Finite Group Databasebeta

← #14280866

Subgroups — #14280866

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91446C211yesmaximal, characteristic
2C5×D3×C22⋊C8C211yesmaximal, characteristic, complemented
3D3×C22⋊#168C211yesmaximal, characteristic, complemented
4#11746289C211yesmaximal, characteristic, complemented
5C3×#64689C211yesmaximal, characteristic, complemented
6#11745951C211yesmaximal, characteristic, complemented
7#11745950C211yesmaximal, characteristic, complemented
8#10600712—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C22×#1203C411yescharacteristic
11C22×#1200C411yescharacteristic
12C2×#6714C2211yescharacteristic
13C2×C5×D3×C8—21no—
14C2×C3×#683C2211yescharacteristic
15C2×(C2×D3)⋊Dic5C411yescharacteristic
16C2×Dic3×Dic5C411yescharacteristic
17#91446—21no—
18#91446—21no—
19#91446—21no—
20#91446—21no—
21C2×D3×#168—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23#91114C2211yescharacteristic
24C5×#830C2211yescharacteristic
25C5×(C2×D3)⋊C8—21no—
26C3×C22⋊#168C2211yescharacteristic
27(C2×D3)⋊#168—21no—
28#68143—51nomaximal, Hall
29C2×C4×C22⋊D5—31no—
30C2×C5×C22⋊C8—31no—
31C2×C22⋊#168—31no—
32#64689—31no—
33#64689D311yescharacteristic, complemented
34#64688—31no—
35#64688—31no—
36C23×D15C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C22×C3×C4×C5C2311yescharacteristic
39C22×Dic15C2×C411yescharacteristic
40C22×C5×Dic3C2×C411yescharacteristic
41C2×C4×C5×D3—42no—
42C2×C4×C5×D3D411yescharacteristic
43C2×C4×C5×D3D411yescharacteristic
44C2×C4×C5×D3D411yescharacteristic
45C2×C4×C5×D3D411yescharacteristic
46C22×C3×Dic5C2×C411yescharacteristic
47C22×C3×Dic5C2×C411yescharacteristic
48C2×#1203—21no—
49C2×#1203—21no—
50C2×#1203—22no—
51C2×#1203C814yescomplemented
52C2×#1200—21no—
53C2×#1200—21no—
54C2×#1200—42no—
55C2×C3×C5×C8—21no—
56#6714—21no—
57#6714—21no—
58C2×C3⋊#168—21no—
59C2×C5×C3⋊C8—21no—
60C5×D3×C8—42no—
61C3×#683—21no—
62C3×#683—21no—
63C2×C3×#168—21no—
64(C2×D3)⋊Dic5—21no—
65(C2×D3)⋊Dic5—21no—
66Dic3×Dic5—21no—
67Dic3×Dic5—21no—
68D3×#168—42no—
69C2×#893—51no—
70D3×C22⋊C8—51no—
71D3×C22⋊C8D511yescharacteristic, complemented
72C3×#324—51no—
73#4528—51no—
74#4468—51no—
75#4468—51no—
76C23×C4×C5—31no—
77C22×C22⋊D5—31no—
78C22×C4×D5—31no—
79C22×C5×C8—61no—
80C2×C22⋊Dic5—31no—
81C4×C22⋊D5—61no—
82C4×C22⋊D5—61no—
83C4×C22⋊D5—61no—
84C4×C22⋊D5—61no—
85C2×#685—31no—
86C2×#683C2×D311yescharacteristic
87C2×C4×Dic5—31no—
88C22×#168—61no—
89C5×C22⋊C8—31no—
90C5×C22⋊C8—61no—
91C5×C22⋊C8C2×D311yescharacteristic
92C22⋊#168—31no—
93C22⋊#168—61no—
94C22⋊#168C2×D311yescharacteristic
95#1459—151noSylow
96C23×C3×C5C22×C411yescharacteristic
97C22×D15—21no—
98C22×D15—21no—
99C22×D15—41no—
100C22×D15—41no—
101C22×D15C2×C812yescomplemented
102C22×C5×D3—41no—
103C22×C5×D3—41no—
104C22×C5×D3C22⋊C411yescharacteristic
105C22×C5×D3C22⋊C411yescharacteristic
106C22×C5×D3C2×C812yes—
107C22×C5×D3M1612yes—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×Dic15—21no—
112C2×Dic15—41no—
113C2×C5×Dic3—22no—
114C2×C5×Dic3C22⋊C411yescharacteristic
115C2×C5×Dic3C22⋊C411yescharacteristic
116C4×C5×D3—22no—
117C4×C5×D3—22no—
118C4×C5×D3—41no—
119C4×C5×D3—41no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—41no—
124C2×C3×Dic5C2×C812yescomplemented
125#1203—24no—
126#1203—24no—
127#1200—42no—
128#1200—42no—
129C3×C5×C8—41no—
130C3⋊#168—41no—
131C3×#168—41no—
132C5×C3⋊C8—41no—
133C22×D12—51no—
134C22×C4×D3—51no—
135C22×C4×D3C2×D511yescharacteristic
136C2×C3×C4⋊C4—51no—
137C2×(C2×D3)⋊C4—51no—
138C2×(C2×D3)⋊C4—51no—
139C2×C4×Dic3—51no—
140C2×D3×C8—21no—
141C2×D3×C8—101no—
142#893—101no—
143#893—101no—
144#893—101no—
145#893—101no—
146C3×C22⋊C8—51no—
147C3×C22⋊C8C2×D511yescharacteristic
148#830—51no—
149#830C2×D511yescharacteristic
150(C2×D3)⋊C8—21no—
151(C2×D3)⋊C8—101no—
152C24×C5—31no—
153C23×D5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×C4×C5—31no—
157C22×C4×C5—31no—
158C22×C4×C5—31no—
159C22×C4×C5—122no—
160C22×C4×C5C22×D311yescharacteristic
161C2×C22⋊D5—34no—
162C2×C22⋊D5—62no—
163C2×C22⋊D5—61no—
164C2×C22⋊D5—61no—
165C22×Dic5—31no—
166C22×Dic5C4×D311yescharacteristic
167C22×Dic5C4×D311yescharacteristic
168C2×C4×D5—61no—
169C2×C4×D5—61no—
170C2×C4×D5—122no—
171C2×C5×C8—21no—
172C2×C5×C8—61no—
173C2×C5×C8—122no—
174C22⋊Dic5—61no—
175C22⋊Dic5—61no—
176#685—61no—
177#685—61no—
178#683—21no—
179#683—21no—
180C4×Dic5—61no—
181C4×Dic5—61no—
182C2×#168—21no—
183C2×#168—61no—
184C2×#168—122no—
185C2×C4×D4—151no—
186C2×C22⋊C8—31no—
187C2×C22⋊C8—151no—
188#324—51no—
189#324—151no—
190#323—151no—
191#323—151no—
192C22×C3×C5—21no—
193C22×C3×C5—21no—
194C22×C3×C5C2×C22⋊C411yescharacteristic
195C22×C3×C5C22×C811yescharacteristic
196C22×C3×C5C2×M1611yescharacteristic
197C2×D15—22no—
198C2×D15—42no—
199C2×D15—41no—
200C2×D15—41no—
201C2×D15—42no—
202C2×C5×D3—21no—
203C2×C5×D3—21no—
204C2×C5×D3—21no—
205C2×C5×D3—21no—
206C2×C5×D3—42no—
207C2×C5×D3—42no—
208C2×C5×D3C22⋊C812yes—
209C2×C5×D3C22⋊C812yes—
210C3×C4×C5—21no—
211C3×C4×C5—21no—
212Dic15—41no—
213C3×Dic5—22no—
214C3×Dic5—41no—
215C5×Dic3—21no—
216C5×Dic3#9912yes—
217C23×D3—51no—
218C23×D3C4×D511yescharacteristic
219C22×C3×C4—51no—
220C22×C3×C4—51no—
221C22×C3×C4C22×D511yescharacteristic
222C22×Dic3—51no—
223C22×Dic3C4×D511yescharacteristic
224C2×D12—54no—
225C2×D12—102no—
226C2×D12—101no—
227C2×D12—101no—
228C2×C4×D3—42no—
229C2×C4×D3—101no—
230C2×C4×D3—101no—
231C2×C4×D3—202no—
232C2×C4×D3D2011yescharacteristic
233C2×C4×D3D2011yescharacteristic
234C2×C4×D3C22⋊D511yescharacteristic
235C2×C4×D3C22⋊D511yescharacteristic
236C2×C3×C8—21no—
237C2×C3×C8—101no—
238C3×C4⋊C4—101no—
239C3×C4⋊C4—101no—
240(C2×D3)⋊C4—101no—
241(C2×D3)⋊C4—101no—
242(C2×D3)⋊C4—101no—
243(C2×D3)⋊C4—101no—
244C4×Dic3—101no—
245C4×Dic3—101no—
246C2×C3⋊C8—21no—
247C2×C3⋊C8—101no—
248D3×C8—42no—
249D3×C8—202no—
250C23×C5—31no—
251C23×C5—31no—
252C23×C5—32no—
253C23×C5—32no—
254C23×C5—121no—
255C23×C5—121no—
256C23×C5C2×C4×D311yescharacteristic
257C22×D5—32no—
258C22×D5—61no—
259C22×D5—61no—
260C22×D5—121no—
261C22×D5—121no—
262C2×C4×C5—31no—
263C2×C4×C5—31no—
264C2×C4×C5—41no—
265C2×C4×C5—62no—
266C2×C4×C5—62no—
267C2×C4×C5—62no—
268C2×C4×C5—121no—
269C2×C4×C5—121no—
270C2×C4×C5D3×D411yescharacteristic
271C2×C4×C5D3×D411yescharacteristic
272C22⋊D5—64no—
273C22⋊D5—64no—
274C2×Dic5—21no—
275C2×Dic5—21no—
276C2×Dic5—21no—
277C2×Dic5—41no—
278C2×Dic5—61no—
279C2×Dic5—121no—
280C2×Dic5D3×C812yescomplemented
281C4×D5—122no—
282C4×D5—122no—
283C5×C8—41no—
284C5×C8—121no—
285#168—41no—
286#168—121no—
287C22×D4—151no—
288C23×C4—31no—
289C23×C4—151no—
290C22×C8—61no—
291C22×C8—301no—
292C4×D4—301no—
293C4×D4—301no—
294C4×D4—301no—
295C4×D4—301no—
296C2×C4⋊C4—51no—
297C2×C22⋊C4—151no—
298C2×C22⋊C4—151no—
299C2×C42—151no—
300C22⋊C8—31no—
301C22⋊C8—51no—
302C22⋊C8—61no—
303C22⋊C8—151no—
304C22⋊C8—301no—
305C22⋊C8D3×D511yescharacteristic
306C2×C3×C5—21no—
307C2×C3×C5—21no—
308C2×C3×C5C2×C22⋊C811yescharacteristic
309C2×C3×C5C2×#9911yescharacteristic
310C2×C3×C5#41311yescharacteristic
311D15—42no—
312C5×D3—22no—
313C5×D3—22no—
314C23×C3C2×C4×D511yescharacteristic
315C22×D3—41no—
316C22×D3—41no—
317C22×D3—52no—
318C22×D3—101no—
319C22×D3—101no—
320C22×D3—201no—
321C22×D3—201no—
322C22×D3C8×D512yes—
323C22×D3#67612yes—
324C22×D3#68511yescharacteristic
325C22×D3#68511yescharacteristic
326C2×C3×C4—41no—
327C2×C3×C4—52no—
328C2×C3×C4—101no—
329C2×C3×C4—101no—
330C2×C3×C4—101no—
331C2×C3×C4—201no—
332C2×C3×C4C2×D2011yescharacteristic
333C2×C3×C4C2×C22⋊D511yescharacteristic
334C2×Dic3—22no—
335C2×Dic3—101no—
336C2×Dic3—201no—
337C2×Dic3#68511yescharacteristic
338C2×Dic3#68511yescharacteristic
339D12—104no—
340D12—104no—
341C4×D3—22no—
342C4×D3—22no—
343C4×D3—41no—
344C4×D3—41no—
345C4×D3—202no—
346C4×D3—202no—
347C3×C8—41no—
348C3×C8—201no—
349C3⋊C8—41no—
350C3⋊C8—201no—
351C22×C5—21no—
352C22×C5—21no—
353C22×C5—32no—
354C22×C5—32no—
355C22×C5—61no—
356C22×C5—61no—
357C22×C5—61no—
358C22×C5—61no—
359C22×C5—122no—
360C22×C5—122no—
361C22×C5D3×C22⋊C411yescharacteristic
362C22×C5C2×D3×C811yescharacteristic
363C22×C5D3×M1611yescharacteristic
364C2×D5—62no—
365C2×D5—122no—
366C2×D5—121no—
367C2×D5—121no—
368C2×D5—122no—
369C4×C5—21no—
370C4×C5—21no—
371C4×C5—32no—
372C4×C5—61no—
373Dic5—22no—
374Dic5—41no—
375Dic5—121no—
376C24—31no—
377C24—151no—
378C2×D4—154no—
379C2×D4—301no—
380C2×D4—301no—
381C2×D4—302no—
382C22×C4—31no—
383C22×C4—31no—
384C22×C4—31no—
385C22×C4—31no—
386C22×C4—31no—
387C22×C4—51no—
388C22×C4—51no—
389C22×C4—122no—
390C22×C4—151no—
391C22×C4—301no—
392C22×C4—301no—
393C22×C4—602no—
394C22×C4C2×D3×D511yescharacteristic
395C2×C8—21no—
396C2×C8—61no—
397C2×C8—101no—
398C2×C8—122no—
399C2×C8—301no—
400C2×C8—602no—
401C4⋊C4—101no—
402C4⋊C4—101no—
403C22⋊C4—301no—
404C22⋊C4—301no—
405C22⋊C4—301no—
406C22⋊C4—301no—
407C42—301no—
408C42—301no—
409C3×C5#145911yescharacteristic, complemented, Hall
410C22×C3—21no—
411C22×C3—21no—
412C22×C3C2×C8×D511yescharacteristic
413C22×C3C2×#67611yescharacteristic
414C22×C3C2×#68511yescharacteristic
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—21no—
418C2×D3—21no—
419C2×D3—42no—
420C2×D3—42no—
421C2×D3—102no—
422C2×D3—202no—
423C2×D3—201no—
424C2×D3—201no—
425C2×D3—202no—
426C2×D3#395212yes—
427C2×D3#395212yes—
428C3×C4—21no—
429C3×C4—21no—
430C3×C4—102no—
431C3×C4—201no—
432Dic3—21no—
433Dic3—201no—
434Dic3#393812yes—
435C2×C5—21no—
436C2×C5—21no—
437C2×C5—62no—
438C2×C5—62no—
439C2×C5D3×C22⋊C811yescharacteristic
440C2×C5D3×#9911yescharacteristic
441C2×C5#475111yescharacteristic
442D5—122no—
443C23—31no—
444C23—31no—
445C23—32no—
446C23—32no—
447C23—121no—
448C23—121no—
449C23—152no—
450C23—301no—
451C23—301no—
452C23—601no—
453C23—601no—
454C23C4×D3×D511yescharacteristic
455D4—304no—
456D4—304no—
457C2×C4—31no—
458C2×C4—31no—
459C2×C4—41no—
460C2×C4—52no—
461C2×C4—62no—
462C2×C4—62no—
463C2×C4—62no—
464C2×C4—101no—
465C2×C4—101no—
466C2×C4—101no—
467C2×C4—121no—
468C2×C4—121no—
469C2×C4—201no—
470C2×C4—301no—
471C2×C4—602no—
472C2×C4—602no—
473C2×C4—601no—
474C2×C4D3×D2011yescharacteristic
475C2×C4D3×C22⋊D511yescharacteristic
476C8—41no—
477C8—121no—
478C8—201no—
479C8—601no—
480C2×C3—21no—
481C2×C3—21no—
482C2×C3C2×#393811yescharacteristic
483C2×C3C2×#395211yescharacteristic
484C2×C3#6542111yescharacteristic
485D3—22no—
486D3—22no—
487D3—202no—
488C5#6814311yescharacteristic, complemented, Sylow
489C22—21no—
490C22—21no—
491C22—32no—
492C22—32no—
493C22—61no—
494C22—61no—
495C22—61no—
496C22—61no—
497C22—122no—
498C22—122no—
499C22—302no—
500C22—602no—
501C22—602no—
502C22—601no—
503C22—601no—
504C22D3×C8×D511yescharacteristic
505C22D3×#67611yescharacteristic
506C22D3×#68511yescharacteristic
507C4—21no—
508C4—21no—
509C4—32no—
510C4—61no—
511C4—102no—
512C4—201no—
513C4—601no—
514C3#1060071211yescharacteristic, complemented, Sylow
515C2—21no—
516C2—21no—
517C2—62no—
518C2—62no—
519C2—602no—
520C2D3×#393811yescharacteristic
521C2D3×#395211yescharacteristic
522C2#1174823511yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC22×C3×C5C22×C8
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#1203C4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1459
LCSG ▷ C22×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. C5×D3×C22⋊C8C2semidirect
3. D3×C22⋊#168C2semidirect
4. #11746289C2semidirect
5. C3×#64689C2semidirect
6. #11745951C2semidirect
7. #11745950C2semidirect
33. #64689D3semidirect
51. C2×#1203C8semidirect
71. D3×C22⋊C8D5semidirect
101. C22×D15C2×C8semidirect
124. C2×C3×Dic5C2×C8semidirect
280. C2×Dic5D3×C8semidirect
409. C3×C5#1459semidirect
488. C5#68143semidirect
514. C3#10600712semidirect

Maximal subgroups

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

subgroupindex
C2×#914462
C5×D3×C22⋊C82
D3×C22⋊#1682
#117462892
C3×#646892
#117459512
#117459502
#106007123
#681435