Finite Group Databasebeta

← C4×#91396 #14319579

Subgroups — C4×#91396 #14319579

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×C42×D15C211yesmaximal, characteristic, complemented
2C2×C4×#1202C211yesmaximal, characteristic
3C2×#91396C212yesmaximal
4C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
5C4×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
6C3×C4×#685C211yesmaximal, characteristic, complemented
7#11748884C212yesmaximal, complemented
8C4×#6667C211yesmaximal, characteristic, complemented
9#11748670C212yesmaximal, complemented
10#11748651C212yesmaximal, complemented
11C4×Dic3×Dic5C211yesmaximal, characteristic, complemented
12C4×#4039—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×C4×D15C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1202C2211yescharacteristic
17C22×D5×Dic3C2212yes—
18C2×C3×C42×C5C2211yescharacteristic
19C2×C4×Dic15C2212yes—
20C2×C4×Dic15C2211yescharacteristic
21C42×D15—24no—
22C2×C5×Dic3⋊C4C2212yes—
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×#685C2212yes—
26C2×C3×C4×Dic5C2211yescharacteristic
27C2×Dic3⋊Dic5C2211yescharacteristic
28C2×#6667C2211yescharacteristic
29C2×#6667C2212yes—
30C2×#6665C2211yescharacteristic
31C2×Dic3×Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33C2×Dic3×Dic5C2212yes—
34C4×#1202C418yescomplemented
35#91396C4116yesdirect product factor
36C4×D5×Dic3—24no—
37C5×C3⋊#95C2212yes—
38C3×#3963C2212yes—
39#90994C2212yes—
40C4×#67⋊C4—51nomaximal, Hall
41C2×#4039—32no—
42C2×C4×D20—31no—
43C2×C42×D5—31no—
44C2×C42×D5—31no—
45C4×C5×C4⋊C4—31no—
46C4⋊C4×Dic5—32no—
47C4×#685—31no—
48C4×#685D311yescharacteristic, complemented
49C42×Dic5—31no—
50#64955—32no—
51#64955—32no—
52C23×D15C2311yescharacteristic
53C23×C3×D5C2311yescharacteristic
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15C2311yescharacteristic
57C22×Dic15C2312yes—
58C2×C4×D15—22no—
59C2×C4×D15—22no—
60C2×C4×D15—24no—
61C2×C4×D15—24no—
62C2×C4×D15C2×C418yescomplemented
63C2×C4×D15C2×C414yescomplemented
64C22×C5×Dic3C2312yes—
65C22×C5×Dic3C2311yescharacteristic
66C22×C5×Dic3C2311yescharacteristic
67C22×C3×Dic5C2312yes—
68C22×C3×Dic5C2311yescharacteristic
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5—22no—
71C2×C3×C4×D5C2×C414yescomplemented
72C2×#1202C2×C418yes—
73C2×#1202C2×C414yes—
74C2×D5×Dic3—24no—
75C2×D5×Dic3—24no—
76C2×D5×Dic3C2×C418yescomplemented
77C3×C42×C5—22no—
78C4×Dic15—24no—
79C4×Dic15D414yescomplemented
80C5×Dic3⋊C4C2×C418yescomplemented
81C4×C5×Dic3—22no—
82C4×C5×Dic3C2×C414yescomplemented
83C3×#685C2×C418yescomplemented
84C3×C4×Dic5—22no—
85Dic3⋊Dic5C2×C414yescomplemented
86#6667C2×C418yescomplemented
87#6667C2×C414yescomplemented
88#6665C2×C414yescomplemented
89Dic3×Dic5—24no—
90Dic3×Dic5—24no—
91Dic3×Dic5C2×C418yescomplemented
92C2×C4×#67—51no—
93C22×C4×Dic3—51no—
94C2×#67⋊C4—52no—
95C2×C42×D3—51no—
96C3×C4×C22⋊C4—51no—
97Dic3×C22⋊C4—52no—
98C4×(C2×D3)⋊C4—51no—
99C4×Dic3⋊C4D511yescharacteristic, complemented
100C42×Dic3—51no—
101#4666—52no—
102#4649—52no—
103C22×D20—31no—
104C22×C4×D5—32no—
105C22×C4×D5—31no—
106C22×C4×D5—32no—
107C22×C4×D5C2×D311yescharacteristic
108C2×C5×C4⋊C4—32no—
109C2×C42×C5—31no—
110C2×C42×C5—31no—
111C2×C42×C5C2×D311yescharacteristic
112C2×#685—31no—
113C2×#685—31no—
114C2×#685—32no—
115C2×#685C2×D312yes—
116C2×C4⋊Dic5—31no—
117C2×C4×Dic5—31no—
118C2×C4×Dic5—32no—
119C2×C4×Dic5—32no—
120C2×C4×Dic5—32no—
121C2×C4×Dic5—32no—
122C2×C4×Dic5C2×D311yescharacteristic
123#4039—316no—
124C4×D20—38no—
125C42×D5—64no—
126C42×D5—64no—
127C5×#95—32no—
128#3963—32no—
129#3963C2×D312yes—
130C42×D4—151noSylow
131C23×C3×C5C2411yescharacteristic
132C22×D15—21no—
133C22×D15—21no—
134C22×D15—22no—
135C22×D15C22×C414yes—
136C22×D15C22×C412yes—
137C22×C3×D5—21no—
138C22×C3×D5—22no—
139C22×C3×D5—21no—
140C22×C3×D5C22×C412yes—
141C22×C3×D5C22×C414yes—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C22×C414yes—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5#4112yes—
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×Dic15C22×C412yes—
151C2×Dic15C22×C414yes—
152C2×Dic15C2×D414yes—
153C2×Dic15#4114yes—
154C4×D15—28no—
155C4×D15—216no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3C22×C412yes—
160C2×C5×Dic3C22×C414yes—
161C2×C5×Dic3C22×C414yes—
162C2×C5×Dic3C22×C412yes—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5C22×C414yes—
168C2×C3×Dic5C22×C412yes—
169C3×C4×D5—28no—
170#1202C42116yescomplemented
171D5×Dic3—216no—
172C23×C3×C4—51no—
173C22×#67—51no—
174C23×Dic3—52no—
175C22×C4×D3—52no—
176C22×C4×D3—51no—
177C2×C3×C22⋊C4—52no—
178C2×C3×C42—51no—
179C2×C3×C42C2×D511yescharacteristic
180C2×#217—51no—
181C4×#67—58no—
182C2×(C2×D3)⋊C4—51no—
183C2×(C2×D3)⋊C4—52no—
184C2×Dic3⋊C4—51no—
185C2×Dic3⋊C4C2×D512yes—
186C2×C4×Dic3—51no—
187C2×C4×Dic3—52no—
188C2×C4×Dic3—52no—
189C2×C4×Dic3—52no—
190C2×C4×Dic3—52no—
191C2×C4×Dic3—104no—
192C2×C4×Dic3C2×D511yescharacteristic
193C2×C4×Dic3C2×D511yescharacteristic
194#67⋊C4—516no—
195C42×D3—104no—
196C3×#95—52no—
197C3⋊#95—52no—
198C3⋊#95C2×D512yes—
199C23×D5—31no—
200C23×D5C22×D311yescharacteristic
201C22×C4×C5—31no—
202C22×C4×C5—32no—
203C22×C4×C5—31no—
204C22×C4×C5C22×D312yes—
205C22×C4×C5C22×D311yescharacteristic
206C22×Dic5—32no—
207C22×Dic5—31no—
208C22×Dic5C22×D311yescharacteristic
209C22×Dic5C22×D312yes—
210C2×D20—34no—
211C2×D20—38no—
212C2×C4×D5—22no—
213C2×C4×D5—22no—
214C2×C4×D5—38no—
215C2×C4×D5—34no—
216C2×C4×D5—38no—
217C2×C4×D5—64no—
218C2×C4×D5—64no—
219C2×C4×D5—64no—
220C2×C4×D5—64no—
221C2×C4×D5—62no—
222C2×C4×D5—62no—
223C2×C4×D5C4×D314yescomplemented
224C5×C4⋊C4—38no—
225C42×C5—22no—
226C42×C5—34no—
227C42×C5—62no—
228#685—34no—
229#685—34no—
230#685—38no—
231#685C4×D318yescomplemented
232C4⋊Dic5—34no—
233C4×Dic5—22no—
234C4×Dic5—34no—
235C4×Dic5—38no—
236C4×Dic5—64no—
237C4×Dic5—64no—
238C4×Dic5—64no—
239C2×C4×D4—151no—
240C2×C4×D4—152no—
241C22×C42—151no—
242C22×C42—151no—
243C4×C4⋊C4—31no—
244C4×C4⋊C4—152no—
245C4×C22⋊C4—51no—
246C4×C22⋊C4—152no—
247C4×C22⋊C4—152no—
248C4×C22⋊C4—151no—
249C43—151no—
250C22×C3×C5C23×C411yescharacteristic
251C22×C3×C5C23×C412yes—
252C22×C3×C5C22×D411yescharacteristic
253C22×C3×C5C2×#4111yescharacteristic
254C22×C3×C5C2×#4112yes—
255C2×D15—22no—
256C2×D15—24no—
257C2×D15—22no—
258C2×D15—24no—
259C2×D15C2×C4214yescomplemented
260C2×C3×D5—24no—
261C2×C3×D5—22no—
262C2×C3×D5—22no—
263C2×C3×D5—24no—
264C2×C3×D5C2×C4214yescomplemented
265C3×C4×C5—24no—
266C3×C4×C5C4×D414yescomplemented
267Dic15—22no—
268Dic15C4×D418yescomplemented
269C3×Dic5—22no—
270C3×Dic5—24no—
271C5×Dic3—24no—
272C5×Dic3—22no—
273C5×Dic3C2×C4214yescomplemented
274C24×C3—51no—
275C23×D3—51no—
276C22×C3×C4—52no—
277C22×C3×C4—51no—
278C22×C3×C4—54no—
279C22×C3×C4—102no—
280C22×C3×C4—102no—
281C22×C3×C4C22×D512yes—
282C22×C3×C4C22×D511yescharacteristic
283C2×#67—58no—
284C2×#67—54no—
285C22×Dic3—52no—
286C22×Dic3—51no—
287C22×Dic3—58no—
288C22×Dic3—104no—
289C22×Dic3—104no—
290C22×Dic3C22×D512yes—
291C22×Dic3C22×D511yescharacteristic
292C22×Dic3C22×D511yescharacteristic
293C2×C4×D3—58no—
294C2×C4×D3—54no—
295C2×C4×D3—104no—
296C2×C4×D3—104no—
297C2×C4×D3—102no—
298C2×C4×D3—102no—
299C3×C22⋊C4—58no—
300C3×C42—22no—
301C3×C42—102no—
302#217—54no—
303(C2×D3)⋊C4—58no—
304(C2×D3)⋊C4—54no—
305Dic3⋊C4—54no—
306Dic3⋊C4C4×D518yescomplemented
307C4×Dic3—22no—
308C4×Dic3—54no—
309C4×Dic3—58no—
310C4×Dic3—104no—
311C4×Dic3—104no—
312C4×Dic3—104no—
313C4×Dic3C4×D514yescomplemented
314C23×C5C23×D311yescharacteristic
315C22×D5—21no—
316C22×D5—21no—
317C22×D5—22no—
318C22×D5—32no—
319C22×D5—34no—
320C22×D5—61no—
321C22×D5—61no—
322C22×D5—62no—
323C22×D5C2×C4×D312yes—
324C22×D5C2×C4×D314yes—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—34no—
328C2×C4×C5—32no—
329C2×C4×C5—32no—
330C2×C4×C5—34no—
331C2×C4×C5—62no—
332C2×C4×C5—62no—
333C2×C4×C5—62no—
334C2×C4×C5C2×C4×D314yes—
335C2×C4×C5C2×C4×D312yes—
336C2×C4×C5D3×D412yes—
337C2×C4×C5#23712yes—
338C2×Dic5—21no—
339C2×Dic5—22no—
340C2×Dic5—21no—
341C2×Dic5—22no—
342C2×Dic5—34no—
343C2×Dic5—34no—
344C2×Dic5—34no—
345C2×Dic5—32no—
346C2×Dic5—61no—
347C2×Dic5—61no—
348C2×Dic5C2×C4×D314yes—
349C2×Dic5C2×C4×D312yes—
350D20—316no—
351C4×D5—28no—
352C4×D5—616no—
353C4×D5—616no—
354C4×D5—68no—
355C22×D4—151no—
356C23×C4—51no—
357C23×C4—152no—
358C23×C4—152no—
359C23×C4—151no—
360C4×D4—158no—
361C4×D4—1516no—
362C2×C4⋊C4—32no—
363C2×C4⋊C4—151no—
364C2×C22⋊C4—52no—
365C2×C22⋊C4—151no—
366C2×C22⋊C4—152no—
367C2×C22⋊C4—151no—
368C2×C42—31no—
369C2×C42—31no—
370C2×C42—51no—
371C2×C42—152no—
372C2×C42—151no—
373C2×C42—152no—
374C2×C42—152no—
375C2×C42—152no—
376C2×C42—304no—
377C2×C42—304no—
378C2×C42D3×D511yescharacteristic
379#95—32no—
380#95—52no—
381#95—152no—
382C2×C3×C5C22×C4211yescharacteristic
383C2×C3×C5C2×C4×D411yescharacteristic
384C2×C3×C5C2×C4×D412yes—
385C2×C3×C5C4×#4111yescharacteristic
386C2×C3×C5C4×#4112yes—
387D15—24no—
388C3×D5—24no—
389C23×C3—52no—
390C23×C3—54no—
391C23×C3—101no—
392C23×C3—101no—
393C23×C3—102no—
394C23×C3C23×D511yescharacteristic
395C22×D3—52no—
396C22×D3—54no—
397C22×D3—101no—
398C22×D3—101no—
399C22×D3—102no—
400C2×C3×C4—22no—
401C2×C3×C4—22no—
402C2×C3×C4—54no—
403C2×C3×C4—52no—
404C2×C3×C4—101no—
405C2×C3×C4—102no—
406C2×C3×C4—101no—
407C2×C3×C4—102no—
408C2×C3×C4—108no—
409C2×C3×C4C2×C4×D514yes—
410C2×C3×C4C2×C4×D512yes—
411C2×C3×C4D4×D512yes—
412C2×C3×C4#71312yes—
413#67—516no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—22no—
417C2×Dic3—54no—
418C2×Dic3—54no—
419C2×Dic3—54no—
420C2×Dic3—52no—
421C2×Dic3—1016no—
422C2×Dic3—101no—
423C2×Dic3—101no—
424C2×Dic3C2×C4×D512yes—
425C2×Dic3C2×C4×D514yes—
426C2×Dic3C2×C4×D514yes—
427C2×Dic3C2×C4×D512yes—
428C4×D3—1016no—
429C4×D3—108no—
430C22×C5C22×C4×D311yescharacteristic
431C22×C5C22×C4×D312yes—
432C22×C5C2×D3×D411yescharacteristic
433C22×C5C2×#23711yescharacteristic
434C22×C5D3×#4112yes—
435C2×D5—22no—
436C2×D5—22no—
437C2×D5—24no—
438C2×D5—24no—
439C2×D5—34no—
440C2×D5—62no—
441C2×D5—62no—
442C2×D5—64no—
443C2×D5—64no—
444C2×D5C42×D314yescomplemented
445C4×C5—24no—
446C4×C5—34no—
447C4×C5—62no—
448C4×C5—64no—
449C4×C5#67⋊C414yescomplemented
450Dic5—22no—
451Dic5—24no—
452Dic5—38no—
453Dic5—62no—
454C24—51no—
455C24—151no—
456C2×D4—154no—
457C2×D4—158no—
458C22×C4—31no—
459C22×C4—31no—
460C22×C4—32no—
461C22×C4—51no—
462C22×C4—52no—
463C22×C4—54no—
464C22×C4—102no—
465C22×C4—102no—
466C22×C4—158no—
467C22×C4—152no—
468C22×C4—151no—
469C22×C4—158no—
470C22×C4—154no—
471C22×C4—304no—
472C22×C4—304no—
473C22×C4—304no—
474C22×C4—304no—
475C22×C4—302no—
476C22×C4—302no—
477C22×C4C2×D3×D512yes—
478C22×C4C2×D3×D511yescharacteristic
479C4⋊C4—38no—
480C4⋊C4—154no—
481C22⋊C4—58no—
482C22⋊C4—154no—
483C22⋊C4—158no—
484C22⋊C4—154no—
485C42—22no—
486C42—34no—
487C42—62no—
488C42—102no—
489C42—158no—
490C42—154no—
491C42—304no—
492C42—304no—
493C42—304no—
494C3×C5C42×D411yescharacteristic, complemented, Hall
495C22×C3—54no—
496C22×C3—102no—
497C22×C3—102no—
498C22×C3—104no—
499C22×C3—104no—
500C22×C3C22×C4×D511yescharacteristic
501C22×C3C22×C4×D512yes—
502C22×C3C2×D4×D511yescharacteristic
503C22×C3C2×#71311yescharacteristic
504C22×C3D5×#4112yes—
505C2×D3—54no—
506C2×D3—102no—
507C2×D3—102no—
508C2×D3—104no—
509C2×D3—104no—
510C3×C4—24no—
511C3×C4—102no—
512C3×C4—104no—
513C3×C4#403914yescomplemented
514Dic3—22no—
515Dic3—24no—
516Dic3—58no—
517Dic3—102no—
518Dic3C42×D514yescomplemented
519C2×C5C2×C42×D311yescharacteristic
520C2×C5C2×#67⋊C411yescharacteristic
521C2×C5#552211yescharacteristic
522C2×C5C4×#23712yes—
523C2×C5C4×D3×D412yes—
524D5—24no—
525D5—64no—
526C23—54no—
527C23—52no—
528C23—101no—
529C23—102no—
530C23—101no—
531C23—152no—
532C23—154no—
533C23—301no—
534C23—302no—
535C23—301no—
536C23C22×D3×D511yescharacteristic
537D4—1516no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—32no—
541C2×C4—34no—
542C2×C4—32no—
543C2×C4—34no—
544C2×C4—54no—
545C2×C4—52no—
546C2×C4—62no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—102no—
550C2×C4—101no—
551C2×C4—102no—
552C2×C4—101no—
553C2×C4—108no—
554C2×C4—154no—
555C2×C4—154no—
556C2×C4—154no—
557C2×C4—152no—
558C2×C4—3016no—
559C2×C4—3016no—
560C2×C4—301no—
561C2×C4—301no—
562C2×C4—308no—
563C2×C4#676612yes—
564C2×C4C4×D3×D514yes—
565C2×C4C4×D3×D512yes—
566C2×C4#679012yes—
567C2×C3—104no—
568C2×C3C2×C42×D511yescharacteristic
569C2×C3C2×#403911yescharacteristic
570C2×C3#6585611yescharacteristic
571C2×C3C4×D4×D512yes—
572C2×C3C4×#71312yes—
573D3—104no—
574C5C4×#67⋊C411yescharacteristic, complemented, Sylow
575C22—54no—
576C22—102no—
577C22—104no—
578C22—104no—
579C22—102no—
580C22—154no—
581C22—302no—
582C22—304no—
583C22—304no—
584C22—302no—
585C22C2×#676611yescharacteristic
586C22C2×C4×D3×D511yescharacteristic
587C22C2×C4×D3×D512yes—
588C22#9201612yes—
589C22C2×#679011yescharacteristic
590C4—24no—
591C4—34no—
592C4—64no—
593C4—62no—
594C4—102no—
595C4—104no—
596C4—158no—
597C4—302no—
598C4#9139614yesdirect product factor
599C3C4×#403911yescharacteristic, complemented, Sylow
600C2—104no—
601C2—304no—
602C2C4×#676612yes—
603C2#1175266711yescharacteristic
604C2C42×D3×D511yescharacteristic
605C2C2×#9139611yescharacteristic
606C2C4×#679012yes—
subgroupG/H
centerC22×C4C2×D3×D5
commutatorC2×C3×C5C22×C42
FrattiniC23C22×D3×D5
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1202C22
hypercenterC2×C42D3×D5
hypocenterC3×C5C42×D4
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C42×D15C2semidirect
4. C2×C4×D5×Dic3C2semidirect
5. C4×C5×Dic3⋊C4C2semidirect
6. C3×C4×#685C2semidirect
7. #11748884C2semidirect
8. C4×#6667C2semidirect
9. #11748670C2semidirect
10. #11748651C2semidirect
11. C4×Dic3×Dic5C2semidirect
34. C4×#1202C4semidirect
35. #91396C4direct (N × H)
48. C4×#685D3semidirect
62. C2×C4×D15C2×C4semidirect
63. C2×C4×D15C2×C4semidirect
71. C2×C3×C4×D5C2×C4semidirect
76. C2×D5×Dic3C2×C4semidirect
79. C4×Dic15D4semidirect
80. C5×Dic3⋊C4C2×C4semidirect
82. C4×C5×Dic3C2×C4semidirect
83. C3×#685C2×C4semidirect
85. Dic3⋊Dic5C2×C4semidirect
86. #6667C2×C4semidirect
87. #6667C2×C4semidirect
88. #6665C2×C4semidirect
91. Dic3×Dic5C2×C4semidirect
99. C4×Dic3⋊C4D5semidirect
170. #1202C42semidirect
223. C2×C4×D5C4×D3semidirect
231. #685C4×D3semidirect
259. C2×D15C2×C42semidirect
264. C2×C3×D5C2×C42semidirect
266. C3×C4×C5C4×D4semidirect
268. Dic15C4×D4semidirect
273. C5×Dic3C2×C42semidirect
306. Dic3⋊C4C4×D5semidirect
313. C4×Dic3C4×D5semidirect
444. C2×D5C42×D3semidirect
449. C4×C5#67⋊C4semidirect
494. C3×C5C42×D4semidirect
513. C3×C4#4039semidirect
518. Dic3C42×D5semidirect
574. C5C4×#67⋊C4semidirect
598. C4#91396direct (N × H)
599. C3C4×#4039semidirect

Maximal subgroups

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

subgroupindex
C2×C42×D152
C2×C4×#12022
C2×#913962
C2×C4×D5×Dic32
C4×C5×Dic3⋊C42
C3×C4×#6852
#117488842
C4×#66672
#117486702
#117486512
C4×Dic3×Dic52
C4×#40393
C4×#67⋊C45