Finite Group Databasebeta

← #14303050

Subgroups — #14303050

Order 1920.

680 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754609C211yesmaximal, characteristic
2#11754120C211yesmaximal, characteristic, complemented
3C2×#91107C211yesmaximal, characteristic, complemented
4C3×#65421C211yesmaximal, characteristic, complemented
5C2×#90960C211yesmaximal, characteristic, complemented
6C5×#4556C211yesmaximal, characteristic, complemented
7#11745988C211yesmaximal, characteristic, complemented
8#10599833—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C5×#926C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16#91572C414yes—
17#91458—21no—
18#91450—22no—
19#91374—21no—
20#91284—22no—
21#91283—22no—
22D5×#208—22no—
23#91107—22no—
24C3×#3956—21no—
25C3×#3955—21no—
26#90960—22no—
27#70137—51nomaximal, Hall
28#66079—31no—
29#65859—31no—
30#65421D311yescharacteristic, complemented
31C2×#3955—31no—
32C2×#3955—31no—
33C5×#344—31no—
34#64753—31no—
35C23×D15C2×C412yes—
36C22×C3×C4×C5C2311yescharacteristic
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×C3×C22⋊D5C2×C412yes—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20D411yescharacteristic
49C2×C3×C4×D5D412yes—
50C2×C3×Dic10D411yescharacteristic
51C2×#1202—24no—
52C3×C5×M16—21no—
53C3×C5×M16—21no—
54C2×C3×C5×C8—21no—
55#6710—21no—
56#6710D412yescomplemented
57C2×C3⋊#168—21no—
58C5×#217C2×C412yes—
59C5×C4⋊Dic3—21no—
60C4×C5×Dic3—21no—
61C5×#208—21no—
62C5×#208D412yescomplemented
63C2×C5×C3⋊C8—21no—
64C3×#681—21no—
65C3×#681—21no—
66C2×C3×#168—21no—
67#6667—24no—
68#6649—24no—
69D5×C3⋊C8—24no—
70#5830—51no—
71#5819—51no—
72C3×#413—51no—
73C2×#823—51no—
74C2×#823—51no—
75#4556—51no—
76#4556D511yescharacteristic, complemented
77C2×#709C2×D311yescharacteristic
78C22×D20—31no—
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81C5×#117—31no—
82C2×#681—31no—
83C2×#681C2×D311yescharacteristic
84#4053—62no—
85D5×M16—62no—
86#4047—62no—
87#4041—62no—
88#4028—34no—
89#4021—61no—
90#4020—61no—
91#3956—21no—
92#3955—21no—
93#3955—62no—
94#3955—62no—
95#1914—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15—22no—
98C22×D15—22no—
99C22×D15—22no—
100C22×D15—82no—
101C22×C3×D5C22⋊C412yes—
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108D60—41no—
109D60—41no—
110D60—41no—
111D60—41no—
112C2×C5×Dic3—22no—
113C3×C22⋊D5—22no—
114C3×C22⋊D5—22no—
115C2×C3×Dic5C22⋊C412yes—
116C3×D20—21no—
117C3×D20—21no—
118C3×C4×D5—22no—
119C3×C4×D5—22no—
120C3×Dic10—21no—
121C3×Dic10—21no—
122#1202—84no—
123C3×C5×C8—41no—
124C3⋊#168—22no—
125C3×#168—41no—
126C5×C3⋊C8—22no—
127C2×C3×#41—51no—
128C22×D12—51no—
129C2×C3×M16—51no—
130C2×C3×M16C2×D511yescharacteristic
131#948—102no—
132#948—102no—
133#947—101no—
134#940—101no—
135#937—54no—
136#930—102no—
137#926C2×D511yescharacteristic
138C2×#208—51no—
139C2×#208—102no—
140C2×#208C2×D511yescharacteristic
141C3×#101—101no—
142C3×#100—101no—
143#823—102no—
144#823—102no—
145C23×D5—32no—
146C22×C4×C5C22×D311yescharacteristic
147C2×C22⋊D5C4×D312yes—
148#709—21no—
149#709—21no—
150#709—21no—
151#709—21no—
152C2×D20—61no—
153C2×D20—61no—
154C2×D20—61no—
155C2×D20—61no—
156C2×D20—61no—
157C2×D20—61no—
158C2×D20—64no—
159C2×D20#6711yescharacteristic
160C2×C4×D5D1212yes—
161C2×Dic10#6711yescharacteristic
162C5×M16—21no—
163C5×M16—21no—
164C5×M16—32no—
165C5×M16—61no—
166C2×C5×C8—21no—
167C2×C5×C8—61no—
168C5×C4⋊C4—61no—
169C5×C22⋊C4—32no—
170C42×C5—61no—
171#685—64no—
172#681—21no—
173#681—21no—
174#681—32no—
175#681—61no—
176C2×#168—21no—
177C2×#168—61no—
178#676—64no—
179C8×D5—64no—
180#568—151no—
181#535—151no—
182#413—51no—
183C2×#100—151no—
184C2×#100—151no—
185#344—31no—
186#344—151no—
187C22×C3×C5—41no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5C4×D411yescharacteristic
190C22×C3×C5C4×D411yescharacteristic
191C2×D15—44no—
192C2×D15—42no—
193C2×D15—82no—
194C2×D15—82no—
195C2×C3×D5—22no—
196C2×C3×D5—42no—
197C3×C4×C5#12011yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12311yescharacteristic
201C3×Dic5—22no—
202C5×Dic3—42no—
203C23×D3—52no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C3×#41—101no—
208C2×C3×Q8—51no—
209C2×C3×D4—52no—
210C2×C3×D4—51no—
211C22×C3×C4—52no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—104no—
214C2×D12—101no—
215C2×D12—101no—
216C2×D12—101no—
217C2×D12—101no—
218C2×D12—101no—
219C2×D12—101no—
220C3×M16—21no—
221C3×M16—21no—
222C3×M16—101no—
223C3×M16—101no—
224C2×C3×C8—21no—
225C2×C3×C8—101no—
226#217C4×D512yes—
227(C2×D3)⋊C4—104no—
228C4⋊Dic3—21no—
229C4×Dic3—21no—
230#208—21no—
231#208—52no—
232#208—104no—
233#208—101no—
234#208D2012yescomplemented
235C2×C3⋊C8—21no—
236C2×C3⋊C8—104no—
237C2×C3⋊C8—101no—
238C23×C5C2×C4×D311yescharacteristic
239C22×D5—62no—
240C22×D5—62no—
241C22×D5—62no—
242C22×D5—242no—
243C22×D5(C2×D3)⋊C412yes—
244C2×C4×C5—62no—
245C2×C4×C5C2×D1211yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5#23711yescharacteristic
249C2×C4×C5#23711yescharacteristic
250C2×C4×C5C2×#6711yescharacteristic
251C22⋊D5—22no—
252C22⋊D5—22no—
253C2×Dic5(C2×D3)⋊C412yes—
254D20—21no—
255D20—21no—
256D20—121no—
257D20—121no—
258D20—121no—
259D20—121no—
260D20—244no—
261C4×D5—22no—
262C4×D5—22no—
263Dic10—21no—
264Dic10—21no—
265C5×C8—41no—
266C5×C8—62no—
267#168—41no—
268#168—62no—
269C2×#41—51no—
270C22×D4—151no—
271#131—302no—
272#131—302no—
273C2×M16—31no—
274C2×M16—51no—
275C2×M16—151no—
276C2×M16—302no—
277C2×M16D3×D511yescharacteristic
278#127—301no—
279#124—301no—
280#121—302no—
281#120—154no—
282#117—31no—
283#101—101no—
284#100—101no—
285#100—302no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—82no—
292C3×D5—42no—
293C23×C3—52no—
294C23×C3C2×C4×D511yescharacteristic
295C22×D3—102no—
296C22×D3—102no—
297C22×D3—102no—
298C22×D3—402no—
299C3×Q8—101no—
300C3×Q8—101no—
301C3×D4—102no—
302C3×D4—102no—
303C3×D4—101no—
304C3×D4—101no—
305C2×C3×C4—52no—
306C2×C3×C4—102no—
307C2×C3×C4—102no—
308C2×C3×C4C2×D2011yescharacteristic
309C2×C3×C4#70911yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4#71311yescharacteristic
314#67—404no—
315C2×Dic3—22no—
316D12—201no—
317D12—201no—
318D12—201no—
319D12—201no—
320C3×C8—41no—
321C3×C8—201no—
322C3⋊C8—22no—
323C3⋊C8—102no—
324C22×C5—41no—
325C22×C5#67⋊C411yescharacteristic
326C22×C5#67⋊C411yescharacteristic
327C22×C5C2×(C2×D3)⋊C411yescharacteristic
328C2×D5—22no—
329C2×D5—42no—
330C2×D5—124no—
331C2×D5—122no—
332C2×D5—242no—
333C2×D5—242no—
334C4×C5—122no—
335C4×C5#88211yescharacteristic
336C4×C5#88611yescharacteristic
337C4×C5#93911yescharacteristic
338C4×C5#93911yescharacteristic
339Dic5—22no—
340C24—152no—
341#41—101no—
342#41—101no—
343#41—101no—
344#41—101no—
345C2×Q8—51no—
346C2×D4—52no—
347C2×D4—51no—
348C2×D4—304no—
349C2×D4—301no—
350C2×D4—301no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4—301no—
354C2×D4—301no—
355C22×C4—52no—
356C22×C4C2×D3×D511yescharacteristic
357M16—21no—
358M16—21no—
359M16—32no—
360M16—61no—
361M16—101no—
362M16—101no—
363M16—152no—
364M16—304no—
365M16—301no—
366C2×C8—21no—
367C2×C8—61no—
368C2×C8—101no—
369C2×C8—304no—
370C2×C8—301no—
371C4⋊C4—61no—
372C22⋊C4—32no—
373C22⋊C4—304no—
374C42—61no—
375C3×C5#191411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—102no—
378C22×C3—202no—
379C22×C3C4×D2011yescharacteristic
380C22×C3D5×C22⋊C411yescharacteristic
381C22×C3#403911yescharacteristic
382C2×D3—204no—
383C2×D3—202no—
384C2×D3—402no—
385C2×D3—402no—
386C3×C4—102no—
387C3×C4#402811yescharacteristic
388C3×C4#403011yescharacteristic
389C3×C4#404011yescharacteristic
390C3×C4#404111yescharacteristic
391Dic3—42no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5#495811yescharacteristic
396D5—42no—
397D5—242no—
398C23—52no—
399C23—302no—
400C23—302no—
401C23—302no—
402C23—1202no—
403C23C4×D3×D511yescharacteristic
404Q8—101no—
405Q8—101no—
406D4—102no—
407D4—102no—
408D4—101no—
409D4—101no—
410D4—601no—
411D4—601no—
412D4—601no—
413D4—601no—
414D4—1204no—
415C2×C4—52no—
416C2×C4—62no—
417C2×C4—102no—
418C2×C4—102no—
419C2×C4#676611yescharacteristic
420C2×C4D5×D1211yescharacteristic
421C2×C4D3×D2011yescharacteristic
422C2×C4#677911yescharacteristic
423C2×C4D5×#6711yescharacteristic
424C2×C4#679011yescharacteristic
425C8—41no—
426C8—62no—
427C8—201no—
428C8—302no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3—202no—
433C2×C3#6495411yescharacteristic
434D3—402no—
435C5#7013711yescharacteristic, complemented, Sylow
436C22—41no—
437C22—102no—
438C22—202no—
439C22—604no—
440C22—602no—
441C22—1202no—
442C22—1202no—
443C22#9139511yescharacteristic
444C22#9139611yescharacteristic
445C22D5×(C2×D3)⋊C411yescharacteristic
446C4—102no—
447C4—122no—
448C4#9140911yescharacteristic
449C4#9141311yescharacteristic
450C4#9147611yescharacteristic
451C4#9155011yescharacteristic
452C3#1059983311yescharacteristic, complemented, Sylow
453C2—21no—
454C2—21no—
455C2—21no—
456C2—202no—
457C2—1202no—
458C2#1174887211yescharacteristic
subgroupG/H
centerC2#11748872
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754609C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1914
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754120C2semidirect
3. C2×#91107C2semidirect
4. C3×#65421C2semidirect
5. C2×#90960C2semidirect
6. C5×#4556C2semidirect
7. #11745988C2semidirect
30. #65421D3semidirect
56. #6710D4semidirect
62. C5×#208D4semidirect
76. #4556D5semidirect
234. #208D20semidirect
375. C3×C5#1914semidirect
435. C5#70137semidirect
452. C3#10599833semidirect

Maximal subgroups

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

subgroupindex
#117546092
#117541202
C2×#911072
C3×#654212
C2×#909602
C5×#45562
#117459882
#105998333
#701375