Finite Group Databasebeta

← #14283168

Subgroups — #14283168

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×#64955C211yesmaximal, characteristic
3#11748499C211yesmaximal, characteristic
4#11746273C211yesmaximal, characteristic, complemented
5C5×#4452C211yesmaximal, characteristic, complemented
6#11745964C211yesmaximal, characteristic, complemented
7#11745962C211yesmaximal, characteristic, complemented
8#10599128—31nomaximal, Hall
9C22×C3×C4×D5C2211yescharacteristic
10C2×D5×Dic6C411yescharacteristic, complemented
11#91813C2211yescharacteristic
12C5×#924C2211yescharacteristic
13C2×C3×#685—21no—
14C2×C3×C4×Dic5—21no—
15#91574—21no—
16D5×#217—21no—
17D5×C4⋊Dic3C411yescharacteristic, complemented
18D5×Dic3⋊C4—21no—
19#91360C411yescharacteristic, complemented
20#91359C411yescharacteristic, complemented
21#91349—21no—
22C2×#6649—21no—
23C3×C5×#95C2211yescharacteristic
24#91114C2211yescharacteristic
25C5×#830C2211yescharacteristic
26C3×#3963C2211yescharacteristic
27#90955—21no—
28#69445—51nomaximal, Hall
29D5×C22⋊Q8—31no—
30#65015—31no—
31#64955D311yescharacteristic
32C5×#328—31no—
33#64758—31no—
34#64687—31no—
35#64672—31no—
36C23×C3×D5D411yescharacteristic
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5C2311yescharacteristic
39C2×Dic30C2×C411yescharacteristic
40C2×C5×Dic6C2×C411yescharacteristic
41C22×C3×Dic5—21no—
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—
52#6719—21no—
53C4⋊Dic15C2×C411yescharacteristic
54#6712—21no—
55C2×C3⋊#168—21no—
56C5×#217—21no—
57C5×C4⋊Dic3C2×C411yescharacteristic
58C5×Dic3⋊C4—21no—
59C2×C5×C3⋊C8—21no—
60C3×#685—24no—
61C3×C4×Dic5—42no—
62Dic3⋊Dic5—21no—
63#6669—21no—
64#6668—21no—
65#6665—21no—
66#6665—21no—
67#6649—42no—
68C2×#924—51no—
69C3×C4×C22⋊C4—51no—
70#5207—51no—
71#4452—51no—
72#4452—51no—
73#4452—51no—
74#4452D511yescharacteristic, complemented
75C2×Q8×D5—31no—
76C22×C4×D5C2×D311yescharacteristic
77C5×C22⋊Q8—31no—
78#4092—31no—
79C2×#685—21no—
80#4070—31no—
81C2×C4×Dic5—21no—
82C2×#676—61no—
83#4043—31no—
84#4042—61no—
85D5×C4⋊C4—31no—
86D5×C4⋊C4—61no—
87D5×C22⋊C4—61no—
88#4024—61no—
89C5×C22⋊C8—31no—
90C5×#95C2×D311yescharacteristic
91#3963C2×D311yescharacteristic
92C22⋊#168—31no—
93#3952—61no—
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—22no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C22×C411yescharacteristic
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×Dic15—21no—
109C2×Dic15—21no—
110Dic30—41no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C5×Dic6—41no—
114C2×C3×Dic5—22no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—41no—
117C2×C3×Dic5—41no—
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⋊#168—41no—
128C5×C3⋊C8—41no—
129C23×C3×C4—51no—
130C22×Dic6—51no—
131C2×C3×C22⋊C4—101no—
132C2×C3×C42—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×#208—101no—
143C3×#95—51no—
144C3×#95C2×D511yescharacteristic
145#830—51no—
146#830—101no—
147#830C2×D511yescharacteristic
148C23×D5#6711yescharacteristic
149C2×C5×Q8—31no—
150C22×C4×C5—21no—
151C22×C4×C5C22×D311yescharacteristic
152C22×Dic5—21no—
153C22×Dic5#6711yescharacteristic
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×D5D1211yescharacteristic
161C2×C4×D5D1211yescharacteristic
162C2×Dic10—31no—
163C2×Dic10—61no—
164C2×C5×C8—61no—
165C5×C4⋊C4—31no—
166C5×C4⋊C4—61no—
167C5×C22⋊C4—61no—
168C22⋊Dic5—61no—
169#685—24no—
170#685—61no—
171#685—61no—
172C4⋊Dic5—31no—
173C4⋊Dic5—61no—
174#683—61no—
175#683—61no—
176#683—61no—
177C4×Dic5—42no—
178C2×#168—61no—
179#676—122no—
180C2×C22⋊Q8—151no—
181#407—151no—
182C4×C22⋊C4—51no—
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—
202C3×C4×C5—42no—
203Dic15—41no—
204Dic15—41no—
205C3×Dic5—21no—
206C3×Dic5—42no—
207C3×Dic5#9912yes—
208C5×Dic3—41no—
209C5×Dic3—41no—
210C24×C3—51no—
211C22×C3×C4—21no—
212C22×C3×C4—51no—
213C22×C3×C4—51no—
214C22×C3×C4—51no—
215C22×C3×C4—51no—
216C22×C3×C4—51no—
217C22×C3×C4—101no—
218C22×C3×C4—202no—
219C22×C3×C4C22×D511yescharacteristic
220C22×Dic3—101no—
221C22×Dic3—101no—
222C2×Dic6—51no—
223C2×Dic6—101no—
224C2×Dic6—202no—
225C2×Dic6C4×D511yescharacteristic
226C3×C22⋊C4—104no—
227C3×C42—202no—
228#217—21no—
229#217—101no—
230#217—101no—
231#217—101no—
232C4⋊Dic3—51no—
233C4⋊Dic3—101no—
234C4⋊Dic3C4×D511yescharacteristic
235Dic3⋊C4—21no—
236Dic3⋊C4—101no—
237Dic3⋊C4—101no—
238Dic3⋊C4—101no—
239#208—202no—
240C2×C3⋊C8—21no—
241C2×C3⋊C8—101no—
242C23×C5C2×#6711yescharacteristic
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—22no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—41no—
254C2×C4×C5—61no—
255C2×C4×C5—61no—
256C2×C4×C5C2×C4×D311yescharacteristic
257C2×C4×C5C2×D1211yescharacteristic
258C2×Dic5—22no—
259C2×Dic5—22no—
260C2×Dic5—41no—
261C2×Dic5—41no—
262C2×Dic5—61no—
263C2×Dic5—61no—
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—121no—
275#168—121no—
276C22×Q8—151no—
277C23×C4—51no—
278C2×M16—301no—
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—101no—
288C2×C22⋊C4—301no—
289C2×C42—101no—
290C22⋊C8—31no—
291C22⋊C8—151no—
292C22⋊C8—301no—
293#95—51no—
294#95D3×D511yescharacteristic
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—22no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4—51no—
314C2×C3×C4—51no—
315C2×C3×C4—102no—
316C2×C3×C4—102no—
317C2×C3×C4—102no—
318C2×C3×C4—102no—
319C2×C3×C4—201no—
320C2×C3×C4—201no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4C2×C4×D511yescharacteristic
324C2×C3×C4D4×D511yescharacteristic
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—101no—
328C2×Dic3—101no—
329C2×Dic3—202no—
330C2×Dic3—202no—
331Dic6—41no—
332Dic6—202no—
333Dic6—201no—
334C3⋊C8—41no—
335C3⋊C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5C2×(C2×D3)⋊C411yescharacteristic
339C22×C5#95111yescharacteristic
340C22×C5#95111yescharacteristic
341C2×D5—21no—
342C2×D5—21no—
343C2×D5—21no—
344C2×D5—21no—
345C2×D5—21no—
346C2×D5—42no—
347C2×D5—42no—
348C2×D5#80512yes—
349C4×C5—21no—
350C4×C5—21no—
351C4×C5—42no—
352C4×C5—121no—
353C4×C5—121no—
354Dic5—21no—
355Dic5—42no—
356Dic5—121no—
357Dic5—121no—
358Dic5#80612yes—
359C24—51no—
360C2×Q8—31no—
361C2×Q8—151no—
362C2×Q8—301no—
363C2×Q8—602no—
364C22×C4—21no—
365C22×C4—51no—
366C22×C4—51no—
367C22×C4—51no—
368C22×C4—51no—
369C22×C4—51no—
370C22×C4—101no—
371C22×C4—202no—
372C22×C4—301no—
373C22×C4—301no—
374C22×C4C2×D3×D511yescharacteristic
375M16—602no—
376C2×C8—61no—
377C2×C8—301no—
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—104no—
387C22⋊C4—301no—
388C22⋊C4—301no—
389C22⋊C4—301no—
390C42—202no—
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—42no—
408C3×C4—52no—
409C3×C4—101no—
410C3×C4—202no—
411Dic3—41no—
412Dic3—41no—
413Dic3—201no—
414Dic3—201no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5C2×#80511yescharacteristic
418C2×C5C2×#80611yescharacteristic
419C2×C5#500411yescharacteristic
420D5—22no—
421D5—41no—
422C23—51no—
423C23—51no—
424C23—102no—
425C23—101no—
426C23—101no—
427C23—201no—
428C23D5×#6711yescharacteristic
429Q8—121no—
430Q8—601no—
431Q8—602no—
432C2×C4—22no—
433C2×C4—41no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—51no—
437C2×C4—51no—
438C2×C4—61no—
439C2×C4—61no—
440C2×C4—102no—
441C2×C4—102no—
442C2×C4—102no—
443C2×C4—102no—
444C2×C4—201no—
445C2×C4—201no—
446C2×C4—201no—
447C2×C4—201no—
448C2×C4—301no—
449C2×C4—301no—
450C2×C4—602no—
451C2×C4—602no—
452C2×C4C4×D3×D511yescharacteristic
453C2×C4D5×D1211yescharacteristic
454C8—121no—
455C8—601no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—102no—
459C2×C3—201no—
460C2×C3D5×#9911yescharacteristic
461C2×C3#6509111yescharacteristic
462C2×C3D5×#10411yescharacteristic
463C5#6944511yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—52no—
467C22—101no—
468C22—101no—
469C22—101no—
470C22—101no—
471C22—101no—
472C22—202no—
473C22—202no—
474C22D5×(C2×D3)⋊C411yescharacteristic
475C22#9148411yescharacteristic
476C22#9150811yescharacteristic
477C4—21no—
478C4—21no—
479C4—42no—
480C4—52no—
481C4—101no—
482C4—121no—
483C4—121no—
484C4—202no—
485C4—601no—
486C4—601no—
487C3#1059912811yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—102no—
491C2—201no—
492C2D5×#80511yescharacteristic
493C2D5×#80611yescharacteristic
494C2#1174748711yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#95C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×C5C23
hypercenter#95D3×D5
hypocenterC3×C5#1508
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #11746273C2semidirect
5. C5×#4452C2semidirect
6. #11745964C2semidirect
7. #11745962C2semidirect
10. C2×D5×Dic6C4semidirect
17. D5×C4⋊Dic3C4semidirect
19. #91360C4semidirect
20. #91359C4semidirect
74. #4452D5semidirect
391. C3×C5#1508semidirect
463. C5#69445semidirect
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×#649552
#117484992
#117462732
C5×#44522
#117459642
#117459622
#105991283
#694455