Finite Group Databasebeta

← #14298555

Subgroups — #14298555

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×C5×#926C211yesmaximal, characteristic
2C4×#6719C211yesmaximal, characteristic
3C3×#65496C211yesmaximal, characteristic
4#11745975C214yesmaximal, complemented
5#10602383—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C2×#6719—21no—
8C2×C4×Dic15C2212yes—
9C2×C5×#217—21no—
10C5×#926—21no—
11C5×#926—21no—
12C5×#926C412yescomplemented
13C5×#926C2212yes—
14C2×C5×C4⋊Dic3C411yescharacteristic, complemented
15C2×C5×C4⋊Dic3C411yescharacteristic, complemented
16C2×C4×C5×Dic3—21no—
17C2×C3×#681C2212yes—
18#91115—21no—
19C3×C22⋊#168—21no—
20C3×C22⋊#168—21no—
21#69975—51nomaximal, Hall
22C2×C5×#117—31no—
23C4×C22⋊Dic5—31no—
24#65496D311yescharacteristic
25#64752—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×Dic15—22no—
35C22×C5×Dic3—21no—
36C22×C5×Dic3—21no—
37#6719—24no—
38C4×Dic15—24no—
39C5×#217—22no—
40C5×#217—22no—
41C5×C4⋊Dic3—21no—
42C5×C4⋊Dic3—21no—
43C5×C4⋊Dic3C2×C412yes—
44C5×C4⋊Dic3C2×C412yes—
45C4×C5×Dic3—22no—
46C4×C5×Dic3—22no—
47C3×#681—24no—
48C2×C3×#168—22no—
49C2×#926D511yescharacteristic
50C3×#407—51no—
51C4×#217—51no—
52#4555—54no—
53C23×C4×C5C2×D311yescharacteristic
54C5×#117—32no—
55C5×#117—32no—
56C5×#117—61no—
57C5×#117—61no—
58C2×C5×C4⋊C4—31no—
59C2×C5×C4⋊C4—31no—
60C2×C5×C22⋊C4—61no—
61C2×C42×C5—61no—
62C2×C22⋊Dic5—61no—
63C2×C4×Dic5—32no—
64C2×#681C2×D312yes—
65#3963—61no—
66C22⋊#168—21no—
67C22⋊#168—21no—
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×Dic15—24no—
86C2×Dic15—42no—
87C2×Dic15—42no—
88C2×C5×Dic3—22no—
89C2×C5×Dic3—22no—
90C2×C5×Dic3—42no—
91C2×C5×Dic3—42no—
92C3×#168—42no—
93C23×C3×C4C2×D511yescharacteristic
94C2×C3×M16—52no—
95C2×#217—21no—
96C2×#217—101no—
97#926—21no—
98#926—21no—
99#926Dic512yescomplemented
100#926C2×D512yes—
101C2×C4⋊Dic3Dic511yescharacteristic, complemented
102C2×C4⋊Dic3Dic511yescharacteristic, complemented
103C2×C4×Dic3—21no—
104C2×C4×Dic3—52no—
105C3×C22⋊C8—101no—
106C3×C22⋊C8—101no—
107C3⋊#95—101no—
108C24×C5D1211yescharacteristic
109C22×C4×C5—24no—
110C22×C4×C5—61no—
111C22×C4×C5—61no—
112C22×C4×C5C4×D311yescharacteristic
113C22×C4×C5C4×D311yescharacteristic
114C22×C4×C5D1211yescharacteristic
115C22×C4×C5#6711yescharacteristic
116C22×C4×C5#6711yescharacteristic
117C22×C4×C5C22×D311yescharacteristic
118C22×Dic5—62no—
119C5×C4⋊C4—32no—
120C5×C4⋊C4—32no—
121C5×C4⋊C4—61no—
122C5×C4⋊C4—61no—
123C5×C22⋊C4—62no—
124C5×C22⋊C4—62no—
125C42×C5—62no—
126C42×C5—62no—
127C22⋊Dic5—64no—
128C4×Dic5—64no—
129#681—24no—
130C2×#168—22no—
131C2×#117—31no—
132#407—51no—
133C4×C22⋊C4—151no—
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—
150Dic15—44no—
151C5×Dic3—42no—
152C5×Dic3—42no—
153C24×C3C22⋊D511yescharacteristic
154C22×C3×C4—24no—
155C22×C3×C4C2×Dic511yescharacteristic
156C22×C3×C4C2×Dic511yescharacteristic
157C22×C3×C4C22⋊D511yescharacteristic
158C22×C3×C4C22⋊D511yescharacteristic
159C22×C3×C4C22⋊D511yescharacteristic
160C22×C3×C4C22×D511yescharacteristic
161C22×Dic3—21no—
162C22×Dic3—21no—
163C22×Dic3—102no—
164C3×M16—104no—
165C2×C3×C8—102no—
166#217—22no—
167#217—22no—
168#217—104no—
169C4⋊Dic3—21no—
170C4⋊Dic3—21no—
171C4⋊Dic3C2×Dic512yes—
172C4⋊Dic3C2×Dic512yes—
173C4×Dic3—22no—
174C4×Dic3—22no—
175C4×Dic3—104no—
176C23×C5—22no—
177C23×C5—22no—
178C23×C5—41no—
179C23×C5(C2×D3)⋊C411yescharacteristic
180C23×C5(C2×D3)⋊C411yescharacteristic
181C23×C5C2×D1211yescharacteristic
182C2×C4×C5—22no—
183C2×C4×C5—22no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—22no—
187C2×C4×C5—62no—
188C2×C4×C5—62no—
189C2×C4×C5—122no—
190C2×C4×C5—122no—
191C2×C4×C5(C2×D3)⋊C411yescharacteristic
192C2×C4×C5(C2×D3)⋊C411yescharacteristic
193C2×C4×C5C2×C4×D311yescharacteristic
194C2×C4×C5#23714yes—
195C2×C4×C5C2×#6711yescharacteristic
196C2×Dic5—64no—
197C2×Dic5—122no—
198C2×Dic5—122no—
199#168—42no—
200C23×C4D3×D511yescharacteristic
201C2×M16—52no—
202#117—32no—
203#117—32no—
204#117—61no—
205#117—61no—
206C2×C4⋊C4—31no—
207C2×C4⋊C4—31no—
208C2×C22⋊C4—61no—
209C2×C22⋊C4—301no—
210C2×C42—61no—
211C2×C42—152no—
212C22⋊C8—101no—
213C22⋊C8—101no—
214#95—301no—
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×C3C22⋊Dic511yescharacteristic
225C23×C3C22⋊Dic511yescharacteristic
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×C4C22⋊Dic511yescharacteristic
233C2×C3×C4C22⋊Dic511yescharacteristic
234C2×C3×C4#70914yes—
235C2×C3×C4C22×Dic511yescharacteristic
236C2×C3×C4C2×C22⋊D511yescharacteristic
237C2×Dic3—22no—
238C2×Dic3—22no—
239C2×Dic3—42no—
240C2×Dic3—42no—
241C2×Dic3—104no—
242C2×Dic3—202no—
243C2×Dic3—202no—
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#82512yes—
254C22×C5#88612yes—
255C22×C5C2×(C2×D3)⋊C411yescharacteristic
256C4×C5—21no—
257C4×C5—21no—
258C4×C5—122no—
259C4×C5—122no—
260C4×C5#87712yes—
261C4×C5#93512yes—
262Dic5—124no—
263C24#120311yescharacteristic
264C22×C4—24no—
265C22×C4—61no—
266C22×C4—61no—
267C22×C4—302no—
268C22×C4D3×Dic511yescharacteristic
269C22×C4D3×Dic511yescharacteristic
270C22×C4#120111yescharacteristic
271C22×C4#120111yescharacteristic
272C22×C4#120311yescharacteristic
273C22×C4C2×D3×D511yescharacteristic
274M16—104no—
275C2×C8—102no—
276C4⋊C4—32no—
277C4⋊C4—32no—
278C4⋊C4—61no—
279C4⋊C4—61no—
280C22⋊C4—62no—
281C22⋊C4—62no—
282C22⋊C4—304no—
283C42—62no—
284C42—62no—
285C42—304no—
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#396912yes—
296C22×C3#407512yes—
297C22×C3C2×C22⋊Dic511yescharacteristic
298C3×C4—21no—
299C3×C4—21no—
300C3×C4#407212yes—
301C3×C4#407512yes—
302Dic3—42no—
303Dic3—42no—
304Dic3—204no—
305C2×C5—22no—
306C2×C5—22no—
307C2×C5—41no—
308C2×C5#494311yescharacteristic
309C2×C5C2×#82511yescharacteristic
310C2×C5#513911yescharacteristic
311C23—22no—
312C23—22no—
313C23—41no—
314C23(C2×D3)⋊Dic511yescharacteristic
315C23(C2×D3)⋊Dic511yescharacteristic
316C23C2×#120311yescharacteristic
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—62no—
323C2×C4—62no—
324C2×C4—122no—
325C2×C4—122no—
326C2×C4—304no—
327C2×C4—602no—
328C2×C4—602no—
329C2×C4(C2×D3)⋊Dic511yescharacteristic
330C2×C4(C2×D3)⋊Dic511yescharacteristic
331C2×C4#677914yes—
332C2×C4C2×D3×Dic511yescharacteristic
333C2×C4C2×#120111yescharacteristic
334C8—202no—
335C2×C3—22no—
336C2×C3—22no—
337C2×C3—41no—
338C2×C3#6550011yescharacteristic
339C2×C3C2×#396911yescharacteristic
340C2×C3#6552511yescharacteristic
341C5#6997511yescharacteristic, complemented, Sylow
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—44no—
350C22#9097812yes—
351C22C2×(C2×D3)⋊Dic511yescharacteristic
352C22#9154212yes—
353C4—21no—
354C4—21no—
355C4—122no—
356C4—122no—
357C4—604no—
358C4#9152912yes—
359C4#9153612yes—
360C3#1060238311yescharacteristic, complemented, Sylow
361C2—22no—
362C2—22no—
363C2—41no—
364C2C2×#9097811yescharacteristic
365C2#1174842411yescharacteristic
366C2#1174947211yescharacteristic
subgroupG/H
centerC2×C4C2×#1201
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. #11745975C2semidirect
12. C5×#926C4semidirect
14. C2×C5×C4⋊Dic3C4semidirect
15. C2×C5×C4⋊Dic3C4semidirect
99. #926Dic5semidirect
101. C2×C4⋊Dic3Dic5semidirect
102. C2×C4⋊Dic3Dic5semidirect
286. C3×C5#1826semidirect
341. C5#69975semidirect
360. C3#10602383semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9262
C4×#67192
C3×#654962
#117459752
#106023833
#699755