Finite Group Databasebeta

← #14283301

Subgroups — #14283301

Order 1920.

548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D15×C22⋊Q8C211yesmaximal, characteristic
2#11750827C211yesmaximal, characteristic
3#11750765C211yesmaximal, characteristic
4C3×C5×#328C211yesmaximal, characteristic, complemented
5#11746359C211yesmaximal, characteristic, complemented
6#11746288C211yesmaximal, characteristic, complemented
7#11746273C211yesmaximal, characteristic, complemented
8#10599129—31nomaximal, Hall
9C2×Q8×D15C411yescharacteristic, complemented
10C22×C4×D15C2211yescharacteristic
11C3×C5×C22⋊Q8C2211yescharacteristic
12#91835C411yescharacteristic, complemented
13C2×#6714—21no—
14#91813C2211yescharacteristic
15C2×#6705—21no—
16#91786C411yescharacteristic, complemented
17#91785—21no—
18C4⋊C4×D15—21no—
19C4⋊C4×D15C411yescharacteristic, complemented
20C22⋊C4×D15—21no—
21#91767—21no—
22C3×C5×C22⋊C8C2211yescharacteristic
23C3×C5×#95C2211yescharacteristic
24#91115—21no—
25#91115C2211yescharacteristic
26#91114C2211yescharacteristic
27#91104—21no—
28#68336—51nomaximal, Hall
29D5×C22⋊Q8—31no—
30#65015—31no—
31#64953—31no—
32C5×#328D311yescharacteristic, complemented
33#64758—31no—
34#64687—31no—
35#64672—31no—
36C23×D15D411yescharacteristic
37C2×C3×C5×Q8C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C22×Dic15D411yescharacteristic
42Q8×D15—42no—
43C2×C4×D15—21no—
44C2×C4×D15—21no—
45C2×C4×D15—42no—
46C2×C4×D15C2×C411yescharacteristic
47C2×C4×D15C2×C411yescharacteristic
48C2×C4×D15D411yescharacteristic
49C2×C4×D15D411yescharacteristic
50C2×Dic30—21no—
51C2×Dic30C2×C411yescharacteristic
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4—21no—
54C3×C5×C4⋊C4C2×C411yescharacteristic
55C3×C5×C22⋊C4—21no—
56#6719—21no—
57#6714—21no—
58#6714—21no—
59#6714—42no—
60C4⋊Dic15—21no—
61C4⋊Dic15C2×C411yescharacteristic
62#6712—21no—
63#6712—21no—
64#6712—21no—
65C2×C3⋊#168—21no—
66#6705—42no—
67D3×C22⋊Q8—51no—
68#4726—51no—
69#4664—51no—
70C3×#328D511yescharacteristic, complemented
71#4538—51no—
72#4467—51no—
73#4452—51no—
74C2×Q8×D5—31no—
75C22×C4×D5—31no—
76C5×C22⋊Q8C2×D311yescharacteristic
77#4092—31no—
78C2×#685—61no—
79#4070—31no—
80C2×#676—61no—
81#4043—31no—
82#4042—61no—
83D5×C4⋊C4—31no—
84D5×C4⋊C4—61no—
85D5×C22⋊C4—61no—
86#4024—61no—
87C5×C22⋊C8C2×D311yescharacteristic
88C5×#95C2×D311yescharacteristic
89#3963—31no—
90#3963—61no—
91C22⋊#168—31no—
92#3952—61no—
93#1511—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C22×D15—21no—
97C22×D15—22no—
98C22×D15—41no—
99C22×D15C22⋊C411yescharacteristic
100C22×D15C22⋊C411yescharacteristic
101C3×C5×Q8—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5—41no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C22×C411yescharacteristic
109C2×C3×C4×C5C2×D411yescharacteristic
110C2×Dic15—21no—
111C2×Dic15—21no—
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15—41no—
115C2×Dic15—41no—
116C2×Dic15C22⋊C411yescharacteristic
117C2×Dic15C22⋊C411yescharacteristic
118C4×D15—22no—
119C4×D15—22no—
120C4×D15—41no—
121C4×D15—41no—
122C4×D15—42no—
123C4×D15—42no—
124Dic30—42no—
125Dic30—41no—
126C3×C5×C8—41no—
127C3⋊#168—41no—
128C2×D3×Q8—51no—
129C22×C4×D3—51no—
130C3×C22⋊Q8C2×D511yescharacteristic
131#946—51no—
132C2×(C2×D3)⋊C4—101no—
133#924—51no—
134C2×ΓL(1,𝔽25)—101no—
135#897—51no—
136#896—101no—
137D3×C4⋊C4—51no—
138D3×C4⋊C4—101no—
139D3×C22⋊C4—101no—
140#878—101no—
141C3×C22⋊C8C2×D511yescharacteristic
142C3×#95C2×D511yescharacteristic
143C3⋊#95—51no—
144C3⋊#95—101no—
145#830—51no—
146(C2×D3)⋊C8—101no—
147C23×D5—31no—
148C2×C5×Q8C4×D311yescharacteristic
149C22×C4×C5—21no—
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—31no—
152C22×Dic5—61no—
153Q8×D5—122no—
154C2×C4×D5—31no—
155C2×C4×D5—31no—
156C2×C4×D5—31no—
157C2×C4×D5—31no—
158C2×C4×D5—61no—
159C2×C4×D5—61no—
160C2×C4×D5—122no—
161C2×Dic10—31no—
162C2×Dic10—61no—
163C2×C5×C8—21no—
164C5×C4⋊C4—21no—
165C5×C4⋊C4C4×D311yescharacteristic
166C5×C22⋊C4—21no—
167C22⋊Dic5—61no—
168#685—61no—
169#685—61no—
170#685—122no—
171C4⋊Dic5—31no—
172C4⋊Dic5—61no—
173#683—61no—
174#683—61no—
175#683—61no—
176C2×#168—61no—
177#676—122no—
178C2×C22⋊Q8—151no—
179#407—151no—
180#381—151no—
181#328—151no—
182#328—151no—
183#328—151no—
184#328D1511yescharacteristic, complemented
185C22×C3×C5—21no—
186C22×C3×C5—21no—
187C22×C3×C5C2×C22⋊C411yescharacteristic
188C22×C3×C5#13711yescharacteristic
189C22×C3×C5#13711yescharacteristic
190C2×D15—21no—
191C2×D15—21no—
192C2×D15—21no—
193C2×D15—21no—
194C2×D15—21no—
195C2×D15—42no—
196C2×D15—42no—
197C2×D15#9912yes—
198C3×C4×C5—21no—
199C3×C4×C5—21no—
200C3×C4×C5—41no—
201C3×C4×C5—41no—
202C3×C4×C5—81no—
203Dic15—21no—
204Dic15—21no—
205Dic15—41no—
206Dic15—41no—
207Dic15—81no—
208C23×D3—51no—
209C2×C3×Q8C4×D511yescharacteristic
210C22×C3×C4—21no—
211C22×C3×C4C22×D511yescharacteristic
212C22×Dic3—51no—
213C22×Dic3—101no—
214D3×Q8—202no—
215C2×C4×D3—51no—
216C2×C4×D3—51no—
217C2×C4×D3—51no—
218C2×C4×D3—51no—
219C2×C4×D3—101no—
220C2×C4×D3—101no—
221C2×C4×D3—202no—
222C2×Dic6—51no—
223C2×Dic6—101no—
224C2×C3×C8—21no—
225C3×C4⋊C4—21no—
226C3×C4⋊C4C4×D511yescharacteristic
227C3×C22⋊C4—21no—
228#217—101no—
229(C2×D3)⋊C4—101no—
230(C2×D3)⋊C4—101no—
231(C2×D3)⋊C4—202no—
232C4⋊Dic3—51no—
233C4⋊Dic3—101no—
234Dic3⋊C4—101no—
235Dic3⋊C4—101no—
236Dic3⋊C4—101no—
237C2×C3⋊C8—101no—
238ΓL(1,𝔽25)—202no—
239C23×C5D3×D411yescharacteristic
240C22×D5—31no—
241C22×D5—31no—
242C22×D5—62no—
243C22×D5—61no—
244C22×D5—61no—
245C22×D5—121no—
246C5×Q8—41no—
247C2×C4×C5—21no—
248C2×C4×C5—21no—
249C2×C4×C5—41no—
250C2×C4×C5—41no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5C2×C4×D311yescharacteristic
254C2×C4×C5D3×D411yescharacteristic
255C2×Dic5—31no—
256C2×Dic5—31no—
257C2×Dic5—61no—
258C2×Dic5—61no—
259C2×Dic5—121no—
260C2×Dic5—121no—
261C2×Dic5—121no—
262C2×Dic5—121no—
263C4×D5—62no—
264C4×D5—62no—
265C4×D5—121no—
266C4×D5—121no—
267C4×D5—122no—
268C4×D5—122no—
269Dic10—122no—
270Dic10—121no—
271C5×C8—41no—
272#168—121no—
273C22×Q8—151no—
274C23×C4—151no—
275C2×M16—301no—
276C22⋊Q8—151no—
277C22⋊Q8—151no—
278C22⋊Q8—151no—
279C22⋊Q8—301no—
280C22⋊Q8—301no—
281C22⋊Q8C2×D1511yescharacteristic
282C2×C4⋊C4—151no—
283C2×C4⋊C4—301no—
284C2×C22⋊C4—301no—
285C2×C22⋊C4—301no—
286C22⋊C8—151no—
287C22⋊C8—301no—
288C22⋊C8C2×D1511yescharacteristic
289#95—151no—
290#95—301no—
291#95C2×D1511yescharacteristic
292C2×C3×C5—21no—
293C2×C3×C5—21no—
294C2×C3×C5C2×#9911yescharacteristic
295C2×C3×C5#41911yescharacteristic
296C2×C3×C5#42111yescharacteristic
297D15—22no—
298D15—41no—
299C23×C3D4×D511yescharacteristic
300C22×D3—51no—
301C22×D3—51no—
302C22×D3—102no—
303C22×D3—101no—
304C22×D3—101no—
305C22×D3—201no—
306C3×Q8—41no—
307C2×C3×C4—21no—
308C2×C3×C4—21no—
309C2×C3×C4—41no—
310C2×C3×C4—41no—
311C2×C3×C4—41no—
312C2×C3×C4—41no—
313C2×C3×C4C2×C4×D511yescharacteristic
314C2×C3×C4D4×D511yescharacteristic
315C2×Dic3—51no—
316C2×Dic3—51no—
317C2×Dic3—101no—
318C2×Dic3—101no—
319C2×Dic3—201no—
320C2×Dic3—201no—
321C2×Dic3—201no—
322C2×Dic3—201no—
323C4×D3—102no—
324C4×D3—102no—
325C4×D3—201no—
326C4×D3—201no—
327C4×D3—202no—
328C4×D3—202no—
329Dic6—202no—
330Dic6—201no—
331C3×C8—41no—
332C3⋊C8—201no—
333C22×C5—21no—
334C22×C5—21no—
335C22×C5D3×C22⋊C411yescharacteristic
336C22×C5#91511yescharacteristic
337C22×C5#91811yescharacteristic
338C2×D5—32no—
339C2×D5—61no—
340C2×D5—61no—
341C2×D5—61no—
342C2×D5—61no—
343C2×D5—61no—
344C2×D5—122no—
345C2×D5—122no—
346C4×C5—21no—
347C4×C5—21no—
348C4×C5—41no—
349C4×C5—41no—
350C4×C5—81no—
351Dic5—61no—
352Dic5—61no—
353Dic5—121no—
354Dic5—121no—
355Dic5—241no—
356C24—151no—
357C2×Q8—151no—
358C2×Q8—301no—
359C2×Q8—602no—
360C2×Q8C4×D1511yescharacteristic
361C22×C4—21no—
362C22×C4—151no—
363C22×C4—151no—
364C22×C4—151no—
365C22×C4—151no—
366C22×C4—151no—
367C22×C4—301no—
368C22×C4—301no—
369C22×C4—301no—
370C22×C4—602no—
371C22×C4C22×D1511yescharacteristic
372M16—602no—
373C2×C8—21no—
374C2×C8—301no—
375C4⋊C4—21no—
376C4⋊C4—151no—
377C4⋊C4—301no—
378C4⋊C4—301no—
379C4⋊C4—301no—
380C4⋊C4—301no—
381C4⋊C4C4×D1511yescharacteristic
382C22⋊C4—21no—
383C22⋊C4—301no—
384C22⋊C4—301no—
385C22⋊C4—301no—
386C22⋊C4—602no—
387C3×C5#151111yescharacteristic, complemented, Hall
388C22×C3—21no—
389C22×C3—21no—
390C22×C3D5×C22⋊C411yescharacteristic
391C22×C3#406111yescharacteristic
392C22×C3#406411yescharacteristic
393C2×D3—52no—
394C2×D3—101no—
395C2×D3—101no—
396C2×D3—101no—
397C2×D3—101no—
398C2×D3—101no—
399C2×D3—202no—
400C2×D3—202no—
401C3×C4—21no—
402C3×C4—21no—
403C3×C4—41no—
404C3×C4—41no—
405C3×C4—81no—
406Dic3—101no—
407Dic3—101no—
408Dic3—201no—
409Dic3—201no—
410Dic3—401no—
411C2×C5—21no—
412C2×C5—21no—
413C2×C5D3×#9911yescharacteristic
414C2×C5#480211yescharacteristic
415C2×C5#482111yescharacteristic
416D5—62no—
417D5—121no—
418C23—151no—
419C23—151no—
420C23—302no—
421C23—301no—
422C23—301no—
423C23—601no—
424C23D4×D1511yescharacteristic
425Q8—41no—
426Q8—601no—
427Q8—602no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—151no—
435C2×C4—151no—
436C2×C4—302no—
437C2×C4—302no—
438C2×C4—301no—
439C2×C4—301no—
440C2×C4—601no—
441C2×C4—601no—
442C2×C4—602no—
443C2×C4—602no—
444C2×C4—601no—
445C2×C4—601no—
446C2×C4—601no—
447C2×C4—601no—
448C2×C4C2×C4×D1511yescharacteristic
449C2×C4D4×D1511yescharacteristic
450C8—41no—
451C8—601no—
452C2×C3—21no—
453C2×C3—21no—
454C2×C3D5×#9911yescharacteristic
455C2×C3#6509111yescharacteristic
456C2×C3#6511011yescharacteristic
457D3—102no—
458D3—201no—
459C5#6833611yescharacteristic, complemented, Sylow
460C22—21no—
461C22—21no—
462C22—152no—
463C22—301no—
464C22—301no—
465C22—301no—
466C22—301no—
467C22—301no—
468C22—602no—
469C22—602no—
470C22C22⋊C4×D1511yescharacteristic
471C22#9180411yescharacteristic
472C22#9180711yescharacteristic
473C4—21no—
474C4—21no—
475C4—41no—
476C4—41no—
477C4—81no—
478C4—301no—
479C4—301no—
480C4—601no—
481C4—601no—
482C4—1201no—
483C3#1059912911yescharacteristic, complemented, Sylow
484C2—21no—
485C2—21no—
486C2—302no—
487C2—601no—
488C2D15×#9911yescharacteristic
489C2#1175090311yescharacteristic
490C2#1175092211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#328C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×D15D4
cosocleC22×C3×C4×C5C23
hypercenter#328D15
hypocenterC3×C5#1511
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
4. C3×C5×#328C2semidirect
5. #11746359C2semidirect
6. #11746288C2semidirect
7. #11746273C2semidirect
9. C2×Q8×D15C4semidirect
12. #91835C4semidirect
16. #91786C4semidirect
19. C4⋊C4×D15C4semidirect
32. C5×#328D3semidirect
70. C3×#328D5semidirect
184. #328D15semidirect
387. C3×C5#1511semidirect
459. C5#68336semidirect
483. C3#10599129semidirect

Maximal subgroups

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

subgroupindex
D15×C22⋊Q82
#117508272
#117507652
C3×C5×#3282
#117463592
#117462882
#117462732
#105991293
#683365