Finite Group Databasebeta

← #14439916

Subgroups — #14439916

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752631C211yesmaximal, characteristic
2#11752562C211yesmaximal, characteristic
3D15×#97C211yesmaximal, characteristic
4C5×#4702C211yesmaximal, characteristic, complemented
5C3×#64991C211yesmaximal, characteristic, complemented
6#11748039C212yesmaximal, complemented
7#11748038C212yesmaximal, complemented
8#11747636C212yesmaximal
9#11747632C212yesmaximal
10#11746970C211yesmaximal, characteristic, complemented
11#11746969C211yesmaximal, characteristic, complemented
12D5×#501—31nomaximal, Hall
13C2×D15⋊Q8—21no—
14C2×C8×D15C2212yes—
15C42×D15C2211yescharacteristic
16C5×#870C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C3×#4016C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91470—21no—
21#91470C2212yes—
22#91437—21no—
23#91437C2211yescharacteristic
24#91437C2212yes—
25#91437C2211yescharacteristic
26#91404—21no—
27#91404—21no—
28#91385—21no—
29#91384C2211yescharacteristic
30#91384C2211yescharacteristic
31#91382—21no—
32#91382—21no—
33C3×C5×#97C2211yescharacteristic
34#91099C2212yes—
35#91087C2211yescharacteristic
36C5×#818C2212yes—
37C5×#817C2212yes—
38C3×#3950C2212yes—
39C3×#3949C2212yes—
40#90989C2212yes—
41#90989C2212yes—
42#90986C2212yes—
43#90986C2212yes—
44D3×#501—51nomaximal, Hall
45D5×C4⋊Q8—31no—
46D5×#125—31no—
47C5×#501—31no—
48#65369—31no—
49#65354—31no—
50D5×#107—32no—
51#65165—32no—
52D5×#106—32no—
53#65145—32no—
54D5×#97—31no—
55#64991D311yescharacteristic, complemented
56C2×C4×D15D411yescharacteristic
57C2×C4×D15D411yescharacteristic
58C2×C4×D15C2311yescharacteristic
59C2×C5×Dic6—21no—
60C2×C3×Dic10—21no—
61C2×#1204—22no—
62C2×#1200—21no—
63C2×#1200—21no—
64C2×#1200—22no—
65D15⋊Q8—44no—
66C2×C3×C5×C8C2312yes—
67C3×C42×C5C2311yescharacteristic
68C4×Dic15D411yescharacteristic
69C4×Dic15D411yescharacteristic
70C4×Dic15C2311yescharacteristic
71C2×C3⋊#168C2312yes—
72C8×D15Q818yescomplemented
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3C2312yes—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×C4⋊Dic3C2311yescharacteristic
77C5×Dic3⋊C4—21no—
78C5×Dic3⋊C4—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2312yes—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×#683—21no—
84C3×#683—21no—
85Dic3⋊Dic5—21no—
86Dic3⋊Dic5—21no—
87#6669—22no—
88#6669—22no—
89#6669—21no—
90#6669—21no—
91#6668—21no—
92#6668—21no—
93D3×C4⋊Q8—51no—
94D3×#125—51no—
95C3×#501—51no—
96#5081—51no—
97#5064—51no—
98D3×#107—52no—
99#4876—52no—
100D3×#106—52no—
101#4856—52no—
102D3×#97—51no—
103#4702D511yescharacteristic, complemented
104C2×Q8×D5—61no—
105C5×C4⋊Q8—31no—
106C5×#125—31no—
107#4090—61no—
108C2×C8×D5—32no—
109D5×C4⋊C4—32no—
110D5×C4⋊C4—31no—
111D5×C4⋊C4—31no—
112D5×C4⋊C4—61no—
113D5×C4⋊C4—61no—
114D5×C4⋊C4—61no—
115#4036—31no—
116#4036—31no—
117#4035—61no—
118#4035—61no—
119#4034—32no—
120#4034—61no—
121C42×D5—31no—
122#4016C2×D311yescharacteristic
123#4015C2×D311yescharacteristic
124C5×#107—32no—
125C5×#106—32no—
126C5×#97C2×D311yescharacteristic
127#3950C2×D312yes—
128#3949C2×D312yes—
129#3947—32no—
130#3940—32no—
131#3940—32no—
132#3939—32no—
133#3939—32no—
134#3935—31no—
135C2×#501—151noSylow
136C22×D15C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2411yescharacteristic
140C2×Dic15C2×D411yescharacteristic
141C2×Dic15C2×D411yescharacteristic
142C2×Dic15C2×D411yescharacteristic
143C4×D15—22no—
144C4×D15—22no—
145C4×D15C2×Q814yes—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—22no—
149C5×Dic6—42no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—22no—
153C3×Dic10—42no—
154#1204—44no—
155#1200—44no—
156#1200—42no—
157#1200—42no—
158C3×C5×C8C2×Q814yescomplemented
159C3⋊#168C2×Q814yescomplemented
160C2×D3×Q8—101no—
161C3×C4⋊Q8—51no—
162C3×#125—51no—
163#944—101no—
164C2×D3×C8—52no—
165D3×C4⋊C4—51no—
166D3×C4⋊C4—52no—
167D3×C4⋊C4—51no—
168D3×C4⋊C4—101no—
169D3×C4⋊C4—101no—
170D3×C4⋊C4—101no—
171#890—51no—
172#890—51no—
173#889—101no—
174#889—101no—
175#888—52no—
176#888—101no—
177C42×D3—51no—
178#870C2×D511yescharacteristic
179#869C2×D511yescharacteristic
180C3×#107—52no—
181C3×#106—52no—
182C3×#97C2×D511yescharacteristic
183#818C2×D512yes—
184#817C2×D512yes—
185#815—52no—
186#808—52no—
187#808—52no—
188#807—52no—
189#807—52no—
190#803—51no—
191C2×C5×Q8—61no—
192Q8×D5—124no—
193C2×C4×D5—31no—
194C2×C4×D5—31no—
195C2×C4×D5—31no—
196C2×C4×D5—62no—
197C2×C4×D5—61no—
198C2×C4×D5—61no—
199C2×Dic10—21no—
200C2×Dic10—62no—
201C2×C5×C8C22×D312yes—
202C5×C4⋊C4—31no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4—32no—
205C5×C4⋊C4—61no—
206C5×C4⋊C4—61no—
207C5×C4⋊C4—61no—
208C42×C5C22×D311yescharacteristic
209C4⋊Dic5—21no—
210C4⋊Dic5—61no—
211C4⋊Dic5—61no—
212C4⋊Dic5C22×D311yescharacteristic
213C4⋊Dic5C22×D312yes—
214C4⋊Dic5C22×D311yescharacteristic
215#683—21no—
216#683—21no—
217#683—61no—
218#683—61no—
219#683—62no—
220#683—62no—
221#683—61no—
222#683—61no—
223C4×Dic5—31no—
224C4×Dic5—31no—
225C4×Dic5—31no—
226C2×#168—32no—
227C8×D5—38no—
228C2×C4⋊Q8—151no—
229C2×#125—151no—
230#501—31no—
231#501—51no—
232#501—152no—
233#501—152no—
234#501—151no—
235#501—151no—
236C2×#107—152no—
237C2×#106—152no—
238C2×#97—151no—
239C22×C3×C5C22×D411yescharacteristic
240C2×D15C4⋊Q812yes—
241C2×D15AGL(1,ℤ/8)12yes—
242C2×D15#13712yes—
243C3×C4×C5—21no—
244C3×C4×C5—21no—
245C3×C4×C5C22×Q812yes—
246Dic15—21no—
247Dic15—21no—
248Dic15C4⋊Q812yes—
249C3×Dic5—42no—
250C3×Dic5—41no—
251C3×Dic5—41no—
252C5×Dic3—42no—
253C5×Dic3—41no—
254C5×Dic3—41no—
255C2×C3×Q8—101no—
256D3×Q8—204no—
257C2×C4×D3—51no—
258C2×C4×D3—51no—
259C2×C4×D3—51no—
260C2×C4×D3—101no—
261C2×C4×D3—101no—
262C2×C4×D3—102no—
263C2×Dic6—21no—
264C2×Dic6—102no—
265C2×C3×C8C22×D512yes—
266C3×C4⋊C4—51no—
267C3×C4⋊C4—52no—
268C3×C4⋊C4—51no—
269C3×C4⋊C4—101no—
270C3×C4⋊C4—101no—
271C3×C4⋊C4—101no—
272C3×C42C22×D511yescharacteristic
273C4⋊Dic3—21no—
274C4⋊Dic3—101no—
275C4⋊Dic3—101no—
276C4⋊Dic3C22×D511yescharacteristic
277C4⋊Dic3C22×D512yes—
278C4⋊Dic3C22×D511yescharacteristic
279Dic3⋊C4—21no—
280Dic3⋊C4—21no—
281Dic3⋊C4—102no—
282Dic3⋊C4—102no—
283Dic3⋊C4—101no—
284Dic3⋊C4—101no—
285Dic3⋊C4—101no—
286Dic3⋊C4—101no—
287C4×Dic3—51no—
288C4×Dic3—51no—
289C4×Dic3—51no—
290C2×C3⋊C8—52no—
291D3×C8—58no—
292C22×D5—31no—
293C5×Q8—122no—
294C2×C4×C5—61no—
295C2×C4×C5—61no—
296C2×C4×C5—62no—
297C2×C4×C5D3×D411yescharacteristic
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5C23×D311yescharacteristic
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—22no—
303C2×Dic5—31no—
304C2×Dic5—31no—
305C2×Dic5—31no—
306C4×D5—34no—
307C4×D5—62no—
308C4×D5—62no—
309C4×D5—122no—
310C4×D5—122no—
311C4×D5—124no—
312Dic10—42no—
313Dic10—124no—
314C5×C8D3×Q814yescomplemented
315#168—34no—
316C22×Q8—301no—
317C22×C8—152no—
318C4⋊Q8—31no—
319C4⋊Q8—51no—
320C4⋊Q8—152no—
321C4⋊Q8—301no—
322C4⋊Q8—301no—
323#125—31no—
324#125—51no—
325#125—151no—
326#125—151no—
327#125—301no—
328#125—301no—
329C2×C4⋊C4—151no—
330C2×C4⋊C4—151no—
331C2×C4⋊C4—152no—
332C2×C4⋊C4—301no—
333C2×C4⋊C4—301no—
334C2×C4⋊C4—301no—
335C2×C42—151no—
336#107—32no—
337#107—52no—
338#107—152no—
339#107—152no—
340#106—32no—
341#106—52no—
342#106—152no—
343#106—152no—
344#97—152no—
345#97—151no—
346#97D3×D511yescharacteristic
347C2×C3×C5C2×C4⋊Q811yescharacteristic
348C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
349C2×C3×C5C2×#13711yescharacteristic
350D15#50114yescomplemented
351C22×D3—51no—
352C3×Q8—202no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4—102no—
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4C23×D511yescharacteristic
359C2×Dic3—21no—
360C2×Dic3—21no—
361C2×Dic3—22no—
362C2×Dic3—51no—
363C2×Dic3—51no—
364C2×Dic3—51no—
365C4×D3—54no—
366C4×D3—102no—
367C4×D3—102no—
368C4×D3—202no—
369C4×D3—202no—
370C4×D3—204no—
371Dic6—42no—
372Dic6—204no—
373C3×C8Q8×D514yescomplemented
374C3⋊C8—54no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—32no—
377C2×D5—32no—
378C2×D5—32no—
379C4×C5—21no—
380C4×C5—21no—
381C4×C5—122no—
382C4×C5—121no—
383C4×C5—121no—
384C4×C5C2×D3×Q812yes—
385Dic5—32no—
386Dic5—42no—
387Dic5—41no—
388Dic5—41no—
389Dic5—61no—
390Dic5—61no—
391C2×Q8—61no—
392C2×Q8—101no—
393C2×Q8—302no—
394C2×Q8—604no—
395C22×C4—151no—
396C22×C4—151no—
397C22×C4—151no—
398C22×C4—301no—
399C22×C4—301no—
400C22×C4—302no—
401C2×C8—152no—
402C2×C8—158no—
403C2×C8C2×D3×D512yes—
404C4⋊C4—31no—
405C4⋊C4—32no—
406C4⋊C4—31no—
407C4⋊C4—51no—
408C4⋊C4—52no—
409C4⋊C4—51no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—61no—
413C4⋊C4—101no—
414C4⋊C4—101no—
415C4⋊C4—101no—
416C4⋊C4—301no—
417C4⋊C4—301no—
418C4⋊C4—302no—
419C4⋊C4—301no—
420C4⋊C4—301no—
421C4⋊C4—301no—
422C4⋊C4—301no—
423C4⋊C4—302no—
424C42—151no—
425C42—151no—
426C42—151no—
427C42C2×D3×D511yescharacteristic
428C3×C5C2×#50111yescharacteristic, complemented, Hall
429C22×C3C2×D4×D511yescharacteristic
430C2×D3—52no—
431C2×D3—52no—
432C2×D3—52no—
433C3×C4—21no—
434C3×C4—21no—
435C3×C4—202no—
436C3×C4—201no—
437C3×C4—201no—
438C3×C4C2×Q8×D512yes—
439Dic3—42no—
440Dic3—41no—
441Dic3—41no—
442Dic3—52no—
443Dic3—101no—
444Dic3—101no—
445C2×C5D3×C4⋊Q811yescharacteristic
446C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
447C2×C5D3×#13711yescharacteristic
448D5—34no—
449C23—151no—
450Q8—122no—
451Q8—202no—
452Q8—604no—
453C2×C4—61no—
454C2×C4—61no—
455C2×C4—62no—
456C2×C4—101no—
457C2×C4—101no—
458C2×C4—102no—
459C2×C4—151no—
460C2×C4—154no—
461C2×C4—151no—
462C2×C4—151no—
463C2×C4—302no—
464C2×C4—302no—
465C2×C4—604no—
466C2×C4—602no—
467C2×C4—602no—
468C2×C4#677711yescharacteristic
469C2×C4#677711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—154no—
472C8D15⋊Q814yescomplemented
473C2×C3D5×C4⋊Q811yescharacteristic
474C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
475C2×C3D5×#13711yescharacteristic
476D3—54no—
477C5D3×#50111yescharacteristic, complemented, Sylow
478C22—152no—
479C22—152no—
480C22—152no—
481C22C2×#677711yescharacteristic
482C4—21no—
483C4—21no—
484C4—122no—
485C4—121no—
486C4—121no—
487C4—152no—
488C4—202no—
489C4—201no—
490C4—201no—
491C4—301no—
492C4—301no—
493C4C2×D15⋊Q812yes—
494C3D5×#50111yescharacteristic, complemented, Sylow
495C2—154no—
496C2#1175256211yescharacteristic
497C2#1175403311yescharacteristic
498C2#1175403411yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
prime radicalC22×D15C2×D4
hypercenter#97D3×D5
hypocenterC3×C5C2×#501
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
4. C5×#4702C2semidirect
5. C3×#64991C2semidirect
6. #11748039C2semidirect
7. #11748038C2semidirect
10. #11746970C2semidirect
11. #11746969C2semidirect
55. #64991D3semidirect
72. C8×D15Q8semidirect
103. #4702D5semidirect
158. C3×C5×C8C2×Q8semidirect
159. C3⋊#168C2×Q8semidirect
314. C5×C8D3×Q8semidirect
350. D15#501semidirect
373. C3×C8Q8×D5semidirect
428. C3×C5C2×#501semidirect
472. C8D15⋊Q8semidirect
477. C5D3×#501semidirect
494. C3D5×#501semidirect

Maximal subgroups

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

subgroupindex
#117526312
#117525622
D15×#972
C5×#47022
C3×#649912
#117480392
#117480382
#117476362
#117476322
#117469702
#117469692
D5×#5013
D3×#5015