Finite Group Databasebeta

← #14298492

Subgroups — #14298492

Order 1920.

600 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×#91781C211yesmaximal, characteristic
2C2×#91104C211yesmaximal, characteristic
3#11751088C211yesmaximal, characteristic
4C3×C5×#340C211yesmaximal, characteristic, complemented
5#11746372C211yesmaximal, characteristic, complemented
6#11746350C211yesmaximal, characteristic, complemented
7#11746350C211yesmaximal, characteristic, complemented
8#10599666—31nomaximal, Hall
9C22×C4×D15C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×#6714—21no—
14C2×#6714—21no—
15C2×C4⋊Dic15C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15—21no—
18C22×C3⋊#168C2211yescharacteristic
19#91781—22no—
20#91781C414yescomplemented
21#91115—21no—
22#91104—22no—
23#68873—51nomaximal, Hall
24C2×#4038—31no—
25C2×#3952—31no—
26#65276—31no—
27C5×#340D311yescharacteristic, complemented
28#64771—31no—
29#64749—31no—
30#64749—31no—
31C23×D15D411yescharacteristic
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×Dic15—21no—
36C22×Dic15—21no—
37C22×Dic15D411yescharacteristic
38C2×C4×D15—21no—
39C2×C4×D15—21no—
40C2×C4×D15—21no—
41C2×C4×D15—21no—
42C2×C4×D15C2×C412yes—
43C2×C4×D15D412yes—
44C2×C3×C5×C8—21no—
45C2×C3×C5×C8—21no—
46C2×C3×C5×C8—21no—
47C3×C5×C4⋊C4—21no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C3×C5×C4⋊C4C2×C412yes—
51#6714—24no—
52#6714—42no—
53C4⋊Dic15—21no—
54C4⋊Dic15—21no—
55C4⋊Dic15—21no—
56C4⋊Dic15C2×C412yes—
57C4×Dic15—24no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C2×#892—51no—
62C2×(C2×D3)⋊C8—51no—
63#4987—51no—
64C3×#340D511yescharacteristic, complemented
65#4551—51no—
66#4529—51no—
67#4529—51no—
68C22×C4×D5—31no—
69C22×C5×C8C2×D311yescharacteristic
70C2×C5×C4⋊C4C2×D311yescharacteristic
71C2×C5×C4⋊C4C2×D311yescharacteristic
72C2×#685—61no—
73C2×#685—61no—
74C2×C4⋊Dic5—31no—
75C2×C4⋊Dic5—31no—
76C2×C4×Dic5—61no—
77C22×#168—31no—
78#4038—34no—
79#4038—62no—
80#3963—61no—
81#3952—62no—
82#1825—151noSylow
83C23×C3×C5C2×D411yescharacteristic
84C22×D15—21no—
85C22×D15—21no—
86C22×D15—21no—
87C22×D15—21no—
88C22×D15—21no—
89C22×D15—21no—
90C22×D15C22⋊C412yes—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—41no—
93C2×C3×C4×C5—41no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5#4111yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—21no—
104C2×Dic15—21no—
105C2×Dic15—22no—
106C2×Dic15—41no—
107C2×Dic15—41no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110C2×Dic15—41no—
111C2×Dic15C22⋊C412yes—
112C4×D15—22no—
113C4×D15—22no—
114C4×D15—22no—
115C4×D15—22no—
116C3×C5×C8—41no—
117C3⋊#168—41no—
118C22×C4×D3—51no—
119C22×C3×C8C2×D511yescharacteristic
120C2×C3×C4⋊C4C2×D511yescharacteristic
121C2×C3×C4⋊C4C2×D511yescharacteristic
122C2×(C2×D3)⋊C4—101no—
123C2×(C2×D3)⋊C4—101no—
124C2×C4⋊Dic3—51no—
125C2×C4⋊Dic3—51no—
126C2×C4×Dic3—101no—
127C22×C3⋊C8—51no—
128#892—54no—
129#892—102no—
130C3⋊#95—101no—
131(C2×D3)⋊C8—102no—
132C23×D5—31no—
133C22×C4×C5—21no—
134C22×C4×C5—21no—
135C22×C4×C5C22×D311yescharacteristic
136C22×Dic5—31no—
137C22×Dic5—61no—
138C22×Dic5—61no—
139C2×C4×D5—32no—
140C2×C4×D5—32no—
141C2×C4×D5—61no—
142C2×C4×D5—61no—
143C2×C4×D5—61no—
144C2×C4×D5—61no—
145C2×C5×C8—21no—
146C2×C5×C8—21no—
147C2×C5×C8—21no—
148C5×C4⋊C4—21no—
149C5×C4⋊C4—21no—
150C5×C4⋊C4—21no—
151C5×C4⋊C4C4×D312yes—
152#685—64no—
153#685—122no—
154C4⋊Dic5—32no—
155C4⋊Dic5—61no—
156C4⋊Dic5—61no—
157C4⋊Dic5—61no—
158C4×Dic5—64no—
159C2×#168—61no—
160C2×#168—61no—
161C2×#168—61no—
162C2×#117—151no—
163C2×C22⋊C8—151no—
164#380—151no—
165#340—151no—
166#340—151no—
167#340—151no—
168#340D1511yescharacteristic, complemented
169C22×C3×C5C2×C22⋊C411yescharacteristic
170C22×C3×C5#12311yescharacteristic
171C22×C3×C5#12311yescharacteristic
172C22×C3×C5#13511yescharacteristic
173C22×C3×C5#13511yescharacteristic
174C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
175C22×C3×C5#13711yescharacteristic
176C2×D15—22no—
177C2×D15—22no—
178C2×D15—22no—
179C2×D15—41no—
180C2×D15—41no—
181C2×D15—41no—
182C2×D15—41no—
183C3×C4×C5—42no—
184C3×C4×C5—81no—
185C3×C4×C5#11711yescharacteristic
186C3×C4×C5#11711yescharacteristic
187C3×C4×C5#12311yescharacteristic
188C3×C4×C5#12311yescharacteristic
189Dic15—22no—
190Dic15—42no—
191Dic15—81no—
192C23×D3—51no—
193C22×C3×C4—21no—
194C22×C3×C4—21no—
195C22×C3×C4C22×D511yescharacteristic
196C22×Dic3—51no—
197C22×Dic3—101no—
198C22×Dic3—101no—
199C2×C4×D3—52no—
200C2×C4×D3—52no—
201C2×C4×D3—101no—
202C2×C4×D3—101no—
203C2×C4×D3—101no—
204C2×C4×D3—101no—
205C2×C3×C8—21no—
206C2×C3×C8—21no—
207C2×C3×C8—21no—
208C3×C4⋊C4—21no—
209C3×C4⋊C4—21no—
210C3×C4⋊C4—21no—
211C3×C4⋊C4C4×D512yes—
212(C2×D3)⋊C4—104no—
213(C2×D3)⋊C4—202no—
214C4⋊Dic3—52no—
215C4⋊Dic3—101no—
216C4⋊Dic3—101no—
217C4⋊Dic3—101no—
218C4×Dic3—104no—
219C2×C3⋊C8—101no—
220C2×C3⋊C8—101no—
221C2×C3⋊C8—101no—
222C23×C5D3×D411yescharacteristic
223C22×D5—32no—
224C22×D5—61no—
225C22×D5—61no—
226C22×D5—61no—
227C22×D5—61no—
228C22×D5—61no—
229C22×D5—61no—
230C2×C4×C5—22no—
231C2×C4×C5—41no—
232C2×C4×C5—41no—
233C2×C4×C5—41no—
234C2×C4×C5—41no—
235C2×C4×C5—41no—
236C2×C4×C5C2×C4×D311yescharacteristic
237C2×C4×C5#23511yescharacteristic
238C2×C4×C5#23511yescharacteristic
239C2×C4×C5D3×D411yescharacteristic
240C2×C4×C5#23711yescharacteristic
241C2×C4×C5#23911yescharacteristic
242C2×Dic5—32no—
243C2×Dic5—61no—
244C2×Dic5—61no—
245C2×Dic5—62no—
246C2×Dic5—121no—
247C2×Dic5—121no—
248C2×Dic5—121no—
249C2×Dic5—121no—
250C2×Dic5—121no—
251C4×D5—62no—
252C4×D5—62no—
253C4×D5—62no—
254C4×D5—62no—
255C5×C8—41no—
256#168—121no—
257C23×C4—151no—
258C22×C8—151no—
259C22×C8C2×D1511yescharacteristic
260#117—154no—
261#117—302no—
262C2×C4⋊C4—151no—
263C2×C4⋊C4—151no—
264C2×C4⋊C4C2×D1511yescharacteristic
265C2×C4⋊C4C2×D1511yescharacteristic
266C2×C22⋊C4—301no—
267C2×C22⋊C4—301no—
268C2×C42—301no—
269C22⋊C8—302no—
270#95—301no—
271C2×C3×C5#38111yescharacteristic
272C2×C3×C5#41611yescharacteristic
273C2×C3×C5#41711yescharacteristic
274C2×C3×C5#48211yescharacteristic
275C2×C3×C5#48211yescharacteristic
276C2×C3×C5#48511yescharacteristic
277C2×C3×C5#48511yescharacteristic
278D15—42no—
279C23×C3D4×D511yescharacteristic
280C22×D3—52no—
281C22×D3—101no—
282C22×D3—101no—
283C22×D3—101no—
284C22×D3—101no—
285C22×D3—101no—
286C22×D3—101no—
287C2×C3×C4—22no—
288C2×C3×C4—41no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4—41no—
293C2×C3×C4C2×C4×D511yescharacteristic
294C2×C3×C4#70911yescharacteristic
295C2×C3×C4#70911yescharacteristic
296C2×C3×C4D4×D511yescharacteristic
297C2×C3×C4#71111yescharacteristic
298C2×C3×C4#71311yescharacteristic
299C2×Dic3—52no—
300C2×Dic3—101no—
301C2×Dic3—101no—
302C2×Dic3—102no—
303C2×Dic3—201no—
304C2×Dic3—201no—
305C2×Dic3—201no—
306C2×Dic3—201no—
307C2×Dic3—201no—
308C4×D3—102no—
309C4×D3—102no—
310C4×D3—102no—
311C4×D3—102no—
312C3×C8—41no—
313C3⋊C8—201no—
314C22×C5D3×C22⋊C411yescharacteristic
315C22×C5#88311yescharacteristic
316C22×C5#89411yescharacteristic
317C22×C5#91211yescharacteristic
318C22×C5#91411yescharacteristic
319C22×C5#91611yescharacteristic
320C22×C5#91811yescharacteristic
321C2×D5—62no—
322C2×D5—62no—
323C2×D5—62no—
324C2×D5—121no—
325C2×D5—121no—
326C2×D5—121no—
327C2×D5—121no—
328C4×C5—42no—
329C4×C5—81no—
330C4×C5#87211yescharacteristic
331C4×C5#88311yescharacteristic
332C4×C5#89211yescharacteristic
333C4×C5#89411yescharacteristic
334Dic5—62no—
335Dic5—122no—
336Dic5—241no—
337C24—151no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—151no—
341C22×C4—152no—
342C22×C4—152no—
343C22×C4—301no—
344C22×C4—301no—
345C22×C4—301no—
346C22×C4—301no—
347C22×C4—301no—
348C22×C4—301no—
349C22×C4C22×D1511yescharacteristic
350C2×C8—21no—
351C2×C8—21no—
352C2×C8—21no—
353C2×C8—301no—
354C2×C8—301no—
355C2×C8—301no—
356C4⋊C4—21no—
357C4⋊C4—21no—
358C4⋊C4—21no—
359C4⋊C4—152no—
360C4⋊C4—301no—
361C4⋊C4—301no—
362C4⋊C4—301no—
363C4⋊C4C4×D1512yes—
364C22⋊C4—304no—
365C22⋊C4—602no—
366C42—304no—
367C3×C5#182511yescharacteristic, complemented, Hall
368C22×C3D5×C22⋊C411yescharacteristic
369C22×C3#402911yescharacteristic
370C22×C3#404011yescharacteristic
371C22×C3#405811yescharacteristic
372C22×C3#406011yescharacteristic
373C22×C3#406211yescharacteristic
374C22×C3#406411yescharacteristic
375C2×D3—102no—
376C2×D3—102no—
377C2×D3—102no—
378C2×D3—201no—
379C2×D3—201no—
380C2×D3—201no—
381C2×D3—201no—
382C3×C4—42no—
383C3×C4—81no—
384C3×C4#401811yescharacteristic
385C3×C4#402911yescharacteristic
386C3×C4#403811yescharacteristic
387C3×C4#404011yescharacteristic
388Dic3—102no—
389Dic3—202no—
390Dic3—401no—
391C2×C5#466411yescharacteristic
392C2×C5#477211yescharacteristic
393C2×C5#478411yescharacteristic
394C2×C5#480311yescharacteristic
395C2×C5#481511yescharacteristic
396C2×C5#486611yescharacteristic
397C2×C5#488811yescharacteristic
398D5—122no—
399C23—152no—
400C23—301no—
401C23—301no—
402C23—301no—
403C23—301no—
404C23—301no—
405C23—301no—
406C23D4×D1511yescharacteristic
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—152no—
414C2×C4—301no—
415C2×C4—301no—
416C2×C4—302no—
417C2×C4—302no—
418C2×C4—302no—
419C2×C4—302no—
420C2×C4—302no—
421C2×C4—601no—
422C2×C4—601no—
423C2×C4—601no—
424C2×C4—601no—
425C2×C4—601no—
426C2×C4C2×C4×D1511yescharacteristic
427C2×C4#681711yescharacteristic
428C2×C4#681711yescharacteristic
429C2×C4D4×D1511yescharacteristic
430C2×C4#681911yescharacteristic
431C2×C4#682111yescharacteristic
432C8—41no—
433C8—601no—
434C2×C3#6495311yescharacteristic
435C2×C3#6506111yescharacteristic
436C2×C3#6507311yescharacteristic
437C2×C3#6509211yescharacteristic
438C2×C3#6510411yescharacteristic
439C2×C3#6515511yescharacteristic
440C2×C3#6517711yescharacteristic
441D3—202no—
442C5#6887311yescharacteristic, complemented, Sylow
443C22—302no—
444C22—302no—
445C22—302no—
446C22—601no—
447C22—601no—
448C22—601no—
449C22—601no—
450C22C22⋊C4×D1511yescharacteristic
451C22#9177211yescharacteristic
452C22#9178311yescharacteristic
453C22#9180111yescharacteristic
454C22#9180311yescharacteristic
455C22#9180511yescharacteristic
456C22#9180711yescharacteristic
457C4—42no—
458C4—81no—
459C4—302no—
460C4—602no—
461C4—1201no—
462C4#9176111yescharacteristic
463C4#9177211yescharacteristic
464C4#9178111yescharacteristic
465C4#9178311yescharacteristic
466C3#1059966611yescharacteristic, complemented, Sylow
467C2—602no—
468C2#1175076511yescharacteristic
469C2#1175087311yescharacteristic
470C2#1175088511yescharacteristic
471C2#1175090411yescharacteristic
472C2#1175091611yescharacteristic
473C2#1175096711yescharacteristic
474C2#1175098911yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#340C2
socleC23×C3×C5C2×D4
prime radicalC23×D15D4
cosocleC22×C3×C4×C5C23
hypercenter#340D15
hypocenterC3×C5#1825
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
4. C3×C5×#340C2semidirect
5. #11746372C2semidirect
6. #11746350C2semidirect
7. #11746350C2semidirect
20. #91781C4semidirect
27. C5×#340D3semidirect
64. C3×#340D5semidirect
168. #340D15semidirect
367. C3×C5#1825semidirect
442. C5#68873semidirect
466. C3#10599666semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×#911042
#117510882
C3×C5×#3402
#117463722
#117463502
#105996663
#688735