Finite Group Databasebeta

← #14327102

Subgroups — #14327102

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic
2C2×#91770C212yesmaximal
3C3×C5×#380C211yesmaximal, characteristic, complemented
4C2×#91115C211yesmaximal, characteristic, complemented
5#11751090C212yesmaximal, complemented
6#11751077C212yesmaximal, complemented
7#11751047C212yesmaximal, complemented
8#11750768C211yesmaximal, characteristic, complemented
9D15×#95C211yesmaximal, characteristic, complemented
10#11750751C211yesmaximal, characteristic, complemented
11#11750750C211yesmaximal, characteristic, complemented
12#10605742—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C23×Dic15C2212yes—
16C22×C4×D15C2212yes—
17C22×C4×D15C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2212yes—
19C2×C3×C5×C22⋊C4C2212yes—
20C2×#6719C2211yescharacteristic
21C4×#1220C418yescomplemented
22C2×#6714C2212yes—
23C2×#6714C2211yescharacteristic
24C2×#6712C2212yes—
25C2×#6712C2212yes—
26C2×#6712C2212yes—
27C2×#6712C2211yescharacteristic
28C2×C4×Dic15C2212yes—
29C2×C4×Dic15C2211yescharacteristic
30#91770—28no—
31C3×C5×#95C2211yescharacteristic
32C3×C5×#95C2211yescharacteristic
33#91115C2211yescharacteristic
34#91115C2211yescharacteristic
35#91115C2212yes—
36#91115C2212yes—
37#91115C2212yes—
38#74011—51nomaximal, Hall
39C2×C4×C22⋊D5—31no—
40C2×#4027—32no—
41C5×#380D311yescharacteristic, complemented
42C2×#3963—31no—
43#65278—32no—
44#65261—32no—
45#65235—32no—
46#64956—31no—
47D5×#95—31no—
48#64939—31no—
49#64938—31no—
50C24×C3×C5C2311yescharacteristic
51C23×D15C2311yescharacteristic
52C22×C3×C4×C5—42no—
53C22×C3×C4×C5C2×C414yescomplemented
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220C2×C414yes—
59C2×#1220D414yes—
60C2×#1220Q814yes—
61C22×Dic15—24no—
62C22×Dic15—24no—
63C22×Dic15—42no—
64C22×Dic15C2312yes—
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2312yes—
68C22×Dic15C2311yescharacteristic
69C2×C4×D15—24no—
70C2×C4×D15—24no—
71C2×C4×D15—42no—
72C2×C4×D15—42no—
73C2×C4×D15C2×C414yescomplemented
74C3×C5×C4⋊C4—42no—
75C3×C5×C22⋊C4—24no—
76#6719C2×C414yescomplemented
77#6714—24no—
78#6714C2×C414yescomplemented
79#6712—24no—
80#6712—24no—
81#6712—42no—
82#6712C2×C414yescomplemented
83C4×Dic15—24no—
84C4×Dic15C2×C414yescomplemented
85C2×C4×#67—51no—
86C2×#67⋊C4—52no—
87C3×#380D511yescharacteristic, complemented
88C2×C3⋊#95—51no—
89#4989—52no—
90#4976—52no—
91#4946—52no—
92#4667—51no—
93D3×#95—51no—
94#4650—51no—
95#4649—51no—
96C23×C4×C5C2×D311yescharacteristic
97C22×C22⋊D5—31no—
98C23×Dic5—32no—
99C22×C4×D5—31no—
100C22×C4×D5—32no—
101C2×C5×C4⋊C4C2×D312yes—
102C2×C5×C22⋊C4C2×D312yes—
103C2×C22⋊Dic5—31no—
104C4×C22⋊D5—38no—
105C2×#685—31no—
106C2×#685—32no—
107C2×#683—31no—
108C2×#683—32no—
109C2×#683—32no—
110C2×#683—32no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—32no—
113#4027—68no—
114C5×#95C2×D311yescharacteristic
115C5×#95C2×D311yescharacteristic
116#3963—31no—
117#3963—31no—
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#2349—151noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5C2×Q812yes—
127C23×C3×C5C2411yescharacteristic
128C22×D15—22no—
129C22×D15—22no—
130C22×D15C22×C412yes—
131C22×D15C2×D412yes—
132C22×D15C2×Q812yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—44no—
142C2×C3×C4×C5C22×C412yes—
143C2×C3×C4×C5C22×C412yes—
144#1220C4⋊C4116yescomplemented
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—22no—
151C2×Dic15—22no—
152C2×Dic15—48no—
153C2×Dic15C22×C412yes—
154C2×Dic15C22×C412yes—
155C2×Dic15C22×C412yes—
156C2×Dic15C2×D412yes—
157C2×Dic15C2×Q812yes—
158C2×Dic15#4114yes—
159C4×D15—44no—
160C4×D15—48no—
161C23×C3×C4C2×D511yescharacteristic
162C22×#67—51no—
163C23×Dic3—52no—
164C22×C4×D3—51no—
165C22×C4×D3—52no—
166C2×C3×C4⋊C4C2×D512yes—
167C2×C3×C22⋊C4C2×D512yes—
168C2×#217—51no—
169C4×#67—58no—
170C2×(C2×D3)⋊C4—51no—
171C2×(C2×D3)⋊C4—52no—
172C2×Dic3⋊C4—51no—
173C2×Dic3⋊C4—52no—
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4—52no—
176C2×C4×Dic3—51no—
177C2×C4×Dic3—52no—
178#67⋊C4—108no—
179C3×#95C2×D511yescharacteristic
180C3×#95C2×D511yescharacteristic
181C3⋊#95—51no—
182C3⋊#95—51no—
183C3⋊#95—52no—
184C3⋊#95—52no—
185C3⋊#95—52no—
186C24×C5C22×D311yescharacteristic
187C23×D5—31no—
188C22×C4×C5—42no—
189C22×C4×C5C4×D314yescomplemented
190C22×C4×C5C22×D312yes—
191C22×C4×C5C22×D312yes—
192C22×C4×C5C22×D311yescharacteristic
193C22×C4×C5C22×D311yescharacteristic
194C2×C22⋊D5—34no—
195C2×C22⋊D5—34no—
196C2×C22⋊D5—34no—
197C22×Dic5—31no—
198C22×Dic5—31no—
199C22×Dic5—31no—
200C22×Dic5—32no—
201C22×Dic5—32no—
202C22×Dic5—64no—
203C22×Dic5—64no—
204C22×Dic5—122no—
205C2×C4×D5—34no—
206C2×C4×D5—64no—
207C2×C4×D5—64no—
208C2×C4×D5—122no—
209C2×C4×D5—122no—
210C5×C4⋊C4—42no—
211C5×C22⋊C4—24no—
212C22⋊Dic5—34no—
213#685—34no—
214#685—64no—
215#683—34no—
216#683—64no—
217#683—64no—
218#683—122no—
219C4×Dic5—34no—
220C4×Dic5—64no—
221C2×C4×D4—151no—
222C2×C4×D4—152no—
223#389—152no—
224#385—152no—
225#385—152no—
226#382—151no—
227#380—151no—
228#380D1511yescharacteristic, complemented
229C4×C4⋊C4—151no—
230C2×#95—151no—
231C2×#95—151no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—24no—
235C22×C3×C5—24no—
236C22×C3×C5C2×C4⋊C414yes—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C22×Q811yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5H(5,𝔽2)12yes—
242C2×D15—22no—
243C2×D15—22no—
244C2×D15—24no—
245C2×D15—24no—
246C2×D15C2×C4⋊C414yes—
247C3×C4×C5—22no—
248C3×C4×C5—22no—
249C3×C4×C5—42no—
250C3×C4×C5—42no—
251Dic15—22no—
252Dic15—22no—
253Dic15—24no—
254Dic15—42no—
255Dic15C2×C4⋊C414yes—
256C24×C3C22×D511yescharacteristic
257C23×D3—51no—
258C22×C3×C4—42no—
259C22×C3×C4C4×D514yescomplemented
260C22×C3×C4C22×D512yes—
261C22×C3×C4C22×D512yes—
262C22×C3×C4C22×D511yescharacteristic
263C22×C3×C4C22×D511yescharacteristic
264C2×#67—54no—
265C2×#67—54no—
266C2×#67—54no—
267C22×Dic3—51no—
268C22×Dic3—52no—
269C22×Dic3—51no—
270C22×Dic3—51no—
271C22×Dic3—52no—
272C22×Dic3—104no—
273C22×Dic3—104no—
274C22×Dic3—202no—
275C2×C4×D3—54no—
276C2×C4×D3—104no—
277C2×C4×D3—104no—
278C2×C4×D3—202no—
279C2×C4×D3—202no—
280C3×C4⋊C4—42no—
281C3×C22⋊C4—24no—
282#217—54no—
283(C2×D3)⋊C4—54no—
284(C2×D3)⋊C4—104no—
285Dic3⋊C4—54no—
286Dic3⋊C4—104no—
287Dic3⋊C4—104no—
288Dic3⋊C4—202no—
289C4×Dic3—54no—
290C4×Dic3—104no—
291C23×C5—22no—
292C23×C5—22no—
293C23×C5C2×C4×D312yes—
294C23×C5D3×D412yes—
295C23×C5D3×Q812yes—
296C23×C5C23×D311yescharacteristic
297C22×D5—32no—
298C22×D5—32no—
299C22×D5—32no—
300C22×D5—62no—
301C22×D5—62no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—44no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5C2×C4×D312yes—
313C22⋊D5—316no—
314C2×Dic5—32no—
315C2×Dic5—32no—
316C2×Dic5—32no—
317C2×Dic5—32no—
318C2×Dic5—32no—
319C2×Dic5—34no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5—128no—
328C4×D5—124no—
329C4×D5—128no—
330C22×D4—151no—
331C23×C4—151no—
332C23×C4—152no—
333C23×C4—152no—
334C23×C4C2×D1511yescharacteristic
335C4×D4—158no—
336C4×D4—308no—
337C2×C4⋊C4—151no—
338C2×C4⋊C4—152no—
339C2×C4⋊C4—152no—
340C2×C4⋊C4—152no—
341C2×C4⋊C4C2×D1512yes—
342C2×C22⋊C4—151no—
343C2×C22⋊C4—151no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4C2×D1512yes—
346C2×C42—151no—
347C2×C42—152no—
348#95—151no—
349#95—151no—
350#95—152no—
351#95—152no—
352#95—152no—
353#95C2×D1511yescharacteristic
354#95C2×D1511yescharacteristic
355C2×C3×C5—24no—
356C2×C3×C5C22×C4⋊C411yescharacteristic
357C2×C3×C5C4×#4111yescharacteristic
358C2×C3×C5#51811yescharacteristic
359C2×C3×C5#54612yes—
360C2×C3×C5#55412yes—
361D15—24no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3C2×C4×D512yes—
365C23×C3D4×D512yes—
366C23×C3Q8×D512yes—
367C23×C3C23×D511yescharacteristic
368C22×D3—52no—
369C22×D3—52no—
370C22×D3—52no—
371C22×D3—102no—
372C22×D3—102no—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—44no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4C2×C4×D512yes—
384#67—516no—
385C2×Dic3—52no—
386C2×Dic3—52no—
387C2×Dic3—52no—
388C2×Dic3—52no—
389C2×Dic3—52no—
390C2×Dic3—54no—
391C2×Dic3—102no—
392C2×Dic3—102no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3—208no—
399C4×D3—204no—
400C4×D3—208no—
401C22×C5—24no—
402C22×C5—22no—
403C22×C5—22no—
404C22×C5—24no—
405C22×C5D3×C4⋊C414yes—
406C22×C5C22×C4×D311yescharacteristic
407C22×C5C2×D3×D411yescharacteristic
408C22×C5#100412yes—
409C22×C5C2×D3×Q811yescharacteristic
410C22×C5D3×#4112yes—
411C2×D5—34no—
412C2×D5—64no—
413C2×D5—62no—
414C2×D5—62no—
415C2×D5—64no—
416C4×C5—22no—
417C4×C5—22no—
418C4×C5—42no—
419C4×C5—42no—
420Dic5—34no—
421Dic5—62no—
422Dic5—62no—
423Dic5—64no—
424Dic5—122no—
425C24—151no—
426C24C22×D1511yescharacteristic
427C2×D4—154no—
428C2×D4—154no—
429C2×D4—154no—
430C22×C4—42no—
431C22×C4—151no—
432C22×C4—152no—
433C22×C4—151no—
434C22×C4—151no—
435C22×C4—154no—
436C22×C4—152no—
437C22×C4—304no—
438C22×C4—304no—
439C22×C4—304no—
440C22×C4—304no—
441C22×C4—602no—
442C22×C4—602no—
443C22×C4—602no—
444C22×C4C4×D1514yescomplemented
445C22×C4C22×D1512yes—
446C22×C4C22×D1512yes—
447C22×C4C22×D1511yescharacteristic
448C22×C4C22×D1511yescharacteristic
449C4⋊C4—42no—
450C4⋊C4—154no—
451C4⋊C4—304no—
452C4⋊C4—304no—
453C4⋊C4—602no—
454C22⋊C4—24no—
455C22⋊C4—154no—
456C22⋊C4—154no—
457C22⋊C4—304no—
458C42—154no—
459C42—304no—
460C3×C5#234911yescharacteristic, complemented, Hall
461C22×C3—22no—
462C22×C3—22no—
463C22×C3—24no—
464C22×C3—24no—
465C22×C3D5×C4⋊C414yes—
466C22×C3C22×C4×D511yescharacteristic
467C22×C3C2×D4×D511yescharacteristic
468C22×C3#414412yes—
469C22×C3C2×Q8×D511yescharacteristic
470C22×C3D5×#4112yes—
471C2×D3—54no—
472C2×D3—102no—
473C2×D3—102no—
474C2×D3—104no—
475C2×D3—104no—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—42no—
479C3×C4—42no—
480Dic3—54no—
481Dic3—102no—
482Dic3—102no—
483Dic3—104no—
484Dic3—202no—
485C2×C5—24no—
486C2×C5#548611yescharacteristic
487C2×C5C2×D3×C4⋊C411yescharacteristic
488C2×C5#552211yescharacteristic
489C2×C5#561012yes—
490C2×C5#563612yes—
491D5—64no—
492C23—22no—
493C23—22no—
494C23—152no—
495C23—152no—
496C23—152no—
497C23—302no—
498C23—302no—
499C23C2×C4×D1512yes—
500C23D4×D1512yes—
501C23Q8×D1512yes—
502C23C23×D1511yescharacteristic
503D4—1516no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—44no—
513C2×C4—152no—
514C2×C4—152no—
515C2×C4—152no—
516C2×C4—152no—
517C2×C4—152no—
518C2×C4—154no—
519C2×C4—302no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4—608no—
528C2×C4—608no—
529C2×C4C2×C4×D1512yes—
530C2×C4C2×C4×D1512yes—
531C2×C3—24no—
532C2×C3#6582011yescharacteristic
533C2×C3C2×D5×C4⋊C411yescharacteristic
534C2×C3#6585611yescharacteristic
535C2×C3#6594412yes—
536C2×C3#6597012yes—
537D3—104no—
538C5#7401111yescharacteristic, complemented, Sylow
539C22—24no—
540C22—24no—
541C22—22no—
542C22—22no—
543C22—154no—
544C22—304no—
545C22—304no—
546C22—302no—
547C22—302no—
548C22C4⋊C4×D1514yes—
549C22C22×C4×D1511yescharacteristic
550C22C2×D4×D1511yescharacteristic
551C22#9209512yes—
552C22C2×Q8×D1511yescharacteristic
553C22#41×D1512yes—
554C4—22no—
555C4—22no—
556C4—42no—
557C4—42no—
558C4—154no—
559C4—304no—
560C4—302no—
561C4—302no—
562C4—602no—
563C3#1060574211yescharacteristic, complemented, Sylow
564C2—24no—
565C2—304no—
566C2#1175624511yescharacteristic
567C2C2×C4⋊C4×D1511yescharacteristic
568C2#1175628111yescharacteristic
569C2#1175636912yes—
570C2#1175639512yes—
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#380C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenter#380D15
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
3. C3×C5×#380C2semidirect
4. C2×#91115C2semidirect
5. #11751090C2semidirect
6. #11751077C2semidirect
7. #11751047C2semidirect
8. #11750768C2semidirect
9. D15×#95C2semidirect
10. #11750751C2semidirect
11. #11750750C2semidirect
21. C4×#1220C4semidirect
41. C5×#380D3semidirect
53. C22×C3×C4×C5C2×C4semidirect
73. C2×C4×D15C2×C4semidirect
76. #6719C2×C4semidirect
78. #6714C2×C4semidirect
82. #6712C2×C4semidirect
84. C4×Dic15C2×C4semidirect
87. C3×#380D5semidirect
144. #1220C4⋊C4semidirect
189. C22×C4×C5C4×D3semidirect
228. #380D15semidirect
259. C22×C3×C4C4×D5semidirect
444. C22×C4C4×D15semidirect
460. C3×C5#2349semidirect
538. C5#74011semidirect
563. C3#10605742semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C2×#917702
C3×C5×#3802
C2×#911152
#117510902
#117510772
#117510472
#117507682
D15×#952
#117507512
#117507502
#106057423
#740115