Finite Group Databasebeta

← #14283180

Subgroups — #14283180

Order 1920.

588 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#924C211yesmaximal, characteristic
2C3×#65015C211yesmaximal, characteristic
3#11748702C211yesmaximal, characteristic
4#11746288C211yesmaximal, characteristic, complemented
5C5×#4467C211yesmaximal, characteristic, complemented
6#11745965C211yesmaximal, characteristic, complemented
7#11745963C211yesmaximal, characteristic, complemented
8#10599128—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×D5×Dic6C411yescharacteristic, complemented
11#91813C2211yescharacteristic
12C5×#924C2211yescharacteristic
13C2×C3×#676—21no—
14#91574—21no—
15D5×#217—21no—
16C2×#6665—21no—
17C2×Dic3×Dic5—21no—
18D5×C4⋊Dic3C411yescharacteristic, complemented
19D5×Dic3⋊C4—21no—
20#91360C411yescharacteristic, complemented
21#91359C411yescharacteristic, complemented
22#91349—21no—
23C3×C5×C22⋊C8C2211yescharacteristic
24#91115C2211yescharacteristic
25C5×C3⋊#95C2211yescharacteristic
26C3×C22⋊#168C2211yescharacteristic
27C3×#3952—21no—
28#69980—51nomaximal, Hall
29D5×C22⋊Q8—31no—
30#65015D311yescharacteristic
31#64955—31no—
32C5×#328—31no—
33#64758—31no—
34#64687—31no—
35#64672—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C22×Dic15—21no—
39C2×Dic30C2×C411yescharacteristic
40C22×C5×Dic3—21no—
41C2×C5×Dic6C2×C411yescharacteristic
42C22×C3×Dic5D411yescharacteristic
43C2×C3×C4×D5—42no—
44C2×C3×C4×D5C2×C411yescharacteristic
45C2×C3×C4×D5C2×C411yescharacteristic
46C2×C3×C4×D5D411yescharacteristic
47C2×C3×C4×D5D411yescharacteristic
48C2×#1204—21no—
49C2×D5×Dic3—21no—
50C2×D5×Dic3—21no—
51D5×Dic6—42no—
52C2×C3×C5×C8—21no—
53#6719—21no—
54C4⋊Dic15C2×C411yescharacteristic
55#6712—21no—
56C5×#217—21no—
57C5×C4⋊Dic3C2×C411yescharacteristic
58C5×Dic3⋊C4—21no—
59C2×C3×#168—21no—
60C3×#676—42no—
61Dic3⋊Dic5—21no—
62#6669—21no—
63#6668—21no—
64#6665—24no—
65#6665—21no—
66#6665—21no—
67Dic3×Dic5—42no—
68C2×#924—51no—
69C3×#407—51no—
70C4×#217—51no—
71#4467—51no—
72#4467—51no—
73#4467—51no—
74#4467D511yescharacteristic, complemented
75C2×Q8×D5—31no—
76C22×C4×D5C2×D311yescharacteristic
77C5×C22⋊Q8—31no—
78#4092—31no—
79C2×#685—61no—
80#4070—31no—
81C2×C4×Dic5—61no—
82C2×#676—21no—
83#4043—31no—
84#4042—61no—
85D5×C4⋊C4—31no—
86D5×C4⋊C4—61no—
87D5×C22⋊C4—61no—
88#4024—61no—
89C5×C22⋊C8C2×D311yescharacteristic
90C5×#95—31no—
91#3963—31no—
92C22⋊#168C2×D311yescharacteristic
93#3952—21no—
94#1508—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C3×D5—21no—
97C22×C3×D5—21no—
98C22×C3×D5—22no—
99C22×C3×D5—41no—
100C22×C3×D5C22⋊C411yescharacteristic
101C22×C3×D5C22⋊C411yescharacteristic
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×Dic15—22no—
106C2×Dic15—21no—
107C2×Dic15—21no—
108C2×Dic15—41no—
109C2×Dic15—41no—
110Dic30—41no—
111C2×C5×Dic3—22no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3—41no—
116C5×Dic6—41no—
117C2×C3×Dic5—22no—
118C2×C3×Dic5C22⋊C411yescharacteristic
119C2×C3×Dic5C22⋊C411yescharacteristic
120C3×C4×D5—22no—
121C3×C4×D5—22no—
122C3×C4×D5—41no—
123C3×C4×D5—41no—
124#1204—42no—
125D5×Dic3—42no—
126D5×Dic3—42no—
127C3×C5×C8—41no—
128C3×#168—41no—
129C23×C3×C4—51no—
130C22×Dic6—51no—
131C2×C3×M16—101no—
132C2×#217—101no—
133C2×#217—101no—
134C2×C4⋊Dic3—51no—
135#924—51no—
136#924—51no—
137#924—51no—
138#924—101no—
139#924—101no—
140#924C2×D511yescharacteristic
141C2×Dic3⋊C4—101no—
142C2×C4×Dic3—101no—
143C3×C22⋊C8—51no—
144C3×C22⋊C8—101no—
145C3×C22⋊C8C2×D511yescharacteristic
146C3⋊#95—51no—
147C3⋊#95C2×D511yescharacteristic
148C23×D5D1211yescharacteristic
149C2×C5×Q8—31no—
150C22×C4×C5—61no—
151C22×C4×C5C22×D311yescharacteristic
152C22×Dic5—61no—
153C22×Dic5D1211yescharacteristic
154Q8×D5—122no—
155C2×C4×D5—42no—
156C2×C4×D5—61no—
157C2×C4×D5—61no—
158C2×C4×D5C4×D311yescharacteristic
159C2×C4×D5C4×D311yescharacteristic
160C2×C4×D5#6711yescharacteristic
161C2×C4×D5#6711yescharacteristic
162C2×Dic10—31no—
163C2×Dic10—61no—
164C2×C5×C8—21no—
165C5×C4⋊C4—31no—
166C5×C4⋊C4—61no—
167C5×C22⋊C4—61no—
168C22⋊Dic5—61no—
169#685—64no—
170#685—61no—
171#685—61no—
172C4⋊Dic5—31no—
173C4⋊Dic5—61no—
174#683—61no—
175#683—61no—
176#683—61no—
177C4×Dic5—122no—
178C2×#168—21no—
179#676—42no—
180C2×C22⋊Q8—151no—
181#407—51no—
182C4×C22⋊C4—151no—
183#328—31no—
184#328—151no—
185#328—151no—
186#328—151no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5C2×C22⋊C411yescharacteristic
190C22×C3×C5#13711yescharacteristic
191C22×C3×C5#13711yescharacteristic
192C2×C3×D5—21no—
193C2×C3×D5—21no—
194C2×C3×D5—21no—
195C2×C3×D5—21no—
196C2×C3×D5—21no—
197C2×C3×D5—42no—
198C2×C3×D5—42no—
199C2×C3×D5#10412yes—
200C3×C4×C5—21no—
201C3×C4×C5—21no—
202Dic15—42no—
203Dic15—41no—
204Dic15—41no—
205C3×Dic5—21no—
206C3×Dic5#9912yes—
207C5×Dic3—42no—
208C5×Dic3—41no—
209C5×Dic3—41no—
210C24×C3—51no—
211C22×C3×C4—51no—
212C22×C3×C4—51no—
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—202no—
217C22×C3×C4C22×D511yescharacteristic
218C22×Dic3—21no—
219C22×Dic3—101no—
220C22×Dic3—101no—
221C22×Dic3—101no—
222C2×Dic6—51no—
223C2×Dic6—101no—
224C2×Dic6—202no—
225C2×Dic6C4×D511yescharacteristic
226C3×M16—202no—
227C2×C3×C8—21no—
228C2×C3×C8—101no—
229#217—21no—
230#217—101no—
231#217—101no—
232#217—104no—
233#217—101no—
234C4⋊Dic3—51no—
235C4⋊Dic3—101no—
236C4⋊Dic3C4×D511yescharacteristic
237Dic3⋊C4—21no—
238Dic3⋊C4—101no—
239Dic3⋊C4—101no—
240Dic3⋊C4—101no—
241C4×Dic3—202no—
242C23×C5C2×D1211yescharacteristic
243C22×D5—21no—
244C22×D5—21no—
245C22×D5—22no—
246C22×D5—41no—
247C22×D5(C2×D3)⋊C411yescharacteristic
248C22×D5(C2×D3)⋊C411yescharacteristic
249C5×Q8—121no—
250C2×C4×C5—41no—
251C2×C4×C5—62no—
252C2×C4×C5—61no—
253C2×C4×C5—61no—
254C2×C4×C5—121no—
255C2×C4×C5—121no—
256C2×C4×C5C2×C4×D311yescharacteristic
257C2×C4×C5C2×#6711yescharacteristic
258C2×Dic5—22no—
259C2×Dic5—62no—
260C2×Dic5—61no—
261C2×Dic5—61no—
262C2×Dic5—121no—
263C2×Dic5—121no—
264C2×Dic5(C2×D3)⋊C411yescharacteristic
265C2×Dic5(C2×D3)⋊C411yescharacteristic
266C4×D5—22no—
267C4×D5—22no—
268C4×D5—41no—
269C4×D5—41no—
270C4×D5—122no—
271C4×D5—122no—
272Dic10—122no—
273Dic10—121no—
274C5×C8—41no—
275#168—41no—
276C22×Q8—151no—
277C23×C4—51no—
278C2×M16—101no—
279C22⋊Q8—31no—
280C22⋊Q8—151no—
281C22⋊Q8—151no—
282C22⋊Q8—151no—
283C22⋊Q8—301no—
284C22⋊Q8—301no—
285C2×C4⋊C4—151no—
286C2×C4⋊C4—301no—
287C2×C22⋊C4—301no—
288C2×C22⋊C4—301no—
289C2×C42—301no—
290C22⋊C8—51no—
291C22⋊C8—101no—
292C22⋊C8D3×D511yescharacteristic
293#95—31no—
294#95—151no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5C2×#9911yescharacteristic
298C2×C3×C5#41911yescharacteristic
299C2×C3×C5C2×#10411yescharacteristic
300C3×D5—22no—
301C3×D5—41no—
302C23×C3—51no—
303C23×C3—51no—
304C23×C3—102no—
305C23×C3—101no—
306C23×C3—101no—
307C23×C3—201no—
308C23×C3D4×D511yescharacteristic
309C2×C3×C4—41no—
310C2×C3×C4—51no—
311C2×C3×C4—51no—
312C2×C3×C4—102no—
313C2×C3×C4—102no—
314C2×C3×C4—102no—
315C2×C3×C4—201no—
316C2×C3×C4—201no—
317C2×C3×C4C2×C4×D511yescharacteristic
318C2×C3×C4D4×D511yescharacteristic
319C2×Dic3—22no—
320C2×Dic3—21no—
321C2×Dic3—21no—
322C2×Dic3—41no—
323C2×Dic3—41no—
324C2×Dic3—102no—
325C2×Dic3—101no—
326C2×Dic3—101no—
327C2×Dic3—202no—
328C2×Dic3—202no—
329C2×Dic3—201no—
330C2×Dic3—201no—
331Dic6—41no—
332Dic6—202no—
333Dic6—201no—
334C3×C8—41no—
335C3×C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5#90911yescharacteristic
339C22×C5#90911yescharacteristic
340C22×C5C2×(C2×D3)⋊C411yescharacteristic
341C2×D5—21no—
342C2×D5—21no—
343C2×D5—21no—
344C2×D5—21no—
345C2×D5—21no—
346C2×D5—42no—
347C2×D5—42no—
348C2×D5#82512yes—
349C4×C5—21no—
350C4×C5—21no—
351C4×C5—122no—
352C4×C5—121no—
353C4×C5—121no—
354Dic5—21no—
355Dic5—122no—
356Dic5—121no—
357Dic5—121no—
358Dic5#80612yes—
359C24—51no—
360C2×Q8—31no—
361C2×Q8—151no—
362C2×Q8—301no—
363C2×Q8—602no—
364C22×C4—51no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—51no—
368C22×C4—51no—
369C22×C4—61no—
370C22×C4—202no—
371C22×C4—301no—
372C22×C4—301no—
373C22×C4—301no—
374C22×C4C2×D3×D511yescharacteristic
375M16—202no—
376C2×C8—21no—
377C2×C8—101no—
378C4⋊C4—31no—
379C4⋊C4—61no—
380C4⋊C4—151no—
381C4⋊C4—301no—
382C4⋊C4—301no—
383C4⋊C4—301no—
384C4⋊C4—301no—
385C22⋊C4—61no—
386C22⋊C4—301no—
387C22⋊C4—301no—
388C22⋊C4—304no—
389C22⋊C4—301no—
390C42—602no—
391C3×C5#150811yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—52no—
395C22×C3—101no—
396C22×C3—101no—
397C22×C3—101no—
398C22×C3—101no—
399C22×C3—101no—
400C22×C3—202no—
401C22×C3—202no—
402C22×C3D5×C22⋊C411yescharacteristic
403C22×C3#406111yescharacteristic
404C22×C3#406411yescharacteristic
405C3×C4—21no—
406C3×C4—21no—
407C3×C4—52no—
408C3×C4—101no—
409Dic3—42no—
410Dic3—41no—
411Dic3—41no—
412Dic3—202no—
413Dic3—201no—
414Dic3—201no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5C2×#80611yescharacteristic
418C2×C5#512011yescharacteristic
419C2×C5C2×#82511yescharacteristic
420D5—22no—
421D5—41no—
422C23—51no—
423C23—51no—
424C23—102no—
425C23—101no—
426C23—101no—
427C23—201no—
428C23D5×D1211yescharacteristic
429Q8—121no—
430Q8—601no—
431Q8—602no—
432C2×C4—41no—
433C2×C4—51no—
434C2×C4—51no—
435C2×C4—62no—
436C2×C4—61no—
437C2×C4—61no—
438C2×C4—102no—
439C2×C4—102no—
440C2×C4—102no—
441C2×C4—121no—
442C2×C4—121no—
443C2×C4—201no—
444C2×C4—201no—
445C2×C4—302no—
446C2×C4—301no—
447C2×C4—301no—
448C2×C4—602no—
449C2×C4—602no—
450C2×C4—601no—
451C2×C4—601no—
452C2×C4C4×D3×D511yescharacteristic
453C2×C4D5×#6711yescharacteristic
454C8—41no—
455C8—201no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—102no—
459C2×C3—201no—
460C2×C3D5×#9911yescharacteristic
461C2×C3#6509111yescharacteristic
462C2×C3D5×#10411yescharacteristic
463C5#6998011yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—52no—
467C22—101no—
468C22—101no—
469C22—101no—
470C22—101no—
471C22—101no—
472C22—202no—
473C22—202no—
474C22#9126011yescharacteristic
475C22#9126111yescharacteristic
476C22D5×(C2×D3)⋊C411yescharacteristic
477C4—21no—
478C4—21no—
479C4—52no—
480C4—101no—
481C4—122no—
482C4—121no—
483C4—121no—
484C4—602no—
485C4—601no—
486C4—601no—
487C3#1059912811yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—102no—
491C2—201no—
492C2D5×#80611yescharacteristic
493C2#1174812211yescharacteristic
494C2D5×#82511yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×C22⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenterC22⋊C8D3×D5
hypocenterC3×C5#1508
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
4. #11746288C2semidirect
5. C5×#4467C2semidirect
6. #11745965C2semidirect
7. #11745963C2semidirect
10. C2×D5×Dic6C4semidirect
18. D5×C4⋊Dic3C4semidirect
20. #91360C4semidirect
21. #91359C4semidirect
74. #4467D5semidirect
391. C3×C5#1508semidirect
463. C5#69980semidirect
487. C3#10599128semidirect

Maximal subgroups

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

subgroupindex
D5×#9242
C3×#650152
#117487022
#117462882
C5×#44672
#117459652
#117459632
#105991283
#699805