Finite Group Databasebeta

← #14301136

Subgroups — #14301136

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
1C22×C5×#204C211yesmaximal, characteristic
2C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
3#11748764C211yesmaximal, characteristic
4C2×#90973C211yesmaximal, characteristic, complemented
5C2×#90967C211yesmaximal, characteristic
6#11746372C211yesmaximal, characteristic, complemented
7C3×#64770C211yesmaximal, characteristic, complemented
8#10602841—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C22×C5×Dic6C2211yescharacteristic
11C22×C3×C5×C8C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×C4⋊Dic15C2211yescharacteristic
14C2×C5×#204—22no—
15C2×C5×#204—22no—
16C2×C5×#204C414yescomplemented
17C2×C3×C4×Dic5C2211yescharacteristic
18C22×C3×#168C2211yescharacteristic
19C2×Dic3⋊Dic5—21no—
20C2×(C2×D3)⋊Dic5—21no—
21C2×(C2×D3)⋊Dic5—21no—
22C2×Dic3×Dic5—21no—
23Dic5×Dic6—22no—
24Dic5×Dic6—22no—
25#90973—22no—
26#90967—22no—
27#68686—51nomaximal, Hall
28C22×C5×SD16—31no—
29C2×Q8×Dic5—31no—
30C2×#3967—31no—
31#65510—31no—
32C2×#3964—31no—
33#64771—31no—
34#64770D311yescharacteristic, complemented
35C23×C5×D3—21no—
36C22×C3×C4×C5C2311yescharacteristic
37C22×Dic15—21no—
38C22×Dic15—21no—
39C22×C5×Dic3—21no—
40C2×C5×D12—21no—
41C2×C5×D12—21no—
42C2×C5×D12—21no—
43C2×C5×D12—21no—
44C2×C5×D12—21no—
45C2×C5×D12C2×C412yes—
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—21no—
49C2×C5×Dic6C2×C412yes—
50C2×C5×Dic6D412yes—
51C2×C5×Dic6D412yes—
52C22×C3×Dic5D411yescharacteristic
53C22×C3×Dic5D411yescharacteristic
54C2×C3×C5×C8—21no—
55C2×C3×C5×C8—21no—
56C2×C3×C5×C8C2×C412yes—
57C4⋊Dic15—21no—
58C4⋊Dic15—21no—
59C4⋊Dic15—21no—
60C4⋊Dic15D412yes—
61C5×#204—28no—
62C3×C4×Dic5—21no—
63C3×C4×Dic5—21no—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66C2×C3×#168—21no—
67Dic3⋊Dic5—24no—
68(C2×D3)⋊Dic5—42no—
69(C2×D3)⋊Dic5—42no—
70Dic3×Dic5—24no—
71C22×#204D511yescharacteristic
72C2×C4×Dic6—51no—
73C2×#821—51no—
74C2×#816—51no—
75#4939—51no—
76C3×#336—51no—
77#4551—51no—
78C22×C5×Q8—31no—
79C22×C5×D4—31no—
80C2×C5×SD16—34no—
81C2×C5×SD16—62no—
82C2×C5×SD16—62no—
83C22×C5×C8C2×D311yescharacteristic
84C2×C22⋊Dic5—61no—
85C2×C22⋊Dic5—61no—
86Q8×Dic5—62no—
87Q8×Dic5—62no—
88C2×C4⋊Dic5—31no—
89C2×C4⋊Dic5—31no—
90C2×C4⋊Dic5—61no—
91C2×C4×Dic5—61no—
92C2×C4×Dic5C2×D311yescharacteristic
93C22×#168C2×D311yescharacteristic
94#3967—62no—
95#3964—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×C5C22×C411yescharacteristic
106C2×C3×C4×C5C2×D411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×C3×C4×C5#4111yescharacteristic
110C2×C3×C4×C5#4111yescharacteristic
111C2×Dic15—22no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C2×Dic15—41no—
117C2×C5×Dic3—22no—
118C2×C5×Dic3—22no—
119C2×C5×Dic3—22no—
120C5×D12—22no—
121C5×D12—22no—
122C5×D12—41no—
123C5×D12—41no—
124C5×Dic6—22no—
125C5×Dic6—22no—
126C5×Dic6—22no—
127C5×Dic6C22⋊C414yescomplemented
128C2×C3×Dic5—21no—
129C2×C3×Dic5—21no—
130C2×C3×Dic5—21no—
131C2×C3×Dic5—21no—
132C2×C3×Dic5—21no—
133C2×C3×Dic5SD1612yescomplemented
134C3×C5×C8—22no—
135C3×#168—41no—
136C22×D12C2×D511yescharacteristic
137C22×Dic6C2×D511yescharacteristic
138C22×C3×C8—51no—
139C22×C3×C8C2×D511yescharacteristic
140C2×C3×C42—51no—
141C2×(C2×D3)⋊C4—101no—
142C2×(C2×D3)⋊C4—101no—
143C2×C4⋊Dic3—51no—
144C2×C4⋊Dic3—51no—
145C2×Dic3⋊C4—101no—
146C2×C4×Dic3—101no—
147C2×#204—22no—
148C2×#204—22no—
149C2×#204Dic514yescomplemented
150C4×Dic6—102no—
151C4×Dic6—102no—
152#821—102no—
153#816—102no—
154C24×C5—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—
161C2×C5×D4—32no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C2×C5×D4—61no—
167C22×C4×C5—61no—
168C22×C4×C5C22×D311yescharacteristic
169C22×Dic5—61no—
170C22×Dic5—61no—
171C22×Dic5D1211yescharacteristic
172C22×Dic5D1211yescharacteristic
173C5×SD16—68no—
174C2×C5×C8—21no—
175C2×C5×C8—21no—
176C2×C5×C8C4×D312yes—
177C22⋊Dic5—122no—
178C22⋊Dic5—122no—
179C4⋊Dic5—32no—
180C4⋊Dic5—64no—
181C4⋊Dic5—61no—
182C4⋊Dic5—61no—
183C4⋊Dic5—61no—
184C4×Dic5—21no—
185C4×Dic5—21no—
186C4×Dic5—64no—
187C2×#168—21no—
188C2×#168—21no—
189C2×#168—21no—
190C22×SD16—31no—
191C2×C4×Q8—151no—
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×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×C5C2×C22⋊C411yescharacteristic
212C3×C4×C5C4×D411yescharacteristic
213C3×C4×C5#12111yescharacteristic
214C3×C4×C5#12311yescharacteristic
215Dic15—42no—
216Dic15—81no—
217C3×Dic5—22no—
218C3×Dic5—41no—
219C5×Dic3—24no—
220C23×D3—21no—
221C22×C3×C4—51no—
222C22×C3×C4—51no—
223C22×C3×C4C22×D511yescharacteristic
224C22×Dic3—21no—
225C22×Dic3—101no—
226C22×Dic3—101no—
227C2×D12—21no—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12C2×Dic512yes—
233C2×Dic6—21no—
234C2×Dic6—21no—
235C2×Dic6—21no—
236C2×Dic6C2×Dic512yes—
237C2×Dic6C22⋊D512yes—
238C2×Dic6C22⋊D512yes—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—101no—
242C2×C3×C8—101no—
243C2×C3×C8—101no—
244C2×C3×C8C2×Dic512yes—
245C3×C42—101no—
246C3×C42—101no—
247(C2×D3)⋊C4—202no—
248(C2×D3)⋊C4—202no—
249C4⋊Dic3—52no—
250C4⋊Dic3—101no—
251C4⋊Dic3—101no—
252C4⋊Dic3—101no—
253Dic3⋊C4—104no—
254C4×Dic3—104no—
255#204—28no—
256C23×C5—62no—
257C23×C5—121no—
258C23×C5—121no—
259C23×C5—121no—
260C23×C5—121no—
261C23×C5—121no—
262C23×C5—121no—
263C23×C5C2×D1211yescharacteristic
264C5×Q8—34no—
265C5×Q8—62no—
266C5×Q8—62no—
267C5×Q8—62no—
268C5×D4—62no—
269C5×D4—62no—
270C5×D4—121no—
271C5×D4—121no—
272C2×C4×C5—62no—
273C2×C4×C5—62no—
274C2×C4×C5—62no—
275C2×C4×C5C2×C4×D311yescharacteristic
276C2×C4×C5#23511yescharacteristic
277C2×C4×C5D3×D411yescharacteristic
278C2×C4×C5D3×D411yescharacteristic
279C2×C4×C5D3×D411yescharacteristic
280C2×C4×C5#23911yescharacteristic
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—62no—
287C2×Dic5—121no—
288C2×Dic5—121no—
289C2×Dic5—121no—
290C2×Dic5—121no—
291C2×Dic5—121no—
292C2×Dic5#20412yescomplemented
293C5×C8—22no—
294#168—41no—
295C22×Q8—31no—
296C22×D4—31no—
297C2×SD16—34no—
298C2×SD16—62no—
299C2×SD16—62no—
300C22×C8—51no—
301C22×C8D3×D511yescharacteristic
302C4×Q8—302no—
303C4×Q8—302no—
304C2×C4⋊C4—151no—
305C2×C4⋊C4—151no—
306C2×C4⋊C4—301no—
307C2×C22⋊C4—301no—
308C2×C22⋊C4—301no—
309C2×C42—51no—
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×C3D4×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—52no—
330C2×C3×C4—101no—
331C2×C3×C4—101no—
332C2×C3×C4—101no—
333C2×C3×C4—101no—
334C2×C3×C4—101no—
335C2×C3×C4D4×D511yescharacteristic
336C2×C3×C4#71111yescharacteristic
337C2×C3×C4#71111yescharacteristic
338C2×C3×C4C22×Dic511yescharacteristic
339C2×C3×C4C2×C22⋊D511yescharacteristic
340C2×C3×C4C2×C22⋊D511yescharacteristic
341C2×Dic3—22no—
342C2×Dic3—22no—
343C2×Dic3—22no—
344C2×Dic3—102no—
345C2×Dic3—201no—
346C2×Dic3—201no—
347C2×Dic3—201no—
348C2×Dic3—201no—
349C2×Dic3—201no—
350D12—22no—
351D12—22no—
352D12—41no—
353D12—41no—
354Dic6—22no—
355Dic6—22no—
356Dic6—22no—
357Dic6C22⋊Dic514yescomplemented
358C3×C8—22no—
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×C5C4×D1211yescharacteristic
368C22×C5#88211yescharacteristic
369C22×C5#89511yescharacteristic
370C22×C5C2×#20411yescharacteristic
371C22×C5#90411yescharacteristic
372C22×C5#90811yescharacteristic
373C22×C5#90911yescharacteristic
374C4×C5—64no—
375C4×C5D3×C22⋊C411yescharacteristic
376C4×C5#88411yescharacteristic
377C4×C5#89311yescharacteristic
378C4×C5#89411yescharacteristic
379Dic5—22no—
380Dic5—41no—
381Dic5—122no—
382Dic5—241no—
383C24—61no—
384C2×Q8—32no—
385C2×Q8—32no—
386C2×Q8—32no—
387C2×Q8—61no—
388C2×Q8—61no—
389C2×Q8—61no—
390C2×D4—32no—
391C2×D4—61no—
392C2×D4—61no—
393C2×D4—61no—
394C2×D4—61no—
395C2×D4—61no—
396C22×C4—51no—
397C22×C4—51no—
398C22×C4—61no—
399C22×C4—301no—
400C22×C4—301no—
401C22×C4C2×D3×D511yescharacteristic
402SD16—68no—
403C2×C8—21no—
404C2×C8—21no—
405C2×C8—101no—
406C2×C8—101no—
407C2×C8—101no—
408C2×C8D3×Dic512yes—
409C4⋊C4—152no—
410C4⋊C4—304no—
411C4⋊C4—301no—
412C4⋊C4—301no—
413C4⋊C4—301no—
414C22⋊C4—602no—
415C22⋊C4—602no—
416C42—101no—
417C42—101no—
418C42—304no—
419C3×C5#188011yescharacteristic, complemented, Hall
420C22×C3D5×SD1611yescharacteristic
421C22×C3#406011yescharacteristic
422C22×C3#406111yescharacteristic
423C22×C3#406211yescharacteristic
424C22×C3D4×Dic511yescharacteristic
425C22×C3#408311yescharacteristic
426C22×C3#408511yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C2×D3—81no—
431C2×D3—81no—
432C2×D3—81no—
433C2×D3—81no—
434C3×C4—102no—
435C3×C4—201no—
436C3×C4D4×Dic511yescharacteristic
437C3×C4#408111yescharacteristic
438C3×C4#408511yescharacteristic
439C3×C4C2×C22⋊Dic511yescharacteristic
440Dic3—24no—
441Dic3—202no—
442Dic3—401no—
443C2×C5—242no—
444C2×C5#466511yescharacteristic
445C2×C5C4×#20411yescharacteristic
446C2×C5#471011yescharacteristic
447C2×C5#473411yescharacteristic
448C2×C5#473811yescharacteristic
449C2×C5#484511yescharacteristic
450C2×C5#484811yescharacteristic
451C23—62no—
452C23—121no—
453C23—121no—
454C23—121no—
455C23—121no—
456C23—121no—
457C23—121no—
458C23D5×D1211yescharacteristic
459Q8—34no—
460Q8—62no—
461Q8—62no—
462Q8—62no—
463D4—62no—
464D4—62no—
465D4—121no—
466D4—121no—
467C2×C4—52no—
468C2×C4—62no—
469C2×C4—62no—
470C2×C4—62no—
471C2×C4—101no—
472C2×C4—101no—
473C2×C4—101no—
474C2×C4—101no—
475C2×C4—101no—
476C2×C4—302no—
477C2×C4—601no—
478C2×C4—601no—
479C2×C4—601no—
480C2×C4—601no—
481C2×C4—601no—
482C2×C4#676811yescharacteristic
483C2×C4#677211yescharacteristic
484C2×C4#677711yescharacteristic
485C2×C4C2×D3×Dic511yescharacteristic
486C2×C4D3×C22⋊D511yescharacteristic
487C2×C4D3×C22⋊D511yescharacteristic
488C8—22no—
489C8—201no—
490C2×C3SD16×Dic511yescharacteristic
491C2×C3#6545211yescharacteristic
492C2×C3#6545311yescharacteristic
493C2×C3#6545511yescharacteristic
494C2×C3#6545911yescharacteristic
495C2×C3#6546111yescharacteristic
496C2×C3#6550911yescharacteristic
497D3—82no—
498C5#6868611yescharacteristic, complemented, Sylow
499C22—122no—
500C22—122no—
501C22—122no—
502C22—241no—
503C22—241no—
504C22—241no—
505C22—241no—
506C22D5×#20411yescharacteristic
507C22#9124911yescharacteristic
508C22#9126011yescharacteristic
509C22#9126911yescharacteristic
510C22Dic5×D1211yescharacteristic
511C22#9141611yescharacteristic
512C22#9147511yescharacteristic
513C4—64no—
514C4—102no—
515C4—201no—
516C4—602no—
517C4—1201no—
518C4#9142311yescharacteristic
519C4#9143511yescharacteristic
520C4#9145311yescharacteristic
521C4D3×C22⋊Dic511yescharacteristic
522C3#1060284111yescharacteristic, complemented, Sylow
523C2—242no—
524C2Dic5×#20411yescharacteristic
525C2#1174776911yescharacteristic
526C2#1174784211yescharacteristic
527C2#1174790011yescharacteristic
528C2#1174796111yescharacteristic
529C2#1174812711yescharacteristic
530C2#1174890111yescharacteristic
subgroupG/H
centerC23D5×D12
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C2×D4
prime radicalC22×C5×D12C22
cosocleC22×C3×C4×C5C23
hypercenterC22×C8D3×D5
hypocenterC3×C5#1880
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×Dic5×Dic6C2semidirect
4. C2×#90973C2semidirect
6. #11746372C2semidirect
7. C3×#64770C2semidirect
16. C2×C5×#204C4semidirect
34. #64770D3semidirect
127. C5×Dic6C22⋊C4semidirect
133. C2×C3×Dic5SD16semidirect
149. C2×#204Dic5semidirect
292. C2×Dic5#204semidirect
357. Dic6C22⋊Dic5semidirect
419. C3×C5#1880semidirect
498. C5#68686semidirect
522. C3#10602841semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2042
C2×Dic5×Dic62
#117487642
C2×#909732
C2×#909672
#117463722
C3×#647702
#106028413
#686865