Finite Group Databasebeta

← #11753185

Subgroups — #11753185

Order 960.

504 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91773C211yesmaximal, characteristic, complemented
2C5×#882C211yesmaximal, characteristic, complemented
3C3×#4025C211yesmaximal, characteristic, complemented
4#91570C211yesmaximal, characteristic, complemented
5#91570C211yesmaximal, characteristic, complemented
6#91558C211yesmaximal, characteristic, complemented
7#91557C211yesmaximal, characteristic, complemented
8#91466C211yesmaximal, characteristic, complemented
9#91451C211yesmaximal, characteristic, complemented
10#91438C211yesmaximal, characteristic, complemented
11#91423C211yesmaximal, characteristic, complemented
12#91420C211yesmaximal, characteristic, complemented
13#91416C211yesmaximal, characteristic, complemented
14#91372C211yesmaximal, characteristic, complemented
15#91355C211yesmaximal, characteristic, complemented
16#65929—31nomaximal, Hall
17C23×C5×D3C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×D60C2211yescharacteristic, complemented
21C2×C4×D15C2211yescharacteristic, complemented
22C2×C5×#67C2211yescharacteristic
23C2×C5×D12C2211yescharacteristic
24C2×C5×D12C2211yescharacteristic
25C2×#1203C2211yescharacteristic
26C2×#1203C2211yescharacteristic
27C2×#1203C2211yescharacteristic
28C2×#1203C2211yescharacteristic
29C2×#1203C2211yescharacteristic, complemented
30C2×#1203C2211yescharacteristic, complemented
31C2×#1200C2211yescharacteristic, complemented
32C2×D3×Dic5C2211yescharacteristic, complemented
33C3×C5×C22⋊C4C2211yescharacteristic
34#6714C2211yescharacteristic, complemented
35#6712C2211yescharacteristic, complemented
36C5×(C2×D3)⋊C4C2211yescharacteristic
37C5×(C2×D3)⋊C4C2211yescharacteristic
38C3×C22⋊Dic5C2211yescharacteristic
39C3×C22⋊Dic5C2211yescharacteristic
40C3×C4⋊Dic5C2211yescharacteristic, complemented
41C3×#683C2211yescharacteristic, complemented
42C3×#683C2211yescharacteristic, complemented
43C3×C4×Dic5C2211yescharacteristic, complemented
44Dic3⋊Dic5C2211yescharacteristic, complemented
45#6669C2211yescharacteristic, complemented
46#6667C2211yescharacteristic, complemented
47(C2×D3)⋊Dic5C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49(C2×D3)⋊Dic5C2211yescharacteristic
50(C2×D3)⋊Dic5C2211yescharacteristic
51(C2×D3)⋊Dic5C2211yescharacteristic, complemented
52#5711—51nomaximal, Hall
53C5×#120—31no—
54#4099—31no—
55#4099—31no—
56#4086—31no—
57#4085—31no—
58#4085—31no—
59#4084—31no—
60#4084—31no—
61#4081—31no—
62#4030—31no—
63#4030—31no—
64#4029—31no—
65#4029—31no—
66#4025—31no—
67#4025D311yescharacteristic, complemented
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×C5×D3—41no—
72C22×C5×D3—41no—
73C22×C5×D3—41no—
74C22×C5×D3C2311yescharacteristic
75C22×C5×D3C2311yescharacteristic
76C22×C5×D3C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79#1220—41no—
80#1220—41no—
81C2×Dic15C2311yescharacteristic
82C2×Dic15C2311yescharacteristic
83D60—41no—
84C4×D15—41no—
85C5×#67—41no—
86C2×C5×Dic3C2311yescharacteristic
87C5×D12—41no—
88C5×D12—41no—
89C2×C3×Dic5C2311yescharacteristic
90C2×C3×Dic5C2311yescharacteristic
91C2×C3×Dic5C2311yescharacteristic
92C2×C3×Dic5C2311yescharacteristic
93#1203—41no—
94#1203—41no—
95#1203—41no—
96#1203—41no—
97#1203—41no—
98#1203—41no—
99#1200—41no—
100D3×Dic5—41no—
101C3×#126—51no—
102#895—51no—
103#895—51no—
104#895—51no—
105#894—51no—
106#894—51no—
107#894—51no—
108#884—51no—
109#884—51no—
110#884—51no—
111#882—51no—
112#882—51no—
113#882D511yescharacteristic, complemented
114#876—51no—
115#874—51no—
116C24×C5—31no—
117C2×C5×D4—31no—
118C2×C5×D4—31no—
119C2×C5×D4—31no—
120C2×C22⋊D5—31no—
121C2×C22⋊D5—31no—
122C2×C22⋊D5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125C2×C22⋊D5—31no—
126C2×C22⋊D5—31no—
127C2×C22⋊D5—31no—
128C22×Dic5—31no—
129C2×D20—31no—
130C2×C4×D5—31no—
131C2×C4×D5—31no—
132C5×C22⋊C4—31no—
133C5×C22⋊C4—31no—
134C5×C22⋊C4C2×D311yescharacteristic
135C22⋊Dic5—31no—
136C22⋊Dic5—31no—
137C22⋊Dic5—31no—
138C22⋊Dic5—31no—
139C22⋊Dic5—31no—
140C22⋊Dic5C2×D311yescharacteristic
141C22⋊Dic5C2×D311yescharacteristic
142#685—31no—
143#685—31no—
144C4⋊Dic5—31no—
145C4⋊Dic5C2×D311yescharacteristic, complemented
146#683—31no—
147#683—31no—
148#683C2×D311yescharacteristic, complemented
149#683C2×D311yescharacteristic, complemented
150C4×Dic5C2×D311yescharacteristic, complemented
151#560—151noSylow
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5C2411yescharacteristic
156C2×D15—21no—
157C2×D15—21no—
158C2×D15—21no—
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—21no—
162C2×C5×D3—21no—
163C2×C5×D3—21no—
164C2×C5×D3—21no—
165C2×C5×D3—21no—
166C2×C5×D3—21no—
167C2×C5×D3—21no—
168C2×C5×D3—21no—
169C2×C5×D3—21no—
170C2×C5×D3—21no—
171C2×C5×D3—44no—
172C3×C4×C5—21no—
173C3×C4×C5—21no—
174Dic15—21no—
175Dic15—21no—
176C3×Dic5—21no—
177C3×Dic5—21no—
178C3×Dic5—21no—
179C3×Dic5—21no—
180C5×Dic3—21no—
181C23×D3C2×D511yescharacteristic
182C2×#67—51no—
183C2×#67—51no—
184C2×#67C2×D511yescharacteristic
185C2×D12—51no—
186C2×D12—51no—
187C2×D12—51no—
188C2×D12—51no—
189C2×D12—51no—
190C2×D12—51no—
191C2×D12—51no—
192C2×D12C2×D511yescharacteristic
193C2×D12C2×D511yescharacteristic
194C2×C4×D3—51no—
195C2×C4×D3—51no—
196C2×C4×D3—51no—
197C3×C4⋊C4—51no—
198C3×C4⋊C4—51no—
199C3×C4⋊C4—51no—
200C3×C22⋊C4—51no—
201C3×C22⋊C4—51no—
202C3×C22⋊C4C2×D511yescharacteristic
203C3×C42—51no—
204(C2×D3)⋊C4—51no—
205(C2×D3)⋊C4—51no—
206(C2×D3)⋊C4—51no—
207(C2×D3)⋊C4—51no—
208(C2×D3)⋊C4—51no—
209(C2×D3)⋊C4—51no—
210(C2×D3)⋊C4—51no—
211(C2×D3)⋊C4C2×D511yescharacteristic
212(C2×D3)⋊C4C2×D511yescharacteristic
213Dic3⋊C4—51no—
214Dic3⋊C4—51no—
215Dic3⋊C4—51no—
216C23×C5—31no—
217C23×C5—31no—
218C23×C5—31no—
219C23×C5—121no—
220C23×C5—121no—
221C23×C5—121no—
222C23×C5C22×D311yescharacteristic
223C22×D5—31no—
224C22×D5—31no—
225C5×D4—121no—
226C5×D4—121no—
227C5×D4—121no—
228C2×C4×C5—31no—
229C2×C4×C5C22×D311yescharacteristic
230C2×C4×C5C22×D311yescharacteristic
231C22⋊D5—121no—
232C22⋊D5—121no—
233C22⋊D5—121no—
234C22⋊D5—121no—
235C22⋊D5—121no—
236C22⋊D5—121no—
237C22⋊D5—121no—
238C22⋊D5—121no—
239C2×Dic5—31no—
240C2×Dic5—31no—
241C2×Dic5—121no—
242C2×Dic5C22×D311yescharacteristic
243C2×Dic5C22×D311yescharacteristic
244C2×Dic5C22×D311yescharacteristic
245C2×Dic5C22×D311yescharacteristic
246D20—121no—
247C4×D5—121no—
248C4×D5—121no—
249#127—151no—
250#126—51no—
251#126—151no—
252#123—151no—
253#123—151no—
254#123—151no—
255#121—151no—
256#121—151no—
257#121—151no—
258#121—151no—
259#121—151no—
260#121—151no—
261#120—31no—
262#120—151no—
263#120—151no—
264C2×C3×C5—41no—
265C2×C3×C5H(5,𝔽2)11yescharacteristic
266C2×C3×C5H(5,𝔽2)11yescharacteristic
267C2×C3×C5H(5,𝔽2)11yescharacteristic
268D15—41no—
269D15—41no—
270C5×D3—41no—
271C5×D3—41no—
272C5×D3—41no—
273C23×C3C22×D511yescharacteristic
274C22×D3—41no—
275C22×D3—41no—
276C22×D3—41no—
277C22×D3—51no—
278C22×D3—51no—
279C22×D3C22×D511yescharacteristic
280C22×D3C22×D511yescharacteristic
281C22×D3C22×D511yescharacteristic
282C2×C3×C4—51no—
283C2×C3×C4—51no—
284C2×C3×C4—51no—
285C2×C3×C4—51no—
286C2×C3×C4C22×D511yescharacteristic
287C2×C3×C4C22×D511yescharacteristic
288#67—41no—
289#67—201no—
290#67—201no—
291C2×Dic3—51no—
292C2×Dic3—51no—
293C2×Dic3C22×D511yescharacteristic
294D12—41no—
295D12—41no—
296D12—201no—
297D12—201no—
298D12—201no—
299D12—201no—
300D12—201no—
301D12—201no—
302D12—201no—
303C4×D3—201no—
304C4×D3—201no—
305C4×D3—201no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—61no—
310C22×C5—61no—
311C22×C5—61no—
312C22×C5—61no—
313C22×C5—61no—
314C22×C5—61no—
315C22×C5—61no—
316C22×C5—61no—
317C22×C5—61no—
318C22×C5—124no—
319C22×C5C23×D311yescharacteristic
320C2×D5—61no—
321C2×D5—61no—
322C2×D5—61no—
323C2×D5—61no—
324C2×D5—61no—
325C2×D5—61no—
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—61no—
329Dic5—21no—
330Dic5—21no—
331Dic5—21no—
332Dic5—21no—
333Dic5—61no—
334Dic5—61no—
335C24—31no—
336C2×D4—31no—
337C2×D4—31no—
338C2×D4—31no—
339C2×D4—151no—
340C2×D4—151no—
341C2×D4—151no—
342C2×D4—151no—
343C2×D4—151no—
344C2×D4—151no—
345C2×D4—151no—
346C2×D4—151no—
347C2×D4—151no—
348C22×C4—151no—
349C22×C4—151no—
350C22×C4—151no—
351C4⋊C4—51no—
352C4⋊C4—51no—
353C4⋊C4—51no—
354C4⋊C4—151no—
355C4⋊C4—151no—
356C4⋊C4—151no—
357C22⋊C4—31no—
358C22⋊C4—31no—
359C22⋊C4—51no—
360C22⋊C4—51no—
361C22⋊C4—151no—
362C22⋊C4—151no—
363C22⋊C4—151no—
364C22⋊C4—151no—
365C22⋊C4—151no—
366C22⋊C4—151no—
367C22⋊C4—151no—
368C22⋊C4D3×D511yescharacteristic
369C42—51no—
370C3×C5#56011yescharacteristic, complemented, Hall
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3C23×D511yescharacteristic
375C2×D3—21no—
376C2×D3—21no—
377C2×D3—21no—
378C2×D3—21no—
379C2×D3—21no—
380C2×D3—21no—
381C2×D3—21no—
382C2×D3—21no—
383C2×D3—21no—
384C2×D3—44no—
385C2×D3—101no—
386C2×D3—101no—
387C2×D3—101no—
388C2×D3—101no—
389C2×D3—101no—
390C2×D3—101no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—101no—
394C3×C4—101no—
395C3×C4—101no—
396C3×C4—101no—
397Dic3—21no—
398Dic3—101no—
399Dic3—101no—
400C2×C5—41no—
401C2×C5—121no—
402C2×C5—121no—
403C2×C5—121no—
404C2×C5#100911yescharacteristic
405C2×C5#100911yescharacteristic
406C2×C5#100911yescharacteristic
407D5—121no—
408D5—121no—
409C23—31no—
410C23—31no—
411C23—31no—
412C23—121no—
413C23—121no—
414C23—121no—
415C23—151no—
416C23—151no—
417C23C2×D3×D511yescharacteristic
418D4—121no—
419D4—121no—
420D4—121no—
421D4—601no—
422D4—601no—
423D4—601no—
424D4—601no—
425D4—601no—
426D4—601no—
427D4—601no—
428D4—601no—
429D4—601no—
430C2×C4—31no—
431C2×C4—51no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—51no—
435C2×C4—151no—
436C2×C4—151no—
437C2×C4—601no—
438C2×C4—601no—
439C2×C4—601no—
440C2×C4C2×D3×D511yescharacteristic
441C2×C4C2×D3×D511yescharacteristic
442C2×C3—41no—
443C2×C3#414411yescharacteristic
444C2×C3#414411yescharacteristic
445C2×C3#414411yescharacteristic
446D3—41no—
447D3—41no—
448D3—41no—
449D3—201no—
450D3—201no—
451C5#571111yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—61no—
456C22—61no—
457C22—61no—
458C22—61no—
459C22—61no—
460C22—61no—
461C22—61no—
462C22—61no—
463C22—61no—
464C22—124no—
465C22—301no—
466C22—301no—
467C22—301no—
468C22—301no—
469C22—301no—
470C22—301no—
471C22C22×D3×D511yescharacteristic
472C4—21no—
473C4—21no—
474C4—61no—
475C4—101no—
476C4—101no—
477C4—101no—
478C4—101no—
479C4—301no—
480C4—301no—
481C3#6592911yescharacteristic, complemented, Sylow
482C2—41no—
483C2—121no—
484C2—121no—
485C2—121no—
486C2—601no—
487C2—601no—
488C2#9201811yescharacteristic
489C2#9202711yescharacteristic
490C2#9202711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #91773C2semidirect
2. C5×#882C2semidirect
3. C3×#4025C2semidirect
4. #91570C2semidirect
5. #91570C2semidirect
6. #91558C2semidirect
7. #91557C2semidirect
8. #91466C2semidirect
9. #91451C2semidirect
10. #91438C2semidirect
11. #91423C2semidirect
12. #91420C2semidirect
13. #91416C2semidirect
14. #91372C2semidirect
15. #91355C2semidirect
20. C2×D60C22semidirect
21. C2×C4×D15C22semidirect
29. C2×#1203C22semidirect
30. C2×#1203C22semidirect
31. C2×#1200C22semidirect
32. C2×D3×Dic5C22semidirect
34. #6714C22semidirect
35. #6712C22semidirect
40. C3×C4⋊Dic5C22semidirect
41. C3×#683C22semidirect
42. C3×#683C22semidirect
43. C3×C4×Dic5C22semidirect
44. Dic3⋊Dic5C22semidirect
45. #6669C22semidirect
46. #6667C22semidirect
51. (C2×D3)⋊Dic5C22semidirect
67. #4025D3semidirect
113. #882D5semidirect
145. C4⋊Dic5C2×D3semidirect
148. #683C2×D3semidirect
149. #683C2×D3semidirect
150. C4×Dic5C2×D3semidirect
370. C3×C5#560semidirect
451. C5#5711semidirect
481. C3#65929semidirect

Maximal subgroups

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

subgroupindex
#917732
C5×#8822
C3×#40252
#915702
#915582
#915572
#914662
#914512
#914382
#914232
#914202
#914162
#913722
#913552
#659293
#57115