Finite Group Databasebeta

← #11755071

Subgroups — #11755071

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×#6819C211yesmaximal, characteristic, complemented
2C2×D5×#67C211yesmaximal, characteristic, complemented
3C5×#939C211yesmaximal, characteristic, complemented
4C3×#4083C211yesmaximal, characteristic, complemented
5#91577C211yesmaximal, characteristic, complemented
6#91571C211yesmaximal, characteristic, complemented
7#91559C211yesmaximal, characteristic, complemented
8#91556C211yesmaximal, characteristic, complemented
9#91543C211yesmaximal, characteristic, complemented
10C2×#6665C211yesmaximal, characteristic, complemented
11#91533C211yesmaximal, characteristic, complemented
12#91473C211yesmaximal, characteristic, complemented
13#91462C211yesmaximal, characteristic, complemented
14#91431C211yesmaximal, characteristic, complemented
15#91354C211yesmaximal, characteristic, complemented
16#65944—31nomaximal, Hall
17C23×C3×D5C2211yescharacteristic
18C22×D3×D5C2211yescharacteristic
19C2×C3×C5×D4C2211yescharacteristic, complemented
20C2×#1220C2211yescharacteristic
21C2×#1220C2211yescharacteristic, complemented
22C22×Dic15C2211yescharacteristic, complemented
23C22×Dic15C2211yescharacteristic, complemented
24#6819—24no—
25C2×C4×D15C2211yescharacteristic, complemented
26C2×Dic30C2211yescharacteristic, complemented
27C2×C5×#67C2211yescharacteristic
28C2×C5×#67C2211yescharacteristic, complemented
29C22×C5×Dic3C2211yescharacteristic, complemented
30C2×C3×C22⋊D5C2211yescharacteristic
31C2×C3×C22⋊D5C2211yescharacteristic, complemented
32D5×#67—24no—
33C2×#1202C2211yescharacteristic
34C2×#1201C2211yescharacteristic
35C2×#1200C2211yescharacteristic, complemented
36C2×D5×Dic3C2211yescharacteristic
37C5×#217C2211yescharacteristic, complemented
38C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
39C5×Dic3⋊C4C2211yescharacteristic, complemented
40C3×C22⋊Dic5C2211yescharacteristic, complemented
41C3×#685C2211yescharacteristic
42C3×#685C2211yescharacteristic, complemented
43#6669C2211yescharacteristic, complemented
44#6668C2211yescharacteristic, complemented
45#6668C2211yescharacteristic, complemented
46#6667C2211yescharacteristic, complemented
47(C2×D3)⋊Dic5C2211yescharacteristic, complemented
48(C2×D3)⋊Dic5C2211yescharacteristic, complemented
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic
51#6665C2211yescharacteristic, complemented
52#6665C2211yescharacteristic, complemented
53Dic3×Dic5C2211yescharacteristic, complemented
54#5591—51nomaximal, Hall
55C2×#711—31no—
56C2×D4×D5—31no—
57C5×#121—31no—
58#4085—31no—
59#4083—31no—
60#4083D311yescharacteristic, complemented
61#4081—31no—
62C4×C22⋊D5—31no—
63C2×#685—31no—
64#4042—31no—
65#4040—31no—
66#4031—31no—
67#4030—31no—
68#4027—31no—
69D5×C22⋊C4—31no—
70C23×C3×C5C2311yescharacteristic
71C23×C3×C5C2311yescharacteristic
72C22×D15C2311yescharacteristic
73C22×C5×D3C2311yescharacteristic
74C22×C3×D5—22no—
75C22×C3×D5—22no—
76C22×C3×D5—41no—
77C22×C3×D5C2311yescharacteristic
78C22×C3×D5C2311yescharacteristic
79C2×D3×D5—22no—
80C2×D3×D5—22no—
81C2×D3×D5—41no—
82C3×C5×D4—22no—
83C2×C3×C4×C5C2311yescharacteristic
84#1220—22no—
85#1220D414yescomplemented
86C2×Dic15—22no—
87C2×Dic15—22no—
88C2×Dic15C2311yescharacteristic
89C2×Dic15C2311yescharacteristic
90C2×Dic15C2311yescharacteristic
91C4×D15—22no—
92Dic30—22no—
93C5×#67—22no—
94C5×#67—41no—
95C2×C5×Dic3—41no—
96C2×C5×Dic3C2311yescharacteristic
97C2×C5×Dic3C2311yescharacteristic
98C2×C5×Dic3C2311yescharacteristic
99C3×C22⋊D5—22no—
100C3×C22⋊D5—41no—
101C2×C3×Dic5C2311yescharacteristic
102C2×C3×Dic5C2311yescharacteristic
103#1202—22no—
104#1201—22no—
105#1200—41no—
106D5×Dic3—22no—
107C22×#67—51no—
108C2×#237—51no—
109C3×#120—51no—
110C2×#217—51no—
111#939—51no—
112#939D511yescharacteristic, complemented
113#938—51no—
114#937—51no—
115D4×Dic3—51no—
116#886—51no—
117#885—51no—
118#883—51no—
119#67⋊C4—51no—
120D3×C22⋊C4—51no—
121#878—51no—
122C23×D5—31no—
123C23×D5C2×D311yescharacteristic
124C2×C5×D4—31no—
125C2×C5×D4—31no—
126C2×C5×D4C2×D311yescharacteristic, complemented
127C22×C4×C5—31no—
128C2×C22⋊D5—31no—
129C2×C22⋊D5—31no—
130C2×C22⋊D5—31no—
131C2×C22⋊D5C2×D311yescharacteristic
132C2×C22⋊D5C2×D311yescharacteristic, complemented
133C22×Dic5—31no—
134C22×Dic5—31no—
135#711—64no—
136D4×D5—64no—
137C2×D20—31no—
138C2×C4×D5—31no—
139C2×C4×D5—31no—
140C2×C4×D5—31no—
141C2×Dic10—31no—
142C5×C4⋊C4—31no—
143C5×C22⋊C4—31no—
144C5×C22⋊C4—31no—
145C22⋊Dic5—31no—
146C22⋊Dic5—31no—
147C22⋊Dic5C2×D311yescharacteristic, complemented
148#685—31no—
149#685—31no—
150#685—31no—
151#685—31no—
152#685—31no—
153#685C2×D311yescharacteristic
154#685C2×D311yescharacteristic, complemented
155#683—31no—
156#683—31no—
157#683—31no—
158C4×Dic5—31no—
159#546—151noSylow
160C22×C3×C5—21no—
161C22×C3×C5—21no—
162C22×C3×C5—21no—
163C22×C3×C5—21no—
164C22×C3×C5—21no—
165C22×C3×C5C2×D412yes—
166C22×C3×C5C2411yescharacteristic
167C2×D15—21no—
168C2×D15—21no—
169C2×D15C2×D412yes—
170C2×C5×D3—21no—
171C2×C5×D3—21no—
172C2×C5×D3—21no—
173C2×C3×D5—21no—
174C2×C3×D5—21no—
175C2×C3×D5—21no—
176C2×C3×D5—21no—
177C2×C3×D5—21no—
178C2×C3×D5—44no—
179C2×C3×D5#4112yescomplemented
180D3×D5—44no—
181C3×C4×C5—21no—
182Dic15—21no—
183Dic15—21no—
184Dic15C2×D412yes—
185C3×Dic5—21no—
186C3×Dic5—21no—
187C5×Dic3—21no—
188C5×Dic3—21no—
189C5×Dic3—21no—
190C24×C3—51no—
191C23×D3—51no—
192C2×C3×D4—51no—
193C2×C3×D4—51no—
194C2×C3×D4C2×D511yescharacteristic, complemented
195C2×#67—51no—
196C2×#67—51no—
197C2×#67—51no—
198C2×#67—51no—
199C2×#67—104no—
200C2×#67C2×D511yescharacteristic
201C2×#67C2×D511yescharacteristic, complemented
202C22×Dic3—51no—
203C22×Dic3—51no—
204C22×Dic3—51no—
205C22×Dic3C2×D511yescharacteristic, complemented
206#237—104no—
207C2×C4×D3—51no—
208C2×C4×D3—51no—
209C2×Dic6—51no—
210C3×C22⋊C4—51no—
211C3×C22⋊C4—51no—
212C3×C22⋊C4—51no—
213#217—51no—
214#217—51no—
215#217—51no—
216#217—51no—
217#217C2×D511yescharacteristic, complemented
218(C2×D3)⋊C4—51no—
219(C2×D3)⋊C4—51no—
220(C2×D3)⋊C4—51no—
221(C2×D3)⋊C4C2×D511yescharacteristic, complemented
222C4⋊Dic3—51no—
223C4⋊Dic3—51no—
224Dic3⋊C4—51no—
225Dic3⋊C4C2×D511yescharacteristic, complemented
226C4×Dic3—51no—
227C23×C5—31no—
228C23×C5C22×D311yescharacteristic
229C23×C5C22×D311yescharacteristic
230C22×D5—22no—
231C22×D5—22no—
232C22×D5—31no—
233C22×D5—41no—
234C22×D5—62no—
235C22×D5—62no—
236C22×D5—121no—
237C22×D5C22×D311yescharacteristic
238C22×D5C22×D311yescharacteristic
239C5×D4—22no—
240C5×D4—62no—
241C5×D4—121no—
242C2×C4×C5—31no—
243C2×C4×C5—31no—
244C2×C4×C5—31no—
245C2×C4×C5—121no—
246C2×C4×C5C22×D311yescharacteristic
247C22⋊D5—22no—
248C22⋊D5—34no—
249C22⋊D5—41no—
250C22⋊D5—62no—
251C22⋊D5—62no—
252C2×Dic5—31no—
253C2×Dic5—31no—
254C2×Dic5—31no—
255C2×Dic5—62no—
256C2×Dic5—62no—
257C2×Dic5C22×D311yescharacteristic
258C2×Dic5C22×D311yescharacteristic
259D20—62no—
260C4×D5—62no—
261C4×D5—62no—
262C4×D5—121no—
263Dic10—62no—
264C2×#41—151no—
265C22×D4—151no—
266#124—151no—
267#123—151no—
268#123—151no—
269C22⋊Q8—151no—
270#121—31no—
271#121—151no—
272#121—151no—
273#120—51no—
274#120—151no—
275C4×D4—151no—
276C4×D4—151no—
277C2×C22⋊C4—151no—
278C2×C22⋊C4—151no—
279C2×C3×C5—22no—
280C2×C3×C5—41no—
281C2×C3×C5C22×D411yescharacteristic
282C2×C3×C5C2×#4111yescharacteristic
283C2×C3×C5H(5,𝔽2)11yescharacteristic
284D15—22no—
285C3×D5—22no—
286C3×D5—41no—
287C5×D3—41no—
288C23×C3—51no—
289C23×C3—51no—
290C23×C3—102no—
291C23×C3—102no—
292C23×C3—201no—
293C23×C3C22×D511yescharacteristic
294C23×C3C22×D511yescharacteristic
295C22×D3—51no—
296C22×D3—102no—
297C22×D3—102no—
298C22×D3—201no—
299C22×D3C22×D511yescharacteristic
300C3×D4—22no—
301C3×D4—102no—
302C3×D4—201no—
303C2×C3×C4—51no—
304C2×C3×C4—51no—
305C2×C3×C4C22×D511yescharacteristic
306#67—22no—
307#67—41no—
308#67—54no—
309#67—102no—
310#67—102no—
311#67—102no—
312C2×Dic3—41no—
313C2×Dic3—51no—
314C2×Dic3—51no—
315C2×Dic3—51no—
316C2×Dic3—102no—
317C2×Dic3—102no—
318C2×Dic3—102no—
319C2×Dic3C22×D511yescharacteristic
320C2×Dic3C22×D511yescharacteristic
321C2×Dic3C22×D511yescharacteristic
322C4×D3—102no—
323C4×D3—201no—
324Dic6—102no—
325C22×C5—21no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—61no—
331C22×C5—61no—
332C22×C5—61no—
333C22×C5D3×D412yes—
334C22×C5C23×D311yescharacteristic
335C2×D5—21no—
336C2×D5—21no—
337C2×D5—21no—
338C2×D5—21no—
339C2×D5—21no—
340C2×D5—32no—
341C2×D5—44no—
342C2×D5—61no—
343C2×D5—61no—
344C2×D5—124no—
345C2×D5#23712yescomplemented
346C4×C5—21no—
347C4×C5—61no—
348C4×C5—61no—
349C4×C5—61no—
350Dic5—21no—
351Dic5—21no—
352Dic5—32no—
353Dic5—61no—
354Dic5—61no—
355C24—51no—
356C24—151no—
357#41—304no—
358C2×Q8—151no—
359C2×D4—31no—
360C2×D4—31no—
361C2×D4—51no—
362C2×D4—51no—
363C2×D4—151no—
364C2×D4—151no—
365C2×D4—151no—
366C2×D4—151no—
367C2×D4—304no—
368C2×D4D3×D511yescharacteristic, complemented
369C22×C4—31no—
370C22×C4—151no—
371C22×C4—151no—
372C22×C4—151no—
373C22×C4—151no—
374C22×C4—151no—
375C4⋊C4—31no—
376C4⋊C4—151no—
377C4⋊C4—151no—
378C4⋊C4—151no—
379C22⋊C4—31no—
380C22⋊C4—31no—
381C22⋊C4—51no—
382C22⋊C4—51no—
383C22⋊C4—51no—
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—21no—
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—52no—
399C22×C3—101no—
400C22×C3—101no—
401C22×C3—101no—
402C22×C3—101no—
403C22×C3—101no—
404C22×C3—204no—
405C22×C3D4×D512yes—
406C22×C3C23×D511yescharacteristic
407C2×D3—21no—
408C2×D3—21no—
409C2×D3—21no—
410C2×D3—52no—
411C2×D3—101no—
412C2×D3—101no—
413C2×D3—204no—
414C3×C4—21no—
415C3×C4—101no—
416C3×C4—101no—
417Dic3—21no—
418Dic3—21no—
419Dic3—21no—
420Dic3—52no—
421Dic3—101no—
422Dic3—101no—
423C2×C5—22no—
424C2×C5—41no—
425C2×C5—121no—
426C2×C5C2×D3×D411yescharacteristic
427C2×C5C2×#23711yescharacteristic
428C2×C5#100411yescharacteristic
429D5—22no—
430D5—41no—
431D5—62no—
432C23—31no—
433C23—51no—
434C23—51no—
435C23—102no—
436C23—102no—
437C23—151no—
438C23—201no—
439C23—302no—
440C23—302no—
441C23—601no—
442C23C2×D3×D511yescharacteristic
443C23C2×D3×D511yescharacteristic
444Q8—302no—
445D4—22no—
446D4—62no—
447D4—102no—
448D4—121no—
449D4—154no—
450D4—201no—
451D4—302no—
452D4—302no—
453D4—302no—
454C2×C4—31no—
455C2×C4—31no—
456C2×C4—31no—
457C2×C4—51no—
458C2×C4—51no—
459C2×C4—121no—
460C2×C4—151no—
461C2×C4—151no—
462C2×C4—151no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—601no—
468C2×C4C2×D3×D511yescharacteristic
469C2×C3—22no—
470C2×C3—41no—
471C2×C3—102no—
472C2×C3—201no—
473C2×C3C2×D4×D511yescharacteristic
474C2×C3#414411yescharacteristic
475C2×C3D5×#4111yescharacteristic
476D3—41no—
477D3—102no—
478C5#559111yescharacteristic, complemented, Sylow
479C22—21no—
480C22—21no—
481C22—21no—
482C22—21no—
483C22—21no—
484C22—52no—
485C22—61no—
486C22—61no—
487C22—61no—
488C22—101no—
489C22—101no—
490C22—101no—
491C22—101no—
492C22—101no—
493C22—152no—
494C22—204no—
495C22—301no—
496C22—301no—
497C22—604no—
498C22#679012yes—
499C22C22×D3×D511yescharacteristic
500C4—21no—
501C4—61no—
502C4—61no—
503C4—61no—
504C4—101no—
505C4—101no—
506C4—152no—
507C4—301no—
508C4—301no—
509C3#6594411yescharacteristic, complemented, Sylow
510C2—22no—
511C2—41no—
512C2—102no—
513C2—121no—
514C2—201no—
515C2—302no—
516C2D5×#23711yescharacteristic
517C2#9202511yescharacteristic
518C2C2×#679011yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×D4C22
hypercenterC2×D4D3×D5
hypocenterC3×C5#546
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×#6819C2semidirect
2. C2×D5×#67C2semidirect
3. C5×#939C2semidirect
4. C3×#4083C2semidirect
5. #91577C2semidirect
6. #91571C2semidirect
7. #91559C2semidirect
8. #91556C2semidirect
9. #91543C2semidirect
10. C2×#6665C2semidirect
11. #91533C2semidirect
12. #91473C2semidirect
13. #91462C2semidirect
14. #91431C2semidirect
15. #91354C2semidirect
19. C2×C3×C5×D4C22semidirect
21. C2×#1220C22semidirect
22. C22×Dic15C22semidirect
23. C22×Dic15C22semidirect
25. C2×C4×D15C22semidirect
26. C2×Dic30C22semidirect
28. C2×C5×#67C22semidirect
29. C22×C5×Dic3C22semidirect
31. C2×C3×C22⋊D5C22semidirect
35. C2×#1200C22semidirect
37. C5×#217C22semidirect
38. C5×(C2×D3)⋊C4C22semidirect
39. C5×Dic3⋊C4C22semidirect
40. C3×C22⋊Dic5C22semidirect
42. C3×#685C22semidirect
43. #6669C22semidirect
44. #6668C22semidirect
45. #6668C22semidirect
46. #6667C22semidirect
47. (C2×D3)⋊Dic5C22semidirect
48. (C2×D3)⋊Dic5C22semidirect
51. #6665C22semidirect
52. #6665C22semidirect
53. Dic3×Dic5C22semidirect
60. #4083D3semidirect
85. #1220D4semidirect
112. #939D5semidirect
126. C2×C5×D4C2×D3semidirect
132. C2×C22⋊D5C2×D3semidirect
147. C22⋊Dic5C2×D3semidirect
154. #685C2×D3semidirect
179. C2×C3×D5#41semidirect
194. C2×C3×D4C2×D5semidirect
201. C2×#67C2×D5semidirect
205. C22×Dic3C2×D5semidirect
217. #217C2×D5semidirect
221. (C2×D3)⋊C4C2×D5semidirect
225. Dic3⋊C4C2×D5semidirect
345. C2×D5#237semidirect
368. C2×D4D3×D5semidirect
392. C3×C5#546semidirect
478. C5#5591semidirect
509. C3#65944semidirect

Maximal subgroups

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

subgroupindex
C2×#68192
C2×D5×#672
C5×#9392
C3×#40832
#915772
#915712
#915592
#915562
#915432
C2×#66652
#915332
#914732
#914622
#914312
#913542
#659443
#55915