Finite Group Databasebeta

← #14329498

Subgroups — #14329498

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×C3×#4086C211yesmaximal, characteristic
2C2×#91559C212yesmaximal, complemented
3C2×Dic3×C22⋊D5C212yesmaximal, complemented
4#11751321C211yesmaximal, characteristic, complemented
5C5×#5220C211yesmaximal, characteristic, complemented
6#11749489C212yesmaximal, complemented
7#11749489C212yesmaximal, complemented
8#11748896C212yesmaximal, complemented
9#11748638C212yesmaximal, complemented
10#10606410—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C23×Dic15C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C22×C3×C22⋊D5C2212yes—
15C22×C3×C22⋊D5C2212yes—
16C22×C3×D20C2211yescharacteristic
17C22×D5×Dic3C2212yes—
18C2×#6719C2212yes—
19C2×#6719C2211yescharacteristic
20C2×C5×#217C2212yes—
21C2×C5×#217C2211yescharacteristic
22C3×#4086C418yescomplemented
23C2×C3×C4×Dic5C2211yescharacteristic
24#91559—28no—
25Dic3×C22⋊D5—28no—
26C2×#6668C2212yes—
27C2×#6668C2212yes—
28C2×#6665C2212yes—
29C2×#6665C2212yes—
30C2×#6665C2212yes—
31C2×Dic3×Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33#91115C2212yes—
34C5×C3⋊#95C2212yes—
35#83173—51nomaximal, Hall
36C2×#4086D311yescharacteristic
37C2×C4×C22⋊D5—32no—
38C2×#4027—32no—
39C5×#386—31no—
40#65509—31no—
41#65246—32no—
42#65246—32no—
43#64954—32no—
44#64938—32no—
45C24×C3×C5C2311yescharacteristic
46C24×C3×C5C2311yescharacteristic
47C23×C3×D5C2312yes—
48C2×C3×C5×D4—41no—
49C2×C3×C5×D4—41no—
50C2×C3×C5×D4C2×C414yescomplemented
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15—24no—
53C22×Dic15—41no—
54C22×Dic15C2312yes—
55C22×Dic15C2312yes—
56C22×C5×Dic3—24no—
57C22×C5×Dic3—41no—
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2312yes—
60C2×C3×C22⋊D5—24no—
61C2×C3×C22⋊D5—24no—
62C2×C3×C22⋊D5—24no—
63C2×C3×C22⋊D5—24no—
64C2×C3×C22⋊D5C2×C418yescomplemented
65C2×C3×C22⋊D5C2×C418yescomplemented
66C22×C3×Dic5C2312yes—
67C2×C3×D20—41no—
68C2×C3×D20—41no—
69C2×C3×D20C2×C414yescomplemented
70C2×D5×Dic3—24no—
71C2×D5×Dic3—24no—
72C2×D5×Dic3—42no—
73#6719—24no—
74#6719—41no—
75C5×#217—24no—
76C5×#217—41no—
77C3×C4×Dic5C2×C414yescomplemented
78#6668—24no—
79#6668D418yescomplemented
80#6665—24no—
81#6665—24no—
82#6665—42no—
83Dic3×Dic5—24no—
84Dic3×Dic5—24no—
85C2×C3×#127—51no—
86C2×D4×Dic3—52no—
87C2×D4×Dic3—52no—
88#5221—52no—
89#5221—52no—
90#5220—51no—
91#5220—52no—
92#5220D511yescharacteristic, complemented
93C4×C4⋊Dic3—52no—
94C22×C5×D4C2×D311yescharacteristic
95C23×C4×C5—31no—
96C22×C22⋊D5C2×D312yes—
97C22×C22⋊D5C2×D312yes—
98C23×Dic5—31no—
99C22×D20C2×D311yescharacteristic
100C22×C4×D5—32no—
101C2×C5×C22⋊C4—32no—
102C2×C5×C22⋊C4—31no—
103C2×C22⋊Dic5—32no—
104C2×C22⋊Dic5—31no—
105#4086Dic318yescomplemented
106C4×C22⋊D5—68no—
107C2×#685—32no—
108C2×#685—32no—
109C2×#685—32no—
110C2×#683—32no—
111C2×#683—32no—
112C2×C4×Dic5—32no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5C2×D311yescharacteristic
115#4027—68no—
116C5×#95—32no—
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×C3×D5—22no—
131C22×C3×D5—22no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5—22no—
135C22×C3×D5—22no—
136C22×C3×D5C22×C414yes—
137C3×C5×D4—44no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5C22×C412yes—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—44no—
147C2×Dic15C2×D414yes—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—44no—
154C2×C5×Dic3C2×D414yes—
155C3×C22⋊D5—216no—
156C3×C22⋊D5—216no—
157C2×C3×Dic5C22×C414yes—
158C2×C3×Dic5C2×D414yes—
159C2×C3×Dic5#4114yes—
160C3×D20—44no—
161D5×Dic3—48no—
162C22×C3×D4—52no—
163C22×C3×D4—52no—
164C22×C3×D4—51no—
165C22×C3×D4C2×D511yescharacteristic
166C23×Dic3—51no—
167C23×Dic3—52no—
168C23×Dic3C2×D511yescharacteristic
169C3×#127—58no—
170C2×C3×C42—51no—
171C2×#217—52no—
172C2×#217—52no—
173C2×#217—52no—
174C2×#217—51no—
175C2×#217—52no—
176C2×#217C2×D512yes—
177C2×#217C2×D511yescharacteristic
178D4×Dic3—108no—
179D4×Dic3—108no—
180C2×C4⋊Dic3—52no—
181C2×C4⋊Dic3—52no—
182C2×C4×Dic3—52no—
183C2×C4×Dic3—52no—
184C3⋊#95—52no—
185C3⋊#95C2×D512yes—
186C24×C5C22×D311yescharacteristic
187C24×C5C22×D311yescharacteristic
188C23×D5C22×D312yes—
189C2×C5×D4—41no—
190C2×C5×D4—41no—
191C2×C5×D4C2×Dic314yescomplemented
192C22×C4×C5—32no—
193C22×C4×C5—32no—
194C22×C4×C5—64no—
195C22×C4×C5—121no—
196C22×C4×C5C22×D311yescharacteristic
197C2×C22⋊D5—24no—
198C2×C22⋊D5—24no—
199C2×C22⋊D5—24no—
200C2×C22⋊D5—24no—
201C2×C22⋊D5C2×Dic318yescomplemented
202C2×C22⋊D5C2×Dic318yescomplemented
203C22×Dic5—32no—
204C22×Dic5—32no—
205C22×Dic5—64no—
206C22×Dic5—121no—
207C22×Dic5C22×D312yes—
208C2×D20—41no—
209C2×D20—41no—
210C2×D20C2×Dic314yescomplemented
211C2×C4×D5—64no—
212C2×C4×D5—64no—
213C2×C4×D5—122no—
214C5×C22⋊C4—64no—
215C5×C22⋊C4—121no—
216C22⋊Dic5—64no—
217C22⋊Dic5—121no—
218#685—64no—
219#685—64no—
220#685—122no—
221#683—38no—
222#683—64no—
223C4×Dic5—64no—
224C4×Dic5—64no—
225C4×Dic5C2×Dic314yescomplemented
226C2×#127—51no—
227C2×C4×D4—152no—
228C2×C4×D4—152no—
229#390—152no—
230#390—152no—
231#386—31no—
232#386—152no—
233#386—151no—
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×C3×D5—24no—
251C2×C3×D5—24no—
252C2×C3×D5—24no—
253C2×C3×D5—42no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5—42no—
257C3×C4×C5—22no—
258Dic15—24no—
259Dic15—42no—
260C3×Dic5C4×D418yescomplemented
261C5×Dic3—24no—
262C5×Dic3—42no—
263C24×C3—52no—
264C24×C3C22×D511yescharacteristic
265C24×C3C22×D511yescharacteristic
266C2×C3×D4—41no—
267C2×C3×D4—41no—
268C2×C3×D4—58no—
269C2×C3×D4—58no—
270C2×C3×D4—54no—
271C2×C3×D4—104no—
272C2×C3×D4—104no—
273C2×C3×D4—104no—
274C2×C3×D4—104no—
275C2×C3×D4—201no—
276C2×C3×D4—201no—
277C2×C3×D4C4×D514yescomplemented
278C22×C3×C4—52no—
279C22×C3×C4C22×D511yescharacteristic
280C22×Dic3—24no—
281C22×Dic3—41no—
282C22×Dic3—52no—
283C22×Dic3—52no—
284C22×Dic3—104no—
285C22×Dic3—104no—
286C22×Dic3—104no—
287C22×Dic3—202no—
288C22×Dic3—201no—
289C22×Dic3C22×D512yes—
290C22×Dic3C22×D512yes—
291C3×C42—54no—
292#217—24no—
293#217—41no—
294#217—104no—
295#217—104no—
296#217—104no—
297#217—202no—
298#217—201no—
299C4⋊Dic3—58no—
300C4⋊Dic3—104no—
301C4×Dic3—104no—
302C4×Dic3—104no—
303C23×C5—22no—
304C23×C5—22no—
305C23×C5—22no—
306C23×C5—22no—
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5C22×Dic312yes—
312C23×C5C22×Dic312yes—
313C23×C5C23×D311yescharacteristic
314C22×D5—22no—
315C22×D5—22no—
316C22×D5—22no—
317C22×D5—22no—
318C22×D5—22no—
319C22×D5—22no—
320C22×D5C22×Dic314yes—
321C5×D4—44no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—34no—
325C2×C4×C5—62no—
326C2×C4×C5—62no—
327C2×C4×C5—62no—
328C2×C4×C5—62no—
329C2×C4×C5—62no—
330C2×C4×C5—124no—
331C2×C4×C5C22×Dic312yes—
332C22⋊D5—216no—
333C22⋊D5—216no—
334C2×Dic5—34no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5—62no—
338C2×Dic5—62no—
339C2×Dic5—62no—
340C2×Dic5—124no—
341C2×Dic5D3×D414yes—
342C2×Dic5#23714yes—
343C2×Dic5C22×Dic314yes—
344D20—44no—
345C4×D5—128no—
346C22×D4—52no—
347C22×D4—52no—
348C22×D4—51no—
349C22×D4D3×D511yescharacteristic
350C23×C4—31no—
351C23×C4—152no—
352C23×C4—151no—
353#127—58no—
354C4×D4—308no—
355C4×D4—308no—
356C2×C4⋊C4—152no—
357C2×C4⋊C4—152no—
358C2×C22⋊C4—32no—
359C2×C22⋊C4—31no—
360C2×C22⋊C4—152no—
361C2×C22⋊C4—152no—
362C2×C22⋊C4—152no—
363C2×C22⋊C4—152no—
364C2×C22⋊C4—151no—
365C2×C42—51no—
366C2×C42—152no—
367C2×C42—152no—
368#95—32no—
369#95—152no—
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
377C3×D5—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×C3—54no—
387C23×C3—102no—
388C23×C3—102no—
389C23×C3—102no—
390C23×C3—102no—
391C23×C3—102no—
392C23×C3—102no—
393C23×C3C2×C4×D512yes—
394C23×C3C2×C4×D512yes—
395C23×C3C23×D511yescharacteristic
396C3×D4—44no—
397C3×D4—1016no—
398C3×D4—1016no—
399C3×D4—204no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—54no—
403C2×C3×C4—54no—
404C2×C3×C4—54no—
405C2×C3×C4C2×C4×D512yes—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—22no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—44no—
412C2×Dic3—54no—
413C2×Dic3—102no—
414C2×Dic3—102no—
415C2×Dic3—102no—
416C2×Dic3—102no—
417C2×Dic3—102no—
418C2×Dic3—208no—
419C2×Dic3—204no—
420C2×Dic3D4×D514yes—
421C22×C5—24no—
422C22×C5—24no—
423C22×C5—22no—
424C22×C5—22no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5—41no—
428C22×C5—41no—
429C22×C5—42no—
430C22×C5—42no—
431C22×C5C2×D3×D412yes—
432C22×C5C2×#23712yes—
433C22×C5#100411yescharacteristic
434C22×C5#100411yescharacteristic
435C22×C5C23×Dic311yescharacteristic
436C2×D5—24no—
437C2×D5—24no—
438C2×D5—24no—
439C2×D5—42no—
440C2×D5—42no—
441C2×D5—42no—
442C2×D5—42no—
443C4×C5—22no—
444C4×C5—64no—
445C4×C5—122no—
446Dic5—64no—
447Dic5—122no—
448Dic5D4×Dic318yescomplemented
449C24—52no—
450C24C2×D3×D511yescharacteristic
451C24C2×D3×D511yescharacteristic
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—58no—
455C2×D4—58no—
456C2×D4—54no—
457C2×D4—104no—
458C2×D4—104no—
459C2×D4—104no—
460C2×D4—104no—
461C2×D4—201no—
462C2×D4—201no—
463C2×D4D5×Dic314yescomplemented
464C22×C4—32no—
465C22×C4—32no—
466C22×C4—52no—
467C22×C4—64no—
468C22×C4—121no—
469C22×C4—152no—
470C22×C4—152no—
471C22×C4—304no—
472C22×C4—304no—
473C22×C4—304no—
474C22×C4—602no—
475C22×C4—601no—
476C22×C4C2×D3×D511yescharacteristic
477C4⋊C4—158no—
478C4⋊C4—304no—
479C22⋊C4—64no—
480C22⋊C4—121no—
481C22⋊C4—304no—
482C22⋊C4—304no—
483C22⋊C4—304no—
484C22⋊C4—602no—
485C22⋊C4—601no—
486C42—54no—
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×C3—104no—
501C22×C3—104no—
502C22×C3—104no—
503C22×C3—202no—
504C22×C3—202no—
505C22×C3—202no—
506C22×C3—202no—
507C22×C3C22×C4×D511yescharacteristic
508C22×C3C2×D4×D512yes—
509C22×C3#414411yescharacteristic
510C22×C3#414411yescharacteristic
511C22×C3D5×#4112yes—
512C3×C4—22no—
513C3×C4—58no—
514Dic3—24no—
515Dic3—42no—
516Dic3—104no—
517Dic3—202no—
518C2×C5—42no—
519C2×C5—42no—
520C2×C5#571311yescharacteristic
521C2×C5#571711yescharacteristic
522C2×C5#571812yes—
523C2×C5C2×D4×Dic312yes—
524C2×C5#579811yescharacteristic
525D5—44no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—54no—
535C23—102no—
536C23—102no—
537C23—102no—
538C23—102no—
539C23—102no—
540C23—102no—
541C23C2×D5×Dic312yes—
542C23C2×D5×Dic312yes—
543C23C22×D3×D511yescharacteristic
544D4—44no—
545D4—1016no—
546D4—1016no—
547D4—204no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—34no—
551C2×C4—54no—
552C2×C4—54no—
553C2×C4—54no—
554C2×C4—62no—
555C2×C4—62no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—124no—
560C2×C4—154no—
561C2×C4—302no—
562C2×C4—302no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4—302no—
566C2×C4—608no—
567C2×C4—604no—
568C2×C4C2×D5×Dic312yes—
569C2×C3—42no—
570C2×C3—42no—
571C2×C3—204no—
572C2×C3#6582011yescharacteristic
573C2×C3C4×D4×D512yes—
574C2×C3#6592411yescharacteristic
575C2×C3#6593312yes—
576C2×C3#6599811yescharacteristic
577C5#8317311yescharacteristic, complemented, Sylow
578C22—24no—
579C22—24no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—42no—
588C22—104no—
589C22—104no—
590C22—104no—
591C22—202no—
592C22—202no—
593C22—202no—
594C22—202no—
595C22D3×D4×D512yes—
596C22D5×#23712yes—
597C22C22×D5×Dic311yescharacteristic
598C22#9204911yescharacteristic
599C22#9204911yescharacteristic
600C4—22no—
601C4—58no—
602C4—64no—
603C4—122no—
604C4—304no—
605C4—602no—
606C3#1060641011yescharacteristic, complemented, Sylow
607C2—42no—
608C2—42no—
609C2—204no—
610C2D4×D5×Dic312yes—
611C2#1175486311yescharacteristic
612C2#1175492912yes—
613C2#1175505811yescharacteristic
614C2#1175540611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C3×#4086C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2366
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91559C2semidirect
3. C2×Dic3×C22⋊D5C2semidirect
4. #11751321C2semidirect
5. C5×#5220C2semidirect
6. #11749489C2semidirect
7. #11749489C2semidirect
8. #11748896C2semidirect
9. #11748638C2semidirect
22. C3×#4086C4semidirect
50. C2×C3×C5×D4C2×C4semidirect
64. C2×C3×C22⋊D5C2×C4semidirect
65. C2×C3×C22⋊D5C2×C4semidirect
69. C2×C3×D20C2×C4semidirect
77. C3×C4×Dic5C2×C4semidirect
79. #6668D4semidirect
92. #5220D5semidirect
105. #4086Dic3semidirect
191. C2×C5×D4C2×Dic3semidirect
201. C2×C22⋊D5C2×Dic3semidirect
202. C2×C22⋊D5C2×Dic3semidirect
210. C2×D20C2×Dic3semidirect
225. C4×Dic5C2×Dic3semidirect
260. C3×Dic5C4×D4semidirect
277. C2×C3×D4C4×D5semidirect
448. Dic5D4×Dic3semidirect
463. C2×D4D5×Dic3semidirect
489. C3×C5#2366semidirect
577. C5#83173semidirect
606. C3#10606410semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40862
C2×#915592
C2×Dic3×C22⋊D52
#117513212
C5×#52202
#117494892
#117488962
#117486382
#106064103
#831735