Finite Group Databasebeta

← #14287789

Subgroups — #14287789

Order 1920.

544 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 84 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
1C5×#5515C211yesmaximal, characteristic, complemented
2#11751092C211yesmaximal, characteristic, complemented
3#11748554C211yesmaximal, characteristic, complemented
4#11748525C211yesmaximal, characteristic
5C3×#64748C211yesmaximal, characteristic, complemented
6#11745963C211yesmaximal, characteristic, complemented
7#11745957C211yesmaximal, characteristic, complemented
8#10602681—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×#6714—21no—
12C2×#6714—21no—
13C5×#930C2211yescharacteristic
14C5×#929—21no—
15C4×C5×#67—21no—
16C5×#924C2211yescharacteristic
17C5×#898—21no—
18C5×#896—21no—
19C5×#894—21no—
20C5×#889—21no—
21C2×#6660—21no—
22C2×#6654—21no—
23#91115C2211yescharacteristic
24C3×C22⋊#168C2211yescharacteristic
25C3×C22⋊#168C2211yescharacteristic
26#90969—21no—
27#90969—21no—
28#68130—51nomaximal, Hall
29C5×#539—31no—
30#65335—31no—
31#65325—31no—
32#65280—31no—
33#64758—31no—
34#64757—31no—
35#64748D311yescharacteristic, complemented
36C23×D15—21no—
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60—42no—
44C2×C5×#67—21no—
45C2×C5×D12D411yescharacteristic
46C2×C4×C5×D3—21no—
47C2×C5×Dic6D411yescharacteristic
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50#6714—42no—
51#6714—42no—
52C5×#217—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×(C2×D3)⋊C4—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×C4⋊Dic3D411yescharacteristic
58C5×C4⋊Dic3D411yescharacteristic
59C5×Dic3⋊C4—21no—
60C5×Dic3⋊C4—21no—
61C5×Dic3⋊C4—21no—
62C5×Dic3⋊C4—21no—
63C4×C5×Dic3—21no—
64C2×C3×#168—21no—
65C2×C3×#168—21no—
66#6660—42no—
67#6654—42no—
68#5515D511yescharacteristic, complemented
69#4991—51no—
70#4732—51no—
71#4731—51no—
72C3×#324—51no—
73#4470—51no—
74#4467—51no—
75C22×D20—31no—
76C5×#126—61no—
77C5×#125—61no—
78C5×#123—61no—
79C5×#123—61no—
80C5×C22⋊Q8—31no—
81C5×C22⋊Q8—61no—
82C5×#121—31no—
83C4×C5×D4—61no—
84C2×C5×C4⋊C4C2×D311yescharacteristic
85C2×#688—61no—
86C2×#686—61no—
87C2×#685—61no—
88C2×#685—61no—
89#3963—31no—
90C22⋊#168C2×D311yescharacteristic
91C22⋊#168C2×D311yescharacteristic
92#3941—61no—
93#3941—61no—
94#1597—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×D15—22no—
97C22×D15—41no—
98C22×D15—41no—
99C22×D15—41no—
100C22×D15—41no—
101C22×D15—41no—
102C22×D15—41no—
103C22×C5×D3—21no—
104C2×C3×C4×C5—21no—
105C2×C3×C4×C5—21no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—21no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C2×D411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×Dic15—41no—
113C2×Dic15—41no—
114C2×Dic15—41no—
115D60—22no—
116D60—22no—
117D60—41no—
118D60—41no—
119C5×#67—41no—
120C5×#67—41no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C5×D12—41no—
125C4×C5×D3—81no—
126C5×Dic6—41no—
127C3×#168—41no—
128C3×#168—41no—
129C22×D12—51no—
130C2×C3×C4⋊C4C2×D511yescharacteristic
131#930C2×D511yescharacteristic
132#929—21no—
133C4×#67—21no—
134C2×(C2×D3)⋊C4—101no—
135C2×(C2×D3)⋊C4—101no—
136#924C2×D511yescharacteristic
137C2×D24—101no—
138C2×#204—101no—
139#898—21no—
140#896—21no—
141#894—21no—
142#889—21no—
143C3×C22⋊C8—51no—
144C3×C22⋊C8—51no—
145C3⋊#95—51no—
146#821—101no—
147#821—101no—
148C23×D5—61no—
149C2×C5×Q8—31no—
150C2×C5×D4—31no—
151C2×C5×D4—61no—
152C22×C4×C5—61no—
153C22×C4×C5D1211yescharacteristic
154C22×C4×C5D1211yescharacteristic
155C22×C4×C5C22×D311yescharacteristic
156C22×Dic5—61no—
157C2×D20—61no—
158C2×D20—61no—
159C2×D20—122no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—31no—
163C5×C4⋊C4—31no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4—61no—
166C5×C4⋊C4—61no—
167C5×C4⋊C4—61no—
168C5×C22⋊C4—61no—
169C5×C22⋊C4—61no—
170C5×C22⋊C4—61no—
171C5×C22⋊C4—61no—
172C5×C22⋊C4—61no—
173C42×C5—61no—
174#688—122no—
175#686—122no—
176#685—122no—
177#685—122no—
178C2×#168—21no—
179C2×#168—21no—
180#539—31no—
181#450—151no—
182#447—151no—
183#394—151no—
184#328—151no—
185#327—151no—
186#324—51no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5#12011yescharacteristic
190C22×C3×C5#13511yescharacteristic
191C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
192C2×D15—42no—
193C2×D15—42no—
194C2×D15—42no—
195C2×D15—81no—
196C2×D15—81no—
197C2×D15—81no—
198C2×D15—81no—
199C2×C5×D3—41no—
200C2×C5×D3—41no—
201C2×C5×D3—41no—
202C3×C4×C5—21no—
203C3×C4×C5—21no—
204C3×C4×C5—41no—
205C3×C4×C5—41no—
206Dic15—81no—
207C5×Dic3—41no—
208C5×Dic3—41no—
209C5×Dic3—41no—
210C23×D3—101no—
211C22×C3×C4C22⋊D511yescharacteristic
212C22×C3×C4C22⋊D511yescharacteristic
213C22×C3×C4C22×D511yescharacteristic
214C2×#67—21no—
215C22×Dic3—101no—
216C2×D12—101no—
217C2×D12—101no—
218C2×D12—202no—
219C2×D12C22⋊D511yescharacteristic
220C2×C4×D3—21no—
221C2×Dic6C22⋊D511yescharacteristic
222C2×C3×C8—101no—
223C2×C3×C8—101no—
224C3×C4⋊C4—21no—
225C3×C4⋊C4—21no—
226#217—21no—
227(C2×D3)⋊C4—21no—
228(C2×D3)⋊C4—21no—
229(C2×D3)⋊C4—21no—
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—202no—
232(C2×D3)⋊C4—202no—
233C4⋊Dic3C22⋊D511yescharacteristic
234C4⋊Dic3C22⋊D511yescharacteristic
235Dic3⋊C4—21no—
236Dic3⋊C4—21no—
237Dic3⋊C4—21no—
238Dic3⋊C4—21no—
239C4×Dic3—21no—
240D24—202no—
241#204—202no—
242C23×C5—61no—
243C23×C5C2×D1211yescharacteristic
244C22×D5—62no—
245C22×D5—121no—
246C22×D5—121no—
247C22×D5—121no—
248C22×D5—121no—
249C22×D5—121no—
250C22×D5—121no—
251C5×Q8—121no—
252C5×D4—121no—
253C5×D4—121no—
254C5×D4—121no—
255C2×C4×C5—21no—
256C2×C4×C5—21no—
257C2×C4×C5—21no—
258C2×C4×C5—21no—
259C2×C4×C5—41no—
260C2×C4×C5—41no—
261C2×C4×C5—61no—
262C2×C4×C5—61no—
263C2×C4×C5—61no—
264C2×C4×C5—241no—
265C2×C4×C5D3×D411yescharacteristic
266C2×C4×C5D3×D411yescharacteristic
267C2×Dic5—121no—
268C2×Dic5—121no—
269C2×Dic5—121no—
270D20—62no—
271D20—62no—
272D20—121no—
273D20—121no—
274#168—41no—
275#168—41no—
276C22×D4—151no—
277C2×SD16—301no—
278C2×D8—301no—
279#126—61no—
280#125—61no—
281#123—61no—
282#123—61no—
283C22⋊Q8—31no—
284C22⋊Q8—61no—
285#121—31no—
286C4×D4—61no—
287C2×C4⋊C4D3×D511yescharacteristic
288C2×C22⋊C4—301no—
289C2×C22⋊C4—301no—
290#102—301no—
291#102—301no—
292C22⋊C8—51no—
293C22⋊C8—51no—
294#95—151no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5#44911yescharacteristic
298C2×C3×C5#45411yescharacteristic
299C2×C3×C5B(4,𝔽2)11yescharacteristic
300D15—82no—
301C5×D3—81no—
302C23×C3C2×C22⋊D511yescharacteristic
303C22×D3—21no—
304C22×D3—102no—
305C22×D3—201no—
306C22×D3—201no—
307C22×D3—201no—
308C22×D3—201no—
309C22×D3—201no—
310C22×D3—201no—
311C2×C3×C4—21no—
312C2×C3×C4—21no—
313C2×C3×C4—21no—
314C2×C3×C4—21no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4C2×C22⋊D511yescharacteristic
318C2×C3×C4C2×C22⋊D511yescharacteristic
319#67—41no—
320#67—41no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—201no—
325C2×Dic3—201no—
326C2×Dic3—201no—
327D12—41no—
328D12—102no—
329D12—102no—
330D12—201no—
331D12—201no—
332C4×D3—81no—
333Dic6—41no—
334C3×C8—201no—
335C3×C8—201no—
336C22×C5—21no—
337C22×C5—21no—
338C22×C5—121no—
339C22×C5—121no—
340C22×C5—121no—
341C22×C5#88211yescharacteristic
342C22×C5#90411yescharacteristic
343C22×C5#90811yescharacteristic
344C2×D5—122no—
345C2×D5—122no—
346C2×D5—122no—
347C2×D5—241no—
348C2×D5—241no—
349C2×D5—241no—
350C2×D5—241no—
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—121no—
356C4×C5—121no—
357C4×C5—121no—
358Dic5—241no—
359C24—301no—
360C2×Q8—31no—
361C2×D4—31no—
362C2×D4—61no—
363C2×D4—301no—
364C2×D4—301no—
365C2×D4—602no—
366C22×C4—61no—
367C22×C4—301no—
368C22×C4#120311yescharacteristic
369C22×C4#120311yescharacteristic
370C22×C4C2×D3×D511yescharacteristic
371SD16—602no—
372D8—602no—
373C2×C8—101no—
374C2×C8—101no—
375C4⋊C4—21no—
376C4⋊C4—21no—
377C4⋊C4—31no—
378C4⋊C4—31no—
379C4⋊C4—61no—
380C4⋊C4—61no—
381C4⋊C4—61no—
382C4⋊C4—61no—
383C22⋊C4—61no—
384C22⋊C4—61no—
385C22⋊C4—61no—
386C22⋊C4—61no—
387C22⋊C4—61no—
388C22⋊C4—602no—
389C22⋊C4—602no—
390C42—61no—
391C3×C5#159711yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3#409511yescharacteristic
395C22×C3#409611yescharacteristic
396C22×C3#409911yescharacteristic
397C2×D3—41no—
398C2×D3—41no—
399C2×D3—41no—
400C2×D3—202no—
401C2×D3—202no—
402C2×D3—202no—
403C2×D3—401no—
404C2×D3—401no—
405C2×D3—401no—
406C2×D3—401no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—41no—
410C3×C4—41no—
411Dic3—41no—
412Dic3—41no—
413Dic3—41no—
414Dic3—401no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—241no—
418C2×C5#473411yescharacteristic
419C2×C5#474111yescharacteristic
420C2×C5#475311yescharacteristic
421D5—242no—
422C23—61no—
423C23—302no—
424C23—601no—
425C23—601no—
426C23—601no—
427C23—601no—
428C23—601no—
429C23—601no—
430C23C2×#120311yescharacteristic
431Q8—121no—
432D4—121no—
433D4—121no—
434D4—121no—
435D4—302no—
436D4—302no—
437D4—601no—
438D4—601no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—241no—
449C2×C4—601no—
450C2×C4—601no—
451C2×C4—601no—
452C2×C4D3×C22⋊D511yescharacteristic
453C2×C4D3×C22⋊D511yescharacteristic
454C8—201no—
455C8—201no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3#6552711yescharacteristic
459C2×C3#6553311yescharacteristic
460C2×C3#6553411yescharacteristic
461D3—81no—
462D3—402no—
463C5#6813011yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—602no—
470C22—602no—
471C22—602no—
472C22—1201no—
473C22—1201no—
474C22—1201no—
475C22—1201no—
476C22#9130311yescharacteristic
477C22#9130511yescharacteristic
478C22#9157011yescharacteristic
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—121no—
484C4—121no—
485C4—121no—
486C4—1201no—
487C3#1060268111yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—241no—
491C2—1202no—
492C2#1174852111yescharacteristic
493C2#1174917811yescharacteristic
494C2#1174938711yescharacteristic
subgroupG/H
centerC22#91570
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radical#11748525C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#1597
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C5×#5515C2semidirect
2. #11751092C2semidirect
3. #11748554C2semidirect
5. C3×#64748C2semidirect
6. #11745963C2semidirect
7. #11745957C2semidirect
35. #64748D3semidirect
68. #5515D5semidirect
391. C3×C5#1597semidirect
463. C5#68130semidirect
487. C3#10602681semidirect

Maximal subgroups

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

subgroupindex
C5×#55152
#117510922
#117485542
#117485252
C3×#647482
#117459632
#117459572
#106026813
#681305