Finite Group Databasebeta

← #14424502

Subgroups — #14424502

Order 1920.

1464 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92101C211yesmaximal, characteristic, complemented
2C2×C5×#949C211yesmaximal, characteristic, complemented
3#11754606C211yesmaximal, characteristic, complemented
4C22×#6659C211yesmaximal, characteristic, complemented
5C3×#65522C211yesmaximal, characteristic, complemented
6#11749287C214yesmaximal, complemented
7#11749043C214yesmaximal, complemented
8#11748415C211yesmaximal, characteristic, complemented
9#11748349C211yesmaximal, characteristic, complemented
10#10615679—31nomaximal, Hall
11C2×C3×C5×#41C2211yescharacteristic
12#92101—24no—
13#92101—24no—
14C2×Q8×D15C2212yescomplemented
15C2×#6819—22no—
16C2×#6819C2212yescomplemented
17C2×#6817—21no—
18C2×#6817C2211yescharacteristic
19C22×Dic30—21no—
20C22×Dic30C2211yescharacteristic
21C22×C5×D12C2211yescharacteristic
22C5×#949—24no—
23C2×C5×#215C2212yes—
24C2×C5×#213C2212yes—
25C2×C5×#208C2211yescharacteristic
26C3×#4072C2211yescharacteristic
27C22×C3×#168C2211yescharacteristic
28#91570—22no—
29#91466C2214yes—
30#91451—21no—
31#91373—21no—
32C2×#6659—24no—
33C2×#6659C2214yes—
34C3×#3967C2212yescomplemented
35C3×#3964C2212yescomplemented
36#90974C2214yescomplemented
37#90957C2214yescomplemented
38#78836—51nomaximal, Hall
39C2×#4150—31no—
40C2×C5×AGL(1,ℤ/8)—31no—
41#66139—31no—
42C22×#687—31no—
43#65522D311yescharacteristic, complemented
44#65459—34no—
45#65447—34no—
46#65418—31no—
47#65409—31no—
48C23×C5×D3—21no—
49C3×C5×#41—22no—
50C3×C5×#41D414yescomplemented
51C2×C3×C5×Q8C2311yescharacteristic
52C2×C3×C5×D4—21no—
53C2×C3×C5×D4C2311yescharacteristic
54C22×C3×C4×C5—21no—
55C22×C3×C4×C5C2311yescharacteristic
56C2×#1220—22no—
57C2×#1220D412yes—
58C22×Dic15—21no—
59C22×Dic15—22no—
60Q8×D15—24no—
61Q8×D15—24no—
62#6819—216no—
63#6819—24no—
64#6819—24no—
65#6817—28no—
66#6817—22no—
67#6817—22no—
68C2×D60D411yescharacteristic
69C2×C4×D15—22no—
70C2×C4×D15C2312yes—
71C2×Dic30—28no—
72C2×Dic30—21no—
73C2×Dic30—22no—
74C2×Dic30—22no—
75C2×Dic30D411yescharacteristic
76C2×Dic30D414yescomplemented
77C2×Dic30C2312yes—
78C2×C5×D12—22no—
79C2×C5×D12—22no—
80C2×C5×D12—21no—
81C2×C5×D12C2312yes—
82C2×#1203—24no—
83C5×#215—24no—
84C5×#213—24no—
85C5×#208—22no—
86C2×C5×C3⋊C8C2312yes—
87C3×C22⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89C3×C4×Dic5—21no—
90C2×C3×#168—22no—
91C2×C3×#168C2312yes—
92(C2×D3)⋊Dic5—24no—
93#6659—28no—
94C2×#1010—51no—
95C2×#949D511yescharacteristic, complemented
96C22×#204—51no—
97#5525—51no—
98C3×#416—51no—
99#5110—51no—
100#5004—51no—
101#4806—54no—
102#4781—54no—
103C2×C5×#41C2×D311yescharacteristic
104C22×C5×D4—31no—
105#4150—64no—
106#4150—64no—
107C2×Q8×D5—32no—
108C2×#711—32no—
109C2×#711—62no—
110C2×#709—31no—
111C2×#709—61no—
112C22×Dic10—31no—
113C22×Dic10—61no—
114C5×AGL(1,ℤ/8)—64no—
115C2×C5×SD16—32no—
116C2×C5×D8—32no—
117C2×C5×M16—31no—
118#4099—62no—
119#4086—61no—
120#4084—34no—
121#4082—61no—
122C2×#687—34no—
123C2×#687—64no—
124#4072C2×D311yescharacteristic
125C22×#168C2×D311yescharacteristic
126#3967C2×D312yescomplemented
127#3964C2×D312yescomplemented
128#3952—34no—
129#3948—34no—
130#3010—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D411yescharacteristic
133C22×D15C2×D412yes—
134C22×C5×D3—22no—
135C22×C5×D3—42no—
136C22×C5×D3—82no—
137C3×C5×Q8—21no—
138C3×C5×Q8C2×D412yes—
139C3×C5×D4—24no—
140C3×C5×D4—21no—
141C3×C5×D4C2×D412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—24no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5C2411yescharacteristic
148#1220—28no—
149#1220—24no—
150C2×Dic15—28no—
151C2×Dic15—24no—
152C2×Dic15—22no—
153C2×Dic15C2×D412yes—
154D60—22no—
155C4×D15—28no—
156C4×D15—22no—
157C4×D15—22no—
158Dic30—28no—
159Dic30—22no—
160Dic30—24no—
161Dic30—22no—
162Dic30C2×D414yes—
163C5×D12—22no—
164C5×D12—22no—
165C5×D12—42no—
166C2×C3×Dic5—22no—
167#1203—84no—
168C3×#168—22no—
169C5×C3⋊C8—22no—
170C2×C3×#41C2×D511yescharacteristic
171#1010—104no—
172#1010—104no—
173C2×D3×Q8—52no—
174C2×#237—52no—
175C2×#237—102no—
176C2×#235—51no—
177C2×#235—101no—
178C22×D12C2×D511yescharacteristic
179C22×Dic6—51no—
180C22×Dic6—101no—
181C22×C3×C8—51no—
182C3×#117—51no—
183#949—24no—
184C2×#215C2×D512yes—
185C2×#213C2×D512yes—
186C2×#208C2×D511yescharacteristic
187C2×#204—54no—
188C2×#204—104no—
189#895—54no—
190#882—102no—
191#875—101no—
192#874—101no—
193C3×#103—52no—
194C3×#102—52no—
195(C2×D3)⋊C8—54no—
196#810—54no—
197C24×C5—61no—
198C5×#41—22no—
199C5×#41D1214yescomplemented
200C2×C5×Q8C22×D311yescharacteristic
201C2×C5×D4—21no—
202C2×C5×D4—32no—
203C2×C5×D4—62no—
204C2×C5×D4—62no—
205C2×C5×D4—61no—
206C2×C5×D4C22×D311yescharacteristic
207C22×C4×C5—21no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—32no—
210C2×C22⋊D5—64no—
211C2×C22⋊D5—62no—
212C22×Dic5—62no—
213C22×Dic5—61no—
214Q8×D5—64no—
215Q8×D5—64no—
216#711—64no—
217#711—616no—
218#711—64no—
219#709—68no—
220#709—62no—
221#709—62no—
222C2×D20—31no—
223C2×C4×D5—32no—
224C2×C4×D5—62no—
225C2×Dic10—34no—
226C2×Dic10—32no—
227C2×Dic10—31no—
228C2×Dic10—62no—
229C2×Dic10—68no—
230C2×Dic10—62no—
231C2×Dic10—61no—
232C5×SD16—64no—
233C5×D8—64no—
234C5×M16—62no—
235C2×C5×C8—32no—
236C22⋊Dic5—21no—
237C22⋊Dic5—64no—
238#687—68no—
239C4⋊Dic5C22×D312yes—
240C4×Dic5—21no—
241C2×#168—22no—
242C2×#168C22×D312yes—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—31no—
245C22×SD16—151no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—51no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—42no—
255C22×C3×C5#12012yes—
256C22×C3×C5C22×D411yescharacteristic
257C2×D15—22no—
258C2×D15—24no—
259C2×C5×D3—42no—
260C2×C5×D3—44no—
261C2×C5×D3—84no—
262C3×C4×C5—22no—
263C3×C4×C5#12012yes—
264C3×C4×C5C22×D411yescharacteristic
265C3×C4×C5C22×D411yescharacteristic
266Dic15—22no—
267Dic15—24no—
268C3×Dic5—42no—
269C23×D3—21no—
270C3×#41—22no—
271C3×#41C22⋊D514yescomplemented
272C2×C3×Q8C22×D511yescharacteristic
273C2×C3×D4—21no—
274C2×C3×D4C22×D511yescharacteristic
275C22×C3×C4—21no—
276C22×C3×C4C22×D511yescharacteristic
277C2×#67—52no—
278C2×#67—102no—
279C22×Dic3—102no—
280C22×Dic3—101no—
281D3×Q8—104no—
282D3×Q8—104no—
283#237—104no—
284#237—1016no—
285#237—104no—
286#235—108no—
287#235—102no—
288#235—102no—
289C2×D12—22no—
290C2×D12—22no—
291C2×D12—21no—
292C2×D12—51no—
293C2×D12—104no—
294C2×D12C22×D512yes—
295C2×C4×D3—52no—
296C2×C4×D3—102no—
297C2×Dic6—54no—
298C2×Dic6—52no—
299C2×Dic6—51no—
300C2×Dic6—102no—
301C2×Dic6—108no—
302C2×Dic6—101no—
303C2×Dic6—102no—
304C2×C3×C8—52no—
305C2×C3×C8—102no—
306C3×C4⋊C4—52no—
307C3×C22⋊C4—101no—
308C3×C42—101no—
309#215—24no—
310#213—24no—
311(C2×D3)⋊C4—104no—
312#208—22no—
313C2×C3⋊C8C22×D512yes—
314#204—108no—
315C23×C5—21no—
316C23×C5—62no—
317C23×C5—122no—
318C23×C5—242no—
319C23×C5D3×D411yescharacteristic
320C22×D5—32no—
321C5×Q8—21no—
322C5×Q8C2×D1212yes—
323C5×D4—24no—
324C5×D4—21no—
325C5×D4—62no—
326C5×D4—62no—
327C5×D4—122no—
328C5×D4C2×D1212yes—
329C2×C4×C5—21no—
330C2×C4×C5—24no—
331C2×C4×C5C2×D1212yes—
332C2×C4×C5D3×D411yescharacteristic
333C2×C4×C5D3×D412yes—
334C2×C4×C5C23×D311yescharacteristic
335C22⋊D5—68no—
336C22⋊D5—64no—
337C22⋊D5—244no—
338C2×Dic5—22no—
339C2×Dic5—32no—
340C2×Dic5—68no—
341C2×Dic5—64no—
342C2×Dic5—62no—
343D20—62no—
344C4×D5—68no—
345C4×D5—62no—
346C4×D5—62no—
347Dic10—34no—
348Dic10—68no—
349Dic10—64no—
350Dic10—62no—
351Dic10—62no—
352C5×C8—62no—
353#168—22no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—151no—
357C2×#41—152no—
358C2×#41—301no—
359C2×#41—302no—
360C2×#41D3×D511yescharacteristic
361C22×Q8—152no—
362C22×Q8—151no—
363C22×Q8—301no—
364C22×D4—31no—
365AGL(1,ℤ/8)—64no—
366C2×SD16—32no—
367C2×SD16—154no—
368C2×SD16—304no—
369C2×D8—32no—
370C2×M16—31no—
371C22×C8—51no—
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—51no—
377#103—52no—
378#103—154no—
379#102—52no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—42no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386C5×D3—82no—
387C23×C3—21no—
388C23×C3D4×D511yescharacteristic
389C22×D3—22no—
390C22×D3—42no—
391C22×D3—52no—
392C22×D3—82no—
393C3×Q8—21no—
394C3×Q8C2×C22⋊D512yes—
395C3×D4—24no—
396C3×D4—21no—
397C3×D4C2×C22⋊D512yes—
398C2×C3×C4—21no—
399C2×C3×C4—24no—
400C2×C3×C4—102no—
401C2×C3×C4D4×D512yes—
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C23×D511yescharacteristic
405#67—108no—
406#67—104no—
407C2×Dic3—52no—
408C2×Dic3—108no—
409C2×Dic3—102no—
410C2×Dic3—104no—
411D12—22no—
412D12—22no—
413D12—42no—
414D12—102no—
415D12—404no—
416C4×D3—108no—
417C4×D3—102no—
418C4×D3—102no—
419Dic6—54no—
420Dic6—108no—
421Dic6—102no—
422Dic6—104no—
423Dic6—102no—
424C3×C8—102no—
425C3⋊C8—22no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—42no—
429C22×C5—122no—
430C22×C5—124no—
431C22×C5—244no—
432C22×C5#88212yes—
433C22×C5C2×D3×D411yescharacteristic
434C2×D5—62no—
435C2×D5—64no—
436C4×C5—22no—
437C4×C5#88212yes—
438C4×C5C22×D1211yescharacteristic
439C4×C5C2×D3×D411yescharacteristic
440Dic5—42no—
441Dic5—64no—
442Dic5—62no—
443C24—61no—
444#41—22no—
445#41—308no—
446#41—304no—
447#41—3016no—
448#41—304no—
449#41—302no—
450#41—302no—
451#41#120314yescomplemented
452C2×Q8—151no—
453C2×Q8—154no—
454C2×Q8—152no—
455C2×Q8—302no—
456C2×Q8—308no—
457C2×Q8—304no—
458C2×Q8—304no—
459C2×Q8—302no—
460C2×Q8—301no—
461C2×Q8C2×D3×D511yescharacteristic
462C2×D4—21no—
463C2×D4—32no—
464C2×D4—62no—
465C2×D4—62no—
466C2×D4—61no—
467C2×D4—152no—
468C2×D4—151no—
469C2×D4—304no—
470C2×D4—302no—
471C2×D4C2×D3×D511yescharacteristic
472C22×C4—21no—
473C22×C4—152no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4—301no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—64no—
479SD16—308no—
480D8—64no—
481M16—62no—
482C2×C8—32no—
483C2×C8—52no—
484C2×C8—102no—
485C4⋊C4—52no—
486C22⋊C4—101no—
487C22⋊C4—304no—
488C42—101no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—22no—
492C22×C3—42no—
493C22×C3#408312yes—
494C22×C3C2×D4×D511yescharacteristic
495C2×D3—44no—
496C2×D3—42no—
497C2×D3—84no—
498C2×D3—104no—
499C2×D3—102no—
500C3×C4—22no—
501C3×C4—202no—
502C3×C4#408312yes—
503C3×C4C2×D4×D511yescharacteristic
504C3×C4C22×C22⋊D511yescharacteristic
505Dic3—104no—
506Dic3—102no—
507C2×C5—22no—
508C2×C5—42no—
509C2×C5—242no—
510C2×C5C2×#88211yescharacteristic
511C2×C5#577012yes—
512D5—122no—
513C23—21no—
514C23—62no—
515C23—122no—
516C23—152no—
517C23—242no—
518C23#679011yescharacteristic
519Q8—21no—
520Q8—154no—
521Q8—308no—
522Q8—302no—
523Q8—302no—
524Q8—304no—
525Q8C2×#120312yes—
526D4—24no—
527D4—21no—
528D4—62no—
529D4—62no—
530D4—122no—
531D4—308no—
532D4—304no—
533D4—302no—
534D4—1204no—
535D4C2×#120312yes—
536C2×C4—21no—
537C2×C4—24no—
538C2×C4—102no—
539C2×C4—152no—
540C2×C4—308no—
541C2×C4—308no—
542C2×C4—302no—
543C2×C4—304no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4C2×#120312yes—
547C2×C4#679012yes—
548C2×C4#679011yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—102no—
552C2×C3—22no—
553C2×C3—42no—
554C2×C3#6610912yes—
555C2×C3C2×#408311yescharacteristic
556D3—82no—
557D3—202no—
558C5#7883611yescharacteristic, complemented, Sylow
559C22—22no—
560C22—22no—
561C22—42no—
562C22—124no—
563C22—122no—
564C22—244no—
565C22—304no—
566C22—302no—
567C22#9157312yes—
568C22C2×#679011yescharacteristic
569C4—22no—
570C4—202no—
571C4—302no—
572C4—304no—
573C4#9157312yes—
574C4C22×#120311yescharacteristic
575C4C2×#679011yescharacteristic
576C3#1061567911yescharacteristic, complemented, Sylow
577C2—22no—
578C2—42no—
579C2—242no—
580C2—602no—
581C2#1175533312yes—
582C2C2×#9157311yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#92101C2semidirect
2. C2×C5×#949C2semidirect
3. #11754606C2semidirect
4. C22×#6659C2semidirect
5. C3×#65522C2semidirect
6. #11749287C2semidirect
7. #11749043C2semidirect
8. #11748415C2semidirect
9. #11748349C2semidirect
14. C2×Q8×D15C22semidirect
16. C2×#6819C22semidirect
34. C3×#3967C22semidirect
35. C3×#3964C22semidirect
36. #90974C22semidirect
37. #90957C22semidirect
43. #65522D3semidirect
50. C3×C5×#41D4semidirect
76. C2×Dic30D4semidirect
95. C2×#949D5semidirect
126. #3967C2×D3semidirect
127. #3964C2×D3semidirect
199. C5×#41D12semidirect
271. C3×#41C22⋊D5semidirect
451. #41#1203semidirect
489. C3×C5#3010semidirect
558. C5#78836semidirect
576. C3#10615679semidirect

Maximal subgroups

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

subgroupindex
C2×#921012
C2×C5×#9492
#117546062
C22×#66592
C3×#655222
#117492872
#117490432
#117484152
#117483492
#106156793
#788365