Finite Group Databasebeta

← #14305954

Subgroups — #14305954

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91829C211yesmaximal, characteristic
2C2×C3×C5×#102C211yesmaximal, characteristic, complemented
3C2×#91116C211yesmaximal, characteristic, complemented
4C2×#91105C211yesmaximal, characteristic, complemented
5C2×#91099C211yesmaximal, characteristic, complemented
6#11751078C211yesmaximal, characteristic, complemented
7C2×#91093C211yesmaximal, characteristic, complemented
8#10600953—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220—22no—
11C22×D60C2211yescharacteristic
12C22×C3×C5×C8C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14#91829—22no—
15#91829C414yescomplemented
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15C2211yescharacteristic
18C22×C3⋊#168C2211yescharacteristic
19C3×C5×#102—22no—
20#91116—22no—
21#91115—22no—
22#91105—22no—
23#91099—22no—
24#91093—22no—
25#70160—51nomaximal, Hall
26C2×#4086—31no—
27C2×C5×#102D311yescharacteristic, complemented
28C2×#3964—31no—
29C2×#3953—31no—
30C2×#3947—31no—
31#65266—31no—
32C2×#3941—31no—
33C24×C3×C5—21no—
34C23×D15—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C412yes—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×#1220—28no—
44C2×#1220—44no—
45C2×#1220—44no—
46C22×Dic15—21no—
47C22×Dic15D412yes—
48C2×D60—21no—
49C2×D60—21no—
50C2×D60—21no—
51C2×D60—21no—
52C2×D60—21no—
53C2×D60C2×C412yes—
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8D412yescomplemented
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15—21no—
61C4×Dic15C2×C412yes—
62C4×Dic15D412yes—
63C2×C3⋊#168—21no—
64C2×C3⋊#168—21no—
65C2×C3⋊#168D412yescomplemented
66C2×#940—51no—
67C2×C3×#102D511yescharacteristic, complemented
68C2×#832—51no—
69C2×#821—51no—
70C2×#815—51no—
71#4977—51no—
72C2×#809—51no—
73C22×C5×D4C2×D311yescharacteristic
74C22×C22⋊D5—62no—
75C22×D20—31no—
76C22×C5×C8C2×D311yescharacteristic
77C2×C5×C4⋊C4C2×D311yescharacteristic
78#4086—34no—
79#4086—62no—
80C2×C4⋊Dic5—31no—
81C2×C4×Dic5—31no—
82C22×#168—31no—
83C5×#102—22no—
84#3964—62no—
85#3963—62no—
86#3953—62no—
87#3947—62no—
88#3941—62no—
89#1961—151noSylow
90C23×C3×C5—22no—
91C23×C3×C5—41no—
92C23×C3×C5—41no—
93C23×C3×C5—42no—
94C23×C3×C5—42no—
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—22no—
97C22×D15—41no—
98C22×D15—41no—
99C22×D15—42no—
100C22×D15—42no—
101C3×C5×D4—22no—
102C3×C5×D4—22no—
103C3×C5×D4—41no—
104C3×C5×D4—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—42no—
107C2×C3×C4×C5C22×C411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5#4111yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113#1220—416no—
114C2×Dic15—22no—
115C2×Dic15—22no—
116C2×Dic15—41no—
117C2×Dic15—42no—
118C2×Dic15C22⋊C414yes—
119D60—22no—
120D60—22no—
121D60—41no—
122D60—41no—
123C3×C5×C8—22no—
124C3⋊#168—22no—
125C22×C3×D4C2×D511yescharacteristic
126C22×#67—102no—
127C22×D12—51no—
128C22×C3×C8C2×D511yescharacteristic
129C2×C3×C4⋊C4C2×D511yescharacteristic
130#940—54no—
131#940—102no—
132C2×C4⋊Dic3—51no—
133C2×C4×Dic3—51no—
134C22×C3⋊C8—51no—
135C3×#102—22no—
136#832—102no—
137C3⋊#95—102no—
138#821—102no—
139#815—102no—
140#809—102no—
141C24×C5—21no—
142C23×D5—61no—
143C2×C5×D4—21no—
144C2×C5×D4—21no—
145C2×C5×D4—21no—
146C2×C5×D4—21no—
147C2×C5×D4—21no—
148C2×C5×D4C4×D312yes—
149C22×C4×C5—21no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—68no—
152C2×C22⋊D5—124no—
153C2×C22⋊D5—124no—
154C22×Dic5—32no—
155C22×Dic5—61no—
156C2×D20—32no—
157C2×D20—61no—
158C2×D20—61no—
159C2×D20—61no—
160C2×D20—61no—
161C2×D20—61no—
162C2×C5×C8—21no—
163C2×C5×C8—21no—
164C2×C5×C8#6712yescomplemented
165C5×C4⋊C4—21no—
166C5×C4⋊C4—21no—
167C4⋊Dic5—61no—
168C4⋊Dic5—61no—
169C4×Dic5—32no—
170C4×Dic5—32no—
171C2×#168—32no—
172C2×#168—61no—
173C2×#168—61no—
174C2×#127—151no—
175C2×#102—151no—
176C2×#102—151no—
177C2×#102—151no—
178C2×#102D1511yescharacteristic, complemented
179C2×#97—151no—
180#382—151no—
181C22×C3×C5—42no—
182C22×C3×C5—44no—
183C22×C3×C5—82no—
184C22×C3×C5—81no—
185C22×C3×C5—81no—
186C22×C3×C5C2×C22⋊C411yescharacteristic
187C22×C3×C5#12411yescharacteristic
188C22×C3×C5#12711yescharacteristic
189C22×C3×C5AGL(1,ℤ/8)12yes—
190C22×C3×C5AGL(1,ℤ/8)12yes—
191C2×D15—42no—
192C2×D15—44no—
193C2×D15—82no—
194C2×D15—81no—
195C2×D15—81no—
196C3×C4×C5—81no—
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5C4×D411yescharacteristic
199C3×C4×C5#12111yescharacteristic
200C3×C4×C5#12111yescharacteristic
201Dic15—24no—
202Dic15—81no—
203C24×C3—21no—
204C23×D3—101no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4C4×D512yes—
211C22×C3×C4—21no—
212C22×C3×C4C22×D511yescharacteristic
213C2×#67—108no—
214C2×#67—204no—
215C2×#67—204no—
216C22×Dic3—52no—
217C22×Dic3—101no—
218C2×D12—52no—
219C2×D12—101no—
220C2×D12—101no—
221C2×D12—101no—
222C2×D12—101no—
223C2×D12—101no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8C22⋊D512yescomplemented
227C3×C4⋊C4—21no—
228C3×C4⋊C4—21no—
229C4⋊Dic3—101no—
230C4⋊Dic3—101no—
231C4×Dic3—52no—
232C4×Dic3—52no—
233C2×C3⋊C8—52no—
234C2×C3⋊C8—101no—
235C2×C3⋊C8—101no—
236C23×C5—22no—
237C23×C5—41no—
238C23×C5—42no—
239C23×C5—42no—
240C23×C5—41no—
241C23×C5D3×D411yescharacteristic
242C22×D5—62no—
243C22×D5—121no—
244C22×D5—122no—
245C22×D5—122no—
246C22×D5—121no—
247C5×D4—22no—
248C5×D4—22no—
249C5×D4—41no—
250C5×D4—41no—
251C2×C4×C5—42no—
252C2×C4×C5—41no—
253C2×C4×C5C2×C4×D311yescharacteristic
254C2×C4×C5#23511yescharacteristic
255C2×C4×C5D3×D411yescharacteristic
256C2×C4×C5D3×D411yescharacteristic
257C2×C4×C5#23711yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C22⋊D5—1216no—
260C2×Dic5—34no—
261C2×Dic5—62no—
262C2×Dic5—62no—
263C2×Dic5—122no—
264C2×Dic5—121no—
265D20—62no—
266D20—62no—
267D20—121no—
268D20—121no—
269C5×C8—22no—
270#168—62no—
271C22×D4—151no—
272C22×D4—302no—
273C22×D4C2×D1511yescharacteristic
274C22×C8—151no—
275C22×C8C2×D1511yescharacteristic
276#127—154no—
277#127—302no—
278C2×C4⋊C4—151no—
279C2×C4⋊C4C2×D1511yescharacteristic
280C2×C42—151no—
281#102—22no—
282#102—302no—
283#102—302no—
284#102—302no—
285#97—302no—
286#95—302no—
287C2×C3×C5—82no—
288C2×C3×C5#39011yescharacteristic
289C2×C3×C5#41812yes—
290C2×C3×C5#49012yes—
291C2×C3×C5#49611yescharacteristic
292C2×C3×C5#49611yescharacteristic
293D15—82no—
294C23×C3—22no—
295C23×C3—41no—
296C23×C3—42no—
297C23×C3—42no—
298C23×C3—41no—
299C23×C3D4×D511yescharacteristic
300C22×D3—102no—
301C22×D3—201no—
302C22×D3—202no—
303C22×D3—202no—
304C22×D3—201no—
305C3×D4—22no—
306C3×D4—22no—
307C3×D4—41no—
308C3×D4—41no—
309C2×C3×C4—42no—
310C2×C3×C4—41no—
311C2×C3×C4C2×C4×D511yescharacteristic
312C2×C3×C4#70911yescharacteristic
313C2×C3×C4D4×D511yescharacteristic
314C2×C3×C4D4×D511yescharacteristic
315C2×C3×C4#71111yescharacteristic
316C2×C3×C4C2×C22⋊D511yescharacteristic
317#67—2016no—
318C2×Dic3—54no—
319C2×Dic3—102no—
320C2×Dic3—102no—
321C2×Dic3—202no—
322C2×Dic3—201no—
323D12—102no—
324D12—102no—
325D12—201no—
326D12—201no—
327C3×C8—22no—
328C3⋊C8—102no—
329C22×C5—42no—
330C22×C5—44no—
331C22×C5—81no—
332C22×C5—81no—
333C22×C5—82no—
334C22×C5D3×C22⋊C411yescharacteristic
335C22×C5#88511yescharacteristic
336C22×C5#91112yes—
337C22×C5#91412yes—
338C22×C5#94011yescharacteristic
339C2×D5—122no—
340C2×D5—124no—
341C2×D5—241no—
342C2×D5—241no—
343C2×D5—242no—
344C4×C5—81no—
345C4×C5#67⋊C411yescharacteristic
346C4×C5#88411yescharacteristic
347C4×C5C4×#6711yescharacteristic
348C4×C5#93911yescharacteristic
349Dic5—64no—
350Dic5—241no—
351C24—21no—
352C24—301no—
353C2×D4—21no—
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—21no—
357C2×D4—21no—
358C2×D4—152no—
359C2×D4—308no—
360C2×D4—301no—
361C2×D4—301no—
362C2×D4—301no—
363C2×D4—301no—
364C2×D4—301no—
365C2×D4—604no—
366C2×D4—604no—
367C2×D4C4×D1512yes—
368C22×C4—21no—
369C22×C4—152no—
370C22×C4—301no—
371C22×C4C22×D1511yescharacteristic
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—152no—
375C2×C8—301no—
376C2×C8—301no—
377C2×C8#122012yescomplemented
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—301no—
381C4⋊C4—301no—
382C42—152no—
383C42—152no—
384C3×C5#196111yescharacteristic, complemented, Hall
385C22×C3—44no—
386C22×C3—42no—
387C22×C3—82no—
388C22×C3—81no—
389C22×C3—81no—
390C22×C3D5×C22⋊C411yescharacteristic
391C22×C3#403111yescharacteristic
392C22×C3#405712yes—
393C22×C3#406012yes—
394C22×C3#408611yescharacteristic
395C2×D3—204no—
396C2×D3—202no—
397C2×D3—402no—
398C2×D3—401no—
399C2×D3—401no—
400C3×C4—81no—
401C3×C4#402711yescharacteristic
402C3×C4#403011yescharacteristic
403C3×C4C4×C22⋊D511yescharacteristic
404C3×C4#408511yescharacteristic
405Dic3—104no—
406Dic3—401no—
407C2×C5—82no—
408C2×C5#476412yes—
409C2×C5#477012yes—
410C2×C5#495711yescharacteristic
411C2×C5#515411yescharacteristic
412C2×C5#517611yescharacteristic
413D5—242no—
414C23—22no—
415C23—41no—
416C23—42no—
417C23—42no—
418C23—41no—
419C23—302no—
420C23—601no—
421C23—602no—
422C23—602no—
423C23—601no—
424C23D4×D1511yescharacteristic
425D4—22no—
426D4—22no—
427D4—41no—
428D4—41no—
429D4—302no—
430D4—302no—
431D4—6016no—
432D4—601no—
433D4—601no—
434C2×C4—42no—
435C2×C4—41no—
436C2×C4—154no—
437C2×C4—302no—
438C2×C4—302no—
439C2×C4—602no—
440C2×C4—601no—
441C2×C4C2×C4×D1511yescharacteristic
442C2×C4#681711yescharacteristic
443C2×C4D4×D1511yescharacteristic
444C2×C4D4×D1511yescharacteristic
445C2×C4#681911yescharacteristic
446C2×C4C2×#122011yescharacteristic
447C8—22no—
448C8—302no—
449C2×C3—82no—
450C2×C3#6505312yes—
451C2×C3#6505912yes—
452C2×C3#6524611yescharacteristic
453C2×C3#6544311yescharacteristic
454C2×C3#6546511yescharacteristic
455D3—402no—
456C5#7016011yescharacteristic, complemented, Sylow
457C22—42no—
458C22—44no—
459C22—81no—
460C22—81no—
461C22—82no—
462C22—602no—
463C22—604no—
464C22—1201no—
465C22—1201no—
466C22—1202no—
467C22C22⋊C4×D1511yescharacteristic
468C22#9177411yescharacteristic
469C22#9180012yes—
470C22#9180312yes—
471C22#9182911yescharacteristic
472C4—81no—
473C4—304no—
474C4—1201no—
475C4#9177011yescharacteristic
476C4#9177311yescharacteristic
477C4C4×#122011yescharacteristic
478C4#9182811yescharacteristic
479C3#1060095311yescharacteristic, complemented, Sylow
480C2—82no—
481C2—1202no—
482C2#1175086512yes—
483C2#1175087112yes—
484C2#1175105811yescharacteristic
485C2#1175125511yescharacteristic
486C2#1175127711yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#102C2
socleC23×C3×C5C2×D4
prime radicalC2×#91829C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#102D15
hypocenterC3×C5#1961
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#102C2semidirect
3. C2×#91116C2semidirect
4. C2×#91105C2semidirect
5. C2×#91099C2semidirect
6. #11751078C2semidirect
7. C2×#91093C2semidirect
15. #91829C4semidirect
27. C2×C5×#102D3semidirect
56. C2×C3×C5×C8D4semidirect
65. C2×C3⋊#168D4semidirect
67. C2×C3×#102D5semidirect
164. C2×C5×C8#67semidirect
178. C2×#102D15semidirect
226. C2×C3×C8C22⋊D5semidirect
377. C2×C8#1220semidirect
384. C3×C5#1961semidirect
456. C5#70160semidirect
479. C3#10600953semidirect

Maximal subgroups

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

subgroupindex
C2×#918292
C2×C3×C5×#1022
C2×#911162
C2×#911052
C2×#910992
#117510782
C2×#910932
#106009533
#701605