Finite Group Databasebeta

← #11754810

Subgroups — #11754810

Order 960.

584 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#237C211yesmaximal, characteristic, complemented
2C2×#6782C211yesmaximal, characteristic, complemented
3#91828C211yesmaximal, characteristic, complemented
4C3×#4081C211yesmaximal, characteristic, complemented
5#91575C211yesmaximal, characteristic, complemented
6#67⋊Dic5C211yesmaximal, characteristic, complemented
7#91558C211yesmaximal, characteristic, complemented
8#91556C211yesmaximal, characteristic, complemented
9#91555C211yesmaximal, characteristic, complemented
10C2×#6669C211yesmaximal, characteristic, complemented
11#91542C211yesmaximal, characteristic, complemented
12#91424C211yesmaximal, characteristic, complemented
13D3×#683C211yesmaximal, characteristic, complemented
14#91351C211yesmaximal, characteristic, complemented
15#91329C211yesmaximal, characteristic, complemented
16#66158—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C22×Dic15C2211yescharacteristic
21C2×C5×#67C2211yescharacteristic
22C2×C5×#67C2211yescharacteristic
23C22×C5×Dic3C2211yescharacteristic
24C22×C5×Dic3C2211yescharacteristic
25C5×#237—24no—
26C2×C4×C5×D3C2211yescharacteristic
27C2×C5×Dic6C2211yescharacteristic
28C22×C3×Dic5C2211yescharacteristic
29C2×#1204C2211yescharacteristic
30C2×#1203C2211yescharacteristic
31C2×#1200C2211yescharacteristic
32#6782—24no—
33C2×D3×Dic5C2211yescharacteristic
34C2×D3×Dic5C2211yescharacteristic
35#6719C2211yescharacteristic
36#6714C2211yescharacteristic
37#6712C2211yescharacteristic
38C3×C22⋊Dic5C2211yescharacteristic
39C3×C22⋊Dic5C2211yescharacteristic
40C3×C22⋊Dic5C2211yescharacteristic
41C3×#683C2211yescharacteristic
42C3×#683C2211yescharacteristic
43Dic3⋊Dic5C2211yescharacteristic
44#6669C2211yescharacteristic
45#6669C2211yescharacteristic
46#6669C2211yescharacteristic
47#6669C2211yescharacteristic
48#6668C2211yescharacteristic
49#6668C2211yescharacteristic
50#6667C2211yescharacteristic
51#6667C2211yescharacteristic
52(C2×D3)⋊Dic5C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic
54#5655—51nomaximal, Hall
55C2×C5×#41—31no—
56C2×#711—31no—
57#4092—31no—
58#4090—31no—
59#4085—31no—
60#4085—31no—
61#4081—31no—
62#4081D311yescharacteristic, complemented
63D4×Dic5—31no—
64#4075—31no—
65#4075—31no—
66C4×C22⋊D5—31no—
67#4070—31no—
68C2×#683—31no—
69C2×#683—31no—
70C23×C3×C5C2311yescharacteristic
71C23×C3×C5C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C22×C5×D3C2311yescharacteristic
74C3×C5×D4—22no—
75C2×C3×C4×C5C2311yescharacteristic
76#1220—22no—
77#1220—22no—
78C2×Dic15—22no—
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81C2×Dic15C2311yescharacteristic
82C5×#67—22no—
83C5×#67D414yescomplemented
84C2×C5×Dic3—22no—
85C2×C5×Dic3—22no—
86C2×C5×Dic3C2311yescharacteristic
87C2×C5×Dic3C2311yescharacteristic
88C2×C5×Dic3C2311yescharacteristic
89C4×C5×D3—22no—
90C5×Dic6—22no—
91C2×C3×Dic5—22no—
92C2×C3×Dic5C2311yescharacteristic
93C2×C3×Dic5C2311yescharacteristic
94C2×C3×Dic5C2311yescharacteristic
95C2×C3×Dic5C2311yescharacteristic
96#1204—22no—
97#1203—22no—
98#1200—22no—
99D3×Dic5—22no—
100D3×Dic5—22no—
101C2×#237D511yescharacteristic, complemented
102C2×#235—51no—
103C3×#123—51no—
104#939—51no—
105C2×Dic3⋊C4—51no—
106#896—51no—
107#894—51no—
108D3×C4⋊C4—51no—
109#888—51no—
110#886—51no—
111#884—51no—
112#883—51no—
113#67⋊C4—51no—
114#67⋊C4—51no—
115#878—51no—
116C5×#41—64no—
117C2×C5×Q8—31no—
118C2×C5×D4—31no—
119C2×C5×D4—31no—
120C2×C5×D4C2×D311yescharacteristic
121C22×C4×C5—31no—
122C22×C4×C5—31no—
123C22×C4×C5—31no—
124C2×C22⋊D5—31no—
125C2×C22⋊D5—31no—
126C2×C22⋊D5—31no—
127C22×Dic5—31no—
128C22×Dic5—31no—
129C22×Dic5—31no—
130C22×Dic5C2×D311yescharacteristic
131#711—64no—
132C2×C4×D5—31no—
133C2×Dic10—31no—
134C22⋊Dic5—31no—
135C22⋊Dic5—31no—
136C22⋊Dic5C2×D311yescharacteristic
137C22⋊Dic5C2×D311yescharacteristic
138C22⋊Dic5C2×D311yescharacteristic
139#685—31no—
140#685—31no—
141#685—31no—
142C4⋊Dic5—31no—
143#683—31no—
144#683—31no—
145#683—31no—
146#683—31no—
147#683—31no—
148#683—31no—
149#683—31no—
150#683C2×D311yescharacteristic
151#683C2×D311yescharacteristic
152C4×Dic5—31no—
153#547—151noSylow
154C22×C3×C5—21no—
155C22×C3×C5—21no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5—21no—
159C22×C3×C5C2×D412yes—
160C22×C3×C5C2411yescharacteristic
161C2×D15—21no—
162C2×D15—21no—
163C2×D15—21no—
164C2×C5×D3—21no—
165C2×C5×D3—21no—
166C2×C5×D3C2×D412yes—
167C3×C4×C5—21no—
168Dic15—21no—
169Dic15—21no—
170Dic15#4112yescomplemented
171C3×Dic5—21no—
172C3×Dic5—21no—
173C3×Dic5—21no—
174C3×Dic5—21no—
175C5×Dic3—21no—
176C5×Dic3—21no—
177C5×Dic3C2×D412yes—
178C2×C3×D4C2×D511yescharacteristic
179C22×C3×C4—51no—
180C2×#67—51no—
181C2×#67—51no—
182C2×#67C2×D511yescharacteristic
183C2×#67C2×D511yescharacteristic
184C22×Dic3—51no—
185C22×Dic3C2×D511yescharacteristic
186C22×Dic3C2×D511yescharacteristic
187#237—24no—
188#235—104no—
189C2×D12—51no—
190C2×C4×D3—51no—
191C2×C4×D3—51no—
192C2×C4×D3—51no—
193C2×C4×D3C2×D511yescharacteristic
194C2×Dic6—51no—
195C2×Dic6C2×D511yescharacteristic
196C3×C4⋊C4—51no—
197C3×C4⋊C4—51no—
198C3×C22⋊C4—51no—
199C3×C22⋊C4—51no—
200C3×C22⋊C4—51no—
201#217—51no—
202(C2×D3)⋊C4—51no—
203(C2×D3)⋊C4—51no—
204(C2×D3)⋊C4—51no—
205(C2×D3)⋊C4—51no—
206C4⋊Dic3—51no—
207C4⋊Dic3—51no—
208Dic3⋊C4—51no—
209Dic3⋊C4—51no—
210Dic3⋊C4—51no—
211Dic3⋊C4—51no—
212Dic3⋊C4—51no—
213Dic3⋊C4—51no—
214C4×Dic3—51no—
215C23×C5—31no—
216C23×C5C22×D311yescharacteristic
217C23×C5C22×D311yescharacteristic
218C22×D5—31no—
219C5×Q8—62no—
220C5×D4—22no—
221C5×D4—34no—
222C5×D4—62no—
223C2×C4×C5—31no—
224C2×C4×C5—31no—
225C2×C4×C5—31no—
226C2×C4×C5—62no—
227C2×C4×C5—62no—
228C2×C4×C5—62no—
229C2×C4×C5C22×D311yescharacteristic
230C22⋊D5—62no—
231C22⋊D5—62no—
232C22⋊D5—62no—
233C2×Dic5—22no—
234C2×Dic5—31no—
235C2×Dic5—31no—
236C2×Dic5—31no—
237C2×Dic5—62no—
238C2×Dic5—62no—
239C2×Dic5—62no—
240C2×Dic5C22×D311yescharacteristic
241C2×Dic5C22×D311yescharacteristic
242C2×Dic5C22×D311yescharacteristic
243C2×Dic5C22×D311yescharacteristic
244C4×D5—62no—
245Dic10—62no—
246C2×#41—31no—
247C2×#41—151no—
248C4⋊Q8—151no—
249#123—51no—
250#123—151no—
251#123—151no—
252#123—151no—
253C22⋊Q8—151no—
254C22⋊Q8—151no—
255#121—151no—
256#121—151no—
257C4×D4—151no—
258C4×D4—151no—
259C2×C4⋊C4—151no—
260C2×C4⋊C4—151no—
261C2×C3×C5—22no—
262C2×C3×C5—41no—
263C2×C3×C5C22×D411yescharacteristic
264C2×C3×C5C2×#4111yescharacteristic
265C2×C3×C52−1+411yescharacteristic
266D15—41no—
267C5×D3—22no—
268C23×C3C22×D511yescharacteristic
269C23×C3C22×D511yescharacteristic
270C22×D3—51no—
271C22×D3C22×D511yescharacteristic
272C3×D4—22no—
273C2×C3×C4—51no—
274C2×C3×C4—51no—
275C2×C3×C4—51no—
276C2×C3×C4—51no—
277C2×C3×C4—102no—
278C2×C3×C4C22×D511yescharacteristic
279#67—22no—
280#67—102no—
281#67—102no—
282#67C22⋊D514yescomplemented
283C2×Dic3—22no—
284C2×Dic3—22no—
285C2×Dic3—51no—
286C2×Dic3—51no—
287C2×Dic3—51no—
288C2×Dic3—102no—
289C2×Dic3C22×D511yescharacteristic
290C2×Dic3C22×D511yescharacteristic
291C2×Dic3C22×D511yescharacteristic
292D12—102no—
293C4×D3—22no—
294C4×D3—102no—
295C4×D3—102no—
296C4×D3—102no—
297Dic6—22no—
298Dic6—102no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5—32no—
305C22×C5—61no—
306C22×C5—61no—
307C22×C5D3×D412yes—
308C22×C5C23×D311yescharacteristic
309C2×D5—61no—
310C2×D5—61no—
311C2×D5—61no—
312C4×C5—21no—
313C4×C5—32no—
314C4×C5—61no—
315C4×C5—61no—
316Dic5—21no—
317Dic5—21no—
318Dic5—21no—
319Dic5—21no—
320Dic5—32no—
321Dic5—61no—
322Dic5—61no—
323#41—64no—
324#41—304no—
325C2×Q8—31no—
326C2×Q8—151no—
327C2×D4—31no—
328C2×D4—31no—
329C2×D4—151no—
330C2×D4—151no—
331C2×D4—151no—
332C2×D4D3×D511yescharacteristic
333C22×C4—31no—
334C22×C4—31no—
335C22×C4—31no—
336C22×C4—51no—
337C22×C4—151no—
338C22×C4—151no—
339C22×C4—151no—
340C22×C4—151no—
341C4⋊C4—51no—
342C4⋊C4—51no—
343C4⋊C4—151no—
344C4⋊C4—151no—
345C4⋊C4—151no—
346C4⋊C4—151no—
347C4⋊C4—151no—
348C4⋊C4—151no—
349C4⋊C4—151no—
350C4⋊C4—151no—
351C22⋊C4—51no—
352C22⋊C4—51no—
353C22⋊C4—51no—
354C22⋊C4—151no—
355C22⋊C4—151no—
356C22⋊C4—151no—
357C22⋊C4—151no—
358C22⋊C4—151no—
359C42—151no—
360C3×C5#54711yescharacteristic, complemented, Hall
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—21no—
364C22×C3—21no—
365C22×C3—21no—
366C22×C3C2×C22⋊D512yes—
367C22×C3C23×D511yescharacteristic
368C2×D3—21no—
369C2×D3—21no—
370C2×D3—101no—
371C2×D3—101no—
372C2×D3—101no—
373C2×D3C2×C22⋊D512yes—
374C3×C4—21no—
375C3×C4—101no—
376C3×C4—101no—
377C3×C4—101no—
378C3×C4—101no—
379Dic3—21no—
380Dic3—21no—
381Dic3—52no—
382Dic3—101no—
383Dic3—101no—
384Dic3C2×C22⋊D512yes—
385C2×C5—22no—
386C2×C5—41no—
387C2×C5—62no—
388C2×C5C2×D3×D411yescharacteristic
389C2×C5D3×#4111yescharacteristic
390C2×C5#101011yescharacteristic
391D5—121no—
392C23—31no—
393C23—151no—
394C23C2×D3×D511yescharacteristic
395C23C2×D3×D511yescharacteristic
396Q8—62no—
397Q8—302no—
398D4—22no—
399D4—34no—
400D4—62no—
401D4—302no—
402D4—302no—
403D4—302no—
404C2×C4—31no—
405C2×C4—31no—
406C2×C4—31no—
407C2×C4—51no—
408C2×C4—51no—
409C2×C4—51no—
410C2×C4—51no—
411C2×C4—62no—
412C2×C4—62no—
413C2×C4—62no—
414C2×C4—102no—
415C2×C4—151no—
416C2×C4—151no—
417C2×C4—151no—
418C2×C4—302no—
419C2×C4—302no—
420C2×C4—302no—
421C2×C4—302no—
422C2×C4C2×D3×D511yescharacteristic
423C2×C3—22no—
424C2×C3—41no—
425C2×C3D5×#4111yescharacteristic
426C2×C3#415011yescharacteristic
427C2×C3C22×C22⋊D511yescharacteristic
428D3—22no—
429D3—201no—
430C5#565511yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—21no—
434C22—21no—
435C22—21no—
436C22—32no—
437C22—61no—
438C22—61no—
439C22—301no—
440C22—301no—
441C22—301no—
442C22D3×C22⋊D512yes—
443C22C22×D3×D511yescharacteristic
444C4—21no—
445C4—32no—
446C4—61no—
447C4—61no—
448C4—101no—
449C4—101no—
450C4—101no—
451C4—101no—
452C4—152no—
453C4—301no—
454C4—301no—
455C3#6615811yescharacteristic, complemented, Sylow
456C2—22no—
457C2—41no—
458C2—62no—
459C2—601no—
460C2#9202011yescharacteristic
461C2#9202411yescharacteristic
462C2C2×D3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#547
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. C2×C5×#237C2semidirect
2. C2×#6782C2semidirect
3. #91828C2semidirect
4. C3×#4081C2semidirect
5. #91575C2semidirect
6. #67⋊Dic5C2semidirect
7. #91558C2semidirect
8. #91556C2semidirect
9. #91555C2semidirect
10. C2×#6669C2semidirect
11. #91542C2semidirect
12. #91424C2semidirect
13. D3×#683C2semidirect
14. #91351C2semidirect
15. #91329C2semidirect
62. #4081D3semidirect
83. C5×#67D4semidirect
101. C2×#237D5semidirect
170. Dic15#41semidirect
282. #67C22⋊D5semidirect
360. C3×C5#547semidirect
430. C5#5655semidirect
455. C3#66158semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#2372
C2×#67822
#918282
C3×#40812
#915752
#67⋊Dic52
#915582
#915562
#915552
C2×#66692
#915422
#914242
D3×#6832
#913512
#913292
#661583
#56555