Finite Group Databasebeta

← #11753047

Subgroups — #11753047

Order 960.

500 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91770C211yesmaximal, characteristic, complemented
2C5×#878C211yesmaximal, characteristic, complemented
3C3×#4028C211yesmaximal, characteristic, complemented
4#91569C211yesmaximal, characteristic, complemented
5#91564C211yesmaximal, characteristic, complemented
6#91559C211yesmaximal, characteristic, complemented
7C2×#6665C211yesmaximal, characteristic, complemented
8#91465C211yesmaximal, characteristic, complemented
9#91455C211yesmaximal, characteristic, complemented
10#91409C211yesmaximal, characteristic, complemented
11#91407C211yesmaximal, characteristic, complemented
12#91368C211yesmaximal, characteristic, complemented
13#91366C211yesmaximal, characteristic, complemented
14#91361C211yesmaximal, characteristic, complemented
15#91354C211yesmaximal, characteristic, complemented
16#65978—31nomaximal, Hall
17C23×C3×D5C2211yescharacteristic
18C2×#1220C2211yescharacteristic
19C22×Dic15C2211yescharacteristic
20C2×C4×D15C2211yescharacteristic, complemented
21C22×C5×Dic3C2211yescharacteristic
22C2×C5×Dic6C2211yescharacteristic, complemented
23C2×C3×C22⋊D5C2211yescharacteristic
24C2×C3×D20C2211yescharacteristic
25C2×C3×D20C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1202C2211yescharacteristic
28C2×#1202C2211yescharacteristic, complemented
29C2×D5×Dic3C2211yescharacteristic, complemented
30C3×C5×C22⋊C4C2211yescharacteristic
31#6714C2211yescharacteristic, complemented
32#6712C2211yescharacteristic, complemented
33C4×Dic15C2211yescharacteristic, complemented
34C5×#217C2211yescharacteristic
35C5×C4⋊Dic3C2211yescharacteristic, complemented
36C5×Dic3⋊C4C2211yescharacteristic, complemented
37C5×Dic3⋊C4C2211yescharacteristic, complemented
38C3×#685C2211yescharacteristic
39C3×#685C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic, complemented
41#6668C2211yescharacteristic, complemented
42#6667C2211yescharacteristic, complemented
43#6665C2211yescharacteristic
44#6665C2211yescharacteristic
45#6665C2211yescharacteristic
46#6665C2211yescharacteristic
47#6665C2211yescharacteristic
48#6665C2211yescharacteristic
49#6665C2211yescharacteristic, complemented
50#6665C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5593—51nomaximal, Hall
53C5×C22⋊Q8—31no—
54#4093—31no—
55#4093—31no—
56#4076—31no—
57C2×#685—31no—
58#4044—31no—
59#4044—31no—
60#4041—31no—
61#4041—31no—
62#4040—31no—
63#4040—31no—
64#4028—31no—
65#4028D311yescharacteristic, complemented
66#4027—31no—
67#4027—31no—
68C23×C3×C5C2311yescharacteristic
69C22×D15C2311yescharacteristic
70C22×C3×D5—22no—
71C22×C3×D5—41no—
72C22×C3×D5—41no—
73C22×C3×D5C2311yescharacteristic
74C22×C3×D5C2311yescharacteristic
75C22×C3×D5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78#1220—22no—
79C2×Dic15—41no—
80C2×Dic15C2311yescharacteristic
81C2×Dic15C2311yescharacteristic
82C2×Dic15C2311yescharacteristic
83C4×D15—41no—
84C2×C5×Dic3—41no—
85C2×C5×Dic3C2311yescharacteristic
86C2×C5×Dic3C2311yescharacteristic
87C2×C5×Dic3C2311yescharacteristic
88C2×C5×Dic3C2311yescharacteristic
89C5×Dic6—41no—
90C3×C22⋊D5—22no—
91C2×C3×Dic5C2311yescharacteristic
92C3×D20—41no—
93C3×D20—41no—
94#1202—41no—
95#1202—41no—
96#1202—41no—
97D5×Dic3—41no—
98C3×#120—51no—
99#953—51no—
100C2×#217—51no—
101#939—51no—
102#939—51no—
103#938—51no—
104#936—51no—
105#935—51no—
106D4×Dic3—51no—
107#885—51no—
108#883—51no—
109#67⋊C4—51no—
110#879—51no—
111#879—51no—
112#878D511yescharacteristic, complemented
113C23×D5C2×D311yescharacteristic
114C2×C5×Q8—31no—
115C22×C4×C5—31no—
116C2×C22⋊D5—31no—
117C2×C22⋊D5C2×D311yescharacteristic
118C22×Dic5—31no—
119C2×D20—31no—
120C2×D20—31no—
121C2×D20—31no—
122C2×D20C2×D311yescharacteristic
123C2×D20C2×D311yescharacteristic
124C2×C4×D5—31no—
125C2×C4×D5—31no—
126C5×C4⋊C4—31no—
127C5×C4⋊C4—31no—
128C5×C4⋊C4—31no—
129C5×C22⋊C4—31no—
130C5×C22⋊C4C2×D311yescharacteristic
131#685—31no—
132#685—31no—
133#685—31no—
134#685—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685—31no—
140#685—31no—
141#685C2×D311yescharacteristic
142#685C2×D311yescharacteristic
143C4⋊Dic5—31no—
144#683—31no—
145#683—31no—
146C4×Dic5—31no—
147C4×Dic5—31no—
148#538—151noSylow
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5#4112yes—
152C22×C3×C5C2411yescharacteristic
153C2×D15—21no—
154C2×D15—21no—
155C2×D15—21no—
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5—21no—
159C2×C3×D5—21no—
160C2×C3×D5—21no—
161C2×C3×D5—21no—
162C2×C3×D5—21no—
163C2×C3×D5—21no—
164C2×C3×D5—21no—
165C2×C3×D5—44no—
166C3×C4×C5—21no—
167C3×C4×C5—21no—
168Dic15—21no—
169Dic15—21no—
170Dic15—21no—
171C3×Dic5—21no—
172C5×Dic3—21no—
173C5×Dic3—21no—
174C5×Dic3—21no—
175C5×Dic3—21no—
176C24×C3—51no—
177C2×C3×D4—51no—
178C2×C3×D4—51no—
179C2×C3×D4—51no—
180C2×#67—51no—
181C2×#67—51no—
182C2×#67—51no—
183C2×#67—51no—
184C22×Dic3—51no—
185C22×Dic3—51no—
186C22×Dic3C2×D511yescharacteristic
187C2×C4×D3—51no—
188C2×Dic6C2×D511yescharacteristic, complemented
189C3×C22⋊C4—51no—
190C3×C22⋊C4—51no—
191C3×C22⋊C4C2×D511yescharacteristic
192#217—51no—
193#217—51no—
194#217—51no—
195#217—51no—
196#217—51no—
197#217—51no—
198#217—51no—
199#217—51no—
200#217C2×D511yescharacteristic
201(C2×D3)⋊C4—51no—
202(C2×D3)⋊C4—51no—
203C4⋊Dic3—51no—
204C4⋊Dic3C2×D511yescharacteristic, complemented
205Dic3⋊C4—51no—
206Dic3⋊C4—51no—
207Dic3⋊C4C2×D511yescharacteristic, complemented
208Dic3⋊C4C2×D511yescharacteristic, complemented
209C4×Dic3—51no—
210C4×Dic3—51no—
211C23×C5C22×D311yescharacteristic
212C22×D5—22no—
213C22×D5—31no—
214C22×D5—41no—
215C22×D5—41no—
216C22×D5C22×D311yescharacteristic
217C22×D5C22×D311yescharacteristic
218C22×D5C22×D311yescharacteristic
219C5×Q8—121no—
220C2×C4×C5—31no—
221C2×C4×C5—31no—
222C2×C4×C5—31no—
223C2×C4×C5—31no—
224C2×C4×C5—121no—
225C2×C4×C5C22×D311yescharacteristic
226C2×C4×C5C22×D311yescharacteristic
227C22⋊D5—22no—
228C22⋊D5—62no—
229C2×Dic5—31no—
230C2×Dic5—31no—
231C2×Dic5—31no—
232C2×Dic5—121no—
233C2×Dic5C22×D311yescharacteristic
234D20—41no—
235D20—41no—
236D20—121no—
237D20—121no—
238D20—121no—
239C4×D5—121no—
240C4×D5—121no—
241#126—151no—
242#126—151no—
243#124—151no—
244#124—151no—
245#123—151no—
246#123—151no—
247C22⋊Q8—31no—
248#121—151no—
249#121—151no—
250#121—151no—
251#120—51no—
252#120—151no—
253C4×D4—151no—
254C4×D4—151no—
255C2×C22⋊C4—151no—
256C2×C3×C5—22no—
257C2×C3×C5C2×#4111yescharacteristic
258C2×C3×C5H(5,𝔽2)11yescharacteristic
259C2×C3×C5H(5,𝔽2)11yescharacteristic
260D15—41no—
261C3×D5—41no—
262C3×D5—41no—
263C3×D5—41no—
264C23×C3—51no—
265C23×C3—51no—
266C23×C3—51no—
267C23×C3—102no—
268C23×C3—201no—
269C23×C3—201no—
270C23×C3C22×D511yescharacteristic
271C22×D3—51no—
272C3×D4—102no—
273C3×D4—201no—
274C3×D4—201no—
275C2×C3×C4—51no—
276C2×C3×C4C22×D511yescharacteristic
277C2×C3×C4C22×D511yescharacteristic
278#67—102no—
279#67—201no—
280#67—201no—
281#67—201no—
282C2×Dic3—41no—
283C2×Dic3—51no—
284C2×Dic3—51no—
285C2×Dic3—51no—
286C2×Dic3—201no—
287C2×Dic3—201no—
288C2×Dic3C22×D511yescharacteristic
289C2×Dic3C22×D511yescharacteristic
290C2×Dic3C22×D511yescharacteristic
291C2×Dic3C22×D511yescharacteristic
292C4×D3—201no—
293Dic6—41no—
294C22×C5—21no—
295C22×C5—21no—
296C22×C5#23712yes—
297C22×C5C23×D311yescharacteristic
298C2×D5—21no—
299C2×D5—21no—
300C2×D5—21no—
301C2×D5—21no—
302C2×D5—21no—
303C2×D5—21no—
304C2×D5—21no—
305C2×D5—21no—
306C2×D5—21no—
307C2×D5—44no—
308C2×D5—61no—
309C2×D5—61no—
310C2×D5—61no—
311C4×C5—21no—
312C4×C5—21no—
313C4×C5—61no—
314C4×C5—61no—
315C4×C5—61no—
316C4×C5—61no—
317Dic5—21no—
318Dic5—61no—
319Dic5—61no—
320Dic5—61no—
321C24—51no—
322C2×Q8—31no—
323C2×D4—51no—
324C2×D4—51no—
325C2×D4—51no—
326C2×D4—151no—
327C2×D4—151no—
328C2×D4—151no—
329C2×D4—151no—
330C22×C4—31no—
331C22×C4—151no—
332C22×C4—151no—
333C22×C4—151no—
334C4⋊C4—31no—
335C4⋊C4—31no—
336C4⋊C4—31no—
337C4⋊C4—151no—
338C4⋊C4—151no—
339C4⋊C4—151no—
340C22⋊C4—31no—
341C22⋊C4—51no—
342C22⋊C4—51no—
343C22⋊C4—151no—
344C22⋊C4—151no—
345C22⋊C4—151no—
346C22⋊C4—151no—
347C22⋊C4—151no—
348C22⋊C4—151no—
349C22⋊C4—151no—
350C22⋊C4—151no—
351C22⋊C4—151no—
352C22⋊C4—151no—
353C22⋊C4D3×D511yescharacteristic
354C42—151no—
355C42—151no—
356C3×C5#53811yescharacteristic, complemented, Hall
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—101no—
360C22×C3—101no—
361C22×C3—101no—
362C22×C3—101no—
363C22×C3—101no—
364C22×C3—101no—
365C22×C3—101no—
366C22×C3—101no—
367C22×C3—101no—
368C22×C3—204no—
369C22×C3#71312yes—
370C22×C3C23×D511yescharacteristic
371C2×D3—101no—
372C2×D3—101no—
373C2×D3—101no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—101no—
377Dic3—21no—
378Dic3—21no—
379Dic3—21no—
380Dic3—21no—
381Dic3—101no—
382Dic3—101no—
383Dic3—101no—
384C2×C5—22no—
385C2×C5C2×#23711yescharacteristic
386C2×C5#100411yescharacteristic
387C2×C5#100411yescharacteristic
388D5—41no—
389D5—41no—
390D5—41no—
391D5—121no—
392C23—51no—
393C23—51no—
394C23—51no—
395C23—102no—
396C23—151no—
397C23—201no—
398C23—201no—
399C23C2×D3×D511yescharacteristic
400Q8—121no—
401D4—102no—
402D4—201no—
403D4—201no—
404D4—302no—
405D4—601no—
406D4—601no—
407D4—601no—
408C2×C4—31no—
409C2×C4—31no—
410C2×C4—31no—
411C2×C4—31no—
412C2×C4—51no—
413C2×C4—121no—
414C2×C4—151no—
415C2×C4—151no—
416C2×C4—151no—
417C2×C4—601no—
418C2×C4—601no—
419C2×C4—601no—
420C2×C4C2×D3×D511yescharacteristic
421C2×C4C2×D3×D511yescharacteristic
422C2×C3—22no—
423C2×C3—201no—
424C2×C3—201no—
425C2×C3—201no—
426C2×C3#414411yescharacteristic
427C2×C3C2×#71311yescharacteristic
428C2×C3#414911yescharacteristic
429D3—201no—
430C5#559311yescharacteristic, complemented, Sylow
431C22—21no—
432C22—21no—
433C22—101no—
434C22—101no—
435C22—101no—
436C22—101no—
437C22—101no—
438C22—101no—
439C22—101no—
440C22—101no—
441C22—101no—
442C22—204no—
443C22—301no—
444C22—301no—
445C22—301no—
446C22#676612yes—
447C22C22×D3×D511yescharacteristic
448C4—21no—
449C4—21no—
450C4—61no—
451C4—61no—
452C4—61no—
453C4—61no—
454C4—101no—
455C4—301no—
456C4—301no—
457C4—301no—
458C3#6597811yescharacteristic, complemented, Sylow
459C2—22no—
460C2—201no—
461C2—201no—
462C2—201no—
463C2—601no—
464C2C2×#676611yescharacteristic
465C2#9202511yescharacteristic
466C2#9202611yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#538
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×#878C2semidirect
3. C3×#4028C2semidirect
4. #91569C2semidirect
5. #91564C2semidirect
6. #91559C2semidirect
7. C2×#6665C2semidirect
8. #91465C2semidirect
9. #91455C2semidirect
10. #91409C2semidirect
11. #91407C2semidirect
12. #91368C2semidirect
13. #91366C2semidirect
14. #91361C2semidirect
15. #91354C2semidirect
20. C2×C4×D15C22semidirect
22. C2×C5×Dic6C22semidirect
28. C2×#1202C22semidirect
29. C2×D5×Dic3C22semidirect
31. #6714C22semidirect
32. #6712C22semidirect
33. C4×Dic15C22semidirect
35. C5×C4⋊Dic3C22semidirect
36. C5×Dic3⋊C4C22semidirect
37. C5×Dic3⋊C4C22semidirect
40. Dic3⋊Dic5C22semidirect
41. #6668C22semidirect
42. #6667C22semidirect
49. #6665C22semidirect
50. #6665C22semidirect
51. Dic3×Dic5C22semidirect
65. #4028D3semidirect
112. #878D5semidirect
188. C2×Dic6C2×D5semidirect
204. C4⋊Dic3C2×D5semidirect
207. Dic3⋊C4C2×D5semidirect
208. Dic3⋊C4C2×D5semidirect
356. C3×C5#538semidirect
430. C5#5593semidirect
458. C3#65978semidirect

Maximal subgroups

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

subgroupindex
#917702
C5×#8782
C3×#40282
#915692
#915642
#915592
C2×#66652
#914652
#914552
#914092
#914072
#913682
#913662
#913612
#913542
#659783
#55935