Finite Group Databasebeta

← #14330201

Subgroups — #14330201

Order 1920.

1120 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×C3×#4093C211yesmaximal, characteristic
2#11751330C211yesmaximal, characteristic, complemented
3C5×#5229C211yesmaximal, characteristic, complemented
4#11748896C212yesmaximal
5#11748884C212yesmaximal, complemented
6Dic3×#685C212yesmaximal, complemented
7#11748772C212yesmaximal, complemented
8#11748771C212yesmaximal, complemented
9#11748635C212yesmaximal, complemented
10#10608226—31nomaximal, Hall
11C22×C3×C5×Q8C2211yescharacteristic
12C22×C3×D20C2211yescharacteristic
13C22×D5×Dic3C2212yes—
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C4×Dic15C2211yescharacteristic
16C2×C5×C4⋊Dic3C2211yescharacteristic
17C2×C4×C5×Dic3C2211yescharacteristic
18C3×#4093C418yescomplemented
19C2×C3×#685C2212yes—
20C2×C3×#685C2212yes—
21C2×C3×C4×Dic5C2211yescharacteristic
22C2×#6665C2212yes—
23C2×#6665C2212yes—
24C2×#6665C2212yes—
25C2×Dic3×Dic5C2212yes—
26C2×Dic3×Dic5C2212yes—
27#91115C2212yes—
28#91115C2212yes—
29C5×C3⋊#95C2212yes—
30C5×C3⋊#95C2212yes—
31#90994C2212yes—
32#90994C2212yes—
33#82956—51nomaximal, Hall
34C2×#4093D311yescharacteristic
35C5×#391—31no—
36#65519—31no—
37#65279—32no—
38C4×#685—32no—
39#64959—32no—
40#64955—32no—
41#64954—32no—
42#64937—32no—
43C23×C3×D5C2312yes—
44C2×C3×C5×Q8—41no—
45C2×C3×C5×Q8—41no—
46C2×C3×C5×Q8C2×C414yescomplemented
47C22×C3×C4×C5C2311yescharacteristic
48C22×C3×C4×C5C2311yescharacteristic
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15C2312yes—
51C22×Dic15C2312yes—
52C22×C5×Dic3C2312yes—
53C22×C5×Dic3C2312yes—
54C22×C3×Dic5C2312yes—
55C2×C3×D20—41no—
56C2×C3×D20—41no—
57C2×C3×D20C2×C414yes—
58C2×D5×Dic3—24no—
59C2×D5×Dic3—24no—
60C2×D5×Dic3—42no—
61C4⋊Dic15—41no—
62C4×Dic15—41no—
63C5×C4⋊Dic3—41no—
64C4×C5×Dic3—41no—
65C3×#685C2×C418yescomplemented
66C3×#685C2×C418yescomplemented
67C3×C4×Dic5C2×C414yescomplemented
68#6665—24no—
69#6665—24no—
70#6665—42no—
71Dic3×Dic5—24no—
72Dic3×Dic5—24no—
73C2×C3×#124—51no—
74#5229—51no—
75#5229D511yescharacteristic, complemented
76#5220—52no—
77#4951—52no—
78#4951—52no—
79Dic3×C22⋊C4—52no—
80Dic3×C22⋊C4—52no—
81#4932—52no—
82C22×C5×Q8C2×D311yescharacteristic
83C22×D20C2×D311yescharacteristic
84C22×C4×D5—32no—
85C2×C5×C4⋊C4—31no—
86C2×C42×C5—31no—
87#4093Dic318yescomplemented
88C2×#685—32no—
89C2×#685—32no—
90C2×#685—32no—
91C2×#685C2×D312yes—
92C2×#685C2×D312yes—
93C2×C4⋊Dic5—31no—
94C2×C4×Dic5—32no—
95C2×C4×Dic5—32no—
96C2×C4×Dic5—31no—
97C2×C4×Dic5C2×D311yescharacteristic
98C5×#95—32no—
99C5×#95—32no—
100#3963—32no—
101#3963—32no—
102#3963—32no—
103#3963—32no—
104#2372—151noSylow
105C23×C3×C5C2411yescharacteristic
106C22×C3×D5—22no—
107C22×C3×D5—22no—
108C22×C3×D5—22no—
109C22×C3×D5—22no—
110C22×C3×D5—22no—
111C22×C3×D5—22no—
112C22×C3×D5C22×C414yes—
113C3×C5×Q8—44no—
114C2×C3×C4×C5—21no—
115C2×C3×C4×C5—21no—
116C2×C3×C4×C5—21no—
117C2×C3×C4×C5—21no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5C22×C412yes—
121C2×C3×C4×C5C22×C412yes—
122C2×C3×C4×C5C22×C412yes—
123C2×Dic15—22no—
124C2×Dic15—22no—
125C2×Dic15—22no—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15#4114yes—
129C2×C5×Dic3—22no—
130C2×C5×Dic3—22no—
131C2×C5×Dic3—22no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3#4114yes—
135C2×C3×Dic5—22no—
136C2×C3×Dic5—22no—
137C2×C3×Dic5C22×C414yes—
138C3×D20—44no—
139D5×Dic3—48no—
140C22×C3×Q8C2×D511yescharacteristic
141C22×C3×D4—51no—
142C23×Dic3—52no—
143C3×#124—58no—
144C2×C3×C22⋊C4—52no—
145C2×C3×C22⋊C4—52no—
146C2×C3×C42—51no—
147C2×#217—52no—
148C2×#217—52no—
149C2×#217—52no—
150C2×C4⋊Dic3—51no—
151C2×C4⋊Dic3C2×D511yescharacteristic
152C2×C4×Dic3—52no—
153C2×C4×Dic3—52no—
154C2×C4×Dic3—51no—
155C2×C4×Dic3C2×D511yescharacteristic
156C3⋊#95—52no—
157C3⋊#95—52no—
158C3⋊#95—52no—
159C3⋊#95—52no—
160C3⋊#95C2×D512yes—
161C3⋊#95C2×D512yes—
162C23×D5C22×D312yes—
163C2×C5×Q8—41no—
164C2×C5×Q8—41no—
165C2×C5×Q8C2×Dic314yescomplemented
166C22×C4×C5—32no—
167C22×C4×C5—32no—
168C22×C4×C5C22×D311yescharacteristic
169C22×C4×C5C22×D311yescharacteristic
170C22×C4×C5C22×D311yescharacteristic
171C22×Dic5—32no—
172C22×Dic5—32no—
173C22×Dic5C22×D312yes—
174C2×D20—41no—
175C2×D20—41no—
176C2×D20C2×Dic314yes—
177C2×C4×D5—64no—
178C2×C4×D5—64no—
179C2×C4×D5—122no—
180C5×C4⋊C4—121no—
181C42×C5—121no—
182#685—64no—
183#685—64no—
184#685—122no—
185#685C2×Dic318yescomplemented
186#685C2×Dic318yescomplemented
187C4⋊Dic5—121no—
188C4×Dic5—64no—
189C4×Dic5—64no—
190C4×Dic5—121no—
191C4×Dic5C2×Dic314yescomplemented
192C2×#124—51no—
193#391—31no—
194#391—151no—
195#388—152no—
196#388—152no—
197#386—152no—
198C4×C22⋊C4—152no—
199C4×C22⋊C4—152no—
200#376—152no—
201C22×C3×C5C23×C411yescharacteristic
202C22×C3×C5C2×#4112yes—
203C22×C3×C5C2×#4112yes—
204C22×C3×C5H(5,𝔽2)11yescharacteristic
205C22×C3×C5H(5,𝔽2)11yescharacteristic
206C2×C3×D5—24no—
207C2×C3×D5—24no—
208C2×C3×D5—24no—
209C2×C3×D5—42no—
210C2×C3×D5—42no—
211C2×C3×D5—42no—
212C2×C3×D5—42no—
213C3×C4×C5—22no—
214C3×C4×C5—22no—
215C3×C4×C5—22no—
216Dic15—24no—
217Dic15—42no—
218C3×Dic5—24no—
219C5×Dic3—24no—
220C5×Dic3—42no—
221C24×C3—52no—
222C2×C3×Q8—41no—
223C2×C3×Q8—41no—
224C2×C3×Q8C4×D514yescomplemented
225C2×C3×D4—54no—
226C2×C3×D4—201no—
227C2×C3×D4—201no—
228C22×C3×C4—52no—
229C22×C3×C4C22×D511yescharacteristic
230C22×C3×C4C22×D511yescharacteristic
231C22×C3×C4C22×D511yescharacteristic
232C22×Dic3—52no—
233C22×Dic3—52no—
234C22×Dic3—104no—
235C22×Dic3—104no—
236C22×Dic3—202no—
237C22×Dic3C22×D512yes—
238C22×Dic3C22×D512yes—
239C3×C22⋊C4—58no—
240C3×C22⋊C4—58no—
241C3×C42—54no—
242#217—104no—
243#217—104no—
244#217—202no—
245C4⋊Dic3—41no—
246C4⋊Dic3—201no—
247C4×Dic3—41no—
248C4×Dic3—104no—
249C4×Dic3—104no—
250C4×Dic3—201no—
251C23×C5C23×D311yescharacteristic
252C22×D5—22no—
253C22×D5—22no—
254C22×D5—22no—
255C22×D5—22no—
256C22×D5—22no—
257C22×D5—22no—
258C22×D5C22×Dic314yes—
259C5×Q8—44no—
260C2×C4×C5—21no—
261C2×C4×C5—21no—
262C2×C4×C5—21no—
263C2×C4×C5—21no—
264C2×C4×C5—21no—
265C2×C4×C5—21no—
266C2×C4×C5—34no—
267C2×C4×C5—62no—
268C2×C4×C5—62no—
269C2×C4×C5—62no—
270C2×C4×C5—62no—
271C2×C4×C5—62no—
272C2×C4×C5C22×Dic312yes—
273C2×C4×C5C22×Dic312yes—
274C2×C4×C5C22×Dic312yes—
275C2×Dic5—22no—
276C2×Dic5—22no—
277C2×Dic5—34no—
278C2×Dic5—62no—
279C2×Dic5—62no—
280C2×Dic5—62no—
281C2×Dic5—62no—
282C2×Dic5—62no—
283C2×Dic5C22×Dic314yes—
284D20—44no—
285C4×D5—128no—
286C22×Q8D3×D511yescharacteristic
287C22×D4—51no—
288C23×C4—152no—
289#124—58no—
290C2×C4⋊C4—31no—
291C2×C4⋊C4—151no—
292C2×C22⋊C4—52no—
293C2×C22⋊C4—52no—
294C2×C22⋊C4—152no—
295C2×C22⋊C4—152no—
296C2×C22⋊C4—152no—
297C2×C42—31no—
298C2×C42—51no—
299C2×C42—152no—
300C2×C42—152no—
301C2×C42—151no—
302#95—32no—
303#95—32no—
304#95—152no—
305#95—152no—
306#95—152no—
307#95—152no—
308C2×C3×C5C4×#4112yes—
309C2×C3×C5#51811yescharacteristic
310C2×C3×C5#55112yes—
311C2×C3×C5#55511yescharacteristic
312C2×C3×C5#55511yescharacteristic
313C3×D5—44no—
314C23×C3—54no—
315C23×C3—102no—
316C23×C3—102no—
317C23×C3—102no—
318C23×C3—102no—
319C23×C3—102no—
320C23×C3—102no—
321C23×C3C23×D511yescharacteristic
322C3×Q8—44no—
323C3×D4—204no—
324C2×C3×C4—21no—
325C2×C3×C4—21no—
326C2×C3×C4—21no—
327C2×C3×C4—21no—
328C2×C3×C4—21no—
329C2×C3×C4—21no—
330C2×C3×C4—54no—
331C2×C3×C4—102no—
332C2×C3×C4—102no—
333C2×C3×C4C2×C4×D512yes—
334C2×C3×C4C2×C4×D512yes—
335C2×C3×C4C2×C4×D512yes—
336C2×Dic3—22no—
337C2×Dic3—22no—
338C2×Dic3—22no—
339C2×Dic3—22no—
340C2×Dic3—22no—
341C2×Dic3—54no—
342C2×Dic3—102no—
343C2×Dic3—102no—
344C2×Dic3—102no—
345C2×Dic3—102no—
346C2×Dic3—102no—
347C2×Dic3—208no—
348C2×Dic3#71314yes—
349C22×C5#100411yescharacteristic
350C22×C5#100411yescharacteristic
351C22×C5D3×#4112yes—
352C22×C5D3×#4112yes—
353C22×C5C23×Dic311yescharacteristic
354C2×D5—24no—
355C2×D5—24no—
356C2×D5—24no—
357C2×D5—42no—
358C2×D5—42no—
359C2×D5—42no—
360C2×D5—42no—
361C4×C5—22no—
362C4×C5—22no—
363C4×C5—22no—
364C4×C5—64no—
365C4×C5—122no—
366Dic5—24no—
367Dic5—64no—
368Dic5—122no—
369C24—52no—
370C2×Q8—41no—
371C2×Q8—41no—
372C2×Q8D5×Dic314yescomplemented
373C2×D4—54no—
374C2×D4—201no—
375C2×D4—201no—
376C22×C4—32no—
377C22×C4—32no—
378C22×C4—52no—
379C22×C4—152no—
380C22×C4—152no—
381C22×C4—304no—
382C22×C4—304no—
383C22×C4—602no—
384C22×C4C2×D3×D511yescharacteristic
385C22×C4C2×D3×D511yescharacteristic
386C22×C4C2×D3×D511yescharacteristic
387C4⋊C4—121no—
388C4⋊C4—601no—
389C22⋊C4—58no—
390C22⋊C4—58no—
391C22⋊C4—304no—
392C22⋊C4—304no—
393C22⋊C4—602no—
394C42—54no—
395C42—121no—
396C42—304no—
397C42—304no—
398C42—601no—
399C3×C5#237211yescharacteristic, complemented, Hall
400C22×C3—104no—
401C22×C3—104no—
402C22×C3—104no—
403C22×C3—202no—
404C22×C3—202no—
405C22×C3—202no—
406C22×C3—202no—
407C22×C3C22×C4×D511yescharacteristic
408C22×C3#414411yescharacteristic
409C22×C3#414411yescharacteristic
410C22×C3C2×#71312yes—
411C22×C3D5×#4112yes—
412C3×C4—22no—
413C3×C4—22no—
414C3×C4—22no—
415C3×C4—104no—
416Dic3—24no—
417Dic3—42no—
418Dic3—104no—
419Dic3—202no—
420C2×C5#567011yescharacteristic
421C2×C5#567011yescharacteristic
422C2×C5#567912yes—
423C2×C5#579811yescharacteristic
424C2×C5Dic3×#4112yes—
425D5—44no—
426C23—54no—
427C23—102no—
428C23—102no—
429C23—102no—
430C23—102no—
431C23—102no—
432C23—102no—
433C23C22×D3×D511yescharacteristic
434Q8—44no—
435D4—204no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—34no—
443C2×C4—54no—
444C2×C4—62no—
445C2×C4—62no—
446C2×C4—62no—
447C2×C4—62no—
448C2×C4—62no—
449C2×C4—102no—
450C2×C4—102no—
451C2×C4—154no—
452C2×C4—302no—
453C2×C4—302no—
454C2×C4—302no—
455C2×C4—302no—
456C2×C4—302no—
457C2×C4—608no—
458C2×C4C2×D5×Dic312yes—
459C2×C4C2×D5×Dic312yes—
460C2×C4C2×D5×Dic312yes—
461C2×C3—204no—
462C2×C3#6582011yescharacteristic
463C2×C3C4×#71312yes—
464C2×C3#6597112yes—
465C2×C3#6600411yescharacteristic
466C2×C3#6606811yescharacteristic
467C5#8295611yescharacteristic, complemented, Sylow
468C22—104no—
469C22—104no—
470C22—104no—
471C22—202no—
472C22—202no—
473C22—202no—
474C22—202no—
475C22D3×#71312yes—
476C22#9203412yes—
477C22C22×D5×Dic311yescharacteristic
478C22#9204911yescharacteristic
479C22#9204911yescharacteristic
480C4—22no—
481C4—22no—
482C4—22no—
483C4—64no—
484C4—104no—
485C4—122no—
486C4—304no—
487C4—602no—
488C3#1060822611yescharacteristic, complemented, Sylow
489C2—204no—
490C2Dic3×#71312yes—
491C2#1175520711yescharacteristic
492C2#1175521111yescharacteristic
493C2#1175529212yes—
494C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×Q8C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC22×Q8D3×D5
hypocenterC3×C5#2372
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. #11751330C2semidirect
3. C5×#5229C2semidirect
5. #11748884C2semidirect
6. Dic3×#685C2semidirect
7. #11748772C2semidirect
8. #11748771C2semidirect
9. #11748635C2semidirect
18. C3×#4093C4semidirect
46. C2×C3×C5×Q8C2×C4semidirect
65. C3×#685C2×C4semidirect
66. C3×#685C2×C4semidirect
67. C3×C4×Dic5C2×C4semidirect
75. #5229D5semidirect
87. #4093Dic3semidirect
165. C2×C5×Q8C2×Dic3semidirect
185. #685C2×Dic3semidirect
186. #685C2×Dic3semidirect
191. C4×Dic5C2×Dic3semidirect
224. C2×C3×Q8C4×D5semidirect
372. C2×Q8D5×Dic3semidirect
399. C3×C5#2372semidirect
467. C5#82956semidirect
488. C3#10608226semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40932
#117513302
C5×#52292
#117488962
#117488842
Dic3×#6852
#117487722
#117487712
#117486352
#106082263
#829565