Finite Group Databasebeta

← #14326421

Subgroups — #14326421

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91761C211yesmaximal, characteristic
2C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3#11751090C212yesmaximal
4#11751079C212yesmaximal, complemented
5C4×#6714C212yesmaximal
6#11751038C211yesmaximal, characteristic, complemented
7#11751034C212yesmaximal, complemented
8#11750765C211yesmaximal, characteristic
9D15×#95C211yesmaximal, characteristic
10#11750751C211yesmaximal, characteristic, complemented
11#11750749C211yesmaximal, characteristic, complemented
12#10605497—31nomaximal, Hall
13C22×C4×D15C2212yes—
14C22×C4×D15C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2212yes—
16C2×C3×C42×C5C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×#6714C2212yes—
19C2×#6714C2211yescharacteristic
20C2×#6714C2211yescharacteristic
21C2×#6712C2212yes—
22C2×#6712C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C4×Dic15C2212yes—
25C2×C4×Dic15C2211yescharacteristic
26#91761C418yescomplemented
27C3×C5×#95C2211yescharacteristic
28C3×C5×#95C2211yescharacteristic
29#91115C2211yescharacteristic
30#91115C2212yes—
31#91115C2211yescharacteristic
32#91115C2212yes—
33#91115C2212yes—
34#91115C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#73766—51nomaximal, Hall
38C2×#4018—31no—
39C4×C5×C4⋊C4D311yescharacteristic, complemented
40#65278—32no—
41#65267—32no—
42C4×#685—32no—
43#65226—31no—
44#65222—32no—
45#64953—31no—
46D5×#95—31no—
47#64939—31no—
48#64937—31no—
49C23×D15C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2312yes—
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2311yescharacteristic
59C22×Dic15C2311yescharacteristic
60C2×C4×D15—24no—
61C2×C4×D15—24no—
62C2×C4×D15—24no—
63C2×C4×D15—42no—
64C2×C4×D15C2×C414yes—
65C3×C5×C4⋊C4—24no—
66C3×C42×C5—42no—
67C3×C42×C5C2×C414yescomplemented
68#6714—24no—
69#6714C2×C414yes—
70#6714C2×C414yes—
71#6712—42no—
72#6712C2×C414yescomplemented
73#6712C2×C414yescomplemented
74C4×Dic15—24no—
75C4×Dic15C2×C414yescomplemented
76C2×#872—51no—
77C3×C4×C4⋊C4D511yescharacteristic, complemented
78#4989—52no—
79#4978—52no—
80C4×(C2×D3)⋊C4—52no—
81#4937—51no—
82#4933—52no—
83#4664—51no—
84D3×#95—51no—
85#4650—51no—
86#4648—51no—
87C22×C4×D5—31no—
88C22×C4×D5—32no—
89C2×C5×C4⋊C4C2×D312yes—
90C2×C42×C5C2×D312yes—
91C2×C42×C5C2×D311yescharacteristic
92C2×#685—31no—
93C2×#685—31no—
94C2×#685—32no—
95C2×#683—31no—
96C2×#683—31no—
97C2×#683—32no—
98C2×C4×Dic5—31no—
99C2×C4×Dic5—32no—
100#4018—38no—
101C5×#95C2×D311yescharacteristic
102C5×#95C2×D311yescharacteristic
103#3963—31no—
104#3963—32no—
105#3963—31no—
106#3963—32no—
107#3963—32no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#2343—151noSylow
112C23×C3×C5C2411yescharacteristic
113C22×D15—22no—
114C22×D15—21no—
115C22×D15—21no—
116C22×D15C22×C412yes—
117C22×D15#4114yes—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—21no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5C22×C412yes—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5#4114yes—
131C2×Dic15—22no—
132C2×Dic15—22no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15C22×C412yes—
142C2×Dic15C22×C412yes—
143C2×Dic15C22×C412yes—
144C4×D15—28no—
145C4×D15—48no—
146C22×C4×D3—51no—
147C22×C4×D3—52no—
148C2×C3×C4⋊C4C2×D512yes—
149C2×C3×C42C2×D512yes—
150C2×C3×C42C2×D511yescharacteristic
151C2×(C2×D3)⋊C4—51no—
152C2×(C2×D3)⋊C4—51no—
153C2×(C2×D3)⋊C4—52no—
154C2×Dic3⋊C4—51no—
155C2×Dic3⋊C4—51no—
156C2×Dic3⋊C4—52no—
157C2×C4×Dic3—51no—
158C2×C4×Dic3—52no—
159#872—58no—
160C3×#95C2×D511yescharacteristic
161C3×#95C2×D511yescharacteristic
162C3⋊#95—51no—
163C3⋊#95—52no—
164C3⋊#95—51no—
165C3⋊#95—52no—
166C3⋊#95—52no—
167C3⋊#95—52no—
168C3⋊#95—52no—
169C3⋊#95—52no—
170C23×D5—31no—
171C22×C4×C5C22×D312yes—
172C22×C4×C5C22×D311yescharacteristic
173C22×C4×C5C22×D311yescharacteristic
174C22×C4×C5C22×D311yescharacteristic
175C22×C4×C5C22×D312yes—
176C22×Dic5—31no—
177C22×Dic5—31no—
178C22×Dic5—31no—
179C22×Dic5—32no—
180C22×Dic5—32no—
181C2×C4×D5—34no—
182C2×C4×D5—64no—
183C2×C4×D5—64no—
184C2×C4×D5—64no—
185C2×C4×D5—122no—
186C5×C4⋊C4—24no—
187C42×C5—42no—
188C42×C5C4×D314yescomplemented
189#685—34no—
190#685—34no—
191#685—64no—
192#683—34no—
193#683—34no—
194#683—122no—
195C4×Dic5—34no—
196C4×Dic5—64no—
197C2×#117—151no—
198#387—152no—
199#387—152no—
200#385—152no—
201#383—151no—
202#382—151no—
203#381—151no—
204C4×C4⋊C4D1511yescharacteristic, complemented
205C4×C22⋊C4—152no—
206#376—151no—
207C2×#95—151no—
208C22×C3×C5C23×C411yescharacteristic
209C22×C3×C5C2×#4112yes—
210C22×C3×C5C2×#4112yes—
211C22×C3×C5H(5,𝔽2)11yescharacteristic
212C22×C3×C52−1+411yescharacteristic
213C2×D15—22no—
214C2×D15—22no—
215C2×D15—24no—
216C2×D15—24no—
217C2×D15#11714yes—
218C3×C4×C5—22no—
219C3×C4×C5—22no—
220C3×C4×C5—22no—
221C3×C4×C5—24no—
222C3×C4×C5—42no—
223Dic15—22no—
224Dic15—22no—
225Dic15—22no—
226Dic15—42no—
227Dic15—42no—
228C23×D3—51no—
229C22×C3×C4C22×D512yes—
230C22×C3×C4C22×D511yescharacteristic
231C22×C3×C4C22×D511yescharacteristic
232C22×C3×C4C22×D511yescharacteristic
233C22×C3×C4C22×D512yes—
234C22×Dic3—51no—
235C22×Dic3—51no—
236C22×Dic3—51no—
237C22×Dic3—52no—
238C22×Dic3—52no—
239C2×C4×D3—54no—
240C2×C4×D3—104no—
241C2×C4×D3—104no—
242C2×C4×D3—104no—
243C2×C4×D3—202no—
244C3×C4⋊C4—24no—
245C3×C42—42no—
246C3×C42C4×D514yescomplemented
247(C2×D3)⋊C4—54no—
248(C2×D3)⋊C4—54no—
249(C2×D3)⋊C4—104no—
250Dic3⋊C4—54no—
251Dic3⋊C4—54no—
252Dic3⋊C4—202no—
253C4×Dic3—54no—
254C4×Dic3—104no—
255C23×C5C23×D311yescharacteristic
256C22×D5—32no—
257C22×D5—34no—
258C22×D5—62no—
259C22×D5—61no—
260C22×D5—61no—
261C2×C4×C5—22no—
262C2×C4×C5—21no—
263C2×C4×C5—22no—
264C2×C4×C5—21no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5C2×C4×D312yes—
271C2×C4×C5C2×C4×D312yes—
272C2×C4×C5C2×C4×D312yes—
273C2×C4×C5#23514yes—
274C2×Dic5—32no—
275C2×Dic5—32no—
276C2×Dic5—32no—
277C2×Dic5—62no—
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—62no—
281C2×Dic5—62no—
282C2×Dic5—62no—
283C2×Dic5—62no—
284C2×Dic5—62no—
285C2×Dic5—62no—
286C2×Dic5—62no—
287C4×D5—68no—
288C4×D5—128no—
289C23×C4—151no—
290C23×C4—152no—
291#117—158no—
292C2×C4⋊C4—151no—
293C2×C4⋊C4—151no—
294C2×C4⋊C4—152no—
295C2×C4⋊C4C2×D1512yes—
296C2×C22⋊C4—151no—
297C2×C22⋊C4—151no—
298C2×C22⋊C4—152no—
299C2×C42—151no—
300C2×C42—152no—
301C2×C42C2×D1512yes—
302C2×C42C2×D1511yescharacteristic
303#95—151no—
304#95—152no—
305#95—151no—
306#95—152no—
307#95—152no—
308#95—152no—
309#95—152no—
310#95—152no—
311#95C2×D1511yescharacteristic
312#95C2×D1511yescharacteristic
313C2×C3×C5C2×#11711yescharacteristic
314C2×C3×C5C4×#4111yescharacteristic
315C2×C3×C5#52011yescharacteristic
316C2×C3×C5#55112yes—
317C2×C3×C5#55212yes—
318D15—24no—
319C23×C3C23×D511yescharacteristic
320C22×D3—52no—
321C22×D3—54no—
322C22×D3—102no—
323C22×D3—101no—
324C22×D3—101no—
325C2×C3×C4—22no—
326C2×C3×C4—21no—
327C2×C3×C4—22no—
328C2×C3×C4—21no—
329C2×C3×C4—22no—
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4C2×C4×D512yes—
335C2×C3×C4C2×C4×D512yes—
336C2×C3×C4C2×C4×D512yes—
337C2×C3×C4#70914yes—
338C2×Dic3—52no—
339C2×Dic3—52no—
340C2×Dic3—52no—
341C2×Dic3—102no—
342C2×Dic3—101no—
343C2×Dic3—101no—
344C2×Dic3—102no—
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—102no—
348C2×Dic3—102no—
349C2×Dic3—102no—
350C2×Dic3—102no—
351C4×D3—108no—
352C4×D3—208no—
353C22×C5C22×C4×D311yescharacteristic
354C22×C5C2×#23512yes—
355C22×C5#100411yescharacteristic
356C22×C5#100711yescharacteristic
357C22×C5D3×#4112yes—
358C2×D5—34no—
359C2×D5—62no—
360C2×D5—62no—
361C2×D5—64no—
362C2×D5—64no—
363C4×C5—22no—
364C4×C5—22no—
365C4×C5—22no—
366C4×C5—24no—
367C4×C5—42no—
368Dic5—62no—
369Dic5—62no—
370Dic5—62no—
371Dic5—122no—
372Dic5—122no—
373C24—151no—
374C22×C4—151no—
375C22×C4—151no—
376C22×C4—151no—
377C22×C4—154no—
378C22×C4—152no—
379C22×C4—152no—
380C22×C4—304no—
381C22×C4—304no—
382C22×C4—304no—
383C22×C4—602no—
384C22×C4C22×D1512yes—
385C22×C4C22×D1511yescharacteristic
386C22×C4C22×D1511yescharacteristic
387C22×C4C22×D1511yescharacteristic
388C22×C4C22×D1512yes—
389C4⋊C4—24no—
390C4⋊C4—154no—
391C4⋊C4—154no—
392C4⋊C4—602no—
393C22⋊C4—154no—
394C22⋊C4—154no—
395C22⋊C4—304no—
396C42—42no—
397C42—154no—
398C42—304no—
399C42C4×D1514yescomplemented
400C3×C5#234311yescharacteristic, complemented, Hall
401C22×C3C22×C4×D511yescharacteristic
402C22×C3C2×#70912yes—
403C22×C3#414411yescharacteristic
404C22×C3#414711yescharacteristic
405C22×C3D5×#4112yes—
406C2×D3—54no—
407C2×D3—102no—
408C2×D3—102no—
409C2×D3—104no—
410C2×D3—104no—
411C3×C4—22no—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—24no—
415C3×C4—42no—
416Dic3—102no—
417Dic3—102no—
418Dic3—102no—
419Dic3—202no—
420Dic3—202no—
421C2×C5C4×#23511yescharacteristic
422C2×C5#550411yescharacteristic
423C2×C5D3×#11711yescharacteristic
424C2×C5#555612yes—
425C2×C5#558112yes—
426D5—64no—
427C23—152no—
428C23—154no—
429C23—302no—
430C23—301no—
431C23—301no—
432C23C23×D1511yescharacteristic
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—22no—
436C2×C4—21no—
437C2×C4—22no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—152no—
443C2×C4—152no—
444C2×C4—152no—
445C2×C4—308no—
446C2×C4—302no—
447C2×C4—301no—
448C2×C4—301no—
449C2×C4—302no—
450C2×C4—302no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—302no—
454C2×C4—302no—
455C2×C4—302no—
456C2×C4—608no—
457C2×C4C2×C4×D1512yes—
458C2×C4C2×C4×D1512yes—
459C2×C4C2×C4×D1512yes—
460C2×C4#681714yes—
461C2×C3C4×#70911yescharacteristic
462C2×C3#6583811yescharacteristic
463C2×C3D5×#11711yescharacteristic
464C2×C3#6589012yes—
465C2×C3#6591512yes—
466D3—104no—
467C5#7376611yescharacteristic, complemented, Sylow
468C22—154no—
469C22—304no—
470C22—304no—
471C22—302no—
472C22—302no—
473C22C22×C4×D1511yescharacteristic
474C22C2×#681712yes—
475C22#9209511yescharacteristic
476C22#9209811yescharacteristic
477C22#41×D1512yes—
478C4—24no—
479C4—22no—
480C4—22no—
481C4—22no—
482C4—42no—
483C4—302no—
484C4—302no—
485C4—302no—
486C4—602no—
487C4—602no—
488C3#1060549711yescharacteristic, complemented, Sylow
489C2—304no—
490C2C4×#681711yescharacteristic
491C2#1175626311yescharacteristic
492C2D15×#11711yescharacteristic
493C2#1175631512yes—
494C2#1175634012yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C4×C5×C4⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC4×C4⋊C4D15
hypocenterC3×C5#2343
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×C4×C5×C4⋊C4C2semidirect
4. #11751079C2semidirect
6. #11751038C2semidirect
7. #11751034C2semidirect
10. #11750751C2semidirect
11. #11750749C2semidirect
26. #91761C4semidirect
39. C4×C5×C4⋊C4D3semidirect
67. C3×C42×C5C2×C4semidirect
72. #6712C2×C4semidirect
73. #6712C2×C4semidirect
75. C4×Dic15C2×C4semidirect
77. C3×C4×C4⋊C4D5semidirect
188. C42×C5C4×D3semidirect
204. C4×C4⋊C4D15semidirect
246. C3×C42C4×D5semidirect
399. C42C4×D15semidirect
400. C3×C5#2343semidirect
467. C5#73766semidirect
488. C3#10605497semidirect

Maximal subgroups

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

subgroupindex
C2×#917612
C3×C4×C5×C4⋊C42
#117510902
#117510792
C4×#67142
#117510382
#117510342
#117507652
D15×#952
#117507512
#117507492
#106054973
#737665