Finite Group Databasebeta

← #14320608

Subgroups — #14320608

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91761C211yesmaximal, characteristic, complemented
2C2×C4×#1203C211yesmaximal, characteristic
3C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
4C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
5C3×C4×#683C211yesmaximal, characteristic, complemented
6#11748892C212yesmaximal, complemented
7#11748883C212yesmaximal
8C4×#6667C211yesmaximal, characteristic, complemented
9#11748666C212yesmaximal, complemented
10#11748650C212yesmaximal, complemented
11#11748611C211yesmaximal, characteristic, complemented
12#10605169—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×#1203C2211yescharacteristic
16C22×D3×Dic5C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×#6714C2212yes—
19C2×#6712C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21#91761—24no—
22C2×C5×(C2×D3)⋊C4C2212yes—
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C3×#683C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×#6668C2211yescharacteristic
28C2×#6667C2212yes—
29C2×#6667C2211yescharacteristic
30C2×(C2×D3)⋊Dic5C2211yescharacteristic
31C2×Dic3×Dic5C2212yes—
32C4×#1203C418yescomplemented
33C4×D3×Dic5—24no—
34C5×C3⋊#95C2212yes—
35C3×#3963C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73754—51nomaximal, Hall
40C2×C4×C22⋊D5—31no—
41C22×C4×Dic5—31no—
42C2×#4018—31no—
43C4×C5×C22⋊C4—31no—
44#65247—32no—
45#65235—32no—
46C4×#685—31no—
47#65221—31no—
48C4×#683D311yescharacteristic, complemented
49#64958—32no—
50#64941—32no—
51C23×D15C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2312yes—
57C2×C4×D15—22no—
58C2×C4×D15—22no—
59C2×C4×D15C2×C414yescomplemented
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2311yescharacteristic
62C2×C4×C5×D3—22no—
63C2×C4×C5×D3—22no—
64C2×C4×C5×D3C2×C414yes—
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2312yes—
68C2×#1203—24no—
69C2×#1203C2×C414yes—
70C2×D3×Dic5—24no—
71C2×D3×Dic5—24no—
72C2×D3×Dic5—24no—
73C3×C42×C5—22no—
74#6714—24no—
75#6712—24no—
76C4×Dic15D414yescomplemented
77C5×(C2×D3)⋊C4—24no—
78C4×C5×Dic3—22no—
79C3×#683—24no—
80C3×C4×Dic5—22no—
81C3×C4×Dic5C2×C414yescomplemented
82#6668C2×C414yescomplemented
83#6667—24no—
84#6667C2×C414yescomplemented
85(C2×D3)⋊Dic5C2×C414yes—
86Dic3×Dic5—24no—
87C2×C4×D12—51no—
88C2×#872—51no—
89C2×C42×D3—51no—
90C3×C4×C4⋊C4—51no—
91#4990—52no—
92#4989—52no—
93C4×(C2×D3)⋊C4—51no—
94C4×(C2×D3)⋊C4D511yescharacteristic, complemented
95#4932—51no—
96#4665—52no—
97#4654—52no—
98C23×C4×C5—31no—
99C22×C22⋊D5—31no—
100C23×Dic5—32no—
101C22×C4×D5—31no—
102C2×C5×C22⋊C4—32no—
103C2×C42×C5—31no—
104C2×C42×C5C2×D311yescharacteristic
105C2×C22⋊Dic5—31no—
106C4×C22⋊D5—38no—
107C2×#685—31no—
108C2×#685—32no—
109C2×#685—32no—
110C2×#683—31no—
111C2×#683—32no—
112C2×#683C2×D312yes—
113C2×C4×Dic5—31no—
114C2×C4×Dic5—32no—
115C2×C4×Dic5—64no—
116C2×C4×Dic5C2×D311yescharacteristic
117C2×C4×Dic5C2×D311yescharacteristic
118#4018—64no—
119C5×#95—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yes—
124#2290—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×D15—21no—
127C22×D15—22no—
128C22×D15—22no—
129C22×D15—21no—
130C22×D15C22×C412yes—
131C22×C5×D3—21no—
132C22×C5×D3—22no—
133C22×C5×D3—21no—
134C22×C5×D3C22×C412yes—
135C22×C5×D3#4114yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—21no—
146C2×Dic15C22×C412yes—
147C2×Dic15C2×D414yes—
148C4×D15—28no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3C22×C412yes—
155C4×C5×D3—28no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C22×C412yes—
162C2×C3×Dic5#4114yes—
163#1203—28no—
164D3×Dic5—216no—
165C22×D12—51no—
166C22×C4×D3—51no—
167C22×C4×D3—52no—
168C22×C4×D3C2×D511yescharacteristic
169C2×C3×C4⋊C4—52no—
170C2×C3×C42—51no—
171C2×C3×C42—51no—
172C2×C3×C42C2×D511yescharacteristic
173C2×(C2×D3)⋊C4—51no—
174C2×(C2×D3)⋊C4—51no—
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4—52no—
177C2×(C2×D3)⋊C4C2×D512yes—
178C2×C4⋊Dic3—51no—
179C2×Dic3⋊C4—52no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3C2×D511yescharacteristic
183C4×D12—58no—
184#872—104no—
185C42×D3—104no—
186C3×#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95C2×D512yes—
191C24×C5—31no—
192C23×D5—31no—
193C22×C4×C5—31no—
194C22×C4×C5—34no—
195C22×C4×C5—32no—
196C22×C4×C5—62no—
197C22×C4×C5—62no—
198C22×C4×C5C22×D312yes—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—34no—
201C2×C22⋊D5—64no—
202C22×Dic5—31no—
203C22×Dic5—32no—
204C22×Dic5—64no—
205C22×Dic5—64no—
206C22×Dic5—64no—
207C22×Dic5C22×D311yescharacteristic
208C22×Dic5C22×D311yescharacteristic
209C22×Dic5C22×D312yes—
210C2×C4×D5—34no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C5×C22⋊C4—64no—
214C42×C5—22no—
215C42×C5—62no—
216C22⋊Dic5—34no—
217#685—34no—
218#685—64no—
219#685—64no—
220#683—24no—
221#683—34no—
222#683—64no—
223C4×Dic5—22no—
224C4×Dic5—34no—
225C4×Dic5—64no—
226C4×Dic5C4×D314yescomplemented
227C2×C4×D4—151no—
228C2×#117—151no—
229C22×C42—151no—
230#388—152no—
231#387—152no—
232#386—152no—
233#385—152no—
234C4×C4⋊C4—51no—
235C4×C22⋊C4—31no—
236C4×C22⋊C4—151no—
237#376—151no—
238C22×C3×C5C23×C411yescharacteristic
239C22×C3×C5C22×D411yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5C2×#4112yes—
243C2×D15—22no—
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—42no—
247C2×D15—42no—
248C2×C5×D3—22no—
249C2×C5×D3—22no—
250C2×C5×D3—24no—
251C2×C5×D3—24no—
252C2×C5×D3#11714yescomplemented
253C3×C4×C5—42no—
254C3×C4×C5C4×D414yes—
255Dic15—22no—
256Dic15—24no—
257C3×Dic5—22no—
258C3×Dic5—22no—
259C3×Dic5—24no—
260C5×Dic3—22no—
261C5×Dic3—42no—
262C23×D3—51no—
263C23×D3C22×D511yescharacteristic
264C22×C3×C4—51no—
265C22×C3×C4—51no—
266C22×C3×C4—52no—
267C22×C3×C4C22×D512yes—
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—52no—
270C22×Dic3—51no—
271C22×Dic3C22×D512yes—
272C22×Dic3C22×D511yescharacteristic
273C2×D12—54no—
274C2×D12—104no—
275C2×C4×D3—22no—
276C2×C4×D3—22no—
277C2×C4×D3—54no—
278C2×C4×D3—104no—
279C2×C4×D3—104no—
280C2×C4×D3—104no—
281C2×C4×D3—102no—
282C2×C4×D3—102no—
283C2×C4×D3C4×D514yes—
284C3×C4⋊C4—104no—
285C3×C42—22no—
286C3×C42—54no—
287C3×C42—102no—
288(C2×D3)⋊C4—24no—
289(C2×D3)⋊C4—54no—
290(C2×D3)⋊C4—54no—
291(C2×D3)⋊C4—104no—
292(C2×D3)⋊C4—104no—
293C4⋊Dic3—54no—
294Dic3⋊C4—104no—
295C4×Dic3—22no—
296C4×Dic3—54no—
297C4×Dic3—104no—
298C23×C5—32no—
299C23×C5—34no—
300C23×C5—62no—
301C23×C5—61no—
302C23×C5—61no—
303C23×C5C23×D311yescharacteristic
304C22×D5—32no—
305C22×D5—62no—
306C22×D5—61no—
307C22×D5—61no—
308C22×D5—62no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—22no—
312C2×C4×C5—32no—
313C2×C4×C5—61no—
314C2×C4×C5—61no—
315C2×C4×C5—68no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5—62no—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5D3×D412yes—
321C2×C4×C5#23912yes—
322C22⋊D5—68no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—22no—
327C2×Dic5—32no—
328C2×Dic5—34no—
329C2×Dic5—616no—
330C2×Dic5—62no—
331C2×Dic5—61no—
332C2×Dic5—61no—
333C2×Dic5—62no—
334C2×Dic5C2×C4×D312yes—
335C2×Dic5C2×C4×D312yes—
336C2×Dic5#23514yes—
337C4×D5—68no—
338C22×D4—151no—
339C23×C4—31no—
340C23×C4—152no—
341C23×C4—151no—
342C4×D4—158no—
343#117—304no—
344C2×C4⋊C4—52no—
345C2×C4⋊C4—151no—
346C2×C4⋊C4—152no—
347C2×C22⋊C4—32no—
348C2×C22⋊C4—151no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—151no—
356C2×C42—152no—
357C2×C42—304no—
358C2×C42D3×D511yescharacteristic
359#95—32no—
360#95—52no—
361#95—152no—
362#95—152no—
363#95—152no—
364C2×C3×C5C2×#11711yescharacteristic
365C2×C3×C5C2×C4×D411yescharacteristic
366C2×C3×C5C4×#4111yescharacteristic
367C2×C3×C5#52512yes—
368C2×C3×C5#52912yes—
369D15—42no—
370C5×D3—24no—
371C23×C3C23×D511yescharacteristic
372C22×D3—21no—
373C22×D3—21no—
374C22×D3—22no—
375C22×D3—52no—
376C22×D3—102no—
377C22×D3—101no—
378C22×D3—101no—
379C22×D3—102no—
380C22×D3C2×C4×D512yes—
381C22×D3#70914yes—
382C2×C3×C4—22no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—54no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4C2×C4×D512yes—
393C2×C3×C4D4×D512yes—
394C2×C3×C4#71112yes—
395C2×Dic3—21no—
396C2×Dic3—21no—
397C2×Dic3—22no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—52no—
401C2×Dic3—54no—
402C2×Dic3—102no—
403C2×Dic3—101no—
404C2×Dic3—101no—
405C2×Dic3—102no—
406C2×Dic3C2×C4×D512yes—
407D12—108no—
408C4×D3—28no—
409C4×D3—1016no—
410C4×D3—108no—
411C22×C5—34no—
412C22×C5—62no—
413C22×C5—62no—
414C22×C5—64no—
415C22×C5—64no—
416C22×C5C22×C4×D311yescharacteristic
417C22×C5C2×#23512yes—
418C22×C5C2×D3×D411yescharacteristic
419C22×C5C2×#23911yescharacteristic
420C22×C5D3×#4112yes—
421C2×D5—62no—
422C2×D5—62no—
423C2×D5—62no—
424C2×D5—122no—
425C2×D5—122no—
426C4×C5—42no—
427C4×C5—62no—
428C4×C5—122no—
429C4×C5#89314yes—
430Dic5—22no—
431Dic5—22no—
432Dic5—24no—
433Dic5—62no—
434Dic5—64no—
435C24—31no—
436C24—151no—
437C2×D4—154no—
438C2×D4—304no—
439C22×C4—31no—
440C22×C4—34no—
441C22×C4—32no—
442C22×C4—51no—
443C22×C4—52no—
444C22×C4—51no—
445C22×C4—62no—
446C22×C4—62no—
447C22×C4—152no—
448C22×C4—151no—
449C22×C4—154no—
450C22×C4—304no—
451C22×C4—304no—
452C22×C4—304no—
453C22×C4—302no—
454C22×C4—302no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—104no—
458C4⋊C4—154no—
459C4⋊C4—304no—
460C22⋊C4—64no—
461C22⋊C4—154no—
462C22⋊C4—154no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C42—22no—
466C42—54no—
467C42—62no—
468C42—102no—
469C42—154no—
470C42—304no—
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3C22×C4×D511yescharacteristic
473C22×C3C2×#70912yes—
474C22×C3C2×D4×D511yescharacteristic
475C22×C3C2×#71111yescharacteristic
476C22×C3D5×#4112yes—
477C2×D3—22no—
478C2×D3—22no—
479C2×D3—24no—
480C2×D3—24no—
481C2×D3—102no—
482C2×D3—102no—
483C2×D3—102no—
484C2×D3—202no—
485C2×D3—202no—
486C2×D3#401814yescomplemented
487C3×C4—42no—
488C3×C4—102no—
489C3×C4—102no—
490C3×C4—104no—
491C3×C4#402714yes—
492Dic3—22no—
493Dic3—42no—
494Dic3—102no—
495Dic3—104no—
496C2×C5—64no—
497C2×C5C4×#23511yescharacteristic
498C2×C5C2×#89311yescharacteristic
499C2×C5D3×#11711yescharacteristic
500C2×C5#554712yes—
501C2×C5#558012yes—
502D5—122no—
503C23—32no—
504C23—34no—
505C23—61no—
506C23—62no—
507C23—61no—
508C23—152no—
509C23—301no—
510C23—302no—
511C23—302no—
512C23—301no—
513C23C22×D3×D511yescharacteristic
514D4—308no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—32no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—54no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—68no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—102no—
532C2×C4—152no—
533C2×C4—154no—
534C2×C4—3016no—
535C2×C4—301no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—301no—
539C2×C4—308no—
540C2×C4#676812yes—
541C2×C4C4×D3×D512yes—
542C2×C4#679012yes—
543C2×C3C2×#401811yescharacteristic
544C2×C3C2×#402711yescharacteristic
545C2×C3#6585611yescharacteristic
546C2×C3#6587212yes—
547C2×C3#6588112yes—
548D3—24no—
549D3—202no—
550C5#7375411yescharacteristic, complemented, Sylow
551C22—34no—
552C22—62no—
553C22—64no—
554C22—64no—
555C22—62no—
556C22—302no—
557C22—302no—
558C22—302no—
559C22—602no—
560C22—602no—
561C22C2×#676811yescharacteristic
562C22C2×C4×D3×D511yescharacteristic
563C22D5×#23512yes—
564C22D3×#70912yes—
565C22C2×#679011yescharacteristic
566C4—42no—
567C4—62no—
568C4—102no—
569C4—104no—
570C4—102no—
571C4—122no—
572C4—302no—
573C4—304no—
574C4#9140614yes—
575C3#1060516911yescharacteristic, complemented, Sylow
576C2—64no—
577C2—602no—
578C2#1175257912yes—
579C2#1175266511yescharacteristic
580C2D3×#401811yescharacteristic
581C2C2×#9140611yescharacteristic
582C2#1175466312yes—
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91761C2semidirect
3. C2×C4×D3×Dic5C2semidirect
4. C4×C5×(C2×D3)⋊C4C2semidirect
5. C3×C4×#683C2semidirect
6. #11748892C2semidirect
8. C4×#6667C2semidirect
9. #11748666C2semidirect
10. #11748650C2semidirect
11. #11748611C2semidirect
32. C4×#1203C4semidirect
48. C4×#683D3semidirect
59. C2×C4×D15C2×C4semidirect
76. C4×Dic15D4semidirect
81. C3×C4×Dic5C2×C4semidirect
82. #6668C2×C4semidirect
84. #6667C2×C4semidirect
94. C4×(C2×D3)⋊C4D5semidirect
226. C4×Dic5C4×D3semidirect
252. C2×C5×D3#117semidirect
471. C3×C5#2290semidirect
486. C2×D3#4018semidirect
550. C5#73754semidirect
575. C3#10605169semidirect

Maximal subgroups

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

subgroupindex
C2×#917612
C2×C4×#12032
C2×C4×D3×Dic52
C4×C5×(C2×D3)⋊C42
C3×C4×#6832
#117488922
#117488832
C4×#66672
#117486662
#117486502
#117486112
#106051693
#737545