Finite Group Databasebeta

← #14328939

Subgroups — #14328939

Order 1920.

1152 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91813C211yesmaximal, characteristic
2C2×C3×#4072C211yesmaximal, characteristic
3C2×#91340C211yesmaximal, characteristic, complemented
4C4×C5×#217C211yesmaximal, characteristic
5#11749481C212yesmaximal
6#11749480C212yesmaximal
7#11748858C211yesmaximal, characteristic, complemented
8#11748824C212yesmaximal, complemented
9Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
10#11748640C212yesmaximal, complemented
11#11748599C211yesmaximal, characteristic, complemented
12#10605199—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×Dic30C2211yescharacteristic
15C2×#6719C2212yes—
16C2×C4⋊Dic15C2211yescharacteristic
17#91813C418yescomplemented
18C2×#6712C2212yes—
19C2×C5×#217C2211yescharacteristic
20C2×C5×#217C2211yescharacteristic
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×C22⋊Dic5C2212yes—
24C3×#4072—24no—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×C4×Dic5C2212yes—
28C2×#6669C2212yes—
29C2×#6669C2212yes—
30C2×Dic3×Dic5C2212yes—
31C2×Dic3×Dic5C2212yes—
32#91340—24no—
33C5×C3⋊#95C2211yescharacteristic
34C5×C3⋊#95C2211yescharacteristic
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82243—51nomaximal, Hall
40C2×#4072D311yescharacteristic
41C2×#4070—31no—
42C2×C4×Dic10—31no—
43C4×C5×C22⋊C4—31no—
44#65234—32no—
45#65233—32no—
46C4×C4⋊Dic5—31no—
47#65218—31no—
48#65217—31no—
49#64941—32no—
50#64938—32no—
51C24×C3×C5C2311yescharacteristic
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5C2×C414yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15C2312yes—
58C22×Dic15C2312yes—
59C2×Dic30—22no—
60C2×Dic30—22no—
61C2×Dic30C2×C414yes—
62C22×C5×Dic3C2311yescharacteristic
63C22×C5×Dic3C2311yescharacteristic
64C22×C5×Dic3C2311yescharacteristic
65C22×C5×Dic3C2311yescharacteristic
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68#6719C2×C418yes—
69C4⋊Dic15C2×C414yes—
70#6712C2×C418yes—
71C5×#217—22no—
72C5×#217—22no—
73C4×C5×Dic3—22no—
74C4×C5×Dic3—22no—
75C3×C22⋊Dic5—24no—
76C3×C4⋊Dic5—22no—
77C3×C4⋊Dic5D414yes—
78C3×C4×Dic5—24no—
79#6669—24no—
80#6669—24no—
81Dic3×Dic5—24no—
82Dic3×Dic5—24no—
83C2×C3×#117—51no—
84C2×#924—51no—
85C2×#887—51no—
86C4×#217D511yescharacteristic
87Dic3×C4⋊C4—51no—
88#4973—51no—
89#4972—51no—
90#4945—52no—
91#4944—52no—
92#4933—52no—
93C4×Dic3⋊C4—52no—
94C23×C4×C5C2×D311yescharacteristic
95C22×Dic10—31no—
96C2×C5×C22⋊C4—31no—
97C2×C5×C22⋊C4—31no—
98C2×C42×C5—31no—
99C2×C42×C5—31no—
100C2×C22⋊Dic5—32no—
101C2×C22⋊Dic5C2×D312yes—
102#4072—24no—
103C2×C4⋊Dic5—31no—
104C2×C4⋊Dic5C2×D311yescharacteristic
105C2×C4⋊Dic5C2×D311yescharacteristic
106#4070—38no—
107C2×#683—32no—
108C2×#683—32no—
109C2×#683—32no—
110C2×C4×Dic5—32no—
111C2×C4×Dic5—32no—
112C2×C4×Dic5C2×D312yes—
113C4×Dic10—64no—
114C5×#95—31no—
115C5×#95—31no—
116#3963—32no—
117#3963—32no—
118#3963—32no—
119#3963—32no—
120#2362—151noSylow
121C23×C3×C5—21no—
122C23×C3×C5—21no—
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5—21no—
126C23×C3×C5—21no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C2411yescharacteristic
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—28no—
132C2×C3×C4×C5C22×C412yes—
133C2×C3×C4×C5C22×C412yes—
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5#4112yes—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15C22×C414yes—
141C2×Dic15C22×C414yes—
142Dic30—28no—
143C2×C5×Dic3—21no—
144C2×C5×Dic3—21no—
145C2×C5×Dic3—21no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3#4112yes—
154C2×C5×Dic3#4112yes—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C2×D414yes—
161C23×C3×C4C2×D511yescharacteristic
162C22×Dic6—51no—
163C3×#117—104no—
164C2×C3×C4⋊C4—51no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C22⋊C4—52no—
167C2×C3×C42—52no—
168C2×#217—52no—
169C2×#217C2×D511yescharacteristic
170C2×#217C2×D511yescharacteristic
171C2×C4⋊Dic3—51no—
172#924—58no—
173C2×Dic3⋊C4—52no—
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4—52no—
176C2×C4×Dic3—52no—
177C2×C4×Dic3—52no—
178C2×C4×Dic3C2×D511yescharacteristic
179C2×C4×Dic3C2×D511yescharacteristic
180#887—104no—
181C3⋊#95—52no—
182C3⋊#95—52no—
183C3⋊#95—52no—
184C3⋊#95—52no—
185C3⋊#95C2×D511yescharacteristic
186C3⋊#95C2×D511yescharacteristic
187C24×C5C22×D311yescharacteristic
188C22×C4×C5—22no—
189C22×C4×C5—22no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—31no—
193C22×C4×C5—31no—
194C22×C4×C5C4×D314yes—
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—32no—
198C22×Dic5—32no—
199C22×Dic5C22×D312yes—
200C22×Dic5C22×D312yes—
201C2×Dic10—34no—
202C2×Dic10—62no—
203C2×Dic10—62no—
204C5×C22⋊C4—62no—
205C5×C22⋊C4—62no—
206C42×C5—62no—
207C42×C5—62no—
208C22⋊Dic5—24no—
209C22⋊Dic5—38no—
210C4⋊Dic5—22no—
211C4⋊Dic5—34no—
212C4⋊Dic5#6714yes—
213#683—38no—
214#683—64no—
215#683—64no—
216C4×Dic5—24no—
217C4×Dic5—64no—
218C4×Dic5—64no—
219C2×C22⋊Q8—151no—
220C2×C4×Q8—151no—
221C2×#117—51no—
222#391—151no—
223#389—151no—
224#388—152no—
225#388—152no—
226#387—152no—
227C4×C4⋊C4—152no—
228C4×C4⋊C4—151no—
229C4×C22⋊C4—31no—
230C22×C3×C5—22no—
231C22×C3×C5—22no—
232C22×C3×C5—22no—
233C22×C3×C5—41no—
234C22×C3×C5—41no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C52−1+411yescharacteristic
243C22×C3×C52−1+411yescharacteristic
244C3×C4×C5—22no—
245C3×C4×C5C4×D414yes—
246Dic15—24no—
247Dic15—24no—
248C3×Dic5—24no—
249C3×Dic5—42no—
250C5×Dic3—22no—
251C5×Dic3—22no—
252C5×Dic3—41no—
253C5×Dic3—41no—
254C24×C3C22×D511yescharacteristic
255C22×C3×C4—22no—
256C22×C3×C4—22no—
257C22×C3×C4—52no—
258C22×C3×C4—52no—
259C22×C3×C4C4×D514yes—
260C22×C3×C4C22×D511yescharacteristic
261C22×C3×C4C22×D511yescharacteristic
262C22×Dic3—52no—
263C22×Dic3—52no—
264C22×Dic3C22×D511yescharacteristic
265C22×Dic3C22×D511yescharacteristic
266C22×Dic3C22×D511yescharacteristic
267C22×Dic3C22×D511yescharacteristic
268C2×Dic6—54no—
269C2×Dic6—102no—
270C2×Dic6—102no—
271C3×C4⋊C4—54no—
272C3×C4⋊C4—102no—
273C3×C22⋊C4—104no—
274C3×C42—104no—
275#217—22no—
276#217—22no—
277#217—58no—
278C4⋊Dic3—54no—
279Dic3⋊C4—58no—
280Dic3⋊C4—104no—
281Dic3⋊C4—104no—
282C4×Dic3—22no—
283C4×Dic3—22no—
284C4×Dic3—104no—
285C4×Dic3—104no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5C2×C4×D312yes—
293C23×C5C23×D311yescharacteristic
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—28no—
297C2×C4×C5—32no—
298C2×C4×C5—32no—
299C2×C4×C5—61no—
300C2×C4×C5—61no—
301C2×C4×C5—61no—
302C2×C4×C5—61no—
303C2×C4×C5—61no—
304C2×C4×C5—61no—
305C2×C4×C5—61no—
306C2×C4×C5—61no—
307C2×C4×C5—61no—
308C2×C4×C5—61no—
309C2×C4×C5C2×C4×D312yes—
310C2×C4×C5C2×C4×D312yes—
311C2×C4×C5#23512yes—
312C2×C4×C5C2×#6712yes—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—34no—
319C2×Dic5—34no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5C2×#6714yes—
325Dic10—68no—
326C22×Q8—151no—
327C23×C4D3×D511yescharacteristic
328C22⋊Q8—158no—
329C4×Q8—304no—
330#117—104no—
331C2×C4⋊C4—51no—
332C2×C4⋊C4—51no—
333C2×C4⋊C4—152no—
334C2×C4⋊C4—151no—
335C2×C4⋊C4—152no—
336C2×C4⋊C4—152no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—52no—
340C2×C22⋊C4—152no—
341C2×C42—31no—
342C2×C42—31no—
343C2×C42—52no—
344C2×C42—152no—
345C2×C42—152no—
346#95—31no—
347#95—31no—
348#95—152no—
349#95—152no—
350#95—152no—
351#95—152no—
352C2×C3×C5—42no—
353C2×C3×C5C2×C4×D411yescharacteristic
354C2×C3×C5C4×#4111yescharacteristic
355C2×C3×C5#51911yescharacteristic
356C2×C3×C5#54711yescharacteristic
357C2×C3×C5#54811yescharacteristic
358C2×C3×C5#55211yescharacteristic
359C2×C3×C5#55611yescharacteristic
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—21no—
365C23×C3—21no—
366C23×C3C2×C4×D512yes—
367C23×C3C23×D511yescharacteristic
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—28no—
371C2×C3×C4—54no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—102no—
375C2×C3×C4—102no—
376C2×C3×C4—102no—
377C2×C3×C4C2×C4×D512yes—
378C2×C3×C4C2×C4×D512yes—
379C2×C3×C4D4×D512yes—
380C2×C3×C4#71112yes—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—21no—
388C2×Dic3—21no—
389C2×Dic3—21no—
390C2×Dic3—21no—
391C2×Dic3—54no—
392C2×Dic3—54no—
393C2×Dic3—102no—
394C2×Dic3—102no—
395C2×Dic3—102no—
396C2×Dic3—102no—
397C2×Dic3#70912yes—
398C2×Dic3#70912yes—
399Dic6—108no—
400C22×C5—22no—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—41no—
404C22×C5—41no—
405C22×C5—41no—
406C22×C5—41no—
407C22×C5C22×C4×D311yescharacteristic
408C22×C5C2×#23511yescharacteristic
409C22×C5D3×#4111yescharacteristic
410C22×C5D3×#4111yescharacteristic
411C22×C5#101011yescharacteristic
412C22×C5#101011yescharacteristic
413C22×C5C22×#6711yescharacteristic
414C4×C5—22no—
415C4×C5—62no—
416C4×C5—62no—
417C4×C5—121no—
418C4×C5—121no—
419C4×C5C4×#6714yes—
420Dic5—24no—
421Dic5—42no—
422Dic5—64no—
423Dic5—64no—
424C24C2×D3×D511yescharacteristic
425C2×Q8—154no—
426C2×Q8—302no—
427C2×Q8—302no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—31no—
434C22×C4—52no—
435C22×C4—52no—
436C22×C4—152no—
437C22×C4—152no—
438C22×C4#120014yes—
439C22×C4C2×D3×D511yescharacteristic
440C22×C4C2×D3×D511yescharacteristic
441C4⋊C4—54no—
442C4⋊C4—102no—
443C4⋊C4—158no—
444C4⋊C4—154no—
445C4⋊C4—304no—
446C4⋊C4—304no—
447C22⋊C4—62no—
448C22⋊C4—62no—
449C22⋊C4—104no—
450C22⋊C4—158no—
451C42—62no—
452C42—62no—
453C42—104no—
454C42—304no—
455C42—304no—
456C3×C5#236211yescharacteristic, complemented, Hall
457C22×C3—22no—
458C22×C3—22no—
459C22×C3—22no—
460C22×C3—41no—
461C22×C3—41no—
462C22×C3—41no—
463C22×C3—41no—
464C22×C3C22×C4×D511yescharacteristic
465C22×C3C2×#70911yescharacteristic
466C22×C3C2×#70911yescharacteristic
467C22×C3C2×D4×D511yescharacteristic
468C22×C3C2×#71111yescharacteristic
469C22×C3#415011yescharacteristic
470C22×C3#415011yescharacteristic
471C3×C4—22no—
472C3×C4—104no—
473C3×C4—202no—
474C3×C4#402714yes—
475Dic3—22no—
476Dic3—22no—
477Dic3—41no—
478Dic3—41no—
479Dic3—104no—
480Dic3—104no—
481C2×C5—42no—
482C2×C5#551611yescharacteristic
483C2×C5#552211yescharacteristic
484C2×C5#552911yescharacteristic
485C2×C5#553311yescharacteristic
486C2×C5C2×C4×#6711yescharacteristic
487C2×C5#582411yescharacteristic
488C2×C5#583111yescharacteristic
489C23—21no—
490C23—21no—
491C23—21no—
492C23—21no—
493C23—21no—
494C23—21no—
495C23C2×#120012yes—
496C23C22×D3×D511yescharacteristic
497Q8—308no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—28no—
501C2×C4—32no—
502C2×C4—32no—
503C2×C4—54no—
504C2×C4—61no—
505C2×C4—61no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—61no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—61no—
512C2×C4—61no—
513C2×C4—61no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—102no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—154no—
520C2×C4—154no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4#678212yes—
526C2×C4C2×#120012yes—
527C2×C4C2×#120012yes—
528C2×C4D5×#6712yes—
529C2×C3—42no—
530C2×C3C4×#70911yescharacteristic
531C2×C3C2×#402711yescharacteristic
532C2×C3#6585011yescharacteristic
533C2×C3#6587511yescharacteristic
534C2×C3#6587611yescharacteristic
535C2×C3#6588511yescharacteristic
536C2×C3#6588611yescharacteristic
537C5#8224311yescharacteristic, complemented, Sylow
538C22—22no—
539C22—22no—
540C22—22no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22#9200111yescharacteristic
546C22#9200111yescharacteristic
547C22D3×#70911yescharacteristic
548C22D3×#70911yescharacteristic
549C22C2×#678211yescharacteristic
550C22C22×#120011yescharacteristic
551C22C2×D5×#6711yescharacteristic
552C4—22no—
553C4—62no—
554C4—62no—
555C4—104no—
556C4—121no—
557C4—121no—
558C4—202no—
559C4—304no—
560C4—304no—
561C4#9155214yes—
562C3#1060519911yescharacteristic, complemented, Sylow
563C2—42no—
564C2#1175417511yescharacteristic
565C2#1175421311yescharacteristic
566C2#1175430611yescharacteristic
567C2#1175443211yescharacteristic
568C2#1175443611yescharacteristic
569C2#1175452811yescharacteristic
570C2C2×#9155211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#2362
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#91340C2semidirect
7. #11748858C2semidirect
8. #11748824C2semidirect
9. Dic3×C4⋊Dic5C2semidirect
10. #11748640C2semidirect
11. #11748599C2semidirect
17. #91813C4semidirect
456. C3×C5#2362semidirect
537. C5#82243semidirect
562. C3#10605199semidirect

Maximal subgroups

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

subgroupindex
C2×#918132
C2×C3×#40722
C2×#913402
C4×C5×#2172
#117494812
#117494802
#117488582
#117488242
Dic3×C4⋊Dic52
#117486402
#117485992
#106051993
#822435