Finite Group Databasebeta

← #14320871

Subgroups — #14320871

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×C3×#4018C211yesmaximal, characteristic, complemented
2C2×C4×#1201C211yesmaximal, characteristic
3C2×#91371C211yesmaximal, characteristic, complemented
4C4×#6712C211yesmaximal, characteristic, complemented
5C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
6#11748916C212yesmaximal
7#11748718C212yesmaximal, complemented
8#11748712C212yesmaximal, complemented
9C4×#6665C211yesmaximal, characteristic, complemented
10#11748658C212yesmaximal, complemented
11C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
12#10605170—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1201C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×#6712C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19C2×C4×Dic15C2211yescharacteristic
20C2×C5×(C2×D3)⋊C4C2212yes—
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C3×#685C2212yes—
23C2×C3×#683C2212yes—
24C2×C3×C4×Dic5C2211yescharacteristic
25C3×#4018—24no—
26C2×Dic3⋊Dic5C2212yes—
27C2×#6669C2211yescharacteristic
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×(C2×D3)⋊Dic5C2211yescharacteristic
30C2×#6665C2212yes—
31C2×#6665C2211yescharacteristic
32C2×Dic3×Dic5C2212yes—
33C2×Dic3×Dic5C2212yes—
34C4×#1201C418yescomplemented
35#91371—24no—
36#91115C2212yes—
37C5×C3⋊#95C2212yes—
38#90994C2212yes—
39#82225—51nomaximal, Hall
40C2×C4×C22⋊D5—31no—
41C2×#4072—31no—
42C2×#4018D311yescharacteristic, complemented
43C4×C5×C22⋊C4—31no—
44#65246—32no—
45#65233—32no—
46C4×#685—31no—
47C4×#683—31no—
48C42×Dic5—31no—
49#64959—32no—
50#64936—32no—
51C23×C5×D3C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2312yes—
60C2×C4×C5×D3—22no—
61C2×C4×C5×D3—22no—
62C2×C4×C5×D3C2×C414yes—
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2312yes—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C414yes—
68C2×#1201—24no—
69C2×#1201C2×C414yes—
70C3×C42×C5—22no—
71#6712—24no—
72C4×Dic15—22no—
73C4×Dic15C2×C414yes—
74C5×(C2×D3)⋊C4—24no—
75C4×C5×Dic3—22no—
76C3×#685—24no—
77C3×#683—24no—
78C3×C4×Dic5D414yescomplemented
79Dic3⋊Dic5—24no—
80#6669C2×C414yes—
81(C2×D3)⋊Dic5—24no—
82(C2×D3)⋊Dic5C2×C414yes—
83#6665—24no—
84#6665C2×C414yes—
85Dic3×Dic5—24no—
86Dic3×Dic5—24no—
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)⋊C4D511yescharacteristic, complemented
96C4×Dic3⋊C4—51no—
97C42×Dic3—51no—
98C23×C4×C5—31no—
99C22×C22⋊D5—31no—
100C22×C4×D5C2×D311yescharacteristic
101C2×C5×C22⋊C4—32no—
102C2×C42×C5—31no—
103C2×C42×C5C2×D311yescharacteristic
104C2×C22⋊Dic5—31no—
105C2×C22⋊Dic5—32no—
106C4×C22⋊D5—38no—
107C2×#685—31no—
108C2×#685—32no—
109C2×#685C2×D312yes—
110#4072—64no—
111C2×C4⋊Dic5—32no—
112C2×#683—31no—
113C2×#683—32no—
114C2×#683C2×D312yes—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—32no—
118C2×C4×Dic5—32no—
119C2×C4×Dic5C2×D311yescharacteristic
120#4018—24no—
121C5×#95—32no—
122#3963—32no—
123#3963—32no—
124#2293—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×C5×D3—21no—
127C22×C5×D3—22no—
128C22×C5×D3—22no—
129C22×C5×D3—21no—
130C22×C5×D3C22×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×C5—22no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15C22×C412yes—
147C2×Dic15C22×C412yes—
148C2×Dic15#4114yes—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3C22×C412yes—
154C2×C5×Dic3#4114yes—
155C4×C5×D3—28no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C2×D414yes—
162C3×C4×D5—28no—
163#1201—28no—
164C23×C3×C4—51no—
165C22×#67—51no—
166C22×C4×D3C2×D511yescharacteristic
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)⋊C4C2×D512yes—
178C2×Dic3⋊C4—51no—
179C2×Dic3⋊C4—52no—
180C2×Dic3⋊C4—52no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—52no—
184C2×C4×Dic3—52no—
185C2×C4×Dic3C2×D511yescharacteristic
186#872—104no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95C2×D512yes—
190C24×C5—31no—
191C23×D5C22×D311yescharacteristic
192C22×C4×C5—32no—
193C22×C4×C5—31no—
194C22×C4×C5—34no—
195C22×C4×C5—62no—
196C22×C4×C5—62no—
197C22×C4×C5C22×D312yes—
198C22×C4×C5C22×D311yescharacteristic
199C2×C22⋊D5—34no—
200C2×C22⋊D5—64no—
201C22×Dic5—31no—
202C22×Dic5—31no—
203C22×Dic5—32no—
204C22×Dic5C22×D311yescharacteristic
205C22×Dic5C22×D312yes—
206C2×C4×D5—22no—
207C2×C4×D5—22no—
208C2×C4×D5C4×D314yes—
209C5×C22⋊C4—64no—
210C42×C5—22no—
211C42×C5—62no—
212C22⋊Dic5—34no—
213C22⋊Dic5—64no—
214#685—24no—
215#685—34no—
216#685—64no—
217C4⋊Dic5—64no—
218#683—24no—
219#683—34no—
220#683—64no—
221C4×Dic5—34no—
222C4×Dic5—64no—
223C4×Dic5—64no—
224C4×Dic5—62no—
225C4×Dic5#6714yescomplemented
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—31no—
235C4×C22⋊C4—151no—
236C43—151no—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C2×#4112yes—
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4112yes—
242C2×C5×D3—22no—
243C2×C5×D3—22no—
244C2×C5×D3—22no—
245C2×C5×D3—42no—
246C2×C5×D3—42no—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—42no—
251C2×C3×D5—42no—
252C3×C4×C5—42no—
253C3×C4×C5C4×D414yes—
254Dic15—22no—
255Dic15—42no—
256Dic15#11714yescomplemented
257C3×Dic5—22no—
258C3×Dic5—24no—
259C5×Dic3—22no—
260C5×Dic3—24no—
261C24×C3—51no—
262C23×D3C22×D511yescharacteristic
263C22×C3×C4—51no—
264C22×C3×C4—52no—
265C22×C3×C4—54no—
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—51no—
274C22×Dic3—52no—
275C22×Dic3C22×D511yescharacteristic
276C22×Dic3C22×D512yes—
277C2×C4×D3—22no—
278C2×C4×D3—22no—
279C2×C4×D3C4×D514yes—
280C3×C4⋊C4—104no—
281C3×C22⋊C4—104no—
282C3×C42—22no—
283C3×C42—54no—
284#217—54no—
285#217—104no—
286(C2×D3)⋊C4—24no—
287(C2×D3)⋊C4—54no—
288(C2×D3)⋊C4—104no—
289Dic3⋊C4—54no—
290Dic3⋊C4—104no—
291Dic3⋊C4—104no—
292C4×Dic3—22no—
293C4×Dic3—54no—
294C4×Dic3—104no—
295C4×Dic3—102no—
296C4×Dic3—104no—
297C23×C5—32no—
298C23×C5—61no—
299C23×C5—62no—
300C23×C5—62no—
301C23×C5—61no—
302C23×C5C23×D311yescharacteristic
303C22×D5—21no—
304C22×D5—22no—
305C22×D5—22no—
306C22×D5—21no—
307C22×D5C2×C4×D312yes—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—32no—
312C2×C4×C5—34no—
313C2×C4×C5—62no—
314C2×C4×C5—61no—
315C2×C4×C5—62no—
316C2×C4×C5—61no—
317C2×C4×C5—68no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5#23512yes—
320C2×C4×C5C2×#6712yes—
321C22⋊D5—68no—
322C2×Dic5—21no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—21no—
326C2×Dic5—32no—
327C2×Dic5—34no—
328C2×Dic5—32no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5C2×C4×D312yes—
334C2×Dic5C2×#6714yes—
335C4×D5—28no—
336C22×D4—151no—
337C23×C4—31no—
338C23×C4—51no—
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—32no—
347C2×C22⋊C4—52no—
348C2×C22⋊C4—151no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—51no—
354C2×C42—151no—
355C2×C42—152no—
356C2×C42—152no—
357C2×C42—151no—
358C2×C42D3×D511yescharacteristic
359#95—32no—
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—
367C3×D5—42no—
368C5×D3—42no—
369C23×C3—52no—
370C23×C3—102no—
371C23×C3—101no—
372C23×C3—101no—
373C23×C3—102no—
374C23×C3C23×D511yescharacteristic
375C22×D3—22no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—22no—
379C22×D3C2×C4×D512yes—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—52no—
384C2×C3×C4—54no—
385C2×C3×C4—102no—
386C2×C3×C4—101no—
387C2×C3×C4—101no—
388C2×C3×C4—102no—
389C2×C3×C4—108no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4D4×D512yes—
392C2×C3×C4#71112yes—
393#67—108no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—21no—
397C2×Dic3—22no—
398C2×Dic3—52no—
399C2×Dic3—54no—
400C2×Dic3—52no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3C2×C4×D512yes—
406C2×Dic3#70914yes—
407C4×D3—28no—
408C22×C5—62no—
409C22×C5—62no—
410C22×C5—62no—
411C22×C5—122no—
412C22×C5—122no—
413C22×C5C22×C4×D311yescharacteristic
414C22×C5C2×#23511yescharacteristic
415C22×C5D3×#4112yes—
416C22×C5D3×#4112yes—
417C22×C5C22×#6711yescharacteristic
418C2×D5—22no—
419C2×D5—22no—
420C2×D5—22no—
421C2×D5—42no—
422C2×D5—42no—
423C4×C5—42no—
424C4×C5—64no—
425C4×C5—62no—
426C4×C5C4×#6714yes—
427Dic5—22no—
428Dic5—24no—
429Dic5—34no—
430Dic5—62no—
431Dic5—122no—
432C24—31no—
433C24—51no—
434C2×D4—154no—
435C2×D4—304no—
436C22×C4—31no—
437C22×C4—32no—
438C22×C4—34no—
439C22×C4—51no—
440C22×C4—52no—
441C22×C4—54no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—102no—
445C22×C4—102no—
446C22×C4—151no—
447C22×C4—151no—
448C22×C4—152no—
449C22×C4C2×D3×D512yes—
450C22×C4C2×D3×D511yescharacteristic
451C4⋊C4—104no—
452C4⋊C4—154no—
453C4⋊C4—304no—
454C4⋊C4—304no—
455C22⋊C4—64no—
456C22⋊C4—104no—
457C22⋊C4—154no—
458C22⋊C4—154no—
459C22⋊C4—304no—
460C22⋊C4—304no—
461C42—22no—
462C42—54no—
463C42—62no—
464C42—154no—
465C42—304no—
466C42—304no—
467C42—302no—
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×C3C2×#70912yes—
476C22×C3C2×D4×D511yescharacteristic
477C22×C3C2×#71111yescharacteristic
478C22×C3D5×#4112yes—
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—42no—
483C2×D3—42no—
484C3×C4—42no—
485C3×C4—102no—
486C3×C4—104no—
487C3×C4#402714yes—
488Dic3—22no—
489Dic3—24no—
490Dic3—54no—
491Dic3—102no—
492Dic3—202no—
493C2×C5—122no—
494C2×C5D3×#11711yescharacteristic
495C2×C5#552211yescharacteristic
496C2×C5#552812yes—
497C2×C5C2×C4×#6711yescharacteristic
498C2×C5#583212yes—
499D5—42no—
500C23—32no—
501C23—52no—
502C23—61no—
503C23—62no—
504C23—62no—
505C23—61no—
506C23—101no—
507C23—102no—
508C23—102no—
509C23—101no—
510C23C22×D3×D511yescharacteristic
511D4—308no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—32no—
516C2×C4—34no—
517C2×C4—52no—
518C2×C4—54no—
519C2×C4—62no—
520C2×C4—61no—
521C2×C4—62no—
522C2×C4—61no—
523C2×C4—68no—
524C2×C4—101no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—101no—
528C2×C4—108no—
529C2×C4—152no—
530C2×C4—154no—
531C2×C4—152no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4#677212yes—
537C2×C4C4×D3×D512yes—
538C2×C4D5×#6712yes—
539C2×C3—202no—
540C2×C3C4×#70911yescharacteristic
541C2×C3C2×#402711yescharacteristic
542C2×C3D5×#11711yescharacteristic
543C2×C3#6587212yes—
544C2×C3#6588212yes—
545D3—42no—
546C5#8222511yescharacteristic, complemented, Sylow
547C22—62no—
548C22—62no—
549C22—62no—
550C22—102no—
551C22—102no—
552C22—102no—
553C22—122no—
554C22—122no—
555C22—202no—
556C22—202no—
557C22C2×#677211yescharacteristic
558C22C2×C4×D3×D511yescharacteristic
559C22D3×#70912yes—
560C22#9201612yes—
561C22C2×D5×#6711yescharacteristic
562C4—42no—
563C4—62no—
564C4—64no—
565C4—102no—
566C4—104no—
567C4—154no—
568C4—302no—
569C4—602no—
570C4#9144014yes—
571C3#1060517011yescharacteristic, complemented, Sylow
572C2—122no—
573C2—202no—
574C2#1175266611yescharacteristic
575C2#1175269412yes—
576C2#1175272311yescharacteristic
577C2#1175431112yes—
578C2C2×#9144011yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
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×C3×#4018C2semidirect
3. C2×#91371C2semidirect
4. C4×#6712C2semidirect
5. C4×C5×(C2×D3)⋊C4C2semidirect
7. #11748718C2semidirect
8. #11748712C2semidirect
9. C4×#6665C2semidirect
10. #11748658C2semidirect
11. C4×Dic3×Dic5C2semidirect
34. C4×#1201C4semidirect
42. C2×#4018D3semidirect
78. C3×C4×Dic5D4semidirect
95. C4×(C2×D3)⋊C4D5semidirect
225. C4×Dic5#67semidirect
256. Dic15#117semidirect
468. C3×C5#2293semidirect
546. C5#82225semidirect
571. C3#10605170semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40182
C2×C4×#12012
C2×#913712
C4×#67122
C4×C5×(C2×D3)⋊C42
#117489162
#117487182
#117487122
C4×#66652
#117486582
C4×Dic3×Dic52
#106051703
#822255