Finite Group Databasebeta

← #14327347

Subgroups — #14327347

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic
2C22×C4⋊Dic15C211yesmaximal, characteristic, complemented
3C2×#91781C211yesmaximal, characteristic, complemented
4C3×C5×#380C211yesmaximal, characteristic, complemented
5#11751088C211yesmaximal, characteristic, complemented
6#11751078C211yesmaximal, characteristic, complemented
7C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
8#11751059C212yesmaximal
9C22⋊C4×Dic15C212yesmaximal, complemented
10#11750771C212yesmaximal, complemented
11#11750756C212yesmaximal, complemented
12#10605614—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C23×Dic15C2212yes—
16C22×C4×D15C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2212yes—
20C2×#6719C2211yescharacteristic
21C4×#1220C418yescomplemented
22C2×#6714C2212yes—
23C2×#6714C2212yes—
24C2×#6714C2211yescharacteristic
25C2×C4⋊Dic15—24no—
26C2×C4⋊Dic15C2212yes—
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×C4×Dic15C2212yes—
31C2×C4×Dic15C2212yes—
32C2×C4×Dic15C2211yescharacteristic
33#91781—24no—
34C3×C5×#95C2212yes—
35#91115C2212yes—
36#91115C2212yes—
37#91115C2212yes—
38#91115C2212yes—
39#73883—51nomaximal, Hall
40C2×C4×C22⋊D5—31no—
41C22×C4⋊Dic5—31no—
42C2×#4038—31no—
43C5×#380D311yescharacteristic, complemented
44#65276—31no—
45#65266—31no—
46C4⋊C4×Dic5—31no—
47#65247—32no—
48C22⋊C4×Dic5—32no—
49#64959—32no—
50#64944—32no—
51C24×C3×C5C2311yescharacteristic
52C23×D15C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yes—
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C2×#1220—22no—
61C2×#1220—22no—
62C2×#1220C2×C414yes—
63C22×Dic15—24no—
64C22×Dic15—24no—
65C22×Dic15—42no—
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2312yes—
71C2×C4×D15—22no—
72C2×C4×D15—22no—
73C2×C4×D15C2×C414yescomplemented
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C22⋊C4—24no—
77#6719C2×C414yes—
78#6714—24no—
79#6714—42no—
80#6714C2×C414yescomplemented
81C4⋊Dic15—22no—
82C4⋊Dic15—24no—
83C4⋊Dic15D414yescomplemented
84#6712C2×C414yescomplemented
85C4×Dic15—24no—
86C4×Dic15—42no—
87C4×Dic15C2×C414yescomplemented
88C2×C4×#67—51no—
89C22×C4⋊Dic3—51no—
90C2×#892—51no—
91C3×#380D511yescharacteristic, complemented
92#4987—51no—
93#4977—51no—
94Dic3×C4⋊C4—51no—
95#4958—52no—
96Dic3×C22⋊C4—52no—
97#4670—52no—
98#4655—52no—
99C23×C4×C5C2×D311yescharacteristic
100C22×C22⋊D5—31no—
101C23×Dic5—32no—
102C22×C4×D5—31no—
103C2×C5×C4⋊C4C2×D311yescharacteristic
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×C5×C22⋊C4C2×D312yes—
106C2×C22⋊Dic5—31no—
107C4×C22⋊D5—38no—
108C2×#685—31no—
109C2×#685—32no—
110C2×#685—32no—
111C2×C4⋊Dic5—31no—
112C2×C4⋊Dic5—32no—
113C2×C4⋊Dic5—31no—
114C2×C4⋊Dic5—64no—
115C2×#683—31no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—32no—
118C2×C4×Dic5—32no—
119#4038—64no—
120C5×#95C2×D312yes—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#3963—32no—
125#2352—151noSylow
126C23×C3×C5—21no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—21no—
130C23×C3×C5C22×C412yes—
131C23×C3×C5#4112yes—
132C23×C3×C5#4112yes—
133C23×C3×C5C2411yescharacteristic
134C22×D15—21no—
135C22×D15—21no—
136C22×D15—21no—
137C22×D15—21no—
138C22×D15—21no—
139C22×D15—21no—
140C22×D15C22×C412yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—28no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5#4112yes—
154#1220—28no—
155C2×Dic15—21no—
156C2×Dic15—21no—
157C2×Dic15—22no—
158C2×Dic15—21no—
159C2×Dic15—21no—
160C2×Dic15—21no—
161C2×Dic15—22no—
162C2×Dic15—21no—
163C2×Dic15—22no—
164C2×Dic15—22no—
165C2×Dic15—22no—
166C2×Dic15—48no—
167C2×Dic15C22×C412yes—
168C2×Dic15C22×C412yes—
169C2×Dic15C22×C412yes—
170C2×Dic15C2×D414yes—
171C4×D15—28no—
172C23×C3×C4C2×D511yescharacteristic
173C22×#67—51no—
174C23×Dic3—52no—
175C22×C4×D3—51no—
176C2×C3×C4⋊C4C2×D511yescharacteristic
177C2×C3×C4⋊C4C2×D511yescharacteristic
178C2×C3×C22⋊C4C2×D512yes—
179C2×#217—51no—
180C4×#67—58no—
181C2×(C2×D3)⋊C4—51no—
182C2×(C2×D3)⋊C4—52no—
183C2×(C2×D3)⋊C4—52no—
184C2×C4⋊Dic3—51no—
185C2×C4⋊Dic3—52no—
186C2×C4⋊Dic3—51no—
187C2×C4⋊Dic3—104no—
188C2×Dic3⋊C4—51no—
189C2×C4×Dic3—51no—
190C2×C4×Dic3—52no—
191C2×C4×Dic3—52no—
192#892—104no—
193C3×#95C2×D512yes—
194C3⋊#95—52no—
195C3⋊#95—52no—
196C3⋊#95—52no—
197C3⋊#95—52no—
198C24×C5C22×D311yescharacteristic
199C23×D5—31no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5C4×D314yes—
203C22×C4×C5C22×D312yes—
204C22×C4×C5C22×D312yes—
205C22×C4×C5C22×D311yescharacteristic
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—34no—
208C2×C22⋊D5—62no—
209C2×C22⋊D5—62no—
210C22×Dic5—31no—
211C22×Dic5—31no—
212C22×Dic5—32no—
213C22×Dic5—31no—
214C22×Dic5—32no—
215C22×Dic5—64no—
216C22×Dic5—64no—
217C22×Dic5—122no—
218C2×C4×D5—34no—
219C2×C4×D5—62no—
220C2×C4×D5—62no—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—22no—
223C5×C22⋊C4—24no—
224C22⋊Dic5—34no—
225#685—34no—
226#685—64no—
227#685—122no—
228C4⋊Dic5—34no—
229C4⋊Dic5—64no—
230C4⋊Dic5—62no—
231#683—34no—
232C4×Dic5—34no—
233C4×Dic5—64no—
234C4×Dic5—122no—
235C2×C4×D4—151no—
236C2×#117—151no—
237C22×C4⋊C4—151no—
238#388—152no—
239#387—152no—
240#386—152no—
241#382—151no—
242#380—151no—
243#380D1511yescharacteristic, complemented
244C4×C4⋊C4—151no—
245C4×C22⋊C4—152no—
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—22no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5#11714yescomplemented
253C22×C3×C5C23×C411yescharacteristic
254C22×C3×C5C22×D411yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5H(5,𝔽2)11yescharacteristic
259C22×C3×C52−1+411yescharacteristic
260C2×D15—22no—
261C2×D15—22no—
262C2×D15—22no—
263C2×D15—41no—
264C2×D15—41no—
265C2×D15—41no—
266C2×D15—41no—
267C3×C4×C5—22no—
268C3×C4×C5—42no—
269C3×C4×C5—42no—
270C3×C4×C5C4×D414yes—
271Dic15—22no—
272Dic15—22no—
273Dic15—22no—
274Dic15—24no—
275Dic15—42no—
276C24×C3C22×D511yescharacteristic
277C23×D3—51no—
278C22×C3×C4—22no—
279C22×C3×C4—22no—
280C22×C3×C4C4×D514yes—
281C22×C3×C4C22×D512yes—
282C22×C3×C4C22×D512yes—
283C22×C3×C4C22×D511yescharacteristic
284C22×C3×C4C22×D511yescharacteristic
285C2×#67—54no—
286C2×#67—102no—
287C2×#67—102no—
288C22×Dic3—51no—
289C22×Dic3—51no—
290C22×Dic3—51no—
291C22×Dic3—52no—
292C22×Dic3—52no—
293C22×Dic3—104no—
294C22×Dic3—104no—
295C22×Dic3—202no—
296C2×C4×D3—54no—
297C2×C4×D3—102no—
298C2×C4×D3—102no—
299C3×C4⋊C4—22no—
300C3×C4⋊C4—22no—
301C3×C22⋊C4—24no—
302#217—54no—
303(C2×D3)⋊C4—54no—
304(C2×D3)⋊C4—104no—
305(C2×D3)⋊C4—202no—
306C4⋊Dic3—54no—
307C4⋊Dic3—104no—
308C4⋊Dic3—102no—
309Dic3⋊C4—54no—
310C4×Dic3—54no—
311C4×Dic3—104no—
312C4×Dic3—202no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5C2×C4×D312yes—
318C23×C5#23712yes—
319C23×C5#23912yes—
320C23×C5C23×D311yescharacteristic
321C22×D5—32no—
322C22×D5—61no—
323C22×D5—61no—
324C22×D5—61no—
325C22×D5—61no—
326C22×D5—61no—
327C22×D5—61no—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—28no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5C2×C4×D312yes—
338C2×C4×C5C2×C4×D312yes—
339C2×C4×C5D3×D412yes—
340C2×C4×C5#23712yes—
341C22⋊D5—68no—
342C2×Dic5—32no—
343C2×Dic5—32no—
344C2×Dic5—32no—
345C2×Dic5—34no—
346C2×Dic5—61no—
347C2×Dic5—61no—
348C2×Dic5—61no—
349C2×Dic5—62no—
350C2×Dic5—61no—
351C2×Dic5—61no—
352C2×Dic5—62no—
353C2×Dic5—61no—
354C2×Dic5—62no—
355C2×Dic5—62no—
356C2×Dic5—62no—
357C2×Dic5—128no—
358C4×D5—68no—
359C22×D4—151no—
360C23×C4—151no—
361C23×C4—152no—
362C23×C4C2×D1511yescharacteristic
363C4×D4—158no—
364#117—304no—
365C2×C4⋊C4—151no—
366C2×C4⋊C4—151no—
367C2×C4⋊C4—151no—
368C2×C4⋊C4—152no—
369C2×C4⋊C4—304no—
370C2×C4⋊C4C2×D1511yescharacteristic
371C2×C4⋊C4C2×D1511yescharacteristic
372C2×C22⋊C4—151no—
373C2×C22⋊C4—151no—
374C2×C22⋊C4—152no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4C2×D1512yes—
377C2×C42—151no—
378C2×C42—152no—
379C2×C42—152no—
380#95—152no—
381#95—152no—
382#95—152no—
383#95—152no—
384#95C2×D1512yes—
385C2×C3×C5—24no—
386C2×C3×C5C2×#11711yescharacteristic
387C2×C3×C5C2×C4×D411yescharacteristic
388C2×C3×C5#52011yescharacteristic
389C2×C3×C5#54611yescharacteristic
390C2×C3×C5#54811yescharacteristic
391C2×C3×C5#55211yescharacteristic
392C2×C3×C5#55311yescharacteristic
393D15—42no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3C2×C4×D512yes—
399C23×C3#71112yes—
400C23×C3#71312yes—
401C23×C3C23×D511yescharacteristic
402C22×D3—52no—
403C22×D3—101no—
404C22×D3—101no—
405C22×D3—101no—
406C22×D3—101no—
407C22×D3—101no—
408C22×D3—101no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—28no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4C2×C4×D512yes—
419C2×C3×C4C2×C4×D512yes—
420C2×C3×C4D4×D512yes—
421C2×C3×C4#71112yes—
422#67—108no—
423C2×Dic3—52no—
424C2×Dic3—52no—
425C2×Dic3—52no—
426C2×Dic3—54no—
427C2×Dic3—101no—
428C2×Dic3—101no—
429C2×Dic3—101no—
430C2×Dic3—102no—
431C2×Dic3—101no—
432C2×Dic3—101no—
433C2×Dic3—102no—
434C2×Dic3—101no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3—102no—
438C2×Dic3—208no—
439C4×D3—108no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5#89214yescomplemented
447C22×C5C22×C4×D311yescharacteristic
448C22×C5C2×D3×D411yescharacteristic
449C22×C5C2×#23711yescharacteristic
450C22×C5C2×#23711yescharacteristic
451C22×C5C2×#23911yescharacteristic
452C22×C5#100911yescharacteristic
453C22×C5#101011yescharacteristic
454C2×D5—62no—
455C2×D5—62no—
456C2×D5—62no—
457C2×D5—121no—
458C2×D5—121no—
459C2×D5—121no—
460C2×D5—121no—
461C4×C5—22no—
462C4×C5—42no—
463C4×C5—42no—
464C4×C5#67⋊C414yes—
465Dic5—62no—
466Dic5—62no—
467Dic5—62no—
468Dic5—64no—
469Dic5—122no—
470C24—151no—
471C24C22×D1511yescharacteristic
472C2×D4—154no—
473C2×D4—302no—
474C2×D4—302no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—151no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—152no—
481C22×C4—154no—
482C22×C4—152no—
483C22×C4—304no—
484C22×C4—302no—
485C22×C4—302no—
486C22×C4—304no—
487C22×C4—602no—
488C22×C4C4×D1514yes—
489C22×C4C22×D1512yes—
490C22×C4C22×D1512yes—
491C22×C4C22×D1511yescharacteristic
492C22×C4C22×D1511yescharacteristic
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—154no—
496C4⋊C4—154no—
497C4⋊C4—304no—
498C4⋊C4—302no—
499C22⋊C4—24no—
500C22⋊C4—154no—
501C22⋊C4—154no—
502C22⋊C4—304no—
503C22⋊C4—602no—
504C42—154no—
505C42—304no—
506C42—602no—
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3#403814yescomplemented
515C22×C3C22×C4×D511yescharacteristic
516C22×C3C2×D4×D511yescharacteristic
517C22×C3C2×#71111yescharacteristic
518C22×C3C2×#71111yescharacteristic
519C22×C3C2×#71311yescharacteristic
520C22×C3#414911yescharacteristic
521C22×C3#415011yescharacteristic
522C2×D3—102no—
523C2×D3—102no—
524C2×D3—102no—
525C2×D3—201no—
526C2×D3—201no—
527C2×D3—201no—
528C2×D3—201no—
529C3×C4—22no—
530C3×C4—42no—
531C3×C4—42no—
532C3×C4#402714yes—
533Dic3—102no—
534Dic3—102no—
535Dic3—102no—
536Dic3—104no—
537Dic3—202no—
538C2×C5—24no—
539C2×C5C2×#67⋊C411yescharacteristic
540C2×C5C2×#89211yescharacteristic
541C2×C5#552311yescharacteristic
542C2×C5#559811yescharacteristic
543C2×C5#561811yescharacteristic
544C2×C5#563011yescharacteristic
545C2×C5#564211yescharacteristic
546D5—122no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—152no—
552C23—301no—
553C23—301no—
554C23—301no—
555C23—301no—
556C23—301no—
557C23—301no—
558C23C2×C4×D1512yes—
559C23#681912yes—
560C23#682112yes—
561C23C23×D1511yescharacteristic
562D4—308no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—28no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—152no—
573C2×C4—152no—
574C2×C4—152no—
575C2×C4—154no—
576C2×C4—301no—
577C2×C4—301no—
578C2×C4—301no—
579C2×C4—302no—
580C2×C4—301no—
581C2×C4—301no—
582C2×C4—302no—
583C2×C4—301no—
584C2×C4—308no—
585C2×C4—302no—
586C2×C4—302no—
587C2×C4—302no—
588C2×C4—608no—
589C2×C4C2×C4×D1512yes—
590C2×C4C2×C4×D1512yes—
591C2×C4D4×D1512yes—
592C2×C4#681912yes—
593C2×C3—24no—
594C2×C3C2×#402711yescharacteristic
595C2×C3C2×#403811yescharacteristic
596C2×C3#6585711yescharacteristic
597C2×C3#6593211yescharacteristic
598C2×C3#6595211yescharacteristic
599C2×C3#6596411yescharacteristic
600C2×C3#6597611yescharacteristic
601D3—202no—
602C5#7388311yescharacteristic, complemented, Sylow
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—302no—
610C22—302no—
611C22—302no—
612C22—601no—
613C22—601no—
614C22—601no—
615C22—601no—
616C22#9178114yescomplemented
617C22C22×C4×D1511yescharacteristic
618C22C2×D4×D1511yescharacteristic
619C22C2×#681911yescharacteristic
620C22C2×#681911yescharacteristic
621C22C2×#682111yescharacteristic
622C22#9210011yescharacteristic
623C22#9210111yescharacteristic
624C4—22no—
625C4—42no—
626C4—42no—
627C4—304no—
628C4—302no—
629C4—302no—
630C4—302no—
631C4—602no—
632C4#9177014yes—
633C3#1060561411yescharacteristic, complemented, Sylow
634C2—24no—
635C2—602no—
636C2C2×#9177011yescharacteristic
637C2C2×#9178111yescharacteristic
638C2#1175628211yescharacteristic
639C2#1175635711yescharacteristic
640C2#1175637711yescharacteristic
641C2#1175638911yescharacteristic
642C2#1175640111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#380C2
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenter#380D15
hypocenterC3×C5#2352
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #380

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊Dic15C2semidirect
3. C2×#91781C2semidirect
4. C3×C5×#380C2semidirect
5. #11751088C2semidirect
6. #11751078C2semidirect
7. C4⋊C4×Dic15C2semidirect
9. C22⋊C4×Dic15C2semidirect
10. #11750771C2semidirect
11. #11750756C2semidirect
21. C4×#1220C4semidirect
43. C5×#380D3semidirect
73. C2×C4×D15C2×C4semidirect
80. #6714C2×C4semidirect
83. C4⋊Dic15D4semidirect
84. #6712C2×C4semidirect
87. C4×Dic15C2×C4semidirect
91. C3×#380D5semidirect
243. #380D15semidirect
252. C22×C3×C5#117semidirect
446. C22×C5#892semidirect
507. C3×C5#2352semidirect
514. C22×C3#4038semidirect
602. C5#73883semidirect
616. C22#91781semidirect
633. C3#10605614semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C22×C4⋊Dic152
C2×#917812
C3×C5×#3802
#117510882
#117510782
C4⋊C4×Dic152
#117510592
C22⋊C4×Dic152
#117507712
#117507562
#106056143
#738835