Finite Group Databasebeta

← #14287788

Subgroups — #14287788

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
2C3×#65280C211yesmaximal, characteristic, complemented
3#11748527C211yesmaximal, characteristic, complemented
4#11748510C211yesmaximal, characteristic
5#11746349C211yesmaximal, characteristic, complemented
6#11745962C211yesmaximal, characteristic, complemented
7#11745956C211yesmaximal, characteristic, complemented
8#10602681—31nomaximal, Hall
9C22×C3×D20C2211yescharacteristic
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C5×#930C2211yescharacteristic
12C5×#929—21no—
13C4×C5×#67—21no—
14C5×#924C2211yescharacteristic
15C5×#898—21no—
16C5×#896—21no—
17C5×#894—21no—
18C5×#889—21no—
19C2×C3×#685—21no—
20C2×C3×#685—21no—
21C2×#6655—21no—
22C2×#6652—21no—
23#91114C2211yescharacteristic
24#91114C2211yescharacteristic
25C3×#3963C2211yescharacteristic
26#90964—21no—
27#90964—21no—
28#69702—51nomaximal, Hall
29C5×#539—31no—
30#65335—31no—
31#65325—31no—
32#65280D311yescharacteristic, complemented
33#64758—31no—
34#64757—31no—
35#64748—31no—
36C23×C3×D5—21no—
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C22×C3×C4×C5C2311yescharacteristic
40C2×C5×#67—21no—
41C2×C5×D12D411yescharacteristic
42C2×C4×C5×D3—21no—
43C2×C5×Dic6D411yescharacteristic
44C22×C3×Dic5—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20—42no—
48C3×C5×C4⋊C4—21no—
49C3×C5×C4⋊C4—21no—
50C2×C3⋊#168—21no—
51C2×C3⋊#168—21no—
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—
64C3×#685—42no—
65C3×#685—42no—
66#6655—42no—
67#6652—42no—
68#5515D511yescharacteristic, complemented
69C3×#394—51no—
70#5218—51no—
71#5217—51no—
72#4528—51no—
73#4452—51no—
74#4451—51no—
75C22×D20C2×D311yescharacteristic
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—21no—
88C2×#685—21no—
89#3963C2×D311yescharacteristic
90C22⋊#168—31no—
91C22⋊#168—31no—
92#3941—61no—
93#3941—61no—
94#1597—151noSylow
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—21no—
97C22×C3×D5—22no—
98C22×C3×D5—41no—
99C22×C3×D5—41no—
100C22×C3×D5—41no—
101C22×C3×D5—41no—
102C22×C3×D5—41no—
103C22×C3×D5—41no—
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
112C5×#67—41no—
113C5×#67—41no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—21no—
117C5×D12—41no—
118C4×C5×D3—81no—
119C5×Dic6—41no—
120C2×C3×Dic5—41no—
121C2×C3×Dic5—41no—
122C2×C3×Dic5—41no—
123C3×D20—22no—
124C3×D20—22no—
125C3×D20—41no—
126C3×D20—41no—
127C3⋊#168—41no—
128C3⋊#168—41no—
129C22×C3×D4—51no—
130C2×C3×C4⋊C4C2×D511yescharacteristic
131C2×C3×C22⋊C4—101no—
132C2×C3×C22⋊C4—101no—
133C2×#214—101no—
134C2×#213—101no—
135#930C2×D511yescharacteristic
136#929—21no—
137C4×#67—21no—
138#924C2×D511yescharacteristic
139#898—21no—
140#896—21no—
141#894—21no—
142#889—21no—
143C3×#95—51no—
144#832—101no—
145#832—101no—
146#830—51no—
147#830—51no—
148C23×D5—21no—
149C2×C5×Q8—31no—
150C2×C5×D4—31no—
151C2×C5×D4—61no—
152C22×C4×C5—61no—
153C22×C4×C5#6711yescharacteristic
154C22×C4×C5#6711yescharacteristic
155C22×C4×C5C22×D311yescharacteristic
156C22×Dic5—21no—
157C2×D20—21no—
158C2×D20—21no—
159C2×D20—42no—
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—42no—
177#685—42no—
178C2×#168—61no—
179C2×#168—61no—
180#539—31no—
181#450—151no—
182#447—151no—
183#394—51no—
184#328—151no—
185#327—151no—
186#324—151no—
187C22×C3×C5—21no—
188C22×C3×C5—21no—
189C22×C3×C5#12011yescharacteristic
190C22×C3×C5#13511yescharacteristic
191C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
192C2×C5×D3—41no—
193C2×C5×D3—41no—
194C2×C5×D3—41no—
195C2×C3×D5—42no—
196C2×C3×D5—42no—
197C2×C3×D5—42no—
198C2×C3×D5—81no—
199C2×C3×D5—81no—
200C2×C3×D5—81no—
201C2×C3×D5—81no—
202C3×C4×C5—21no—
203C3×C4×C5—21no—
204C3×C4×C5—41no—
205C3×C4×C5—41no—
206C3×Dic5—81no—
207C5×Dic3—41no—
208C5×Dic3—41no—
209C5×Dic3—41no—
210C24×C3—101no—
211C2×C3×D4—101no—
212C2×C3×D4—101no—
213C2×C3×D4—202no—
214C22×C3×C4—101no—
215C22×C3×C4C22⋊D511yescharacteristic
216C22×C3×C4C22⋊D511yescharacteristic
217C22×C3×C4C22×D511yescharacteristic
218C2×#67—21no—
219C2×D12C22⋊D511yescharacteristic
220C2×C4×D3—21no—
221C2×Dic6C22⋊D511yescharacteristic
222C3×C4⋊C4—21no—
223C3×C4⋊C4—21no—
224C3×C22⋊C4—202no—
225C3×C22⋊C4—202no—
226#217—21no—
227#214—202no—
228#213—202no—
229(C2×D3)⋊C4—21no—
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—21no—
232(C2×D3)⋊C4—21no—
233C4⋊Dic3C22⋊D511yescharacteristic
234C4⋊Dic3C22⋊D511yescharacteristic
235Dic3⋊C4—21no—
236Dic3⋊C4—21no—
237Dic3⋊C4—21no—
238Dic3⋊C4—21no—
239C4×Dic3—21no—
240C2×C3⋊C8—101no—
241C2×C3⋊C8—101no—
242C23×C5—61no—
243C23×C5C2×#6711yescharacteristic
244C22×D5—22no—
245C22×D5—41no—
246C22×D5—41no—
247C22×D5—41no—
248C22×D5—41no—
249C22×D5—41no—
250C22×D5—41no—
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—41no—
268C2×Dic5—41no—
269C2×Dic5—41no—
270D20—22no—
271D20—22no—
272D20—41no—
273D20—41no—
274#168—121no—
275#168—121no—
276C22×D4—51no—
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—101no—
289C2×C22⋊C4—101no—
290#102—301no—
291#102—301no—
292C22⋊C8—151no—
293C22⋊C8—151no—
294#95—51no—
295C2×C3×C5—21no—
296C2×C3×C5—21no—
297C2×C3×C5#44911yescharacteristic
298C2×C3×C5#45411yescharacteristic
299C2×C3×C5B(4,𝔽2)11yescharacteristic
300C3×D5—82no—
301C5×D3—81no—
302C23×C3—102no—
303C23×C3—201no—
304C23×C3—201no—
305C23×C3—201no—
306C23×C3—201no—
307C23×C3—201no—
308C23×C3—201no—
309C23×C3C2×C22⋊D511yescharacteristic
310C22×D3—21no—
311C3×D4—102no—
312C3×D4—102no—
313C3×D4—201no—
314C3×D4—201no—
315C2×C3×C4—21no—
316C2×C3×C4—21no—
317C2×C3×C4—21no—
318C2×C3×C4—21no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—201no—
322C2×C3×C4—201no—
323C2×C3×C4—201no—
324C2×C3×C4C2×C22⋊D511yescharacteristic
325C2×C3×C4C2×C22⋊D511yescharacteristic
326#67—41no—
327#67—41no—
328C2×Dic3—21no—
329C2×Dic3—21no—
330C2×Dic3—21no—
331D12—41no—
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#93211yescharacteristic
342C22×C5#93711yescharacteristic
343C22×C5#95011yescharacteristic
344C2×D5—42no—
345C2×D5—42no—
346C2×D5—42no—
347C2×D5—81no—
348C2×D5—81no—
349C2×D5—81no—
350C2×D5—81no—
351C4×C5—21no—
352C4×C5—21no—
353C4×C5—41no—
354C4×C5—41no—
355C4×C5—121no—
356C4×C5—121no—
357C4×C5—121no—
358Dic5—81no—
359C24—101no—
360C2×Q8—31no—
361C2×D4—31no—
362C2×D4—61no—
363C2×D4—101no—
364C2×D4—101no—
365C2×D4—202no—
366C22×C4—61no—
367C22×C4—101no—
368C22×C4#120111yescharacteristic
369C22×C4#120111yescharacteristic
370C22×C4C2×D3×D511yescharacteristic
371SD16—602no—
372D8—602no—
373C2×C8—301no—
374C2×C8—301no—
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—202no—
389C22⋊C4—202no—
390C42—61no—
391C3×C5#159711yescharacteristic, complemented, Hall
392C22×C3—21no—
393C22×C3—21no—
394C22×C3—202no—
395C22×C3—202no—
396C22×C3—202no—
397C22×C3—401no—
398C22×C3—401no—
399C22×C3—401no—
400C22×C3—401no—
401C22×C3#409511yescharacteristic
402C22×C3#409611yescharacteristic
403C22×C3#409911yescharacteristic
404C2×D3—41no—
405C2×D3—41no—
406C2×D3—41no—
407C3×C4—21no—
408C3×C4—21no—
409C3×C4—41no—
410C3×C4—41no—
411C3×C4—401no—
412Dic3—41no—
413Dic3—41no—
414Dic3—41no—
415C2×C5—21no—
416C2×C5—21no—
417C2×C5—241no—
418C2×C5#503211yescharacteristic
419C2×C5#503711yescharacteristic
420C2×C5#506211yescharacteristic
421D5—82no—
422C23—61no—
423C23—102no—
424C23—201no—
425C23—201no—
426C23—201no—
427C23—201no—
428C23—201no—
429C23—201no—
430C23C2×#120111yescharacteristic
431Q8—121no—
432D4—102no—
433D4—102no—
434D4—121no—
435D4—121no—
436D4—121no—
437D4—201no—
438D4—201no—
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—201no—
449C2×C4—201no—
450C2×C4—201no—
451C2×C4—241no—
452C2×C4D3×C22⋊D511yescharacteristic
453C2×C4D3×C22⋊D511yescharacteristic
454C8—601no—
455C8—601no—
456C2×C3—21no—
457C2×C3—21no—
458C2×C3—402no—
459C2×C3#6552711yescharacteristic
460C2×C3#6553311yescharacteristic
461C2×C3#6553411yescharacteristic
462D3—81no—
463C5#6970211yescharacteristic, complemented, Sylow
464C22—21no—
465C22—21no—
466C22—121no—
467C22—121no—
468C22—121no—
469C22—202no—
470C22—202no—
471C22—202no—
472C22—401no—
473C22—401no—
474C22—401no—
475C22—401no—
476C22#9129711yescharacteristic
477C22#9129811yescharacteristic
478C22#9156811yescharacteristic
479C4—21no—
480C4—21no—
481C4—41no—
482C4—41no—
483C4—121no—
484C4—121no—
485C4—121no—
486C4—401no—
487C3#1060268111yescharacteristic, complemented, Sylow
488C2—21no—
489C2—21no—
490C2—241no—
491C2—402no—
492C2#1174851711yescharacteristic
493C2#1174917711yescharacteristic
494C2#1174938611yescharacteristic
subgroupG/H
centerC22#91568
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5#120
prime radical#11748510C2
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. C3×#65280C2semidirect
3. #11748527C2semidirect
5. #11746349C2semidirect
6. #11745962C2semidirect
7. #11745956C2semidirect
32. #65280D3semidirect
68. #5515D5semidirect
391. C3×C5#1597semidirect
463. C5#69702semidirect
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
C3×#652802
#117485272
#117485102
#117463492
#117459622
#117459562
#106026813
#697025