Finite Group Databasebeta

← #11754758

Subgroups — #11754758

Order 960.

660 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
1C2×#6779C211yesmaximal, characteristic, complemented
2C22×D5×Dic3C211yesmaximal, characteristic, complemented
3#91828C211yesmaximal, characteristic, complemented
4C5×D4×Dic3C211yesmaximal, characteristic, complemented
5C3×#4083C211yesmaximal, characteristic, complemented
6#91576C211yesmaximal, characteristic, complemented
7#91564C211yesmaximal, characteristic, complemented
8#91556C211yesmaximal, characteristic, complemented
9Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
10#91550C211yesmaximal, characteristic, complemented
11#91548C211yesmaximal, characteristic, complemented
12#91430C211yesmaximal, characteristic, complemented
13#91413C211yesmaximal, characteristic, complemented
14#91395C211yesmaximal, characteristic, complemented
15#91393C211yesmaximal, characteristic, complemented
16#65881—31nomaximal, Hall
17C23×C3×D5C2211yescharacteristic
18C2×C3×C5×D4C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×#1220C2211yescharacteristic, complemented
21C22×Dic15C2211yescharacteristic
22C22×C5×Dic3C2211yescharacteristic
23C22×C5×Dic3C2211yescharacteristic, complemented
24C2×C3×C22⋊D5C2211yescharacteristic
25C2×C3×C22⋊D5C2211yescharacteristic
26C2×#1204C2211yescharacteristic, complemented
27C2×#1202C2211yescharacteristic
28C2×#1202C2211yescharacteristic
29C2×#1200C2211yescharacteristic, complemented
30#6779—24no—
31C2×D5×Dic3—24no—
32C2×D5×Dic3C2211yescharacteristic
33C2×D5×Dic3C2211yescharacteristic
34C2×D5×Dic3C2211yescharacteristic
35C2×D5×Dic3C2211yescharacteristic
36#6719C2211yescharacteristic, complemented
37#6714C2211yescharacteristic, complemented
38#6712C2211yescharacteristic, complemented
39C5×#217C2211yescharacteristic
40C5×#217C2211yescharacteristic, complemented
41C5×C4⋊Dic3C2211yescharacteristic, complemented
42C4×C5×Dic3C2211yescharacteristic, complemented
43C3×C22⋊Dic5C2211yescharacteristic
44C3×#685C2211yescharacteristic
45C3×#685C2211yescharacteristic
46Dic3⋊Dic5C2211yescharacteristic, complemented
47#6669C2211yescharacteristic, complemented
48#6669C2211yescharacteristic, complemented
49#6668C2211yescharacteristic, complemented
50#6667C2211yescharacteristic, complemented
51#6665C2211yescharacteristic
52#6665C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic, complemented
54#5586—51nomaximal, Hall
55C2×#709—31no—
56C22×C4×D5—31no—
57C4×C5×D4—31no—
58#4085—31no—
59#4083D311yescharacteristic, complemented
60C4×C22⋊D5—31no—
61C4×C22⋊D5—31no—
62#4042—31no—
63#4040—31no—
64#4030—31no—
65#4029—31no—
66#4028—31no—
67#4024—31no—
68C4×D20—31no—
69#4018—31no—
70C23×C3×C5C2311yescharacteristic
71C23×C3×C5C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C22×C3×D5—22no—
74C22×C3×D5—22no—
75C22×C3×D5—22no—
76C22×C3×D5C2311yescharacteristic
77C22×C3×D5C2311yescharacteristic
78C3×C5×D4—22no—
79C2×C3×C4×C5C2311yescharacteristic
80#1220—22no—
81#1220—22no—
82C2×Dic15—22no—
83C2×Dic15C2311yescharacteristic
84C2×Dic15C2311yescharacteristic
85C2×Dic15C2311yescharacteristic
86C2×C5×Dic3—22no—
87C2×C5×Dic3—22no—
88C2×C5×Dic3C2311yescharacteristic
89C2×C5×Dic3C2311yescharacteristic
90C2×C5×Dic3C2311yescharacteristic
91C2×C5×Dic3C2311yescharacteristic
92C3×C22⋊D5—22no—
93C3×C22⋊D5—22no—
94C2×C3×Dic5C2311yescharacteristic
95C2×C3×Dic5C2311yescharacteristic
96#1204—22no—
97#1202—22no—
98#1202—22no—
99#1200—22no—
100D5×Dic3—22no—
101D5×Dic3—22no—
102D5×Dic3—22no—
103D5×Dic3D414yescomplemented
104C23×Dic3—51no—
105C2×#237—51no—
106C3×#120—51no—
107#953—51no—
108#939—51no—
109#939—51no—
110#935—51no—
111D4×Dic3—51no—
112D4×Dic3D511yescharacteristic, complemented
113#886—51no—
114#67⋊C4—51no—
115#67⋊C4—51no—
116#878—51no—
117#878—51no—
118#877—51no—
119C23×D5C2×D311yescharacteristic
120C2×C5×D4C2×D311yescharacteristic
121C22×C4×C5—31no—
122C22×C4×C5—31no—
123C2×C22⋊D5—31no—
124C2×C22⋊D5—31no—
125C2×C22⋊D5C2×D311yescharacteristic
126C2×C22⋊D5C2×D311yescharacteristic
127C22×Dic5—31no—
128#709—64no—
129C2×D20—31no—
130C2×D20—31no—
131C2×C4×D5—31no—
132C2×C4×D5—31no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—64no—
137C2×Dic10—31no—
138C5×C4⋊C4—31no—
139C5×C22⋊C4—31no—
140C5×C22⋊C4—31no—
141C42×C5—31no—
142C22⋊Dic5—31no—
143C22⋊Dic5C2×D311yescharacteristic
144#685—31no—
145#685—31no—
146#685—31no—
147#685—31no—
148#685C2×D311yescharacteristic
149#685C2×D311yescharacteristic
150C4⋊Dic5—31no—
151#683—31no—
152#683—31no—
153#683—31no—
154#683—31no—
155C4×Dic5—31no—
156#525—151noSylow
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5—21no—
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5#4112yescomplemented
163C22×C3×C5C2411yescharacteristic
164C2×D15—21no—
165C2×D15—21no—
166C2×D15—21no—
167C2×C3×D5—28no—
168C2×C3×D5—21no—
169C2×C3×D5—21no—
170C2×C3×D5—21no—
171C2×C3×D5—21no—
172C2×C3×D5C2×D412yes—
173C2×C3×D5#4112yescomplemented
174C3×C4×C5—21no—
175Dic15—21no—
176Dic15—21no—
177Dic15C2×D412yes—
178C3×Dic5—21no—
179C3×Dic5—21no—
180C5×Dic3—21no—
181C5×Dic3—21no—
182C5×Dic3—21no—
183C5×Dic3C2×D412yes—
184C24×C3—51no—
185C2×C3×D4—51no—
186C2×C3×D4—51no—
187C2×C3×D4C2×D511yescharacteristic
188C2×#67—51no—
189C2×#67—51no—
190C2×#67—51no—
191C2×#67—51no—
192C22×Dic3—51no—
193C22×Dic3—51no—
194C22×Dic3—51no—
195C22×Dic3—51no—
196C22×Dic3—51no—
197C22×Dic3—104no—
198C22×Dic3C2×D511yescharacteristic
199C22×Dic3C2×D511yescharacteristic, complemented
200#237—104no—
201C2×C4×D3—51no—
202C2×Dic6—51no—
203C3×C22⋊C4—51no—
204C3×C22⋊C4—51no—
205C3×C22⋊C4—51no—
206#217—51no—
207#217—51no—
208#217—51no—
209#217C2×D511yescharacteristic
210#217C2×D511yescharacteristic, complemented
211(C2×D3)⋊C4—51no—
212(C2×D3)⋊C4—51no—
213C4⋊Dic3—51no—
214C4⋊Dic3C2×D511yescharacteristic, complemented
215Dic3⋊C4—51no—
216Dic3⋊C4—51no—
217Dic3⋊C4—51no—
218Dic3⋊C4—51no—
219C4×Dic3—51no—
220C4×Dic3C2×D511yescharacteristic, complemented
221C23×C5C22×D311yescharacteristic
222C23×C5C22×D311yescharacteristic
223C22×D5—22no—
224C22×D5—22no—
225C22×D5—22no—
226C22×D5—31no—
227C22×D5C22×D311yescharacteristic
228C22×D5C22×D311yescharacteristic
229C5×D4—22no—
230C2×C4×C5—31no—
231C2×C4×C5—31no—
232C2×C4×C5—31no—
233C2×C4×C5—31no—
234C2×C4×C5—62no—
235C2×C4×C5—62no—
236C2×C4×C5C22×D311yescharacteristic
237C22⋊D5—22no—
238C22⋊D5—22no—
239C22⋊D5—62no—
240C22⋊D5—62no—
241C2×Dic5—31no—
242C2×Dic5—31no—
243C2×Dic5—31no—
244C2×Dic5—62no—
245C2×Dic5C22×D311yescharacteristic
246C2×Dic5C22×D311yescharacteristic
247D20—62no—
248D20—62no—
249C4×D5—34no—
250C4×D5—62no—
251C4×D5—62no—
252C4×D5—62no—
253C4×D5—62no—
254Dic10—62no—
255C2×#41—151no—
256C23×C4—151no—
257#123—151no—
258#123—151no—
259C22⋊Q8—151no—
260C22⋊Q8—151no—
261#121—151no—
262#121—151no—
263#120—51no—
264#120—151no—
265C4×D4—31no—
266C4×D4—151no—
267C4×D4—151no—
268C4×D4—151no—
269#117—151no—
270C2×C3×C5—22no—
271C2×C3×C5—41no—
272C2×C3×C5C22×D411yescharacteristic
273C2×C3×C5C2×#4111yescharacteristic
274C2×C3×C5C2×#4111yescharacteristic
275D15—41no—
276C3×D5—22no—
277C3×D5—22no—
278C23×C3—51no—
279C23×C3—51no—
280C23×C3—102no—
281C23×C3—102no—
282C23×C3—102no—
283C23×C3C22×D511yescharacteristic
284C23×C3C22×D511yescharacteristic
285C22×D3—51no—
286C3×D4—22no—
287C3×D4—102no—
288C3×D4—102no—
289C2×C3×C4—51no—
290C2×C3×C4—51no—
291C2×C3×C4C22×D511yescharacteristic
292#67—102no—
293#67—102no—
294#67—102no—
295#67—102no—
296C2×Dic3—22no—
297C2×Dic3—22no—
298C2×Dic3—51no—
299C2×Dic3—54no—
300C2×Dic3—51no—
301C2×Dic3—51no—
302C2×Dic3—102no—
303C2×Dic3—102no—
304C2×Dic3—102no—
305C2×Dic3—102no—
306C2×Dic3C22×D511yescharacteristic
307C2×Dic3C22×D511yescharacteristic
308C2×Dic3C22×D511yescharacteristic
309C2×Dic3C22×D511yescharacteristic
310C4×D3—102no—
311Dic6—102no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—21no—
317C22×C5#23712yescomplemented
318C22×C5C23×D311yescharacteristic
319C2×D5—28no—
320C2×D5—21no—
321C2×D5—21no—
322C2×D5—21no—
323C2×D5—21no—
324C2×D5—61no—
325C2×D5—61no—
326C2×D5—61no—
327C2×D5D3×D412yes—
328C2×D5#23712yescomplemented
329C4×C5—21no—
330C4×C5—32no—
331C4×C5—61no—
332C4×C5—61no—
333C4×C5—61no—
334Dic5—21no—
335Dic5—21no—
336Dic5—32no—
337Dic5—61no—
338Dic5—61no—
339C24—51no—
340#41—304no—
341C2×Q8—151no—
342C2×D4—51no—
343C2×D4—51no—
344C2×D4—151no—
345C2×D4—151no—
346C2×D4—151no—
347C2×D4—151no—
348C2×D4D3×D511yescharacteristic
349C22×C4—31no—
350C22×C4—31no—
351C22×C4—151no—
352C22×C4—151no—
353C22×C4—151no—
354C22×C4—151no—
355C22×C4—151no—
356C22×C4—151no—
357C22×C4—304no—
358C4⋊C4—31no—
359C4⋊C4—151no—
360C4⋊C4—151no—
361C4⋊C4—151no—
362C4⋊C4—151no—
363C4⋊C4—151no—
364C22⋊C4—31no—
365C22⋊C4—31no—
366C22⋊C4—51no—
367C22⋊C4—51no—
368C22⋊C4—51no—
369C22⋊C4—151no—
370C22⋊C4—151no—
371C22⋊C4—151no—
372C22⋊C4—151no—
373C22⋊C4—151no—
374C42—31no—
375C42—151no—
376C3×C5#52511yescharacteristic, complemented, Hall
377C22×C3—21no—
378C22×C3—21no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—52no—
383C22×C3—52no—
384C22×C3—108no—
385C22×C3—101no—
386C22×C3—101no—
387C22×C3—101no—
388C22×C3—101no—
389C22×C3#70912yescomplemented
390C22×C3C23×D511yescharacteristic
391C2×D3—101no—
392C2×D3—101no—
393C2×D3—101no—
394C3×C4—21no—
395C3×C4—101no—
396C3×C4—101no—
397Dic3—21no—
398Dic3—21no—
399Dic3—21no—
400Dic3—52no—
401Dic3—101no—
402Dic3—101no—
403Dic3D4×D512yes—
404C2×C5—22no—
405C2×C5—41no—
406C2×C5C2×D3×D411yescharacteristic
407C2×C5C2×#23711yescharacteristic
408C2×C5C2×#23711yescharacteristic
409D5—22no—
410D5—22no—
411D5—121no—
412C23—51no—
413C23—51no—
414C23—102no—
415C23—102no—
416C23—102no—
417C23—151no—
418C23C2×D3×D511yescharacteristic
419C23C2×D3×D511yescharacteristic
420Q8—302no—
421D4—22no—
422D4—102no—
423D4—102no—
424D4—302no—
425D4—302no—
426D4—302no—
427D4—302no—
428C2×C4—31no—
429C2×C4—31no—
430C2×C4—31no—
431C2×C4—31no—
432C2×C4—51no—
433C2×C4—51no—
434C2×C4—62no—
435C2×C4—62no—
436C2×C4—154no—
437C2×C4—151no—
438C2×C4—151no—
439C2×C4—151no—
440C2×C4—302no—
441C2×C4—302no—
442C2×C4—302no—
443C2×C4—302no—
444C2×C4—302no—
445C2×C4C2×D3×D511yescharacteristic
446C2×C3—22no—
447C2×C3—41no—
448C2×C3—102no—
449C2×C3—102no—
450C2×C3C2×#70911yescharacteristic
451C2×C3C2×D4×D511yescharacteristic
452C2×C3D5×#4111yescharacteristic
453D3—201no—
454C5#558611yescharacteristic, complemented, Sylow
455C22—21no—
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—52no—
461C22—52no—
462C22—108no—
463C22—101no—
464C22—101no—
465C22—101no—
466C22—101no—
467C22—301no—
468C22—301no—
469C22—301no—
470C22#677912yescomplemented
471C22C22×D3×D511yescharacteristic
472C4—21no—
473C4—32no—
474C4—61no—
475C4—61no—
476C4—61no—
477C4—101no—
478C4—101no—
479C4—152no—
480C4—301no—
481C4—301no—
482C3#6588111yescharacteristic, complemented, Sylow
483C2—22no—
484C2—41no—
485C2—102no—
486C2—102no—
487C2—601no—
488C2D3×D4×D511yescharacteristic
489C2D5×#23711yescharacteristic
490C2C2×#677911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#525
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. C2×#6779C2semidirect
2. C22×D5×Dic3C2semidirect
3. #91828C2semidirect
4. C5×D4×Dic3C2semidirect
5. C3×#4083C2semidirect
6. #91576C2semidirect
7. #91564C2semidirect
8. #91556C2semidirect
9. Dic3×C22⋊D5C2semidirect
10. #91550C2semidirect
11. #91548C2semidirect
12. #91430C2semidirect
13. #91413C2semidirect
14. #91395C2semidirect
15. #91393C2semidirect
20. C2×#1220C22semidirect
23. C22×C5×Dic3C22semidirect
26. C2×#1204C22semidirect
29. C2×#1200C22semidirect
36. #6719C22semidirect
37. #6714C22semidirect
38. #6712C22semidirect
40. C5×#217C22semidirect
41. C5×C4⋊Dic3C22semidirect
42. C4×C5×Dic3C22semidirect
46. Dic3⋊Dic5C22semidirect
47. #6669C22semidirect
48. #6669C22semidirect
49. #6668C22semidirect
50. #6667C22semidirect
53. Dic3×Dic5C22semidirect
59. #4083D3semidirect
103. D5×Dic3D4semidirect
112. D4×Dic3D5semidirect
162. C22×C3×C5#41semidirect
173. C2×C3×D5#41semidirect
199. C22×Dic3C2×D5semidirect
210. #217C2×D5semidirect
214. C4⋊Dic3C2×D5semidirect
220. C4×Dic3C2×D5semidirect
317. C22×C5#237semidirect
328. C2×D5#237semidirect
376. C3×C5#525semidirect
389. C22×C3#709semidirect
454. C5#5586semidirect
470. C22#6779semidirect
482. C3#65881semidirect

Maximal subgroups

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

subgroupindex
C2×#67792
C22×D5×Dic32
#918282
C5×D4×Dic32
C3×#40832
#915762
#915642
#915562
Dic3×C22⋊D52
#915502
#915482
#914302
#914132
#913952
#913932
#658813
#55865