Finite Group Databasebeta

← #14297535

Subgroups — #14297535

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4027C211yesmaximal, characteristic
2#11749506C212yesmaximal, complemented
3C2×#90995C212yesmaximal
4#11746347C211yesmaximal, characteristic, complemented
5C5×#4526C211yesmaximal, characteristic, complemented
6#10599752—31nomaximal, Hall
7C22×C3×C22⋊D5C2211yescharacteristic
8C23×C3×Dic5C2211yescharacteristic
9C22×C3×C4×D5C411yescharacteristic, complemented
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×#6719C2212yes—
12C2×C5×#217C2212yes—
13C2×C3×#685C411yescharacteristic, complemented
14C2×C3×#683C411yescharacteristic, complemented
15C2×C3×C4×Dic5C411yescharacteristic, complemented
16C3×#4027—22no—
17C3×#4027—22no—
18C2×#6668—22no—
19#90995—24no—
20#90994—22no—
21#71619—51nomaximal, Hall
22C2×#4027D311yescharacteristic
23C2×#3938—32no—
24#65231—32no—
25C5×#342—31no—
26#64746—31no—
27C24×C3×C5C2311yescharacteristic
28C23×C3×D5C2×C411yescharacteristic
29C22×C3×C4×C5C2×C411yescharacteristic
30C22×C3×C4×C5C2×C411yescharacteristic
31C22×Dic15—22no—
32C22×C5×Dic3—22no—
33C2×C3×C22⋊D5—22no—
34C2×C3×C22⋊D5—22no—
35C2×C3×C22⋊D5D412yes—
36C2×C3×C22⋊D5Q812yes—
37C22×C3×Dic5—42no—
38C22×C3×Dic5C2×C411yescharacteristic
39C22×C3×Dic5C2×C411yescharacteristic
40C22×C3×Dic5C2×C411yescharacteristic
41C22×C3×Dic5D412yes—
42C22×C3×Dic5D412yes—
43C2×C3×C4×D5—21no—
44C2×C3×C4×D5—21no—
45C2×C3×C4×D5—42no—
46C3×C5×C22⋊C4—22no—
47#6719—22no—
48#6719—22no—
49C5×#217—22no—
50C5×#217—22no—
51C3×#685—22no—
52C3×#683—22no—
53C3×C4×Dic5—21no—
54C3×C4×Dic5—21no—
55#6668—44no—
56C2×C3×C4×D4—51no—
57C2×#834—52no—
58#5212—52no—
59#4526—51no—
60#4526D511yescharacteristic, complemented
61C22×C22⋊D5C2×D311yescharacteristic
62C23×Dic5C2×D311yescharacteristic
63C22×C4×D5Dic311yescharacteristic, complemented
64C2×C5×C22⋊C4—32no—
65C2×C5×C22⋊C4C2×D311yescharacteristic
66C2×C22⋊Dic5—32no—
67C2×#685Dic311yescharacteristic, complemented
68C2×#683—62no—
69C2×#683Dic311yescharacteristic, complemented
70C2×C4×Dic5Dic311yescharacteristic, complemented
71#4027—22no—
72#4027—22no—
73#3963—62no—
74#3938—64no—
75#1799—151noSylow
76C23×C3×C5—41no—
77C23×C3×C5—41no—
78C23×C3×C5C22×C411yescharacteristic
79C23×C3×C5C2×D412yes—
80C23×C3×C5C2×D411yescharacteristic
81C23×C3×C5C2×Q811yescharacteristic
82C23×C3×C5#4112yes—
83C22×C3×D5—21no—
84C22×C3×D5—21no—
85C22×C3×D5—41no—
86C22×C3×D5—41no—
87C22×C3×D5C4⋊C412yescomplemented
88C2×C3×C4×C5—21no—
89C2×C3×C4×C5—21no—
90C2×C3×C4×C5—41no—
91C2×C3×C4×C5—41no—
92C2×Dic15—42no—
93C2×Dic15—42no—
94C2×Dic15—42no—
95C2×C5×Dic3—42no—
96C2×C5×Dic3—42no—
97C2×C5×Dic3—42no—
98C3×C22⋊D5—24no—
99C3×C22⋊D5—24no—
100C2×C3×Dic5—21no—
101C2×C3×Dic5—21no—
102C2×C3×Dic5—24no—
103C2×C3×Dic5—22no—
104C2×C3×Dic5—41no—
105C2×C3×Dic5—42no—
106C2×C3×Dic5C22⋊C411yescharacteristic
107C2×C3×Dic5C22⋊C412yes—
108C2×C3×Dic5C22⋊C411yescharacteristic
109C2×C3×Dic5C4⋊C412yescomplemented
110C3×C4×D5—42no—
111C3×C4×D5—42no—
112C22×C3×D4—51no—
113C23×C3×C4—51no—
114C23×C3×C4—51no—
115C3×C4×D4—102no—
116C3×C4×D4—102no—
117C2×C3×C4⋊C4—51no—
118C2×C3×C22⋊C4—51no—
119C2×C3×C22⋊C4C2×D511yescharacteristic
120C2×C3×C42—51no—
121C2×#217—52no—
122C2×#217C2×D512yes—
123C2×C4⋊Dic3—102no—
124#834—104no—
125C3⋊#95—102no—
126C24×C5C22×D311yescharacteristic
127C23×D5C2×Dic311yescharacteristic
128C22×C4×C5—62no—
129C22×C4×C5C2×Dic311yescharacteristic
130C22×C4×C5C2×Dic311yescharacteristic
131C2×C22⋊D5—22no—
132C2×C22⋊D5—22no—
133C2×C22⋊D5Dic612yes—
134C2×C22⋊D5D1212yes—
135C22×Dic5—42no—
136C22×Dic5—62no—
137C22×Dic5C2×Dic311yescharacteristic
138C22×Dic5C2×Dic311yescharacteristic
139C22×Dic5C2×Dic311yescharacteristic
140C22×Dic5#6712yes—
141C22×Dic5#6712yes—
142C2×C4×D5—21no—
143C2×C4×D5—21no—
144C2×C4×D5—42no—
145C5×C22⋊C4—22no—
146C5×C22⋊C4—62no—
147C5×C22⋊C4—62no—
148C22⋊Dic5—62no—
149C22⋊Dic5—62no—
150#685—22no—
151#683—22no—
152#683—124no—
153C4×Dic5—21no—
154C4×Dic5—21no—
155C2×C4×D4—51no—
156C2×#99—152no—
157#380—152no—
158#342—31no—
159#342—151no—
160C22×C3×C5—22no—
161C22×C3×C5—21no—
162C22×C3×C5—22no—
163C22×C3×C5—21no—
164C22×C3×C5—41no—
165C22×C3×C5—41no—
166C22×C3×C5—42no—
167C22×C3×C5C2×C22⋊C411yescharacteristic
168C22×C3×C5C2×C4⋊C411yescharacteristic
169C22×C3×C5#11711yescharacteristic
170C22×C3×C5#12112yes—
171C22×C3×C5C22⋊Q812yes—
172C2×C3×D5—22no—
173C2×C3×D5—42no—
174C2×C3×D5—41no—
175C2×C3×D5—41no—
176C2×C3×D5—42no—
177C3×C4×C5—41no—
178C3×C4×C5—41no—
179Dic15—82no—
180C3×Dic5—22no—
181C3×Dic5—21no—
182C3×Dic5—22no—
183C3×Dic5#9912yescomplemented
184C5×Dic3—82no—
185C24×C3—51no—
186C24×C3C22×D511yescharacteristic
187C2×C3×D4—52no—
188C2×C3×D4—52no—
189C2×C3×D4—102no—
190C2×C3×D4—102no—
191C22×C3×C4—51no—
192C22×C3×C4—51no—
193C22×C3×C4—52no—
194C22×C3×C4—51no—
195C22×C3×C4—52no—
196C22×C3×C4—101no—
197C22×C3×C4—101no—
198C22×C3×C4—202no—
199C22×C3×C4—202no—
200C22×C3×C4C4×D511yescharacteristic
201C22×C3×C4C4×D511yescharacteristic
202C22×Dic3—22no—
203C22×Dic3—102no—
204C3×C4⋊C4—102no—
205C3×C22⋊C4—22no—
206C3×C22⋊C4—102no—
207C3×C42—101no—
208C3×C42—101no—
209#217—22no—
210#217—22no—
211#217—102no—
212#217—102no—
213C4⋊Dic3—204no—
214C23×C5—41no—
215C23×C5—41no—
216C23×C5C2×Dic611yescharacteristic
217C23×C5C2×D1211yescharacteristic
218C23×C5#23512yes—
219C23×C5C22×Dic311yescharacteristic
220C23×C5C2×#6712yes—
221C22×D5—21no—
222C22×D5—21no—
223C22×D5—41no—
224C22×D5—41no—
225C22×D5C4⋊Dic312yescomplemented
226C2×C4×C5—21no—
227C2×C4×C5—21no—
228C2×C4×C5—41no—
229C2×C4×C5—41no—
230C2×C4×C5—122no—
231C2×C4×C5—122no—
232C2×C4×C5—122no—
233C22⋊D5—24no—
234C22⋊D5—24no—
235C2×Dic5—21no—
236C2×Dic5—21no—
237C2×Dic5—24no—
238C2×Dic5—22no—
239C2×Dic5—41no—
240C2×Dic5—42no—
241C2×Dic5—122no—
242C2×Dic5—122no—
243C2×Dic5—122no—
244C2×Dic5C4⋊Dic312yescomplemented
245C2×Dic5#21711yescharacteristic
246C2×Dic5#21712yes—
247C2×Dic5#21711yescharacteristic
248C4×D5—42no—
249C4×D5—42no—
250C22×D4—51no—
251C23×C4—51no—
252C23×C4—51no—
253C4×D4—102no—
254C4×D4—102no—
255C2×C4⋊C4—51no—
256C2×C4⋊C4—302no—
257C2×C22⋊C4—32no—
258C2×C22⋊C4—51no—
259C2×C22⋊C4—152no—
260C2×C22⋊C4D3×D511yescharacteristic
261C2×C42—51no—
262#99—304no—
263#95—302no—
264C2×C3×C5—22no—
265C2×C3×C5—21no—
266C2×C3×C5—21no—
267C2×C3×C5—22no—
268C2×C3×C5#38011yescharacteristic
269C2×C3×C5C2×#9911yescharacteristic
270C2×C3×C5#41011yescharacteristic
271C3×D5—42no—
272C23×C3—41no—
273C23×C3—41no—
274C23×C3—52no—
275C23×C3—101no—
276C23×C3—101no—
277C23×C3—201no—
278C23×C3—201no—
279C23×C3C2×C4×D511yescharacteristic
280C23×C3#70912yes—
281C23×C3D4×D511yescharacteristic
282C23×C3D4×D512yes—
283C23×C3Q8×D511yescharacteristic
284C3×D4—104no—
285C3×D4—104no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—51no—
291C2×C3×C4—51no—
292C2×C3×C4—52no—
293C2×C3×C4—52no—
294C2×C3×C4—104no—
295C2×C3×C4—102no—
296C2×C3×C4—101no—
297C2×C3×C4—101no—
298C2×C3×C4—202no—
299C2×C3×C4—202no—
300C2×C3×C4—201no—
301C2×C3×C4—202no—
302C2×Dic3—42no—
303C2×Dic3—42no—
304C2×Dic3—42no—
305C2×Dic3—202no—
306C2×Dic3—202no—
307C2×Dic3—202no—
308C22×C5—22no—
309C22×C5—21no—
310C22×C5—22no—
311C22×C5—21no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5—42no—
315C22×C5#92412yes—
316C22×C5C2×C4⋊Dic311yescharacteristic
317C22×C5#92611yescharacteristic
318C22×C5#93012yes—
319C22×C5C2×#21711yescharacteristic
320C2×D5—22no—
321C2×D5—42no—
322C2×D5—41no—
323C2×D5—41no—
324C2×D5—42no—
325C4×C5—41no—
326C4×C5—41no—
327C4×C5—242no—
328Dic5—22no—
329Dic5—21no—
330Dic5—22no—
331Dic5—242no—
332Dic5#83412yescomplemented
333C24—51no—
334C24C2×D3×D511yescharacteristic
335C2×D4—52no—
336C2×D4—52no—
337C2×D4—102no—
338C2×D4—102no—
339C22×C4—51no—
340C22×C4—51no—
341C22×C4—52no—
342C22×C4—51no—
343C22×C4—52no—
344C22×C4—62no—
345C22×C4—101no—
346C22×C4—101no—
347C22×C4—202no—
348C22×C4—202no—
349C22×C4—302no—
350C22×C4D5×Dic311yescharacteristic
351C22×C4D5×Dic311yescharacteristic
352C4⋊C4—102no—
353C4⋊C4—604no—
354C22⋊C4—22no—
355C22⋊C4—62no—
356C22⋊C4—62no—
357C22⋊C4—102no—
358C22⋊C4—302no—
359C22⋊C4—302no—
360C42—101no—
361C42—101no—
362C3×C5#179911yescharacteristic, complemented, Hall
363C22×C3—22no—
364C22×C3—21no—
365C22×C3—22no—
366C22×C3—21no—
367C22×C3—42no—
368C22×C3—41no—
369C22×C3—41no—
370C22×C3—102no—
371C22×C3—202no—
372C22×C3—202no—
373C22×C3—201no—
374C22×C3—201no—
375C22×C3#401811yescharacteristic
376C22×C3D5×C22⋊C411yescharacteristic
377C22×C3#403012yes—
378C22×C3D5×C4⋊C411yescharacteristic
379C22×C3#404212yes—
380C3×C4—41no—
381C3×C4—41no—
382C3×C4—52no—
383C3×C4—102no—
384C3×C4—101no—
385C3×C4—102no—
386Dic3—82no—
387Dic3—402no—
388C2×C5—22no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—22no—
392C2×C5#521211yescharacteristic
393C2×C5C2×#83411yescharacteristic
394C2×C5#524011yescharacteristic
395D5—42no—
396C23—41no—
397C23—41no—
398C23—52no—
399C23—101no—
400C23—101no—
401C23—201no—
402C23—201no—
403C23D5×Dic611yescharacteristic
404C23#677112yes—
405C23D5×D1211yescharacteristic
406C23C2×D5×Dic311yescharacteristic
407C23D5×#6712yes—
408D4—104no—
409D4—104no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—51no—
415C2×C4—52no—
416C2×C4—51no—
417C2×C4—52no—
418C2×C4—104no—
419C2×C4—102no—
420C2×C4—101no—
421C2×C4—101no—
422C2×C4—122no—
423C2×C4—122no—
424C2×C4—122no—
425C2×C4—202no—
426C2×C4—202no—
427C2×C4—202no—
428C2×C4—201no—
429C2×C4—602no—
430C2×C4—602no—
431C2×C4—602no—
432C2×C3—22no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—22no—
436C2×C3—202no—
437C2×C3#6495611yescharacteristic
438C2×C3#6502911yescharacteristic
439C2×C3D5×#9911yescharacteristic
440C5#7161911yescharacteristic, complemented, Sylow
441C22—21no—
442C22—22no—
443C22—21no—
444C22—22no—
445C22—41no—
446C22—42no—
447C22—41no—
448C22—102no—
449C22—202no—
450C22—202no—
451C22—201no—
452C22—201no—
453C22#9134912yes—
454C22#9135711yescharacteristic
455C22D5×C4⋊Dic311yescharacteristic
456C22#9144812yes—
457C22D5×#21711yescharacteristic
458C4—41no—
459C4—41no—
460C4—52no—
461C4—101no—
462C4—102no—
463C4—102no—
464C4—242no—
465C4—1202no—
466C3#1059975211yescharacteristic, complemented, Sylow
467C2—22no—
468C2—21no—
469C2—21no—
470C2—22no—
471C2—202no—
472C2#1174873811yescharacteristic
473C2D5×#83411yescharacteristic
474C2#1174917211yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×C22⋊D5C22
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1799
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11749506C2semidirect
4. #11746347C2semidirect
5. C5×#4526C2semidirect
9. C22×C3×C4×D5C4semidirect
13. C2×C3×#685C4semidirect
14. C2×C3×#683C4semidirect
15. C2×C3×C4×Dic5C4semidirect
60. #4526D5semidirect
63. C22×C4×D5Dic3semidirect
67. C2×#685Dic3semidirect
69. C2×#683Dic3semidirect
70. C2×C4×Dic5Dic3semidirect
87. C22×C3×D5C4⋊C4semidirect
109. C2×C3×Dic5C4⋊C4semidirect
183. C3×Dic5#99semidirect
225. C22×D5C4⋊Dic3semidirect
244. C2×Dic5C4⋊Dic3semidirect
332. Dic5#834semidirect
362. C3×C5#1799semidirect
440. C5#71619semidirect
466. C3#10599752semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40272
#117495062
C2×#909952
#117463472
C5×#45262
#105997523
#716195