Finite Group Databasebeta

← #14319946

Subgroups — #14319946

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C4×D5C211yesmaximal, characteristic
2C2×#91357C212yesmaximal, complemented
3C4×#6719C211yesmaximal, characteristic, complemented
4C4×C5×#217C211yesmaximal, characteristic, complemented
5#11749506C212yesmaximal, complemented
6#11749488C212yesmaximal
7#11748738C212yesmaximal, complemented
8#11748737C212yesmaximal, complemented
9C4×#6665C212yesmaximal, complemented
10#10605292—31nomaximal, Hall
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×Dic5C2211yescharacteristic
14C22×C3×C4×D5—28no—
15C22×C3×C4×D5C418yescomplemented
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C2×#6719C2212yes—
21C2×C4×Dic15C2212yescomplemented
22C2×C5×#217C2212yes—
23C2×C4×C5×Dic3C2212yescomplemented
24C2×#6668C2214yescomplemented
25C2×#6665C2214yes—
26C2×#6665C2214yes—
27#91357—28no—
28#91115C2212yescomplemented
29C5×C3⋊#95C2212yescomplemented
30#90994C2214yescomplemented
31#84027—51nomaximal, Hall
32C23×C4×D5D311yescharacteristic
33C2×#4018—32no—
34C4×C5×C22⋊C4—31no—
35C4×C22⋊Dic5—31no—
36#65244—32no—
37#65231—32no—
38C4×#685—32no—
39#64956—32no—
40#64953—32no—
41C24×C3×C5C2311yescharacteristic
42C23×C3×D5—24no—
43C23×C3×D5—24no—
44C23×C3×D5—24no—
45C23×C3×D5C2×C414yes—
46C23×C3×D5C2311yescharacteristic
47C23×C3×D5C2311yescharacteristic
48C22×C3×C4×C5—24no—
49C22×C3×C4×C5C2×C414yes—
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2314yes—
53C22×C5×Dic3C2314yes—
54C22×C3×Dic5—24no—
55C22×C3×Dic5C2×C414yes—
56C22×C3×Dic5C2311yescharacteristic
57C22×C3×Dic5C2311yescharacteristic
58C2×C3×C4×D5—24no—
59C2×C3×C4×D5—24no—
60C2×C3×C4×D5—24no—
61C2×C3×C4×D5—232no—
62C2×C3×C4×D5C2×C414yes—
63C2×C3×C4×D5C2×C414yes—
64C2×C3×C4×D5C2×C414yes—
65C2×C3×C4×D5C2×C414yes—
66C2×C3×C4×D5D418yes—
67#6719—24no—
68C4×Dic15—24no—
69C5×#217—24no—
70C4×C5×Dic3—24no—
71#6668—28no—
72#6665—28no—
73#6665—28no—
74C24×C3×C4—51no—
75C2×#926—52no—
76#5247—52no—
77#5212—52no—
78#5212—52no—
79#5211—52no—
80C4×#217—51no—
81C4×#217—52no—
82C4×#217D511yescharacteristic, complemented
83C24×D5C2×D311yescharacteristic
84C23×C4×C5C2×D311yescharacteristic
85C23×Dic5C2×D311yescharacteristic
86C22×C4×D5—28no—
87C22×C4×D5Dic318yescomplemented
88C22×C4×D5C2×D311yescharacteristic
89C22×C4×D5C2×D311yescharacteristic
90C22×C4×D5C2×D311yescharacteristic
91C22×C4×D5C2×D311yescharacteristic
92C2×C5×C22⋊C4—32no—
93C2×C42×C5—32no—
94C2×C22⋊Dic5—32no—
95C2×#685—34no—
96C2×#685—34no—
97C2×#683—34no—
98C2×C4×Dic5—32no—
99#4018—68no—
100C5×#95—32no—
101#3963—32no—
102#3963—34no—
103#2280—151noSylow
104C23×C3×C5—22no—
105C23×C3×C5—22no—
106C23×C3×C5C22×C412yes—
107C23×C3×C5#4114yes—
108C23×C3×C5C2411yescharacteristic
109C22×C3×D5—232no—
110C22×C3×D5—28no—
111C22×C3×D5—22no—
112C22×C3×D5—22no—
113C22×C3×D5—22no—
114C22×C3×D5—22no—
115C22×C3×D5—28no—
116C22×C3×D5—28no—
117C22×C3×D5C22×C412yes—
118C22×C3×D5C22×C412yes—
119C22×C3×D5C2×D414yes—
120C22×C3×D5#4114yes—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—28no—
123C2×C3×C4×C5C22×C412yes—
124C2×C3×C4×C5C22×C412yes—
125C2×C3×C4×C5C2×D414yes—
126C2×Dic15—24no—
127C2×Dic15—24no—
128C2×Dic15—24no—
129C2×C5×Dic3—24no—
130C2×C5×Dic3—24no—
131C2×C5×Dic3—24no—
132C2×C3×Dic5—22no—
133C2×C3×Dic5—28no—
134C2×C3×Dic5C22×C412yes—
135C2×C3×Dic5C22×C412yes—
136C2×C3×Dic5C2×D414yes—
137C3×C4×D5—28no—
138C3×C4×D5—28no—
139C3×C4×D5—28no—
140C3×C4×D5C22⋊C4116yescomplemented
141C25×C3—51no—
142C23×C3×C4—51no—
143C23×C3×C4—51no—
144C23×C3×C4—58no—
145C23×C3×C4—51no—
146C23×C3×C4—51no—
147C23×C3×C4—51no—
148C23×C3×C4—108no—
149C23×C3×C4C2×D511yescharacteristic
150C2×#217—52no—
151C2×#217—54no—
152C2×#217—54no—
153C2×#217C2×D512yes—
154#926—108no—
155C2×C4⋊Dic3—54no—
156C2×C4×Dic3—52no—
157C2×C4×Dic3C2×D512yescomplemented
158C3⋊#95—52no—
159C3⋊#95—54no—
160C3⋊#95C2×D512yescomplemented
161C24×C5C22×D311yescharacteristic
162C23×D5—24no—
163C23×D5—24no—
164C23×D5—24no—
165C23×D5C2×Dic314yes—
166C23×D5C22×D311yescharacteristic
167C23×D5C22×D311yescharacteristic
168C22×C4×C5—24no—
169C22×C4×C5—34no—
170C22×C4×C5C2×Dic314yes—
171C22×C4×C5C22×D311yescharacteristic
172C22×C4×C5C22×D311yescharacteristic
173C22×Dic5—24no—
174C22×Dic5—34no—
175C22×Dic5C2×Dic314yes—
176C22×Dic5C22×D311yescharacteristic
177C22×Dic5C22×D311yescharacteristic
178C2×C4×D5—24no—
179C2×C4×D5—24no—
180C2×C4×D5—24no—
181C2×C4×D5—232no—
182C2×C4×D5C2×Dic314yes—
183C2×C4×D5C2×Dic314yes—
184C2×C4×D5C2×Dic314yes—
185C2×C4×D5C2×Dic314yes—
186C2×C4×D5#6718yes—
187C5×C22⋊C4—64no—
188C42×C5—64no—
189C22⋊Dic5—64no—
190#685—68no—
191#685—68no—
192#683—68no—
193C4×Dic5—64no—
194C24×C4—51no—
195C2×#117—152no—
196#381—152no—
197#380—152no—
198#380—152no—
199#379—152no—
200C4×C22⋊C4—31no—
201C4×C22⋊C4—152no—
202C4×C22⋊C4—151no—
203C22×C3×C5—22no—
204C22×C3×C5—22no—
205C22×C3×C5—28no—
206C22×C3×C5#11714yescomplemented
207C22×C3×C5C23×C411yescharacteristic
208C22×C3×C5C22×D412yes—
209C22×C3×C5C2×#4112yes—
210C22×C3×C5C2×#4112yes—
211C2×C3×D5—232no—
212C2×C3×D5—22no—
213C2×C3×D5—22no—
214C2×C3×D5—22no—
215C2×C3×D5—22no—
216C2×C3×D5—28no—
217C2×C3×D5—28no—
218C2×C3×D5C2×C22⋊C414yes—
219C2×C3×D5#11714yescomplemented
220C3×C4×C5—22no—
221C3×C4×C5C2×C22⋊C414yes—
222Dic15—44no—
223C3×Dic5—22no—
224C3×Dic5C2×C22⋊C414yes—
225C5×Dic3—44no—
226C24×C3—51no—
227C24×C3—51no—
228C24×C3—54no—
229C24×C3—104no—
230C24×C3—104no—
231C24×C3—104no—
232C24×C3C22×D511yescharacteristic
233C22×C3×C4—24no—
234C22×C3×C4—51no—
235C22×C3×C4—54no—
236C22×C3×C4—58no—
237C22×C3×C4—54no—
238C22×C3×C4—51no—
239C22×C3×C4—54no—
240C22×C3×C4—54no—
241C22×C3×C4—54no—
242C22×C3×C4—104no—
243C22×C3×C4—1032no—
244C22×C3×C4—104no—
245C22×C3×C4—104no—
246C22×C3×C4—104no—
247C22×C3×C4C4×D514yes—
248C22×C3×C4C22×D511yescharacteristic
249C22×C3×C4C22×D511yescharacteristic
250C22×Dic3—54no—
251C22×Dic3C22×D514yes—
252#217—24no—
253#217—108no—
254#217—108no—
255#217—104no—
256C4⋊Dic3—108no—
257C4×Dic3—24no—
258C4×Dic3—104no—
259C23×C5—22no—
260C23×C5—22no—
261C23×C5#23514yes—
262C23×C5C22×Dic312yes—
263C23×C5C23×D311yescharacteristic
264C22×D5—232no—
265C22×D5—28no—
266C22×D5—22no—
267C22×D5—22no—
268C22×D5—22no—
269C22×D5—22no—
270C22×D5—28no—
271C22×D5—28no—
272C22×D5#23514yes—
273C22×D5C22×Dic312yes—
274C22×D5C22×Dic312yes—
275C22×D5C2×#6714yes—
276C2×C4×C5—22no—
277C2×C4×C5—28no—
278C2×C4×C5—64no—
279C2×C4×C5—64no—
280C2×C4×C5—64no—
281C2×C4×C5C22×Dic312yes—
282C2×C4×C5C22×Dic312yes—
283C2×C4×C5C2×#6714yes—
284C2×Dic5—22no—
285C2×Dic5—28no—
286C2×Dic5—64no—
287C2×Dic5—64no—
288C2×Dic5—64no—
289C2×Dic5C22×Dic312yes—
290C2×Dic5C22×Dic312yes—
291C2×Dic5C2×#6714yes—
292C4×D5—28no—
293C4×D5—28no—
294C4×D5—28no—
295C4×D5#217116yescomplemented
296C25—51no—
297C23×C4—51no—
298C23×C4—51no—
299C23×C4—58no—
300C23×C4—51no—
301C23×C4—51no—
302C23×C4—51no—
303C23×C4—108no—
304C23×C4D3×D511yescharacteristic
305#117—308no—
306C2×C4⋊C4—154no—
307C2×C22⋊C4—32no—
308C2×C22⋊C4—154no—
309C2×C22⋊C4—154no—
310C2×C22⋊C4—152no—
311C2×C42—32no—
312C2×C42—152no—
313#95—32no—
314#95—154no—
315#95—152no—
316C2×C3×C5—24no—
317C2×C3×C5C22×C22⋊C411yescharacteristic
318C2×C3×C5C2×#11711yescharacteristic
319C2×C3×C5C2×#11711yescharacteristic
320C2×C3×C5#52514yes—
321C3×D5—24no—
322C3×D5—24no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3—52no—
326C23×C3—52no—
327C23×C3—54no—
328C23×C3—54no—
329C23×C3—108no—
330C23×C3—108no—
331C23×C3—1032no—
332C23×C3—102no—
333C23×C3—102no—
334C23×C3—102no—
335C23×C3—102no—
336C23×C3—108no—
337C23×C3C2×C4×D512yes—
338C23×C3#70914yes—
339C23×C3C23×D511yescharacteristic
340C2×C3×C4—22no—
341C2×C3×C4—28no—
342C2×C3×C4—52no—
343C2×C3×C4—54no—
344C2×C3×C4—516no—
345C2×C3×C4—52no—
346C2×C3×C4—108no—
347C2×C3×C4—108no—
348C2×C3×C4—108no—
349C2×C3×C4—102no—
350C2×C3×C4—108no—
351C2×C3×C4C2×C4×D512yes—
352C2×C3×C4C2×C4×D512yes—
353C2×C3×C4D4×D514yes—
354C2×Dic3—24no—
355C2×Dic3—24no—
356C2×Dic3—24no—
357C2×Dic3—104no—
358C2×Dic3—104no—
359C2×Dic3—104no—
360C22×C5—22no—
361C22×C5—28no—
362C22×C5—22no—
363C22×C5#92614yescomplemented
364C22×C5C2×#23512yes—
365C22×C5C2×#23512yes—
366C22×C5C23×Dic311yescharacteristic
367C22×C5C22×#6712yes—
368C2×D5—232no—
369C2×D5—22no—
370C2×D5—22no—
371C2×D5—22no—
372C2×D5—28no—
373C2×D5—28no—
374C2×D5—22no—
375C2×D5#92614yescomplemented
376C2×D5C2×#21714yes—
377C4×C5—22no—
378C4×C5—124no—
379C4×C5C2×#21714yes—
380Dic5—22no—
381Dic5—124no—
382Dic5C2×#21714yes—
383C24—51no—
384C24—51no—
385C24—54no—
386C24—104no—
387C24—104no—
388C24—104no—
389C24C2×D3×D511yescharacteristic
390C22×C4—24no—
391C22×C4—34no—
392C22×C4—51no—
393C22×C4—54no—
394C22×C4—58no—
395C22×C4—54no—
396C22×C4—51no—
397C22×C4—54no—
398C22×C4—54no—
399C22×C4—54no—
400C22×C4—104no—
401C22×C4—1032no—
402C22×C4—104no—
403C22×C4—104no—
404C22×C4—104no—
405C22×C4—154no—
406C22×C4D5×Dic314yes—
407C22×C4C2×D3×D511yescharacteristic
408C22×C4C2×D3×D511yescharacteristic
409C4⋊C4—308no—
410C22⋊C4—64no—
411C22⋊C4—308no—
412C22⋊C4—308no—
413C22⋊C4—304no—
414C42—64no—
415C42—304no—
416C3×C5#228011yescharacteristic, complemented, Hall
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—28no—
420C22×C3—54no—
421C22×C3—54no—
422C22×C3—1032no—
423C22×C3—102no—
424C22×C3—102no—
425C22×C3—102no—
426C22×C3—102no—
427C22×C3—108no—
428C22×C3—108no—
429C22×C3#401814yescomplemented
430C22×C3C22×C4×D511yescharacteristic
431C22×C3C2×#70912yes—
432C22×C3C2×D4×D512yes—
433C22×C3D5×#4112yes—
434C3×C4—22no—
435C3×C4—54no—
436C3×C4—102no—
437C3×C4D5×C22⋊C414yes—
438Dic3—44no—
439Dic3—204no—
440C2×C5—24no—
441C2×C5C2×#92611yescharacteristic
442C2×C5C2×#92611yescharacteristic
443C2×C5#579114yes—
444C2×C5C22×#21711yescharacteristic
445D5—24no—
446D5—24no—
447C23—22no—
448C23—22no—
449C23—54no—
450C23—52no—
451C23—52no—
452C23—54no—
453C23—108no—
454C23—108no—
455C23—1032no—
456C23—102no—
457C23—102no—
458C23—102no—
459C23—102no—
460C23—108no—
461C23#677114yes—
462C23C2×D5×Dic312yes—
463C23C22×D3×D511yescharacteristic
464C2×C4—22no—
465C2×C4—28no—
466C2×C4—52no—
467C2×C4—54no—
468C2×C4—516no—
469C2×C4—52no—
470C2×C4—64no—
471C2×C4—64no—
472C2×C4—64no—
473C2×C4—108no—
474C2×C4—108no—
475C2×C4—108no—
476C2×C4—102no—
477C2×C4—108no—
478C2×C4—304no—
479C2×C4—304no—
480C2×C4—304no—
481C2×C4C2×D5×Dic312yes—
482C2×C4C2×D5×Dic312yes—
483C2×C4D5×#6714yes—
484C2×C3—24no—
485C2×C3—104no—
486C2×C3—104no—
487C2×C3C2×#401811yescharacteristic
488C2×C3C2×D5×C22⋊C411yescharacteristic
489C2×C3D5×#11711yescharacteristic
490C2×C3#6588114yes—
491C5#8402711yescharacteristic, complemented, Sylow
492C22—28no—
493C22—22no—
494C22—22no—
495C22—54no—
496C22—54no—
497C22—1032no—
498C22—108no—
499C22—108no—
500C22—102no—
501C22—102no—
502C22—102no—
503C22—102no—
504C22#9135714yescomplemented
505C22C2×#677112yes—
506C22D5×#23512yes—
507C22C22×D5×Dic311yescharacteristic
508C22C2×D5×#6712yes—
509C4—22no—
510C4—54no—
511C4—102no—
512C4—124no—
513C4—604no—
514C4D5×#21714yes—
515C3#1060529211yescharacteristic, complemented, Sylow
516C2—24no—
517C2—104no—
518C2—104no—
519C2C2×#9135711yescharacteristic
520C2D5×#92611yescharacteristic
521C2#1175452514yes—
522C2C2×D5×#21711yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×#91357C2semidirect
3. C4×#6719C2semidirect
4. C4×C5×#217C2semidirect
5. #11749506C2semidirect
7. #11748738C2semidirect
8. #11748737C2semidirect
9. C4×#6665C2semidirect
15. C22×C3×C4×D5C4semidirect
21. C2×C4×Dic15C22semidirect
23. C2×C4×C5×Dic3C22semidirect
24. C2×#6668C22semidirect
28. #91115C22semidirect
29. C5×C3⋊#95C22semidirect
30. #90994C22semidirect
82. C4×#217D5semidirect
87. C22×C4×D5Dic3semidirect
140. C3×C4×D5C22⋊C4semidirect
157. C2×C4×Dic3C2×D5semidirect
160. C3⋊#95C2×D5semidirect
206. C22×C3×C5#117semidirect
219. C2×C3×D5#117semidirect
295. C4×D5#217semidirect
363. C22×C5#926semidirect
375. C2×D5#926semidirect
416. C3×C5#2280semidirect
429. C22×C3#4018semidirect
491. C5#84027semidirect
504. C22#91357semidirect
515. C3#10605292semidirect

Maximal subgroups

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

subgroupindex
C23×C3×C4×D52
C2×#913572
C4×#67192
C4×C5×#2172
#117495062
#117494882
#117487382
#117487372
C4×#66652
#106052923
#840275