Finite Group Databasebeta

← #14326729

Subgroups — #14326729

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Dic3C211yesmaximal, characteristic
2C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
3C5×#4928C211yesmaximal, characteristic, complemented
4C3×C4×#685C211yesmaximal, characteristic
5#11748884C212yesmaximal
6#11748878C212yesmaximal
7#11748842C211yesmaximal, characteristic, complemented
8#11748810C212yesmaximal, complemented
9#11748759C211yesmaximal, characteristic
10Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#11748655C212yesmaximal, complemented
12#10607932—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C22×D5×Dic3C2212yes—
15C2×C3×C42×C5C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2212yes—
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C5×Dic3⋊C4C2212yes—
22C2×C3×#685C2211yescharacteristic
23C2×C3×#685C2211yescharacteristic
24C2×C3×C4×Dic5C2211yescharacteristic
25C2×Dic3⋊Dic5C2212yes—
26C2×#6668C2212yes—
27C2×#6665C2212yes—
28C2×Dic3×Dic5C2212yes—
29D5×C4⋊Dic3C418yescomplemented
30#91115C2212yes—
31C5×C3⋊#95C2212yes—
32C3×#3963C2211yescharacteristic
33C3×#3963C2211yescharacteristic
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73457—51nomaximal, Hall
38C2×D5×C4⋊C4—31no—
39C5×#389—31no—
40#65276—32no—
41#65276—31no—
42#65274—31no—
43#65267—32no—
44C4⋊C4×Dic5—31no—
45C4×#685D311yescharacteristic
46C4×C4⋊Dic5—31no—
47#64955—32no—
48#64944—32no—
49C23×C3×D5C2311yescharacteristic
50C22×C3×C4×C5C2311yescharacteristic
51C22×C3×C4×C5C2311yescharacteristic
52C22×C3×C4×C5C2311yescharacteristic
53C22×Dic15C2312yes—
54C22×Dic15C2312yes—
55C22×C5×Dic3C2312yes—
56C22×C5×Dic3C2312yes—
57C22×C3×Dic5C2311yescharacteristic
58C22×C3×Dic5C2311yescharacteristic
59C22×C3×Dic5C2311yescharacteristic
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5C2×C414yes—
63C2×D5×Dic3—42no—
64C2×D5×Dic3—42no—
65C2×D5×Dic3C2×C418yes—
66C3×C42×C5—22no—
67C4⋊Dic15—22no—
68C4⋊Dic15C2×C414yes—
69C4×Dic15—42no—
70C5×C4⋊Dic3—22no—
71C5×C4⋊Dic3C2×C414yes—
72C5×Dic3⋊C4—42no—
73C3×#685—22no—
74C3×#685Q814yes—
75C3×C4×Dic5—22no—
76Dic3⋊Dic5—42no—
77#6668C2×C418yes—
78#6665—24no—
79Dic3×Dic5—42no—
80C22×C4⋊Dic3—51no—
81C3×C4×C22⋊C4—51no—
82#5212—51no—
83#4942—52no—
84Dic3×C22⋊C4—52no—
85C4×C4⋊Dic3—51no—
86C4×C4⋊Dic3—51no—
87#4928—51no—
88#4928D511yescharacteristic, complemented
89#4654—52no—
90#4654—52no—
91C22×C4×D5—32no—
92C22×C4×D5C2×D311yescharacteristic
93C2×C5×C4⋊C4—31no—
94C2×C5×C4⋊C4—31no—
95C2×C5×C4⋊C4—32no—
96C2×C42×C5C2×D311yescharacteristic
97C2×#685—32no—
98C2×#685C2×D311yescharacteristic
99C2×#685C2×D311yescharacteristic
100C2×C4⋊Dic5—31no—
101C2×C4⋊Dic5—31no—
102C2×C4⋊Dic5—32no—
103C2×#683—32no—
104C2×C4×Dic5—32no—
105C2×C4×Dic5—32no—
106C2×C4×Dic5C2×D311yescharacteristic
107D5×C4⋊C4—38no—
108C5×#95—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963—32no—
113#3963C2×D311yescharacteristic
114#3963C2×D311yescharacteristic
115#2345—151noSylow
116C23×C3×C5C2411yescharacteristic
117C22×C3×D5—21no—
118C22×C3×D5—21no—
119C22×C3×D5—21no—
120C22×C3×D5—21no—
121C22×C3×D5C22×C412yes—
122C22×C3×D5C2×Q812yes—
123C22×C3×D5#4112yes—
124C2×C3×C4×C5—21no—
125C2×C3×C4×C5—21no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—21no—
129C2×C3×C4×C5C22×C412yes—
130C2×C3×C4×C5C2×Q812yes—
131C2×C3×C4×C5#4112yes—
132C2×C3×C4×C5#4112yes—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15C22×C414yes—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3C22×C414yes—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5C22×C412yes—
153C2×C3×Dic5C2×Q812yes—
154C3×C4×D5—28no—
155D5×Dic3—48no—
156C23×C3×C4—51no—
157C23×Dic3—52no—
158C2×C3×C22⋊C4—51no—
159C2×C3×C22⋊C4—51no—
160C2×C3×C42—51no—
161C2×C3×C42C2×D511yescharacteristic
162C2×#217—52no—
163C2×C4⋊Dic3—51no—
164C2×C4⋊Dic3—52no—
165C2×C4⋊Dic3—58no—
166C2×C4⋊Dic3—51no—
167C2×C4⋊Dic3C2×D511yescharacteristic
168C2×C4⋊Dic3C2×D511yescharacteristic
169C2×Dic3⋊C4—52no—
170C2×Dic3⋊C4C2×D512yes—
171C2×C4×Dic3—52no—
172C2×C4×Dic3—52no—
173C3×#95—51no—
174C3×#95—51no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C3⋊#95—52no—
178C3⋊#95—52no—
179C3⋊#95C2×D512yes—
180C23×D5C22×D311yescharacteristic
181C22×C4×C5—32no—
182C22×C4×C5—32no—
183C22×C4×C5C22×D311yescharacteristic
184C22×C4×C5C22×D311yescharacteristic
185C22×C4×C5C22×D311yescharacteristic
186C22×Dic5—32no—
187C22×Dic5—32no—
188C22×Dic5C22×D311yescharacteristic
189C22×Dic5C22×D311yescharacteristic
190C22×Dic5C22×D311yescharacteristic
191C2×C4×D5—22no—
192C2×C4×D5—22no—
193C2×C4×D5—38no—
194C2×C4×D5—122no—
195C2×C4×D5—122no—
196C2×C4×D5C4×D314yes—
197C5×C4⋊C4—34no—
198C5×C4⋊C4—62no—
199C5×C4⋊C4—122no—
200C42×C5—22no—
201#685—22no—
202#685—64no—
203#685Dic614yes—
204C4⋊Dic5—34no—
205C4⋊Dic5—62no—
206C4⋊Dic5—122no—
207#683—38no—
208C4×Dic5—22no—
209C4×Dic5—122no—
210C4×Dic5—122no—
211C22×C4⋊C4—151no—
212#389—31no—
213#389—151no—
214#387—152no—
215#387—152no—
216#380—152no—
217#380—151no—
218C4×C4⋊C4—151no—
219C4×C4⋊C4—151no—
220C4×C22⋊C4—51no—
221C4×C22⋊C4—152no—
222C22×C3×C5C23×C411yescharacteristic
223C22×C3×C5C22×Q811yescharacteristic
224C22×C3×C5C2×#4111yescharacteristic
225C22×C3×C5C2×#4111yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5H(5,𝔽2)11yescharacteristic
228C22×C3×C5H(5,𝔽2)11yescharacteristic
229C2×C3×D5—22no—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—22no—
233C2×C3×D5—22no—
234C2×C3×D5—22no—
235C2×C3×D5C4×Q814yes—
236C3×C4×C5—22no—
237C3×C4×C5—41no—
238C3×C4×C5#11714yes—
239Dic15—24no—
240Dic15—42no—
241C3×Dic5—22no—
242C3×Dic5—22no—
243C3×Dic5—41no—
244C5×Dic3—24no—
245C5×Dic3—42no—
246C24×C3—51no—
247C22×C3×C4—51no—
248C22×C3×C4—51no—
249C22×C3×C4—54no—
250C22×C3×C4—51no—
251C22×C3×C4—102no—
252C22×C3×C4—102no—
253C22×C3×C4C22×D511yescharacteristic
254C22×C3×C4C22×D511yescharacteristic
255C22×C3×C4C22×D511yescharacteristic
256C22×Dic3—52no—
257C22×Dic3—58no—
258C22×Dic3—52no—
259C22×Dic3—202no—
260C22×Dic3—202no—
261C22×Dic3C22×D512yes—
262C22×Dic3C22×D512yes—
263C3×C22⋊C4—54no—
264C3×C22⋊C4—102no—
265C3×C42—22no—
266C3×C42—102no—
267#217—104no—
268C4⋊Dic3—22no—
269C4⋊Dic3—54no—
270C4⋊Dic3—58no—
271C4⋊Dic3—102no—
272C4⋊Dic3C4×D514yes—
273Dic3⋊C4—42no—
274Dic3⋊C4—202no—
275C4×Dic3—202no—
276C4×Dic3—202no—
277C23×C5C23×D311yescharacteristic
278C22×D5—21no—
279C22×D5—21no—
280C22×D5—21no—
281C22×D5—21no—
282C22×D5C2×Dic612yes—
283C22×D5C2×C4×D312yes—
284C22×D5#23512yes—
285C2×C4×C5—21no—
286C2×C4×C5—21no—
287C2×C4×C5—21no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—34no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5—62no—
295C2×C4×C5—62no—
296C2×C4×C5C2×Dic612yes—
297C2×C4×C5C2×C4×D312yes—
298C2×C4×C5#23712yes—
299C2×C4×C5#23712yes—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—21no—
303C2×Dic5—21no—
304C2×Dic5—21no—
305C2×Dic5—21no—
306C2×Dic5—21no—
307C2×Dic5—34no—
308C2×Dic5—62no—
309C2×Dic5—62no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5—62no—
313C2×Dic5C2×Dic612yes—
314C2×Dic5C2×C4×D312yes—
315C4×D5—28no—
316C4×D5—128no—
317C23×C4—51no—
318C23×C4—152no—
319C2×C4⋊C4—31no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—32no—
322C2×C4⋊C4—158no—
323C2×C4⋊C4—152no—
324C2×C4⋊C4—151no—
325C2×C4⋊C4—151no—
326C2×C4⋊C4—152no—
327C2×C22⋊C4—51no—
328C2×C22⋊C4—51no—
329C2×C22⋊C4—152no—
330C2×C42—51no—
331C2×C42—152no—
332C2×C42—152no—
333C2×C42D3×D511yescharacteristic
334#95—32no—
335#95—51no—
336#95—51no—
337#95—152no—
338#95—152no—
339#95—152no—
340#95—152no—
341C2×C3×C5C2×#11711yescharacteristic
342C2×C3×C5C2×C4×Q811yescharacteristic
343C2×C3×C5#51811yescharacteristic
344C2×C3×C5#55311yescharacteristic
345C2×C3×C5#55311yescharacteristic
346C2×C3×C5#55411yescharacteristic
347C2×C3×C5#55411yescharacteristic
348C3×D5—24no—
349C23×C3—52no—
350C23×C3—52no—
351C23×C3—52no—
352C23×C3—101no—
353C23×C3—101no—
354C23×C3—101no—
355C23×C3—101no—
356C23×C3C23×D511yescharacteristic
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—52no—
363C2×C3×C4—52no—
364C2×C3×C4—101no—
365C2×C3×C4—101no—
366C2×C3×C4—101no—
367C2×C3×C4—101no—
368C2×C3×C4—108no—
369C2×C3×C4—101no—
370C2×C3×C4—101no—
371C2×C3×C4—101no—
372C2×C3×C4C2×C4×D512yes—
373C2×C3×C4#71112yes—
374C2×C3×C4Q8×D512yes—
375C2×C3×C4#71312yes—
376C2×Dic3—22no—
377C2×Dic3—22no—
378C2×Dic3—22no—
379C2×Dic3—22no—
380C2×Dic3—22no—
381C2×Dic3—54no—
382C2×Dic3—102no—
383C2×Dic3—102no—
384C2×Dic3—102no—
385C2×Dic3—102no—
386C2×Dic3—102no—
387C2×Dic3—208no—
388C2×Dic3C2×C4×D514yes—
389C22×C5C22×Dic611yescharacteristic
390C22×C5C22×C4×D311yescharacteristic
391C22×C5C2×#23511yescharacteristic
392C22×C5C2×#23711yescharacteristic
393C22×C5C2×#23711yescharacteristic
394C22×C5#100911yescharacteristic
395C22×C5#100911yescharacteristic
396C2×D5—22no—
397C2×D5—22no—
398C2×D5—22no—
399C2×D5—22no—
400C2×D5—22no—
401C2×D5—22no—
402C2×D5C4×Dic614yes—
403C4×C5—22no—
404C4×C5—41no—
405C4×C5—64no—
406C4×C5—122no—
407C4×C5#87714yes—
408Dic5—22no—
409Dic5—22no—
410Dic5—41no—
411Dic5—64no—
412Dic5—122no—
413C24—51no—
414C22×C4—32no—
415C22×C4—32no—
416C22×C4—51no—
417C22×C4—51no—
418C22×C4—54no—
419C22×C4—51no—
420C22×C4—102no—
421C22×C4—102no—
422C22×C4—158no—
423C22×C4—152no—
424C22×C4—152no—
425C22×C4—602no—
426C22×C4—602no—
427C22×C4C2×D3×D511yescharacteristic
428C22×C4C2×D3×D511yescharacteristic
429C22×C4C2×D3×D511yescharacteristic
430C4⋊C4—34no—
431C4⋊C4—62no—
432C4⋊C4—122no—
433C4⋊C4—158no—
434C4⋊C4—154no—
435C4⋊C4—302no—
436C4⋊C4—602no—
437C22⋊C4—54no—
438C22⋊C4—102no—
439C22⋊C4—304no—
440C42—22no—
441C42—102no—
442C42—602no—
443C42—602no—
444C3×C5#234511yescharacteristic, complemented, Hall
445C22×C3—54no—
446C22×C3—102no—
447C22×C3—102no—
448C22×C3—102no—
449C22×C3—102no—
450C22×C3—102no—
451C22×C3—102no—
452C22×C3C22×C4×D511yescharacteristic
453C22×C3C2×#71111yescharacteristic
454C22×C3#414411yescharacteristic
455C22×C3C2×Q8×D511yescharacteristic
456C22×C3C2×#71311yescharacteristic
457C22×C3D5×#4111yescharacteristic
458C22×C3#414911yescharacteristic
459C3×C4—22no—
460C3×C4—41no—
461C3×C4—102no—
462C3×C4—102no—
463C3×C4—201no—
464C3×C4#403814yes—
465Dic3—24no—
466Dic3—42no—
467Dic3—104no—
468Dic3—202no—
469C2×C5C2×C4×Dic611yescharacteristic
470C2×C5C2×#87711yescharacteristic
471C2×C5#552111yescharacteristic
472C2×C5#554311yescharacteristic
473C2×C5#554311yescharacteristic
474C2×C5#556511yescharacteristic
475C2×C5#556511yescharacteristic
476D5—24no—
477C23—52no—
478C23—52no—
479C23—52no—
480C23—101no—
481C23—101no—
482C23—101no—
483C23—101no—
484C23C22×D3×D511yescharacteristic
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—34no—
491C2×C4—52no—
492C2×C4—52no—
493C2×C4—62no—
494C2×C4—62no—
495C2×C4—62no—
496C2×C4—62no—
497C2×C4—62no—
498C2×C4—101no—
499C2×C4—101no—
500C2×C4—101no—
501C2×C4—101no—
502C2×C4—108no—
503C2×C4—101no—
504C2×C4—101no—
505C2×C4—101no—
506C2×C4—154no—
507C2×C4—302no—
508C2×C4—302no—
509C2×C4—302no—
510C2×C4—302no—
511C2×C4—302no—
512C2×C4—608no—
513C2×C4D5×Dic612yes—
514C2×C4#676612yes—
515C2×C4C4×D3×D512yes—
516C2×C4#678012yes—
517C2×C3—104no—
518C2×C3C2×#403811yescharacteristic
519C2×C3#6587911yescharacteristic
520C2×C3C4×Q8×D511yescharacteristic
521C2×C3#6594811yescharacteristic
522C2×C3#6596911yescharacteristic
523C2×C3#6602911yescharacteristic
524C2×C3#6606411yescharacteristic
525C5#7345711yescharacteristic, complemented, Sylow
526C22—54no—
527C22—102no—
528C22—102no—
529C22—102no—
530C22—102no—
531C22—102no—
532C22—102no—
533C22C2×D5×Dic611yescharacteristic
534C22C2×#676611yescharacteristic
535C22C2×C4×D3×D511yescharacteristic
536C22D5×#23511yescharacteristic
537C22#9201811yescharacteristic
538C22#9201911yescharacteristic
539C22C2×#678011yescharacteristic
540C4—22no—
541C4—41no—
542C4—64no—
543C4—102no—
544C4—102no—
545C4—122no—
546C4—201no—
547C4—304no—
548C4—602no—
549C4#9139414yes—
550C3#1060793211yescharacteristic, complemented, Sylow
551C2—104no—
552C2C4×D5×Dic611yescharacteristic
553C2#1175257711yescharacteristic
554C2#1175264811yescharacteristic
555C2#1175272511yescharacteristic
556C2C2×#9139411yescharacteristic
557C2#1175440611yescharacteristic
558C2#1175451011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#2345
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. C4×C4⋊Dic15C2semidirect
3. C5×#4928C2semidirect
7. #11748842C2semidirect
8. #11748810C2semidirect
10. Dic5×C4⋊Dic3C2semidirect
11. #11748655C2semidirect
29. D5×C4⋊Dic3C4semidirect
88. #4928D5semidirect
444. C3×C5#2345semidirect
525. C5#73457semidirect
550. C3#10607932semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Dic32
C4×C4⋊Dic152
C5×#49282
C3×C4×#6852
#117488842
#117488782
#117488422
#117488102
#117487592
Dic5×C4⋊Dic32
#117486552
#106079323
#734575