Finite Group Databasebeta

← #14326732

Subgroups — #14326732

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×C5×D3×C4⋊C4C211yesmaximal, characteristic
2C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
3C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
4#11748868C211yesmaximal, characteristic, complemented
5#11748842C211yesmaximal, characteristic, complemented
6#11748786C211yesmaximal, characteristic
7#11748782C212yesmaximal
8C4×(C2×D3)⋊Dic5C212yesmaximal
9C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic
10#11748605C212yesmaximal, complemented
11#11748573C212yesmaximal, complemented
12#10613891—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×C4×C5×D3C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15C2211yescharacteristic
18C2×C4×Dic15C2212yes—
19C2×C5×C4⋊Dic3C2211yescharacteristic
20C2×C5×Dic3⋊C4C2212yes—
21C5×D3×C4⋊C4C418yescomplemented
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C2×C3×C4×Dic5C2211yescharacteristic
24C2×C3×C4×Dic5C2212yes—
25C2×Dic3⋊Dic5C2212yes—
26C2×Dic3⋊Dic5C2212yes—
27C2×(C2×D3)⋊Dic5C2211yescharacteristic
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×(C2×D3)⋊Dic5C2211yescharacteristic
30#91115C2212yes—
31C3×#3963C2212yes—
32#90994C2212yes—
33#90994C2211yescharacteristic
34#90994C2212yes—
35#90994C2211yescharacteristic
36#90994C2212yes—
37#73768—51nomaximal, Hall
38C22×C5×C4⋊C4—31no—
39#65501—31no—
40#65501—32no—
41C4×C22⋊Dic5—31no—
42C4×C22⋊Dic5—32no—
43#65274—31no—
44#65274—31no—
45#65270—32no—
46#65270—32no—
47C4⋊C4×Dic5—31no—
48C4⋊C4×Dic5D311yescharacteristic, complemented
49C23×C5×D3C2311yescharacteristic
50C22×C3×C4×C5C2312yes—
51C22×C3×C4×C5C2311yescharacteristic
52C22×Dic15C2312yes—
53C22×Dic15C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×C5×Dic3C2311yescharacteristic
56C22×C5×Dic3C2312yes—
57C2×C4×C5×D3—22no—
58C2×C4×C5×D3—22no—
59C2×C4×C5×D3—42no—
60C2×C4×C5×D3—42no—
61C2×C4×C5×D3C2×C414yes—
62C2×C4×C5×D3C2×C418yes—
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2311yescharacteristic
66C3×C5×C4⋊C4C2×C414yes—
67C4⋊Dic15—22no—
68C4×Dic15—22no—
69C4×Dic15—42no—
70C5×C4⋊Dic3C2×C414yes—
71C5×Dic3⋊C4C2×C418yes—
72C3×C4⋊Dic5—22no—
73C3×C4×Dic5—22no—
74C3×C4×Dic5—42no—
75Dic3⋊Dic5—42no—
76Dic3⋊Dic5—42no—
77(C2×D3)⋊Dic5—22no—
78(C2×D3)⋊Dic5—24no—
79(C2×D3)⋊Dic5Q814yes—
80C2×D3×C4⋊C4D511yescharacteristic
81C3×C4×C4⋊C4—51no—
82#4987—51no—
83Dic3×C4⋊C4—51no—
84#4972—51no—
85C4×(C2×D3)⋊C4—51no—
86C4×(C2×D3)⋊C4—52no—
87#4933—52no—
88#4928—51no—
89#4667—52no—
90#4652—52no—
91C23×C4×C5—31no—
92C23×C4×C5—32no—
93C2×C5×C4⋊C4—32no—
94C2×C5×C4⋊C4—31no—
95C2×C5×C4⋊C4—38no—
96C2×C5×C4⋊C4C2×D311yescharacteristic
97C2×C22⋊Dic5—31no—
98C2×C22⋊Dic5—32no—
99C2×C22⋊Dic5—31no—
100C2×C4⋊Dic5—31no—
101C2×C4⋊Dic5—32no—
102C2×C4⋊Dic5—32no—
103C2×C4⋊Dic5C2×D311yescharacteristic
104C2×C4×Dic5—31no—
105C2×C4×Dic5—32no—
106C2×C4×Dic5C2×D311yescharacteristic
107C2×C4×Dic5C2×D312yes—
108#3963—32no—
109#3963—31no—
110#3963—31no—
111#3963—32no—
112#3963—32no—
113#3963—32no—
114#3963C2×D312yes—
115#2345—151noSylow
116C23×C3×C5C2411yescharacteristic
117C22×C5×D3—21no—
118C22×C5×D3—21no—
119C22×C5×D3—21no—
120C22×C5×D3—21no—
121C22×C5×D3C22×C412yes—
122C22×C5×D3C2×Q812yes—
123C22×C5×D3#4112yes—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5C22×C414yes—
127C2×C3×C4×C5C22×C412yes—
128C2×C3×C4×C5#4112yes—
129C2×C3×C4×C5#4112yes—
130C2×Dic15—21no—
131C2×Dic15—21no—
132C2×Dic15—22no—
133C2×Dic15—21no—
134C2×Dic15—21no—
135C2×Dic15—22no—
136C2×Dic15—21no—
137C2×Dic15—22no—
138C2×Dic15C2×Q812yes—
139C2×C5×Dic3—21no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3C22×C412yes—
144C2×C5×Dic3C22×C414yes—
145C4×C5×D3—28no—
146C4×C5×D3—48no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5C2×Q812yes—
156C22×C4×D3C2×D511yescharacteristic
157C22×C4×D3C2×D512yes—
158C2×C3×C4⋊C4—51no—
159C2×C3×C4⋊C4C2×D511yescharacteristic
160C2×C3×C42—51no—
161C2×C3×C42—52no—
162C2×(C2×D3)⋊C4—51no—
163C2×(C2×D3)⋊C4—51no—
164C2×(C2×D3)⋊C4—52no—
165C2×C4⋊Dic3—51no—
166C2×C4⋊Dic3C2×D511yescharacteristic
167C2×Dic3⋊C4—52no—
168C2×Dic3⋊C4—52no—
169C2×Dic3⋊C4C2×D512yes—
170C2×C4×Dic3—51no—
171C2×C4×Dic3—52no—
172D3×C4⋊C4Dic518yescomplemented
173C3×#95—52no—
174C3⋊#95—52no—
175C3⋊#95—51no—
176C3⋊#95—52no—
177C3⋊#95—52no—
178C3⋊#95—52no—
179C3⋊#95—51no—
180C24×C5—31no—
181C22×C4×C5—31no—
182C22×C4×C5—32no—
183C22×C4×C5—34no—
184C22×C4×C5—38no—
185C22×C4×C5—62no—
186C22×C4×C5—62no—
187C22×C4×C5—122no—
188C22×C4×C5—122no—
189C22×C4×C5C22×D312yes—
190C22×C4×C5C22×D311yescharacteristic
191C22×Dic5—31no—
192C22×Dic5—31no—
193C22×Dic5—32no—
194C22×Dic5C22×D312yes—
195C22×Dic5C22×D311yescharacteristic
196C22×Dic5C22×D311yescharacteristic
197C5×C4⋊C4—38no—
198C5×C4⋊C4—34no—
199C5×C4⋊C4C4×D314yes—
200C22⋊Dic5—34no—
201C22⋊Dic5—62no—
202C22⋊Dic5—64no—
203C4⋊Dic5—22no—
204C4⋊Dic5—62no—
205C4⋊Dic5—122no—
206C4⋊Dic5—122no—
207C4×Dic5—22no—
208C4×Dic5—42no—
209C4×Dic5—62no—
210C4×Dic5—122no—
211C22×C4⋊C4—31no—
212#389—151no—
213#389—151no—
214#387—152no—
215#387—152no—
216#380—152no—
217#380—151no—
218C4×C4⋊C4—51no—
219C4×C4⋊C4—151no—
220C4×C22⋊C4—151no—
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×C5×D3—22no—
230C2×C5×D3—22no—
231C2×C5×D3—22no—
232C2×C5×D3—22no—
233C2×C5×D3—22no—
234C2×C5×D3—22no—
235C2×C5×D3C4×Q814yes—
236C3×C4×C5—24no—
237C3×C4×C5#11714yes—
238Dic15—22no—
239Dic15—42no—
240Dic15—41no—
241C3×Dic5—22no—
242C3×Dic5—41no—
243C3×Dic5—42no—
244C5×Dic3—22no—
245C5×Dic3—24no—
246C23×D3C22×D511yescharacteristic
247C22×C3×C4—51no—
248C22×C3×C4—52no—
249C22×C3×C4—51no—
250C22×C3×C4C22×D512yes—
251C22×C3×C4C22×D511yescharacteristic
252C22×Dic3—51no—
253C22×Dic3—51no—
254C22×Dic3—52no—
255C22×Dic3C22×D511yescharacteristic
256C22×Dic3C22×D512yes—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—42no—
260C2×C4×D3—42no—
261C2×C4×D3C2×Dic514yes—
262C2×C4×D3C2×Dic518yes—
263C3×C4⋊C4—102no—
264C3×C4⋊C4C2×Dic514yes—
265C3×C42—102no—
266C3×C42—202no—
267(C2×D3)⋊C4—54no—
268(C2×D3)⋊C4—102no—
269(C2×D3)⋊C4—104no—
270C4⋊Dic3—102no—
271C4⋊Dic3C2×Dic514yes—
272Dic3⋊C4—202no—
273Dic3⋊C4—202no—
274Dic3⋊C4C2×Dic518yes—
275C4×Dic3—102no—
276C4×Dic3—202no—
277C23×C5—32no—
278C23×C5—32no—
279C23×C5—32no—
280C23×C5—61no—
281C23×C5—61no—
282C23×C5—61no—
283C23×C5—61no—
284C23×C5C23×D311yescharacteristic
285C2×C4×C5—22no—
286C2×C4×C5—22no—
287C2×C4×C5—32no—
288C2×C4×C5—34no—
289C2×C4×C5—61no—
290C2×C4×C5—61no—
291C2×C4×C5—62no—
292C2×C4×C5—62no—
293C2×C4×C5—68no—
294C2×C4×C5—128no—
295C2×C4×C5C2×C4×D314yes—
296C2×C4×C5C2×C4×D312yes—
297C2×C4×C5#23512yes—
298C2×C4×C5#23512yes—
299C2×Dic5—21no—
300C2×Dic5—21no—
301C2×Dic5—21no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—21no—
305C2×Dic5—22no—
306C2×Dic5—21no—
307C2×Dic5—32no—
308C2×Dic5—61no—
309C2×Dic5—61no—
310C2×Dic5—61no—
311C2×Dic5—62no—
312C2×Dic5—61no—
313C2×Dic5—62no—
314C2×Dic5—61no—
315C2×Dic5—62no—
316C2×Dic5D3×Q812yes—
317C23×C4—31no—
318C23×C4—32no—
319C2×C4⋊C4—32no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—38no—
322C2×C4⋊C4—51no—
323C2×C4⋊C4—151no—
324C2×C4⋊C4—152no—
325C2×C4⋊C4—152no—
326C2×C4⋊C4D3×D511yescharacteristic
327C2×C22⋊C4—151no—
328C2×C22⋊C4—151no—
329C2×C22⋊C4—152no—
330C2×C42—51no—
331C2×C42—52no—
332C2×C42—151no—
333C2×C42—152no—
334#95—52no—
335#95—151no—
336#95—151no—
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
348C5×D3—24no—
349C23×C3C23×D511yescharacteristic
350C22×D3—21no—
351C22×D3—21no—
352C22×D3—21no—
353C22×D3—21no—
354C22×D3Q8×D512yes—
355C22×D3#71312yes—
356C22×D3C22×Dic512yes—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—52no—
360C2×C3×C4—101no—
361C2×C3×C4—101no—
362C2×C3×C4—101no—
363C2×C3×C4—102no—
364C2×C3×C4—101no—
365C2×C3×C4—102no—
366C2×C3×C4—102no—
367C2×C3×C4—101no—
368C2×C3×C4#70912yes—
369C2×C3×C4#70912yes—
370C2×C3×C4C22×Dic514yes—
371C2×C3×C4C22×Dic512yes—
372C2×Dic3—21no—
373C2×Dic3—21no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—52no—
377C2×Dic3—101no—
378C2×Dic3—101no—
379C2×Dic3—101no—
380C2×Dic3—102no—
381C2×Dic3—102no—
382C2×Dic3—101no—
383C2×Dic3—101no—
384C2×Dic3—102no—
385C2×Dic3C22×Dic512yes—
386C2×Dic3C22×Dic514yes—
387C4×D3—28no—
388C4×D3—48no—
389C22×C5—34no—
390C22×C5—62no—
391C22×C5—62no—
392C22×C5—62no—
393C22×C5—62no—
394C22×C5—62no—
395C22×C5—62no—
396C22×C5C22×C4×D311yescharacteristic
397C22×C5C2×#23511yescharacteristic
398C22×C5C2×#23511yescharacteristic
399C22×C5#100411yescharacteristic
400C22×C5C2×D3×Q811yescharacteristic
401C22×C5D3×#4111yescharacteristic
402C22×C5#100911yescharacteristic
403C4×C5—24no—
404C4×C5—62no—
405C4×C5—64no—
406C4×C5#87214yes—
407Dic5—22no—
408Dic5—41no—
409Dic5—42no—
410Dic5—62no—
411Dic5—122no—
412Dic5—121no—
413C24—31no—
414C22×C4—31no—
415C22×C4—32no—
416C22×C4—34no—
417C22×C4—38no—
418C22×C4—51no—
419C22×C4—51no—
420C22×C4—52no—
421C22×C4—62no—
422C22×C4—62no—
423C22×C4—122no—
424C22×C4—122no—
425C22×C4—151no—
426C22×C4—151no—
427C22×C4—152no—
428C22×C4C2×D3×D512yes—
429C22×C4C2×D3×D511yescharacteristic
430C4⋊C4—38no—
431C4⋊C4—34no—
432C4⋊C4—102no—
433C4⋊C4—302no—
434C4⋊C4—602no—
435C4⋊C4—602no—
436C4⋊C4D3×Dic514yes—
437C22⋊C4—154no—
438C22⋊C4—302no—
439C22⋊C4—304no—
440C42—102no—
441C42—202no—
442C42—302no—
443C42—602no—
444C3×C5#234511yescharacteristic, complemented, Hall
445C22×C3C2×#70911yescharacteristic
446C22×C3C2×#70911yescharacteristic
447C22×C3#414411yescharacteristic
448C22×C3#414411yescharacteristic
449C22×C3C2×Q8×D511yescharacteristic
450C22×C3C2×#71311yescharacteristic
451C22×C3C23×Dic511yescharacteristic
452C2×D3—22no—
453C2×D3—22no—
454C2×D3—22no—
455C2×D3—22no—
456C2×D3—22no—
457C2×D3—22no—
458C2×D3Q8×Dic514yes—
459C3×C4—24no—
460C3×C4—102no—
461C3×C4—201no—
462C3×C4—202no—
463C3×C4#407214yes—
464Dic3—22no—
465Dic3—24no—
466Dic3—102no—
467Dic3—202no—
468Dic3—201no—
469C2×C5—64no—
470C2×C5C2×#87211yescharacteristic
471C2×C5#551111yescharacteristic
472C2×C5#553011yescharacteristic
473C2×C5#554511yescharacteristic
474C2×C5#555811yescharacteristic
475C2×C5C4×D3×Q811yescharacteristic
476C2×C5#557911yescharacteristic
477C23—32no—
478C23—32no—
479C23—32no—
480C23—61no—
481C23—61no—
482C23—61no—
483C23—61no—
484C23C22×D3×D511yescharacteristic
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—32no—
488C2×C4—34no—
489C2×C4—52no—
490C2×C4—61no—
491C2×C4—61no—
492C2×C4—62no—
493C2×C4—62no—
494C2×C4—68no—
495C2×C4—101no—
496C2×C4—101no—
497C2×C4—101no—
498C2×C4—102no—
499C2×C4—102no—
500C2×C4—101no—
501C2×C4—101no—
502C2×C4—102no—
503C2×C4—128no—
504C2×C4—152no—
505C2×C4—301no—
506C2×C4—301no—
507C2×C4—301no—
508C2×C4—302no—
509C2×C4—301no—
510C2×C4—302no—
511C2×C4—302no—
512C2×C4—301no—
513C2×C4#677112yes—
514C2×C4#677112yes—
515C2×C4C2×D3×Dic514yes—
516C2×C4C2×D3×Dic512yes—
517C2×C3#6584511yescharacteristic
518C2×C3#6584511yescharacteristic
519C2×C3#6584811yescharacteristic
520C2×C3#6584811yescharacteristic
521C2×C3C2×#407211yescharacteristic
522C2×C3#6613211yescharacteristic
523C2×C3C2×Q8×Dic511yescharacteristic
524D3—24no—
525C5#7376811yescharacteristic, complemented, Sylow
526C22—34no—
527C22—62no—
528C22—62no—
529C22—62no—
530C22—62no—
531C22—62no—
532C22—62no—
533C22C2×#677111yescharacteristic
534C22C2×#677111yescharacteristic
535C22#9202511yescharacteristic
536C22#9202711yescharacteristic
537C22D3×Q8×D511yescharacteristic
538C22D3×#71311yescharacteristic
539C22C22×D3×Dic511yescharacteristic
540C4—24no—
541C4—62no—
542C4—64no—
543C4—102no—
544C4—201no—
545C4—202no—
546C4—302no—
547C4—602no—
548C4—601no—
549C4#9137114yes—
550C3#1061389111yescharacteristic, complemented, Sylow
551C2—64no—
552C2#1175370511yescharacteristic
553C2#1175371511yescharacteristic
554C2#1175377311yescharacteristic
555C2#1175377611yescharacteristic
556C2C2×#9137111yescharacteristic
557C2#1175491411yescharacteristic
558C2D3×Q8×Dic511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2345
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C4⋊C4×Dic15C2semidirect
3. C3×C4⋊C4×Dic5C2semidirect
4. #11748868C2semidirect
5. #11748842C2semidirect
10. #11748605C2semidirect
11. #11748573C2semidirect
21. C5×D3×C4⋊C4C4semidirect
48. C4⋊C4×Dic5D3semidirect
172. D3×C4⋊C4Dic5semidirect
444. C3×C5#2345semidirect
525. C5#73768semidirect
550. C3#10613891semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C4⋊C42
C4⋊C4×Dic152
C3×C4⋊C4×Dic52
#117488682
#117488422
#117487862
#117487822
C4×(C2×D3)⋊Dic52
#117486052
#117485732
#106138913
#737685