Finite Group Databasebeta

← #13105239

Subgroups — #13105239

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×D5×C22⋊D5C211yesmaximal, characteristic, complemented
2C2×#87873C211yesmaximal, characteristic, complemented
3#11717204C211yesmaximal, characteristic, complemented
4C5×#4029C211yesmaximal, characteristic, complemented
5C5×D5×C22⋊C4C211yesmaximal, characteristic, complemented
6#11717095C211yesmaximal, characteristic, complemented
7#11717089C211yesmaximal, characteristic, complemented
8#11717071C211yesmaximal, characteristic, complemented
9#11717041C211yesmaximal, characteristic, complemented
10D5×#685C211yesmaximal, characteristic, complemented
11#11717027C211yesmaximal, characteristic, complemented
12#11717014C211yesmaximal, characteristic, complemented
13#11716999C211yesmaximal, characteristic, complemented
14#11716997C211yesmaximal, characteristic, complemented
15#11716968C211yesmaximal, characteristic, complemented
16C23×C5×D5C2211yescharacteristic
17C22×D52C2211yescharacteristic
18C2×C22⋊(C5⋊D5)C2211yescharacteristic
19C2×C22⋊(C5⋊D5)C2211yescharacteristic, complemented
20C2×C4⋊(C5⋊D5)C2211yescharacteristic, complemented
21C2×C4×C5⋊D5C2211yescharacteristic, complemented
22C2×C5×C22⋊D5C2211yescharacteristic
23C2×C4×C5×D5C2211yescharacteristic, complemented
24C2×C4×C5×D5C2211yescharacteristic, complemented
25C2×C4×C5×D5C2211yescharacteristic, complemented
26D5×C22⋊D5—24no—
27C2×#6039C2211yescharacteristic, complemented
28C2×#6038C2211yescharacteristic
29C2×#6038C2211yescharacteristic
30C2×#6038C2211yescharacteristic, complemented
31C2×#6038C2211yescharacteristic, complemented
32C2×#6037C2211yescharacteristic
33C2×D5×Dic5C2211yescharacteristic
34C2×D5×Dic5C2211yescharacteristic, complemented
35#87873—24no—
36C52×C22⋊C4C2211yescharacteristic, complemented
37#87808C2211yescharacteristic, complemented
38#87806C2211yescharacteristic, complemented
39C5×C22⋊Dic5C2211yescharacteristic, complemented
40C5×C22⋊Dic5C2211yescharacteristic, complemented
41C5×#685C2211yescharacteristic
42C5×#685C2211yescharacteristic
43C5×#685C2211yescharacteristic, complemented
44C5×C4⋊Dic5C2211yescharacteristic, complemented
45C5×#683C2211yescharacteristic, complemented
46#87781C2211yescharacteristic, complemented
47#87779C2211yescharacteristic, complemented
48#87779C2211yescharacteristic, complemented
49#87779C2211yescharacteristic, complemented
50#87778C2211yescharacteristic
51#87778C2211yescharacteristic, complemented
52Dic52C2211yescharacteristic, complemented
53#65988—51nomaximal
54#65824—51nomaximal
55C23×C52C2311yescharacteristic
56C22×C5⋊D5C2311yescharacteristic
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—
67C2×C4×C52C2311yescharacteristic
68C2×C4×C52C2311yescharacteristic
69C22⋊(C5⋊D5)—22no—
70C22⋊(C5⋊D5)—41no—
71C2×#1039C2311yescharacteristic
72C2×#1039C2311yescharacteristic
73C4⋊(C5⋊D5)—41no—
74C4×C5⋊D5—22no—
75C5×C22⋊D5—22no—
76C2×C5×Dic5C2311yescharacteristic
77C2×C5×Dic5C2311yescharacteristic
78C2×C5×Dic5C2311yescharacteristic
79C2×C5×Dic5C2311yescharacteristic
80C2×C5×Dic5C2311yescharacteristic
81C4×C5×D5—22no—
82C4×C5×D5—22no—
83C4×C5×D5—41no—
84#6039—22no—
85#6038—22no—
86#6038—22no—
87#6038—22no—
88#6038—22no—
89#6037D414yescomplemented
90D5×Dic5—22no—
91D5×Dic5—41no—
92C22×C22⋊D5—51no—
93C2×D4×D5—51no—
94C2×#709—51no—
95C2×#709—51no—
96C5×#123—51no—
97C2×C5×C22⋊C4—51no—
98#4099—51no—
99#4085—51no—
100#4076—51no—
101#4075—51no—
102C4×C22⋊D5—51no—
103C2×#685—51no—
104#4042—51no—
105#4041—51no—
106#4040—51no—
107#4039—51no—
108#4031—51no—
109#4031—51no—
110#4030—51no—
111#4030—51no—
112#4030—51no—
113#4030—102no—
114#4029D511yescharacteristic, complemented
115#4028—51no—
116#4028—51no—
117#4028—51no—
118#4027—51no—
119#4027—51no—
120D5×C22⋊C4—51no—
121D5×C22⋊C4D511yescharacteristic, complemented
122#4024—51no—
123C22×C52—21no—
124C22×C52—21no—
125C22×C52—21no—
126C22×C52C2411yescharacteristic
127C2×C5⋊D5—21no—
128C2×C5⋊D5—21no—
129C2×C5⋊D5—21no—
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—44no—
140C2×C5×D5C2×D412yes—
141C2×C5×D5C2×D412yes—
142C2×C5×D5#4112yescomplemented
143D52—44no—
144C4×C52—21no—
145C4×C52—21no—
146#1039—21no—
147#1039C2×D412yes—
148C5×Dic5—21no—
149C5×Dic5—21no—
150C5×Dic5—21no—
151C5×Dic5—21no—
152C5×Dic5—21no—
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—
161C2×C22⋊D5—51no—
162C2×C22⋊D5—51no—
163C2×C22⋊D5—51no—
164C2×C22⋊D5—51no—
165C2×C22⋊D5—51no—
166C2×C22⋊D5—51no—
167C2×C22⋊D5—51no—
168C2×C22⋊D5—51no—
169C2×C22⋊D5—51no—
170C2×C22⋊D5—51no—
171C2×C22⋊D5—102no—
172C2×C22⋊D5—102no—
173C2×C22⋊D5—104no—
174C2×C22⋊D5C2×D511yescharacteristic
175C22×Dic5—51no—
176C22×Dic5—51no—
177D4×D5—104no—
178#709—104no—
179#709—104no—
180C2×D20—51no—
181C2×D20—51no—
182C2×D20—51no—
183C2×D20—51no—
184C2×D20—51no—
185C2×D20—51no—
186C2×D20—102no—
187C2×C4×D5—51no—
188C2×C4×D5—51no—
189C2×C4×D5—51no—
190C2×C4×D5—51no—
191C2×C4×D5—102no—
192C2×C4×D5C2×D511yescharacteristic, complemented
193C2×C4×D5C2×D511yescharacteristic, complemented
194C2×C4×D5C2×D511yescharacteristic, complemented
195C2×Dic10—51no—
196C2×Dic10—51no—
197C5×C4⋊C4—51no—
198C5×C4⋊C4—51no—
199C5×C22⋊C4—22no—
200C5×C22⋊C4—51no—
201C5×C22⋊C4—51no—
202C5×C22⋊C4—51no—
203C5×C22⋊C4—51no—
204C5×C22⋊C4—51no—
205C5×C22⋊C4C2×D511yescharacteristic, complemented
206C5×C22⋊C4C2×D511yescharacteristic, complemented
207C22⋊Dic5—51no—
208C22⋊Dic5—51no—
209C22⋊Dic5C2×D511yescharacteristic, complemented
210C22⋊Dic5C2×D511yescharacteristic, complemented
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—51no—
221#685—102no—
222#685C2×D511yescharacteristic
223#685C2×D511yescharacteristic
224#685C2×D511yescharacteristic, complemented
225C4⋊Dic5C2×D511yescharacteristic, complemented
226#683—51no—
227#683—51no—
228#683—51no—
229#683—51no—
230#683—102no—
231#683C2×D511yescharacteristic, complemented
232C4×Dic5—51no—
233C4×Dic5—51no—
234#546—251noSylow
235C2×C52—41no—
236C2×C52C22×D411yescharacteristic
237C2×C52C2×#4111yescharacteristic
238C2×C52H(5,𝔽2)11yescharacteristic
239C5⋊D5—41no—
240C5⋊D5—41no—
241C5×D5—22no—
242C5×D5—22no—
243C5×D5—22no—
244C23×C5—22no—
245C23×C5—51no—
246C23×C5—51no—
247C23×C5—51no—
248C23×C5—102no—
249C23×C5—102no—
250C23×C5—201no—
251C23×C5C22×D511yescharacteristic
252C23×C5C22×D511yescharacteristic
253C22×D5—22no—
254C22×D5—22no—
255C22×D5—41no—
256C22×D5—51no—
257C22×D5—51no—
258C22×D5—51no—
259C22×D5—51no—
260C22×D5—102no—
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×D4—102no—
272C2×C4×C5—22no—
273C2×C4×C5—22no—
274C2×C4×C5—51no—
275C2×C4×C5—51no—
276C2×C4×C5—51no—
277C2×C4×C5—51no—
278C2×C4×C5—51no—
279C2×C4×C5—102no—
280C2×C4×C5—102no—
281C2×C4×C5—201no—
282C2×C4×C5C22×D511yescharacteristic
283C2×C4×C5C22×D511yescharacteristic
284C2×C4×C5C22×D511yescharacteristic
285C2×C4×C5C22×D511yescharacteristic
286C22⋊D5—22no—
287C22⋊D5—54no—
288C22⋊D5—54no—
289C22⋊D5—102no—
290C22⋊D5—102no—
291C22⋊D5—102no—
292C22⋊D5—102no—
293C22⋊D5—102no—
294C22⋊D5—102no—
295C22⋊D5—204no—
296C22⋊D5—201no—
297C22⋊D5—201no—
298C22⋊D5—204no—
299C2×Dic5—51no—
300C2×Dic5—51no—
301C2×Dic5—51no—
302C2×Dic5—51no—
303C2×Dic5—102no—
304C2×Dic5—102no—
305C2×Dic5—102no—
306C2×Dic5—201no—
307C2×Dic5C22×D511yescharacteristic
308C2×Dic5C22×D511yescharacteristic
309C2×Dic5C22×D511yescharacteristic
310C2×Dic5C22×D511yescharacteristic
311C2×Dic5C22×D511yescharacteristic
312D20—102no—
313D20—102no—
314D20—102no—
315D20—102no—
316D20—201no—
317D20—201no—
318D20—204no—
319C4×D5—22no—
320C4×D5—22no—
321C4×D5—41no—
322C4×D5—102no—
323C4×D5—102no—
324C4×D5—102no—
325C4×D5—204no—
326C4×D5—201no—
327Dic10—102no—
328Dic10—102no—
329C2×#41—251no—
330C22×D4—251no—
331#124—251no—
332#123—51no—
333#123—251no—
334C22⋊Q8—251no—
335#121—251no—
336#121—251no—
337#121—251no—
338#120—251no—
339#120—251no—
340C4×D4—251no—
341C4×D4—251no—
342C2×C22⋊C4—51no—
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—22no—
352C22×C5—42no—
353C22×C5—42no—
354C22×C5—42no—
355C22×C5—52no—
356C22×C5—52no—
357C22×C5—52no—
358C22×C5—101no—
359C22×C5—101no—
360C22×C5—101no—
361C22×C5—101no—
362C22×C5—101no—
363C22×C5—101no—
364C22×C5—204no—
365C22×C5C23×D511yescharacteristic
366C22×C5C23×D511yescharacteristic
367C2×D5—21no—
368C2×D5—21no—
369C2×D5—21no—
370C2×D5—21no—
371C2×D5—21no—
372C2×D5—21no—
373C2×D5—44no—
374C2×D5—104no—
375C2×D5—101no—
376C2×D5—101no—
377C2×D5—101no—
378C2×D5—101no—
379C2×D5—101no—
380C2×D5—101no—
381C2×D5—101no—
382C2×D5—101no—
383C2×D5—101no—
384C2×D5—101no—
385C2×D5—101no—
386C2×D5—101no—
387C2×D5—202no—
388C2×D5—202no—
389C2×D5—202no—
390C2×D5—202no—
391C2×D5—202no—
392C2×D5—204no—
393C2×D5—204no—
394C2×D5#70912yescomplemented
395C2×D5D4×D512yes—
396C2×D5D4×D512yes—
397C4×C5—21no—
398C4×C5—21no—
399C4×C5—21no—
400C4×C5—21no—
401C4×C5—42no—
402C4×C5—42no—
403C4×C5—101no—
404C4×C5—101no—
405C4×C5—101no—
406C4×C5—101no—
407C4×C5—101no—
408Dic5—21no—
409Dic5—21no—
410Dic5—21no—
411Dic5—21no—
412Dic5—21no—
413Dic5—52no—
414Dic5—52no—
415Dic5—104no—
416Dic5—101no—
417Dic5—101no—
418Dic5—202no—
419C24—51no—
420C24—251no—
421#41—504no—
422C2×Q8—251no—
423C2×D4—51no—
424C2×D4—251no—
425C2×D4—251no—
426C2×D4—251no—
427C2×D4—251no—
428C2×D4—251no—
429C2×D4—251no—
430C2×D4—251no—
431C2×D4—251no—
432C2×D4—504no—
433C22×C4—51no—
434C22×C4—51no—
435C22×C4—51no—
436C22×C4—251no—
437C22×C4—251no—
438C22×C4—251no—
439C4⋊C4—51no—
440C4⋊C4—51no—
441C4⋊C4—251no—
442C4⋊C4—251no—
443C22⋊C4—51no—
444C22⋊C4—51no—
445C22⋊C4—51no—
446C22⋊C4—51no—
447C22⋊C4—51no—
448C22⋊C4—251no—
449C22⋊C4—251no—
450C22⋊C4—251no—
451C22⋊C4—251no—
452C22⋊C4—251no—
453C22⋊C4—251no—
454C22⋊C4D5211yescharacteristic, complemented
455C42—251no—
456C2×C5—22no—
457C2×C5—22no—
458C2×C5—22no—
459C2×C5—41no—
460C2×C5—41no—
461C2×C5—82no—
462C2×C5—102no—
463C2×C5—102no—
464C2×C5—102no—
465C2×C5C2×#70911yescharacteristic
466C2×C5C2×D4×D511yescharacteristic
467C2×C5C2×D4×D511yescharacteristic
468C2×C5#414411yescharacteristic
469C2×C5D5×#4111yescharacteristic
470C2×C5#414911yescharacteristic
471D5—22no—
472D5—22no—
473D5—22no—
474D5—204no—
475D5—201no—
476D5—201no—
477D5—201no—
478D5—201no—
479D5—402no—
480C23—51no—
481C23—51no—
482C23—51no—
483C23—102no—
484C23—102no—
485C23—201no—
486C23—251no—
487C23—251no—
488C23—502no—
489C23—502no—
490C23—1001no—
491C23C2×D5211yescharacteristic
492Q8—502no—
493D4—102no—
494D4—254no—
495D4—502no—
496D4—502no—
497D4—502no—
498D4—502no—
499D4—502no—
500D4—1001no—
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—201no—
510C2×C4—251no—
511C2×C4—251no—
512C2×C4—502no—
513C2×C4—502no—
514C2×C4—1001no—
515C2×C4C2×D5211yescharacteristic
516C2×C4C2×D5211yescharacteristic
517C5—22no—
518C5#6582411yescharacteristic, complemented
519C5#6598811yescharacteristic, complemented
520C22—21no—
521C22—21no—
522C22—21no—
523C22—52no—
524C22—52no—
525C22—52no—
526C22—101no—
527C22—101no—
528C22—101no—
529C22—101no—
530C22—101no—
531C22—101no—
532C22—204no—
533C22—501no—
534C22—501no—
535C22—501no—
536C22—501no—
537C22—501no—
538C22—501no—
539C22—1004no—
540C22C22×D5211yescharacteristic
541C4—21no—
542C4—21no—
543C4—101no—
544C4—101no—
545C4—101no—
546C4—101no—
547C4—101no—
548C4—252no—
549C4—501no—
550C2—41no—
551C2—102no—
552C2—102no—
553C2—102no—
554C2—1001no—
555C2—1001no—
556C2D5×#70911yescharacteristic
557C2D4×D5211yescharacteristic
558C2#1171747911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D52
commutator, socle, cosocleC22×C52C24
FittingC52×C22⋊C4C22
hypercenterC22⋊C4D52
hypocenterC52#546
LCSG ▷ C22×C52 ▷ C52
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D5×C22⋊D5C2semidirect
2. C2×#87873C2semidirect
3. #11717204C2semidirect
4. C5×#4029C2semidirect
5. C5×D5×C22⋊C4C2semidirect
6. #11717095C2semidirect
7. #11717089C2semidirect
8. #11717071C2semidirect
9. #11717041C2semidirect
10. D5×#685C2semidirect
11. #11717027C2semidirect
12. #11717014C2semidirect
13. #11716999C2semidirect
14. #11716997C2semidirect
15. #11716968C2semidirect
19. C2×C22⋊(C5⋊D5)C22semidirect
20. C2×C4⋊(C5⋊D5)C22semidirect
21. C2×C4×C5⋊D5C22semidirect
23. C2×C4×C5×D5C22semidirect
24. C2×C4×C5×D5C22semidirect
25. C2×C4×C5×D5C22semidirect
27. C2×#6039C22semidirect
30. C2×#6038C22semidirect
31. C2×#6038C22semidirect
34. C2×D5×Dic5C22semidirect
36. C52×C22⋊C4C22semidirect
37. #87808C22semidirect
38. #87806C22semidirect
39. C5×C22⋊Dic5C22semidirect
40. C5×C22⋊Dic5C22semidirect
43. C5×#685C22semidirect
44. C5×C4⋊Dic5C22semidirect
45. C5×#683C22semidirect
46. #87781C22semidirect
47. #87779C22semidirect
48. #87779C22semidirect
49. #87779C22semidirect
51. #87778C22semidirect
52. Dic52C22semidirect
89. #6037D4semidirect
114. #4029D5semidirect
121. D5×C22⋊C4D5semidirect
142. C2×C5×D5#41semidirect
192. C2×C4×D5C2×D5semidirect
193. C2×C4×D5C2×D5semidirect
194. C2×C4×D5C2×D5semidirect
205. C5×C22⋊C4C2×D5semidirect
206. C5×C22⋊C4C2×D5semidirect
209. C22⋊Dic5C2×D5semidirect
210. C22⋊Dic5C2×D5semidirect
224. #685C2×D5semidirect
225. C4⋊Dic5C2×D5semidirect
231. #683C2×D5semidirect
344. C52#546semidirect
394. C2×D5#709semidirect
454. C22⋊C4D52semidirect
518. C5#65824semidirect
519. C5#65988semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊D52
C2×#878732
#117172042
C5×#40292
C5×D5×C22⋊C42
#117170952
#117170892
#117170712
#117170412
D5×#6852
#117170272
#117170142
#117169992
#117169972
#117169682
#659885
#658245