Finite Group Databasebeta

← #11756414

Subgroups — #11756414

Order 960.

584 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#6819C211yesmaximal, characteristic, complemented
2C2×#6817C211yesmaximal, characteristic, complemented
3C3×C5×#123C211yesmaximal, characteristic, complemented
4#91828C211yesmaximal, characteristic, complemented
5C2×#6712C211yesmaximal, characteristic, complemented
6#91785C211yesmaximal, characteristic, complemented
7#91783C211yesmaximal, characteristic, complemented
8C4⋊C4×D15C211yesmaximal, characteristic, complemented
9#91777C211yesmaximal, characteristic, complemented
10#91775C211yesmaximal, characteristic, complemented
11#91773C211yesmaximal, characteristic, complemented
12#91772C211yesmaximal, characteristic, complemented
13#91770C211yesmaximal, characteristic, complemented
14#91770C211yesmaximal, characteristic, complemented
15#91767C211yesmaximal, characteristic, complemented
16#65989—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C22×C3×C4×C5C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×#1220C2211yescharacteristic
21C2×#1220C2211yescharacteristic
22C2×#1220C2211yescharacteristic
23C22×Dic15C2211yescharacteristic
24C22×Dic15C2211yescharacteristic
25C22×Dic15C2211yescharacteristic
26#6819—24no—
27#6817—24no—
28C2×D60C2211yescharacteristic
29C2×C4×D15C2211yescharacteristic
30C2×C4×D15C2211yescharacteristic
31C2×C4×D15C2211yescharacteristic
32C2×C4×D15C2211yescharacteristic
33C2×Dic30C2211yescharacteristic
34C2×Dic30C2211yescharacteristic
35C3×C5×C4⋊C4C2211yescharacteristic
36C3×C5×C4⋊C4C2211yescharacteristic
37C3×C5×C22⋊C4C2211yescharacteristic
38C3×C5×C22⋊C4C2211yescharacteristic
39C3×C5×C22⋊C4C2211yescharacteristic
40#6719C2211yescharacteristic
41#6714C2211yescharacteristic
42#6714C2211yescharacteristic
43#6714C2211yescharacteristic
44#6714C2211yescharacteristic
45C4⋊Dic15C2211yescharacteristic
46C4⋊Dic15C2211yescharacteristic
47#6712C2211yescharacteristic
48#6712C2211yescharacteristic
49#6712C2211yescharacteristic
50#6712C2211yescharacteristic
51#6712C2211yescharacteristic
52#6712C2211yescharacteristic
53C4×Dic15C2211yescharacteristic
54#5655—51nomaximal, Hall
55C2×#711—31no—
56C2×#709—31no—
57C5×#123D311yescharacteristic, complemented
58#4085—31no—
59C2×#683—31no—
60#4042—31no—
61#4040—31no—
62D5×C4⋊C4—31no—
63#4034—31no—
64#4032—31no—
65#4030—31no—
66#4029—31no—
67#4027—31no—
68#4027—31no—
69#4024—31no—
70C23×C3×C5C2311yescharacteristic
71C23×C3×C5C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C22×D15C2311yescharacteristic
74C3×C5×D4—22no—
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79C2×C3×C4×C5C2311yescharacteristic
80C2×C3×C4×C5C2311yescharacteristic
81#1220—22no—
82#1220—22no—
83#1220—22no—
84#1220D414yescomplemented
85C2×Dic15—22no—
86C2×Dic15—22no—
87C2×Dic15—22no—
88C2×Dic15C2311yescharacteristic
89C2×Dic15C2311yescharacteristic
90C2×Dic15C2311yescharacteristic
91C2×Dic15C2311yescharacteristic
92C2×Dic15C2311yescharacteristic
93C2×Dic15C2311yescharacteristic
94D60—22no—
95C4×D15—22no—
96C4×D15—22no—
97C4×D15—22no—
98C4×D15—22no—
99Dic30—22no—
100Dic30—22no—
101C2×#237—51no—
102C2×#235—51no—
103C3×#123D511yescharacteristic, complemented
104#939—51no—
105C2×Dic3⋊C4—51no—
106#896—51no—
107#894—51no—
108D3×C4⋊C4—51no—
109#888—51no—
110#886—51no—
111#884—51no—
112#883—51no—
113#67⋊C4—51no—
114#67⋊C4—51no—
115#878—51no—
116C2×C5×D4C2×D311yescharacteristic
117C22×C4×C5C2×D311yescharacteristic
118C2×C22⋊D5—31no—
119C2×C22⋊D5—31no—
120C2×C22⋊D5—31no—
121C2×C22⋊D5—31no—
122C22×Dic5—31no—
123C22×Dic5—31no—
124C22×Dic5—31no—
125#711—64no—
126#709—64no—
127C2×D20—31no—
128C2×C4×D5—31no—
129C2×C4×D5—31no—
130C2×C4×D5—31no—
131C2×C4×D5—31no—
132C2×Dic10—31no—
133C2×Dic10—31no—
134C5×C4⋊C4C2×D311yescharacteristic
135C5×C4⋊C4C2×D311yescharacteristic
136C5×C22⋊C4C2×D311yescharacteristic
137C5×C22⋊C4C2×D311yescharacteristic
138C5×C22⋊C4C2×D311yescharacteristic
139C22⋊Dic5—31no—
140#685—31no—
141#685—31no—
142#685—31no—
143#685—31no—
144C4⋊Dic5—31no—
145C4⋊Dic5—31no—
146#683—31no—
147#683—31no—
148#683—31no—
149#683—31no—
150#683—31no—
151#683—31no—
152C4×Dic5—31no—
153#547—151noSylow
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5C2×D412yes—
160C22×C3×C5C2411yescharacteristic
161C2×D15—21no—
162C2×D15—21no—
163C2×D15—21no—
164C2×D15—21no—
165C2×D15—21no—
166C2×D15C2×D412yes—
167C3×C4×C5—21no—
168C3×C4×C5—21no—
169C3×C4×C5—21no—
170C3×C4×C5—21no—
171C3×C4×C5—21no—
172Dic15—21no—
173Dic15—21no—
174Dic15—21no—
175Dic15—21no—
176Dic15C2×D412yes—
177Dic15#4112yescomplemented
178C2×C3×D4C2×D511yescharacteristic
179C22×C3×C4C2×D511yescharacteristic
180C2×#67—51no—
181C2×#67—51no—
182C2×#67—51no—
183C2×#67—51no—
184C22×Dic3—51no—
185C22×Dic3—51no—
186C22×Dic3—51no—
187#237—104no—
188#235—104no—
189C2×D12—51no—
190C2×C4×D3—51no—
191C2×C4×D3—51no—
192C2×C4×D3—51no—
193C2×C4×D3—51no—
194C2×Dic6—51no—
195C2×Dic6—51no—
196C3×C4⋊C4C2×D511yescharacteristic
197C3×C4⋊C4C2×D511yescharacteristic
198C3×C22⋊C4C2×D511yescharacteristic
199C3×C22⋊C4C2×D511yescharacteristic
200C3×C22⋊C4C2×D511yescharacteristic
201#217—51no—
202(C2×D3)⋊C4—51no—
203(C2×D3)⋊C4—51no—
204(C2×D3)⋊C4—51no—
205(C2×D3)⋊C4—51no—
206C4⋊Dic3—51no—
207C4⋊Dic3—51no—
208Dic3⋊C4—51no—
209Dic3⋊C4—51no—
210Dic3⋊C4—51no—
211Dic3⋊C4—51no—
212Dic3⋊C4—51no—
213Dic3⋊C4—51no—
214C4×Dic3—51no—
215C23×C5C22×D311yescharacteristic
216C23×C5C22×D311yescharacteristic
217C22×D5—31no—
218C22×D5—31no—
219C5×D4—22no—
220C2×C4×C5—22no—
221C2×C4×C5C22×D311yescharacteristic
222C2×C4×C5C22×D311yescharacteristic
223C2×C4×C5C22×D311yescharacteristic
224C2×C4×C5C22×D311yescharacteristic
225C2×C4×C5C22×D311yescharacteristic
226C22⋊D5—34no—
227C22⋊D5—62no—
228C22⋊D5—62no—
229C22⋊D5—62no—
230C2×Dic5—31no—
231C2×Dic5—31no—
232C2×Dic5—31no—
233C2×Dic5—31no—
234C2×Dic5—31no—
235C2×Dic5—31no—
236C2×Dic5—62no—
237C2×Dic5—62no—
238C2×Dic5—62no—
239D20—62no—
240C4×D5—62no—
241C4×D5—62no—
242C4×D5—62no—
243C4×D5—62no—
244Dic10—62no—
245Dic10—62no—
246C2×#41—151no—
247C2×#41—151no—
248C4⋊Q8—151no—
249#123—151no—
250#123—151no—
251#123—151no—
252#123D1511yescharacteristic, complemented
253C22⋊Q8—151no—
254C22⋊Q8—151no—
255#121—151no—
256#121—151no—
257C4×D4—151no—
258C4×D4—151no—
259C2×C4⋊C4—151no—
260C2×C4⋊C4—151no—
261C2×C3×C5—22no—
262C2×C3×C5—41no—
263C2×C3×C5C22×D411yescharacteristic
264C2×C3×C5C2×#4111yescharacteristic
265C2×C3×C52−1+411yescharacteristic
266D15—22no—
267D15—41no—
268C23×C3C22×D511yescharacteristic
269C23×C3C22×D511yescharacteristic
270C22×D3—51no—
271C22×D3—51no—
272C3×D4—22no—
273C2×C3×C4—22no—
274C2×C3×C4C22×D511yescharacteristic
275C2×C3×C4C22×D511yescharacteristic
276C2×C3×C4C22×D511yescharacteristic
277C2×C3×C4C22×D511yescharacteristic
278C2×C3×C4C22×D511yescharacteristic
279#67—54no—
280#67—102no—
281#67—102no—
282#67—102no—
283C2×Dic3—51no—
284C2×Dic3—51no—
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—51no—
289C2×Dic3—102no—
290C2×Dic3—102no—
291C2×Dic3—102no—
292D12—102no—
293C4×D3—102no—
294C4×D3—102no—
295C4×D3—102no—
296C4×D3—102no—
297Dic6—102no—
298Dic6—102no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5D3×D412yes—
305C22×C5C23×D311yescharacteristic
306C2×D5—32no—
307C2×D5—61no—
308C2×D5—61no—
309C2×D5—61no—
310C2×D5—61no—
311C2×D5—61no—
312C4×C5—21no—
313C4×C5—21no—
314C4×C5—21no—
315C4×C5—21no—
316C4×C5—21no—
317Dic5—32no—
318Dic5—32no—
319Dic5—61no—
320Dic5—61no—
321Dic5—61no—
322Dic5—61no—
323#41—304no—
324#41—304no—
325C2×Q8—151no—
326C2×Q8—151no—
327C2×D4—151no—
328C2×D4—151no—
329C2×D4—151no—
330C2×D4—151no—
331C2×D4—151no—
332C2×D4C2×D1511yescharacteristic
333C22×C4—151no—
334C22×C4—151no—
335C22×C4—151no—
336C22×C4—151no—
337C22×C4—151no—
338C22×C4—151no—
339C22×C4—151no—
340C22×C4C2×D1511yescharacteristic
341C4⋊C4—151no—
342C4⋊C4—151no—
343C4⋊C4—151no—
344C4⋊C4—151no—
345C4⋊C4—151no—
346C4⋊C4—151no—
347C4⋊C4—151no—
348C4⋊C4—151no—
349C4⋊C4C2×D1511yescharacteristic
350C4⋊C4C2×D1511yescharacteristic
351C22⋊C4—151no—
352C22⋊C4—151no—
353C22⋊C4—151no—
354C22⋊C4—151no—
355C22⋊C4—151no—
356C22⋊C4C2×D1511yescharacteristic
357C22⋊C4C2×D1511yescharacteristic
358C22⋊C4C2×D1511yescharacteristic
359C42—151no—
360C3×C5#54711yescharacteristic, complemented, Hall
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3D4×D512yes—
367C22×C3C23×D511yescharacteristic
368C2×D3—52no—
369C2×D3—101no—
370C2×D3—101no—
371C2×D3—101no—
372C2×D3—101no—
373C2×D3—101no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379Dic3—52no—
380Dic3—52no—
381Dic3—101no—
382Dic3—101no—
383Dic3—101no—
384Dic3—101no—
385C2×C5—22no—
386C2×C5—41no—
387C2×C5C2×D3×D411yescharacteristic
388C2×C5D3×#4111yescharacteristic
389C2×C5#101011yescharacteristic
390D5—62no—
391D5—121no—
392C23—151no—
393C23—151no—
394C23C22×D1511yescharacteristic
395C23C22×D1511yescharacteristic
396Q8—302no—
397Q8—302no—
398D4—22no—
399D4—154no—
400D4—302no—
401D4—302no—
402D4—302no—
403D4—302no—
404C2×C4—22no—
405C2×C4—151no—
406C2×C4—151no—
407C2×C4—151no—
408C2×C4—151no—
409C2×C4—151no—
410C2×C4—151no—
411C2×C4—302no—
412C2×C4—302no—
413C2×C4—302no—
414C2×C4—302no—
415C2×C4—302no—
416C2×C4—302no—
417C2×C4—302no—
418C2×C4C22×D1511yescharacteristic
419C2×C4C22×D1511yescharacteristic
420C2×C4C22×D1511yescharacteristic
421C2×C4C22×D1511yescharacteristic
422C2×C4C22×D1511yescharacteristic
423C2×C3—22no—
424C2×C3—41no—
425C2×C3C2×D4×D511yescharacteristic
426C2×C3D5×#4111yescharacteristic
427C2×C3#415011yescharacteristic
428D3—102no—
429D3—201no—
430C5#565511yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—152no—
437C22—301no—
438C22—301no—
439C22—301no—
440C22—301no—
441C22—301no—
442C22D4×D1512yes—
443C22C23×D1511yescharacteristic
444C4—21no—
445C4—21no—
446C4—21no—
447C4—21no—
448C4—21no—
449C4—152no—
450C4—152no—
451C4—301no—
452C4—301no—
453C4—301no—
454C4—301no—
455C3#6598911yescharacteristic, complemented, Sylow
456C2—22no—
457C2—41no—
458C2—302no—
459C2—601no—
460C2C2×D4×D1511yescharacteristic
461C2#41×D1511yescharacteristic
462C2#9210111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#123C2
hypercenter#123D15
hypocenterC3×C5#547
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C2×#6819C2semidirect
2. C2×#6817C2semidirect
3. C3×C5×#123C2semidirect
4. #91828C2semidirect
5. C2×#6712C2semidirect
6. #91785C2semidirect
7. #91783C2semidirect
8. C4⋊C4×D15C2semidirect
9. #91777C2semidirect
10. #91775C2semidirect
11. #91773C2semidirect
12. #91772C2semidirect
13. #91770C2semidirect
14. #91770C2semidirect
15. #91767C2semidirect
57. C5×#123D3semidirect
84. #1220D4semidirect
103. C3×#123D5semidirect
177. Dic15#41semidirect
252. #123D15semidirect
360. C3×C5#547semidirect
430. C5#5655semidirect
455. C3#65989semidirect

Maximal subgroups

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

subgroupindex
C2×#68192
C2×#68172
C3×C5×#1232
#918282
C2×#67122
#917852
#917832
C4⋊C4×D152
#917772
#917752
#917732
#917722
#917702
#917672
#659893
#56555