Finite Group Databasebeta

← #14416723

Subgroups — #14416723

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91821C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
3#11754414C211yesmaximal, characteristic, complemented
4C5×#5215C211yesmaximal, characteristic, complemented
5#11749004C212yesmaximal, complemented
6#11748998C212yesmaximal, complemented
7#11748979C212yesmaximal, complemented
8#11748975C212yesmaximal, complemented
9#11748470C211yesmaximal, characteristic, complemented
10#11748413C211yesmaximal, characteristic, complemented
11Dic5×#208C211yesmaximal, characteristic, complemented
12#10610645—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C23×C3×Dic5—21no—
16C2×#6716C2212yes—
17#91821C418yescomplemented
18C2×#6715C2212yes—
19C2×#6710C2211yescharacteristic
20C5×#926C2211yescharacteristic
21C2×C5×#208C2211yescharacteristic
22C2×C3×C22⋊Dic5—21no—
23C3×D4×Dic5—21no—
24C3×D4×Dic5—21no—
25C3×D4×Dic5C2212yes—
26C3×D4×Dic5C2212yes—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29#91552—21no—
30#91552—21no—
31#91418C2211yescharacteristic, complemented
32#91418C2211yescharacteristic, complemented
33C4×#1200—21no—
34#91386—21no—
35#91333C2211yescharacteristic, complemented
36#91333C2211yescharacteristic, complemented
37C5×#832C2212yes—
38C5×#832C2212yes—
39#90989C2212yescomplemented
40#90986C2212yescomplemented
41#90974C2212yescomplemented
42#90968C2212yescomplemented
43#90952C2212yescomplemented
44Dic5×C3⋊C8C2212yescomplemented
45C4×#932—51nomaximal, Hall
46C2×D4×Dic5D311yescharacteristic, complemented
47C2×#4078—31no—
48#65856—31no—
49C5×#418—31no—
50#65422—31no—
51M16×Dic5—31no—
52#65284—31no—
53#65074—32no—
54#65047—32no—
55#65046—32no—
56#65045—32no—
57C24×C3×C5—21no—
58C2×C3×C5×D4—21no—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4C2×C414yescomplemented
61C2×C3×C5×D4C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64#6817—22no—
65#6817C2×C414yescomplemented
66C2×D60C2311yescharacteristic
67C2×C4×D15—21no—
68C2×Dic30C2311yescharacteristic
69C22×C3×Dic5—21no—
70C22×C3×Dic5—22no—
71C22×C3×Dic5—22no—
72C22×C3×Dic5—44no—
73C22×C3×Dic5D411yescharacteristic
74C22×C3×Dic5D411yescharacteristic
75C2×#1200—21no—
76C2×#1200—21no—
77#6716C2×C418yescomplemented
78#6715C2×C418yescomplemented
79#6710C2×C414yescomplemented
80C2×C3⋊#168C2312yes—
81C5×#217—21no—
82C5×C4⋊Dic3C2311yescharacteristic
83C5×C4⋊Dic3C2311yescharacteristic
84C4×C5×Dic3—21no—
85C5×#208—22no—
86C2×C5×C3⋊C8C2312yes—
87C3×C22⋊Dic5—22no—
88C3×C22⋊Dic5—22no—
89C3×C4⋊Dic5—21no—
90C3×C4⋊Dic5C2312yes—
91C3×C4×Dic5D411yescharacteristic
92C3×C4×Dic5D411yescharacteristic
93C3×C4×Dic5C2311yescharacteristic
94C3×C4×Dic5C2311yescharacteristic
95#6669—21no—
96#6669—21no—
97#6667—21no—
98#6667—21no—
99Dic3×Dic5—21no—
100Dic3×Dic5—21no—
101C2×C3×C4×D4—51no—
102C2×#932—51no—
103C4×#235—51no—
104#5215D511yescharacteristic, complemented
105#5018—52no—
106C4×#214—52no—
107#5014—52no—
108C4×#213—52no—
109#4966—51no—
110#4964—51no—
111C4×#208—51no—
112C22×C5×D4C2×D311yescharacteristic
113C23×Dic5—21no—
114C2×#709—31no—
115C2×C5×M16—31no—
116C5×#117—31no—
117C2×C22⋊Dic5—21no—
118D4×Dic5—21no—
119D4×Dic5—21no—
120D4×Dic5C2×D312yes—
121D4×Dic5C2×D312yes—
122C2×#687—32no—
123#4078—38no—
124C2×#686—32no—
125C2×C4⋊Dic5C2×D311yescharacteristic
126C2×C4×Dic5C2×D311yescharacteristic
127C2×#681—31no—
128#4039—31no—
129#4039—31no—
130#4033—31no—
131#4033—31no—
132#4027—61no—
133#4027—61no—
134#4018—61no—
135C42×D5—61no—
136C5×#102—32no—
137C5×#102—32no—
138#3953—32no—
139#3948—32no—
140#3947—32no—
141C8×Dic5—32no—
142#3940—32no—
143#3939—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5—24no—
146C23×C3×C5—22no—
147C23×C3×C5—42no—
148C23×C3×C5—42no—
149C23×C3×C5C2×D411yescharacteristic
150C22×D15—21no—
151C3×C5×D4—24no—
152C3×C5×D4—22no—
153C3×C5×D4C22×C414yes—
154C2×C3×C4×C5C22×C412yes—
155C2×C3×C4×C5C2×D411yescharacteristic
156C2×C3×C4×C5#4112yes—
157C2×C3×C4×C5C2411yescharacteristic
158#1220—24no—
159C2×Dic15—21no—
160D60—21no—
161D60C22×C412yescomplemented
162C4×D15—24no—
163Dic30—21no—
164Dic30C22×C412yescomplemented
165C2×C5×Dic3—21no—
166C2×C5×Dic3—21no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—41no—
170C2×C3×Dic5—44no—
171C2×C3×Dic5—42no—
172C2×C3×Dic5—44no—
173C2×C3×Dic5C2×D411yescharacteristic
174C2×C3×Dic5C2×D411yescharacteristic
175C2×C3×Dic5C2×D411yescharacteristic
176C2×C3×Dic5C2×D411yescharacteristic
177#1200—42no—
178#1200—42no—
179C3⋊#168C22×C414yescomplemented
180C5×C3⋊C8—22no—
181C22×C3×D4C2×D511yescharacteristic
182C23×C3×C4—101no—
183C2×#235—51no—
184C3×C4×D4—52no—
185C3×C4×D4—52no—
186C3×C4×D4—101no—
187C3×C4×D4—101no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C22⋊C4—101no—
190C2×C3×C42—51no—
191C2×#214—52no—
192#932—58no—
193C2×#213—52no—
194C4×#67—101no—
195C4×#67—101no—
196#926C2×D511yescharacteristic
197C2×#208—51no—
198C2×#208C2×D511yescharacteristic
199C4×D12—51no—
200C4×D12—51no—
201#872—101no—
202C42×D3—101no—
203C4×Dic6—51no—
204C4×Dic6—51no—
205#832C2×D512yes—
206#832C2×D512yes—
207#810—52no—
208#809—52no—
209#808—52no—
210#807—52no—
211#803—52no—
212C4×C3⋊C8—52no—
213C24×C5—21no—
214C2×C5×D4—22no—
215C2×C5×D4—21no—
216C2×C5×D4C4×D314yescomplemented
217C2×C5×D4C22×D312yes—
218C22×C4×C5C22×D311yescharacteristic
219C2×C22⋊D5—61no—
220C22×Dic5—21no—
221C22×Dic5—22no—
222C22×Dic5—22no—
223C22×Dic5—44no—
224C22×Dic5#6711yescharacteristic
225C22×Dic5#6711yescharacteristic
226#709—34no—
227#709—62no—
228C2×D20—31no—
229C2×C4×D5—61no—
230C2×C4×D5—61no—
231C2×C4×D5—61no—
232C2×Dic10—31no—
233C5×M16—62no—
234C2×C5×C8—32no—
235C5×C4⋊C4—31no—
236C5×C4⋊C4—31no—
237C5×C22⋊C4—61no—
238C42×C5—61no—
239C22⋊Dic5—22no—
240C22⋊Dic5—22no—
241#687—38no—
242#686—38no—
243#685—61no—
244#685—61no—
245C4⋊Dic5—21no—
246C4⋊Dic5C22×D312yes—
247#683—61no—
248#683—61no—
249C4×Dic5—61no—
250C4×Dic5—61no—
251C4×Dic5#6711yescharacteristic
252C4×Dic5#6711yescharacteristic
253C4×Dic5C22×D311yescharacteristic
254C4×Dic5C22×D311yescharacteristic
255#681—34no—
256C2×#168—32no—
257C2×AGL(1,ℤ/8)—151no—
258C4×#41—151no—
259C2×C4×D4—51no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—31no—
266#417—151no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5—24no—
271C22×C3×C5—48no—
272C22×C3×C5—42no—
273C22×C3×C5—42no—
274C22×C3×C5C4×D412yes—
275C22×C3×C5C22×D411yescharacteristic
276C2×D15—22no—
277C2×D15—41no—
278C2×D15—41no—
279C3×C4×C5C4×D412yes—
280C3×C4×C5C23×C411yescharacteristic
281C3×C4×C5C2×#4111yescharacteristic
282Dic15—22no—
283C3×Dic5—21no—
284C3×Dic5—21no—
285C3×Dic5—21no—
286C3×Dic5—42no—
287C3×Dic5AGL(1,ℤ/8)12yescomplemented
288C5×Dic3—41no—
289C5×Dic3—41no—
290C24×C3—21no—
291C2×C3×D4—21no—
292C2×C3×D4—22no—
293C2×C3×D4C4×D514yescomplemented
294C2×C3×D4C22×D512yes—
295C22×C3×C4—51no—
296C22×C3×C4—51no—
297C22×C3×C4—102no—
298C22×C3×C4—102no—
299C22×C3×C4—101no—
300C22×C3×C4—204no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—101no—
303#235—54no—
304#235—102no—
305C2×D12—51no—
306C2×C4×D3—101no—
307C2×C4×D3—101no—
308C2×C4×D3—101no—
309C2×Dic6—51no—
310C3×C4⋊C4—52no—
311C3×C4⋊C4—101no—
312C3×C22⋊C4—102no—
313C3×C22⋊C4—102no—
314C3×C42—51no—
315C3×C42—51no—
316C3×C42—51no—
317C3×C42—51no—
318#217—21no—
319#214—58no—
320#213—58no—
321(C2×D3)⋊C4—101no—
322(C2×D3)⋊C4—101no—
323C4⋊Dic3C22×D511yescharacteristic
324C4⋊Dic3C22×D511yescharacteristic
325Dic3⋊C4—101no—
326Dic3⋊C4—101no—
327C4×Dic3—21no—
328C4×Dic3—101no—
329C4×Dic3—101no—
330#208—22no—
331#208—54no—
332C2×C3⋊C8—52no—
333C2×C3⋊C8C22×D512yes—
334C23×C5—24no—
335C23×C5—22no—
336C23×C5—42no—
337C23×C5—42no—
338C23×C5C2×#6711yescharacteristic
339C22×D5—61no—
340C5×D4—24no—
341C5×D4—22no—
342C5×D4C2×C4×D314yes—
343C2×C4×C5—61no—
344C2×C4×C5—61no—
345C2×C4×C5C2×C4×D312yes—
346C2×C4×C5#23512yes—
347C2×C4×C5C2×#6711yescharacteristic
348C2×C4×C5C23×D311yescharacteristic
349C22⋊D5—64no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—41no—
353C2×Dic5—44no—
354C2×Dic5—42no—
355C2×Dic5—44no—
356C2×Dic5—61no—
357C2×Dic5C2×#6711yescharacteristic
358C2×Dic5C2×#6711yescharacteristic
359C2×Dic5C2×#6711yescharacteristic
360C2×Dic5C2×#6711yescharacteristic
361D20—32no—
362D20—61no—
363C4×D5—64no—
364C4×D5—122no—
365C4×D5—122no—
366Dic10—32no—
367Dic10—61no—
368C5×C8—62no—
369#168—34no—
370C2×#41—151no—
371C22×D4D3×D511yescharacteristic
372C23×C4—101no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—31no—
377C2×M16—151no—
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—52no—
381C4×D4—52no—
382C4×D4—101no—
383C4×D4—101no—
384C4×D4—151no—
385C4×D4—151no—
386C4×D4—301no—
387C4×D4—301no—
388#117—31no—
389#117—301no—
390C2×C4⋊C4—51no—
391C2×C22⋊C4—101no—
392C2×C42—51no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—152no—
397#102—32no—
398#102—32no—
399#102—152no—
400#97—152no—
401C4×C8—152no—
402C2×C3×C5—22no—
403C2×C3×C5—44no—
404C2×C3×C5C2×C4×D411yescharacteristic
405C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
406C2×C3×C5#57511yescharacteristic
407D15—42no—
408C23×C3—22no—
409C23×C3—24no—
410C23×C3—42no—
411C23×C3—42no—
412C23×C3D4×D511yescharacteristic
413C22×D3—101no—
414C3×D4—22no—
415C3×D4—24no—
416C3×D4C2×C4×D514yes—
417C2×C3×C4—51no—
418C2×C3×C4—51no—
419C2×C3×C4—51no—
420C2×C3×C4—51no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4—204no—
424C2×C3×C4—201no—
425C2×C3×C4—204no—
426C2×C3×C4—202no—
427C2×C3×C4C2×C4×D512yes—
428C2×C3×C4D4×D511yescharacteristic
429C2×C3×C4#71112yes—
430C2×C3×C4C23×D511yescharacteristic
431#67—104no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—101no—
435D12—52no—
436D12—101no—
437C4×D3—104no—
438C4×D3—202no—
439C4×D3—202no—
440Dic6—52no—
441Dic6—101no—
442C3⋊C8—22no—
443C3⋊C8—54no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—24no—
447C22×C5—48no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5C4×#6712yes—
451C22×C5C22×#6711yescharacteristic
452C2×D5—62no—
453C2×D5—121no—
454C2×D5—121no—
455C4×C5—121no—
456C4×C5—121no—
457C4×C5C4×#6712yes—
458C4×C5C22×C4×D311yescharacteristic
459C4×C5C2×#23511yescharacteristic
460Dic5—21no—
461Dic5—21no—
462Dic5—21no—
463Dic5—42no—
464Dic5—62no—
465Dic5#93212yescomplemented
466C24—21no—
467#41—154no—
468#41—302no—
469C2×Q8—151no—
470C2×D4—22no—
471C2×D4—21no—
472C2×D4—151no—
473C2×D4—301no—
474C2×D4#120014yescomplemented
475C2×D4C2×D3×D512yes—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—102no—
479C22×C4—102no—
480C22×C4—101no—
481C22×C4—204no—
482C22×C4—301no—
483C22×C4—301no—
484C22×C4—301no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—62no—
489M16—154no—
490C2×C8—32no—
491C2×C8—152no—
492C4⋊C4—31no—
493C4⋊C4—31no—
494C4⋊C4—52no—
495C4⋊C4—101no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C22⋊C4—61no—
499C22⋊C4—102no—
500C22⋊C4—102no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—51no—
504C42—51no—
505C42—51no—
506C42—51no—
507C42—61no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—24no—
514C22×C3—48no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3#402712yes—
518C22×C3C2×D4×D511yescharacteristic
519C2×D3—102no—
520C2×D3—201no—
521C2×D3—201no—
522C3×C4—52no—
523C3×C4—101no—
524C3×C4—101no—
525C3×C4—101no—
526C3×C4—202no—
527C3×C4#402712yes—
528C3×C4C22×C4×D511yescharacteristic
529C3×C4C2×#71111yescharacteristic
530Dic3—41no—
531Dic3—41no—
532Dic3—102no—
533C2×C5—22no—
534C2×C5—44no—
535C2×C5C2×C4×#6711yescharacteristic
536C2×C5C2×#93211yescharacteristic
537C2×C5#582211yescharacteristic
538D5—122no—
539C23—22no—
540C23—24no—
541C23—42no—
542C23—42no—
543C23—301no—
544C23D5×#6711yescharacteristic
545Q8—152no—
546Q8—301no—
547D4—22no—
548D4—24no—
549D4—152no—
550D4—304no—
551D4—301no—
552D4C2×#120014yes—
553C2×C4—51no—
554C2×C4—51no—
555C2×C4—51no—
556C2×C4—51no—
557C2×C4—61no—
558C2×C4—61no—
559C2×C4—102no—
560C2×C4—102no—
561C2×C4—204no—
562C2×C4—201no—
563C2×C4—204no—
564C2×C4—202no—
565C2×C4—301no—
566C2×C4—304no—
567C2×C4—602no—
568C2×C4—602no—
569C2×C4#678212yes—
570C2×C4C2×#120012yes—
571C2×C4D5×#6711yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—62no—
574C8—154no—
575C2×C3—22no—
576C2×C3—44no—
577C2×C3C2×#402711yescharacteristic
578C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
579C2×C3#6610711yescharacteristic
580D3—202no—
581C5C4×#93211yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—24no—
585C22—48no—
586C22—42no—
587C22—42no—
588C22—302no—
589C22—601no—
590C22—601no—
591C22#9155212yes—
592C22C2×D5×#6711yescharacteristic
593C4—52no—
594C4—101no—
595C4—101no—
596C4—101no—
597C4—121no—
598C4—121no—
599C4—202no—
600C4—302no—
601C4#9155212yes—
602C4C2×#678211yescharacteristic
603C4C22×#120011yescharacteristic
604C3#1061064511yescharacteristic, complemented, Sylow
605C2—22no—
606C2—44no—
607C2—602no—
608C2D5×#93211yescharacteristic
609C2#1175469011yescharacteristic
610C2C2×#9155211yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91821C2
cosocleC2×C3×C4×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic5C2semidirect
3. #11754414C2semidirect
4. C5×#5215C2semidirect
5. #11749004C2semidirect
6. #11748998C2semidirect
7. #11748979C2semidirect
8. #11748975C2semidirect
9. #11748470C2semidirect
10. #11748413C2semidirect
11. Dic5×#208C2semidirect
17. #91821C4semidirect
31. #91418C22semidirect
32. #91418C22semidirect
35. #91333C22semidirect
36. #91333C22semidirect
39. #90989C22semidirect
40. #90986C22semidirect
41. #90974C22semidirect
42. #90968C22semidirect
43. #90952C22semidirect
44. Dic5×C3⋊C8C22semidirect
46. C2×D4×Dic5D3semidirect
60. C2×C3×C5×D4C2×C4semidirect
65. #6817C2×C4semidirect
77. #6716C2×C4semidirect
78. #6715C2×C4semidirect
79. #6710C2×C4semidirect
104. #5215D5semidirect
161. D60C22×C4semidirect
164. Dic30C22×C4semidirect
179. C3⋊#168C22×C4semidirect
216. C2×C5×D4C4×D3semidirect
287. C3×Dic5AGL(1,ℤ/8)semidirect
293. C2×C3×D4C4×D5semidirect
465. Dic5#932semidirect
474. C2×D4#1200semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
581. C5C4×#932semidirect
604. C3#10610645semidirect

Maximal subgroups

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

subgroupindex
C2×#918212
C2×C3×D4×Dic52
#117544142
C5×#52152
#117490042
#117489982
#117489792
#117489752
#117484702
#117484132
Dic5×#2082
#106106453
C4×#9325