Finite Group Databasebeta

← #14321136

Subgroups — #14321136

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C42×C5×D3C211yesmaximal, characteristic
2C2×#91338C211yesmaximal, characteristic
3C2×#91338C211yesmaximal, characteristic
4#11751029C211yesmaximal, characteristic, complemented
5C3×#65217C211yesmaximal, characteristic, complemented
6#11748858C211yesmaximal, characteristic, complemented
7#11748857C211yesmaximal, characteristic, complemented
8#11748722C212yesmaximal
9#11748716C212yesmaximal
10#11748645C212yesmaximal, complemented
11Dic3×#683C212yesmaximal, complemented
12#10613800—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C2×C3×C42×C5C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×#6712C2212yes—
20C2×C4×C5×Dic3C2211yescharacteristic
21C2×C4×C5×Dic3C2211yescharacteristic
22C2×C4×C5×Dic3C2211yescharacteristic
23C42×C5×D3—24no—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×#683C2212yes—
27C2×#6669C2212yes—
28C2×#6668C2212yes—
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×(C2×D3)⋊Dic5C2212yes—
31C2×Dic3×Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33#91338—24no—
34#91338C418yescomplemented
35#91115C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#75963—51nomaximal, Hall
40C22×C42×C5—31no—
41C2×#4072—31no—
42C2×#4072—31no—
43#65499—32no—
44#65499—32no—
45C4×#683—32no—
46C4×#683—32no—
47#65217—31no—
48#65217—31no—
49#65217—31no—
50#65217D311yescharacteristic, complemented
51C23×C5×D3C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2311yescharacteristic
60C2×C4×C5×D3—22no—
61C2×C4×C5×D3—22no—
62C2×C4×C5×D3—22no—
63C2×C4×C5×D3—22no—
64C2×C4×C5×D3—22no—
65C2×C4×C5×D3—22no—
66C2×C4×C5×D3C2×C414yes—
67C2×C4×C5×D3D414yes—
68C2×C4×C5×D3Q814yes—
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2312yes—
71C3×C42×C5—22no—
72C4⋊Dic15—22no—
73C4⋊Dic15C2×C414yescomplemented
74#6712—24no—
75C4×C5×Dic3—22no—
76C4×C5×Dic3—22no—
77C4×C5×Dic3—22no—
78C3×C4⋊Dic5—22no—
79C3×C4⋊Dic5C2×C414yescomplemented
80C3×#683—24no—
81#6669—24no—
82#6668—24no—
83(C2×D3)⋊Dic5—24no—
84(C2×D3)⋊Dic5C2×C418yes—
85Dic3×Dic5—24no—
86Dic3×Dic5C2×C418yescomplemented
87C2×#892—51no—
88C2×#892—51no—
89C2×C42×D3D511yescharacteristic
90C3×#389—51no—
91#4989—52no—
92#4984—51no—
93Dic3×C4⋊C4—52no—
94#4972—51no—
95#4928—51no—
96#4668—52no—
97#4649—52no—
98C23×C4×C5—31no—
99C23×C4×C5—31no—
100C23×C4×C5—31no—
101C2×C42×C5—31no—
102C2×C42×C5—31no—
103C2×C42×C5—31no—
104C2×C42×C5—64no—
105C2×C42×C5C2×D311yescharacteristic
106C2×C22⋊Dic5—32no—
107C2×C22⋊Dic5—32no—
108#4072—38no—
109#4072—64no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—31no—
112C2×C4⋊Dic5C2×D311yescharacteristic
113C2×C4⋊Dic5C2×D311yescharacteristic
114C2×#683—32no—
115C2×#683—32no—
116C2×#683—32no—
117C2×#683C2×D312yes—
118C2×C4×Dic5—32no—
119C2×C4×Dic5—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963C2×D312yes—
124#2296—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×C5×D3—21no—
127C22×C5×D3—21no—
128C22×C5×D3—21no—
129C22×C5×D3—21no—
130C22×C5×D3C22×C412yes—
131C22×C5×D3C2×D412yes—
132C22×C5×D3C2×Q812yes—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×C3×C4×C5C2×D412yes—
139C2×C3×C4×C5C2×Q812yes—
140C2×C3×C4×C5#4112yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15C22×C414yes—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3C22×C412yes—
153C2×C5×Dic3C2×D412yes—
154C2×C5×Dic3C2×Q812yes—
155C2×C5×Dic3#4112yes—
156C2×C5×Dic3#4112yes—
157C4×C5×D3—28no—
158C4×C5×D3—28no—
159C4×C5×D3C4⋊C4116yescomplemented
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5C22×C414yes—
166C22×C4×D3C2×D511yescharacteristic
167C22×C4×D3C2×D511yescharacteristic
168C22×C4×D3C2×D511yescharacteristic
169C2×C3×C4⋊C4—51no—
170C2×C3×C4⋊C4—51no—
171C2×C3×C4⋊C4—52no—
172C2×C3×C42C2×D511yescharacteristic
173C2×(C2×D3)⋊C4—52no—
174C2×(C2×D3)⋊C4—52no—
175C2×C4⋊Dic3—51no—
176C2×C4⋊Dic3—51no—
177C2×C4⋊Dic3—52no—
178C2×Dic3⋊C4—52no—
179C2×Dic3⋊C4—52no—
180C2×C4×Dic3—52no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3C2×D511yescharacteristic
183C2×C4×Dic3C2×D511yescharacteristic
184C2×C4×Dic3C2×D511yescharacteristic
185#892—58no—
186#892—104no—
187C42×D3—24no—
188C3×#95—52no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C3⋊#95—52no—
192C24×C5—31no—
193C22×C4×C5—31no—
194C22×C4×C5—34no—
195C22×C4×C5—34no—
196C22×C4×C5—34no—
197C22×C4×C5—31no—
198C22×C4×C5—31no—
199C22×C4×C5—62no—
200C22×C4×C5—62no—
201C22×C4×C5—62no—
202C22×C4×C5—62no—
203C22×C4×C5—62no—
204C22×C4×C5—62no—
205C22×C4×C5C22×D311yescharacteristic
206C22×C4×C5C22×D311yescharacteristic
207C22×C4×C5C22×D311yescharacteristic
208C22×Dic5—32no—
209C22×Dic5—32no—
210C22×Dic5C22×D312yes—
211C22×Dic5C22×D312yes—
212C42×C5—22no—
213C42×C5—62no—
214C42×C5—62no—
215C42×C5—62no—
216C22⋊Dic5—38no—
217C22⋊Dic5—64no—
218C4⋊Dic5—22no—
219C4⋊Dic5—34no—
220C4⋊Dic5—62no—
221C4⋊Dic5C4×D314yescomplemented
222#683—24no—
223#683—64no—
224#683—64no—
225#683—64no—
226C4×Dic5—38no—
227C4×Dic5—64no—
228C2×#117—151no—
229C2×#117—151no—
230C22×C42—31no—
231#389—51no—
232#389—151no—
233#389—151no—
234#389—151no—
235#385—152no—
236#385—152no—
237C4×C4⋊C4—152no—
238C4×C4⋊C4—152no—
239C22×C3×C5C23×C411yescharacteristic
240C22×C3×C5C22×D411yescharacteristic
241C22×C3×C5C22×Q811yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C22×C3×C5C2×#4111yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5C2×#4111yescharacteristic
246C2×C5×D3—22no—
247C2×C5×D3—22no—
248C2×C5×D3—22no—
249C2×C5×D3—22no—
250C2×C5×D3—22no—
251C2×C5×D3—22no—
252C2×C5×D3C2×C4⋊C414yes—
253C3×C4×C5—22no—
254C3×C4×C5—22no—
255C3×C4×C5C2×C4⋊C414yes—
256Dic15—24no—
257Dic15—42no—
258C3×Dic5—24no—
259C3×Dic5—42no—
260C5×Dic3—22no—
261C5×Dic3—22no—
262C5×Dic3C2×C4⋊C414yes—
263C23×D3C22×D511yescharacteristic
264C22×C3×C4—52no—
265C22×C3×C4—52no—
266C22×C3×C4C22×D511yescharacteristic
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—52no—
270C22×Dic3—52no—
271C22×Dic3C22×D511yescharacteristic
272C22×Dic3C22×D511yescharacteristic
273C22×Dic3C22×D511yescharacteristic
274C2×C4×D3—22no—
275C2×C4×D3—22no—
276C2×C4×D3—22no—
277C2×C4×D3—22no—
278C2×C4×D3—22no—
279C2×C4×D3—22no—
280C2×C4×D3Dic1014yes—
281C2×C4×D3C4×D514yes—
282C2×C4×D3C22⋊D514yes—
283C3×C4⋊C4—54no—
284C3×C4⋊C4—104no—
285C3×C4⋊C4—102no—
286C3×C42—22no—
287(C2×D3)⋊C4—58no—
288(C2×D3)⋊C4—104no—
289C4⋊Dic3—54no—
290C4⋊Dic3—102no—
291C4⋊Dic3—104no—
292Dic3⋊C4—104no—
293Dic3⋊C4—104no—
294C4×Dic3—22no—
295C4×Dic3—22no—
296C4×Dic3—22no—
297C4×Dic3—58no—
298C4×Dic3—104no—
299C23×C5—32no—
300C23×C5—32no—
301C23×C5—32no—
302C23×C5—61no—
303C23×C5—61no—
304C23×C5—61no—
305C23×C5—61no—
306C23×C5C23×D311yescharacteristic
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—32no—
312C2×C4×C5—32no—
313C2×C4×C5—32no—
314C2×C4×C5—316no—
315C2×C4×C5—32no—
316C2×C4×C5—32no—
317C2×C4×C5—68no—
318C2×C4×C5—68no—
319C2×C4×C5—61no—
320C2×C4×C5—61no—
321C2×C4×C5—61no—
322C2×C4×C5—61no—
323C2×C4×C5C2×C4×D312yes—
324C2×C4×C5D3×D412yes—
325C2×C4×C5#23712yes—
326C2×C4×C5D3×Q812yes—
327C2×C4×C5#23912yes—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—22no—
331C2×Dic5—22no—
332C2×Dic5—22no—
333C2×Dic5—34no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5—62no—
338C2×Dic5—62no—
339C2×Dic5C2×C4×D314yes—
340C23×C4—31no—
341C23×C4—31no—
342C23×C4—31no—
343#117—158no—
344#117—304no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4—51no—
347C2×C4⋊C4—52no—
348C2×C4⋊C4—151no—
349C2×C4⋊C4—152no—
350C2×C4⋊C4—152no—
351C2×C4⋊C4—151no—
352C2×C4⋊C4—152no—
353C2×C22⋊C4—152no—
354C2×C22⋊C4—152no—
355C2×C42—31no—
356C2×C42—31no—
357C2×C42—31no—
358C2×C42—64no—
359C2×C42—152no—
360C2×C42—152no—
361C2×C42D3×D511yescharacteristic
362#95—52no—
363#95—152no—
364#95—152no—
365#95—152no—
366C2×C3×C5C22×C4⋊C411yescharacteristic
367C2×C3×C5C4×#4111yescharacteristic
368C2×C3×C5C4×#4111yescharacteristic
369C2×C3×C5#52511yescharacteristic
370C2×C3×C5#52511yescharacteristic
371C2×C3×C5#53311yescharacteristic
372C2×C3×C5#53311yescharacteristic
373C5×D3—24no—
374C23×C3C23×D511yescharacteristic
375C22×D3—21no—
376C22×D3—21no—
377C22×D3—21no—
378C22×D3—21no—
379C22×D3C2×Dic1012yes—
380C22×D3C2×C4×D512yes—
381C22×D3C2×C22⋊D512yes—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—54no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4C2×Dic1012yes—
393C2×C3×C4C2×C4×D512yes—
394C2×C3×C4#70912yes—
395C2×C3×C4#70912yes—
396C2×C3×C4C2×C22⋊D512yes—
397C2×Dic3—21no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—54no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3C2×Dic1012yes—
408C2×Dic3C2×C4×D512yes—
409C2×Dic3#70912yes—
410C2×Dic3#70912yes—
411C2×Dic3C2×C22⋊D512yes—
412C4×D3—28no—
413C4×D3—28no—
414C4×D3#683116yescomplemented
415C22×C5—34no—
416C22×C5—62no—
417C22×C5—62no—
418C22×C5—62no—
419C22×C5—62no—
420C22×C5—62no—
421C22×C5—62no—
422C22×C5C22×C4×D311yescharacteristic
423C22×C5C2×D3×D411yescharacteristic
424C22×C5C2×#23711yescharacteristic
425C22×C5C2×D3×Q811yescharacteristic
426C22×C5C2×#23911yescharacteristic
427C22×C5D3×#4111yescharacteristic
428C22×C5D3×#4111yescharacteristic
429C4×C5—22no—
430C4×C5—22no—
431C4×C5—34no—
432C4×C5—62no—
433C4×C5—62no—
434C4×C5D3×C4⋊C414yes—
435Dic5—24no—
436Dic5—42no—
437Dic5—64no—
438Dic5—122no—
439C24—31no—
440C22×C4—31no—
441C22×C4—34no—
442C22×C4—34no—
443C22×C4—34no—
444C22×C4—31no—
445C22×C4—31no—
446C22×C4—52no—
447C22×C4—52no—
448C22×C4—62no—
449C22×C4—62no—
450C22×C4—62no—
451C22×C4—62no—
452C22×C4—62no—
453C22×C4—62no—
454C22×C4—152no—
455C22×C4—152no—
456C22×C4C2×D3×D511yescharacteristic
457C22×C4C2×D3×D511yescharacteristic
458C22×C4C2×D3×D511yescharacteristic
459C4⋊C4—54no—
460C4⋊C4—104no—
461C4⋊C4—102no—
462C4⋊C4—154no—
463C4⋊C4—304no—
464C4⋊C4—304no—
465C4⋊C4—304no—
466C4⋊C4—302no—
467C22⋊C4—158no—
468C22⋊C4—304no—
469C42—22no—
470C42—62no—
471C42—62no—
472C42—62no—
473C42—158no—
474C42—304no—
475C3×C5#229611yescharacteristic, complemented, Hall
476C22×C3C22×Dic1011yescharacteristic
477C22×C3C22×C4×D511yescharacteristic
478C22×C3C2×#70911yescharacteristic
479C22×C3C2×#70911yescharacteristic
480C22×C3C2×#70911yescharacteristic
481C22×C3C2×#70911yescharacteristic
482C22×C3C22×C22⋊D511yescharacteristic
483C2×D3—22no—
484C2×D3—22no—
485C2×D3—22no—
486C2×D3—22no—
487C2×D3—22no—
488C2×D3—22no—
489C2×D3C2×#68314yes—
490C3×C4—22no—
491C3×C4—22no—
492C3×C4—104no—
493C3×C4—202no—
494C3×C4C2×#68314yes—
495Dic3—22no—
496Dic3—22no—
497Dic3—104no—
498Dic3—202no—
499Dic3C2×#68314yes—
500C2×C5—64no—
501C2×C5C2×D3×C4⋊C411yescharacteristic
502C2×C5C4×#23711yescharacteristic
503C2×C5C4×#23911yescharacteristic
504C2×C5#560611yescharacteristic
505C2×C5#562711yescharacteristic
506C2×C5#568811yescharacteristic
507C2×C5#572811yescharacteristic
508C23—32no—
509C23—32no—
510C23—32no—
511C23—61no—
512C23—61no—
513C23—61no—
514C23—61no—
515C23C22×D3×D511yescharacteristic
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—32no—
523C2×C4—316no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—54no—
527C2×C4—68no—
528C2×C4—68no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—102no—
534C2×C4—102no—
535C2×C4—102no—
536C2×C4—102no—
537C2×C4—102no—
538C2×C4—154no—
539C2×C4—302no—
540C2×C4—302no—
541C2×C4—302no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4#676512yes—
545C2×C4D3×Dic1012yes—
546C2×C4#676912yes—
547C2×C4C4×D3×D512yes—
548C2×C4D3×C22⋊D512yes—
549C2×C3#6580411yescharacteristic
550C2×C3#6580411yescharacteristic
551C2×C3C4×#70911yescharacteristic
552C2×C3C4×#70911yescharacteristic
553C2×C3C22×#68311yescharacteristic
554C2×C3#6612511yescharacteristic
555C2×C3#6612511yescharacteristic
556D3—24no—
557C5#7596311yescharacteristic, complemented, Sylow
558C22—34no—
559C22—62no—
560C22—62no—
561C22—62no—
562C22—62no—
563C22—62no—
564C22—62no—
565C22C2×#676511yescharacteristic
566C22C2×D3×Dic1011yescharacteristic
567C22C2×#676911yescharacteristic
568C22C2×C4×D3×D511yescharacteristic
569C22D3×#70911yescharacteristic
570C22D3×#70911yescharacteristic
571C22C2×D3×C22⋊D511yescharacteristic
572C4—22no—
573C4—22no—
574C4—34no—
575C4—62no—
576C4—62no—
577C4—104no—
578C4—202no—
579C4—304no—
580C4—602no—
581C4D3×#68314yes—
582C3#1061380011yescharacteristic, complemented, Sylow
583C2—64no—
584C2#1175246611yescharacteristic
585C2#1175247811yescharacteristic
586C2C4×#676511yescharacteristic
587C2C4×#676911yescharacteristic
588C2C2×D3×#68311yescharacteristic
589C2#1175434111yescharacteristic
590C2#1175435211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2296
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #11751029C2semidirect
5. C3×#65217C2semidirect
6. #11748858C2semidirect
7. #11748857C2semidirect
10. #11748645C2semidirect
11. Dic3×#683C2semidirect
34. #91338C4semidirect
50. #65217D3semidirect
73. C4⋊Dic15C2×C4semidirect
79. C3×C4⋊Dic5C2×C4semidirect
86. Dic3×Dic5C2×C4semidirect
159. C4×C5×D3C4⋊C4semidirect
221. C4⋊Dic5C4×D3semidirect
414. C4×D3#683semidirect
475. C3×C5#2296semidirect
557. C5#75963semidirect
582. C3#10613800semidirect

Maximal subgroups

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

subgroupindex
C2×C42×C5×D32
C2×#913382
#117510292
C3×#652172
#117488582
#117488572
#117487222
#117487162
#117486452
Dic3×#6832
#106138003
#759635