Finite Group Databasebeta

← #14321720

Subgroups — #14321720

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C5×Dic3C211yesmaximal, characteristic, complemented
2C2×#91556C211yesmaximal, characteristic
3C2×#91542C211yesmaximal, characteristic
4#11751314C211yesmaximal, characteristic
5C3×#65499C211yesmaximal, characteristic, complemented
6Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
7#11749472C211yesmaximal, characteristic, complemented
8#11748881C212yesmaximal, complemented
9#11748807C212yesmaximal, complemented
10#11748728C212yesmaximal, complemented
11Dic3×#683C212yesmaximal, complemented
12C4×#4075—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C23×C5×Dic3C2211yescharacteristic
17C22×#1200C2211yescharacteristic
18C2×#6719C2211yescharacteristic
19C2×#6714C2212yes—
20C2×C4×C5×Dic3—24no—
21C2×C4×C5×Dic3C2212yes—
22C2×C4×C5×Dic3C2212yes—
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×#683C2212yes—
26#91556—24no—
27C2×#6669C2211yescharacteristic
28#91542C418yescomplemented
29C2×#6668C2212yes—
30C2×#6667C2211yescharacteristic
31C2×#6667C2212yes—
32C2×Dic3×Dic5C2212yes—
33C2×Dic3×Dic5C2211yescharacteristic
34#91115C2212yes—
35C3×#3963C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#74380—51nomaximal, Hall
40C22×C42×C5—31no—
41C2×#4075—31no—
42C2×C4×C22⋊D5—31no—
43#65502—31no—
44#65500—31no—
45#65499D311yescharacteristic, complemented
46C4×C22⋊Dic5—31no—
47#65229—32no—
48C4×#685—32no—
49#65222—32no—
50C4×#683—32no—
51C24×C3×C5C2311yescharacteristic
52C23×D15C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—24no—
55C22×C3×C4×C5C2312yes—
56C2×#1220—22no—
57C2×#1220—22no—
58C2×#1220C2×C414yes—
59C22×Dic15C2312yes—
60C22×Dic15C2311yescharacteristic
61C22×C5×Dic3—22no—
62C22×C5×Dic3—22no—
63C22×C5×Dic3—24no—
64C22×C5×Dic3C2×C414yescomplemented
65C22×C5×Dic3D414yes—
66C22×C5×Dic3C2312yes—
67C22×C5×Dic3C2311yescharacteristic
68C22×C5×Dic3C2311yescharacteristic
69C22×C3×Dic5C2311yescharacteristic
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2312yes—
72C2×#1200—22no—
73C2×#1200—24no—
74#6719—22no—
75#6714—24no—
76C4×C5×Dic3—24no—
77C4×C5×Dic3—24no—
78C3×C22⋊Dic5—22no—
79C3×C22⋊Dic5C2×C414yescomplemented
80C3×#683—24no—
81#6669—22no—
82#6668C2×C418yescomplemented
83#6667—22no—
84#6667C2×C418yescomplemented
85Dic3×Dic5—22no—
86Dic3×Dic5—24no—
87C22×C4×Dic3D511yescharacteristic, complemented
88C2×#886—51no—
89C2×#67⋊C4—51no—
90C3×#385—51no—
91#5213—51no—
92#4990—52no—
93Dic3×C4⋊C4—52no—
94#4943—51no—
95Dic3×C22⋊C4—51no—
96#4666—52no—
97#4654—52no—
98C23×C4×C5—31no—
99C23×C4×C5—31no—
100C23×C4×C5C2×D311yescharacteristic
101C22×C22⋊D5—31no—
102C22×C4×D5—31no—
103C2×C42×C5—32no—
104C2×C42×C5—32no—
105C2×C42×C5—64no—
106C2×C22⋊Dic5—31no—
107C2×C22⋊Dic5C2×D311yescharacteristic
108C2×C22⋊Dic5C2×D311yescharacteristic
109#4075—38no—
110C4×C22⋊D5—64no—
111C2×#685—32no—
112C2×#685—32no—
113C2×#685—31no—
114C2×#683—32no—
115C2×#683—31no—
116C2×#683C2×D312yes—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—32no—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yes—
124C4×#123—151noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C2×D412yes—
129C23×C3×C5#4112yes—
130C23×C3×C5C2411yescharacteristic
131C22×D15—21no—
132C22×D15—22no—
133C22×D15—22no—
134C22×D15—21no—
135C22×D15C22×C412yes—
136C2×C3×C4×C5—28no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5#4114yes—
140#1220—28no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15C22×C412yes—
147C2×C5×Dic3—28no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—28no—
152C2×C5×Dic3C22×C414yes—
153C2×C5×Dic3C2×D412yes—
154C2×C5×Dic3C2×D412yes—
155C2×C5×Dic3#4114yes—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5C22×C414yes—
163#1200—44no—
164C23×C3×C4C2×D511yescharacteristic
165C22×#67—51no—
166C23×Dic3C2×D511yescharacteristic
167C23×Dic3C2×D511yescharacteristic
168C22×C4×D3—51no—
169C2×C3×C4⋊C4—52no—
170C2×C3×C22⋊C4—51no—
171C2×C3×C22⋊C4—51no—
172C2×#217—51no—
173C2×(C2×D3)⋊C4—52no—
174C2×(C2×D3)⋊C4—52no—
175C2×(C2×D3)⋊C4—51no—
176C2×C4⋊Dic3—52no—
177C2×Dic3⋊C4—51no—
178C2×C4×Dic3—24no—
179C2×C4×Dic3—52no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3C2×D512yes—
182C2×C4×Dic3C2×D512yes—
183#886—58no—
184#67⋊C4—104no—
185C3×#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C24×C5C22×D311yescharacteristic
191C23×D5—31no—
192C22×C4×C5—22no—
193C22×C4×C5—24no—
194C22×C4×C5—31no—
195C22×C4×C5—34no—
196C22×C4×C5—34no—
197C22×C4×C5—32no—
198C22×C4×C5—31no—
199C22×C4×C5—64no—
200C22×C4×C5—62no—
201C22×C4×C5—62no—
202C22×C4×C5C22×D312yes—
203C2×C22⋊D5—34no—
204C2×C22⋊D5—62no—
205C2×C22⋊D5—62no—
206C22×Dic5—31no—
207C22×Dic5—32no—
208C22×Dic5C22×D311yescharacteristic
209C22×Dic5C22×D311yescharacteristic
210C22×Dic5C22×D312yes—
211C2×C4×D5—64no—
212C2×C4×D5—62no—
213C42×C5—64no—
214C42×C5—64no—
215C22⋊Dic5—22no—
216C22⋊Dic5—62no—
217C22⋊Dic5C4×D314yescomplemented
218#685—38no—
219#685—62no—
220#685—64no—
221#683—24no—
222#683—38no—
223#683—62no—
224C4×Dic5—64no—
225C4×Dic5—62no—
226C2×#123—151no—
227C2×C4×D4—151no—
228C22×C42—31no—
229#388—152no—
230#387—152no—
231#386—151no—
232#385—51no—
233#381—151no—
234C4×C4⋊C4—152no—
235C4×C22⋊C4—152no—
236C4×C22⋊C4—151no—
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5C4×D414yes—
242C22×C3×C5C23×C411yescharacteristic
243C22×C3×C5C22×D411yescharacteristic
244C22×C3×C5C2×#4112yes—
245C22×C3×C5C2×#4111yescharacteristic
246C22×C3×C5C2×#4112yes—
247C2×D15—22no—
248C2×D15—24no—
249C2×D15—41no—
250C2×D15—41no—
251C2×D15—42no—
252C3×C4×C5—24no—
253Dic15—22no—
254Dic15—42no—
255C3×Dic5—24no—
256C3×Dic5—41no—
257C3×Dic5—41no—
258C5×Dic3—24no—
259C5×Dic3—22no—
260C5×Dic3#12314yescomplemented
261C24×C3C22×D511yescharacteristic
262C23×D3—51no—
263C22×C3×C4—22no—
264C22×C3×C4—24no—
265C22×C3×C4—52no—
266C22×C3×C4—51no—
267C22×C3×C4—51no—
268C22×C3×C4C22×D512yes—
269C2×#67—54no—
270C2×#67—102no—
271C2×#67—102no—
272C22×Dic3—22no—
273C22×Dic3—22no—
274C22×Dic3—24no—
275C22×Dic3—51no—
276C22×Dic3—52no—
277C22×Dic3C4×D514yescomplemented
278C22×Dic3C22⋊D514yes—
279C22×Dic3C22×D512yes—
280C22×Dic3C22×D511yescharacteristic
281C22×Dic3C22×D511yescharacteristic
282C2×C4×D3—104no—
283C2×C4×D3—102no—
284C3×C4⋊C4—104no—
285C3×C22⋊C4—54no—
286C3×C22⋊C4—102no—
287#217—102no—
288(C2×D3)⋊C4—58no—
289(C2×D3)⋊C4—104no—
290(C2×D3)⋊C4—102no—
291C4⋊Dic3—58no—
292Dic3⋊C4—102no—
293C4×Dic3—24no—
294C4×Dic3—24no—
295C4×Dic3—104no—
296C4×Dic3—102no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5C2×C4×D312yes—
300C23×C5D3×D412yes—
301C23×C5#23912yes—
302C23×C5C23×D311yescharacteristic
303C22×D5—32no—
304C22×D5—61no—
305C22×D5—62no—
306C22×D5—61no—
307C22×D5—62no—
308C2×C4×C5—28no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—32no—
312C2×C4×C5—34no—
313C2×C4×C5—34no—
314C2×C4×C5—32no—
315C2×C4×C5—68no—
316C2×C4×C5—68no—
317C2×C4×C5—62no—
318C2×C4×C5—62no—
319C2×C4×C5—62no—
320C2×C4×C5#23714yes—
321C22⋊D5—68no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—22no—
327C2×Dic5—22no—
328C2×Dic5—32no—
329C2×Dic5—61no—
330C2×Dic5—61no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5C2×C4×D314yes—
335C4×D5—124no—
336C22×D4—151no—
337C23×C4—31no—
338C23×C4—31no—
339C23×C4—151no—
340C23×C4D3×D511yescharacteristic
341#123—158no—
342C4×D4—304no—
343C2×C4⋊C4—52no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—151no—
346C2×C22⋊C4—51no—
347C2×C22⋊C4—51no—
348C2×C22⋊C4—152no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—151no—
351C2×C22⋊C4—152no—
352C2×C42—32no—
353C2×C42—32no—
354C2×C42—64no—
355C2×C42—151no—
356C2×C42—152no—
357#95—52no—
358#95—152no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5—24no—
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5C4×#4112yes—
365C2×C3×C5C2×#12311yescharacteristic
366C2×C3×C5#52511yescharacteristic
367C2×C3×C5#52912yes—
368D15—42no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3C2×C4×D512yes—
372C23×C3#70912yes—
373C23×C3C2×C22⋊D512yes—
374C23×C3C23×D511yescharacteristic
375C22×D3—52no—
376C22×D3—102no—
377C22×D3—102no—
378C22×D3—101no—
379C22×D3—101no—
380C2×C3×C4—28no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—54no—
384C2×C3×C4—102no—
385C2×C3×C4—102no—
386C2×C3×C4—102no—
387C2×C3×C4—102no—
388C2×C3×C4—101no—
389C2×C3×C4—101no—
390C2×C3×C4#70914yes—
391#67—108no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—28no—
396C2×Dic3—28no—
397C2×Dic3—52no—
398C2×Dic3—101no—
399C2×Dic3—101no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3C2×C4×D514yes—
404C2×Dic3#70914yes—
405C2×Dic3C2×C22⋊D512yes—
406C2×Dic3C2×C22⋊D512yes—
407C4×D3—204no—
408C22×C5—22no—
409C22×C5—24no—
410C22×C5—22no—
411C22×C5—24no—
412C22×C5#89314yes—
413C22×C5C22×C4×D311yescharacteristic
414C22×C5C2×D3×D411yescharacteristic
415C22×C5C2×#23712yes—
416C22×C5C2×#23911yescharacteristic
417C22×C5D3×#4112yes—
418C2×D5—62no—
419C2×D5—64no—
420C2×D5—121no—
421C2×D5—121no—
422C2×D5—122no—
423C4×C5—24no—
424C4×C5—34no—
425C4×C5—62no—
426C4×C5—64no—
427Dic5—24no—
428Dic5—41no—
429Dic5—41no—
430Dic5—62no—
431Dic5—122no—
432C24—151no—
433C24C2×D3×D511yescharacteristic
434C2×D4—154no—
435C2×D4—302no—
436C2×D4—302no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—31no—
440C22×C4—34no—
441C22×C4—34no—
442C22×C4—32no—
443C22×C4—31no—
444C22×C4—52no—
445C22×C4—51no—
446C22×C4—51no—
447C22×C4—64no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—151no—
451C22×C4—152no—
452C22×C4—302no—
453C22×C4—304no—
454C22×C4C2×D3×D512yes—
455C4⋊C4—104no—
456C4⋊C4—158no—
457C4⋊C4—302no—
458C22⋊C4—54no—
459C22⋊C4—102no—
460C22⋊C4—158no—
461C22⋊C4—302no—
462C22⋊C4—302no—
463C22⋊C4—304no—
464C42—64no—
465C42—64no—
466C42—302no—
467C42—304no—
468C3×C5C4×#12311yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3C4×C22⋊D514yes—
474C22×C3C22×C4×D511yescharacteristic
475C22×C3C2×#70911yescharacteristic
476C22×C3C2×#70912yes—
477C22×C3C2×#70912yes—
478C22×C3C22×C22⋊D511yescharacteristic
479C2×D3—104no—
480C2×D3—102no—
481C2×D3—202no—
482C2×D3—201no—
483C2×D3—201no—
484C3×C4—24no—
485C3×C4—104no—
486C3×C4—201no—
487C3×C4—201no—
488Dic3—24no—
489Dic3—22no—
490Dic3—102no—
491Dic3—202no—
492Dic3#407514yescomplemented
493C2×C5—24no—
494C2×C5C2×#89311yescharacteristic
495C2×C5C4×#23712yes—
496C2×C5#558611yescharacteristic
497C2×C5#562412yes—
498C2×C5D3×#12311yescharacteristic
499D5—122no—
500C23—22no—
501C23—22no—
502C23—152no—
503C23—301no—
504C23—302no—
505C23—302no—
506C23—301no—
507C23#676912yes—
508C23C4×D3×D512yes—
509C23D3×C22⋊D512yes—
510C23C22×D3×D511yescharacteristic
511D4—308no—
512C2×C4—28no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—34no—
516C2×C4—32no—
517C2×C4—34no—
518C2×C4—32no—
519C2×C4—54no—
520C2×C4—68no—
521C2×C4—68no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—102no—
526C2×C4—102no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—152no—
532C2×C4—301no—
533C2×C4—301no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—604no—
538C2×C4#677914yes—
539C2×C3—24no—
540C2×C3C4×#70912yes—
541C2×C3#6581312yes—
542C2×C3C2×C4×C22⋊D511yescharacteristic
543C2×C3C2×#407511yescharacteristic
544C2×C3#6612511yescharacteristic
545D3—202no—
546C5#7438011yescharacteristic, complemented, Sylow
547C22—24no—
548C22—22no—
549C22—22no—
550C22—24no—
551C22—302no—
552C22—304no—
553C22—601no—
554C22—601no—
555C22—602no—
556C22#9144614yes—
557C22C2×#676911yescharacteristic
558C22C2×C4×D3×D511yescharacteristic
559C22D3×#70912yes—
560C22C2×#677912yes—
561C22C2×D3×C22⋊D511yescharacteristic
562C4—24no—
563C4—34no—
564C4—64no—
565C4—62no—
566C4—104no—
567C4—201no—
568C4—201no—
569C4—302no—
570C4—602no—
571C3C4×#407511yescharacteristic, complemented, Sylow
572C2—24no—
573C2—602no—
574C2C4×#677912yes—
575C2#1175444012yes—
576C2C2×#9144611yescharacteristic
577C2D3×#407511yescharacteristic
578C2#1175538811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C4×#123
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C5×Dic3C2semidirect
5. C3×#65499C2semidirect
6. Dic3×C22⋊Dic5C2semidirect
7. #11749472C2semidirect
8. #11748881C2semidirect
9. #11748807C2semidirect
10. #11748728C2semidirect
11. Dic3×#683C2semidirect
28. #91542C4semidirect
45. #65499D3semidirect
64. C22×C5×Dic3C2×C4semidirect
79. C3×C22⋊Dic5C2×C4semidirect
82. #6668C2×C4semidirect
84. #6667C2×C4semidirect
87. C22×C4×Dic3D5semidirect
217. C22⋊Dic5C4×D3semidirect
260. C5×Dic3#123semidirect
277. C22×Dic3C4×D5semidirect
468. C3×C5C4×#123semidirect
492. Dic3#4075semidirect
546. C5#74380semidirect
571. C3C4×#4075semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C5×Dic32
C2×#915562
C2×#915422
#117513142
C3×#654992
Dic3×C22⋊Dic52
#117494722
#117488812
#117488072
#117487282
Dic3×#6832
C4×#40753
#743805