Finite Group Databasebeta

← #14303054

Subgroups — #14303054

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
1C5×#5745C211yesmaximal, characteristic, complemented
2#11754610C211yesmaximal, characteristic
3C2×#91107C211yesmaximal, characteristic, complemented
4C2×#90960C211yesmaximal, characteristic, complemented
5#11748355C211yesmaximal, characteristic, complemented
6C3×#64779C211yesmaximal, characteristic, complemented
7#11745993C211yesmaximal, characteristic, complemented
8#10602823—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C5×#235C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C5×#907—22no—
15C5×D3×M16—22no—
16C5×#901—22no—
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91573C414yes—
20#91460—22no—
21#91451—21no—
22#91375—21no—
23#91107—22no—
24#90962—21no—
25#90960—22no—
26#90959—21no—
27#69040—51nomaximal, Hall
28C5×#568—31no—
29#66164—31no—
30#65526—31no—
31C2×#3955—31no—
32C2×#3955—31no—
33#64779—31no—
34#64779D311yescharacteristic, complemented
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×C5×#67C2×C412yes—
44C5×#235—21no—
45C5×#235—21no—
46C5×#235—21no—
47C5×#235—21no—
48C2×C5×D12D411yescharacteristic
49C2×C4×C5×D3D412yes—
50C2×C5×Dic6D411yescharacteristic
51C2×#1203—24no—
52C3×C5×M16—21no—
53C3×C5×M16D412yescomplemented
54C2×C3×C5×C8—21no—
55#6710—21no—
56#6710—21no—
57C2×C3⋊#168—21no—
58C5×#208—21no—
59C5×#208D412yescomplemented
60C2×C5×C3⋊C8—21no—
61C5×ΓL(1,𝔽25)—24no—
62C5×D3×C8—24no—
63C3×C22⋊Dic5C2×C412yes—
64C3×C4⋊Dic5—21no—
65C3×C4×Dic5—21no—
66C3×#681—21no—
67C3×#681—21no—
68C2×C3×#168—21no—
69#6667—24no—
70#5745D511yescharacteristic, complemented
71#5525—51no—
72#5132—51no—
73C2×#823—51no—
74C2×#823—51no—
75C3×#344—51no—
76#4533—51no—
77C2×C5×#41—31no—
78C22×D20—31no—
79C5×#131—62no—
80C5×#131—62no—
81C2×C5×M16—31no—
82C2×C5×M16—62no—
83C2×C5×M16C2×D311yescharacteristic
84#4093—61no—
85#4086—61no—
86#4083—34no—
87#4076—62no—
88#4072C2×D311yescharacteristic
89C2×#681—31no—
90C2×#681C2×D311yescharacteristic
91#3968—61no—
92#3965—61no—
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×C5×D3C22⋊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—
112C5×#67—22no—
113C5×#67—22no—
114C2×C5×Dic3C22⋊C412yes—
115C5×D12—21no—
116C5×D12—21no—
117C4×C5×D3—22no—
118C4×C5×D3—22no—
119C5×Dic6—21no—
120C5×Dic6—21no—
121C2×C3×Dic5—22no—
122#1203—84no—
123C3×C5×C8—22no—
124C3⋊#168—41no—
125C3×#168—41no—
126C5×C3⋊C8—22no—
127C2×#235C2×D511yescharacteristic
128C22×D12—51no—
129C2×C3×M16—51no—
130C2×C3×M16C2×D511yescharacteristic
131C3×#117—51no—
132C2×#208—51no—
133C2×#208C2×D511yescharacteristic
134#907—22no—
135D3×M16—22no—
136#901—22no—
137#895—102no—
138#882—54no—
139#875—101no—
140#874—101no—
141#824—101no—
142#823—101no—
143#823—102no—
144#823—102no—
145C23×D5—32no—
146C5×#41—61no—
147C5×#41—61no—
148C5×#41—61no—
149C5×#41—61no—
150C2×C5×Q8—31no—
151C2×C5×D4—32no—
152C2×C5×D4—31no—
153C22×C4×C5—32no—
154C22×C4×C5C22×D311yescharacteristic
155C2×C22⋊D5—64no—
156C2×D20—61no—
157C2×D20—61no—
158C2×D20—61no—
159C2×D20—61no—
160C2×D20—61no—
161C2×D20—61no—
162C5×M16—21no—
163C5×M16—32no—
164C5×M16—64no—
165C5×M16—61no—
166C5×M16D1212yescomplemented
167C2×C5×C8—21no—
168C2×C5×C8—64no—
169C2×C5×C8—61no—
170C22⋊Dic5C4×D312yes—
171#685—64no—
172C4⋊Dic5—21no—
173C4×Dic5—21no—
174#681—21no—
175#681—21no—
176#681—61no—
177#681—61no—
178C2×#168—21no—
179C2×#168—61no—
180#568—31no—
181#535—151no—
182#413—151no—
183C2×#100—151no—
184C2×#100—151no—
185#344—51no—
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×C5×D3—22no—
196C2×C5×D3—42no—
197C3×C4×C5#12011yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12311yescharacteristic
201C3×Dic5—42no—
202C5×Dic3—22no—
203C23×D3—52no—
204C22×C3×C4C22×D511yescharacteristic
205C2×#67C4×D512yes—
206#235—21no—
207#235—21no—
208#235—21no—
209#235—21no—
210C2×D12—101no—
211C2×D12—101no—
212C2×D12—101no—
213C2×D12—101no—
214C2×D12—101no—
215C2×D12—101no—
216C2×D12—104no—
217C2×D12D2011yescharacteristic
218C2×C4×D3C22⋊D512yes—
219C2×Dic6D2011yescharacteristic
220C3×M16—21no—
221C3×M16—101no—
222C3×M16—101no—
223C3×M16C22⋊D512yescomplemented
224C2×C3×C8—21no—
225C2×C3×C8—101no—
226C3×C4⋊C4—101no—
227C3×C22⋊C4—52no—
228C3×C42—101no—
229(C2×D3)⋊C4—104no—
230#208—21no—
231#208—101no—
232#208—101no—
233#208C22⋊D512yescomplemented
234C2×C3⋊C8—21no—
235C2×C3⋊C8—101no—
236ΓL(1,𝔽25)—24no—
237D3×C8—24no—
238C23×C5—32no—
239C23×C5C2×C4×D311yescharacteristic
240C22×D5—62no—
241C22×D5—62no—
242C22×D5—62no—
243C22×D5—242no—
244C5×Q8—61no—
245C5×Q8—61no—
246C5×D4—62no—
247C5×D4—62no—
248C5×D4—61no—
249C5×D4—61no—
250C2×C4×C5—32no—
251C2×C4×C5—62no—
252C2×C4×C5—62no—
253C2×C4×C5C2×D1211yescharacteristic
254C2×C4×C5#23511yescharacteristic
255C2×C4×C5D3×D411yescharacteristic
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5D3×D411yescharacteristic
258C2×C4×C5#23911yescharacteristic
259C22⋊D5—244no—
260C2×Dic5—22no—
261D20—121no—
262D20—121no—
263D20—121no—
264D20—121no—
265C5×C8—22no—
266C5×C8—62no—
267#168—41no—
268#168—121no—
269C2×#41—31no—
270C22×D4—151no—
271#131—62no—
272#131—62no—
273C2×M16—31no—
274C2×M16—51no—
275C2×M16—62no—
276C2×M16—151no—
277C2×M16D3×D511yescharacteristic
278#127—301no—
279#124—301no—
280#121—302no—
281#120—154no—
282#117—51no—
283#101—301no—
284#100—302no—
285#100—301no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—82no—
292C5×D3—42no—
293C23×C3C2×C4×D511yescharacteristic
294C22×D3—102no—
295C22×D3—102no—
296C22×D3—102no—
297C22×D3—402no—
298C22×D3#68512yes—
299C2×C3×C4—102no—
300C2×C3×C4C2×D2011yescharacteristic
301C2×C3×C4#70911yescharacteristic
302C2×C3×C4#70911yescharacteristic
303C2×C3×C4C2×C22⋊D511yescharacteristic
304C2×C3×C4C2×C22⋊D511yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306#67—22no—
307#67—22no—
308C2×Dic3#68512yes—
309D12—21no—
310D12—21no—
311D12—201no—
312D12—201no—
313D12—201no—
314D12—201no—
315D12—404no—
316C4×D3—22no—
317C4×D3—22no—
318Dic6—21no—
319Dic6—21no—
320C3×C8—22no—
321C3×C8—201no—
322C3⋊C8—22no—
323C3⋊C8—201no—
324C22×C5—41no—
325C22×C5—62no—
326C22×C5—122no—
327C22×C5C4×D1211yescharacteristic
328C22×C5D3×C22⋊C411yescharacteristic
329C22×C5#89311yescharacteristic
330C2×D5—124no—
331C2×D5—122no—
332C2×D5—242no—
333C2×D5—242no—
334C4×C5—62no—
335C4×C5#88211yescharacteristic
336C4×C5#88411yescharacteristic
337C4×C5#89411yescharacteristic
338C4×C5#89511yescharacteristic
339Dic5—42no—
340C24—152no—
341#41—61no—
342#41—61no—
343#41—61no—
344#41—61no—
345C2×Q8—31no—
346C2×D4—32no—
347C2×D4—31no—
348C2×D4—304no—
349C2×D4—301no—
350C2×D4—301no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4—301no—
354C2×D4—301no—
355C22×C4—32no—
356C22×C4C2×D3×D511yescharacteristic
357M16—21no—
358M16—32no—
359M16—64no—
360M16—61no—
361M16—101no—
362M16—101no—
363M16—301no—
364M16—301no—
365M16#120312yescomplemented
366C2×C8—21no—
367C2×C8—64no—
368C2×C8—61no—
369C2×C8—101no—
370C2×C8—301no—
371C4⋊C4—101no—
372C22⋊C4—52no—
373C22⋊C4—304no—
374C42—101no—
375C3×C5#191411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3C2×#68511yescharacteristic
378C22×C3C4×C22⋊D511yescharacteristic
379C22×C3C4×C22⋊D511yescharacteristic
380C2×D3—22no—
381C2×D3—42no—
382C2×D3—204no—
383C2×D3—202no—
384C2×D3—402no—
385C2×D3—402no—
386C3×C4—202no—
387C3×C4#407511yescharacteristic
388C3×C4#407611yescharacteristic
389C3×C4#407611yescharacteristic
390C3×C4#409911yescharacteristic
391Dic3—22no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5—122no—
396C2×C5#466511yescharacteristic
397D5—242no—
398C23—32no—
399C23—302no—
400C23—302no—
401C23—302no—
402C23—1202no—
403C23C4×D3×D511yescharacteristic
404Q8—61no—
405Q8—61no—
406D4—62no—
407D4—62no—
408D4—61no—
409D4—61no—
410D4—601no—
411D4—601no—
412D4—601no—
413D4—601no—
414D4—1204no—
415C2×C4—32no—
416C2×C4—62no—
417C2×C4—62no—
418C2×C4—102no—
419C2×C4#676911yescharacteristic
420C2×C4#677111yescharacteristic
421C2×C4D3×D2011yescharacteristic
422C2×C4C2×#120311yescharacteristic
423C2×C4D3×C22⋊D511yescharacteristic
424C2×C4D3×C22⋊D511yescharacteristic
425C8—22no—
426C8—62no—
427C8—201no—
428C8—601no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3#6550211yescharacteristic
433D3—42no—
434D3—402no—
435C5#6904011yescharacteristic, complemented, Sylow
436C22—41no—
437C22—62no—
438C22—122no—
439C22—604no—
440C22—602no—
441C22—1202no—
442C22—1202no—
443C22C4×#120311yescharacteristic
444C22#9144611yescharacteristic
445C22D3×#68511yescharacteristic
446C4—62no—
447C4—202no—
448C4#9135111yescharacteristic
449C4#9145411yescharacteristic
450C4#9146011yescharacteristic
451C4#9157011yescharacteristic
452C3#1060282311yescharacteristic, complemented, Sylow
453C2—21no—
454C2—21no—
455C2—21no—
456C2—122no—
457C2—1202no—
458C2#1174891411yescharacteristic
subgroupG/H
centerC2#11748914
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754610C2
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
1. C5×#5745C2semidirect
3. C2×#91107C2semidirect
4. C2×#90960C2semidirect
5. #11748355C2semidirect
6. C3×#64779C2semidirect
7. #11745993C2semidirect
34. #64779D3semidirect
53. C3×C5×M16D4semidirect
59. C5×#208D4semidirect
70. #5745D5semidirect
166. C5×M16D12semidirect
223. C3×M16C22⋊D5semidirect
233. #208C22⋊D5semidirect
365. M16#1203semidirect
375. C3×C5#1914semidirect
435. C5#69040semidirect
452. C3#10602823semidirect

Maximal subgroups

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

subgroupindex
C5×#57452
#117546102
C2×#911072
C2×#909602
#117483552
C3×#647792
#117459932
#106028233
#690405