Finite Group Databasebeta

← #11753431

Subgroups — #11753431

Order 960.

560 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D15⋊Q8C211yesmaximal, characteristic, complemented
2C2×D5×Dic6C211yesmaximal, characteristic, complemented
3#91785C211yesmaximal, characteristic, complemented
4C5×#888C211yesmaximal, characteristic, complemented
5C3×#4042C211yesmaximal, characteristic, complemented
6#91444C211yesmaximal, characteristic
7#91430C211yesmaximal, characteristic, complemented
8#91424C211yesmaximal, characteristic, complemented
9#91421C211yesmaximal, characteristic, complemented
10#91419C211yesmaximal, characteristic, complemented
11#91396C211yesmaximal, characteristic
12#91395C211yesmaximal, characteristic
13#91328C211yesmaximal, characteristic, complemented
14#91327C211yesmaximal, characteristic, complemented
15#91324C211yesmaximal, characteristic, complemented
16#66061—31nomaximal, Hall
17C2×C4×D15C2211yescharacteristic
18C2×Dic30C2211yescharacteristic
19C2×C5×Dic6C2211yescharacteristic
20C2×C5×Dic6C2211yescharacteristic
21C2×C3×C4×D5C2211yescharacteristic
22C2×C3×Dic10C2211yescharacteristic
23C2×#1204C2211yescharacteristic
24C2×#1204C2211yescharacteristic
25C2×#1204C2211yescharacteristic
26C2×#1202C2211yescharacteristic
27C2×#1200C2211yescharacteristic
28C2×#1200C2211yescharacteristic
29C2×D5×Dic3C2211yescharacteristic
30C2×D5×Dic3C2211yescharacteristic
31D15⋊Q8—24no—
32D5×Dic6—24no—
33C3×C5×C4⋊C4C2211yescharacteristic
34#6714C2211yescharacteristic
35#6714C2211yescharacteristic
36#6712C2211yescharacteristic
37#6712C2211yescharacteristic
38C5×C4⋊Dic3C2211yescharacteristic
39C5×Dic3⋊C4C2211yescharacteristic
40C5×Dic3⋊C4C2211yescharacteristic
41C4×C5×Dic3C2211yescharacteristic
42C3×#685C2211yescharacteristic
43C3×#685C2211yescharacteristic
44C3×#683C2211yescharacteristic
45C3×#683C2211yescharacteristic
46Dic3⋊Dic5C2211yescharacteristic
47Dic3⋊Dic5C2211yescharacteristic
48#6669C2211yescharacteristic
49#6668C2211yescharacteristic
50#6667C2211yescharacteristic
51#6665C2211yescharacteristic
52Dic3×Dic5C2211yescharacteristic
53Dic3×Dic5C2211yescharacteristic
54#5632—51nomaximal, Hall
55C2×Q8×D5—31no—
56C2×Q8×D5—31no—
57C5×C4⋊Q8—31no—
58#4092—31no—
59#4092—31no—
60#4042—31no—
61#4042—31no—
62#4042—31no—
63#4042D311yescharacteristic, complemented
64#4039—31no—
65#4039—31no—
66#4034—31no—
67#4034—31no—
68C4×D20—31no—
69C4×Dic10—31no—
70C22×D15C2311yescharacteristic
71C22×C3×D5C2311yescharacteristic
72C2×C3×C4×C5C2311yescharacteristic
73C2×C3×C4×C5C2311yescharacteristic
74C2×C3×C4×C5C2311yescharacteristic
75C2×Dic15C2311yescharacteristic
76C2×Dic15C2311yescharacteristic
77C2×Dic15C2311yescharacteristic
78C4×D15—22no—
79Dic30—22no—
80C2×C5×Dic3C2311yescharacteristic
81C2×C5×Dic3C2311yescharacteristic
82C2×C5×Dic3C2311yescharacteristic
83C2×C5×Dic3C2311yescharacteristic
84C5×Dic6—22no—
85C5×Dic6—22no—
86C2×C3×Dic5C2311yescharacteristic
87C2×C3×Dic5C2311yescharacteristic
88C2×C3×Dic5C2311yescharacteristic
89C3×C4×D5—22no—
90C3×Dic10—22no—
91#1204—22no—
92#1204—22no—
93#1204D414yescomplemented
94#1202Q814yescomplemented
95#1200—22no—
96#1200—22no—
97D5×Dic3—22no—
98D5×Dic3—22no—
99C2×D3×Q8—51no—
100C22×Dic6—51no—
101C3×C22⋊Q8—51no—
102#944—51no—
103C4×#67—51no—
104#897—51no—
105#896—51no—
106#896—51no—
107#888—51no—
108#888D511yescharacteristic, complemented
109#887—51no—
110#67⋊C4—51no—
111#67⋊C4—51no—
112#878—51no—
113#878—51no—
114C2×C5×Q8—31no—
115C2×C5×Q8—31no—
116Q8×D5—64no—
117Q8×D5—64no—
118C2×D20—31no—
119C2×C4×D5—31no—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×C4×D5C2×D311yescharacteristic
125C2×Dic10—31no—
126C2×Dic10—31no—
127C2×Dic10—31no—
128C2×Dic10—31no—
129C2×Dic10C2×D311yescharacteristic
130C5×C4⋊C4—31no—
131C5×C4⋊C4—31no—
132C5×C4⋊C4—31no—
133C5×C4⋊C4C2×D311yescharacteristic
134C42×C5—31no—
135#685—31no—
136#685—31no—
137#685—31no—
138#685—31no—
139#685C2×D311yescharacteristic
140#685C2×D311yescharacteristic
141C4⋊Dic5—31no—
142C4⋊Dic5—31no—
143#683—31no—
144#683—31no—
145#683—31no—
146#683—31no—
147#683C2×D311yescharacteristic
148#683C2×D311yescharacteristic
149C4×Dic5—31no—
150C4×Dic5—31no—
151D4×Q8—151noSylow
152C22×C3×C5C2411yescharacteristic
153C2×D15—21no—
154C2×D15—21no—
155C2×D15C2×Q812yescomplemented
156C2×C3×D5—21no—
157C2×C3×D5—21no—
158C2×C3×D5C2×Q812yescomplemented
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162Dic15—21no—
163Dic15—21no—
164Dic15C2×D412yes—
165C3×Dic5—21no—
166C3×Dic5—21no—
167C3×Dic5C2×D412yes—
168C5×Dic3—21no—
169C5×Dic3—21no—
170C5×Dic3C2×D412yes—
171C5×Dic3C2×Q812yescomplemented
172C2×C3×Q8—51no—
173C22×C3×C4—51no—
174C2×#67—51no—
175C22×Dic3—51no—
176C22×Dic3—51no—
177D3×Q8—104no—
178C2×C4×D3—51no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×Dic6—51no—
182C2×Dic6—51no—
183C2×Dic6—51no—
184C2×Dic6—51no—
185C2×Dic6—104no—
186C2×Dic6C2×D511yescharacteristic
187C2×Dic6C2×D511yescharacteristic
188C3×C4⋊C4—51no—
189C3×C4⋊C4—51no—
190C3×C4⋊C4C2×D511yescharacteristic
191C3×C22⋊C4—51no—
192C3×C22⋊C4—51no—
193#217—51no—
194(C2×D3)⋊C4—51no—
195(C2×D3)⋊C4—51no—
196(C2×D3)⋊C4—51no—
197C4⋊Dic3—51no—
198C4⋊Dic3C2×D511yescharacteristic
199Dic3⋊C4—51no—
200Dic3⋊C4—51no—
201Dic3⋊C4—51no—
202Dic3⋊C4—51no—
203Dic3⋊C4—51no—
204Dic3⋊C4C2×D511yescharacteristic
205Dic3⋊C4C2×D511yescharacteristic
206C4×Dic3—51no—
207C4×Dic3—51no—
208C4×Dic3C2×D511yescharacteristic
209C22×D5—31no—
210C22×D5C22×D311yescharacteristic
211C5×Q8—62no—
212C5×Q8—62no—
213C2×C4×C5—31no—
214C2×C4×C5—31no—
215C2×C4×C5—31no—
216C2×C4×C5—31no—
217C2×C4×C5C22×D311yescharacteristic
218C2×C4×C5C22×D311yescharacteristic
219C2×C4×C5C22×D311yescharacteristic
220C2×Dic5—31no—
221C2×Dic5—31no—
222C2×Dic5—31no—
223C2×Dic5C22×D311yescharacteristic
224C2×Dic5C22×D311yescharacteristic
225C2×Dic5C22×D311yescharacteristic
226D20—34no—
227C4×D5—22no—
228C4×D5—62no—
229C4×D5—62no—
230C4×D5—62no—
231C4×D5—62no—
232C4×D5—62no—
233Dic10—22no—
234Dic10—34no—
235Dic10—62no—
236Dic10—62no—
237Dic10—62no—
238C22×Q8—151no—
239C22×Q8—151no—
240C4⋊Q8—31no—
241C4⋊Q8—151no—
242C4⋊Q8—151no—
243C22⋊Q8—51no—
244C22⋊Q8—151no—
245C22⋊Q8—151no—
246C22⋊Q8—151no—
247C22⋊Q8—151no—
248C22⋊Q8—151no—
249C4×Q8—151no—
250C4×D4—151no—
251C4×D4—151no—
252C4×D4—151no—
253C2×C3×C5C22×D411yescharacteristic
254C2×C3×C5C22×Q811yescharacteristic
255C2×C3×C52−1+411yescharacteristic
256D15—22no—
257C3×D5—22no—
258C23×C3—51no—
259C22×D3—51no—
260C3×Q8—102no—
261C2×C3×C4—51no—
262C2×C3×C4—51no—
263C2×C3×C4—51no—
264C2×C3×C4—102no—
265C2×C3×C4C22×D511yescharacteristic
266C2×C3×C4C22×D511yescharacteristic
267C2×C3×C4C22×D511yescharacteristic
268#67—54no—
269C2×Dic3—51no—
270C2×Dic3—51no—
271C2×Dic3—51no—
272C2×Dic3—102no—
273C2×Dic3—102no—
274C2×Dic3C22×D511yescharacteristic
275C2×Dic3C22×D511yescharacteristic
276C2×Dic3C22×D511yescharacteristic
277C2×Dic3C22×D511yescharacteristic
278C4×D3—102no—
279C4×D3—102no—
280C4×D3—102no—
281Dic6—22no—
282Dic6—22no—
283Dic6—54no—
284Dic6—102no—
285Dic6—102no—
286Dic6—102no—
287C22×C5C23×D311yescharacteristic
288C2×D5—21no—
289C2×D5—21no—
290C2×D5—32no—
291C2×D5—61no—
292C2×D5—61no—
293C2×D5D3×Q812yescomplemented
294C4×C5—21no—
295C4×C5—21no—
296C4×C5—21no—
297C4×C5—32no—
298C4×C5—32no—
299C4×C5—61no—
300C4×C5—61no—
301Dic5—21no—
302Dic5—21no—
303Dic5—32no—
304Dic5—61no—
305Dic5—61no—
306Dic5D3×D412yes—
307C2×Q8—31no—
308C2×Q8—31no—
309C2×Q8—51no—
310C2×Q8—151no—
311C2×Q8—151no—
312C2×Q8—151no—
313C2×Q8—151no—
314C2×Q8—304no—
315C2×Q8—304no—
316C2×D4—151no—
317C22×C4—51no—
318C22×C4—151no—
319C22×C4—151no—
320C22×C4—151no—
321C22×C4—151no—
322C22×C4—151no—
323C4⋊C4—31no—
324C4⋊C4—31no—
325C4⋊C4—31no—
326C4⋊C4—51no—
327C4⋊C4—51no—
328C4⋊C4—151no—
329C4⋊C4—151no—
330C4⋊C4—151no—
331C4⋊C4—151no—
332C4⋊C4—151no—
333C4⋊C4—151no—
334C4⋊C4D3×D511yescharacteristic
335C22⋊C4—51no—
336C22⋊C4—51no—
337C22⋊C4—151no—
338C22⋊C4—151no—
339C22⋊C4—151no—
340C22⋊C4—151no—
341C42—31no—
342C42—151no—
343C42—151no—
344C3×C5D4×Q811yescharacteristic, complemented, Hall
345C22×C3—52no—
346C22×C3—101no—
347C22×C3—101no—
348C22×C3C23×D511yescharacteristic
349C2×D3—52no—
350C2×D3—101no—
351C2×D3—101no—
352C3×C4—21no—
353C3×C4—21no—
354C3×C4—21no—
355C3×C4—52no—
356C3×C4—101no—
357C3×C4—101no—
358Dic3—21no—
359Dic3—21no—
360Dic3—52no—
361Dic3—101no—
362Dic3—101no—
363Dic3D4×D512yes—
364Dic3Q8×D512yescomplemented
365C2×C5C2×D3×D411yescharacteristic
366C2×C5C2×D3×Q811yescharacteristic
367C2×C5#101011yescharacteristic
368D5—22no—
369D5—62no—
370C23—51no—
371C23—151no—
372Q8—62no—
373Q8—62no—
374Q8—102no—
375Q8—154no—
376Q8—302no—
377Q8—302no—
378Q8—302no—
379D4—154no—
380C2×C4—31no—
381C2×C4—31no—
382C2×C4—31no—
383C2×C4—31no—
384C2×C4—51no—
385C2×C4—51no—
386C2×C4—51no—
387C2×C4—102no—
388C2×C4—151no—
389C2×C4—151no—
390C2×C4—151no—
391C2×C4—302no—
392C2×C4—302no—
393C2×C4—302no—
394C2×C4—302no—
395C2×C4—302no—
396C2×C4C2×D3×D511yescharacteristic
397C2×C4C2×D3×D511yescharacteristic
398C2×C4C2×D3×D511yescharacteristic
399C2×C3—102no—
400C2×C3C2×D4×D511yescharacteristic
401C2×C3C2×Q8×D511yescharacteristic
402C2×C3#414711yescharacteristic
403D3—102no—
404C5#563211yescharacteristic, complemented, Sylow
405C22—52no—
406C22—101no—
407C22—101no—
408C22—152no—
409C22—301no—
410C22—301no—
411C22C22×D3×D511yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—32no—
416C4—32no—
417C4—52no—
418C4—61no—
419C4—61no—
420C4—101no—
421C4—101no—
422C4—152no—
423C4—301no—
424C4—301no—
425C3#6606111yescharacteristic, complemented, Sylow
426C2—102no—
427C2—302no—
428C2#9200011yescharacteristic
429C2D3×D4×D511yescharacteristic
430C2D3×Q8×D511yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×D5
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×C4⋊C4C22
prime radicalC2×#1202C22
hypercenterC4⋊C4D3×D5
hypocenterC3×C5D4×Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D15⋊Q8C2semidirect
2. C2×D5×Dic6C2semidirect
3. #91785C2semidirect
4. C5×#888C2semidirect
5. C3×#4042C2semidirect
7. #91430C2semidirect
8. #91424C2semidirect
9. #91421C2semidirect
10. #91419C2semidirect
13. #91328C2semidirect
14. #91327C2semidirect
15. #91324C2semidirect
63. #4042D3semidirect
93. #1204D4semidirect
94. #1202Q8semidirect
108. #888D5semidirect
155. C2×D15C2×Q8semidirect
158. C2×C3×D5C2×Q8semidirect
171. C5×Dic3C2×Q8semidirect
293. C2×D5D3×Q8semidirect
344. C3×C5D4×Q8semidirect
364. Dic3Q8×D5semidirect
404. C5#5632semidirect
425. C3#66061semidirect

Maximal subgroups

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

subgroupindex
C2×D15⋊Q82
C2×D5×Dic62
#917852
C5×#8882
C3×#40422
#914442
#914302
#914242
#914212
#914192
#913962
#913952
#913282
#913272
#913242
#660613
#56325