Finite Group Databasebeta

← #14298428

Subgroups — #14298428

Order 1920.

688 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×C4⋊C4×D15C211yesmaximal, 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#10599664—31nomaximal, Hall
9C22×C4×D15—21no—
10C22×C4×D15C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C4⋊C4C2211yescharacteristic
14C2×#6714—21no—
15C2×C4⋊Dic15C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×#6712—21no—
18C22×C3⋊#168C2211yescharacteristic
19C4⋊C4×D15—22no—
20C4⋊C4×D15C414yescomplemented
21#91115—21no—
22#91104—22no—
23#68871—51nomaximal, Hall
24C2×D5×C4⋊C4—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×D15—24no—
43C2×C4×D15—42no—
44C2×C4×D15—42no—
45C2×C4×D15C2×C412yes—
46C2×C4×D15D412yes—
47C2×C3×C5×C8—21no—
48C2×C3×C5×C8—21no—
49C2×C3×C5×C8—21no—
50C3×C5×C4⋊C4—21no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C4⋊C4C2×C412yes—
54#6714—42no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15—21no—
58C4⋊Dic15C2×C412yes—
59#6712—24no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C2×D3×C4⋊C4—51no—
64C2×(C2×D3)⋊C8—51no—
65#4987—51no—
66C3×#340D511yescharacteristic, complemented
67#4551—51no—
68#4529—51no—
69#4529—51no—
70C22×C4×D5—31no—
71C22×C4×D5—61no—
72C22×C5×C8C2×D311yescharacteristic
73C2×C5×C4⋊C4C2×D311yescharacteristic
74C2×C5×C4⋊C4C2×D311yescharacteristic
75C2×#685—61no—
76C2×C4⋊Dic5—31no—
77C2×C4⋊Dic5—31no—
78C2×#683—61no—
79C22×#168—31no—
80D5×C4⋊C4—34no—
81D5×C4⋊C4—62no—
82#3963—61no—
83#3952—62no—
84#1823—151noSylow
85C23×C3×C5C2×D411yescharacteristic
86C22×D15—21no—
87C22×D15—21no—
88C22×D15—21no—
89C22×D15—21no—
90C22×D15C22⋊C412yes—
91C22×D15D812yes—
92C22×D15SD1612yes—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5—41no—
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×Dic15—21no—
106C2×Dic15—21no—
107C2×Dic15—22no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110C2×Dic15—41no—
111C2×Dic15—41no—
112C2×Dic15—41no—
113C2×Dic15C22⋊C412yes—
114C4×D15—22no—
115C4×D15—22no—
116C4×D15—22no—
117C4×D15—22no—
118C4×D15—48no—
119C3×C5×C8—41no—
120C3⋊#168—41no—
121C22×C4×D3—51no—
122C22×C4×D3—101no—
123C22×C3×C8C2×D511yescharacteristic
124C2×C3×C4⋊C4C2×D511yescharacteristic
125C2×C3×C4⋊C4C2×D511yescharacteristic
126C2×(C2×D3)⋊C4—101no—
127C2×C4⋊Dic3—51no—
128C2×C4⋊Dic3—51no—
129C2×Dic3⋊C4—101no—
130C22×C3⋊C8—51no—
131D3×C4⋊C4—54no—
132D3×C4⋊C4—102no—
133C3⋊#95—101no—
134(C2×D3)⋊C8—102no—
135C23×D5—31no—
136C22×C4×C5—21no—
137C22×C4×C5—21no—
138C22×C4×C5C22×D311yescharacteristic
139C22×Dic5—31no—
140C22×Dic5—61no—
141C22×Dic5—61no—
142C2×C4×D5—32no—
143C2×C4×D5—32no—
144C2×C4×D5—61no—
145C2×C4×D5—61no—
146C2×C4×D5—61no—
147C2×C4×D5—61no—
148C2×C4×D5—64no—
149C2×C4×D5—122no—
150C2×C4×D5—122no—
151C2×C5×C8—21no—
152C2×C5×C8—21no—
153C2×C5×C8—21no—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4C4×D312yes—
158#685—122no—
159C4⋊Dic5—32no—
160C4⋊Dic5—61no—
161C4⋊Dic5—61no—
162C4⋊Dic5—61no—
163#683—64no—
164C2×#168—61no—
165C2×#168—61no—
166C2×#168—61no—
167C22×C4⋊C4—151no—
168C2×C22⋊C8—151no—
169#380—151no—
170#340—151no—
171#340—151no—
172#340—151no—
173#340D1511yescharacteristic, complemented
174C22×C3×C5C2×C22⋊C411yescharacteristic
175C22×C3×C5#12311yescharacteristic
176C22×C3×C5#12311yescharacteristic
177C22×C3×C5C2×D811yescharacteristic
178C22×C3×C5C2×SD1611yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C22×C3×C5#13711yescharacteristic
181C2×D15—22no—
182C2×D15—22no—
183C2×D15—22no—
184C2×D15—22no—
185C2×D15—22no—
186C2×D15—22no—
187C2×D15#10214yes—
188C3×C4×C5—42no—
189C3×C4×C5—81no—
190C3×C4×C5#11711yescharacteristic
191C3×C4×C5#11711yescharacteristic
192C3×C4×C5#12311yescharacteristic
193C3×C4×C5#12311yescharacteristic
194Dic15—22no—
195Dic15—42no—
196Dic15—81no—
197C23×D3—51no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4C22×D511yescharacteristic
201C22×Dic3—51no—
202C22×Dic3—101no—
203C22×Dic3—101no—
204C2×C4×D3—52no—
205C2×C4×D3—52no—
206C2×C4×D3—101no—
207C2×C4×D3—101no—
208C2×C4×D3—101no—
209C2×C4×D3—101no—
210C2×C4×D3—104no—
211C2×C4×D3—202no—
212C2×C4×D3—202no—
213C2×C3×C8—21no—
214C2×C3×C8—21no—
215C2×C3×C8—21no—
216C3×C4⋊C4—21no—
217C3×C4⋊C4—21no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4C4×D512yes—
220(C2×D3)⋊C4—202no—
221C4⋊Dic3—52no—
222C4⋊Dic3—101no—
223C4⋊Dic3—101no—
224C4⋊Dic3—101no—
225Dic3⋊C4—104no—
226C2×C3⋊C8—101no—
227C2×C3⋊C8—101no—
228C2×C3⋊C8—101no—
229C23×C5D3×D411yescharacteristic
230C22×D5—32no—
231C22×D5—32no—
232C22×D5—32no—
233C22×D5—61no—
234C22×D5—61no—
235C22×D5—61no—
236C22×D5—61no—
237C2×C4×C5—22no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—41no—
242C2×C4×C5—41no—
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5#23511yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×C4×C5#23911yescharacteristic
249C2×Dic5—32no—
250C2×Dic5—61no—
251C2×Dic5—61no—
252C2×Dic5—62no—
253C2×Dic5—121no—
254C2×Dic5—121no—
255C2×Dic5—121no—
256C2×Dic5—121no—
257C2×Dic5—121no—
258C4×D5—62no—
259C4×D5—62no—
260C4×D5—62no—
261C4×D5—62no—
262C4×D5—128no—
263C5×C8—41no—
264#168—121no—
265C23×C4—151no—
266C23×C4—301no—
267C22×C8—151no—
268C22×C8C2×D1511yescharacteristic
269C2×C4⋊C4—151no—
270C2×C4⋊C4—154no—
271C2×C4⋊C4—151no—
272C2×C4⋊C4—302no—
273C2×C4⋊C4—301no—
274C2×C4⋊C4C2×D1511yescharacteristic
275C2×C4⋊C4C2×D1511yescharacteristic
276C2×C22⋊C4—301no—
277C22⋊C8—302no—
278#95—301no—
279C2×C3×C5#38111yescharacteristic
280C2×C3×C5C2×#10211yescharacteristic
281C2×C3×C5#41911yescharacteristic
282C2×C3×C5#48011yescharacteristic
283C2×C3×C5#48011yescharacteristic
284C2×C3×C5#48311yescharacteristic
285C2×C3×C5#48311yescharacteristic
286D15—24no—
287C23×C3D4×D511yescharacteristic
288C22×D3—52no—
289C22×D3—52no—
290C22×D3—52no—
291C22×D3—101no—
292C22×D3—101no—
293C22×D3—101no—
294C22×D3—101no—
295C2×C3×C4—22no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4—41no—
300C2×C3×C4—41no—
301C2×C3×C4C2×C4×D511yescharacteristic
302C2×C3×C4#70911yescharacteristic
303C2×C3×C4#70911yescharacteristic
304C2×C3×C4D4×D511yescharacteristic
305C2×C3×C4#71111yescharacteristic
306C2×C3×C4#71311yescharacteristic
307C2×Dic3—52no—
308C2×Dic3—101no—
309C2×Dic3—101no—
310C2×Dic3—102no—
311C2×Dic3—201no—
312C2×Dic3—201no—
313C2×Dic3—201no—
314C2×Dic3—201no—
315C2×Dic3—201no—
316C4×D3—102no—
317C4×D3—102no—
318C4×D3—102no—
319C4×D3—102no—
320C4×D3—208no—
321C3×C8—41no—
322C3⋊C8—201no—
323C22×C5D3×C22⋊C411yescharacteristic
324C22×C5#88311yescharacteristic
325C22×C5#89411yescharacteristic
326C22×C5D3×D811yescharacteristic
327C22×C5D3×SD1611yescharacteristic
328C22×C5#91511yescharacteristic
329C22×C5#91811yescharacteristic
330C2×D5—34no—
331C2×D5—62no—
332C2×D5—62no—
333C2×D5—62no—
334C2×D5—62no—
335C2×D5—62no—
336C2×D5—62no—
337C4×C5—42no—
338C4×C5—81no—
339C4×C5#87211yescharacteristic
340C4×C5#88311yescharacteristic
341C4×C5#89211yescharacteristic
342C4×C5#89411yescharacteristic
343Dic5—62no—
344Dic5—122no—
345Dic5—241no—
346C24—151no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—151no—
350C22×C4—152no—
351C22×C4—152no—
352C22×C4—304no—
353C22×C4—301no—
354C22×C4—301no—
355C22×C4—301no—
356C22×C4—301no—
357C22×C4—301no—
358C22×C4—301no—
359C22×C4—602no—
360C22×C4—602no—
361C22×C4C22×D1511yescharacteristic
362C2×C8—21no—
363C2×C8—21no—
364C2×C8—21no—
365C2×C8—301no—
366C2×C8—301no—
367C2×C8—301no—
368C4⋊C4—21no—
369C4⋊C4—21no—
370C4⋊C4—21no—
371C4⋊C4—152no—
372C4⋊C4—304no—
373C4⋊C4—301no—
374C4⋊C4—301no—
375C4⋊C4—301no—
376C4⋊C4C4×D1512yes—
377C22⋊C4—602no—
378C3×C5#182311yescharacteristic, complemented, Hall
379C22×C3D5×C22⋊C411yescharacteristic
380C22×C3#402911yescharacteristic
381C22×C3#404011yescharacteristic
382C22×C3D5×D811yescharacteristic
383C22×C3D5×SD1611yescharacteristic
384C22×C3#406111yescharacteristic
385C22×C3#406411yescharacteristic
386C2×D3—54no—
387C2×D3—102no—
388C2×D3—102no—
389C2×D3—102no—
390C2×D3—102no—
391C2×D3—102no—
392C2×D3—102no—
393C3×C4—42no—
394C3×C4—81no—
395C3×C4#401811yescharacteristic
396C3×C4#402911yescharacteristic
397C3×C4#403811yescharacteristic
398C3×C4#404011yescharacteristic
399Dic3—102no—
400Dic3—202no—
401Dic3—401no—
402C2×C5#466411yescharacteristic
403C2×C5D3×#10211yescharacteristic
404C2×C5#477411yescharacteristic
405C2×C5#480211yescharacteristic
406C2×C5#480511yescharacteristic
407C2×C5#486211yescharacteristic
408C2×C5#488211yescharacteristic
409D5—64no—
410C23—152no—
411C23—152no—
412C23—152no—
413C23—301no—
414C23—301no—
415C23—301no—
416C23—301no—
417C23D4×D1511yescharacteristic
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—152no—
425C2×C4—301no—
426C2×C4—301no—
427C2×C4—302no—
428C2×C4—302no—
429C2×C4—302no—
430C2×C4—302no—
431C2×C4—302no—
432C2×C4—608no—
433C2×C4—601no—
434C2×C4—601no—
435C2×C4—601no—
436C2×C4—601no—
437C2×C4—601no—
438C2×C4C2×C4×D1511yescharacteristic
439C2×C4#681711yescharacteristic
440C2×C4#681711yescharacteristic
441C2×C4D4×D1511yescharacteristic
442C2×C4#681911yescharacteristic
443C2×C4#682111yescharacteristic
444C8—41no—
445C8—601no—
446C2×C3#6495311yescharacteristic
447C2×C3D5×#10211yescharacteristic
448C2×C3#6506311yescharacteristic
449C2×C3#6509111yescharacteristic
450C2×C3#6509411yescharacteristic
451C2×C3#6515111yescharacteristic
452C2×C3#6517111yescharacteristic
453D3—104no—
454C5#6887111yescharacteristic, complemented, Sylow
455C22—154no—
456C22—302no—
457C22—302no—
458C22—302no—
459C22—302no—
460C22—302no—
461C22—302no—
462C22C22⋊C4×D1511yescharacteristic
463C22#9177211yescharacteristic
464C22#9178311yescharacteristic
465C22D8×D1511yescharacteristic
466C22SD16×D1511yescharacteristic
467C22#9180411yescharacteristic
468C22#9180711yescharacteristic
469C4—42no—
470C4—81no—
471C4—302no—
472C4—602no—
473C4—1201no—
474C4#9176111yescharacteristic
475C4#9177211yescharacteristic
476C4#9178111yescharacteristic
477C4#9178311yescharacteristic
478C3#1059966411yescharacteristic, complemented, Sylow
479C2—304no—
480C2#1175076511yescharacteristic
481C2D15×#10211yescharacteristic
482C2#1175087511yescharacteristic
483C2#1175090311yescharacteristic
484C2#1175090611yescharacteristic
485C2#1175096311yescharacteristic
486C2#1175098311yescharacteristic
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#1823
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. C4⋊C4×D15C4semidirect
27. C5×#340D3semidirect
66. C3×#340D5semidirect
173. #340D15semidirect
378. C3×C5#1823semidirect
454. C5#68871semidirect
478. C3#10599664semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D152
C2×#911042
#117510882
C3×C5×#3402
#117463722
#117463502
#105996643
#688715