Finite Group Databasebeta

← #11754587

Subgroups — #11754587

Order 960.

468 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
1C2×C4×Dic15C211yesmaximal, characteristic, complemented
2C4×C5×#67C211yesmaximal, characteristic, complemented
3C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4#91576C211yesmaximal, characteristic, complemented
5#91571C211yesmaximal, characteristic
6#91543C211yesmaximal, characteristic, complemented
7#91537C211yesmaximal, characteristic, complemented
8C4×#1204C211yesmaximal, characteristic, complemented
9#91464C211yesmaximal, characteristic, complemented
10C4×#1201C211yesmaximal, characteristic, complemented
11#91382C211yesmaximal, characteristic, complemented
12#91371C211yesmaximal, characteristic, complemented
13#91367C211yesmaximal, characteristic, complemented
14#91366C211yesmaximal, characteristic, complemented
15#91357C211yesmaximal, characteristic, complemented
16#65872—31nomaximal, Hall
17C22×C3×C4×C5C2211yescharacteristic
18C22×Dic15C2211yescharacteristic
19C22×Dic15C2211yescharacteristic
20C2×C5×#67C2211yescharacteristic
21C2×C4×C5×D3C2211yescharacteristic
22C2×C3×C22⋊D5C2211yescharacteristic
23C2×C3×C4×D5C2211yescharacteristic
24C2×#1204C2211yescharacteristic
25C2×#1201C2211yescharacteristic
26C4×Dic15C2211yescharacteristic
27C4×Dic15C2211yescharacteristic
28C4×Dic15C2211yescharacteristic
29C4×Dic15C2211yescharacteristic
30C5×#217C2211yescharacteristic
31C5×(C2×D3)⋊C4C2211yescharacteristic
32C5×Dic3⋊C4C2211yescharacteristic
33C4×C5×Dic3C2211yescharacteristic
34C3×C22⋊Dic5C2211yescharacteristic
35C3×#685C2211yescharacteristic
36C3×#683C2211yescharacteristic
37C3×C4×Dic5C2211yescharacteristic
38Dic3⋊Dic5C2211yescharacteristic
39Dic3⋊Dic5C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6669C2211yescharacteristic
43#6668C2211yescharacteristic
44#6668C2211yescharacteristic
45#6668C2211yescharacteristic
46(C2×D3)⋊Dic5C2211yescharacteristic
47(C2×D3)⋊Dic5C2211yescharacteristic
48(C2×D3)⋊Dic5C2211yescharacteristic
49#6665C2211yescharacteristic
50#6665C2211yescharacteristic
51#6665C2211yescharacteristic
52#5538—51nomaximal, Hall
53C4×C5×D4—31no—
54#4085—31no—
55#4081—31no—
56C4×C22⋊D5—31no—
57C4×C22⋊D5D311yescharacteristic, complemented
58#4072—31no—
59C2×C4×Dic5—31no—
60#4044—31no—
61#4035—31no—
62#4032—31no—
63#4031—31no—
64#4025—31no—
65#4024—31no—
66#4018—31no—
67C4×Dic10—31no—
68C23×C3×C5C2311yescharacteristic
69C22×C5×D3C2311yescharacteristic
70C22×C3×D5C2311yescharacteristic
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×Dic15—22no—
75C2×Dic15—22no—
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×Dic15C2311yescharacteristic
79C2×Dic15C2311yescharacteristic
80C5×#67—22no—
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C4×C5×D3—22no—
85C3×C22⋊D5—22no—
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C3×C4×D5—22no—
90#1204—22no—
91#1201—22no—
92C3×C4×D4—51no—
93#939—51no—
94#935—51no—
95C4×#67—51no—
96C4×#67D511yescharacteristic, complemented
97#926—51no—
98C2×C4×Dic3—51no—
99#898—51no—
100#889—51no—
101#886—51no—
102#885—51no—
103#879—51no—
104#878—51no—
105#872—51no—
106C4×Dic6—51no—
107C2×C5×D4—31no—
108C22×C4×C5—31no—
109C22×C4×C5C2×D311yescharacteristic
110C2×C22⋊D5—31no—
111C2×C22⋊D5C2×D311yescharacteristic
112C22×Dic5—31no—
113C22×Dic5—31no—
114C2×C4×D5C2×D311yescharacteristic
115C2×Dic10—31no—
116C5×C4⋊C4—31no—
117C5×C22⋊C4—31no—
118C5×C22⋊C4—31no—
119C42×C5—31no—
120C22⋊Dic5—31no—
121C22⋊Dic5—31no—
122C22⋊Dic5—31no—
123C22⋊Dic5C2×D311yescharacteristic
124#685—31no—
125#685—31no—
126#685—31no—
127#685C2×D311yescharacteristic
128C4⋊Dic5—31no—
129C4⋊Dic5—31no—
130C4⋊Dic5—31no—
131#683—31no—
132#683—31no—
133#683—31no—
134#683—31no—
135#683—31no—
136#683C2×D311yescharacteristic
137C4×Dic5—31no—
138C4×Dic5—31no—
139C4×Dic5—31no—
140C4×Dic5—31no—
141C4×Dic5C2×D311yescharacteristic
142#529—151noSylow
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5#4112yes—
146C22×C3×C5C2411yescharacteristic
147C2×C5×D3—21no—
148C2×C5×D3—21no—
149C2×C5×D3—21no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5—21no—
153C3×C4×C5—21no—
154C3×C4×C5#4112yes—
155Dic15—21no—
156Dic15—21no—
157Dic15—21no—
158Dic15#4112yes—
159C3×Dic5—21no—
160C3×Dic5—21no—
161C3×Dic5—21no—
162C5×Dic3—21no—
163C5×Dic3—21no—
164C5×Dic3—21no—
165C2×C3×D4—51no—
166C22×C3×C4—51no—
167C22×C3×C4C2×D511yescharacteristic
168C2×#67—51no—
169C2×#67C2×D511yescharacteristic
170C22×Dic3—51no—
171C22×Dic3—51no—
172C2×C4×D3C2×D511yescharacteristic
173C2×Dic6—51no—
174C3×C4⋊C4—51no—
175C3×C22⋊C4—51no—
176C3×C22⋊C4—51no—
177C3×C42—51no—
178#217—51no—
179#217—51no—
180#217—51no—
181#217C2×D511yescharacteristic
182(C2×D3)⋊C4—51no—
183(C2×D3)⋊C4—51no—
184(C2×D3)⋊C4—51no—
185(C2×D3)⋊C4C2×D511yescharacteristic
186C4⋊Dic3—51no—
187C4⋊Dic3—51no—
188C4⋊Dic3—51no—
189Dic3⋊C4—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4—51no—
193Dic3⋊C4—51no—
194Dic3⋊C4C2×D511yescharacteristic
195C4×Dic3—51no—
196C4×Dic3—51no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C4×Dic3C2×D511yescharacteristic
200C23×C5—31no—
201C23×C5C22×D311yescharacteristic
202C22×D5C22×D311yescharacteristic
203C5×D4—62no—
204C2×C4×C5—22no—
205C2×C4×C5—31no—
206C2×C4×C5—31no—
207C2×C4×C5—31no—
208C2×C4×C5—62no—
209C2×C4×C5C22×D311yescharacteristic
210C2×C4×C5C22×D311yescharacteristic
211C22⋊D5—22no—
212C22⋊D5—62no—
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5—31no—
216C2×Dic5—31no—
217C2×Dic5—62no—
218C2×Dic5—62no—
219C2×Dic5C22×D311yescharacteristic
220C2×Dic5C22×D311yescharacteristic
221C2×Dic5C22×D311yescharacteristic
222C4×D5—22no—
223Dic10—62no—
224#126—151no—
225#126—151no—
226#125—151no—
227#124—151no—
228#123—151no—
229#123—151no—
230C22⋊Q8—151no—
231#121—151no—
232C4×Q8—151no—
233C4×D4—31no—
234C4×D4—51no—
235C4×D4—151no—
236#117—151no—
237#117—151no—
238C2×C42—151no—
239C2×C3×C5—22no—
240C2×C3×C5C2×#4111yescharacteristic
241C2×C3×C5C2×#4111yescharacteristic
242C2×C3×C5C2×#4111yescharacteristic
243C3×D5—41no—
244C5×D3—41no—
245C23×C3—51no—
246C23×C3C22×D511yescharacteristic
247C22×D3C22×D511yescharacteristic
248C3×D4—102no—
249C2×C3×C4—22no—
250C2×C3×C4—51no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—102no—
254C2×C3×C4C22×D511yescharacteristic
255C2×C3×C4C22×D511yescharacteristic
256#67—22no—
257#67—102no—
258C2×Dic3—51no—
259C2×Dic3—51no—
260C2×Dic3—51no—
261C2×Dic3—51no—
262C2×Dic3—102no—
263C2×Dic3—102no—
264C2×Dic3C22×D511yescharacteristic
265C2×Dic3C22×D511yescharacteristic
266C2×Dic3C22×D511yescharacteristic
267C4×D3—22no—
268Dic6—102no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—61no—
272C22×C5—61no—
273C22×C5—61no—
274C22×C5#23512yes—
275C22×C5C23×D311yescharacteristic
276C2×D5—21no—
277C2×D5—21no—
278C2×D5—21no—
279C4×C5—21no—
280C4×C5—61no—
281C4×C5—61no—
282C4×C5—61no—
283C4×C5#23712yes—
284Dic5—21no—
285Dic5—21no—
286Dic5—21no—
287Dic5—32no—
288Dic5—61no—
289Dic5—61no—
290Dic5—61no—
291C2×Q8—151no—
292C2×D4—31no—
293C2×D4—51no—
294C2×D4—151no—
295C22×C4—31no—
296C22×C4—51no—
297C22×C4—151no—
298C22×C4—151no—
299C22×C4D3×D511yescharacteristic
300C4⋊C4—31no—
301C4⋊C4—51no—
302C4⋊C4—151no—
303C4⋊C4—151no—
304C4⋊C4—151no—
305C4⋊C4—151no—
306C4⋊C4—151no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—151no—
310C22⋊C4—31no—
311C22⋊C4—31no—
312C22⋊C4—51no—
313C22⋊C4—51no—
314C22⋊C4—151no—
315C22⋊C4—151no—
316C22⋊C4—151no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4—151no—
320C42—31no—
321C42—51no—
322C42—151no—
323C42—151no—
324C42—151no—
325C42—151no—
326C3×C5#52911yescharacteristic, complemented, Hall
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—101no—
330C22×C3—101no—
331C22×C3—101no—
332C22×C3#70912yes—
333C22×C3C23×D511yescharacteristic
334C2×D3—21no—
335C2×D3—21no—
336C2×D3—21no—
337C3×C4—21no—
338C3×C4—101no—
339C3×C4—101no—
340C3×C4—101no—
341C3×C4#71112yes—
342Dic3—21no—
343Dic3—21no—
344Dic3—21no—
345Dic3—52no—
346Dic3—101no—
347Dic3—101no—
348Dic3—101no—
349C2×C5—22no—
350C2×C5—121no—
351C2×C5C2×#23511yescharacteristic
352C2×C5C2×#23711yescharacteristic
353C2×C5D3×#4111yescharacteristic
354D5—41no—
355C23—31no—
356C23—51no—
357C23C2×D3×D511yescharacteristic
358Q8—302no—
359D4—62no—
360D4—102no—
361D4—302no—
362C2×C4—22no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—51no—
369C2×C4—62no—
370C2×C4—102no—
371C2×C4—151no—
372C2×C4—151no—
373C2×C4—151no—
374C2×C4—151no—
375C2×C4—302no—
376C2×C4—302no—
377C2×C4C2×D3×D511yescharacteristic
378C2×C4C2×D3×D511yescharacteristic
379C2×C3—22no—
380C2×C3—201no—
381C2×C3C2×#70911yescharacteristic
382C2×C3C2×#71111yescharacteristic
383C2×C3D5×#4111yescharacteristic
384D3—41no—
385C5#553811yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—61no—
389C22—61no—
390C22—61no—
391C22—101no—
392C22—101no—
393C22—101no—
394C22#677112yes—
395C22C22×D3×D511yescharacteristic
396C4—21no—
397C4—61no—
398C4—61no—
399C4—61no—
400C4—101no—
401C4—101no—
402C4—101no—
403C4—152no—
404C4—301no—
405C4—301no—
406C4—301no—
407C4#678012yes—
408C3#6587211yescharacteristic, complemented, Sylow
409C2—22no—
410C2—121no—
411C2—201no—
412C2C2×#677111yescharacteristic
413C2#9201611yescharacteristic
414C2C2×#678011yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FrattiniC22C22×D3×D5
FittingC22×C3×C4×C5C22
prime radical#91571C2
hypercenterC22×C4D3×D5
hypocenterC3×C5#529
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic15C2semidirect
2. C4×C5×#67C2semidirect
3. C3×C4×C22⋊D5C2semidirect
4. #91576C2semidirect
6. #91543C2semidirect
7. #91537C2semidirect
8. C4×#1204C2semidirect
9. #91464C2semidirect
10. C4×#1201C2semidirect
11. #91382C2semidirect
12. #91371C2semidirect
13. #91367C2semidirect
14. #91366C2semidirect
15. #91357C2semidirect
57. C4×C22⋊D5D3semidirect
96. C4×#67D5semidirect
326. C3×C5#529semidirect
385. C5#5538semidirect
408. C3#65872semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Dic152
C4×C5×#672
C3×C4×C22⋊D52
#915762
#915712
#915432
#915372
C4×#12042
#914642
C4×#12012
#913822
#913712
#913672
#913662
#913572
#658723
#55385