Finite Group Databasebeta

← #14323614

Subgroups — #14323614

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×C4⋊Dic3C211yesmaximal, characteristic, complemented
2C2×C3×#4075C211yesmaximal, characteristic
3C2×Dic3×C22⋊D5C211yesmaximal, characteristic
4#11751312C211yesmaximal, characteristic, complemented
5#11749511C211yesmaximal, characteristic, complemented
6#11749495C211yesmaximal, characteristic
7Dic3×C22⋊Dic5C211yesmaximal, characteristic, complemented
8#11748899C212yesmaximal, complemented
9#11748771C212yesmaximal, complemented
10#11748690C212yesmaximal, complemented
11#11748681C212yesmaximal, complemented
12#10613889—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C22×C3×C22⋊D5C2211yescharacteristic
17C22×D5×Dic3C2211yescharacteristic
18C2×#6719C2211yescharacteristic
19C2×#6719C2211yescharacteristic
20C2×C5×C4⋊Dic3—24no—
21C2×C5×C4⋊Dic3C2212yes—
22C2×C5×C4⋊Dic3C2212yes—
23C2×C3×C22⋊Dic5C2211yescharacteristic
24C3×#4075C418yescomplemented
25C2×C3×#685C2212yes—
26C2×C3×#683C2212yes—
27Dic3×C22⋊D5—24no—
28C2×#6668C2211yescharacteristic
29C2×#6668C2212yes—
30C2×#6665C2211yescharacteristic
31C2×#6665C2212yes—
32C2×Dic3×Dic5C2211yescharacteristic
33C2×Dic3×Dic5C2212yes—
34#91115C2212yes—
35#91115C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82836—51nomaximal, Hall
40C22×C5×C4⋊C4—31no—
41C2×#4075D311yescharacteristic
42C2×C4×C22⋊D5—31no—
43#65502—31no—
44#65500—31no—
45#65499—31no—
46C4×C22⋊Dic5—31no—
47#65279—32no—
48#65278—32no—
49#65267—32no—
50#65261—32no—
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
56C22×C3×C4×C5C2312yes—
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×Dic15C2311yescharacteristic
60C22×C5×Dic3—22no—
61C22×C5×Dic3—42no—
62C22×C5×Dic3—42no—
63C22×C5×Dic3D414yes—
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2311yescharacteristic
66C22×C5×Dic3C2311yescharacteristic
67C2×C3×C22⋊D5—22no—
68C2×C3×C22⋊D5—22no—
69C2×C3×C22⋊D5C2×C414yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2311yescharacteristic
72C2×D5×Dic3—22no—
73C2×D5×Dic3—42no—
74#6719—22no—
75#6719—22no—
76C5×C4⋊Dic3—24no—
77C5×C4⋊Dic3—24no—
78C3×C22⋊Dic5C2×C414yescomplemented
79C3×#685C2×C418yescomplemented
80C3×#683C2×C418yescomplemented
81#6668—22no—
82#6668—42no—
83#6665—22no—
84#6665—42no—
85Dic3×Dic5—22no—
86Dic3×Dic5—42no—
87C2×C3×#123—51no—
88C2×D4×Dic3—51no—
89C22×C4⋊Dic3D511yescharacteristic, complemented
90#5220—51no—
91#5211—51no—
92#4984—52no—
93#4980—52no—
94#4951—52no—
95#4950—51no—
96#4950—52no—
97Dic3×C22⋊C4—51no—
98C23×C4×C5—31no—
99C23×C4×C5—31no—
100C23×C4×C5C2×D311yescharacteristic
101C22×C22⋊D5C2×D311yescharacteristic
102C22×C4×D5—31no—
103C2×C5×C4⋊C4—32no—
104C2×C5×C4⋊C4—32no—
105C2×C5×C4⋊C4—64no—
106C2×C22⋊Dic5—31no—
107C2×C22⋊Dic5—31no—
108C2×C22⋊Dic5C2×D311yescharacteristic
109#4075Dic318yescomplemented
110C4×C22⋊D5—64no—
111C2×#685—31no—
112C2×#685—32no—
113C2×#685C2×D312yes—
114C2×#683—31no—
115C2×#683—32no—
116C2×#683C2×D312yes—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—32no—
119#3963—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2322—151noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5C22×C412yes—
128C23×C3×C5C2×D412yes—
129C23×C3×C5#4112yes—
130C23×C3×C5C2411yescharacteristic
131C22×C3×D5—21no—
132C22×C3×D5—21no—
133C22×C3×D5—22no—
134C22×C3×D5—22no—
135C22×C3×D5C22×C412yes—
136C2×C3×C4×C5—28no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5C22×C414yes—
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—44no—
153C2×C5×Dic3—44no—
154C2×C5×Dic3C2×D412yes—
155C2×C5×Dic3C2×D412yes—
156C3×C22⋊D5—28no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5C22×C412yes—
162C2×C3×Dic5C22×C414yes—
163D5×Dic3—44no—
164C22×C3×D4—51no—
165C23×C3×C4C2×D511yescharacteristic
166C23×Dic3—51no—
167C23×Dic3C2×D511yescharacteristic
168C23×Dic3C2×D511yescharacteristic
169C3×#123—58no—
170C2×C3×C4⋊C4—52no—
171C2×C3×C22⋊C4—51no—
172C2×C3×C22⋊C4—52no—
173C2×#217—51no—
174C2×#217—51no—
175C2×#217—51no—
176C2×#217—52no—
177D4×Dic3—104no—
178C2×C4⋊Dic3—24no—
179C2×C4⋊Dic3—51no—
180C2×C4⋊Dic3—52no—
181C2×C4⋊Dic3C2×D512yes—
182C2×C4⋊Dic3C2×D512yes—
183C2×C4×Dic3—51no—
184C2×C4×Dic3—52no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C24×C5C22×D311yescharacteristic
191C23×D5C22×D311yescharacteristic
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5—31no—
195C22×C4×C5—31no—
196C22×C4×C5—34no—
197C22×C4×C5—32no—
198C22×C4×C5—62no—
199C22×C4×C5—122no—
200C22×C4×C5—122no—
201C22×C4×C5C2×Dic314yescomplemented
202C22×C4×C5C22×D312yes—
203C2×C22⋊D5—22no—
204C2×C22⋊D5—22no—
205C2×C22⋊D5C2×Dic314yes—
206C22×Dic5—31no—
207C22×Dic5—31no—
208C22×Dic5—32no—
209C22×Dic5C22×D312yes—
210C22×Dic5C22×D311yescharacteristic
211C2×C4×D5—62no—
212C2×C4×D5—122no—
213C5×C4⋊C4—64no—
214C5×C4⋊C4—64no—
215C22⋊Dic5—62no—
216C22⋊Dic5—62no—
217C22⋊Dic5C2×Dic314yescomplemented
218#685—62no—
219#685—122no—
220#685C2×Dic318yescomplemented
221#683—62no—
222#683—122no—
223#683C2×Dic318yescomplemented
224C4×Dic5—62no—
225C4×Dic5—122no—
226C2×#123—51no—
227C2×C4×D4—151no—
228C22×C4⋊C4—31no—
229#389—152no—
230#388—152no—
231#387—152no—
232#386—151no—
233#385—152no—
234#385—151no—
235#381—151no—
236C4×C22⋊C4—151no—
237C22×C3×C5—24no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—24no—
241C22×C3×C5C4×D414yes—
242C22×C3×C5C23×C411yescharacteristic
243C22×C3×C5C22×D411yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5H(5,𝔽2)12yes—
246C22×C3×C52−1+412yes—
247C2×C3×D5—22no—
248C2×C3×D5—24no—
249C2×C3×D5—41no—
250C2×C3×D5—41no—
251C2×C3×D5—42no—
252C3×C4×C5—24no—
253Dic15—41no—
254Dic15—41no—
255Dic15—42no—
256C3×Dic5—22no—
257C3×Dic5—24no—
258C5×Dic3—22no—
259C5×Dic3—22no—
260C5×Dic3—42no—
261C24×C3—51no—
262C24×C3C22×D511yescharacteristic
263C2×C3×D4—54no—
264C2×C3×D4—102no—
265C2×C3×D4—102no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—52no—
269C22×C3×C4—51no—
270C22×C3×C4C4×D514yescomplemented
271C22×C3×C4C22×D512yes—
272C22×Dic3—22no—
273C22×Dic3—42no—
274C22×Dic3—42no—
275C22×Dic3—52no—
276C22×Dic3—51no—
277C22×Dic3—51no—
278C22×Dic3—102no—
279C22×Dic3—202no—
280C22×Dic3C22⋊D514yes—
281C22×Dic3C22×D512yes—
282C22×Dic3C22×D511yescharacteristic
283C22×Dic3C22×D511yescharacteristic
284C3×C4⋊C4—58no—
285C3×C22⋊C4—54no—
286C3×C22⋊C4—58no—
287#217—102no—
288#217—102no—
289#217—102no—
290#217—202no—
291C4⋊Dic3—24no—
292C4⋊Dic3—24no—
293C4⋊Dic3—102no—
294C4⋊Dic3—202no—
295C4×Dic3—102no—
296C4×Dic3—202no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5D3×D412yes—
300C23×C5#23712yes—
301C23×C5C22×Dic312yes—
302C23×C5C23×D311yescharacteristic
303C22×D5—21no—
304C22×D5—21no—
305C22×D5—22no—
306C22×D5—22no—
307C22×D5C22×Dic312yes—
308C2×C4×C5—28no—
309C2×C4×C5—22no—
310C2×C4×C5—22no—
311C2×C4×C5—32no—
312C2×C4×C5—32no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5—124no—
319C2×C4×C5—124no—
320C2×C4×C5C22×Dic314yes—
321C22⋊D5—28no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—22no—
325C2×Dic5—22no—
326C2×Dic5—61no—
327C2×Dic5—61no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5C22×Dic312yes—
334C2×Dic5C22×Dic314yes—
335C4×D5—124no—
336C22×D4—51no—
337C23×C4—31no—
338C23×C4—31no—
339C23×C4—151no—
340C23×C4D3×D511yescharacteristic
341#123—58no—
342C4×D4—304no—
343C2×C4⋊C4—32no—
344C2×C4⋊C4—32no—
345C2×C4⋊C4—52no—
346C2×C4⋊C4—64no—
347C2×C4⋊C4—151no—
348C2×C4⋊C4—152no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—52no—
351C2×C22⋊C4—151no—
352C2×C22⋊C4—151no—
353C2×C22⋊C4—151no—
354C2×C22⋊C4—152no—
355C2×C42—151no—
356C2×C42—152no—
357#95—152no—
358#95—152no—
359#95—152no—
360#95—152no—
361#95—152no—
362C2×C3×C5—24no—
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5#52012yes—
365C2×C3×C5#53411yescharacteristic
366C2×C3×C5#53611yescharacteristic
367C2×C3×C5#53912yes—
368C3×D5—42no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—52no—
372C23×C3—101no—
373C23×C3—102no—
374C23×C3—102no—
375C23×C3—101no—
376C23×C3C2×C4×D512yes—
377C23×C3#70912yes—
378C23×C3C2×C22⋊D512yes—
379C23×C3C23×D511yescharacteristic
380C3×D4—108no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—28no—
384C2×C3×C4—54no—
385C2×C3×C4—52no—
386C2×C3×C4—101no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—101no—
390C2×C3×C4C2×C4×D514yes—
391C2×Dic3—22no—
392C2×Dic3—22no—
393C2×Dic3—22no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—44no—
397C2×Dic3—44no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—101no—
404C2×Dic3—101no—
405C2×Dic3—204no—
406C2×Dic3C2×C22⋊D512yes—
407C2×Dic3C2×C22⋊D512yes—
408C22×C5—22no—
409C22×C5—22no—
410C22×C5—24no—
411C22×C5—24no—
412C22×C5D4×Dic314yes—
413C22×C5C2×D3×D411yescharacteristic
414C22×C5C2×#23711yescharacteristic
415C22×C5#100912yes—
416C22×C5#101012yes—
417C22×C5C23×Dic311yescharacteristic
418C2×D5—22no—
419C2×D5—24no—
420C2×D5—41no—
421C2×D5—41no—
422C2×D5—42no—
423C4×C5—24no—
424C4×C5—62no—
425C4×C5—62no—
426C4×C5—122no—
427Dic5—22no—
428Dic5—24no—
429Dic5—121no—
430Dic5—121no—
431Dic5—122no—
432C24—51no—
433C24C2×D3×D511yescharacteristic
434C2×D4—54no—
435C2×D4—102no—
436C2×D4—102no—
437C22×C4—22no—
438C22×C4—22no—
439C22×C4—31no—
440C22×C4—31no—
441C22×C4—34no—
442C22×C4—32no—
443C22×C4—52no—
444C22×C4—51no—
445C22×C4—62no—
446C22×C4—122no—
447C22×C4—122no—
448C22×C4—151no—
449C22×C4—152no—
450C22×C4—151no—
451C22×C4—302no—
452C22×C4—602no—
453C22×C4D5×Dic314yescomplemented
454C22×C4C2×D3×D512yes—
455C4⋊C4—58no—
456C4⋊C4—64no—
457C4⋊C4—64no—
458C4⋊C4—302no—
459C4⋊C4—602no—
460C22⋊C4—54no—
461C22⋊C4—58no—
462C22⋊C4—302no—
463C22⋊C4—302no—
464C22⋊C4—302no—
465C22⋊C4—602no—
466C42—302no—
467C42—602no—
468C3×C5#232211yescharacteristic, complemented, Hall
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—22no—
472C22×C3—22no—
473C22×C3—104no—
474C22×C3—102no—
475C22×C3—202no—
476C22×C3—201no—
477C22×C3—201no—
478C22×C3C4×C22⋊D514yes—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C2×#70911yescharacteristic
481C22×C3#414412yes—
482C22×C3#414712yes—
483C22×C3C22×C22⋊D511yescharacteristic
484C3×C4—24no—
485C3×C4—104no—
486C3×C4—102no—
487Dic3—22no—
488Dic3—22no—
489Dic3—42no—
490Dic3—202no—
491Dic3—201no—
492Dic3—201no—
493C2×C5—24no—
494C2×C5#564811yescharacteristic
495C2×C5#565311yescharacteristic
496C2×C5#566512yes—
497C2×C5C2×D4×Dic311yescharacteristic
498C2×C5#582712yes—
499D5—42no—
500C23—22no—
501C23—22no—
502C23—52no—
503C23—102no—
504C23—102no—
505C23—101no—
506C23—101no—
507C23C2×D5×Dic312yes—
508C23#677912yes—
509C23D3×C22⋊D512yes—
510C23C22×D3×D511yescharacteristic
511D4—108no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—28no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—54no—
518C2×C4—52no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—102no—
525C2×C4—102no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—124no—
529C2×C4—124no—
530C2×C4—302no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—301no—
536C2×C4—301no—
537C2×C4—604no—
538C2×C4C2×D5×Dic314yes—
539C2×C3—24no—
540C2×C3—202no—
541C2×C3#6583812yes—
542C2×C3#6584912yes—
543C2×C3C2×C4×C22⋊D511yescharacteristic
544C2×C3#6613811yescharacteristic
545C2×C3#6615011yescharacteristic
546C5#8283611yescharacteristic, complemented, Sylow
547C22—24no—
548C22—24no—
549C22—22no—
550C22—22no—
551C22—104no—
552C22—102no—
553C22—202no—
554C22—201no—
555C22—201no—
556C22Dic3×C22⋊D514yes—
557C22#9200012yes—
558C22#9201812yes—
559C22C22×D5×Dic311yescharacteristic
560C22C2×#677911yescharacteristic
561C22C2×D3×C22⋊D511yescharacteristic
562C4—24no—
563C4—62no—
564C4—62no—
565C4—104no—
566C4—102no—
567C4—122no—
568C4—602no—
569C4—601no—
570C4—601no—
571C3#1061388911yescharacteristic, complemented, Sylow
572C2—24no—
573C2—202no—
574C2#1175434011yescharacteristic
575C2#1175449912yes—
576C2#1175450112yes—
577C2#1175465311yescharacteristic
578C2C2×Dic3×C22⋊D511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2322
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C5×C4⋊Dic3C2semidirect
4. #11751312C2semidirect
5. #11749511C2semidirect
7. Dic3×C22⋊Dic5C2semidirect
8. #11748899C2semidirect
9. #11748771C2semidirect
10. #11748690C2semidirect
11. #11748681C2semidirect
24. C3×#4075C4semidirect
55. C22×C3×C4×C5C2×C4semidirect
78. C3×C22⋊Dic5C2×C4semidirect
79. C3×#685C2×C4semidirect
80. C3×#683C2×C4semidirect
89. C22×C4⋊Dic3D5semidirect
109. #4075Dic3semidirect
201. C22×C4×C5C2×Dic3semidirect
217. C22⋊Dic5C2×Dic3semidirect
220. #685C2×Dic3semidirect
223. #683C2×Dic3semidirect
270. C22×C3×C4C4×D5semidirect
453. C22×C4D5×Dic3semidirect
468. C3×C5#2322semidirect
546. C5#82836semidirect
571. C3#10613889semidirect

Maximal subgroups

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

subgroupindex
C22×C5×C4⋊Dic32
C2×C3×#40752
C2×Dic3×C22⋊D52
#117513122
#117495112
#117494952
Dic3×C22⋊Dic52
#117488992
#117487712
#117486902
#117486812
#106138893
#828365