Finite Group Databasebeta

← #14320875

Subgroups — #14320875

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91761C211yesmaximal, characteristic, complemented
2C2×C3×#4018C211yesmaximal, characteristic, complemented
3C2×C4×#1202C211yesmaximal, characteristic
4C42×C5×Dic3C211yesmaximal, characteristic, complemented
5#11748912C212yesmaximal
6#11748820C212yesmaximal, complemented
7C4×Dic3⋊Dic5C211yesmaximal, characteristic, complemented
8#11748728C212yesmaximal, complemented
9C4×#6667C211yesmaximal, characteristic, complemented
10#11748706C212yesmaximal, complemented
11C4×#6665C211yesmaximal, characteristic, complemented
12#10605030—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1202C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×#6714C2212yes—
18C2×#6712C2212yes—
19C2×C4×Dic15C2211yescharacteristic
20#91761—24no—
21C2×C4×C5×Dic3C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C4×C5×Dic3C2212yes—
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×#685C2212yes—
26C2×C3×#683C2212yes—
27C2×C3×C4×Dic5C2211yescharacteristic
28C3×#4018—24no—
29C2×Dic3⋊Dic5C2212yes—
30C2×Dic3⋊Dic5C2211yescharacteristic
31C2×#6667C2212yes—
32C2×#6667C2211yescharacteristic
33C2×#6665C2212yes—
34C2×#6665C2211yescharacteristic
35C4×#1202C418yescomplemented
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82225—51nomaximal, Hall
40C2×C4×D20—31no—
41C2×#4018—31no—
42C2×#4018D311yescharacteristic, complemented
43C43×C5—31no—
44#65229—32no—
45#65229—32no—
46#65228—32no—
47C4×#685—31no—
48C4×#685—31no—
49C4×C4⋊Dic5—31no—
50#65217—32no—
51C23×D15C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C2×C4×D15—22no—
58C2×C4×D15—22no—
59C2×C4×D15C2×C414yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2312yes—
62C22×C5×Dic3C2311yescharacteristic
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C414yes—
68C2×#1202—24no—
69C2×#1202C2×C414yes—
70C3×C42×C5D414yescomplemented
71#6714—24no—
72#6712—24no—
73C4×Dic15—22no—
74C4×C5×Dic3—22no—
75C4×C5×Dic3—24no—
76C4×C5×Dic3—24no—
77C4×C5×Dic3C2×C414yes—
78C3×#685—24no—
79C3×#683—24no—
80C3×C4×Dic5—22no—
81Dic3⋊Dic5—24no—
82Dic3⋊Dic5C2×C414yes—
83#6667—24no—
84#6667C2×C414yes—
85#6665—24no—
86#6665C2×C414yes—
87C2×C3×#117—51no—
88C2×C4×#67—51no—
89C2×#872—51no—
90C4×#217—51no—
91#4990—52no—
92#4976—52no—
93#4957—52no—
94#4945—52no—
95C4×(C2×D3)⋊C4—51no—
96C4×Dic3⋊C4—51no—
97C42×Dic3D511yescharacteristic, complemented
98C22×D20—31no—
99C22×C4×D5—31no—
100C22×C4×D5C2×D311yescharacteristic
101C2×C42×C5—31no—
102C2×C42×C5—32no—
103C2×C42×C5—31no—
104C2×C42×C5—32no—
105C2×C42×C5C2×D311yescharacteristic
106C2×#685—31no—
107C2×#685—31no—
108C2×#685—32no—
109C2×#685—32no—
110C2×#685—32no—
111C2×#685C2×D312yes—
112C2×C4⋊Dic5—31no—
113C2×C4⋊Dic5—32no—
114C2×#683—32no—
115C2×#683C2×D312yes—
116C2×C4×Dic5—31no—
117C2×C4×Dic5C2×D311yescharacteristic
118C4×D20—38no—
119#4018—24no—
120#4018—64no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2293—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×D15—21no—
127C22×D15—22no—
128C22×D15—22no—
129C22×D15—21no—
130C22×D15C22×C412yes—
131C22×C3×D5—21no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5—21no—
135C22×C3×D5C22×C412yes—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C412yes—
139C2×C3×C4×C5C2×D414yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15C22×C412yes—
148C4×D15—28no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3C22×C412yes—
153C2×C5×Dic3C22×C412yes—
154C2×C5×Dic3#4114yes—
155C2×C5×Dic3#4114yes—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5C22×C412yes—
162C3×C4×D5—28no—
163#1202—28no—
164C23×C3×C4—51no—
165C22×#67—51no—
166C22×C4×D3—51no—
167C3×#117—104no—
168C2×C3×C4⋊C4—52no—
169C2×C3×C22⋊C4—52no—
170C2×C3×C42—51no—
171C2×C3×C42C2×D511yescharacteristic
172C2×#217—51no—
173C2×#217—52no—
174C4×#67—58no—
175C2×(C2×D3)⋊C4—51no—
176C2×(C2×D3)⋊C4—52no—
177C2×(C2×D3)⋊C4—52no—
178C2×Dic3⋊C4—51no—
179C2×Dic3⋊C4—52no—
180C2×Dic3⋊C4—52no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3C2×D511yescharacteristic
183C2×C4×Dic3C2×D512yes—
184C2×C4×Dic3C2×D512yes—
185C2×C4×Dic3C2×D511yescharacteristic
186#872—104no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C23×D5—31no—
191C23×D5C22×D311yescharacteristic
192C22×C4×C5—31no—
193C22×C4×C5—31no—
194C22×C4×C5—32no—
195C22×C4×C5C22×D312yes—
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—31no—
198C22×Dic5—32no—
199C22×Dic5C22×D312yes—
200C22×Dic5C22×D311yescharacteristic
201C2×D20—34no—
202C2×D20—64no—
203C2×C4×D5—22no—
204C2×C4×D5—22no—
205C2×C4×D5—34no—
206C2×C4×D5—62no—
207C2×C4×D5—62no—
208C2×C4×D5C4×D314yes—
209C42×C5—34no—
210C42×C5—64no—
211C42×C5—64no—
212C42×C5—62no—
213C42×C5#6714yescomplemented
214#685—24no—
215#685—34no—
216#685—34no—
217#685—64no—
218#685—64no—
219#685—64no—
220C4⋊Dic5—34no—
221C4⋊Dic5—64no—
222#683—24no—
223#683—64no—
224C4×Dic5—22no—
225C4×Dic5—62no—
226C2×C4×D4—151no—
227C2×#117—51no—
228C2×#117—151no—
229#390—152no—
230#389—152no—
231#388—152no—
232#388—152no—
233C4×C4⋊C4—151no—
234C4×C22⋊C4—151no—
235C4×C22⋊C4—151no—
236C43—31no—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5C2×#4112yes—
242C2×D15—22no—
243C2×D15—22no—
244C2×D15—22no—
245C2×D15—42no—
246C2×D15—42no—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—42no—
251C2×C3×D5—42no—
252C3×C4×C5—24no—
253C3×C4×C5C4×D414yes—
254Dic15—22no—
255Dic15—42no—
256C3×Dic5—22no—
257C3×Dic5—42no—
258C5×Dic3—22no—
259C5×Dic3—24no—
260C5×Dic3#11714yescomplemented
261C24×C3—51no—
262C23×D3—51no—
263C22×C3×C4—51no—
264C22×C3×C4—54no—
265C22×C3×C4—52no—
266C22×C3×C4—102no—
267C22×C3×C4—102no—
268C22×C3×C4C22×D512yes—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—54no—
271C2×#67—104no—
272C22×Dic3—51no—
273C22×Dic3—52no—
274C22×Dic3C22×D511yescharacteristic
275C22×Dic3C22×D512yes—
276C22×Dic3C22×D511yescharacteristic
277C2×C4×D3—54no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C3×C4⋊C4—104no—
281C3×C22⋊C4—104no—
282C3×C42—102no—
283C3×C42D2014yescomplemented
284#217—54no—
285#217—104no—
286(C2×D3)⋊C4—54no—
287(C2×D3)⋊C4—104no—
288(C2×D3)⋊C4—104no—
289Dic3⋊C4—54no—
290Dic3⋊C4—104no—
291Dic3⋊C4—104no—
292C4×Dic3—22no—
293C4×Dic3—24no—
294C4×Dic3—24no—
295C4×Dic3—102no—
296C4×Dic3C4×D514yes—
297C23×C5C23×D311yescharacteristic
298C22×D5—21no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—21no—
302C22×D5—32no—
303C22×D5—61no—
304C22×D5—62no—
305C22×D5—62no—
306C22×D5—61no—
307C22×D5C2×C4×D312yes—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—32no—
311C2×C4×C5—34no—
312C2×C4×C5—32no—
313C2×C4×C5—34no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5C2×C4×D312yes—
318C2×C4×C5#23512yes—
319C2×C4×C5C2×#6714yes—
320C2×C4×C5C2×#6712yes—
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—32no—
327C2×Dic5—61no—
328C2×Dic5—61no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5C2×C4×D312yes—
333D20—68no—
334C4×D5—28no—
335C4×D5—68no—
336C22×D4—151no—
337C23×C4—51no—
338C23×C4—151no—
339C4×D4—158no—
340#117—104no—
341#117—304no—
342C2×C4⋊C4—52no—
343C2×C4⋊C4—151no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—152no—
346C2×C22⋊C4—52no—
347C2×C22⋊C4—151no—
348C2×C22⋊C4—151no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—32no—
354C2×C42—32no—
355C2×C42—31no—
356C2×C42—51no—
357C2×C42—151no—
358C2×C42D3×D511yescharacteristic
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5C2×#11711yescharacteristic
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5C4×#4111yescharacteristic
365C2×C3×C5#52912yes—
366C2×C3×C5#53212yes—
367D15—42no—
368C3×D5—42no—
369C23×C3—52no—
370C23×C3—101no—
371C23×C3—102no—
372C23×C3—102no—
373C23×C3—101no—
374C23×C3C23×D511yescharacteristic
375C22×D3—52no—
376C22×D3—101no—
377C22×D3—102no—
378C22×D3—101no—
379C22×D3—102no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—52no—
383C2×C3×C4—101no—
384C2×C3×C4—101no—
385C2×C3×C4—108no—
386C2×C3×C4—102no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4C2×C4×D512yes—
390C2×C3×C4C2×D2014yes—
391C2×C3×C4C2×D2012yes—
392C2×C3×C4#70912yes—
393#67—108no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—52no—
398C2×Dic3—101no—
399C2×Dic3—101no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3C2×C4×D512yes—
404C2×Dic3C2×C4×D512yes—
405C2×Dic3#70914yes—
406C2×Dic3#70914yes—
407C4×D3—108no—
408C22×C5C22×C4×D311yescharacteristic
409C22×C5C2×#23511yescharacteristic
410C22×C5D3×#4112yes—
411C22×C5D3×#4112yes—
412C22×C5C22×#6711yescharacteristic
413C2×D5—22no—
414C2×D5—22no—
415C2×D5—22no—
416C2×D5—42no—
417C2×D5—42no—
418C2×D5—62no—
419C2×D5—62no—
420C2×D5—62no—
421C2×D5—122no—
422C2×D5—122no—
423C4×C5—24no—
424C4×C5—34no—
425C4×C5—62no—
426C4×C5—64no—
427C4×C5C4×#6714yes—
428Dic5—22no—
429Dic5—42no—
430Dic5—62no—
431Dic5—122no—
432C24—51no—
433C24—151no—
434C2×D4—154no—
435C2×D4—304no—
436C22×C4—31no—
437C22×C4—31no—
438C22×C4—32no—
439C22×C4—51no—
440C22×C4—54no—
441C22×C4—52no—
442C22×C4—102no—
443C22×C4—102no—
444C22×C4—151no—
445C22×C4—154no—
446C22×C4—152no—
447C22×C4—302no—
448C22×C4—302no—
449C22×C4C2×D3×D512yes—
450C22×C4C2×D3×D511yescharacteristic
451C4⋊C4—104no—
452C4⋊C4—154no—
453C4⋊C4—304no—
454C4⋊C4—304no—
455C22⋊C4—104no—
456C22⋊C4—154no—
457C22⋊C4—154no—
458C22⋊C4—304no—
459C22⋊C4—304no—
460C22⋊C4—304no—
461C42—34no—
462C42—64no—
463C42—64no—
464C42—62no—
465C42—102no—
466C42—302no—
467C42#120214yescomplemented
468C3×C5#229311yescharacteristic, complemented, Hall
469C22×C3—102no—
470C22×C3—102no—
471C22×C3—102no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3C22×C4×D511yescharacteristic
475C22×C3C22×D2011yescharacteristic
476C22×C3C2×#70911yescharacteristic
477C22×C3C2×#70912yes—
478C22×C3C2×#70912yes—
479C2×D3—102no—
480C2×D3—102no—
481C2×D3—102no—
482C2×D3—202no—
483C2×D3—202no—
484C3×C4—24no—
485C3×C4—102no—
486C3×C4—202no—
487C3×C4C4×D2014yes—
488Dic3—22no—
489Dic3—24no—
490Dic3—102no—
491Dic3—202no—
492Dic3#401814yescomplemented
493C2×C5D3×#11711yescharacteristic
494C2×C5#552211yescharacteristic
495C2×C5#552812yes—
496C2×C5C2×C4×#6711yescharacteristic
497C2×C5#583212yes—
498D5—42no—
499D5—122no—
500C23—52no—
501C23—101no—
502C23—102no—
503C23—102no—
504C23—101no—
505C23—152no—
506C23—301no—
507C23—302no—
508C23—302no—
509C23—301no—
510C23C22×D3×D511yescharacteristic
511D4—308no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—32no—
515C2×C4—34no—
516C2×C4—32no—
517C2×C4—34no—
518C2×C4—52no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—108no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—152no—
529C2×C4—301no—
530C2×C4—301no—
531C2×C4—308no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4#677112yes—
536C2×C4C4×D3×D512yes—
537C2×C4C2×#120214yes—
538C2×C4C2×#120212yes—
539C2×C3—202no—
540C2×C3C2×#401811yescharacteristic
541C2×C3C2×C4×D2011yescharacteristic
542C2×C3C4×#70911yescharacteristic
543C2×C3#6581112yes—
544C2×C3#6581312yes—
545D3—202no—
546C5#8222511yescharacteristic, complemented, Sylow
547C22—102no—
548C22—102no—
549C22—102no—
550C22—202no—
551C22—202no—
552C22—302no—
553C22—302no—
554C22—302no—
555C22—602no—
556C22—602no—
557C22C2×#677111yescharacteristic
558C22C2×C4×D3×D511yescharacteristic
559C22D3×#70912yes—
560C22D3×#70912yes—
561C22C22×#120211yescharacteristic
562C4—24no—
563C4—34no—
564C4—62no—
565C4—64no—
566C4—102no—
567C4—202no—
568C4—302no—
569C4—602no—
570C4C4×#120214yes—
571C3#1060503011yescharacteristic, complemented, Sylow
572C2—202no—
573C2—602no—
574C2#1175266611yescharacteristic
575C2#1175269312yes—
576C2D3×#401811yescharacteristic
577C2C2×C4×#120211yescharacteristic
578C2#1175458112yes—
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2293
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
2. C2×C3×#4018C2semidirect
4. C42×C5×Dic3C2semidirect
6. #11748820C2semidirect
7. C4×Dic3⋊Dic5C2semidirect
8. #11748728C2semidirect
9. C4×#6667C2semidirect
10. #11748706C2semidirect
11. C4×#6665C2semidirect
35. C4×#1202C4semidirect
42. C2×#4018D3semidirect
70. C3×C42×C5D4semidirect
97. C42×Dic3D5semidirect
213. C42×C5#67semidirect
260. C5×Dic3#117semidirect
283. C3×C42D20semidirect
467. C42#1202semidirect
468. C3×C5#2293semidirect
492. Dic3#4018semidirect
546. C5#82225semidirect
571. C3#10605030semidirect

Maximal subgroups

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

subgroupindex
C2×#917612
C2×C3×#40182
C2×C4×#12022
C42×C5×Dic32
#117489122
#117488202
C4×Dic3⋊Dic52
#117487282
C4×#66672
#117487062
C4×#66652
#106050303
#822255