Finite Group Databasebeta

← #14298558

Subgroups — #14298558

Order 1920.

612 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4072C211yesmaximal, characteristic
2#11751308C211yesmaximal, characteristic
3C4×C5×#217C211yesmaximal, characteristic
4#11745974C214yesmaximal, complemented
5#10600235—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C2×#6710C2212yes—
8C2×C5×#217—21no—
9C2×C4×C5×Dic3C2212yes—
10C2×C3×C22⋊Dic5—21no—
11C3×#4072—21no—
12C3×#4072—21no—
13C3×#4072C412yescomplemented
14C3×#4072C2212yes—
15C2×C3×C4⋊Dic5C411yescharacteristic, complemented
16C2×C3×C4⋊Dic5C411yescharacteristic, complemented
17C2×C3×C4×Dic5—21no—
18#91114—21no—
19#91114—21no—
20C5×C3⋊#95—21no—
21#71590—51nomaximal, Hall
22C2×#4072D311yescharacteristic
23C4×C5×C22⋊C4—31no—
24#65496—31no—
25#64743—34no—
26C24×C3×C5D411yescharacteristic
27C22×C3×C4×C5—24no—
28C22×C3×C4×C5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D411yescharacteristic
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5C2311yescharacteristic
34C22×C5×Dic3—22no—
35C22×C3×Dic5—21no—
36C22×C3×Dic5—21no—
37#6710—24no—
38C2×C3⋊#168—22no—
39C5×#217—24no—
40C4×C5×Dic3—24no—
41C3×C22⋊Dic5—22no—
42C3×C22⋊Dic5—22no—
43C3×C4⋊Dic5—21no—
44C3×C4⋊Dic5—21no—
45C3×C4⋊Dic5C2×C412yes—
46C3×C4⋊Dic5C2×C412yes—
47C3×C4×Dic5—22no—
48C3×C4×Dic5—22no—
49C2×C3×#117—51no—
50C4×#217D511yescharacteristic
51#5207—51no—
52#4532—54no—
53C23×C4×C5C2×D311yescharacteristic
54C2×C5×C22⋊C4—61no—
55C2×C42×C5—32no—
56C2×C22⋊Dic5—21no—
57#4072—21no—
58#4072—21no—
59#4072Dic312yescomplemented
60#4072C2×D312yes—
61C2×C4⋊Dic5Dic311yescharacteristic, complemented
62C2×C4⋊Dic5Dic311yescharacteristic, complemented
63C2×C4×Dic5—21no—
64C2×#681—32no—
65C5×#95—61no—
66C22⋊#168—61no—
67C22⋊#168—61no—
68#1826—151noSylow
69C23×C3×C5—22no—
70C23×C3×C5—22no—
71C23×C3×C5—41no—
72C23×C3×C5C22⋊C411yescharacteristic
73C23×C3×C5C22⋊C411yescharacteristic
74C23×C3×C5C2×D411yescharacteristic
75C2×C3×C4×C5—22no—
76C2×C3×C4×C5—22no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—22no—
79C2×C3×C4×C5—22no—
80C2×C3×C4×C5C22⋊C411yescharacteristic
81C2×C3×C4×C5C22⋊C411yescharacteristic
82C2×C3×C4×C5C22×C411yescharacteristic
83C2×C3×C4×C5C2×D411yescharacteristic
84C2×C3×C4×C5#4114yes—
85C2×C5×Dic3—24no—
86C2×C5×Dic3—42no—
87C2×C5×Dic3—42no—
88C2×C3×Dic5—22no—
89C2×C3×Dic5—22no—
90C2×C3×Dic5—42no—
91C2×C3×Dic5—42no—
92C3⋊#168—42no—
93C23×C3×C4C2×D511yescharacteristic
94C3×#117—52no—
95C3×#117—52no—
96C3×#117—101no—
97C3×#117—101no—
98C2×C3×C4⋊C4—51no—
99C2×C3×C4⋊C4—51no—
100C2×C3×C22⋊C4—101no—
101C2×C3×C42—101no—
102C2×#217—21no—
103C2×C4×Dic3C2×D512yes—
104C2×#208—52no—
105C3⋊#95—21no—
106#830—101no—
107#830—101no—
108C24×C5#6711yescharacteristic
109C22×C4×C5—24no—
110C22×C4×C5—62no—
111C22×C4×C5C2×Dic311yescharacteristic
112C22×C4×C5C2×Dic311yescharacteristic
113C22×C4×C5#6711yescharacteristic
114C22×C4×C5#6711yescharacteristic
115C22×C4×C5#6711yescharacteristic
116C22×C4×C5C22×D311yescharacteristic
117C22×Dic5—21no—
118C22×Dic5—21no—
119C5×C22⋊C4—64no—
120C42×C5—64no—
121C22⋊Dic5—22no—
122C22⋊Dic5—22no—
123C4⋊Dic5—21no—
124C4⋊Dic5—21no—
125C4⋊Dic5C2×Dic312yes—
126C4⋊Dic5C2×Dic312yes—
127C4×Dic5—22no—
128C4×Dic5—22no—
129#681—64no—
130C2×#168—62no—
131C2×#117—51no—
132#407—151no—
133C4×C22⋊C4—31no—
134#339—154no—
135C22×C3×C5—21no—
136C22×C3×C5—21no—
137C22×C3×C5—21no—
138C22×C3×C5—21no—
139C22×C3×C5—21no—
140C22×C3×C5—21no—
141C22×C3×C5—21no—
142C22×C3×C5—44no—
143C22×C3×C5#10412yes—
144C22×C3×C5C2×C22⋊C411yescharacteristic
145C22×C3×C5#12312yes—
146C3×C4×C5—21no—
147C3×C4×C5—21no—
148C3×C4×C5#11712yes—
149C3×C4×C5#12312yes—
150C3×Dic5—42no—
151C3×Dic5—42no—
152C5×Dic3—44no—
153C24×C3C22⋊D511yescharacteristic
154C22×C3×C4—24no—
155C22×C3×C4—101no—
156C22×C3×C4—101no—
157C22×C3×C4C4×D511yescharacteristic
158C22×C3×C4C4×D511yescharacteristic
159C22×C3×C4D2011yescharacteristic
160C22×C3×C4D2011yescharacteristic
161C22×C3×C4C22⋊D511yescharacteristic
162C22×C3×C4C22×D511yescharacteristic
163C22×Dic3—22no—
164C3×C4⋊C4—52no—
165C3×C4⋊C4—52no—
166C3×C4⋊C4—101no—
167C3×C4⋊C4—101no—
168C3×C22⋊C4—102no—
169C3×C22⋊C4—102no—
170C3×C42—102no—
171C3×C42—102no—
172#217—24no—
173C4×Dic3—24no—
174#208—104no—
175C2×C3⋊C8—102no—
176C23×C5—22no—
177C23×C5—22no—
178C23×C5—41no—
179C23×C5#21711yescharacteristic
180C23×C5#21711yescharacteristic
181C23×C5C2×#6711yescharacteristic
182C2×C4×C5—22no—
183C2×C4×C5—22no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—22no—
187C2×C4×C5—64no—
188C2×C4×C5—122no—
189C2×C4×C5—122no—
190C2×C4×C5#21711yescharacteristic
191C2×C4×C5#21711yescharacteristic
192C2×C4×C5#23514yes—
193C2×C4×C5C22×Dic311yescharacteristic
194C2×C4×C5C2×#6711yescharacteristic
195C2×Dic5—22no—
196C2×Dic5—22no—
197C2×Dic5—42no—
198C2×Dic5—42no—
199#168—122no—
200C23×C4D3×D511yescharacteristic
201C2×M16—152no—
202#117—52no—
203#117—52no—
204#117—101no—
205#117—101no—
206C2×C4⋊C4—51no—
207C2×C4⋊C4—51no—
208C2×C22⋊C4—61no—
209C2×C22⋊C4—101no—
210C2×C42—32no—
211C2×C42—101no—
212C22⋊C8—301no—
213C22⋊C8—301no—
214#95—61no—
215C2×C3×C5—22no—
216C2×C3×C5—22no—
217C2×C3×C5—41no—
218C2×C3×C5#38111yescharacteristic
219C2×C3×C5C2×#10411yescharacteristic
220C2×C3×C5#42111yescharacteristic
221C23×C3—22no—
222C23×C3—22no—
223C23×C3—41no—
224C23×C3#68511yescharacteristic
225C23×C3#68511yescharacteristic
226C23×C3C2×C22⋊D511yescharacteristic
227C2×C3×C4—22no—
228C2×C3×C4—22no—
229C2×C3×C4—22no—
230C2×C3×C4—22no—
231C2×C3×C4—22no—
232C2×C3×C4—102no—
233C2×C3×C4—102no—
234C2×C3×C4—202no—
235C2×C3×C4—202no—
236C2×C3×C4#68511yescharacteristic
237C2×C3×C4#68511yescharacteristic
238C2×C3×C4C2×C4×D511yescharacteristic
239C2×C3×C4C2×D2011yescharacteristic
240C2×C3×C4#71114yes—
241C2×Dic3—24no—
242C2×Dic3—42no—
243C2×Dic3—42no—
244C3⋊C8—202no—
245C22×C5—21no—
246C22×C5—21no—
247C22×C5—21no—
248C22×C5—21no—
249C22×C5—21no—
250C22×C5—21no—
251C22×C5—21no—
252C22×C5—44no—
253C22×C5#83712yes—
254C22×C5#92912yes—
255C22×C5C2×#21711yescharacteristic
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—124no—
259C4×C5#92612yes—
260C4×C5#92912yes—
261Dic5—42no—
262Dic5—42no—
263C24#120111yescharacteristic
264C22×C4—24no—
265C22×C4—62no—
266C22×C4—101no—
267C22×C4—101no—
268C22×C4D5×Dic311yescharacteristic
269C22×C4D5×Dic311yescharacteristic
270C22×C4#120111yescharacteristic
271C22×C4#120211yescharacteristic
272C22×C4#120211yescharacteristic
273C22×C4C2×D3×D511yescharacteristic
274M16—304no—
275C2×C8—302no—
276C4⋊C4—52no—
277C4⋊C4—52no—
278C4⋊C4—101no—
279C4⋊C4—101no—
280C22⋊C4—64no—
281C22⋊C4—102no—
282C22⋊C4—102no—
283C42—64no—
284C42—102no—
285C42—102no—
286C3×C5#182611yescharacteristic, complemented, Hall
287C22×C3—21no—
288C22×C3—21no—
289C22×C3—21no—
290C22×C3—21no—
291C22×C3—21no—
292C22×C3—21no—
293C22×C3—21no—
294C22×C3—44no—
295C22×C3#393712yes—
296C22×C3C2×#68511yescharacteristic
297C22×C3#408112yes—
298C3×C4—21no—
299C3×C4—21no—
300C3×C4—202no—
301C3×C4—202no—
302C3×C4#402312yes—
303C3×C4#403212yes—
304Dic3—44no—
305C2×C5—22no—
306C2×C5—22no—
307C2×C5—41no—
308C2×C5#521111yescharacteristic
309C2×C5C2×#83711yescharacteristic
310C2×C5#523611yescharacteristic
311C23—22no—
312C23—22no—
313C23—41no—
314C23#666511yescharacteristic
315C23#666511yescharacteristic
316C23C2×#120111yescharacteristic
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—64no—
323C2×C4—102no—
324C2×C4—102no—
325C2×C4—122no—
326C2×C4—122no—
327C2×C4—202no—
328C2×C4—202no—
329C2×C4#666511yescharacteristic
330C2×C4#666511yescharacteristic
331C2×C4C2×D5×Dic311yescharacteristic
332C2×C4#678214yes—
333C2×C4C2×#120211yescharacteristic
334C8—602no—
335C2×C3—22no—
336C2×C3—22no—
337C2×C3—41no—
338C2×C3C2×#393711yescharacteristic
339C2×C3#6523211yescharacteristic
340C2×C3#6529411yescharacteristic
341C5#7159011yescharacteristic, complemented, Sylow
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—44no—
350C22#9097712yes—
351C22C2×#666511yescharacteristic
352C22#9153912yes—
353C4—21no—
354C4—21no—
355C4—124no—
356C4—202no—
357C4—202no—
358C4#9152812yes—
359C4#9154612yes—
360C3#1060023511yescharacteristic, complemented, Sylow
361C2—22no—
362C2—22no—
363C2—41no—
364C2C2×#9097711yescharacteristic
365C2#1174842111yescharacteristic
366C2#1174947111yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1826
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #11745974C2semidirect
13. C3×#4072C4semidirect
15. C2×C3×C4⋊Dic5C4semidirect
16. C2×C3×C4⋊Dic5C4semidirect
59. #4072Dic3semidirect
61. C2×C4⋊Dic5Dic3semidirect
62. C2×C4⋊Dic5Dic3semidirect
286. C3×C5#1826semidirect
341. C5#71590semidirect
360. C3#10600235semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40722
#117513082
C4×C5×#2172
#117459742
#106002353
#715905