Finite Group Databasebeta

← #11754997

Subgroups — #11754997

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#91826C211yesmaximal, characteristic, complemented
2C5×#938C211yesmaximal, characteristic, complemented
3C3×#4085C211yesmaximal, characteristic, complemented
4#91573C211yesmaximal, characteristic, complemented
5#91572C211yesmaximal, characteristic, complemented
6#91567C211yesmaximal, characteristic, complemented
7#91566C211yesmaximal, characteristic, complemented
8#91550C211yesmaximal, characteristic, complemented
9#91549C211yesmaximal, characteristic, complemented
10#91546C211yesmaximal, characteristic, complemented
11#91531C211yesmaximal, characteristic, complemented
12#91454C211yesmaximal, characteristic, complemented
13#91413C211yesmaximal, characteristic, complemented
14#91351C211yesmaximal, characteristic, complemented
15#91337C211yesmaximal, characteristic, complemented
16#65954—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C2×C3×C5×D4C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×#1220C2211yescharacteristic
21C2×C5×#67C2211yescharacteristic
22C2×C5×#67C2211yescharacteristic, complemented
23C2×C4×C5×D3C2211yescharacteristic, complemented
24C2×C3×C22⋊D5C2211yescharacteristic
25C2×C3×C22⋊D5C2211yescharacteristic, complemented
26C22×C3×Dic5C2211yescharacteristic, complemented
27C2×#1203C2211yescharacteristic
28C2×#1203C2211yescharacteristic
29C2×#1202C2211yescharacteristic
30C2×#1202C2211yescharacteristic
31C2×#1201C2211yescharacteristic, complemented
32C2×D5×Dic3C2211yescharacteristic, complemented
33#6719C2211yescharacteristic
34#6714C2211yescharacteristic
35#6714C2211yescharacteristic
36C5×#217C2211yescharacteristic
37C5×#217C2211yescharacteristic, complemented
38C5×C4⋊Dic3C2211yescharacteristic, complemented
39C3×C22⋊Dic5C2211yescharacteristic
40C3×#685C2211yescharacteristic, complemented
41C3×#683C2211yescharacteristic, complemented
42Dic3⋊Dic5C2211yescharacteristic, complemented
43Dic3⋊Dic5C2211yescharacteristic, complemented
44#6669C2211yescharacteristic, complemented
45#6668C2211yescharacteristic, complemented
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic
50(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5620—51nomaximal, Hall
53C5×#121—31no—
54#4086—31no—
55#4085—31no—
56#4085D311yescharacteristic, complemented
57#4084—31no—
58#4083—31no—
59#4083—31no—
60#4076—31no—
61#4075—31no—
62#4044—31no—
63#4040—31no—
64#4032—31no—
65#4030—31no—
66#4028—31no—
67#4025—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C22×D15—41no—
71C22×D15—41no—
72C22×D15—41no—
73C22×D15C2311yescharacteristic
74C22×D15C2311yescharacteristic
75C22×C5×D3C2311yescharacteristic
76C22×C3×D5C2311yescharacteristic
77C3×C5×D4—41no—
78C2×C3×C4×C5C2311yescharacteristic
79#1220—41no—
80#1220—41no—
81C2×Dic15C2311yescharacteristic
82C2×Dic15C2311yescharacteristic
83C5×#67—41no—
84C5×#67—41no—
85C2×C5×Dic3C2311yescharacteristic
86C2×C5×Dic3C2311yescharacteristic
87C2×C5×Dic3C2311yescharacteristic
88C4×C5×D3—41no—
89C3×C22⋊D5—41no—
90C3×C22⋊D5—41no—
91C2×C3×Dic5—41no—
92C2×C3×Dic5C2311yescharacteristic
93C2×C3×Dic5C2311yescharacteristic
94C2×C3×Dic5C2311yescharacteristic
95#1203—41no—
96#1203—41no—
97#1202—41no—
98#1202—41no—
99#1201—41no—
100D5×Dic3—41no—
101C3×#121—51no—
102#940—51no—
103#939—51no—
104#939—51no—
105#938D511yescharacteristic, complemented
106#937—51no—
107#937—51no—
108#930—51no—
109#929—51no—
110#898—51no—
111#894—51no—
112#886—51no—
113#884—51no—
114#882—51no—
115#879—51no—
116C23×D5—31no—
117C2×C5×D4—31no—
118C2×C5×D4—31no—
119C2×C5×D4C2×D311yescharacteristic
120C22×C4×C5—31no—
121C2×C22⋊D5—31no—
122C2×C22⋊D5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125C2×C22⋊D5—31no—
126C2×C22⋊D5C2×D311yescharacteristic
127C2×C22⋊D5C2×D311yescharacteristic, complemented
128C22×Dic5C2×D311yescharacteristic, complemented
129C2×D20—31no—
130C2×D20—31no—
131C2×C4×D5—31no—
132C5×C4⋊C4—31no—
133C5×C22⋊C4—31no—
134C5×C22⋊C4—31no—
135C22⋊Dic5—31no—
136C22⋊Dic5—31no—
137C22⋊Dic5C2×D311yescharacteristic
138#685—31no—
139#685—31no—
140#685—31no—
141#685—31no—
142#685—31no—
143#685—31no—
144#685C2×D311yescharacteristic, complemented
145C4⋊Dic5—31no—
146C4⋊Dic5—31no—
147#683—31no—
148#683—31no—
149#683C2×D311yescharacteristic, complemented
150C4×Dic5—31no—
151#560—151noSylow
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5C2411yescharacteristic
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—21no—
162C2×D15—21no—
163C2×D15—21no—
164C2×D15—21no—
165C2×D15—44no—
166C2×C5×D3—21no—
167C2×C5×D3—21no—
168C2×C5×D3—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C3×C4×C5—21no—
173Dic15—21no—
174Dic15—21no—
175C3×Dic5—21no—
176C3×Dic5—21no—
177C3×Dic5—21no—
178C5×Dic3—21no—
179C5×Dic3—21no—
180C5×Dic3—21no—
181C23×D3—51no—
182C2×C3×D4—51no—
183C2×C3×D4—51no—
184C2×C3×D4C2×D511yescharacteristic
185C22×C3×C4—51no—
186C2×#67—51no—
187C2×#67—51no—
188C2×#67—51no—
189C2×#67—51no—
190C2×#67—51no—
191C2×#67C2×D511yescharacteristic
192C2×#67C2×D511yescharacteristic, complemented
193C22×Dic3—51no—
194C2×D12—51no—
195C2×D12—51no—
196C2×C4×D3C2×D511yescharacteristic, complemented
197C3×C4⋊C4—51no—
198C3×C22⋊C4—51no—
199C3×C22⋊C4—51no—
200#217—51no—
201#217C2×D511yescharacteristic
202#217C2×D511yescharacteristic, complemented
203(C2×D3)⋊C4—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—
210C4⋊Dic3—51no—
211C4⋊Dic3C2×D511yescharacteristic, complemented
212Dic3⋊C4—51no—
213Dic3⋊C4—51no—
214Dic3⋊C4—51no—
215C4×Dic3—51no—
216C23×C5—31no—
217C23×C5C22×D311yescharacteristic
218C23×C5C22×D311yescharacteristic
219C22×D5—31no—
220C22×D5—31no—
221C22×D5—121no—
222C22×D5—121no—
223C22×D5—121no—
224C22×D5C22×D311yescharacteristic
225C5×D4—41no—
226C5×D4—121no—
227C5×D4—121no—
228C2×C4×C5—31no—
229C2×C4×C5—31no—
230C2×C4×C5—31no—
231C2×C4×C5—121no—
232C2×C4×C5C22×D311yescharacteristic
233C22⋊D5—41no—
234C22⋊D5—41no—
235C22⋊D5—121no—
236C22⋊D5—121no—
237C22⋊D5—121no—
238C22⋊D5—121no—
239C22⋊D5—121no—
240C2×Dic5—31no—
241C2×Dic5—31no—
242C2×Dic5—41no—
243C2×Dic5C22×D311yescharacteristic
244C2×Dic5C22×D311yescharacteristic
245C2×Dic5C22×D311yescharacteristic
246D20—121no—
247D20—121no—
248C4×D5—121no—
249#127—151no—
250#126—151no—
251#126—151no—
252#123—151no—
253#123—151no—
254#123—151no—
255#121—31no—
256#121—51no—
257#121—151no—
258#121—151no—
259#121—151no—
260#121—151no—
261#120—151no—
262#120—151no—
263#120—151no—
264C2×C3×C5—41no—
265C2×C3×C5—41no—
266C2×C3×C5H(5,𝔽2)11yescharacteristic
267C2×C3×C5H(5,𝔽2)11yescharacteristic
268C2×C3×C5H(5,𝔽2)11yescharacteristic
269D15—41no—
270D15—41no—
271C3×D5—41no—
272C5×D3—41no—
273C23×C3—51no—
274C23×C3C22×D511yescharacteristic
275C23×C3C22×D511yescharacteristic
276C22×D3—51no—
277C22×D3—51no—
278C22×D3—201no—
279C22×D3—201no—
280C22×D3—201no—
281C22×D3C22×D511yescharacteristic
282C3×D4—41no—
283C3×D4—201no—
284C3×D4—201no—
285C2×C3×C4—51no—
286C2×C3×C4—51no—
287C2×C3×C4—51no—
288C2×C3×C4—201no—
289C2×C3×C4C22×D511yescharacteristic
290#67—41no—
291#67—41no—
292#67—201no—
293#67—201no—
294#67—201no—
295#67—201no—
296#67—201no—
297C2×Dic3—51no—
298C2×Dic3—51no—
299C2×Dic3—201no—
300C2×Dic3C22×D511yescharacteristic
301C2×Dic3C22×D511yescharacteristic
302C2×Dic3C22×D511yescharacteristic
303D12—201no—
304D12—201no—
305C4×D3—41no—
306C22×C5—21no—
307C22×C5—21no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—61no—
313C22×C5—61no—
314C22×C5—61no—
315C22×C5C23×D311yescharacteristic
316C2×D5—21no—
317C2×D5—21no—
318C2×D5—21no—
319C2×D5—61no—
320C2×D5—61no—
321C2×D5—61no—
322C2×D5—61no—
323C2×D5—61no—
324C2×D5—61no—
325C2×D5—124no—
326C4×C5—21no—
327C4×C5—61no—
328C4×C5—61no—
329C4×C5—61no—
330Dic5—21no—
331Dic5—21no—
332Dic5—21no—
333Dic5—61no—
334Dic5—61no—
335C24—151no—
336C2×D4—31no—
337C2×D4—31no—
338C2×D4—51no—
339C2×D4—51no—
340C2×D4—151no—
341C2×D4—151no—
342C2×D4—151no—
343C2×D4—151no—
344C2×D4—151no—
345C2×D4—151no—
346C2×D4—151no—
347C2×D4D3×D511yescharacteristic
348C22×C4—31no—
349C22×C4—51no—
350C22×C4—151no—
351C4⋊C4—31no—
352C4⋊C4—51no—
353C4⋊C4—151no—
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⋊C4—151no—
369C42—151no—
370C3×C5#56011yescharacteristic, complemented, Hall
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—101no—
378C22×C3—101no—
379C22×C3—101no—
380C22×C3C23×D511yescharacteristic
381C2×D3—21no—
382C2×D3—21no—
383C2×D3—21no—
384C2×D3—101no—
385C2×D3—101no—
386C2×D3—101no—
387C2×D3—101no—
388C2×D3—101no—
389C2×D3—101no—
390C2×D3—204no—
391C3×C4—21no—
392C3×C4—101no—
393C3×C4—101no—
394C3×C4—101no—
395Dic3—21no—
396Dic3—21no—
397Dic3—21no—
398Dic3—101no—
399Dic3—101no—
400C2×C5—41no—
401C2×C5—41no—
402C2×C5—121no—
403C2×C5#100411yescharacteristic
404C2×C5#100411yescharacteristic
405C2×C5#100911yescharacteristic
406D5—41no—
407D5—121no—
408D5—121no—
409C23—31no—
410C23—51no—
411C23—151no—
412C23—151no—
413C23—601no—
414C23—601no—
415C23—601no—
416C23C2×D3×D511yescharacteristic
417C23C2×D3×D511yescharacteristic
418D4—41no—
419D4—121no—
420D4—121no—
421D4—201no—
422D4—201no—
423D4—601no—
424D4—601no—
425D4—601no—
426D4—601no—
427D4—601no—
428D4—601no—
429D4—601no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—31no—
433C2×C4—51no—
434C2×C4—51no—
435C2×C4—51no—
436C2×C4—121no—
437C2×C4—151no—
438C2×C4—151no—
439C2×C4—201no—
440C2×C4—601no—
441C2×C4C2×D3×D511yescharacteristic
442C2×C3—41no—
443C2×C3—41no—
444C2×C3—201no—
445C2×C3#414411yescharacteristic
446C2×C3#414411yescharacteristic
447C2×C3#414911yescharacteristic
448D3—41no—
449D3—201no—
450D3—201no—
451C5#562011yescharacteristic, complemented, Sylow
452C22—21no—
453C22—21no—
454C22—21no—
455C22—21no—
456C22—21no—
457C22—21no—
458C22—61no—
459C22—61no—
460C22—61no—
461C22—101no—
462C22—101no—
463C22—101no—
464C22—301no—
465C22—301no—
466C22—301no—
467C22—301no—
468C22—301no—
469C22—301no—
470C22—604no—
471C22C22×D3×D511yescharacteristic
472C4—21no—
473C4—61no—
474C4—61no—
475C4—61no—
476C4—101no—
477C4—101no—
478C4—101no—
479C4—301no—
480C4—301no—
481C3#6595411yescharacteristic, complemented, Sylow
482C2—41no—
483C2—41no—
484C2—121no—
485C2—201no—
486C2—601no—
487C2—601no—
488C2#9202611yescharacteristic
489C2#9202711yescharacteristic
490C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#560
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. #91826C2semidirect
2. C5×#938C2semidirect
3. C3×#4085C2semidirect
4. #91573C2semidirect
5. #91572C2semidirect
6. #91567C2semidirect
7. #91566C2semidirect
8. #91550C2semidirect
9. #91549C2semidirect
10. #91546C2semidirect
11. #91531C2semidirect
12. #91454C2semidirect
13. #91413C2semidirect
14. #91351C2semidirect
15. #91337C2semidirect
22. C2×C5×#67C22semidirect
23. C2×C4×C5×D3C22semidirect
25. C2×C3×C22⋊D5C22semidirect
26. C22×C3×Dic5C22semidirect
31. C2×#1201C22semidirect
32. C2×D5×Dic3C22semidirect
37. C5×#217C22semidirect
38. C5×C4⋊Dic3C22semidirect
40. C3×#685C22semidirect
41. C3×#683C22semidirect
42. Dic3⋊Dic5C22semidirect
43. Dic3⋊Dic5C22semidirect
44. #6669C22semidirect
45. #6668C22semidirect
50. (C2×D3)⋊Dic5C22semidirect
51. Dic3×Dic5C22semidirect
56. #4085D3semidirect
105. #938D5semidirect
127. C2×C22⋊D5C2×D3semidirect
128. C22×Dic5C2×D3semidirect
144. #685C2×D3semidirect
149. #683C2×D3semidirect
192. C2×#67C2×D5semidirect
196. C2×C4×D3C2×D5semidirect
202. #217C2×D5semidirect
211. C4⋊Dic3C2×D5semidirect
370. C3×C5#560semidirect
451. C5#5620semidirect
481. C3#65954semidirect

Maximal subgroups

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

subgroupindex
#918262
C5×#9382
C3×#40852
#915732
#915722
#915672
#915662
#915502
#915492
#915462
#915312
#914542
#914132
#913512
#913372
#659543
#56205