Finite Group Databasebeta

← #14322442

Subgroups — #14322442

Order 1920.

2208 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×D12C211yesmaximal, characteristic
2C2×C3×#4018C211yesmaximal, characteristic, complemented
3C2×#91358C211yesmaximal, characteristic, complemented
4#11751040C211yesmaximal, characteristic, complemented
5C5×#4939C211yesmaximal, characteristic, complemented
6#11748940C214yesmaximal, complemented
7#11748909C214yesmaximal, complemented
8#11748768C211yesmaximal, characteristic, complemented
9#11748764C211yesmaximal, characteristic, complemented
10#10608159—31nomaximal, Hall
11C23×D3×D5C2212yes—
12C22×D60C2211yescharacteristic
13C22×C5×D12C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1203C2212yes—
16C2×D5×D12—24no—
17C2×D5×D12—24no—
18C2×D5×D12C418yescomplemented
19C2×C3×C42×C5C2211yescharacteristic, complemented
20C2×#6714C2214yescomplemented
21C2×C4⋊Dic15C2211yescharacteristic, complemented
22C2×C5×(C2×D3)⋊C4C2214yescomplemented
23C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
24C2×C3×#685C2212yes—
25C2×C3×#683C2212yescomplemented
26C2×C3×C4×Dic5C2211yescharacteristic, complemented
27C3×#4018—24no—
28C2×#6667C2214yescomplemented
29C2×(C2×D3)⋊Dic5C2214yescomplemented
30C2×#6665C2212yes—
31C2×Dic3×Dic5C2212yescomplemented
32#91358—24no—
33#82269—51nomaximal, Hall
34C22×D4×D5—31no—
35C2×#4038—31no—
36C2×#4018D311yescharacteristic, complemented
37C5×#390—31no—
38#65510—31no—
39#65277—31no—
40#65246—34no—
41#65244—34no—
42#65228—31no—
43C23×D15C2312yes—
44C23×C5×D3C2312yes—
45C23×C3×D5C2311yescharacteristic
46C22×D3×D5—24no—
47C22×D3×D5—24no—
48C22×D3×D5—44no—
49C22×D3×D5—44no—
50C22×D3×D5C2×C418yes—
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C2×D60—22no—
55C2×D60—22no—
56C2×D60C2×C414yes—
57C22×C5×Dic3C2312yes—
58C2×C5×D12—22no—
59C2×C5×D12—22no—
60C2×C5×D12C2×C414yes—
61C22×C3×Dic5C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C2×C3×C4×D5C2×C414yes—
64C2×C3×C4×D5D414yes—
65C2×C3×C4×D5D414yes—
66C2×#1203—24no—
67C2×#1203—24no—
68C2×#1203C2×C418yes—
69D5×D12—232no—
70C3×C42×C5—22no—
71#6714—44no—
72C4⋊Dic15—22no—
73C5×(C2×D3)⋊C4—44no—
74C5×C4⋊Dic3—22no—
75C3×#685—24no—
76C3×#683—24no—
77C3×C4×Dic5—22no—
78#6667—44no—
79(C2×D3)⋊Dic5—44no—
80#6665—24no—
81Dic3×Dic5—24no—
82C23×D12—51no—
83C2×C3×#117—51no—
84C2×#926—51no—
85#4988—54no—
86#4955—54no—
87#4939—51no—
88#4939—51no—
89#4939—51no—
90#4939D511yescharacteristic, complemented
91C24×D5—32no—
92C22×C5×D4—31no—
93C22×C22⋊D5—32no—
94C2×D4×D5—38no—
95C2×D4×D5—64no—
96C2×D4×D5—64no—
97C22×D20—31no—
98C22×C4×D5C2×D311yescharacteristic
99C2×C5×C4⋊C4—31no—
100C2×C5×C22⋊C4—34no—
101C2×C42×C5C2×D311yescharacteristic, complemented
102C2×C22⋊Dic5—34no—
103C2×#685—32no—
104C2×#685—34no—
105C2×#685—34no—
106C2×#685C2×D312yes—
107C2×C4⋊Dic5—31no—
108C2×#683C2×D312yescomplemented
109C2×C4×Dic5—32no—
110C2×C4×Dic5C2×D311yescharacteristic, complemented
111#4038—64no—
112#4018—24no—
113#2309—151noSylow
114C23×C3×C5C2411yescharacteristic
115C22×D15—22no—
116C22×D15—22no—
117C22×D15—24no—
118C22×D15—24no—
119C22×D15C22×C414yes—
120C22×C5×D3—22no—
121C22×C5×D3—22no—
122C22×C5×D3—24no—
123C22×C5×D3—24no—
124C22×C5×D3C22×C414yes—
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5C22×C412yes—
128C22×C3×D5C2×D412yes—
129C22×C3×D5C2×D412yes—
130C2×D3×D5—216no—
131C2×D3×D5—416no—
132C2×D3×D5—48no—
133C2×D3×D5—416no—
134C2×D3×D5—48no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×D412yes—
141C2×Dic15—22no—
142C2×Dic15—24no—
143D60—28no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—24no—
146C5×D12—28no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5C22×C412yes—
151C2×C3×Dic5C2×D412yes—
152C2×C3×Dic5C2×D412yes—
153C3×C4×D5C22⋊C4116yescomplemented
154#1203—216no—
155C24×D3—52no—
156C23×C3×C4—51no—
157C22×D12—52no—
158C22×D12—51no—
159C22×D12—58no—
160C22×D12—104no—
161C22×D12—104no—
162C22×D12C2×D511yescharacteristic
163C3×#117—104no—
164C2×C3×C4⋊C4—52no—
165C2×C3×C22⋊C4—52no—
166C2×C3×C42—51no—
167C2×C3×C42C2×D511yescharacteristic, complemented
168C2×#217—52no—
169C2×(C2×D3)⋊C4—54no—
170C2×(C2×D3)⋊C4—54no—
171C2×(C2×D3)⋊C4—54no—
172C2×(C2×D3)⋊C4C2×D514yescomplemented
173#926—104no—
174C2×C4⋊Dic3—51no—
175C2×C4⋊Dic3C2×D511yescharacteristic, complemented
176C2×C4×Dic3—52no—
177C24×C5—32no—
178C23×D5—32no—
179C23×D5—38no—
180C23×D5—64no—
181C23×D5—64no—
182C23×D5—124no—
183C23×D5—124no—
184C23×D5C22×D311yescharacteristic
185C2×C5×D4—34no—
186C2×C5×D4—62no—
187C2×C5×D4—62no—
188C22×C4×C5—32no—
189C22×C4×C5C22×D312yes—
190C22×C4×C5C22×D311yescharacteristic
191C2×C22⋊D5—38no—
192C2×C22⋊D5—64no—
193C2×C22⋊D5—64no—
194C22×Dic5—32no—
195C22×Dic5C22×D312yes—
196C22×Dic5C22×D311yescharacteristic
197D4×D5—632no—
198C2×D20—34no—
199C2×D20—62no—
200C2×D20—62no—
201C2×C4×D5C4×D314yes—
202C2×C4×D5D1214yes—
203C2×C4×D5#6714yes—
204C5×C4⋊C4—62no—
205C5×C22⋊C4—124no—
206C42×C5—22no—
207C22⋊Dic5—124no—
208#685—24no—
209#685—64no—
210#685—124no—
211#685—124no—
212C4⋊Dic5—62no—
213#683—24no—
214C4×Dic5—22no—
215C4×Dic5—64no—
216C23×D4—151no—
217C2×#117—51no—
218C2×#117—151no—
219#390—31no—
220#390—151no—
221#390—151no—
222#390—154no—
223#390—151no—
224#379—154no—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C22×D411yescharacteristic
227C22×C3×C5C22×D411yescharacteristic
228C22×C3×C5H(5,𝔽2)12yes—
229C22×C3×C5H(5,𝔽2)12yes—
230C2×D15—24no—
231C2×D15—28no—
232C2×D15—42no—
233C2×D15—44no—
234C2×D15—42no—
235C2×C5×D3—24no—
236C2×C5×D3—28no—
237C2×C5×D3—42no—
238C2×C5×D3—44no—
239C2×C5×D3—42no—
240C2×C3×D5—24no—
241C2×C3×D5—22no—
242C2×C3×D5—24no—
243C2×C3×D5—22no—
244C2×C3×D5C2×C22⋊C414yes—
245D3×D5—432no—
246C3×C4×C5—42no—
247C3×C4×C5C2×C22⋊C414yes—
248Dic15—42no—
249C3×Dic5—42no—
250C3×Dic5C2×C22⋊C414yes—
251C5×Dic3—42no—
252C24×C3—51no—
253C23×D3—52no—
254C23×D3—58no—
255C23×D3—104no—
256C23×D3—104no—
257C23×D3—204no—
258C23×D3—204no—
259C23×D3C22×D512yes—
260C22×C3×C4—51no—
261C22×C3×C4—54no—
262C22×C3×C4—54no—
263C22×C3×C4—54no—
264C22×C3×C4—52no—
265C22×C3×C4C22×D512yes—
266C22×C3×C4C22×D511yescharacteristic
267C22×Dic3—52no—
268C22×Dic3C22×D512yes—
269C2×D12—22no—
270C2×D12—22no—
271C2×D12—58no—
272C2×D12—54no—
273C2×D12—1032no—
274C2×D12—104no—
275C2×D12—104no—
276C2×D12—102no—
277C2×D12—102no—
278C2×D12C4×D514yes—
279C3×C4⋊C4—104no—
280C3×C22⋊C4—104no—
281C3×C42—22no—
282C3×C42—102no—
283#217—104no—
284(C2×D3)⋊C4—44no—
285(C2×D3)⋊C4—204no—
286(C2×D3)⋊C4—204no—
287(C2×D3)⋊C4—204no—
288C4⋊Dic3—22no—
289C4⋊Dic3—102no—
290C4×Dic3—104no—
291C23×C5—34no—
292C23×C5—62no—
293C23×C5—64no—
294C23×C5—64no—
295C23×C5—62no—
296C23×C5C23×D311yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—34no—
300C22×D5—62no—
301C22×D5—64no—
302C22×D5—64no—
303C22×D5—62no—
304C22×D5—616no—
305C22×D5—1216no—
306C22×D5—128no—
307C22×D5—128no—
308C22×D5—1216no—
309C22×D5C2×C4×D312yes—
310C22×D5C2×D1212yes—
311C22×D5C2×#6712yes—
312C5×D4—68no—
313C2×C4×C5—22no—
314C2×C4×C5—22no—
315C2×C4×C5—22no—
316C2×C4×C5—62no—
317C2×C4×C5—64no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5C2×D1212yes—
320C2×C4×C5C2×#6712yes—
321C22⋊D5—616no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—22no—
325C2×Dic5—62no—
326C2×Dic5—64no—
327C2×Dic5C2×C4×D312yes—
328C2×Dic5C2×D1212yes—
329C2×Dic5C2×#6712yes—
330D20—68no—
331C4×D5(C2×D3)⋊C4116yescomplemented
332C25—152no—
333C22×D4—31no—
334C22×D4—158no—
335C22×D4—152no—
336C22×D4—151no—
337C22×D4—304no—
338C22×D4—304no—
339C23×C4—51no—
340#117—104no—
341#117—304no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—52no—
344C2×C4⋊C4—151no—
345C2×C22⋊C4—34no—
346C2×C22⋊C4—52no—
347C2×C22⋊C4—152no—
348C2×C22⋊C4—154no—
349C2×C22⋊C4—154no—
350C2×C22⋊C4—154no—
351C2×C42—51no—
352C2×C42—152no—
353C2×C42D3×D511yescharacteristic, complemented
354C2×C3×C5C22×C22⋊C411yescharacteristic
355C2×C3×C5#51812yes—
356C2×C3×C5#53511yescharacteristic
357C2×C3×C5#53512yes—
358C2×C3×C5#53511yescharacteristic
359D15—44no—
360C3×D5—24no—
361C5×D3—44no—
362C23×C3—52no—
363C23×C3—52no—
364C23×C3—52no—
365C23×C3—102no—
366C23×C3—102no—
367C23×C3C23×D511yescharacteristic
368C22×D3—22no—
369C22×D3—22no—
370C22×D3—24no—
371C22×D3—24no—
372C22×D3—54no—
373C22×D3—1016no—
374C22×D3—102no—
375C22×D3—102no—
376C22×D3—104no—
377C22×D3—104no—
378C22×D3—2016no—
379C22×D3—208no—
380C22×D3—2016no—
381C22×D3—208no—
382C22×D3C2×C4×D514yes—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—52no—
387C2×C3×C4—52no—
388C2×C3×C4—52no—
389C2×C3×C4—516no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4C2×C4×D512yes—
394C2×C3×C4D4×D512yes—
395C2×C3×C4D4×D512yes—
396C2×Dic3—22no—
397C2×Dic3—24no—
398C2×Dic3—102no—
399C2×Dic3—104no—
400D12—28no—
401D12—1016no—
402D12—108no—
403C22×C5—68no—
404C22×C5—64no—
405C22×C5—122no—
406C22×C5—122no—
407C22×C5—124no—
408C22×C5C22×C4×D311yescharacteristic
409C22×C5C22×D1211yescharacteristic
410C22×C5#100912yes—
411C22×C5#100912yes—
412C22×C5C22×#6711yescharacteristic
413C2×D5—24no—
414C2×D5—22no—
415C2×D5—22no—
416C2×D5—24no—
417C2×D5—68no—
418C2×D5—64no—
419C2×D5—1232no—
420C2×D5—122no—
421C2×D5—122no—
422C2×D5—124no—
423C2×D5C2×(C2×D3)⋊C414yes—
424C4×C5—42no—
425C4×C5—122no—
426C4×C5C2×(C2×D3)⋊C414yes—
427Dic5—42no—
428Dic5—122no—
429Dic5C2×(C2×D3)⋊C414yes—
430C24—32no—
431C24—51no—
432C24—158no—
433C24—152no—
434C24—304no—
435C24—304no—
436C24—604no—
437C24—604no—
438C2×D4—34no—
439C2×D4—62no—
440C2×D4—62no—
441C2×D4—158no—
442C2×D4—154no—
443C2×D4—3032no—
444C2×D4—304no—
445C2×D4—304no—
446C2×D4—302no—
447C2×D4—302no—
448C22×C4—32no—
449C22×C4—51no—
450C22×C4—54no—
451C22×C4—54no—
452C22×C4—54no—
453C22×C4—52no—
454C22×C4—152no—
455C22×C4C2×D3×D512yes—
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—62no—
458C4⋊C4—104no—
459C4⋊C4—302no—
460C22⋊C4—104no—
461C22⋊C4—124no—
462C22⋊C4—304no—
463C22⋊C4—604no—
464C22⋊C4—604no—
465C22⋊C4—604no—
466C42—22no—
467C42—102no—
468C42—304no—
469C3×C5#230911yescharacteristic, complemented, Hall
470C22×C3—54no—
471C22×C3—102no—
472C22×C3—104no—
473C22×C3—104no—
474C22×C3—102no—
475C22×C3C22×C4×D511yescharacteristic
476C22×C3C2×D4×D511yescharacteristic
477C22×C3C2×D4×D511yescharacteristic
478C22×C3#414412yes—
479C22×C3#414912yes—
480C2×D3—24no—
481C2×D3—28no—
482C2×D3—42no—
483C2×D3—44no—
484C2×D3—42no—
485C2×D3—104no—
486C2×D3—108no—
487C2×D3—2032no—
488C2×D3—202no—
489C2×D3—204no—
490C2×D3—202no—
491C3×C4—42no—
492C3×C4—54no—
493C3×C4—202no—
494C3×C4D5×C22⋊C414yes—
495Dic3—42no—
496Dic3—202no—
497C2×C5—124no—
498C2×C5#552112yes—
499C2×C5#552511yescharacteristic
500C2×C5#552511yescharacteristic
501C2×C5C22×(C2×D3)⋊C411yescharacteristic
502C2×C5#583012yes—
503D5—24no—
504D5—124no—
505C23—34no—
506C23—52no—
507C23—52no—
508C23—52no—
509C23—62no—
510C23—64no—
511C23—64no—
512C23—62no—
513C23—102no—
514C23—102no—
515C23—154no—
516C23—3016no—
517C23—302no—
518C23—304no—
519C23—304no—
520C23—302no—
521C23—6016no—
522C23—608no—
523C23—608no—
524C23—6016no—
525C23C22×D3×D511yescharacteristic
526D4—68no—
527D4—3016no—
528D4—308no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—52no—
533C2×C4—52no—
534C2×C4—52no—
535C2×C4—516no—
536C2×C4—62no—
537C2×C4—64no—
538C2×C4—102no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—302no—
542C2×C4—304no—
543C2×C4C4×D3×D512yes—
544C2×C4D5×D1212yes—
545C2×C4D5×#6712yes—
546C2×C3—104no—
547C2×C3C2×D5×C22⋊C411yescharacteristic
548C2×C3#6587912yes—
549C2×C3#6594112yes—
550C2×C3#6600811yescharacteristic
551C2×C3#6604911yescharacteristic
552D3—44no—
553D3—204no—
554C5#8226911yescharacteristic, complemented, Sylow
555C22—54no—
556C22—68no—
557C22—64no—
558C22—104no—
559C22—102no—
560C22—102no—
561C22—104no—
562C22—122no—
563C22—122no—
564C22—124no—
565C22—308no—
566C22—304no—
567C22—6032no—
568C22—602no—
569C22—602no—
570C22—604no—
571C22C2×C4×D3×D511yescharacteristic
572C22C2×D5×D1211yescharacteristic
573C22#9201812yes—
574C22#9201912yes—
575C22C2×D5×#6711yescharacteristic
576C4—42no—
577C4—54no—
578C4—122no—
579C4—202no—
580C4—602no—
581C4D5×(C2×D3)⋊C414yes—
582C3#1060815911yescharacteristic, complemented, Sylow
583C2—104no—
584C2—124no—
585C2—604no—
586C2#1175272512yes—
587C2#1175273311yescharacteristic
588C2#1175273411yescharacteristic
589C2C2×D5×(C2×D3)⋊C411yescharacteristic
590C2#1175463512yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×D5×D12C2
hypercenterC2×C42D3×D5
hypocenterC3×C5#2309
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4018C2semidirect
3. C2×#91358C2semidirect
4. #11751040C2semidirect
5. C5×#4939C2semidirect
6. #11748940C2semidirect
7. #11748909C2semidirect
8. #11748768C2semidirect
9. #11748764C2semidirect
18. C2×D5×D12C4semidirect
19. C2×C3×C42×C5C22semidirect
20. C2×#6714C22semidirect
21. C2×C4⋊Dic15C22semidirect
22. C2×C5×(C2×D3)⋊C4C22semidirect
23. C2×C5×C4⋊Dic3C22semidirect
25. C2×C3×#683C22semidirect
26. C2×C3×C4×Dic5C22semidirect
28. C2×#6667C22semidirect
29. C2×(C2×D3)⋊Dic5C22semidirect
31. C2×Dic3×Dic5C22semidirect
36. C2×#4018D3semidirect
90. #4939D5semidirect
101. C2×C42×C5C2×D3semidirect
108. C2×#683C2×D3semidirect
110. C2×C4×Dic5C2×D3semidirect
153. C3×C4×D5C22⋊C4semidirect
167. C2×C3×C42C2×D5semidirect
172. C2×(C2×D3)⋊C4C2×D5semidirect
175. C2×C4⋊Dic3C2×D5semidirect
331. C4×D5(C2×D3)⋊C4semidirect
353. C2×C42D3×D5semidirect
469. C3×C5#2309semidirect
554. C5#82269semidirect
582. C3#10608159semidirect

Maximal subgroups

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

subgroupindex
C22×D5×D122
C2×C3×#40182
C2×#913582
#117510402
C5×#49392
#117489402
#117489092
#117487682
#117487642
#106081593
#822695