Finite Group Databasebeta

← #11754990

Subgroups — #11754990

Order 960.

440 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#91824C211yesmaximal, characteristic, complemented
2C5×#938C211yesmaximal, characteristic, complemented
3C3×#4085C211yesmaximal, characteristic, complemented
4#91576C211yesmaximal, characteristic, complemented
5#91574C211yesmaximal, characteristic, complemented
6#91571C211yesmaximal, characteristic, complemented
7#91549C211yesmaximal, characteristic, complemented
8#91548C211yesmaximal, characteristic, complemented
9#91539C211yesmaximal, characteristic, complemented
10#91534C211yesmaximal, characteristic, complemented
11#91525C211yesmaximal, characteristic, complemented
12#91452C211yesmaximal, characteristic, complemented
13#91430C211yesmaximal, characteristic, complemented
14#91352C211yesmaximal, characteristic, complemented
15#91336C211yesmaximal, characteristic, complemented
16#65955—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C2×C5×#67C2211yescharacteristic
20C2×C5×#67C2211yescharacteristic
21C2×C4×C5×D3C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C22⋊D5C2211yescharacteristic
24C22×C3×Dic5C2211yescharacteristic
25C2×#1204C2211yescharacteristic
26C2×#1204C2211yescharacteristic
27C2×#1201C2211yescharacteristic
28C2×D5×Dic3C2211yescharacteristic
29#6719C2211yescharacteristic
30#6719C2211yescharacteristic
31#6719C2211yescharacteristic
32#6712C2211yescharacteristic
33#6712C2211yescharacteristic
34C5×#217C2211yescharacteristic
35C5×#217C2211yescharacteristic
36C5×C4⋊Dic3C2211yescharacteristic
37C3×C22⋊Dic5C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×#683C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42#6669C2211yescharacteristic
43#6669C2211yescharacteristic
44#6669C2211yescharacteristic
45#6668C2211yescharacteristic
46(C2×D3)⋊Dic5C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5621—51nomaximal, Hall
53C5×#121—31no—
54#4085—31no—
55#4085D311yescharacteristic, complemented
56#4084—31no—
57#4082—31no—
58#4081—31no—
59#4081—31no—
60#4075—31no—
61#4070—31no—
62#4042—31no—
63#4035—31no—
64#4031—31no—
65#4029—31no—
66#4024—31no—
67#4024—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C3×C5×D4—41no—
73C2×C3×C4×C5C2311yescharacteristic
74C2×Dic15—41no—
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C5×#67—41no—
80C5×#67—41no—
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C4×C5×D3—41no—
85C3×C22⋊D5—41no—
86C3×C22⋊D5—41no—
87C2×C3×Dic5—41no—
88C2×C3×Dic5C2311yescharacteristic
89C2×C3×Dic5C2311yescharacteristic
90C2×C3×Dic5C2311yescharacteristic
91#1204—41no—
92#1204—41no—
93#1201—41no—
94D5×Dic3—41no—
95C3×#121—51no—
96#939—51no—
97#939—51no—
98#938D511yescharacteristic, complemented
99#936—51no—
100#935—51no—
101#935—51no—
102#929—51no—
103#924—51no—
104#896—51no—
105#889—51no—
106#885—51no—
107#883—51no—
108#878—51no—
109#878—51no—
110C2×C5×D4—31no—
111C2×C5×D4—31no—
112C2×C5×D4C2×D311yescharacteristic
113C22×C4×C5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5C2×D311yescharacteristic
116C2×C22⋊D5C2×D311yescharacteristic
117C22×Dic5—31no—
118C22×Dic5C2×D311yescharacteristic
119C2×C4×D5—31no—
120C2×Dic10—31no—
121C2×Dic10—31no—
122C5×C4⋊C4—31no—
123C5×C22⋊C4—31no—
124C5×C22⋊C4—31no—
125C22⋊Dic5—31no—
126C22⋊Dic5—31no—
127C22⋊Dic5—31no—
128C22⋊Dic5—31no—
129C22⋊Dic5—31no—
130C22⋊Dic5—31no—
131C22⋊Dic5C2×D311yescharacteristic
132#685—31no—
133#685—31no—
134#685C2×D311yescharacteristic
135C4⋊Dic5—31no—
136C4⋊Dic5—31no—
137#683—31no—
138#683—31no—
139#683—31no—
140#683—31no—
141#683—31no—
142#683—31no—
143#683C2×D311yescharacteristic
144C4×Dic5—31no—
145#562—151noSylow
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5C2411yescharacteristic
153C2×C5×D3—21no—
154C2×C5×D3—21no—
155C2×C5×D3—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C3×C4×C5—21no—
160Dic15—21no—
161Dic15—21no—
162Dic15—21no—
163Dic15—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C5×Dic3—21no—
168C5×Dic3—21no—
169C5×Dic3—21no—
170C2×C3×D4—51no—
171C2×C3×D4—51no—
172C2×C3×D4C2×D511yescharacteristic
173C22×C3×C4—51no—
174C2×#67—51no—
175C2×#67C2×D511yescharacteristic
176C2×#67C2×D511yescharacteristic
177C22×Dic3—51no—
178C22×Dic3—51no—
179C2×C4×D3C2×D511yescharacteristic
180C2×Dic6—51no—
181C2×Dic6—51no—
182C3×C4⋊C4—51no—
183C3×C22⋊C4—51no—
184C3×C22⋊C4—51no—
185#217—51no—
186#217—51no—
187#217—51no—
188#217—51no—
189#217—51no—
190#217C2×D511yescharacteristic
191#217C2×D511yescharacteristic
192(C2×D3)⋊C4—51no—
193(C2×D3)⋊C4—51no—
194(C2×D3)⋊C4—51no—
195C4⋊Dic3—51no—
196C4⋊Dic3C2×D511yescharacteristic
197Dic3⋊C4—51no—
198Dic3⋊C4—51no—
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4—51no—
203Dic3⋊C4—51no—
204C4×Dic3—51no—
205C23×C5—31no—
206C23×C5C22×D311yescharacteristic
207C23×C5C22×D311yescharacteristic
208C22×D5C22×D311yescharacteristic
209C5×D4—41no—
210C5×D4—121no—
211C5×D4—121no—
212C2×C4×C5—31no—
213C2×C4×C5—31no—
214C2×C4×C5—31no—
215C2×C4×C5—121no—
216C2×C4×C5C22×D311yescharacteristic
217C22⋊D5—41no—
218C22⋊D5—41no—
219C22⋊D5—121no—
220C2×Dic5—31no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—41no—
225C2×Dic5—121no—
226C2×Dic5C22×D311yescharacteristic
227C2×Dic5C22×D311yescharacteristic
228C2×Dic5C22×D311yescharacteristic
229C4×D5—121no—
230Dic10—121no—
231Dic10—121no—
232#125—151no—
233#124—151no—
234#124—151no—
235#123—151no—
236#123—151no—
237#123—151no—
238#123—151no—
239C22⋊Q8—151no—
240C22⋊Q8—151no—
241C22⋊Q8—151no—
242C22⋊Q8—151no—
243#121—31no—
244#121—51no—
245#121—151no—
246#121—151no—
247C2×C3×C5—41no—
248C2×C3×C5—41no—
249C2×C3×C5H(5,𝔽2)11yescharacteristic
250C2×C3×C5H(5,𝔽2)11yescharacteristic
251C2×C3×C52−1+411yescharacteristic
252C3×D5—41no—
253C5×D3—41no—
254C23×C3—51no—
255C23×C3C22×D511yescharacteristic
256C23×C3C22×D511yescharacteristic
257C22×D3C22×D511yescharacteristic
258C3×D4—41no—
259C3×D4—201no—
260C3×D4—201no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—201no—
265C2×C3×C4C22×D511yescharacteristic
266#67—41no—
267#67—41no—
268#67—201no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—201no—
274C2×Dic3—201no—
275C2×Dic3C22×D511yescharacteristic
276C2×Dic3C22×D511yescharacteristic
277C2×Dic3C22×D511yescharacteristic
278C4×D3—41no—
279Dic6—201no—
280Dic6—201no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5—21no—
287C22×C5—61no—
288C22×C5—61no—
289C22×C5—61no—
290C22×C5C23×D311yescharacteristic
291C2×D5—21no—
292C2×D5—21no—
293C2×D5—21no—
294C4×C5—21no—
295C4×C5—61no—
296C4×C5—61no—
297C4×C5—61no—
298Dic5—21no—
299Dic5—21no—
300Dic5—21no—
301Dic5—61no—
302Dic5—61no—
303Dic5—61no—
304Dic5—61no—
305C2×Q8—151no—
306C2×Q8—151no—
307C2×D4—31no—
308C2×D4—31no—
309C2×D4—51no—
310C2×D4—51no—
311C2×D4—151no—
312C2×D4D3×D511yescharacteristic
313C22×C4—31no—
314C22×C4—51no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—31no—
318C4⋊C4—51no—
319C4⋊C4—151no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4—151no—
325C4⋊C4—151no—
326C4⋊C4—151no—
327C22⋊C4—31no—
328C22⋊C4—31no—
329C22⋊C4—51no—
330C22⋊C4—51no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4—151no—
336C22⋊C4—151no—
337C22⋊C4—151no—
338C22⋊C4—151no—
339C42—151no—
340C3×C5#56211yescharacteristic, complemented, Hall
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—101no—
348C22×C3—101no—
349C22×C3—101no—
350C22×C3C23×D511yescharacteristic
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—21no—
354C3×C4—21no—
355C3×C4—101no—
356C3×C4—101no—
357C3×C4—101no—
358Dic3—21no—
359Dic3—21no—
360Dic3—21no—
361Dic3—101no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365C2×C5—41no—
366C2×C5—41no—
367C2×C5—121no—
368C2×C5#100411yescharacteristic
369C2×C5#100411yescharacteristic
370C2×C5#101011yescharacteristic
371D5—41no—
372C23—31no—
373C23—51no—
374C23C2×D3×D511yescharacteristic
375C23C2×D3×D511yescharacteristic
376Q8—601no—
377Q8—601no—
378D4—41no—
379D4—121no—
380D4—121no—
381D4—201no—
382D4—201no—
383D4—601no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—121no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—151no—
395C2×C4—201no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C2×D3×D511yescharacteristic
399C2×C3—41no—
400C2×C3—41no—
401C2×C3—201no—
402C2×C3#414411yescharacteristic
403C2×C3#414411yescharacteristic
404C2×C3#415011yescharacteristic
405D3—41no—
406C5#562111yescharacteristic, complemented, Sylow
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—61no—
414C22—61no—
415C22—61no—
416C22—101no—
417C22—101no—
418C22—101no—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—61no—
422C4—61no—
423C4—61no—
424C4—101no—
425C4—101no—
426C4—101no—
427C4—301no—
428C4—301no—
429C4—301no—
430C4—301no—
431C3#6595511yescharacteristic, complemented, Sylow
432C2—41no—
433C2—41no—
434C2—121no—
435C2—201no—
436C2#9202011yescharacteristic
437C2#9202511yescharacteristic
438C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#562
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. #91824C2semidirect
2. C5×#938C2semidirect
3. C3×#4085C2semidirect
4. #91576C2semidirect
5. #91574C2semidirect
6. #91571C2semidirect
7. #91549C2semidirect
8. #91548C2semidirect
9. #91539C2semidirect
10. #91534C2semidirect
11. #91525C2semidirect
12. #91452C2semidirect
13. #91430C2semidirect
14. #91352C2semidirect
15. #91336C2semidirect
55. #4085D3semidirect
98. #938D5semidirect
340. C3×C5#562semidirect
406. C5#5621semidirect
431. C3#65955semidirect

Maximal subgroups

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

subgroupindex
#918242
C5×#9382
C3×#40852
#915762
#915742
#915712
#915492
#915482
#915392
#915342
#915252
#914522
#914302
#913522
#913362
#659553
#56215