Finite Group Databasebeta

← #14412673

Subgroups — #14412673

Order 1920.

1556 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4149C211yesmaximal, characteristic
2#11754499C211yesmaximal, characteristic, complemented
3C2×#91284C211yesmaximal, characteristic, complemented
4#11751334C211yesmaximal, characteristic, complemented
5C5×#5232C211yesmaximal, characteristic, complemented
6#11749207C212yesmaximal, complemented
7#11749198C212yesmaximal, complemented
8#11748962C212yesmaximal, complemented
9D5×#832C212yesmaximal, complemented
10#11748367C211yesmaximal, characteristic, complemented
11C2×#90964C211yesmaximal, characteristic, complemented
12#10610613—31nomaximal, Hall
13C2×C3×C5×#41C2211yescharacteristic
14C3×#4149—24no—
15C3×#4149C418yescomplemented
16C2×C3×#713C2212yes—
17C2×C3×D4×D5—22no—
18C2×C3×D4×D5C2212yes—
19C2×C3×#709—21no—
20C2×C3×#709C2211yescharacteristic
21C22×C3×D20—21no—
22C22×C3×D20C2211yescharacteristic
23#91815C2211yescharacteristic, complemented
24C22×C3⋊#168C2211yescharacteristic, complemented
25C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
26C2×C5×#208C2211yescharacteristic, complemented
27Dic3×C22⋊D5—22no—
28#91434—21no—
29D5×C4⋊Dic3C2212yescomplemented
30#91358C2212yescomplemented
31#91331—21no—
32C2×#6649C2212yescomplemented
33#91284—24no—
34C2×D5×C3⋊C8C2212yescomplemented
35#91119C2211yescharacteristic, complemented
36#91119C2211yescharacteristic, complemented
37#91116C2211yescharacteristic, complemented
38#91116C2211yescharacteristic, complemented
39C5×#835C2212yescomplemented
40C5×#832C2212yescomplemented
41#90965C2212yescomplemented
42#90965C2212yescomplemented
43#90964C2212yescomplemented
44#90964C2212yescomplemented
45#84099—51nomaximal, Hall
46C2×#4149D311yescharacteristic
47C2×#4053—31no—
48#65838—31no—
49C5×#417—31no—
50#65522—31no—
51#65420—31no—
52C2×#3941—31no—
53#65093—32no—
54#65092—32no—
55#65059—32no—
56D5×#102—32no—
57C23×C3×D5—21no—
58C23×C3×D5—22no—
59C3×C5×#41—22no—
60C3×C5×#41C2×C414yescomplemented
61C2×C3×C5×Q8C2311yescharacteristic
62C2×C3×C5×D4—21no—
63C2×C3×C5×D4C2311yescharacteristic
64C22×C3×C4×C5—21no—
65C22×C3×C4×C5C2311yescharacteristic
66C22×C5×Dic3—21no—
67C2×C3×C22⋊D5—22no—
68C2×C3×C22⋊D5D412yes—
69C3×#713—24no—
70C3×#713C2×C418yescomplemented
71C3×D4×D5—216no—
72C3×D4×D5—24no—
73C3×D4×D5C2×C418yescomplemented
74C3×#709—28no—
75C3×#709C2×C414yes—
76C3×#709D414yes—
77C2×C3×D20—22no—
78C2×C3×D20—21no—
79C2×C3×D20—22no—
80C2×C3×D20—28no—
81C2×C3×D20C2×C414yescomplemented
82C2×C3×D20D411yescharacteristic
83C2×C3×D20C2312yes—
84C2×C3×C4×D5—22no—
85C2×C3×C4×D5C2312yes—
86C2×C3×Dic10D411yescharacteristic
87C2×D5×Dic3—22no—
88#6719—21no—
89C4⋊Dic15C2311yescharacteristic
90C4⋊Dic15C2311yescharacteristic
91C4×Dic15—21no—
92C2×C3⋊#168—22no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×C4⋊Dic3—21no—
96C5×C4⋊Dic3C2312yes—
97C5×#208—22no—
98C2×C5×C3⋊C8C2312yes—
99#6668—22no—
100#6665—22no—
101Dic3×Dic5—22no—
102#6649—24no—
103D5×C3⋊C8—24no—
104C2×C3×H(5,𝔽2)—51no—
105#5827—51no—
106C2×#948—51no—
107#5233—51no—
108#5233—52no—
109#5232—52no—
110#5232D511yescharacteristic, complemented
111#5215—51no—
112#5215—52no—
113C2×#832—51no—
114C2×#832—52no—
115C2×C5×#41C2×D311yescharacteristic
116#4149—24no—
117#4149Dic318yescomplemented
118C2×#713C2×D312yes—
119C2×D4×D5—22no—
120C2×D4×D5C2×D312yes—
121C2×#709—21no—
122C2×#709C2×D311yescharacteristic
123C22×D20—21no—
124C22×D20C2×D311yescharacteristic
125C2×C5×M16—31no—
126C2×C5×C4⋊C4—31no—
127C4×C22⋊D5—62no—
128#4072—31no—
129C22×#168—31no—
130#4053—64no—
131C2×#676—32no—
132C2×C8×D5—32no—
133#4039—61no—
134#4038—32no—
135D5×C4⋊C4—32no—
136#4033—61no—
137C5×#103—32no—
138C5×#102—32no—
139#3967—31no—
140#3967—31no—
141#3964—31no—
142#3964—31no—
143#3953—32no—
144#3953—32no—
145#3941—32no—
146#3941—32no—
147#2897—151noSylow
148C23×C3×C5—21no—
149C23×C3×C5C2×D411yescharacteristic
150C22×C3×D5—22no—
151C22×C3×D5—24no—
152C22×C3×D5—28no—
153C22×C3×D5—82no—
154C22×C3×D5—82no—
155C22×C3×D5—81no—
156C22×C3×D5—81no—
157C22×C3×D5C2×D412yes—
158C3×C5×Q8—21no—
159C3×C5×Q8C22×C412yes—
160C3×C5×D4—24no—
161C3×C5×D4—21no—
162C3×C5×D4C22×C412yes—
163C2×C3×C4×C5—21no—
164C2×C3×C4×C5—24no—
165C2×C3×C4×C5C22×C412yes—
166C2×C3×C4×C5C2×D411yescharacteristic
167C2×C3×C4×C5C2×D412yes—
168C2×C3×C4×C5C2411yescharacteristic
169C2×Dic15—21no—
170C2×Dic15—21no—
171C2×C5×Dic3—22no—
172C2×C5×Dic3—81no—
173C3×C22⋊D5—28no—
174C3×C22⋊D5C22⋊C418yes—
175C2×C3×Dic5C2×D412yes—
176C3×D20—28no—
177C3×D20—24no—
178C3×D20—22no—
179C3×D20C22⋊C414yes—
180C3×D20C22×C414yes—
181C3×C4×D5—28no—
182C3×C4×D5C22×C414yes—
183C3×C4×D5C2×D414yes—
184C3×Dic10C22⋊C414yes—
185D5×Dic3—82no—
186C3⋊#168—21no—
187C3⋊#168—21no—
188C5×C3⋊C8—22no—
189C3×H(5,𝔽2)—58no—
190C3×H(5,𝔽2)—104no—
191C2×C3×#41—51no—
192C2×C3×#41—52no—
193C2×C3×#41—101no—
194C2×C3×#41C2×D511yescharacteristic
195C22×C3×D4—52no—
196C22×C3×D4—51no—
197C22×C3×D4—101no—
198C22×C3×D4—102no—
199#948—104no—
200Q8×Dic3—101no—
201D4×Dic3—101no—
202D4×Dic3—102no—
203#926—51no—
204#926—52no—
205C2×C4⋊Dic3—52no—
206C2×C4⋊Dic3C2×D511yescharacteristic, complemented
207C2×#208—52no—
208C2×#208C2×D511yescharacteristic, complemented
209C22×C3⋊C8—51no—
210C22×C3⋊C8—52no—
211#835—51no—
212#835—51no—
213#835C2×D512yescomplemented
214#832—51no—
215#832—51no—
216#832—52no—
217#832—52no—
218#832—52no—
219#832—52no—
220#832C2×D512yescomplemented
221C23×D5—21no—
222C23×D5—22no—
223C5×#41—22no—
224C5×#41C2×Dic314yescomplemented
225C2×C5×Q8C22×D311yescharacteristic
226C2×C5×D4—21no—
227C2×C5×D4C22×D311yescharacteristic
228C22×C4×C5—21no—
229C22×C4×C5—61no—
230C22×C4×C5C22×D311yescharacteristic
231C2×C22⋊D5—22no—
232C2×C22⋊D5#6712yes—
233#713—24no—
234#713C2×Dic318yescomplemented
235D4×D5—216no—
236D4×D5—24no—
237D4×D5C2×Dic318yescomplemented
238#709—28no—
239#709C2×Dic314yes—
240#709#6714yes—
241C2×D20—22no—
242C2×D20—21no—
243C2×D20—22no—
244C2×D20—28no—
245C2×D20C2×Dic314yescomplemented
246C2×D20#6711yescharacteristic
247C2×D20C22×D312yes—
248C2×C4×D5—22no—
249C2×C4×D5—62no—
250C2×C4×D5C22×D312yes—
251C2×Dic10#6711yescharacteristic
252C5×M16—62no—
253C2×C5×C8—32no—
254C5×C4⋊C4—32no—
255C5×C4⋊C4—61no—
256C22⋊Dic5—61no—
257#685—62no—
258C4⋊Dic5—31no—
259C4⋊Dic5—31no—
260#683—62no—
261C4×Dic5—61no—
262C4×Dic5—62no—
263C2×#168—31no—
264C2×#168—31no—
265C2×#168—62no—
266#676—64no—
267C8×D5—64no—
268C2×H(5,𝔽2)—51no—
269C2×#131—151no—
270#520—151no—
271#418—152no—
272#418—151no—
273#417—31no—
274#417—152no—
275#416—152no—
276#416—151no—
277C2×#102—152no—
278C2×#102—151no—
279C22×C3×C5—21no—
280C22×C3×C5—21no—
281C22×C3×C5—22no—
282C22×C3×C5—41no—
283C22×C3×C5—41no—
284C22×C3×C5C2×C22⋊C412yes—
285C22×C3×C5C22×D411yescharacteristic
286C2×C3×D5—22no—
287C2×C3×D5—22no—
288C2×C3×D5—24no—
289C2×C3×D5—42no—
290C2×C3×D5—42no—
291C2×C3×D5—88no—
292C2×C3×D5—84no—
293C2×C3×D5C2×C22⋊C414yes—
294C3×C4×C5—22no—
295C3×C4×C5C2×C22⋊C412yes—
296C3×C4×C5C23×C411yescharacteristic
297C3×C4×C5C22×D411yescharacteristic
298Dic15—41no—
299Dic15—41no—
300C3×Dic5C2×C22⋊C414yes—
301C5×Dic3—42no—
302C24×C3—102no—
303C24×C3—101no—
304C3×#41—22no—
305C3×#41—54no—
306C3×#41—54no—
307C3×#41—58no—
308C3×#41—108no—
309C3×#41—104no—
310C3×#41C4×D514yescomplemented
311C2×C3×Q8—51no—
312C2×C3×Q8C22×D511yescharacteristic
313C2×C3×D4—21no—
314C2×C3×D4—52no—
315C2×C3×D4—58no—
316C2×C3×D4—54no—
317C2×C3×D4—51no—
318C2×C3×D4—52no—
319C2×C3×D4—108no—
320C2×C3×D4—102no—
321C2×C3×D4—104no—
322C2×C3×D4—102no—
323C2×C3×D4—1016no—
324C2×C3×D4—101no—
325C2×C3×D4—102no—
326C2×C3×D4C22×D511yescharacteristic
327C22×C3×C4—21no—
328C22×C3×C4—52no—
329C22×C3×C4—102no—
330C22×C3×C4C22×D511yescharacteristic
331C22×Dic3—21no—
332C22×Dic3—102no—
333#217—102no—
334#217—101no—
335C4⋊Dic3—21no—
336C4⋊Dic3—51no—
337C4⋊Dic3—51no—
338C4⋊Dic3—102no—
339C4⋊Dic3C22×D512yes—
340C4×Dic3—102no—
341C4×Dic3—101no—
342#208—22no—
343#208—104no—
344C2×C3⋊C8—51no—
345C2×C3⋊C8—51no—
346C2×C3⋊C8—104no—
347C2×C3⋊C8—102no—
348C2×C3⋊C8C22×D512yes—
349C23×C5—21no—
350C23×C5C2×#6711yescharacteristic
351C22×D5—22no—
352C22×D5—24no—
353C22×D5—28no—
354C22×D5—82no—
355C22×D5—82no—
356C22×D5—81no—
357C22×D5—81no—
358C22×D5C2×#6712yes—
359C5×Q8—21no—
360C5×Q8C22×Dic312yes—
361C5×D4—24no—
362C5×D4—21no—
363C5×D4C22×Dic312yes—
364C2×C4×C5—21no—
365C2×C4×C5—24no—
366C2×C4×C5—62no—
367C2×C4×C5—241no—
368C2×C4×C5C22×Dic312yes—
369C2×C4×C5C2×#6711yescharacteristic
370C2×C4×C5C2×#6712yes—
371C2×C4×C5C23×D311yescharacteristic
372C22⋊D5—28no—
373C22⋊D5#21718yes—
374C2×Dic5—61no—
375C2×Dic5—61no—
376C2×Dic5C2×#6712yes—
377D20—28no—
378D20—24no—
379D20—22no—
380D20#21714yes—
381D20C22×Dic314yes—
382C4×D5—28no—
383C4×D5—242no—
384C4×D5C22×Dic314yes—
385C4×D5C2×#6714yes—
386Dic10#21714yes—
387C5×C8—62no—
388#168—61no—
389#168—61no—
390H(5,𝔽2)—58no—
391H(5,𝔽2)—104no—
392C2×#41—51no—
393C2×#41—52no—
394C2×#41—101no—
395C2×#41D3×D511yescharacteristic
396C22×D4—52no—
397C22×D4—51no—
398C22×D4—101no—
399C22×D4—102no—
400#131—304no—
401C2×M16—31no—
402C2×M16—152no—
403C22×C8—152no—
404C22×C8—151no—
405C4×Q8—301no—
406C4×D4—301no—
407C4×D4—302no—
408#117—152no—
409#117—151no—
410C2×C4⋊C4—31no—
411C2×C4⋊C4—152no—
412#103—32no—
413#103—151no—
414#103—151no—
415#102—32no—
416#102—152no—
417#102—152no—
418#102—152no—
419#102—152no—
420#102—151no—
421#102—151no—
422C2×C3×C5—22no—
423C2×C3×C5—42no—
424C2×C3×C5C22×C22⋊C411yescharacteristic
425C2×C3×C5#57611yescharacteristic
426C2×C3×C5#57711yescharacteristic
427C3×D5—24no—
428C3×D5—44no—
429C23×C3—21no—
430C23×C3—52no—
431C23×C3—108no—
432C23×C3—102no—
433C23×C3—104no—
434C23×C3—401no—
435C23×C3—401no—
436C23×C3—402no—
437C23×C3—402no—
438C23×C3D4×D511yescharacteristic
439C3×Q8—21no—
440C3×Q8—54no—
441C3×Q8C2×C4×D512yes—
442C3×D4—24no—
443C3×D4—21no—
444C3×D4—58no—
445C3×D4—54no—
446C3×D4—54no—
447C3×D4—108no—
448C3×D4—108no—
449C3×D4—102no—
450C3×D4—104no—
451C3×D4C2×C4×D512yes—
452C2×C3×C4—21no—
453C2×C3×C4—24no—
454C2×C3×C4—52no—
455C2×C3×C4—54no—
456C2×C3×C4—54no—
457C2×C3×C4—108no—
458C2×C3×C4C2×C4×D512yes—
459C2×C3×C4D4×D512yes—
460C2×C3×C4D4×D511yescharacteristic
461C2×C3×C4C23×D511yescharacteristic
462C2×Dic3—22no—
463C2×Dic3—81no—
464C2×Dic3—101no—
465C2×Dic3—101no—
466C2×Dic3—402no—
467C3⋊C8—22no—
468C3⋊C8—101no—
469C3⋊C8—101no—
470C22×C5—21no—
471C22×C5—21no—
472C22×C5—22no—
473C22×C5—41no—
474C22×C5—41no—
475C22×C5C2×#21712yes—
476C22×C5C22×#6711yescharacteristic
477C2×D5—22no—
478C2×D5—22no—
479C2×D5—24no—
480C2×D5—42no—
481C2×D5—42no—
482C2×D5—88no—
483C2×D5—84no—
484C2×D5C2×#21714yes—
485C4×C5—22no—
486C4×C5—122no—
487C4×C5C2×#21712yes—
488C4×C5C23×Dic311yescharacteristic
489C4×C5C22×#6711yescharacteristic
490Dic5—121no—
491Dic5—121no—
492Dic5C2×#21714yes—
493C24—102no—
494C24—101no—
495#41—22no—
496#41—54no—
497#41—54no—
498#41—58no—
499#41—108no—
500#41—104no—
501#41D5×Dic314yescomplemented
502C2×Q8—51no—
503C2×Q8C2×D3×D511yescharacteristic
504C2×D4—21no—
505C2×D4—52no—
506C2×D4—58no—
507C2×D4—54no—
508C2×D4—51no—
509C2×D4—52no—
510C2×D4—108no—
511C2×D4—102no—
512C2×D4—104no—
513C2×D4—102no—
514C2×D4—1016no—
515C2×D4—101no—
516C2×D4—102no—
517C2×D4C2×D3×D511yescharacteristic
518C22×C4—21no—
519C22×C4—52no—
520C22×C4—61no—
521C22×C4—102no—
522C22×C4—302no—
523C22×C4C2×D3×D511yescharacteristic
524M16—62no—
525M16—304no—
526C2×C8—32no—
527C2×C8—151no—
528C2×C8—151no—
529C2×C8—304no—
530C2×C8—302no—
531C4⋊C4—32no—
532C4⋊C4—61no—
533C4⋊C4—151no—
534C4⋊C4—151no—
535C4⋊C4—302no—
536C22⋊C4—302no—
537C22⋊C4—301no—
538C42—302no—
539C42—301no—
540C3×C5#289711yescharacteristic, complemented, Hall
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—22no—
544C22×C3—41no—
545C22×C3—41no—
546C22×C3—54no—
547C22×C3—102no—
548C22×C3—102no—
549C22×C3—104no—
550C22×C3—202no—
551C22×C3—202no—
552C22×C3—404no—
553C22×C3—408no—
554C22×C3D5×C22⋊C412yes—
555C22×C3C2×D4×D511yescharacteristic
556C3×C4—22no—
557C3×C4—54no—
558C3×C4D5×C22⋊C412yes—
559C3×C4C22×C4×D511yescharacteristic
560C3×C4C2×D4×D511yescharacteristic
561Dic3—42no—
562Dic3—201no—
563Dic3—201no—
564C2×C5—22no—
565C2×C5—42no—
566C2×C5#583511yescharacteristic
567C2×C5#583611yescharacteristic
568C2×C5C22×#21711yescharacteristic
569D5—24no—
570D5—44no—
571C23—21no—
572C23—52no—
573C23—108no—
574C23—102no—
575C23—104no—
576C23—401no—
577C23—401no—
578C23—402no—
579C23—402no—
580C23D5×#6711yescharacteristic
581Q8—21no—
582Q8—54no—
583Q8C2×D5×Dic312yes—
584D4—24no—
585D4—21no—
586D4—58no—
587D4—54no—
588D4—54no—
589D4—108no—
590D4—108no—
591D4—102no—
592D4—104no—
593D4C2×D5×Dic312yes—
594C2×C4—21no—
595C2×C4—24no—
596C2×C4—52no—
597C2×C4—54no—
598C2×C4—54no—
599C2×C4—62no—
600C2×C4—108no—
601C2×C4—241no—
602C2×C4—301no—
603C2×C4—301no—
604C2×C4—1202no—
605C2×C4C2×D5×Dic312yes—
606C2×C4D5×#6712yes—
607C2×C4D5×#6711yescharacteristic
608C2×C4C22×D3×D511yescharacteristic
609C8—62no—
610C8—301no—
611C8—301no—
612C2×C3—22no—
613C2×C3—42no—
614C2×C3—104no—
615C2×C3—204no—
616C2×C3C2×D5×C22⋊C411yescharacteristic
617C2×C3#6610811yescharacteristic
618C2×C3#6611211yescharacteristic
619C5#8409911yescharacteristic, complemented, Sylow
620C22—21no—
621C22—21no—
622C22—22no—
623C22—41no—
624C22—41no—
625C22—54no—
626C22—102no—
627C22—102no—
628C22—104no—
629C22—202no—
630C22—202no—
631C22—404no—
632C22—408no—
633C22D5×#21712yes—
634C22C2×D5×#6711yescharacteristic
635C4—22no—
636C4—54no—
637C4—122no—
638C4—601no—
639C4—601no—
640C4D5×#21712yes—
641C4C22×D5×Dic311yescharacteristic
642C4C2×D5×#6711yescharacteristic
643C3#1061061311yescharacteristic, complemented, Sylow
644C2—22no—
645C2—42no—
646C2—104no—
647C2—204no—
648C2#1175531611yescharacteristic
649C2#1175533511yescharacteristic
650C2C2×D5×#21711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4149C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#41D3×D5
hypocenterC3×C5#2897
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11754499C2semidirect
3. C2×#91284C2semidirect
4. #11751334C2semidirect
5. C5×#5232C2semidirect
6. #11749207C2semidirect
7. #11749198C2semidirect
8. #11748962C2semidirect
9. D5×#832C2semidirect
10. #11748367C2semidirect
11. C2×#90964C2semidirect
15. C3×#4149C4semidirect
23. #91815C22semidirect
24. C22×C3⋊#168C22semidirect
25. C2×C5×C4⋊Dic3C22semidirect
26. C2×C5×#208C22semidirect
29. D5×C4⋊Dic3C22semidirect
30. #91358C22semidirect
32. C2×#6649C22semidirect
34. C2×D5×C3⋊C8C22semidirect
35. #91119C22semidirect
36. #91119C22semidirect
37. #91116C22semidirect
38. #91116C22semidirect
39. C5×#835C22semidirect
40. C5×#832C22semidirect
41. #90965C22semidirect
42. #90965C22semidirect
43. #90964C22semidirect
44. #90964C22semidirect
60. C3×C5×#41C2×C4semidirect
70. C3×#713C2×C4semidirect
73. C3×D4×D5C2×C4semidirect
81. C2×C3×D20C2×C4semidirect
110. #5232D5semidirect
117. #4149Dic3semidirect
206. C2×C4⋊Dic3C2×D5semidirect
208. C2×#208C2×D5semidirect
213. #835C2×D5semidirect
220. #832C2×D5semidirect
224. C5×#41C2×Dic3semidirect
234. #713C2×Dic3semidirect
237. D4×D5C2×Dic3semidirect
245. C2×D20C2×Dic3semidirect
310. C3×#41C4×D5semidirect
501. #41D5×Dic3semidirect
540. C3×C5#2897semidirect
619. C5#84099semidirect
643. C3#10610613semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41492
#117544992
C2×#912842
#117513342
C5×#52322
#117492072
#117491982
#117489622
D5×#8322
#117483672
C2×#909642
#106106133
#840995