Finite Group Databasebeta

← #14302015

Subgroups — #14302015

Order 1920.

716 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#926C211yesmaximal, characteristic, complemented
2C3×#66125C211yesmaximal, characteristic
3#11751308C211yesmaximal, characteristic, complemented
4C2×#90977C212yesmaximal, complemented
5#11745974C212yesmaximal, complemented
6#10602384—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×#709C2211yescharacteristic
9C2×#6710C2212yes—
10C2×C5×#217—21no—
11C5×#926—24no—
12C2×C5×C4⋊Dic3—21no—
13C2×C4×C5×Dic3C2212yes—
14C3×#4099—21no—
15C3×#4076C412yescomplemented
16C3×#4075—21no—
17C3×C4×C22⋊D5—22no—
18C3×#4072C2211yescharacteristic
19C3×#4070C412yescomplemented
20#91114—22no—
21#90977—24no—
22#71712—51nomaximal, Hall
23C2×C5×#117—31no—
24#66125D311yescharacteristic
25#65496—31no—
26C2×#3937—32no—
27#64743—32no—
28C24×C3×C5D411yescharacteristic
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5C2×C412yes—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C22×C5×Dic3—22no—
36C2×C3×C22⋊D5—22no—
37C2×C3×C22⋊D5—21no—
38C3×#709—22no—
39C3×#709—22no—
40C2×C3×D20C2×C411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×Dic10C2×C411yescharacteristic
43#6710—22no—
44#6710—22no—
45C2×C3⋊#168—22no—
46C5×#217—24no—
47C5×C4⋊Dic3—24no—
48C4×C5×Dic3—22no—
49C4×C5×Dic3D414yescomplemented
50C3×C22⋊Dic5—22no—
51C3×C22⋊Dic5—21no—
52C3×#685—22no—
53C3×C4⋊Dic5C2×C412yes—
54C3×#683—22no—
55C3×C4×Dic5—21no—
56C3×#525—51no—
57C2×#926D511yescharacteristic, complemented
58C2×#837—52no—
59#5207—51no—
60#4532—52no—
61C23×C4×C5C2×D311yescharacteristic
62C2×#709C2×D311yescharacteristic
63C5×#117—64no—
64C2×C5×C4⋊C4—61no—
65C2×C5×C22⋊C4—61no—
66C2×C42×C5—32no—
67#4099—21no—
68#4076Dic312yescomplemented
69#4075—21no—
70C4×C22⋊D5—22no—
71#4072C2×D311yescharacteristic
72#4070Dic312yescomplemented
73C2×#681—32no—
74C22⋊#168—62no—
75#3937—64no—
76#1897—151noSylow
77C23×C3×C5—21no—
78C23×C3×C5—21no—
79C23×C3×C5—42no—
80C23×C3×C5C22⋊C412yes—
81C23×C3×C5C2×D411yescharacteristic
82C22×C3×D5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—24no—
86C2×C3×C4×C5—24no—
87C2×C3×C4×C5C22⋊C412yes—
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D412yes—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4112yes—
92C2×C5×Dic3—24no—
93C2×C5×Dic3—44no—
94C3×C22⋊D5—44no—
95C3×C22⋊D5—41no—
96C3×C22⋊D5—41no—
97C2×C3×Dic5—22no—
98C2×C3×Dic5—21no—
99C3×D20—22no—
100C3×C4×D5—42no—
101C3×Dic10—22no—
102C3⋊#168—42no—
103C2×C3×#41—51no—
104C23×C3×C4C2×D511yescharacteristic
105C3×#123—101no—
106C3×C22⋊Q8—52no—
107C3×#121—52no—
108C3×#120—101no—
109C3×C4×D4—102no—
110C3×#117—51no—
111C2×#217—21no—
112#926—24no—
113C2×C4⋊Dic3—21no—
114C2×C4×Dic3C2×D512yes—
115C2×#208—52no—
116#837—104no—
117#830—102no—
118C24×C5#6711yescharacteristic
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—62no—
122C22×C4×C5C2×Dic312yes—
123C22×C4×C5#6711yescharacteristic
124C22×C4×C5#6712yes—
125C22×C4×C5C22×D311yescharacteristic
126C2×C22⋊D5—22no—
127C2×C22⋊D5—21no—
128#709—22no—
129#709—22no—
130C2×D20C2×Dic311yescharacteristic
131C2×C4×D5—21no—
132C2×Dic10C2×Dic311yescharacteristic
133C5×C4⋊C4—64no—
134C5×C22⋊C4—64no—
135C42×C5—34no—
136C42×C5—62no—
137C22⋊Dic5—22no—
138C22⋊Dic5—21no—
139#685—22no—
140C4⋊Dic5C2×Dic312yes—
141#683—22no—
142C4×Dic5—21no—
143#681—62no—
144#681—62no—
145C2×#168—62no—
146#525—51no—
147C2×#117—31no—
148C2×#104—152no—
149#407—151no—
150#339—152no—
151C22×C3×C5—22no—
152C22×C3×C5—22no—
153C22×C3×C5—22no—
154C22×C3×C5—22no—
155C22×C3×C5—42no—
156C22×C3×C5—42no—
157C22×C3×C5C2×C22⋊C411yescharacteristic
158C22×C3×C5#12011yescharacteristic
159C22×C3×C5#12311yescharacteristic
160C2×C3×D5—41no—
161C2×C3×D5—42no—
162C3×C4×C5—22no—
163C3×C4×C5C4×D412yes—
164C3×C4×C5#12112yes—
165C3×Dic5—41no—
166C3×Dic5—42no—
167C5×Dic3—44no—
168C24×C3C22⋊D511yescharacteristic
169C3×#41—102no—
170C3×#41—102no—
171C2×C3×Q8—51no—
172C2×C3×D4—51no—
173C2×C3×D4—102no—
174C2×C3×D4—101no—
175C22×C3×C4—22no—
176C22×C3×C4—22no—
177C22×C3×C4—101no—
178C22×C3×C4C4×D512yes—
179C22×C3×C4D2012yes—
180C22×C3×C4C22⋊D511yescharacteristic
181C22×C3×C4C22×D511yescharacteristic
182C22×Dic3—22no—
183C3×C4⋊C4—52no—
184C3×C4⋊C4—102no—
185C3×C22⋊C4—102no—
186C3×C22⋊C4—101no—
187C3×C22⋊C4—102no—
188C3×C42—101no—
189#217—24no—
190C4⋊Dic3—24no—
191C4×Dic3—22no—
192C4×Dic3C22⋊D514yescomplemented
193#208—102no—
194#208—102no—
195C2×C3⋊C8—102no—
196C23×C5—21no—
197C23×C5—21no—
198C23×C5—42no—
199C23×C5#21712yes—
200C23×C5C2×#6711yescharacteristic
201C22×D5—21no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—24no—
205C2×C4×C5—24no—
206C2×C4×C5—64no—
207C2×C4×C5—124no—
208C2×C4×C5#21712yes—
209C2×C4×C5D3×D412yes—
210C2×C4×C5#23712yes—
211C2×C4×C5C22×Dic311yescharacteristic
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—44no—
214C22⋊D5—41no—
215C22⋊D5—41no—
216C2×Dic5—22no—
217C2×Dic5—21no—
218D20—22no—
219C4×D5—42no—
220Dic10—22no—
221#168—122no—
222C2×#41—51no—
223C23×C4D3×D511yescharacteristic
224C2×M16—152no—
225#123—101no—
226C22⋊Q8—52no—
227#121—52no—
228#120—101no—
229C4×D4—102no—
230#117—51no—
231#117—64no—
232C2×C4⋊C4—61no—
233C2×C22⋊C4—61no—
234C2×C42—32no—
235#104—304no—
236C22⋊C8—302no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5—42no—
240C2×C3×C5#38611yescharacteristic
241C2×C3×C5#42112yes—
242C3×D5—81no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—42no—
246C23×C3—101no—
247C23×C3#68512yes—
248C23×C3C2×C22⋊D511yescharacteristic
249C3×Q8—102no—
250C3×D4—102no—
251C3×D4—204no—
252C3×D4—201no—
253C3×D4—201no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—24no—
257C2×C3×C4—24no—
258C2×C3×C4—102no—
259C2×C3×C4—101no—
260C2×C3×C4—202no—
261C2×C3×C4#68512yes—
262C2×C3×C4C2×C4×D511yescharacteristic
263C2×C3×C4C2×D2011yescharacteristic
264C2×C3×C4#70912yes—
265C2×C3×C4C2×C22⋊D512yes—
266C2×Dic3—24no—
267C2×Dic3—44no—
268C3⋊C8—202no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—22no—
272C22×C5—22no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5#93511yescharacteristic
276C22×C5#93711yescharacteristic
277C22×C5C2×#21711yescharacteristic
278C2×D5—41no—
279C2×D5—42no—
280C4×C5—22no—
281C4×C5—124no—
282C4×C5D4×Dic312yes—
283C4×C5#93912yes—
284Dic5—41no—
285Dic5—42no—
286C24#120111yescharacteristic
287#41—102no—
288#41—102no—
289C2×Q8—51no—
290C2×D4—51no—
291C2×D4—102no—
292C2×D4—101no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—62no—
296C22×C4—101no—
297C22×C4D5×Dic312yes—
298C22×C4#120111yescharacteristic
299C22×C4#120212yes—
300C22×C4C2×D3×D511yescharacteristic
301M16—302no—
302M16—302no—
303C2×C8—302no—
304C4⋊C4—52no—
305C4⋊C4—64no—
306C4⋊C4—102no—
307C22⋊C4—64no—
308C22⋊C4—102no—
309C22⋊C4—101no—
310C22⋊C4—102no—
311C42—34no—
312C42—62no—
313C42—101no—
314C3×C5#189711yescharacteristic, complemented, Hall
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3—202no—
322C22×C3—201no—
323C22×C3C2×#68511yescharacteristic
324C22×C3#407511yescharacteristic
325C22×C3#409911yescharacteristic
326C3×C4—22no—
327C3×C4—202no—
328C3×C4—201no—
329C3×C4C4×C22⋊D512yes—
330C3×C4#407612yes—
331Dic3—44no—
332C2×C5—21no—
333C2×C5—21no—
334C2×C5—42no—
335C2×C5#522011yescharacteristic
336C2×C5#523612yes—
337D5—81no—
338C23—21no—
339C23—21no—
340C23—42no—
341C23—101no—
342C23#666512yes—
343C23C2×#120111yescharacteristic
344Q8—102no—
345D4—102no—
346D4—204no—
347D4—201no—
348D4—201no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—64no—
354C2×C4—102no—
355C2×C4—101no—
356C2×C4—124no—
357C2×C4—202no—
358C2×C4#666512yes—
359C2×C4C2×D5×Dic311yescharacteristic
360C2×C4#677912yes—
361C2×C4C2×#120211yescharacteristic
362C2×C4D3×C22⋊D512yes—
363C8—602no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—42no—
367C2×C3—401no—
368C2×C3#6529412yes—
369C2×C3#6550211yescharacteristic
370C5#7171211yescharacteristic, complemented, Sylow
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—202no—
378C22—201no—
379C22C2×#666511yescharacteristic
380C22#9153611yescharacteristic
381C22#9156811yescharacteristic
382C4—22no—
383C4—124no—
384C4—202no—
385C4—201no—
386C4Dic3×C22⋊D512yes—
387C4#9156912yes—
388C3#1060238411yescharacteristic, complemented, Sylow
389C2—21no—
390C2—21no—
391C2—42no—
392C2—401no—
393C2#1174842112yes—
394C2#1174949511yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC3×#66125C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1897
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
1. C2×C5×#926C2semidirect
3. #11751308C2semidirect
4. C2×#90977C2semidirect
5. #11745974C2semidirect
15. C3×#4076C4semidirect
19. C3×#4070C4semidirect
49. C4×C5×Dic3D4semidirect
57. C2×#926D5semidirect
68. #4076Dic3semidirect
72. #4070Dic3semidirect
192. C4×Dic3C22⋊D5semidirect
314. C3×C5#1897semidirect
370. C5#71712semidirect
388. C3#10602384semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9262
C3×#661252
#117513082
C2×#909772
#117459742
#106023843
#717125