Finite Group Databasebeta

← #14302014

Subgroups — #14302014

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
1#11756550C211yesmaximal, characteristic
2C2×C5×#926C211yesmaximal, characteristic, complemented
3C3×#65496C211yesmaximal, characteristic, complemented
4C2×#90980C212yesmaximal, complemented
5#11745976C212yesmaximal, complemented
6#10602384—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×#6817C2211yescharacteristic
9#91842—21no—
10#91819C412yescomplemented
11#91818—21no—
12C4×#1220—22no—
13#91815C2211yescharacteristic
14#91813C412yescomplemented
15C2×C5×#217—21no—
16C5×#926—24no—
17C2×C5×C4⋊Dic3—21no—
18C2×C4×C5×Dic3C2212yes—
19C2×C3×#681C2212yes—
20C3×C22⋊#168—22no—
21#90980—24no—
22#69966—51nomaximal, Hall
23C2×C5×#117—31no—
24#66125—31no—
25#65496D311yescharacteristic, complemented
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
35C2×#1220—22no—
36C2×#1220—21no—
37#6817—22no—
38#6817—22no—
39C2×D60C2×C411yescharacteristic
40C2×C4×D15—21no—
41C2×Dic30C2×C411yescharacteristic
42C22×C5×Dic3—22no—
43#6719—22no—
44#6719—21no—
45#6714—22no—
46C4⋊Dic15C2×C412yes—
47#6712—22no—
48C4×Dic15—21no—
49C5×#217—24no—
50C5×C4⋊Dic3—24no—
51C4×C5×Dic3—22no—
52C4×C5×Dic3D414yescomplemented
53C3×#681—22no—
54C3×#681—22no—
55C2×C3×#168—22no—
56#5791—51no—
57C2×#926D511yescharacteristic, complemented
58C3×#407—51no—
59C2×#825—52no—
60#4555—52no—
61C23×C4×C5C2×D311yescharacteristic
62C2×#709—31no—
63C5×#117—64no—
64C2×C5×C4⋊C4—61no—
65C2×C5×C22⋊C4—61no—
66C2×C42×C5—32no—
67#4099—61no—
68#4076—32no—
69#4075—61no—
70C4×C22⋊D5—62no—
71#4072—31no—
72#4070—32no—
73C2×#681C2×D312yes—
74C22⋊#168—22no—
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×D15—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—
92#1220—44no—
93#1220—41no—
94#1220—41no—
95C2×Dic15—22no—
96C2×Dic15—21no—
97D60—22no—
98C4×D15—42no—
99Dic30—22no—
100C2×C5×Dic3—24no—
101C2×C5×Dic3—44no—
102C3×#168—42no—
103C23×C3×C4C2×D511yescharacteristic
104C2×#235—51no—
105C2×C3×M16—52no—
106#953—101no—
107C2×#217—21no—
108#930—52no—
109#929—101no—
110C4×#67—102no—
111#926—24no—
112#926—51no—
113C2×C4⋊Dic3—21no—
114#924—52no—
115C2×C4×Dic3C2×D512yes—
116C3×C22⋊C8—102no—
117#825—104no—
118C24×C5D1211yescharacteristic
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5—62no—
122C22×C4×C5C4×D312yes—
123C22×C4×C5D1211yescharacteristic
124C22×C4×C5#6712yes—
125C22×C4×C5C22×D311yescharacteristic
126C2×C22⋊D5—62no—
127C2×C22⋊D5—61no—
128#709—62no—
129#709—62no—
130C2×D20—31no—
131C2×C4×D5—61no—
132C2×Dic10—31no—
133C5×C4⋊C4—64no—
134C5×C22⋊C4—64no—
135C42×C5—34no—
136C42×C5—62no—
137C22⋊Dic5—62no—
138C22⋊Dic5—61no—
139#685—62no—
140C4⋊Dic5—32no—
141#683—62no—
142C4×Dic5—61no—
143#681—22no—
144#681—22no—
145C2×#168—22no—
146#525—151no—
147C2×#117—31no—
148C2×#104—152no—
149#407—51no—
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×D15—41no—
161C2×D15—42no—
162C3×C4×C5—22no—
163C3×C4×C5C4×D412yes—
164C3×C4×C5#12112yes—
165Dic15—41no—
166Dic15—42no—
167C5×Dic3—44no—
168C24×C3C22⋊D511yescharacteristic
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4C4×D512yes—
172C22×C3×C4D2012yes—
173C22×C3×C4C22⋊D511yescharacteristic
174C22×C3×C4C22×D511yescharacteristic
175C2×#67—102no—
176C2×#67—101no—
177C22×Dic3—22no—
178#235—102no—
179#235—102no—
180C2×D12—51no—
181C2×C4×D3—101no—
182C2×Dic6—51no—
183C3×M16—102no—
184C3×M16—102no—
185C2×C3×C8—102no—
186#217—24no—
187#217—102no—
188#217—101no—
189(C2×D3)⋊C4—102no—
190C4⋊Dic3—24no—
191C4⋊Dic3—52no—
192Dic3⋊C4—102no—
193C4×Dic3—22no—
194C4×Dic3—101no—
195C4×Dic3C22⋊D514yescomplemented
196C23×C5—21no—
197C23×C5—21no—
198C23×C5—42no—
199C23×C5(C2×D3)⋊C412yes—
200C23×C5C2×D1211yescharacteristic
201C22×D5—61no—
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(C2×D3)⋊C412yes—
209C2×C4×C5C2×C4×D311yescharacteristic
210C2×C4×C5D3×D412yes—
211C2×C4×C5#23712yes—
212C2×C4×C5C2×#6711yescharacteristic
213C22⋊D5—124no—
214C22⋊D5—121no—
215C22⋊D5—121no—
216C2×Dic5—62no—
217C2×Dic5—61no—
218D20—62no—
219C4×D5—122no—
220Dic10—62no—
221#168—42no—
222C2×#41—151no—
223C23×C4D3×D511yescharacteristic
224C2×M16—52no—
225#123—301no—
226C22⋊Q8—152no—
227#121—152no—
228#120—301no—
229C4×D4—302no—
230#117—64no—
231#117—151no—
232C2×C4⋊C4—61no—
233C2×C22⋊C4—61no—
234C2×C42—32no—
235#104—304no—
236C22⋊C8—102no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5—42no—
240C2×C3×C5#38611yescharacteristic
241C2×C3×C5#42112yes—
242D15—81no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—42no—
246C23×C3#68512yes—
247C23×C3C2×C22⋊D511yescharacteristic
248C22×D3—101no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
253C2×C3×C4#68512yes—
254C2×C3×C4C2×C4×D511yescharacteristic
255C2×C3×C4C2×D2011yescharacteristic
256C2×C3×C4#70912yes—
257C2×C3×C4C2×C22⋊D512yes—
258#67—204no—
259#67—201no—
260#67—201no—
261C2×Dic3—24no—
262C2×Dic3—44no—
263C2×Dic3—102no—
264C2×Dic3—101no—
265D12—102no—
266C4×D3—202no—
267Dic6—102no—
268C3×C8—202no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—22no—
272C22×C5—22no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5#88211yescharacteristic
276C22×C5#88611yescharacteristic
277C22×C5C2×(C2×D3)⋊C411yescharacteristic
278C2×D5—122no—
279C2×D5—121no—
280C4×C5—22no—
281C4×C5—124no—
282C4×C5#67⋊C412yes—
283C4×C5#93912yes—
284Dic5—122no—
285Dic5—121no—
286C24#120311yescharacteristic
287#41—302no—
288#41—302no—
289C2×Q8—151no—
290C2×D4—151no—
291C2×D4—302no—
292C2×D4—301no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—62no—
296C22×C4—301no—
297C22×C4#120012yes—
298C22×C4#120212yes—
299C22×C4#120311yescharacteristic
300C22×C4C2×D3×D511yescharacteristic
301M16—102no—
302M16—102no—
303C2×C8—102no—
304C4⋊C4—64no—
305C4⋊C4—152no—
306C4⋊C4—302no—
307C22⋊C4—64no—
308C22⋊C4—302no—
309C22⋊C4—301no—
310C22⋊C4—302no—
311C42—34no—
312C42—62no—
313C42—301no—
314C3×C5#189711yescharacteristic, complemented, Hall
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3C2×#68511yescharacteristic
322C22×C3#407511yescharacteristic
323C22×C3#409911yescharacteristic
324C2×D3—202no—
325C2×D3—201no—
326C3×C4—22no—
327C3×C4C4×C22⋊D512yes—
328C3×C4#407612yes—
329Dic3—44no—
330Dic3—202no—
331Dic3—201no—
332C2×C5—21no—
333C2×C5—21no—
334C2×C5—42no—
335C2×C5#495811yescharacteristic
336C2×C5#513912yes—
337D5—241no—
338C23—21no—
339C23—21no—
340C23—42no—
341C23—301no—
342C23#666712yes—
343C23C2×#120311yescharacteristic
344Q8—302no—
345D4—302no—
346D4—604no—
347D4—601no—
348D4—601no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—64no—
354C2×C4—124no—
355C2×C4—302no—
356C2×C4—301no—
357C2×C4—602no—
358C2×C4#666712yes—
359C2×C4#677912yes—
360C2×C4C2×#120011yescharacteristic
361C2×C4C2×#120211yescharacteristic
362C2×C4D3×C22⋊D512yes—
363C8—202no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—42no—
367C2×C3#6529412yes—
368C2×C3#6550211yescharacteristic
369D3—401no—
370C5#6996611yescharacteristic, complemented, Sylow
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—602no—
378C22—601no—
379C22C2×#666711yescharacteristic
380C22#9154211yescharacteristic
381C22#9157011yescharacteristic
382C4—22no—
383C4—124no—
384C4—602no—
385C4—601no—
386C4#9155612yes—
387C4#9156912yes—
388C3#1060238411yescharacteristic, complemented, Sylow
389C2—21no—
390C2—21no—
391C2—42no—
392C2—1201no—
393C2#1174842812yes—
394C2#1174949811yescharacteristic
subgroupG/H
centerC2×C4C2×#1202
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756550C2
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
2. C2×C5×#926C2semidirect
3. C3×#65496C2semidirect
4. C2×#90980C2semidirect
5. #11745976C2semidirect
10. #91819C4semidirect
14. #91813C4semidirect
25. #65496D3semidirect
52. C4×C5×Dic3D4semidirect
57. C2×#926D5semidirect
195. C4×Dic3C22⋊D5semidirect
314. C3×C5#1897semidirect
370. C5#69966semidirect
388. C3#10602384semidirect

Maximal subgroups

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

subgroupindex
#117565502
C2×C5×#9262
C3×#654962
C2×#909802
#117459762
#106023843
#699665