Finite Group Databasebeta

← #11756254

Subgroups — #11756254

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
1C2×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
2#91842C211yesmaximal, characteristic
3C2×#6719C211yesmaximal, characteristic, complemented
4#91818C211yesmaximal, characteristic, complemented
5C4×#1220C211yesmaximal, characteristic, complemented
6#91815C211yesmaximal, characteristic, complemented
7#91813C211yesmaximal, characteristic, complemented
8#91775C211yesmaximal, characteristic, complemented
9#91774C211yesmaximal, characteristic, complemented
10#91772C211yesmaximal, characteristic, complemented
11#91770C211yesmaximal, characteristic, complemented
12#91768C211yesmaximal, characteristic, complemented
13#91768C211yesmaximal, characteristic, complemented
14#91767C211yesmaximal, characteristic, complemented
15#91766C211yesmaximal, characteristic, complemented
16#65829—31nomaximal, Hall
17C24×C3×C5C2211yescharacteristic
18C22×C3×C4×C5C2211yescharacteristic
19C22×C3×C4×C5C2211yescharacteristic
20C2×#1220C2211yescharacteristic
21C2×#1220C2211yescharacteristic
22C2×#1220C2211yescharacteristic
23C22×Dic15C2211yescharacteristic
24C22×Dic15C2211yescharacteristic
25C2×C4×D15C2211yescharacteristic, complemented
26C2×Dic30C2211yescharacteristic, complemented
27C3×C5×C22⋊C4C2211yescharacteristic
28C3×C5×C22⋊C4C2211yescharacteristic
29C3×C5×C22⋊C4C2211yescharacteristic
30C3×C5×C22⋊C4C2211yescharacteristic
31#6719C2211yescharacteristic
32#6719C2211yescharacteristic
33#6719C2211yescharacteristic
34#6719C2211yescharacteristic
35#6719C2211yescharacteristic
36#6719C2211yescharacteristic
37#6719C2211yescharacteristic
38#6714C2211yescharacteristic, complemented
39#6714C2211yescharacteristic, complemented
40#6714C2211yescharacteristic, complemented
41C4⋊Dic15C2211yescharacteristic, complemented
42C4⋊Dic15C2211yescharacteristic, complemented
43C4⋊Dic15C2211yescharacteristic, complemented
44#6712C2211yescharacteristic, complemented
45#6712C2211yescharacteristic, complemented
46#6712C2211yescharacteristic, complemented
47#6712C2211yescharacteristic, complemented
48#6712C2211yescharacteristic, complemented
49C4×Dic15C2211yescharacteristic, complemented
50C4×Dic15C2211yescharacteristic, complemented
51C4×Dic15C2211yescharacteristic, complemented
52#5495—51nomaximal, Hall
53C2×C5×C22⋊C4D311yescharacteristic, complemented
54#4099—31no—
55C2×C22⋊Dic5—31no—
56#4075—31no—
57C4×C22⋊D5—31no—
58#4072—31no—
59#4070—31no—
60#4032—31no—
61#4031—31no—
62#4029—31no—
63#4027—31no—
64#4025—31no—
65#4025—31no—
66#4024—31no—
67#4023—31no—
68C23×C3×C5—22no—
69C23×C3×C5—22no—
70C23×C3×C5—41no—
71C23×C3×C5C2311yescharacteristic
72C23×C3×C5C2311yescharacteristic
73C23×C3×C5C2311yescharacteristic
74C22×D15C2311yescharacteristic
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—41no—
77C2×C3×C4×C5C2311yescharacteristic
78C2×C3×C4×C5C2311yescharacteristic
79C2×C3×C4×C5C2311yescharacteristic
80C2×C3×C4×C5C2311yescharacteristic
81#1220—22no—
82#1220—22no—
83#1220—41no—
84C2×Dic15—22no—
85C2×Dic15—41no—
86C2×Dic15C2311yescharacteristic
87C2×Dic15C2311yescharacteristic
88C2×Dic15C2311yescharacteristic
89C2×Dic15C2311yescharacteristic
90C2×Dic15C2311yescharacteristic
91C2×Dic15C2311yescharacteristic
92C2×Dic15C2311yescharacteristic
93C4×D15—41no—
94Dic30—41no—
95C2×C3×C22⋊C4D511yescharacteristic, complemented
96#953—51no—
97C2×#217—51no—
98#929—51no—
99C4×#67—51no—
100#926—51no—
101#924—51no—
102#886—51no—
103#885—51no—
104#883—51no—
105#67⋊C4—51no—
106#879—51no—
107#879—51no—
108#878—51no—
109#877—51no—
110C24×C5C2×D311yescharacteristic
111C22×C4×C5C2×D311yescharacteristic
112C22×C4×C5C2×D311yescharacteristic
113C2×C22⋊D5—31no—
114C2×C22⋊D5—31no—
115C2×C22⋊D5—31no—
116C22×Dic5—31no—
117C22×Dic5—31no—
118C2×C4×D5—31no—
119C2×Dic10—31no—
120C5×C22⋊C4C2×D311yescharacteristic
121C5×C22⋊C4C2×D311yescharacteristic
122C5×C22⋊C4C2×D311yescharacteristic
123C5×C22⋊C4C2×D311yescharacteristic
124C22⋊Dic5—31no—
125C22⋊Dic5—31no—
126C22⋊Dic5—31no—
127C22⋊Dic5—31no—
128C22⋊Dic5—31no—
129C22⋊Dic5—31no—
130C22⋊Dic5—31no—
131#685—31no—
132#685—31no—
133#685—31no—
134C4⋊Dic5—31no—
135C4⋊Dic5—31no—
136C4⋊Dic5—31no—
137#683—31no—
138#683—31no—
139#683—31no—
140#683—31no—
141#683—31no—
142C4×Dic5—31no—
143C4×Dic5—31no—
144C4×Dic5—31no—
145#551—151noSylow
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—21no—
151C22×C3×C5—21no—
152C22×C3×C5—21no—
153C22×C3×C5—44no—
154C22×C3×C5#4112yes—
155C22×C3×C5#4112yes—
156C22×C3×C5C2411yescharacteristic
157C2×D15—21no—
158C2×D15—21no—
159C2×D15—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×C4×C5—21no—
163C3×C4×C5—21no—
164Dic15—21no—
165Dic15—21no—
166Dic15—21no—
167Dic15—21no—
168Dic15—21no—
169Dic15—21no—
170Dic15—21no—
171C24×C3C2×D511yescharacteristic
172C22×C3×C4C2×D511yescharacteristic
173C22×C3×C4C2×D511yescharacteristic
174C2×#67—51no—
175C2×#67—51no—
176C2×#67—51no—
177C22×Dic3—51no—
178C22×Dic3—51no—
179C2×C4×D3—51no—
180C2×Dic6—51no—
181C3×C22⋊C4C2×D511yescharacteristic
182C3×C22⋊C4C2×D511yescharacteristic
183C3×C22⋊C4C2×D511yescharacteristic
184C3×C22⋊C4C2×D511yescharacteristic
185#217—51no—
186#217—51no—
187#217—51no—
188#217—51no—
189#217—51no—
190#217—51no—
191#217—51no—
192(C2×D3)⋊C4—51no—
193(C2×D3)⋊C4—51no—
194(C2×D3)⋊C4—51no—
195C4⋊Dic3—51no—
196C4⋊Dic3—51no—
197C4⋊Dic3—51no—
198Dic3⋊C4—51no—
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4—51no—
203C4×Dic3—51no—
204C4×Dic3—51no—
205C4×Dic3—51no—
206C23×C5—22no—
207C23×C5—22no—
208C23×C5—41no—
209C23×C5C22×D311yescharacteristic
210C23×C5C22×D311yescharacteristic
211C23×C5C22×D311yescharacteristic
212C22×D5—31no—
213C2×C4×C5—22no—
214C2×C4×C5—41no—
215C2×C4×C5C22×D311yescharacteristic
216C2×C4×C5C22×D311yescharacteristic
217C2×C4×C5C22×D311yescharacteristic
218C2×C4×C5C22×D311yescharacteristic
219C22⋊D5—62no—
220C22⋊D5—62no—
221C22⋊D5—121no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5—31no—
227C2×Dic5—31no—
228C2×Dic5—31no—
229C2×Dic5—62no—
230C2×Dic5—121no—
231C4×D5—121no—
232Dic10—121no—
233#126—151no—
234#126—151no—
235#124—151no—
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—151no—
245#117—151no—
246C2×C22⋊C4—151no—
247C2×C22⋊C4D1511yescharacteristic, complemented
248C2×C3×C5—22no—
249C2×C3×C5—22no—
250C2×C3×C5—41no—
251C2×C3×C5C2×#4111yescharacteristic
252C2×C3×C5C2×#4111yescharacteristic
253C2×C3×C5H(5,𝔽2)11yescharacteristic
254D15—41no—
255C23×C3—22no—
256C23×C3—22no—
257C23×C3—41no—
258C23×C3C22×D511yescharacteristic
259C23×C3C22×D511yescharacteristic
260C23×C3C22×D511yescharacteristic
261C22×D3—51no—
262C2×C3×C4—22no—
263C2×C3×C4—41no—
264C2×C3×C4C22×D511yescharacteristic
265C2×C3×C4C22×D511yescharacteristic
266C2×C3×C4C22×D511yescharacteristic
267C2×C3×C4C22×D511yescharacteristic
268#67—102no—
269#67—102no—
270#67—201no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3—51no—
275C2×Dic3—51no—
276C2×Dic3—51no—
277C2×Dic3—51no—
278C2×Dic3—102no—
279C2×Dic3—201no—
280C4×D3—201no—
281Dic6—201no—
282C22×C5—21no—
283C22×C5—21no—
284C22×C5—21no—
285C22×C5—21no—
286C22×C5—21no—
287C22×C5—21no—
288C22×C5—21no—
289C22×C5—44no—
290C22×C5#23512yes—
291C22×C5#23712yes—
292C22×C5C23×D311yescharacteristic
293C2×D5—61no—
294C2×D5—61no—
295C2×D5—61no—
296C4×C5—21no—
297C4×C5—21no—
298C4×C5—21no—
299C4×C5—21no—
300Dic5—61no—
301Dic5—61no—
302Dic5—61no—
303Dic5—61no—
304Dic5—61no—
305Dic5—61no—
306Dic5—61no—
307C24C2×D1511yescharacteristic
308C2×Q8—151no—
309C2×D4—151no—
310C2×D4—151no—
311C2×D4—151no—
312C22×C4—151no—
313C22×C4—151no—
314C22×C4—151no—
315C22×C4C2×D1511yescharacteristic
316C22×C4C2×D1511yescharacteristic
317C4⋊C4—151no—
318C4⋊C4—151no—
319C4⋊C4—151no—
320C4⋊C4—151no—
321C4⋊C4—151no—
322C4⋊C4—151no—
323C4⋊C4—151no—
324C4⋊C4—151no—
325C22⋊C4—151no—
326C22⋊C4—151no—
327C22⋊C4—151no—
328C22⋊C4—151no—
329C22⋊C4—151no—
330C22⋊C4—151no—
331C22⋊C4—151no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4C2×D1511yescharacteristic
336C22⋊C4C2×D1511yescharacteristic
337C22⋊C4C2×D1511yescharacteristic
338C22⋊C4C2×D1511yescharacteristic
339C42—151no—
340C42—151no—
341C42—151no—
342C3×C5#55111yescharacteristic, complemented, Hall
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—44no—
351C22×C3#70912yes—
352C22×C3#71112yes—
353C22×C3C23×D511yescharacteristic
354C2×D3—101no—
355C2×D3—101no—
356C2×D3—101no—
357C3×C4—21no—
358C3×C4—21no—
359C3×C4—21no—
360C3×C4—21no—
361Dic3—101no—
362Dic3—101no—
363Dic3—101no—
364Dic3—101no—
365Dic3—101no—
366Dic3—101no—
367Dic3—101no—
368C2×C5—22no—
369C2×C5—22no—
370C2×C5—41no—
371C2×C5C2×#23511yescharacteristic
372C2×C5C2×#23711yescharacteristic
373C2×C5#100411yescharacteristic
374D5—121no—
375C23—22no—
376C23—22no—
377C23—41no—
378C23—151no—
379C23C22×D1511yescharacteristic
380C23C22×D1511yescharacteristic
381C23C22×D1511yescharacteristic
382Q8—601no—
383D4—302no—
384D4—302no—
385D4—601no—
386C2×C4—22no—
387C2×C4—41no—
388C2×C4—151no—
389C2×C4—151no—
390C2×C4—151no—
391C2×C4—151no—
392C2×C4—151no—
393C2×C4—151no—
394C2×C4—151no—
395C2×C4—302no—
396C2×C4—601no—
397C2×C4—601no—
398C2×C4C22×D1511yescharacteristic
399C2×C4C22×D1511yescharacteristic
400C2×C4C22×D1511yescharacteristic
401C2×C4C22×D1511yescharacteristic
402C2×C3—22no—
403C2×C3—22no—
404C2×C3—41no—
405C2×C3C2×#70911yescharacteristic
406C2×C3C2×#71111yescharacteristic
407C2×C3#414411yescharacteristic
408D3—201no—
409C5#549511yescharacteristic, complemented, Sylow
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—44no—
418C22—301no—
419C22—301no—
420C22—301no—
421C22#681712yes—
422C22#681912yes—
423C22C23×D1511yescharacteristic
424C4—21no—
425C4—21no—
426C4—21no—
427C4—21no—
428C4—301no—
429C4—301no—
430C4—301no—
431C4—301no—
432C4—301no—
433C4—301no—
434C4—301no—
435C3#6582911yescharacteristic, complemented, Sylow
436C2—22no—
437C2—22no—
438C2—41no—
439C2—601no—
440C2C2×#681711yescharacteristic
441C2C2×#681911yescharacteristic
442C2#9209511yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×C22⋊C4C2
prime radical#91842C2
hypercenterC2×C22⋊C4D15
hypocenterC3×C5#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×C22⋊C4C2semidirect
3. C2×#6719C2semidirect
4. #91818C2semidirect
5. C4×#1220C2semidirect
6. #91815C2semidirect
7. #91813C2semidirect
8. #91775C2semidirect
9. #91774C2semidirect
10. #91772C2semidirect
11. #91770C2semidirect
12. #91768C2semidirect
13. #91768C2semidirect
14. #91767C2semidirect
15. #91766C2semidirect
25. C2×C4×D15C22semidirect
26. C2×Dic30C22semidirect
38. #6714C22semidirect
39. #6714C22semidirect
40. #6714C22semidirect
41. C4⋊Dic15C22semidirect
42. C4⋊Dic15C22semidirect
43. C4⋊Dic15C22semidirect
44. #6712C22semidirect
45. #6712C22semidirect
46. #6712C22semidirect
47. #6712C22semidirect
48. #6712C22semidirect
49. C4×Dic15C22semidirect
50. C4×Dic15C22semidirect
51. C4×Dic15C22semidirect
53. C2×C5×C22⋊C4D3semidirect
95. C2×C3×C22⋊C4D5semidirect
247. C2×C22⋊C4D15semidirect
342. C3×C5#551semidirect
409. C5#5495semidirect
435. C3#65829semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×C22⋊C42
#918422
C2×#67192
#918182
C4×#12202
#918152
#918132
#917752
#917742
#917722
#917702
#917682
#917672
#917662
#658293
#54955