Finite Group Databasebeta

← #11756421

Subgroups — #11756421

Order 960.

432 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#123C211yesmaximal, characteristic, complemented
2#91828C211yesmaximal, characteristic
3#91825C211yesmaximal, characteristic, complemented
4C4×#1220C211yesmaximal, characteristic, complemented
5#91813C211yesmaximal, characteristic, complemented
6#91787C211yesmaximal, characteristic, complemented
7#91785C211yesmaximal, characteristic, complemented
8#91777C211yesmaximal, characteristic, complemented
9#91776C211yesmaximal, characteristic, complemented
10#91774C211yesmaximal, characteristic, complemented
11#91774C211yesmaximal, characteristic, complemented
12#91772C211yesmaximal, characteristic, complemented
13#91768C211yesmaximal, characteristic, complemented
14#91767C211yesmaximal, characteristic, complemented
15#91766C211yesmaximal, characteristic, complemented
16#65996—31nomaximal, Hall
17C2×C3×C5×D4C2211yescharacteristic
18C22×C3×C4×C5C2211yescharacteristic
19C2×#1220C2211yescharacteristic
20C2×#1220C2211yescharacteristic
21C22×Dic15C2211yescharacteristic
22C2×C4×D15C2211yescharacteristic
23C2×Dic30C2211yescharacteristic
24C2×Dic30C2211yescharacteristic
25C2×Dic30C2211yescharacteristic
26C3×C5×C4⋊C4C2211yescharacteristic
27C3×C5×C4⋊C4C2211yescharacteristic
28C3×C5×C22⋊C4C2211yescharacteristic
29C3×C5×C22⋊C4C2211yescharacteristic
30C3×C5×C22⋊C4C2211yescharacteristic
31#6719C2211yescharacteristic
32#6719C2211yescharacteristic
33#6719C2211yescharacteristic
34#6719C2211yescharacteristic
35#6719C2211yescharacteristic
36#6714C2211yescharacteristic
37#6714C2211yescharacteristic
38#6714C2211yescharacteristic
39#6714C2211yescharacteristic
40C4⋊Dic15C2211yescharacteristic
41C4⋊Dic15C2211yescharacteristic
42#6712C2211yescharacteristic
43#6712C2211yescharacteristic
44#6712C2211yescharacteristic
45#6712C2211yescharacteristic
46#6712C2211yescharacteristic
47#6712C2211yescharacteristic
48C4×Dic15C2211yescharacteristic
49C4×Dic15C2211yescharacteristic
50C4×Dic15C2211yescharacteristic
51C4×Dic15C2211yescharacteristic
52#5662—51nomaximal, Hall
53C5×#123D311yescharacteristic, complemented
54#4085—31no—
55#4082—31no—
56C4×C22⋊D5—31no—
57#4070—31no—
58#4044—31no—
59#4042—31no—
60#4034—31no—
61#4033—31no—
62#4031—31no—
63#4031—31no—
64#4029—31no—
65#4025—31no—
66#4024—31no—
67#4023—31no—
68C23×C3×C5C2311yescharacteristic
69C23×C3×C5C2311yescharacteristic
70C22×D15C2311yescharacteristic
71C3×C5×D4—41no—
72C2×C3×C4×C5—41no—
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×C3×C4×C5C2311yescharacteristic
76C2×C3×C4×C5C2311yescharacteristic
77C2×C3×C4×C5C2311yescharacteristic
78#1220—22no—
79#1220—41no—
80C2×Dic15—22no—
81C2×Dic15C2311yescharacteristic
82C2×Dic15C2311yescharacteristic
83C2×Dic15C2311yescharacteristic
84C2×Dic15C2311yescharacteristic
85C2×Dic15C2311yescharacteristic
86C2×Dic15C2311yescharacteristic
87C2×Dic15C2311yescharacteristic
88C4×D15—41no—
89Dic30—22no—
90Dic30—41no—
91Dic30—41no—
92C3×#123D511yescharacteristic, complemented
93#939—51no—
94#936—51no—
95C4×#67—51no—
96#924—51no—
97#898—51no—
98#896—51no—
99#888—51no—
100#887—51no—
101#885—51no—
102#885—51no—
103#883—51no—
104#879—51no—
105#878—51no—
106#877—51no—
107C2×C5×D4C2×D311yescharacteristic
108C22×C4×C5C2×D311yescharacteristic
109C2×C22⋊D5—31no—
110C2×C22⋊D5—31no—
111C22×Dic5—31no—
112C2×C4×D5—31no—
113C2×Dic10—31no—
114C2×Dic10—31no—
115C2×Dic10—31no—
116C5×C4⋊C4C2×D311yescharacteristic
117C5×C4⋊C4C2×D311yescharacteristic
118C5×C22⋊C4C2×D311yescharacteristic
119C5×C22⋊C4C2×D311yescharacteristic
120C5×C22⋊C4C2×D311yescharacteristic
121C22⋊Dic5—31no—
122C22⋊Dic5—31no—
123C22⋊Dic5—31no—
124C22⋊Dic5—31no—
125C22⋊Dic5—31no—
126#685—31no—
127#685—31no—
128#685—31no—
129#685—31no—
130C4⋊Dic5—31no—
131C4⋊Dic5—31no—
132#683—31no—
133#683—31no—
134#683—31no—
135#683—31no—
136#683—31no—
137#683—31no—
138C4×Dic5—31no—
139C4×Dic5—31no—
140C4×Dic5—31no—
141C4×Dic5—31no—
142#542—151noSylow
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5C2411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15—21no—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155C3×C4×C5—21no—
156C3×C4×C5—21no—
157C3×C4×C5—21no—
158Dic15—21no—
159Dic15—21no—
160Dic15—21no—
161Dic15—21no—
162Dic15—21no—
163Dic15—21no—
164Dic15#4112yes—
165C2×C3×D4C2×D511yescharacteristic
166C22×C3×C4C2×D511yescharacteristic
167C2×#67—51no—
168C2×#67—51no—
169C22×Dic3—51no—
170C2×C4×D3—51no—
171C2×Dic6—51no—
172C2×Dic6—51no—
173C2×Dic6—51no—
174C3×C4⋊C4C2×D511yescharacteristic
175C3×C4⋊C4C2×D511yescharacteristic
176C3×C22⋊C4C2×D511yescharacteristic
177C3×C22⋊C4C2×D511yescharacteristic
178C3×C22⋊C4C2×D511yescharacteristic
179#217—51no—
180#217—51no—
181#217—51no—
182#217—51no—
183#217—51no—
184(C2×D3)⋊C4—51no—
185(C2×D3)⋊C4—51no—
186(C2×D3)⋊C4—51no—
187(C2×D3)⋊C4—51no—
188C4⋊Dic3—51no—
189C4⋊Dic3—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4—51no—
193Dic3⋊C4—51no—
194Dic3⋊C4—51no—
195Dic3⋊C4—51no—
196C4×Dic3—51no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C4×Dic3—51no—
200C23×C5C22×D311yescharacteristic
201C23×C5C22×D311yescharacteristic
202C22×D5—31no—
203C5×D4—41no—
204C2×C4×C5—41no—
205C2×C4×C5C22×D311yescharacteristic
206C2×C4×C5C22×D311yescharacteristic
207C2×C4×C5C22×D311yescharacteristic
208C2×C4×C5C22×D311yescharacteristic
209C2×C4×C5C22×D311yescharacteristic
210C22⋊D5—62no—
211C22⋊D5—121no—
212C2×Dic5—31no—
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5—31no—
216C2×Dic5—31no—
217C2×Dic5—31no—
218C2×Dic5—31no—
219C2×Dic5—62no—
220C4×D5—121no—
221Dic10—62no—
222Dic10—121no—
223Dic10—121no—
224C4⋊Q8—151no—
225#126—151no—
226#126—151no—
227#124—151no—
228#124—151no—
229#124—151no—
230#123—151no—
231#123D1511yescharacteristic, complemented
232C22⋊Q8—151no—
233C22⋊Q8—151no—
234C22⋊Q8—151no—
235#121—151no—
236C4×Q8—151no—
237C4×D4—151no—
238#117—151no—
239C2×C3×C5—41no—
240C2×C3×C5—41no—
241C2×C3×C5C2×#4111yescharacteristic
242C2×C3×C5H(5,𝔽2)11yescharacteristic
243C2×C3×C52−1+411yescharacteristic
244D15—41no—
245C23×C3C22×D511yescharacteristic
246C23×C3C22×D511yescharacteristic
247C22×D3—51no—
248C3×D4—41no—
249C2×C3×C4—41no—
250C2×C3×C4C22×D511yescharacteristic
251C2×C3×C4C22×D511yescharacteristic
252C2×C3×C4C22×D511yescharacteristic
253C2×C3×C4C22×D511yescharacteristic
254C2×C3×C4C22×D511yescharacteristic
255#67—102no—
256#67—201no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3—51no—
260C2×Dic3—51no—
261C2×Dic3—51no—
262C2×Dic3—51no—
263C2×Dic3—51no—
264C2×Dic3—102no—
265C4×D3—201no—
266Dic6—102no—
267Dic6—201no—
268Dic6—201no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5C23×D311yescharacteristic
276C2×D5—61no—
277C2×D5—61no—
278C2×D5—61no—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—21no—
283C4×C5—21no—
284Dic5—32no—
285Dic5—61no—
286Dic5—61no—
287Dic5—61no—
288Dic5—61no—
289Dic5—61no—
290Dic5—61no—
291C2×Q8—151no—
292C2×Q8—151no—
293C2×Q8—151no—
294C2×D4—151no—
295C2×D4—151no—
296C2×D4C2×D1511yescharacteristic
297C22×C4—151no—
298C22×C4—151no—
299C22×C4C2×D1511yescharacteristic
300C4⋊C4—151no—
301C4⋊C4—151no—
302C4⋊C4—151no—
303C4⋊C4—151no—
304C4⋊C4—151no—
305C4⋊C4—151no—
306C4⋊C4—151no—
307C4⋊C4—151no—
308C4⋊C4C2×D1511yescharacteristic
309C4⋊C4C2×D1511yescharacteristic
310C22⋊C4—151no—
311C22⋊C4—151no—
312C22⋊C4—151no—
313C22⋊C4—151no—
314C22⋊C4—151no—
315C22⋊C4—151no—
316C22⋊C4—151no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4C2×D1511yescharacteristic
320C22⋊C4C2×D1511yescharacteristic
321C22⋊C4C2×D1511yescharacteristic
322C42—151no—
323C42—151no—
324C42—151no—
325C42—151no—
326C3×C5#54211yescharacteristic, complemented, Hall
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—21no—
331C22×C3—21no—
332C22×C3—21no—
333C22×C3C23×D511yescharacteristic
334C2×D3—101no—
335C2×D3—101no—
336C2×D3—101no—
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—21no—
340C3×C4—21no—
341C3×C4—21no—
342Dic3—52no—
343Dic3—101no—
344Dic3—101no—
345Dic3—101no—
346Dic3—101no—
347Dic3—101no—
348Dic3—101no—
349C2×C5—41no—
350C2×C5—41no—
351C2×C5#100411yescharacteristic
352C2×C5D3×#4111yescharacteristic
353C2×C5#101011yescharacteristic
354D5—121no—
355C23—151no—
356C23C22×D1511yescharacteristic
357C23C22×D1511yescharacteristic
358Q8—302no—
359Q8—601no—
360Q8—601no—
361D4—41no—
362D4—302no—
363D4—601no—
364C2×C4—41no—
365C2×C4—151no—
366C2×C4—151no—
367C2×C4—151no—
368C2×C4—151no—
369C2×C4—151no—
370C2×C4—151no—
371C2×C4—151no—
372C2×C4—302no—
373C2×C4—601no—
374C2×C4C22×D1511yescharacteristic
375C2×C4C22×D1511yescharacteristic
376C2×C4C22×D1511yescharacteristic
377C2×C4C22×D1511yescharacteristic
378C2×C4C22×D1511yescharacteristic
379C2×C3—41no—
380C2×C3—41no—
381C2×C3#414411yescharacteristic
382C2×C3D5×#4111yescharacteristic
383C2×C3#415011yescharacteristic
384D3—201no—
385C5#566211yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—21no—
390C22—21no—
391C22—21no—
392C22—301no—
393C22—301no—
394C22—301no—
395C22C23×D1511yescharacteristic
396C4—21no—
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—152no—
402C4—301no—
403C4—301no—
404C4—301no—
405C4—301no—
406C4—301no—
407C4—301no—
408C3#6599611yescharacteristic, complemented, Sylow
409C2—41no—
410C2—41no—
411C2—601no—
412C2#9209511yescharacteristic
413C2#41×D1511yescharacteristic
414C2#9210111yescharacteristic
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#123C2
prime radical#91828C2
hypercenter#123D15
hypocenterC3×C5#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #123

Complements

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

NH ≅ G/Ntype
1. C3×C5×#123C2semidirect
3. #91825C2semidirect
4. C4×#1220C2semidirect
5. #91813C2semidirect
6. #91787C2semidirect
7. #91785C2semidirect
8. #91777C2semidirect
9. #91776C2semidirect
10. #91774C2semidirect
11. #91774C2semidirect
12. #91772C2semidirect
13. #91768C2semidirect
14. #91767C2semidirect
15. #91766C2semidirect
53. C5×#123D3semidirect
92. C3×#123D5semidirect
231. #123D15semidirect
326. C3×C5#542semidirect
385. C5#5662semidirect
408. C3#65996semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1232
#918282
#918252
C4×#12202
#918132
#917872
#917852
#917772
#917762
#917742
#917722
#917682
#917672
#917662
#659963
#56625