Finite Group Databasebeta

← #14323960

Subgroups — #14323960

Order 1920.

1336 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×#91784C211yesmaximal, characteristic
2C2×#91428C211yesmaximal, characteristic, complemented
3C2×#91386C211yesmaximal, characteristic, complemented
4C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×#65274C211yesmaximal, characteristic, complemented
6#11748904C212yesmaximal, complemented
7#11748898C212yesmaximal, complemented
8#11748854C212yesmaximal, complemented
9#11748799C211yesmaximal, characteristic, complemented
10#11748789C212yesmaximal, complemented
11#11748768C211yesmaximal, characteristic, complemented
12#10605494—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C22×D60C2212yes—
15C22×C4×D15C2211yescharacteristic
16C22×#1200C2212yes—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×#6714C2212yes—
19#91784C418yescomplemented
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C4×C5×Dic3C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4⋊Dic5C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×#6669C2211yescharacteristic
27C2×#6669C2211yescharacteristic
28C2×#6667C2211yescharacteristic
29C2×#6667C2211yescharacteristic
30C2×#6667C2212yes—
31C2×#6667C2212yes—
32C2×#6667C2212yes—
33C2×#6667C2212yes—
34#91428—24no—
35#91386—24no—
36C5×C3⋊#95C2212yes—
37C3×#3963C2212yes—
38#90994C2212yes—
39#76198—51nomaximal, Hall
40C2×#4041—31no—
41C2×C4×D20—31no—
42C2×#4018—31no—
43C4×C5×C4⋊C4—31no—
44#65277—31no—
45#65276—31no—
46#65274D311yescharacteristic, complemented
47#65229—32no—
48#65228—32no—
49#64957—32no—
50#64954—32no—
51C23×D15C2312yes—
52C23×D15C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C2×D60—22no—
57C2×D60—22no—
58C2×D60—42no—
59C2×D60—42no—
60C2×D60C2×C414yes—
61C2×D60C2×C418yescomplemented
62C2×C4×D15—22no—
63C2×C4×D15—22no—
64C2×C4×D15C2×C414yescomplemented
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2311yescharacteristic
67C22×C5×Dic3C2311yescharacteristic
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2311yescharacteristic
70C22×C3×Dic5C2311yescharacteristic
71C2×#1200—24no—
72C2×#1200—42no—
73C2×#1200—42no—
74C3×C5×C4⋊C4C2×C414yescomplemented
75#6714C2×C418yescomplemented
76C5×C4⋊Dic3—22no—
77C4×C5×Dic3—42no—
78C4×C5×Dic3D414yescomplemented
79C3×C4⋊Dic5—22no—
80C3×C4⋊Dic5—42no—
81C3×C4×Dic5—22no—
82#6669—22no—
83#6669—22no—
84#6667—24no—
85#6667—22no—
86#6667—22no—
87#6667—42no—
88#6667—42no—
89#6667—42no—
90C2×#895—51no—
91C2×#893—51no—
92C2×#872—51no—
93C3×#389—51no—
94#4989—52no—
95#4988—52no—
96#4987—51no—
97Dic3×C4⋊C4D511yescharacteristic, complemented
98#4939—51no—
99#4669—52no—
100#4665—52no—
101C22×D20—31no—
102C22×D20—32no—
103C22×C4×D5—31no—
104C22×C4×D5—32no—
105C2×C5×C4⋊C4—31no—
106C2×C5×C4⋊C4C2×D311yescharacteristic
107C2×C42×C5—31no—
108C2×C42×C5—32no—
109C2×#685—32no—
110C2×#685—31no—
111C2×#685—31no—
112C2×#685—32no—
113C2×#685—32no—
114C2×#685—32no—
115C2×#685—32no—
116C2×C4⋊Dic5C2×D311yescharacteristic
117C2×C4⋊Dic5C2×D312yes—
118C2×#683—31no—
119C2×#683—31no—
120C2×C4×Dic5C2×D311yescharacteristic
121#4041—38no—
122C4×D20—64no—
123#4018—64no—
124C5×#95—32no—
125#3963—32no—
126#3963C2×D312yes—
127#2324—151noSylow
128C23×C3×C5C2411yescharacteristic
129C22×D15—21no—
130C22×D15—22no—
131C22×D15—21no—
132C22×D15—22no—
133C22×D15—21no—
134C22×D15—22no—
135C22×D15—22no—
136C22×D15—22no—
137C22×D15—21no—
138C22×D15—21no—
139C22×D15—22no—
140C22×D15—21no—
141C22×D15C22×C414yes—
142C22×D15C22×C412yes—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C22×C414yes—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5#4112yes—
149C2×Dic15—21no—
150C2×Dic15—21no—
151C2×Dic15C22×C412yes—
152D60—28no—
153D60—48no—
154C4×D15—28no—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3C2×D412yes—
163C2×C5×Dic3C2×D412yes—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—21no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—21no—
173#1200—48no—
174C22×D12—51no—
175C22×D12—52no—
176C22×C4×D3—51no—
177C22×C4×D3—52no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C4⋊C4—52no—
180C2×C3×C4⋊C4C2×D511yescharacteristic
181C2×C3×C42—51no—
182C2×(C2×D3)⋊C4—52no—
183C2×(C2×D3)⋊C4—51no—
184C2×(C2×D3)⋊C4—52no—
185C2×(C2×D3)⋊C4—51no—
186C2×(C2×D3)⋊C4—52no—
187C2×(C2×D3)⋊C4—52no—
188C2×(C2×D3)⋊C4—52no—
189C2×C4⋊Dic3C2×D511yescharacteristic
190C2×Dic3⋊C4—51no—
191C2×Dic3⋊C4—51no—
192C2×C4×Dic3C2×D512yes—
193C2×C4×Dic3C2×D511yescharacteristic
194#895—58no—
195#893—104no—
196#872—104no—
197C3×#95—52no—
198C3⋊#95—52no—
199C3⋊#95C2×D512yes—
200C23×D5—32no—
201C23×D5—31no—
202C22×C4×C5—31no—
203C22×C4×C5—31no—
204C22×C4×C5—32no—
205C22×C4×C5C22×D312yes—
206C22×C4×C5C22×D311yescharacteristic
207C22×Dic5—31no—
208C22×Dic5C22×D312yes—
209C22×Dic5C22×D311yescharacteristic
210C22×Dic5C22×D311yescharacteristic
211C2×D20—34no—
212C2×D20—38no—
213C2×D20—62no—
214C2×D20—62no—
215C2×D20—122no—
216C2×D20—122no—
217C2×C4×D5—34no—
218C2×C4×D5—62no—
219C2×C4×D5—62no—
220C2×C4×D5—64no—
221C2×C4×D5—122no—
222C2×C4×D5—122no—
223C5×C4⋊C4—62no—
224C5×C4⋊C4C4×D314yescomplemented
225C42×C5—34no—
226C42×C5—122no—
227#685—38no—
228#685—62no—
229#685—62no—
230#685—64no—
231#685—122no—
232#685—122no—
233#685—122no—
234C4⋊Dic5—22no—
235C4⋊Dic5—42no—
236#683—62no—
237#683—62no—
238C4×Dic5—22no—
239C2×#121—151no—
240C2×C4×D4—151no—
241C2×#117—151no—
242#390—152no—
243#390—151no—
244#389—51no—
245#388—152no—
246#386—152no—
247#385—152no—
248#380—151no—
249C4×C4⋊C4—31no—
250C22×C3×C5C23×C411yescharacteristic
251C22×C3×C5C22×D411yescharacteristic
252C22×C3×C5C2×#4111yescharacteristic
253C22×C3×C5H(5,𝔽2)11yescharacteristic
254C22×C3×C5H(5,𝔽2)11yescharacteristic
255C22×C3×C5H(5,𝔽2)11yescharacteristic
256C22×C3×C52−1+411yescharacteristic
257C2×D15—22no—
258C2×D15—24no—
259C2×D15—22no—
260C2×D15—24no—
261C2×D15—22no—
262C2×D15—24no—
263C2×D15—42no—
264C2×D15—41no—
265C2×D15—41no—
266C2×D15—42no—
267C2×D15—41no—
268C2×D15—42no—
269C2×D15—41no—
270C2×D15—42no—
271C3×C4×C5—24no—
272C3×C4×C5C4×D414yes—
273Dic15—22no—
274C3×Dic5—42no—
275C3×Dic5—41no—
276C3×Dic5—41no—
277C5×Dic3—22no—
278C5×Dic3—22no—
279C5×Dic3—42no—
280C23×D3—52no—
281C23×D3—51no—
282C22×C3×C4—52no—
283C22×C3×C4—51no—
284C22×C3×C4—51no—
285C22×C3×C4C22×D512yes—
286C22×C3×C4C22×D511yescharacteristic
287C22×Dic3—51no—
288C22×Dic3C22×D512yes—
289C22×Dic3C22×D511yescharacteristic
290C22×Dic3C22×D511yescharacteristic
291C2×D12—54no—
292C2×D12—58no—
293C2×D12—102no—
294C2×D12—102no—
295C2×D12—202no—
296C2×D12—202no—
297C2×C4×D3—54no—
298C2×C4×D3—102no—
299C2×C4×D3—102no—
300C2×C4×D3—104no—
301C2×C4×D3—202no—
302C2×C4×D3—202no—
303C3×C4⋊C4—102no—
304C3×C4⋊C4—202no—
305C3×C4⋊C4C4×D514yescomplemented
306C3×C42—102no—
307(C2×D3)⋊C4—58no—
308(C2×D3)⋊C4—102no—
309(C2×D3)⋊C4—102no—
310(C2×D3)⋊C4—104no—
311(C2×D3)⋊C4—202no—
312(C2×D3)⋊C4—202no—
313(C2×D3)⋊C4—202no—
314C4⋊Dic3—22no—
315Dic3⋊C4—102no—
316Dic3⋊C4—102no—
317C4×Dic3—42no—
318C4×Dic3D2014yescomplemented
319C23×C5C23×D311yescharacteristic
320C22×D5—34no—
321C22×D5—32no—
322C22×D5—61no—
323C22×D5—62no—
324C22×D5—62no—
325C22×D5—61no—
326C22×D5—61no—
327C22×D5—62no—
328C22×D5—62no—
329C22×D5—61no—
330C22×D5—61no—
331C22×D5—62no—
332C22×D5—62no—
333C22×D5—61no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—32no—
337C2×C4×C5—32no—
338C2×C4×C5—61no—
339C2×C4×C5—61no—
340C2×C4×C5—61no—
341C2×C4×C5—61no—
342C2×C4×C5—62no—
343C2×C4×C5—62no—
344C2×C4×C5—62no—
345C2×C4×C5C2×C4×D314yes—
346C2×C4×C5C2×C4×D312yes—
347C2×C4×C5D3×D412yes—
348C2×C4×C5#23912yes—
349C2×Dic5—21no—
350C2×Dic5—21no—
351C2×Dic5—22no—
352C2×Dic5—21no—
353C2×Dic5—22no—
354C2×Dic5—21no—
355C2×Dic5—21no—
356C2×Dic5—21no—
357C2×Dic5—22no—
358C2×Dic5—32no—
359C2×Dic5—61no—
360C2×Dic5—61no—
361D20—68no—
362D20—128no—
363C4×D5—68no—
364C4×D5—128no—
365C22×D4—151no—
366C22×D4—152no—
367C23×C4—152no—
368C23×C4—151no—
369#121—158no—
370C4×D4—304no—
371#117—304no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—52no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4D3×D511yescharacteristic
378C2×C22⋊C4—152no—
379C2×C22⋊C4—151no—
380C2×C22⋊C4—151no—
381C2×C22⋊C4—152no—
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C42—31no—
386C2×C42—32no—
387C2×C42—51no—
388#95—32no—
389#95—52no—
390#95—152no—
391C2×C3×C5C2×C4×D411yescharacteristic
392C2×C3×C5#51811yescharacteristic
393C2×C3×C5#52011yescharacteristic
394C2×C3×C5#53511yescharacteristic
395C2×C3×C5#53711yescharacteristic
396C2×C3×C5#54011yescharacteristic
397C2×C3×C5#54211yescharacteristic
398D15—42no—
399D15—44no—
400C23×C3C23×D511yescharacteristic
401C22×D3—54no—
402C22×D3—52no—
403C22×D3—101no—
404C22×D3—102no—
405C22×D3—101no—
406C22×D3—102no—
407C22×D3—102no—
408C22×D3—101no—
409C22×D3—102no—
410C22×D3—101no—
411C22×D3—101no—
412C22×D3—102no—
413C22×D3—102no—
414C22×D3—101no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—101no—
418C2×C3×C4—101no—
419C2×C3×C4—102no—
420C2×C3×C4—101no—
421C2×C3×C4—101no—
422C2×C3×C4—101no—
423C2×C3×C4—102no—
424C2×C3×C4—101no—
425C2×C3×C4—102no—
426C2×C3×C4C2×C4×D514yes—
427C2×C3×C4C2×C4×D512yes—
428C2×C3×C4C2×D2012yes—
429C2×C3×C4#70912yes—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—52no—
438C2×Dic3—101no—
439C2×Dic3—101no—
440C2×Dic3C2×D2012yes—
441C2×Dic3C2×D2012yes—
442D12—108no—
443D12—208no—
444C4×D3—108no—
445C4×D3—208no—
446C22×C5C22×C4×D311yescharacteristic
447C22×C5C2×D3×D411yescharacteristic
448C22×C5#100411yescharacteristic
449C22×C5C2×#23911yescharacteristic
450C22×C5#100711yescharacteristic
451C22×C5#100911yescharacteristic
452C22×C5#100911yescharacteristic
453C2×D5—62no—
454C2×D5—64no—
455C2×D5—62no—
456C2×D5—64no—
457C2×D5—64no—
458C2×D5—62no—
459C2×D5—121no—
460C2×D5—122no—
461C2×D5—122no—
462C2×D5—121no—
463C2×D5—122no—
464C2×D5—121no—
465C2×D5—121no—
466C2×D5—122no—
467C4×C5—24no—
468C4×C5—62no—
469C4×C5—62no—
470C4×C5—122no—
471C4×C5#89314yes—
472Dic5—42no—
473Dic5—41no—
474Dic5—41no—
475Dic5—62no—
476C24—152no—
477C24—151no—
478C2×D4—154no—
479C2×D4—158no—
480C2×D4—302no—
481C2×D4—302no—
482C2×D4—602no—
483C2×D4—602no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—32no—
487C22×C4—51no—
488C22×C4—52no—
489C22×C4—51no—
490C22×C4—151no—
491C22×C4—154no—
492C22×C4—304no—
493C22×C4—302no—
494C22×C4—302no—
495C22×C4—602no—
496C22×C4—602no—
497C22×C4C2×D3×D512yes—
498C22×C4C2×D3×D511yescharacteristic
499C4⋊C4—62no—
500C4⋊C4—102no—
501C4⋊C4—202no—
502C4⋊C4—302no—
503C4⋊C4—302no—
504C4⋊C4#120014yescomplemented
505C22⋊C4—158no—
506C22⋊C4—302no—
507C22⋊C4—302no—
508C22⋊C4—304no—
509C22⋊C4—602no—
510C22⋊C4—602no—
511C22⋊C4—602no—
512C42—34no—
513C42—102no—
514C42—122no—
515C3×C5#232411yescharacteristic, complemented, Hall
516C22×C3C22×C4×D511yescharacteristic
517C22×C3C22×D2011yescharacteristic
518C22×C3C2×#70911yescharacteristic
519C22×C3#414411yescharacteristic
520C22×C3#414711yescharacteristic
521C22×C3#414911yescharacteristic
522C22×C3#414911yescharacteristic
523C2×D3—102no—
524C2×D3—104no—
525C2×D3—102no—
526C2×D3—104no—
527C2×D3—104no—
528C2×D3—102no—
529C2×D3—201no—
530C2×D3—202no—
531C2×D3—202no—
532C2×D3—201no—
533C2×D3—201no—
534C2×D3—202no—
535C2×D3—201no—
536C2×D3—202no—
537C3×C4—24no—
538C3×C4—201no—
539C3×C4—202no—
540C3×C4—201no—
541C3×C4C4×D2014yes—
542Dic3—22no—
543Dic3—22no—
544Dic3—42no—
545Dic3—102no—
546C2×C5C2×#89311yescharacteristic
547C2×C5#554511yescharacteristic
548C2×C5#557411yescharacteristic
549C2×C5#560711yescharacteristic
550C2×C5#562911yescharacteristic
551C2×C5#569711yescharacteristic
552C2×C5#573311yescharacteristic
553D5—122no—
554D5—124no—
555C23—154no—
556C23—152no—
557C23—301no—
558C23—302no—
559C23—301no—
560C23—302no—
561C23—302no—
562C23—301no—
563C23—302no—
564C23—301no—
565C23—302no—
566C23—301no—
567C23—301no—
568C23—302no—
569C23C22×D3×D511yescharacteristic
570D4—308no—
571D4—608no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—32no—
575C2×C4—32no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—61no—
579C2×C4—61no—
580C2×C4—62no—
581C2×C4—62no—
582C2×C4—62no—
583C2×C4—101no—
584C2×C4—101no—
585C2×C4—102no—
586C2×C4—101no—
587C2×C4—102no—
588C2×C4—101no—
589C2×C4—101no—
590C2×C4—101no—
591C2×C4—102no—
592C2×C4—152no—
593C2×C4—301no—
594C2×C4—301no—
595C2×C4—308no—
596C2×C4—608no—
597C2×C4#676912yes—
598C2×C4D3×D2012yes—
599C2×C4C2×#120014yes—
600C2×C4C2×#120012yes—
601C2×C3C2×C4×D2011yescharacteristic
602C2×C3#6584411yescharacteristic
603C2×C3#6585911yescharacteristic
604C2×C3#6587911yescharacteristic
605C2×C3#6589611yescharacteristic
606C2×C3#6590811yescharacteristic
607C2×C3#6591611yescharacteristic
608D3—202no—
609D3—204no—
610C5#7619811yescharacteristic, complemented, Sylow
611C22—302no—
612C22—304no—
613C22—304no—
614C22—302no—
615C22—302no—
616C22—304no—
617C22—601no—
618C22—602no—
619C22—602no—
620C22—601no—
621C22—601no—
622C22—602no—
623C22—601no—
624C22—602no—
625C22C2×#676911yescharacteristic
626C22C2×D3×D2011yescharacteristic
627C22#9202611yescharacteristic
628C22#9202711yescharacteristic
629C22#9202911yescharacteristic
630C22#9203511yescharacteristic
631C22C22×#120011yescharacteristic
632C4—24no—
633C4—62no—
634C4—62no—
635C4—122no—
636C4—202no—
637C4—201no—
638C4—201no—
639C4—302no—
640C4#9142814yes—
641C3#1060549411yescharacteristic, complemented, Sylow
642C2—602no—
643C2—604no—
644C2#1175339011yescharacteristic
645C2#1175369411yescharacteristic
646C2#1175382311yescharacteristic
647C2#1175388211yescharacteristic
648C2C2×#9142811yescharacteristic
649C2#1175492211yescharacteristic
650C2#1175514911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91784C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2324
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91428C2semidirect
3. C2×#91386C2semidirect
4. C5×Dic3×C4⋊C4C2semidirect
5. C3×#65274C2semidirect
6. #11748904C2semidirect
7. #11748898C2semidirect
8. #11748854C2semidirect
9. #11748799C2semidirect
10. #11748789C2semidirect
11. #11748768C2semidirect
19. #91784C4semidirect
46. #65274D3semidirect
61. C2×D60C2×C4semidirect
64. C2×C4×D15C2×C4semidirect
74. C3×C5×C4⋊C4C2×C4semidirect
75. #6714C2×C4semidirect
78. C4×C5×Dic3D4semidirect
97. Dic3×C4⋊C4D5semidirect
224. C5×C4⋊C4C4×D3semidirect
305. C3×C4⋊C4C4×D5semidirect
318. C4×Dic3D20semidirect
504. C4⋊C4#1200semidirect
515. C3×C5#2324semidirect
610. C5#76198semidirect
641. C3#10605494semidirect

Maximal subgroups

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

subgroupindex
C2×#917842
C2×#914282
C2×#913862
C5×Dic3×C4⋊C42
C3×#652742
#117489042
#117488982
#117488542
#117487992
#117487892
#117487682
#106054943
#761985