Finite Group Databasebeta

← #14460054

Subgroups — #14460054

Order 1920.

772 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#11752561C211yesmaximal, characteristic
2#11752491C211yesmaximal, characteristic, complemented
3#11750947C211yesmaximal, characteristic, complemented
4C5×#4834C211yesmaximal, characteristic, complemented
5C3×#65138C211yesmaximal, characteristic, complemented
6#11748152C212yesmaximal, complemented
7#11747952C212yesmaximal, complemented
8#11747684C212yesmaximal, complemented
9#11747643C212yesmaximal, complemented
10C4×#6658C211yesmaximal, characteristic, complemented
11#11746920C211yesmaximal, characteristic, complemented
12#10611173—31nomaximal, Hall
13C2×#6769C2212yes—
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C2×C5×D3×C8C2212yes—
17C4×C5×D12C2211yescharacteristic
18C2×C3×Dic20C2212yes—
19C3×#4015C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21#91466—21no—
22#91438—22no—
23#91437—21no—
24#91373—21no—
25#91369C2212yes—
26#91369C2212yes—
27#91342—22no—
28#91338C2212yes—
29#91333—21no—
30C2×#6658C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic
32#91105C2212yes—
33#91102C2212yes—
34C5×(C2×D3)⋊C8C2212yes—
35C4×C5×C3⋊C8C2211yescharacteristic
36C3×#3948C2212yes—
37#90987C2211yescharacteristic
38#90971C2212yes—
39#90971C2212yes—
40#90971C2211yescharacteristic
41#90968C2211yescharacteristic
42#80492—51nomaximal, Hall
43#65885—31no—
44#65876—31no—
45C5×C8×D4—31no—
46#65405—32no—
47#65402—32no—
48#65138D311yescharacteristic, complemented
49#65135—31no—
50#65022—32no—
51#65012—32no—
52C4×#677—31no—
53#64970—31no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30—21no—
57C2×C5×D12D411yescharacteristic
58C2×C4×C5×D3C2312yes—
59C2×C3×Dic10C2312yes—
60C2×C3×Dic10C2311yescharacteristic
61C2×#1203—22no—
62C2×#1200—22no—
63#6769—24no—
64#6769—42no—
65C2×C3×C5×C8C2312yes—
66C3×C42×C5C2311yescharacteristic
67#6714—21no—
68C4⋊Dic15—21no—
69C4⋊Dic15C2312yes—
70C4⋊Dic15C2311yescharacteristic
71C5×(C2×D3)⋊C4D412yes—
72C5×C4⋊Dic3D411yescharacteristic
73C2×C5×C3⋊C8C2311yescharacteristic
74C2×C5×C3⋊C8C2311yescharacteristic
75C5×D3×C8—42no—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#683—21no—
80C3×C4×Dic5—21no—
81C3×Dic20—42no—
82#6669—22no—
83#6669—22no—
84(C2×D3)⋊Dic5—22no—
85(C2×D3)⋊Dic5—22no—
86(C2×D3)⋊Dic5—22no—
87Dic3×Dic5—22no—
88#6658—22no—
89#5726—51no—
90#5584—51no—
91C3×#462—51no—
92#5188—52no—
93#5187—52no—
94#5079—51no—
95C4×#215—51no—
96#4846—51no—
97#4834D511yescharacteristic, complemented
98#4814—52no—
99#4804—52no—
100C2×#709—32no—
101C22×C5×C8—32no—
102C4×C5×D4—31no—
103#4084—61no—
104#4082—61no—
105#4072—32no—
106#4070—32no—
107#4070—32no—
108C2×Dic20C2×D312yes—
109C2×#677—31no—
110D5×C4⋊C4—61no—
111#4033—61no—
112#4029—62no—
113#4025—62no—
114C4×D20—31no—
115#4015—31no—
116#4015C2×D311yescharacteristic
117C4×Dic10C2×D311yescharacteristic
118C5×C4⋊C8C2×D311yescharacteristic
119C5×C22⋊C8—32no—
120C4×C5×C8—31no—
121#3953—32no—
122#3953—31no—
123#3950—32no—
124#3949—31no—
125#3948—32no—
126#3948—31no—
127#3948—32no—
128#3948C2×D312yes—
129#3302—151noSylow
130C22×D15—21no—
131C22×C5×D3C2×D412yes—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136C2×Dic15—21no—
137D60—21no—
138D60#4112yes—
139C4×D15—42no—
140Dic30—42no—
141C2×C5×Dic3C2×D412yes—
142C5×D12—22no—
143C4×C5×D3—22no—
144C4×C5×D3—22no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—22no—
148C3×Dic10—21no—
149C3×Dic10—22no—
150C3×Dic10—21no—
151C3×Dic10—22no—
152#1203—44no—
153#1200—44no—
154C3×C5×C8—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#239—52no—
158C2×C3×Q16—52no—
159C3×C4⋊Q8—51no—
160C3×C4×Q8—51no—
161#946—52no—
162#946—52no—
163C2×#215—51no—
164C2×D3×C8C2×D512yes—
165#898—102no—
166#895—101no—
167#894—102no—
168#892—52no—
169D3×C4⋊C4—101no—
170#875—101no—
171C4×D12—51no—
172C4×D12C2×D511yescharacteristic
173#869—51no—
174C4×Dic6—101no—
175C3×C4⋊C8C2×D511yescharacteristic
176C3×#103—52no—
177#835—52no—
178#835—51no—
179#835—52no—
180#821—52no—
181(C2×D3)⋊C8C2×D512yes—
182#818—52no—
183#809—51no—
184#808—51no—
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×D4—31no—
187C22×C4×C5—32no—
188C2×C22⋊D5—62no—
189#709—64no—
190#709—122no—
191C2×D20—31no—
192C2×C4×D5—62no—
193C2×C4×D5—61no—
194C2×Dic10—61no—
195C2×Dic10C22×D312yes—
196C2×Dic10C22×D311yescharacteristic
197C2×C5×C8—31no—
198C2×C5×C8—31no—
199C2×C5×C8—122no—
200C2×C5×C8C22×D312yes—
201C5×C4⋊C4—31no—
202C5×C22⋊C4—32no—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—62no—
205C22⋊Dic5—62no—
206C22⋊Dic5—62no—
207#685—61no—
208C4⋊Dic5—21no—
209C4⋊Dic5—21no—
210C4⋊Dic5—32no—
211C4⋊Dic5—31no—
212C4⋊Dic5—61no—
213C4⋊Dic5C22×D311yescharacteristic
214#683—21no—
215#683—62no—
216#683—62no—
217C4×Dic5—21no—
218C4×Dic5—62no—
219Dic20—42no—
220#677—62no—
221#556—151no—
222#547—151no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—51no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—31no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—22no—
234C2×D15—41no—
235C2×D15—41no—
236C2×C5×D3—22no—
237C2×C5×D3—22no—
238C2×C5×D3—22no—
239C3×C4×C5—21no—
240C3×C4×C5#13512yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C5H(5,𝔽2)11yescharacteristic
243Dic15—42no—
244Dic15—41no—
245C3×Dic5—42no—
246C3×Dic5—41no—
247C3×Dic5—41no—
248C5×Dic3—22no—
249C2×C3×Q8—52no—
250C2×C3×Q8—51no—
251#239—104no—
252#239—202no—
253C2×D12—51no—
254C2×D12—102no—
255C2×D12D2011yescharacteristic
256C2×C4×D3—101no—
257C2×C4×D3—102no—
258C2×C4×D3C22×D512yes—
259C2×Dic6—101no—
260C3×Q16—202no—
261C2×C3×C8C22×D512yes—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—101no—
264C3×C4⋊C4—101no—
265C3×C4⋊C4—101no—
266C3×C42—101no—
267C3×C42C22×D511yescharacteristic
268#215—102no—
269(C2×D3)⋊C4—102no—
270(C2×D3)⋊C4—102no—
271(C2×D3)⋊C4—102no—
272(C2×D3)⋊C4—101no—
273(C2×D3)⋊C4D2012yes—
274C4⋊Dic3—51no—
275C4⋊Dic3—52no—
276C4⋊Dic3—101no—
277C4⋊Dic3D2011yescharacteristic
278Dic3⋊C4—102no—
279Dic3⋊C4—102no—
280C4×Dic3—102no—
281C2×C3⋊C8C22×D511yescharacteristic
282C2×C3⋊C8C22×D511yescharacteristic
283D3×C8—42no—
284C23×C5—32no—
285C22×D5—61no—
286C5×D4—62no—
287C2×C4×C5—32no—
288C2×C4×C5—62no—
289C2×C4×C5—62no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—22no—
297C2×Dic5—62no—
298C2×Dic5—61no—
299D20—32no—
300D20—61no—
301C4×D5—124no—
302C4×D5—122no—
303Dic10—21no—
304Dic10—22no—
305Dic10—21no—
306Dic10—22no—
307Dic10—122no—
308C5×C8—22no—
309C5×C8—61no—
310C5×C8—61no—
311C2×#41—152no—
312C2×Q16—52no—
313C2×SD16—151no—
314C22×C8—32no—
315C4⋊Q8—51no—
316C4⋊Q8—151no—
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—51no—
324C4×Q8—301no—
325C4×D4—31no—
326C4×D4—151no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—151no—
331C4⋊C8D3×D511yescharacteristic
332#103—52no—
333#103—152no—
334#103—151no—
335#103—152no—
336#102—151no—
337#102—152no—
338C22⋊C8—32no—
339C4×C8—31no—
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343D15—42no—
344C5×D3—42no—
345C22×D3—101no—
346C22×D3C2×D2012yes—
347C3×Q8—101no—
348C3×Q8—102no—
349C3×Q8—101no—
350C3×Q8—102no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4—102no—
354C2×C3×C4C2×D2011yescharacteristic
355C2×C3×C4C2×D2011yescharacteristic
356C2×C3×C4C23×D511yescharacteristic
357C2×Dic3—102no—
358C2×Dic3—101no—
359C2×Dic3C2×D2012yes—
360D12—22no—
361D12—52no—
362D12—101no—
363D12—204no—
364C4×D3—22no—
365C4×D3—22no—
366C4×D3—204no—
367C4×D3—202no—
368Dic6—202no—
369C3×C8—22no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C22×C5—62no—
373C22×C5—62no—
374C22×C5—62no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—62no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—62no—
381C4×C5#91912yes—
382C4×C5#100411yescharacteristic
383C4×C5D3×#4111yescharacteristic
384Dic5—41no—
385Dic5—42no—
386Dic5—41no—
387Dic5—122no—
388Dic5—121no—
389#41—304no—
390#41—602no—
391C2×Q8—52no—
392C2×Q8—51no—
393C2×Q8—301no—
394C2×D4—31no—
395C2×D4—151no—
396C2×D4—302no—
397C22×C4—32no—
398C22×C4—302no—
399C22×C4—301no—
400Q16—202no—
401SD16—302no—
402C2×C8—31no—
403C2×C8—31no—
404C2×C8—122no—
405C2×C8C2×D3×D512yes—
406C4⋊C4—31no—
407C4⋊C4—51no—
408C4⋊C4—101no—
409C4⋊C4—101no—
410C4⋊C4—101no—
411C4⋊C4—152no—
412C4⋊C4—151no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—32no—
417C22⋊C4—302no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—301no—
421C42—101no—
422C42—302no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3C22×D2011yescharacteristic
426C2×D3—22no—
427C2×D3—22no—
428C2×D3—22no—
429C2×D3—102no—
430C2×D3—201no—
431C2×D3—201no—
432C3×C4—21no—
433C3×C4—201no—
434C3×C4—202no—
435C3×C4—201no—
436C3×C4#405012yes—
437C3×C4#414411yescharacteristic
438C3×C4D5×#4111yescharacteristic
439Dic3—22no—
440Dic3—202no—
441Dic3—201no—
442C2×C5—122no—
443C2×C5#561211yescharacteristic
444C2×C5C2×#91911yescharacteristic
445C2×C5#577911yescharacteristic
446D5—122no—
447C23—32no—
448C23—301no—
449Q8—101no—
450Q8—102no—
451Q8—101no—
452Q8—102no—
453Q8—602no—
454D4—62no—
455D4—152no—
456D4—301no—
457D4—604no—
458C2×C4—32no—
459C2×C4—62no—
460C2×C4—62no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—102no—
464C2×C4—302no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D3×D2011yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—22no—
472C8—61no—
473C8—61no—
474C2×C3#6588811yescharacteristic
475C2×C3C2×#405011yescharacteristic
476C2×C3#6608711yescharacteristic
477D3—42no—
478D3—202no—
479C5#8049211yescharacteristic, complemented, Sylow
480C22—62no—
481C22—62no—
482C22—62no—
483C22—302no—
484C22—601no—
485C22—601no—
486C22C2×D3×D2011yescharacteristic
487C4—21no—
488C4—62no—
489C4—201no—
490C4—202no—
491C4—201no—
492C4—601no—
493C4—602no—
494C4#9127512yes—
495C4#9202511yescharacteristic
496C4#9203411yescharacteristic
497C3#1061117311yescharacteristic, complemented, Sylow
498C2—122no—
499C2—602no—
500C2#1175388311yescharacteristic
501C2C2×#9127511yescharacteristic
502C2#1175404211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11752561C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3302
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. #11752491C2semidirect
3. #11750947C2semidirect
4. C5×#4834C2semidirect
5. C3×#65138C2semidirect
6. #11748152C2semidirect
7. #11747952C2semidirect
8. #11747684C2semidirect
9. #11747643C2semidirect
10. C4×#6658C2semidirect
11. #11746920C2semidirect
48. #65138D3semidirect
97. #4834D5semidirect
424. C3×C5#3302semidirect
479. C5#80492semidirect
497. C3#10611173semidirect

Maximal subgroups

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

subgroupindex
#117525612
#117524912
#117509472
C5×#48342
C3×#651382
#117481522
#117479522
#117476842
#117476432
C4×#66582
#117469202
#106111733
#804925