Finite Group Databasebeta

← #14427858

Subgroups — #14427858

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C8×D5C211yesmaximal, characteristic, complemented
2#11754564C211yesmaximal, characteristic, complemented
3#11754563C211yesmaximal, characteristic, complemented
4C2×#91303C211yesmaximal, characteristic, complemented
5#11751214C211yesmaximal, characteristic, complemented
6C5×#5113C211yesmaximal, characteristic, complemented
7#11748458C211yesmaximal, characteristic, complemented
8#11747939C212yesmaximal, complemented
9#11747938C212yesmaximal, complemented
10#11747893C212yesmaximal, complemented
11#11747892C212yesmaximal, complemented
12#10610569—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17#91815C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C22×C3×#168C2211yescharacteristic
20C2×C3×C8×D5—24no—
21C2×C3×C8×D5C2212yes—
22C2×C3×C8×D5C2212yes—
23#91564—21no—
24#91563—21no—
25#91546—21no—
26#91539—21no—
27#91450C2212yes—
28#91449C2212yes—
29C4×#1202—22no—
30C4×#1201—22no—
31#91360C2212yes—
32#91359C2212yes—
33C2×#6663C2211yescharacteristic, complemented
34C2×#6660C2211yescharacteristic, complemented
35C2×#6659C2211yescharacteristic, complemented
36#91303—24no—
37C2×#6654C2211yescharacteristic, complemented
38#91105C2212yescomplemented
39#91100C2212yescomplemented
40C5×#821C2212yescomplemented
41C5×#816C2212yescomplemented
42#90988C2212yescomplemented
43#90985C2212yescomplemented
44#83742—51nomaximal, Hall
45#66162—31no—
46C2×#4096—31no—
47C22×C8×D5D311yescharacteristic, complemented
48#65858—31no—
49C5×#416—31no—
50#65402—31no—
51#65287—31no—
52#65102—32no—
53#65096—32no—
54#65067—32no—
55#65064—32no—
56C23×C3×D5D411yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817—22no—
61C2×D60C2311yescharacteristic
62C2×C4×D15—21no—
63C2×Dic30C2311yescharacteristic
64C2×C5×#67—21no—
65C5×#235—22no—
66C5×#235—22no—
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—21no—
69C2×C5×Dic6C2311yescharacteristic
70C22×C3×Dic5D411yescharacteristic
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5D412yes—
74C2×C3×C4×D5C2312yes—
75C2×#1202—22no—
76C2×#1201—22no—
77C2×C3×C5×C8—22no—
78C2×C3×C5×C8C2312yes—
79#6719—21no—
80C4⋊Dic15C2312yes—
81C4×Dic15—21no—
82C5×#217—21no—
83C5×C4⋊Dic3C2312yes—
84C4×C5×Dic3—21no—
85C2×C3×#168D414yescomplemented
86C2×C3×#168C2311yescharacteristic
87C2×C3×#168C2311yescharacteristic
88C3×C8×D5—24no—
89C3×C8×D5—24no—
90Dic3⋊Dic5—22no—
91#6669—22no—
92#6667—22no—
93(C2×D3)⋊Dic5—22no—
94#6665—22no—
95#6665—22no—
96#6663—22no—
97#6660—22no—
98#6659—22no—
99#6654—22no—
100C23×C3×C8—51no—
101#5791—51no—
102#5791—51no—
103C2×#904—51no—
104#5116—52no—
105#5115—52no—
106#5114—52no—
107#5114—52no—
108#5113—51no—
109#5113D511yescharacteristic, complemented
110#5106—51no—
111C2×C5×#41—31no—
112C2×#709—31no—
113C22×C4×D5C2×D311yescharacteristic
114C22×C5×C8C2×D311yescharacteristic
115C5×#117—31no—
116#4096—64no—
117#4092—32no—
118C2×#689—31no—
119C2×#688—31no—
120#4084—32no—
121#4083—61no—
122#4081—61no—
123C2×#687—31no—
124C2×#686—31no—
125C4×C22⋊D5—62no—
126#4072—31no—
127C22×#168C2×D311yescharacteristic
128C2×C8×D5—24no—
129C2×C8×D5C2×D312yes—
130C2×C8×D5C2×D312yes—
131#4043—32no—
132#4041—32no—
133#4032—61no—
134#4028—61no—
135C4×D20—62no—
136C5×#103—32no—
137C5×#102—32no—
138#3953—32no—
139#3948—32no—
140#3940—32no—
141#3939—32no—
142#3050—151noSylow
143C23×C3×C5C2×D411yescharacteristic
144C22×D15—21no—
145C22×C5×D3—21no—
146C22×C3×D5—22no—
147C22×C3×D5—24no—
148C22×C3×D5C2×D412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5C2411yescharacteristic
153#1220—42no—
154C2×Dic15—21no—
155C2×Dic15—22no—
156D60—21no—
157D60—21no—
158C4×D15—42no—
159Dic30—21no—
160Dic30—21no—
161C5×#67—42no—
162C2×C5×Dic3—21no—
163C2×C5×Dic3—22no—
164C5×D12—21no—
165C5×D12—21no—
166C4×C5×D3—42no—
167C5×Dic6—21no—
168C5×Dic6—21no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5C2×D412yes—
171C3×C4×D5—24no—
172C3×C4×D5—22no—
173C3×C4×D5—22no—
174#1202—44no—
175#1201—44no—
176C3×C5×C8—22no—
177C3×#168C2×D412yes—
178C3×#168C2×D412yes—
179C23×C3×C4—51no—
180C2×#235—51no—
181C2×#235C2×D511yescharacteristic
182C22×C3×C8—51no—
183C22×C3×C8—52no—
184C22×C3×C8—52no—
185C22×C3×C8—104no—
186C22×C3×C8C2×D511yescharacteristic
187#953—101no—
188#953—101no—
189#930—52no—
190#930—52no—
191#929—101no—
192#929—101no—
193C4×#67—102no—
194C4×#67—102no—
195#926—51no—
196#926C2×D511yescharacteristic
197#924—52no—
198#924—52no—
199C2×Dic12—51no—
200#904—104no—
201C2×D24—51no—
202C2×#204—51no—
203C2×#204—51no—
204#821—52no—
205#821C2×D512yescomplemented
206#818—52no—
207#817—52no—
208#816—52no—
209#816C2×D512yescomplemented
210C23×D5D1211yescharacteristic
211C5×#41—62no—
212C5×#41—62no—
213C2×C5×Q8—31no—
214C2×C5×D4—31no—
215C2×C5×D4—61no—
216C22×C4×C5—61no—
217C22×C4×C5C22×D311yescharacteristic
218C2×C22⋊D5—61no—
219C2×C22⋊D5—62no—
220C22×Dic5D1211yescharacteristic
221#709—62no—
222#709—62no—
223C2×D20—31no—
224C2×D20—62no—
225C2×C4×D5—22no—
226C2×C4×D5—22no—
227C2×C4×D5—61no—
228C2×C4×D5D1212yes—
229C2×C4×D5C22×D312yes—
230C2×Dic10—31no—
231C2×C5×C8—22no—
232C2×C5×C8C22×D312yes—
233C5×C4⋊C4—32no—
234C5×C22⋊C4—61no—
235C42×C5—61no—
236C22⋊Dic5—61no—
237C22⋊Dic5—62no—
238#689—62no—
239#688—62no—
240#687—62no—
241#686—62no—
242#685—62no—
243#685—62no—
244#685—62no—
245C4⋊Dic5—32no—
246C4⋊Dic5—62no—
247#683—62no—
248C4×Dic5—61no—
249C2×#168#6714yescomplemented
250C2×#168C22×D311yescharacteristic
251C2×#168C22×D311yescharacteristic
252C8×D5—24no—
253C8×D5—24no—
254C2×#135—151no—
255C23×C8—51no—
256#525—151no—
257#525—151no—
258#467—152no—
259#466—152no—
260#465—152no—
261#465—152no—
262#427—151no—
263#416—31no—
264#416—151no—
265C22×C3×C5—22no—
266C22×C3×C5#12112yes—
267C22×C3×C5C22×D411yescharacteristic
268C2×D15—41no—
269C2×D15—42no—
270C2×C5×D3—41no—
271C2×C5×D3—42no—
272C2×C3×D5—28no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5#13514yescomplemented
276C3×C4×C5#12112yes—
277C3×C4×C5C22×D411yescharacteristic
278C3×C4×C5C2×#4111yescharacteristic
279Dic15—41no—
280Dic15—42no—
281C3×Dic5—22no—
282C5×Dic3—41no—
283C5×Dic3—42no—
284C24×C3—51no—
285C22×C3×C4—51no—
286C22×C3×C4—52no—
287C22×C3×C4—52no—
288C22×C3×C4—102no—
289C22×C3×C4—102no—
290C22×C3×C4C22×D511yescharacteristic
291C2×#67—21no—
292C2×#67—102no—
293C2×#67—102no—
294C2×#67—101no—
295#235—22no—
296#235—22no—
297#235—102no—
298#235—102no—
299C2×D12—51no—
300C2×D12C22×D511yescharacteristic
301C2×C4×D3—21no—
302C2×C4×D3—101no—
303C2×Dic6—51no—
304C2×Dic6C22×D511yescharacteristic
305C2×C3×C8—22no—
306C2×C3×C8—54no—
307C2×C3×C8—51no—
308C2×C3×C8—51no—
309C2×C3×C8—104no—
310C2×C3×C8—104no—
311C2×C3×C8C22×D512yes—
312#217—21no—
313#217—102no—
314#217—102no—
315#217—101no—
316(C2×D3)⋊C4—102no—
317(C2×D3)⋊C4—102no—
318C4⋊Dic3—52no—
319C4⋊Dic3C22×D512yes—
320Dic3⋊C4—102no—
321Dic3⋊C4—102no—
322C4×Dic3—21no—
323C4×Dic3—101no—
324Dic12—102no—
325D24—102no—
326#204—102no—
327#204—102no—
328C23×C5—61no—
329C23×C5C2×D1211yescharacteristic
330C22×D5—22no—
331C22×D5—24no—
332C22×D5—61no—
333C22×D5C2×D1212yes—
334C5×Q8—61no—
335C5×Q8—61no—
336C5×D4—61no—
337C5×D4—61no—
338C5×D4—122no—
339C2×C4×C5—61no—
340C2×C4×C5—62no—
341C2×C4×C5—122no—
342C2×C4×C5C2×D1211yescharacteristic
343C2×C4×C5#23512yes—
344C2×C4×C5C2×#6712yes—
345C2×C4×C5C23×D311yescharacteristic
346C22⋊D5—122no—
347C22⋊D5—124no—
348C2×Dic5—22no—
349C2×Dic5—62no—
350C2×Dic5—61no—
351C2×Dic5C2×D1212yes—
352D20—61no—
353D20—61no—
354D20—124no—
355C4×D5—24no—
356C4×D5—22no—
357C4×D5—22no—
358C4×D5—122no—
359Dic10—61no—
360Dic10—61no—
361C5×C8—22no—
362#168C2×#6712yes—
363#168C2×#6712yes—
364C2×#41—31no—
365C2×#41—151no—
366C23×C4—51no—
367#135—304no—
368C2×Q16—151no—
369C2×SD16—151no—
370C2×SD16—151no—
371C2×D8—151no—
372C22×C8—51no—
373C22×C8—52no—
374C22×C8—52no—
375C22×C8—104no—
376C22×C8D3×D511yescharacteristic
377#123—301no—
378#123—301no—
379C22⋊Q8—152no—
380C22⋊Q8—152no—
381#121—152no—
382#121—152no—
383#120—301no—
384#120—301no—
385C4×D4—302no—
386C4×D4—302no—
387#117—31no—
388#117—151no—
389#107—152no—
390#106—152no—
391#103—32no—
392#103—152no—
393#102—32no—
394#102—152no—
395C2×C3×C5—22no—
396C2×C3×C5C2×#12111yescharacteristic
397C2×C3×C5C2×#13512yes—
398D15—81no—
399C3×D5—24no—
400C5×D3—81no—
401C23×C3—52no—
402C23×C3—104no—
403C23×C3—102no—
404C23×C3D4×D511yescharacteristic
405C22×D3—21no—
406C22×D3—101no—
407C2×C3×C4—52no—
408C2×C3×C4—102no—
409C2×C3×C4—102no—
410C2×C3×C4—102no—
411C2×C3×C4—104no—
412C2×C3×C4#70912yes—
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4D4×D512yes—
415C2×C3×C4C23×D511yescharacteristic
416#67—42no—
417#67—204no—
418#67—204no—
419#67—202no—
420C2×Dic3—22no—
421C2×Dic3—21no—
422C2×Dic3—102no—
423C2×Dic3—101no—
424D12—21no—
425D12—21no—
426D12—101no—
427D12—101no—
428C4×D3—42no—
429C4×D3—202no—
430Dic6—21no—
431Dic6—21no—
432Dic6—101no—
433Dic6—101no—
434C3×C8—22no—
435C3×C8—52no—
436C3×C8—52no—
437C22×C5—22no—
438C22×C5—122no—
439C22×C5—121no—
440C22×C5#93012yes—
441C22×C5C22×D1211yescharacteristic
442C2×D5—28no—
443C2×D5—22no—
444C2×D5—22no—
445C2×D5—122no—
446C2×D5—121no—
447C2×D5#90414yescomplemented
448C4×C5—122no—
449C4×C5—121no—
450C4×C5#93012yes—
451C4×C5C2×#23511yescharacteristic
452C4×C5C22×#6711yescharacteristic
453Dic5—22no—
454Dic5—122no—
455Dic5—121no—
456C24—51no—
457#41—62no—
458#41—62no—
459#41—302no—
460#41—302no—
461C2×Q8—31no—
462C2×Q8—151no—
463C2×D4—31no—
464C2×D4—61no—
465C2×D4—151no—
466C2×D4—302no—
467C2×D4—302no—
468C2×D4—301no—
469C22×C4—51no—
470C22×C4—52no—
471C22×C4—52no—
472C22×C4—61no—
473C22×C4—102no—
474C22×C4—102no—
475C22×C4—301no—
476C22×C4C2×D3×D511yescharacteristic
477Q16—302no—
478SD16—302no—
479SD16—302no—
480D8—302no—
481C2×C8—22no—
482C2×C8—54no—
483C2×C8—51no—
484C2×C8—51no—
485C2×C8—104no—
486C2×C8—104no—
487C2×C8C2×D3×D512yes—
488C4⋊C4—32no—
489C4⋊C4—152no—
490C4⋊C4—302no—
491C4⋊C4—302no—
492C22⋊C4—61no—
493C22⋊C4—302no—
494C22⋊C4—302no—
495C22⋊C4—302no—
496C22⋊C4—302no—
497C22⋊C4—301no—
498C42—61no—
499C42—301no—
500C3×C5#305011yescharacteristic, complemented, Hall
501C22×C3—22no—
502C22×C3—54no—
503C22×C3—108no—
504C22×C3—102no—
505C22×C3—102no—
506C22×C3#403012yes—
507C22×C3C2×D4×D511yescharacteristic
508C2×D3—41no—
509C2×D3—42no—
510C2×D3—201no—
511C2×D3—202no—
512C3×C4—102no—
513C3×C4#403012yes—
514C3×C4C2×#70911yescharacteristic
515C3×C4C2×D4×D511yescharacteristic
516Dic3—41no—
517Dic3—42no—
518Dic3—201no—
519Dic3—202no—
520C2×C5—22no—
521C2×C5—241no—
522C2×C5C2×#90412yes—
523C2×C5C2×#93011yescharacteristic
524D5—24no—
525D5—241no—
526C23—52no—
527C23—61no—
528C23—104no—
529C23—102no—
530C23—301no—
531C23D5×D1211yescharacteristic
532Q8—61no—
533Q8—61no—
534Q8—301no—
535Q8—301no—
536D4—61no—
537D4—61no—
538D4—122no—
539D4—301no—
540D4—301no—
541D4—604no—
542D4—604no—
543D4—602no—
544C2×C4—52no—
545C2×C4—62no—
546C2×C4—61no—
547C2×C4—102no—
548C2×C4—104no—
549C2×C4—102no—
550C2×C4—102no—
551C2×C4—122no—
552C2×C4—302no—
553C2×C4—301no—
554C2×C4—602no—
555C2×C4#677112yes—
556C2×C4D5×D1211yescharacteristic
557C2×C4D5×#6712yes—
558C2×C4C22×D3×D511yescharacteristic
559C8—22no—
560C8—52no—
561C8—52no—
562C2×C3—22no—
563C2×C3—104no—
564C2×C3C2×#403011yescharacteristic
565C2×C3D5×#13512yes—
566D3—81no—
567D3—401no—
568C5#8374211yescharacteristic, complemented, Sylow
569C22—22no—
570C22—54no—
571C22—108no—
572C22—102no—
573C22—102no—
574C22—121no—
575C22—122no—
576C22—601no—
577C22—602no—
578C22#9144812yes—
579C22C2×D5×D1211yescharacteristic
580C4—102no—
581C4—121no—
582C4—122no—
583C4—601no—
584C4—602no—
585C4#9144812yes—
586C4C2×#677111yescharacteristic
587C4C2×D5×#6711yescharacteristic
588C3#1061056911yescharacteristic, complemented, Sylow
589C2—22no—
590C2—104no—
591C2—241no—
592C2—1201no—
593C2D5×#90412yes—
594C2C2×#9144811yescharacteristic
subgroupG/H
centerC2×C4D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
hypercenterC22×C8D3×D5
hypocenterC3×C5#3050
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C8×D5C2semidirect
2. #11754564C2semidirect
3. #11754563C2semidirect
4. C2×#91303C2semidirect
5. #11751214C2semidirect
6. C5×#5113C2semidirect
7. #11748458C2semidirect
8. #11747939C2semidirect
9. #11747938C2semidirect
10. #11747893C2semidirect
11. #11747892C2semidirect
33. C2×#6663C22semidirect
34. C2×#6660C22semidirect
35. C2×#6659C22semidirect
37. C2×#6654C22semidirect
38. #91105C22semidirect
39. #91100C22semidirect
40. C5×#821C22semidirect
41. C5×#816C22semidirect
42. #90988C22semidirect
43. #90985C22semidirect
47. C22×C8×D5D3semidirect
85. C2×C3×#168D4semidirect
109. #5113D5semidirect
205. #821C2×D5semidirect
209. #816C2×D5semidirect
249. C2×#168#67semidirect
275. C2×C3×D5#135semidirect
447. C2×D5#904semidirect
500. C3×C5#3050semidirect
568. C5#83742semidirect
588. C3#10610569semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C8×D52
#117545642
#117545632
C2×#913032
#117512142
C5×#51132
#117484582
#117479392
#117479382
#117478932
#117478922
#106105693
#837425