Finite Group Databasebeta

← #14281193

Subgroups — #14281193

Order 1920.

560 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91447C211yesmaximal, characteristic
2C3×D5×C22⋊C8C211yesmaximal, characteristic, complemented
3#11748499C211yesmaximal, characteristic, complemented
4#11746290C211yesmaximal, characteristic, complemented
5C5×#4468C211yesmaximal, characteristic, complemented
6#11745953C211yesmaximal, characteristic, complemented
7#11745949C211yesmaximal, characteristic, complemented
8#10598915—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C22×#1201C411yescharacteristic
11C2×#6712C2211yescharacteristic
12C2×C5×(C2×D3)⋊C4C2211yescharacteristic
13C2×C3×C8×D5—21no—
14C2×Dic3⋊Dic5C411yescharacteristic
15C2×(C2×D3)⋊Dic5C411yescharacteristic
16C2×#6665C411yescharacteristic
17#91447—21no—
18#91447—21no—
19#91447—21no—
20#91447—21no—
21C2×#6649—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26C3×#3952—21no—
27#90955—21no—
28#69920—51nomaximal, Hall
29C2×#4029—31no—
30#65015—31no—
31D5×C22⋊C8D311yescharacteristic, complemented
32C5×#323—31no—
33#64745—31no—
34#64689—31no—
35#64689—31no—
36C23×C5×D3C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C22×Dic15C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C3×Dic5C2×C411yescharacteristic
43C2×C3×C4×D5—42no—
44C2×C3×C4×D5D411yescharacteristic
45C2×C3×C4×D5D411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×#1201—21no—
49C2×#1201—21no—
50C2×#1201—42no—
51C2×C3×C5×C8—21no—
52#6712—21no—
53#6712—21no—
54C2×C3⋊#168—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×(C2×D3)⋊C4—21no—
57C2×C5×C3⋊C8—21no—
58C2×C3×#168—21no—
59C3×C8×D5—42no—
60Dic3⋊Dic5—21no—
61Dic3⋊Dic5—21no—
62(C2×D3)⋊Dic5—21no—
63(C2×D3)⋊Dic5—21no—
64#6665—21no—
65#6665—21no—
66#6649—42no—
67C2×#929—51no—
68C2×C3×C22⋊C8—51no—
69#5207—51no—
70#4469—51no—
71#4469—51no—
72#4468—51no—
73#4468D511yescharacteristic, complemented
74C22×C22⋊D5—31no—
75C22×C4×D5C2×D311yescharacteristic
76C2×C5×C22⋊C4—31no—
77C2×C22⋊Dic5—31no—
78C2×#685—31no—
79C2×C4⋊Dic5—31no—
80C2×#683—31no—
81C2×#676—61no—
82C2×C8×D5—21no—
83#4029—61no—
84#4029—61no—
85#4029—61no—
86#4029—61no—
87C5×C22⋊C8—31no—
88C5×C22⋊C8C2×D311yescharacteristic
89C22⋊#168—31no—
90C22⋊#168C2×D311yescharacteristic
91#3952—21no—
92#3952—61no—
93#1468—151noSylow
94C23×C3×C5C22×C411yescharacteristic
95C22×C5×D3—21no—
96C22×C5×D3—21no—
97C22×C5×D3—21no—
98C22×C5×D3—41no—
99C22×C5×D3—41no—
100C22×C3×D5—21no—
101C22×C3×D5—21no—
102C22×C3×D5—22no—
103C22×C3×D5—41no—
104C22×C3×D5C22⋊C411yescharacteristic
105C22×C3×D5C22⋊C411yescharacteristic
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5C2×D411yescharacteristic
109C2×Dic15—21no—
110C2×Dic15—21no—
111C2×Dic15—21no—
112C2×Dic15—21no—
113C2×Dic15—41no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—41no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5C22⋊C411yescharacteristic
118C2×C3×Dic5C22⋊C411yescharacteristic
119C3×C4×D5—22no—
120C3×C4×D5—22no—
121C3×C4×D5—41no—
122C3×C4×D5—41no—
123#1201—42no—
124#1201—42no—
125C3×C5×C8—41no—
126C3⋊#168—41no—
127C3×#168—41no—
128C5×C3⋊C8—41no—
129C23×C3×C4—51no—
130C22×#67—51no—
131C22×C3×C8—101no—
132C2×#217—51no—
133#929—101no—
134#929—101no—
135#929—101no—
136#929—101no—
137C2×(C2×D3)⋊C4—51no—
138C2×(C2×D3)⋊C4C2×D511yescharacteristic
139C2×Dic3⋊C4—51no—
140C2×Dic3⋊C4—51no—
141C2×#208—101no—
142C3×C22⋊C8—51no—
143C3×C22⋊C8—101no—
144C3×C22⋊C8C2×D511yescharacteristic
145#830—51no—
146#830—101no—
147#830C2×D511yescharacteristic
148C24×C5—31no—
149C23×D5C4×D311yescharacteristic
150C22×C4×C5—31no—
151C22×C4×C5C22×D311yescharacteristic
152C2×C22⋊D5—61no—
153C2×C22⋊D5—61no—
154C2×C22⋊D5—122no—
155C22×Dic5—31no—
156C22×Dic5—31no—
157C22×Dic5C4×D311yescharacteristic
158C2×C4×D5—42no—
159C2×C4×D5D1211yescharacteristic
160C2×C4×D5D1211yescharacteristic
161C2×C4×D5#6711yescharacteristic
162C2×C4×D5#6711yescharacteristic
163C2×C5×C8—21no—
164C2×C5×C8—61no—
165C5×C22⋊C4—61no—
166C5×C22⋊C4—61no—
167C22⋊Dic5—61no—
168C22⋊Dic5—61no—
169#685—61no—
170#685—61no—
171C4⋊Dic5—61no—
172C4⋊Dic5—61no—
173#683—61no—
174#683—61no—
175C2×#168—21no—
176C2×#168—61no—
177#676—122no—
178C8×D5—42no—
179C2×#123—151no—
180#407—151no—
181C2×C22⋊C8—51no—
182#324—151no—
183#324—151no—
184#323—31no—
185#323—151no—
186C22×C3×C5—21no—
187C22×C3×C5—21no—
188C22×C3×C5C2×C22⋊C411yescharacteristic
189C22×C3×C5#13111yescharacteristic
190C22×C3×C5#13111yescharacteristic
191C2×C5×D3—41no—
192C2×C5×D3—41no—
193C2×C5×D3—41no—
194C2×C5×D3—81no—
195C2×C5×D3—81no—
196C2×C3×D5—21no—
197C2×C3×D5—21no—
198C2×C3×D5—21no—
199C2×C3×D5—21no—
200C2×C3×D5—21no—
201C2×C3×D5—42no—
202C2×C3×D5—42no—
203C2×C3×D5#9912yes—
204C3×C4×C5—21no—
205C3×C4×C5—21no—
206Dic15—41no—
207Dic15—41no—
208C3×Dic5—21no—
209C3×Dic5—21no—
210C5×Dic3—41no—
211C24×C3—51no—
212C23×D3C4×D511yescharacteristic
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—51no—
217C22×C3×C4—51no—
218C22×C3×C4—202no—
219C22×C3×C4C22×D511yescharacteristic
220C2×#67—101no—
221C2×#67—101no—
222C2×#67—202no—
223C22×Dic3—51no—
224C22×Dic3—51no—
225C22×Dic3C4×D511yescharacteristic
226C2×C3×C8—21no—
227C2×C3×C8—101no—
228C2×C3×C8—202no—
229#217—101no—
230#217—101no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—21no—
233(C2×D3)⋊C4—101no—
234(C2×D3)⋊C4—101no—
235Dic3⋊C4—101no—
236Dic3⋊C4—101no—
237Dic3⋊C4—101no—
238Dic3⋊C4—101no—
239#208—202no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—101no—
242C23×C5—61no—
243C23×C5—61no—
244C23×C5—61no—
245C23×C5—121no—
246C23×C5—121no—
247C23×C5C2×C4×D311yescharacteristic
248C22×D5—21no—
249C22×D5—21no—
250C22×D5—22no—
251C22×D5—41no—
252C22×D5(C2×D3)⋊C411yescharacteristic
253C22×D5(C2×D3)⋊C411yescharacteristic
254C2×C4×C5—41no—
255C2×C4×C5—61no—
256C2×C4×C5—121no—
257C2×C4×C5C2×D1211yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C22⋊D5—122no—
260C22⋊D5—122no—
261C2×Dic5—41no—
262C2×Dic5—61no—
263C2×Dic5—61no—
264C2×Dic5—61no—
265C2×Dic5—61no—
266C2×Dic5—121no—
267C2×Dic5(C2×D3)⋊C411yescharacteristic
268C2×Dic5(C2×D3)⋊C411yescharacteristic
269C4×D5—22no—
270C4×D5—22no—
271C4×D5—41no—
272C4×D5—41no—
273C5×C8—41no—
274C5×C8—121no—
275#168—41no—
276#168—121no—
277C22×D4—151no—
278C23×C4—51no—
279C2×M16—301no—
280C22×C8—101no—
281#123—301no—
282#123—301no—
283#123—301no—
284#123—301no—
285C2×C4⋊C4—151no—
286C2×C4⋊C4—151no—
287C2×C22⋊C4—31no—
288C2×C22⋊C4—151no—
289C2×C22⋊C4—151no—
290C22⋊C8—31no—
291C22⋊C8—51no—
292C22⋊C8—101no—
293C22⋊C8—151no—
294C22⋊C8—301no—
295C22⋊C8D3×D511yescharacteristic
296C2×C3×C5—21no—
297C2×C3×C5—21no—
298C2×C3×C5#40811yescharacteristic
299C2×C3×C5C2×#9911yescharacteristic
300C2×C3×C5#41311yescharacteristic
301C3×D5—22no—
302C3×D5—41no—
303C5×D3—81no—
304C23×C3—51no—
305C23×C3—51no—
306C23×C3—102no—
307C23×C3—101no—
308C23×C3—101no—
309C23×C3—201no—
310C23×C3C2×C4×D511yescharacteristic
311C22×D3—21no—
312C22×D3—21no—
313C22×D3—21no—
314C22×D3—41no—
315C22×D3—41no—
316C2×C3×C4—41no—
317C2×C3×C4—51no—
318C2×C3×C4—51no—
319C2×C3×C4—102no—
320C2×C3×C4—102no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4—201no—
324C2×C3×C4D4×D511yescharacteristic
325C2×C3×C4D4×D511yescharacteristic
326#67—202no—
327#67—202no—
328C2×Dic3—21no—
329C2×Dic3—41no—
330C2×Dic3—101no—
331C2×Dic3—101no—
332C2×Dic3—101no—
333C2×Dic3—101no—
334C2×Dic3—201no—
335C3×C8—41no—
336C3×C8—201no—
337C3⋊C8—41no—
338C3⋊C8—201no—
339C22×C5—21no—
340C22×C5—21no—
341C22×C5—121no—
342C22×C5—121no—
343C22×C5—121no—
344C22×C5—241no—
345C22×C5—241no—
346C22×C5#90111yescharacteristic
347C22×C5#90111yescharacteristic
348C22×C5C2×(C2×D3)⋊C411yescharacteristic
349C2×D5—21no—
350C2×D5—21no—
351C2×D5—21no—
352C2×D5—21no—
353C2×D5—21no—
354C2×D5—42no—
355C2×D5—42no—
356C2×D5#80612yes—
357C4×C5—21no—
358C4×C5—21no—
359C4×C5—121no—
360Dic5—21no—
361Dic5—21no—
362Dic5—121no—
363Dic5—121no—
364C24—31no—
365C24—51no—
366C2×D4—301no—
367C2×D4—301no—
368C2×D4—602no—
369C22×C4—31no—
370C22×C4—51no—
371C22×C4—51no—
372C22×C4—51no—
373C22×C4—51no—
374C22×C4—51no—
375C22×C4—151no—
376C22×C4—151no—
377C22×C4—202no—
378C22×C4C2×D3×D511yescharacteristic
379M16—602no—
380C2×C8—21no—
381C2×C8—61no—
382C2×C8—101no—
383C2×C8—202no—
384C2×C8—301no—
385C4⋊C4—301no—
386C4⋊C4—301no—
387C4⋊C4—301no—
388C4⋊C4—301no—
389C22⋊C4—61no—
390C22⋊C4—61no—
391C22⋊C4—301no—
392C22⋊C4—301no—
393C22⋊C4—301no—
394C22⋊C4—301no—
395C3×C5#146811yescharacteristic, complemented, Hall
396C22×C3—21no—
397C22×C3—21no—
398C22×C3—52no—
399C22×C3—101no—
400C22×C3—101no—
401C22×C3—101no—
402C22×C3—101no—
403C22×C3—101no—
404C22×C3—202no—
405C22×C3—202no—
406C22×C3D5×C22⋊C411yescharacteristic
407C22×C3#404711yescharacteristic
408C22×C3#405311yescharacteristic
409C2×D3—41no—
410C2×D3—41no—
411C2×D3—41no—
412C2×D3—81no—
413C2×D3—81no—
414C3×C4—21no—
415C3×C4—21no—
416C3×C4—101no—
417C3×C4—101no—
418Dic3—41no—
419Dic3—201no—
420Dic3—201no—
421C2×C5—21no—
422C2×C5—21no—
423C2×C5—241no—
424C2×C5C2×#80611yescharacteristic
425C2×C5#511011yescharacteristic
426C2×C5#513211yescharacteristic
427D5—22no—
428D5—41no—
429C23—51no—
430C23—51no—
431C23—61no—
432C23—61no—
433C23—61no—
434C23—102no—
435C23—101no—
436C23—101no—
437C23—121no—
438C23—121no—
439C23—201no—
440C23C4×D3×D511yescharacteristic
441D4—602no—
442D4—602no—
443C2×C4—41no—
444C2×C4—51no—
445C2×C4—51no—
446C2×C4—61no—
447C2×C4—102no—
448C2×C4—102no—
449C2×C4—121no—
450C2×C4—201no—
451C2×C4—201no—
452C2×C4—201no—
453C2×C4—301no—
454C2×C4—301no—
455C2×C4—301no—
456C2×C4—301no—
457C2×C4—601no—
458C2×C4D5×D1211yescharacteristic
459C2×C4D5×#6711yescharacteristic
460C8—41no—
461C8—121no—
462C8—201no—
463C8—601no—
464C2×C3—21no—
465C2×C3—21no—
466C2×C3—102no—
467C2×C3—201no—
468C2×C3#6501611yescharacteristic
469C2×C3D5×#9911yescharacteristic
470C2×C3#6503411yescharacteristic
471D3—81no—
472C5#6992011yescharacteristic, complemented, Sylow
473C22—21no—
474C22—21no—
475C22—52no—
476C22—101no—
477C22—101no—
478C22—101no—
479C22—101no—
480C22—101no—
481C22—121no—
482C22—121no—
483C22—121no—
484C22—202no—
485C22—202no—
486C22—241no—
487C22—241no—
488C22#9126511yescharacteristic
489C22#9126611yescharacteristic
490C22D5×(C2×D3)⋊C411yescharacteristic
491C4—21no—
492C4—21no—
493C4—101no—
494C4—101no—
495C4—121no—
496C4—601no—
497C4—601no—
498C3#1059891511yescharacteristic, complemented, Sylow
499C2—21no—
500C2—21no—
501C2—102no—
502C2—201no—
503C2—241no—
504C2D5×#80611yescharacteristic
505C2#1174813411yescharacteristic
506C2#1174823011yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1201C4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1468
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C3×D5×C22⋊C8C2semidirect
3. #11748499C2semidirect
4. #11746290C2semidirect
5. C5×#4468C2semidirect
6. #11745953C2semidirect
7. #11745949C2semidirect
31. D5×C22⋊C8D3semidirect
73. #4468D5semidirect
395. C3×C5#1468semidirect
472. C5#69920semidirect
498. C3#10598915semidirect

Maximal subgroups

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

subgroupindex
C2×#914472
C3×D5×C22⋊C82
#117484992
#117462902
C5×#44682
#117459532
#117459492
#105989153
#699205