Finite Group Databasebeta

← #14326268

Subgroups — #14326268

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×C22⋊C4C211yesmaximal, characteristic
2C22×(C2×D3)⋊Dic5C211yesmaximal, characteristic
3C2×#91532C211yesmaximal, characteristic, complemented
4#11751044C211yesmaximal, characteristic, complemented
5C3×#65231C211yesmaximal, characteristic, complemented
6#11749496C211yesmaximal, characteristic
7Dic5×#217C211yesmaximal, characteristic, complemented
8#11748721C212yesmaximal, complemented
9#11748719C212yesmaximal, complemented
10#11748718C212yesmaximal, complemented
11#11748716C212yesmaximal, complemented
12#10613829—31nomaximal, Hall
13C24×C5×D3C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C22×C4×C5×D3C2212yes—
16C23×C3×Dic5C2211yescharacteristic
17C2×C3×C5×C22⋊C4C2211yescharacteristic
18C2×#6719C2211yescharacteristic
19C2×C5×#217C2211yescharacteristic
20C2×C5×(C2×D3)⋊C4C2212yes—
21C5×D3×C22⋊C4—24no—
22C2×C3×C22⋊Dic5C2211yescharacteristic
23C2×C3×#683C2212yescomplemented
24C2×#6669C2212yescomplemented
25C2×(C2×D3)⋊Dic5C418yescomplemented
26C2×(C2×D3)⋊Dic5C2212yes—
27C2×(C2×D3)⋊Dic5C2212yes—
28C2×(C2×D3)⋊Dic5C2211yescharacteristic
29C2×(C2×D3)⋊Dic5C2211yescharacteristic
30C2×(C2×D3)⋊Dic5C2211yescharacteristic
31C2×(C2×D3)⋊Dic5C2211yescharacteristic
32#91532—24no—
33C2×Dic3×Dic5C2212yescomplemented
34C2×Dic3×Dic5C2212yescomplemented
35#91115C2212yescomplemented
36#91115C2212yescomplemented
37C3×#3963C2212yescomplemented
38#90994C2212yescomplemented
39#74009—51nomaximal, Hall
40C22×C5×C22⋊C4—31no—
41C22×C22⋊Dic5—31no—
42C2×#4023—31no—
43#65536—31no—
44#65499—32no—
45C4×C22⋊Dic5—32no—
46#65234—32no—
47#65233—32no—
48#65232—31no—
49#65231D311yescharacteristic, complemented
50C22⋊C4×Dic5—31no—
51C24×C3×C5C2311yescharacteristic
52C23×C5×D3—22no—
53C23×C5×D3—22no—
54C23×C5×D3—24no—
55C23×C5×D3—42no—
56C23×C5×D3C2×C414yes—
57C23×C5×D3C2311yescharacteristic
58C23×C5×D3C2311yescharacteristic
59C22×C3×C4×C5C2312yes—
60C22×Dic15—22no—
61C22×Dic15—22no—
62C22×Dic15C2×C414yescomplemented
63C22×Dic15C2312yes—
64C22×Dic15C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×C5×Dic3C2312yes—
67C2×C4×C5×D3—24no—
68C2×C4×C5×D3—24no—
69C2×C4×C5×D3—42no—
70C22×C3×Dic5—42no—
71C22×C3×Dic5C2×C414yescomplemented
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2311yescharacteristic
74C22×C3×Dic5C2311yescharacteristic
75C3×C5×C22⋊C4—22no—
76#6719—22no—
77C5×#217D414yes—
78C5×(C2×D3)⋊C4—24no—
79C3×C22⋊Dic5—22no—
80C3×#683—42no—
81#6669—24no—
82(C2×D3)⋊Dic5—24no—
83(C2×D3)⋊Dic5—42no—
84(C2×D3)⋊Dic5C2×C414yes—
85(C2×D3)⋊Dic5C2×C414yes—
86(C2×D3)⋊Dic5C2×C414yescomplemented
87(C2×D3)⋊Dic5C2×C414yescomplemented
88Dic3×Dic5—24no—
89Dic3×Dic5—42no—
90C22×(C2×D3)⋊C4—51no—
91C2×D3×C22⋊C4D511yescharacteristic
92C2×#877—51no—
93C3×#380—51no—
94C4×#217—51no—
95#4990—52no—
96#4989—52no—
97#4955—51no—
98#4943—51no—
99#4669—52no—
100#4666—52no—
101C25×C5—31no—
102C23×C4×C5—32no—
103C23×Dic5—31no—
104C23×Dic5C2×D311yescharacteristic
105C2×C5×C22⋊C4—31no—
106C2×C5×C22⋊C4—32no—
107C2×C5×C22⋊C4—64no—
108C2×C5×C22⋊C4C2×D311yescharacteristic
109C2×C22⋊Dic5—38no—
110C2×C22⋊Dic5—31no—
111C2×C22⋊Dic5—31no—
112C2×C22⋊Dic5—31no—
113C2×C22⋊Dic5—31no—
114C2×C22⋊Dic5—31no—
115C2×C22⋊Dic5—32no—
116C2×C22⋊Dic5—32no—
117C2×C22⋊Dic5C2×D311yescharacteristic
118C2×#683—32no—
119C2×#683C2×D312yescomplemented
120C2×C4×Dic5—32no—
121C2×C4×Dic5—32no—
122#4023—64no—
123#3963—32no—
124#3963—32no—
125#3963—32no—
126#3963C2×D312yescomplemented
127#2342—151noSylow
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5C22×C412yes—
131C23×C3×C5C2×D412yes—
132C23×C3×C5#4112yes—
133C23×C3×C5C2411yescharacteristic
134C22×C5×D3—21no—
135C22×C5×D3—21no—
136C22×C5×D3—22no—
137C22×C5×D3—28no—
138C22×C5×D3—21no—
139C22×C5×D3—22no—
140C22×C5×D3—21no—
141C22×C5×D3—22no—
142C22×C5×D3—28no—
143C22×C5×D3—44no—
144C22×C5×D3—48no—
145C22×C5×D3—48no—
146C22×C5×D3C22×C412yes—
147C22×C5×D3C22×C412yes—
148C22×C5×D3#4114yes—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—22no—
152C2×Dic15—28no—
153C2×Dic15—21no—
154C2×Dic15—21no—
155C2×Dic15—21no—
156C2×Dic15—21no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15C22×C412yes—
161C2×Dic15C22×C412yes—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3C2×D414yes—
165C4×C5×D3—48no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—44no—
172C2×C3×Dic5C22×C412yes—
173C2×C3×Dic5C22×C412yes—
174C24×D3C2×D511yescharacteristic
175C23×C3×C4—51no—
176C23×Dic3—51no—
177C22×C4×D3C2×D512yes—
178C2×C3×C4⋊C4—52no—
179C2×C3×C22⋊C4—51no—
180C2×C3×C22⋊C4C2×D511yescharacteristic
181C2×#217—51no—
182C2×#217C2×D511yescharacteristic
183C2×(C2×D3)⋊C4—58no—
184C2×(C2×D3)⋊C4—51no—
185C2×(C2×D3)⋊C4—51no—
186C2×(C2×D3)⋊C4—51no—
187C2×(C2×D3)⋊C4—51no—
188C2×(C2×D3)⋊C4—52no—
189C2×(C2×D3)⋊C4—52no—
190C2×(C2×D3)⋊C4C2×D512yes—
191C2×Dic3⋊C4—52no—
192C2×C4×Dic3—52no—
193C2×C4×Dic3—52no—
194D3×C22⋊C4—24no—
195#877—104no—
196C3×#95—52no—
197C3⋊#95—52no—
198C3⋊#95—52no—
199C3⋊#95—52no—
200C24×C5—31no—
201C24×C5—31no—
202C24×C5—34no—
203C24×C5—64no—
204C24×C5—62no—
205C24×C5—62no—
206C24×C5—122no—
207C24×C5C22×D311yescharacteristic
208C22×C4×C5—32no—
209C22×C4×C5—64no—
210C22×C4×C5—64no—
211C22×C4×C5—122no—
212C22×C4×C5C22×D312yes—
213C22×Dic5—34no—
214C22×Dic5—31no—
215C22×Dic5—31no—
216C22×Dic5—32no—
217C22×Dic5—42no—
218C22×Dic5—62no—
219C22×Dic5—62no—
220C22×Dic5C4×D314yescomplemented
221C22×Dic5C22×D312yes—
222C22×Dic5C22×D311yescharacteristic
223C22×Dic5C22×D311yescharacteristic
224C5×C22⋊C4—22no—
225C5×C22⋊C4—34no—
226C5×C22⋊C4—64no—
227C22⋊Dic5—22no—
228C22⋊Dic5—34no—
229C22⋊Dic5—34no—
230C22⋊Dic5—34no—
231C22⋊Dic5—34no—
232C22⋊Dic5—64no—
233C22⋊Dic5—62no—
234C22⋊Dic5—122no—
235#683—42no—
236#683—64no—
237C4×Dic5—64no—
238C4×Dic5—122no—
239C2×#117—151no—
240C22×C22⋊C4—31no—
241C22×C22⋊C4—151no—
242#388—152no—
243#388—152no—
244#385—152no—
245#381—151no—
246#380—51no—
247#379—151no—
248C4×C22⋊C4—152no—
249C4×C22⋊C4—151no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—24no—
253C22×C3×C5—24no—
254C22×C3×C5C4×D414yes—
255C22×C3×C5C23×C411yescharacteristic
256C22×C3×C5C22×D411yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5C2×#4112yes—
259C22×C3×C5H(5,𝔽2)12yes—
260C2×C5×D3—22no—
261C2×C5×D3—22no—
262C2×C5×D3—24no—
263C2×C5×D3—24no—
264C2×C5×D3—22no—
265C2×C5×D3—22no—
266C2×C5×D3—22no—
267C2×C5×D3—416no—
268C2×C5×D3—42no—
269C2×C5×D3—42no—
270C2×C5×D3#11714yescomplemented
271C3×C4×C5—42no—
272Dic15—22no—
273Dic15—22no—
274Dic15—42no—
275C3×Dic5—22no—
276C3×Dic5—22no—
277C3×Dic5—42no—
278C5×Dic3—24no—
279C24×C3C22×D511yescharacteristic
280C23×D3—22no—
281C23×D3—22no—
282C23×D3—24no—
283C23×D3—42no—
284C23×D3C4×D514yes—
285C23×D3C22×D511yescharacteristic
286C23×D3C22×D511yescharacteristic
287C22×C3×C4—51no—
288C22×C3×C4—51no—
289C22×C3×C4—54no—
290C22×C3×C4—52no—
291C22×C3×C4—202no—
292C22×C3×C4C22×D512yes—
293C22×Dic3—54no—
294C22×Dic3—51no—
295C22×Dic3—51no—
296C22×Dic3—52no—
297C22×Dic3—102no—
298C22×Dic3—102no—
299C22×Dic3C22×D512yes—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—42no—
303C3×C4⋊C4—202no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—102no—
306#217—102no—
307#217C22⋊D514yes—
308(C2×D3)⋊C4—24no—
309(C2×D3)⋊C4—54no—
310(C2×D3)⋊C4—54no—
311(C2×D3)⋊C4—54no—
312(C2×D3)⋊C4—54no—
313(C2×D3)⋊C4—104no—
314(C2×D3)⋊C4—202no—
315Dic3⋊C4—104no—
316C4×Dic3—104no—
317C4×Dic3—202no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—32no—
321C23×C5—34no—
322C23×C5—32no—
323C23×C5—68no—
324C23×C5—61no—
325C23×C5—62no—
326C23×C5—61no—
327C23×C5—68no—
328C23×C5—61no—
329C23×C5—62no—
330C23×C5—61no—
331C23×C5—62no—
332C23×C5—124no—
333C23×C5—128no—
334C23×C5—128no—
335C23×C5C2×C4×D312yes—
336C23×C5D3×D412yes—
337C23×C5#23912yes—
338C23×C5C23×D311yescharacteristic
339C2×C4×C5—22no—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—34no—
343C2×C4×C5—62no—
344C2×C4×C5—62no—
345C2×C4×C5—128no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—32no—
352C2×Dic5—32no—
353C2×Dic5—44no—
354C2×Dic5—68no—
355C2×Dic5—61no—
356C2×Dic5—61no—
357C2×Dic5—61no—
358C2×Dic5—61no—
359C2×Dic5—62no—
360C2×Dic5—62no—
361C2×Dic5—62no—
362C2×Dic5C2×C4×D312yes—
363C2×Dic5C2×C4×D312yes—
364C25—31no—
365C23×C4—32no—
366C23×C4—51no—
367C23×C4—151no—
368#117—304no—
369C2×C4⋊C4—52no—
370C2×C4⋊C4—152no—
371C2×C22⋊C4—31no—
372C2×C22⋊C4—32no—
373C2×C22⋊C4—51no—
374C2×C22⋊C4—64no—
375C2×C22⋊C4—151no—
376C2×C22⋊C4—151no—
377C2×C22⋊C4—151no—
378C2×C22⋊C4—151no—
379C2×C22⋊C4—158no—
380C2×C22⋊C4—152no—
381C2×C22⋊C4—151no—
382C2×C22⋊C4—152no—
383C2×C22⋊C4D3×D511yescharacteristic
384C2×C42—152no—
385C2×C42—152no—
386#95—52no—
387#95—152no—
388#95—152no—
389#95—152no—
390C2×C3×C5—24no—
391C2×C3×C5C2×#11711yescharacteristic
392C2×C3×C5C2×C4×D411yescharacteristic
393C2×C3×C5#51811yescharacteristic
394C2×C3×C5#54612yes—
395C2×C3×C5#55112yes—
396C5×D3—24no—
397C5×D3—42no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3C2×C4×D512yes—
401C23×C3#70912yes—
402C23×C3C2×C22⋊D512yes—
403C23×C3C23×D511yescharacteristic
404C22×D3—21no—
405C22×D3—22no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—21no—
411C22×D3—28no—
412C22×D3—28no—
413C22×D3—44no—
414C22×D3—48no—
415C22×D3—48no—
416C22×D3C2×C4×D512yes—
417C22×D3C2×C4×D512yes—
418C22×D3#71114yes—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—52no—
423C2×C3×C4—52no—
424C2×C3×C4—102no—
425C2×C3×C4—102no—
426C2×C3×C4—102no—
427C2×C3×C4—102no—
428C2×C3×C4—102no—
429C2×C3×C4—204no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—52no—
433C2×Dic3—52no—
434C2×Dic3—101no—
435C2×Dic3—101no—
436C2×Dic3—101no—
437C2×Dic3—101no—
438C2×Dic3—108no—
439C2×Dic3—102no—
440C2×Dic3—102no—
441C2×Dic3—102no—
442C2×Dic3C2×C22⋊D514yes—
443C4×D3—48no—
444C22×C5—24no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—24no—
448C22×C5—34no—
449C22×C5—64no—
450C22×C5—62no—
451C22×C5—62no—
452C22×C5—64no—
453C22×C5—62no—
454C22×C5—62no—
455C22×C5—62no—
456C22×C5—1216no—
457C22×C5—122no—
458C22×C5—122no—
459C22×C5#89314yes—
460C22×C5C22×C4×D311yescharacteristic
461C22×C5C2×D3×D411yescharacteristic
462C22×C5#100412yes—
463C22×C5C2×#23911yescharacteristic
464C22×C5D3×#4112yes—
465C4×C5—42no—
466C4×C5—64no—
467Dic5—22no—
468Dic5—22no—
469Dic5—42no—
470Dic5—62no—
471Dic5—62no—
472Dic5—122no—
473C24—31no—
474C24—31no—
475C24—34no—
476C24—64no—
477C24—62no—
478C24—62no—
479C24—122no—
480C24C2×D3×D511yescharacteristic
481C22×C4—32no—
482C22×C4—51no—
483C22×C4—51no—
484C22×C4—54no—
485C22×C4—52no—
486C22×C4—64no—
487C22×C4—64no—
488C22×C4—122no—
489C22×C4—154no—
490C22×C4—151no—
491C22×C4—151no—
492C22×C4—152no—
493C22×C4—202no—
494C22×C4—302no—
495C22×C4—302no—
496C22×C4C2×D3×D512yes—
497C4⋊C4—202no—
498C4⋊C4—304no—
499C22⋊C4—22no—
500C22⋊C4—34no—
501C22⋊C4—64no—
502C22⋊C4—102no—
503C22⋊C4—154no—
504C22⋊C4—154no—
505C22⋊C4—154no—
506C22⋊C4—154no—
507C22⋊C4—304no—
508C22⋊C4—302no—
509C22⋊C4—602no—
510C42—304no—
511C42—602no—
512C3×C5#234211yescharacteristic, complemented, Hall
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—24no—
516C22×C3—24no—
517C22×C3C4×C22⋊D514yes—
518C22×C3C22×C4×D511yescharacteristic
519C22×C3C2×#70911yescharacteristic
520C22×C3C2×#71112yes—
521C22×C3#414412yes—
522C22×C3C22×C22⋊D511yescharacteristic
523C2×D3—22no—
524C2×D3—24no—
525C2×D3—22no—
526C2×D3—24no—
527C2×D3—22no—
528C2×D3—22no—
529C2×D3—22no—
530C2×D3—416no—
531C2×D3—42no—
532C2×D3—42no—
533C2×D3#402314yescomplemented
534C3×C4—42no—
535C3×C4—102no—
536C3×C4—102no—
537C3×C4—202no—
538Dic3—24no—
539Dic3—102no—
540Dic3—102no—
541Dic3—202no—
542C2×C5—24no—
543C2×C5—64no—
544C2×C5—122no—
545C2×C5#548611yescharacteristic
546C2×C5C2×#89311yescharacteristic
547C2×C5D3×#11711yescharacteristic
548C2×C5#561012yes—
549C2×C5#563712yes—
550C23—22no—
551C23—22no—
552C23—32no—
553C23—34no—
554C23—32no—
555C23—68no—
556C23—61no—
557C23—62no—
558C23—61no—
559C23—68no—
560C23—61no—
561C23—62no—
562C23—62no—
563C23—61no—
564C23—124no—
565C23—128no—
566C23—128no—
567C23#676912yes—
568C23C4×D3×D512yes—
569C23D3×C22⋊D512yes—
570C23C22×D3×D511yescharacteristic
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—34no—
575C2×C4—52no—
576C2×C4—52no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—102no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—128no—
585C2×C4—152no—
586C2×C4—152no—
587C2×C4—204no—
588C2×C4—308no—
589C2×C4—301no—
590C2×C4—301no—
591C2×C4—301no—
592C2×C4—301no—
593C2×C4—302no—
594C2×C4—302no—
595C2×C4—302no—
596C2×C3—24no—
597C2×C3C2×#402311yescharacteristic
598C2×C3#6582011yescharacteristic
599C2×C3#6582912yes—
600C2×C3C2×C4×C22⋊D511yescharacteristic
601C2×C3#6614012yes—
602D3—24no—
603D3—42no—
604C5#7400911yescharacteristic, complemented, Sylow
605C22—24no—
606C22—22no—
607C22—22no—
608C22—24no—
609C22—34no—
610C22—62no—
611C22—64no—
612C22—62no—
613C22—64no—
614C22—62no—
615C22—62no—
616C22—62no—
617C22—1216no—
618C22—122no—
619C22—122no—
620C22#9144614yes—
621C22C2×#676911yescharacteristic
622C22C2×C4×D3×D511yescharacteristic
623C22D3×#71112yes—
624C22#9202512yes—
625C22C2×D3×C22⋊D511yescharacteristic
626C4—42no—
627C4—64no—
628C4—102no—
629C4—102no—
630C4—202no—
631C4—302no—
632C4—302no—
633C4—602no—
634C3#1061382911yescharacteristic, complemented, Sylow
635C2—24no—
636C2—64no—
637C2—122no—
638C2D3×#402311yescharacteristic
639C2#1175300512yes—
640C2#1175306511yescharacteristic
641C2C2×#9144611yescharacteristic
642C2#1175494212yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C5×D3C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2342
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#91532C2semidirect
4. #11751044C2semidirect
5. C3×#65231C2semidirect
7. Dic5×#217C2semidirect
8. #11748721C2semidirect
9. #11748719C2semidirect
10. #11748718C2semidirect
11. #11748716C2semidirect
23. C2×C3×#683C22semidirect
24. C2×#6669C22semidirect
25. C2×(C2×D3)⋊Dic5C4semidirect
33. C2×Dic3×Dic5C22semidirect
34. C2×Dic3×Dic5C22semidirect
35. #91115C22semidirect
36. #91115C22semidirect
37. C3×#3963C22semidirect
38. #90994C22semidirect
49. #65231D3semidirect
62. C22×Dic15C2×C4semidirect
71. C22×C3×Dic5C2×C4semidirect
86. (C2×D3)⋊Dic5C2×C4semidirect
87. (C2×D3)⋊Dic5C2×C4semidirect
119. C2×#683C2×D3semidirect
126. #3963C2×D3semidirect
220. C22×Dic5C4×D3semidirect
270. C2×C5×D3#117semidirect
512. C3×C5#2342semidirect
533. C2×D3#4023semidirect
604. C5#74009semidirect
634. C3#10613829semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×C22⋊C42
C22×(C2×D3)⋊Dic52
C2×#915322
#117510442
C3×#652312
#117494962
Dic5×#2172
#117487212
#117487192
#117487182
#117487162
#106138293
#740095