Finite Group Databasebeta

← #14459105

Subgroups — #14459105

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#547C211yesmaximal, characteristic
2D4×Dic30C211yesmaximal, characteristic, complemented
3#11751195C211yesmaximal, characteristic, complemented
4#11751194C211yesmaximal, characteristic, complemented
5#11751142C212yesmaximal, complemented
6#11751141C212yesmaximal, complemented
7#11751120C211yesmaximal, characteristic, complemented
8C4×#6716C211yesmaximal, characteristic, complemented
9D4×C3⋊#168C211yesmaximal, characteristic, complemented
10#11751072C212yesmaximal, complemented
11C2×#91094C212yesmaximal, complemented
12#10615262—31nomaximal, Hall
13C2×C3×C5×#41—21no—
14C22×Dic30C2212yes—
15C3×C5×C4⋊Q8C2211yescharacteristic
16C3×C5×#123—22no—
17C3×C5×C22⋊Q8—21no—
18C3×C5×#121C2212yes—
19C3×C4×C5×D4C2211yescharacteristic
20C3×C4×C5×D4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2212yes—
22D4×Dic15—21no—
23C2×#6716C2211yescharacteristic
24C2×#6716C2212yes—
25#91813C2212yes—
26C22×C3⋊#168C2212yes—
27#91777—21no—
28#91767—22no—
29#91758C2211yescharacteristic
30C4×Dic30C2211yescharacteristic
31#91116C2211yescharacteristic
32#91114C2212yes—
33#91094C2212yes—
34#91094C2212yes—
35#91094C2212yes—
36#91094C2211yescharacteristic
37#91094C2212yes—
38#91092C2212yes—
39#91092C2211yescharacteristic
40C4⋊(C3⋊#168)C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#83531—51nomaximal, Hall
43C5×#547D311yescharacteristic
44D4×Dic10—31no—
45#65383—31no—
46#65382—31no—
47#65330—32no—
48#65329—32no—
49#65308—31no—
50C4×#687—31no—
51D4×#168—31no—
52#65260—32no—
53C2×#3942—32no—
54C3×C5×#41—44no—
55C2×C3×C5×Q8—21no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4D411yescharacteristic
58C2×C3×C5×D4C2311yescharacteristic
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5C2312yes—
62C22×Dic15—22no—
63C2×Dic30—24no—
64C2×Dic30—22no—
65C2×Dic30—42no—
66C2×Dic30C2312yes—
67C2×Dic30C2311yescharacteristic
68C3×C5×C4⋊C4—22no—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4D411yescharacteristic
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C4⋊C4C2312yes—
73C3×C5×C22⋊C4—21no—
74C3×C5×C22⋊C4—22no—
75C3×C5×C22⋊C4D412yes—
76C3×C42×C5C2311yescharacteristic
77#6719—22no—
78#6716—22no—
79#6716—42no—
80C4⋊Dic15—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15C2311yescharacteristic
83#6712—21no—
84#6712—22no—
85C4×Dic15—21no—
86C2×C3⋊#168—42no—
87C2×C3⋊#168C2311yescharacteristic
88C2×C3⋊#168C2312yes—
89C2×C3⋊#168C2311yescharacteristic
90C3×#547D511yescharacteristic
91D4×Dic6—51no—
92#5094—51no—
93#5093—51no—
94#5041—52no—
95#5040—52no—
96#5019—51no—
97C4×#214—51no—
98D4×C3⋊C8—51no—
99#4971—52no—
100C2×#810—52no—
101C2×C5×#41—21no—
102C22×Dic10—32no—
103C5×C4⋊Q8C2×D311yescharacteristic
104C5×#123—22no—
105C5×C22⋊Q8—21no—
106C5×#121C2×D312yes—
107C4×C5×D4C2×D311yescharacteristic
108C4×C5×D4C2×D311yescharacteristic
109C2×C5×C4⋊C4C2×D312yes—
110D4×Dic5—61no—
111C2×#687—31no—
112C2×#687—32no—
113#4070—32no—
114C22×#168—32no—
115#4034—61no—
116#4024—62no—
117#4015—31no—
118C4×Dic10—31no—
119#3964—31no—
120C22⋊#168—32no—
121#3942—31no—
122#3942—32no—
123#3942—32no—
124#3942—32no—
125#3942—32no—
126#3940—31no—
127#3940—32no—
128C4⋊#168—31no—
129C4×#168—31no—
130#3298—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5C2×D412yes—
133C3×C5×Q8—42no—
134C3×C5×D4—21no—
135C3×C5×D4—21no—
136C3×C5×D4—44no—
137C3×C5×D4SD1614yescomplemented
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—44no—
143C2×C3×C4×C5—42no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2411yescharacteristic
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×Dic15—22no—
151C2×Dic15—44no—
152Dic30—21no—
153Dic30—22no—
154Dic30—22no—
155Dic30—44no—
156Dic30#4112yescomplemented
157C3⋊#168—21no—
158C3⋊#168—21no—
159C3⋊#168—22no—
160C2×C3×#41—21no—
161C22×Dic6—52no—
162C3×C4⋊Q8C2×D511yescharacteristic
163C3×#123—22no—
164C3×C22⋊Q8—21no—
165C3×#121C2×D512yes—
166C3×C4×D4C2×D511yescharacteristic
167C3×C4×D4C2×D511yescharacteristic
168C2×C3×C4⋊C4C2×D512yes—
169D4×Dic3—101no—
170C2×#214—51no—
171C2×#214—52no—
172#924—52no—
173C22×C3⋊C8—52no—
174#888—101no—
175#878—102no—
176#869—51no—
177C4×Dic6—51no—
178#832—51no—
179#830—52no—
180#810—51no—
181#810—52no—
182#810—52no—
183#810—52no—
184#810—52no—
185#808—51no—
186#808—52no—
187C4⋊(C3⋊C8)—51no—
188C4×C3⋊C8—51no—
189C5×#41—44no—
190C2×C5×Q8—21no—
191C2×C5×D4—22no—
192C2×C5×D4#6711yescharacteristic
193C2×C5×D4C22×D311yescharacteristic
194C22×C4×C5—22no—
195C22×C4×C5—21no—
196C22×C4×C5C22×D312yes—
197C22×Dic5—62no—
198C2×Dic10—31no—
199C2×Dic10—32no—
200C2×Dic10—64no—
201C2×Dic10—62no—
202C2×Dic10—122no—
203C5×C4⋊C4—22no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4#6711yescharacteristic
206C5×C4⋊C4C22×D311yescharacteristic
207C5×C4⋊C4C22×D312yes—
208C5×C22⋊C4—21no—
209C5×C22⋊C4—22no—
210C5×C22⋊C4#6712yes—
211C42×C5C22×D311yescharacteristic
212C22⋊Dic5—62no—
213#687—62no—
214#687—122no—
215C4⋊Dic5—31no—
216C4⋊Dic5—61no—
217C4⋊Dic5—61no—
218#683—61no—
219#683—62no—
220C4×Dic5—61no—
221C2×#168—31no—
222C2×#168—31no—
223C2×#168—32no—
224C2×#168—122no—
225D4×Q8—151no—
226#547D1511yescharacteristic
227#487—151no—
228#483—152no—
229#475—151no—
230#465—152no—
231#461—151no—
232#448—152no—
233C4×SD16—151no—
234C8×D4—151no—
235C2×#103—152no—
236C22×C3×C5—22no—
237C22×C3×C5—22no—
238C22×C3×C5—41no—
239C22×C3×C5—41no—
240C22×C3×C5—41no—
241C22×C3×C5C2×SD1614yes—
242C22×C3×C5C22×D411yescharacteristic
243C3×C4×C5—22no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5—42no—
247C3×C4×C5C2×SD1612yes—
248C3×C4×C5C2×#4111yescharacteristic
249C3×C4×C5H(5,𝔽2)11yescharacteristic
250Dic15—22no—
251Dic15—42no—
252Dic15—41no—
253C3×#41—44no—
254C2×C3×Q8—21no—
255C2×C3×D4—22no—
256C2×C3×D4C22⋊D511yescharacteristic
257C2×C3×D4C22×D511yescharacteristic
258C22×C3×C4—22no—
259C22×C3×C4—21no—
260C22×C3×C4C22×D512yes—
261C22×Dic3—102no—
262C2×Dic6—51no—
263C2×Dic6—52no—
264C2×Dic6—104no—
265C2×Dic6—102no—
266C2×Dic6—202no—
267C3×C4⋊C4—22no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4C22⋊D511yescharacteristic
270C3×C4⋊C4C22×D511yescharacteristic
271C3×C4⋊C4C22×D512yes—
272C3×C22⋊C4—21no—
273C3×C22⋊C4—22no—
274C3×C22⋊C4C22⋊D512yes—
275C3×C42C22×D511yescharacteristic
276#217—102no—
277#214—102no—
278#214—202no—
279C4⋊Dic3—51no—
280C4⋊Dic3—101no—
281C4⋊Dic3—101no—
282Dic3⋊C4—101no—
283Dic3⋊C4—102no—
284C4×Dic3—101no—
285C2×C3⋊C8—51no—
286C2×C3⋊C8—51no—
287C2×C3⋊C8—52no—
288C2×C3⋊C8—202no—
289C23×C5—21no—
290C23×C5C2×#6712yes—
291C5×Q8—42no—
292C5×D4—21no—
293C5×D4—21no—
294C5×D4—44no—
295C5×D4#21414yescomplemented
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—21no—
299C2×C4×C5—22no—
300C2×C4×C5—44no—
301C2×C4×C5—42no—
302C2×C4×C5C2×#6711yescharacteristic
303C2×C4×C5C2×#6712yes—
304C2×C4×C5C2×#6711yescharacteristic
305C2×C4×C5C23×D311yescharacteristic
306C2×Dic5—61no—
307C2×Dic5—61no—
308C2×Dic5—62no—
309C2×Dic5—124no—
310Dic10—32no—
311Dic10—61no—
312Dic10—62no—
313Dic10—62no—
314Dic10—124no—
315#168—61no—
316#168—61no—
317#168—62no—
318C2×#41—21no—
319C22×Q8—152no—
320C2×SD16—151no—
321C2×SD16—152no—
322C22×C8—152no—
323C4⋊Q8—151no—
324C4⋊Q8—301no—
325C4⋊Q8C2×D1511yescharacteristic
326#123—22no—
327C22⋊Q8—21no—
328C22⋊Q8—152no—
329C22⋊Q8—302no—
330#121C2×D1512yes—
331C4×Q8—151no—
332C4×D4—301no—
333C4×D4C2×D1511yescharacteristic
334C4×D4C2×D1511yescharacteristic
335C2×C4⋊C4C2×D1512yes—
336#106—151no—
337#106—152no—
338C4⋊C8—151no—
339#103—151no—
340#103—152no—
341#103—152no—
342#103—152no—
343#103—152no—
344#102—151no—
345C22⋊C8—152no—
346C4×C8—151no—
347C2×C3×C5—24no—
348C2×C3×C5—81no—
349C2×C3×C5#54611yescharacteristic
350C2×C3×C5C22×SD1611yescharacteristic
351C2×C3×C5#57811yescharacteristic
352C23×C3—21no—
353C23×C3C2×C22⋊D512yes—
354C3×Q8—42no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—44no—
358C3×D4#68714yescomplemented
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—21no—
362C2×C3×C4—22no—
363C2×C3×C4—44no—
364C2×C3×C4—42no—
365C2×C3×C4C2×C22⋊D511yescharacteristic
366C2×C3×C4C2×C22⋊D512yes—
367C2×C3×C4C2×C22⋊D511yescharacteristic
368C2×C3×C4C23×D511yescharacteristic
369C2×Dic3—101no—
370C2×Dic3—101no—
371C2×Dic3—102no—
372C2×Dic3—204no—
373Dic6—52no—
374Dic6—101no—
375Dic6—102no—
376Dic6—102no—
377Dic6—204no—
378C3⋊C8—101no—
379C3⋊C8—101no—
380C3⋊C8—102no—
381C22×C5—22no—
382C22×C5—22no—
383C22×C5—41no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5C2×#21414yes—
387C22×C5C22×#6711yescharacteristic
388C4×C5—22no—
389C4×C5—21no—
390C4×C5—41no—
391C4×C5—42no—
392C4×C5C2×#21412yes—
393C4×C5D3×#4111yescharacteristic
394C4×C5#100911yescharacteristic
395Dic5—62no—
396Dic5—122no—
397Dic5—121no—
398#41—44no—
399C2×Q8—21no—
400C2×Q8—151no—
401C2×Q8—152no—
402C2×Q8—304no—
403C2×Q8—302no—
404C2×Q8—602no—
405C2×D4—22no—
406C2×D4#122011yescharacteristic
407C2×D4C22×D1511yescharacteristic
408C22×C4—22no—
409C22×C4—21no—
410C22×C4—302no—
411C22×C4C22×D1512yes—
412SD16—302no—
413SD16—602no—
414C2×C8—151no—
415C2×C8—151no—
416C2×C8—152no—
417C2×C8—602no—
418C4⋊C4—22no—
419C4⋊C4—21no—
420C4⋊C4—151no—
421C4⋊C4—301no—
422C4⋊C4—301no—
423C4⋊C4—302no—
424C4⋊C4—301no—
425C4⋊C4#122011yescharacteristic
426C4⋊C4C22×D1511yescharacteristic
427C4⋊C4C22×D1512yes—
428C22⋊C4—21no—
429C22⋊C4—22no—
430C22⋊C4—302no—
431C22⋊C4#122012yes—
432C42—301no—
433C42C22×D1511yescharacteristic
434C3×C5#329811yescharacteristic, complemented, Hall
435C22×C3—22no—
436C22×C3—22no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3C2×#68714yes—
441C22×C3C22×C22⋊D511yescharacteristic
442C3×C4—22no—
443C3×C4—21no—
444C3×C4—41no—
445C3×C4—42no—
446C3×C4C2×#68712yes—
447C3×C4D5×#4111yescharacteristic
448C3×C4#414911yescharacteristic
449Dic3—102no—
450Dic3—202no—
451Dic3—201no—
452C2×C5—24no—
453C2×C5—81no—
454C2×C5C22×#21411yescharacteristic
455C2×C5#582911yescharacteristic
456C2×C5#583811yescharacteristic
457C23—21no—
458C23C2×#122012yes—
459Q8—42no—
460Q8—152no—
461Q8—301no—
462Q8—302no—
463Q8—302no—
464Q8—604no—
465D4—21no—
466D4—21no—
467D4—44no—
468D4#671614yescomplemented
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—21no—
472C2×C4—22no—
473C2×C4—44no—
474C2×C4—42no—
475C2×C4—301no—
476C2×C4—301no—
477C2×C4—302no—
478C2×C4—604no—
479C2×C4C2×#122011yescharacteristic
480C2×C4C2×#122012yes—
481C2×C4C2×#122011yescharacteristic
482C2×C4C23×D1511yescharacteristic
483C8—301no—
484C8—301no—
485C8—302no—
486C2×C3—24no—
487C2×C3—81no—
488C2×C3C22×#68711yescharacteristic
489C2×C3#6616311yescharacteristic
490C2×C3#6617211yescharacteristic
491C5#8353111yescharacteristic, complemented, Sylow
492C22—22no—
493C22—22no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22C2×#671614yes—
498C22C22×#122011yescharacteristic
499C4—22no—
500C4—21no—
501C4—41no—
502C4—42no—
503C4—302no—
504C4—602no—
505C4—601no—
506C4C2×#671612yes—
507C4#41×D1511yescharacteristic
508C4#9210011yescharacteristic
509C3#1061526211yescharacteristic, complemented, Sylow
510C2—24no—
511C2—81no—
512C2C22×#671611yescharacteristic
513C2#1175658811yescharacteristic
514C2#1175659711yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
Fitting, prime radicalC3×C5×#547C2
socleC22×C3×C5C22×D4
hypercenter#547D15
hypocenterC3×C5#3298
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
2. D4×Dic30C2semidirect
3. #11751195C2semidirect
4. #11751194C2semidirect
5. #11751142C2semidirect
6. #11751141C2semidirect
7. #11751120C2semidirect
8. C4×#6716C2semidirect
9. D4×C3⋊#168C2semidirect
10. #11751072C2semidirect
11. C2×#91094C2semidirect
137. C3×C5×D4SD16semidirect
156. Dic30#41semidirect
295. C5×D4#214semidirect
358. C3×D4#687semidirect
434. C3×C5#3298semidirect
468. D4#6716semidirect
491. C5#83531semidirect
509. C3#10615262semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5472
D4×Dic302
#117511952
#117511942
#117511422
#117511412
#117511202
C4×#67162
D4×C3⋊#1682
#117510722
C2×#910942
#106152623
#835315