Finite Group Databasebeta

← #14329453

Subgroups — #14329453

Order 1920.

1664 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91829C211yesmaximal, characteristic
2C2×C4×#1220C212yesmaximal, complemented
3C2×#91770C212yesmaximal, complemented
4C3×C5×#386C211yesmaximal, characteristic, complemented
5#11751321C211yesmaximal, characteristic, complemented
6#11751058C212yesmaximal, complemented
7#11751058C212yesmaximal, complemented
8#11750766C212yesmaximal, complemented
9#11750750C212yesmaximal, complemented
10#10606410—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C22×#1220C2212yes—
14C22×#1220C2212yes—
15C23×Dic15C2211yescharacteristic
16C22×D60C2211yescharacteristic
17C22×C4×D15C2212yes—
18C2×C3×C5×C22⋊C4C2212yes—
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×#6719C2212yes—
21C2×#6719C2211yescharacteristic
22#91829C418yescomplemented
23C4×#1220—28no—
24C2×#6714C2212yes—
25C2×#6714C2212yes—
26C2×#6714C2212yes—
27C2×#6712C2212yes—
28C2×#6712C2212yes—
29C2×C4×Dic15C2212yes—
30C2×C4×Dic15C2212yes—
31C2×C4×Dic15C2211yescharacteristic
32#91770—28no—
33C3×C5×#95C2212yes—
34#91115C2212yes—
35#74679—51nomaximal, Hall
36C2×#4086—31no—
37C2×C4×C22⋊D5—32no—
38C2×#4027—32no—
39C5×#386D311yescharacteristic, complemented
40#65509—31no—
41#65246—32no—
42#65246—32no—
43#64954—32no—
44#64938—32no—
45C24×C3×C5C2311yescharacteristic
46C24×C3×C5C2311yescharacteristic
47C23×D15C2312yes—
48C2×C3×C5×D4—41no—
49C2×C3×C5×D4—41no—
50C2×C3×C5×D4C2×C414yescomplemented
51C22×C3×C4×C5—24no—
52C22×C3×C4×C5—41no—
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2312yes—
56C2×#1220—24no—
57C2×#1220—24no—
58C2×#1220—24no—
59C2×#1220—24no—
60C2×#1220C2×C418yescomplemented
61C2×#1220C2×C418yescomplemented
62C22×Dic15—24no—
63C22×Dic15—41no—
64C22×Dic15C2312yes—
65C22×Dic15C2312yes—
66C22×Dic15C2312yes—
67C2×D60—41no—
68C2×D60—41no—
69C2×D60C2×C414yescomplemented
70C2×C4×D15—24no—
71C2×C4×D15—24no—
72C2×C4×D15—42no—
73C3×C5×C22⋊C4—24no—
74C3×C5×C22⋊C4—41no—
75#6719—24no—
76#6719—41no—
77#6714—24no—
78#6714—24no—
79#6714—42no—
80#6712—24no—
81#6712D418yescomplemented
82C4×Dic15—24no—
83C4×Dic15—24no—
84C4×Dic15C2×C414yescomplemented
85C2×#940—51no—
86C2×C4×#67—52no—
87C2×#67⋊C4—52no—
88C3×#386D511yescharacteristic, complemented
89#5220—51no—
90#4957—52no—
91#4957—52no—
92#4665—52no—
93#4649—52no—
94C22×C5×D4C2×D311yescharacteristic
95C23×C4×C5C2×D311yescharacteristic
96C22×C22⋊D5—32no—
97C22×C22⋊D5—32no—
98C23×Dic5—31no—
99C22×D20—31no—
100C22×C4×D5—32no—
101C2×C5×C22⋊C4C2×D312yes—
102C2×C5×C22⋊C4C2×D311yescharacteristic
103C2×C22⋊Dic5—32no—
104C2×C22⋊Dic5—31no—
105#4086—38no—
106C4×C22⋊D5—68no—
107C2×#685—32no—
108C2×#685—32no—
109C2×#685—32no—
110C2×#683—32no—
111C2×#683—32no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—32no—
115#4027—68no—
116C5×#95C2×D312yes—
117#3963—32no—
118#2366—151noSylow
119C23×C3×C5—22no—
120C23×C3×C5—22no—
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5—21no—
126C23×C3×C5—21no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C22×C412yes—
129C23×C3×C5C2411yescharacteristic
130C22×D15—22no—
131C22×D15—22no—
132C22×D15—22no—
133C22×D15—22no—
134C22×D15—22no—
135C22×D15—22no—
136C22×D15C22×C414yes—
137C3×C5×D4—44no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—44no—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C2×D414yes—
148#1220—216no—
149#1220—216no—
150C2×Dic15—22no—
151C2×Dic15—22no—
152C2×Dic15—22no—
153C2×Dic15—22no—
154C2×Dic15—22no—
155C2×Dic15—44no—
156C2×Dic15C22×C414yes—
157C2×Dic15C2×D414yes—
158C2×Dic15C2×D414yes—
159C2×Dic15#4114yes—
160D60—44no—
161C4×D15—48no—
162C22×C3×D4C2×D511yescharacteristic
163C23×C3×C4C2×D511yescharacteristic
164C22×#67—52no—
165C22×#67—52no—
166C23×Dic3—51no—
167C22×D12—51no—
168C22×C4×D3—52no—
169C2×C3×C22⋊C4C2×D512yes—
170C2×C3×C22⋊C4C2×D511yescharacteristic
171C2×#217—52no—
172C2×#217—51no—
173#940—58no—
174C4×#67—108no—
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4—52no—
177C2×(C2×D3)⋊C4—52no—
178C2×Dic3⋊C4—52no—
179C2×Dic3⋊C4—52no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3—52no—
183#67⋊C4—108no—
184C3×#95C2×D512yes—
185C3⋊#95—52no—
186C24×C5C22×D311yescharacteristic
187C24×C5C22×D311yescharacteristic
188C23×D5—32no—
189C2×C5×D4—41no—
190C2×C5×D4—41no—
191C2×C5×D4C4×D314yescomplemented
192C22×C4×C5—24no—
193C22×C4×C5—41no—
194C22×C4×C5C22×D312yes—
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D312yes—
197C2×C22⋊D5—38no—
198C2×C22⋊D5—38no—
199C2×C22⋊D5—64no—
200C2×C22⋊D5—64no—
201C2×C22⋊D5—64no—
202C2×C22⋊D5—64no—
203C22×Dic5—32no—
204C22×Dic5—32no—
205C22×Dic5—32no—
206C22×Dic5—64no—
207C22×Dic5—121no—
208C2×D20—34no—
209C2×D20—121no—
210C2×D20—121no—
211C2×C4×D5—64no—
212C2×C4×D5—64no—
213C2×C4×D5—122no—
214C5×C22⋊C4—24no—
215C5×C22⋊C4—41no—
216C22⋊Dic5—64no—
217C22⋊Dic5—121no—
218#685—64no—
219#685—64no—
220#685—122no—
221#683—38no—
222#683—64no—
223C4×Dic5—34no—
224C4×Dic5—64no—
225C4×Dic5—64no—
226C2×#127—151no—
227C2×C4×D4—152no—
228C2×C4×D4—152no—
229#390—152no—
230#390—152no—
231#386—151no—
232#386—152no—
233#386D1511yescharacteristic, complemented
234C4×C4⋊C4—152no—
235C22×C3×C5—24no—
236C22×C3×C5—24no—
237C22×C3×C5—22no—
238C22×C3×C5—22no—
239C22×C3×C5—41no—
240C22×C3×C5—41no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5C23×C411yescharacteristic
246C22×C3×C5C22×D412yes—
247C22×C3×C5C2×#4112yes—
248C22×C3×C5H(5,𝔽2)11yescharacteristic
249C22×C3×C5H(5,𝔽2)11yescharacteristic
250C2×D15—24no—
251C2×D15—24no—
252C2×D15—24no—
253C2×D15—42no—
254C2×D15—42no—
255C2×D15—42no—
256C2×D15—42no—
257C3×C4×C5—22no—
258C3×C4×C5—24no—
259C3×C4×C5—42no—
260Dic15—24no—
261Dic15—42no—
262Dic15C4×D418yescomplemented
263C24×C3C22×D511yescharacteristic
264C24×C3C22×D511yescharacteristic
265C23×D3—52no—
266C2×C3×D4—41no—
267C2×C3×D4—41no—
268C2×C3×D4C4×D514yescomplemented
269C22×C3×C4—24no—
270C22×C3×C4—41no—
271C22×C3×C4C22×D512yes—
272C22×C3×C4C22×D511yescharacteristic
273C22×C3×C4C22×D512yes—
274C2×#67—58no—
275C2×#67—58no—
276C2×#67—104no—
277C2×#67—104no—
278C2×#67—104no—
279C2×#67—104no—
280C22×Dic3—52no—
281C22×Dic3—52no—
282C22×Dic3—52no—
283C22×Dic3—104no—
284C22×Dic3—201no—
285C2×D12—54no—
286C2×D12—201no—
287C2×D12—201no—
288C2×C4×D3—104no—
289C2×C4×D3—104no—
290C2×C4×D3—202no—
291C3×C22⋊C4—24no—
292C3×C22⋊C4—41no—
293#217—104no—
294#217—201no—
295(C2×D3)⋊C4—104no—
296(C2×D3)⋊C4—104no—
297(C2×D3)⋊C4—202no—
298Dic3⋊C4—58no—
299Dic3⋊C4—104no—
300C4×Dic3—54no—
301C4×Dic3—104no—
302C4×Dic3—104no—
303C23×C5—22no—
304C23×C5—22no—
305C23×C5—21no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—22no—
310C23×C5—22no—
311C23×C5C2×C4×D312yes—
312C23×C5C2×C4×D312yes—
313C23×C5C23×D311yescharacteristic
314C22×D5—34no—
315C22×D5—62no—
316C22×D5—62no—
317C22×D5—62no—
318C22×D5—62no—
319C22×D5—62no—
320C22×D5—62no—
321C5×D4—44no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—21no—
325C2×C4×C5—21no—
326C2×C4×C5—22no—
327C2×C4×C5—22no—
328C2×C4×C5—22no—
329C2×C4×C5—44no—
330C2×C4×C5C2×C4×D312yes—
331C2×C4×C5D3×D414yes—
332C22⋊D5—616no—
333C22⋊D5—616no—
334C2×Dic5—34no—
335C2×Dic5—34no—
336C2×Dic5—34no—
337C2×Dic5—34no—
338C2×Dic5—62no—
339C2×Dic5—62no—
340C2×Dic5—62no—
341C2×Dic5—62no—
342C2×Dic5—62no—
343C2×Dic5—124no—
344D20—124no—
345C4×D5—128no—
346C22×D4—152no—
347C22×D4—152no—
348C22×D4—151no—
349C22×D4C2×D1511yescharacteristic
350C23×C4—151no—
351C23×C4—152no—
352C23×C4C2×D1511yescharacteristic
353#127—158no—
354C4×D4—308no—
355C4×D4—308no—
356C2×C4⋊C4—152no—
357C2×C4⋊C4—152no—
358C2×C22⋊C4—152no—
359C2×C22⋊C4—152no—
360C2×C22⋊C4—152no—
361C2×C22⋊C4—151no—
362C2×C22⋊C4—152no—
363C2×C22⋊C4C2×D1512yes—
364C2×C22⋊C4C2×D1511yescharacteristic
365C2×C42—151no—
366C2×C42—152no—
367C2×C42—152no—
368#95—152no—
369#95C2×D1512yes—
370C2×C3×C5—42no—
371C2×C3×C5—42no—
372C2×C3×C5C2×C4×D412yes—
373C2×C3×C5#51811yescharacteristic
374C2×C3×C5D4211yescharacteristic
375C2×C3×C5#55012yes—
376C2×C3×C5#55911yescharacteristic
377D15—44no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—22no—
385C23×C3—22no—
386C23×C3C2×C4×D512yes—
387C23×C3C2×C4×D512yes—
388C23×C3C23×D511yescharacteristic
389C22×D3—54no—
390C22×D3—102no—
391C22×D3—102no—
392C22×D3—102no—
393C22×D3—102no—
394C22×D3—102no—
395C22×D3—102no—
396C3×D4—44no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—44no—
405C2×C3×C4C2×C4×D512yes—
406C2×C3×C4D4×D514yes—
407#67—1016no—
408#67—1016no—
409C2×Dic3—54no—
410C2×Dic3—54no—
411C2×Dic3—54no—
412C2×Dic3—54no—
413C2×Dic3—102no—
414C2×Dic3—102no—
415C2×Dic3—102no—
416C2×Dic3—102no—
417C2×Dic3—102no—
418C2×Dic3—204no—
419D12—204no—
420C4×D3—208no—
421C22×C5—22no—
422C22×C5—22no—
423C22×C5—24no—
424C22×C5—24no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5—41no—
429C22×C5—42no—
430C22×C5—42no—
431C22×C5C22×C4×D311yescharacteristic
432C22×C5C2×D3×D412yes—
433C22×C5#100411yescharacteristic
434C22×C5#100411yescharacteristic
435C22×C5D3×#4112yes—
436C2×D5—64no—
437C2×D5—64no—
438C2×D5—64no—
439C2×D5—122no—
440C2×D5—122no—
441C2×D5—122no—
442C2×D5—122no—
443C4×C5—22no—
444C4×C5—24no—
445C4×C5—42no—
446Dic5—38no—
447Dic5—64no—
448Dic5—122no—
449C24—152no—
450C24C22×D1511yescharacteristic
451C24C22×D1511yescharacteristic
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—158no—
455C2×D4—158no—
456C2×D4—154no—
457C2×D4—304no—
458C2×D4—304no—
459C2×D4—304no—
460C2×D4—304no—
461C2×D4—601no—
462C2×D4—601no—
463C2×D4C4×D1514yescomplemented
464C22×C4—24no—
465C22×C4—41no—
466C22×C4—152no—
467C22×C4—152no—
468C22×C4—152no—
469C22×C4—304no—
470C22×C4—304no—
471C22×C4—304no—
472C22×C4—602no—
473C22×C4—601no—
474C22×C4C22×D1512yes—
475C22×C4C22×D1511yescharacteristic
476C22×C4C22×D1512yes—
477C4⋊C4—158no—
478C4⋊C4—304no—
479C22⋊C4—24no—
480C22⋊C4—41no—
481C22⋊C4—304no—
482C22⋊C4—304no—
483C22⋊C4—304no—
484C22⋊C4—602no—
485C22⋊C4—601no—
486C42—154no—
487C42—304no—
488C42—304no—
489C3×C5#236611yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—24no—
493C22×C3—24no—
494C22×C3—41no—
495C22×C3—41no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3C22×C4×D511yescharacteristic
501C22×C3C2×D4×D512yes—
502C22×C3#414411yescharacteristic
503C22×C3#414411yescharacteristic
504C22×C3D5×#4112yes—
505C2×D3—104no—
506C2×D3—104no—
507C2×D3—104no—
508C2×D3—202no—
509C2×D3—202no—
510C2×D3—202no—
511C2×D3—202no—
512C3×C4—22no—
513C3×C4—24no—
514C3×C4—42no—
515Dic3—58no—
516Dic3—104no—
517Dic3—202no—
518C2×C5—42no—
519C2×C5—42no—
520C2×C5#548611yescharacteristic
521C2×C5C4×D3×D412yes—
522C2×C5#559011yescharacteristic
523C2×C5#559912yes—
524C2×C5#566411yescharacteristic
525D5—124no—
526C23—22no—
527C23—22no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—22no—
533C23—22no—
534C23—154no—
535C23—302no—
536C23—302no—
537C23—302no—
538C23—302no—
539C23—302no—
540C23—302no—
541C23C2×C4×D1512yes—
542C23C2×C4×D1512yes—
543C23C23×D1511yescharacteristic
544D4—44no—
545D4—3016no—
546D4—3016no—
547D4—604no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—44no—
556C2×C4—154no—
557C2×C4—154no—
558C2×C4—154no—
559C2×C4—154no—
560C2×C4—302no—
561C2×C4—302no—
562C2×C4—302no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4—608no—
566C2×C4—604no—
567C2×C4C2×C4×D1512yes—
568C2×C4D4×D1514yes—
569C2×C3—42no—
570C2×C3—42no—
571C2×C3#6582011yescharacteristic
572C2×C3C4×D4×D512yes—
573C2×C3#6592411yescharacteristic
574C2×C3#6593312yes—
575C2×C3#6599811yescharacteristic
576D3—204no—
577C5#7467911yescharacteristic, complemented, Sylow
578C22—24no—
579C22—24no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—42no—
585C22—42no—
586C22—41no—
587C22—41no—
588C22—304no—
589C22—304no—
590C22—304no—
591C22—602no—
592C22—602no—
593C22—602no—
594C22—602no—
595C22C22×C4×D1511yescharacteristic
596C22C2×D4×D1512yes—
597C22#9209511yescharacteristic
598C22#9209511yescharacteristic
599C22#41×D1512yes—
600C4—24no—
601C4—22no—
602C4—42no—
603C4—158no—
604C4—304no—
605C4—602no—
606C3#1060641011yescharacteristic, complemented, Sylow
607C2—42no—
608C2—42no—
609C2—604no—
610C2#1175624511yescharacteristic
611C2C4×D4×D1512yes—
612C2#1175634911yescharacteristic
613C2#1175635812yes—
614C2#1175642311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C5×#386C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91829C2
hypercenter#386D15
hypocenterC3×C5#2366
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1220C2semidirect
3. C2×#91770C2semidirect
4. C3×C5×#386C2semidirect
5. #11751321C2semidirect
6. #11751058C2semidirect
7. #11751058C2semidirect
8. #11750766C2semidirect
9. #11750750C2semidirect
22. #91829C4semidirect
39. C5×#386D3semidirect
50. C2×C3×C5×D4C2×C4semidirect
60. C2×#1220C2×C4semidirect
61. C2×#1220C2×C4semidirect
69. C2×D60C2×C4semidirect
81. #6712D4semidirect
84. C4×Dic15C2×C4semidirect
88. C3×#386D5semidirect
191. C2×C5×D4C4×D3semidirect
233. #386D15semidirect
262. Dic15C4×D4semidirect
268. C2×C3×D4C4×D5semidirect
463. C2×D4C4×D15semidirect
489. C3×C5#2366semidirect
577. C5#74679semidirect
606. C3#10606410semidirect

Maximal subgroups

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

subgroupindex
C2×#918292
C2×C4×#12202
C2×#917702
C3×C5×#3862
#117513212
#117510582
#117507662
#117507502
#106064103
#746795