Finite Group Databasebeta

← #14313544

Subgroups — #14313544

Order 1920.

476 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 86 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
1#11754812C211yesmaximal, characteristic
2C5×#4740C211yesmaximal, characteristic
3#11749173C211yesmaximal, characteristic
4#11746294C211yesmaximal, characteristic, complemented
5C3×#64693C211yesmaximal, characteristic, complemented
6#11746011C211yesmaximal, characteristic, complemented
7#11746009C211yesmaximal, characteristic, complemented
8#10600852—31nomaximal, Hall
9C2×C5×#237C2211yescharacteristic
10C2×D3×Dic10C411yescharacteristic, complemented
11#91825C2211yescharacteristic
12C5×#877—21no—
13C3×#4082C2211yescharacteristic
14#91575—21no—
15#91575—21no—
16#91555—21no—
17#91555—21no—
18#91529—21no—
19#91385C411yescharacteristic, complemented
20#91376C411yescharacteristic, complemented
21#91371C411yescharacteristic, complemented
22C3×C5×#99C2211yescharacteristic
23#91118C2211yescharacteristic
24C5×#834C2211yescharacteristic
25C5×#806—21no—
26C3×#3966C2211yescharacteristic
27#90996—21no—
28#69159—51nomaximal, Hall
29#66159—31no—
30C5×#410—31no—
31#65529—31no—
32#64693—31no—
33#64693—31no—
34#64693—31no—
35#64693D311yescharacteristic, complemented
36C2×C3×C5×D4C2311yescharacteristic
37C2×Dic30C2×C411yescharacteristic
38C2×C5×#67D411yescharacteristic
39C2×C5×#67D411yescharacteristic
40C22×C5×Dic3D411yescharacteristic
41C22×C5×Dic3D411yescharacteristic
42C5×#237—41no—
43C5×#237—41no—
44C2×C4×C5×D3C2×C411yescharacteristic
45C2×C5×Dic6C2×C411yescharacteristic
46C2×C3×Dic10C2×C411yescharacteristic
47C2×#1204—21no—
48C2×D3×Dic5—21no—
49D3×Dic10—41no—
50D3×Dic10—41no—
51C3×C5×C22⋊C4—21no—
52#6719—21no—
53#6719—21no—
54#6719—21no—
55C4×Dic15C2×C411yescharacteristic
56C5×#217—21no—
57C5×Dic3⋊C4—41no—
58C4×C5×Dic3—41no—
59C3×C22⋊Dic5—21no—
60C3×C22⋊Dic5—21no—
61C3×C22⋊Dic5—21no—
62C3×C4×Dic5C2×C411yescharacteristic
63Dic3⋊Dic5—21no—
64Dic3⋊Dic5—41no—
65#6669—21no—
66#6669—21no—
67#6668—21no—
68#6668—21no—
69(C2×D3)⋊Dic5—21no—
70Dic3×Dic5—41no—
71#5675—51no—
72#4740—51no—
73#4740D511yescharacteristic
74C3×#354—51no—
75#4541—51no—
76#4473—51no—
77#4473—51no—
78C2×C5×#41—31no—
79C22×Dic10—31no—
80C5×#117—61no—
81#4090—31no—
82#4090—31no—
83#4082—31no—
84#4082C2×D311yescharacteristic
85#4081—61no—
86#4081—61no—
87#4072—31no—
88#4072—61no—
89#4070—61no—
90#4070—61no—
91C5×#99—31no—
92C5×#99—61no—
93C5×#99C2×D311yescharacteristic
94#3966—31no—
95#3966—61no—
96#3966C2×D311yescharacteristic
97#2129—151noSylow
98C23×C3×C5C2×D411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3C22⋊C411yescharacteristic
101C3×C5×D4—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5C22×C411yescharacteristic
104C2×Dic15—21no—
105C2×Dic15—21no—
106C2×Dic15—41no—
107Dic30—41no—
108C5×#67—41no—
109C5×#67—41no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—41no—
115C2×C5×Dic3C22⋊C411yescharacteristic
116C2×C5×Dic3C22⋊C411yescharacteristic
117C2×C5×Dic3C22⋊C411yescharacteristic
118C4×C5×D3—21no—
119C4×C5×D3—21no—
120C5×Dic6—41no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—41no—
124C3×Dic10—41no—
125#1204—41no—
126#1204—41no—
127D3×Dic5—42no—
128C2×D3×Q8—51no—
129C2×#237C2×D511yescharacteristic
130C3×#124—51no—
131#944—51no—
132#936—51no—
133#883—101no—
134#883—101no—
135#878—101no—
136#878—101no—
137#877—21no—
138#877—101no—
139#872—51no—
140#869—51no—
141C3×#99—51no—
142C3×#99C2×D511yescharacteristic
143#834—51no—
144#834C2×D511yescharacteristic
145#806—21no—
146#806—101no—
147C5×#41—121no—
148C5×#41—121no—
149C2×C5×Q8—31no—
150C2×C5×D4—31no—
151C2×C5×D4—31no—
152C2×C5×D4C22×D311yescharacteristic
153C22×C4×C5—31no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×Dic5—61no—
157C2×Dic10—31no—
158C2×Dic10—61no—
159C2×Dic10—121no—
160C2×Dic10—121no—
161C2×Dic10C4×D311yescharacteristic
162C5×C4⋊C4—121no—
163C5×C22⋊C4—21no—
164C5×C22⋊C4—61no—
165C42×C5—121no—
166C22⋊Dic5—21no—
167C22⋊Dic5—21no—
168C22⋊Dic5—21no—
169C22⋊Dic5—61no—
170C22⋊Dic5—61no—
171C22⋊Dic5—61no—
172C22⋊Dic5—61no—
173C4⋊Dic5—61no—
174C4⋊Dic5—121no—
175#683—61no—
176#683—61no—
177#683—61no—
178#683—61no—
179C4×Dic5—31no—
180C4×Dic5—121no—
181C4×Dic5C4×D311yescharacteristic
182#536—151no—
183#410—31no—
184#410—151no—
185#354—51no—
186#354—151no—
187#354—151no—
188#354—151no—
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5C2×C22⋊C411yescharacteristic
194C2×C5×D3—21no—
195C2×C5×D3—41no—
196C3×C4×C5—21no—
197C3×C4×C5—81no—
198Dic15—41no—
199Dic15—41no—
200Dic15—81no—
201C3×Dic5—41no—
202C3×Dic5—41no—
203C3×Dic5—81no—
204C5×Dic3—21no—
205C5×Dic3—21no—
206C5×Dic3—81no—
207C5×Dic3#9911yescharacteristic
208C5×Dic3#9911yescharacteristic
209C2×C3×Q8—51no—
210C2×C3×D4C22×D511yescharacteristic
211C2×#67D2011yescharacteristic
212C2×#67C22⋊D511yescharacteristic
213C22×Dic3D2011yescharacteristic
214C22×Dic3C22⋊D511yescharacteristic
215D3×Q8—201no—
216D3×Q8—201no—
217#237—41no—
218#237—41no—
219C2×C4×D3—101no—
220C2×C4×D3C4×D511yescharacteristic
221C2×Dic6—51no—
222C2×Dic6—101no—
223C2×Dic6C4×D511yescharacteristic
224C3×C22⋊C4—21no—
225C3×C22⋊C4—101no—
226C3×C22⋊C4—101no—
227C3×C22⋊C4—101no—
228C3×C42—51no—
229#217—21no—
230#217—101no—
231#217—101no—
232#217—101no—
233(C2×D3)⋊C4—101no—
234C4⋊Dic3—101no—
235C4⋊Dic3—101no—
236Dic3⋊C4—41no—
237Dic3⋊C4—101no—
238Dic3⋊C4—101no—
239Dic3⋊C4—101no—
240Dic3⋊C4—201no—
241C4×Dic3—41no—
242C4×Dic3—51no—
243C4×Dic3—201no—
244C23×C5—31no—
245C23×C5D3×D411yescharacteristic
246C23×C5D3×D411yescharacteristic
247C5×Q8—121no—
248C5×D4—41no—
249C5×D4—121no—
250C5×D4—121no—
251C2×C4×C5—31no—
252C2×C4×C5—31no—
253C2×C4×C5—31no—
254C2×C4×C5—41no—
255C2×C4×C5—61no—
256C2×C4×C5—61no—
257C2×C4×C5—61no—
258C2×C4×C5—61no—
259C2×C4×C5—61no—
260C2×C4×C5—61no—
261C2×C4×C5—121no—
262C2×C4×C5C2×C4×D311yescharacteristic
263C2×Dic5—21no—
264C2×Dic5—21no—
265C2×Dic5—41no—
266C2×Dic5—61no—
267C2×Dic5—61no—
268C2×Dic5—122no—
269C2×Dic5—121no—
270Dic10—41no—
271Dic10—121no—
272Dic10—121no—
273Dic10—121no—
274C2×#41—31no—
275C22×Q8—151no—
276C4⋊Q8—151no—
277C4⋊Q8—151no—
278#124—51no—
279#124—151no—
280#123—301no—
281#123—301no—
282C22⋊Q8—301no—
283C22⋊Q8—301no—
284#117—61no—
285#117—151no—
286#117—301no—
287#99—31no—
288#99—51no—
289#99—61no—
290#99—151no—
291#99—301no—
292#99D3×D511yescharacteristic
293C2×C3×C5—21no—
294C2×C3×C5—41no—
295C2×C3×C5—41no—
296C2×C3×C5C2×#9911yescharacteristic
297C5×D3—41no—
298C23×C3C2×D2011yescharacteristic
299C23×C3C2×C22⋊D511yescharacteristic
300C22×D3#68511yescharacteristic
301C3×Q8—201no—
302C3×D4—41no—
303C2×C3×C4—41no—
304C2×C3×C4—101no—
305C2×C3×C4—101no—
306C2×C3×C4—201no—
307C2×C3×C4C2×C4×D511yescharacteristic
308#67—41no—
309#67—41no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—21no—
314C2×Dic3—41no—
315C2×Dic3—101no—
316C2×Dic3—101no—
317C2×Dic3—201no—
318C2×Dic3#68511yescharacteristic
319C2×Dic3#68511yescharacteristic
320C2×Dic3#68511yescharacteristic
321C4×D3—21no—
322C4×D3—21no—
323C4×D3—202no—
324Dic6—41no—
325Dic6—201no—
326Dic6—201no—
327Dic6—201no—
328C22×C5—21no—
329C22×C5—21no—
330C22×C5—41no—
331C22×C5—41no—
332C22×C5—61no—
333C22×C5—121no—
334C22×C5D3×C22⋊C411yescharacteristic
335C4×C5—21no—
336C4×C5—31no—
337C4×C5—31no—
338C4×C5—61no—
339C4×C5—61no—
340C4×C5—81no—
341C4×C5—241no—
342Dic5—41no—
343Dic5—41no—
344Dic5—81no—
345Dic5—121no—
346Dic5—121no—
347Dic5—241no—
348#41—121no—
349#41—121no—
350C2×Q8—31no—
351C2×Q8—51no—
352C2×Q8—151no—
353C2×Q8—301no—
354C2×Q8—601no—
355C2×Q8—601no—
356C2×D4—31no—
357C2×D4—31no—
358C2×D4C2×D3×D511yescharacteristic
359C22×C4—31no—
360C22×C4—31no—
361C22×C4—31no—
362C22×C4—301no—
363C4⋊C4—121no—
364C4⋊C4—301no—
365C4⋊C4—301no—
366C4⋊C4—301no—
367C4⋊C4—301no—
368C4⋊C4—301no—
369C4⋊C4—601no—
370C22⋊C4—21no—
371C22⋊C4—61no—
372C22⋊C4—101no—
373C22⋊C4—101no—
374C22⋊C4—101no—
375C22⋊C4—301no—
376C22⋊C4—301no—
377C22⋊C4—301no—
378C22⋊C4—301no—
379C42—51no—
380C42—121no—
381C42—151no—
382C42—601no—
383C3×C5#212911yescharacteristic, complemented, Hall
384C22×C3—21no—
385C22×C3—21no—
386C22×C3—41no—
387C22×C3—41no—
388C22×C3C2×#68511yescharacteristic
389C2×D3—21no—
390C2×D3—41no—
391C3×C4—21no—
392C3×C4—81no—
393C3×C4—201no—
394C3×C4—201no—
395C3×C4—401no—
396Dic3—21no—
397Dic3—21no—
398Dic3—81no—
399Dic3—201no—
400Dic3—201no—
401Dic3—401no—
402Dic3#393811yescharacteristic
403Dic3#393811yescharacteristic
404C2×C5—21no—
405C2×C5—41no—
406C2×C5—41no—
407C2×C5—121no—
408C2×C5D3×#9911yescharacteristic
409C23—31no—
410C23D3×D2011yescharacteristic
411C23D3×C22⋊D511yescharacteristic
412Q8—121no—
413Q8—201no—
414Q8—601no—
415Q8—601no—
416Q8—601no—
417D4—41no—
418D4—121no—
419D4—121no—
420C2×C4—31no—
421C2×C4—31no—
422C2×C4—31no—
423C2×C4—41no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—61no—
429C2×C4—61no—
430C2×C4—101no—
431C2×C4—101no—
432C2×C4—121no—
433C2×C4—201no—
434C2×C4—301no—
435C2×C4—301no—
436C2×C4—602no—
437C2×C4—601no—
438C2×C4C4×D3×D511yescharacteristic
439C2×C3—21no—
440C2×C3—41no—
441C2×C3—41no—
442C2×C3C2×#393811yescharacteristic
443D3—41no—
444C5#6915911yescharacteristic, complemented, Sylow
445C22—21no—
446C22—21no—
447C22—41no—
448C22—41no—
449C22—61no—
450C22—121no—
451C22D3×#68511yescharacteristic
452C4—21no—
453C4—31no—
454C4—31no—
455C4—61no—
456C4—61no—
457C4—81no—
458C4—201no—
459C4—201no—
460C4—241no—
461C4—401no—
462C4—601no—
463C4—601no—
464C4—1201no—
465C3#1060085211yescharacteristic, complemented, Sylow
466C2—21no—
467C2—41no—
468C2—41no—
469C2—121no—
470C2D3×#393811yescharacteristic
subgroupG/H
centerC2D3×#3938
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×D4C2×D3×D5
FittingC3×C5×#99C22
socleC2×C3×C5C2×#99
prime radicalC2×C5×#237C22
cosocleC2×C3×C5×D4C23
hypercenter#99D3×D5
hypocenterC3×C5#2129
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
4. #11746294C2semidirect
5. C3×#64693C2semidirect
6. #11746011C2semidirect
7. #11746009C2semidirect
10. C2×D3×Dic10C4semidirect
19. #91385C4semidirect
20. #91376C4semidirect
21. #91371C4semidirect
35. #64693D3semidirect
383. C3×C5#2129semidirect
444. C5#69159semidirect
465. C3#10600852semidirect

Maximal subgroups

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

subgroupindex
#117548122
C5×#47402
#117491732
#117462942
C3×#646932
#117460112
#117460092
#106008523
#691595