Finite Group Databasebeta

← #14287896

Subgroups — #14287896

Order 1920.

640 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 640 conjugacy classes of subgroups — too many to draw. Only its 83 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#11756376C211yesmaximal, characteristic, complemented
2C3×C5×#447C211yesmaximal, characteristic, complemented
3#11751324C211yesmaximal, characteristic, complemented
4#11751319C211yesmaximal, characteristic, complemented
5#11746358C211yesmaximal, characteristic, complemented
6#11746289C211yesmaximal, characteristic, complemented
7#11746288C211yesmaximal, characteristic, complemented
8#10601762—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×#1220—21no—
11C2×C3×C5×D8—21no—
12C3×C5×#121C2211yescharacteristic
13C2×#6719—21no—
14#91828—21no—
15#91826—21no—
16D4×Dic15—21no—
17C2×#6716—21no—
18C2×#6714C2211yescharacteristic
19#91813C2211yescharacteristic
20#91787—21no—
21#91775—21no—
22#91774—21no—
23C3×C5×#102—21no—
24C3×C5×C22⋊C8C2211yescharacteristic
25#91116—21no—
26#91115C2211yescharacteristic
27#91114C2211yescharacteristic
28#70969—51nomaximal, Hall
29#65951—31no—
30C5×#447D311yescharacteristic, complemented
31#65512—31no—
32#65507—31no—
33#64757—31no—
34#64688—31no—
35#64687—31no—
36C24×C3×C5—21no—
37C23×D15D411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—42no—
42C2×C3×C5×D4D411yescharacteristic, complemented
43C22×C3×C4×C5C2311yescharacteristic
44C2×#1220—21no—
45C2×#1220—21no—
46C2×#1220—42no—
47C2×#1220—42no—
48C2×#1220—42no—
49C22×Dic15—21no—
50C22×Dic15—21no—
51C22×Dic15D411yescharacteristic
52C2×Dic30D411yescharacteristic, complemented
53C3×C5×D8—42no—
54C2×C3×C5×C8—21no—
55C3×C5×C4⋊C4D411yescharacteristic, complemented
56C3×C5×C22⋊C4—21no—
57#6719—21no—
58#6719—21no—
59#6719—42no—
60#6716—42no—
61#6714—21no—
62#6714—21no—
63#6714—21no—
64#6714—21no—
65C4⋊Dic15—21no—
66C4⋊Dic15D411yescharacteristic, complemented
67#6712—21no—
68C4×Dic15—21no—
69C2×C3⋊#168—21no—
70#5617—51no—
71C3×#447D511yescharacteristic, complemented
72#5223—51no—
73#5218—51no—
74#4537—51no—
75#4468—51no—
76#4467—51no—
77C22×C5×D4C2×D311yescharacteristic
78C22×C22⋊D5—61no—
79C2×C5×D8—21no—
80C5×#121C2×D311yescharacteristic
81C2×C22⋊Dic5—61no—
82#4085—61no—
83#4083—61no—
84D4×Dic5—61no—
85C2×#687—61no—
86C2×#685—31no—
87#4070—31no—
88#4044—61no—
89#4032—61no—
90#4031—61no—
91C5×#102—21no—
92C5×C22⋊C8C2×D311yescharacteristic
93#3964—61no—
94#3963—31no—
95C22⋊#168—31no—
96#1600—151noSylow
97C23×C3×C5—22no—
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5C2×D411yescharacteristic
106C22×D15—21no—
107C22×D15—21no—
108C22×D15—21no—
109C22×D15—41no—
110C22×D15—41no—
111C3×C5×D4—22no—
112C3×C5×D4—22no—
113C3×C5×D4—41no—
114C3×C5×D4—41no—
115C3×C5×D4—41no—
116C3×C5×D4—41no—
117C3×C5×D4—41no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—41no—
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D411yescharacteristic
122#1220—48no—
123#1220—81no—
124#1220—81no—
125C2×Dic15—22no—
126C2×Dic15—21no—
127C2×Dic15—21no—
128C2×Dic15—21no—
129C2×Dic15—41no—
130C2×Dic15—41no—
131C2×Dic15—41no—
132C2×Dic15—81no—
133Dic30—41no—
134C3×C5×C8—41no—
135C3⋊#168—41no—
136C22×C3×D4C2×D511yescharacteristic
137C22×#67—101no—
138C2×C3×D8—21no—
139C3×#121C2×D511yescharacteristic
140C2×#217—101no—
141#939—101no—
142#937—101no—
143D4×Dic3—101no—
144C2×#214—101no—
145C2×(C2×D3)⋊C4—51no—
146#924—51no—
147#898—101no—
148#886—101no—
149#885—101no—
150C3×#102—21no—
151C3×C22⋊C8C2×D511yescharacteristic
152#832—101no—
153C3⋊#95—51no—
154#830—51no—
155C24×C5—21no—
156C23×D5—31no—
157C2×C5×D4—21no—
158C2×C5×D4—21no—
159C2×C5×D4—21no—
160C2×C5×D4—42no—
161C2×C5×D4#6711yescharacteristic, complemented
162C22×C4×C5C22×D311yescharacteristic
163C2×C22⋊D5—61no—
164C2×C22⋊D5—61no—
165C2×C22⋊D5—122no—
166C2×C22⋊D5—122no—
167C2×C22⋊D5—122no—
168C22×Dic5—31no—
169C22×Dic5—61no—
170C22×Dic5—61no—
171C2×Dic10—31no—
172C5×D8—42no—
173C2×C5×C8—21no—
174C5×C4⋊C4#6711yescharacteristic, complemented
175C5×C22⋊C4—21no—
176C22⋊Dic5—61no—
177C22⋊Dic5—61no—
178C22⋊Dic5—122no—
179#687—122no—
180#685—61no—
181#685—61no—
182#685—61no—
183#685—61no—
184C4⋊Dic5—31no—
185C4⋊Dic5—61no—
186#683—61no—
187C4×Dic5—61no—
188C2×#168—61no—
189#538—151no—
190#450—151no—
191#447D1511yescharacteristic, complemented
192#392—151no—
193#328—151no—
194#327—151no—
195#323—151no—
196C22×C3×C5—21no—
197C22×C3×C5—21no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—41no—
201C22×C3×C5—41no—
202C22×C3×C5—41no—
203C22×C3×C5—42no—
204C22×C3×C5—81no—
205C22×C3×C5—81no—
206C22×C3×C5—81no—
207C22×C3×C5—81no—
208C22×C3×C5#12011yescharacteristic
209C22×C3×C5#13511yescharacteristic
210C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
211C2×D15—42no—
212C2×D15—41no—
213C2×D15—41no—
214C2×D15—41no—
215C2×D15—81no—
216C3×C4×C5—21no—
217C3×C4×C5—21no—
218C3×C4×C5—41no—
219Dic15—42no—
220Dic15—41no—
221Dic15—41no—
222Dic15—41no—
223C24×C3—21no—
224C23×D3—51no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—42no—
229C2×C3×D4C22⋊D511yescharacteristic, complemented
230C22×C3×C4C22×D511yescharacteristic
231C2×#67—101no—
232C2×#67—101no—
233C2×#67—202no—
234C2×#67—202no—
235C2×#67—202no—
236C22×Dic3—51no—
237C22×Dic3—101no—
238C22×Dic3—101no—
239C2×Dic6—51no—
240C3×D8—42no—
241C2×C3×C8—21no—
242C3×C4⋊C4C22⋊D511yescharacteristic, complemented
243C3×C22⋊C4—21no—
244#217—101no—
245#217—101no—
246#217—202no—
247#214—202no—
248(C2×D3)⋊C4—101no—
249(C2×D3)⋊C4—101no—
250(C2×D3)⋊C4—101no—
251(C2×D3)⋊C4—101no—
252C4⋊Dic3—51no—
253C4⋊Dic3—101no—
254Dic3⋊C4—101no—
255C4×Dic3—101no—
256C2×C3⋊C8—101no—
257C23×C5—22no—
258C23×C5—21no—
259C23×C5—41no—
260C23×C5—41no—
261C23×C5—41no—
262C23×C5—41no—
263C23×C5—41no—
264C23×C5—41no—
265C23×C5D3×D411yescharacteristic
266C22×D5—61no—
267C22×D5—61no—
268C22×D5—61no—
269C22×D5—121no—
270C22×D5—121no—
271C5×D4—22no—
272C5×D4—22no—
273C5×D4—41no—
274C5×D4—41no—
275C5×D4—41no—
276C5×D4—41no—
277C5×D4—41no—
278C2×C4×C5—21no—
279C2×C4×C5—41no—
280C2×C4×C5D3×D411yescharacteristic
281C2×C4×C5C2×#6711yescharacteristic
282C22⋊D5—128no—
283C22⋊D5—241no—
284C22⋊D5—241no—
285C2×Dic5—62no—
286C2×Dic5—61no—
287C2×Dic5—61no—
288C2×Dic5—61no—
289C2×Dic5—121no—
290C2×Dic5—121no—
291C2×Dic5—121no—
292C2×Dic5—241no—
293Dic10—121no—
294C5×C8—41no—
295#168—121no—
296C22×D4—301no—
297C22×D4C2×D1511yescharacteristic
298C2×SD16—301no—
299C2×D8—21no—
300#126—301no—
301#124—301no—
302#123—301no—
303C22⋊Q8—151no—
304#121—301no—
305#121C2×D1511yescharacteristic
306#120—301no—
307C4×D4—301no—
308C2×C22⋊C4—151no—
309C2×C22⋊C4—301no—
310#102—21no—
311#102—301no—
312C22⋊C8—151no—
313C22⋊C8C2×D1511yescharacteristic
314#95—151no—
315C2×C3×C5—21no—
316C2×C3×C5—21no—
317C2×C3×C5—81no—
318C2×C3×C5—82no—
319C2×C3×C5#44911yescharacteristic
320C2×C3×C5#45311yescharacteristic
321C2×C3×C5B(4,𝔽2)11yescharacteristic
322D15—81no—
323C23×C3—22no—
324C23×C3—21no—
325C23×C3—41no—
326C23×C3—41no—
327C23×C3—41no—
328C23×C3—41no—
329C23×C3—41no—
330C23×C3—41no—
331C23×C3D4×D511yescharacteristic
332C22×D3—101no—
333C22×D3—101no—
334C22×D3—101no—
335C22×D3—201no—
336C22×D3—201no—
337C3×D4—22no—
338C3×D4—22no—
339C3×D4—41no—
340C3×D4—41no—
341C3×D4—41no—
342C3×D4—41no—
343C3×D4—41no—
344C2×C3×C4—21no—
345C2×C3×C4—41no—
346C2×C3×C4D4×D511yescharacteristic
347C2×C3×C4C2×C22⋊D511yescharacteristic
348#67—208no—
349#67—401no—
350#67—401no—
351C2×Dic3—102no—
352C2×Dic3—101no—
353C2×Dic3—101no—
354C2×Dic3—101no—
355C2×Dic3—201no—
356C2×Dic3—201no—
357C2×Dic3—201no—
358C2×Dic3—401no—
359Dic6—201no—
360C3×C8—41no—
361C3⋊C8—201no—
362C22×C5—21no—
363C22×C5—21no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—41no—
367C22×C5—41no—
368C22×C5—41no—
369C22×C5—42no—
370C22×C5—81no—
371C22×C5—81no—
372C22×C5—81no—
373C22×C5—81no—
374C22×C5#91111yescharacteristic
375C22×C5#91211yescharacteristic
376C22×C5#93711yescharacteristic
377C2×D5—122no—
378C2×D5—121no—
379C2×D5—121no—
380C2×D5—121no—
381C2×D5—241no—
382C4×C5—21no—
383C4×C5—21no—
384C4×C5—41no—
385Dic5—122no—
386Dic5—121no—
387Dic5—121no—
388Dic5—121no—
389C24—21no—
390C24—151no—
391C2×Q8—151no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—42no—
396C2×D4—301no—
397C2×D4—301no—
398C2×D4—602no—
399C2×D4—602no—
400C2×D4—602no—
401C2×D4#122011yescharacteristic, complemented
402C22×C4—151no—
403C22×C4—301no—
404C22×C4—301no—
405C22×C4C22×D1511yescharacteristic
406SD16—602no—
407D8—42no—
408C2×C8—21no—
409C2×C8—301no—
410C4⋊C4—151no—
411C4⋊C4—301no—
412C4⋊C4—301no—
413C4⋊C4#122011yescharacteristic, complemented
414C22⋊C4—21no—
415C22⋊C4—301no—
416C22⋊C4—301no—
417C22⋊C4—301no—
418C22⋊C4—301no—
419C22⋊C4—301no—
420C22⋊C4—301no—
421C22⋊C4—602no—
422C42—301no—
423C3×C5#160011yescharacteristic, complemented, Hall
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—42no—
427C22×C3—42no—
428C22×C3—41no—
429C22×C3—42no—
430C22×C3—41no—
431C22×C3—41no—
432C22×C3—81no—
433C22×C3—81no—
434C22×C3—81no—
435C22×C3—81no—
436C22×C3#405711yescharacteristic
437C22×C3#405811yescharacteristic
438C22×C3#408311yescharacteristic
439C2×D3—202no—
440C2×D3—201no—
441C2×D3—201no—
442C2×D3—201no—
443C2×D3—401no—
444C3×C4—21no—
445C3×C4—21no—
446C3×C4—41no—
447Dic3—202no—
448Dic3—201no—
449Dic3—201no—
450Dic3—201no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—82no—
454C2×C5—81no—
455C2×C5#503211yescharacteristic
456C2×C5#515811yescharacteristic
457C2×C5#519811yescharacteristic
458D5—241no—
459C23—22no—
460C23—21no—
461C23—41no—
462C23—41no—
463C23—41no—
464C23—41no—
465C23—41no—
466C23—41no—
467C23—301no—
468C23—301no—
469C23—301no—
470C23—601no—
471C23—601no—
472C23D4×D1511yescharacteristic
473Q8—601no—
474D4—22no—
475D4—22no—
476D4—41no—
477D4—41no—
478D4—41no—
479D4—41no—
480D4—41no—
481D4—608no—
482D4—1201no—
483D4—1201no—
484C2×C4—21no—
485C2×C4—41no—
486C2×C4—302no—
487C2×C4—301no—
488C2×C4—301no—
489C2×C4—301no—
490C2×C4—601no—
491C2×C4—601no—
492C2×C4—601no—
493C2×C4—1201no—
494C2×C4D4×D1511yescharacteristic
495C2×C4C2×#122011yescharacteristic
496C8—41no—
497C8—601no—
498C2×C3—21no—
499C2×C3—21no—
500C2×C3—82no—
501C2×C3—81no—
502C2×C3#6532111yescharacteristic
503C2×C3#6544711yescharacteristic
504C2×C3#6548711yescharacteristic
505D3—401no—
506C5#7096911yescharacteristic, complemented, Sylow
507C22—21no—
508C22—21no—
509C22—42no—
510C22—42no—
511C22—41no—
512C22—41no—
513C22—42no—
514C22—41no—
515C22—81no—
516C22—81no—
517C22—81no—
518C22—81no—
519C22—602no—
520C22—601no—
521C22—601no—
522C22—601no—
523C22—1201no—
524C22#9180011yescharacteristic
525C22#9180111yescharacteristic
526C22#9182611yescharacteristic
527C4—21no—
528C4—21no—
529C4—41no—
530C4—602no—
531C4—601no—
532C4—601no—
533C4—601no—
534C3#1060176211yescharacteristic, complemented, Sylow
535C2—21no—
536C2—21no—
537C2—82no—
538C2—81no—
539C2—1201no—
540C2#1175113311yescharacteristic
541C2#1175125911yescharacteristic
542C2#1175129911yescharacteristic
subgroupG/H
centerC22#91826
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C22×D15
FittingC3×C5×#447C2
socleC22×C3×C5#120
hypercenter#447D15
hypocenterC3×C5#1600
LCSG ▷ C22×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #11756376C2semidirect
2. C3×C5×#447C2semidirect
3. #11751324C2semidirect
4. #11751319C2semidirect
5. #11746358C2semidirect
6. #11746289C2semidirect
7. #11746288C2semidirect
30. C5×#447D3semidirect
42. C2×C3×C5×D4D4semidirect
52. C2×Dic30D4semidirect
55. C3×C5×C4⋊C4D4semidirect
66. C4⋊Dic15D4semidirect
71. C3×#447D5semidirect
161. C2×C5×D4#67semidirect
174. C5×C4⋊C4#67semidirect
191. #447D15semidirect
229. C2×C3×D4C22⋊D5semidirect
242. C3×C4⋊C4C22⋊D5semidirect
401. C2×D4#1220semidirect
413. C4⋊C4#1220semidirect
423. C3×C5#1600semidirect
506. C5#70969semidirect
534. C3#10601762semidirect

Maximal subgroups

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

subgroupindex
#117563762
C3×C5×#4472
#117513242
#117513192
#117463582
#117462892
#117462882
#106017623
#709695