Finite Group Databasebeta

← #14424475

Subgroups — #14424475

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×#92004C211yesmaximal, characteristic, complemented
2#11756564C211yesmaximal, characteristic, complemented
3C2×C5×#932C211yesmaximal, characteristic, complemented
4C22×C3×#687C211yesmaximal, characteristic, complemented
5#11749161C214yesmaximal, complemented
6#11749156C214yesmaximal, complemented
7#11748400C211yesmaximal, characteristic, complemented
8#11748388C211yesmaximal, characteristic, complemented
9#11748349C211yesmaximal, characteristic, complemented
10#10615679—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C2×#6817C2211yescharacteristic
13C2×C5×#235C2211yescharacteristic
14C22×C3×Dic10C2211yescharacteristic
15C2×#6782—22no—
16C2×D15⋊Q8C2212yescomplemented
17C2×#6769—21no—
18#92004—24no—
19#92004—24no—
20C2×#6768C2212yescomplemented
21C2×D3×Dic10—21no—
22#91842—22no—
23#91829—21no—
24#91827C2214yes—
25#91825—21no—
26#91815C2211yescharacteristic
27C2×C5×#214C2212yes—
28C5×#932—24no—
29C2×C5×#213C2212yes—
30C2×C5×#208C2211yescharacteristic
31C2×C3×#687—24no—
32C2×C3×#687C2214yes—
33C22×C3×#168C2211yescharacteristic
34#90973C2212yescomplemented
35#90971C2214yescomplemented
36#90967C2212yescomplemented
37#90957C2214yescomplemented
38#83860—51nomaximal, Hall
39C2×#4150—31no—
40C2×C5×AGL(1,ℤ/8)—31no—
41#66139—31no—
42C22×#687D311yescharacteristic, complemented
43#65522—31no—
44#65459—34no—
45#65447—34no—
46#65418—31no—
47#65409—31no—
48C24×C3×C5—21no—
49C2×C3×C5×D4—22no—
50C2×C3×C5×D4—22no—
51C2×C3×C5×D4—21no—
52C2×C3×C5×D4C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C2×#1220—24no—
55C2×#1220D412yes—
56#6817—22no—
57#6817—22no—
58C2×D60D411yescharacteristic
59C2×C4×D15C2312yes—
60C2×Dic30D411yescharacteristic
61C2×C5×#67—21no—
62C5×#235—22no—
63C5×#235D414yescomplemented
64C2×C5×D12C2311yescharacteristic
65C2×C4×C5×D3—21no—
66C2×C5×Dic6C2311yescharacteristic
67C22×C3×Dic5—21no—
68C2×C3×Dic10—21no—
69C2×C3×Dic10—22no—
70C2×C3×Dic10D414yescomplemented
71C2×C3×Dic10C2312yes—
72C2×#1204—22no—
73C2×#1203—22no—
74C2×#1200—22no—
75#6782—216no—
76C2×D3×Dic5—22no—
77D15⋊Q8—24no—
78D15⋊Q8—24no—
79#6769—28no—
80#6768—24no—
81#6768—24no—
82D3×Dic10—28no—
83#6719—21no—
84#6719—24no—
85C4⋊Dic15C2312yes—
86C4×Dic15—21no—
87C5×#214—24no—
88C5×#213—24no—
89C5×#208—22no—
90C2×C5×C3⋊C8C2312yes—
91C3×#687—28no—
92C2×C3×#168—22no—
93C2×C3×#168C2312yes—
94C2×#1007—51no—
95C22×C3×SD16—51no—
96#5805—51no—
97C2×#932D511yescharacteristic, complemented
98#5225—51no—
99#5172—54no—
100#5170—54no—
101#5113—51no—
102#5110—51no—
103C2×C5×#41—31no—
104C22×C5×D4C2×D311yescharacteristic
105#4150—64no—
106#4150—64no—
107C2×Q8×D5—32no—
108C2×#711—32no—
109C2×#711—62no—
110C2×#709—31no—
111C2×#709—61no—
112C22×Dic10—61no—
113C22×Dic10C2×D311yescharacteristic
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—24no—
123C2×#687C2×D314yes—
124#4072—31no—
125C22×#168C2×D311yescharacteristic
126#3967—32no—
127#3964—32no—
128#3952—34no—
129#3948—34no—
130#3010—151noSylow
131C23×C3×C5—22no—
132C23×C3×C5—42no—
133C23×C3×C5—82no—
134C23×C3×C5C2×D411yescharacteristic
135C22×D15C2×D412yes—
136C22×C5×D3—21no—
137C3×C5×D4—22no—
138C3×C5×D4—22no—
139C3×C5×D4—42no—
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2411yescharacteristic
144#1220—24no—
145#1220—84no—
146C2×Dic15—22no—
147C2×Dic15C2×D412yes—
148D60—22no—
149C4×D15—22no—
150C4×D15—22no—
151Dic30—22no—
152C5×#67—24no—
153C2×C5×Dic3—21no—
154C5×D12—21no—
155C5×D12C2×D412yes—
156C4×C5×D3—24no—
157C5×Dic6—21no—
158C5×Dic6C2×D412yes—
159C2×C3×Dic5—24no—
160C2×C3×Dic5—22no—
161C3×Dic10—24no—
162C3×Dic10—22no—
163C3×Dic10C2×D414yes—
164#1204—28no—
165#1203—28no—
166#1200—28no—
167D3×Dic5—28no—
168C3×#168—22no—
169C5×C3⋊C8—22no—
170C22×C3×Q8—51no—
171C22×C3×D4C2×D511yescharacteristic
172#1007—104no—
173#1007—104no—
174C2×#239—52no—
175C2×#239—101no—
176C2×D3×Q8—52no—
177C2×D3×Q8—101no—
178C2×#235—51no—
179C2×#235—102no—
180C2×#235C2×D511yescharacteristic
181C2×C3×SD16—54no—
182C2×C3×SD16—104no—
183C22×C3×C8—51no—
184#953—102no—
185#940—101no—
186#938—54no—
187#936—101no—
188C2×#214C2×D512yes—
189#932—24no—
190C2×#213C2×D512yes—
191#926—51no—
192C2×#208C2×D511yescharacteristic
193#835—54no—
194#821—52no—
195(C2×D3)⋊C8—54no—
196#816—52no—
197C24×C5—21no—
198C5×#41—34no—
199C5×#41—62no—
200C2×C5×Q8—31no—
201C2×C5×D4—22no—
202C2×C5×D4—21no—
203C2×C5×D4—22no—
204C2×C5×D4—31no—
205C2×C5×D4—61no—
206C2×C5×D4C22×D312yes—
207C22×C4×C5—61no—
208C22×C4×C5C22×D311yescharacteristic
209C2×C22⋊D5—32no—
210C2×C22⋊D5—62no—
211C2×C22⋊D5—64no—
212C22×Dic5—21no—
213C22×Dic5—62no—
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—21no—
226C2×Dic10—22no—
227C2×Dic10—31no—
228C2×Dic10—68no—
229C2×Dic10—62no—
230C2×Dic10#6714yescomplemented
231C2×Dic10C22×D312yes—
232C5×SD16—64no—
233C5×D8—64no—
234C5×M16—62no—
235C2×C5×C8—32no—
236C22⋊Dic5—64no—
237C22⋊Dic5—61no—
238#687—28no—
239C4⋊Dic5—32no—
240C4×Dic5—61no—
241C2×#168—22no—
242C2×#168C22×D312yes—
243C2×2−1+4—151no—
244C2×AGL(1,ℤ/8)—31no—
245C22×SD16—51no—
246#535—151no—
247#449—154no—
248#448—154no—
249#419—151no—
250#416—151no—
251#408—151no—
252C22×C3×C5—22no—
253C22×C3×C5—42no—
254C22×C3×C5—44no—
255C22×C3×C5—84no—
256C22×C3×C5#12012yes—
257C22×C3×C5C22×D411yescharacteristic
258C2×D15—22no—
259C2×D15—24no—
260C2×C5×D3—22no—
261C2×C5×D3—42no—
262C3×C4×C5#12012yes—
263C3×C4×C5C22×D411yescharacteristic
264C3×C4×C5C22×D411yescharacteristic
265Dic15—22no—
266Dic15—42no—
267C3×Dic5—24no—
268C5×Dic3—22no—
269C24×C3—21no—
270C2×C3×Q8—54no—
271C2×C3×Q8—52no—
272C2×C3×Q8—101no—
273C2×C3×Q8—102no—
274C2×C3×D4—22no—
275C2×C3×D4—21no—
276C2×C3×D4—22no—
277C2×C3×D4C22×D512yes—
278C22×C3×C4—101no—
279C22×C3×C4C22×D511yescharacteristic
280C2×#67—21no—
281C2×#67—52no—
282C2×#67—104no—
283#239—108no—
284#239—104no—
285#239—104no—
286D3×Q8—104no—
287D3×Q8—108no—
288D3×Q8—104no—
289#235—22no—
290#235—1016no—
291#235—102no—
292#235—102no—
293#235C22⋊D514yescomplemented
294C2×D12—51no—
295C2×D12—102no—
296C2×D12C22×D511yescharacteristic
297C2×C4×D3—21no—
298C2×C4×D3—52no—
299C2×C4×D3—102no—
300C2×C4×D3—102no—
301C2×Dic6—51no—
302C2×Dic6—102no—
303C2×Dic6C22×D511yescharacteristic
304C3×SD16—108no—
305C2×C3×C8—52no—
306C2×C3×C8—102no—
307#217—104no—
308#217—101no—
309#214—24no—
310#213—24no—
311C4⋊Dic3—52no—
312C4×Dic3—101no—
313#208—22no—
314C2×C3⋊C8C22×D512yes—
315C23×C5—22no—
316C23×C5—42no—
317C23×C5—61no—
318C23×C5—82no—
319C23×C5D3×D411yescharacteristic
320C22×D5—32no—
321C5×Q8—32no—
322C5×Q8—61no—
323C5×D4—22no—
324C5×D4—22no—
325C5×D4—32no—
326C5×D4—42no—
327C5×D4—64no—
328C5×D4—61no—
329C2×C4×C5—61no—
330C2×C4×C5—64no—
331C2×C4×C5D3×D412yes—
332C2×C4×C5D3×D411yescharacteristic
333C2×C4×C5C2×#6712yes—
334C2×C4×C5C23×D311yescharacteristic
335C22⋊D5—68no—
336C22⋊D5—64no—
337C22⋊D5—244no—
338C2×Dic5—24no—
339C2×Dic5—22no—
340C2×Dic5—32no—
341C2×Dic5—68no—
342C2×Dic5—62no—
343D20—62no—
344C4×D5—68no—
345C4×D5—62no—
346C4×D5—62no—
347Dic10—24no—
348Dic10—22no—
349Dic10—68no—
350Dic10—62no—
351Dic10C2×#6714yes—
352C5×C8—62no—
353#168—22no—
3542−1+4—304no—
3552−1+4—304no—
356C2×#41—31no—
357C2×#41—151no—
358C2×#41—152no—
359C2×#41—301no—
360C2×#41—302no—
361C22×Q8—51no—
362C22×Q8—152no—
363C22×Q8—301no—
364C22×D4D3×D511yescharacteristic
365AGL(1,ℤ/8)—64no—
366C2×SD16—32no—
367C2×SD16—54no—
368C2×SD16—104no—
369C2×D8—32no—
370C2×M16—31no—
371C22×C8—51no—
372#127—301no—
373#124—301no—
374#121—154no—
375#120—302no—
376#117—151no—
377#103—154no—
378#103—152no—
379#102—152no—
380C22⋊C8—154no—
381C2×C3×C5—22no—
382C2×C3×C5—82no—
383C2×C3×C5C2×#12011yescharacteristic
384C2×C3×C5#57712yes—
385D15—42no—
386C5×D3—42no—
387C23×C3—22no—
388C23×C3—42no—
389C23×C3—82no—
390C23×C3D4×D511yescharacteristic
391C22×D3—21no—
392C22×D3—52no—
393C3×Q8—54no—
394C3×Q8—102no—
395C3×Q8—104no—
396C3×D4—22no—
397C3×D4—22no—
398C3×D4—42no—
399C2×C3×C4—102no—
400C2×C3×C4—104no—
401C2×C3×C4D4×D512yes—
402C2×C3×C4D4×D511yescharacteristic
403C2×C3×C4C2×C22⋊D512yes—
404C2×C3×C4C23×D511yescharacteristic
405#67—24no—
406#67—104no—
407#67—404no—
408C2×Dic3—21no—
409C2×Dic3—52no—
410C2×Dic3—102no—
411D12—21no—
412D12—108no—
413D12—102no—
414D12C2×C22⋊D512yes—
415C4×D3—24no—
416C4×D3—108no—
417C4×D3—108no—
418C4×D3—102no—
419C4×D3—102no—
420Dic6—21no—
421Dic6—108no—
422Dic6—102no—
423Dic6C2×C22⋊D512yes—
424C3×C8—102no—
425C3⋊C8—22no—
426C22×C5—22no—
427C22×C5—44no—
428C22×C5—42no—
429C22×C5—62no—
430C22×C5—84no—
431C22×C5—122no—
432C22×C5#93712yes—
433C22×C5C2×D3×D411yescharacteristic
434C2×D5—64no—
435C2×D5—62no—
436C4×C5—62no—
437C4×C5#93712yes—
438C4×C5C2×D3×D411yescharacteristic
439C4×C5C22×#6711yescharacteristic
440Dic5—24no—
441Dic5—62no—
442Dic5—122no—
443C24—21no—
444#41—34no—
445#41—62no—
446#41—308no—
447#41—3016no—
448#41—304no—
449#41—304no—
450#41—302no—
451#41—302no—
452C2×Q8—31no—
453C2×Q8—54no—
454C2×Q8—52no—
455C2×Q8—102no—
456C2×Q8—101no—
457C2×Q8—151no—
458C2×Q8—302no—
459C2×Q8—308no—
460C2×Q8—304no—
461C2×Q8—304no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—31no—
466C2×D4—61no—
467C2×D4—152no—
468C2×D4—151no—
469C2×D4—302no—
470C2×D4—304no—
471C2×D4C2×D3×D512yes—
472C22×C4—61no—
473C22×C4—101no—
474C22×C4—152no—
475C22×C4—302no—
476C22×C4—302no—
477C22×C4C2×D3×D511yescharacteristic
478SD16—64no—
479SD16—108no—
480D8—64no—
481M16—62no—
482C2×C8—32no—
483C2×C8—52no—
484C2×C8—102no—
485C4⋊C4—152no—
486C22⋊C4—304no—
487C22⋊C4—301no—
488C42—301no—
489C3×C5#301011yescharacteristic, complemented, Hall
490C22×C3—22no—
491C22×C3—44no—
492C22×C3—42no—
493C22×C3—84no—
494C22×C3#408312yes—
495C22×C3C2×D4×D511yescharacteristic
496C2×D3—22no—
497C2×D3—42no—
498C2×D3—104no—
499C2×D3—102no—
500C3×C4—104no—
501C3×C4#408312yes—
502C3×C4C2×D4×D511yescharacteristic
503C3×C4C22×C22⋊D511yescharacteristic
504Dic3—22no—
505Dic3—102no—
506Dic3—202no—
507C2×C5—22no—
508C2×C5—82no—
509C2×C5—122no—
510C2×C5#576212yes—
511C2×C5C2×#93711yescharacteristic
512D5—122no—
513C23—22no—
514C23—42no—
515C23—61no—
516C23—82no—
517C23—152no—
518C23#679011yescharacteristic
519Q8—32no—
520Q8—54no—
521Q8—61no—
522Q8—102no—
523Q8—104no—
524Q8—308no—
525Q8—302no—
526D4—22no—
527D4—22no—
528D4—32no—
529D4—42no—
530D4—64no—
531D4—61no—
532D4—308no—
533D4—304no—
534D4—302no—
535D4—1204no—
536C2×C4—61no—
537C2×C4—64no—
538C2×C4—102no—
539C2×C4—104no—
540C2×C4—152no—
541C2×C4—308no—
542C2×C4—308no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4D5×#6712yes—
547C2×C4D3×C22⋊D512yes—
548C2×C4#679011yescharacteristic
549C2×C4C22×D3×D511yescharacteristic
550C8—62no—
551C8—102no—
552C2×C3—22no—
553C2×C3—82no—
554C2×C3#6610912yes—
555C2×C3C2×#408311yescharacteristic
556D3—42no—
557D3—202no—
558C5#8386011yescharacteristic, complemented, Sylow
559C22—22no—
560C22—42no—
561C22—44no—
562C22—62no—
563C22—84no—
564C22—122no—
565C22—302no—
566C22—304no—
567C22#9157712yes—
568C22C2×#679011yescharacteristic
569C4—62no—
570C4—104no—
571C4—302no—
572C4—602no—
573C4#9157712yes—
574C4C2×D5×#6711yescharacteristic
575C4C2×D3×C22⋊D511yescharacteristic
576C3#1061567911yescharacteristic, complemented, Sylow
577C2—22no—
578C2—82no—
579C2—122no—
580C2—602no—
581C2#1175472812yes—
582C2C2×#9157711yescharacteristic
subgroupG/H
centerC22C2×#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C22×D4
hypercenterC22×D4D3×D5
hypocenterC3×C5#3010
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#92004C2semidirect
2. #11756564C2semidirect
3. C2×C5×#932C2semidirect
4. C22×C3×#687C2semidirect
5. #11749161C2semidirect
6. #11749156C2semidirect
7. #11748400C2semidirect
8. #11748388C2semidirect
9. #11748349C2semidirect
16. C2×D15⋊Q8C22semidirect
20. C2×#6768C22semidirect
34. #90973C22semidirect
35. #90971C22semidirect
36. #90967C22semidirect
37. #90957C22semidirect
42. C22×#687D3semidirect
63. C5×#235D4semidirect
70. C2×C3×Dic10D4semidirect
97. C2×#932D5semidirect
230. C2×Dic10#67semidirect
293. #235C22⋊D5semidirect
489. C3×C5#3010semidirect
558. C5#83860semidirect
576. C3#10615679semidirect

Maximal subgroups

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

subgroupindex
C2×#920042
#117565642
C2×C5×#9322
C22×C3×#6872
#117491612
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