Finite Group Databasebeta

← #14283282

Subgroups — #14283282

Order 1920.

652 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#930C211yesmaximal, characteristic
2#11751308C211yesmaximal, characteristic, complemented
3C3×#65500C211yesmaximal, characteristic, complemented
4#11745956C214yesmaximal, complemented
5#10602467—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C22×C5×#67—21no—
8C22×C5×D12C411yescharacteristic, complemented
9C2×#6710—21no—
10C5×#930—21no—
11C5×#930—21no—
12C5×#930C412yescomplemented
13C5×#930C2212yes—
14C2×C5×(C2×D3)⋊C4—21no—
15C2×C5×C4⋊Dic3C411yescharacteristic, complemented
16C2×C3×C22⋊Dic5—21no—
17#91114—21no—
18#91114C2212yescomplemented
19C3×#3963—21no—
20C3×#3963C2212yescomplemented
21#69531—51nomaximal, Hall
22C2×C5×#121—31no—
23#65500D311yescharacteristic, complemented
24#65496—31no—
25#64757—34no—
26C24×C3×C5D411yescharacteristic
27C23×C5×D3—21no—
28C22×C3×C4×C5—42no—
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D411yescharacteristic
34C22×C3×C4×C5C2311yescharacteristic
35C2×C5×#67—22no—
36C2×C5×#67—22no—
37C2×C5×#67—44no—
38C22×C5×Dic3—21no—
39C2×C5×D12—21no—
40C2×C5×D12—42no—
41C2×C5×D12C2×C412yes—
42C22×C3×Dic5—22no—
43#6710—42no—
44C2×C3⋊#168—22no—
45C5×(C2×D3)⋊C4—22no—
46C5×(C2×D3)⋊C4—22no—
47C5×C4⋊Dic3—21no—
48C5×C4⋊Dic3C2×C412yes—
49C3×C22⋊Dic5—42no—
50C2×#930D511yescharacteristic
51C3×#381—51no—
52#5207—51no—
53#4451—54no—
54C22×C5×D4—31no—
55C22×C5×D4—61no—
56C23×C4×C5C2×D311yescharacteristic
57C5×#121—32no—
58C5×#121—32no—
59C5×#121—61no—
60C5×#121—61no—
61C2×C5×C4⋊C4—31no—
62C2×C5×C22⋊C4—61no—
63C2×C22⋊Dic5—21no—
64C2×#681—61no—
65#3963—21no—
66#3963C2×D312yescomplemented
67C22⋊#168—32no—
68C22⋊#168—61no—
69#1510—151noSylow
70C23×C3×C5—22no—
71C23×C3×C5—22no—
72C23×C3×C5—41no—
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C22⋊C411yescharacteristic
75C23×C3×C5C2×D411yescharacteristic
76C22×C5×D3—22no—
77C22×C5×D3—42no—
78C22×C5×D3—42no—
79C22×C5×D3—42no—
80C2×C3×C4×C5—22no—
81C2×C3×C4×C5—22no—
82C2×C3×C4×C5—41no—
83C2×C3×C4×C5—41no—
84C2×C3×C4×C5—41no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C22⋊C411yescharacteristic
87C2×C3×C4×C5C22⋊C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C5×#67—44no—
91C5×#67—44no—
92C2×C5×Dic3—22no—
93C2×C5×Dic3—42no—
94C5×D12—42no—
95C5×D12—42no—
96C2×C3×Dic5—42no—
97C2×C3×Dic5—42no—
98C2×C3×Dic5—42no—
99C3⋊#168—42no—
100C23×C3×C4C2×D511yescharacteristic
101C22×#67—21no—
102C22×D12Dic511yescharacteristic, complemented
103C2×C3×C22⋊C4—101no—
104#930—21no—
105#930—21no—
106#930Dic512yescomplemented
107#930C2×D512yes—
108C2×(C2×D3)⋊C4—21no—
109C2×C4⋊Dic3Dic511yescharacteristic, complemented
110C2×#208—101no—
111C3×#95—52no—
112C3×#95—101no—
113#830—52no—
114#830—101no—
115C24×C5—61no—
116C24×C5#6711yescharacteristic
117C2×C5×D4—32no—
118C2×C5×D4—62no—
119C2×C5×D4—62no—
120C2×C5×D4—61no—
121C2×C5×D4—122no—
122C2×C5×D4—124no—
123C22×C4×C5—42no—
124C22×C4×C5—61no—
125C22×C4×C5C4×D311yescharacteristic
126C22×C4×C5C4×D311yescharacteristic
127C22×C4×C5D1211yescharacteristic
128C22×C4×C5D1211yescharacteristic
129C22×C4×C5#6711yescharacteristic
130C22×C4×C5C22×D311yescharacteristic
131C22×Dic5—22no—
132C5×C4⋊C4—32no—
133C5×C4⋊C4—61no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C22⋊Dic5—42no—
137#681—122no—
138C2×#168—62no—
139C2×#121—31no—
140#407—151no—
141#381—51no—
142#327—154no—
143C22×C3×C5—21no—
144C22×C3×C5—21no—
145C22×C3×C5—21no—
146C22×C3×C5—21no—
147C22×C3×C5—21no—
148C22×C3×C5—21no—
149C22×C3×C5—21no—
150C22×C3×C5—44no—
151C22×C3×C5#9912yes—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C22×C3×C5AGL(1,ℤ/8)12yes—
154C2×C5×D3—42no—
155C2×C5×D3—42no—
156C2×C5×D3—42no—
157C2×C5×D3—84no—
158C3×C4×C5—21no—
159C3×C4×C5—21no—
160C3×C4×C5—21no—
161C3×C4×C5—21no—
162C3×Dic5—82no—
163C5×Dic3—42no—
164C24×C3C22⋊D511yescharacteristic
165C23×D3—21no—
166C22×C3×C4—42no—
167C22×C3×C4—102no—
168C22×C3×C4C2×Dic511yescharacteristic
169C22×C3×C4C2×Dic511yescharacteristic
170C22×C3×C4C22⋊D511yescharacteristic
171C22×C3×C4C22⋊D511yescharacteristic
172C22×C3×C4C22⋊D511yescharacteristic
173C22×C3×C4C22×D511yescharacteristic
174C2×#67—22no—
175C2×#67—22no—
176C2×#67—44no—
177C22×Dic3—21no—
178C2×D12—21no—
179C2×D12—42no—
180C2×D12C2×Dic512yes—
181C3×C22⋊C4—202no—
182(C2×D3)⋊C4—22no—
183(C2×D3)⋊C4—22no—
184C4⋊Dic3—21no—
185C4⋊Dic3C2×Dic512yes—
186#208—202no—
187C2×C3⋊C8—102no—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—41no—
191C23×C5—62no—
192C23×C5—122no—
193C23×C5—122no—
194C23×C5—122no—
195C23×C5(C2×D3)⋊C411yescharacteristic
196C23×C5(C2×D3)⋊C411yescharacteristic
197C23×C5C2×#6711yescharacteristic
198C5×D4—122no—
199C5×D4—122no—
200C5×D4—124no—
201C5×D4—124no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—41no—
207C2×C4×C5—41no—
208C2×C4×C5—62no—
209C2×C4×C5—122no—
210C2×C4×C5(C2×D3)⋊C411yescharacteristic
211C2×C4×C5(C2×D3)⋊C411yescharacteristic
212C2×C4×C5C2×C4×D311yescharacteristic
213C2×C4×C5C2×D1211yescharacteristic
214C2×Dic5—42no—
215C2×Dic5—42no—
216C2×Dic5—42no—
217#168—122no—
218C22×D4—31no—
219C22×D4—61no—
220C23×C4D3×D511yescharacteristic
221C2×M16—301no—
222#121—32no—
223#121—32no—
224#121—61no—
225#121—61no—
226C2×C4⋊C4—31no—
227C2×C22⋊C4—61no—
228C2×C22⋊C4—101no—
229C22⋊C8—152no—
230C22⋊C8—301no—
231#95—52no—
232#95—101no—
233C2×C3×C5—22no—
234C2×C3×C5—22no—
235C2×C3×C5—41no—
236C2×C3×C5C2×#9911yescharacteristic
237C2×C3×C5#41811yescharacteristic
238C2×C3×C5#42111yescharacteristic
239C5×D3—82no—
240C23×C3—22no—
241C23×C3—22no—
242C23×C3—41no—
243C23×C3C22⋊Dic511yescharacteristic
244C23×C3C22⋊Dic511yescharacteristic
245C23×C3C2×C22⋊D511yescharacteristic
246C22×D3—22no—
247C22×D3—42no—
248C22×D3—42no—
249C22×D3—42no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—41no—
253C2×C3×C4—41no—
254C2×C3×C4—41no—
255C2×C3×C4—41no—
256C2×C3×C4—202no—
257C2×C3×C4—202no—
258C2×C3×C4—202no—
259C2×C3×C4C22⋊Dic511yescharacteristic
260C2×C3×C4C22⋊Dic511yescharacteristic
261C2×C3×C4C22×Dic511yescharacteristic
262C2×C3×C4C2×C22⋊D511yescharacteristic
263#67—44no—
264#67—44no—
265C2×Dic3—22no—
266C2×Dic3—42no—
267D12—42no—
268D12—42no—
269C3⋊C8—202no—
270C22×C5—21no—
271C22×C5—21no—
272C22×C5—21no—
273C22×C5—21no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—44no—
278C22×C5—122no—
279C22×C5—122no—
280C22×C5—122no—
281C22×C5—244no—
282C22×C5#80612yes—
283C22×C5C2×(C2×D3)⋊C411yescharacteristic
284C22×C5#94912yes—
285C4×C5—21no—
286C4×C5—21no—
287C4×C5—21no—
288C4×C5—21no—
289C4×C5—122no—
290Dic5—82no—
291C24—61no—
292C24#120111yescharacteristic
293C2×D4—32no—
294C2×D4—62no—
295C2×D4—62no—
296C2×D4—61no—
297C2×D4—122no—
298C2×D4—124no—
299C22×C4—42no—
300C22×C4—61no—
301C22×C4—102no—
302C22×C4D3×Dic511yescharacteristic
303C22×C4D3×Dic511yescharacteristic
304C22×C4#120111yescharacteristic
305C22×C4#120311yescharacteristic
306C22×C4#120311yescharacteristic
307C22×C4C2×D3×D511yescharacteristic
308M16—602no—
309C2×C8—302no—
310C4⋊C4—32no—
311C4⋊C4—61no—
312C22⋊C4—62no—
313C22⋊C4—62no—
314C22⋊C4—202no—
315C3×C5#151011yescharacteristic, complemented, Hall
316C22×C3—21no—
317C22×C3—21no—
318C22×C3—21no—
319C22×C3—21no—
320C22×C3—21no—
321C22×C3—21no—
322C22×C3—21no—
323C22×C3—44no—
324C22×C3#396612yes—
325C22×C3#407812yes—
326C22×C3C2×C22⋊Dic511yescharacteristic
327C2×D3—42no—
328C2×D3—42no—
329C2×D3—42no—
330C2×D3—84no—
331C3×C4—21no—
332C3×C4—21no—
333C3×C4—21no—
334C3×C4—21no—
335C3×C4—402no—
336Dic3—42no—
337C2×C5—22no—
338C2×C5—22no—
339C2×C5—41no—
340C2×C5—242no—
341C2×C5C2×#80611yescharacteristic
342C2×C5#500111yescharacteristic
343C2×C5#500511yescharacteristic
344C23—22no—
345C23—22no—
346C23—41no—
347C23—62no—
348C23—122no—
349C23—122no—
350C23—122no—
351C23(C2×D3)⋊Dic511yescharacteristic
352C23(C2×D3)⋊Dic511yescharacteristic
353C23C2×#120111yescharacteristic
354D4—122no—
355D4—122no—
356D4—124no—
357D4—124no—
358C2×C4—22no—
359C2×C4—22no—
360C2×C4—41no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—62no—
365C2×C4—122no—
366C2×C4—202no—
367C2×C4—202no—
368C2×C4—202no—
369C2×C4(C2×D3)⋊Dic511yescharacteristic
370C2×C4(C2×D3)⋊Dic511yescharacteristic
371C2×C4C2×D3×Dic511yescharacteristic
372C2×C4C2×#120311yescharacteristic
373C8—602no—
374C2×C3—22no—
375C2×C3—22no—
376C2×C3—41no—
377C2×C3#6550411yescharacteristic
378C2×C3C2×#396611yescharacteristic
379C2×C3#6552511yescharacteristic
380D3—82no—
381C5#6953111yescharacteristic, complemented, Sylow
382C22—21no—
383C22—21no—
384C22—21no—
385C22—21no—
386C22—21no—
387C22—21no—
388C22—21no—
389C22—44no—
390C22—122no—
391C22—122no—
392C22—122no—
393C22—244no—
394C22#9099612yes—
395C22#9129912yes—
396C22C2×(C2×D3)⋊Dic511yescharacteristic
397C4—21no—
398C4—21no—
399C4—21no—
400C4—21no—
401C4—122no—
402C4—402no—
403C3#1060246711yescharacteristic, complemented, Sylow
404C2—22no—
405C2—22no—
406C2—41no—
407C2—242no—
408C2#1174838611yescharacteristic
409C2#1174842511yescharacteristic
410C2C2×#9099611yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×#930C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1510
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751308C2semidirect
3. C3×#65500C2semidirect
4. #11745956C2semidirect
8. C22×C5×D12C4semidirect
12. C5×#930C4semidirect
15. C2×C5×C4⋊Dic3C4semidirect
18. #91114C22semidirect
20. C3×#3963C22semidirect
23. #65500D3semidirect
66. #3963C2×D3semidirect
102. C22×D12Dic5semidirect
106. #930Dic5semidirect
109. C2×C4⋊Dic3Dic5semidirect
315. C3×C5#1510semidirect
381. C5#69531semidirect
403. C3#10602467semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9302
#117513082
C3×#655002
#117459562
#106024673
#695315