Finite Group Databasebeta

← #14460014

Subgroups — #14460014

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#11756301C211yesmaximal, characteristic, complemented
2C3×#65885C211yesmaximal, characteristic
3C5×D4×C3⋊C8C211yesmaximal, characteristic, complemented
4#11748560C212yesmaximal, complemented
5#11748531C212yesmaximal, complemented
6#11748446C212yesmaximal, complemented
7#11748365C212yesmaximal, complemented
8#11747104C211yesmaximal, characteristic, complemented
9C4×#6657C211yesmaximal, characteristic, complemented
10#11746920C211yesmaximal, characteristic, complemented
11#11746889C211yesmaximal, characteristic, complemented
12#10611173—31nomaximal, Hall
13C2×C3×#709C2212yes—
14C3×C4×C5×D4C2211yescharacteristic
15#91825—21no—
16#91815C2212yes—
17#91813C2212yes—
18#91776—21no—
19#91768—22no—
20#91758C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C22×C5×C3⋊C8C2212yes—
23C3×#4084—21no—
24C3×#4070C2212yes—
25C3×D5×C4⋊C4—21no—
26C3×#4029—22no—
27C3×C4×D20C2211yescharacteristic
28C3×#4015C2211yescharacteristic
29C2×#6662C2212yes—
30C2×#6657C2211yescharacteristic
31C5×#830C2212yes—
32C5×C4⋊(C3⋊C8)C2211yescharacteristic
33C4×C5×C3⋊C8C2211yescharacteristic
34#90990C2212yes—
35#90987C2211yescharacteristic
36#90974C2211yescharacteristic
37#90971C2212yes—
38#90971C2212yes—
39#90971C2212yes—
40#90965C2211yescharacteristic
41#90965C2212yes—
42#83510—51nomaximal, Hall
43#65885D311yescharacteristic
44#65876—31no—
45C5×C8×D4—31no—
46#65405—32no—
47#65402—32no—
48#65138—31no—
49#65135—31no—
50#65022—32no—
51#65012—32no—
52C4×#677—31no—
53#64970—31no—
54C2×C3×C5×D4D411yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×Dic30—21no—
57C2×Dic30C2311yescharacteristic
58C2×C3×C22⋊D5—22no—
59C3×#709—24no—
60C3×#709—42no—
61C2×C3×D20C2311yescharacteristic
62C2×C3×C4×D5—21no—
63C2×C3×C4×D5—22no—
64C2×C3×Dic10C2312yes—
65C3×C5×C4⋊C4D411yescharacteristic
66C3×C5×C22⋊C4D412yes—
67C3×C42×C5C2311yescharacteristic
68#6719—22no—
69#6719—22no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2312yes—
73#6712—21no—
74#6712—22no—
75C4×Dic15—21no—
76C4×Dic15—22no—
77C2×C5×C3⋊C8—42no—
78C2×C5×C3⋊C8C2311yescharacteristic
79C2×C5×C3⋊C8C2312yes—
80C2×C5×C3⋊C8C2311yescharacteristic
81C3×C22⋊Dic5—22no—
82C3×#685—21no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×#683—22no—
87#6662—42no—
88#6657—22no—
89C3×#547—51no—
90#5542—51no—
91#5239—52no—
92#5233—52no—
93#5090—51no—
94#5079—51no—
95#5051—52no—
96#5045—52no—
97C4×#214—51no—
98D4×C3⋊C8D511yescharacteristic, complemented
99#5007—51no—
100C2×#709C2×D312yes—
101C22×C5×C8—32no—
102C4×C5×D4C2×D311yescharacteristic
103#4084—21no—
104#4082—61no—
105#4072—32no—
106#4070—32no—
107#4070C2×D312yes—
108C2×Dic20—32no—
109C2×#677—31no—
110D5×C4⋊C4—21no—
111#4033—61no—
112#4029—22no—
113#4025—62no—
114C4×D20C2×D311yescharacteristic
115#4015—31no—
116#4015C2×D311yescharacteristic
117C4×Dic10—31no—
118C5×C4⋊C8—31no—
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—32no—
127#3948—32no—
128#3948—31no—
129#3302—151noSylow
130C23×C3×C5C2×D412yes—
131C22×C3×D5—21no—
132C3×C5×D4—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—21no—
140C2×Dic15—21no—
141C2×Dic15—22no—
142Dic30—21no—
143Dic30—21no—
144Dic30—42no—
145C3×C22⋊D5—44no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—22no—
148C3×D20—21no—
149C3×D20#4112yes—
150C3×C4×D5—44no—
151C3×C4×D5—42no—
152C3×Dic10—22no—
153C3×Dic10—22no—
154C5×C3⋊C8—21no—
155C5×C3⋊C8—22no—
156C5×C3⋊C8—21no—
157C2×C3×#41—52no—
158C3×C4⋊Q8—51no—
159C3×#123—102no—
160C3×C22⋊Q8—52no—
161C3×#121—101no—
162C3×C4×D4—51no—
163C3×C4×D4C2×D511yescharacteristic
164C2×C3×C4⋊C4—101no—
165C2×#216—52no—
166#936—101no—
167C2×#214—51no—
168#926—52no—
169#924—52no—
170C22×C3⋊C8C2×D512yes—
171#887—101no—
172#879—102no—
173#869—51no—
174C4×Dic6—51no—
175#835—52no—
176#835—52no—
177#835—52no—
178#832—51no—
179#832—52no—
180#830C2×D512yes—
181#810—51no—
182#808—51no—
183#807—52no—
184C4⋊(C3⋊C8)C2×D511yescharacteristic
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×D4#6711yescharacteristic
187C22×C4×C5C22×D312yes—
188C2×C22⋊D5—22no—
189#709—24no—
190#709—42no—
191C2×D20C22×D311yescharacteristic
192C2×C4×D5—22no—
193C2×C4×D5—21no—
194C2×Dic10—31no—
195C2×Dic10—61no—
196C2×Dic10C22×D312yes—
197C2×C5×C8—31no—
198C2×C5×C8—32no—
199C2×C5×C8—31no—
200C2×C5×C8—122no—
201C5×C4⋊C4#6711yescharacteristic
202C5×C22⋊C4#6712yes—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—22no—
205C22⋊Dic5—62no—
206C22⋊Dic5—62no—
207#685—21no—
208C4⋊Dic5—21no—
209C4⋊Dic5—21no—
210C4⋊Dic5—31no—
211C4⋊Dic5—32no—
212C4⋊Dic5—61no—
213C4⋊Dic5C22×D311yescharacteristic
214#683—22no—
215#683—61no—
216#683—62no—
217C4×Dic5—61no—
218C4×Dic5—62no—
219Dic20—122no—
220#677—62no—
221#556—151no—
222#547—51no—
223#487—151no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—151no—
230C8×D4—31no—
231#416—152no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—22no—
235C22×C3×C5C22×D411yescharacteristic
236C2×C3×D5—22no—
237C2×C3×D5—41no—
238C2×C3×D5—41no—
239C3×C4×C5—22no—
240C3×C4×C5—21no—
241C3×C4×C5#13512yes—
242C3×C4×C5C2×#4111yescharacteristic
243C3×C4×C5H(5,𝔽2)11yescharacteristic
244Dic15—41no—
245Dic15—42no—
246Dic15—41no—
247C3×Dic5—42no—
248C3×Dic5—41no—
249C3×#41—104no—
250C3×#41—202no—
251C2×C3×Q8—52no—
252C2×C3×D4—51no—
253C2×C3×D4—102no—
254C2×C3×D4D2011yescharacteristic
255C22×C3×C4—101no—
256C22×C3×C4—102no—
257C22×C3×C4C22×D512yes—
258C2×Dic6—51no—
259C2×Dic6—101no—
260C3×C4⋊C4—51no—
261C3×C4⋊C4—102no—
262C3×C4⋊C4—101no—
263C3×C4⋊C4—101no—
264C3×C4⋊C4D2011yescharacteristic
265C3×C22⋊C4—102no—
266C3×C22⋊C4—101no—
267C3×C22⋊C4D2012yes—
268C3×C42C22×D511yescharacteristic
269#217—102no—
270#217—102no—
271#216—202no—
272#214—102no—
273C4⋊Dic3—52no—
274C4⋊Dic3—51no—
275C4⋊Dic3—101no—
276Dic3⋊C4—101no—
277Dic3⋊C4—102no—
278C4×Dic3—101no—
279C4×Dic3—102no—
280C2×C3⋊C8—42no—
281C2×C3⋊C8C22×D511yescharacteristic
282C2×C3⋊C8C22×D511yescharacteristic
283C2×C3⋊C8C22×D512yes—
284C23×C5C2×#6712yes—
285C22×D5—21no—
286C5×D4—22no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5C2×#6712yes—
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—44no—
294C2×Dic5—21no—
295C2×Dic5—22no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298C2×Dic5—62no—
299D20—21no—
300D20#23712yes—
301C4×D5—44no—
302C4×D5—42no—
303Dic10—22no—
304Dic10—22no—
305Dic10—61no—
306Dic10—61no—
307Dic10—122no—
308C5×C8—61no—
309C5×C8—62no—
310C5×C8—61no—
311C2×#41—52no—
312C2×Q16—152no—
313C2×SD16—151no—
314C22×C8—32no—
315C4⋊Q8—51no—
316C4⋊Q8—151no—
317#126—302no—
318#124—301no—
319#123—102no—
320C22⋊Q8—52no—
321C22⋊Q8—152no—
322#121—101no—
323C4×Q8—151no—
324C4×Q8—301no—
325C4×D4—51no—
326C4×D4D3×D511yescharacteristic
327#117—152no—
328C2×C4⋊C4—101no—
329#107—152no—
330#106—151no—
331C4⋊C8—31no—
332#103—151no—
333#103—152no—
334#103—152no—
335#103—152no—
336#102—151no—
337#102—152no—
338C22⋊C8—32no—
339C4×C8—31no—
340C2×C3×C5—42no—
341C2×C3×C5#54611yescharacteristic
342C2×C3×C5C2×#13511yescharacteristic
343C2×C3×C5#57811yescharacteristic
344C3×D5—42no—
345C23×C3—101no—
346C23×C3C2×D2012yes—
347C3×Q8—102no—
348C3×Q8—102no—
349C3×D4—22no—
350C3×D4—52no—
351C3×D4—101no—
352C3×D4—204no—
353C2×C3×C4—22no—
354C2×C3×C4—22no—
355C2×C3×C4—101no—
356C2×C3×C4—102no—
357C2×C3×C4—204no—
358C2×C3×C4—202no—
359C2×C3×C4C2×D2012yes—
360C2×C3×C4C2×D2011yescharacteristic
361C2×C3×C4C2×D2011yescharacteristic
362C2×C3×C4C23×D511yescharacteristic
363C2×Dic3—101no—
364C2×Dic3—101no—
365C2×Dic3—102no—
366Dic6—101no—
367Dic6—101no—
368Dic6—202no—
369C3⋊C8—21no—
370C3⋊C8—22no—
371C3⋊C8—21no—
372C22×C5—22no—
373C22×C5—22no—
374C22×C5—22no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—22no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—22no—
380C4×C5—21no—
381C4×C5#95012yes—
382C4×C5C2×#23711yescharacteristic
383C4×C5#100411yescharacteristic
384Dic5—42no—
385Dic5—41no—
386Dic5—121no—
387Dic5—122no—
388Dic5—121no—
389#41—104no—
390#41—202no—
391C2×Q8—52no—
392C2×Q8—151no—
393C2×Q8—301no—
394C2×D4—51no—
395C2×D4—102no—
396C2×D4#120211yescharacteristic
397C22×C4—101no—
398C22×C4—102no—
399C22×C4C2×D3×D512yes—
400Q16—602no—
401SD16—302no—
402C2×C8—31no—
403C2×C8—31no—
404C2×C8—32no—
405C2×C8—122no—
406C4⋊C4—51no—
407C4⋊C4—101no—
408C4⋊C4—102no—
409C4⋊C4—101no—
410C4⋊C4—151no—
411C4⋊C4—152no—
412C4⋊C4—301no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4#120211yescharacteristic
416C22⋊C4—102no—
417C22⋊C4—101no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4#120212yes—
421C42—302no—
422C42—301no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—22no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—102no—
429C22×C3—201no—
430C22×C3—201no—
431C22×C3C22×D2011yescharacteristic
432C3×C4—21no—
433C3×C4—22no—
434C3×C4—201no—
435C3×C4—202no—
436C3×C4#405012yes—
437C3×C4#414411yescharacteristic
438C3×C4D5×#4111yescharacteristic
439Dic3—202no—
440Dic3—201no—
441Dic3—201no—
442C2×C5—42no—
443C2×C5#580611yescharacteristic
444C2×C5C2×#95011yescharacteristic
445C2×C5#583811yescharacteristic
446D5—42no—
447C23—101no—
448C23C2×#120212yes—
449Q8—102no—
450Q8—102no—
451Q8—301no—
452Q8—301no—
453Q8—602no—
454D4—22no—
455D4—52no—
456D4—101no—
457D4—204no—
458C2×C4—22no—
459C2×C4—22no—
460C2×C4—101no—
461C2×C4—102no—
462C2×C4—204no—
463C2×C4—202no—
464C2×C4—301no—
465C2×C4—302no—
466C2×C4—301no—
467C2×C4C2×#120212yes—
468C2×C4C2×#120211yescharacteristic
469C2×C4C2×#120211yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—61no—
472C8—61no—
473C8—62no—
474C2×C3—42no—
475C2×C3—202no—
476C2×C3#6588811yescharacteristic
477C2×C3C2×#405011yescharacteristic
478C2×C3#6608711yescharacteristic
479C5#8351011yescharacteristic, complemented, Sylow
480C22—22no—
481C22—22no—
482C22—22no—
483C22—102no—
484C22—201no—
485C22—201no—
486C22C22×#120211yescharacteristic
487C4—21no—
488C4—22no—
489C4—201no—
490C4—202no—
491C4—601no—
492C4—602no—
493C4—601no—
494C4#9131112yes—
495C4D5×#23711yescharacteristic
496C4#9202511yescharacteristic
497C3#1061117311yescharacteristic, complemented, Sylow
498C2—42no—
499C2—202no—
500C2C2×#9131111yescharacteristic
501C2#1175496311yescharacteristic
502C2#1175531211yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC3×#65885C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3302
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
1. #11756301C2semidirect
3. C5×D4×C3⋊C8C2semidirect
4. #11748560C2semidirect
5. #11748531C2semidirect
6. #11748446C2semidirect
7. #11748365C2semidirect
8. #11747104C2semidirect
9. C4×#6657C2semidirect
10. #11746920C2semidirect
11. #11746889C2semidirect
98. D4×C3⋊C8D5semidirect
424. C3×C5#3302semidirect
479. C5#83510semidirect
497. C3#10611173semidirect

Maximal subgroups

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

subgroupindex
#117563012
C3×#658852
C5×D4×C3⋊C82
#117485602
#117485312
#117484462
#117483652
#117471042
C4×#66572
#117469202
#117468892
#106111733
#835105