Finite Group Databasebeta

← #11754639

Subgroups — #11754639

Order 960.

668 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#709C211yesmaximal, characteristic, complemented
2C2×#6790C211yesmaximal, characteristic, complemented
3C2×#6714C211yesmaximal, characteristic, complemented
4C5×#929C211yesmaximal, characteristic, complemented
5#91572C211yesmaximal, characteristic, complemented
6#91571C211yesmaximal, characteristic, complemented
7#91559C211yesmaximal, characteristic, complemented
8#91474C211yesmaximal, characteristic, complemented
9D5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
10#91448C211yesmaximal, characteristic, complemented
11#91444C211yesmaximal, characteristic, complemented
12#91411C211yesmaximal, characteristic, complemented
13#91409C211yesmaximal, characteristic, complemented
14#91348C211yesmaximal, characteristic, complemented
15#91326C211yesmaximal, characteristic, complemented
16#65988—31nomaximal, Hall
17C23×D15C2211yescharacteristic
18C22×D3×D5C2211yescharacteristic
19C22×C3×C4×C5C2211yescharacteristic, complemented
20C22×Dic15C2211yescharacteristic, complemented
21C2×C5×#67C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C22⋊D5C2211yescharacteristic, complemented
24C3×#709—24no—
25C2×C3×D20C2211yescharacteristic, complemented
26C2×C3×C4×D5C2211yescharacteristic, complemented
27C2×C3×C4×D5C2211yescharacteristic, complemented
28C2×C3×Dic10C2211yescharacteristic, complemented
29#6790—24no—
30C2×#1203C2211yescharacteristic
31C2×#1202C2211yescharacteristic
32C2×#1202C2211yescharacteristic
33C2×#1202C2211yescharacteristic, complemented
34C2×#1201C2211yescharacteristic, complemented
35C2×#1200C2211yescharacteristic
36C2×D5×Dic3C2211yescharacteristic, complemented
37#6714C2211yescharacteristic
38#6714C2211yescharacteristic
39#6714C2211yescharacteristic, complemented
40#6714C2211yescharacteristic, complemented
41C5×#217C2211yescharacteristic, complemented
42C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C5×Dic3⋊C4C2211yescharacteristic, complemented
45C5×Dic3⋊C4C2211yescharacteristic, complemented
46#6669C2211yescharacteristic, complemented
47#6668C2211yescharacteristic, complemented
48#6667C2211yescharacteristic
49#6667C2211yescharacteristic, complemented
50(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51#6665C2211yescharacteristic, complemented
52#6665C2211yescharacteristic, complemented
53Dic3×Dic5C2211yescharacteristic, complemented
54#5829—51nomaximal, Hall
55C2×D4×D5—31no—
56C2×#709D311yescharacteristic, complemented
57C5×#123—31no—
58#4085—31no—
59C2×#685—31no—
60#4042—31no—
61#4041—31no—
62#4040—31no—
63#4039—31no—
64#4031—31no—
65#4030—31no—
66#4028—31no—
67#4028—31no—
68#4027—31no—
69D5×C22⋊C4—31no—
70C23×C3×C5C2311yescharacteristic
71C22×D15—22no—
72C22×D15—22no—
73C22×D15—41no—
74C22×D15C2311yescharacteristic
75C22×D15C2311yescharacteristic
76C22×C5×D3C2311yescharacteristic
77C22×C3×D5C2311yescharacteristic
78C22×C3×D5C2311yescharacteristic
79C2×D3×D5—22no—
80C2×D3×D5—22no—
81C2×D3×D5—41no—
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5C2311yescharacteristic
84C2×C3×C4×C5C2311yescharacteristic
85C2×Dic15—41no—
86C2×Dic15C2311yescharacteristic
87C2×Dic15C2311yescharacteristic
88C5×#67—22no—
89C2×C5×Dic3C2311yescharacteristic
90C2×C5×Dic3C2311yescharacteristic
91C2×C5×Dic3C2311yescharacteristic
92C3×C22⋊D5—22no—
93C3×C22⋊D5D414yescomplemented
94C2×C3×Dic5C2311yescharacteristic
95C2×C3×Dic5C2311yescharacteristic
96C3×D20—22no—
97C3×C4×D5—22no—
98C3×C4×D5—22no—
99C3×Dic10—22no—
100#1203—22no—
101#1202—22no—
102#1202—22no—
103#1202—41no—
104#1201—41no—
105#1200—22no—
106D5×Dic3—41no—
107C2×C3×#41—51no—
108C2×D3×D4—51no—
109#947—51no—
110#946—51no—
111#939—51no—
112#939—51no—
113#937—51no—
114#937—51no—
115D4×Dic3—51no—
116#930—51no—
117#929—51no—
118#929D511yescharacteristic, complemented
119C4×#67—51no—
120C2×(C2×D3)⋊C4—51no—
121C2×(C2×D3)⋊C4—51no—
122C23×D5—31no—
123C23×D5—31no—
124C2×C5×D4—31no—
125C22×C4×C5C2×D311yescharacteristic, complemented
126C2×C22⋊D5—31no—
127C2×C22⋊D5—31no—
128C2×C22⋊D5C2×D311yescharacteristic
129C2×C22⋊D5C2×D311yescharacteristic, complemented
130C22×Dic5—31no—
131D4×D5—64no—
132#709—24no—
133C2×D20—31no—
134C2×D20—31no—
135C2×D20—31no—
136C2×D20C2×D311yescharacteristic, complemented
137C2×C4×D5—31no—
138C2×C4×D5—31no—
139C2×C4×D5C2×D311yescharacteristic, complemented
140C2×C4×D5C2×D311yescharacteristic, complemented
141C2×Dic10C2×D311yescharacteristic, complemented
142C5×C4⋊C4—31no—
143C5×C4⋊C4—31no—
144C5×C22⋊C4—31no—
145C5×C22⋊C4—31no—
146C5×C22⋊C4—31no—
147C22⋊Dic5—31no—
148#685—31no—
149#685—31no—
150#685—31no—
151#685—31no—
152#685—31no—
153#685—31no—
154#685—31no—
155#685—31no—
156#683—31no—
157#683—31no—
158C4×Dic5—31no—
159#546—151noSylow
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5C2×D412yes—
163C22×C3×C5C2411yescharacteristic
164C2×D15—21no—
165C2×D15—21no—
166C2×D15—21no—
167C2×D15—21no—
168C2×D15—21no—
169C2×D15—44no—
170C2×D15#4112yescomplemented
171C2×C5×D3—21no—
172C2×C5×D3—21no—
173C2×C5×D3—21no—
174C2×C3×D5—21no—
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5—21no—
179C2×C3×D5C2×D412yes—
180D3×D5—44no—
181C3×C4×C5—21no—
182C3×C4×C5—21no—
183Dic15—21no—
184Dic15—21no—
185C3×Dic5—21no—
186C3×Dic5C2×D412yes—
187C5×Dic3—21no—
188C5×Dic3—21no—
189C5×Dic3—21no—
190C23×D3—51no—
191C23×D3—51no—
192C3×#41—104no—
193C2×C3×Q8—51no—
194C2×C3×D4—51no—
195C2×C3×D4—51no—
196C2×C3×D4—51no—
197C22×C3×C4—51no—
198C22×C3×C4—51no—
199C22×C3×C4C2×D511yescharacteristic, complemented
200C2×#67—51no—
201C2×#67—51no—
202C2×#67—51no—
203C2×#67—51no—
204C2×#67C2×D511yescharacteristic
205C22×Dic3—51no—
206C22×Dic3—51no—
207D3×D4—104no—
208C2×D12—51no—
209C2×C4×D3—51no—
210#217—51no—
211#217—51no—
212#217C2×D511yescharacteristic, complemented
213(C2×D3)⋊C4—51no—
214(C2×D3)⋊C4—51no—
215(C2×D3)⋊C4—51no—
216(C2×D3)⋊C4—51no—
217(C2×D3)⋊C4—51no—
218(C2×D3)⋊C4—51no—
219(C2×D3)⋊C4—51no—
220(C2×D3)⋊C4C2×D511yescharacteristic, complemented
221(C2×D3)⋊C4C2×D511yescharacteristic, complemented
222C4⋊Dic3—51no—
223Dic3⋊C4—51no—
224Dic3⋊C4C2×D511yescharacteristic, complemented
225Dic3⋊C4C2×D511yescharacteristic, complemented
226C4×Dic3—51no—
227C23×C5—31no—
228C23×C5C22×D311yescharacteristic
229C22×D5—31no—
230C22×D5—31no—
231C22×D5—62no—
232C22×D5—62no—
233C22×D5—62no—
234C22×D5—62no—
235C22×D5—121no—
236C22×D5—121no—
237C22×D5C22×D311yescharacteristic
238C22×D5C22×D311yescharacteristic
239C5×D4—62no—
240C2×C4×C5—22no—
241C2×C4×C5—31no—
242C2×C4×C5—31no—
243C2×C4×C5—31no—
244C2×C4×C5C22×D311yescharacteristic
245C2×C4×C5C22×D311yescharacteristic
246C22⋊D5—22no—
247C22⋊D5—62no—
248C22⋊D5—121no—
249C22⋊D5#6714yescomplemented
250C2×Dic5—31no—
251C2×Dic5—31no—
252C2×Dic5—121no—
253C2×Dic5C22×D311yescharacteristic
254C2×Dic5C22×D311yescharacteristic
255D20—22no—
256D20—62no—
257D20—62no—
258D20—121no—
259C4×D5—22no—
260C4×D5—22no—
261C4×D5—62no—
262C4×D5—121no—
263Dic10—22no—
264C2×#41—51no—
265C22×D4—151no—
266#124—151no—
267#123—31no—
268#123—151no—
269C22⋊Q8—151no—
270#121—151no—
271#121—151no—
272#121—151no—
273#120—151no—
274#120—151no—
275C4×D4—151no—
276C4×D4—151no—
277C2×C22⋊C4—151no—
278C2×C22⋊C4—151no—
279C2×C3×C5—22no—
280C2×C3×C5C22×D411yescharacteristic
281C2×C3×C5C2×#4111yescharacteristic
282C2×C3×C5H(5,𝔽2)11yescharacteristic
283D15—22no—
284D15—41no—
285C3×D5—22no—
286C3×D5—41no—
287C5×D3—41no—
288C23×C3—51no—
289C23×C3—51no—
290C23×C3C22×D511yescharacteristic
291C22×D3—51no—
292C22×D3—51no—
293C22×D3—102no—
294C22×D3—102no—
295C22×D3—102no—
296C22×D3—102no—
297C22×D3—201no—
298C22×D3—201no—
299C22×D3C22×D511yescharacteristic
300C3×Q8—102no—
301C3×D4—54no—
302C3×D4—102no—
303C3×D4—102no—
304C2×C3×C4—22no—
305C2×C3×C4—51no—
306C2×C3×C4—51no—
307C2×C3×C4—102no—
308C2×C3×C4—102no—
309C2×C3×C4C22×D511yescharacteristic
310C2×C3×C4C22×D511yescharacteristic
311#67—22no—
312#67—102no—
313#67—102no—
314#67—201no—
315#67—201no—
316C2×Dic3—51no—
317C2×Dic3—51no—
318C2×Dic3—201no—
319C2×Dic3—201no—
320C2×Dic3C22×D511yescharacteristic
321C2×Dic3C22×D511yescharacteristic
322C2×Dic3C22×D511yescharacteristic
323D12—102no—
324C4×D3—102no—
325C22×C5—21no—
326C22×C5—21no—
327C22×C5—61no—
328C22×C5—61no—
329C22×C5—61no—
330C22×C5C2×#6712yes—
331C22×C5C23×D311yescharacteristic
332C2×D5—21no—
333C2×D5—21no—
334C2×D5—21no—
335C2×D5—21no—
336C2×D5—21no—
337C2×D5—32no—
338C2×D5—61no—
339C2×D5—61no—
340C2×D5—61no—
341C2×D5—61no—
342C2×D5—61no—
343C2×D5—124no—
344C2×D5—124no—
345C2×D5C2×#6712yes—
346C4×C5—21no—
347C4×C5—21no—
348C4×C5—61no—
349C4×C5—61no—
350C4×C5—61no—
351Dic5—21no—
352Dic5—61no—
353Dic5—61no—
354Dic5C2×#6712yes—
355C24—151no—
356C24—151no—
357#41—104no—
358C2×Q8—51no—
359C2×D4—31no—
360C2×D4—51no—
361C2×D4—51no—
362C2×D4—51no—
363C2×D4—151no—
364C2×D4—151no—
365C2×D4—151no—
366C2×D4—151no—
367C2×D4—151no—
368C2×D4—304no—
369C22×C4—51no—
370C22×C4—51no—
371C22×C4—151no—
372C22×C4—151no—
373C22×C4—151no—
374C22×C4D3×D511yescharacteristic, complemented
375C4⋊C4—31no—
376C4⋊C4—31no—
377C4⋊C4—151no—
378C4⋊C4—151no—
379C22⋊C4—31no—
380C22⋊C4—31no—
381C22⋊C4—31no—
382C22⋊C4—151no—
383C22⋊C4—151no—
384C22⋊C4—151no—
385C22⋊C4—151no—
386C22⋊C4—151no—
387C22⋊C4—151no—
388C22⋊C4—151no—
389C22⋊C4—151no—
390C22⋊C4—151no—
391C42—151no—
392C3×C5#54611yescharacteristic, complemented, Hall
393C22×C3—21no—
394C22×C3—21no—
395C22×C3—52no—
396C22×C3—101no—
397C22×C3—101no—
398C22×C3—101no—
399C22×C3—101no—
400C22×C3—101no—
401C22×C3D4×D512yes—
402C22×C3C23×D511yescharacteristic
403C2×D3—21no—
404C2×D3—21no—
405C2×D3—21no—
406C2×D3—52no—
407C2×D3—101no—
408C2×D3—101no—
409C2×D3—101no—
410C2×D3—101no—
411C2×D3—101no—
412C2×D3—204no—
413C2×D3—204no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—52no—
417C3×C4—101no—
418Dic3—21no—
419Dic3—21no—
420Dic3—21no—
421Dic3—101no—
422Dic3—101no—
423C2×C5—22no—
424C2×C5—121no—
425C2×C5D3×#4111yescharacteristic
426C2×C5#100911yescharacteristic
427C2×C5C22×#6711yescharacteristic
428D5—22no—
429D5—41no—
430D5—62no—
431D5—121no—
432C23—31no—
433C23—51no—
434C23—51no—
435C23—151no—
436C23—151no—
437C23—302no—
438C23—302no—
439C23—302no—
440C23—302no—
441C23—601no—
442C23—601no—
443C23C2×D3×D511yescharacteristic
444Q8—102no—
445D4—54no—
446D4—62no—
447D4—102no—
448D4—102no—
449D4—302no—
450D4—302no—
451D4—302no—
452D4—601no—
453D4—601no—
454C2×C4—22no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—31no—
458C2×C4—51no—
459C2×C4—51no—
460C2×C4—102no—
461C2×C4—102no—
462C2×C4—151no—
463C2×C4—151no—
464C2×C4—302no—
465C2×C4—601no—
466C2×C4—601no—
467C2×C4C2×D3×D511yescharacteristic
468C2×C4C2×D3×D511yescharacteristic
469C2×C3—22no—
470C2×C3—102no—
471C2×C3—201no—
472C2×C3C2×D4×D511yescharacteristic
473C2×C3D5×#4111yescharacteristic
474C2×C3#414911yescharacteristic
475D3—41no—
476D3—102no—
477D3—201no—
478C5#582911yescharacteristic, complemented, Sylow
479C22—21no—
480C22—21no—
481C22—52no—
482C22—61no—
483C22—61no—
484C22—61no—
485C22—101no—
486C22—101no—
487C22—101no—
488C22—101no—
489C22—101no—
490C22—152no—
491C22—301no—
492C22—301no—
493C22—301no—
494C22—301no—
495C22—301no—
496C22—604no—
497C22—604no—
498C22D5×#6712yes—
499C22C22×D3×D511yescharacteristic
500C4—21no—
501C4—21no—
502C4—52no—
503C4—61no—
504C4—61no—
505C4—61no—
506C4—101no—
507C4—301no—
508C4—301no—
509C3#6598811yescharacteristic, complemented, Sylow
510C2—22no—
511C2—102no—
512C2—121no—
513C2—201no—
514C2—302no—
515C2—601no—
516C2#9201611yescharacteristic
517C2#9201911yescharacteristic
518C2C2×D5×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC22×C3×C4×C5C22
hypercenterC22×C4D3×D5
hypocenterC3×C5#546
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. C2×C3×#709C2semidirect
2. C2×#6790C2semidirect
3. C2×#6714C2semidirect
4. C5×#929C2semidirect
5. #91572C2semidirect
6. #91571C2semidirect
7. #91559C2semidirect
8. #91474C2semidirect
9. D5×(C2×D3)⋊C4C2semidirect
10. #91448C2semidirect
11. #91444C2semidirect
12. #91411C2semidirect
13. #91409C2semidirect
14. #91348C2semidirect
15. #91326C2semidirect
19. C22×C3×C4×C5C22semidirect
20. C22×Dic15C22semidirect
23. C2×C3×C22⋊D5C22semidirect
25. C2×C3×D20C22semidirect
26. C2×C3×C4×D5C22semidirect
27. C2×C3×C4×D5C22semidirect
28. C2×C3×Dic10C22semidirect
33. C2×#1202C22semidirect
34. C2×#1201C22semidirect
36. C2×D5×Dic3C22semidirect
39. #6714C22semidirect
40. #6714C22semidirect
41. C5×#217C22semidirect
42. C5×(C2×D3)⋊C4C22semidirect
43. C5×(C2×D3)⋊C4C22semidirect
44. C5×Dic3⋊C4C22semidirect
45. C5×Dic3⋊C4C22semidirect
46. #6669C22semidirect
47. #6668C22semidirect
49. #6667C22semidirect
50. (C2×D3)⋊Dic5C22semidirect
51. #6665C22semidirect
52. #6665C22semidirect
53. Dic3×Dic5C22semidirect
56. C2×#709D3semidirect
93. C3×C22⋊D5D4semidirect
118. #929D5semidirect
125. C22×C4×C5C2×D3semidirect
129. C2×C22⋊D5C2×D3semidirect
136. C2×D20C2×D3semidirect
139. C2×C4×D5C2×D3semidirect
140. C2×C4×D5C2×D3semidirect
141. C2×Dic10C2×D3semidirect
170. C2×D15#41semidirect
199. C22×C3×C4C2×D5semidirect
212. #217C2×D5semidirect
220. (C2×D3)⋊C4C2×D5semidirect
221. (C2×D3)⋊C4C2×D5semidirect
224. Dic3⋊C4C2×D5semidirect
225. Dic3⋊C4C2×D5semidirect
249. C22⋊D5#67semidirect
374. C22×C4D3×D5semidirect
392. C3×C5#546semidirect
478. C5#5829semidirect
509. C3#65988semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#7092
C2×#67902
C2×#67142
C5×#9292
#915722
#915712
#915592
#914742
D5×(C2×D3)⋊C42
#914482
#914442
#914112
#914092
#913482
#913262
#659883
#58295