Finite Group Databasebeta

← #14480744

Subgroups — #14480744

Order 1920.

3112 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92016C212yesmaximal, complemented
2C2×#91781C211yesmaximal, characteristic, complemented
3C5×#5510C211yesmaximal, characteristic, complemented
4C3×#65844C211yesmaximal, characteristic, complemented
5#11754674C214yesmaximal, complemented
6#11754607C212yesmaximal, complemented
7#11754386C214yesmaximal, complemented
8#11753889C214yesmaximal, complemented
9#11753886C214yesmaximal, complemented
10#11753885C214yesmaximal, complemented
11#11753697C214yesmaximal, complemented
12#10618264—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C2×C5×#235C2212yescomplemented
15C2×C3×#709C2212yescomplemented
16C2×#6790C2214yes—
17C2×#6780C2214yescomplemented
18#92016—216no—
19C2×#6777C2212yescomplemented
20C2×C4×D3×D5C2214yescomplemented
21C2×#6771C2214yes—
22C2×D15⋊Q8C2212yescomplemented
23C2×#6768C2212yes—
24C2×#6766C2212yes—
25C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
26C2×#6714C2212yes—
27C2×C4⋊Dic15C2211yescharacteristic, complemented
28C2×C4×Dic15C2212yescomplemented
29#91781C2214yescomplemented
30#91781C2214yescomplemented
31C5×#930C2214yescomplemented
32C5×#897C2214yescomplemented
33C5×#895C2214yescomplemented
34C3×#4076C2214yescomplemented
35C3×#4043C2214yescomplemented
36C3×#4041C2214yescomplemented
37#91571C2218yescomplemented
38#91475C2218yescomplemented
39#91474C2218yescomplemented
40#91470C2214yescomplemented
41#91464C2218yescomplemented
42#91463C2214yescomplemented
43#91456C2214yescomplemented
44#91449C2214yescomplemented
45#91442C2218yescomplemented
46#91438C2218yescomplemented
47#91435C2214yescomplemented
48#91434C2214yescomplemented
49#91369C2214yescomplemented
50#91359C2214yescomplemented
51#91356C2218yescomplemented
52#86363—51nomaximal, Hall
53C2×D5×#41—32no—
54C5×#537—31no—
55#66167—32no—
56#65962—34no—
57#65961—34no—
58#65941—34no—
59#65940—34no—
60#65939—34no—
61#65930—34no—
62#65844D311yescharacteristic, complemented
63C2×#4038—31no—
64C23×D15C2311yescharacteristic
65C22×D3×D5C2314yes—
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2311yescharacteristic
68C22×Dic15C2312yes—
69C22×Dic15C2311yescharacteristic
70C2×C4×D15D418yescomplemented
71C2×C4×D15C2312yes—
72C2×C4×D15C2312yes—
73C2×C5×#67C2314yes—
74C5×#235—28no—
75C2×C5×D12C2312yes—
76C2×C5×D12C2314yes—
77C2×C4×C5×D3C2314yes—
78C2×C5×Dic6C2312yes—
79C2×C3×C22⋊D5C2314yes—
80C3×#709—28no—
81C2×C3×D20C2312yes—
82C2×C3×D20C2314yes—
83C2×C3×C4×D5C2314yes—
84C2×C3×Dic10C2312yes—
85#6790—216no—
86C2×#1204C2314yes—
87C2×#1203C2314yes—
88C2×#1202C2314yes—
89C2×#1201C2314yes—
90C2×#1201C2318yes—
91C2×#1200C2314yes—
92C2×D3×Dic5C2314yes—
93#6780—216no—
94C2×D5×Dic3C2314yes—
95#6777—28no—
96C4×D3×D5—216no—
97#6771—216no—
98D15⋊Q8—28no—
99#6768—28no—
100#6766—28no—
101C3×C5×C4⋊C4C2314yes—
102#6714C2318yes—
103C4⋊Dic15C2314yes—
104C4×Dic15C2314yes—
105C4×Dic15C2314yes—
106C5×(C2×D3)⋊C4C2318yes—
107C5×C4⋊Dic3C2314yes—
108C3×#685C2318yes—
109C3×C4⋊Dic5C2314yes—
110#6669C2318yes—
111(C2×D3)⋊Dic5C2318yes—
112#6665C2318yes—
113C2×D3×#41—52no—
114C3×#537—51no—
115#5833—52no—
116#5628—54no—
117#5627—54no—
118#5607—54no—
119#5606—54no—
120#5605—54no—
121#5596—54no—
122#5510D511yescharacteristic, complemented
123C2×#892—51no—
124C2×C5×#41—32no—
125D5×#41—616no—
126C2×#713—32no—
127C2×Q8×D5—32no—
128C2×#711—34no—
129C2×#711—32no—
130C2×D4×D5—34no—
131C2×D4×D5—32no—
132C2×#709—34no—
133C2×#709C2×D312yescomplemented
134C22×C4×D5—31no—
135C22×C4×D5—34no—
136C5×C22⋊Q8—34no—
137C5×#121—34no—
138C5×#121—34no—
139C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
140#4092—34no—
141#4086—34no—
142#4085—38no—
143#4084—34no—
144#4083—38no—
145D4×Dic5—34no—
146#4076—34no—
147#4076C2×D314yescomplemented
148C2×#685—32no—
149C2×C4⋊Dic5—31no—
150#4070—34no—
151C2×C4×Dic5—32no—
152#4043C2×D314yescomplemented
153#4041C2×D314yescomplemented
154#4040—38no—
155#4039—34no—
156#4038—34no—
157#4038—34no—
158#4034—34no—
159#4031—38no—
160#4029—38no—
161#4028—38no—
162#4027—38no—
163#3449—151noSylow
164C23×C3×C5C2411yescharacteristic
165C22×D15—41no—
166C22×D15—41no—
167C22×D15C2×D414yes—
168C22×D15C2412yes—
169C22×C5×D3C2414yes—
170C22×C3×D5C2414yes—
171C2×D3×D5—28no—
172C2×D3×D5—44no—
173C2×D3×D5—44no—
174C2×C3×C4×C5—42no—
175C2×C3×C4×C5C2×D414yes—
176C2×C3×C4×C5C2414yes—
177C2×C3×C4×C5C2412yes—
178C2×Dic15—42no—
179C2×Dic15C2×D414yes—
180C2×Dic15C2414yes—
181C2×Dic15C2411yescharacteristic
182C2×Dic15C2411yescharacteristic
183C4×D15C2×D418yes—
184C4×D15C2×D418yes—
185C5×#67—28no—
186C2×C5×Dic3C2414yes—
187C5×D12—24no—
188C5×D12—44no—
189C4×C5×D3—28no—
190C5×Dic6—24no—
191C3×C22⋊D5—28no—
192C2×C3×Dic5C2414yes—
193C3×D20—24no—
194C3×D20—44no—
195C3×C4×D5—28no—
196C3×Dic10—24no—
197#1204—28no—
198#1203—28no—
199#1202—28no—
200#1201—28no—
201#1201—48no—
202#1200—28no—
203D3×Dic5—28no—
204D5×Dic3—28no—
205C2×C3×#41—52no—
206D3×#41—1016no—
207C2×#239—52no—
208C2×D3×Q8—52no—
209C2×#237—54no—
210C2×#237—52no—
211C2×D3×D4—54no—
212C2×D3×D4—52no—
213C2×#235—54no—
214C2×#235C2×D512yescomplemented
215C22×C4×D3—51no—
216C22×C4×D3—54no—
217C3×C22⋊Q8—54no—
218C3×#121—54no—
219C3×#121—54no—
220C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
221#946—54no—
222#940—54no—
223#939—58no—
224#938—54no—
225#937—58no—
226D4×Dic3—54no—
227#930—54no—
228#930C2×D514yescomplemented
229C2×(C2×D3)⋊C4—52no—
230C2×C4⋊Dic3—51no—
231#924—54no—
232C2×C4×Dic3—52no—
233#897C2×D514yescomplemented
234#895C2×D514yescomplemented
235#894—58no—
236#893—54no—
237#892—54no—
238#892—54no—
239#888—54no—
240#885—58no—
241#883—58no—
242#882—58no—
243#67⋊C4—58no—
244C23×D5—31no—
245C23×D5—34no—
246C5×#41—68no—
247C2×C5×Q8—32no—
248C2×C5×D4—34no—
249C2×C5×D4—32no—
250C2×C5×D4—34no—
251C22×C4×C5—34no—
252C22×C4×C5C22×D312yes—
253C22×C4×C5C22×D311yescharacteristic
254C2×C22⋊D5—34no—
255C2×C22⋊D5—38no—
256C2×C22⋊D5—34no—
257C2×C22⋊D5C22×D314yes—
258C22×Dic5—31no—
259C22×Dic5—32no—
260C22×Dic5—34no—
261#713—68no—
262Q8×D5—68no—
263#711—68no—
264#711—616no—
265D4×D5—68no—
266D4×D5—616no—
267#709—28no—
268#709—616no—
269C2×D20—34no—
270C2×D20C22×D312yes—
271C2×D20C22×D314yes—
272C2×C4×D5—38no—
273C2×C4×D5—32no—
274C2×C4×D5—32no—
275C2×C4×D5—34no—
276C2×C4×D5—34no—
277C2×C4×D5—616no—
278C2×C4×D5C22×D314yes—
279C2×Dic10—34no—
280C2×Dic10C22×D312yes—
281C5×C4⋊C4—34no—
282C5×C4⋊C4C22×D314yes—
283C5×C22⋊C4—38no—
284C22⋊Dic5—38no—
285#685—38no—
286#685—38no—
287#685C22×D318yes—
288C4⋊Dic5—34no—
289C4⋊Dic5C22×D314yes—
290#683—38no—
291C4×Dic5—34no—
292C4×Dic5—34no—
293C22×#41—152no—
294#537—31no—
295#537—51no—
296#537—152no—
297#536—154no—
298#535—154no—
299#534—154no—
300#532—154no—
301#525—154no—
302#525—154no—
303C2×#117—151no—
304C22×C3×C5—21no—
305C22×C3×C5—21no—
306C22×C3×C5C22×D412yes—
307C22×C3×C5C2511yescharacteristic
308C2×D15—22no—
309C2×D15—22no—
310C2×D15—44no—
311C2×D15C22×D414yes—
312C2×C5×D3—24no—
313C2×C5×D3—24no—
314C2×C5×D3—24no—
315C2×C3×D5—24no—
316C2×C3×D5—24no—
317C2×C3×D5—24no—
318D3×D5—416no—
319C3×C4×C5—24no—
320C3×C4×C5C22×D414yes—
321Dic15—24no—
322Dic15C22×D412yes—
323Dic15C22×D412yes—
324C3×Dic5—24no—
325C5×Dic3—24no—
326C23×D3—51no—
327C23×D3—54no—
328C3×#41—108no—
329C2×C3×Q8—52no—
330C2×C3×D4—54no—
331C2×C3×D4—52no—
332C2×C3×D4—54no—
333C22×C3×C4—54no—
334C22×C3×C4C22×D512yes—
335C22×C3×C4C22×D511yescharacteristic
336C2×#67—54no—
337C2×#67—58no—
338C2×#67—54no—
339C2×#67C22×D514yes—
340C22×Dic3—51no—
341C22×Dic3—52no—
342C22×Dic3—54no—
343#239—108no—
344D3×Q8—108no—
345#237—108no—
346#237—1016no—
347D3×D4—108no—
348D3×D4—1016no—
349#235—28no—
350#235—1016no—
351C2×D12—54no—
352C2×D12C22×D512yes—
353C2×D12C22×D514yes—
354C2×C4×D3—58no—
355C2×C4×D3—52no—
356C2×C4×D3—52no—
357C2×C4×D3—54no—
358C2×C4×D3—54no—
359C2×C4×D3—1016no—
360C2×C4×D3C22×D514yes—
361C2×Dic6—54no—
362C2×Dic6C22×D512yes—
363C3×C4⋊C4—54no—
364C3×C4⋊C4C22×D514yes—
365C3×C22⋊C4—58no—
366#217—58no—
367(C2×D3)⋊C4—58no—
368(C2×D3)⋊C4—58no—
369(C2×D3)⋊C4C22×D518yes—
370C4⋊Dic3—54no—
371C4⋊Dic3C22×D514yes—
372Dic3⋊C4—58no—
373C4×Dic3—54no—
374C4×Dic3—54no—
375C23×C5—34no—
376C23×C5C23×D311yescharacteristic
377C22×D5—32no—
378C22×D5—34no—
379C22×D5—68no—
380C22×D5—124no—
381C22×D5—124no—
382C22×D5—121no—
383C22×D5—121no—
384C22×D5C23×D314yes—
385C5×Q8—64no—
386C5×D4—68no—
387C5×D4—64no—
388C5×D4—124no—
389C2×C4×C5—34no—
390C2×C4×C5—42no—
391C2×C4×C5—68no—
392C2×C4×C5D3×D414yes—
393C2×C4×C5C23×D314yes—
394C2×C4×C5C23×D312yes—
395C22⋊D5—28no—
396C22⋊D5—68no—
397C22⋊D5—68no—
398C22⋊D5—128no—
399C2×Dic5—34no—
400C2×Dic5—31no—
401C2×Dic5—31no—
402C2×Dic5—34no—
403C2×Dic5—68no—
404C2×Dic5—122no—
405C2×Dic5C23×D314yes—
406D20—24no—
407D20—44no—
408D20—68no—
409C4×D5—28no—
410C4×D5—38no—
411C4×D5—38no—
412C4×D5—68no—
413C4×D5—68no—
414Dic10—24no—
415Dic10—68no—
416C2×#41—32no—
417C2×#41—52no—
418C2×#41—154no—
419C2×#41—154no—
420C2×#41—152no—
421C2×#41—152no—
422C2×#41—3016no—
423C22×Q8—152no—
424C22×D4—154no—
425C22×D4—152no—
426C23×C4—154no—
427C23×C4—151no—
428C4⋊Q8—154no—
429#127—154no—
430#124—158no—
431#123—158no—
432#123—158no—
433C22⋊Q8—34no—
434C22⋊Q8—54no—
435C22⋊Q8—154no—
436C22⋊Q8—154no—
437#121—34no—
438#121—34no—
439#121—54no—
440#121—54no—
441#121—154no—
442#121—154no—
443#121—158no—
444#120—158no—
445#120—158no—
446C4×D4—158no—
447C4×D4—154no—
448C4×D4—154no—
449#117—154no—
450#117—154no—
451C2×C4⋊C4—151no—
452C2×C4⋊C4D3×D511yescharacteristic, complemented
453C2×C22⋊C4—152no—
454C2×C42—152no—
455C2×C3×C5—22no—
456C2×C3×C5C23×D411yescharacteristic
457C2×C3×C5#58511yescharacteristic
458C2×C3×C5#58511yescharacteristic
459D15—24no—
460C3×D5—44no—
461C5×D3—44no—
462C23×C3—54no—
463C23×C3C23×D511yescharacteristic
464C22×D3—52no—
465C22×D3—54no—
466C22×D3—108no—
467C22×D3—204no—
468C22×D3—204no—
469C22×D3—201no—
470C22×D3—201no—
471C22×D3C23×D514yes—
472C3×Q8—104no—
473C3×D4—108no—
474C3×D4—104no—
475C3×D4—204no—
476C2×C3×C4—42no—
477C2×C3×C4—54no—
478C2×C3×C4—108no—
479C2×C3×C4D4×D514yes—
480C2×C3×C4C23×D514yes—
481C2×C3×C4C23×D512yes—
482#67—28no—
483#67—108no—
484#67—108no—
485#67—208no—
486C2×Dic3—54no—
487C2×Dic3—51no—
488C2×Dic3—51no—
489C2×Dic3—54no—
490C2×Dic3—108no—
491C2×Dic3—202no—
492C2×Dic3C23×D514yes—
493D12—24no—
494D12—44no—
495D12—108no—
496C4×D3—28no—
497C4×D3—58no—
498C4×D3—58no—
499C4×D3—108no—
500C4×D3—108no—
501Dic6—24no—
502Dic6—108no—
503C22×C5—21no—
504C22×C5—21no—
505C22×C5—64no—
506C22×C5—64no—
507C22×C5—64no—
508C22×C5C2×D3×D412yes—
509C22×C5C24×D311yescharacteristic
510C2×D5—24no—
511C2×D5—24no—
512C2×D5—24no—
513C2×D5—34no—
514C2×D5—62no—
515C2×D5—62no—
516C2×D5—1216no—
517C2×D5—124no—
518C4×C5—24no—
519C4×C5—64no—
520C4×C5C2×D3×D414yes—
521Dic5—24no—
522Dic5—32no—
523Dic5—32no—
524Dic5—64no—
525C24—154no—
526C24—151no—
527#41—68no—
528#41—108no—
529#41—3016no—
530#41—3016no—
531#41—308no—
532#41—308no—
533C2×Q8—32no—
534C2×Q8—52no—
535C2×Q8—154no—
536C2×Q8—308no—
537C2×D4—34no—
538C2×D4—32no—
539C2×D4—34no—
540C2×D4—54no—
541C2×D4—52no—
542C2×D4—54no—
543C2×D4—154no—
544C2×D4—154no—
545C2×D4—154no—
546C2×D4—158no—
547C2×D4—308no—
548C2×D4—3016no—
549C22×C4—34no—
550C22×C4—54no—
551C22×C4—154no—
552C22×C4—154no—
553C22×C4—154no—
554C22×C4—151no—
555C22×C4—158no—
556C22×C4—152no—
557C22×C4—152no—
558C22×C4—152no—
559C22×C4—3016no—
560C22×C4C2×D3×D512yes—
561C22×C4C2×D3×D511yescharacteristic
562C4⋊C4—34no—
563C4⋊C4—54no—
564C4⋊C4—158no—
565C4⋊C4—154no—
566C4⋊C4C2×D3×D514yes—
567C22⋊C4—38no—
568C22⋊C4—58no—
569C22⋊C4—158no—
570C22⋊C4—158no—
571C22⋊C4—158no—
572C42—154no—
573C42—154no—
574C3×C5#344911yescharacteristic, complemented, Hall
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—104no—
578C22×C3—104no—
579C22×C3—104no—
580C22×C3C2×D4×D512yes—
581C22×C3C24×D511yescharacteristic
582C2×D3—24no—
583C2×D3—24no—
584C2×D3—24no—
585C2×D3—54no—
586C2×D3—102no—
587C2×D3—102no—
588C2×D3—2016no—
589C2×D3—204no—
590C3×C4—24no—
591C3×C4—104no—
592C3×C4C2×D4×D514yes—
593Dic3—24no—
594Dic3—52no—
595Dic3—52no—
596Dic3—104no—
597C2×C5—22no—
598C2×C5—124no—
599C2×C5C22×D3×D411yescharacteristic
600C2×C5#596611yescharacteristic
601C2×C5#596811yescharacteristic
602D5—44no—
603D5—64no—
604C23—34no—
605C23—54no—
606C23—152no—
607C23—154no—
608C23—308no—
609C23—601no—
610C23—601no—
611C23—604no—
612C23—604no—
613C23C22×D3×D511yescharacteristic
614Q8—64no—
615Q8—104no—
616Q8—308no—
617D4—68no—
618D4—64no—
619D4—108no—
620D4—104no—
621D4—124no—
622D4—204no—
623D4—308no—
624D4—308no—
625D4—308no—
626D4—608no—
627C2×C4—34no—
628C2×C4—42no—
629C2×C4—54no—
630C2×C4—68no—
631C2×C4—108no—
632C2×C4—154no—
633C2×C4—151no—
634C2×C4—151no—
635C2×C4—158no—
636C2×C4—158no—
637C2×C4—154no—
638C2×C4—308no—
639C2×C4—308no—
640C2×C4—308no—
641C2×C4—602no—
642C2×C4#677714yes—
643C2×C4C22×D3×D514yes—
644C2×C4C22×D3×D512yes—
645C2×C3—22no—
646C2×C3—204no—
647C2×C3C22×D4×D511yescharacteristic
648C2×C3#6628511yescharacteristic
649C2×C3#6628711yescharacteristic
650D3—44no—
651D3—104no—
652C5#8636311yescharacteristic, complemented, Sylow
653C22—21no—
654C22—21no—
655C22—64no—
656C22—64no—
657C22—64no—
658C22—104no—
659C22—104no—
660C22—104no—
661C22—154no—
662C22—302no—
663C22—302no—
664C22—604no—
665C22—6016no—
666C22C2×#677712yes—
667C22C23×D3×D511yescharacteristic
668C4—24no—
669C4—64no—
670C4—104no—
671C4—152no—
672C4—152no—
673C4—304no—
674C4C2×#677714yes—
675C3#1061826411yescharacteristic, complemented, Sylow
676C2—22no—
677C2—124no—
678C2—204no—
679C2—304no—
680C2C22×#677711yescharacteristic
681C2#1175703611yescharacteristic
682C2#1175705011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC2×C3×C5×C4⋊C4C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#3449
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#92016C2semidirect
2. C2×#91781C2semidirect
3. C5×#5510C2semidirect
4. C3×#65844C2semidirect
5. #11754674C2semidirect
6. #11754607C2semidirect
7. #11754386C2semidirect
8. #11753889C2semidirect
9. #11753886C2semidirect
10. #11753885C2semidirect
11. #11753697C2semidirect
14. C2×C5×#235C22semidirect
15. C2×C3×#709C22semidirect
17. C2×#6780C22semidirect
19. C2×#6777C22semidirect
20. C2×C4×D3×D5C22semidirect
22. C2×D15⋊Q8C22semidirect
25. C2×C3×C5×C4⋊C4C22semidirect
27. C2×C4⋊Dic15C22semidirect
28. C2×C4×Dic15C22semidirect
29. #91781C22semidirect
30. #91781C22semidirect
31. C5×#930C22semidirect
32. C5×#897C22semidirect
33. C5×#895C22semidirect
34. C3×#4076C22semidirect
35. C3×#4043C22semidirect
36. C3×#4041C22semidirect
37. #91571C22semidirect
38. #91475C22semidirect
39. #91474C22semidirect
40. #91470C22semidirect
41. #91464C22semidirect
42. #91463C22semidirect
43. #91456C22semidirect
44. #91449C22semidirect
45. #91442C22semidirect
46. #91438C22semidirect
47. #91435C22semidirect
48. #91434C22semidirect
49. #91369C22semidirect
50. #91359C22semidirect
51. #91356C22semidirect
62. #65844D3semidirect
70. C2×C4×D15D4semidirect
122. #5510D5semidirect
133. C2×#709C2×D3semidirect
139. C2×C5×C4⋊C4C2×D3semidirect
147. #4076C2×D3semidirect
152. #4043C2×D3semidirect
153. #4041C2×D3semidirect
214. C2×#235C2×D5semidirect
220. C2×C3×C4⋊C4C2×D5semidirect
228. #930C2×D5semidirect
233. #897C2×D5semidirect
234. #895C2×D5semidirect
452. C2×C4⋊C4D3×D5semidirect
574. C3×C5#3449semidirect
652. C5#86363semidirect
675. C3#10618264semidirect

Maximal subgroups

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

subgroupindex
C2×#920162
C2×#917812
C5×#55102
C3×#658442
#117546742
#117546072
#117543862
#117538892
#117538862
#117538852
#117536972
#106182643
#863635