Finite Group Databasebeta

← #14327377

Subgroups — #14327377

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×#1201C211yesmaximal, characteristic
2C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#91338C211yesmaximal, characteristic, complemented
4C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
5C5×#4987C211yesmaximal, characteristic, complemented
6C3×#65276C211yesmaximal, characteristic, complemented
7#11748906C212yesmaximal
8#11748884C212yesmaximal, complemented
9#11748724C212yesmaximal, complemented
10#11748649C212yesmaximal, complemented
11#11748623C211yesmaximal, characteristic, complemented
12#10605743—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1201C2211yescharacteristic
16C22×D5×Dic3C2212yes—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4×Dic15C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21C2×C5×(C2×D3)⋊C4C2212yes—
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C3×#685C2212yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×#6669C2211yescharacteristic
26C2×#6668C2212yes—
27C2×(C2×D3)⋊Dic5C2212yes—
28C2×(C2×D3)⋊Dic5C2211yescharacteristic
29C2×#6665C2211yescharacteristic
30C2×Dic3×Dic5C2212yes—
31C4×#1201C418yescomplemented
32D5×C4⋊Dic3—24no—
33#91338—24no—
34#91115C2212yes—
35C5×C3⋊#95C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73883—51nomaximal, Hall
40C2×C4×C22⋊D5—31no—
41C2×#4072—31no—
42C2×D5×C4⋊C4—31no—
43C5×#380—31no—
44#65276D311yescharacteristic, complemented
45#65266—31no—
46C4⋊C4×Dic5—31no—
47#65245—32no—
48#65233—32no—
49#64955—32no—
50#64941—32no—
51C23×C5×D3C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2312yes—
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2311yescharacteristic
60C2×C4×C5×D3—22no—
61C2×C4×C5×D3—22no—
62C2×C4×C5×D3C2×C414yescomplemented
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5C2×C414yes—
68C2×#1201—22no—
69C2×#1201—22no—
70C2×#1201C2×C414yes—
71C2×D5×Dic3—24no—
72C2×D5×Dic3—24no—
73C2×D5×Dic3—42no—
74C3×C5×C4⋊C4—22no—
75C4⋊Dic15D414yescomplemented
76C4×Dic15—42no—
77C4×Dic15C2×C414yescomplemented
78C5×(C2×D3)⋊C4—42no—
79C5×C4⋊Dic3—22no—
80C3×#685—24no—
81C3×C4⋊Dic5—22no—
82#6669C2×C414yescomplemented
83#6668—24no—
84(C2×D3)⋊Dic5—24no—
85(C2×D3)⋊Dic5C2×C414yescomplemented
86#6665C2×C414yes—
87Dic3×Dic5—24no—
88C2×C4×#67—51no—
89C22×C4⋊Dic3—51no—
90C2×#892—51no—
91C3×#380—51no—
92#4987D511yescharacteristic, complemented
93#4977—51no—
94Dic3×C4⋊C4—51no—
95#4958—52no—
96Dic3×C22⋊C4—52no—
97#4670—52no—
98#4655—52no—
99C23×C4×C5—31no—
100C22×C22⋊D5—31no—
101C22×C4×D5—32no—
102C22×C4×D5C2×D311yescharacteristic
103C2×C5×C4⋊C4—31no—
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×C5×C22⋊C4—32no—
106C2×C22⋊Dic5—31no—
107C2×C22⋊Dic5—32no—
108C4×C22⋊D5—38no—
109C2×#685—31no—
110C2×#685C2×D312yes—
111#4072—64no—
112C2×C4⋊Dic5—31no—
113C2×C4⋊Dic5C2×D311yescharacteristic
114C2×#683—31no—
115C2×#683—32no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5—32no—
118C2×C4×Dic5—32no—
119D5×C4⋊C4—64no—
120C5×#95—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#3963C2×D312yes—
125#2352—151noSylow
126C23×C3×C5C2411yescharacteristic
127C22×C5×D3—21no—
128C22×C5×D3—21no—
129C22×C5×D3—21no—
130C22×C5×D3—21no—
131C22×C5×D3—21no—
132C22×C5×D3—21no—
133C22×C5×D3C22×C412yes—
134C22×C3×D5—21no—
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5—21no—
138C22×C3×D5C22×C412yes—
139C22×C3×D5#4112yes—
140C22×C3×D5#4112yes—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5#4112yes—
147C2×Dic15—22no—
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×Dic15—21no—
151C2×Dic15—22no—
152C2×Dic15—21no—
153C2×Dic15C22×C412yes—
154C2×Dic15C22×C412yes—
155C2×Dic15C2×D414yes—
156C2×C5×Dic3—21no—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3C22×C412yes—
162C4×C5×D3—28no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5C22×C412yes—
169C3×C4×D5—28no—
170#1201—28no—
171D5×Dic3—48no—
172C23×C3×C4—51no—
173C22×#67—51no—
174C23×Dic3—52no—
175C22×C4×D3C2×D511yescharacteristic
176C2×C3×C4⋊C4—51no—
177C2×C3×C4⋊C4C2×D511yescharacteristic
178C2×C3×C22⋊C4—52no—
179C2×#217—51no—
180C4×#67—58no—
181C2×(C2×D3)⋊C4—51no—
182C2×(C2×D3)⋊C4—52no—
183C2×(C2×D3)⋊C4C2×D512yes—
184C2×C4⋊Dic3—51no—
185C2×C4⋊Dic3—52no—
186C2×C4⋊Dic3—104no—
187C2×C4⋊Dic3C2×D511yescharacteristic
188C2×Dic3⋊C4—51no—
189C2×C4×Dic3—51no—
190C2×C4×Dic3—52no—
191C2×C4×Dic3—52no—
192#892—104no—
193C3×#95—52no—
194C3⋊#95—52no—
195C3⋊#95—52no—
196C3⋊#95—52no—
197C3⋊#95C2×D512yes—
198C24×C5—31no—
199C23×D5C22×D311yescharacteristic
200C22×C4×C5—31no—
201C22×C4×C5—34no—
202C22×C4×C5—32no—
203C22×C4×C5—62no—
204C22×C4×C5—62no—
205C22×C4×C5C22×D312yes—
206C22×C4×C5C22×D311yescharacteristic
207C2×C22⋊D5—34no—
208C2×C22⋊D5—62no—
209C2×C22⋊D5—62no—
210C22×Dic5—32no—
211C22×Dic5—31no—
212C22×Dic5—31no—
213C22×Dic5C22×D312yes—
214C22×Dic5C22×D311yescharacteristic
215C2×C4×D5—22no—
216C2×C4×D5—22no—
217C2×C4×D5—64no—
218C2×C4×D5—64no—
219C2×C4×D5—122no—
220C2×C4×D5C4×D314yes—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—62no—
223C5×C22⋊C4—122no—
224C22⋊Dic5—34no—
225C22⋊Dic5—64no—
226#685—24no—
227#685—34no—
228C4⋊Dic5—22no—
229C4⋊Dic5—34no—
230#683—34no—
231#683—64no—
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—31no—
243#380—51no—
244C4×C4⋊C4—151no—
245C4×C22⋊C4—152no—
246C22×C3×C5C23×C411yescharacteristic
247C22×C3×C5C22×D411yescharacteristic
248C22×C3×C5C2×#4111yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5C2×#4111yescharacteristic
251C22×C3×C5H(5,𝔽2)11yescharacteristic
252C22×C3×C52−1+411yescharacteristic
253C2×C5×D3—22no—
254C2×C5×D3—22no—
255C2×C5×D3—22no—
256C2×C5×D3—41no—
257C2×C5×D3—41no—
258C2×C5×D3—41no—
259C2×C5×D3—41no—
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—22no—
263C2×C3×D5—22no—
264C2×C3×D5—22no—
265C2×C3×D5—22no—
266C2×C3×D5#11714yescomplemented
267C3×C4×C5—42no—
268C3×C4×C5C4×D414yes—
269Dic15—22no—
270Dic15—22no—
271Dic15—24no—
272C3×Dic5—22no—
273C3×Dic5—42no—
274C5×Dic3—22no—
275C5×Dic3—42no—
276C24×C3—51no—
277C23×D3C22×D511yescharacteristic
278C22×C3×C4—51no—
279C22×C3×C4—54no—
280C22×C3×C4—52no—
281C22×C3×C4—102no—
282C22×C3×C4—102no—
283C22×C3×C4C22×D512yes—
284C22×C3×C4C22×D511yescharacteristic
285C2×#67—54no—
286C2×#67—102no—
287C2×#67—102no—
288C22×Dic3—51no—
289C22×Dic3—51no—
290C22×Dic3—52no—
291C22×Dic3—104no—
292C22×Dic3—104no—
293C22×Dic3—202no—
294C22×Dic3C22×D512yes—
295C22×Dic3C22×D511yescharacteristic
296C2×C4×D3—22no—
297C2×C4×D3—22no—
298C2×C4×D3C4×D514yescomplemented
299C3×C4⋊C4—22no—
300C3×C4⋊C4—102no—
301C3×C22⋊C4—104no—
302#217—54no—
303(C2×D3)⋊C4—42no—
304(C2×D3)⋊C4—54no—
305(C2×D3)⋊C4—104no—
306C4⋊Dic3—22no—
307C4⋊Dic3—54no—
308C4⋊Dic3—104no—
309Dic3⋊C4—54no—
310C4×Dic3—54no—
311C4×Dic3—104no—
312C4×Dic3—202no—
313C23×C5—32no—
314C23×C5—61no—
315C23×C5—61no—
316C23×C5—61no—
317C23×C5—61no—
318C23×C5—61no—
319C23×C5—61no—
320C23×C5C23×D311yescharacteristic
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5—21no—
325C22×D5C2×C4×D312yes—
326C22×D5#23712yes—
327C22×D5#23912yes—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—32no—
332C2×C4×C5—61no—
333C2×C4×C5—61no—
334C2×C4×C5—68no—
335C2×C4×C5—62no—
336C2×C4×C5—62no—
337C2×C4×C5—62no—
338C2×C4×C5C2×C4×D312yes—
339C2×C4×C5D3×D412yes—
340C2×C4×C5#23712yes—
341C22⋊D5—68no—
342C2×Dic5—21no—
343C2×Dic5—21no—
344C2×Dic5—22no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—32no—
348C2×Dic5—32no—
349C2×Dic5—34no—
350C2×Dic5—61no—
351C2×Dic5—62no—
352C2×Dic5—61no—
353C2×Dic5—61no—
354C2×Dic5—62no—
355C2×Dic5—61no—
356C2×Dic5C2×C4×D312yes—
357C4×D5—28no—
358C4×D5—128no—
359C22×D4—151no—
360C23×C4—31no—
361C23×C4—51no—
362C23×C4—152no—
363C4×D4—158no—
364#117—304no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—151no—
368C2×C4⋊C4—151no—
369C2×C4⋊C4—152no—
370C2×C4⋊C4—304no—
371C2×C4⋊C4D3×D511yescharacteristic
372C2×C22⋊C4—32no—
373C2×C22⋊C4—52no—
374C2×C22⋊C4—151no—
375C2×C22⋊C4—151no—
376C2×C22⋊C4—152no—
377C2×C42—151no—
378C2×C42—152no—
379C2×C42—152no—
380#95—32no—
381#95—52no—
382#95—152no—
383#95—152no—
384#95—152no—
385C2×C3×C5C2×#11711yescharacteristic
386C2×C3×C5C2×C4×D411yescharacteristic
387C2×C3×C5#52011yescharacteristic
388C2×C3×C5#54611yescharacteristic
389C2×C3×C5#54811yescharacteristic
390C2×C3×C5#55211yescharacteristic
391C2×C3×C5#55311yescharacteristic
392C3×D5—24no—
393C5×D3—42no—
394C23×C3—52no—
395C23×C3—52no—
396C23×C3—52no—
397C23×C3—101no—
398C23×C3—101no—
399C23×C3—101no—
400C23×C3—101no—
401C23×C3C23×D511yescharacteristic
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3C2×C4×D512yes—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—52no—
413C2×C3×C4—101no—
414C2×C3×C4—101no—
415C2×C3×C4—108no—
416C2×C3×C4—102no—
417C2×C3×C4—102no—
418C2×C3×C4—102no—
419C2×C3×C4C2×C4×D512yes—
420C2×C3×C4D4×D512yes—
421C2×C3×C4#71112yes—
422#67—108no—
423C2×Dic3—21no—
424C2×Dic3—21no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—54no—
431C2×Dic3—101no—
432C2×Dic3—102no—
433C2×Dic3—101no—
434C2×Dic3—102no—
435C2×Dic3—101no—
436C2×Dic3—101no—
437C2×Dic3—208no—
438C2×Dic3C2×C4×D512yes—
439C4×D3—28no—
440C22×C5—62no—
441C22×C5—62no—
442C22×C5—62no—
443C22×C5—121no—
444C22×C5—121no—
445C22×C5—121no—
446C22×C5—121no—
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—22no—
455C2×D5—22no—
456C2×D5—22no—
457C2×D5—22no—
458C2×D5—22no—
459C2×D5—22no—
460C2×D5#89214yescomplemented
461C4×C5—42no—
462C4×C5—62no—
463C4×C5—122no—
464C4×C5#67⋊C414yes—
465Dic5—22no—
466Dic5—42no—
467Dic5—62no—
468Dic5—62no—
469Dic5—64no—
470C24—31no—
471C24—51no—
472C2×D4—154no—
473C2×D4—302no—
474C2×D4—302no—
475C22×C4—31no—
476C22×C4—34no—
477C22×C4—32no—
478C22×C4—51no—
479C22×C4—54no—
480C22×C4—52no—
481C22×C4—62no—
482C22×C4—62no—
483C22×C4—102no—
484C22×C4—102no—
485C22×C4—151no—
486C22×C4—151no—
487C22×C4—152no—
488C22×C4—304no—
489C22×C4—304no—
490C22×C4—602no—
491C22×C4C2×D3×D512yes—
492C22×C4C2×D3×D511yescharacteristic
493C4⋊C4—22no—
494C4⋊C4—62no—
495C4⋊C4—102no—
496C4⋊C4—154no—
497C4⋊C4—154no—
498C4⋊C4—304no—
499C22⋊C4—104no—
500C22⋊C4—122no—
501C22⋊C4—154no—
502C22⋊C4—154no—
503C22⋊C4—304no—
504C42—154no—
505C42—304no—
506C42—602no—
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—54no—
509C22×C3—102no—
510C22×C3—102no—
511C22×C3—102no—
512C22×C3—102no—
513C22×C3—102no—
514C22×C3—102no—
515C22×C3C22×C4×D511yescharacteristic
516C22×C3C2×D4×D511yescharacteristic
517C22×C3C2×#71111yescharacteristic
518C22×C3#414411yescharacteristic
519C22×C3#414711yescharacteristic
520C22×C3D5×#4111yescharacteristic
521C22×C3D5×#4111yescharacteristic
522C2×D3—22no—
523C2×D3—22no—
524C2×D3—22no—
525C2×D3—41no—
526C2×D3—41no—
527C2×D3—41no—
528C2×D3—41no—
529C3×C4—42no—
530C3×C4—102no—
531C3×C4—202no—
532C3×C4#402714yes—
533Dic3—22no—
534Dic3—42no—
535Dic3—102no—
536Dic3—102no—
537Dic3—104no—
538C2×C5—122no—
539C2×C5C2×#67⋊C411yescharacteristic
540C2×C5C2×#89211yescharacteristic
541C2×C5#552311yescharacteristic
542C2×C5#559811yescharacteristic
543C2×C5#561811yescharacteristic
544C2×C5#563011yescharacteristic
545C2×C5#564211yescharacteristic
546D5—24no—
547C23—32no—
548C23—52no—
549C23—52no—
550C23—52no—
551C23—61no—
552C23—61no—
553C23—61no—
554C23—61no—
555C23—61no—
556C23—61no—
557C23—101no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23C22×D3×D511yescharacteristic
562D4—308no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—32no—
567C2×C4—52no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—68no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—108no—
577C2×C4—102no—
578C2×C4—102no—
579C2×C4—102no—
580C2×C4—152no—
581C2×C4—152no—
582C2×C4—154no—
583C2×C4—301no—
584C2×C4—301no—
585C2×C4—302no—
586C2×C4—301no—
587C2×C4—302no—
588C2×C4—301no—
589C2×C4—608no—
590C2×C4C4×D3×D512yes—
591C2×C4#677712yes—
592C2×C4#678012yes—
593C2×C3—104no—
594C2×C3C2×#402711yescharacteristic
595C2×C3#6583811yescharacteristic
596C2×C3D5×#11711yescharacteristic
597C2×C3#6594611yescharacteristic
598C2×C3#6594811yescharacteristic
599C2×C3#6596711yescharacteristic
600C2×C3#6597311yescharacteristic
601D3—42no—
602C5#7388311yescharacteristic, complemented, Sylow
603C22—54no—
604C22—62no—
605C22—62no—
606C22—62no—
607C22—102no—
608C22—102no—
609C22—102no—
610C22—102no—
611C22—102no—
612C22—102no—
613C22—121no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22C2×C4×D3×D511yescharacteristic
618C22C2×#677711yescharacteristic
619C22D5×#23711yescharacteristic
620C22#9202711yescharacteristic
621C22#9202811yescharacteristic
622C22D5×#23911yescharacteristic
623C22C2×#678011yescharacteristic
624C4—42no—
625C4—62no—
626C4—102no—
627C4—122no—
628C4—202no—
629C4—302no—
630C4—304no—
631C4—302no—
632C4#9144214yes—
633C3#1060574311yescharacteristic, complemented, Sylow
634C2—104no—
635C2—122no—
636C2#1175366911yescharacteristic
637C2#1175369811yescharacteristic
638C2D5×#89211yescharacteristic
639C2#1175388711yescharacteristic
640C2C2×#9144211yescharacteristic
641C2#1175496211yescharacteristic
642C2#1175519311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2352
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×D5×C4⋊Dic3C2semidirect
3. C2×#91338C2semidirect
4. C4⋊C4×Dic15C2semidirect
5. C5×#4987C2semidirect
6. C3×#65276C2semidirect
8. #11748884C2semidirect
9. #11748724C2semidirect
10. #11748649C2semidirect
11. #11748623C2semidirect
31. C4×#1201C4semidirect
44. #65276D3semidirect
62. C2×C4×C5×D3C2×C4semidirect
75. C4⋊Dic15D4semidirect
77. C4×Dic15C2×C4semidirect
82. #6669C2×C4semidirect
85. (C2×D3)⋊Dic5C2×C4semidirect
92. #4987D5semidirect
266. C2×C3×D5#117semidirect
298. C2×C4×D3C4×D5semidirect
460. C2×D5#892semidirect
507. C3×C5#2352semidirect
602. C5#73883semidirect
633. C3#10605743semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12012
C2×D5×C4⋊Dic32
C2×#913382
C4⋊C4×Dic152
C5×#49872
C3×#652762
#117489062
#117488842
#117487242
#117486492
#117486232
#106057433
#738835