Finite Group Databasebeta

← #11753012

Subgroups — #11753012

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#91770C211yesmaximal, characteristic, complemented
2C5×#885C211yesmaximal, characteristic, complemented
3C3×#4031C211yesmaximal, characteristic, complemented
4#91571C211yesmaximal, characteristic, complemented
5#91558C211yesmaximal, characteristic, complemented
6#91550C211yesmaximal, characteristic, complemented
7#91532C211yesmaximal, characteristic, complemented
8#91461C211yesmaximal, characteristic, complemented
9#91455C211yesmaximal, characteristic, complemented
10#91442C211yesmaximal, characteristic, complemented
11#91398C211yesmaximal, characteristic, complemented
12#91393C211yesmaximal, characteristic, complemented
13#91386C211yesmaximal, characteristic, complemented
14#91385C211yesmaximal, characteristic, complemented
15#91326C211yesmaximal, characteristic, complemented
16#66004—31nomaximal, Hall
17C2×#1220C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C2×C4×D15C2211yescharacteristic
20C2×C5×#67C2211yescharacteristic
21C2×C5×Dic6C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×Dic10C2211yescharacteristic
24C2×#1203C2211yescharacteristic
25C2×#1202C2211yescharacteristic
26C2×#1201C2211yescharacteristic
27C2×D3×Dic5C2211yescharacteristic
28C2×D5×Dic3C2211yescharacteristic
29C3×C5×C22⋊C4C2211yescharacteristic
30#6714C2211yescharacteristic
31#6712C2211yescharacteristic
32C4×Dic15C2211yescharacteristic
33C5×#217C2211yescharacteristic
34C5×(C2×D3)⋊C4C2211yescharacteristic
35C5×(C2×D3)⋊C4C2211yescharacteristic
36C4×C5×Dic3C2211yescharacteristic
37C3×C22⋊Dic5C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×#685C2211yescharacteristic
40C3×C4×Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6669C2211yescharacteristic
44#6669C2211yescharacteristic
45#6669C2211yescharacteristic
46#6667C2211yescharacteristic
47#6667C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49#6665C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5670—51nomaximal, Hall
53C5×#124—31no—
54#4093—31no—
55#4090—31no—
56#4085—31no—
57#4085—31no—
58#4031—31no—
59#4031D311yescharacteristic, complemented
60#4030—31no—
61#4030—31no—
62#4027—31no—
63#4027—31no—
64#4023—31no—
65#4023—31no—
66#4018—31no—
67#4018—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74#1220—22no—
75C2×Dic15—22no—
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C4×D15—22no—
80C5×#67—41no—
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C5×Dic6—41no—
85C3×C22⋊D5—41no—
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C3×Dic10—41no—
90#1203—41no—
91#1202—41no—
92#1201—22no—
93D3×Dic5—22no—
94D5×Dic3—22no—
95C3×#124—51no—
96#947—51no—
97#944—51no—
98#939—51no—
99#939—51no—
100#885—51no—
101#885D511yescharacteristic, complemented
102#884—51no—
103#884—51no—
104#67⋊C4—51no—
105#67⋊C4—51no—
106#877—51no—
107#877—51no—
108#872—51no—
109#872—51no—
110C2×C5×Q8—31no—
111C2×C5×D4—31no—
112C2×C22⋊D5—31no—
113C2×C22⋊D5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5C2×D311yescharacteristic
116C22×Dic5—31no—
117C22×Dic5—31no—
118C2×D20—31no—
119C2×C4×D5—31no—
120C2×C4×D5—31no—
121C2×Dic10C2×D311yescharacteristic
122C5×C22⋊C4—31no—
123C5×C22⋊C4—31no—
124C5×C22⋊C4—31no—
125C5×C22⋊C4C2×D311yescharacteristic
126C42×C5—31no—
127C22⋊Dic5—31no—
128C22⋊Dic5C2×D311yescharacteristic
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685C2×D311yescharacteristic
134#685C2×D311yescharacteristic
135#683—31no—
136#683—31no—
137#683—31no—
138#683—31no—
139#683—31no—
140#683—31no—
141C4×Dic5—31no—
142C4×Dic5—31no—
143C4×Dic5—31no—
144C4×Dic5C2×D311yescharacteristic
145#555—151noSylow
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5C2411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15—21no—
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—
160C3×C4×C5—21no—
161Dic15—21no—
162Dic15#4112yes—
163Dic15#4112yes—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C5×Dic3—21no—
168C5×Dic3—21no—
169C5×Dic3—21no—
170C2×C3×Q8—51no—
171C2×C3×D4—51no—
172C2×#67—51no—
173C2×#67—51no—
174C2×#67—51no—
175C2×#67C2×D511yescharacteristic
176C22×Dic3—51no—
177C22×Dic3—51no—
178C2×D12—51no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×Dic6C2×D511yescharacteristic
182C3×C22⋊C4—51no—
183C3×C22⋊C4—51no—
184C3×C22⋊C4—51no—
185C3×C22⋊C4C2×D511yescharacteristic
186C3×C42—51no—
187#217—51no—
188#217C2×D511yescharacteristic
189(C2×D3)⋊C4—51no—
190(C2×D3)⋊C4—51no—
191(C2×D3)⋊C4—51no—
192(C2×D3)⋊C4—51no—
193(C2×D3)⋊C4C2×D511yescharacteristic
194(C2×D3)⋊C4C2×D511yescharacteristic
195Dic3⋊C4—51no—
196Dic3⋊C4—51no—
197Dic3⋊C4—51no—
198Dic3⋊C4—51no—
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201C4×Dic3—51no—
202C4×Dic3—51no—
203C4×Dic3—51no—
204C4×Dic3C2×D511yescharacteristic
205C23×C5—31no—
206C23×C5C22×D311yescharacteristic
207C22×D5—31no—
208C22×D5C22×D311yescharacteristic
209C5×Q8—121no—
210C5×D4—121no—
211C2×C4×C5—31no—
212C2×C4×C5—31no—
213C2×C4×C5—31no—
214C2×C4×C5C22×D311yescharacteristic
215C2×C4×C5C22×D311yescharacteristic
216C22⋊D5—41no—
217C22⋊D5—62no—
218C22⋊D5—62no—
219C22⋊D5—121no—
220C2×Dic5—31no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5—62no—
224C2×Dic5—62no—
225C2×Dic5C22×D311yescharacteristic
226C2×Dic5C22×D311yescharacteristic
227C2×Dic5C22×D311yescharacteristic
228D20—121no—
229C4×D5—62no—
230C4×D5—62no—
231Dic10—41no—
232C4⋊Q8—151no—
233#124—31no—
234#124—51no—
235#124—151no—
236#124—151no—
237#121—151no—
238#121—151no—
239#121—151no—
240#121—151no—
241C4×D4—151no—
242C4×D4—151no—
243#117—151no—
244#117—151no—
245#117—151no—
246#117—151no—
247C2×C3×C5—41no—
248C2×C3×C5C2×#4111yescharacteristic
249C2×C3×C5C2×#4111yescharacteristic
250C2×C3×C5H(5,𝔽2)11yescharacteristic
251D15—41no—
252C3×D5—41no—
253C5×D3—41no—
254C23×C3—51no—
255C23×C3C22×D511yescharacteristic
256C22×D3—51no—
257C22×D3C22×D511yescharacteristic
258C3×Q8—201no—
259C3×D4—201no—
260C2×C3×C4—51no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4C22×D511yescharacteristic
264C2×C3×C4C22×D511yescharacteristic
265#67—41no—
266#67—102no—
267#67—102no—
268#67—201no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—102no—
273C2×Dic3—102no—
274C2×Dic3C22×D511yescharacteristic
275C2×Dic3C22×D511yescharacteristic
276C2×Dic3C22×D511yescharacteristic
277D12—201no—
278C4×D3—102no—
279C4×D3—102no—
280Dic6—41no—
281C22×C5—21no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—61no—
285C22×C5—61no—
286C22×C5—61no—
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—21no—
296C4×C5—61no—
297C4×C5—61no—
298C4×C5—61no—
299Dic5—21no—
300Dic5—21no—
301Dic5—21no—
302Dic5—32no—
303Dic5—32no—
304Dic5—61no—
305C2×Q8—31no—
306C2×Q8—51no—
307C2×D4—31no—
308C2×D4—51no—
309C2×D4—151no—
310C2×D4—151no—
311C2×D4—151no—
312C2×D4—151no—
313C22×C4—151no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—151no—
318C4⋊C4—151no—
319C4⋊C4—151no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C22⋊C4—31no—
324C22⋊C4—31no—
325C22⋊C4—31no—
326C22⋊C4—51no—
327C22⋊C4—51no—
328C22⋊C4—51no—
329C22⋊C4—151no—
330C22⋊C4—151no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4D3×D511yescharacteristic
335C42—31no—
336C42—51no—
337C42—151no—
338C42—151no—
339C42—151no—
340C3×C5#55511yescharacteristic, complemented, Hall
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3—101no—
347C22×C3C23×D511yescharacteristic
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—101no—
352C2×D3—101no—
353C2×D3—101no—
354C3×C4—21no—
355C3×C4—21no—
356C3×C4—101no—
357C3×C4—101no—
358C3×C4—101no—
359Dic3—21no—
360Dic3—21no—
361Dic3—21no—
362Dic3—52no—
363Dic3—52no—
364Dic3—101no—
365C2×C5—41no—
366C2×C5—121no—
367C2×C5#100411yescharacteristic
368C2×C5D3×#4111yescharacteristic
369C2×C5D3×#4111yescharacteristic
370D5—41no—
371D5—121no—
372C23—31no—
373C23—51no—
374C23—151no—
375C23C2×D3×D511yescharacteristic
376Q8—121no—
377Q8—201no—
378D4—121no—
379D4—201no—
380D4—302no—
381D4—302no—
382D4—601no—
383D4—601no—
384C2×C4—31no—
385C2×C4—31no—
386C2×C4—31no—
387C2×C4—51no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—151no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—302no—
394C2×C4—302no—
395C2×C4—302no—
396C2×C4—302no—
397C2×C4C2×D3×D511yescharacteristic
398C2×C4C2×D3×D511yescharacteristic
399C2×C3—41no—
400C2×C3—201no—
401C2×C3#414411yescharacteristic
402C2×C3D5×#4111yescharacteristic
403C2×C3D5×#4111yescharacteristic
404D3—41no—
405D3—201no—
406C5#567011yescharacteristic, complemented, Sylow
407C22—21no—
408C22—21no—
409C22—21no—
410C22—61no—
411C22—61no—
412C22—61no—
413C22—101no—
414C22—101no—
415C22—101no—
416C22—301no—
417C22—301no—
418C22—301no—
419C22C22×D3×D511yescharacteristic
420C4—21no—
421C4—21no—
422C4—61no—
423C4—61no—
424C4—61no—
425C4—101no—
426C4—101no—
427C4—101no—
428C4—152no—
429C4—152no—
430C4—301no—
431C3#6600411yescharacteristic, complemented, Sylow
432C2—41no—
433C2—121no—
434C2—201no—
435C2—601no—
436C2#9201611yescharacteristic
437C2#9202411yescharacteristic
438C2#9202511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#555
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #91770C2semidirect
2. C5×#885C2semidirect
3. C3×#4031C2semidirect
4. #91571C2semidirect
5. #91558C2semidirect
6. #91550C2semidirect
7. #91532C2semidirect
8. #91461C2semidirect
9. #91455C2semidirect
10. #91442C2semidirect
11. #91398C2semidirect
12. #91393C2semidirect
13. #91386C2semidirect
14. #91385C2semidirect
15. #91326C2semidirect
59. #4031D3semidirect
101. #885D5semidirect
340. C3×C5#555semidirect
406. C5#5670semidirect
431. C3#66004semidirect

Maximal subgroups

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

subgroupindex
#917702
C5×#8852
C3×#40312
#915712
#915582
#915502
#915322
#914612
#914552
#914422
#913982
#913932
#913862
#913852
#913262
#660043
#56705