Finite Group Databasebeta

← C4×#91552 #14319581

Subgroups — C4×#91552 #14319581

Order 1920.

1848 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#1220C211yesmaximal, characteristic
2C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
3C2×#91552C212yesmaximal
4C2×C4×#1200C211yesmaximal, characteristic, complemented
5C4×C5×#217C211yesmaximal, characteristic, complemented
6Dic5×#217C212yesmaximal, complemented
7#11748875C212yesmaximal, complemented
8C4×#6669C211yesmaximal, characteristic, complemented
9C4×#6667C211yesmaximal, characteristic, complemented
10#11748640C212yesmaximal, complemented
11C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
12C4×#4027—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×#1220C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C23×C3×Dic5C2212yes—
17C22×#1200C2212yes—
18C2×#6719C2211yescharacteristic
19C4×#1220C418yescomplemented
20C2×#6714C2211yescharacteristic
21C2×#6712C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C5×#217C2212yes—
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C3×C4×Dic5—24no—
27C2×C3×C4×Dic5C2212yes—
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30#91552C4116yesdirect product factor
31C2×#6669C2212yes—
32C2×#6667C2212yes—
33C2×Dic3×Dic5C2212yes—
34C2×Dic3×Dic5C2212yes—
35C2×Dic3×Dic5C2212yes—
36C4×#1200—24no—
37C5×C3⋊#95C2212yes—
38#90994C2212yes—
39#90994C2212yes—
40C42×#67—51nomaximal, Hall
41C2×C4×C22⋊D5—31no—
42C22×C4×Dic5D311yescharacteristic, complemented
43C2×#4027—32no—
44C2×C42×D5—31no—
45C4×C5×C22⋊C4—31no—
46C22⋊C4×Dic5—32no—
47C4×#685—31no—
48C4×#683—31no—
49C42×Dic5—31no—
50#64955—32no—
51#64938—32no—
52C24×C3×C5C2311yescharacteristic
53C23×D15C2311yescharacteristic
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5C2×C414yescomplemented
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C2×#1220C2×C418yes—
60C2×#1220C2×C414yes—
61C22×Dic15C2311yescharacteristic
62C22×Dic15C2311yescharacteristic
63C22×Dic15C2311yescharacteristic
64C2×C4×D15—22no—
65C2×C4×D15—22no—
66C2×C4×D15C2×C414yescomplemented
67C22×C5×Dic3C2312yes—
68C22×C5×Dic3C2312yes—
69C22×C3×Dic5—24no—
70C22×C3×Dic5—24no—
71C22×C3×Dic5C2×C418yescomplemented
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2312yes—
74C2×#1200—24no—
75C2×#1200—24no—
76C2×#1200C2×C418yescomplemented
77#6719C2×C414yescomplemented
78#6714C2×C414yescomplemented
79#6712C2×C414yescomplemented
80C4×Dic15C2×C414yescomplemented
81C5×#217C2×C418yescomplemented
82C4×C5×Dic3—22no—
83C4×C5×Dic3—22no—
84C3×C4×Dic5—22no—
85C3×C4×Dic5—24no—
86C3×C4×Dic5D414yescomplemented
87#6669C2×C418yescomplemented
88#6667C2×C418yescomplemented
89Dic3×Dic5—24no—
90Dic3×Dic5—24no—
91Dic3×Dic5C2×C418yescomplemented
92C22×C3×C42—51no—
93C2×C4×#67—51no—
94C2×C4×#67—52no—
95C2×C42×D3—51no—
96C4×#217—52no—
97C4×#217D511yescharacteristic, complemented
98C4×(C2×D3)⋊C4—51no—
99C4×(C2×D3)⋊C4—52no—
100C4×Dic3⋊C4—51no—
101C4×Dic3⋊C4—52no—
102C42×Dic3—51no—
103C23×C4×C5C2×D311yescharacteristic
104C22×C22⋊D5—31no—
105C23×Dic5C2×D312yes—
106C22×C4×D5—31no—
107C22×C4×D5—32no—
108C2×C5×C22⋊C4—32no—
109C2×C42×C5—31no—
110C2×C42×C5—31no—
111C2×C22⋊Dic5—31no—
112C4×C22⋊D5—38no—
113C2×#685—31no—
114C2×#685—32no—
115C2×#683—31no—
116C2×#683—32no—
117C2×C4×Dic5—24no—
118C2×C4×Dic5—31no—
119C2×C4×Dic5—32no—
120C2×C4×Dic5—32no—
121C2×C4×Dic5—32no—
122C2×C4×Dic5C2×D312yes—
123C2×C4×Dic5C2×D311yescharacteristic
124C2×C4×Dic5C2×D311yescharacteristic
125#4027—316no—
126C42×D5—64no—
127C5×#95—32no—
128#3963—32no—
129#3963—32no—
130C42×D4—151noSylow
131C23×C3×C5—21no—
132C23×C3×C5—22no—
133C23×C3×C5—21no—
134C23×C3×C5C22×C414yes—
135C23×C3×C5C22×C412yes—
136C23×C3×C5C2411yescharacteristic
137C22×D15—21no—
138C22×D15—22no—
139C22×D15—21no—
140C22×D15C22×C414yes—
141C22×D15C22×C412yes—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—28no—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5#4112yes—
149#1220C42116yescomplemented
150C2×Dic15—21no—
151C2×Dic15—22no—
152C2×Dic15—21no—
153C2×Dic15C22×C412yes—
154C2×Dic15C22×C412yes—
155C2×Dic15C22×C414yes—
156C2×Dic15C22×C412yes—
157C4×D15—28no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3C22×C414yes—
163C2×C5×Dic3C22×C414yes—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—216no—
167C2×C3×Dic5C22×C414yes—
168C2×C3×Dic5C22×C414yes—
169C2×C3×Dic5C2×D414yes—
170C2×C3×Dic5#4114yes—
171#1200—216no—
172C23×C3×C4—52no—
173C23×C3×C4C2×D511yescharacteristic
174C22×#67—51no—
175C22×C4×D3—51no—
176C22×C4×D3—52no—
177C2×C3×C42—51no—
178C2×C3×C42—52no—
179C2×C3×C42—51no—
180C2×C3×C42—104no—
181C2×#217—51no—
182C2×#217C2×D512yes—
183C4×#67—58no—
184C4×#67—516no—
185C2×(C2×D3)⋊C4—51no—
186C2×(C2×D3)⋊C4—52no—
187C2×Dic3⋊C4—51no—
188C2×Dic3⋊C4—52no—
189C2×C4×Dic3—51no—
190C2×C4×Dic3—52no—
191C2×C4×Dic3—52no—
192C2×C4×Dic3—52no—
193C2×C4×Dic3C2×D511yescharacteristic
194C2×C4×Dic3C2×D511yescharacteristic
195C42×D3—104no—
196C3⋊#95—52no—
197C3⋊#95—52no—
198C3⋊#95C2×D512yes—
199C24×C5C22×D311yescharacteristic
200C23×D5—31no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—32no—
204C22×C4×C5—32no—
205C22×C4×C5C4×D314yescomplemented
206C22×C4×C5C22×D311yescharacteristic
207C22×C4×C5C22×D311yescharacteristic
208C2×C22⋊D5—38no—
209C2×C22⋊D5—34no—
210C22×Dic5—24no—
211C22×Dic5—24no—
212C22×Dic5—31no—
213C22×Dic5—31no—
214C22×Dic5—31no—
215C22×Dic5C4×D318yescomplemented
216C22×Dic5C22×D312yes—
217C22×Dic5C22×D312yes—
218C2×C4×D5—34no—
219C2×C4×D5—38no—
220C2×C4×D5—62no—
221C2×C4×D5—62no—
222C2×C4×D5—64no—
223C2×C4×D5—64no—
224C5×C22⋊C4—38no—
225C42×C5—62no—
226C42×C5—62no—
227C22⋊Dic5—34no—
228#685—34no—
229#685—38no—
230#683—34no—
231#683—38no—
232C4×Dic5—22no—
233C4×Dic5—24no—
234C4×Dic5—34no—
235C4×Dic5—38no—
236C4×Dic5—64no—
237C4×Dic5—64no—
238C4×Dic5#6714yescomplemented
239C2×C4×D4—152no—
240C2×C4×D4—151no—
241C22×C42—51no—
242C22×C42—151no—
243C4×C4⋊C4—152no—
244C4×C4⋊C4—151no—
245C4×C22⋊C4—31no—
246C4×C22⋊C4—152no—
247C4×C22⋊C4—151no—
248C4×C22⋊C4—152no—
249C43—151no—
250C22×C3×C5—24no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—24no—
254C22×C3×C5C2×C4214yescomplemented
255C22×C3×C5C23×C412yes—
256C22×C3×C5C23×C411yescharacteristic
257C22×C3×C5C22×D411yescharacteristic
258C22×C3×C5C2×#4111yescharacteristic
259C22×C3×C5C2×#4112yes—
260C2×D15—24no—
261C2×D15—22no—
262C2×D15—22no—
263C2×D15—24no—
264C2×D15C2×C4214yescomplemented
265C3×C4×C5—22no—
266C3×C4×C5C4×D414yescomplemented
267Dic15—22no—
268Dic15—22no—
269Dic15C2×C4214yescomplemented
270C3×Dic5—24no—
271C3×Dic5C4×D418yescomplemented
272C5×Dic3—24no—
273C5×Dic3—24no—
274C24×C3C22×D511yescharacteristic
275C23×D3—51no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4—52no—
279C22×C3×C4—58no—
280C22×C3×C4—52no—
281C22×C3×C4—104no—
282C22×C3×C4—104no—
283C22×C3×C4C4×D514yescomplemented
284C22×C3×C4C22×D511yescharacteristic
285C22×C3×C4C22×D511yescharacteristic
286C2×#67—58no—
287C2×#67—54no—
288C22×Dic3—51no—
289C22×Dic3—51no—
290C22×Dic3—51no—
291C22×Dic3C22×D512yes—
292C22×Dic3C22×D512yes—
293C2×C4×D3—54no—
294C2×C4×D3—58no—
295C2×C4×D3—104no—
296C2×C4×D3—104no—
297C2×C4×D3—102no—
298C2×C4×D3—102no—
299C3×C42—54no—
300C3×C42—104no—
301C3×C42—102no—
302#217—54no—
303#217C4×D518yescomplemented
304(C2×D3)⋊C4—54no—
305(C2×D3)⋊C4—58no—
306Dic3⋊C4—54no—
307Dic3⋊C4—58no—
308C4×Dic3—22no—
309C4×Dic3—22no—
310C4×Dic3—54no—
311C4×Dic3—58no—
312C4×Dic3—104no—
313C4×Dic3—104no—
314C23×C5—22no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5C2×C4×D314yes—
318C23×C5C2×C4×D312yes—
319C23×C5C23×D311yescharacteristic
320C22×D5—34no—
321C22×D5—32no—
322C22×D5—62no—
323C22×D5—61no—
324C22×D5—61no—
325C2×C4×C5—21no—
326C2×C4×C5—21no—
327C2×C4×C5—28no—
328C2×C4×C5—34no—
329C2×C4×C5—34no—
330C2×C4×C5—62no—
331C2×C4×C5—62no—
332C2×C4×C5—62no—
333C2×C4×C5—62no—
334C2×C4×C5C2×C4×D312yes—
335C2×C4×C5C2×C4×D312yes—
336C2×C4×C5#23512yes—
337C2×C4×C5C2×#6712yes—
338C22⋊D5—316no—
339C2×Dic5—22no—
340C2×Dic5—22no—
341C2×Dic5—216no—
342C2×Dic5—34no—
343C2×Dic5—32no—
344C2×Dic5—32no—
345C2×Dic5—32no—
346C2×Dic5—62no—
347C2×Dic5—61no—
348C2×Dic5—61no—
349C2×Dic5C2×C4×D314yes—
350C2×Dic5C2×C4×D314yes—
351C2×Dic5#23514yes—
352C2×Dic5C2×#6714yes—
353C4×D5—68no—
354C4×D5—616no—
355C22×D4—151no—
356C23×C4—52no—
357C23×C4—152no—
358C23×C4—151no—
359C23×C4D3×D511yescharacteristic
360C4×D4—1516no—
361C4×D4—158no—
362C2×C4⋊C4—152no—
363C2×C4⋊C4—151no—
364C2×C22⋊C4—32no—
365C2×C22⋊C4—152no—
366C2×C22⋊C4—151no—
367C2×C22⋊C4—151no—
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—51no—
371C2×C42—52no—
372C2×C42—51no—
373C2×C42—104no—
374C2×C42—152no—
375C2×C42—151no—
376C2×C42—152no—
377C2×C42—152no—
378C2×C42—304no—
379#95—32no—
380#95—152no—
381#95—152no—
382C2×C3×C5—24no—
383C2×C3×C5C22×C4211yescharacteristic
384C2×C3×C5C2×C4×D411yescharacteristic
385C2×C3×C5C2×C4×D412yes—
386C2×C3×C5C4×#4111yescharacteristic
387C2×C3×C5C4×#4112yes—
388D15—24no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—22no—
392C23×C3C2×C4×D514yes—
393C23×C3C2×C4×D512yes—
394C23×C3C23×D511yescharacteristic
395C22×D3—54no—
396C22×D3—52no—
397C22×D3—101no—
398C22×D3—101no—
399C22×D3—102no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—28no—
403C2×C3×C4—54no—
404C2×C3×C4—54no—
405C2×C3×C4—54no—
406C2×C3×C4—54no—
407C2×C3×C4—1016no—
408C2×C3×C4—102no—
409C2×C3×C4—102no—
410C2×C3×C4C2×C4×D512yes—
411C2×C3×C4C2×C4×D512yes—
412C2×C3×C4D4×D512yes—
413C2×C3×C4#71112yes—
414#67—516no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—22no—
418C2×Dic3—22no—
419C2×Dic3—54no—
420C2×Dic3—52no—
421C2×Dic3—52no—
422C2×Dic3—52no—
423C2×Dic3—101no—
424C2×Dic3—101no—
425C2×Dic3—102no—
426C2×Dic3C2×C4×D514yes—
427C2×Dic3C2×C4×D514yes—
428C4×D3—1016no—
429C4×D3—108no—
430C22×C5—24no—
431C22×C5—22no—
432C22×C5—24no—
433C22×C5—22no—
434C22×C5C42×D314yescomplemented
435C22×C5C22×C4×D312yes—
436C22×C5C22×C4×D311yescharacteristic
437C22×C5C2×#23512yes—
438C22×C5C2×#23511yescharacteristic
439C22×C5C22×#6711yescharacteristic
440C2×D5—34no—
441C2×D5—64no—
442C2×D5—62no—
443C2×D5—62no—
444C2×D5—64no—
445C4×C5—22no—
446C4×C5—64no—
447C4×C5—64no—
448C4×C5C4×#6714yescomplemented
449Dic5—24no—
450Dic5—34no—
451Dic5—62no—
452Dic5—62no—
453Dic5C4×#6718yescomplemented
454C24—151no—
455C24C2×D3×D511yescharacteristic
456C2×D4—158no—
457C2×D4—154no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—52no—
463C22×C4—58no—
464C22×C4—52no—
465C22×C4—104no—
466C22×C4—104no—
467C22×C4—158no—
468C22×C4—151no—
469C22×C4—151no—
470C22×C4—151no—
471C22×C4—154no—
472C22×C4—304no—
473C22×C4—304no—
474C22×C4—302no—
475C22×C4—302no—
476C22×C4#120014yescomplemented
477C22×C4C2×D3×D511yescharacteristic
478C22×C4C2×D3×D511yescharacteristic
479C4⋊C4—158no—
480C4⋊C4—154no—
481C22⋊C4—38no—
482C22⋊C4—158no—
483C22⋊C4—154no—
484C22⋊C4—154no—
485C42—54no—
486C42—62no—
487C42—62no—
488C42—104no—
489C42—102no—
490C42—158no—
491C42—154no—
492C42—304no—
493C42—304no—
494C3×C5C42×D411yescharacteristic, complemented, Hall
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3C42×D514yescomplemented
500C22×C3C22×C4×D512yes—
501C22×C3C22×C4×D511yescharacteristic
502C22×C3C2×D4×D511yescharacteristic
503C22×C3C2×#71111yescharacteristic
504C22×C3D5×#4112yes—
505C2×D3—54no—
506C2×D3—102no—
507C2×D3—102no—
508C2×D3—104no—
509C2×D3—104no—
510C3×C4—22no—
511C3×C4—58no—
512C3×C4—104no—
513C3×C4#402714yescomplemented
514Dic3—24no—
515Dic3—24no—
516Dic3—54no—
517Dic3—102no—
518Dic3—102no—
519C2×C5—24no—
520C2×C5C2×C42×D311yescharacteristic
521C2×C5C4×#23512yes—
522C2×C5C4×#23511yescharacteristic
523C2×C5C2×C4×#6711yescharacteristic
524C2×C5C2×C4×#6712yes—
525D5—64no—
526C23—22no—
527C23—21no—
528C23—21no—
529C23—154no—
530C23—152no—
531C23—302no—
532C23—301no—
533C23—301no—
534C23C4×D3×D514yes—
535C23C2×#120012yes—
536C23C22×D3×D511yescharacteristic
537D4—1516no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—28no—
541C2×C4—34no—
542C2×C4—34no—
543C2×C4—54no—
544C2×C4—54no—
545C2×C4—54no—
546C2×C4—54no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—1016no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—154no—
555C2×C4—152no—
556C2×C4—152no—
557C2×C4—152no—
558C2×C4—3016no—
559C2×C4—302no—
560C2×C4—301no—
561C2×C4—301no—
562C2×C4—308no—
563C2×C4#678212yes—
564C2×C4C2×#120012yes—
565C2×C4C2×#120012yes—
566C2×C4D5×#6712yes—
567C2×C3—24no—
568C2×C3C2×C42×D511yescharacteristic
569C2×C3C2×#402711yescharacteristic
570C2×C3#6585611yescharacteristic
571C2×C3C4×#71112yes—
572C2×C3C4×D4×D512yes—
573D3—104no—
574C5C42×#6711yescharacteristic, complemented, Sylow
575C22—24no—
576C22—22no—
577C22—24no—
578C22—22no—
579C22—154no—
580C22—304no—
581C22—302no—
582C22—304no—
583C22—302no—
584C22C4×#120014yescomplemented
585C22C2×C4×D3×D512yes—
586C22D5×#23512yes—
587C22C2×#678211yescharacteristic
588C22C22×#120011yescharacteristic
589C22C2×D5×#6711yescharacteristic
590C4—22no—
591C4—58no—
592C4—64no—
593C4—64no—
594C4—104no—
595C4—154no—
596C4—302no—
597C4—302no—
598C4#9155214yesdirect product factor
599C3C4×#402711yescharacteristic, complemented, Sylow
600C2—24no—
601C2—304no—
602C2C4×#678212yes—
603C2C2×C4×#120011yescharacteristic
604C2#1175441411yescharacteristic
605C2C4×D5×#6712yes—
606C2C2×#9155211yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC2×C3×C5C22×C42
FrattiniC23C22×D3×D5
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1220C22
hypercenterC23×C4D3×D5
hypocenterC3×C5C42×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C4×Dic5C2semidirect
4. C2×C4×#1200C2semidirect
5. C4×C5×#217C2semidirect
6. Dic5×#217C2semidirect
7. #11748875C2semidirect
8. C4×#6669C2semidirect
9. C4×#6667C2semidirect
10. #11748640C2semidirect
11. C4×Dic3×Dic5C2semidirect
19. C4×#1220C4semidirect
30. #91552C4direct (N × H)
42. C22×C4×Dic5D3semidirect
56. C22×C3×C4×C5C2×C4semidirect
66. C2×C4×D15C2×C4semidirect
71. C22×C3×Dic5C2×C4semidirect
76. C2×#1200C2×C4semidirect
77. #6719C2×C4semidirect
78. #6714C2×C4semidirect
79. #6712C2×C4semidirect
80. C4×Dic15C2×C4semidirect
81. C5×#217C2×C4semidirect
86. C3×C4×Dic5D4semidirect
87. #6669C2×C4semidirect
88. #6667C2×C4semidirect
91. Dic3×Dic5C2×C4semidirect
97. C4×#217D5semidirect
149. #1220C42semidirect
205. C22×C4×C5C4×D3semidirect
215. C22×Dic5C4×D3semidirect
238. C4×Dic5#67semidirect
254. C22×C3×C5C2×C42semidirect
264. C2×D15C2×C42semidirect
266. C3×C4×C5C4×D4semidirect
269. Dic15C2×C42semidirect
271. C3×Dic5C4×D4semidirect
283. C22×C3×C4C4×D5semidirect
303. #217C4×D5semidirect
434. C22×C5C42×D3semidirect
448. C4×C5C4×#67semidirect
453. Dic5C4×#67semidirect
476. C22×C4#1200semidirect
494. C3×C5C42×D4semidirect
499. C22×C3C42×D5semidirect
513. C3×C4#4027semidirect
574. C5C42×#67semidirect
584. C22C4×#1200semidirect
598. C4#91552direct (N × H)
599. C3C4×#4027semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#12202
C22×C3×C4×Dic52
C2×#915522
C2×C4×#12002
C4×C5×#2172
Dic5×#2172
#117488752
C4×#66692
C4×#66672
#117486402
C4×Dic3×Dic52
C4×#40273
C42×#675