Finite Group Databasebeta

← #14303052

Subgroups — #14303052

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#11756504C211yesmaximal, characteristic, complemented
2#11754606C211yesmaximal, characteristic
3C2×C5×#823C211yesmaximal, characteristic, complemented
4#11748357C211yesmaximal, characteristic, complemented
5C2×#90959C211yesmaximal, characteristic, complemented
6C3×#64779C211yesmaximal, characteristic, complemented
7#11745992C211yesmaximal, characteristic, complemented
8#10600882—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13#91796—22no—
14M16×D15—22no—
15#91790—22no—
16C2×C5×#208C2211yescharacteristic
17C3×#4072C2211yescharacteristic
18C2×C3×#681C2211yescharacteristic
19#91570C414yes—
20#91466—22no—
21#91451—21no—
22#91373—21no—
23C5×#823—22no—
24#90963—21no—
25#90960—21no—
26#90959—22no—
27#69040—51nomaximal, Hall
28#66139—31no—
29#66079—31no—
30C2×C5×#100—31no—
31C2×#3965—31no—
32#65421—31no—
33#64779D311yescharacteristic, complemented
34#64776—31no—
35C23×C5×D3C2×C412yes—
36C22×C3×C4×C5C2311yescharacteristic
37C2×#1220C2×C412yes—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41#6817—21no—
42C2×D60D411yescharacteristic
43C2×C4×D15D412yes—
44C2×Dic30D411yescharacteristic
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12—21no—
51C2×#1203—24no—
52C3×C5×M16—21no—
53C3×C5×M16D412yescomplemented
54C2×C3×C5×C8—21no—
55#6710—21no—
56#6710D412yescomplemented
57C2×C3⋊#168—21no—
58#6705—24no—
59C8×D15—24no—
60C5×#208—21no—
61C5×#208—21no—
62C2×C5×C3⋊C8—21no—
63C3×C22⋊Dic5C2×C412yes—
64C3×C4⋊Dic5—21no—
65C3×C4×Dic5—21no—
66C3×#681—21no—
67C3×#681—21no—
68C2×C3×#168—21no—
69(C2×D3)⋊Dic5—24no—
70#5745—51no—
71#5525—51no—
72#5132—51no—
73C2×#823—51no—
74C2×#823D511yescharacteristic, complemented
75C3×#344—51no—
76#4533—51no—
77C22×C5×D4—31no—
78C2×#709—31no—
79C2×C5×M16—31no—
80C2×C5×M16C2×D311yescharacteristic
81#4099—34no—
82#4086—61no—
83#4084—62no—
84#4082—61no—
85#4072C2×D311yescharacteristic
86C2×#681—31no—
87C2×#681C2×D311yescharacteristic
88#4053—62no—
89D5×M16—62no—
90#4047—62no—
91C5×#100—62no—
92#3965—62no—
93#3956—61no—
94#3955—61no—
95#1914—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15C22⋊C412yes—
98C22×C5×D3—22no—
99C22×C5×D3—22no—
100C22×C5×D3—22no—
101C22×C5×D3—82no—
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
108#1220—22no—
109#1220—22no—
110C2×Dic15C22⋊C412yes—
111D60—21no—
112D60—21no—
113C4×D15—22no—
114C4×D15—22no—
115Dic30—21no—
116Dic30—21no—
117C5×D12—41no—
118C5×D12—41no—
119C5×D12—41no—
120C5×D12—41no—
121C2×C3×Dic5—22no—
122#1203—84no—
123C3×C5×C8—22no—
124C3⋊#168—22no—
125C3×#168—41no—
126C5×C3⋊C8—41no—
127C2×#235—51no—
128C22×D12C2×D511yescharacteristic
129C2×C3×M16—51no—
130C2×C3×M16C2×D511yescharacteristic
131C3×#117—51no—
132C2×#208—51no—
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—22no—
143#823—101no—
144#823—102no—
145C24×C5—32no—
146C2×C5×D4—61no—
147C2×C5×D4—61no—
148C2×C5×D4—61no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—61no—
152C22×C4×C5C22×D311yescharacteristic
153C2×C22⋊D5—32no—
154C2×C22⋊D5—64no—
155#709—61no—
156#709—61no—
157#709—61no—
158#709—61no—
159C2×D20—31no—
160C2×C4×D5—32no—
161C2×Dic10—31no—
162C5×M16—21no—
163C5×M16—61no—
164C5×M16—61no—
165C5×M16D1212yescomplemented
166C2×C5×C8—21no—
167C2×C5×C8—61no—
168C22⋊Dic5—64no—
169C22⋊Dic5C4×D312yes—
170C4⋊Dic5—21no—
171C4×Dic5—21no—
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—151no—
183C2×#100—31no—
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—22no—
192C2×D15—42no—
193C2×C5×D3—44no—
194C2×C5×D3—42no—
195C2×C5×D3—82no—
196C2×C5×D3—82no—
197C3×C4×C5#12011yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12311yescharacteristic
201Dic15—22no—
202C3×Dic5—42no—
203C23×D3C4×D512yes—
204C22×C3×C4C22×D511yescharacteristic
205C2×#67—52no—
206#235—101no—
207#235—101no—
208#235—101no—
209#235—101no—
210C2×D12—21no—
211C2×D12—21no—
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12—21no—
216C2×D12—51no—
217C2×D12—104no—
218C2×C4×D3—52no—
219C2×Dic6—51no—
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—21no—
232#208—52no—
233#208—101no—
234C2×C3⋊C8—21no—
235C2×C3⋊C8—101no—
236ΓL(1,𝔽25)—104no—
237D3×C8—104no—
238C23×C5—62no—
239C23×C5—62no—
240C23×C5—62no—
241C23×C5—242no—
242C23×C5C2×C4×D311yescharacteristic
243C22×D5—32no—
244C5×D4—121no—
245C5×D4—121no—
246C5×D4—121no—
247C5×D4—121no—
248C2×C4×C5C2×D1211yescharacteristic
249C2×C4×C5#23511yescharacteristic
250C2×C4×C5D3×D411yescharacteristic
251C2×C4×C5D3×D411yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5#23911yescharacteristic
254C22⋊D5—62no—
255C22⋊D5—62no—
256C22⋊D5—244no—
257C2×Dic5—22no—
258C2×Dic5—32no—
259D20—61no—
260D20—61no—
261C4×D5—62no—
262C4×D5—62no—
263Dic10—61no—
264Dic10—61no—
265C5×C8—22no—
266C5×C8—121no—
267#168—41no—
268#168—62no—
269C2×#41—151no—
270C22×D4—31no—
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—51no—
283#101—301no—
284#100—62no—
285#100—301no—
286#100—302no—
287C2×C3×C5—21no—
288C2×C3×C5—21no—
289C2×C3×C5—21no—
290C2×C3×C5#38611yescharacteristic
291D15—42no—
292C5×D3—82no—
293C23×C3C2×C4×D511yescharacteristic
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—22no—
297C22×D3—52no—
298C22×D3—82no—
299C2×C3×C4—102no—
300C2×C3×C4#70911yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4#71111yescharacteristic
305C2×C3×C4C2×C22⋊D511yescharacteristic
306#67—102no—
307#67—102no—
308C2×Dic3—52no—
309D12—41no—
310D12—41no—
311D12—41no—
312D12—41no—
313D12—101no—
314D12—101no—
315D12—404no—
316C4×D3—102no—
317C4×D3—102no—
318Dic6—101no—
319Dic6—101no—
320C3×C8—22no—
321C3×C8—201no—
322C3⋊C8—41no—
323C3⋊C8—102no—
324C22×C5—41no—
325C22×C5—124no—
326C22×C5—122no—
327C22×C5—242no—
328C22×C5—242no—
329C22×C5C4×D1211yescharacteristic
330C22×C5D3×C22⋊C411yescharacteristic
331C22×C5#89311yescharacteristic
332C2×D5—62no—
333C2×D5—122no—
334C4×C5#88211yescharacteristic
335C4×C5#88411yescharacteristic
336C4×C5#89411yescharacteristic
337C4×C5#89511yescharacteristic
338Dic5—42no—
339Dic5—62no—
340C24—32no—
341#41—301no—
342#41—301no—
343#41—301no—
344#41—301no—
345C2×Q8—151no—
346C2×D4—61no—
347C2×D4—61no—
348C2×D4—61no—
349C2×D4—61no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—152no—
353C2×D4—151no—
354C2×D4—304no—
355C22×C4—152no—
356C22×C4C2×D3×D511yescharacteristic
357M16—21no—
358M16—61no—
359M16—61no—
360M16—101no—
361M16—101no—
362M16—152no—
363M16—304no—
364M16—301no—
365M16#120312yescomplemented
366C2×C8—21no—
367C2×C8—61no—
368C2×C8—101no—
369C2×C8—304no—
370C2×C8—301no—
371C4⋊C4—101no—
372C22⋊C4—52no—
373C22⋊C4—304no—
374C42—101no—
375C3×C5#191411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3D5×C22⋊C411yescharacteristic
378C22×C3#402711yescharacteristic
379C22×C3C4×C22⋊D511yescharacteristic
380C2×D3—44no—
381C2×D3—42no—
382C2×D3—82no—
383C2×D3—82no—
384C2×D3—102no—
385C2×D3—202no—
386C3×C4—202no—
387C3×C4#402911yescharacteristic
388C3×C4#403011yescharacteristic
389C3×C4#408311yescharacteristic
390C3×C4#408411yescharacteristic
391Dic3—102no—
392C2×C5—21no—
393C2×C5—21no—
394C2×C5—21no—
395C2×C5—242no—
396C2×C5#466511yescharacteristic
397D5—122no—
398C23—62no—
399C23—62no—
400C23—62no—
401C23—152no—
402C23—242no—
403C23C4×D3×D511yescharacteristic
404Q8—301no—
405Q8—301no—
406D4—121no—
407D4—121no—
408D4—121no—
409D4—121no—
410D4—302no—
411D4—302no—
412D4—301no—
413D4—301no—
414D4—1204no—
415C2×C4—102no—
416C2×C4—152no—
417C2×C4—302no—
418C2×C4—302no—
419C2×C4#676811yescharacteristic
420C2×C4#677111yescharacteristic
421C2×C4#677711yescharacteristic
422C2×C4C2×#120311yescharacteristic
423C2×C4#679011yescharacteristic
424C2×C4#679011yescharacteristic
425C8—22no—
426C8—121no—
427C8—201no—
428C8—302no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—21no—
432C2×C3#6524511yescharacteristic
433D3—82no—
434D3—202no—
435C5#6904011yescharacteristic, complemented, Sylow
436C22—41no—
437C22—124no—
438C22—122no—
439C22—242no—
440C22—242no—
441C22—302no—
442C22—602no—
443C22#9140611yescharacteristic
444C22C4×#120311yescharacteristic
445C22#9147311yescharacteristic
446C4—202no—
447C4—302no—
448C4#9135511yescharacteristic
449C4#9146111yescharacteristic
450C4#9146611yescharacteristic
451C4#9157311yescharacteristic
452C3#1060088211yescharacteristic, complemented, Sylow
453C2—21no—
454C2—21no—
455C2—21no—
456C2—242no—
457C2—602no—
458C2#1174891811yescharacteristic
subgroupG/H
centerC2#11748918
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radical#11754606C2
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. #11756504C2semidirect
3. C2×C5×#823C2semidirect
4. #11748357C2semidirect
5. C2×#90959C2semidirect
6. C3×#64779C2semidirect
7. #11745992C2semidirect
33. #64779D3semidirect
53. C3×C5×M16D4semidirect
56. #6710D4semidirect
74. C2×#823D5semidirect
165. C5×M16D12semidirect
223. C3×M16C22⋊D5semidirect
365. M16#1203semidirect
375. C3×C5#1914semidirect
435. C5#69040semidirect
452. C3#10600882semidirect

Maximal subgroups

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

subgroupindex
#117565042
#117546062
C2×C5×#8232
#117483572
C2×#909592
C3×#647792
#117459922
#106008823
#690405