Finite Group Databasebeta

← #14471940

Subgroups — #14471940

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752554C211yesmaximal, characteristic
2#11752472C211yesmaximal, characteristic, complemented
3C8×Dic30C211yesmaximal, characteristic, complemented
4C4×C5×#204C211yesmaximal, characteristic, complemented
5C3×#64983C211yesmaximal, characteristic, complemented
6#11748011C212yesmaximal, complemented
7#11748001C212yesmaximal, complemented
8#11747802C212yesmaximal, complemented
9#11747735C212yesmaximal, complemented
10#11747068C211yesmaximal, characteristic, complemented
11#11746882C211yesmaximal, characteristic, complemented
12#10611353—31nomaximal, Hall
13C2×#6765—21no—
14C4×Dic30C2211yescharacteristic
15C2×C5×#204C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×#4020C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91470C2212yes—
21#91469—21no—
22#91463C2212yes—
23#91456—21no—
24#91434C2212yes—
25#91408—22no—
26#91344C2212yes—
27#91340—21no—
28#91327—22no—
29C2×#6655C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#821C2211yescharacteristic
35C5×#817C2211yescharacteristic
36C5×#816C2211yescharacteristic
37C3×#3953C2212yes—
38C3×#3953C2212yes—
39#90986C2212yes—
40#90966C2212yes—
41#90964C2212yes—
42#81588—51nomaximal, Hall
43Q8×Dic10—31no—
44#65887—31no—
45C4×C5×SD16—31no—
46#65452—32no—
47#65316—31no—
48#65297—31no—
49#65159—32no—
50#65077—32no—
51#65049—32no—
52#64983D311yescharacteristic, complemented
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C4×C5×D3—21no—
57C2×C5×Dic6C2311yescharacteristic
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20C2312yes—
61C2×C3×Dic10—21no—
62C2×#1204—22no—
63C2×#1201—22no—
64C2×#1201—22no—
65C2×D5×Dic3—22no—
66#6765—44no—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C42×C5C2311yescharacteristic
70C4⋊Dic15D411yescharacteristic
71#6712D412yes—
72C4×Dic15C2312yes—
73C2×C3⋊#168C2312yes—
74C5×(C2×D3)⋊C4—21no—
75C5×C4⋊Dic3C2311yescharacteristic
76C5×C4⋊Dic3C2311yescharacteristic
77C5×Dic3⋊C4—21no—
78C4×C5×Dic3—21no—
79C5×#204—22no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2312yes—
82Dic3⋊Dic5—22no—
83#6669—22no—
84#6665—22no—
85Dic3×Dic5—22no—
86#6655—24no—
87#5722—51no—
88#5718—51no—
89C3×#486—51no—
90#5084—51no—
91#5075—51no—
92#4762—52no—
93#4761—52no—
94#4760—52no—
95#4758—52no—
96C4×#204D511yescharacteristic, complemented
97C8×Dic6—51no—
98C2×#709—61no—
99C2×C5×SD16—31no—
100C4×C5×Q8—31no—
101C4×C5×D4—31no—
102Q8×Dic5—32no—
103C2×#688—32no—
104#4086—32no—
105#4076—61no—
106#4039—32no—
107#4034—32no—
108#4034—62no—
109#4030—62no—
110#4020C2×D311yescharacteristic
111#4015—61no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×#106—31no—
116C5×#103—31no—
117C5×#102—31no—
118C4×C5×C8C2×D311yescharacteristic
119#3964—32no—
120#3953C2×D312yes—
121#3953C2×D312yes—
122#3946—32no—
123C8×Dic5—32no—
124#3941—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3362—151noSylow
128C22×C5×D3—21no—
129C22×C3×D5—22no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15C2×D412yes—
134C2×Dic15C2×D412yes—
135Dic30SD1614yescomplemented
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3—21no—
139C5×D12—21no—
140C5×D12—21no—
141C4×C5×D3—42no—
142C5×Dic6—21no—
143C5×Dic6#4112yescomplemented
144C2×C3×Dic5—22no—
145C3×D20—22no—
146C3×D20—22no—
147C3×D20—42no—
148C3×D20—81no—
149C3×Dic10—81no—
150#1204—82no—
151#1201—44no—
152#1201—82no—
153D5×Dic3—44no—
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C3⋊#168—22no—
157C2×#237—101no—
158C3×C4⋊Q8—51no—
159C3×#127—51no—
160#944—102no—
161#940—52no—
162#939—102no—
163#938—101no—
164D4×Dic3—52no—
165C2×#214—52no—
166C2×#204C2×D511yescharacteristic
167#888—52no—
168#888—101no—
169#887—52no—
170#887—101no—
171C4×D12C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6C2×D511yescharacteristic
174C3×#102—52no—
175C3×#102—52no—
176C3×C4×C8C2×D511yescharacteristic
177#832—52no—
178#821C2×D511yescharacteristic
179#817C2×D511yescharacteristic
180#816C2×D511yescharacteristic
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809—52no—
184#808—52no—
185C4⋊(C3⋊C8)—51no—
186C2×C5×Q8—31no—
187C2×C5×D4—31no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—21no—
193C2×D20—21no—
194C2×D20C22×D312yes—
195C2×C4×D5—62no—
196C2×Dic10—21no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C5×SD16—62no—
200C2×C5×C8C22×D311yescharacteristic
201C2×C5×C8C22×D311yescharacteristic
202C5×C4⋊C4—31no—
203C5×C4⋊C4—31no—
204C5×C4⋊C4—61no—
205C5×C22⋊C4—61no—
206C42×C5—61no—
207C42×C5C22×D311yescharacteristic
208#688—64no—
209#685—62no—
210C4⋊Dic5—21no—
211C4⋊Dic5—31no—
212C4⋊Dic5—62no—
213C4⋊Dic5C22×D312yes—
214#683—32no—
215#683—62no—
216C4×Dic5—32no—
217C4×Dic5—62no—
218C2×#168—32no—
219Q82—151no—
220#550—151no—
221#486—51no—
222#486—152no—
223#476—152no—
224#476—151no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—31no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×C5×D3—41no—
232C2×C5×D3—41no—
233C2×C5×D3—41no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—42no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—22no—
242Dic15C2×SD1614yes—
243C3×Dic5—42no—
244C5×Dic3—22no—
245C5×Dic3—41no—
246C5×Dic3—41no—
247C2×C3×Q8—101no—
248C2×C3×D4—52no—
249C2×C3×D4—101no—
250C2×C3×D4—101no—
251C2×#67—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—204no—
255C2×D12C22×D511yescharacteristic
256C2×C4×D3—21no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6C22×D511yescharacteristic
260C2×C3×C8C22×D511yescharacteristic
261C2×C3×C8C22×D511yescharacteristic
262C3×C4⋊C4—52no—
263C3×C4⋊C4—101no—
264C3×C42C22×D511yescharacteristic
265#217—102no—
266#214—104no—
267(C2×D3)⋊C4—21no—
268C4⋊Dic3—51no—
269C4⋊Dic3C22×D511yescharacteristic
270C4⋊Dic3C22×D511yescharacteristic
271Dic3⋊C4—21no—
272Dic3⋊C4—52no—
273Dic3⋊C4—102no—
274Dic3⋊C4—102no—
275C4×Dic3—21no—
276C4×Dic3—52no—
277C4×Dic3—102no—
278C2×C3⋊C8—52no—
279#204—22no—
280C23×C5—61no—
281C22×D5—22no—
282C5×Q8—32no—
283C5×Q8—61no—
284C5×D4—61no—
285C5×D4—61no—
286C2×C4×C5—61no—
287C2×C4×C5—61no—
288C2×C4×C5—61no—
289C2×C4×C5—122no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—22no—
296C2×Dic5—32no—
297C2×Dic5—32no—
298D20—22no—
299D20—22no—
300D20—42no—
301D20—81no—
302C4×D5—124no—
303Dic10—34no—
304Dic10—81no—
305Dic10—242no—
306C5×C8—21no—
307C5×C8—21no—
308#168—62no—
309C2×#41—301no—
310C2×SD16—31no—
311C2×SD16—152no—
312C4⋊Q8—51no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—51no—
317#127—152no—
318#121—302no—
319#121—301no—
320C4×Q8—31no—
321C4×Q8—151no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—31no—
325C4×D4—152no—
326#106—31no—
327#106—152no—
328C4⋊C8—152no—
329C4⋊C8—151no—
330#103—31no—
331#102—31no—
332#102—52no—
333#102—52no—
334#102—152no—
335#102—152no—
336C4×C8—152no—
337C4×C8D3×D511yescharacteristic
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341C3×D5—82no—
342C5×D3—81no—
343C23×C3—102no—
344C22×D3—21no—
345C3×Q8—401no—
346C3×D4—102no—
347C3×D4—102no—
348C3×D4—202no—
349C3×D4—401no—
350C2×C3×C4—102no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—21no—
359C2×Dic3—52no—
360C2×Dic3—52no—
361C2×Dic3—204no—
362D12—21no—
363D12—21no—
364C4×D3—42no—
365Dic6—21no—
366Dic6—54no—
367Dic6—402no—
368Dic6#70912yescomplemented
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—102no—
372C22×C5—121no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—42no—
377C2×D5—42no—
378C2×D5—42no—
379C4×C5—21no—
380C4×C5—62no—
381C4×C5—121no—
382C4×C5—121no—
383C4×C5D3×SD1612yes—
384C4×C5D3×#4111yescharacteristic
385C4×C5#101011yescharacteristic
386Dic5—34no—
387Dic5—42no—
388Dic5—62no—
389#41—604no—
390C2×Q8—31no—
391C2×Q8—101no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—31no—
395C2×D4—52no—
396C2×D4—101no—
397C2×D4—101no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—61no—
401C22×C4—302no—
402SD16—62no—
403SD16—304no—
404C2×C8—152no—
405C2×C8C2×D3×D511yescharacteristic
406C2×C8C2×D3×D511yescharacteristic
407C4⋊C4—31no—
408C4⋊C4—31no—
409C4⋊C4—52no—
410C4⋊C4—61no—
411C4⋊C4—101no—
412C4⋊C4—152no—
413C4⋊C4—151no—
414C4⋊C4—302no—
415C4⋊C4—302no—
416C22⋊C4—61no—
417C22⋊C4—302no—
418C42—61no—
419C42—152no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—202no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—41no—
428C2×D3—41no—
429C2×D3—41no—
430C3×C4—21no—
431C3×C4—202no—
432C3×C4D5×SD1612yes—
433C3×C4C2×#70911yescharacteristic
434C3×C4#415011yescharacteristic
435Dic3—22no—
436Dic3—41no—
437Dic3—41no—
438Dic3—54no—
439Dic3—102no—
440C2×C5—241no—
441C2×C5#567711yescharacteristic
442C2×C5#575711yescharacteristic
443C2×C5C2×D3×SD1611yescharacteristic
444D5—82no—
445C23—61no—
446C23—102no—
447Q8—32no—
448Q8—61no—
449Q8—154no—
450Q8—401no—
451Q8—1202no—
452D4—61no—
453D4—61no—
454D4—102no—
455D4—102no—
456D4—202no—
457D4—401no—
458D4—604no—
459D4—1202no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—61no—
463C2×C4—102no—
464C2×C4—122no—
465C2×C4—152no—
466C2×C4—152no—
467C2×C4—604no—
468C2×C4#677711yescharacteristic
469C2×C4#677711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—21no—
472C8—21no—
473C8—302no—
474C2×C3—402no—
475C2×C3#6588611yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610311yescharacteristic
478D3—81no—
479C5#8158811yescharacteristic, complemented, Sylow
480C22—121no—
481C22—121no—
482C22—121no—
483C22—202no—
484C22—202no—
485C22—202no—
486C22C2×#677711yescharacteristic
487C4—21no—
488C4—62no—
489C4—121no—
490C4—121no—
491C4—154no—
492C4—202no—
493C4—302no—
494C4#9125512yes—
495C4#9200111yescharacteristic
496C4D3×#70911yescharacteristic
497C3#1061135311yescharacteristic, complemented, Sylow
498C2—241no—
499C2—402no—
500C2#1175255511yescharacteristic
501C2C2×#9125511yescharacteristic
502C2#1175398111yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11752554C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
2. #11752472C2semidirect
3. C8×Dic30C2semidirect
4. C4×C5×#204C2semidirect
5. C3×#64983C2semidirect
6. #11748011C2semidirect
7. #11748001C2semidirect
8. #11747802C2semidirect
9. #11747735C2semidirect
10. #11747068C2semidirect
11. #11746882C2semidirect
52. #64983D3semidirect
96. C4×#204D5semidirect
135. Dic30SD16semidirect
143. C5×Dic6#41semidirect
368. Dic6#709semidirect
422. C3×C5#3362semidirect
479. C5#81588semidirect
497. C3#10611353semidirect

Maximal subgroups

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

subgroupindex
#117525542
#117524722
C8×Dic302
C4×C5×#2042
C3×#649832
#117480112
#117480012
#117478022
#117477352
#117470682
#117468822
#106113533
#815885