Finite Group Databasebeta

← #11755411

Subgroups — #11755411

Order 960.

500 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91842C211yesmaximal, characteristic, complemented
2C5×#953C211yesmaximal, characteristic, complemented
3C2×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
4#91574C211yesmaximal, characteristic, complemented
5#91566C211yesmaximal, characteristic, complemented
6#91562C211yesmaximal, characteristic, complemented
7#91558C211yesmaximal, characteristic, complemented
8#91557C211yesmaximal, characteristic, complemented
9#91555C211yesmaximal, characteristic, complemented
10#91552C211yesmaximal, characteristic, complemented
11Dic5×#67C211yesmaximal, characteristic, complemented
12#91531C211yesmaximal, characteristic, complemented
13#91530C211yesmaximal, characteristic, complemented
14#91526C211yesmaximal, characteristic, complemented
15#91525C211yesmaximal, characteristic, complemented
16#65927—31nomaximal, Hall
17C24×C3×C5C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×#1220C2211yescharacteristic
21C2×C5×#67C2211yescharacteristic
22C2×C5×#67C2211yescharacteristic
23C2×C5×#67C2211yescharacteristic
24C22×C3×Dic5C2211yescharacteristic
25C22×C3×Dic5C2211yescharacteristic
26C2×#1204C2211yescharacteristic, complemented
27C2×#1203C2211yescharacteristic, complemented
28C2×#1200C2211yescharacteristic, complemented
29C2×D3×Dic5C2211yescharacteristic, complemented
30#6719C2211yescharacteristic
31#6719C2211yescharacteristic
32#6719C2211yescharacteristic
33C5×#217C2211yescharacteristic
34C5×#217C2211yescharacteristic
35C5×#217C2211yescharacteristic
36C3×C22⋊Dic5C2211yescharacteristic
37C3×C22⋊Dic5C2211yescharacteristic
38C3×C22⋊Dic5C2211yescharacteristic
39C3×C22⋊Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic, complemented
41Dic3⋊Dic5C2211yescharacteristic, complemented
42#6669C2211yescharacteristic, complemented
43#6669C2211yescharacteristic, complemented
44#6668C2211yescharacteristic, complemented
45#6668C2211yescharacteristic, complemented
46#6667C2211yescharacteristic, complemented
47#6667C2211yescharacteristic, complemented
48(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49(C2×D3)⋊Dic5C2211yescharacteristic, complemented
50Dic3×Dic5C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5494—51nomaximal, Hall
53C5×#120—31no—
54#4099—31no—
55C2×C22⋊Dic5D311yescharacteristic, complemented
56#4085—31no—
57#4085—31no—
58#4084—31no—
59#4082—31no—
60#4081—31no—
61D4×Dic5—31no—
62#4031—31no—
63#4029—31no—
64#4027—31no—
65#4025—31no—
66#4025—31no—
67#4024—31no—
68C23×C3×C5—22no—
69C23×C3×C5—41no—
70C23×C3×C5—41no—
71C23×C3×C5C2311yescharacteristic
72C23×C3×C5C2311yescharacteristic
73C23×C3×C5C2311yescharacteristic
74C22×D15C2311yescharacteristic
75C22×C5×D3C2311yescharacteristic
76#1220—22no—
77#1220—41no—
78#1220—41no—
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81C2×Dic15C2311yescharacteristic
82C5×#67—22no—
83C5×#67—41no—
84C5×#67—41no—
85C2×C5×Dic3C2311yescharacteristic
86C2×C5×Dic3C2311yescharacteristic
87C2×C5×Dic3C2311yescharacteristic
88C2×C3×Dic5—41no—
89C2×C3×Dic5—41no—
90C2×C3×Dic5C2311yescharacteristic
91C2×C3×Dic5C2311yescharacteristic
92C2×C3×Dic5C2311yescharacteristic
93C2×C3×Dic5C2311yescharacteristic
94#1204—41no—
95#1203—41no—
96#1200—41no—
97D3×Dic5—41no—
98C2×C3×C22⋊C4—51no—
99#953—51no—
100#953D511yescharacteristic, complemented
101#930—51no—
102C4×#67—51no—
103C4×#67—51no—
104#924—51no—
105#885—51no—
106#885—51no—
107#884—51no—
108#884—51no—
109#883—51no—
110#883—51no—
111#879—51no—
112#879—51no—
113C24×C5C2×D311yescharacteristic
114C2×C5×D4—31no—
115C2×C5×D4—31no—
116C2×C5×D4—31no—
117C2×C22⋊D5—31no—
118C2×C22⋊D5—31no—
119C2×C22⋊D5—31no—
120C2×C22⋊D5—31no—
121C22×Dic5—31no—
122C22×Dic5C2×D311yescharacteristic
123C22×Dic5C2×D311yescharacteristic
124C2×C4×D5—31no—
125C2×Dic10—31no—
126C5×C22⋊C4—31no—
127C5×C22⋊C4—31no—
128C5×C22⋊C4—31no—
129C22⋊Dic5—31no—
130C22⋊Dic5—31no—
131C22⋊Dic5—31no—
132C22⋊Dic5—31no—
133C22⋊Dic5—31no—
134C22⋊Dic5C2×D311yescharacteristic
135C22⋊Dic5C2×D311yescharacteristic
136C22⋊Dic5C2×D311yescharacteristic
137C22⋊Dic5C2×D311yescharacteristic
138#685—31no—
139#685—31no—
140C4⋊Dic5—31no—
141C4⋊Dic5—31no—
142#683—31no—
143#683—31no—
144#683—31no—
145#683—31no—
146C4×Dic5—31no—
147C4×Dic5—31no—
148#538—151noSylow
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5—21no—
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—44no—
158C22×C3×C5#4112yes—
159C22×C3×C5C2411yescharacteristic
160C2×D15—21no—
161C2×D15—21no—
162C2×D15—21no—
163C2×C5×D3—21no—
164C2×C5×D3—21no—
165C2×C5×D3—21no—
166Dic15—21no—
167Dic15—21no—
168Dic15—21no—
169C3×Dic5—21no—
170C3×Dic5—21no—
171C3×Dic5—21no—
172C3×Dic5—21no—
173C5×Dic3—21no—
174C5×Dic3—21no—
175C5×Dic3—21no—
176C24×C3C2×D511yescharacteristic
177C22×C3×C4—51no—
178C22×C3×C4—51no—
179C2×#67—51no—
180C2×#67—51no—
181C2×#67—51no—
182C2×#67C2×D511yescharacteristic
183C2×#67C2×D511yescharacteristic
184C2×#67C2×D511yescharacteristic
185C2×D12—51no—
186C2×C4×D3—51no—
187C2×C4×D3—51no—
188C2×Dic6—51no—
189C3×C22⋊C4—51no—
190C3×C22⋊C4—51no—
191C3×C22⋊C4—51no—
192C3×C22⋊C4—51no—
193#217—51no—
194#217—51no—
195#217—51no—
196#217C2×D511yescharacteristic
197#217C2×D511yescharacteristic
198#217C2×D511yescharacteristic
199(C2×D3)⋊C4—51no—
200(C2×D3)⋊C4—51no—
201(C2×D3)⋊C4—51no—
202(C2×D3)⋊C4—51no—
203C4⋊Dic3—51no—
204C4⋊Dic3—51no—
205Dic3⋊C4—51no—
206Dic3⋊C4—51no—
207Dic3⋊C4—51no—
208Dic3⋊C4—51no—
209C4×Dic3—51no—
210C4×Dic3—51no—
211C23×C5—22no—
212C23×C5—31no—
213C23×C5—41no—
214C23×C5—41no—
215C23×C5C22×D311yescharacteristic
216C23×C5C22×D311yescharacteristic
217C23×C5C22×D311yescharacteristic
218C22×D5—31no—
219C5×D4—62no—
220C5×D4—121no—
221C5×D4—121no—
222C2×C4×C5—31no—
223C2×C4×C5—31no—
224C2×C4×C5—31no—
225C22⋊D5—62no—
226C22⋊D5—121no—
227C22⋊D5—121no—
228C22⋊D5—121no—
229C2×Dic5—31no—
230C2×Dic5—31no—
231C2×Dic5—31no—
232C2×Dic5—41no—
233C2×Dic5—41no—
234C2×Dic5—121no—
235C2×Dic5C22×D311yescharacteristic
236C2×Dic5C22×D311yescharacteristic
237C2×Dic5C22×D311yescharacteristic
238C2×Dic5C22×D311yescharacteristic
239C4×D5—121no—
240Dic10—121no—
241#126—151no—
242#126—151no—
243#124—151no—
244#124—151no—
245#123—151no—
246#123—151no—
247C22⋊Q8—151no—
248#121—151no—
249#121—151no—
250#121—151no—
251#120—31no—
252#120—151no—
253C4×D4—151no—
254C4×D4—151no—
255C2×C22⋊C4—51no—
256C2×C3×C5—22no—
257C2×C3×C5—41no—
258C2×C3×C5—41no—
259C2×C3×C5C2×#4111yescharacteristic
260C2×C3×C5H(5,𝔽2)11yescharacteristic
261C2×C3×C5H(5,𝔽2)11yescharacteristic
262D15—41no—
263C5×D3—41no—
264C23×C3—22no—
265C23×C3—41no—
266C23×C3—41no—
267C23×C3C22×D511yescharacteristic
268C23×C3C22×D511yescharacteristic
269C23×C3C22×D511yescharacteristic
270C22×D3—51no—
271C22×D3C22×D511yescharacteristic
272C2×C3×C4—51no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—201no—
277C2×C3×C4—201no—
278#67—22no—
279#67—41no—
280#67—41no—
281#67—102no—
282#67—201no—
283#67—201no—
284C2×Dic3—51no—
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3C22×D511yescharacteristic
288C2×Dic3C22×D511yescharacteristic
289C2×Dic3C22×D511yescharacteristic
290D12—201no—
291C4×D3—201no—
292C4×D3—201no—
293Dic6—201no—
294C22×C5—21no—
295C22×C5—21no—
296C22×C5—21no—
297C22×C5—21no—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—44no—
303C22×C5—61no—
304C22×C5—61no—
305C22×C5—61no—
306C22×C5#23512yes—
307C22×C5C23×D311yescharacteristic
308C2×D5—61no—
309C2×D5—61no—
310C2×D5—61no—
311C4×C5—61no—
312C4×C5—61no—
313C4×C5—61no—
314Dic5—21no—
315Dic5—21no—
316Dic5—21no—
317Dic5—21no—
318Dic5—61no—
319Dic5—61no—
320Dic5—61no—
321C24D3×D511yescharacteristic
322C2×Q8—151no—
323C2×D4—31no—
324C2×D4—31no—
325C2×D4—31no—
326C2×D4—151no—
327C2×D4—151no—
328C2×D4—151no—
329C2×D4—151no—
330C22×C4—51no—
331C22×C4—51no—
332C22×C4—151no—
333C22×C4—151no—
334C4⋊C4—151no—
335C4⋊C4—151no—
336C4⋊C4—151no—
337C4⋊C4—151no—
338C4⋊C4—151no—
339C4⋊C4—151no—
340C22⋊C4—31no—
341C22⋊C4—31no—
342C22⋊C4—31no—
343C22⋊C4—51no—
344C22⋊C4—51no—
345C22⋊C4—51no—
346C22⋊C4—51no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4—151no—
351C22⋊C4—151no—
352C22⋊C4—151no—
353C22⋊C4—151no—
354C42—151no—
355C42—151no—
356C3×C5#53811yescharacteristic, complemented, Hall
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—44no—
366C22×C3#71112yes—
367C22×C3C23×D511yescharacteristic
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—21no—
371C2×D3—101no—
372C2×D3—101no—
373C2×D3—101no—
374C3×C4—101no—
375C3×C4—101no—
376C3×C4—101no—
377C3×C4—101no—
378Dic3—21no—
379Dic3—21no—
380Dic3—21no—
381Dic3—101no—
382Dic3—101no—
383Dic3—101no—
384C2×C5—22no—
385C2×C5—41no—
386C2×C5—41no—
387C2×C5—121no—
388C2×C5C2×#23511yescharacteristic
389C2×C5#100411yescharacteristic
390C2×C5#100411yescharacteristic
391D5—121no—
392C23—22no—
393C23—31no—
394C23—41no—
395C23—41no—
396C23—151no—
397C23C2×D3×D511yescharacteristic
398C23C2×D3×D511yescharacteristic
399C23C2×D3×D511yescharacteristic
400Q8—601no—
401D4—62no—
402D4—121no—
403D4—121no—
404D4—302no—
405D4—601no—
406D4—601no—
407D4—601no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—51no—
412C2×C4—51no—
413C2×C4—51no—
414C2×C4—51no—
415C2×C4—151no—
416C2×C4—151no—
417C2×C4—151no—
418C2×C4—201no—
419C2×C4—201no—
420C2×C4—601no—
421C2×C4—601no—
422C2×C3—22no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3C2×#71111yescharacteristic
426C2×C3#414411yescharacteristic
427C2×C3#414411yescharacteristic
428D3—41no—
429D3—201no—
430C5#549411yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—21no—
437C22—21no—
438C22—21no—
439C22—44no—
440C22—61no—
441C22—61no—
442C22—61no—
443C22—301no—
444C22—301no—
445C22—301no—
446C22#678212yes—
447C22C22×D3×D511yescharacteristic
448C4—61no—
449C4—61no—
450C4—61no—
451C4—101no—
452C4—101no—
453C4—101no—
454C4—101no—
455C4—301no—
456C4—301no—
457C4—301no—
458C3#6592711yescharacteristic, complemented, Sylow
459C2—22no—
460C2—41no—
461C2—41no—
462C2—121no—
463C2—601no—
464C2C2×#678211yescharacteristic
465C2#9204911yescharacteristic
466C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC24×C3×C5C22
hypercenterC24D3×D5
hypocenterC3×C5#538
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. #91842C2semidirect
2. C5×#953C2semidirect
3. C2×C3×C22⋊Dic5C2semidirect
4. #91574C2semidirect
5. #91566C2semidirect
6. #91562C2semidirect
7. #91558C2semidirect
8. #91557C2semidirect
9. #91555C2semidirect
10. #91552C2semidirect
11. Dic5×#67C2semidirect
12. #91531C2semidirect
13. #91530C2semidirect
14. #91526C2semidirect
15. #91525C2semidirect
26. C2×#1204C22semidirect
27. C2×#1203C22semidirect
28. C2×#1200C22semidirect
29. C2×D3×Dic5C22semidirect
40. Dic3⋊Dic5C22semidirect
41. Dic3⋊Dic5C22semidirect
42. #6669C22semidirect
43. #6669C22semidirect
44. #6668C22semidirect
45. #6668C22semidirect
46. #6667C22semidirect
47. #6667C22semidirect
48. (C2×D3)⋊Dic5C22semidirect
49. (C2×D3)⋊Dic5C22semidirect
50. Dic3×Dic5C22semidirect
51. Dic3×Dic5C22semidirect
55. C2×C22⋊Dic5D3semidirect
100. #953D5semidirect
356. C3×C5#538semidirect
430. C5#5494semidirect
458. C3#65927semidirect

Maximal subgroups

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

subgroupindex
#918422
C5×#9532
C2×C3×C22⋊Dic52
#915742
#915662
#915622
#915582
#915572
#915552
#915522
Dic5×#672
#915312
#915302
#915262
#915252
#659273
#54945