Finite Group Databasebeta

← #14320628

Subgroups — #14320628

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91815C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
3C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
4C4×C5×#217C211yesmaximal, characteristic, complemented
5#11749518C212yesmaximal
6#11749486C212yesmaximal, complemented
7#11748900C212yesmaximal, complemented
8C4×#6668C211yesmaximal, characteristic, complemented
9C4×#6665C211yesmaximal, characteristic, complemented
10#11748691C212yesmaximal, complemented
11#11748611C211yesmaximal, characteristic, complemented
12#10605293—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×D5×Dic3C2212yes—
17C2×#6719C2212yes—
18#91815—24no—
19C2×C4⋊Dic15C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×C5×#217C2212yes—
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C3×C4×C22⋊D5C418yescomplemented
27C2×C3×#685C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×#6668C2212yes—
31C2×#6665C2212yes—
32C2×Dic3×Dic5C2212yes—
33C4×D5×Dic3—24no—
34C5×C3⋊#95C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82318—51nomaximal, Hall
40C2×C4×C22⋊D5D311yescharacteristic
41C2×#4072—31no—
42C2×C42×D5—31no—
43C4×C5×C22⋊C4—31no—
44#65245—32no—
45#65234—32no—
46C4×#685—31no—
47#65221—31no—
48C4×#683—31no—
49#64957—32no—
50#64944—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×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15C2312yes—
59C22×Dic15C2312yes—
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2312yes—
62C2×C3×C22⋊D5—24no—
63C2×C3×C22⋊D5C2×C414yes—
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5C2×C414yes—
70C2×D5×Dic3—24no—
71C2×D5×Dic3—24no—
72C2×D5×Dic3—24no—
73#6719—24no—
74C4⋊Dic15—24no—
75C4×Dic15—22no—
76C4×Dic15D414yescomplemented
77C5×#217—24no—
78C4×C5×Dic3—22no—
79C4×C5×Dic3—22no—
80C3×C22⋊Dic5C2×C414yescomplemented
81C3×#685C2×C414yes—
82C3×#683C2×C414yescomplemented
83C3×C4×Dic5C2×C414yescomplemented
84#6668—24no—
85#6665—24no—
86Dic3×Dic5—24no—
87C2×C3×C4×D4—51no—
88C2×#926—51no—
89C22×C4×Dic3—51no—
90#5220—52no—
91C4×#217—51no—
92C4×#217D511yescharacteristic, complemented
93#4980—52no—
94#4951—52no—
95#4950—52no—
96C4×C4⋊Dic3—51no—
97#4932—51no—
98C23×C4×C5C2×D311yescharacteristic
99C22×C22⋊D5C2×D311yescharacteristic
100C22×C4×D5—32no—
101C22×C4×D5C2×D311yescharacteristic
102C2×C5×C22⋊C4—32no—
103C2×C42×C5—31no—
104C2×C42×C5—31no—
105C2×C22⋊Dic5—32no—
106C2×C22⋊Dic5C2×D311yescharacteristic
107C4×C22⋊D5Dic318yescomplemented
108C2×#685—32no—
109C2×#685C2×D311yescharacteristic
110#4072—64no—
111C2×C4⋊Dic5—32no—
112C2×#683—32no—
113C2×#683C2×D311yescharacteristic
114C2×C4×Dic5—31no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—32no—
117C2×C4×Dic5C2×D311yescharacteristic
118C42×D5—64no—
119C5×#95—32no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2290—151noSylow
125C23×C3×C5—21no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—21no—
129C23×C3×C5C22×C412yes—
130C23×C3×C5C2411yescharacteristic
131C22×C3×D5—21no—
132C22×C3×D5—22no—
133C22×C3×D5—21no—
134C22×C3×D5C22×C412yes—
135C22×C3×D5#4114yes—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—28no—
139C2×C3×C4×C5C22×C412yes—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C2×D412yes—
142C2×C3×C4×C5#4112yes—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15C2×D414yes—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—22no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—22no—
154C2×C5×Dic3#4114yes—
155C3×C22⋊D5—28no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C22×C412yes—
162C2×C3×Dic5C22×C412yes—
163C3×C4×D5—28no—
164D5×Dic3—216no—
165C22×C3×D4—51no—
166C23×C3×C4—51no—
167C23×C3×C4C2×D511yescharacteristic
168C23×Dic3—52no—
169C3×C4×D4—58no—
170C2×C3×C4⋊C4—51no—
171C2×C3×C22⋊C4—51no—
172C2×C3×C22⋊C4—51no—
173C2×C3×C42—51no—
174C2×#217—52no—
175C2×#217—52no—
176C2×#217C2×D512yes—
177#926—104no—
178C2×C4⋊Dic3—52no—
179C2×C4⋊Dic3—52no—
180C2×C4×Dic3—51no—
181C2×C4×Dic3—51no—
182C2×C4×Dic3—52no—
183C2×C4×Dic3—104no—
184C2×C4×Dic3C2×D511yescharacteristic
185C2×C4×Dic3C2×D511yescharacteristic
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95C2×D512yes—
191C24×C5C22×D311yescharacteristic
192C23×D5C22×D311yescharacteristic
193C22×C4×C5—22no—
194C22×C4×C5—22no—
195C22×C4×C5—32no—
196C22×C4×C5—32no—
197C22×C4×C5C2×Dic314yescomplemented
198C22×C4×C5C22×D311yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—24no—
201C2×C22⋊D5C2×Dic314yes—
202C22×Dic5—32no—
203C22×Dic5—32no—
204C22×Dic5C22×D311yescharacteristic
205C22×Dic5C22×D311yescharacteristic
206C22×Dic5C22×D311yescharacteristic
207C2×C4×D5—22no—
208C2×C4×D5—22no—
209C2×C4×D5—64no—
210C2×C4×D5—64no—
211C2×C4×D5—64no—
212C2×C4×D5C2×Dic314yes—
213C5×C22⋊C4—64no—
214C42×C5—62no—
215C42×C5—62no—
216C22⋊Dic5—64no—
217C22⋊Dic5C2×Dic314yescomplemented
218#685—64no—
219#685C2×Dic314yes—
220C4⋊Dic5—64no—
221#683—64no—
222#683C2×Dic314yescomplemented
223C4×Dic5—34no—
224C4×Dic5—64no—
225C4×Dic5—62no—
226C4×Dic5C2×Dic314yescomplemented
227C2×C4×D4—51no—
228C2×#117—151no—
229C22×C42—151no—
230#388—152no—
231#387—152no—
232#386—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C22⋊C4—31no—
236C4×C22⋊C4—151no—
237#376—151no—
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—22no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5C23×C411yescharacteristic
244C22×C3×C5C22×D411yescharacteristic
245C22×C3×C5C2×#4112yes—
246C22×C3×C5C2×#4111yescharacteristic
247C22×C3×C5C2×#4112yes—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—24no—
251C2×C3×D5—24no—
252C2×C3×D5#11714yescomplemented
253C3×C4×C5—22no—
254C3×C4×C5C4×D414yes—
255Dic15—24no—
256Dic15—42no—
257C3×Dic5—22no—
258C3×Dic5—22no—
259C3×Dic5—22no—
260C5×Dic3—24no—
261C5×Dic3—42no—
262C24×C3—51no—
263C24×C3C22×D511yescharacteristic
264C2×C3×D4—54no—
265C2×C3×D4—104no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—54no—
272C22×C3×C4—102no—
273C22×C3×C4—102no—
274C22×C3×C4C4×D514yescomplemented
275C22×C3×C4C22×D511yescharacteristic
276C22×C3×C4C22×D511yescharacteristic
277C22×Dic3—52no—
278C22×Dic3—52no—
279C22×Dic3—104no—
280C22×Dic3—104no—
281C22×Dic3—104no—
282C22×Dic3C22×D512yes—
283C22×Dic3C22×D512yes—
284C3×C4⋊C4—54no—
285C3×C22⋊C4—54no—
286C3×C22⋊C4—54no—
287C3×C42—54no—
288#217—24no—
289#217—104no—
290#217—104no—
291C4⋊Dic3—104no—
292C4⋊Dic3—104no—
293C4×Dic3—22no—
294C4×Dic3—22no—
295C4×Dic3—54no—
296C4×Dic3—104no—
297C4×Dic3—102no—
298C23×C5—22no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—22no—
302C23×C5C22×Dic312yes—
303C23×C5C23×D311yescharacteristic
304C22×D5—21no—
305C22×D5—21no—
306C22×D5—22no—
307C22×D5#23514yes—
308C22×D5C22×Dic312yes—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—28no—
312C2×C4×C5—34no—
313C2×C4×C5—62no—
314C2×C4×C5—62no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5—62no—
318C2×C4×C5D3×D412yes—
319C2×C4×C5#23712yes—
320C2×C4×C5C22×Dic312yes—
321C2×C4×C5C22×Dic312yes—
322C22⋊D5—28no—
323C2×Dic5—22no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—22no—
327C2×Dic5—34no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5C22×Dic312yes—
334C2×Dic5C22×Dic312yes—
335C2×Dic5C22×Dic312yes—
336C4×D5—28no—
337C4×D5—616no—
338C22×D4—51no—
339C23×C4—51no—
340C23×C4—152no—
341C23×C4D3×D511yescharacteristic
342C4×D4—58no—
343#117—304no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—152no—
346C2×C4⋊C4—152no—
347C2×C22⋊C4—32no—
348C2×C22⋊C4—51no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C42—31no—
353C2×C42—31no—
354C2×C42—51no—
355C2×C42—151no—
356C2×C42—152no—
357C2×C42—151no—
358C2×C42—304no—
359#95—32no—
360#95—152no—
361#95—152no—
362#95—152no—
363#95—152no—
364C2×C3×C5—42no—
365C2×C3×C5C2×#11711yescharacteristic
366C2×C3×C5C2×C4×D411yescharacteristic
367C2×C3×C5C4×#4111yescharacteristic
368C2×C3×C5#52512yes—
369C2×C3×C5#52912yes—
370C3×D5—24no—
371C23×C3—22no—
372C23×C3—21no—
373C23×C3—21no—
374C23×C3—22no—
375C23×C3—52no—
376C23×C3—54no—
377C23×C3—102no—
378C23×C3—101no—
379C23×C3—101no—
380C23×C3C2×C4×D512yes—
381C23×C3C23×D511yescharacteristic
382C3×D4—108no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—28no—
386C2×C3×C4—52no—
387C2×C3×C4—52no—
388C2×C3×C4—52no—
389C2×C3×C4—102no—
390C2×C3×C4—101no—
391C2×C3×C4—101no—
392C2×C3×C4—102no—
393C2×C3×C4—108no—
394C2×C3×C4C2×C4×D512yes—
395C2×C3×C4C2×C4×D512yes—
396C2×C3×C4D4×D512yes—
397C2×C3×C4#71112yes—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—22no—
403C2×Dic3—54no—
404C2×Dic3—1016no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—102no—
408C2×Dic3—102no—
409C2×Dic3—102no—
410C2×Dic3#70914yes—
411C22×C5—22no—
412C22×C5—22no—
413C22×C5—22no—
414C22×C5—42no—
415C22×C5—42no—
416C22×C5C2×#23512yes—
417C22×C5C2×D3×D411yescharacteristic
418C22×C5C2×#23711yescharacteristic
419C22×C5D3×#4112yes—
420C22×C5C23×Dic311yescharacteristic
421C2×D5—24no—
422C2×D5—22no—
423C2×D5—24no—
424C2×D5—22no—
425C2×D5#92614yescomplemented
426C4×C5—22no—
427C4×C5—64no—
428C4×C5—122no—
429C4×C5D4×Dic314yes—
430Dic5—22no—
431Dic5—22no—
432Dic5—22no—
433Dic5—64no—
434Dic5—122no—
435C24—51no—
436C24C2×D3×D511yescharacteristic
437C2×D4—54no—
438C2×D4—104no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—32no—
442C22×C4—32no—
443C22×C4—51no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—54no—
447C22×C4—102no—
448C22×C4—102no—
449C22×C4—152no—
450C22×C4—152no—
451C22×C4—304no—
452C22×C4—304no—
453C22×C4—304no—
454C22×C4D5×Dic314yescomplemented
455C22×C4C2×D3×D511yescharacteristic
456C22×C4C2×D3×D511yescharacteristic
457C4⋊C4—54no—
458C4⋊C4—304no—
459C4⋊C4—304no—
460C22⋊C4—54no—
461C22⋊C4—54no—
462C22⋊C4—64no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C42—54no—
466C42—62no—
467C42—62no—
468C42—154no—
469C42—304no—
470C42—302no—
471C3×C5#229011yescharacteristic, complemented, Hall
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—22no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—54no—
478C22×C3—102no—
479C22×C3—102no—
480C22×C3—104no—
481C22×C3—104no—
482C22×C3C22×C4×D511yescharacteristic
483C22×C3C2×#70912yes—
484C22×C3C2×D4×D511yescharacteristic
485C22×C3C2×#71111yescharacteristic
486C22×C3D5×#4112yes—
487C3×C4—22no—
488C3×C4—102no—
489C3×C4—102no—
490C3×C4—102no—
491C3×C4#402714yes—
492Dic3—24no—
493Dic3—42no—
494Dic3—104no—
495Dic3—202no—
496C2×C5—42no—
497C2×C5#553812yes—
498C2×C5#554712yes—
499C2×C5C2×#92611yescharacteristic
500C2×C5C2×D4×Dic311yescharacteristic
501C2×C5Dic3×#4111yescharacteristic
502D5—24no—
503C23—22no—
504C23—22no—
505C23—21no—
506C23—21no—
507C23—54no—
508C23—52no—
509C23—102no—
510C23—101no—
511C23—101no—
512C23C2×D5×Dic312yes—
513C23C22×D3×D511yescharacteristic
514D4—108no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—28no—
518C2×C4—34no—
519C2×C4—52no—
520C2×C4—52no—
521C2×C4—52no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—108no—
532C2×C4—154no—
533C2×C4—3016no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—302no—
538C2×C4—302no—
539C2×C4C2×D5×Dic312yes—
540C2×C4C2×D5×Dic312yes—
541C2×C4#678012yes—
542C2×C4#679012yes—
543C2×C3—42no—
544C2×C3—104no—
545C2×C3C4×#70911yescharacteristic
546C2×C3C2×#402711yescharacteristic
547C2×C3D5×#11711yescharacteristic
548C2×C3#6588112yes—
549C2×C3#6589112yes—
550C5#8231811yescharacteristic, complemented, Sylow
551C22—22no—
552C22—22no—
553C22—22no—
554C22—42no—
555C22—42no—
556C22—54no—
557C22—102no—
558C22—104no—
559C22—104no—
560C22—102no—
561C22D5×#23512yes—
562C22D3×#70912yes—
563C22C22×D5×Dic311yescharacteristic
564C22C2×#678011yescharacteristic
565C22C2×#679011yescharacteristic
566C4—22no—
567C4—64no—
568C4—102no—
569C4—102no—
570C4—102no—
571C4—122no—
572C4—304no—
573C4—602no—
574C4#9155914yes—
575C3#1060529311yescharacteristic, complemented, Sylow
576C2—42no—
577C2—104no—
578C2D5×#92611yescharacteristic
579C2#1175439512yes—
580C2Dic3×#70911yescharacteristic
581C2#1175466312yes—
582C2C2×#9155911yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2290
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×#91815C2semidirect
3. C2×C4×D5×Dic3C2semidirect
4. C4×C5×#217C2semidirect
6. #11749486C2semidirect
7. #11748900C2semidirect
8. C4×#6668C2semidirect
9. C4×#6665C2semidirect
10. #11748691C2semidirect
11. #11748611C2semidirect
26. C3×C4×C22⋊D5C4semidirect
55. C22×C3×C4×C5C2×C4semidirect
76. C4×Dic15D4semidirect
80. C3×C22⋊Dic5C2×C4semidirect
82. C3×#683C2×C4semidirect
83. C3×C4×Dic5C2×C4semidirect
92. C4×#217D5semidirect
107. C4×C22⋊D5Dic3semidirect
197. C22×C4×C5C2×Dic3semidirect
217. C22⋊Dic5C2×Dic3semidirect
222. #683C2×Dic3semidirect
226. C4×Dic5C2×Dic3semidirect
252. C2×C3×D5#117semidirect
274. C22×C3×C4C4×D5semidirect
425. C2×D5#926semidirect
454. C22×C4D5×Dic3semidirect
471. C3×C5#2290semidirect
550. C5#82318semidirect
575. C3#10605293semidirect

Maximal subgroups

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

subgroupindex
C2×#918152
C2×C3×C4×C22⋊D52
C2×C4×D5×Dic32
C4×C5×#2172
#117495182
#117494862
#117489002
C4×#66682
C4×#66652
#117486912
#117486112
#106052933
#823185