D5—21no—
380C2×D5—21no—
381C2×D5—21no—
382C2×D5—21no—
383C2×D5—44no—
384C2×D5—101no—
385C2×D5—101no—
386C2×D5—101no—
387C2×D5—101no—
388C2×D5—101no—
389C2×D5—101no—
390C2×D5—202no—
391C2×D5—202no—
392C2×D5—202no—
393C2×D5—204no—
394C2×D5—204no—
395C2×D5#71112yescomplemented
396C2×D5C2×C22⋊D512yes—
397C4×C5—21no—
398C4×C5—21no—
399C4×C5—42no—
400C4×C5—52no—
401C4×C5—101no—
402C4×C5—101no—
403C4×C5—101no—
404C4×C5—101no—
405Dic5—21no—
406Dic5—21no—
407Dic5—21no—
408Dic5—21no—
409Dic5—104no—
410Dic5—101no—
411Dic5—101no—
412Dic5—101no—
413Dic5—101no—
414Dic5—101no—
415Dic5—101no—
416Dic5—202no—
417Dic5—202no—
418Dic5C2×C22⋊D512yes—
419C24—51no—
420C24—251no—
421#41—104no—
422C2×Q8—51no—
423C2×D4—51no—
424C2×D4—51no—
425C2×D4—51no—
426C2×D4—51no—
427C2×D4—251no—
428C2×D4—251no—
429C2×D4—251no—
430C2×D4—251no—
431C2×D4—504no—
432C2×D4D5211yescharacteristic, complemented
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—251no—
437C22×C4—251no—
438C22×C4—251no—
439C4⋊C4—251no—
440C4⋊C4—251no—
441C4⋊C4—251no—
442C4⋊C4—251no—
443C22⋊C4—51no—
444C22⋊C4—51no—
445C22⋊C4—51no—
446C22⋊C4—251no—
447C22⋊C4—251no—
448C22⋊C4—251no—
449C22⋊C4—251no—
450C22⋊C4—251no—
451C22⋊C4—251no—
452C22⋊C4—251no—
453C22⋊C4—251no—
454C22⋊C4—251no—
455C42—251no—
456C2×C5—22no—
457C2×C5—22no—
458C2×C5—22no—
459C2×C5—22no—
460C2×C5—22no—
461C2×C5—44no—
462C2×C5—41no—
463C2×C5—41no—
464C2×C5—82no—
465C2×C5—102no—
466C2×C5—102no—
467C2×C5—201no—
468C2×C5C2×D4×D511yescharacteristic
469C2×C5C2×#71111yescharacteristic
470C2×C5#414411yescharacteristic
471C2×C5D5×#4111yescharacteristic
472C2×C5#414911yescharacteristic
473C2×C5C22×C22⋊D511yescharacteristic
474D5—22no—
475D5—22no—
476D5—41no—
477D5—201no—
478D5—201no—
479D5—402no—
480C23—51no—
481C23—51no—
482C23—51no—
483C23—102no—
484C23—102no—
485C23—201no—
486C23—251no—
487C23—502no—
488C23—502no—
489C23—1001no—
490C23C2×D5211yescharacteristic
491C23C2×D5211yescharacteristic
492Q8—102no—
493D4—22no—
494D4—54no—
495D4—102no—
496D4—102no—
497D4—201no—
498D4—502no—
499D4—502no—
500D4—502no—
501D4—1001no—
502C2×C4—51no—
503C2×C4—51no—
504C2×C4—51no—
505C2×C4—51no—
506C2×C4—51no—
507C2×C4—102no—
508C2×C4—102no—
509C2×C4—102no—
510C2×C4—251no—
511C2×C4—251no—
512C2×C4—251no—
513C2×C4—502no—
514C2×C4—1001no—
515C2×C4—1001no—
516C2×C4C2×D5211yescharacteristic
517C5—22no—
518C5#6592511yescharacteristic, complemented
519C5#6616311yescharacteristic, complemented
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—52no—
526C22—52no—
527C22—101no—
528C22—101no—
529C22—101no—
530C22—101no—
531C22—101no—
532C22—101no—
533C22—101no—
534C22—204no—
535C22—501no—
536C22—501no—
537C22—501no—
538C22—1004no—
539C22D5×C22⋊D512yes—
540C22C22×D5211yescharacteristic
541C4—21no—
542C4—52no—
543C4—101no—
544C4—101no—
545C4—101no—
546C4—101no—
547C4—501no—
548C4—501no—
549C4—501no—
550C2—22no—
551C2—41no—
552C2—102no—
553C2—102no—
554C2—201no—
555C2—1001no—
556C2D5×#71111yescharacteristic
557C2#1171747911yescharacteristic
558C2C2×D5×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC2×C52×D4C22
hypercenterC2×D4D52
hypocenterC52#546
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#711C2semidirect
2. C2×D5×C22⋊D5C2semidirect
3. #11717259C2semidirect
4. C5×#4083C2semidirect
5. #11717101C2semidirect
6. #11717096C2semidirect
7. #11717091C2semidirect
8. Dic5×C22⋊D5C2semidirect
9. #11717088C2semidirect
10. #11717084C2semidirect
11. C2×#87778C2semidirect
12. D5×#685C2semidirect
13. #11717025C2semidirect
14. #11717023C2semidirect
15. #11717006C2semidirect
18. C2×C52×D4C22semidirect
20. C2×C22⋊(C5⋊D5)C22semidirect
21. C22×#1039C22semidirect
24. C2×C5×C22⋊D5C22semidirect
25. C2×C5×C22⋊D5C22semidirect
26. C22×C5×Dic5C22semidirect
27. C22×C5×Dic5C22semidirect
29. C2×C4×C5×D5C22semidirect
30. C2×C5×Dic10C22semidirect
35. C2×D5×Dic5C22semidirect
36. C22⋊#1039C22semidirect
37. #87808C22semidirect
38. #87806C22semidirect
39. C5×C22⋊Dic5C22semidirect
41. C5×#685C22semidirect
42. #87780C22semidirect
43. #87780C22semidirect
44. #87780C22semidirect
45. #87779C22semidirect
46. #87779C22semidirect
49. #87778C22semidirect
50. #87778C22semidirect
51. #87778C22semidirect
52. Dic52C22semidirect
78. C5×C22⋊D5D4semidirect
94. C2×#711D5semidirect
108. #4083D5semidirect
142. C2×C5×D5#41semidirect
164. C2×C5×D4C2×D5semidirect
165. C2×C5×D4C2×D5semidirect
181. C2×C22⋊D5C2×D5semidirect
182. C2×C22⋊D5C2×D5semidirect
188. C22×Dic5C2×D5semidirect
189. C22×Dic5C2×D5semidirect
195. C2×C4×D5C2×D5semidirect
196. C2×Dic10C2×D5semidirect
208. C22⋊Dic5C2×D5semidirect
222. #685C2×D5semidirect
302. C22⋊D5C22⋊D5semidirect
344. C52#546semidirect
395. C2×D5#711semidirect
432. C2×D4D52semidirect
518. C5#65925semidirect
519. C5#66163semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#7112
C2×D5×C22⋊D52
#117172592
C5×#40832
#117171012
#117170962
#117170912
Dic5×C22⋊D52
#117170882
#117170842
C2×#877782
D5×#6852
#117170252
#117170232
#117170062
#661635
#659255