Finite Group Databasebeta

← #14331629

Subgroups — #14331629

Order 1920.

1888 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6819C211yesmaximal, characteristic, complemented
2C2×#91559C212yesmaximal, complemented
3C2×#91396C211yesmaximal, characteristic, complemented
4C5×#5222C211yesmaximal, characteristic, complemented
5C3×#65512C211yesmaximal, characteristic, complemented
6#11749522C212yesmaximal, complemented
7#11749510C212yesmaximal, complemented
8#11749487C212yesmaximal, complemented
9#11748793C211yesmaximal, characteristic, complemented
10#11748670C211yesmaximal, characteristic, complemented
11#11748578C211yesmaximal, characteristic, complemented
12#10608620—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C22×#1220C2212yes—
15C23×Dic15C2212yes—
16C2×#6819—28no—
17C2×#6819—24no—
18C22×C4×D15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C3×C22⋊D5C2212yes—
21C22×#1202C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C2×C5×#217C2212yes—
24C2×C5×#217C2212yes—
25C2×C5×Dic3⋊C4C2211yescharacteristic
26C2×C3×C22⋊Dic5C2212yes—
27C2×C3×#685C2211yescharacteristic
28#91559—28no—
29C2×#6668C2212yes—
30C2×#6667C2211yescharacteristic
31C2×#6667C2212yes—
32C2×#6665C2212yes—
33C2×Dic3×Dic5C2211yescharacteristic
34C2×Dic3×Dic5C2212yes—
35#91396—24no—
36C5×C3⋊#95C2211yescharacteristic
37C3×#3963C2211yescharacteristic
38#90994C2212yes—
39#90994C2212yes—
40#76665—51nomaximal, Hall
41C22×#711—31no—
42C2×#4039—31no—
43C2×#4027—32no—
44C5×#394—31no—
45#65512D311yescharacteristic, complemented
46#65268—31no—
47#65249—32no—
48#65248—32no—
49C22⋊C4×Dic5—32no—
50#64962—31no—
51#64955—31no—
52C24×C3×C5C2312yes—
53C23×D15C2311yescharacteristic
54C23×C3×D5C2311yescharacteristic
55C2×C3×C5×D4—24no—
56C2×C3×C5×D4—22no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—24no—
59C2×#1220—24no—
60C2×#1220—24no—
61C22×Dic15—24no—
62C22×Dic15—24no—
63C22×Dic15D418yescomplemented
64C22×Dic15C2312yes—
65C22×Dic15C2311yescharacteristic
66#6819—232no—
67C2×C4×D15—24no—
68C2×C4×D15D414yescomplemented
69C2×Dic30—22no—
70C2×Dic30—24no—
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C22×C5×Dic3C2311yescharacteristic
74C2×C3×C22⋊D5—24no—
75C2×C3×C22⋊D5—24no—
76C2×C3×C22⋊D5—24no—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2312yes—
79C2×#1202—22no—
80C2×#1202—22no—
81C2×#1202—22no—
82C2×D5×Dic3—22no—
83C2×D5×Dic3—24no—
84C5×#217—24no—
85C5×#217—24no—
86C5×Dic3⋊C4—22no—
87C3×C22⋊Dic5—24no—
88C3×#685—22no—
89#6668—24no—
90#6667—22no—
91#6667—24no—
92#6665—24no—
93Dic3×Dic5—22no—
94Dic3×Dic5—24no—
95C22×#237—51no—
96C2×D4×Dic3—52no—
97C2×#67⋊C4—51no—
98C3×#392—51no—
99#5223—52no—
100#5222D511yescharacteristic, complemented
101#4961—52no—
102#4947—51no—
103Dic3×C22⋊C4—52no—
104#4666—51no—
105#4656—51no—
106C22×C5×D4C2×D311yescharacteristic
107C22×C22⋊D5—32no—
108C22×C22⋊D5C2×D312yes—
109C23×Dic5—32no—
110C2×#711—64no—
111C2×#711—68no—
112C22×D20—31no—
113C22×C4×D5—31no—
114C22×C4×D5—31no—
115C22×Dic10—31no—
116C2×C5×C4⋊C4—31no—
117C2×C5×C22⋊C4—32no—
118C2×C5×C22⋊C4—32no—
119C2×C22⋊Dic5C2×D312yes—
120C2×#685—32no—
121C2×#685—31no—
122C2×#685—32no—
123C2×#685C2×D311yescharacteristic
124C2×#683—32no—
125C2×C4×Dic5—32no—
126C2×C4×Dic5—31no—
127#4039—64no—
128#4027—68no—
129C5×#95—31no—
130#3963—32no—
131#3963—32no—
132#3963C2×D311yescharacteristic
133#2388—151noSylow
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5C2×D414yes—
141C23×C3×C5C2411yescharacteristic
142C22×D15—22no—
143C22×D15—22no—
144C22×D15—21no—
145C22×D15—21no—
146C22×D15C2×D412yes—
147C22×C3×D5—22no—
148C22×C3×D5—21no—
149C22×C3×D5—21no—
150C22×C3×D5—22no—
151C22×C3×D5#4112yescomplemented
152C3×C5×D4—28no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5C2×D412yes—
155#1220—216no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—216no—
159C2×Dic15C2×D414yes—
160C2×Dic15C2×D414yes—
161C2×Dic15C2×D412yes—
162C4×D15—28no—
163Dic30—28no—
164C2×C5×Dic3—21no—
165C2×C5×Dic3—21no—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—21no—
168C2×C5×Dic3—22no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3—22no—
171C2×C5×Dic3#4112yescomplemented
172C3×C22⋊D5—216no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—21no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5#4114yescomplemented
178#1202—28no—
179D5×Dic3—44no—
180C22×C3×D4—52no—
181C22×C3×D4C2×D511yescharacteristic
182C22×#67—52no—
183C22×#67—51no—
184C23×Dic3—52no—
185C23×Dic3—51no—
186C2×#237—104no—
187C2×#237—108no—
188C22×C4×D3—51no—
189C22×Dic6—51no—
190C2×C3×C22⋊C4—52no—
191C2×C3×C22⋊C4—51no—
192C2×#217—52no—
193C2×#217C2×D512yes—
194C2×#217C2×D512yes—
195D4×Dic3—108no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—51no—
198C2×C4⋊Dic3—52no—
199C2×Dic3⋊C4C2×D511yescharacteristic
200C2×C4×Dic3—52no—
201C2×C4×Dic3—51no—
202#67⋊C4—104no—
203C3×#95—51no—
204C3⋊#95—52no—
205C3⋊#95—52no—
206C3⋊#95C2×D511yescharacteristic
207C24×C5C22×D312yes—
208C23×D5—31no—
209C23×D5C22×D311yescharacteristic
210C2×C5×D4—24no—
211C2×C5×D4—22no—
212C22×C4×C5—31no—
213C22×C4×C5—31no—
214C22×C4×C5—32no—
215C22×C4×C5C22×D311yescharacteristic
216C2×C22⋊D5—24no—
217C2×C22⋊D5—24no—
218C2×C22⋊D5—24no—
219C2×C22⋊D5—64no—
220C2×C22⋊D5—64no—
221C2×C22⋊D5—64no—
222C22×Dic5—31no—
223C22×Dic5—38no—
224C22×Dic5—32no—
225C22×Dic5—64no—
226C22×Dic5—64no—
227C22×Dic5C22×D311yescharacteristic
228C22×Dic5C22×D312yes—
229#711—632no—
230C2×D20—62no—
231C2×D20—62no—
232C2×D20—62no—
233C2×C4×D5—34no—
234C2×C4×D5—64no—
235C2×C4×D5—64no—
236C2×C4×D5—62no—
237C2×Dic10—64no—
238C2×Dic10—62no—
239C5×C4⋊C4—62no—
240C5×C22⋊C4—64no—
241C5×C22⋊C4—64no—
242C22⋊Dic5—24no—
243#685—22no—
244#685—62no—
245#685—64no—
246#685—64no—
247#683—64no—
248C4×Dic5—64no—
249C4×Dic5—62no—
250C22×#41—151no—
251C2×C4×D4—152no—
252C2×C4×D4—151no—
253#395—151no—
254#394—31no—
255#394—152no—
256#393—151no—
257#392—51no—
258#392—152no—
259C4×C22⋊C4—151no—
260C4×C22⋊C4—152no—
261C22×C3×C5—24no—
262C22×C3×C5—24no—
263C22×C3×C5—24no—
264C22×C3×C5—42no—
265C22×C3×C5—42no—
266C22×C3×C5—42no—
267C22×C3×C5—42no—
268C22×C3×C5C22×D411yescharacteristic
269C22×C3×C5C22×D412yes—
270C22×C3×C5C2×#4111yescharacteristic
271C22×C3×C5C2×#4111yescharacteristic
272C22×C3×C5C2×#4112yes—
273C2×D15—22no—
274C2×D15—22no—
275C2×D15—22no—
276C2×D15—42no—
277C2×D15—42no—
278C2×C3×D5—22no—
279C2×C3×D5—24no—
280C2×C3×D5—41no—
281C2×C3×D5—42no—
282C2×C3×D5—41no—
283C3×C4×C5—22no—
284Dic15—24no—
285Dic15#12014yes—
286C3×Dic5—24no—
287C3×Dic5—41no—
288C5×Dic3—22no—
289C5×Dic3—41no—
290C5×Dic3—42no—
291C24×C3—51no—
292C24×C3C22×D512yes—
293C23×D3—51no—
294C2×C3×D4—24no—
295C2×C3×D4—22no—
296C2×C3×D4—104no—
297C2×C3×D4—104no—
298C2×C3×D4—104no—
299C22×C3×C4—52no—
300C22×C3×C4—51no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—102no—
303C2×#67—102no—
304C2×#67—104no—
305C2×#67—104no—
306C2×#67—104no—
307C2×#67—102no—
308C22×Dic3—51no—
309C22×Dic3—58no—
310C22×Dic3—52no—
311C22×Dic3—102no—
312C22×Dic3—104no—
313C22×Dic3—104no—
314C22×Dic3—104no—
315C22×Dic3C22×D512yes—
316C22×Dic3C22×D511yescharacteristic
317C22×Dic3C22×D511yescharacteristic
318#237—1032no—
319C2×C4×D3—54no—
320C2×C4×D3—104no—
321C2×Dic6—104no—
322C2×Dic6—102no—
323C3×C22⋊C4—104no—
324C3×C22⋊C4—102no—
325#217—24no—
326#217—24no—
327#217—104no—
328(C2×D3)⋊C4—104no—
329(C2×D3)⋊C4—102no—
330C4⋊Dic3—104no—
331Dic3⋊C4—22no—
332C4×Dic3—102no—
333C4×Dic3—104no—
334C23×C5—22no—
335C23×C5—22no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5D3×D414yes—
341C23×C5C23×D311yescharacteristic
342C22×D5—21no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—21no—
346C22×D5—32no—
347C22×D5—62no—
348C22×D5—62no—
349C22×D5—61no—
350C22×D5—61no—
351C22×D5#23712yescomplemented
352C5×D4—28no—
353C2×C4×C5—22no—
354C2×C4×C5—32no—
355C2×C4×C5—61no—
356C2×C4×C5—61no—
357C2×C4×C5—62no—
358C2×C4×C5—62no—
359C2×C4×C5—61no—
360C2×C4×C5—62no—
361C2×C4×C5—62no—
362C2×C4×C5D3×D412yes—
363C22⋊D5—216no—
364C22⋊D5—616no—
365C2×Dic5—22no—
366C2×Dic5—22no—
367C2×Dic5—21no—
368C2×Dic5—22no—
369C2×Dic5—32no—
370C2×Dic5—34no—
371C2×Dic5—34no—
372C2×Dic5—616no—
373C2×Dic5—62no—
374C2×Dic5—62no—
375C2×Dic5#23714yescomplemented
376D20—68no—
377C4×D5—68no—
378C4×D5—124no—
379Dic10—68no—
380C2×#41—308no—
381C2×#41—304no—
382C22×Q8—151no—
383C22×D4—52no—
384C22×D4—151no—
385C22×D4—152no—
386C22×D4D3×D511yescharacteristic
387C23×C4—151no—
388C23×C4—152no—
389C23×C4—151no—
390C4×D4—308no—
391C4×D4—304no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—152no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—32no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—51no—
398C2×C22⋊C4—151no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—152no—
401C2×C42—151no—
402C2×C42—152no—
403#95—31no—
404#95—51no—
405#95—152no—
406#95—152no—
407C2×C3×C5—44no—
408C2×C3×C5C2×#12011yescharacteristic
409C2×C3×C5#52511yescharacteristic
410C2×C3×C5#52512yes—
411C2×C3×C5#53212yes—
412C2×C3×C5#53211yescharacteristic
413D15—42no—
414C3×D5—42no—
415C23×C3—22no—
416C23×C3—22no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—22no—
421C23×C3—52no—
422C23×C3—102no—
423C23×C3—101no—
424C23×C3—101no—
425C23×C3—102no—
426C23×C3D4×D514yes—
427C23×C3C23×D511yescharacteristic
428C22×D3—52no—
429C22×D3—102no—
430C22×D3—101no—
431C22×D3—102no—
432C22×D3—101no—
433C3×D4—28no—
434C3×D4—1016no—
435C2×C3×C4—22no—
436C2×C3×C4—54no—
437C2×C3×C4—102no—
438C2×C3×C4—102no—
439C2×C3×C4—101no—
440C2×C3×C4—102no—
441C2×C3×C4D4×D512yes—
442#67—108no—
443#67—1016no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—22no—
447C2×Dic3—21no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—22no—
451C2×Dic3—52no—
452C2×Dic3—54no—
453C2×Dic3—54no—
454C2×Dic3—1016no—
455C2×Dic3—102no—
456C2×Dic3—102no—
457C2×Dic3—204no—
458C2×Dic3#71112yescomplemented
459C4×D3—108no—
460Dic6—108no—
461C22×C5—24no—
462C22×C5—24no—
463C22×C5—24no—
464C22×C5—42no—
465C22×C5—42no—
466C22×C5—42no—
467C22×C5—42no—
468C22×C5C2×D3×D411yescharacteristic
469C22×C5C2×D3×D412yes—
470C22×C5C2×#23712yes—
471C22×C5C2×#23711yescharacteristic
472C22×C5D3×#4111yescharacteristic
473C2×D5—24no—
474C2×D5—22no—
475C2×D5—41no—
476C2×D5—41no—
477C2×D5—42no—
478C2×D5—62no—
479C2×D5—62no—
480C2×D5—62no—
481C2×D5—122no—
482C2×D5—122no—
483C4×C5—22no—
484C4×C5—62no—
485C4×C5—121no—
486C4×C5—122no—
487Dic5—24no—
488Dic5—34no—
489Dic5—41no—
490Dic5—64no—
491C24—51no—
492C24—151no—
493C24C2×D3×D512yes—
494#41—3032no—
495C2×Q8—304no—
496C2×Q8—302no—
497C2×D4—24no—
498C2×D4—22no—
499C2×D4—104no—
500C2×D4—104no—
501C2×D4—104no—
502C2×D4—302no—
503C2×D4—302no—
504C2×D4—302no—
505C2×D4—304no—
506C2×D4—304no—
507C2×D4—304no—
508C22×C4—31no—
509C22×C4—32no—
510C22×C4—31no—
511C22×C4—52no—
512C22×C4—51no—
513C22×C4—151no—
514C22×C4—158no—
515C22×C4—152no—
516C22×C4—154no—
517C22×C4—304no—
518C22×C4—304no—
519C22×C4—302no—
520C22×C4—304no—
521C22×C4—304no—
522C22×C4C2×D3×D511yescharacteristic
523C4⋊C4—62no—
524C4⋊C4—304no—
525C22⋊C4—64no—
526C22⋊C4—64no—
527C22⋊C4—104no—
528C22⋊C4—102no—
529C22⋊C4—304no—
530C22⋊C4—302no—
531C22⋊C4—304no—
532C42—302no—
533C42—304no—
534C3×C5#238811yescharacteristic, complemented, Hall
535C22×C3—24no—
536C22×C3—24no—
537C22×C3—24no—
538C22×C3—42no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—42no—
542C22×C3—102no—
543C22×C3—104no—
544C22×C3—201no—
545C22×C3—202no—
546C22×C3—201no—
547C22×C3C2×D4×D512yes—
548C22×C3C2×D4×D511yescharacteristic
549C22×C3C2×#71111yescharacteristic
550C22×C3D5×#4112yes—
551C22×C3D5×#4111yescharacteristic
552C2×D3—102no—
553C2×D3—102no—
554C2×D3—102no—
555C2×D3—202no—
556C2×D3—202no—
557C3×C4—22no—
558C3×C4—104no—
559C3×C4—201no—
560Dic3—22no—
561Dic3—41no—
562Dic3—42no—
563Dic3—54no—
564Dic3—104no—
565C2×C5—44no—
566C2×C5#558612yes—
567C2×C5D3×#12011yescharacteristic
568C2×C5#559612yes—
569C2×C5#560611yescharacteristic
570C2×C5#571611yescharacteristic
571D5—42no—
572D5—122no—
573C23—22no—
574C23—22no—
575C23—22no—
576C23—22no—
577C23—22no—
578C23—22no—
579C23—52no—
580C23—102no—
581C23—101no—
582C23—101no—
583C23—102no—
584C23—152no—
585C23—302no—
586C23—301no—
587C23—301no—
588C23—302no—
589C23#679014yes—
590C23C22×D3×D511yescharacteristic
591Q8—308no—
592D4—28no—
593D4—1016no—
594D4—308no—
595D4—3016no—
596C2×C4—22no—
597C2×C4—32no—
598C2×C4—54no—
599C2×C4—61no—
600C2×C4—61no—
601C2×C4—62no—
602C2×C4—62no—
603C2×C4—62no—
604C2×C4—62no—
605C2×C4—61no—
606C2×C4—102no—
607C2×C4—102no—
608C2×C4—102no—
609C2×C4—101no—
610C2×C4—152no—
611C2×C4—154no—
612C2×C4—154no—
613C2×C4—308no—
614C2×C4—3016no—
615C2×C4—302no—
616C2×C4—302no—
617C2×C4—604no—
618C2×C4#679012yes—
619C2×C3—44no—
620C2×C3—202no—
621C2×C3D5×#12011yescharacteristic
622C2×C3#6593012yes—
623C2×C3#6594011yescharacteristic
624C2×C3#6599012yes—
625C2×C3#6600211yescharacteristic
626D3—202no—
627C5#7666511yescharacteristic, complemented, Sylow
628C22—24no—
629C22—24no—
630C22—24no—
631C22—42no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—102no—
636C22—104no—
637C22—202no—
638C22—201no—
639C22—201no—
640C22—302no—
641C22—302no—
642C22—302no—
643C22—602no—
644C22—602no—
645C22D5×#23711yescharacteristic
646C22D5×#23712yes—
647C22D3×#71111yescharacteristic
648C22C2×#679011yescharacteristic
649C22C2×#679012yes—
650C4—22no—
651C4—62no—
652C4—104no—
653C4—122no—
654C4—121no—
655C4—154no—
656C4—201no—
657C4—304no—
658C3#1060862011yescharacteristic, complemented, Sylow
659C2—44no—
660C2—202no—
661C2—602no—
662C2#1175481512yes—
663C2#1175482012yes—
664C2#1175482211yescharacteristic
665C2#1175507011yescharacteristic
666C2#1175544111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC22×C3×C5×D4C22
hypercenterC22×D4D3×D5
hypocenterC3×C5#2388
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6819C2semidirect
2. C2×#91559C2semidirect
3. C2×#91396C2semidirect
4. C5×#5222C2semidirect
5. C3×#65512C2semidirect
6. #11749522C2semidirect
7. #11749510C2semidirect
8. #11749487C2semidirect
9. #11748793C2semidirect
10. #11748670C2semidirect
11. #11748578C2semidirect
45. #65512D3semidirect
63. C22×Dic15D4semidirect
68. C2×C4×D15D4semidirect
100. #5222D5semidirect
151. C22×C3×D5#41semidirect
171. C2×C5×Dic3#41semidirect
177. C2×C3×Dic5#41semidirect
351. C22×D5#237semidirect
375. C2×Dic5#237semidirect
458. C2×Dic3#711semidirect
534. C3×C5#2388semidirect
627. C5#76665semidirect
658. C3#10608620semidirect

Maximal subgroups

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

subgroupindex
C22×#68192
C2×#915592
C2×#913962
C5×#52222
C3×#655122
#117495222
#117495102
#117494872
#117487932
#117486702
#117485782
#106086203
#766655