Finite Group Databasebeta

← #14298412

Subgroups — #14298412

Order 1920.

544 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91347C211yesmaximal, characteristic
2#11751227C211yesmaximal, characteristic
3#11748351C211yesmaximal, characteristic
4C5×#4554C211yesmaximal, characteristic, complemented
5C3×#64774C211yesmaximal, characteristic, complemented
6#11745986C211yesmaximal, characteristic, complemented
7#11745985C211yesmaximal, characteristic, complemented
8#10599784—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11C2×#6710C2211yescharacteristic
12C2×C5×C4⋊Dic3C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C3×C4⋊Dic5C2211yescharacteristic
15C2×C3×#681C2211yescharacteristic
16C2×#6667C412yes—
17C2×Dic3×Dic5C412yes—
18#91347—22no—
19#91347—22no—
20#91104—22no—
21#90957—22no—
22#68991—51nomaximal, Hall
23C2×#4038—31no—
24#65415—31no—
25#65415—31no—
26C5×#343—31no—
27#64774—31no—
28#64774D311yescharacteristic, complemented
29#64750—31no—
30C23×D15C2×C411yescharacteristic
31C22×C3×C4×C5C2311yescharacteristic
32C22×Dic15C2×C411yescharacteristic
33C2×C4×D15—21no—
34C2×C4×D15—21no—
35C2×C4×D15—21no—
36C2×C4×D15—21no—
37C2×C4×D15D412yes—
38C2×C4×D15D412yes—
39C22×C5×Dic3C2×C412yes—
40C22×C3×Dic5C2×C412yes—
41C3×C5×M16—21no—
42C3×C5×M16—21no—
43C2×C3×C5×C8—21no—
44#6710—21no—
45#6710—21no—
46C2×C3⋊#168—21no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3—21no—
49C5×#208—21no—
50C5×#208—21no—
51C2×C5×C3⋊C8—21no—
52C3×C4⋊Dic5—21no—
53C3×C4⋊Dic5—21no—
54C3×#681—21no—
55C3×#681—21no—
56C2×C3×#168—21no—
57#6667—24no—
58Dic3×Dic5—24no—
59C2×#892—51no—
60#5126—51no—
61#5126—51no—
62C3×#343—51no—
63#4554—51no—
64#4554D511yescharacteristic, complemented
65#4530—51no—
66C22×C4×D5—31no—
67C2×C5×M16—31no—
68C2×C5×M16C2×D311yescharacteristic
69C2×C5×C4⋊C4—31no—
70C2×#685—32no—
71C2×C4⋊Dic5C2×D311yescharacteristic
72C2×C4×Dic5—32no—
73C2×#681—31no—
74C2×#681C2×D311yescharacteristic
75#4038—62no—
76#4038—62no—
77#3952—62no—
78#3952—62no—
79#1822—151noSylow
80C23×C3×C5C22×C411yescharacteristic
81C22×D15—21no—
82C22×D15—21no—
83C22×D15—41no—
84C22×D15—41no—
85C22×D15C22⋊C412yes—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5#4111yescharacteristic
89C2×C3×C4×C5#4111yescharacteristic
90C2×C3×C4×C5#4111yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C2×Dic15—21no—
93C2×Dic15—21no—
94C2×Dic15C22⋊C412yes—
95C4×D15—22no—
96C4×D15—22no—
97C4×D15—22no—
98C4×D15—22no—
99C2×C5×Dic3—22no—
100C2×C5×Dic3—42no—
101C2×C3×Dic5—22no—
102C2×C3×Dic5—42no—
103C3×C5×C8—41no—
104C3⋊#168—41no—
105C3×#168—41no—
106C5×C3⋊C8—41no—
107C22×C4×D3—51no—
108C2×C3×M16—51no—
109C2×C3×M16C2×D511yescharacteristic
110C2×C3×C4⋊C4—51no—
111C2×(C2×D3)⋊C4—52no—
112C2×C4⋊Dic3C2×D511yescharacteristic
113C2×C4×Dic3—52no—
114C2×#208—51no—
115C2×#208C2×D511yescharacteristic
116#892—102no—
117#892—102no—
118(C2×D3)⋊C8—102no—
119(C2×D3)⋊C8—102no—
120C23×D5—31no—
121C22×C4×C5—32no—
122C22×C4×C5C22×D311yescharacteristic
123C22×Dic5—31no—
124C22×Dic5C4×D312yes—
125C2×C4×D5—32no—
126C2×C4×D5—32no—
127C2×C4×D5—61no—
128C2×C4×D5—61no—
129C2×C4×D5—61no—
130C2×C4×D5—61no—
131C5×M16—21no—
132C5×M16—21no—
133C5×M16—61no—
134C5×M16—61no—
135C2×C5×C8—21no—
136C2×C5×C8—61no—
137C5×C4⋊C4—61no—
138C5×C4⋊C4—61no—
139#685—64no—
140C4⋊Dic5—21no—
141C4⋊Dic5—21no—
142C4×Dic5—64no—
143#681—21no—
144#681—21no—
145#681—61no—
146#681—61no—
147C2×#168—21no—
148C2×#168—61no—
149C2×#117—151no—
150#407—151no—
151#407—151no—
152#343—31no—
153#343—51no—
154#343—151no—
155#343—151no—
156C22×C3×C5—21no—
157C22×C3×C5—21no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C22×C3×C5#11711yescharacteristic
160C22×C3×C5#11711yescharacteristic
161C2×D15—22no—
162C2×D15—22no—
163C2×D15—22no—
164C2×D15—42no—
165C2×D15—42no—
166C3×C4×C5#12311yescharacteristic
167C3×C4×C5#12311yescharacteristic
168C3×C4×C5#12311yescharacteristic
169C3×C4×C5#12311yescharacteristic
170Dic15—22no—
171C3×Dic5—42no—
172C5×Dic3—42no—
173C23×D3—51no—
174C22×C3×C4—52no—
175C22×C3×C4C22×D511yescharacteristic
176C22×Dic3—51no—
177C22×Dic3C4×D512yes—
178C2×C4×D3—52no—
179C2×C4×D3—52no—
180C2×C4×D3—101no—
181C2×C4×D3—101no—
182C2×C4×D3—101no—
183C2×C4×D3—101no—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—101no—
187C3×M16—101no—
188C2×C3×C8—21no—
189C2×C3×C8—101no—
190C3×C4⋊C4—101no—
191C3×C4⋊C4—101no—
192(C2×D3)⋊C4—104no—
193C4⋊Dic3—21no—
194C4⋊Dic3—21no—
195C4×Dic3—104no—
196#208—21no—
197#208—21no—
198#208—101no—
199#208—101no—
200C2×C3⋊C8—21no—
201C2×C3⋊C8—101no—
202C23×C5C2×C4×D311yescharacteristic
203C22×D5—32no—
204C22×D5—61no—
205C22×D5—61no—
206C22×D5—121no—
207C22×D5—121no—
208C2×C4×C5—62no—
209C2×C4×C5—122no—
210C2×C4×C5#23511yescharacteristic
211C2×C4×C5#23511yescharacteristic
212C2×C4×C5D3×D411yescharacteristic
213C2×C4×C5D3×D411yescharacteristic
214C2×C4×C5#23711yescharacteristic
215C2×C4×C5#23911yescharacteristic
216C2×Dic5—22no—
217C2×Dic5—32no—
218C2×Dic5—42no—
219C2×Dic5—61no—
220C2×Dic5—61no—
221C4×D5—62no—
222C4×D5—62no—
223C4×D5—62no—
224C4×D5—62no—
225C5×C8—41no—
226C5×C8—121no—
227#168—41no—
228#168—121no—
229C23×C4—151no—
230C2×M16—31no—
231C2×M16—51no—
232C2×M16—151no—
233C2×M16D3×D511yescharacteristic
234#117—302no—
235#117—302no—
236C2×C4⋊C4—31no—
237C2×C4⋊C4—51no—
238C2×C22⋊C4—152no—
239C2×C42—152no—
240C22⋊C8—302no—
241C22⋊C8—302no—
242C2×C3×C5—21no—
243C2×C3×C5—21no—
244C2×C3×C5#38111yescharacteristic
245C2×C3×C5#41311yescharacteristic
246C2×C3×C5#41311yescharacteristic
247D15—42no—
248C23×C3C2×C4×D511yescharacteristic
249C22×D3—52no—
250C22×D3—101no—
251C22×D3—101no—
252C22×D3—201no—
253C22×D3—201no—
254C2×C3×C4—102no—
255C2×C3×C4—202no—
256C2×C3×C4#70911yescharacteristic
257C2×C3×C4#70911yescharacteristic
258C2×C3×C4D4×D511yescharacteristic
259C2×C3×C4D4×D511yescharacteristic
260C2×C3×C4#71111yescharacteristic
261C2×C3×C4#71311yescharacteristic
262C2×Dic3—22no—
263C2×Dic3—42no—
264C2×Dic3—52no—
265C2×Dic3—101no—
266C2×Dic3—101no—
267C4×D3—102no—
268C4×D3—102no—
269C4×D3—102no—
270C4×D3—102no—
271C3×C8—41no—
272C3×C8—201no—
273C3⋊C8—41no—
274C3⋊C8—201no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5#87211yescharacteristic
278C22×C5D3×C22⋊C411yescharacteristic
279C22×C5#89211yescharacteristic
280C2×D5—62no—
281C2×D5—62no—
282C2×D5—62no—
283C2×D5—122no—
284C2×D5—122no—
285C4×C5—122no—
286C4×C5#88311yescharacteristic
287C4×C5#88311yescharacteristic
288C4×C5#89411yescharacteristic
289C4×C5#89411yescharacteristic
290Dic5—42no—
291Dic5—62no—
292C24—151no—
293C22×C4—32no—
294C22×C4—52no—
295C22×C4—151no—
296C22×C4—152no—
297C22×C4—152no—
298C22×C4—301no—
299C22×C4—301no—
300C22×C4—301no—
301C22×C4—301no—
302C22×C4C2×D3×D511yescharacteristic
303M16—21no—
304M16—21no—
305M16—61no—
306M16—61no—
307M16—101no—
308M16—101no—
309M16—301no—
310M16—301no—
311C2×C8—21no—
312C2×C8—61no—
313C2×C8—101no—
314C2×C8—301no—
315C4⋊C4—61no—
316C4⋊C4—61no—
317C4⋊C4—101no—
318C4⋊C4—101no—
319C22⋊C4—304no—
320C42—304no—
321C3×C5#182211yescharacteristic, complemented, Hall
322C22×C3—21no—
323C22×C3—21no—
324C22×C3#401811yescharacteristic
325C22×C3D5×C22⋊C411yescharacteristic
326C22×C3#403811yescharacteristic
327C2×D3—102no—
328C2×D3—102no—
329C2×D3—102no—
330C2×D3—202no—
331C2×D3—202no—
332C3×C4—202no—
333C3×C4#402911yescharacteristic
334C3×C4#402911yescharacteristic
335C3×C4#404011yescharacteristic
336C3×C4#404011yescharacteristic
337Dic3—42no—
338Dic3—102no—
339C2×C5—21no—
340C2×C5—21no—
341C2×C5#466411yescharacteristic
342C2×C5#474511yescharacteristic
343C2×C5#475111yescharacteristic
344D5—122no—
345C23—152no—
346C23—301no—
347C23—301no—
348C23—601no—
349C23—601no—
350C23C4×D3×D511yescharacteristic
351C2×C4—62no—
352C2×C4—102no—
353C2×C4—122no—
354C2×C4—152no—
355C2×C4—202no—
356C2×C4—301no—
357C2×C4—301no—
358C2×C4—302no—
359C2×C4—302no—
360C2×C4—302no—
361C2×C4—302no—
362C2×C4#676911yescharacteristic
363C2×C4#677311yescharacteristic
364C2×C4#677711yescharacteristic
365C2×C4#677911yescharacteristic
366C2×C4#678211yescharacteristic
367C2×C4#679011yescharacteristic
368C8—41no—
369C8—121no—
370C8—201no—
371C8—601no—
372C2×C3—21no—
373C2×C3—21no—
374C2×C3#6495311yescharacteristic
375C2×C3#6503411yescharacteristic
376C2×C3#6504011yescharacteristic
377D3—202no—
378C5#6899111yescharacteristic, complemented, Sylow
379C22—21no—
380C22—21no—
381C22—302no—
382C22—302no—
383C22—302no—
384C22—602no—
385C22—602no—
386C22#9140211yescharacteristic
387C22#9140311yescharacteristic
388C22#9147311yescharacteristic
389C4—122no—
390C4—202no—
391C4—302no—
392C4#9135611yescharacteristic
393C4#9143311yescharacteristic
394C4#9143811yescharacteristic
395C4#9156211yescharacteristic
396C3#1059978411yescharacteristic, complemented, Sylow
397C2—21no—
398C2—21no—
399C2—602no—
400C2#1174823811yescharacteristic
401C2#1174823911yescharacteristic
402C2#1174888911yescharacteristic
subgroupG/H
centerC22#91473
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D15C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. C5×#4554C2semidirect
5. C3×#64774C2semidirect
6. #11745986C2semidirect
7. #11745985C2semidirect
28. #64774D3semidirect
64. #4554D5semidirect
321. C3×C5#1822semidirect
378. C5#68991semidirect
396. C3#10599784semidirect

Maximal subgroups

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

subgroupindex
C2×#913472
#117512272
#117483512
C5×#45542
C3×#647742
#117459862
#117459852
#105997843
#689915