Finite Group Databasebeta

← #14301129

Subgroups — #14301129

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×C4×C5×Dic6C211yesmaximal, characteristic, complemented
2C22×#6660C211yesmaximal, characteristic
3#11751040C211yesmaximal, characteristic
4C2×#90973C211yesmaximal, characteristic, complemented
5C2×#90969C211yesmaximal, characteristic
6C3×#64744C211yesmaximal, characteristic, complemented
7#11745981C211yesmaximal, characteristic, complemented
8#10602426—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6714—21no—
13C2×#6714—21no—
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×Dic3⋊C4—21no—
17C2×C4×C5×Dic3—21no—
18C4×C5×Dic6—22no—
19C4×C5×Dic6—22no—
20C22×C3×#168C2211yescharacteristic
21C22×C3×#168C2211yescharacteristic
22C2×#6660—22no—
23C2×#6660—22no—
24C2×#6660C414yescomplemented
25#90973—22no—
26#90969—22no—
27#68686—51nomaximal, Hall
28C2×C4×C5×Q8—31no—
29C22×#688—31no—
30C2×#3967—31no—
31C2×#3941—31no—
32#65228—31no—
33#64749—31no—
34#64744D311yescharacteristic, complemented
35C23×D15—21no—
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15—21no—
40C2×D60—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60—21no—
45C2×D60C2×C412yes—
46C22×C5×Dic3—21no—
47C22×C5×Dic3—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6—21no—
50C2×C5×Dic6—21no—
51C2×C5×Dic6C2×C412yes—
52C2×C5×Dic6D412yes—
53C2×C5×Dic6D412yes—
54C3×C42×C5—21no—
55C3×C42×C5—21no—
56#6714—42no—
57#6714—42no—
58C4⋊Dic15—21no—
59C4⋊Dic15—21no—
60C5×C4⋊Dic3—21no—
61C5×C4⋊Dic3D412yes—
62C5×Dic3⋊C4—24no—
63C4×C5×Dic3—24no—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67C2×C3×#168—21no—
68C2×C3×#168—21no—
69C2×C3×#168C2×C412yes—
70#6660—28no—
71C22×#204—51no—
72C2×C4×Dic6D511yescharacteristic, complemented
73C2×#821—51no—
74C2×#816—51no—
75#4939—51no—
76C3×#336—51no—
77#4551—51no—
78C22×C5×Q8—31no—
79C22×D20—31no—
80C4×C5×Q8—62no—
81C4×C5×Q8—62no—
82C2×C5×C4⋊C4—31no—
83C2×C5×C4⋊C4—61no—
84C2×C42×C5—61no—
85C2×C42×C5C2×D311yescharacteristic
86C2×#688—34no—
87C2×#688—62no—
88C2×#688—62no—
89C2×#685—61no—
90C2×#685—61no—
91C2×C4⋊Dic5—31no—
92C22×#168C2×D311yescharacteristic
93C22×#168C2×D311yescharacteristic
94#3967—62no—
95#3941—62no—
96#1880—151noSylow
97C23×C3×C5C2×D411yescharacteristic
98C22×D15—22no—
99C22×D15—41no—
100C22×D15—41no—
101C22×D15—41no—
102C22×D15—41no—
103C22×D15—41no—
104C22×D15—41no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5SD1612yescomplemented
111C2×C3×C4×C5C22×C411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5C2×D411yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C3×C4×C5#4111yescharacteristic
117C2×Dic15—41no—
118C2×Dic15—41no—
119C2×Dic15—41no—
120D60—22no—
121D60—22no—
122D60—41no—
123D60—41no—
124C2×C5×Dic3—22no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—22no—
127C2×C5×Dic3—22no—
128C2×C5×Dic3—41no—
129C2×C5×Dic3—41no—
130C5×Dic6—22no—
131C5×Dic6—22no—
132C5×Dic6—22no—
133C5×Dic6C22⋊C414yescomplemented
134C3×#168—22no—
135C3×#168—41no—
136C22×D12—51no—
137C22×Dic6C2×D511yescharacteristic
138C22×C3×C8—51no—
139C22×C3×C8—51no—
140C2×C3×C42C2×D511yescharacteristic
141C2×(C2×D3)⋊C4—101no—
142C2×(C2×D3)⋊C4—101no—
143C2×C4⋊Dic3—51no—
144C2×C4⋊Dic3C2×D511yescharacteristic
145C2×Dic3⋊C4—21no—
146C2×C4×Dic3—21no—
147C2×#204—54no—
148C2×#204—102no—
149C2×#204—102no—
150C4×Dic6—22no—
151C4×Dic6—22no—
152#821—102no—
153#816—102no—
154C23×D5—61no—
155C2×C5×Q8—32no—
156C2×C5×Q8—32no—
157C2×C5×Q8—32no—
158C2×C5×Q8—61no—
159C2×C5×Q8—61no—
160C2×C5×Q8—61no—
161C22×C4×C5—61no—
162C22×C4×C5—61no—
163C22×C4×C5D1211yescharacteristic
164C22×C4×C5D1211yescharacteristic
165C22×C4×C5C22×D311yescharacteristic
166C22×Dic5—61no—
167C2×D20—32no—
168C2×D20—61no—
169C2×D20—61no—
170C2×D20—61no—
171C2×D20—61no—
172C2×D20—61no—
173C5×C4⋊C4—32no—
174C5×C4⋊C4—64no—
175C5×C4⋊C4—61no—
176C42×C5—21no—
177C42×C5—21no—
178C42×C5—64no—
179#688—68no—
180#685—122no—
181#685—122no—
182C4⋊Dic5—61no—
183C4⋊Dic5—61no—
184C2×#168—21no—
185C2×#168—21no—
186C2×#168—21no—
187C2×#168—21no—
188C2×#168—21no—
189C2×#168C4×D312yes—
190C22×SD16—151no—
191C2×C4×Q8—31no—
192C2×#103—151no—
193C2×#102—151no—
194#390—151no—
195#340—151no—
196#336—51no—
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×D15—42no—
205C2×D15—42no—
206C2×D15—42no—
207C2×D15—81no—
208C2×D15—81no—
209C2×D15—81no—
210C2×D15—81no—
211C3×C4×C5—22no—
212C3×C4×C5—41no—
213C3×C4×C5C2×C22⋊C411yescharacteristic
214C3×C4×C5C4×D411yescharacteristic
215C3×C4×C5#12111yescharacteristic
216C3×C4×C5#12311yescharacteristic
217Dic15—81no—
218C5×Dic3—24no—
219C5×Dic3—42no—
220C23×D3—101no—
221C22×C3×C4C22⋊D511yescharacteristic
222C22×C3×C4C22⋊D511yescharacteristic
223C22×C3×C4C22×D511yescharacteristic
224C22×Dic3—21no—
225C22×Dic3—21no—
226C22×Dic3—101no—
227C2×D12—52no—
228C2×D12—101no—
229C2×D12—101no—
230C2×D12—101no—
231C2×D12—101no—
232C2×D12—101no—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6C4×D512yes—
237C2×Dic6D2012yes—
238C2×Dic6C22⋊D512yes—
239C2×C3×C8—52no—
240C2×C3×C8—101no—
241C2×C3×C8—101no—
242C2×C3×C8—101no—
243C2×C3×C8—101no—
244C2×C3×C8—101no—
245C3×C42—21no—
246C3×C42—21no—
247(C2×D3)⋊C4—202no—
248(C2×D3)⋊C4—202no—
249C4⋊Dic3—21no—
250C4⋊Dic3—101no—
251C4⋊Dic3—101no—
252C4⋊Dic3C22⋊D512yes—
253Dic3⋊C4—24no—
254C4×Dic3—24no—
255#204—108no—
256C23×C5C2×D1211yescharacteristic
257C22×D5—62no—
258C22×D5—121no—
259C22×D5—121no—
260C22×D5—121no—
261C22×D5—121no—
262C22×D5—121no—
263C22×D5—121no—
264C5×Q8—34no—
265C5×Q8—62no—
266C5×Q8—62no—
267C5×Q8—62no—
268C2×C4×C5—21no—
269C2×C4×C5—21no—
270C2×C4×C5—21no—
271C2×C4×C5—21no—
272C2×C4×C5—21no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5—62no—
276C2×C4×C5—62no—
277C2×C4×C5—121no—
278C2×C4×C5—121no—
279C2×C4×C5#20412yescomplemented
280C2×C4×C5C2×C4×D311yescharacteristic
281C2×C4×C5#23511yescharacteristic
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5#23911yescharacteristic
286C2×Dic5—121no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289D20—62no—
290D20—62no—
291D20—121no—
292D20—121no—
293#168—22no—
294#168—41no—
295C22×Q8—31no—
296C22×D4—151no—
297C2×SD16—154no—
298C2×SD16—302no—
299C2×SD16—302no—
300C22×C8—51no—
301C22×C8—51no—
302C4×Q8—62no—
303C4×Q8—62no—
304C2×C4⋊C4—31no—
305C2×C4⋊C4—61no—
306C2×C4⋊C4—151no—
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—61no—
310C2×C42D3×D511yescharacteristic
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
320D15—82no—
321C23×C3C2×C22⋊D511yescharacteristic
322C22×D3—102no—
323C22×D3—201no—
324C22×D3—201no—
325C22×D3—201no—
326C22×D3—201no—
327C22×D3—201no—
328C22×D3—201no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—21no—
333C2×C3×C4—21no—
334C2×C3×C4#68812yescomplemented
335C2×C3×C4C2×C4×D511yescharacteristic
336C2×C3×C4C2×D2011yescharacteristic
337C2×C3×C4#70911yescharacteristic
338C2×C3×C4#70911yescharacteristic
339C2×C3×C4C2×C22⋊D511yescharacteristic
340C2×C3×C4C2×C22⋊D511yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—22no—
345C2×Dic3—41no—
346C2×Dic3—41no—
347C2×Dic3—201no—
348C2×Dic3—201no—
349C2×Dic3—201no—
350D12—102no—
351D12—102no—
352D12—201no—
353D12—201no—
354Dic6—22no—
355Dic6—22no—
356Dic6—22no—
357Dic6#68514yescomplemented
358C3×C8—102no—
359C3×C8—201no—
360C22×C5C4×D1211yescharacteristic
361C22×C5#88211yescharacteristic
362C22×C5#89511yescharacteristic
363C22×C5C2×#20411yescharacteristic
364C22×C5#90411yescharacteristic
365C22×C5#90811yescharacteristic
366C22×C5#90911yescharacteristic
367C2×D5—122no—
368C2×D5—122no—
369C2×D5—122no—
370C2×D5—241no—
371C2×D5—241no—
372C2×D5—241no—
373C2×D5—241no—
374C4×C5—22no—
375C4×C5—41no—
376C4×C5—64no—
377C4×C5—122no—
378C4×C5D3×C22⋊C411yescharacteristic
379C4×C5#88411yescharacteristic
380C4×C5#89311yescharacteristic
381C4×C5#89411yescharacteristic
382Dic5—241no—
383C24—301no—
384C2×Q8—32no—
385C2×Q8—32no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×D4—152no—
391C2×D4—301no—
392C2×D4—301no—
393C2×D4—301no—
394C2×D4—301no—
395C2×D4—301no—
396C22×C4—61no—
397C22×C4—61no—
398C22×C4—301no—
399C22×C4#120311yescharacteristic
400C22×C4#120311yescharacteristic
401C22×C4C2×D3×D511yescharacteristic
402SD16—308no—
403C2×C8—52no—
404C2×C8—101no—
405C2×C8—101no—
406C2×C8—101no—
407C2×C8—101no—
408C2×C8—101no—
409C4⋊C4—32no—
410C4⋊C4—64no—
411C4⋊C4—61no—
412C4⋊C4—301no—
413C4⋊C4—301no—
414C22⋊C4—602no—
415C22⋊C4—602no—
416C42—21no—
417C42—21no—
418C42—64no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3C4×C22⋊D511yescharacteristic
421C22×C3#407611yescharacteristic
422C22×C3C2×#68811yescharacteristic
423C22×C3#408811yescharacteristic
424C22×C3#409511yescharacteristic
425C22×C3#409611yescharacteristic
426C22×C3#409911yescharacteristic
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C2×D3—401no—
431C2×D3—401no—
432C2×D3—401no—
433C2×D3—401no—
434C3×C4—22no—
435C3×C4—41no—
436C3×C4C2×#68511yescharacteristic
437C3×C4C4×C22⋊D511yescharacteristic
438C3×C4#407511yescharacteristic
439C3×C4#407611yescharacteristic
440Dic3—24no—
441Dic3—42no—
442Dic3—401no—
443C2×C5#466511yescharacteristic
444C2×C5C4×#20411yescharacteristic
445C2×C5#471011yescharacteristic
446C2×C5#473411yescharacteristic
447C2×C5#473811yescharacteristic
448C2×C5#484511yescharacteristic
449C2×C5#484811yescharacteristic
450D5—242no—
451C23—302no—
452C23—601no—
453C23—601no—
454C23—601no—
455C23—601no—
456C23—601no—
457C23—601no—
458C23C2×#120311yescharacteristic
459Q8—34no—
460Q8—62no—
461Q8—62no—
462Q8—62no—
463D4—302no—
464D4—302no—
465D4—601no—
466D4—601no—
467C2×C4—21no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—62no—
473C2×C4—62no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4—121no—
477C2×C4—121no—
478C2×C4—601no—
479C2×C4—601no—
480C2×C4—601no—
481C2×C4#666012yescomplemented
482C2×C4#676911yescharacteristic
483C2×C4#677111yescharacteristic
484C2×C4C4×D3×D511yescharacteristic
485C2×C4D3×D2011yescharacteristic
486C2×C4D3×C22⋊D511yescharacteristic
487C2×C4D3×C22⋊D511yescharacteristic
488C8—102no—
489C8—201no—
490C2×C3C4×#68811yescharacteristic
491C2×C3#6531511yescharacteristic
492C2×C3#6531611yescharacteristic
493C2×C3#6531711yescharacteristic
494C2×C3#6550211yescharacteristic
495C2×C3#6551611yescharacteristic
496C2×C3#6552711yescharacteristic
497D3—402no—
498C5#6868611yescharacteristic, complemented, Sylow
499C22—602no—
500C22—602no—
501C22—602no—
502C22—1201no—
503C22—1201no—
504C22—1201no—
505C22—1201no—
506C22#9130311yescharacteristic
507C22#9130511yescharacteristic
508C22C2×#666011yescharacteristic
509C22#9132111yescharacteristic
510C22C4×#120311yescharacteristic
511C22#9146011yescharacteristic
512C22#9157011yescharacteristic
513C4—22no—
514C4—41no—
515C4—64no—
516C4—122no—
517C4—1201no—
518C4#9135111yescharacteristic
519C4#9144611yescharacteristic
520C4#9145411yescharacteristic
521C4D3×#68511yescharacteristic
522C3#1060242611yescharacteristic, complemented, Sylow
523C2—1202no—
524C2C4×#666011yescharacteristic
525C2#1174705811yescharacteristic
526C2#1174707811yescharacteristic
527C2#1174710211yescharacteristic
528C2#1174852111yescharacteristic
529C2#1174854411yescharacteristic
530C2#1174891411yescharacteristic
subgroupG/H
centerC23C2×#1203
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C2×D4
prime radicalC22×D60C22
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×Dic6C2semidirect
4. C2×#90973C2semidirect
6. C3×#64744C2semidirect
7. #11745981C2semidirect
24. C2×#6660C4semidirect
34. #64744D3semidirect
72. C2×C4×Dic6D5semidirect
110. C2×C3×C4×C5SD16semidirect
133. C5×Dic6C22⋊C4semidirect
279. C2×C4×C5#204semidirect
334. C2×C3×C4#688semidirect
357. Dic6#685semidirect
419. C3×C5#1880semidirect
481. C2×C4#6660semidirect
498. C5#68686semidirect
522. C3#10602426semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×Dic62
C22×#66602
#117510402
C2×#909732
C2×#909692
C3×#647442
#117459812
#106024263
#686865