Finite Group Databasebeta

← #14301401

Subgroups — #14301401

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756591C211yesmaximal, characteristic
2C3×#66153C211yesmaximal, characteristic, complemented
3C5×#5240C211yesmaximal, characteristic, complemented
4#11748428C212yesmaximal, complemented
5#11745975C212yesmaximal, complemented
6#10600838—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C2×#6817C2211yescharacteristic
9#91836C411yescharacteristic, complemented
10#91833C411yescharacteristic, complemented
11#91829C411yescharacteristic, complemented
12#91828—22no—
13#91825C411yescharacteristic, complemented
14C4×#1220—22no—
15C2×C4×Dic15C2211yescharacteristic
16C5×#926C2212yes—
17C3×#4094—24no—
18C2×C3×#681—22no—
19C2×C3×#681C2212yes—
20C5×#834—22no—
21#90980—24no—
22#72021—51nomaximal, Hall
23#66166—31no—
24#66153D311yescharacteristic, complemented
25C5×#410—31no—
26#65294—32no—
27#64752—32no—
28C3×C5×#41—22no—
29C3×C5×#41—22no—
30C2×C3×C5×Q8C2×C411yescharacteristic
31C2×C3×C5×D4C2×C411yescharacteristic
32C2×C3×C5×D4D412yes—
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220—22no—
36C2×#1220—21no—
37C22×Dic15—21no—
38#6817—22no—
39#6817—22no—
40C2×D60C2×C411yescharacteristic
41C2×C4×D15—21no—
42C2×Dic30C2×C411yescharacteristic
43#6719—22no—
44#6714—22no—
45#6712—22no—
46C4×Dic15—21no—
47C4×Dic15C2×C411yescharacteristic
48C4×Dic15C2×C411yescharacteristic
49C5×#217—22no—
50C5×C4⋊Dic3—22no—
51C4×C5×Dic3—22no—
52C3×#681—24no—
53C3×#681—22no—
54C3×#681D414yescomplemented
55C2×C3×#168—24no—
56C2×C3×#168—22no—
57C3×#568—51no—
58#5832—51no—
59#5240D511yescharacteristic, complemented
60#5139—52no—
61#4555—52no—
62C2×C5×#41C2×D311yescharacteristic
63C2×#709—31no—
64C5×#117—32no—
65#4094—24no—
66#4093—31no—
67#4090—31no—
68#4086—31no—
69#4085—62no—
70#4082—31no—
71C4×C22⋊D5—62no—
72C2×C4×Dic5—31no—
73C2×#681—22no—
74C2×#681C2×D312yes—
75C5×#99—62no—
76#3937—64no—
77#1884—151noSylow
78C23×C3×C5C22⋊C412yes—
79C23×C3×C5C2×D411yescharacteristic
80C22×D15—21no—
81C3×C5×Q8—22no—
82C3×C5×D4—24no—
83C3×C5×D4—22no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22⋊C412yes—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D412yes—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5#4112yes—
91#1220—44no—
92#1220—42no—
93C2×Dic15—21no—
94C2×Dic15—21no—
95C2×Dic15—21no—
96C2×Dic15—42no—
97D60—22no—
98C4×D15—41no—
99C4×D15—41no—
100Dic30—22no—
101C2×C5×Dic3—42no—
102C3×#168—24no—
103C2×C3×#41C2×D511yescharacteristic
104C2×#235—51no—
105C3×#131—104no—
106C2×C3×M16—52no—
107C2×C3×M16—102no—
108#947—51no—
109#944—51no—
110#940—51no—
111#939—102no—
112#936—51no—
113C4×#67—102no—
114#926C2×D512yes—
115C2×C4×Dic3—51no—
116#834—22no—
117#825—104no—
118C5×#41—22no—
119C5×#41—22no—
120C2×C5×Q8C4×D311yescharacteristic
121C2×C5×D4C4×D311yescharacteristic
122C2×C5×D4D1212yes—
123C22×C4×C5#6712yes—
124C22×C4×C5C22×D311yescharacteristic
125C2×C22⋊D5—62no—
126C2×C22⋊D5—61no—
127C22×Dic5—61no—
128#709—62no—
129#709—62no—
130C2×D20—31no—
131C2×C4×D5—61no—
132C2×Dic10—31no—
133C5×C4⋊C4—62no—
134C5×C22⋊C4—62no—
135C42×C5—62no—
136C22⋊Dic5—62no—
137#685—62no—
138#683—62no—
139C4×Dic5—31no—
140C4×Dic5—31no—
141C4×Dic5—61no—
142#681—24no—
143#681—22no—
144#681#6714yescomplemented
145C2×#168—24no—
146C2×#168—22no—
147#568—51no—
148#532—151no—
149#421—152no—
150#410—31no—
151#339—152no—
152C22×C3×C5—22no—
153C22×C3×C5—41no—
154C22×C3×C5—42no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C22×C3×C5#12112yes—
157C2×D15—42no—
158C2×D15—41no—
159C3×C4×C5—22no—
160C3×C4×C5C4×D412yes—
161C3×C4×C5#12011yescharacteristic
162C3×C4×C5#12311yescharacteristic
163Dic15—22no—
164Dic15—41no—
165Dic15—41no—
166C5×Dic3—82no—
167C3×#41—22no—
168C3×#41—22no—
169C2×C3×Q8C4×D511yescharacteristic
170C2×C3×D4C4×D511yescharacteristic
171C2×C3×D4C22⋊D512yes—
172C22×C3×C4D2012yes—
173C22×C3×C4C22×D511yescharacteristic
174C2×#67—102no—
175C2×#67—101no—
176C22×Dic3—101no—
177#235—102no—
178#235—102no—
179C2×D12—51no—
180C2×C4×D3—101no—
181C2×Dic6—51no—
182C3×M16—54no—
183C3×M16—104no—
184C3×M16—102no—
185C2×C3×C8—104no—
186C2×C3×C8—102no—
187#217—22no—
188#217—102no—
189(C2×D3)⋊C4—102no—
190C4⋊Dic3—22no—
191Dic3⋊C4—102no—
192C4×Dic3—22no—
193C4×Dic3—51no—
194C4×Dic3—51no—
195C4×Dic3—101no—
196C23×C5(C2×D3)⋊C412yes—
197C23×C5C2×D1211yescharacteristic
198C22×D5—61no—
199C5×Q8—22no—
200C5×D4—24no—
201C5×D4—22no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—122no—
205C2×C4×C5(C2×D3)⋊C412yes—
206C2×C4×C5C2×C4×D311yescharacteristic
207C2×C4×C5#23512yes—
208C2×C4×C5C2×#6711yescharacteristic
209C2×C4×C5C2×#6712yes—
210C22⋊D5—124no—
211C22⋊D5—122no—
212C2×Dic5—61no—
213C2×Dic5—61no—
214C2×Dic5—61no—
215C2×Dic5—122no—
216D20—62no—
217C4×D5—121no—
218C4×D5—121no—
219Dic10—62no—
220#168—24no—
221C2×#41—151no—
222C2×#41D3×D511yescharacteristic
223#131—104no—
224C2×M16—52no—
225C2×M16—102no—
226C4⋊Q8—151no—
227#127—151no—
228#124—151no—
229#124—151no—
230#121—302no—
231C4×D4—302no—
232#117—32no—
233C2×C42—151no—
234#104—304no—
235#99—62no—
236C2×C3×C5—22no—
237C2×C3×C5—21no—
238C2×C3×C5—42no—
239C2×C3×C5#38611yescharacteristic
240D15—81no—
241C23×C3#68512yes—
242C23×C3C2×C22⋊D511yescharacteristic
243C22×D3—101no—
244C3×Q8—22no—
245C3×D4—24no—
246C3×D4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—22no—
249C2×C3×C4#68512yes—
250C2×C3×C4C2×C4×D511yescharacteristic
251C2×C3×C4C2×D2011yescharacteristic
252C2×C3×C4D4×D512yes—
253C2×C3×C4#71112yes—
254#67—204no—
255#67—202no—
256C2×Dic3—42no—
257C2×Dic3—101no—
258C2×Dic3—101no—
259C2×Dic3—101no—
260C2×Dic3—202no—
261D12—102no—
262C4×D3—201no—
263C4×D3—201no—
264Dic6—102no—
265C3×C8—104no—
266C22×C5—22no—
267C22×C5—41no—
268C22×C5—42no—
269C22×C5C2×(C2×D3)⋊C411yescharacteristic
270C22×C5#93012yes—
271C2×D5—122no—
272C2×D5—121no—
273C4×C5—22no—
274C4×C5—242no—
275C4×C5C4×#6712yes—
276C4×C5#92911yescharacteristic
277C4×C5#95311yescharacteristic
278Dic5—62no—
279Dic5—121no—
280Dic5—121no—
281#41—22no—
282#41—22no—
283#41—302no—
284#41—302no—
285C2×Q8—151no—
286C2×Q8#120011yescharacteristic
287C2×D4—151no—
288C2×D4—302no—
289C2×D4—301no—
290C2×D4#120011yescharacteristic
291C2×D4#120312yes—
292C22×C4—301no—
293C22×C4—301no—
294C22×C4#120212yes—
295C22×C4C2×D3×D511yescharacteristic
296M16—54no—
297M16—104no—
298M16—102no—
299C2×C8—104no—
300C2×C8—102no—
301C4⋊C4—62no—
302C4⋊C4—302no—
303C22⋊C4—62no—
304C22⋊C4—302no—
305C22⋊C4—302no—
306C42—62no—
307C42—151no—
308C42—151no—
309C42—301no—
310C3×C5#188411yescharacteristic, complemented, Hall
311C22×C3—22no—
312C22×C3—41no—
313C22×C3—42no—
314C22×C3C2×#68511yescharacteristic
315C22×C3#408512yes—
316C2×D3—202no—
317C2×D3—201no—
318C3×C4—22no—
319C3×C4#402712yes—
320C3×C4#402811yescharacteristic
321C3×C4#403211yescharacteristic
322Dic3—82no—
323Dic3—102no—
324Dic3—201no—
325Dic3—201no—
326C2×C5—21no—
327C2×C5—22no—
328C2×C5—42no—
329C2×C5#521311yescharacteristic
330D5—241no—
331C23—301no—
332C23#666712yes—
333C23C2×#120311yescharacteristic
334Q8—22no—
335Q8—302no—
336D4—24no—
337D4—22no—
338D4—302no—
339D4—604no—
340D4—602no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—122no—
344C2×C4—301no—
345C2×C4—301no—
346C2×C4—301no—
347C2×C4—602no—
348C2×C4—601no—
349C2×C4—601no—
350C2×C4#666712yes—
351C2×C4#678212yes—
352C2×C4C2×#120011yescharacteristic
353C2×C4C2×#120211yescharacteristic
354C2×C4D5×#6712yes—
355C8—104no—
356C2×C3—22no—
357C2×C3—21no—
358C2×C3—42no—
359C2×C3#6524711yescharacteristic
360D3—401no—
361C5#7202111yescharacteristic, complemented, Sylow
362C22—22no—
363C22—41no—
364C22—42no—
365C22—602no—
366C22—601no—
367C22C2×#666711yescharacteristic
368C22#9156612yes—
369C4—22no—
370C4—242no—
371C4—302no—
372C4—601no—
373C4—601no—
374C4#9154611yescharacteristic
375C4#9155212yes—
376C4#9156411yescharacteristic
377C3#1060083811yescharacteristic, complemented, Sylow
378C2—22no—
379C2—21no—
380C2—42no—
381C2—1201no—
382C2#1174949411yescharacteristic
subgroupG/H
centerC4#91564
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#386
prime radical#11756591C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C3×#66153C2semidirect
3. C5×#5240C2semidirect
4. #11748428C2semidirect
5. #11745975C2semidirect
9. #91836C4semidirect
10. #91833C4semidirect
11. #91829C4semidirect
13. #91825C4semidirect
24. #66153D3semidirect
54. C3×#681D4semidirect
59. #5240D5semidirect
144. #681#67semidirect
310. C3×C5#1884semidirect
361. C5#72021semidirect
377. C3#10600838semidirect

Maximal subgroups

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

subgroupindex
#117565912
C3×#661532
C5×#52402
#117484282
#117459752
#106008383
#720215