Finite Group Databasebeta

← #14327717

Subgroups — #14327717

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91434C211yesmaximal, characteristic
2C2×#91393C212yesmaximal, complemented
3C4×#6712C211yesmaximal, characteristic, complemented
4C4×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#65228C211yesmaximal, characteristic
6#11748885C212yesmaximal, complemented
7#11748866C211yesmaximal, characteristic, complemented
8#11748796C211yesmaximal, characteristic
9#11748708C212yesmaximal, complemented
10#11748705C212yesmaximal, complemented
11#11748699C211yesmaximal, characteristic, complemented
12#10605370—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C22×D5×Dic3C2212yes—
15C2×C3×C42×C5C2211yescharacteristic
16C2×#6712C2211yescharacteristic
17C2×#6712C2211yescharacteristic
18C2×C4×Dic15C2211yescharacteristic
19C2×C4×Dic15C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C4×C5×Dic3C2212yes—
23C2×C3×#685C2212yes—
24C2×C3×#685C2212yes—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×#6669C2212yes—
27C2×#6669C2212yes—
28C2×#6665C2212yes—
29C2×#6665C2212yes—
30C2×#6665C2212yes—
31C2×Dic3×Dic5C2212yes—
32#91434C418yescomplemented
33#91393—28no—
34#91115C2211yescharacteristic
35#91115C2211yescharacteristic
36C5×C3⋊#95C2212yes—
37#90994C2212yes—
38#76302—51nomaximal, Hall
39C2×#4039—31no—
40C2×#4018—32no—
41C4×C5×C4⋊C4—31no—
42#65277—31no—
43#65265—31no—
44C4⋊C4×Dic5—31no—
45#65229—32no—
46#65228D311yescharacteristic
47C4×#683—31no—
48#64958—32no—
49#64956—32no—
50C23×C3×D5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2312yes—
60C22×C3×Dic5C2312yes—
61C2×C3×D20—22no—
62C2×C3×D20—22no—
63C2×C3×D20C2×C414yes—
64C2×D5×Dic3—24no—
65C2×D5×Dic3—24no—
66C2×D5×Dic3C2×C418yes—
67C3×C42×C5—22no—
68#6712—22no—
69#6712D414yescomplemented
70C4×Dic15—22no—
71C4×Dic15C2×C414yes—
72C5×C4⋊Dic3—22no—
73C5×C4⋊Dic3C2×C414yes—
74C4×C5×Dic3—24no—
75C3×#685—24no—
76C3×#685—42no—
77C3×C4⋊Dic5—22no—
78#6669—24no—
79#6669—42no—
80#6665—24no—
81#6665—42no—
82#6665C2×C418yes—
83Dic3×Dic5—24no—
84C2×D4×Dic3—51no—
85C2×#877—52no—
86C3×#390—51no—
87#5221—51no—
88#4975—51no—
89Dic3×C4⋊C4—51no—
90#4945—52no—
91#4944—52no—
92#4942—52no—
93C4×C4⋊Dic3D511yescharacteristic, complemented
94C4×Dic3⋊C4—51no—
95C22×D20C2×D311yescharacteristic
96C22×C4×D5—32no—
97C2×C5×C4⋊C4—31no—
98C2×C5×C4⋊C4—31no—
99C2×C42×C5—32no—
100C2×C42×C5C2×D311yescharacteristic
101C2×#685—32no—
102C2×#685—32no—
103C2×#685—32no—
104C2×#685C2×D312yes—
105C2×#685C2×D312yes—
106C2×C4⋊Dic5C2×D311yescharacteristic
107C2×#683—31no—
108C2×#683—31no—
109C2×#683—32no—
110C2×#683—32no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5—31no—
113C2×C4×Dic5—32no—
114#4039—38no—
115#4018—68no—
116C5×#95—32no—
117#3963—31no—
118#3963—31no—
119#3963—32no—
120#2354—151noSylow
121C23×C3×C5C2411yescharacteristic
122C22×C3×D5—22no—
123C22×C3×D5—22no—
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5C22×C414yes—
129C2×C3×C4×C5—21no—
130C2×C3×C4×C5—21no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5C22×C412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5#4112yes—
137C2×C3×C4×C5#4112yes—
138C2×Dic15—21no—
139C2×Dic15—21no—
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145C2×Dic15C22×C412yes—
146C2×Dic15C22×C412yes—
147C2×Dic15C2×D412yes—
148C2×Dic15C2×D412yes—
149C2×Dic15#4112yes—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3C22×C414yes—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C3×D20—28no—
160D5×Dic3—216no—
161C22×C3×D4—51no—
162C23×Dic3—52no—
163C2×C3×C4⋊C4—51no—
164C2×C3×C22⋊C4—52no—
165C2×C3×C22⋊C4—52no—
166C2×C3×C42C2×D511yescharacteristic
167C2×#217—52no—
168C2×#217—52no—
169C2×#217—52no—
170D4×Dic3—58no—
171C2×C4⋊Dic3C2×D511yescharacteristic
172C2×C4⋊Dic3C2×D511yescharacteristic
173C2×Dic3⋊C4—51no—
174C2×Dic3⋊C4—51no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—52no—
177C2×C4×Dic3—51no—
178C2×C4×Dic3—51no—
179C2×C4×Dic3—52no—
180C2×C4×Dic3C2×D512yes—
181#877—108no—
182C3⋊#95—51no—
183C3⋊#95—51no—
184C3⋊#95—52no—
185C3⋊#95C2×D512yes—
186C23×D5C22×D312yes—
187C22×C4×C5—32no—
188C22×C4×C5—32no—
189C22×C4×C5C22×D311yescharacteristic
190C22×C4×C5C22×D311yescharacteristic
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—31no—
193C22×Dic5—31no—
194C22×Dic5—31no—
195C22×Dic5—31no—
196C22×Dic5C22×D312yes—
197C2×D20—22no—
198C2×D20—22no—
199C2×D20C4×D314yes—
200C2×C4×D5—38no—
201C2×C4×D5—64no—
202C2×C4×D5—64no—
203C5×C4⋊C4—34no—
204C5×C4⋊C4—62no—
205C42×C5—22no—
206C42×C5—64no—
207#685—24no—
208#685—38no—
209#685—42no—
210#685—64no—
211#685—122no—
212C4⋊Dic5—22no—
213#683—34no—
214#683—64no—
215#683—62no—
216#683—122no—
217C4×Dic5—34no—
218C4×Dic5—64no—
219C4×Dic5—62no—
220C2×C4×D4—151no—
221C2×#117—152no—
222#390—51no—
223#390—151no—
224#388—152no—
225#388—152no—
226#384—151no—
227#380—152no—
228C4×C4⋊C4—31no—
229C4×C4⋊C4—151no—
230C4×C4⋊C4—151no—
231C22×C3×C5C23×C411yescharacteristic
232C22×C3×C5C22×D411yescharacteristic
233C22×C3×C5C2×#4111yescharacteristic
234C22×C3×C5C2×#4111yescharacteristic
235C22×C3×C5C2×#4111yescharacteristic
236C22×C3×C5H(5,𝔽2)11yescharacteristic
237C22×C3×C52−1+411yescharacteristic
238C2×C3×D5—24no—
239C2×C3×D5—24no—
240C2×C3×D5—24no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C2×C3×D5—42no—
245C3×C4×C5—22no—
246C3×C4×C5—41no—
247C3×C4×C5#11714yescomplemented
248Dic15—22no—
249Dic15—22no—
250Dic15—41no—
251Dic15C4×D414yes—
252C3×Dic5—42no—
253C5×Dic3—24no—
254C5×Dic3—42no—
255C24×C3—52no—
256C2×C3×D4—54no—
257C2×C3×D4—102no—
258C2×C3×D4—102no—
259C22×C3×C4—52no—
260C22×C3×C4C22×D511yescharacteristic
261C22×C3×C4C22×D511yescharacteristic
262C22×C3×C4C22×D511yescharacteristic
263C22×Dic3—51no—
264C22×Dic3—51no—
265C22×Dic3—51no—
266C22×Dic3—58no—
267C22×Dic3—51no—
268C22×Dic3—104no—
269C22×Dic3—104no—
270C22×Dic3C22×D512yes—
271C22×Dic3C22×D512yes—
272C3×C4⋊C4—102no—
273C3×C22⋊C4—104no—
274C3×C22⋊C4—202no—
275C3×C42—22no—
276#217—58no—
277#217—104no—
278#217—202no—
279C4⋊Dic3—22no—
280C4⋊Dic3C4×D514yes—
281Dic3⋊C4—54no—
282Dic3⋊C4—104no—
283Dic3⋊C4—102no—
284Dic3⋊C4—202no—
285C4×Dic3—24no—
286C4×Dic3—54no—
287C4×Dic3—104no—
288C4×Dic3—102no—
289C23×C5C23×D311yescharacteristic
290C22×D5—22no—
291C22×D5—22no—
292C22×D5—22no—
293C22×D5—22no—
294C22×D5—22no—
295C22×D5—22no—
296C22×D5C2×C4×D314yes—
297C2×C4×C5—21no—
298C2×C4×C5—21no—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—34no—
303C2×C4×C5—62no—
304C2×C4×C5—62no—
305C2×C4×C5—62no—
306C2×C4×C5—62no—
307C2×C4×C5—62no—
308C2×C4×C5C2×C4×D312yes—
309C2×C4×C5D3×D412yes—
310C2×C4×C5#23712yes—
311C2×C4×C5#23712yes—
312C2×Dic5—22no—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—32no—
316C2×Dic5—32no—
317C2×Dic5—32no—
318C2×Dic5—32no—
319C2×Dic5—32no—
320C2×Dic5—61no—
321C2×Dic5—61no—
322C2×Dic5—61no—
323C2×Dic5—61no—
324C2×Dic5—61no—
325C2×Dic5—61no—
326C2×Dic5—61no—
327D20—28no—
328C4×D5—616no—
329C22×D4—51no—
330C23×C4—152no—
331C4×D4—158no—
332#117—308no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—151no—
337C2×C4⋊C4—152no—
338C2×C4⋊C4—151no—
339C2×C4⋊C4—152no—
340C2×C22⋊C4—52no—
341C2×C22⋊C4—52no—
342C2×C22⋊C4—152no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4—152no—
345C2×C42—32no—
346C2×C42—151no—
347C2×C42—152no—
348C2×C42—151no—
349C2×C42D3×D511yescharacteristic
350#95—32no—
351#95—152no—
352#95—151no—
353#95—151no—
354C2×C3×C5C2×#11711yescharacteristic
355C2×C3×C5C2×C4×D411yescharacteristic
356C2×C3×C5#52011yescharacteristic
357C2×C3×C5#54711yescharacteristic
358C2×C3×C5#55011yescharacteristic
359C2×C3×C5#55511yescharacteristic
360C2×C3×C5#55611yescharacteristic
361C3×D5—44no—
362C23×C3—54no—
363C23×C3—102no—
364C23×C3—102no—
365C23×C3—102no—
366C23×C3—102no—
367C23×C3—102no—
368C23×C3—102no—
369C23×C3C23×D511yescharacteristic
370C3×D4—108no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—102no—
379C2×C3×C4C2×C4×D512yes—
380C2×C3×C4#70912yes—
381C2×C3×C4#70912yes—
382C2×C3×C4D4×D512yes—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—22no—
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—52no—
389C2×Dic3—52no—
390C2×Dic3—52no—
391C2×Dic3—52no—
392C2×Dic3—52no—
393C2×Dic3—1016no—
394C2×Dic3—101no—
395C2×Dic3—101no—
396C2×Dic3—101no—
397C2×Dic3—101no—
398C2×Dic3—101no—
399C2×Dic3—101no—
400C2×Dic3—101no—
401C2×Dic3C2×C4×D514yes—
402C22×C5C22×C4×D311yescharacteristic
403C22×C5C2×D3×D411yescharacteristic
404C22×C5C2×#23711yescharacteristic
405C22×C5C2×#23711yescharacteristic
406C22×C5#100411yescharacteristic
407C22×C5D3×#4111yescharacteristic
408C22×C5#101011yescharacteristic
409C2×D5—24no—
410C2×D5—24no—
411C2×D5—24no—
412C2×D5—42no—
413C2×D5—42no—
414C2×D5—42no—
415C2×D5—42no—
416C4×C5—22no—
417C4×C5—41no—
418C4×C5—64no—
419C4×C5—122no—
420C4×C5#87714yescomplemented
421Dic5—34no—
422Dic5—42no—
423Dic5—62no—
424Dic5—62no—
425Dic5—121no—
426C24—52no—
427C2×D4—54no—
428C2×D4—102no—
429C2×D4—102no—
430C22×C4—32no—
431C22×C4—32no—
432C22×C4—52no—
433C22×C4—158no—
434C22×C4—151no—
435C22×C4—151no—
436C22×C4—151no—
437C22×C4—151no—
438C22×C4—304no—
439C22×C4—304no—
440C22×C4C2×D3×D511yescharacteristic
441C22×C4C2×D3×D511yescharacteristic
442C22×C4C2×D3×D511yescharacteristic
443C4⋊C4—34no—
444C4⋊C4—62no—
445C4⋊C4—102no—
446C4⋊C4—154no—
447C4⋊C4—302no—
448C4⋊C4—304no—
449C4⋊C4—602no—
450C22⋊C4—104no—
451C22⋊C4—158no—
452C22⋊C4—202no—
453C22⋊C4—304no—
454C22⋊C4—602no—
455C42—22no—
456C42—64no—
457C42—154no—
458C42—304no—
459C42—302no—
460C3×C5#235411yescharacteristic, complemented, Hall
461C22×C3—104no—
462C22×C3—104no—
463C22×C3—104no—
464C22×C3—202no—
465C22×C3—202no—
466C22×C3—202no—
467C22×C3—202no—
468C22×C3C22×C4×D511yescharacteristic
469C22×C3C2×#70911yescharacteristic
470C22×C3C2×#70911yescharacteristic
471C22×C3C2×D4×D511yescharacteristic
472C22×C3#414711yescharacteristic
473C22×C3D5×#4111yescharacteristic
474C22×C3#414911yescharacteristic
475C3×C4—22no—
476C3×C4—41no—
477C3×C4—202no—
478C3×C4#401814yescomplemented
479Dic3—24no—
480Dic3—42no—
481Dic3—54no—
482Dic3—102no—
483Dic3—102no—
484Dic3—201no—
485C2×C5C2×#87711yescharacteristic
486C2×C5C4×D3×D411yescharacteristic
487C2×C5#554611yescharacteristic
488C2×C5#561111yescharacteristic
489C2×C5#561611yescharacteristic
490C2×C5#567111yescharacteristic
491C2×C5#571811yescharacteristic
492D5—44no—
493C23—54no—
494C23—102no—
495C23—102no—
496C23—102no—
497C23—102no—
498C23—102no—
499C23—102no—
500C23C22×D3×D511yescharacteristic
501D4—108no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—34no—
508C2×C4—62no—
509C2×C4—62no—
510C2×C4—62no—
511C2×C4—62no—
512C2×C4—62no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—152no—
517C2×C4—152no—
518C2×C4—152no—
519C2×C4—152no—
520C2×C4—152no—
521C2×C4—3016no—
522C2×C4—301no—
523C2×C4—301no—
524C2×C4—301no—
525C2×C4—301no—
526C2×C4—301no—
527C2×C4—301no—
528C2×C4—301no—
529C2×C4#676512yes—
530C2×C4C4×D3×D512yes—
531C2×C4#677712yes—
532C2×C4#677912yes—
533C2×C3—204no—
534C2×C3C2×#401811yescharacteristic
535C2×C3#6584111yescharacteristic
536C2×C3#6586611yescharacteristic
537C2×C3C4×D4×D511yescharacteristic
538C2×C3#6588711yescharacteristic
539C2×C3#6590211yescharacteristic
540C2×C3#6590811yescharacteristic
541C5#7630211yescharacteristic, complemented, Sylow
542C22—104no—
543C22—104no—
544C22—104no—
545C22—202no—
546C22—202no—
547C22—202no—
548C22—202no—
549C22C2×#676511yescharacteristic
550C22#9200011yescharacteristic
551C22C2×C4×D3×D511yescharacteristic
552C22C2×#677711yescharacteristic
553C22#9201611yescharacteristic
554C22#9201711yescharacteristic
555C22C2×#677911yescharacteristic
556C4—22no—
557C4—41no—
558C4—64no—
559C4—122no—
560C4—154no—
561C4—202no—
562C4—302no—
563C4—302no—
564C4—601no—
565C4#9139314yescomplemented
566C3#1060537011yescharacteristic, complemented, Sylow
567C2—204no—
568C2#1175252011yescharacteristic
569C2#1175255411yescharacteristic
570C2#1175261911yescharacteristic
571C2C4×#677711yescharacteristic
572C2C2×#9139311yescharacteristic
573C2#1175438511yescharacteristic
574C2#1175444711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2354
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#91393C2semidirect
3. C4×#6712C2semidirect
4. C4×C5×C4⋊Dic3C2semidirect
6. #11748885C2semidirect
7. #11748866C2semidirect
9. #11748708C2semidirect
10. #11748705C2semidirect
11. #11748699C2semidirect
32. #91434C4semidirect
69. #6712D4semidirect
93. C4×C4⋊Dic3D5semidirect
247. C3×C4×C5#117semidirect
420. C4×C5#877semidirect
460. C3×C5#2354semidirect
478. C3×C4#4018semidirect
541. C5#76302semidirect
565. C4#91393semidirect
566. C3#10605370semidirect

Maximal subgroups

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

subgroupindex
C2×#914342
C2×#913932
C4×#67122
C4×C5×C4⋊Dic32
C3×#652282
#117488852
#117488662
#117487962
#117487082
#117487052
#117486992
#106053703
#763025