Finite Group Databasebeta

← #14329583

Subgroups — #14329583

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×Dic6C211yesmaximal, characteristic, complemented
2C2×#91434C211yesmaximal, characteristic
3C2×#91368C211yesmaximal, characteristic
4C4×#6712C211yesmaximal, characteristic, complemented
5C3×#65228C211yesmaximal, characteristic
6#11748891C212yesmaximal, complemented
7Dic3×#685C212yesmaximal, complemented
8#11748711C212yesmaximal, complemented
9#11748706C212yesmaximal, complemented
10#11748699C211yesmaximal, characteristic, complemented
11#11748607C211yesmaximal, characteristic, complemented
12#10614197—31nomaximal, Hall
13C22×C5×Dic6C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×D5×Dic3C2212yes—
16C2×C3×C42×C5C2211yescharacteristic
17C2×#6712C2211yescharacteristic
18C2×#6712C2211yescharacteristic
19C2×C4×Dic15C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C5×Dic3⋊C4C2212yes—
23C2×C4×C5×Dic3C2212yes—
24C4×C5×Dic6—24no—
25C2×C3×#685C2212yes—
26C2×C3×#685C2212yes—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×#6665C2212yes—
29C2×#6665C2212yes—
30C2×#6665C2212yes—
31C2×Dic3×Dic5C2212yes—
32#91434—24no—
33#91368C418yescomplemented
34#91115C2211yescharacteristic
35#91115C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#76307—51nomaximal, Hall
40C2×C4×C5×Q8—31no—
41C2×#4093—31no—
42C2×#4039—31no—
43#65519—31no—
44#65279—32no—
45#65278—32no—
46C4⋊C4×Dic5—31no—
47#65229—32no—
48#65228D311yescharacteristic
49C4×#685—32no—
50C4×#683—31no—
51C23×C3×D5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2311yescharacteristic
59C22×C5×Dic3C2312yes—
60C22×C5×Dic3C2312yes—
61C2×C5×Dic6—22no—
62C2×C5×Dic6—22no—
63C2×C5×Dic6C2×C414yescomplemented
64C22×C3×Dic5C2312yes—
65C2×C3×D20—22no—
66C2×C3×D20—22no—
67C2×C3×D20C2×C414yes—
68C2×D5×Dic3—24no—
69C2×D5×Dic3—24no—
70C2×D5×Dic3—42no—
71C3×C42×C5—22no—
72#6712—22no—
73#6712—22no—
74C4×Dic15—22no—
75C4×Dic15C2×C414yescomplemented
76C5×C4⋊Dic3D414yes—
77C5×Dic3⋊C4—24no—
78C4×C5×Dic3—24no—
79C3×#685—24no—
80C3×#685—42no—
81C3×C4⋊Dic5—22no—
82#6665—24no—
83#6665C2×C418yescomplemented
84#6665C2×C418yescomplemented
85Dic3×Dic5—42no—
86C2×#936—51no—
87C2×D4×Dic3—51no—
88C2×C4×Dic6D511yescharacteristic, complemented
89C3×#390—51no—
90Dic3×C4⋊C4—51no—
91#4973—51no—
92#4946—52no—
93#4945—52no—
94#4944—52no—
95Dic3×C22⋊C4—52no—
96C4×Dic3⋊C4—51no—
97C22×C5×Q8—31no—
98C22×D20C2×D311yescharacteristic
99C22×C4×D5—32no—
100C4×C5×Q8—64no—
101C2×C5×C4⋊C4—31no—
102C2×C5×C4⋊C4—32no—
103C2×C42×C5—32no—
104C2×C42×C5C2×D311yescharacteristic
105#4093—38no—
106C2×#685—32no—
107C2×#685—32no—
108C2×#685—32no—
109C2×#685C2×D312yes—
110C2×#685C2×D312yes—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C2×#683—31no—
113C2×#683—31no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—32no—
117#4039—64no—
118#3963—31no—
119#3963—31no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#2367—151noSylow
124C23×C3×C5C2411yescharacteristic
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5—22no—
129C22×C3×D5—22no—
130C22×C3×D5—22no—
131C22×C3×D5C22×C414yes—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5#4112yes—
140C2×C3×C4×C5#4112yes—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145C2×Dic15—21no—
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×Dic15C22×C412yes—
151C2×Dic15C22×C412yes—
152C2×Dic15#4112yes—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3C22×C414yes—
158C2×C5×Dic3C2×D414yes—
159C5×Dic6—28no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C3×D20—28no—
164D5×Dic3—48no—
165C22×C3×D4—51no—
166C23×Dic3—52no—
167C22×Dic6C2×D511yescharacteristic
168C2×C3×C4⋊C4—51no—
169C2×C3×C22⋊C4—52no—
170C2×C3×C22⋊C4—52no—
171C2×C3×C42C2×D511yescharacteristic
172C2×#217—52no—
173C2×#217—52no—
174C2×#217—52no—
175#936—58no—
176D4×Dic3—104no—
177C2×C4⋊Dic3C2×D511yescharacteristic
178C2×Dic3⋊C4—51no—
179C2×Dic3⋊C4—51no—
180C2×Dic3⋊C4C2×D512yes—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—52no—
184C2×C4×Dic3C2×D512yes—
185C4×Dic6—24no—
186C3⋊#95—51no—
187C3⋊#95—51no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C23×D5C22×D312yes—
192C2×C5×Q8—34no—
193C2×C5×Q8—62no—
194C2×C5×Q8—62no—
195C22×C4×C5—32no—
196C22×C4×C5—32no—
197C22×C4×C5C22×D311yescharacteristic
198C22×C4×C5C22×D311yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C22×Dic5—31no—
201C22×Dic5—31no—
202C22×Dic5—31no—
203C22×Dic5—31no—
204C22×Dic5C22×D312yes—
205C2×D20—22no—
206C2×D20—22no—
207C2×D20C4×D314yes—
208C2×C4×D5—64no—
209C2×C4×D5—64no—
210C2×C4×D5—122no—
211C5×C4⋊C4—34no—
212C5×C4⋊C4—64no—
213C42×C5—22no—
214C42×C5—64no—
215#685—24no—
216#685—38no—
217#685—38no—
218#685—42no—
219#685—64no—
220C4⋊Dic5—22no—
221#683—62no—
222#683—62no—
223C4×Dic5—34no—
224C4×Dic5—62no—
225C4×Dic5—122no—
226C2×#124—151no—
227C2×C4×Q8—31no—
228C2×C4×D4—151no—
229#391—151no—
230#390—51no—
231#388—152no—
232#388—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C4⋊C4—151no—
236C4×C22⋊C4—152no—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5H(5,𝔽2)11yescharacteristic
243C22×C3×C52−1+411yescharacteristic
244C2×C3×D5—24no—
245C2×C3×D5—24no—
246C2×C3×D5—24no—
247C2×C3×D5—42no—
248C2×C3×D5—42no—
249C2×C3×D5—42no—
250C2×C3×D5—42no—
251C3×C4×C5—22no—
252C3×C4×C5—41no—
253C3×C4×C5C4×D414yes—
254Dic15—22no—
255Dic15—22no—
256Dic15—22no—
257Dic15—41no—
258C3×Dic5—42no—
259C5×Dic3—24no—
260C5×Dic3—24no—
261C24×C3—52no—
262C2×C3×D4—54no—
263C2×C3×D4—102no—
264C2×C3×D4—102no—
265C22×C3×C4—52no—
266C22×C3×C4C22×D511yescharacteristic
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—51no—
270C22×Dic3—51no—
271C22×Dic3—51no—
272C22×Dic3—51no—
273C22×Dic3—104no—
274C22×Dic3—104no—
275C22×Dic3—202no—
276C22×Dic3C22×D512yes—
277C22×Dic3C22×D512yes—
278C2×Dic6—22no—
279C2×Dic6—22no—
280C2×Dic6C4×D514yescomplemented
281C3×C4⋊C4—102no—
282C3×C22⋊C4—104no—
283C3×C22⋊C4—202no—
284C3×C42—22no—
285#217—58no—
286#217—58no—
287#217—104no—
288C4⋊Dic3C22⋊D514yes—
289Dic3⋊C4—24no—
290Dic3⋊C4—102no—
291Dic3⋊C4—102no—
292C4×Dic3—24no—
293C4×Dic3—54no—
294C4×Dic3—102no—
295C4×Dic3—202no—
296C23×C5C23×D311yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—22no—
302C22×D5—22no—
303C22×D5C2×C4×D314yes—
304C5×Q8—68no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—34no—
311C2×C4×C5—34no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5C2×C4×D312yes—
317C2×C4×C5D3×D412yes—
318C2×C4×C5#23712yes—
319C2×C4×C5#23712yes—
320C2×Dic5—22no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—32no—
324C2×Dic5—32no—
325C2×Dic5—32no—
326C2×Dic5—61no—
327C2×Dic5—61no—
328C2×Dic5—61no—
329C2×Dic5—61no—
330C2×Dic5—61no—
331C2×Dic5—61no—
332C2×Dic5—61no—
333C2×Dic5—61no—
334C2×Dic5—61no—
335D20—28no—
336C4×D5—128no—
337C22×Q8—31no—
338C22×D4—51no—
339C23×C4—152no—
340#124—158no—
341C4×Q8—64no—
342C4×D4—304no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—32no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—151no—
347C2×C4⋊C4—151no—
348C2×C22⋊C4—52no—
349C2×C22⋊C4—52no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C22⋊C4—152no—
353C2×C42—32no—
354C2×C42—151no—
355C2×C42—151no—
356C2×C42—152no—
357C2×C42D3×D511yescharacteristic
358#95—152no—
359#95—152no—
360#95—152no—
361#95—151no—
362#95—151no—
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5C4×#4111yescharacteristic
365C2×C3×C5#52011yescharacteristic
366C2×C3×C5#54611yescharacteristic
367C2×C3×C5#54811yescharacteristic
368C2×C3×C5#55611yescharacteristic
369C2×C3×C5#55911yescharacteristic
370C3×D5—44no—
371C23×C3—54no—
372C23×C3—102no—
373C23×C3—102no—
374C23×C3—102no—
375C23×C3—102no—
376C23×C3—102no—
377C23×C3—102no—
378C23×C3C23×D511yescharacteristic
379C3×D4—108no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4—102no—
388C2×C3×C4C2×C4×D512yes—
389C2×C3×C4#70912yes—
390C2×C3×C4#71312yes—
391C2×C3×C4C2×C22⋊D512yes—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—52no—
397C2×Dic3—52no—
398C2×Dic3—52no—
399C2×Dic3—101no—
400C2×Dic3—101no—
401C2×Dic3—101no—
402C2×Dic3—101no—
403C2×Dic3—101no—
404C2×Dic3—101no—
405C2×Dic3—101no—
406C2×Dic3—101no—
407C2×Dic3—101no—
408C2×Dic3—208no—
409C2×Dic3C2×C4×D514yes—
410C2×Dic3C2×C22⋊D514yes—
411Dic6—28no—
412C22×C5C22×C4×D311yescharacteristic
413C22×C5C2×D3×D411yescharacteristic
414C22×C5C2×#23711yescharacteristic
415C22×C5C2×#23711yescharacteristic
416C22×C5#100411yescharacteristic
417C22×C5D3×#4111yescharacteristic
418C22×C5#101011yescharacteristic
419C2×D5—24no—
420C2×D5—24no—
421C2×D5—24no—
422C2×D5—42no—
423C2×D5—42no—
424C2×D5—42no—
425C2×D5—42no—
426C4×C5—22no—
427C4×C5—41no—
428C4×C5—64no—
429C4×C5—64no—
430C4×C5#67⋊C414yes—
431Dic5—42no—
432Dic5—62no—
433Dic5—62no—
434Dic5—62no—
435Dic5—121no—
436C24—52no—
437C2×Q8—34no—
438C2×Q8—62no—
439C2×Q8—62no—
440C2×D4—54no—
441C2×D4—102no—
442C2×D4—102no—
443C22×C4—32no—
444C22×C4—32no—
445C22×C4—52no—
446C22×C4—151no—
447C22×C4—151no—
448C22×C4—151no—
449C22×C4—151no—
450C22×C4—304no—
451C22×C4—304no—
452C22×C4—602no—
453C22×C4C2×D3×D511yescharacteristic
454C22×C4C2×D3×D511yescharacteristic
455C22×C4C2×D3×D511yescharacteristic
456C4⋊C4—34no—
457C4⋊C4—64no—
458C4⋊C4—102no—
459C4⋊C4—302no—
460C4⋊C4—302no—
461C22⋊C4—104no—
462C22⋊C4—158no—
463C22⋊C4—158no—
464C22⋊C4—202no—
465C22⋊C4—304no—
466C42—22no—
467C42—64no—
468C42—154no—
469C42—302no—
470C42—602no—
471C3×C5#236711yescharacteristic, complemented, Hall
472C22×C3—104no—
473C22×C3—104no—
474C22×C3—104no—
475C22×C3—202no—
476C22×C3—202no—
477C22×C3—202no—
478C22×C3—202no—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C2×#70911yescharacteristic
481C22×C3C2×#71311yescharacteristic
482C22×C3#414711yescharacteristic
483C22×C3D5×#4111yescharacteristic
484C22×C3#414911yescharacteristic
485C22×C3C22×C22⋊D511yescharacteristic
486C3×C4—22no—
487C3×C4—41no—
488C3×C4—202no—
489C3×C4C4×C22⋊D514yes—
490Dic3—24no—
491Dic3—24no—
492Dic3—102no—
493Dic3—102no—
494Dic3—102no—
495Dic3—201no—
496C2×C5C2×#67⋊C411yescharacteristic
497C2×C5C4×#23711yescharacteristic
498C2×C5#554611yescharacteristic
499C2×C5#559811yescharacteristic
500C2×C5#561211yescharacteristic
501C2×C5#567111yescharacteristic
502C2×C5#571311yescharacteristic
503D5—44no—
504C23—54no—
505C23—102no—
506C23—102no—
507C23—102no—
508C23—102no—
509C23—102no—
510C23—102no—
511C23C22×D3×D511yescharacteristic
512Q8—68no—
513D4—108no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—34no—
520C2×C4—34no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—152no—
529C2×C4—152no—
530C2×C4—152no—
531C2×C4—301no—
532C2×C4—301no—
533C2×C4—301no—
534C2×C4—301no—
535C2×C4—301no—
536C2×C4—301no—
537C2×C4—301no—
538C2×C4—301no—
539C2×C4—301no—
540C2×C4—608no—
541C2×C4#676512yes—
542C2×C4#676612yes—
543C2×C4C4×D3×D512yes—
544C2×C4D3×C22⋊D512yes—
545C2×C3—204no—
546C2×C3#6590211yescharacteristic
547C2×C3C4×#71311yescharacteristic
548C2×C3#6590811yescharacteristic
549C2×C3#6591911yescharacteristic
550C2×C3C2×C4×C22⋊D511yescharacteristic
551C2×C3#6615111yescharacteristic
552C2×C3#6616311yescharacteristic
553C5#7630711yescharacteristic, complemented, Sylow
554C22—104no—
555C22—104no—
556C22—104no—
557C22—202no—
558C22—202no—
559C22—202no—
560C22—202no—
561C22C2×#676511yescharacteristic
562C22C2×#676611yescharacteristic
563C22#9200011yescharacteristic
564C22C2×C4×D3×D511yescharacteristic
565C22#9201611yescharacteristic
566C22#9201711yescharacteristic
567C22C2×D3×C22⋊D511yescharacteristic
568C4—22no—
569C4—41no—
570C4—64no—
571C4—64no—
572C4—202no—
573C4—302no—
574C4—302no—
575C4—302no—
576C4—601no—
577C4#9144114yes—
578C3#1061419711yescharacteristic, complemented, Sylow
579C2—204no—
580C2C4×#676611yescharacteristic
581C2#1175252011yescharacteristic
582C2#1175261911yescharacteristic
583C2#1175263611yescharacteristic
584C2#1175434411yescharacteristic
585C2C2×#9144111yescharacteristic
586C2#1175465811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2367
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×Dic6C2semidirect
4. C4×#6712C2semidirect
6. #11748891C2semidirect
7. Dic3×#685C2semidirect
8. #11748711C2semidirect
9. #11748706C2semidirect
10. #11748699C2semidirect
11. #11748607C2semidirect
33. #91368C4semidirect
63. C2×C5×Dic6C2×C4semidirect
75. C4×Dic15C2×C4semidirect
83. #6665C2×C4semidirect
84. #6665C2×C4semidirect
88. C2×C4×Dic6D5semidirect
280. C2×Dic6C4×D5semidirect
471. C3×C5#2367semidirect
553. C5#76307semidirect
578. C3#10614197semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×Dic62
C2×#914342
C2×#913682
C4×#67122
C3×#652282
#117488912
Dic3×#6852
#117487112
#117487062
#117486992
#117486072
#106141973
#763075