Finite Group Databasebeta

← #14320168

Subgroups — #14320168

Order 1920.

1312 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×#91400C212yesmaximal
2C2×C4×D3×Dic5C211yesmaximal, characteristic
3C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
4C5×#4987C211yesmaximal, characteristic
5C3×#65265C211yesmaximal, characteristic, complemented
6#11748874C212yesmaximal
7#11748834C211yesmaximal, characteristic, complemented
8#11748786C211yesmaximal, characteristic
9#11748699C211yesmaximal, characteristic, complemented
10#11748642C212yesmaximal, complemented
11#11748637C212yesmaximal, complemented
12#10605595—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×D3×Dic5C2211yescharacteristic
15C22×D3×Dic5C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2212yes—
19C2×C4×Dic15C2211yescharacteristic
20C2×C5×(C2×D3)⋊C4C2212yes—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×#683C2212yes—
24C2×C3×#683C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×#6668C2212yes—
27C2×#6668C2212yes—
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2211yescharacteristic
31C2×Dic3×Dic5C2211yescharacteristic
32#91400—28no—
33C4×D3×Dic5C418yescomplemented
34#91115C2212yes—
35C5×C3⋊#95C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#74318—51nomaximal, Hall
39C22×C4×Dic5—31no—
40C2×#4023—32no—
41C5×#380—31no—
42#65501—31no—
43#65265—31no—
44#65265D311yescharacteristic, complemented
45C4⋊C4×Dic5—31no—
46C4⋊C4×Dic5—31no—
47#65231—32no—
48#64939—32no—
49#64938—32no—
50C23×C5×D3C2311yescharacteristic
51C22×C3×C4×C5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×C5×Dic3C2312yes—
57C22×C5×Dic3C2311yescharacteristic
58C2×C4×C5×D3—22no—
59C2×C4×C5×D3—22no—
60C2×C4×C5×D3C2×C414yes—
61C22×C3×Dic5C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C2×D3×Dic5—22no—
65C2×D3×Dic5—22no—
66C2×D3×Dic5C2×C414yes—
67C2×D3×Dic5C2×C414yes—
68C2×D3×Dic5D414yes—
69C2×D3×Dic5Q814yes—
70C3×C5×C4⋊C4—22no—
71C4⋊Dic15—22no—
72C4×Dic15—24no—
73C4×Dic15C2×C414yes—
74C5×(C2×D3)⋊C4—24no—
75C5×C4⋊Dic3—22no—
76C3×C4⋊Dic5—22no—
77C3×#683—24no—
78C3×#683—24no—
79C3×C4×Dic5C2×C414yes—
80#6668—24no—
81#6668—24no—
82(C2×D3)⋊Dic5—24no—
83Dic3×Dic5—24no—
84Dic3×Dic5C2×C414yes—
85Dic3×Dic5C2×C414yes—
86C2×#892—52no—
87C2×C42×D3—51no—
88C3×#384—51no—
89#4987—51no—
90#4987—52no—
91#4987D511yescharacteristic
92#4977—52no—
93Dic3×C4⋊C4—51no—
94Dic3×C4⋊C4—51no—
95Dic3×C4⋊C4—52no—
96#4935—51no—
97C23×C4×C5—31no—
98C23×Dic5—31no—
99C23×Dic5—31no—
100C2×C5×C4⋊C4—31no—
101C2×C5×C4⋊C4C2×D311yescharacteristic
102C2×C5×C22⋊C4—32no—
103C2×C22⋊Dic5—32no—
104C2×C4⋊Dic5—31no—
105C2×C4⋊Dic5C2×D311yescharacteristic
106C2×#683—32no—
107C2×#683—32no—
108C2×#683C2×D312yes—
109C2×#683C2×D312yes—
110C2×C4×Dic5—31no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—38no—
114C2×C4×Dic5—32no—
115C2×C4×Dic5—32no—
116C2×C4×Dic5C2×D311yescharacteristic
117#4023—68no—
118C5×#95—32no—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#2285—151noSylow
123C23×C3×C5C2411yescharacteristic
124C22×C5×D3—21no—
125C22×C5×D3—21no—
126C22×C5×D3—21no—
127C22×C5×D3—21no—
128C22×C5×D3C22×C412yes—
129C22×C5×D3C2×D412yes—
130C22×C5×D3C2×Q812yes—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5C22×C412yes—
135C2×C3×C4×C5#4112yes—
136C2×C3×C4×C5#4112yes—
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15C22×C412yes—
143C2×Dic15C22×C412yes—
144C2×Dic15C2×D412yes—
145C2×Dic15C2×Q812yes—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3C22×C412yes—
152C4×C5×D3—28no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5C22×C412yes—
157C2×C3×Dic5C22×C412yes—
158C2×C3×Dic5C2×D412yes—
159C2×C3×Dic5C2×Q812yes—
160C2×C3×Dic5#4112yes—
161C2×C3×Dic5#4112yes—
162D3×Dic5—28no—
163D3×Dic5C4⋊C4116yescomplemented
164C22×C4×D3—51no—
165C22×C4×D3—51no—
166C22×C4×D3C2×D511yescharacteristic
167C2×C3×C4⋊C4—52no—
168C2×C3×C4⋊C4—51no—
169C2×C3×C4⋊C4—52no—
170C2×C3×C4⋊C4C2×D511yescharacteristic
171C2×C3×C42—51no—
172C2×(C2×D3)⋊C4—52no—
173C2×(C2×D3)⋊C4C2×D512yes—
174C2×C4⋊Dic3—51no—
175C2×C4⋊Dic3—52no—
176C2×C4⋊Dic3—52no—
177C2×C4⋊Dic3C2×D511yescharacteristic
178C2×C4×Dic3—51no—
179C2×C4×Dic3—51no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3—52no—
183#892—108no—
184C42×D3—58no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95C2×D512yes—
189C24×C5—31no—
190C22×C4×C5—31no—
191C22×C4×C5—34no—
192C22×C4×C5—32no—
193C22×C4×C5—62no—
194C22×C4×C5—62no—
195C22×C4×C5C22×D312yes—
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—31no—
198C22×Dic5—34no—
199C22×Dic5—34no—
200C22×Dic5—34no—
201C22×Dic5—31no—
202C22×Dic5—34no—
203C22×Dic5—32no—
204C22×Dic5—62no—
205C22×Dic5—62no—
206C22×Dic5C22×D312yes—
207C22×Dic5C22×D311yescharacteristic
208C22×Dic5C22×D311yescharacteristic
209C5×C4⋊C4—22no—
210C5×C4⋊C4—62no—
211C5×C22⋊C4—64no—
212C22⋊Dic5—64no—
213C4⋊Dic5—22no—
214C4⋊Dic5—62no—
215#683—24no—
216#683—24no—
217#683—64no—
218#683—64no—
219C4×Dic5—34no—
220C4×Dic5—34no—
221C4×Dic5—34no—
222C4×Dic5—64no—
223C4×Dic5—64no—
224C4×Dic5C4×D314yes—
225C2×#117—152no—
226C22×C42—151no—
227#384—51no—
228#384—151no—
229#382—152no—
230#380—31no—
231#380—152no—
232#380—151no—
233C4×C4⋊C4—152no—
234C4×C4⋊C4—151no—
235C4×C4⋊C4—151no—
236C22×C3×C5C23×C411yescharacteristic
237C22×C3×C5C22×D411yescharacteristic
238C22×C3×C5C22×Q811yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C2×C5×D3—22no—
244C2×C5×D3—22no—
245C2×C5×D3—22no—
246C2×C5×D3—22no—
247C2×C5×D3—22no—
248C2×C5×D3—22no—
249C2×C5×D3C2×C4⋊C414yes—
250C3×C4×C5—42no—
251C3×C4×C5#11714yescomplemented
252Dic15—22no—
253Dic15—42no—
254Dic15C2×C4⋊C414yes—
255C3×Dic5—42no—
256C3×Dic5C2×C4⋊C414yes—
257C3×Dic5#11714yescomplemented
258C5×Dic3—22no—
259C5×Dic3—42no—
260C23×D3C22×D511yescharacteristic
261C22×C3×C4—51no—
262C22×C3×C4—51no—
263C22×C3×C4—52no—
264C22×C3×C4C22×D512yes—
265C22×C3×C4C22×D511yescharacteristic
266C22×Dic3—51no—
267C22×Dic3—51no—
268C22×Dic3—52no—
269C22×Dic3C22×D512yes—
270C22×Dic3C22×D511yescharacteristic
271C2×C4×D3—22no—
272C2×C4×D3—22no—
273C2×C4×D3—54no—
274C2×C4×D3—54no—
275C2×C4×D3—54no—
276C2×C4×D3—54no—
277C2×C4×D3—102no—
278C2×C4×D3—102no—
279C2×C4×D3C4×D514yes—
280C3×C4⋊C4—22no—
281C3×C4⋊C4—104no—
282C3×C4⋊C4—104no—
283C3×C4⋊C4—102no—
284C3×C42—54no—
285(C2×D3)⋊C4—24no—
286(C2×D3)⋊C4—104no—
287C4⋊Dic3—22no—
288C4⋊Dic3—104no—
289C4⋊Dic3—104no—
290C4⋊Dic3—102no—
291C4×Dic3—54no—
292C4×Dic3—54no—
293C4×Dic3—54no—
294C4×Dic3—104no—
295C4×Dic3—104no—
296C23×C5—32no—
297C23×C5—32no—
298C23×C5—32no—
299C23×C5—61no—
300C23×C5—61no—
301C23×C5—61no—
302C23×C5—61no—
303C23×C5C23×D311yescharacteristic
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—32no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—68no—
311C2×C4×C5—62no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5C2×C4×D312yes—
315C2×C4×C5#23712yes—
316C2×C4×C5#23912yes—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—32no—
321C2×Dic5—32no—
322C2×Dic5—32no—
323C2×Dic5—316no—
324C2×Dic5—32no—
325C2×Dic5—61no—
326C2×Dic5—61no—
327C2×Dic5—68no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5C2×C4×D312yes—
332C2×Dic5C2×C4×D312yes—
333C2×Dic5D3×D412yes—
334C2×Dic5#23712yes—
335C2×Dic5D3×Q812yes—
336C2×Dic5#23912yes—
337C23×C4—31no—
338C23×C4—151no—
339C23×C4—151no—
340#117—308no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—52no—
343C2×C4⋊C4—52no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C4⋊C4—151no—
348C2×C4⋊C4D3×D511yescharacteristic
349C2×C22⋊C4—32no—
350C2×C22⋊C4—152no—
351C2×C42—51no—
352C2×C42—158no—
353C2×C42—151no—
354C2×C42—151no—
355C2×C42—151no—
356C2×C42—152no—
357C2×C42—152no—
358#95—32no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5C22×C4⋊C411yescharacteristic
363C2×C3×C5C2×#11711yescharacteristic
364C2×C3×C5C2×#11711yescharacteristic
365C2×C3×C5#53211yescharacteristic
366C2×C3×C5#53211yescharacteristic
367C2×C3×C5#53311yescharacteristic
368C2×C3×C5#53311yescharacteristic
369C5×D3—24no—
370C23×C3C23×D511yescharacteristic
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—21no—
374C22×D3—21no—
375C22×D3C2×C4×D512yes—
376C22×D3D4×D512yes—
377C22×D3Q8×D512yes—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—52no—
382C2×C3×C4—52no—
383C2×C3×C4—52no—
384C2×C3×C4—52no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4#71112yes—
392C2×C3×C4#71112yes—
393C2×Dic3—21no—
394C2×Dic3—21no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—22no—
398C2×Dic3—52no—
399C2×Dic3—52no—
400C2×Dic3—52no—
401C2×Dic3—52no—
402C2×Dic3—101no—
403C2×Dic3—101no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3C2×C4×D512yes—
408C4×D3—28no—
409C4×D3—516no—
410C4×D3—108no—
411C22×C5—34no—
412C22×C5—62no—
413C22×C5—62no—
414C22×C5—62no—
415C22×C5—62no—
416C22×C5—62no—
417C22×C5—62no—
418C22×C5C22×C4×D311yescharacteristic
419C22×C5C2×D3×D411yescharacteristic
420C22×C5C2×#23711yescharacteristic
421C22×C5C2×#23711yescharacteristic
422C22×C5C2×D3×Q811yescharacteristic
423C22×C5C2×#23911yescharacteristic
424C22×C5C2×#23911yescharacteristic
425C4×C5—42no—
426C4×C5—62no—
427C4×C5—122no—
428C4×C5#89214yescomplemented
429Dic5—34no—
430Dic5—42no—
431Dic5—62no—
432Dic5—122no—
433Dic5D3×C4⋊C414yes—
434Dic5#89214yescomplemented
435C24—31no—
436C22×C4—31no—
437C22×C4—34no—
438C22×C4—32no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—52no—
442C22×C4—62no—
443C22×C4—62no—
444C22×C4—154no—
445C22×C4—154no—
446C22×C4—154no—
447C22×C4—154no—
448C22×C4—151no—
449C22×C4—151no—
450C22×C4—152no—
451C22×C4—302no—
452C22×C4—302no—
453C22×C4C2×D3×D512yes—
454C22×C4C2×D3×D511yescharacteristic
455C4⋊C4—22no—
456C4⋊C4—62no—
457C4⋊C4—104no—
458C4⋊C4—104no—
459C4⋊C4—102no—
460C4⋊C4—304no—
461C4⋊C4—304no—
462C4⋊C4—302no—
463C22⋊C4—64no—
464C22⋊C4—304no—
465C42—54no—
466C42—154no—
467C42—154no—
468C42—154no—
469C42—304no—
470C42—304no—
471C3×C5#228511yescharacteristic, complemented, Hall
472C22×C3C22×C4×D511yescharacteristic
473C22×C3C2×D4×D511yescharacteristic
474C22×C3C2×#71111yescharacteristic
475C22×C3C2×#71111yescharacteristic
476C22×C3C2×Q8×D511yescharacteristic
477C22×C3D5×#4111yescharacteristic
478C22×C3D5×#4111yescharacteristic
479C2×D3—22no—
480C2×D3—22no—
481C2×D3—22no—
482C2×D3—22no—
483C2×D3—22no—
484C2×D3—22no—
485C2×D3D5×C4⋊C414yes—
486C3×C4—42no—
487C3×C4—54no—
488C3×C4—54no—
489C3×C4—202no—
490C3×C4#402314yescomplemented
491Dic3—22no—
492Dic3—42no—
493Dic3—54no—
494Dic3—102no—
495Dic3—202no—
496C2×C5—64no—
497C2×C5C2×D3×C4⋊C411yescharacteristic
498C2×C5C2×#89211yescharacteristic
499C2×C5C2×#89211yescharacteristic
500C2×C5#571611yescharacteristic
501C2×C5#572511yescharacteristic
502C2×C5#572811yescharacteristic
503C2×C5#572811yescharacteristic
504C23—32no—
505C23—32no—
506C23—32no—
507C23—61no—
508C23—61no—
509C23—61no—
510C23—61no—
511C23C22×D3×D511yescharacteristic
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—32no—
516C2×C4—52no—
517C2×C4—52no—
518C2×C4—52no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—52no—
522C2×C4—61no—
523C2×C4—61no—
524C2×C4—68no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—62no—
528C2×C4—102no—
529C2×C4—102no—
530C2×C4—102no—
531C2×C4—1516no—
532C2×C4—152no—
533C2×C4—152no—
534C2×C4—152no—
535C2×C4—152no—
536C2×C4—308no—
537C2×C4—301no—
538C2×C4—301no—
539C2×C4—302no—
540C2×C4—302no—
541C2×C4—302no—
542C2×C4#676812yes—
543C2×C4C4×D3×D512yes—
544C2×C4#678012yes—
545C2×C3C2×#402311yescharacteristic
546C2×C3C2×D5×C4⋊C411yescharacteristic
547C2×C3D5×#11711yescharacteristic
548C2×C3#6593011yescharacteristic
549C2×C3#6593011yescharacteristic
550C2×C3#6595611yescharacteristic
551C2×C3#6595611yescharacteristic
552D3—24no—
553C5#7431811yescharacteristic, complemented, Sylow
554C22—34no—
555C22—62no—
556C22—62no—
557C22—62no—
558C22—62no—
559C22—62no—
560C22—62no—
561C22C2×#676811yescharacteristic
562C22C2×C4×D3×D511yescharacteristic
563C22D3×D4×D511yescharacteristic
564C22D5×#23711yescharacteristic
565C22D3×Q8×D511yescharacteristic
566C22D5×#23911yescharacteristic
567C22C2×#678011yescharacteristic
568C4—42no—
569C4—54no—
570C4—54no—
571C4—62no—
572C4—122no—
573C4—154no—
574C4—202no—
575C4—302no—
576C4—602no—
577C4#9140014yescomplemented
578C3#1060559511yescharacteristic, complemented, Sylow
579C2—64no—
580C2#1175342311yescharacteristic
581C2#1175345911yescharacteristic
582C2D3×D5×C4⋊C411yescharacteristic
583C2D5×#89211yescharacteristic
584C2C2×#9140011yescharacteristic
585C2#1175477111yescharacteristic
586C2#1175518111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2285
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
3. C4⋊C4×Dic15C2semidirect
5. C3×#65265C2semidirect
7. #11748834C2semidirect
9. #11748699C2semidirect
10. #11748642C2semidirect
11. #11748637C2semidirect
33. C4×D3×Dic5C4semidirect
44. #65265D3semidirect
163. D3×Dic5C4⋊C4semidirect
251. C3×C4×C5#117semidirect
257. C3×Dic5#117semidirect
428. C4×C5#892semidirect
434. Dic5#892semidirect
471. C3×C5#2285semidirect
490. C3×C4#4023semidirect
553. C5#74318semidirect
577. C4#91400semidirect
578. C3#10605595semidirect

Maximal subgroups

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

subgroupindex
C2×#914002
C2×C4×D3×Dic52
C4⋊C4×Dic152
C5×#49872
C3×#652652
#117488742
#117488342
#117487862
#117486992
#117486422
#117486372
#106055953
#743185