Finite Group Databasebeta

← #10613843

Subgroups — #10613843

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
1C22×C5×C22⋊C4C211yesmaximal, characteristic
2C2×#4025C211yesmaximal, characteristic, complemented
3#65536C211yesmaximal, characteristic
4#65536C211yesmaximal, characteristic
5#65501C211yesmaximal, characteristic, complemented
6#65499C211yesmaximal, characteristic, complemented
7#65499C211yesmaximal, characteristic, complemented
8C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
9#65242C211yesmaximal, characteristic, complemented
10#65241C211yesmaximal, characteristic, complemented
11#65241C211yesmaximal, characteristic, complemented
12#65240C211yesmaximal, characteristic, complemented
13#65237C211yesmaximal, characteristic, complemented
14#65234C211yesmaximal, characteristic, complemented
15#65233C211yesmaximal, characteristic, complemented
16C25×C5C2211yescharacteristic
17C23×C4×C5C2211yescharacteristic
18C23×C4×C5C2211yescharacteristic
19C2×C5×C22⋊C4—24no—
20C2×C5×C22⋊C4C2211yescharacteristic
21C2×C5×C22⋊C4C2211yescharacteristic
22C2×C5×C22⋊C4C2211yescharacteristic
23C2×C5×C22⋊C4C2211yescharacteristic
24C2×C22⋊Dic5C2211yescharacteristic
25C2×C22⋊Dic5C2211yescharacteristic
26C2×C22⋊Dic5C2211yescharacteristic
27C2×C22⋊Dic5C2211yescharacteristic
28C2×C22⋊Dic5C2211yescharacteristic
29C2×C22⋊Dic5C2211yescharacteristic
30C2×C22⋊Dic5C2211yescharacteristic
31C2×C22⋊Dic5C2211yescharacteristic
32C2×C22⋊Dic5C2211yescharacteristic
33C2×C22⋊Dic5C2211yescharacteristic
34C2×C22⋊Dic5C2211yescharacteristic
35C2×C22⋊Dic5C2211yescharacteristic
36C2×C4⋊Dic5C2211yescharacteristic, complemented
37C2×C4⋊Dic5C2211yescharacteristic, complemented
38C2×#683C2211yescharacteristic, complemented
39C2×#683C2211yescharacteristic, complemented
40C2×#683C2211yescharacteristic, complemented
41C2×#683C2211yescharacteristic, complemented
42C2×C4×Dic5C2211yescharacteristic, complemented
43C2×C4×Dic5C2211yescharacteristic, complemented
44#4025—24no—
45#3963C2211yescharacteristic, complemented
46#3963C2211yescharacteristic, complemented
47#3963C2211yescharacteristic, complemented
48#3963C2211yescharacteristic, complemented
49#3963C2211yescharacteristic, complemented
50#3963C2211yescharacteristic, complemented
51#3963C2211yescharacteristic, complemented
52#3963C2211yescharacteristic, complemented
53#2480—51nomaximal, Sylow
54C24×C5—22no—
55C24×C5—22no—
56C24×C5—22no—
57C24×C5—22no—
58C24×C5—22no—
59C24×C5—41no—
60C24×C5—41no—
61C24×C5C2311yescharacteristic
62C24×C5C2311yescharacteristic
63C24×C5C2311yescharacteristic
64C22×C4×C5—22no—
65C22×C4×C5—22no—
66C22×C4×C5—22no—
67C22×C4×C5—22no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5C2311yescharacteristic
71C22×C4×C5C2311yescharacteristic
72C22×C4×C5C2311yescharacteristic
73C22×C4×C5C2311yescharacteristic
74C22×Dic5C2311yescharacteristic
75C22×Dic5C2311yescharacteristic
76C22×Dic5C2311yescharacteristic
77C22×Dic5C2311yescharacteristic
78C22×Dic5C2311yescharacteristic
79C22×Dic5C2311yescharacteristic
80C22×Dic5C2311yescharacteristic
81C22×Dic5C2311yescharacteristic
82C5×C22⋊C4—22no—
83C5×C22⋊C4—22no—
84C5×C22⋊C4—22no—
85C5×C22⋊C4D414yes—
86C22⋊Dic5—22no—
87C22⋊Dic5—22no—
88C22⋊Dic5—22no—
89C22⋊Dic5—22no—
90C22⋊Dic5—22no—
91C22⋊Dic5—22no—
92C22⋊Dic5—22no—
93C22⋊Dic5—22no—
94C22⋊Dic5—41no—
95C22⋊Dic5—41no—
96C22⋊Dic5—41no—
97C22⋊Dic5—41no—
98C4⋊Dic5—22no—
99C4⋊Dic5—41no—
100#683—22no—
101#683—22no—
102#683—41no—
103#683—41no—
104C4×Dic5—22no—
105C4×Dic5—41no—
106C2×#126—51no—
107C22×C22⋊C4D511yescharacteristic
108#397—51no—
109#397—51no—
110#397—51no—
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—28no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—21no—
136C23×C5—21no—
137C23×C5—21no—
138C23×C5—44no—
139C23×C5—44no—
140C23×C5—44no—
141C23×C5—44no—
142C23×C5—44no—
143C23×C5—44no—
144C23×C5C2×D412yes—
145C23×C5#4112yes—
146C23×C5#4112yes—
147C23×C5#4112yes—
148C23×C5#4112yes—
149C23×C5C2411yescharacteristic
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—44no—
161C2×C4×C5—44no—
162C2×C4×C5C2×D412yes—
163C2×C4×C5C2×D412yes—
164C2×Dic5—21no—
165C2×Dic5—21no—
166C2×Dic5—21no—
167C2×Dic5—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×Dic5—21no—
185C2×Dic5—21no—
186C2×Dic5—21no—
187C2×Dic5—21no—
188C25C2×D511yescharacteristic
189C23×C4C2×D511yescharacteristic
190C23×C4C2×D511yescharacteristic
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⋊C4—51no—
198C2×C22⋊C4—24no—
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⋊C4C2×D511yescharacteristic
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#95—51no—
223#95—51no—
224#95—51no—
225C22×C5—22no—
226C22×C5—22no—
227C22×C5—22no—
228C22×C5—22no—
229C22×C5—22no—
230C22×C5—22no—
231C22×C5—22no—
232C22×C5—22no—
233C22×C5—22no—
234C22×C5—22no—
235C22×C5—22no—
236C22×C5—22no—
237C22×C5—416no—
238C22×C5—41no—
239C22×C5—41no—
240C22×C5—41no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5—41no—
244C22×C5—41no—
245C22×C5—41no—
246C22×C5#12614yescomplemented
247C22×C5C22×D411yescharacteristic
248C22×C5C2×#4111yescharacteristic
249C22×C5C2×#4111yescharacteristic
250C22×C5C2×#4111yescharacteristic
251C22×C5C2×#4111yescharacteristic
252C22×C5H(5,𝔽2)11yescharacteristic
253C22×C5H(5,𝔽2)11yescharacteristic
254C4×C5—22no—
255C4×C5—22no—
256C4×C5—41no—
257C4×C5—41no—
258Dic5—41no—
259Dic5—41no—
260Dic5—41no—
261Dic5—41no—
262Dic5—41no—
263Dic5—41no—
264Dic5—41no—
265Dic5—41no—
266C24—22no—
267C24—22no—
268C24—22no—
269C24—22no—
270C24—22no—
271C24—41no—
272C24—41no—
273C24C22×D511yescharacteristic
274C24C22×D511yescharacteristic
275C24C22×D511yescharacteristic
276C22×C4—22no—
277C22×C4—22no—
278C22×C4—22no—
279C22×C4—22no—
280C22×C4—41no—
281C22×C4—41no—
282C22×C4—51no—
283C22×C4—51no—
284C22×C4—51no—
285C22×C4—51no—
286C22×C4—51no—
287C22×C4—51no—
288C22×C4—51no—
289C22×C4—51no—
290C22×C4C22×D511yescharacteristic
291C22×C4C22×D511yescharacteristic
292C22×C4C22×D511yescharacteristic
293C22×C4C22×D511yescharacteristic
294C4⋊C4—102no—
295C4⋊C4—102no—
296C4⋊C4—102no—
297C4⋊C4—201no—
298C4⋊C4—201no—
299C4⋊C4—201no—
300C22⋊C4—22no—
301C22⋊C4—22no—
302C22⋊C4—22no—
303C22⋊C4—102no—
304C22⋊C4—102no—
305C22⋊C4—102no—
306C22⋊C4—102no—
307C22⋊C4—102no—
308C22⋊C4—102no—
309C22⋊C4—102no—
310C22⋊C4—102no—
311C22⋊C4—201no—
312C22⋊C4—201no—
313C22⋊C4—201no—
314C22⋊C4—201no—
315C22⋊C4C22⋊D514yes—
316C42—102no—
317C42—201no—
318C2×C5—24no—
319C2×C5—42no—
320C2×C5—42no—
321C2×C5#52511yescharacteristic
322C2×C5C2×#12611yescharacteristic
323C2×C5#53811yescharacteristic
324C2×C5#54611yescharacteristic
325C2×C5#54611yescharacteristic
326C2×C5#55111yescharacteristic
327C2×C5#55111yescharacteristic
328C23—21no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—28no—
333C23—21no—
334C23—21no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—44no—
346C23—44no—
347C23—44no—
348C23—44no—
349C23—44no—
350C23—44no—
351C23#70912yes—
352C23#70912yes—
353C23#71112yes—
354C23#71112yes—
355C23C2×C22⋊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—44no—
368C2×C4—44no—
369C2×C4—101no—
370C2×C4—101no—
371C2×C4—101no—
372C2×C4—101no—
373C2×C4—101no—
374C2×C4—101no—
375C2×C4—101no—
376C2×C4—101no—
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×C4C2×C22⋊D512yes—
394C2×C4C2×C22⋊D512yes—
395C5#248011yescharacteristic, complemented, Sylow
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—416no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—41no—
416C22—41no—
417C22#402514yescomplemented
418C22C2×#70911yescharacteristic
419C22C2×#70911yescharacteristic
420C22C2×#71111yescharacteristic
421C22C2×#71111yescharacteristic
422C22#414411yescharacteristic
423C22#414411yescharacteristic
424C22C22×C22⋊D511yescharacteristic
425C4—22no—
426C4—22no—
427C4—41no—
428C4—41no—
429C4—201no—
430C4—201no—
431C4—201no—
432C4—201no—
433C4—201no—
434C4—201no—
435C4—201no—
436C4—201no—
437C2—24no—
438C2—42no—
439C2—42no—
440C2C2×#402511yescharacteristic
441C2#6582811yescharacteristic
442C2#6582911yescharacteristic
443C2#6582911yescharacteristic
444C2#6612511yescharacteristic
445C2#6614011yescharacteristic
446C2#6614011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D5
commutator, socle, cosocleC23×C5C24
FittingC22×C5×C22⋊C4C2
prime radicalC25×C5C22
hypercenterC22×C22⋊C4D5
hypocenterC5#2480
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#4025C2semidirect
5. #65501C2semidirect
6. #65499C2semidirect
7. #65499C2semidirect
8. C4×C22⋊Dic5C2semidirect
9. #65242C2semidirect
10. #65241C2semidirect
11. #65241C2semidirect
12. #65240C2semidirect
13. #65237C2semidirect
14. #65234C2semidirect
15. #65233C2semidirect
36. C2×C4⋊Dic5C22semidirect
37. C2×C4⋊Dic5C22semidirect
38. C2×#683C22semidirect
39. C2×#683C22semidirect
40. C2×#683C22semidirect
41. C2×#683C22semidirect
42. C2×C4×Dic5C22semidirect
43. C2×C4×Dic5C22semidirect
45. #3963C22semidirect
46. #3963C22semidirect
47. #3963C22semidirect
48. #3963C22semidirect
49. #3963C22semidirect
50. #3963C22semidirect
51. #3963C22semidirect
52. #3963C22semidirect
246. C22×C5#126semidirect
395. C5#2480semidirect
417. C22#4025semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊C42
C2×#40252
#655362
#655012
#654992
C4×C22⋊Dic52
#652422
#652412
#652402
#652372
#652342
#652332
#24805