Finite Group Databasebeta

← C2×#11748102 #14411652

Subgroups — C2×#11748102 #14411652

Order 1920.

2016 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D3×D5C211yesmaximal, characteristic
2C22×C5×ΓL(1,𝔽25)C211yesmaximal, characteristic, complemented
3C22×#6650C211yesmaximal, characteristic, complemented
4C2×#91104C211yesmaximal, characteristic, complemented
5C2×C3×#3952C211yesmaximal, characteristic, complemented
6C2×#90957C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11748102C218yesmaximal, direct product factor
9C2×#65415—31nomaximal, Hall
10C23×D3×D5C411yescharacteristic
11C22×C4×D15C2211yescharacteristic
12C22×C4×C5×D3C2211yescharacteristic
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1200C411yescharacteristic
15C22×D3×Dic5C411yescharacteristic
16C22×D5×Dic3C411yescharacteristic
17C2×C4×D3×D5—24no—
18C2×C4×D3×D5—24no—
19C2×C4×D3×D5C414yes—
20C2×C4×D3×D5C2214yes—
21C22×C3×C5×C8C2211yescharacteristic, complemented
22C22×C3⋊#168C2211yescharacteristic, complemented
23C22×C5×C3⋊C8C2211yescharacteristic, complemented
24C2×C5×ΓL(1,𝔽25)—24no—
25C2×C5×ΓL(1,𝔽25)C2214yescomplemented
26C22×C3×#168C2211yescharacteristic, complemented
27C2×#6650—24no—
28C2×#6650C2214yescomplemented
29#91104C2214yescomplemented
30C3×#3952C2214yescomplemented
31#90957C2214yescomplemented
32#90955C2214yescomplemented
33C2×#4726—51nomaximal, Hall
34C23×C4×D5—31no—
35C22×C5×M16—31no—
36C22×#681—31no—
37#65415—38no—
38C2×#3952—31no—
39C2×#3952—31no—
40C2×#3952—31no—
41C2×#3952D311yescharacteristic, complemented
42C23×D15C2×C411yescharacteristic
43C23×C5×D3C2×C411yescharacteristic
44C23×C3×D5C2×C411yescharacteristic
45C22×D3×D5—24no—
46C22×D3×D5—24no—
47C22×D3×D5—24no—
48C22×D3×D5C2×C414yes—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15C2×C411yescharacteristic
51C2×C4×D15—22no—
52C2×C4×D15—22no—
53C2×C4×D15C2×C412yes—
54C2×C4×D15C2312yes—
55C22×C5×Dic3C2×C411yescharacteristic
56C2×C4×C5×D3C2×C412yes—
57C2×C4×C5×D3D414yes—
58C2×C4×C5×D3D414yes—
59C2×C4×C5×D3C2312yes—
60C22×C3×Dic5C2×C411yescharacteristic
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5C2×C412yes—
64C2×C3×C4×D5C2312yes—
65C2×#1200—24no—
66C2×#1200C2×C414yes—
67C2×D3×Dic5—24no—
68C2×D3×Dic5C2×C414yes—
69C2×D5×Dic3—24no—
70C2×D5×Dic3C2×C414yes—
71C4×D3×D5—216no—
72C4×D3×D5—28no—
73C4×D3×D5—28no—
74C2×C3×C5×C8—22no—
75C2×C3×C5×C8C2312yescomplemented
76C2×C3⋊#168—22no—
77C2×C3⋊#168C2312yescomplemented
78C2×C5×C3⋊C8—22no—
79C2×C5×C3⋊C8C2312yescomplemented
80C5×ΓL(1,𝔽25)—28no—
81C2×C3×#168—22no—
82C2×C3×#168C2312yescomplemented
83#6650—28no—
84C23×C4×D3—51no—
85C22×ΓL(1,𝔽25)—51no—
86C22×ΓL(1,𝔽25)D511yescharacteristic, complemented
87C2×C3×C22⋊C8—51no—
88C2×#830—51no—
89C2×(C2×D3)⋊C8—51no—
90C2×(C2×D3)⋊C8—51no—
91#4726—58no—
92C24×D5—31no—
93C23×C4×C5—31no—
94C23×Dic5—31no—
95C22×C4×D5—31no—
96C22×C4×D5—31no—
97C22×C4×D5—31no—
98C22×C4×D5—34no—
99C22×C4×D5—34no—
100C22×C4×D5—64no—
101C22×C4×D5—64no—
102C22×C4×D5C2×D311yescharacteristic
103C2×C5×M16—34no—
104C2×C5×M16—64no—
105C22×C5×C8—31no—
106C22×C5×C8C2×D311yescharacteristic, complemented
107C2×#681—34no—
108C2×#681—64no—
109C22×#168—31no—
110C22×#168C2×D311yescharacteristic, complemented
111#3952—34no—
112#3952—34no—
113#3952—34no—
114#3952C2×D314yescomplemented
115C2×#407—151noSylow
116C23×C3×C5C22×C411yescharacteristic
117C22×D15—22no—
118C22×D15—22no—
119C22×D15M1614yescomplemented
120C22×D15C22×C412yes—
121C22×C5×D3—22no—
122C22×C5×D3—22no—
123C22×C5×D3C22⋊C414yes—
124C22×C5×D3C22×C412yes—
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5M1614yescomplemented
128C22×C3×D5C22×C412yes—
129C2×D3×D5—232no—
130C2×D3×D5—28no—
131C2×D3×D5—28no—
132C2×D3×D5—28no—
133C2×C3×C4×C5C22×C411yescharacteristic
134C2×C3×C4×C5C2×D412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—22no—
138C2×Dic15C22×C412yes—
139C4×D15—24no—
140C4×D15—22no—
141C4×D15—22no—
142C2×C5×Dic3C22⋊C414yes—
143C2×C5×Dic3C22×C412yes—
144C4×C5×D3C22⋊C418yes—
145C4×C5×D3C2×D414yes—
146C4×C5×D3C2×D414yes—
147C2×C3×Dic5—22no—
148C2×C3×Dic5C22×C412yes—
149C3×C4×D5—24no—
150C3×C4×D5—22no—
151C3×C4×D5—22no—
152#1200—28no—
153D3×Dic5—28no—
154D5×Dic3—28no—
155C3×C5×C8—22no—
156C3⋊#168—22no—
157C3×#168—22no—
158C5×C3⋊C8—22no—
159C24×D3—51no—
160C23×C3×C4—51no—
161C23×Dic3—51no—
162C22×C4×D3—51no—
163C22×C4×D3—51no—
164C22×C4×D3—51no—
165C22×C4×D3—54no—
166C22×C4×D3—54no—
167C22×C4×D3—104no—
168C22×C4×D3—104no—
169C22×C4×D3C2×D511yescharacteristic
170C22×C3×C8—51no—
171C22×C3×C8C2×D511yescharacteristic, complemented
172C22×C3⋊C8—51no—
173C22×C3⋊C8C2×D511yescharacteristic, complemented
174C2×ΓL(1,𝔽25)—24no—
175C2×ΓL(1,𝔽25)—54no—
176C2×ΓL(1,𝔽25)—104no—
177C2×ΓL(1,𝔽25)C2×D514yescomplemented
178C3×C22⋊C8—54no—
179#830—54no—
180(C2×D3)⋊C8—54no—
181(C2×D3)⋊C8—54no—
182C24×C5—31no—
183C23×D5—31no—
184C23×D5—34no—
185C23×D5—64no—
186C23×D5—64no—
187C23×D5—64no—
188C23×D5C4×D311yescharacteristic
189C22×C4×C5—31no—
190C22×C4×C5—32no—
191C22×C4×C5—34no—
192C22×C4×C5—34no—
193C22×C4×C5—32no—
194C22×C4×C5C22×D311yescharacteristic
195C22×Dic5—31no—
196C22×Dic5—34no—
197C22×Dic5—64no—
198C22×Dic5C4×D311yescharacteristic
199C2×C4×D5—22no—
200C2×C4×D5—22no—
201C2×C4×D5—34no—
202C2×C4×D5—32no—
203C2×C4×D5—32no—
204C2×C4×D5—34no—
205C2×C4×D5—616no—
206C2×C4×D5—68no—
207C2×C4×D5—68no—
208C2×C4×D5—64no—
209C2×C4×D5—64no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×C4×D5C4×D312yes—
213C2×C4×D5C22×D312yes—
214C5×M16—68no—
215C2×C5×C8—22no—
216C2×C5×C8—32no—
217C2×C5×C8—62no—
218C2×C5×C8C22×D312yescomplemented
219#681—68no—
220C2×#168—22no—
221C2×#168—32no—
222C2×#168—62no—
223C2×#168C22×D312yescomplemented
224C24×C4—151no—
225C22×M16—31no—
226C22×M16—151no—
227#407—158no—
228C2×C22⋊C8—51no—
229C2×C22⋊C8—151no—
230C2×C22⋊C8—151no—
231C2×C22⋊C8—151no—
232C22×C3×C5C2×C22⋊C412yes—
233C22×C3×C5C2×M1612yes—
234C22×C3×C5C2×M1612yes—
235C22×C3×C5C23×C411yescharacteristic
236C2×D15—22no—
237C2×D15—22no—
238C2×D15—28no—
239C2×D15C2×M1614yescomplemented
240C2×C5×D3—22no—
241C2×C5×D3—22no—
242C2×C5×D3—28no—
243C2×C5×D3C2×C22⋊C414yes—
244C2×C3×D5—22no—
245C2×C3×D5—22no—
246C2×C3×D5—28no—
247C2×C3×D5C2×M1614yescomplemented
248D3×D5—232no—
249C3×C4×C5C2×C22⋊C412yes—
250C3×C4×C5C22×D411yescharacteristic
251C3×C4×C5C22×D411yescharacteristic
252Dic15—22no—
253C3×Dic5—22no—
254C5×Dic3C2×C22⋊C414yes—
255C24×C3—51no—
256C23×D3—51no—
257C23×D3—54no—
258C23×D3—104no—
259C23×D3—104no—
260C23×D3—104no—
261C23×D3C4×D511yescharacteristic
262C22×C3×C4—51no—
263C22×C3×C4—52no—
264C22×C3×C4—52no—
265C22×C3×C4—102no—
266C22×C3×C4—102no—
267C22×C3×C4C22×D511yescharacteristic
268C22×Dic3—51no—
269C22×Dic3—54no—
270C22×Dic3—104no—
271C22×Dic3C4×D511yescharacteristic
272C2×C4×D3—54no—
273C2×C4×D3—52no—
274C2×C4×D3—52no—
275C2×C4×D3—54no—
276C2×C4×D3—104no—
277C2×C4×D3—102no—
278C2×C4×D3—102no—
279C2×C4×D3—104no—
280C2×C4×D3—1016no—
281C2×C4×D3—108no—
282C2×C4×D3—108no—
283C2×C4×D3C4×D512yes—
284C2×C4×D3D2014yes—
285C2×C4×D3C22⋊D514yes—
286C2×C4×D3C22×D512yes—
287C2×C3×C8—22no—
288C2×C3×C8—52no—
289C2×C3×C8—102no—
290C2×C3×C8C22×D512yescomplemented
291C2×C3⋊C8—22no—
292C2×C3⋊C8—52no—
293C2×C3⋊C8—102no—
294C2×C3⋊C8C22×D512yescomplemented
295ΓL(1,𝔽25)—28no—
296ΓL(1,𝔽25)—108no—
297C23×C5—34no—
298C23×C5—32no—
299C23×C5—62no—
300C23×C5—62no—
301C23×C5C2×C4×D311yescharacteristic
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—34no—
305C22×D5—32no—
306C22×D5—68no—
307C22×D5—68no—
308C22×D5—632no—
309C22×D5—62no—
310C22×D5—62no—
311C22×D5—68no—
312C22×D5ΓL(1,𝔽25)14yescomplemented
313C22×D5C2×C4×D312yes—
314C2×C4×C5—34no—
315C2×C4×C5—32no—
316C2×C4×C5—38no—
317C2×C4×C5—34no—
318C2×C4×C5—34no—
319C2×C4×C5C2×C4×D311yescharacteristic
320C2×C4×C5D3×D412yes—
321C2×C4×C5D3×D412yes—
322C2×C4×C5C23×D311yescharacteristic
323C2×Dic5—22no—
324C2×Dic5—32no—
325C2×Dic5—68no—
326C2×Dic5—62no—
327C2×Dic5C2×C4×D312yes—
328C4×D5—24no—
329C4×D5—22no—
330C4×D5—22no—
331C4×D5—68no—
332C4×D5—68no—
333C4×D5—64no—
334C4×D5—62no—
335C4×D5—62no—
336C5×C8—22no—
337C5×C8—62no—
338#168—22no—
339#168—62no—
340C25—151no—
341C23×C4—31no—
342C23×C4—51no—
343C23×C4—154no—
344C23×C4—151no—
345C23×C4—154no—
346C23×C4—151no—
347C23×C4—151no—
348C23×C4—151no—
349C23×C4—304no—
350C23×C4—304no—
351C2×M16—34no—
352C2×M16—64no—
353C2×M16—154no—
354C2×M16—304no—
355C22×C8—31no—
356C22×C8—51no—
357C22×C8—151no—
358C22×C8D3×D511yescharacteristic, complemented
359C22⋊C8—54no—
360C22⋊C8—154no—
361C22⋊C8—154no—
362C22⋊C8—154no—
363C2×C3×C5#40714yescomplemented
364C2×C3×C5C22×C22⋊C411yescharacteristic
365C2×C3×C5C22×M1611yescharacteristic
366C2×C3×C5C22×M1611yescharacteristic
367D15—24no—
368C3×D5—24no—
369C5×D3—24no—
370C23×C3—52no—
371C23×C3—54no—
372C23×C3—102no—
373C23×C3—102no—
374C23×C3C2×C4×D511yescharacteristic
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—52no—
378C22×D3—54no—
379C22×D3—108no—
380C22×D3—108no—
381C22×D3—1032no—
382C22×D3—102no—
383C22×D3—102no—
384C22×D3—108no—
385C22×D3#68514yes—
386C22×D3C2×C4×D512yes—
387C2×C3×C4—52no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—104no—
392C2×C3×C4C2×C4×D511yescharacteristic
393C2×C3×C4C2×D2012yes—
394C2×C3×C4C2×C22⋊D512yes—
395C2×C3×C4C23×D511yescharacteristic
396C2×Dic3—52no—
397C2×Dic3—102no—
398C2×Dic3—108no—
399C2×Dic3#68514yes—
400C2×Dic3C2×C4×D512yes—
401C4×D3—108no—
402C4×D3—102no—
403C4×D3—102no—
404C4×D3—104no—
405C4×D3—108no—
406C4×D3#68518yes—
407C4×D3C2×D2014yes—
408C4×D3C2×C22⋊D514yes—
409C3×C8—22no—
410C3×C8—102no—
411C3⋊C8—22no—
412C3⋊C8—102no—
413C22×C5—34no—
414C22×C5—62no—
415C22×C5—62no—
416C22×C5—68no—
417C22×C5D3×C22⋊C412yes—
418C22×C5C2×ΓL(1,𝔽25)12yes—
419C22×C5D3×M1612yes—
420C22×C5C22×C4×D311yescharacteristic
421C2×D5—22no—
422C2×D5—22no—
423C2×D5—28no—
424C2×D5—34no—
425C2×D5—632no—
426C2×D5—62no—
427C2×D5—62no—
428C2×D5—68no—
429C2×D5C2×ΓL(1,𝔽25)14yescomplemented
430C4×C5—34no—
431C4×C5D3×C22⋊C412yes—
432C4×C5C2×D3×D411yescharacteristic
433C4×C5C2×D3×D411yescharacteristic
434Dic5—22no—
435Dic5—62no—
436C24—31no—
437C24—51no—
438C24—154no—
439C24—151no—
440C24—304no—
441C24—304no—
442C24—304no—
443C22×C4—31no—
444C22×C4—32no—
445C22×C4—34no—
446C22×C4—34no—
447C22×C4—32no—
448C22×C4—51no—
449C22×C4—52no—
450C22×C4—52no—
451C22×C4—102no—
452C22×C4—102no—
453C22×C4—154no—
454C22×C4—154no—
455C22×C4—154no—
456C22×C4—151no—
457C22×C4—152no—
458C22×C4—152no—
459C22×C4—304no—
460C22×C4—3016no—
461C22×C4—308no—
462C22×C4—308no—
463C22×C4—304no—
464C22×C4—304no—
465C22×C4—302no—
466C22×C4—302no—
467C22×C4C2×D3×D511yescharacteristic
468M16—68no—
469M16—308no—
470C2×C8—22no—
471C2×C8—32no—
472C2×C8—52no—
473C2×C8—62no—
474C2×C8—102no—
475C2×C8—152no—
476C2×C8—302no—
477C2×C8C2×D3×D512yescomplemented
478C3×C5C2×#40711yescharacteristic, complemented, Hall
479C22×C3—54no—
480C22×C3—102no—
481C22×C3—102no—
482C22×C3—108no—
483C22×C3D5×M1612yes—
484C22×C3D5×M1612yes—
485C22×C3C2×#68512yes—
486C22×C3C22×C4×D511yescharacteristic
487C2×D3—22no—
488C2×D3—22no—
489C2×D3—28no—
490C2×D3—54no—
491C2×D3—1032no—
492C2×D3—102no—
493C2×D3—102no—
494C2×D3—108no—
495C2×D3C2×#68514yes—
496C3×C4—102no—
497C3×C4C2×#68512yes—
498C3×C4C22×D2011yescharacteristic
499C3×C4C22×C22⋊D511yescharacteristic
500Dic3—102no—
501Dic3C2×#68514yes—
502C2×C5—64no—
503C2×C5#472614yescomplemented
504C2×C5C2×D3×C22⋊C411yescharacteristic
505C2×C5C22×ΓL(1,𝔽25)11yescharacteristic
506C2×C5C2×D3×M1611yescharacteristic
507D5—24no—
508D5—64no—
509C23—34no—
510C23—32no—
511C23—52no—
512C23—54no—
513C23—62no—
514C23—62no—
515C23—102no—
516C23—102no—
517C23—152no—
518C23—154no—
519C23—308no—
520C23—308no—
521C23—308no—
522C23—3032no—
523C23—302no—
524C23—302no—
525C23C4×D3×D511yescharacteristic
526C2×C4—34no—
527C2×C4—32no—
528C2×C4—38no—
529C2×C4—34no—
530C2×C4—34no—
531C2×C4—52no—
532C2×C4—102no—
533C2×C4—104no—
534C2×C4—102no—
535C2×C4—102no—
536C2×C4—152no—
537C2×C4—308no—
538C2×C4—308no—
539C2×C4—308no—
540C2×C4—302no—
541C2×C4—304no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4C4×D3×D511yescharacteristic
545C2×C4D3×D2012yes—
546C2×C4D3×C22⋊D512yes—
547C2×C4C22×D3×D511yescharacteristic
548C8—22no—
549C8—62no—
550C8—102no—
551C8—302no—
552C2×C3—104no—
553C2×C3#6541514yescomplemented
554C2×C3C2×D5×M1611yescharacteristic
555C2×C3C2×D5×M1611yescharacteristic
556C2×C3C22×#68511yescharacteristic
557D3—24no—
558D3—104no—
559C5C2×#472611yescharacteristic, complemented, Sylow
560C22—34no—
561C22—54no—
562C22—68no—
563C22—62no—
564C22—62no—
565C22—108no—
566C22—102no—
567C22—102no—
568C22—154no—
569C22—3032no—
570C22—308no—
571C22—302no—
572C22—302no—
573C22D5×ΓL(1,𝔽25)12yes—
574C22#9124612yes—
575C22D3×#68512yes—
576C22C2×C4×D3×D511yescharacteristic
577C4—34no—
578C4—102no—
579C4—302no—
580C4D3×#68512yes—
581C4C2×D3×D2011yescharacteristic
582C4C2×D3×C22⋊D511yescharacteristic
583C3C2×#6541511yescharacteristic, complemented, Sylow
584C2—64no—
585C2—104no—
586C2—304no—
587C2#1174810214yesdirect product factor
588C2C2×D5×ΓL(1,𝔽25)11yescharacteristic
589C2C2×#9124611yescharacteristic
590C2C2×D3×#68511yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC22×C3×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC23×C3×C5C22×C4
prime radicalC23×D3×D5C4
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5C2×#407
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C22×C5×ΓL(1,𝔽25)C2semidirect
3. C22×#6650C2semidirect
4. C2×#91104C2semidirect
5. C2×C3×#3952C2semidirect
6. C2×#90957C2semidirect
7. C2×#90955C2semidirect
8. #11748102C2direct (N × H)
21. C22×C3×C5×C8C22semidirect
22. C22×C3⋊#168C22semidirect
23. C22×C5×C3⋊C8C22semidirect
25. C2×C5×ΓL(1,𝔽25)C22semidirect
26. C22×C3×#168C22semidirect
28. C2×#6650C22semidirect
29. #91104C22semidirect
30. C3×#3952C22semidirect
31. #90957C22semidirect
32. #90955C22semidirect
41. C2×#3952D3semidirect
75. C2×C3×C5×C8C23semidirect
77. C2×C3⋊#168C23semidirect
79. C2×C5×C3⋊C8C23semidirect
82. C2×C3×#168C23semidirect
86. C22×ΓL(1,𝔽25)D5semidirect
106. C22×C5×C8C2×D3semidirect
110. C22×#168C2×D3semidirect
114. #3952C2×D3semidirect
119. C22×D15M16semidirect
127. C22×C3×D5M16semidirect
171. C22×C3×C8C2×D5semidirect
173. C22×C3⋊C8C2×D5semidirect
177. C2×ΓL(1,𝔽25)C2×D5semidirect
218. C2×C5×C8C22×D3semidirect
223. C2×#168C22×D3semidirect
239. C2×D15C2×M16semidirect
247. C2×C3×D5C2×M16semidirect
290. C2×C3×C8C22×D5semidirect
294. C2×C3⋊C8C22×D5semidirect
312. C22×D5ΓL(1,𝔽25)semidirect
358. C22×C8D3×D5semidirect
363. C2×C3×C5#407semidirect
429. C2×D5C2×ΓL(1,𝔽25)semidirect
477. C2×C8C2×D3×D5semidirect
478. C3×C5C2×#407semidirect
503. C2×C5#4726semidirect
553. C2×C3#65415semidirect
559. C5C2×#4726semidirect
583. C3C2×#65415semidirect
587. C2#11748102direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C22×C5×ΓL(1,𝔽25)2
C22×#66502
C2×#911042
C2×C3×#39522
C2×#909572
C2×#909552
#117481022
C2×#654153
C2×#47265