Finite Group Databasebeta

← #14412023

Subgroups — #14412023

Order 1920.

1432 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92004C211yesmaximal, characteristic
2C3×#65850C211yesmaximal, characteristic, complemented
3#11754188C211yesmaximal, characteristic, complemented
4#11751107C211yesmaximal, characteristic, complemented
5C5×#5006C211yesmaximal, characteristic, complemented
6#11748626C211yesmaximal, characteristic, complemented
7#11748625C211yesmaximal, characteristic, complemented
8#11747129C218yesmaximal, complemented
9#10610420—31nomaximal, Hall
10C2×#6817C2211yescharacteristic
11C2×C5×#235C2211yescharacteristic
12C22×C3×Dic10C2211yescharacteristic
13C2×#6782C2214yes—
14C2×D15⋊Q8C412yescomplemented
15C2×#6769C412yescomplemented
16#92004—22no—
17#92004—22no—
18#92004—22no—
19#92004—22no—
20C2×#6768C412yescomplemented
21C2×D3×Dic10C412yescomplemented
22C3×C5×#117C2211yescharacteristic
23#91815C2211yescharacteristic
24C5×#926C2211yescharacteristic
25C3×#4072C2211yescharacteristic
26C3×#4033—22no—
27C3×#4023C2214yes—
28C3×C4×Dic10—22no—
29#91528C2214yes—
30#91331—22no—
31Dic3×Dic10—22no—
32#91090C2214yes—
33C5×#806C2214yes—
34#90997C2214yes—
35#90996C2214yes—
36#82556—51nomaximal, Hall
37C2×#4150—31no—
38#65850—31no—
39#65850D311yescharacteristic, complemented
40C5×#410—31no—
41#65529—31no—
42#65295—31no—
43#65295—31no—
44#65029—38no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×#1220C2312yes—
47#6817—21no—
48#6817—21no—
49#6817—21no—
50#6817—21no—
51C2×D60C2×C411yescharacteristic
52C2×C4×D15C2×C412yes—
53C2×Dic30C2×C411yescharacteristic
54C2×C5×#67C2312yes—
55C5×#235—21no—
56C5×#235—21no—
57C5×#235—21no—
58C5×#235—21no—
59C2×C5×D12C2×C411yescharacteristic
60C2×C4×C5×D3C2×C412yes—
61C2×C5×Dic6C2×C411yescharacteristic
62C22×C3×Dic5C2312yes—
63C2×C3×Dic10C2×C412yes—
64C2×C3×Dic10C2×C412yes—
65C2×C3×Dic10D412yes—
66C2×C3×Dic10D412yes—
67C2×C3×Dic10D412yes—
68C2×C3×Dic10D412yes—
69C2×#1204C2×C414yes—
70C2×#1203C2×C414yes—
71C2×#1200C2×C414yes—
72#6782—28no—
73#6782—28no—
74C2×D3×Dic5C2×C414yes—
75D15⋊Q8—24no—
76D15⋊Q8—24no—
77#6769—24no—
78#6769—24no—
79#6768—24no—
80#6768—24no—
81D3×Dic10—24no—
82D3×Dic10—24no—
83C3×C5×C4⋊C4—21no—
84C3×C5×C22⋊C4C2312yes—
85C3×C42×C5—21no—
86#6719C2312yes—
87C4⋊Dic15—21no—
88C4×Dic15—21no—
89C5×#217C2312yes—
90C5×C4⋊Dic3—21no—
91C4×C5×Dic3—21no—
92C3×C22⋊Dic5C2312yes—
93C3×C4⋊Dic5—21no—
94C3×#683—24no—
95C3×C4×Dic5—21no—
96C3×C4×Dic5—24no—
97#6668—24no—
98Dic3×Dic5—24no—
99C2×#1007—51no—
100C3×#519—51no—
101#5812—51no—
102#5006—51no—
103#5006—51no—
104#5006—51no—
105#5006—58no—
106#5006D511yescharacteristic, complemented
107C2×C5×#41—31no—
108#4150—62no—
109#4150—62no—
110#4150—62no—
111#4150—62no—
112C2×Q8×D5—32no—
113C2×#711—34no—
114C2×#711—32no—
115C2×#709—31no—
116C2×#709—32no—
117C22×Dic10—32no—
118C22×Dic10C2×D311yescharacteristic
119C5×#117—31no—
120C5×#117C2×D311yescharacteristic
121#4072—31no—
122#4072C2×D311yescharacteristic
123#4033—22no—
124#4033—62no—
125#4023—34no—
126#4023C2×D314yes—
127C4×Dic10—22no—
128C4×Dic10—62no—
129C5×#99—34no—
130#3966—34no—
131#3938—34no—
132#3938—34no—
133#2884—151noSylow
134C23×C3×C5C2411yescharacteristic
135C22×D15C22×C412yes—
136C22×C5×D3C22×C412yes—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C22×C411yescharacteristic
139C2×C3×C4×C5C22×C411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2×D411yescharacteristic
144#1220—22no—
145#1220—22no—
146C2×Dic15—22no—
147C2×Dic15C22×C412yes—
148D60—21no—
149D60—21no—
150C4×D15—22no—
151C4×D15—22no—
152Dic30—21no—
153Dic30—21no—
154C5×#67—22no—
155C5×#67—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3C22×C412yes—
158C5×D12—21no—
159C5×D12—21no—
160C4×C5×D3—22no—
161C4×C5×D3—22no—
162C5×Dic6—21no—
163C5×Dic6—21no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5C22×C414yes—
166C2×C3×Dic5C2×D414yes—
167C2×C3×Dic5C2×D414yes—
168C3×Dic10C22⋊C414yes—
169C3×Dic10C22⋊C414yes—
170C3×Dic10C22⋊C414yes—
171C3×Dic10C22⋊C414yes—
172#1204—28no—
173#1203—28no—
174#1200—28no—
175D3×Dic5—28no—
176C22×C3×Q8—51no—
177#1007—102no—
178#1007—102no—
179#1007—102no—
180#1007—102no—
181C2×#239—52no—
182C2×#239—52no—
183C2×D3×Q8—52no—
184C2×D3×Q8—52no—
185C2×#235—51no—
186C2×#235—54no—
187C2×#235C2×D511yescharacteristic
188C3×C4×Q8—102no—
189C3×C4×Q8—102no—
190C3×#117—51no—
191C3×#117—54no—
192C3×#117C2×D511yescharacteristic
193Q8×Dic3—102no—
194Q8×Dic3—102no—
195#926—51no—
196#926—54no—
197#926C2×D511yescharacteristic
198#806—54no—
199#806—54no—
200#806—54no—
201#806C2×D514yes—
202C5×#41—61no—
203C5×#41—61no—
204C5×#41—61no—
205C5×#41—61no—
206C2×C5×Q8—31no—
207C2×C5×D4—32no—
208C2×C5×D4—31no—
209C22×C4×C5—32no—
210C22×C4×C5C22×D311yescharacteristic
211C2×C22⋊D5—32no—
212C2×C22⋊D5—34no—
213C22×Dic5—34no—
214C22×Dic5C22×D312yes—
215Q8×D5—64no—
216Q8×D5—64no—
217#711—68no—
218#711—68no—
219#711—64no—
220#711—64no—
221#709—61no—
222#709—61no—
223#709—61no—
224#709—61no—
225#709—64no—
226#709—64no—
227C2×D20—31no—
228C2×C4×D5—32no—
229C2×C4×D5—34no—
230C2×Dic10—31no—
231C2×Dic10—34no—
232C2×Dic10—64no—
233C2×Dic10—64no—
234C2×Dic10C4×D312yes—
235C2×Dic10C4×D312yes—
236C2×Dic10D1212yes—
237C2×Dic10D1212yes—
238C2×Dic10#6712yes—
239C2×Dic10#6712yes—
240C5×C4⋊C4—21no—
241C5×C4⋊C4—61no—
242C5×C22⋊C4—32no—
243C5×C22⋊C4C22×D312yes—
244C42×C5—21no—
245C42×C5—61no—
246C22⋊Dic5—32no—
247C22⋊Dic5C22×D312yes—
248C4⋊Dic5—21no—
249C4⋊Dic5—61no—
250#683—24no—
251#683—64no—
252C4×Dic5—21no—
253C4×Dic5—24no—
254C4×Dic5—61no—
255C4×Dic5—64no—
256C2×2−1+4—151no—
257#519—51no—
258#519—151no—
259#410—31no—
260#410—158no—
261#410—151no—
262#410—151no—
263#410—151no—
264C22×C3×C5—41no—
265C22×C3×C5C23×C411yescharacteristic
266C22×C3×C5C22×D411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C2×D15—22no—
269C2×D15—42no—
270C2×C5×D3—22no—
271C2×C5×D3—42no—
272C3×C4×C5—42no—
273C3×C4×C5C2×C22⋊C411yescharacteristic
274C3×C4×C5C2×C22⋊C411yescharacteristic
275C3×C4×C5C2×C22⋊C411yescharacteristic
276C3×C4×C5C2×C22⋊C411yescharacteristic
277Dic15—22no—
278Dic15—42no—
279C3×Dic5—42no—
280C3×Dic5C2×C22⋊C418yes—
281C5×Dic3—22no—
282C5×Dic3—42no—
283C2×C3×Q8—52no—
284C2×C3×Q8—52no—
285C2×C3×Q8—52no—
286C2×C3×Q8—52no—
287C2×C3×Q8—52no—
288C2×C3×Q8—52no—
289C22×C3×C4—52no—
290C22×C3×C4C22×D511yescharacteristic
291C2×#67—52no—
292C2×#67C22×D512yes—
293#239—104no—
294#239—104no—
295#239—104no—
296#239—104no—
297D3×Q8—104no—
298D3×Q8—104no—
299D3×Q8—104no—
300D3×Q8—104no—
301#235—21no—
302#235—21no—
303#235—21no—
304#235—21no—
305#235—108no—
306#235—108no—
307#235—101no—
308#235—101no—
309#235—101no—
310#235—101no—
311C2×D12—54no—
312C2×D12—51no—
313C2×D12C4×D511yescharacteristic
314C2×C4×D3—54no—
315C2×C4×D3—52no—
316C2×C4×D3—54no—
317C2×C4×D3C4×D512yes—
318C2×Dic6—51no—
319C2×Dic6—54no—
320C2×Dic6C4×D511yescharacteristic
321C3×C4⋊C4—21no—
322C3×C4⋊C4—104no—
323C3×C4⋊C4—101no—
324C3×C22⋊C4—52no—
325C3×C22⋊C4C22×D512yes—
326C3×C42—21no—
327C3×C42—104no—
328C3×C42—101no—
329#217—52no—
330#217C22×D512yes—
331C4⋊Dic3—21no—
332C4⋊Dic3—104no—
333C4⋊Dic3—101no—
334C4×Dic3—21no—
335C4×Dic3—104no—
336C4×Dic3—101no—
337C23×C5—32no—
338C23×C5C23×D311yescharacteristic
339C22×D5—32no—
340C5×Q8—61no—
341C5×Q8—61no—
342C5×D4—62no—
343C5×D4—62no—
344C5×D4—61no—
345C5×D4—61no—
346C2×C4×C5—22no—
347C2×C4×C5—32no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5—62no—
351C2×C4×C5C2×C4×D311yescharacteristic
352C2×C4×C5C2×C4×D311yescharacteristic
353C2×C4×C5C2×D1211yescharacteristic
354C2×C4×C5C2×D1211yescharacteristic
355C2×C4×C5C2×#6711yescharacteristic
356C2×C4×C5C2×#6711yescharacteristic
357C22⋊D5—62no—
358C22⋊D5—62no—
359C22⋊D5—68no—
360C2×Dic5—22no—
361C2×Dic5—32no—
362C2×Dic5—68no—
363C2×Dic5—62no—
364C2×Dic5C2×C4×D314yes—
365C2×Dic5C2×D1214yes—
366C2×Dic5C2×#6714yes—
367D20—61no—
368D20—61no—
369C4×D5—62no—
370C4×D5—62no—
371C4×D5—68no—
372Dic10—61no—
373Dic10—61no—
374Dic10—68no—
375Dic10(C2×D3)⋊C414yes—
376Dic10(C2×D3)⋊C414yes—
377Dic10(C2×D3)⋊C414yes—
378Dic10(C2×D3)⋊C414yes—
3792−1+4—302no—
3802−1+4—302no—
3812−1+4—302no—
3822−1+4—302no—
383C2×#41—31no—
384C2×#41—152no—
385C2×#41—154no—
386C2×#41—152no—
387C2×#41—151no—
388C22×Q8—51no—
389C22×Q8—152no—
390C22×Q8—152no—
391C4×Q8—102no—
392C4×Q8—102no—
393C4×Q8—302no—
394C4×Q8—302no—
395#117—31no—
396#117—51no—
397#117—54no—
398#117—154no—
399#117—151no—
400#117D3×D511yescharacteristic
401#99—34no—
402#99—154no—
403#99—154no—
404#99—154no—
405C2×C3×C5—21no—
406C2×C3×C5—21no—
407C2×C3×C5—21no—
408C2×C3×C5C22×C22⋊C411yescharacteristic
409D15—42no—
410C5×D3—42no—
411C23×C3C23×D511yescharacteristic
412C22×D3—52no—
413C22×D3C2×C4×D512yes—
414C3×Q8—54no—
415C3×Q8—54no—
416C3×Q8—54no—
417C3×Q8—54no—
418C2×C3×C4—22no—
419C2×C3×C4—54no—
420C2×C3×C4—54no—
421C2×C3×C4—54no—
422C2×C3×C4—102no—
423C2×C3×C4C2×C4×D511yescharacteristic
424C2×C3×C4C2×C4×D511yescharacteristic
425C2×C3×C4D4×D511yescharacteristic
426C2×C3×C4D4×D511yescharacteristic
427C2×C3×C4D4×D511yescharacteristic
428C2×C3×C4D4×D511yescharacteristic
429#67—22no—
430#67—22no—
431#67—102no—
432#67—102no—
433C2×Dic3—22no—
434C2×Dic3—52no—
435C2×Dic3—102no—
436C2×Dic3C2×C4×D512yes—
437D12—21no—
438D12—21no—
439D12—108no—
440D12—101no—
441D12—101no—
442C4×D3—22no—
443C4×D3—22no—
444C4×D3—108no—
445C4×D3—108no—
446C4×D3—102no—
447C4×D3—102no—
448Dic6—21no—
449Dic6—21no—
450Dic6—108no—
451Dic6—101no—
452Dic6—101no—
453C22×C5—41no—
454C22×C5—62no—
455C22×C5—122no—
456C22×C5C22×C4×D311yescharacteristic
457C22×C5C22×D1211yescharacteristic
458C22×C5C22×#6711yescharacteristic
459C2×D5—62no—
460C2×D5—122no—
461C4×C5—42no—
462C4×C5—62no—
463C4×C5—122no—
464C4×C5C2×(C2×D3)⋊C411yescharacteristic
465C4×C5C2×(C2×D3)⋊C411yescharacteristic
466C4×C5C2×(C2×D3)⋊C411yescharacteristic
467C4×C5C2×(C2×D3)⋊C411yescharacteristic
468Dic5—42no—
469Dic5—62no—
470Dic5—122no—
471Dic5C2×(C2×D3)⋊C418yes—
472#41—61no—
473#41—61no—
474#41—61no—
475#41—61no—
476#41—308no—
477#41—308no—
478#41—304no—
479#41—304no—
480#41—304no—
481#41—304no—
482#41—301no—
483#41—301no—
484#41—301no—
485#41—301no—
486C2×Q8—31no—
487C2×Q8—52no—
488C2×Q8—52no—
489C2×Q8—52no—
490C2×Q8—52no—
491C2×Q8—52no—
492C2×Q8—52no—
493C2×Q8—154no—
494C2×Q8—151no—
495C2×Q8—304no—
496C2×Q8—304no—
497C2×Q8—304no—
498C2×Q8—304no—
499C2×D4—32no—
500C2×D4—31no—
501C2×D4—154no—
502C2×D4—152no—
503C2×D4—151no—
504C22×C4—32no—
505C22×C4—52no—
506C22×C4—154no—
507C22×C4—154no—
508C22×C4—152no—
509C22×C4C2×D3×D511yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—61no—
512C4⋊C4—104no—
513C4⋊C4—101no—
514C4⋊C4—304no—
515C4⋊C4—301no—
516C22⋊C4—32no—
517C22⋊C4—52no—
518C22⋊C4—152no—
519C22⋊C4C2×D3×D512yes—
520C42—21no—
521C42—61no—
522C42—104no—
523C42—101no—
524C42—304no—
525C42—301no—
526C3×C5#288411yescharacteristic, complemented, Hall
527C22×C3—41no—
528C22×C3C22×C4×D511yescharacteristic
529C22×C3C2×D4×D511yescharacteristic
530C22×C3C2×D4×D511yescharacteristic
531C2×D3—22no—
532C2×D3—42no—
533C2×D3—102no—
534C2×D3—202no—
535C3×C4—42no—
536C3×C4—58no—
537C3×C4—202no—
538C3×C4D5×C22⋊C411yescharacteristic
539C3×C4D5×C22⋊C411yescharacteristic
540C3×C4D5×C22⋊C411yescharacteristic
541C3×C4D5×C22⋊C411yescharacteristic
542Dic3—22no—
543Dic3—42no—
544Dic3—102no—
545Dic3—202no—
546C2×C5—21no—
547C2×C5—21no—
548C2×C5—21no—
549C2×C5—122no—
550C2×C5C22×(C2×D3)⋊C411yescharacteristic
551D5—122no—
552C23—32no—
553C23—152no—
554C23C22×D3×D511yescharacteristic
555Q8—54no—
556Q8—54no—
557Q8—54no—
558Q8—54no—
559Q8—61no—
560Q8—61no—
561Q8—308no—
562Q8—301no—
563Q8—301no—
564D4—62no—
565D4—62no—
566D4—61no—
567D4—61no—
568D4—308no—
569D4—302no—
570D4—302no—
571D4—301no—
572D4—301no—
573C2×C4—22no—
574C2×C4—32no—
575C2×C4—54no—
576C2×C4—54no—
577C2×C4—54no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—62no—
581C2×C4—102no—
582C2×C4—152no—
583C2×C4—308no—
584C2×C4—308no—
585C2×C4—302no—
586C2×C4—302no—
587C2×C4—302no—
588C2×C4C4×D3×D511yescharacteristic
589C2×C4C4×D3×D511yescharacteristic
590C2×C4D5×D1211yescharacteristic
591C2×C4D5×D1211yescharacteristic
592C2×C4D5×#6711yescharacteristic
593C2×C4D5×#6711yescharacteristic
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—21no—
597C2×C3C2×D5×C22⋊C411yescharacteristic
598D3—42no—
599D3—202no—
600C5#8255611yescharacteristic, complemented, Sylow
601C22—41no—
602C22—62no—
603C22—122no—
604C22—302no—
605C22—602no—
606C22C2×C4×D3×D511yescharacteristic
607C22C2×D5×D1211yescharacteristic
608C22C2×D5×#6711yescharacteristic
609C4—42no—
610C4—58no—
611C4—62no—
612C4—122no—
613C4—202no—
614C4—302no—
615C4—602no—
616C4D5×(C2×D3)⋊C411yescharacteristic
617C4D5×(C2×D3)⋊C411yescharacteristic
618C4D5×(C2×D3)⋊C411yescharacteristic
619C4D5×(C2×D3)⋊C411yescharacteristic
620C3#1061042011yescharacteristic, complemented, Sylow
621C2—21no—
622C2—21no—
623C2—21no—
624C2—122no—
625C2—602no—
626C2C2×D5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC2C2×D5×(C2×D3)⋊C4
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92004C2
cosocleC23×C3×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2884
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#65850C2semidirect
3. #11754188C2semidirect
4. #11751107C2semidirect
5. C5×#5006C2semidirect
6. #11748626C2semidirect
7. #11748625C2semidirect
8. #11747129C2semidirect
14. C2×D15⋊Q8C4semidirect
15. C2×#6769C4semidirect
20. C2×#6768C4semidirect
21. C2×D3×Dic10C4semidirect
39. #65850D3semidirect
106. #5006D5semidirect
526. C3×C5#2884semidirect
600. C5#82556semidirect
620. C3#10610420semidirect

Maximal subgroups

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

subgroupindex
C2×#920042
C3×#658502
#117541882
#117511072
C5×#50062
#117486262
#117486252
#117471292
#106104203
#825565