Finite Group Databasebeta

← #14303011

Subgroups — #14303011

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5798C211yesmaximal, characteristic, complemented
2C3×#66138C211yesmaximal, characteristic
3C2×#91118C211yesmaximal, characteristic, complemented
4C2×#90995C212yesmaximal, complemented
5#11746020C212yesmaximal, complemented
6#10602449—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C3×C22⋊D5C2211yescharacteristic
9C2×#6719C2212yes—
10C2×C5×#217—21no—
11C2×C5×#217C2212yes—
12C5×D4×Dic3—24no—
13C5×#926—21no—
14C3×#4099—21no—
15C2×C3×C22⋊Dic5C2211yescharacteristic
16C3×#4085—22no—
17C3×#4083C412yescomplemented
18C3×#4081C412yescomplemented
19C3×#4075—21no—
20#91118—22no—
21#90995—24no—
22#71848—51nomaximal, Hall
23C5×#518—31no—
24#66138D311yescharacteristic
25C2×#3966—31no—
26C2×#3938—32no—
27#64747—32no—
28C24×C3×C5D411yescharacteristic
29C24×C3×C5C2311yescharacteristic
30C23×C3×D5C2×C411yescharacteristic, complemented
31C2×C3×C5×D4—22no—
32C2×C3×C5×D4—22no—
33C2×C3×C5×D4C2×C412yes—
34C2×C3×C5×D4D412yes—
35C22×C3×C4×C5D411yescharacteristic
36C22×Dic15—22no—
37C22×C5×Dic3—22no—
38C22×C5×Dic3—22no—
39C2×C3×C22⋊D5—21no—
40C2×C3×C22⋊D5—21no—
41C2×C3×C22⋊D5—22no—
42C2×C3×C22⋊D5—22no—
43C2×C3×C22⋊D5—22no—
44C22×C3×Dic5—21no—
45C22×C3×Dic5C2×C411yescharacteristic, complemented
46#6719—22no—
47#6719—22no—
48C5×#217—22no—
49C5×#217—22no—
50C5×#217D414yescomplemented
51C5×C4⋊Dic3—22no—
52C4×C5×Dic3—22no—
53C3×C22⋊Dic5—22no—
54C3×C22⋊Dic5—21no—
55C3×C22⋊Dic5C2×C412yescomplemented
56C3×#685—22no—
57C3×#683—22no—
58C3×#534—51no—
59#5798D511yescharacteristic, complemented
60C2×#834—51no—
61C2×#834—52no—
62#4527—52no—
63C22×C5×D4C2×D311yescharacteristic
64C22×C22⋊D5C2×D311yescharacteristic
65C4×C5×D4—64no—
66C5×#117—61no—
67C2×C5×C22⋊C4—32no—
68C2×C5×C22⋊C4—61no—
69#4099—21no—
70C2×C22⋊Dic5—32no—
71C2×C22⋊Dic5C2×D311yescharacteristic
72#4085—22no—
73#4083Dic312yescomplemented
74#4081Dic312yescomplemented
75#4075—21no—
76#3966—62no—
77#3938—64no—
78#1913—151noSylow
79C23×C3×C5—21no—
80C23×C3×C5—21no—
81C23×C3×C5—81no—
82C23×C3×C5—81no—
83C23×C3×C5C22⋊C412yes—
84C23×C3×C5C22×C411yescharacteristic
85C23×C3×C5C2×D411yescharacteristic
86C23×C3×C5C2×D411yescharacteristic
87C23×C3×C5C2×D412yes—
88C23×C3×C5#4112yes—
89C22×C3×D5—21no—
90C22×C3×D5—22no—
91C22×C3×D5—81no—
92C3×C5×D4—24no—
93C3×C5×D4—24no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5C22⋊C412yes—
97C2×Dic15—42no—
98C2×Dic15—82no—
99C2×C5×Dic3—24no—
100C2×C5×Dic3—82no—
101C2×C5×Dic3—82no—
102C3×C22⋊D5—41no—
103C3×C22⋊D5—42no—
104C3×C22⋊D5—41no—
105C3×C22⋊D5—82no—
106C2×C3×Dic5—21no—
107C2×C3×Dic5—22no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5—81no—
110C22×C3×D4—51no—
111C22×C3×D4C2×D511yescharacteristic
112C3×#123—52no—
113C3×#123—101no—
114C3×#121—102no—
115C3×#120—52no—
116C3×#120—101no—
117C2×C3×C22⋊C4—51no—
118C2×#217—21no—
119C2×#217—52no—
120C2×#217C2×D512yes—
121D4×Dic3—24no—
122#926—21no—
123#834—102no—
124#834—104no—
125C24×C5#6711yescharacteristic
126C24×C5C22×D311yescharacteristic
127C23×D5C2×Dic311yescharacteristic, complemented
128C2×C5×D4—22no—
129C2×C5×D4—22no—
130C2×C5×D4C2×Dic312yes—
131C2×C5×D4#6712yes—
132C22×C4×C5—62no—
133C22×C4×C5—62no—
134C22×C4×C5#6711yescharacteristic
135C2×C22⋊D5—22no—
136C2×C22⋊D5—22no—
137C2×C22⋊D5—21no—
138C2×C22⋊D5—21no—
139C2×C22⋊D5—22no—
140C22×Dic5—21no—
141C22×Dic5—62no—
142C22×Dic5C2×Dic311yescharacteristic, complemented
143C5×C4⋊C4—62no—
144C5×C22⋊C4—34no—
145C5×C22⋊C4—62no—
146C5×C22⋊C4—62no—
147C42×C5—62no—
148C22⋊Dic5—22no—
149C22⋊Dic5—21no—
150C22⋊Dic5—62no—
151C22⋊Dic5—62no—
152C22⋊Dic5C2×Dic312yescomplemented
153#685—22no—
154#683—22no—
155#534—51no—
156#518—31no—
157C2×#99—152no—
158C2×#99—151no—
159#342—152no—
160C22×C3×C5—22no—
161C22×C3×C5—41no—
162C22×C3×C5—42no—
163C22×C3×C5—42no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—42no—
167C22×C3×C5—42no—
168C22×C3×C5—81no—
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C22×C3×C5C4×D412yes—
171C22×C3×C5#12011yescharacteristic
172C22×C3×C5#12112yes—
173C22×C3×C5#12311yescharacteristic
174C2×C3×D5—42no—
175C2×C3×D5—41no—
176C2×C3×D5—82no—
177C3×C4×C5—22no—
178Dic15—82no—
179C3×Dic5—42no—
180C3×Dic5—41no—
181C5×Dic3—44no—
182C24×C3—51no—
183C24×C3C22⋊D511yescharacteristic
184C24×C3C22×D511yescharacteristic
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—101no—
188C2×C3×D4—102no—
189C2×C3×D4—102no—
190C2×C3×D4—101no—
191C2×C3×D4—102no—
192C2×C3×D4C4×D512yes—
193C2×C3×D4D2012yes—
194C22×C3×C4—51no—
195C22×C3×C4—101no—
196C22×C3×C4C22⋊D511yescharacteristic
197C22×Dic3—22no—
198C22×Dic3—22no—
199C22×Dic3—102no—
200C3×C4⋊C4—102no—
201C3×C22⋊C4—52no—
202C3×C22⋊C4—102no—
203C3×C22⋊C4—101no—
204C3×C22⋊C4—102no—
205#217—22no—
206#217—22no—
207#217—102no—
208#217—102no—
209#217C22⋊D514yescomplemented
210C4⋊Dic3—22no—
211C4×Dic3—22no—
212C23×C5—21no—
213C23×C5—21no—
214C23×C5—81no—
215C23×C5—81no—
216C23×C5#21712yes—
217C23×C5D3×D412yes—
218C23×C5#23712yes—
219C23×C5C22×Dic311yescharacteristic
220C23×C5C2×#6711yescharacteristic
221C23×C5C2×#6711yescharacteristic
222C22×D5—21no—
223C22×D5—22no—
224C22×D5—81no—
225C5×D4—24no—
226C5×D4—24no—
227C2×C4×C5—21no—
228C2×C4×C5—21no—
229C2×C4×C5—64no—
230C2×C4×C5—242no—
231C2×C4×C5—242no—
232C2×C4×C5#21712yes—
233C22⋊D5—41no—
234C22⋊D5—41no—
235C22⋊D5—42no—
236C22⋊D5—82no—
237C2×Dic5—22no—
238C2×Dic5—21no—
239C2×Dic5—22no—
240C2×Dic5—81no—
241C2×Dic5—122no—
242C2×Dic5—242no—
243C22×D4—51no—
244C22×D4D3×D511yescharacteristic
245#123—52no—
246#123—101no—
247#121—102no—
248#120—52no—
249#120—101no—
250C4×D4—64no—
251#117—61no—
252C2×C22⋊C4—32no—
253C2×C22⋊C4—51no—
254C2×C22⋊C4—61no—
255C2×C22⋊C4—152no—
256#99—304no—
257#99—302no—
258C2×C3×C5—21no—
259C2×C3×C5—21no—
260C2×C3×C5—22no—
261C2×C3×C5—22no—
262C2×C3×C5—21no—
263C2×C3×C5—42no—
264C2×C3×C5#38611yescharacteristic
265C3×D5—81no—
266C23×C3—21no—
267C23×C3—21no—
268C23×C3—81no—
269C23×C3—81no—
270C23×C3—101no—
271C23×C3—102no—
272C23×C3—401no—
273C23×C3#68512yes—
274C23×C3C2×C4×D511yescharacteristic
275C23×C3C2×D2011yescharacteristic
276C23×C3#70912yes—
277C23×C3C2×C22⋊D511yescharacteristic
278C23×C3C2×C22⋊D512yes—
279C3×D4—24no—
280C3×D4—24no—
281C3×D4—201no—
282C3×D4—201no—
283C3×D4—202no—
284C3×D4—402no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—102no—
288C2×C3×C4—101no—
289C2×C3×C4—102no—
290C2×C3×C4—401no—
291C2×C3×C4#68512yes—
292C2×Dic3—24no—
293C2×Dic3—82no—
294C2×Dic3—82no—
295C2×Dic3—202no—
296C2×Dic3—402no—
297C22×C5—22no—
298C22×C5—41no—
299C22×C5—42no—
300C22×C5—42no—
301C22×C5—41no—
302C22×C5—41no—
303C22×C5—42no—
304C22×C5—42no—
305C22×C5—81no—
306C22×C5D4×Dic312yes—
307C22×C5#93511yescharacteristic
308C22×C5#93711yescharacteristic
309C22×C5#93912yes—
310C22×C5C2×#21711yescharacteristic
311C2×D5—42no—
312C2×D5—41no—
313C2×D5—82no—
314C4×C5—22no—
315C4×C5—124no—
316Dic5—42no—
317Dic5—41no—
318Dic5—242no—
319C24—51no—
320C24#120111yescharacteristic
321C24C2×D3×D511yescharacteristic
322C2×D4—22no—
323C2×D4—22no—
324C2×D4—102no—
325C2×D4—101no—
326C2×D4—101no—
327C2×D4—102no—
328C2×D4—102no—
329C2×D4D5×Dic312yes—
330C2×D4#120212yes—
331C22×C4—51no—
332C22×C4—62no—
333C22×C4—62no—
334C22×C4—101no—
335C22×C4—302no—
336C22×C4#120111yescharacteristic
337C4⋊C4—62no—
338C4⋊C4—102no—
339C22⋊C4—34no—
340C22⋊C4—52no—
341C22⋊C4—62no—
342C22⋊C4—62no—
343C22⋊C4—102no—
344C22⋊C4—101no—
345C22⋊C4—102no—
346C22⋊C4—302no—
347C22⋊C4—302no—
348C42—62no—
349C3×C5#191311yescharacteristic, complemented, Hall
350C22×C3—22no—
351C22×C3—42no—
352C22×C3—42no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3—41no—
356C22×C3—42no—
357C22×C3—42no—
358C22×C3—81no—
359C22×C3—202no—
360C22×C3—201no—
361C22×C3—402no—
362C22×C3C2×#68511yescharacteristic
363C22×C3C4×C22⋊D512yes—
364C22×C3#407511yescharacteristic
365C22×C3#407612yes—
366C22×C3#409911yescharacteristic
367C3×C4—22no—
368C3×C4—202no—
369C3×C4—201no—
370Dic3—44no—
371Dic3—402no—
372C2×C5—21no—
373C2×C5—22no—
374C2×C5—21no—
375C2×C5—22no—
376C2×C5—21no—
377C2×C5—42no—
378C2×C5#522011yescharacteristic
379D5—81no—
380C23—21no—
381C23—21no—
382C23—81no—
383C23—81no—
384C23—101no—
385C23—102no—
386C23—401no—
387C23#666512yes—
388C23C2×D5×Dic311yescharacteristic
389C23#677912yes—
390C23C2×#120111yescharacteristic
391C23C2×#120211yescharacteristic
392C23D3×C22⋊D512yes—
393D4—24no—
394D4—24no—
395D4—201no—
396D4—201no—
397D4—202no—
398D4—402no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—64no—
402C2×C4—102no—
403C2×C4—101no—
404C2×C4—102no—
405C2×C4—242no—
406C2×C4—242no—
407C2×C4—401no—
408C2×C4—602no—
409C2×C4—1202no—
410C2×C4#666512yes—
411C2×C3—21no—
412C2×C3—22no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—22no—
416C2×C3—42no—
417C2×C3—401no—
418C2×C3#6550211yescharacteristic
419C5#7184811yescharacteristic, complemented, Sylow
420C22—22no—
421C22—42no—
422C22—41no—
423C22—42no—
424C22—41no—
425C22—41no—
426C22—42no—
427C22—42no—
428C22—81no—
429C22—202no—
430C22—201no—
431C22—402no—
432C22C2×#666511yescharacteristic
433C22#9153611yescharacteristic
434C22Dic3×C22⋊D512yes—
435C22#9156811yescharacteristic
436C22#9156912yes—
437C4—22no—
438C4—124no—
439C4—202no—
440C4—201no—
441C4—1202no—
442C3#1060244911yescharacteristic, complemented, Sylow
443C2—21no—
444C2—21no—
445C2—22no—
446C2—21no—
447C2—22no—
448C2—42no—
449C2—401no—
450C2#1174949511yescharacteristic
subgroupG/H
centerC2#11749495
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC2×C3×C5#386
prime radicalC3×#66138C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C5×#5798C2semidirect
3. C2×#91118C2semidirect
4. C2×#90995C2semidirect
5. #11746020C2semidirect
17. C3×#4083C4semidirect
18. C3×#4081C4semidirect
30. C23×C3×D5C2×C4semidirect
45. C22×C3×Dic5C2×C4semidirect
50. C5×#217D4semidirect
55. C3×C22⋊Dic5C2×C4semidirect
59. #5798D5semidirect
73. #4083Dic3semidirect
74. #4081Dic3semidirect
127. C23×D5C2×Dic3semidirect
142. C22×Dic5C2×Dic3semidirect
152. C22⋊Dic5C2×Dic3semidirect
209. #217C22⋊D5semidirect
349. C3×C5#1913semidirect
419. C5#71848semidirect
442. C3#10602449semidirect

Maximal subgroups

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

subgroupindex
C5×#57982
C3×#661382
C2×#911182
C2×#909952
#117460202
#106024493
#718485