Finite Group Databasebeta

← #11755409

Subgroups — #11755409

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×#6719C211yesmaximal, characteristic, complemented
2C2×C5×#217C211yesmaximal, characteristic, complemented
3C3×#4099C211yesmaximal, characteristic
4#91576C211yesmaximal, characteristic, complemented
5#91575C211yesmaximal, characteristic, complemented
6#91559C211yesmaximal, characteristic, complemented
7Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
8#91548C211yesmaximal, characteristic, complemented
9#91537C211yesmaximal, characteristic, complemented
10#91536C211yesmaximal, characteristic, complemented
11#91534C211yesmaximal, characteristic, complemented
12#91532C211yesmaximal, characteristic, complemented
13#91531C211yesmaximal, characteristic, complemented
14#91530C211yesmaximal, characteristic, complemented
15#91529C211yesmaximal, characteristic, complemented
16#65829—31nomaximal, Hall
17C24×C3×C5C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C22×Dic15C2211yescharacteristic
20C22×C5×Dic3C2211yescharacteristic
21C22×C5×Dic3C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C22⋊D5C2211yescharacteristic
24C2×C3×C22⋊D5C2211yescharacteristic
25C2×#1204C2211yescharacteristic, complemented
26C2×D5×Dic3C2211yescharacteristic, complemented
27#6719C2211yescharacteristic
28#6719C2211yescharacteristic
29#6719C2211yescharacteristic
30#6719C2211yescharacteristic
31C5×#217C2211yescharacteristic
32C5×#217C2211yescharacteristic
33C5×#217C2211yescharacteristic
34C5×#217C2211yescharacteristic
35C3×C22⋊Dic5C2211yescharacteristic
36C3×C22⋊Dic5C2211yescharacteristic
37C3×C22⋊Dic5C2211yescharacteristic
38Dic3⋊Dic5C2211yescharacteristic, complemented
39Dic3⋊Dic5C2211yescharacteristic, complemented
40Dic3⋊Dic5C2211yescharacteristic, complemented
41#6669C2211yescharacteristic, complemented
42#6669C2211yescharacteristic, complemented
43#6669C2211yescharacteristic, complemented
44#6668C2211yescharacteristic, complemented
45#6668C2211yescharacteristic, complemented
46#6665C2211yescharacteristic, complemented
47#6665C2211yescharacteristic, complemented
48#6665C2211yescharacteristic, complemented
49Dic3×Dic5C2211yescharacteristic, complemented
50Dic3×Dic5C2211yescharacteristic, complemented
51Dic3×Dic5C2211yescharacteristic, complemented
52#5587—51nomaximal, Hall
53C2×C5×C22⋊C4—31no—
54#4099D311yescharacteristic
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×C3×D5C2311yescharacteristic
75C2×Dic15—22no—
76C2×Dic15—41no—
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80C2×Dic15C2311yescharacteristic
81C2×C5×Dic3—22no—
82C2×C5×Dic3—41no—
83C2×C5×Dic3C2311yescharacteristic
84C2×C5×Dic3C2311yescharacteristic
85C2×C5×Dic3C2311yescharacteristic
86C2×C5×Dic3C2311yescharacteristic
87C3×C22⋊D5—22no—
88C3×C22⋊D5—22no—
89C3×C22⋊D5—41no—
90C2×C3×Dic5C2311yescharacteristic
91C2×C3×Dic5C2311yescharacteristic
92C2×C3×Dic5C2311yescharacteristic
93#1204—41no—
94D5×Dic3—41no—
95C3×#120—51no—
96C2×#217—51no—
97C2×#217D511yescharacteristic, complemented
98#936—51no—
99#935—51no—
100#935—51no—
101#935—51no—
102D4×Dic3—51no—
103D4×Dic3—51no—
104#879—51no—
105#879—51no—
106#878—51no—
107#878—51no—
108#877—51no—
109#877—51no—
110C24×C5C2×D311yescharacteristic
111C22×C4×C5—31no—
112C22×C4×C5—31no—
113C2×C22⋊D5C2×D311yescharacteristic
114C2×C22⋊D5C2×D311yescharacteristic
115C2×C22⋊D5C2×D311yescharacteristic
116C22×Dic5—31no—
117C22×Dic5—31no—
118C2×C4×D5—31no—
119C2×Dic10—31no—
120C5×C22⋊C4—31no—
121C5×C22⋊C4—31no—
122C5×C22⋊C4—31no—
123C5×C22⋊C4—31no—
124C22⋊Dic5—31no—
125C22⋊Dic5—31no—
126C22⋊Dic5—31no—
127C22⋊Dic5—31no—
128C22⋊Dic5C2×D311yescharacteristic
129C22⋊Dic5C2×D311yescharacteristic
130C22⋊Dic5C2×D311yescharacteristic
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×C3×D5—21no—
158C2×C3×D5—21no—
159C2×C3×D5—21no—
160Dic15—21no—
161Dic15—21no—
162Dic15—21no—
163Dic15—21no—
164C3×Dic5—21no—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C5×Dic3—21no—
168C5×Dic3—21no—
169C5×Dic3—21no—
170C5×Dic3—21no—
171C24×C3C2×D511yescharacteristic
172C2×C3×D4—51no—
173C2×C3×D4—51no—
174C2×C3×D4—51no—
175C22×Dic3—51no—
176C22×Dic3—51no—
177C22×Dic3—51no—
178C22×Dic3C2×D511yescharacteristic
179C22×Dic3C2×D511yescharacteristic
180C2×Dic6—51no—
181C3×C22⋊C4—51no—
182C3×C22⋊C4—51no—
183C3×C22⋊C4—51no—
184#217—51no—
185#217—51no—
186#217—51no—
187#217—51no—
188#217—51no—
189#217—51no—
190#217—51no—
191#217C2×D511yescharacteristic
192#217C2×D511yescharacteristic
193#217C2×D511yescharacteristic
194#217C2×D511yescharacteristic
195C4⋊Dic3—51no—
196C4⋊Dic3—51no—
197Dic3⋊C4—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×D5C22×D311yescharacteristic
213C2×C4×C5—31no—
214C2×C4×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5—62no—
218C2×C4×C5—121no—
219C22⋊D5—22no—
220C22⋊D5—22no—
221C22⋊D5—41no—
222C2×Dic5—31no—
223C2×Dic5—31no—
224C2×Dic5—31no—
225C2×Dic5—31no—
226C2×Dic5—62no—
227C2×Dic5—121no—
228C2×Dic5C22×D311yescharacteristic
229C2×Dic5C22×D311yescharacteristic
230C2×Dic5C22×D311yescharacteristic
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—51no—
242C4×D4—151no—
243C4×D4—151no—
244#117—151no—
245#117—151no—
246C2×C22⋊C4—31no—
247C2×C22⋊C4—151no—
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
254C3×D5—41no—
255C23×C3—22no—
256C23×C3—22no—
257C23×C3—41no—
258C23×C3—51no—
259C23×C3C22×D511yescharacteristic
260C23×C3C22×D511yescharacteristic
261C23×C3C22×D511yescharacteristic
262C3×D4—102no—
263C3×D4—102no—
264C3×D4—201no—
265C2×C3×C4—51no—
266C2×C3×C4—51no—
267C2×C3×C4—51no—
268C2×Dic3—22no—
269C2×Dic3—41no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—51no—
273C2×Dic3—51no—
274C2×Dic3—102no—
275C2×Dic3—201no—
276C2×Dic3—201no—
277C2×Dic3C22×D511yescharacteristic
278C2×Dic3C22×D511yescharacteristic
279C2×Dic3C22×D511yescharacteristic
280C2×Dic3C22×D511yescharacteristic
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#23712yes—
291C22×C5#23712yes—
292C22×C5C23×D311yescharacteristic
293C2×D5—21no—
294C2×D5—21no—
295C2×D5—21no—
296C4×C5—61no—
297C4×C5—61no—
298C4×C5—61no—
299C4×C5—61no—
300Dic5—21no—
301Dic5—21no—
302Dic5—21no—
303Dic5—61no—
304Dic5—61no—
305Dic5—61no—
306Dic5—61no—
307C24D3×D511yescharacteristic
308C2×Q8—151no—
309C2×D4—51no—
310C2×D4—51no—
311C2×D4—51no—
312C22×C4—31no—
313C22×C4—31no—
314C22×C4—151no—
315C22×C4—151no—
316C22×C4—151no—
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—31no—
326C22⋊C4—31no—
327C22⋊C4—31no—
328C22⋊C4—31no—
329C22⋊C4—51no—
330C22⋊C4—51no—
331C22⋊C4—51no—
332C22⋊C4—151no—
333C22⋊C4—151no—
334C22⋊C4—151no—
335C22⋊C4—151no—
336C22⋊C4—151no—
337C22⋊C4—151no—
338C22⋊C4—151no—
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—101no—
352C22×C3—101no—
353C22×C3—101no—
354C22×C3#70912yes—
355C22×C3#71112yes—
356C22×C3C23×D511yescharacteristic
357C3×C4—101no—
358C3×C4—101no—
359C3×C4—101no—
360Dic3—21no—
361Dic3—21no—
362Dic3—21no—
363Dic3—21no—
364Dic3—101no—
365Dic3—101no—
366Dic3—101no—
367Dic3—101no—
368C2×C5—22no—
369C2×C5—22no—
370C2×C5—41no—
371C2×C5C2×#23711yescharacteristic
372C2×C5C2×#23711yescharacteristic
373C2×C5#100411yescharacteristic
374D5—41no—
375C23—22no—
376C23—22no—
377C23—41no—
378C23—51no—
379C23C2×D3×D511yescharacteristic
380C23C2×D3×D511yescharacteristic
381C23C2×D3×D511yescharacteristic
382Q8—601no—
383D4—102no—
384D4—102no—
385D4—201no—
386C2×C4—31no—
387C2×C4—31no—
388C2×C4—31no—
389C2×C4—31no—
390C2×C4—51no—
391C2×C4—51no—
392C2×C4—51no—
393C2×C4—62no—
394C2×C4—121no—
395C2×C4—151no—
396C2×C4—151no—
397C2×C4—151no—
398C2×C4—151no—
399C2×C4—302no—
400C2×C4—601no—
401C2×C4—601no—
402C2×C3—22no—
403C2×C3—22no—
404C2×C3—41no—
405C2×C3—201no—
406C2×C3C2×#70911yescharacteristic
407C2×C3C2×#71111yescharacteristic
408C2×C3#414411yescharacteristic
409C5#558711yescharacteristic, complemented, Sylow
410C22—21no—
411C22—21no—
412C22—21no—
413C22—21no—
414C22—21no—
415C22—21no—
416C22—21no—
417C22—44no—
418C22—101no—
419C22—101no—
420C22—101no—
421C22#677912yes—
422C22#678012yes—
423C22C22×D3×D511yescharacteristic
424C4—61no—
425C4—61no—
426C4—61no—
427C4—61no—
428C4—101no—
429C4—101no—
430C4—101no—
431C4—301no—
432C4—301no—
433C4—301no—
434C4—301no—
435C3#6582911yescharacteristic, complemented, Sylow
436C2—22no—
437C2—22no—
438C2—41no—
439C2—201no—
440C2C2×#677911yescharacteristic
441C2C2×#678011yescharacteristic
442C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC24×C3×C5C22
prime radicalC3×#4099C2
hypercenterC24D3×D5
hypocenterC3×C5#551
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C2×#6719C2semidirect
2. C2×C5×#217C2semidirect
4. #91576C2semidirect
5. #91575C2semidirect
6. #91559C2semidirect
7. Dic3×C22⋊D5C2semidirect
8. #91548C2semidirect
9. #91537C2semidirect
10. #91536C2semidirect
11. #91534C2semidirect
12. #91532C2semidirect
13. #91531C2semidirect
14. #91530C2semidirect
15. #91529C2semidirect
25. C2×#1204C22semidirect
26. C2×D5×Dic3C22semidirect
38. Dic3⋊Dic5C22semidirect
39. Dic3⋊Dic5C22semidirect
40. Dic3⋊Dic5C22semidirect
41. #6669C22semidirect
42. #6669C22semidirect
43. #6669C22semidirect
44. #6668C22semidirect
45. #6668C22semidirect
46. #6665C22semidirect
47. #6665C22semidirect
48. #6665C22semidirect
49. Dic3×Dic5C22semidirect
50. Dic3×Dic5C22semidirect
51. Dic3×Dic5C22semidirect
97. C2×#217D5semidirect
342. C3×C5#551semidirect
409. C5#5587semidirect
435. C3#65829semidirect

Maximal subgroups

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

subgroupindex
C2×#67192
C2×C5×#2172
C3×#40992
#915762
#915752
#915592
Dic3×C22⋊D52
#915482
#915372
#915362
#915342
#915322
#915312
#915302
#915292
#658293
#55875