Finite Group Databasebeta

← #11752910

Subgroups — #11752910

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
1#91766C211yesmaximal, characteristic, complemented
2C5×#879C211yesmaximal, characteristic, complemented
3C3×#4030C211yesmaximal, characteristic
4#91559C211yesmaximal, characteristic, complemented
5#91559C211yesmaximal, characteristic, complemented
6#91548C211yesmaximal, characteristic, complemented
7#91534C211yesmaximal, characteristic, complemented
8#91434C211yesmaximal, characteristic, complemented
9#91407C211yesmaximal, characteristic, complemented
10#91394C211yesmaximal, characteristic, complemented
11C4×D5×Dic3C211yesmaximal, characteristic, complemented
12#91363C211yesmaximal, characteristic, complemented
13#91349C211yesmaximal, characteristic, complemented
14#91335C211yesmaximal, characteristic, complemented
15#91325C211yesmaximal, characteristic, complemented
16#66040—31nomaximal, Hall
17C22×Dic15C2211yescharacteristic
18C2×C3×C22⋊D5C2211yescharacteristic
19C2×C3×C22⋊D5C2211yescharacteristic
20C2×C3×D20C2211yescharacteristic
21C2×C3×C4×D5C2211yescharacteristic
22C2×#1204C2211yescharacteristic
23C2×D5×Dic3C2211yescharacteristic
24C2×D5×Dic3C2211yescharacteristic
25C2×D5×Dic3C2211yescharacteristic
26C3×C5×C22⋊C4C2211yescharacteristic
27#6719C2211yescharacteristic
28#6712C2211yescharacteristic
29#6712C2211yescharacteristic
30C4×Dic15C2211yescharacteristic
31C4×Dic15C2211yescharacteristic
32C5×#217C2211yescharacteristic
33C5×#217C2211yescharacteristic
34C5×C4⋊Dic3C2211yescharacteristic
35C5×Dic3⋊C4C2211yescharacteristic
36C5×Dic3⋊C4C2211yescharacteristic
37C4×C5×Dic3C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×#683C2211yescharacteristic
40Dic3⋊Dic5C2211yescharacteristic
41#6669C2211yescharacteristic
42#6668C2211yescharacteristic
43#6668C2211yescharacteristic
44#6665C2211yescharacteristic
45#6665C2211yescharacteristic
46#6665C2211yescharacteristic
47#6665C2211yescharacteristic
48#6665C2211yescharacteristic
49Dic3×Dic5C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5600—51nomaximal, Hall
53C5×#126—31no—
54#4042—31no—
55#4040—31no—
56#4039—31no—
57#4038—31no—
58#4035—31no—
59#4033—31no—
60#4031—31no—
61#4030D311yescharacteristic
62#4029—31no—
63#4027—31no—
64#4027—31no—
65#4023—31no—
66#4022—31no—
67C42×D5—31no—
68C23×C3×C5C2311yescharacteristic
69C22×C3×D5C2311yescharacteristic
70C22×C3×D5C2311yescharacteristic
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×Dic15—22no—
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C3×C22⋊D5—22no—
83C3×C22⋊D5—22no—
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C3×D20—22no—
87C3×C4×D5—22no—
88#1204—22no—
89D5×Dic3—22no—
90D5×Dic3—22no—
91D5×Dic3—22no—
92C3×#121—51no—
93#936—51no—
94#935—51no—
95#935—51no—
96D4×Dic3—51no—
97D4×Dic3—51no—
98D4×Dic3—51no—
99#924—51no—
100C2×C4×Dic3—51no—
101#890—51no—
102#887—51no—
103#879—51no—
104#879D511yescharacteristic, complemented
105#877—51no—
106#877—51no—
107C2×C22⋊D5C2×D311yescharacteristic
108C2×C22⋊D5C2×D311yescharacteristic
109C22×Dic5—31no—
110C2×D20C2×D311yescharacteristic
111C2×C4×D5—31no—
112C2×C4×D5—31no—
113C2×C4×D5—31no—
114C2×C4×D5C2×D311yescharacteristic
115C2×Dic10—31no—
116C5×C4⋊C4—31no—
117C5×C4⋊C4—31no—
118C5×C4⋊C4—31no—
119C5×C22⋊C4—31no—
120C5×C22⋊C4—31no—
121C5×C22⋊C4C2×D311yescharacteristic
122C42×C5—31no—
123C22⋊Dic5—31no—
124#685—31no—
125#685—31no—
126#685—31no—
127#685—31no—
128#685—31no—
129#685C2×D311yescharacteristic
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×Dic5—31no—
142#529—151noSylow
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5C2411yescharacteristic
147C2×C3×D5—21no—
148C2×C3×D5—21no—
149C2×C3×D5—21no—
150C2×C3×D5—21no—
151C2×C3×D5—21no—
152C2×C3×D5#4112yes—
153C3×C4×C5—21no—
154C3×C4×C5—21no—
155Dic15—21no—
156Dic15—21no—
157Dic15—21no—
158Dic15#4112yes—
159C3×Dic5—21no—
160C3×Dic5#4112yes—
161C5×Dic3—21no—
162C5×Dic3—21no—
163C5×Dic3—21no—
164C5×Dic3—21no—
165C2×C3×D4—51no—
166C2×C3×D4—51no—
167C2×C3×D4—51no—
168C22×C3×C4—51no—
169C22×Dic3—51no—
170C22×Dic3—51no—
171C22×Dic3—51no—
172C22×Dic3—51no—
173C2×Dic6—51no—
174C3×C4⋊C4—51no—
175C3×C22⋊C4—51no—
176C3×C22⋊C4C2×D511yescharacteristic
177#217—51no—
178#217—51no—
179#217—51no—
180#217—51no—
181#217—51no—
182#217—51no—
183#217C2×D511yescharacteristic
184#217C2×D511yescharacteristic
185C4⋊Dic3—51no—
186C4⋊Dic3—51no—
187C4⋊Dic3C2×D511yescharacteristic
188Dic3⋊C4—51no—
189Dic3⋊C4—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4C2×D511yescharacteristic
193Dic3⋊C4C2×D511yescharacteristic
194C4×Dic3—51no—
195C4×Dic3—51no—
196C4×Dic3—51no—
197C4×Dic3—51no—
198C4×Dic3—51no—
199C4×Dic3C2×D511yescharacteristic
200C23×C5C22×D311yescharacteristic
201C22×D5C22×D311yescharacteristic
202C22×D5C22×D311yescharacteristic
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5—31no—
206C2×C4×C5—31no—
207C2×C4×C5C22×D311yescharacteristic
208C2×C4×C5C22×D311yescharacteristic
209C22⋊D5—22no—
210C22⋊D5—22no—
211C2×Dic5—31no—
212C2×Dic5—31no—
213C2×Dic5—31no—
214C2×Dic5—31no—
215C2×Dic5—62no—
216C2×Dic5C22×D311yescharacteristic
217C2×Dic5C22×D311yescharacteristic
218D20—22no—
219C4×D5—22no—
220C4×D5—62no—
221C4×D5—62no—
222C4×D5—62no—
223Dic10—62no—
224#126—31no—
225#126—151no—
226#125—151no—
227#124—151no—
228#123—151no—
229#123—151no—
230C22⋊Q8—151no—
231#121—51no—
232C4×Q8—151no—
233C4×D4—151no—
234C4×D4—151no—
235C4×D4—151no—
236#117—151no—
237#117—151no—
238C2×C42—151no—
239C2×C3×C5—41no—
240C2×C3×C5C2×#4111yescharacteristic
241C2×C3×C5C2×#4111yescharacteristic
242C2×C3×C5C2×#4111yescharacteristic
243C3×D5—22no—
244C3×D5—41no—
245C23×C3—51no—
246C23×C3—51no—
247C23×C3C22×D511yescharacteristic
248C3×D4—102no—
249C3×D4—102no—
250C3×D4—102no—
251C2×C3×C4—51no—
252C2×C3×C4—51no—
253C2×C3×C4—102no—
254C2×C3×C4C22×D511yescharacteristic
255C2×C3×C4C22×D511yescharacteristic
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—51no—
259C2×Dic3—51no—
260C2×Dic3—102no—
261C2×Dic3—102no—
262C2×Dic3—102no—
263C2×Dic3—102no—
264C2×Dic3C22×D511yescharacteristic
265C2×Dic3C22×D511yescharacteristic
266C2×Dic3C22×D511yescharacteristic
267C2×Dic3C22×D511yescharacteristic
268Dic6—102no—
269C22×C5—21no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5C23×D311yescharacteristic
273C2×D5—21no—
274C2×D5—21no—
275C2×D5—21no—
276C2×D5—21no—
277C2×D5—21no—
278C2×D5#23712yes—
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—61no—
282C4×C5—61no—
283C4×C5—61no—
284C4×C5—61no—
285Dic5—21no—
286Dic5—32no—
287Dic5—61no—
288Dic5—61no—
289Dic5—61no—
290Dic5#23712yes—
291C2×Q8—151no—
292C2×D4—51no—
293C2×D4—51no—
294C2×D4—51no—
295C22×C4—51no—
296C22×C4—151no—
297C22×C4—151no—
298C22×C4—151no—
299C22×C4—151no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—51no—
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—151no—
314C22⋊C4—151no—
315C22⋊C4—151no—
316C22⋊C4—151no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4D3×D511yescharacteristic
320C42—31no—
321C42—151no—
322C42—151no—
323C42—151no—
324C42—151no—
325C42—151no—
326C3×C5#52911yescharacteristic, complemented, Hall
327C22×C3—21no—
328C22×C3—21no—
329C22×C3—21no—
330C22×C3—52no—
331C22×C3—101no—
332C22×C3—101no—
333C22×C3—101no—
334C22×C3—101no—
335C22×C3—101no—
336C22×C3C23×D511yescharacteristic
337C3×C4—21no—
338C3×C4—21no—
339C3×C4—52no—
340C3×C4—101no—
341Dic3—21no—
342Dic3—21no—
343Dic3—21no—
344Dic3—21no—
345Dic3—52no—
346Dic3—101no—
347Dic3—101no—
348Dic3—101no—
349C2×C5—41no—
350C2×C5C2×#23711yescharacteristic
351C2×C5C2×#23711yescharacteristic
352C2×C5D3×#4111yescharacteristic
353D5—22no—
354D5—41no—
355C23—51no—
356C23—51no—
357C23C2×D3×D511yescharacteristic
358Q8—302no—
359D4—102no—
360D4—102no—
361D4—102no—
362C2×C4—31no—
363C2×C4—31no—
364C2×C4—31no—
365C2×C4—31no—
366C2×C4—51no—
367C2×C4—51no—
368C2×C4—102no—
369C2×C4—151no—
370C2×C4—151no—
371C2×C4—151no—
372C2×C4—151no—
373C2×C4—302no—
374C2×C4—302no—
375C2×C4—302no—
376C2×C4—302no—
377C2×C4C2×D3×D511yescharacteristic
378C2×C4C2×D3×D511yescharacteristic
379C2×C3—41no—
380C2×C3—102no—
381C2×C3—201no—
382C2×C3D5×#4111yescharacteristic
383C2×C3D5×#4111yescharacteristic
384C2×C3D5×#4111yescharacteristic
385C5#560011yescharacteristic, complemented, Sylow
386C22—21no—
387C22—21no—
388C22—21no—
389C22—52no—
390C22—101no—
391C22—101no—
392C22—101no—
393C22—101no—
394C22—101no—
395C22C22×D3×D511yescharacteristic
396C4—21no—
397C4—21no—
398C4—52no—
399C4—61no—
400C4—61no—
401C4—61no—
402C4—61no—
403C4—101no—
404C4—152no—
405C4—301no—
406C4—301no—
407C4—301no—
408C3#6604011yescharacteristic, complemented, Sylow
409C2—41no—
410C2—102no—
411C2—201no—
412C2#9201611yescharacteristic
413C2D5×#23711yescharacteristic
414C2D5×#23711yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C22⋊C4C22
prime radicalC3×#4030C2
hypercenterC22⋊C4D3×D5
hypocenterC3×C5#529
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. #91766C2semidirect
2. C5×#879C2semidirect
4. #91559C2semidirect
5. #91559C2semidirect
6. #91548C2semidirect
7. #91534C2semidirect
8. #91434C2semidirect
9. #91407C2semidirect
10. #91394C2semidirect
11. C4×D5×Dic3C2semidirect
12. #91363C2semidirect
13. #91349C2semidirect
14. #91335C2semidirect
15. #91325C2semidirect
104. #879D5semidirect
326. C3×C5#529semidirect
385. C5#5600semidirect
408. C3#66040semidirect

Maximal subgroups

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

subgroupindex
#917662
C5×#8792
C3×#40302
#915592
#915482
#915342
#914342
#914072
#913942
C4×D5×Dic32
#913632
#913492
#913352
#913252
#660403
#56005