Finite Group Databasebeta

← #10609213

Subgroups — #10609213

Order 640.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C22⋊C4C211yesmaximal, characteristic
2C2×#4025C211yesmaximal, characteristic, complemented
3C5×#397C211yesmaximal, characteristic, complemented
4#65279C211yesmaximal, characteristic, complemented
5#65278C211yesmaximal, characteristic, complemented
6#65244C211yesmaximal, characteristic
7#65244C211yesmaximal, characteristic
8#65241C211yesmaximal, characteristic, complemented
9#65234C211yesmaximal, characteristic, complemented
10#64965C211yesmaximal, characteristic, complemented
11#64964C211yesmaximal, characteristic, complemented
12#64959C211yesmaximal, characteristic, complemented
13#64957C211yesmaximal, characteristic, complemented
14#64956C211yesmaximal, characteristic, complemented
15#64955C211yesmaximal, characteristic, complemented
16C24×D5C2211yescharacteristic
17C22×C4×D5C2211yescharacteristic
18C22×C4×D5C2211yescharacteristic
19C2×C5×C4⋊C4C2211yescharacteristic, complemented
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C5×C22⋊C4C2211yescharacteristic
22C2×C5×C22⋊C4C2211yescharacteristic
23C2×C22⋊Dic5C2211yescharacteristic
24C2×C22⋊Dic5C2211yescharacteristic
25C2×C22⋊Dic5C2211yescharacteristic
26C2×#685C2211yescharacteristic
27C2×#685C2211yescharacteristic
28C2×#685C2211yescharacteristic
29C2×#685C2211yescharacteristic
30C2×#685C2211yescharacteristic
31C2×#685C2211yescharacteristic
32C2×#685C2211yescharacteristic
33C2×#685C2211yescharacteristic
34C2×#685C2211yescharacteristic
35C2×#685C2211yescharacteristic
36C2×C4⋊Dic5C2211yescharacteristic, complemented
37C2×#683C2211yescharacteristic, complemented
38C2×#683C2211yescharacteristic, complemented
39C2×#683C2211yescharacteristic, complemented
40C2×#683C2211yescharacteristic, complemented
41C2×C4×Dic5C2211yescharacteristic, complemented
42C2×C4×Dic5C2211yescharacteristic, complemented
43D5×C22⋊C4—24no—
44#4025—24no—
45C5×#95C2211yescharacteristic, complemented
46C5×#95C2211yescharacteristic, complemented
47C5×#95C2211yescharacteristic, complemented
48#3963C2211yescharacteristic, complemented
49#3963C2211yescharacteristic, complemented
50#3963C2211yescharacteristic, complemented
51#3963C2211yescharacteristic, complemented
52#3963C2211yescharacteristic, complemented
53#2480—51nomaximal, Sylow
54C24×C5C2311yescharacteristic
55C23×D5—22no—
56C23×D5—22no—
57C23×D5—22no—
58C23×D5—22no—
59C23×D5—22no—
60C23×D5—41no—
61C23×D5—41no—
62C23×D5C2311yescharacteristic
63C23×D5C2311yescharacteristic
64C22×C4×C5C2311yescharacteristic
65C22×C4×C5C2311yescharacteristic
66C22×C4×C5C2311yescharacteristic
67C22×C4×C5C2311yescharacteristic
68C22×C4×C5C2311yescharacteristic
69C22×C4×C5C2311yescharacteristic
70C22×Dic5C2311yescharacteristic
71C22×Dic5C2311yescharacteristic
72C22×Dic5C2311yescharacteristic
73C22×Dic5C2311yescharacteristic
74C22×Dic5C2311yescharacteristic
75C22×Dic5C2311yescharacteristic
76C2×C4×D5—22no—
77C2×C4×D5—22no—
78C2×C4×D5—22no—
79C2×C4×D5—22no—
80C2×C4×D5—41no—
81C2×C4×D5—41no—
82C5×C4⋊C4—41no—
83C5×C22⋊C4—22no—
84C5×C22⋊C4—22no—
85C5×C22⋊C4—41no—
86C22⋊Dic5—22no—
87C22⋊Dic5—41no—
88C22⋊Dic5D414yes—
89#685—22no—
90#685—22no—
91#685—22no—
92#685—22no—
93#685—22no—
94#685—22no—
95#685—22no—
96#685—22no—
97#685—41no—
98#685—41no—
99C4⋊Dic5—22no—
100#683—22no—
101#683—22no—
102#683—41no—
103#683—41no—
104C4×Dic5—22no—
105C4×Dic5—41no—
106C2×#126—51no—
107C22×C22⋊C4—51no—
108#397—51no—
109#397—51no—
110#397D511yescharacteristic, complemented
111#396—51no—
112#388—51no—
113#388—51no—
114#388—51no—
115#385—51no—
116#385—51no—
117#380—51no—
118#379—51no—
119#379—51no—
120C4×C22⋊C4—51no—
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5C2×D412yes—
128C23×C5C2411yescharacteristic
129C22×D5—21no—
130C22×D5—21no—
131C22×D5—21no—
132C22×D5—21no—
133C22×D5—28no—
134C22×D5—21no—
135C22×D5—21no—
136C22×D5—21no—
137C22×D5—21no—
138C22×D5—21no—
139C22×D5—21no—
140C22×D5—44no—
141C22×D5—44no—
142C22×D5—44no—
143C22×D5—44no—
144C22×D5—44no—
145C22×D5—44no—
146C22×D5#4112yes—
147C22×D5#4112yes—
148C22×D5#4112yes—
149C22×D5#4112yes—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—21no—
168C2×Dic5—21no—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—21no—
172C2×Dic5—21no—
173C2×Dic5—21no—
174C2×Dic5—21no—
175C2×Dic5—21no—
176C2×Dic5—21no—
177C2×Dic5—21no—
178C2×Dic5—21no—
179C2×Dic5—21no—
180C2×Dic5—21no—
181C2×Dic5—21no—
182C2×Dic5—21no—
183C2×Dic5—21no—
184C2×Dic5C2×D412yes—
185C2×Dic5C2×D412yes—
186C4×D5—44no—
187C4×D5—44no—
188C25—51no—
189C23×C4—51no—
190C23×C4—51no—
191#126—104no—
192C2×C4⋊C4—51no—
193C2×C4⋊C4—51no—
194C2×C4⋊C4—51no—
195C2×C4⋊C4—51no—
196C2×C4⋊C4—51no—
197C2×C4⋊C4C2×D511yescharacteristic, complemented
198C2×C22⋊C4—51no—
199C2×C22⋊C4—51no—
200C2×C22⋊C4—51no—
201C2×C22⋊C4—51no—
202C2×C22⋊C4—51no—
203C2×C22⋊C4—51no—
204C2×C22⋊C4—51no—
205C2×C22⋊C4—51no—
206C2×C22⋊C4—51no—
207C2×C22⋊C4—51no—
208C2×C22⋊C4—51no—
209C2×C22⋊C4—51no—
210C2×C22⋊C4—51no—
211C2×C22⋊C4—104no—
212C2×C22⋊C4C2×D511yescharacteristic
213C2×C22⋊C4C2×D511yescharacteristic
214C2×C22⋊C4C2×D511yescharacteristic
215C2×C42—51no—
216C2×C42—51no—
217#95—51no—
218#95—51no—
219#95—51no—
220#95—51no—
221#95—51no—
222#95C2×D511yescharacteristic, complemented
223#95C2×D511yescharacteristic, complemented
224#95C2×D511yescharacteristic, complemented
225C22×C5—22no—
226C22×C5—22no—
227C22×C5—22no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5—41no—
231C22×C5—41no—
232C22×C5C22×D411yescharacteristic
233C22×C5C2×#4111yescharacteristic
234C22×C5C2×#4111yescharacteristic
235C22×C5C2×#4111yescharacteristic
236C22×C5C2×#4111yescharacteristic
237C22×C5H(5,𝔽2)11yescharacteristic
238C22×C5H(5,𝔽2)11yescharacteristic
239C2×D5—22no—
240C2×D5—22no—
241C2×D5—22no—
242C2×D5—22no—
243C2×D5—22no—
244C2×D5—22no—
245C2×D5—22no—
246C2×D5—22no—
247C2×D5—22no—
248C2×D5—416no—
249C2×D5—41no—
250C2×D5—41no—
251C2×D5—41no—
252C2×D5—41no—
253C2×D5#12614yescomplemented
254C4×C5—41no—
255C4×C5—41no—
256C4×C5—41no—
257C4×C5—41no—
258C4×C5—41no—
259C4×C5—41no—
260Dic5—22no—
261Dic5—22no—
262Dic5—41no—
263Dic5—41no—
264Dic5—41no—
265Dic5—41no—
266C24—51no—
267C24—51no—
268C24—102no—
269C24—102no—
270C24—102no—
271C24—102no—
272C24—102no—
273C24—201no—
274C24—201no—
275C24C22×D511yescharacteristic
276C22×C4—51no—
277C22×C4—51no—
278C22×C4—51no—
279C22×C4—51no—
280C22×C4—51no—
281C22×C4—51no—
282C22×C4—102no—
283C22×C4—102no—
284C22×C4—102no—
285C22×C4—102no—
286C22×C4—201no—
287C22×C4—201no—
288C22×C4C22×D511yescharacteristic
289C22×C4C22×D511yescharacteristic
290C22×C4C22×D511yescharacteristic
291C22×C4C22×D511yescharacteristic
292C22×C4C22×D511yescharacteristic
293C22×C4C22×D511yescharacteristic
294C4⋊C4—41no—
295C4⋊C4—102no—
296C4⋊C4—102no—
297C4⋊C4—102no—
298C4⋊C4—201no—
299C4⋊C4—201no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—41no—
303C22⋊C4—54no—
304C22⋊C4—102no—
305C22⋊C4—102no—
306C22⋊C4—102no—
307C22⋊C4—102no—
308C22⋊C4—102no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C22⋊C4—102no—
312C22⋊C4—102no—
313C22⋊C4—201no—
314C22⋊C4—201no—
315C22⋊C4—201no—
316C42—102no—
317C42—201no—
318C2×C5—42no—
319C2×C5#52511yescharacteristic
320C2×C5C2×#12611yescharacteristic
321C2×C5#53811yescharacteristic
322C2×C5#54611yescharacteristic
323C2×C5#54611yescharacteristic
324C2×C5#55111yescharacteristic
325C2×C5#55111yescharacteristic
326D5—24no—
327D5—42no—
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—21no—
334C23—52no—
335C23—52no—
336C23—52no—
337C23—52no—
338C23—108no—
339C23—101no—
340C23—101no—
341C23—101no—
342C23—101no—
343C23—101no—
344C23—101no—
345C23—101no—
346C23—101no—
347C23—101no—
348C23—101no—
349C23—204no—
350C23—204no—
351C23—204no—
352C23—204no—
353C23—204no—
354C23—204no—
355C23D4×D512yes—
356C23C23×D511yescharacteristic
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—52no—
376C2×C4—52no—
377C2×C4—101no—
378C2×C4—101no—
379C2×C4—101no—
380C2×C4—101no—
381C2×C4—101no—
382C2×C4—101no—
383C2×C4—101no—
384C2×C4—101no—
385C2×C4—101no—
386C2×C4—101no—
387C2×C4—101no—
388C2×C4—101no—
389C2×C4—101no—
390C2×C4—101no—
391C2×C4—101no—
392C2×C4—101no—
393C2×C4—204no—
394C2×C4—204no—
395C5#248011yescharacteristic, complemented, Sylow
396C22—22no—
397C22—22no—
398C22—22no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—54no—
404C22—102no—
405C22—102no—
406C22—102no—
407C22—102no—
408C22—102no—
409C22—102no—
410C22—102no—
411C22—102no—
412C22—102no—
413C22—2016no—
414C22—201no—
415C22—201no—
416C22—201no—
417C22—201no—
418C22C2×D4×D511yescharacteristic
419C22#414411yescharacteristic
420C22D5×#4111yescharacteristic
421C22D5×#4111yescharacteristic
422C22D5×#4111yescharacteristic
423C22D5×#4111yescharacteristic
424C22#414911yescharacteristic
425C4—41no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—102no—
432C4—102no—
433C4—201no—
434C4—201no—
435C4—201no—
436C4—201no—
437C2—42no—
438C2—104no—
439C2—202no—
440C2#6594411yescharacteristic
441C2#6598811yescharacteristic
442C2#6599011yescharacteristic
443C2#6599311yescharacteristic
444C2#6601211yescharacteristic
445C2D5×#12611yescharacteristic
446C2#6603911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC5×#397C2
prime radicalC24×D5C22
hypercenter#397D5
hypocenterC5#2480
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
2. C2×#4025C2semidirect
3. C5×#397C2semidirect
4. #65279C2semidirect
5. #65278C2semidirect
8. #65241C2semidirect
9. #65234C2semidirect
10. #64965C2semidirect
11. #64964C2semidirect
12. #64959C2semidirect
13. #64957C2semidirect
14. #64956C2semidirect
15. #64955C2semidirect
19. C2×C5×C4⋊C4C22semidirect
36. C2×C4⋊Dic5C22semidirect
37. C2×#683C22semidirect
38. C2×#683C22semidirect
39. C2×#683C22semidirect
40. C2×#683C22semidirect
41. C2×C4×Dic5C22semidirect
42. C2×C4×Dic5C22semidirect
45. C5×#95C22semidirect
46. C5×#95C22semidirect
47. C5×#95C22semidirect
48. #3963C22semidirect
49. #3963C22semidirect
50. #3963C22semidirect
51. #3963C22semidirect
52. #3963C22semidirect
110. #397D5semidirect
197. C2×C4⋊C4C2×D5semidirect
222. #95C2×D5semidirect
223. #95C2×D5semidirect
224. #95C2×D5semidirect
253. C2×D5#126semidirect
395. C5#2480semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊C42
C2×#40252
C5×#3972
#652792
#652782
#652442
#652412
#652342
#649652
#649642
#649592
#649572
#649562
#649552
#24805