Finite Group Databasebeta

← #11754996

Subgroups — #11754996

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#91827C211yesmaximal, characteristic, complemented
2C5×#935C211yesmaximal, characteristic, complemented
3C3×#4085C211yesmaximal, characteristic, complemented
4#91575C211yesmaximal, characteristic, complemented
5#91574C211yesmaximal, characteristic, complemented
6#91569C211yesmaximal, characteristic, complemented
7#91550C211yesmaximal, characteristic, complemented
8#91548C211yesmaximal, characteristic, complemented
9#91546C211yesmaximal, characteristic, complemented
10#91534C211yesmaximal, characteristic, complemented
11#91526C211yesmaximal, characteristic, complemented
12#91422C211yesmaximal, characteristic, complemented
13#91377C211yesmaximal, characteristic, complemented
14#91354C211yesmaximal, characteristic, complemented
15#91343C211yesmaximal, characteristic, complemented
16#66001—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×C4×D15C2211yescharacteristic
21C22×C5×Dic3C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C22⋊D5C2211yescharacteristic
24C22×C3×Dic5C2211yescharacteristic
25C2×#1204C2211yescharacteristic
26C2×#1204C2211yescharacteristic
27C2×#1202C2211yescharacteristic
28C2×D5×Dic3C2211yescharacteristic
29#6719C2211yescharacteristic
30#6719C2211yescharacteristic
31C4⋊Dic15C2211yescharacteristic
32C5×#217C2211yescharacteristic
33C5×#217C2211yescharacteristic
34C5×#217C2211yescharacteristic
35C5×Dic3⋊C4C2211yescharacteristic
36C5×Dic3⋊C4C2211yescharacteristic
37C3×C22⋊Dic5C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×#683C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41Dic3⋊Dic5C2211yescharacteristic
42Dic3⋊Dic5C2211yescharacteristic
43#6669C2211yescharacteristic
44#6669C2211yescharacteristic
45#6668C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48#6667C2211yescharacteristic
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5621—51nomaximal, Hall
53C5×#123—31no—
54#4085D311yescharacteristic, complemented
55#4084—31no—
56#4076—31no—
57#4070—31no—
58#4043—31no—
59#4042—31no—
60#4040—31no—
61#4036—31no—
62#4032—31no—
63#4031—31no—
64#4031—31no—
65#4030—31no—
66#4029—31no—
67#4024—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C3×C5×D4—41no—
73C2×C3×C4×C5C2311yescharacteristic
74#1220—41no—
75#1220—41no—
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C4×D15—41no—
80C2×C5×Dic3—41no—
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
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#1202—41no—
94D5×Dic3—41no—
95C3×#121—51no—
96#939—51no—
97#939—51no—
98#938—51no—
99#936—51no—
100#935—51no—
101#935D511yescharacteristic, complemented
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×D4C2×D311yescharacteristic
111C22×C4×C5—31no—
112C2×C22⋊D5—31no—
113C2×C22⋊D5—31no—
114C2×C22⋊D5C2×D311yescharacteristic
115C2×C22⋊D5C2×D311yescharacteristic
116C22×Dic5C2×D311yescharacteristic
117C2×D20—31no—
118C2×C4×D5—31no—
119C2×C4×D5—31no—
120C2×Dic10—31no—
121C2×Dic10—31no—
122C5×C4⋊C4—31no—
123C5×C4⋊C4—31no—
124C5×C22⋊C4—31no—
125C5×C22⋊C4—31no—
126C5×C22⋊C4—31no—
127C22⋊Dic5—31no—
128C22⋊Dic5—31no—
129C22⋊Dic5C2×D311yescharacteristic
130#685—31no—
131#685—31no—
132#685—31no—
133#685—31no—
134#685—31no—
135#685C2×D311yescharacteristic
136C4⋊Dic5—31no—
137C4⋊Dic5—31no—
138C4⋊Dic5—31no—
139C4⋊Dic5—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×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C3×C4×C5—21no—
160Dic15—21no—
161Dic15—21no—
162Dic15—21no—
163C3×Dic5—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C5×Dic3—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×#67—51no—
176C2×#67—51no—
177C22×Dic3—51no—
178C22×Dic3C2×D511yescharacteristic
179C2×C4×D3—51no—
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#217C2×D511yescharacteristic
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⋊Dic3—51no—
197Dic3⋊C4—51no—
198Dic3⋊C4—51no—
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4C2×D511yescharacteristic
203Dic3⋊C4C2×D511yescharacteristic
204C4×Dic3—51no—
205C23×C5C22×D311yescharacteristic
206C23×C5C22×D311yescharacteristic
207C22×D5—31no—
208C22×D5C22×D311yescharacteristic
209C5×D4—41no—
210C2×C4×C5—31no—
211C2×C4×C5—31no—
212C2×C4×C5—31no—
213C2×C4×C5—31no—
214C2×C4×C5—121no—
215C2×C4×C5C22×D311yescharacteristic
216C22⋊D5—41no—
217C22⋊D5—41no—
218C22⋊D5—121no—
219C22⋊D5—121no—
220C2×Dic5—31no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—41no—
224C2×Dic5C22×D311yescharacteristic
225C2×Dic5C22×D311yescharacteristic
226C2×Dic5C22×D311yescharacteristic
227D20—121no—
228C4×D5—121no—
229C4×D5—121no—
230Dic10—121no—
231Dic10—121no—
232#125—151no—
233#124—151no—
234#124—151no—
235#123—31no—
236#123—151no—
237#123—151no—
238#123—151no—
239C22⋊Q8—151no—
240C22⋊Q8—151no—
241C22⋊Q8—151no—
242C22⋊Q8—151no—
243#121—51no—
244#121—151no—
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
252D15—41no—
253C3×D5—41no—
254C23×C3—51no—
255C23×C3C22×D511yescharacteristic
256C23×C3C22×D511yescharacteristic
257C22×D3—51no—
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—201no—
267#67—201no—
268#67—201no—
269C2×Dic3—41no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—201no—
274C2×Dic3C22×D511yescharacteristic
275C2×Dic3C22×D511yescharacteristic
276C2×Dic3C22×D511yescharacteristic
277C2×Dic3C22×D511yescharacteristic
278C4×D3—201no—
279Dic6—201no—
280Dic6—201no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5—21no—
287C22×C5C23×D311yescharacteristic
288C2×D5—21no—
289C2×D5—21no—
290C2×D5—21no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5—61no—
294C4×C5—21no—
295C4×C5—61no—
296C4×C5—61no—
297C4×C5—61no—
298C4×C5—61no—
299Dic5—21no—
300Dic5—21no—
301Dic5—21no—
302Dic5—61no—
303Dic5—61no—
304Dic5—61no—
305C2×Q8—151no—
306C2×Q8—151no—
307C2×D4—51no—
308C2×D4—51no—
309C2×D4—151no—
310C2×D4—151no—
311C2×D4—151no—
312C2×D4D3×D511yescharacteristic
313C22×C4—31no—
314C22×C4—51no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—31no—
318C4⋊C4—31no—
319C4⋊C4—51no—
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—31no—
330C22⋊C4—51no—
331C22⋊C4—51no—
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—101no—
352C2×D3—101no—
353C2×D3—101no—
354C3×C4—21no—
355C3×C4—101no—
356C3×C4—101no—
357C3×C4—101no—
358Dic3—21no—
359Dic3—21no—
360Dic3—21no—
361Dic3—21no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365C2×C5—41no—
366C2×C5—41no—
367C2×C5#100411yescharacteristic
368C2×C5#100411yescharacteristic
369C2×C5#101011yescharacteristic
370D5—41no—
371D5—121no—
372C23—51no—
373C23—151no—
374C23C2×D3×D511yescharacteristic
375C23C2×D3×D511yescharacteristic
376Q8—601no—
377Q8—601no—
378D4—41no—
379D4—201no—
380D4—201no—
381D4—601no—
382D4—601no—
383D4—601no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—51no—
391C2×C4—121no—
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#414911yescharacteristic
404C2×C3#415011yescharacteristic
405D3—201no—
406C5#562111yescharacteristic, complemented, Sylow
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—21no—
413C22—101no—
414C22—101no—
415C22—101no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—61no—
422C4—61no—
423C4—61no—
424C4—61no—
425C4—101no—
426C4—101no—
427C4—101no—
428C4—301no—
429C4—301no—
430C4—301no—
431C3#6600111yescharacteristic, complemented, Sylow
432C2—41no—
433C2—41no—
434C2—201no—
435C2—601no—
436C2#9202011yescharacteristic
437C2#9202611yescharacteristic
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. #91827C2semidirect
2. C5×#935C2semidirect
3. C3×#4085C2semidirect
4. #91575C2semidirect
5. #91574C2semidirect
6. #91569C2semidirect
7. #91550C2semidirect
8. #91548C2semidirect
9. #91546C2semidirect
10. #91534C2semidirect
11. #91526C2semidirect
12. #91422C2semidirect
13. #91377C2semidirect
14. #91354C2semidirect
15. #91343C2semidirect
54. #4085D3semidirect
101. #935D5semidirect
340. C3×C5#562semidirect
406. C5#5621semidirect
431. C3#66001semidirect

Maximal subgroups

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

subgroupindex
#918272
C5×#9352
C3×#40852
#915752
#915742
#915692
#915502
#915482
#915462
#915342
#915262
#914222
#913772
#913542
#913432
#660013
#56215