Finite Group Databasebeta

← #11755178

Subgroups — #11755178

Order 960.

456 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#91835C211yesmaximal, characteristic, complemented
2C5×#944C211yesmaximal, characteristic, complemented
3C3×#4092C211yesmaximal, characteristic, complemented
4#91444C211yesmaximal, characteristic
5#91429C211yesmaximal, characteristic, complemented
6#91424C211yesmaximal, characteristic, complemented
7#91422C211yesmaximal, characteristic, complemented
8#91421C211yesmaximal, characteristic, complemented
9#91404C211yesmaximal, characteristic, complemented
10#91396C211yesmaximal, characteristic
11#91395C211yesmaximal, characteristic
12D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
13#91346C211yesmaximal, characteristic, complemented
14#91343C211yesmaximal, characteristic, complemented
15#91324C211yesmaximal, characteristic, complemented
16#66064—31nomaximal, Hall
17C2×C3×C5×Q8C2211yescharacteristic
18C2×C4×D15C2211yescharacteristic
19C2×C5×Dic6C2211yescharacteristic
20C2×C3×C4×D5C2211yescharacteristic
21C2×#1204C2211yescharacteristic
22C2×#1202C2211yescharacteristic
23C2×#1200C2211yescharacteristic
24C2×#1200C2211yescharacteristic
25C2×D5×Dic3C2211yescharacteristic
26C2×D5×Dic3C2211yescharacteristic
27#6714C2211yescharacteristic
28#6714C2211yescharacteristic
29C4⋊Dic15C2211yescharacteristic
30#6712C2211yescharacteristic
31#6712C2211yescharacteristic
32C5×Dic3⋊C4C2211yescharacteristic
33C5×Dic3⋊C4C2211yescharacteristic
34C5×Dic3⋊C4C2211yescharacteristic
35C5×Dic3⋊C4C2211yescharacteristic
36C4×C5×Dic3C2211yescharacteristic
37C3×#685C2211yescharacteristic
38C3×#685C2211yescharacteristic
39C3×C4⋊Dic5C2211yescharacteristic
40C3×#683C2211yescharacteristic
41C3×#683C2211yescharacteristic
42Dic3⋊Dic5C2211yescharacteristic
43Dic3⋊Dic5C2211yescharacteristic
44Dic3⋊Dic5C2211yescharacteristic
45Dic3⋊Dic5C2211yescharacteristic
46#6669C2211yescharacteristic
47#6668C2211yescharacteristic
48#6667C2211yescharacteristic
49#6665C2211yescharacteristic
50Dic3×Dic5C2211yescharacteristic
51Dic3×Dic5C2211yescharacteristic
52#5636—51nomaximal, Hall
53C5×C4⋊Q8—31no—
54#4092—31no—
55#4092—31no—
56#4092—31no—
57#4092D311yescharacteristic, complemented
58#4043—31no—
59#4043—31no—
60#4039—31no—
61#4039—31no—
62D5×C4⋊C4—31no—
63D5×C4⋊C4—31no—
64#4036—31no—
65#4036—31no—
66C4×D20—31no—
67C4×Dic10—31no—
68C22×D15C2311yescharacteristic
69C22×C3×D5C2311yescharacteristic
70C3×C5×Q8—41no—
71C2×C3×C4×C5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×Dic15C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C4×D15—41no—
78C2×C5×Dic3C2311yescharacteristic
79C2×C5×Dic3C2311yescharacteristic
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C5×Dic6—41no—
83C2×C3×Dic5C2311yescharacteristic
84C2×C3×Dic5C2311yescharacteristic
85C2×C3×Dic5C2311yescharacteristic
86C3×C4×D5—41no—
87#1204—22no—
88#1202Q814yescomplemented
89#1200—22no—
90#1200—41no—
91D5×Dic3—22no—
92D5×Dic3—41no—
93C3×C22⋊Q8—51no—
94#946—51no—
95#944D511yescharacteristic, complemented
96C4×#67—51no—
97C2×Dic3⋊C4—51no—
98#896—51no—
99#896—51no—
100D3×C4⋊C4—51no—
101#889—51no—
102#889—51no—
103#887—51no—
104#67⋊C4—51no—
105#67⋊C4—51no—
106#878—51no—
107#878—51no—
108C2×C5×Q8—31no—
109C2×C5×Q8C2×D311yescharacteristic
110C2×D20—31no—
111C2×C4×D5—31no—
112C2×C4×D5—31no—
113C2×C4×D5—31no—
114C2×C4×D5—31no—
115C2×C4×D5—31no—
116C2×C4×D5C2×D311yescharacteristic
117C2×Dic10—31no—
118C5×C4⋊C4—31no—
119C5×C4⋊C4—31no—
120C5×C4⋊C4—31no—
121C5×C4⋊C4—31no—
122C42×C5—31no—
123#685—31no—
124#685—31no—
125#685—31no—
126#685—31no—
127#685C2×D311yescharacteristic
128#685C2×D311yescharacteristic
129C4⋊Dic5—31no—
130C4⋊Dic5—31no—
131C4⋊Dic5—31no—
132C4⋊Dic5—31no—
133C4⋊Dic5—31no—
134C4⋊Dic5C2×D311yescharacteristic
135#683—31no—
136#683—31no—
137#683—31no—
138#683—31no—
139#683C2×D311yescharacteristic
140#683C2×D311yescharacteristic
141C4×Dic5—31no—
142C4×Dic5—31no—
143#554—151noSylow
144C22×C3×C5C2411yescharacteristic
145C2×D15—21no—
146C2×D15—21no—
147C2×D15C2×Q812yes—
148C2×C3×D5—21no—
149C2×C3×D5—21no—
150C2×C3×D5C2×Q812yes—
151C3×C4×C5—21no—
152C3×C4×C5—21no—
153C3×C4×C5—21no—
154Dic15—21no—
155Dic15—21no—
156Dic15—21no—
157C3×Dic5—21no—
158C3×Dic5—21no—
159C3×Dic5—21no—
160C5×Dic3—21no—
161C5×Dic3—21no—
162C5×Dic3C2×Q812yes—
163C5×Dic3#4112yes—
164C2×C3×Q8C2×D511yescharacteristic
165C22×C3×C4—51no—
166C2×#67—51no—
167C22×Dic3—51no—
168C22×Dic3—51no—
169C2×C4×D3—51no—
170C2×C4×D3—51no—
171C2×C4×D3—51no—
172C2×Dic6—51no—
173C2×Dic6C2×D511yescharacteristic
174C3×C4⋊C4—51no—
175C3×C4⋊C4—51no—
176C3×C4⋊C4—51no—
177C3×C22⋊C4—51no—
178C3×C22⋊C4—51no—
179#217—51no—
180(C2×D3)⋊C4—51no—
181(C2×D3)⋊C4—51no—
182(C2×D3)⋊C4—51no—
183C4⋊Dic3—51no—
184C4⋊Dic3—51no—
185Dic3⋊C4—51no—
186Dic3⋊C4—51no—
187Dic3⋊C4—51no—
188Dic3⋊C4—51no—
189Dic3⋊C4—51no—
190Dic3⋊C4—51no—
191Dic3⋊C4—51no—
192Dic3⋊C4C2×D511yescharacteristic
193Dic3⋊C4C2×D511yescharacteristic
194Dic3⋊C4C2×D511yescharacteristic
195Dic3⋊C4C2×D511yescharacteristic
196C4×Dic3—51no—
197C4×Dic3—51no—
198C4×Dic3C2×D511yescharacteristic
199C22×D5—31no—
200C22×D5C22×D311yescharacteristic
201C5×Q8—41no—
202C5×Q8—121no—
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5—31no—
206C2×C4×C5—31no—
207C2×C4×C5C22×D311yescharacteristic
208C2×C4×C5C22×D311yescharacteristic
209C2×C4×C5C22×D311yescharacteristic
210C2×Dic5—31no—
211C2×Dic5—31no—
212C2×Dic5—31no—
213C2×Dic5C22×D311yescharacteristic
214C2×Dic5C22×D311yescharacteristic
215C2×Dic5C22×D311yescharacteristic
216D20—34no—
217C4×D5—41no—
218C4×D5—62no—
219C4×D5—62no—
220C4×D5—121no—
221C4×D5—121no—
222C4×D5—121no—
223Dic10—62no—
224C4⋊Q8—31no—
225#125—151no—
226#125—151no—
227C22⋊Q8—51no—
228C22⋊Q8—151no—
229C22⋊Q8—151no—
230C22⋊Q8—151no—
231C22⋊Q8—151no—
232C22⋊Q8—151no—
233C4×Q8—151no—
234C4×D4—151no—
235C4×D4—151no—
236C4×D4—151no—
237C2×C4⋊C4—151no—
238C2×C4⋊C4—151no—
239C2×C3×C5C22×Q811yescharacteristic
240C2×C3×C5C2×#4111yescharacteristic
241C2×C3×C5H(5,𝔽2)11yescharacteristic
242D15—22no—
243C3×D5—22no—
244C23×C3—51no—
245C22×D3—51no—
246C3×Q8—41no—
247C2×C3×C4—51no—
248C2×C3×C4—51no—
249C2×C3×C4—51no—
250C2×C3×C4—201no—
251C2×C3×C4C22×D511yescharacteristic
252C2×C3×C4C22×D511yescharacteristic
253C2×C3×C4C22×D511yescharacteristic
254#67—54no—
255C2×Dic3—51no—
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—102no—
259C2×Dic3—201no—
260C2×Dic3C22×D511yescharacteristic
261C2×Dic3C22×D511yescharacteristic
262C2×Dic3C22×D511yescharacteristic
263C2×Dic3C22×D511yescharacteristic
264C4×D3—102no—
265C4×D3—201no—
266C4×D3—201no—
267Dic6—41no—
268Dic6—102no—
269C22×C5C23×D311yescharacteristic
270C2×D5—21no—
271C2×D5—21no—
272C2×D5—32no—
273C2×D5—61no—
274C2×D5—61no—
275C2×D5D3×Q812yes—
276C4×C5—21no—
277C4×C5—21no—
278C4×C5—21no—
279C4×C5—32no—
280C4×C5—32no—
281C4×C5—61no—
282C4×C5—61no—
283Dic5—21no—
284Dic5—21no—
285Dic5—21no—
286Dic5—61no—
287Dic5—61no—
288Dic5—61no—
289C2×Q8—31no—
290C2×Q8—151no—
291C2×Q8D3×D511yescharacteristic
292C2×D4—151no—
293C22×C4—51no—
294C22×C4—151no—
295C22×C4—151no—
296C22×C4—151no—
297C22×C4—151no—
298C22×C4—151no—
299C4⋊C4—31no—
300C4⋊C4—31no—
301C4⋊C4—31no—
302C4⋊C4—31no—
303C4⋊C4—51no—
304C4⋊C4—51no—
305C4⋊C4—51no—
306C4⋊C4—151no—
307C4⋊C4—151no—
308C4⋊C4—151no—
309C4⋊C4—151no—
310C4⋊C4—151no—
311C4⋊C4—151no—
312C4⋊C4—151no—
313C4⋊C4—151no—
314C4⋊C4—151no—
315C22⋊C4—51no—
316C22⋊C4—51no—
317C22⋊C4—151no—
318C22⋊C4—151no—
319C22⋊C4—151no—
320C22⋊C4—151no—
321C42—31no—
322C42—151no—
323C42—151no—
324C3×C5#55411yescharacteristic, complemented, Hall
325C22×C3—52no—
326C22×C3—101no—
327C22×C3—101no—
328C22×C3C23×D511yescharacteristic
329C2×D3—52no—
330C2×D3—101no—
331C2×D3—101no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—101no—
336C3×C4—101no—
337C3×C4—101no—
338Dic3—21no—
339Dic3—21no—
340Dic3—101no—
341Dic3—101no—
342Dic3—101no—
343Dic3Q8×D512yes—
344Dic3#71312yes—
345C2×C5#100411yescharacteristic
346C2×C5C2×D3×Q811yescharacteristic
347C2×C5D3×#4111yescharacteristic
348D5—22no—
349D5—62no—
350C23—51no—
351C23—151no—
352Q8—41no—
353Q8—121no—
354Q8—302no—
355D4—154no—
356C2×C4—31no—
357C2×C4—31no—
358C2×C4—31no—
359C2×C4—31no—
360C2×C4—51no—
361C2×C4—51no—
362C2×C4—51no—
363C2×C4—151no—
364C2×C4—151no—
365C2×C4—151no—
366C2×C4—201no—
367C2×C4—302no—
368C2×C4—302no—
369C2×C4—601no—
370C2×C4—601no—
371C2×C4—601no—
372C2×C4C2×D3×D511yescharacteristic
373C2×C4C2×D3×D511yescharacteristic
374C2×C4C2×D3×D511yescharacteristic
375C2×C3—102no—
376C2×C3#414411yescharacteristic
377C2×C3C2×Q8×D511yescharacteristic
378C2×C3C2×#71311yescharacteristic
379D3—102no—
380C5#563611yescharacteristic, complemented, Sylow
381C22—52no—
382C22—101no—
383C22—101no—
384C22—152no—
385C22—301no—
386C22—301no—
387C22C22×D3×D511yescharacteristic
388C4—21no—
389C4—21no—
390C4—21no—
391C4—32no—
392C4—32no—
393C4—61no—
394C4—61no—
395C4—101no—
396C4—101no—
397C4—101no—
398C4—301no—
399C4—301no—
400C4—301no—
401C3#6606411yescharacteristic, complemented, Sylow
402C2—102no—
403C2—302no—
404C2D3×Q8×D511yescharacteristic
405C2D3×#71311yescharacteristic
406C2#9204911yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC2×C3×C5×Q8C22
prime radicalC2×#1202C22
hypercenterC2×Q8D3×D5
hypocenterC3×C5#554
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
1. #91835C2semidirect
2. C5×#944C2semidirect
3. C3×#4092C2semidirect
5. #91429C2semidirect
6. #91424C2semidirect
7. #91422C2semidirect
8. #91421C2semidirect
9. #91404C2semidirect
12. D5×Dic3⋊C4C2semidirect
13. #91346C2semidirect
14. #91343C2semidirect
15. #91324C2semidirect
57. #4092D3semidirect
88. #1202Q8semidirect
95. #944D5semidirect
324. C3×C5#554semidirect
380. C5#5636semidirect
401. C3#66064semidirect

Maximal subgroups

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

subgroupindex
#918352
C5×#9442
C3×#40922
#914442
#914292
#914242
#914222
#914212
#914042
#913962
#913952
D5×Dic3⋊C42
#913462
#913432
#913242
#660643
#56365