Finite Group Databasebeta

← #11752760

Subgroups — #11752760

Order 960.

496 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91761C211yesmaximal, characteristic, complemented
2C5×#875C211yesmaximal, characteristic, complemented
3C3×#4018C211yesmaximal, characteristic, complemented
4#91475C211yesmaximal, characteristic
5#91473C211yesmaximal, characteristic, complemented
6D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
7#91447C211yesmaximal, characteristic, complemented
8#91442C211yesmaximal, characteristic, complemented
9#91424C211yesmaximal, characteristic, complemented
10#91423C211yesmaximal, characteristic, complemented
11#91421C211yesmaximal, characteristic, complemented
12#91405C211yesmaximal, characteristic, complemented
13#91372C211yesmaximal, characteristic, complemented
14#91367C211yesmaximal, characteristic, complemented
15#91355C211yesmaximal, characteristic, complemented
16#66013—31nomaximal, Hall
17C22×D3×D5C2211yescharacteristic
18C2×C4×D15C2211yescharacteristic
19C2×C5×D12C2211yescharacteristic
20C2×C5×Dic6C2211yescharacteristic, complemented
21C2×C3×C4×D5C2211yescharacteristic
22C2×#1203C2211yescharacteristic
23C2×#1201C2211yescharacteristic
24C2×#1200C2211yescharacteristic
25C2×D3×Dic5C2211yescharacteristic, complemented
26C2×D5×Dic3C2211yescharacteristic
27C3×C42×C5C2211yescharacteristic, complemented
28#6714C2211yescharacteristic
29#6714C2211yescharacteristic
30#6712C2211yescharacteristic, complemented
31#6712C2211yescharacteristic, complemented
32C4×Dic15C2211yescharacteristic, complemented
33C5×(C2×D3)⋊C4C2211yescharacteristic
34C5×(C2×D3)⋊C4C2211yescharacteristic
35C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
36C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C3×#685C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×#683C2211yescharacteristic, complemented
40C3×#683C2211yescharacteristic, complemented
41C3×C4×Dic5C2211yescharacteristic, complemented
42Dic3⋊Dic5C2211yescharacteristic, complemented
43Dic3⋊Dic5C2211yescharacteristic, complemented
44#6669C2211yescharacteristic, complemented
45#6668C2211yescharacteristic, complemented
46#6667C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49(C2×D3)⋊Dic5C2211yescharacteristic
50(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51#6665C2211yescharacteristic
52#5527—51nomaximal, Hall
53C5×#124—31no—
54#4092—31no—
55#4092—31no—
56#4083—31no—
57#4081—31no—
58#4029—31no—
59#4029—31no—
60#4027—31no—
61#4027—31no—
62D5×C22⋊C4—31no—
63D5×C22⋊C4—31no—
64#4025—31no—
65#4025—31no—
66#4018—31no—
67#4018D311yescharacteristic, complemented
68C22×D15C2311yescharacteristic
69C22×C5×D3C2311yescharacteristic
70C22×C5×D3C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C2×D3×D5—22no—
73C2×D3×D5—22no—
74C2×D3×D5—41no—
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81C4×D15—22no—
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C5×D12—41no—
85C5×Dic6—41no—
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C3×C4×D5—22no—
90#1203—22no—
91#1201—22no—
92#1200—41no—
93D3×Dic5—41no—
94D5×Dic3—41no—
95C3×#117—51no—
96#929—51no—
97C2×(C2×D3)⋊C4—51no—
98#898—51no—
99#896—51no—
100#894—51no—
101#894—51no—
102#882—51no—
103#67⋊C4—51no—
104D3×C22⋊C4—51no—
105#878—51no—
106#876—51no—
107#875D511yescharacteristic, complemented
108C4×D12—51no—
109#872—51no—
110C23×D5—31no—
111C2×C5×Q8—31no—
112C2×C5×D4—31no—
113C2×C22⋊D5—31no—
114C2×C22⋊D5—31no—
115C22×Dic5—31no—
116C2×C4×D5—31no—
117C2×C4×D5—31no—
118C2×C4×D5—31no—
119C2×C4×D5C2×D311yescharacteristic
120C5×C22⋊C4—31no—
121C5×C22⋊C4—31no—
122C5×C22⋊C4—31no—
123C5×C22⋊C4—31no—
124C42×C5C2×D311yescharacteristic, complemented
125C22⋊Dic5—31no—
126C22⋊Dic5—31no—
127C22⋊Dic5—31no—
128C22⋊Dic5—31no—
129#685—31no—
130#685—31no—
131#685—31no—
132#685—31no—
133#685C2×D311yescharacteristic
134#685C2×D311yescharacteristic
135C4⋊Dic5—31no—
136C4⋊Dic5—31no—
137#683—31no—
138#683—31no—
139#683—31no—
140#683—31no—
141#683C2×D311yescharacteristic, complemented
142#683C2×D311yescharacteristic, complemented
143C4×Dic5—31no—
144C4×Dic5C2×D311yescharacteristic, complemented
145#551—151noSylow
146C22×C3×C5C2411yescharacteristic
147C2×D15—21no—
148C2×D15—21no—
149C2×D15#4112yes—
150C2×C5×D3—21no—
151C2×C5×D3—21no—
152C2×C5×D3—21no—
153C2×C5×D3—21no—
154C2×C5×D3—21no—
155C2×C5×D3—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5#4112yes—
159D3×D5—44no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163Dic15—21no—
164Dic15—21no—
165Dic15—21no—
166C3×Dic5—21no—
167C3×Dic5—21no—
168C3×Dic5—21no—
169C5×Dic3—21no—
170C5×Dic3—21no—
171C23×D3—51no—
172C22×C3×C4—51no—
173C2×#67—51no—
174C22×Dic3—51no—
175C2×D12—51no—
176C2×D12C2×D511yescharacteristic
177C2×C4×D3—51no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×Dic6C2×D511yescharacteristic, complemented
181C3×C4⋊C4—51no—
182C3×C4⋊C4—51no—
183C3×C22⋊C4—51no—
184C3×C22⋊C4—51no—
185C3×C42—51no—
186C3×C42C2×D511yescharacteristic, complemented
187#217—51no—
188(C2×D3)⋊C4—51no—
189(C2×D3)⋊C4—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)⋊C4C2×D511yescharacteristic
196(C2×D3)⋊C4C2×D511yescharacteristic
197(C2×D3)⋊C4C2×D511yescharacteristic, complemented
198(C2×D3)⋊C4C2×D511yescharacteristic, complemented
199C4⋊Dic3—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4—51no—
203Dic3⋊C4—51no—
204Dic3⋊C4—51no—
205C4×Dic3—51no—
206C23×C5—31no—
207C23×C5—31no—
208C22×D5—31no—
209C22×D5—62no—
210C22×D5—62no—
211C22×D5—121no—
212C22×D5C22×D311yescharacteristic
213C5×Q8—121no—
214C5×D4—121no—
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5C22×D311yescharacteristic
218C2×C4×C5C22×D311yescharacteristic
219C2×C4×C5C22×D311yescharacteristic
220C22⋊D5—62no—
221C22⋊D5—62no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—121no—
226C2×Dic5C22×D311yescharacteristic
227C2×Dic5C22×D311yescharacteristic
228C2×Dic5C22×D311yescharacteristic
229C4×D5—22no—
230C4×D5—62no—
231C4×D5—121no—
232C4×D5—121no—
233#126—151no—
234#126—151no—
235#124—31no—
236#123—151no—
237#123—151no—
238#123—151no—
239C22⋊Q8—151no—
240C22⋊Q8—151no—
241#120—151no—
242C4×D4—151no—
243C4×D4—151no—
244#117—51no—
245#117—151no—
246C2×C22⋊C4—151no—
247C2×C22⋊C4—151no—
248C2×C3×C5C2×#4111yescharacteristic
249C2×C3×C5C2×#4111yescharacteristic
250C2×C3×C5H(5,𝔽2)11yescharacteristic
251D15—22no—
252C3×D5—22no—
253C5×D3—41no—
254C5×D3—41no—
255C23×C3—51no—
256C22×D3—51no—
257C22×D3—102no—
258C22×D3—102no—
259C22×D3—201no—
260C22×D3C22×D511yescharacteristic
261C22×D3C22×D511yescharacteristic
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—51no—
265C2×C3×C4—102no—
266C2×C3×C4C22×D511yescharacteristic
267C2×C3×C4C22×D511yescharacteristic
268C2×C3×C4C22×D511yescharacteristic
269#67—102no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—201no—
274C2×Dic3C22×D511yescharacteristic
275C2×Dic3C22×D511yescharacteristic
276D12—41no—
277D12—102no—
278C4×D3—102no—
279C4×D3—201no—
280C4×D3—201no—
281Dic6—41no—
282C22×C5—61no—
283C22×C5—61no—
284C22×C5—61no—
285C22×C5—61no—
286C22×C5—61no—
287C22×C5—61no—
288C22×C5C23×D311yescharacteristic
289C2×D5—21no—
290C2×D5—21no—
291C2×D5—32no—
292C2×D5—61no—
293C2×D5—61no—
294C2×D5—124no—
295C2×D5#23512yes—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—61no—
300C4×C5—61no—
301Dic5—21no—
302Dic5—21no—
303Dic5—21no—
304Dic5—61no—
305Dic5—61no—
306Dic5—61no—
307C24—151no—
308C2×Q8—31no—
309C2×D4—31no—
310C2×D4—151no—
311C2×D4—151no—
312C22×C4—51no—
313C22×C4—151no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
317C4⋊C4—51no—
318C4⋊C4—51no—
319C4⋊C4—151no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4—151no—
325C22⋊C4—31no—
326C22⋊C4—31no—
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—51no—
340C42—151no—
341C42D3×D511yescharacteristic, complemented
342C3×C5#55111yescharacteristic, complemented, Hall
343C22×C3—52no—
344C22×C3—101no—
345C22×C3—101no—
346C22×C3C23×D511yescharacteristic
347C2×D3—21no—
348C2×D3—21no—
349C2×D3—21no—
350C2×D3—21no—
351C2×D3—21no—
352C2×D3—21no—
353C2×D3—52no—
354C2×D3—101no—
355C2×D3—101no—
356C2×D3—204no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—101no—
361C3×C4—101no—
362C3×C4—101no—
363Dic3—21no—
364Dic3—21no—
365Dic3—101no—
366Dic3—101no—
367Dic3—101no—
368C2×C5—121no—
369C2×C5—121no—
370C2×C5C2×#23511yescharacteristic
371C2×C5D3×#4111yescharacteristic
372C2×C5#100911yescharacteristic
373D5—22no—
374D5—62no—
375C23—31no—
376C23—31no—
377C23—51no—
378C23—151no—
379C23—302no—
380C23—302no—
381C23—601no—
382Q8—121no—
383D4—121no—
384D4—302no—
385D4—302no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—51no—
389C2×C4—51no—
390C2×C4—51no—
391C2×C4—102no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—151no—
395C2×C4—302no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4—601no—
399C2×C4C2×D3×D511yescharacteristic
400C2×C4C2×D3×D511yescharacteristic
401C2×C4C2×D3×D511yescharacteristic
402C2×C3—102no—
403C2×C3#414411yescharacteristic
404C2×C3D5×#4111yescharacteristic
405C2×C3D5×#4111yescharacteristic
406D3—41no—
407D3—41no—
408D3—102no—
409C5#552711yescharacteristic, complemented, Sylow
410C22—52no—
411C22—61no—
412C22—61no—
413C22—61no—
414C22—61no—
415C22—61no—
416C22—61no—
417C22—101no—
418C22—101no—
419C22—152no—
420C22—301no—
421C22—301no—
422C22—604no—
423C22C22×D3×D511yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—61no—
428C4—61no—
429C4—101no—
430C4—101no—
431C4—101no—
432C4—301no—
433C4—301no—
434C4—301no—
435C3#6601311yescharacteristic, complemented, Sylow
436C2—102no—
437C2—121no—
438C2—121no—
439C2—302no—
440C2D5×#23511yescharacteristic
441C2#9201611yescharacteristic
442C2#9201811yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C42×C5C22
prime radical#91475C2
hypercenterC42D3×D5
hypocenterC3×C5#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #91761C2semidirect
2. C5×#875C2semidirect
3. C3×#4018C2semidirect
5. #91473C2semidirect
6. D5×(C2×D3)⋊C4C2semidirect
7. #91447C2semidirect
8. #91442C2semidirect
9. #91424C2semidirect
10. #91423C2semidirect
11. #91421C2semidirect
12. #91405C2semidirect
13. #91372C2semidirect
14. #91367C2semidirect
15. #91355C2semidirect
20. C2×C5×Dic6C22semidirect
25. C2×D3×Dic5C22semidirect
27. C3×C42×C5C22semidirect
30. #6712C22semidirect
31. #6712C22semidirect
32. C4×Dic15C22semidirect
35. C5×(C2×D3)⋊C4C22semidirect
36. C5×(C2×D3)⋊C4C22semidirect
39. C3×#683C22semidirect
40. C3×#683C22semidirect
41. C3×C4×Dic5C22semidirect
42. Dic3⋊Dic5C22semidirect
43. Dic3⋊Dic5C22semidirect
44. #6669C22semidirect
45. #6668C22semidirect
50. (C2×D3)⋊Dic5C22semidirect
67. #4018D3semidirect
107. #875D5semidirect
124. C42×C5C2×D3semidirect
141. #683C2×D3semidirect
142. #683C2×D3semidirect
144. C4×Dic5C2×D3semidirect
180. C2×Dic6C2×D5semidirect
186. C3×C42C2×D5semidirect
197. (C2×D3)⋊C4C2×D5semidirect
198. (C2×D3)⋊C4C2×D5semidirect
341. C42D3×D5semidirect
342. C3×C5#551semidirect
409. C5#5527semidirect
435. C3#66013semidirect

Maximal subgroups

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

subgroupindex
#917612
C5×#8752
C3×#40182
#914752
#914732
D5×(C2×D3)⋊C42
#914472
#914422
#914242
#914232
#914212
#914052
#913722
#913672
#913552
#660133
#55275