Finite Group Databasebeta

← #14299485

Subgroups — #14299485

Order 1920.

632 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91338C211yesmaximal, characteristic
2C5×#4987C211yesmaximal, characteristic
3C2×#90989C211yesmaximal, characteristic, complemented
4C2×#90985C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊#168C211yesmaximal, characteristic
6#11746350C211yesmaximal, characteristic, complemented
7C3×#64749C211yesmaximal, characteristic, complemented
8#10600299—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C4⋊Dic15C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×(C2×D3)⋊C4—21no—
14C2×C5×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic5C2211yescharacteristic
16C22×C3×#168C2211yescharacteristic
17C2×(C2×D3)⋊Dic5—21no—
18C2×Dic3×Dic5—21no—
19#91338—22no—
20#91338—22no—
21C5×C3⋊#95—21no—
22#90989—22no—
23#90985—22no—
24(C2×D3)⋊#168C414yescomplemented
25#68876—51nomaximal, Hall
26C2×#4072—31no—
27C5×#380—31no—
28C2×C22⋊#168—31no—
29C2×#3940—31no—
30C2×#3939—31no—
31#64749—31no—
32#64749D311yescharacteristic, complemented
33C23×C5×D3D411yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C22×C5×Dic3—21no—
38C22×C5×Dic3D411yescharacteristic
39C2×C4×C5×D3—21no—
40C2×C4×C5×D3—21no—
41C2×C4×C5×D3—21no—
42C2×C4×C5×D3—21no—
43C2×C4×C5×D3C2×C412yes—
44C2×C4×C5×D3Q812yes—
45C22×C3×Dic5—21no—
46C3×C5×C4⋊C4—21no—
47C3×C5×C4⋊C4—21no—
48C4⋊Dic15—21no—
49C4⋊Dic15D412yes—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
52C2×C3⋊#168C2×C412yes—
53C5×(C2×D3)⋊C4—42no—
54C5×C4⋊Dic3—21no—
55C5×C4⋊Dic3—21no—
56C3×C4⋊Dic5—21no—
57C3×C4⋊Dic5D412yes—
58C2×C3×#168—21no—
59C2×C3×#168—21no—
60C2×C3×#168C2×C412yes—
61(C2×D3)⋊Dic5—24no—
62Dic3×Dic5—24no—
63C2×#892—51no—
64C2×(C2×D3)⋊C8—51no—
65C2×#817—51no—
66#4987D511yescharacteristic
67C2×#807—51no—
68C3×#340—51no—
69#4529—51no—
70C23×C4×C5—31no—
71C2×C5×C4⋊C4—31no—
72C2×C5×C4⋊C4C2×D311yescharacteristic
73C2×C5×C22⋊C4—61no—
74C2×C22⋊Dic5—61no—
75#4072—62no—
76#4072—62no—
77C2×C4⋊Dic5—31no—
78C2×C4⋊Dic5C2×D311yescharacteristic
79C2×C4×Dic5—61no—
80C22×#168—31no—
81C22×#168C2×D311yescharacteristic
82C5×#95—61no—
83C22⋊#168—34no—
84#3940—62no—
85#3939—62no—
86#1854—151noSylow
87C23×C3×C5C2×D411yescharacteristic
88C22×C5×D3—21no—
89C22×C5×D3—21no—
90C22×C5×D3—21no—
91C22×C5×D3—21no—
92C22×C5×D3—21no—
93C22×C5×D3—21no—
94C22×C5×D3C4⋊C412yes—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5—41no—
98C2×C3×C4×C5C22×C411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5C2×Q811yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×Dic15—22no—
105C2×Dic15—41no—
106C2×Dic15—41no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—41no—
110C2×C5×Dic3—41no—
111C2×C5×Dic3—41no—
112C2×C5×Dic3C4⋊C412yes—
113C4×C5×D3—22no—
114C4×C5×D3—22no—
115C4×C5×D3—22no—
116C4×C5×D3—22no—
117C2×C3×Dic5—22no—
118C2×C3×Dic5—41no—
119C2×C3×Dic5—41no—
120C3⋊#168—22no—
121C3×#168—22no—
122C22×C4×D3C2×D511yescharacteristic
123C22×C3×C8—51no—
124C2×C3×C4⋊C4—51no—
125C2×C3×C4⋊C4C2×D511yescharacteristic
126C2×(C2×D3)⋊C4—21no—
127C2×(C2×D3)⋊C4—101no—
128C2×C4⋊Dic3—51no—
129C2×C4⋊Dic3C2×D511yescharacteristic
130C2×C4×Dic3—101no—
131C22×C3⋊C8—51no—
132#892—102no—
133#892—102no—
134C3⋊#95—21no—
135(C2×D3)⋊C8—54no—
136#817—102no—
137#807—102no—
138C24×C5—31no—
139C22×C4×C5—21no—
140C22×C4×C5—31no—
141C22×C4×C5—32no—
142C22×C4×C5—32no—
143C22×C4×C5—61no—
144C22×C4×C5—61no—
145C22×C4×C5—61no—
146C22×C4×C5—61no—
147C22×C4×C5—61no—
148C22×C4×C5C22×D311yescharacteristic
149C22×Dic5—21no—
150C22×Dic5—61no—
151C5×C4⋊C4—21no—
152C5×C4⋊C4—21no—
153C5×C4⋊C4—61no—
154C5×C4⋊C4—61no—
155C5×C22⋊C4—122no—
156C22⋊Dic5—64no—
157C4⋊Dic5—21no—
158C4⋊Dic5—32no—
159C4⋊Dic5—61no—
160C4⋊Dic5D1212yes—
161C4×Dic5—64no—
162C2×#168—21no—
163C2×#168—21no—
164C2×#168—32no—
165C2×#168—61no—
166C2×#168—61no—
167C2×#168C4×D312yes—
168C2×#117—151no—
169C2×#107—151no—
170C2×#106—151no—
171C2×C22⋊C8—151no—
172#380—31no—
173#340—51no—
174#340—151no—
175C22×C3×C5C2×C4⋊C411yescharacteristic
176C22×C3×C5#12011yescharacteristic
177C22×C3×C5#12311yescharacteristic
178C22×C3×C5#13511yescharacteristic
179C22×C3×C5#13511yescharacteristic
180C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
181C22×C3×C5#13711yescharacteristic
182C2×C5×D3—22no—
183C2×C5×D3—22no—
184C2×C5×D3—22no—
185C2×C5×D3—41no—
186C2×C5×D3—41no—
187C2×C5×D3—41no—
188C2×C5×D3—41no—
189C3×C4×C5—81no—
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C4×D411yescharacteristic
192C3×C4×C5C22⋊Q811yescharacteristic
193C3×C4×C5C22⋊Q811yescharacteristic
194Dic15—42no—
195C3×Dic5—42no—
196C5×Dic3—22no—
197C5×Dic3—81no—
198C23×D3C22⋊D511yescharacteristic
199C22×C3×C4—21no—
200C22×C3×C4—101no—
201C22×C3×C4C22×D511yescharacteristic
202C22×Dic3—21no—
203C22×Dic3—101no—
204C22×Dic3C22⋊D511yescharacteristic
205C2×C4×D3—21no—
206C2×C4×D3—21no—
207C2×C4×D3—21no—
208C2×C4×D3—21no—
209C2×C4×D3Dic1012yes—
210C2×C4×D3C4×D512yes—
211C2×C3×C8—52no—
212C2×C3×C8—101no—
213C2×C3×C8—101no—
214C3×C4⋊C4—21no—
215C3×C4⋊C4—21no—
216C3×C4⋊C4—52no—
217C3×C4⋊C4—101no—
218(C2×D3)⋊C4—42no—
219(C2×D3)⋊C4—104no—
220C4⋊Dic3—21no—
221C4⋊Dic3—21no—
222C4⋊Dic3—52no—
223C4⋊Dic3—101no—
224C4×Dic3—104no—
225C2×C3⋊C8—52no—
226C2×C3⋊C8—101no—
227C2×C3⋊C8—101no—
228C23×C5—32no—
229C23×C5—61no—
230C23×C5—61no—
231C23×C5—61no—
232C23×C5—61no—
233C23×C5—61no—
234C23×C5—61no—
235C23×C5D3×D411yescharacteristic
236C2×C4×C5—32no—
237C2×C4×C5—41no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—61no—
241C2×C4×C5—61no—
242C2×C4×C5—62no—
243C2×C4×C5—62no—
244C2×C4×C5—62no—
245C2×C4×C5—62no—
246C2×C4×C5—121no—
247C2×C4×C5—121no—
248C2×C4×C5—121no—
249C2×C4×C5C2×C4×D311yescharacteristic
250C2×C4×C5C2×D1211yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5#23711yescharacteristic
254C2×C4×C5D3×Q811yescharacteristic
255C2×Dic5—22no—
256C2×Dic5—41no—
257C2×Dic5—41no—
258C2×Dic5—62no—
259C2×Dic5—121no—
260C2×Dic5—121no—
261#168—22no—
262#168—62no—
263C23×C4—31no—
264C22×C8—51no—
265C22×C8—151no—
266#117—302no—
267#117—302no—
268C2×C4⋊C4—31no—
269C2×C4⋊C4—51no—
270C2×C4⋊C4—151no—
271C2×C4⋊C4D3×D511yescharacteristic
272C2×C22⋊C4—61no—
273C2×C22⋊C4—301no—
274C2×C42—301no—
275#107—302no—
276#106—302no—
277C22⋊C8—154no—
278#95—61no—
279C2×C3×C5#38511yescharacteristic
280C2×C3×C5#42711yescharacteristic
281C2×C3×C5#42811yescharacteristic
282C2×C3×C5#44911yescharacteristic
283C2×C3×C5#45211yescharacteristic
284C2×C3×C5#48211yescharacteristic
285C2×C3×C5#48511yescharacteristic
286C5×D3—42no—
287C23×C3C2×C22⋊D511yescharacteristic
288C22×D3—21no—
289C22×D3—21no—
290C22×D3—21no—
291C22×D3—21no—
292C22×D3—21no—
293C22×D3—21no—
294C22×D3#68312yes—
295C2×C3×C4—41no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—102no—
299C2×C3×C4—201no—
300C2×C3×C4—201no—
301C2×C3×C4C2×Dic1011yescharacteristic
302C2×C3×C4C2×C4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4D4×D511yescharacteristic
305C2×C3×C4#71111yescharacteristic
306C2×C3×C4#71111yescharacteristic
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—41no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—102no—
313C2×Dic3—201no—
314C2×Dic3—201no—
315C2×Dic3#68312yes—
316C4×D3—22no—
317C4×D3—22no—
318C4×D3—22no—
319C4×D3—22no—
320C3×C8—102no—
321C3⋊C8—102no—
322C22×C5—62no—
323C22×C5—62no—
324C22×C5—62no—
325C22×C5—121no—
326C22×C5—121no—
327C22×C5—121no—
328C22×C5—121no—
329C22×C5#88211yescharacteristic
330C22×C5#88311yescharacteristic
331C22×C5D3×C4⋊C411yescharacteristic
332C22×C5#91111yescharacteristic
333C22×C5#91611yescharacteristic
334C22×C5#91611yescharacteristic
335C22×C5#91811yescharacteristic
336C4×C5—62no—
337C4×C5—81no—
338C4×C5—241no—
339C4×C5C4×D1211yescharacteristic
340C4×C5#67⋊C411yescharacteristic
341C4×C5#89611yescharacteristic
342C4×C5#89711yescharacteristic
343Dic5—42no—
344Dic5—122no—
345C24—31no—
346C22×C4—21no—
347C22×C4—31no—
348C22×C4—32no—
349C22×C4—32no—
350C22×C4—61no—
351C22×C4—61no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4—61no—
355C22×C4—101no—
356C22×C4—301no—
357C22×C4C2×D3×D511yescharacteristic
358C2×C8—52no—
359C2×C8—101no—
360C2×C8—101no—
361C2×C8—152no—
362C2×C8—301no—
363C2×C8—301no—
364C4⋊C4—21no—
365C4⋊C4—21no—
366C4⋊C4—52no—
367C4⋊C4—61no—
368C4⋊C4—61no—
369C4⋊C4—101no—
370C4⋊C4—152no—
371C4⋊C4—301no—
372C22⋊C4—122no—
373C22⋊C4—304no—
374C42—304no—
375C3×C5#185411yescharacteristic, complemented, Hall
376C22×C3C2×#68311yescharacteristic
377C22×C3#407811yescharacteristic
378C22×C3#408111yescharacteristic
379C22×C3#408311yescharacteristic
380C22×C3#408811yescharacteristic
381C22×C3#409611yescharacteristic
382C22×C3#409611yescharacteristic
383C2×D3—22no—
384C2×D3—22no—
385C2×D3—22no—
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—41no—
389C2×D3—41no—
390C3×C4—81no—
391C3×C4—202no—
392C3×C4#402411yescharacteristic
393C3×C4#402411yescharacteristic
394C3×C4#402711yescharacteristic
395C3×C4#402711yescharacteristic
396Dic3—22no—
397Dic3—81no—
398Dic3—202no—
399C2×C5—122no—
400C2×C5#466811yescharacteristic
401C2×C5#477911yescharacteristic
402C2×C5#478111yescharacteristic
403C2×C5#480811yescharacteristic
404C2×C5#481511yescharacteristic
405C2×C5#486011yescharacteristic
406C2×C5#488111yescharacteristic
407C23—32no—
408C23—61no—
409C23—61no—
410C23—61no—
411C23—61no—
412C23—61no—
413C23—61no—
414C23D3×C22⋊D511yescharacteristic
415C2×C4—32no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—41no—
419C2×C4—61no—
420C2×C4—61no—
421C2×C4—62no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—102no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—121no—
429C2×C4—201no—
430C2×C4—201no—
431C2×C4—302no—
432C2×C4—601no—
433C2×C4—601no—
434C2×C4D3×Dic1011yescharacteristic
435C2×C4C4×D3×D511yescharacteristic
436C2×C4D5×D1211yescharacteristic
437C2×C4#677711yescharacteristic
438C2×C4#678011yescharacteristic
439C2×C4#678211yescharacteristic
440C8—102no—
441C8—302no—
442C2×C3#6523511yescharacteristic
443C2×C3#6525311yescharacteristic
444C2×C3#6528711yescharacteristic
445C2×C3#6532411yescharacteristic
446C2×C3#6532611yescharacteristic
447C2×C3#6533411yescharacteristic
448C2×C3#6533611yescharacteristic
449D3—42no—
450C5#6887611yescharacteristic, complemented, Sylow
451C22—62no—
452C22—62no—
453C22—62no—
454C22—121no—
455C22—121no—
456C22—121no—
457C22—121no—
458C22D3×#68311yescharacteristic
459C22#9147511yescharacteristic
460C22#9149411yescharacteristic
461C22#9149511yescharacteristic
462C22#9151711yescharacteristic
463C22#9152011yescharacteristic
464C22#9155511yescharacteristic
465C4—62no—
466C4—81no—
467C4—202no—
468C4—241no—
469C4—602no—
470C4#9140511yescharacteristic
471C4#9141711yescharacteristic
472C4#9143611yescharacteristic
473C4#9144211yescharacteristic
474C3#1060029911yescharacteristic, complemented, Sylow
475C2—122no—
476C2#1174743711yescharacteristic
477C2#1174745411yescharacteristic
478C2#1174751511yescharacteristic
479C2#1174751611yescharacteristic
480C2#1174889311yescharacteristic
481C2#1174896811yescharacteristic
482C2#1174921211yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC23×C5×D3D4
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1854
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#90989C2semidirect
4. C2×#90985C2semidirect
6. #11746350C2semidirect
7. C3×#64749C2semidirect
24. (C2×D3)⋊#168C4semidirect
32. #64749D3semidirect
375. C3×C5#1854semidirect
450. C5#68876semidirect
474. C3#10600299semidirect

Maximal subgroups

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

subgroupindex
C2×#913382
C5×#49872
C2×#909892
C2×#909852
C2×(C2×D3)⋊#1682
#117463502
C3×#647492
#106002993
#688765