Finite Group Databasebeta

← #14424138

Subgroups — #14424138

Order 1920.

1508 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6772C211yesmaximal, characteristic
2D5×#924C211yesmaximal, characteristic, complemented
3C2×#91260C212yesmaximal, complemented
4#11750840C211yesmaximal, characteristic, complemented
5C5×#4731C211yesmaximal, characteristic, complemented
6C3×#65015C211yesmaximal, characteristic, complemented
7#11748565C211yesmaximal, characteristic, complemented
8#11748543C211yesmaximal, characteristic, complemented
9#11748164C212yesmaximal, complemented
10#11748155C212yesmaximal, complemented
11#11747605C212yesmaximal, complemented
12#10611878—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C22×C5×D12C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1201—21no—
17C22×D3×Dic5—21no—
18C2×#6772—21no—
19C2×#6772—21no—
20C2×#6772—28no—
21C2×#6772C2212yes—
22C2×#6772C2212yes—
23C2×D5×Dic6C2211yescharacteristic, complemented
24#91813C2211yescharacteristic
25C2×Dic60C2212yescomplemented
26C5×#924C2211yescharacteristic
27C2×C5×#204C2212yescomplemented
28C2×C3×#676C2212yescomplemented
29#91574—21no—
30D5×#217—21no—
31D5×C4⋊Dic3C2211yescharacteristic, complemented
32D5×Dic3⋊C4—21no—
33#91360C2211yescharacteristic, complemented
34#91359C2211yescharacteristic, complemented
35#91349—21no—
36C2×#6663C2212yescomplemented
37C2×#6659C2212yescomplemented
38#91260—28no—
39C3×C5×C22⋊C8C2211yescharacteristic
40#91100C2212yescomplemented
41C5×#821C2212yescomplemented
42C3×C22⋊#168C2211yescharacteristic
43C3×#3952C2212yescomplemented
44#90975C2212yescomplemented
45#90967C2212yescomplemented
46#78640—51nomaximal, Hall
47C22×#711—31no—
48C2×#4061—32no—
49D5×C22⋊Q8—31no—
50C5×#450—31no—
51#65507—31no—
52#65462—32no—
53#65339—31no—
54#65072—32no—
55#65060—32no—
56#65028—31no—
57#65015D311yescharacteristic, complemented
58C23×C5×D3—21no—
59C23×C3×D5D411yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15—21no—
62C2×Dic30—21no—
63C2×Dic30—24no—
64C2×Dic30C2311yescharacteristic
65C2×Dic30C2312yes—
66C2×C5×D12—21no—
67C2×C5×D12—24no—
68C2×C5×D12C2312yes—
69C2×C5×Dic6C2311yescharacteristic
70C22×C3×Dic5D411yescharacteristic
71C2×C3×C4×D5—24no—
72C2×C3×C4×D5D411yescharacteristic
73C2×C3×C4×D5D411yescharacteristic
74C2×C3×C4×D5C2311yescharacteristic
75C2×C3×C4×D5C2311yescharacteristic
76C2×#1204—21no—
77C2×#1201—28no—
78C2×#1201—22no—
79C2×#1201—22no—
80C2×D3×Dic5—28no—
81C2×D3×Dic5—22no—
82C2×D3×Dic5—22no—
83C2×D5×Dic3—21no—
84C2×D5×Dic3—21no—
85#6772—28no—
86#6772—28no—
87#6772—24no—
88#6772—24no—
89#6772—24no—
90#6772D418yes—
91D5×Dic6—24no—
92C2×C3×C5×C8C2312yes—
93#6719—21no—
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96Dic60—24no—
97C5×#217—21no—
98C5×C4⋊Dic3C2311yescharacteristic
99C5×Dic3⋊C4—21no—
100C5×#204—24no—
101C2×C3×#168C2312yes—
102C3×#676—24no—
103Dic3⋊Dic5—21no—
104#6669—21no—
105#6668—21no—
106#6665—21no—
107#6665—21no—
108#6663—24no—
109#6659—24no—
110C22×#235—51no—
111C2×#924—51no—
112C2×#909—52no—
113C3×#407—51no—
114#5133—52no—
115#4739—51no—
116#4739—51no—
117#4733—52no—
118#4733—52no—
119#4731—51no—
120#4731D511yescharacteristic, complemented
121C22×C5×D4—31no—
122C22×C22⋊D5—61no—
123C23×Dic5—61no—
124C2×Q8×D5—31no—
125C2×#711—32no—
126C2×#711—32no—
127C2×#711—68no—
128C2×#711—61no—
129C2×#711—61no—
130C22×C4×D5C2×D311yescharacteristic
131C22×Dic10—31no—
132C2×C5×SD16—32no—
133C5×C22⋊Q8—31no—
134#4092—31no—
135C2×#689—32no—
136C2×#687—32no—
137#4070—31no—
138#4061—68no—
139C2×Dic20—32no—
140C2×#676C2×D312yescomplemented
141#4043—31no—
142#4042—61no—
143D5×C4⋊C4—31no—
144D5×C4⋊C4—61no—
145D5×C22⋊C4—61no—
146#4024—61no—
147C5×#102—32no—
148C5×C22⋊C8C2×D311yescharacteristic
149#3964—32no—
150C22⋊#168C2×D311yescharacteristic
151#3952C2×D312yescomplemented
152#3948—32no—
153#3942—32no—
154#3007—151noSylow
155C23×C3×C5C2×D411yescharacteristic
156C22×C5×D3—24no—
157C22×C5×D3—22no—
158C22×C5×D3—42no—
159C22×C5×D3—42no—
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5—41no—
163C22×C3×D5C2×D411yescharacteristic
164C22×C3×D5C2×D411yescharacteristic
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5C2×D411yescharacteristic
167C2×C3×C4×C5C2411yescharacteristic
168C2×Dic15—24no—
169C2×Dic15—22no—
170C2×Dic15—21no—
171C2×Dic15—21no—
172Dic30—24no—
173Dic30—22no—
174Dic30—22no—
175Dic30C2×D414yes—
176C2×C5×Dic3—21no—
177C2×C5×Dic3—21no—
178C5×D12—24no—
179C5×D12—22no—
180C5×D12C2×D414yes—
181C5×Dic6—22no—
182C2×C3×Dic5—22no—
183C2×C3×Dic5C2×D411yescharacteristic
184C2×C3×Dic5C2×D411yescharacteristic
185C3×C4×D5—22no—
186C3×C4×D5—22no—
187C3×C4×D5—22no—
188C3×C4×D5C2×D414yes—
189#1204—42no—
190#1201—28no—
191#1201—28no—
192D3×Dic5—28no—
193D3×Dic5—28no—
194D5×Dic3—42no—
195D5×Dic3—42no—
196C3×C5×C8—22no—
197C3×#168—22no—
198C23×C3×C4—51no—
199C22×#67—101no—
200C2×#235—52no—
201C2×#235—52no—
202C2×#235—108no—
203C2×#235—101no—
204C2×#235—101no—
205C22×D12C2×D511yescharacteristic
206C22×C4×D3—101no—
207C22×Dic6—51no—
208C22×Dic6—51no—
209C2×C3×M16—52no—
210C2×#217—101no—
211C2×C4⋊Dic3—51no—
212#924—51no—
213#924—51no—
214#924—51no—
215#924—101no—
216#924—101no—
217#924C2×D511yescharacteristic
218C2×Dic3⋊C4—101no—
219#909—108no—
220C2×Dic12—52no—
221C2×Dic12—52no—
222C2×#204—52no—
223C2×#204C2×D512yescomplemented
224C3×C22⋊C8—51no—
225C3×C22⋊C8—52no—
226C3×C22⋊C8C2×D511yescharacteristic
227#821—52no—
228#821C2×D512yescomplemented
229#816—52no—
230#816—52no—
231C24×C5—61no—
232C23×D5D1211yescharacteristic
233C2×C5×Q8—31no—
234C2×C5×D4—32no—
235C2×C5×D4—64no—
236C2×C5×D4—61no—
237C22×C4×C5C22×D311yescharacteristic
238C2×C22⋊D5—68no—
239C2×C22⋊D5—62no—
240C2×C22⋊D5—62no—
241C22×Dic5—68no—
242C22×Dic5—61no—
243C22×Dic5—62no—
244C22×Dic5—62no—
245C22×Dic5D1211yescharacteristic
246Q8×D5—64no—
247#711—38no—
248#711—64no—
249#711—64no—
250#711—68no—
251#711—68no—
252#711—64no—
253C2×C4×D5—24no—
254C2×C4×D5—61no—
255C2×C4×D5—61no—
256C2×C4×D5D1211yescharacteristic
257C2×C4×D5D1211yescharacteristic
258C2×C4×D5C22×D311yescharacteristic
259C2×C4×D5C22×D311yescharacteristic
260C2×Dic10—32no—
261C2×Dic10—31no—
262C2×Dic10—64no—
263C2×Dic10—61no—
264C2×Dic10—61no—
265C5×SD16—64no—
266C2×C5×C8C22×D312yes—
267C5×C4⋊C4—31no—
268C5×C4⋊C4—61no—
269C5×C22⋊C4—61no—
270C22⋊Dic5—61no—
271#689—64no—
272#687—64no—
273#685—61no—
274#685—61no—
275C4⋊Dic5—31no—
276C4⋊Dic5—61no—
277#683—61no—
278#683—61no—
279#683—61no—
280C2×#168C22×D312yes—
281Dic20—64no—
282#676—24no—
283C22×#41—151no—
284C2×#137—152no—
285C2×C22⋊Q8—151no—
286#452—152no—
287#452—152no—
288#451—151no—
289#451—151no—
290#450—31no—
291#450—151no—
292#417—152no—
293#407—51no—
294C22×C3×C5—21no—
295C22×C3×C5—21no—
296C22×C3×C5#13712yescomplemented
297C22×C3×C5C22×D411yescharacteristic
298C2×C5×D3—24no—
299C2×C5×D3—48no—
300C2×C5×D3—42no—
301C2×C5×D3—42no—
302C2×C3×D5—21no—
303C2×C3×D5—21no—
304C2×C3×D5—21no—
305C2×C3×D5—21no—
306C2×C3×D5—21no—
307C2×C3×D5—44no—
308C2×C3×D5#12012yes—
309C3×C4×C5—21no—
310C3×C4×C5C22×D412yes—
311Dic15—24no—
312Dic15—41no—
313Dic15—41no—
314C3×Dic5—21no—
315C3×Dic5#12012yes—
316C5×Dic3—41no—
317C5×Dic3—41no—
318C24×C3—51no—
319C23×D3—21no—
320C22×C3×C4—51no—
321C22×C3×C4—51no—
322C22×C3×C4—51no—
323C22×C3×C4—51no—
324C22×C3×C4—51no—
325C22×C3×C4—104no—
326C22×C3×C4C22×D511yescharacteristic
327C2×#67—102no—
328C2×#67—102no—
329C2×#67—108no—
330C22×Dic3—101no—
331C22×Dic3—101no—
332C22×Dic3—101no—
333#235—58no—
334#235—104no—
335#235—104no—
336#235—108no—
337#235—108no—
338#235—104no—
339C2×D12—21no—
340C2×D12—24no—
341C2×D12C22×D512yes—
342C2×C4×D3—102no—
343C2×C4×D3—102no—
344C2×C4×D3—108no—
345C2×Dic6—52no—
346C2×Dic6—51no—
347C2×Dic6—104no—
348C2×Dic6—104no—
349C2×Dic6—101no—
350C2×Dic6—101no—
351C2×Dic6C22×D511yescharacteristic
352C3×M16—104no—
353C2×C3×C8—52no—
354C2×C3×C8C22×D512yes—
355#217—21no—
356#217—101no—
357#217—101no—
358#217—101no—
359C4⋊Dic3—51no—
360C4⋊Dic3—101no—
361C4⋊Dic3C22×D511yescharacteristic
362Dic3⋊C4—21no—
363Dic3⋊C4—101no—
364Dic3⋊C4—101no—
365Dic3⋊C4—101no—
366Dic12—104no—
367Dic12—104no—
368#204—24no—
369#204—104no—
370C23×C5—64no—
371C23×C5—62no—
372C23×C5—122no—
373C23×C5—122no—
374C23×C5C2×D1211yescharacteristic
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—41no—
378C22×D5C2×D1211yescharacteristic
379C22×D5C2×D1211yescharacteristic
380C5×Q8—62no—
381C5×D4—34no—
382C5×D4—64no—
383C5×D4—62no—
384C2×C4×C5—22no—
385C2×C4×C5—61no—
386C2×C4×C5—61no—
387C2×C4×C5C2×D1211yescharacteristic
388C2×C4×C5C23×D311yescharacteristic
389C22⋊D5—68no—
390C22⋊D5—68no—
391C2×Dic5—22no—
392C2×Dic5—68no—
393C2×Dic5—64no—
394C2×Dic5—62no—
395C2×Dic5—68no—
396C2×Dic5—61no—
397C2×Dic5—61no—
398C2×Dic5C2×D1211yescharacteristic
399C2×Dic5C2×D1211yescharacteristic
400C4×D5—22no—
401C4×D5—22no—
402C4×D5—22no—
403C4×D5—122no—
404C4×D5—122no—
405C4×D5D3×D414yes—
406Dic10—34no—
407Dic10—64no—
408Dic10—62no—
409Dic10—62no—
410Dic10—122no—
411C5×C8—22no—
412#168—22no—
413C2×#41—152no—
414C2×#41—152no—
415C2×#41—301no—
416C2×#41—301no—
417C2×#41—308no—
418C22×Q8—151no—
419C22×Q8—151no—
420C22×D4—31no—
421C22×D4—301no—
422C23×C4—51no—
423C23×C4—301no—
424#137—308no—
425C2×Q16—152no—
426C2×Q16—152no—
427C2×SD16—32no—
428C2×SD16—152no—
429C2×M16—52no—
430C22⋊Q8—31no—
431C22⋊Q8—151no—
432C22⋊Q8—151no—
433C22⋊Q8—151no—
434C22⋊Q8—301no—
435C22⋊Q8—301no—
436C2×C4⋊C4—151no—
437C2×C4⋊C4—301no—
438C2×C22⋊C4—301no—
439#103—152no—
440#103—152no—
441#102—32no—
442#102—152no—
443C22⋊C8—51no—
444C22⋊C8—52no—
445C22⋊C8D3×D511yescharacteristic
446C2×C3×C5—22no—
447C2×C3×C5C2×#12011yescharacteristic
448C2×C3×C5C2×#13711yescharacteristic
449C2×C3×C5#57511yescharacteristic
450C3×D5—22no—
451C3×D5—41no—
452C5×D3—44no—
453C23×C3—51no—
454C23×C3—51no—
455C23×C3—102no—
456C23×C3—102no—
457C23×C3—201no—
458C23×C3D4×D511yescharacteristic
459C22×D3—24no—
460C22×D3—22no—
461C22×D3—42no—
462C22×D3—42no—
463C2×C3×C4—22no—
464C2×C3×C4—51no—
465C2×C3×C4—54no—
466C2×C3×C4—51no—
467C2×C3×C4—102no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—102no—
471C2×C3×C4D4×D511yescharacteristic
472C2×C3×C4C23×D511yescharacteristic
473#67—108no—
474#67—108no—
475C2×Dic3—21no—
476C2×Dic3—21no—
477C2×Dic3—104no—
478C2×Dic3—102no—
479C2×Dic3—101no—
480C2×Dic3—101no—
481C2×Dic3—202no—
482C2×Dic3—202no—
483D12—24no—
484D12—22no—
485D12D4×D514yes—
486C4×D3—108no—
487C4×D3—108no—
488Dic6—22no—
489Dic6—54no—
490Dic6—104no—
491Dic6—102no—
492Dic6—102no—
493Dic6—202no—
494C3×C8—22no—
495C3×C8—102no—
496C22×C5—21no—
497C22×C5—21no—
498C22×C5—64no—
499C22×C5—128no—
500C22×C5—122no—
501C22×C5—122no—
502C22×C5#90912yescomplemented
503C22×C5C22×D1211yescharacteristic
504C2×D5—21no—
505C2×D5—21no—
506C2×D5—21no—
507C2×D5—21no—
508C2×D5—21no—
509C2×D5—44no—
510C2×D5#88212yes—
511C4×C5—21no—
512C4×C5—121no—
513C4×C5—121no—
514C4×C5C2×D3×D412yes—
515Dic5—21no—
516Dic5—64no—
517Dic5—121no—
518Dic5—121no—
519Dic5#88212yes—
520C24—51no—
521C24—61no—
522#41—158no—
523#41—304no—
524#41—304no—
525#41—304no—
526#41—308no—
527#41—308no—
528C2×Q8—31no—
529C2×Q8—152no—
530C2×Q8—151no—
531C2×Q8—304no—
532C2×Q8—301no—
533C2×Q8—304no—
534C2×Q8—301no—
535C2×D4—32no—
536C2×D4—64no—
537C2×D4—61no—
538C2×D4—302no—
539C2×D4—302no—
540C2×D4—308no—
541C22×C4—51no—
542C22×C4—51no—
543C22×C4—51no—
544C22×C4—51no—
545C22×C4—51no—
546C22×C4—104no—
547C22×C4—302no—
548C22×C4—302no—
549C22×C4—301no—
550C22×C4—301no—
551C22×C4—308no—
552C22×C4—301no—
553C22×C4C2×D3×D511yescharacteristic
554Q16—304no—
555Q16—304no—
556SD16—64no—
557SD16—304no—
558M16—104no—
559C2×C8—52no—
560C2×C8C2×D3×D512yes—
561C4⋊C4—31no—
562C4⋊C4—61no—
563C4⋊C4—151no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C22⋊C4—61no—
569C22⋊C4—301no—
570C22⋊C4—301no—
571C22⋊C4—301no—
572C3×C5#300711yescharacteristic, complemented, Hall
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—52no—
576C22×C3—101no—
577C22×C3—101no—
578C22×C3—101no—
579C22×C3—101no—
580C22×C3—101no—
581C22×C3—204no—
582C22×C3#406112yescomplemented
583C22×C3C2×D4×D511yescharacteristic
584C2×D3—24no—
585C2×D3—48no—
586C2×D3—42no—
587C2×D3—42no—
588C3×C4—21no—
589C3×C4—52no—
590C3×C4—101no—
591C3×C4C2×D4×D512yes—
592Dic3—41no—
593Dic3—41no—
594Dic3—104no—
595Dic3—201no—
596Dic3—201no—
597C2×C5—22no—
598C2×C5—124no—
599C2×C5C2×#88211yescharacteristic
600C2×C5C2×#90911yescharacteristic
601C2×C5#574811yescharacteristic
602D5—22no—
603D5—41no—
604C23—51no—
605C23—51no—
606C23—64no—
607C23—62no—
608C23—102no—
609C23—102no—
610C23—122no—
611C23—122no—
612C23—201no—
613C23D5×D1211yescharacteristic
614Q8—62no—
615Q8—154no—
616Q8—304no—
617Q8—302no—
618Q8—302no—
619Q8—602no—
620D4—34no—
621D4—64no—
622D4—62no—
623D4—308no—
624D4—308no—
625C2×C4—22no—
626C2×C4—51no—
627C2×C4—54no—
628C2×C4—51no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—102no—
632C2×C4—102no—
633C2×C4—102no—
634C2×C4—102no—
635C2×C4—308no—
636C2×C4—308no—
637C2×C4—304no—
638C2×C4—302no—
639C2×C4—301no—
640C2×C4—301no—
641C2×C4—602no—
642C2×C4—602no—
643C2×C4D5×D1211yescharacteristic
644C2×C4C22×D3×D511yescharacteristic
645C8—22no—
646C8—102no—
647C2×C3—22no—
648C2×C3—102no—
649C2×C3—201no—
650C2×C3D5×#12011yescharacteristic
651C2×C3C2×#406111yescharacteristic
652C2×C3#6610711yescharacteristic
653D3—44no—
654C5#7864011yescharacteristic, complemented, Sylow
655C22—21no—
656C22—21no—
657C22—52no—
658C22—64no—
659C22—101no—
660C22—101no—
661C22—101no—
662C22—101no—
663C22—101no—
664C22—128no—
665C22—122no—
666C22—122no—
667C22—204no—
668C22#9126012yescomplemented
669C22C2×D5×D1211yescharacteristic
670C4—21no—
671C4—52no—
672C4—101no—
673C4—121no—
674C4—121no—
675C4—304no—
676C4—601no—
677C4—601no—
678C4D3×D4×D512yes—
679C3#1061187811yescharacteristic, complemented, Sylow
680C2—22no—
681C2—102no—
682C2—124no—
683C2—201no—
684C2D5×#88211yescharacteristic
685C2C2×#9126011yescharacteristic
686C2#1175402211yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC22×#6772C2
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#3007
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. D5×#924C2semidirect
3. C2×#91260C2semidirect
4. #11750840C2semidirect
5. C5×#4731C2semidirect
6. C3×#65015C2semidirect
7. #11748565C2semidirect
8. #11748543C2semidirect
9. #11748164C2semidirect
10. #11748155C2semidirect
11. #11747605C2semidirect
23. C2×D5×Dic6C22semidirect
25. C2×Dic60C22semidirect
27. C2×C5×#204C22semidirect
28. C2×C3×#676C22semidirect
31. D5×C4⋊Dic3C22semidirect
33. #91360C22semidirect
34. #91359C22semidirect
36. C2×#6663C22semidirect
37. C2×#6659C22semidirect
40. #91100C22semidirect
41. C5×#821C22semidirect
43. C3×#3952C22semidirect
44. #90975C22semidirect
45. #90967C22semidirect
57. #65015D3semidirect
120. #4731D5semidirect
140. C2×#676C2×D3semidirect
151. #3952C2×D3semidirect
223. C2×#204C2×D5semidirect
228. #821C2×D5semidirect
296. C22×C3×C5#137semidirect
502. C22×C5#909semidirect
572. C3×C5#3007semidirect
582. C22×C3#4061semidirect
654. C5#78640semidirect
668. C22#91260semidirect
679. C3#10611878semidirect

Maximal subgroups

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

subgroupindex
C22×#67722
D5×#9242
C2×#912602
#117508402
C5×#47312
C3×#650152
#117485652
#117485432
#117481642
#117481552
#117476052
#106118783
#786405