Finite Group Databasebeta

← #11753757

Subgroups — #11753757

Order 960.

472 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91783C211yesmaximal, characteristic, complemented
2C5×#887C211yesmaximal, characteristic, complemented
3C3×#4040C211yesmaximal, characteristic, complemented
4#91458C211yesmaximal, characteristic
5#91455C211yesmaximal, characteristic, complemented
6#91455C211yesmaximal, characteristic, complemented
7#91444C211yesmaximal, characteristic, complemented
8C4×#1202C211yesmaximal, characteristic, complemented
9#91433C211yesmaximal, characteristic, complemented
10#91407C211yesmaximal, characteristic, complemented
11#91396C211yesmaximal, characteristic, complemented
12#91395C211yesmaximal, characteristic, complemented
13#91353C211yesmaximal, characteristic, complemented
14#91353C211yesmaximal, characteristic, complemented
15#91324C211yesmaximal, characteristic, complemented
16#65919—31nomaximal, Hall
17C2×D60C2211yescharacteristic
18C2×C4×D15C2211yescharacteristic
19C2×C5×Dic6C2211yescharacteristic
20C2×C3×D20C2211yescharacteristic
21C2×C3×C4×D5C2211yescharacteristic
22C2×#1204C2211yescharacteristic
23C2×#1202C2211yescharacteristic
24C2×#1202C2211yescharacteristic
25C2×#1202C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1200C2211yescharacteristic
28C2×D5×Dic3C2211yescharacteristic
29C3×C5×C4⋊C4C2211yescharacteristic
30#6714C2211yescharacteristic
31#6714C2211yescharacteristic
32#6714C2211yescharacteristic
33#6712C2211yescharacteristic
34C5×Dic3⋊C4C2211yescharacteristic
35C5×Dic3⋊C4C2211yescharacteristic
36C4×C5×Dic3C2211yescharacteristic
37C4×C5×Dic3C2211yescharacteristic
38C4×C5×Dic3C2211yescharacteristic
39C3×#685C2211yescharacteristic
40C3×#685C2211yescharacteristic
41C3×#685C2211yescharacteristic
42C3×#683C2211yescharacteristic
43Dic3⋊Dic5C2211yescharacteristic
44#6667C2211yescharacteristic
45#6667C2211yescharacteristic
46#6667C2211yescharacteristic
47#6665C2211yescharacteristic
48#6665C2211yescharacteristic
49#6665C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5664—51nomaximal, Hall
53C4×C5×Q8—31no—
54#4093—31no—
55#4093—31no—
56#4040—31no—
57#4040—31no—
58#4040—31no—
59#4040D311yescharacteristic, complemented
60#4039—31no—
61#4039—31no—
62#4021—31no—
63#4021—31no—
64#4020—31no—
65C4×D20—31no—
66C4×D20—31no—
67C4×Dic10—31no—
68C22×D15C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C3×D5C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77D60—41no—
78C4×D15—41no—
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C5×Dic6—22no—
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C3×D20—41no—
87C3×C4×D5—41no—
88#1204—22no—
89#1202—22no—
90#1202—22no—
91#1202—22no—
92#1202—22no—
93#1200—41no—
94D5×Dic3—41no—
95C3×#123—51no—
96#940—51no—
97#935—51no—
98C4×#67—51no—
99C4×#67—51no—
100#894—51no—
101#894—51no—
102#887—51no—
103#887D511yescharacteristic, complemented
104#885—51no—
105#885—51no—
106#885—51no—
107#885—51no—
108#67⋊C4—51no—
109#67⋊C4—51no—
110C2×C5×Q8—31no—
111C2×D20—31no—
112C2×D20—31no—
113C2×D20—31no—
114C2×D20—31no—
115C2×D20—31no—
116C2×D20C2×D311yescharacteristic
117C2×C4×D5—31no—
118C2×C4×D5—31no—
119C2×C4×D5—31no—
120C2×C4×D5C2×D311yescharacteristic
121C2×Dic10—31no—
122C5×C4⋊C4—31no—
123C5×C4⋊C4—31no—
124C5×C4⋊C4C2×D311yescharacteristic
125C42×C5—31no—
126C42×C5—31no—
127C42×C5—31no—
128#685—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685—31no—
134#685—31no—
135#685—31no—
136#685—31no—
137#685C2×D311yescharacteristic
138#685C2×D311yescharacteristic
139#685C2×D311yescharacteristic
140C4⋊Dic5—31no—
141#683—31no—
142#683C2×D311yescharacteristic
143C4×Dic5—31no—
144C4×Dic5—31no—
145#559—151noSylow
146C22×C3×C5C2411yescharacteristic
147C2×D15—21no—
148C2×D15—21no—
149C2×D15—21no—
150C2×D15—21no—
151C2×D15—21no—
152C2×D15—21no—
153C2×C3×D5—21no—
154C2×C3×D5—21no—
155C2×C3×D5—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162Dic15—21no—
163Dic15—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C5×Dic3—21no—
167C5×Dic3—21no—
168C5×Dic3#4112yes—
169C5×Dic3#4112yes—
170C2×C3×D4—51no—
171C22×C3×C4—51no—
172C2×#67—51no—
173C2×#67—51no—
174C2×#67—51no—
175C2×#67—51no—
176C22×Dic3—51no—
177C2×D12—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×Dic6—51no—
181C2×Dic6C2×D511yescharacteristic
182C3×C4⋊C4—51no—
183C3×C4⋊C4C2×D511yescharacteristic
184C3×C22⋊C4—51no—
185C3×C22⋊C4—51no—
186C3×C22⋊C4—51no—
187#217—51no—
188#217—51no—
189#217—51no—
190(C2×D3)⋊C4—51no—
191(C2×D3)⋊C4—51no—
192(C2×D3)⋊C4—51no—
193(C2×D3)⋊C4—51no—
194(C2×D3)⋊C4—51no—
195(C2×D3)⋊C4—51no—
196Dic3⋊C4—51no—
197Dic3⋊C4—51no—
198Dic3⋊C4C2×D511yescharacteristic
199Dic3⋊C4C2×D511yescharacteristic
200C4×Dic3—51no—
201C4×Dic3—51no—
202C4×Dic3C2×D511yescharacteristic
203C4×Dic3C2×D511yescharacteristic
204C4×Dic3C2×D511yescharacteristic
205C22×D5—31no—
206C22×D5—31no—
207C22×D5C22×D311yescharacteristic
208C22×D5C22×D311yescharacteristic
209C5×Q8—62no—
210C2×C4×C5—31no—
211C2×C4×C5—31no—
212C2×C4×C5—31no—
213C2×C4×C5—31no—
214C2×C4×C5C22×D311yescharacteristic
215C2×C4×C5C22×D311yescharacteristic
216C2×C4×C5C22×D311yescharacteristic
217C2×Dic5—31no—
218C2×Dic5—31no—
219C2×Dic5C22×D311yescharacteristic
220C2×Dic5C22×D311yescharacteristic
221D20—41no—
222D20—62no—
223D20—62no—
224D20—62no—
225D20—62no—
226D20—121no—
227C4×D5—41no—
228C4×D5—121no—
229C4×D5—121no—
230C4×D5—121no—
231Dic10—62no—
232#127—151no—
233#124—151no—
234#124—151no—
235#124—151no—
236#124—151no—
237#123—51no—
238#123—151no—
239#123—151no—
240#123—151no—
241C4×Q8—31no—
242C4×Q8—151no—
243C4×D4—151no—
244C4×D4—151no—
245C4×D4—151no—
246C4×D4—151no—
247C2×C3×C5C2×#4111yescharacteristic
248C2×C3×C5C2×#4111yescharacteristic
249C2×C3×C5H(5,𝔽2)11yescharacteristic
250D15—41no—
251D15—41no—
252C3×D5—41no—
253C3×D5—41no—
254C23×C3—51no—
255C23×C3—51no—
256C22×D3—51no—
257C22×D3—51no—
258C3×D4—201no—
259C2×C3×C4—51no—
260C2×C3×C4—51no—
261C2×C3×C4—201no—
262C2×C3×C4C22×D511yescharacteristic
263C2×C3×C4C22×D511yescharacteristic
264C2×C3×C4C22×D511yescharacteristic
265#67—102no—
266#67—102no—
267#67—102no—
268#67—102no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3—201no—
272C2×Dic3C22×D511yescharacteristic
273C2×Dic3C22×D511yescharacteristic
274C2×Dic3C22×D511yescharacteristic
275C2×Dic3C22×D511yescharacteristic
276D12—201no—
277C4×D3—201no—
278C4×D3—201no—
279Dic6—22no—
280Dic6—102no—
281C22×C5C23×D311yescharacteristic
282C2×D5—21no—
283C2×D5—21no—
284C2×D5—21no—
285C2×D5—21no—
286C2×D5—21no—
287C2×D5—21no—
288C2×D5—61no—
289C2×D5—61no—
290C2×D5—61no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—32no—
298C4×C5—32no—
299C4×C5—61no—
300C4×C5—61no—
301Dic5—21no—
302Dic5—21no—
303Dic5—61no—
304Dic5—61no—
305C2×Q8—31no—
306C2×Q8—151no—
307C2×D4—51no—
308C2×D4—151no—
309C2×D4—151no—
310C2×D4—151no—
311C2×D4—151no—
312C2×D4—151no—
313C22×C4—51no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—31no—
318C4⋊C4—31no—
319C4⋊C4—51no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4D3×D511yescharacteristic
323C22⋊C4—51no—
324C22⋊C4—51no—
325C22⋊C4—51no—
326C22⋊C4—151no—
327C22⋊C4—151no—
328C22⋊C4—151no—
329C22⋊C4—151no—
330C22⋊C4—151no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C42—31no—
336C42—31no—
337C42—31no—
338C42—151no—
339C42—151no—
340C3×C5#55911yescharacteristic, complemented, Hall
341C22×C3—101no—
342C22×C3—101no—
343C22×C3—101no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3—101no—
347C22×C3C23×D511yescharacteristic
348C2×D3—101no—
349C2×D3—101no—
350C2×D3—101no—
351C2×D3—101no—
352C2×D3—101no—
353C2×D3—101no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—21no—
357C3×C4—101no—
358C3×C4—101no—
359Dic3—21no—
360Dic3—21no—
361Dic3—101no—
362Dic3—101no—
363Dic3#70912yes—
364Dic3#71312yes—
365C2×C5#100411yescharacteristic
366C2×C5D3×#4111yescharacteristic
367C2×C5D3×#4111yescharacteristic
368D5—41no—
369D5—41no—
370D5—121no—
371D5—121no—
372C23—51no—
373C23—51no—
374C23—151no—
375C23—151no—
376Q8—62no—
377Q8—302no—
378D4—201no—
379D4—302no—
380D4—302no—
381D4—302no—
382D4—302no—
383D4—601no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—151no—
391C2×C4—151no—
392C2×C4—201no—
393C2×C4—601no—
394C2×C4—601no—
395C2×C4—601no—
396C2×C4C2×D3×D511yescharacteristic
397C2×C4C2×D3×D511yescharacteristic
398C2×C4C2×D3×D511yescharacteristic
399C2×C3—201no—
400C2×C3—201no—
401C2×C3C2×#70911yescharacteristic
402C2×C3C2×#71311yescharacteristic
403C2×C3#414911yescharacteristic
404D3—201no—
405D3—201no—
406C5#566411yescharacteristic, complemented, Sylow
407C22—101no—
408C22—101no—
409C22—101no—
410C22—101no—
411C22—101no—
412C22—101no—
413C22—301no—
414C22—301no—
415C22—301no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—21no—
422C4—21no—
423C4—32no—
424C4—32no—
425C4—61no—
426C4—61no—
427C4—101no—
428C4—101no—
429C4—301no—
430C4—301no—
431C3#6591911yescharacteristic, complemented, Sylow
432C2—201no—
433C2—201no—
434C2—601no—
435C2—601no—
436C2D3×#70911yescharacteristic
437C2#9202611yescharacteristic
438C2D3×#71311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radical#91458C2
hypercenterC4⋊C4D3×D5
hypocenterC3×C5#559
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #91783C2semidirect
2. C5×#887C2semidirect
3. C3×#4040C2semidirect
5. #91455C2semidirect
6. #91455C2semidirect
7. #91444C2semidirect
8. C4×#1202C2semidirect
9. #91433C2semidirect
10. #91407C2semidirect
11. #91396C2semidirect
12. #91395C2semidirect
13. #91353C2semidirect
14. #91353C2semidirect
15. #91324C2semidirect
59. #4040D3semidirect
103. #887D5semidirect
340. C3×C5#559semidirect
406. C5#5664semidirect
431. C3#65919semidirect

Maximal subgroups

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

subgroupindex
#917832
C5×#8872
C3×#40402
#914582
#914552
#914442
C4×#12022
#914332
#914072
#913962
#913952
#913532
#913242
#659193
#56645