Finite Group Databasebeta

← #14319913

Subgroups — #14319913

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×C4×D15C211yesmaximal, characteristic
2C2×#91761C212yesmaximal, complemented
3C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
4C4×#6719C211yesmaximal, characteristic, complemented
5#11751056C212yesmaximal
6#11751043C212yesmaximal, complemented
7C4×#6714C212yesmaximal, complemented
8#11750768C212yesmaximal, complemented
9#11750765C212yesmaximal, complemented
10#10605292—31nomaximal, Hall
11C24×D15C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×Dic15C2211yescharacteristic
14C22×C4×D15—28no—
15C22×C4×D15C418yescomplemented
16C22×C4×D15C2211yescharacteristic
17C22×C4×D15C2211yescharacteristic
18C22×C4×D15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2212yes—
21C2×C3×C42×C5C2212yescomplemented
22C2×#6719C2212yes—
23C2×#6714C2214yes—
24C2×#6714C2214yes—
25C2×#6712C2214yescomplemented
26C2×C4×Dic15C2212yescomplemented
27#91761—28no—
28C3×C5×#95C2212yescomplemented
29#91115C2212yescomplemented
30#91115C2214yescomplemented
31#73561—51nomaximal, Hall
32C23×C4×D5—31no—
33C2×#4018—32no—
34C4×C5×C22⋊C4D311yescharacteristic, complemented
35C4×C22⋊Dic5—31no—
36#65244—32no—
37#65231—32no—
38C4×#685—32no—
39#64956—32no—
40#64953—32no—
41C24×C3×C5C2311yescharacteristic
42C23×D15—24no—
43C23×D15—24no—
44C23×D15—24no—
45C23×D15C2×C414yes—
46C23×D15C2311yescharacteristic
47C23×D15C2311yescharacteristic
48C22×C3×C4×C5—24no—
49C22×C3×C4×C5C2×C414yes—
50C22×C3×C4×C5C2314yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15—24no—
54C22×Dic15C2×C414yes—
55C22×Dic15C2314yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C2×C4×D15—24no—
59C2×C4×D15—24no—
60C2×C4×D15—24no—
61C2×C4×D15—232no—
62C2×C4×D15C2×C414yes—
63C2×C4×D15C2×C414yes—
64C2×C4×D15C2×C414yes—
65C2×C4×D15C2×C414yes—
66C2×C4×D15D418yes—
67C3×C5×C22⋊C4—24no—
68C3×C42×C5—24no—
69#6719—24no—
70#6714—28no—
71#6714—28no—
72#6712—28no—
73C4×Dic15—24no—
74C23×C4×D3—51no—
75C2×#872—52no—
76C3×C4×C22⋊C4D511yescharacteristic, complemented
77C4×#217—51no—
78#4955—52no—
79#4942—52no—
80C4×(C2×D3)⋊C4—52no—
81#4667—52no—
82#4664—52no—
83C24×D5—31no—
84C23×C4×C5C2×D311yescharacteristic
85C23×Dic5—31no—
86C22×C4×D5—31no—
87C22×C4×D5—38no—
88C22×C4×D5—31no—
89C22×C4×D5—31no—
90C22×C4×D5—31no—
91C22×C4×D5—68no—
92C2×C5×C22⋊C4C2×D312yes—
93C2×C42×C5C2×D312yescomplemented
94C2×C22⋊Dic5—32no—
95C2×#685—34no—
96C2×#685—34no—
97C2×#683—34no—
98C2×C4×Dic5—32no—
99#4018—68no—
100C5×#95C2×D312yescomplemented
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×D15—232no—
110C22×D15—28no—
111C22×D15—22no—
112C22×D15—22no—
113C22×D15—22no—
114C22×D15—22no—
115C22×D15—28no—
116C22×D15—28no—
117C22×D15C22×C412yes—
118C22×D15C22×C412yes—
119C22×D15C2×D414yes—
120C22×D15#4114yes—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—28no—
123C2×C3×C4×C5—24no—
124C2×C3×C4×C5—24no—
125C2×C3×C4×C5—24no—
126C2×C3×C4×C5C22×C412yes—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C2×D414yes—
129C2×Dic15—22no—
130C2×Dic15—28no—
131C2×Dic15—24no—
132C2×Dic15—24no—
133C2×Dic15—24no—
134C2×Dic15C22×C412yes—
135C2×Dic15C22×C412yes—
136C2×Dic15C2×D414yes—
137C4×D15—28no—
138C4×D15—28no—
139C4×D15—28no—
140C4×D15C22⋊C4116yescomplemented
141C24×D3—51no—
142C23×C3×C4C2×D511yescharacteristic
143C23×Dic3—51no—
144C22×C4×D3—51no—
145C22×C4×D3—58no—
146C22×C4×D3—51no—
147C22×C4×D3—51no—
148C22×C4×D3—51no—
149C22×C4×D3—108no—
150C2×C3×C22⋊C4C2×D512yes—
151C2×C3×C42C2×D512yescomplemented
152C2×#217—52no—
153C2×(C2×D3)⋊C4—54no—
154C2×(C2×D3)⋊C4—54no—
155C2×Dic3⋊C4—54no—
156C2×C4×Dic3—52no—
157#872—108no—
158C3×#95C2×D512yescomplemented
159C3⋊#95—52no—
160C3⋊#95—54no—
161C24×C5C22×D311yescharacteristic
162C23×D5—31no—
163C23×D5—31no—
164C23×D5—34no—
165C23×D5—64no—
166C23×D5—64no—
167C23×D5—64no—
168C22×C4×C5—24no—
169C22×C4×C5C4×D314yes—
170C22×C4×C5C22×D314yes—
171C22×C4×C5C22×D311yescharacteristic
172C22×C4×C5C22×D311yescharacteristic
173C22×Dic5—31no—
174C22×Dic5—34no—
175C22×Dic5—31no—
176C22×Dic5—34no—
177C22×Dic5—64no—
178C2×C4×D5—34no—
179C2×C4×D5—38no—
180C2×C4×D5—34no—
181C2×C4×D5—34no—
182C2×C4×D5—34no—
183C2×C4×D5—632no—
184C2×C4×D5—64no—
185C2×C4×D5—64no—
186C2×C4×D5—64no—
187C5×C22⋊C4—24no—
188C42×C5—24no—
189C22⋊Dic5—64no—
190#685—68no—
191#685—68no—
192#683—68no—
193C4×Dic5—64no—
194C24×C4—151no—
195C2×#117—152no—
196#381—152no—
197#380—152no—
198#380—152no—
199#379—152no—
200C4×C22⋊C4—151no—
201C4×C22⋊C4—152no—
202C4×C22⋊C4D1511yescharacteristic, complemented
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×D15—232no—
212C2×D15—22no—
213C2×D15—22no—
214C2×D15—22no—
215C2×D15—22no—
216C2×D15—28no—
217C2×D15—28no—
218C2×D15C2×C22⋊C414yes—
219C2×D15#11714yescomplemented
220C3×C4×C5—22no—
221C3×C4×C5—44no—
222C3×C4×C5C2×C22⋊C414yes—
223Dic15—22no—
224Dic15—44no—
225Dic15C2×C22⋊C414yes—
226C24×C3C22×D511yescharacteristic
227C23×D3—51no—
228C23×D3—51no—
229C23×D3—54no—
230C23×D3—104no—
231C23×D3—104no—
232C23×D3—104no—
233C22×C3×C4—24no—
234C22×C3×C4C4×D514yes—
235C22×C3×C4C22×D514yes—
236C22×C3×C4C22×D511yescharacteristic
237C22×C3×C4C22×D511yescharacteristic
238C22×Dic3—51no—
239C22×Dic3—54no—
240C22×Dic3—51no—
241C22×Dic3—54no—
242C22×Dic3—104no—
243C2×C4×D3—54no—
244C2×C4×D3—58no—
245C2×C4×D3—54no—
246C2×C4×D3—54no—
247C2×C4×D3—54no—
248C2×C4×D3—1032no—
249C2×C4×D3—104no—
250C2×C4×D3—104no—
251C2×C4×D3—104no—
252C3×C22⋊C4—24no—
253C3×C42—24no—
254#217—104no—
255(C2×D3)⋊C4—108no—
256(C2×D3)⋊C4—108no—
257Dic3⋊C4—108no—
258C4×Dic3—104no—
259C23×C5—22no—
260C23×C5—22no—
261C23×C5C2×C4×D312yes—
262C23×C5#23514yes—
263C23×C5C23×D311yescharacteristic
264C22×D5—32no—
265C22×D5—32no—
266C22×D5—34no—
267C22×D5—34no—
268C22×D5—68no—
269C22×D5—68no—
270C22×D5—632no—
271C22×D5—68no—
272C22×D5—62no—
273C22×D5—62no—
274C22×D5—62no—
275C22×D5—62no—
276C2×C4×C5—22no—
277C2×C4×C5—28no—
278C2×C4×C5—24no—
279C2×C4×C5—24no—
280C2×C4×C5—24no—
281C2×C4×C5C2×C4×D312yes—
282C2×C4×C5C2×C4×D312yes—
283C2×C4×C5D3×D414yes—
284C2×Dic5—32no—
285C2×Dic5—34no—
286C2×Dic5—32no—
287C2×Dic5—68no—
288C2×Dic5—62no—
289C2×Dic5—64no—
290C2×Dic5—64no—
291C2×Dic5—64no—
292C4×D5—316no—
293C4×D5—68no—
294C4×D5—68no—
295C4×D5—68no—
296C25—151no—
297C23×C4—151no—
298C23×C4—151no—
299C23×C4—158no—
300C23×C4—151no—
301C23×C4—151no—
302C23×C4—151no—
303C23×C4—308no—
304C23×C4C2×D1511yescharacteristic
305#117—308no—
306C2×C4⋊C4—154no—
307C2×C22⋊C4—152no—
308C2×C22⋊C4—154no—
309C2×C22⋊C4—154no—
310C2×C22⋊C4C2×D1512yes—
311C2×C42—152no—
312C2×C42C2×D1512yescomplemented
313#95—154no—
314#95—152no—
315#95C2×D1512yescomplemented
316C2×C3×C5—24no—
317C2×C3×C5C22×C22⋊C411yescharacteristic
318C2×C3×C5C2×#11711yescharacteristic
319C2×C3×C5C2×#11711yescharacteristic
320C2×C3×C5#52514yes—
321D15—24no—
322D15—24no—
323C23×C3—22no—
324C23×C3—22no—
325C23×C3C2×C4×D512yes—
326C23×C3#70914yes—
327C23×C3C23×D511yescharacteristic
328C22×D3—52no—
329C22×D3—52no—
330C22×D3—54no—
331C22×D3—54no—
332C22×D3—108no—
333C22×D3—108no—
334C22×D3—1032no—
335C22×D3—102no—
336C22×D3—102no—
337C22×D3—102no—
338C22×D3—102no—
339C22×D3—108no—
340C2×C3×C4—22no—
341C2×C3×C4—28no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4C2×C4×D512yes—
346C2×C3×C4C2×C4×D512yes—
347C2×C3×C4D4×D514yes—
348C2×Dic3—52no—
349C2×Dic3—54no—
350C2×Dic3—52no—
351C2×Dic3—108no—
352C2×Dic3—102no—
353C2×Dic3—104no—
354C2×Dic3—104no—
355C2×Dic3—104no—
356C4×D3—516no—
357C4×D3—108no—
358C4×D3—108no—
359C4×D3—108no—
360C22×C5—22no—
361C22×C5—22no—
362C22×C5—28no—
363C22×C5#87214yescomplemented
364C22×C5C22×C4×D311yescharacteristic
365C22×C5C2×#23512yes—
366C22×C5C2×D3×D412yes—
367C22×C5D3×#4112yes—
368C2×D5—34no—
369C2×D5—34no—
370C2×D5—632no—
371C2×D5—62no—
372C2×D5—62no—
373C2×D5—62no—
374C2×D5—62no—
375C2×D5—68no—
376C2×D5—68no—
377C4×C5—22no—
378C4×C5—44no—
379C4×C5D3×C22⋊C414yes—
380Dic5—34no—
381Dic5—62no—
382Dic5—124no—
383C24—151no—
384C24—151no—
385C24—154no—
386C24—304no—
387C24—304no—
388C24—304no—
389C24C22×D1511yescharacteristic
390C22×C4—24no—
391C22×C4—151no—
392C22×C4—154no—
393C22×C4—158no—
394C22×C4—154no—
395C22×C4—151no—
396C22×C4—154no—
397C22×C4—154no—
398C22×C4—154no—
399C22×C4—154no—
400C22×C4—304no—
401C22×C4—3032no—
402C22×C4—304no—
403C22×C4—304no—
404C22×C4—304no—
405C22×C4C4×D1514yes—
406C22×C4C22×D1514yes—
407C22×C4C22×D1511yescharacteristic
408C22×C4C22×D1511yescharacteristic
409C4⋊C4—308no—
410C22⋊C4—24no—
411C22⋊C4—308no—
412C22⋊C4—308no—
413C22⋊C4—304no—
414C42—24no—
415C42—304no—
416C3×C5#228011yescharacteristic, complemented, Hall
417C22×C3—22no—
418C22×C3—22no—
419C22×C3—28no—
420C22×C3#401814yescomplemented
421C22×C3C22×C4×D511yescharacteristic
422C22×C3C2×#70912yes—
423C22×C3C2×D4×D512yes—
424C22×C3D5×#4112yes—
425C2×D3—54no—
426C2×D3—54no—
427C2×D3—1032no—
428C2×D3—102no—
429C2×D3—102no—
430C2×D3—102no—
431C2×D3—102no—
432C2×D3—108no—
433C2×D3—108no—
434C3×C4—22no—
435C3×C4—44no—
436C3×C4D5×C22⋊C414yes—
437Dic3—54no—
438Dic3—102no—
439Dic3—204no—
440C2×C5—24no—
441C2×C5C2×#87211yescharacteristic
442C2×C5C2×D3×C22⋊C411yescharacteristic
443C2×C5D3×#11711yescharacteristic
444C2×C5#554714yes—
445D5—64no—
446D5—64no—
447C23—22no—
448C23—22no—
449C23—152no—
450C23—152no—
451C23—154no—
452C23—154no—
453C23—308no—
454C23—308no—
455C23—3032no—
456C23—308no—
457C23—302no—
458C23—302no—
459C23—302no—
460C23—302no—
461C23C2×C4×D1512yes—
462C23#681714yes—
463C23C23×D1511yescharacteristic
464C2×C4—22no—
465C2×C4—28no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—152no—
470C2×C4—154no—
471C2×C4—1516no—
472C2×C4—152no—
473C2×C4—308no—
474C2×C4—308no—
475C2×C4—308no—
476C2×C4—302no—
477C2×C4—308no—
478C2×C4—304no—
479C2×C4—304no—
480C2×C4—304no—
481C2×C4C2×C4×D1512yes—
482C2×C4C2×C4×D1512yes—
483C2×C4D4×D1514yes—
484C2×C3—24no—
485C2×C3C2×#401811yescharacteristic
486C2×C3C2×D5×C22⋊C411yescharacteristic
487C2×C3D5×#11711yescharacteristic
488C2×C3#6588114yes—
489D3—104no—
490D3—104no—
491C5#7356111yescharacteristic, complemented, Sylow
492C22—28no—
493C22—22no—
494C22—22no—
495C22—154no—
496C22—154no—
497C22—3032no—
498C22—308no—
499C22—308no—
500C22—302no—
501C22—302no—
502C22—302no—
503C22—302no—
504C22#9176114yescomplemented
505C22C22×C4×D1511yescharacteristic
506C22C2×#681712yes—
507C22C2×D4×D1512yes—
508C22#41×D1512yes—
509C4—22no—
510C4—44no—
511C4—154no—
512C4—302no—
513C4—604no—
514C4C22⋊C4×D1514yes—
515C3#1060529211yescharacteristic, complemented, Sylow
516C2—24no—
517C2—304no—
518C2—304no—
519C2C2×#9176111yescharacteristic
520C2C2×C22⋊C4×D1511yescharacteristic
521C2D15×#11711yescharacteristic
522C2#1175630614yes—
subgroupG/H
centerC22×C4C22×D15
commutatorC22×C3×C5C23×C4
FrattiniC23C23×D15
FittingC3×C4×C5×C22⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC24×D15C22
hypercenterC4×C22⋊C4D15
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91761C2semidirect
3. C3×C4×C5×C22⋊C4C2semidirect
4. C4×#6719C2semidirect
6. #11751043C2semidirect
7. C4×#6714C2semidirect
8. #11750768C2semidirect
9. #11750765C2semidirect
15. C22×C4×D15C4semidirect
21. C2×C3×C42×C5C22semidirect
25. C2×#6712C22semidirect
26. C2×C4×Dic15C22semidirect
28. C3×C5×#95C22semidirect
29. #91115C22semidirect
30. #91115C22semidirect
34. C4×C5×C22⋊C4D3semidirect
76. C3×C4×C22⋊C4D5semidirect
93. C2×C42×C5C2×D3semidirect
100. C5×#95C2×D3semidirect
140. C4×D15C22⋊C4semidirect
151. C2×C3×C42C2×D5semidirect
158. C3×#95C2×D5semidirect
202. C4×C22⋊C4D15semidirect
206. C22×C3×C5#117semidirect
219. C2×D15#117semidirect
312. C2×C42C2×D15semidirect
315. #95C2×D15semidirect
363. C22×C5#872semidirect
416. C3×C5#2280semidirect
420. C22×C3#4018semidirect
491. C5#73561semidirect
504. C22#91761semidirect
515. C3#10605292semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D152
C2×#917612
C3×C4×C5×C22⋊C42
C4×#67192
#117510562
#117510432
C4×#67142
#117507682
#117507652
#106052923
#735615