Finite Group Databasebeta

← #14303067

Subgroups — #14303067

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#11756284C211yesmaximal, characteristic
2#11754130C211yesmaximal, characteristic, complemented
3#11748357C211yesmaximal, characteristic, complemented
4C2×#90960C211yesmaximal, characteristic, complemented
5C2×#90960C211yesmaximal, characteristic, complemented
6C5×#4533C211yesmaximal, characteristic, complemented
7C3×#64753C211yesmaximal, characteristic, complemented
8#10599833—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91784—22no—
13#91771C414yes—
14#91764—21no—
15#91763—21no—
16C2×C5×#208C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20#91292—22no—
21#91291—22no—
22#91290—22no—
23#90963—21no—
24#90960—21no—
25#90960—22no—
26#90960—22no—
27#69040—51nomaximal, Hall
28#66079—31no—
29#65859—31no—
30#65421—31no—
31C2×#3955—31no—
32C2×#3955—31no—
33C5×#344—31no—
34#64753D311yescharacteristic, complemented
35C23×D15C2×C412yes—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220C2×C412yes—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41#6817—21no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60—21no—
46C2×D60—21no—
47C2×D60—21no—
48C2×D60—24no—
49C2×D60D411yescharacteristic
50C2×C4×D15D412yes—
51C2×Dic30D411yescharacteristic
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4C2×C412yes—
54C3×C42×C5—21no—
55#6714—24no—
56C5×#208—21no—
57C5×#208—21no—
58C5×#208—21no—
59C5×#208D412yescomplemented
60C2×C5×C3⋊C8—21no—
61C2×C5×C3⋊C8—21no—
62C3×#681—21no—
63C3×#681—21no—
64C3×#681—21no—
65C3×#681D412yescomplemented
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68#6651—24no—
69#6648—24no—
70#5745—51no—
71#5525—51no—
72#5132—51no—
73C2×#823—51no—
74C2×#823—51no—
75C3×#344—51no—
76#4533D511yescharacteristic, complemented
77C2×#709—31no—
78C22×D20—31no—
79C2×C5×M16—31no—
80C2×C5×M16—31no—
81C5×#117C2×D311yescharacteristic
82C2×#681C2×D311yescharacteristic
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—61no—
92#3955—62no—
93#3955—61no—
94#3955—62no—
95#1914—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15—22no—
98C22×D15—22no—
99C22×D15—22no—
100C22×D15—82no—
101C22×D15C22⋊C412yes—
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5#4111yescharacteristic
108C2×C3×C4×C5#4111yescharacteristic
109#1220—22no—
110#1220—22no—
111C2×Dic15C22⋊C412yes—
112D60—21no—
113D60—21no—
114D60—41no—
115D60—41no—
116D60—41no—
117D60—41no—
118D60—84no—
119C4×D15—22no—
120C4×D15—22no—
121Dic30—21no—
122Dic30—21no—
123C3×#168—22no—
124C3×#168—41no—
125C5×C3⋊C8—22no—
126C5×C3⋊C8—41no—
127C2×#235—51no—
128C22×D12—51no—
129C2×C3×M16—51no—
130C2×C3×M16—51no—
131C3×#117C2×D511yescharacteristic
132C2×#208C2×D511yescharacteristic
133C2×#208C2×D511yescharacteristic
134#907—102no—
135D3×M16—102no—
136#901—102no—
137#895—102no—
138#882—54no—
139#875—101no—
140#874—101no—
141#824—101no—
142#823—102no—
143#823—101no—
144#823—102no—
145C23×D5—32no—
146C22×C4×C5C22×D311yescharacteristic
147C2×C22⋊D5—32no—
148#709—61no—
149#709—61no—
150#709—61no—
151#709—61no—
152C2×D20—31no—
153C2×D20—61no—
154C2×D20—61no—
155C2×D20—61no—
156C2×D20—61no—
157C2×D20—61no—
158C2×D20—61no—
159C2×D20—64no—
160C2×C4×D5—32no—
161C2×Dic10—31no—
162C5×M16—32no—
163C5×M16—61no—
164C5×M16—61no—
165C5×M16—61no—
166C2×C5×C8—61no—
167C2×C5×C8—61no—
168C5×C4⋊C4—21no—
169C5×C22⋊C4C4×D312yes—
170C42×C5—21no—
171#685—64no—
172#681—21no—
173#681—21no—
174#681—21no—
175#681D1212yescomplemented
176C2×#168—21no—
177C2×#168—21no—
178#676—64no—
179C8×D5—64no—
180#568—151no—
181#535—151no—
182#413—151no—
183C2×#100—151no—
184C2×#100—151no—
185#344—31no—
186#344—51no—
187C22×C3×C5—41no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5C4×D411yescharacteristic
190C22×C3×C5C4×D411yescharacteristic
191C2×D15—22no—
192C2×D15—42no—
193C2×D15—44no—
194C2×D15—42no—
195C2×D15—82no—
196C2×D15—82no—
197C3×C4×C5—42no—
198C3×C4×C5#12011yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12111yescharacteristic
201C3×C4×C5#12311yescharacteristic
202Dic15—22no—
203C23×D3—52no—
204C22×C3×C4C22×D511yescharacteristic
205C2×#67—52no—
206#235—101no—
207#235—101no—
208#235—101no—
209#235—101no—
210C2×D12—51no—
211C2×D12—101no—
212C2×D12—101no—
213C2×D12—101no—
214C2×D12—101no—
215C2×D12—101no—
216C2×D12—101no—
217C2×D12—104no—
218C2×C4×D3—52no—
219C2×Dic6—51no—
220C3×M16—52no—
221C3×M16—101no—
222C3×M16—101no—
223C3×M16—101no—
224C2×C3×C8—101no—
225C2×C3×C8—101no—
226C3×C4⋊C4—21no—
227C3×C22⋊C4C4×D512yes—
228C3×C42—21no—
229(C2×D3)⋊C4—104no—
230#208—21no—
231#208—21no—
232#208—21no—
233#208D2012yescomplemented
234C2×C3⋊C8—21no—
235C2×C3⋊C8—21no—
236ΓL(1,𝔽25)—104no—
237D3×C8—104no—
238C23×C5C2×C4×D311yescharacteristic
239C22×D5—32no—
240C22×D5—62no—
241C22×D5—62no—
242C22×D5—62no—
243C22×D5—242no—
244C2×C4×C5—22no—
245C2×C4×C5C2×D1211yescharacteristic
246C2×C4×C5#23511yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5D3×D411yescharacteristic
250C2×C4×C5#23911yescharacteristic
251C22⋊D5—62no—
252C22⋊D5—62no—
253C2×Dic5—32no—
254D20—61no—
255D20—61no—
256D20—121no—
257D20—121no—
258D20—121no—
259D20—121no—
260D20—244no—
261C4×D5—62no—
262C4×D5—62no—
263Dic10—61no—
264Dic10—61no—
265C5×C8—62no—
266C5×C8—121no—
267#168—22no—
268#168—41no—
269C2×#41—151no—
270C22×D4—151no—
271#131—302no—
272#131—302no—
273C2×M16—31no—
274C2×M16—31no—
275C2×M16—51no—
276C2×M16—51no—
277C2×M16—302no—
278#127—301no—
279#124—301no—
280#121—302no—
281#120—154no—
282#117D3×D511yescharacteristic
283#101—301no—
284#100—302no—
285#100—302no—
286#100—301no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—42no—
292D15—82no—
293C23×C3C2×C4×D511yescharacteristic
294C22×D3—52no—
295C22×D3—102no—
296C22×D3—102no—
297C22×D3—102no—
298C22×D3—402no—
299C2×C3×C4—22no—
300C2×C3×C4C2×D2011yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4D4×D511yescharacteristic
305C2×C3×C4#71311yescharacteristic
306#67—102no—
307#67—102no—
308C2×Dic3—52no—
309D12—101no—
310D12—101no—
311D12—201no—
312D12—201no—
313D12—201no—
314D12—201no—
315D12—404no—
316C4×D3—102no—
317C4×D3—102no—
318Dic6—101no—
319Dic6—101no—
320C3×C8—102no—
321C3×C8—201no—
322C3⋊C8—22no—
323C3⋊C8—41no—
324C22×C5—41no—
325C22×C5C4×D1211yescharacteristic
326C22×C5D3×C22⋊C411yescharacteristic
327C22×C5#89311yescharacteristic
328C2×D5—62no—
329C2×D5—122no—
330C2×D5—124no—
331C2×D5—122no—
332C2×D5—242no—
333C2×D5—242no—
334C4×C5—42no—
335C4×C5#88211yescharacteristic
336C4×C5#88411yescharacteristic
337C4×C5#89411yescharacteristic
338C4×C5#89511yescharacteristic
339Dic5—62no—
340C24—152no—
341#41—301no—
342#41—301no—
343#41—301no—
344#41—301no—
345C2×Q8—151no—
346C2×D4—152no—
347C2×D4—151no—
348C2×D4—304no—
349C2×D4—301no—
350C2×D4—301no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4—301no—
354C2×D4—301no—
355C22×C4—152no—
356C22×C4C2×D3×D511yescharacteristic
357M16—32no—
358M16—52no—
359M16—61no—
360M16—61no—
361M16—61no—
362M16—101no—
363M16—101no—
364M16—101no—
365M16—304no—
366C2×C8—61no—
367C2×C8—61no—
368C2×C8—101no—
369C2×C8—101no—
370C2×C8—304no—
371C4⋊C4—21no—
372C22⋊C4—304no—
373C22⋊C4#120012yes—
374C42—21no—
375C3×C5#191411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3C4×D2011yescharacteristic
378C22×C3D5×C22⋊C411yescharacteristic
379C22×C3#403911yescharacteristic
380C2×D3—102no—
381C2×D3—202no—
382C2×D3—204no—
383C2×D3—202no—
384C2×D3—402no—
385C2×D3—402no—
386C3×C4—42no—
387C3×C4#402811yescharacteristic
388C3×C4#403011yescharacteristic
389C3×C4#404011yescharacteristic
390C3×C4#404111yescharacteristic
391Dic3—102no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5#466511yescharacteristic
396D5—122no—
397D5—242no—
398C23—152no—
399C23—302no—
400C23—302no—
401C23—302no—
402C23—1202no—
403C23C2×#120011yescharacteristic
404Q8—301no—
405Q8—301no—
406D4—302no—
407D4—302no—
408D4—301no—
409D4—301no—
410D4—601no—
411D4—601no—
412D4—601no—
413D4—601no—
414D4—1204no—
415C2×C4—22no—
416C2×C4—152no—
417C2×C4—302no—
418C2×C4—302no—
419C2×C4#676911yescharacteristic
420C2×C4#677311yescharacteristic
421C2×C4D5×D1211yescharacteristic
422C2×C4D3×D2011yescharacteristic
423C2×C4#679011yescharacteristic
424C2×C4#679011yescharacteristic
425C8—62no—
426C8—102no—
427C8—121no—
428C8—201no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3#6495411yescharacteristic
433D3—202no—
434D3—402no—
435C5#6904011yescharacteristic, complemented, Sylow
436C22—41no—
437C22—302no—
438C22—602no—
439C22—604no—
440C22—602no—
441C22—1202no—
442C22—1202no—
443C22#9141811yescharacteristic
444C22#9142811yescharacteristic
445C22#9156111yescharacteristic
446C4—42no—
447C4—302no—
448C4#9142011yescharacteristic
449C4#9143311yescharacteristic
450C4#9145911yescharacteristic
451C4#9147611yescharacteristic
452C3#1059983311yescharacteristic, complemented, Sylow
453C2—21no—
454C2—21no—
455C2—21no—
456C2—602no—
457C2—1202no—
458C2#1174890411yescharacteristic
subgroupG/H
centerC2#11748904
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radical#11756284C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1914
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11754130C2semidirect
3. #11748357C2semidirect
4. C2×#90960C2semidirect
5. C2×#90960C2semidirect
6. C5×#4533C2semidirect
7. C3×#64753C2semidirect
34. #64753D3semidirect
59. C5×#208D4semidirect
65. C3×#681D4semidirect
76. #4533D5semidirect
175. #681D12semidirect
233. #208D20semidirect
375. C3×C5#1914semidirect
435. C5#69040semidirect
452. C3#10599833semidirect

Maximal subgroups

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

subgroupindex
#117562842
#117541302
#117483572
C2×#909602
C5×#45332
C3×#647532
#105998333
#690405