Finite Group Databasebeta

← #14301125

Subgroups — #14301125

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91340C211yesmaximal, characteristic, complemented
2C22×#6659C211yesmaximal, characteristic
3C2×#91094C211yesmaximal, characteristic, complemented
4C5×#4988C211yesmaximal, characteristic
5C2×#90966C211yesmaximal, characteristic
6C3×#64749C211yesmaximal, characteristic, complemented
7#11745967C211yesmaximal, characteristic, complemented
8#10600453—31nomaximal, Hall
9C22×Dic30C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C2×C5×(C2×D3)⋊C4—21no—
14C2×C5×(C2×D3)⋊C4—21no—
15C2×C4×C5×Dic3C2211yescharacteristic
16C2×C3×C4⋊Dic5C2211yescharacteristic
17C22×C3×#168C2211yescharacteristic
18C2×#6669—21no—
19C2×Dic3×Dic5—21no—
20#91340—22no—
21#91340—22no—
22C2×#6659—22no—
23C2×#6659—22no—
24C2×#6659C414yescomplemented
25#91094—22no—
26#90966—22no—
27#68909—51nomaximal, Hall
28C22×#687—31no—
29C2×C4×Dic10—31no—
30C5×#390—31no—
31C2×#3964—31no—
32C2×#3942—31no—
33#64749D311yescharacteristic, complemented
34#64744—31no—
35C23×C5×D3—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30—21no—
40C2×Dic30—21no—
41C2×Dic30—21no—
42C2×Dic30C2×C412yes—
43C2×Dic30D412yes—
44C2×Dic30D412yes—
45C22×C5×Dic3D411yescharacteristic
46C22×C5×Dic3D411yescharacteristic
47C2×C5×D12—21no—
48C2×C5×D12—21no—
49C2×C5×D12—21no—
50C2×C5×D12—21no—
51C2×C5×D12—21no—
52C2×C5×D12C2×C412yes—
53C22×C3×Dic5—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C4⋊C4—21no—
56C2×C3⋊#168—21no—
57C2×C3⋊#168—21no—
58C2×C3⋊#168—21no—
59C5×(C2×D3)⋊C4—42no—
60C5×(C2×D3)⋊C4—42no—
61C4×C5×Dic3—21no—
62C4×C5×Dic3—21no—
63C3×C4⋊Dic5—21no—
64C3×C4⋊Dic5D412yes—
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67C2×C3×#168C2×C412yes—
68#6669—24no—
69Dic3×Dic5—24no—
70#6659—28no—
71C22×#204—51no—
72C2×#887—51no—
73#4988D511yescharacteristic
74C2×#810—51no—
75C2×#809—51no—
76C3×#340—51no—
77#4550—51no—
78C22×C5×D4—31no—
79C22×Dic10—31no—
80C2×C5×C4⋊C4C2×D311yescharacteristic
81C2×C5×C22⋊C4—61no—
82C2×C5×C22⋊C4—61no—
83C2×C42×C5—31no—
84C2×#687—34no—
85C2×#687—62no—
86C2×#687—62no—
87C2×C4⋊Dic5C2×D311yescharacteristic
88C2×#683—61no—
89C2×C4×Dic5—61no—
90C22×#168—31no—
91C22×#168C2×D311yescharacteristic
92C4×Dic10—62no—
93C4×Dic10—62no—
94#3964—62no—
95#3942—62no—
96#1880—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×C5×D3—22no—
99C22×C5×D3—41no—
100C22×C5×D3—41no—
101C22×C5×D3—41no—
102C22×C5×D3—41no—
103C22×C5×D3—41no—
104C22×C5×D3—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5#4111yescharacteristic
113C2×C3×C4×C5#4111yescharacteristic
114C2×Dic15—22no—
115C2×Dic15—22no—
116C2×Dic15—22no—
117Dic30—22no—
118Dic30—22no—
119Dic30—22no—
120Dic30C22⋊C414yescomplemented
121C2×C5×Dic3—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—21no—
125C2×C5×Dic3—21no—
126C2×C5×Dic3SD1612yescomplemented
127C5×D12—22no—
128C5×D12—22no—
129C5×D12—41no—
130C5×D12—41no—
131C2×C3×Dic5—22no—
132C2×C3×Dic5—41no—
133C2×C3×Dic5—41no—
134C3⋊#168—41no—
135C3×#168—22no—
136C22×D12C2×D511yescharacteristic
137C22×Dic6—51no—
138C22×C3×C8—51no—
139C2×C3×C4⋊C4—51no—
140C2×C3×C4⋊C4C2×D511yescharacteristic
141C2×(C2×D3)⋊C4—21no—
142C2×(C2×D3)⋊C4—21no—
143C2×Dic3⋊C4—101no—
144C2×C4×Dic3—101no—
145C2×C4×Dic3C2×D511yescharacteristic
146C22×C3⋊C8—51no—
147C2×#204—54no—
148C2×#204—102no—
149C2×#204—102no—
150#887—102no—
151#887—102no—
152#810—102no—
153#809—102no—
154C24×C5—61no—
155C2×C5×D4—32no—
156C2×C5×D4—61no—
157C2×C5×D4—61no—
158C2×C5×D4—61no—
159C2×C5×D4—61no—
160C2×C5×D4—61no—
161C22×C4×C5—21no—
162C22×C4×C5—31no—
163C22×C4×C5—31no—
164C22×C4×C5C22×D311yescharacteristic
165C22×Dic5—21no—
166C22×Dic5—61no—
167C2×Dic10—32no—
168C2×Dic10—32no—
169C2×Dic10—32no—
170C2×Dic10—61no—
171C2×Dic10—61no—
172C2×Dic10—61no—
173C5×C4⋊C4—21no—
174C5×C4⋊C4—21no—
175C5×C22⋊C4—122no—
176C5×C22⋊C4—122no—
177C42×C5—61no—
178C42×C5—61no—
179#687—68no—
180C4⋊Dic5—21no—
181C4⋊Dic5D1212yes—
182#683—64no—
183C4×Dic5—64no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168—61no—
187C2×#168—61no—
188C2×#168—61no—
189C2×#168C4×D312yes—
190C22×SD16—151no—
191C2×C4×Q8—151no—
192C2×#103—151no—
193C2×#102—151no—
194#390—31no—
195#340—51no—
196#336—151no—
197C22×C3×C5C4×D411yescharacteristic
198C22×C3×C5#12011yescharacteristic
199C22×C3×C5#12111yescharacteristic
200C22×C3×C5C2×SD1611yescharacteristic
201C22×C3×C5#13511yescharacteristic
202C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
203C22×C3×C5#13711yescharacteristic
204C2×C5×D3—42no—
205C2×C5×D3—42no—
206C2×C5×D3—42no—
207C2×C5×D3—81no—
208C2×C5×D3—81no—
209C2×C5×D3—81no—
210C2×C5×D3—81no—
211C3×C4×C5—81no—
212C3×C4×C5C2×C22⋊C411yescharacteristic
213C3×C4×C5C4×D411yescharacteristic
214C3×C4×C5#12111yescharacteristic
215C3×C4×C5#12311yescharacteristic
216Dic15—24no—
217C3×Dic5—42no—
218C5×Dic3—22no—
219C5×Dic3—41no—
220C23×D3—21no—
221C22×C3×C4—21no—
222C22×C3×C4—101no—
223C22×C3×C4C22×D511yescharacteristic
224C22×Dic3—101no—
225C22×Dic3C22⋊D511yescharacteristic
226C22×Dic3C22⋊D511yescharacteristic
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12C4×D512yes—
233C2×Dic6—52no—
234C2×Dic6—52no—
235C2×Dic6—52no—
236C2×Dic6—101no—
237C2×Dic6—101no—
238C2×Dic6—101no—
239C2×C3×C8—52no—
240C2×C3×C8—101no—
241C2×C3×C8—101no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—52no—
245C3×C4⋊C4—101no—
246(C2×D3)⋊C4—42no—
247(C2×D3)⋊C4—42no—
248Dic3⋊C4—104no—
249C4×Dic3—21no—
250C4×Dic3—21no—
251C4×Dic3—104no—
252C2×C3⋊C8—101no—
253C2×C3⋊C8—101no—
254C2×C3⋊C8—101no—
255#204—108no—
256C23×C5—62no—
257C23×C5—121no—
258C23×C5—121no—
259C23×C5—121no—
260C23×C5—121no—
261C23×C5—121no—
262C23×C5—121no—
263C23×C5D3×D411yescharacteristic
264C5×D4—62no—
265C5×D4—62no—
266C5×D4—121no—
267C5×D4—121no—
268C2×C4×C5—32no—
269C2×C4×C5—41no—
270C2×C4×C5—41no—
271C2×C4×C5—41no—
272C2×C4×C5—61no—
273C2×C4×C5—61no—
274C2×C4×C5—61no—
275C2×C4×C5—61no—
276C2×C4×C5—61no—
277C2×C4×C5C2×C4×D311yescharacteristic
278C2×C4×C5C2×D1211yescharacteristic
279C2×C4×C5#23511yescharacteristic
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5D3×D411yescharacteristic
282C2×C4×C5#23911yescharacteristic
283C2×Dic5—22no—
284C2×Dic5—41no—
285C2×Dic5—41no—
286C2×Dic5—62no—
287C2×Dic5—62no—
288C2×Dic5—62no—
289Dic10—34no—
290Dic10—62no—
291Dic10—62no—
292Dic10—62no—
293#168—22no—
294#168—121no—
295C22×Q8—151no—
296C22×D4—31no—
297C2×SD16—154no—
298C2×SD16—302no—
299C2×SD16—302no—
300C22×C8—51no—
301C22×C8—151no—
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—51no—
305C2×C4⋊C4—301no—
306C2×C4⋊C4D3×D511yescharacteristic
307C2×C22⋊C4—61no—
308C2×C22⋊C4—61no—
309C2×C42—31no—
310C2×C42—301no—
311#103—302no—
312#102—302no—
313C2×C3×C5#38611yescharacteristic
314C2×C3×C5C4×SD1611yescharacteristic
315C2×C3×C5#44011yescharacteristic
316C2×C3×C5#44811yescharacteristic
317C2×C3×C5#44911yescharacteristic
318C2×C3×C5#46011yescharacteristic
319C2×C3×C5#46411yescharacteristic
320C5×D3—82no—
321C23×C3C2×C22⋊D511yescharacteristic
322C22×D3—22no—
323C22×D3—41no—
324C22×D3—41no—
325C22×D3—41no—
326C22×D3—41no—
327C22×D3—41no—
328C22×D3—41no—
329C2×C3×C4—41no—
330C2×C3×C4—41no—
331C2×C3×C4—41no—
332C2×C3×C4—102no—
333C2×C3×C4—201no—
334C2×C3×C4—201no—
335C2×C3×C4C2×C4×D511yescharacteristic
336C2×C3×C4#70911yescharacteristic
337C2×C3×C4D4×D511yescharacteristic
338C2×C3×C4D4×D511yescharacteristic
339C2×C3×C4D4×D511yescharacteristic
340C2×C3×C4#71111yescharacteristic
341C2×Dic3—21no—
342C2×Dic3—21no—
343C2×Dic3—21no—
344C2×Dic3—21no—
345C2×Dic3—21no—
346C2×Dic3—102no—
347C2×Dic3—102no—
348C2×Dic3—102no—
349C2×Dic3#68712yescomplemented
350D12—22no—
351D12—22no—
352D12—41no—
353D12—41no—
354Dic6—54no—
355Dic6—102no—
356Dic6—102no—
357Dic6—102no—
358C3×C8—102no—
359C3⋊C8—201no—
360C22×C5—122no—
361C22×C5—122no—
362C22×C5—122no—
363C22×C5—241no—
364C22×C5—241no—
365C22×C5—241no—
366C22×C5—241no—
367C22×C5#88211yescharacteristic
368C22×C5#88411yescharacteristic
369C22×C5#89311yescharacteristic
370C22×C5#91111yescharacteristic
371C22×C5D3×SD1611yescharacteristic
372C22×C5#91611yescharacteristic
373C22×C5#91811yescharacteristic
374C4×C5—62no—
375C4×C5—81no—
376C4×C5—121no—
377C4×C5C4×D1211yescharacteristic
378C4×C5D3×C22⋊C411yescharacteristic
379C4×C5#89411yescharacteristic
380C4×C5#89511yescharacteristic
381Dic5—42no—
382Dic5—64no—
383C24—61no—
384C2×Q8—152no—
385C2×Q8—152no—
386C2×Q8—152no—
387C2×Q8—301no—
388C2×Q8—301no—
389C2×Q8—301no—
390C2×D4—32no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C22×C4—21no—
397C22×C4—31no—
398C22×C4—31no—
399C22×C4—101no—
400C22×C4—301no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—308no—
403C2×C8—52no—
404C2×C8—101no—
405C2×C8—101no—
406C2×C8—301no—
407C2×C8—301no—
408C2×C8—301no—
409C4⋊C4—21no—
410C4⋊C4—21no—
411C4⋊C4—52no—
412C4⋊C4—101no—
413C4⋊C4—304no—
414C22⋊C4—122no—
415C22⋊C4—122no—
416C42—61no—
417C42—61no—
418C42—304no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3C4×C22⋊D511yescharacteristic
421C22×C3#407811yescharacteristic
422C22×C3C2×#68711yescharacteristic
423C22×C3#408311yescharacteristic
424C22×C3#408411yescharacteristic
425C22×C3#409611yescharacteristic
426C22×C3#409711yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C2×D3—81no—
431C2×D3—81no—
432C2×D3—81no—
433C2×D3—81no—
434C3×C4—81no—
435C3×C4—202no—
436C3×C4D5×C22⋊C411yescharacteristic
437C3×C4#402711yescharacteristic
438C3×C4#402911yescharacteristic
439C3×C4#403011yescharacteristic
440Dic3—22no—
441Dic3—41no—
442Dic3—104no—
443C2×C5—242no—
444C2×C5#466511yescharacteristic
445C2×C5#476211yescharacteristic
446C2×C5#478111yescharacteristic
447C2×C5#479811yescharacteristic
448C2×C5#480611yescharacteristic
449C2×C5#485211yescharacteristic
450C2×C5#488911yescharacteristic
451C23—62no—
452C23—121no—
453C23—121no—
454C23—121no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23D3×C22⋊D511yescharacteristic
459Q8—154no—
460Q8—302no—
461Q8—302no—
462Q8—302no—
463D4—62no—
464D4—62no—
465D4—121no—
466D4—121no—
467C2×C4—32no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—61no—
476C2×C4—102no—
477C2×C4—201no—
478C2×C4—201no—
479C2×C4—302no—
480C2×C4—302no—
481C2×C4—302no—
482C2×C4#676911yescharacteristic
483C2×C4C4×D3×D511yescharacteristic
484C2×C4D5×D1211yescharacteristic
485C2×C4#677711yescharacteristic
486C2×C4#678211yescharacteristic
487C2×C4#679011yescharacteristic
488C8—102no—
489C8—601no—
490C2×C3#6524511yescharacteristic
491C2×C3C4×#68711yescharacteristic
492C2×C3#6530711yescharacteristic
493C2×C3#6532611yescharacteristic
494C2×C3#6532911yescharacteristic
495C2×C3#6534311yescharacteristic
496C2×C3#6536411yescharacteristic
497D3—82no—
498C5#6890911yescharacteristic, complemented, Sylow
499C22—122no—
500C22—122no—
501C22—122no—
502C22—241no—
503C22—241no—
504C22—241no—
505C22—241no—
506C22#9144611yescharacteristic
507C22#9147511yescharacteristic
508C22D3×#68711yescharacteristic
509C22#9149411yescharacteristic
510C22#9151011yescharacteristic
511C22#9151711yescharacteristic
512C22#9155711yescharacteristic
513C4—62no—
514C4—81no—
515C4—121no—
516C4—202no—
517C4—304no—
518C4#9140511yescharacteristic
519C4#9142011yescharacteristic
520C4#9143811yescharacteristic
521C4#9147311yescharacteristic
522C3#1060045311yescharacteristic, complemented, Sylow
523C2—242no—
524C2#1174727711yescharacteristic
525C2#1174747311yescharacteristic
526C2#1174749411yescharacteristic
527C2#1174751511yescharacteristic
528C2#1174891911yescharacteristic
529C2#1174901311yescharacteristic
530C2#1174925811yescharacteristic
subgroupG/H
centerC23D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91340C2semidirect
3. C2×#91094C2semidirect
6. C3×#64749C2semidirect
7. #11745967C2semidirect
24. C2×#6659C4semidirect
33. #64749D3semidirect
120. Dic30C22⋊C4semidirect
126. C2×C5×Dic3SD16semidirect
349. C2×Dic3#687semidirect
419. C3×C5#1880semidirect
498. C5#68909semidirect
522. C3#10600453semidirect

Maximal subgroups

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

subgroupindex
C2×#913402
C22×#66592
C2×#910942
C5×#49882
C2×#909662
C3×#647492
#117459672
#106004533
#689095