Finite Group Databasebeta

← D5×#3195 #12969906

Subgroups — D5×#3195 #12969906

Order 1280.

2322 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C22⋊Q8C212yesmaximal
2C5×#3195C211yesmaximal, characteristic, complemented
3#10614473C212yesmaximal, complemented
4#10613180C214yesmaximal, complemented
5D5×#483C214yesmaximal, complemented
6#10612639C214yesmaximal, complemented
7D5×#470C214yesmaximal, complemented
8#10611920C214yesmaximal, complemented
9D5×#451C214yesmaximal, complemented
10#10610377C211yesmaximal, characteristic, complemented
11D5×#407C211yesmaximal, characteristic
12C22×Q8×D5C2212yes—
13C23×C4×D5C2211yescharacteristic
14C2×C5×C22⋊Q8C2212yes—
15C2×#4092C2212yes—
16C2×#4070C2212yes—
17C2×D5×Q16C2214yescomplemented
18C2×D5×M16C2212yes—
19D5×C22⋊Q8—22no—
20D5×C22⋊Q8—22no—
21D5×C22⋊Q8—22no—
22D5×C22⋊Q8—22no—
23D5×C22⋊Q8C2214yes—
24D5×C22⋊Q8C2214yes—
25D5×C22⋊Q8C2214yes—
26D5×C22⋊Q8C2214yes—
27C2×#4043C2212yes—
28C2×#4042—22no—
29C2×D5×C4⋊C4—22no—
30C2×D5×C4⋊C4C2212yes—
31C2×D5×C22⋊C4—22no—
32C2×#4024—22no—
33C5×#483C2214yescomplemented
34C5×#470C2214yescomplemented
35C5×#451C2214yescomplemented
36C5×#407C2211yescharacteristic
37#65517C2214yescomplemented
38#65496C2211yescharacteristic
39#65478C2214yescomplemented
40#65475C2218yescomplemented
41#65426C2214yescomplemented
42#65415C2212yes—
43#65341C2218yescomplemented
44#65339C2214yescomplemented
45#65332C2214yescomplemented
46#65260C2214yescomplemented
47#65157C2214yescomplemented
48#65151C2218yescomplemented
49D5×#106C2214yescomplemented
50#65105C2218yescomplemented
51#65097C2218yescomplemented
52#65094C2218yescomplemented
53D5×#103C2218yescomplemented
54#65028C2214yescomplemented
55#65015C2214yes—
56D5×C22⋊C8C2214yes—
57#65010C2214yescomplemented
58C2×#3195—51nomaximal, Sylow
59C24×D5D411yescharacteristic
60C22×C5×Q8C2312yes—
61C23×C4×C5C2311yescharacteristic
62C23×Dic5D411yescharacteristic
63C2×Q8×D5—22no—
64C2×Q8×D5—22no—
65C2×Q8×D5—48no—
66C2×Q8×D5C2314yes—
67C2×Q8×D5C2314yes—
68C22×C4×D5—22no—
69C22×C4×D5—22no—
70C22×C4×D5—44no—
71C22×C4×D5D412yes—
72C22×C4×D5D412yes—
73C22×C4×D5D411yescharacteristic
74C22×C4×D5D411yescharacteristic
75C22×C4×D5C2311yescharacteristic
76C22×C4×D5C2312yes—
77C22×C4×D5C2312yes—
78C22×C4×D5C2311yescharacteristic
79C22×Dic10—22no—
80C22×Dic10C2312yes—
81C2×C5×Q16C2314yescomplemented
82C2×C5×M16C2312yes—
83C5×C22⋊Q8—22no—
84C5×C22⋊Q8—22no—
85C5×C22⋊Q8C2314yes—
86C5×C22⋊Q8C2314yes—
87C2×C5×C4⋊C4—22no—
88C2×C5×C4⋊C4C2312yes—
89C2×C5×C22⋊C4—22no—
90C2×C22⋊Dic5—22no—
91#4092—22no—
92#4092—22no—
93#4092C2314yes—
94#4092C2314yes—
95C2×#689C2318yescomplemented
96C2×#685—22no—
97C2×#685—22no—
98C2×C4⋊Dic5—22no—
99C2×C4⋊Dic5C2312yes—
100#4070—22no—
101#4070—22no—
102#4070C2314yes—
103#4070C2314yes—
104C2×#683—22no—
105C2×#683—22no—
106C2×#683—22no—
107C2×#681C2312yes—
108D5×Q16—48no—
109D5×M16—44no—
110C2×Dic20C2314yescomplemented
111C2×#676C2314yes—
112C2×C8×D5C2314yes—
113#4043—22no—
114#4043—22no—
115#4043C2314yes—
116#4043C2314yes—
117#4042—24no—
118#4042—24no—
119#4042—24no—
120#4042—24no—
121D5×C4⋊C4—24no—
122D5×C4⋊C4—24no—
123D5×C4⋊C4—24no—
124D5×C4⋊C4—24no—
125D5×C4⋊C4—22no—
126D5×C4⋊C4—22no—
127D5×C4⋊C4C2314yes—
128D5×C4⋊C4C2314yes—
129D5×C22⋊C4—24no—
130D5×C22⋊C4—24no—
131D5×C22⋊C4—24no—
132D5×C22⋊C4—24no—
133#4024—24no—
134#4024—24no—
135#4024—24no—
136#4024—24no—
137C5×#106C2314yescomplemented
138C5×#103C2318yescomplemented
139C5×C22⋊C8C2314yes—
140#3967C2318yescomplemented
141C22⋊#168C2314yes—
142#3952C2318yes—
143#3949C2314yescomplemented
144#3948C2318yescomplemented
145#3942C2318yescomplemented
146#3940C2318yescomplemented
147C22×C22⋊Q8—52no—
148#3195—54no—
149#3195—54no—
150#3195—54no—
151#3195—51no—
152#3195—52no—
153#3195D511yescharacteristic, direct product factor
154C2×#483—54no—
155C2×#470—54no—
156C2×#451—54no—
157C2×#407—51no—
158C24×C5C2×D411yescharacteristic
159C23×D5—28no—
160C23×D5—42no—
161C23×D5C2×D411yescharacteristic
162C23×D5C2×D411yescharacteristic
163C23×D5C2×D412yes—
164C23×D5C2×D412yes—
165C2×C5×Q8—22no—
166C2×C5×Q8—44no—
167C2×C5×Q8C2414yes—
168C22×C4×C5—22no—
169C22×C4×C5—22no—
170C22×C4×C5—42no—
171C22×C4×C5C2×D412yes—
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2412yes—
174C22×C4×C5C2411yescharacteristic
175C22×Dic5—22no—
176C22×Dic5—22no—
177C22×Dic5—42no—
178C22×Dic5C2×D412yes—
179C22×Dic5C2×D411yescharacteristic
180C22×Dic5C2×D411yescharacteristic
181C22×Dic5C2×D412yes—
182Q8×D5—216no—
183Q8×D5—48no—
184Q8×D5—48no—
185Q8×D5—48no—
186C2×C4×D5—28no—
187C2×C4×D5—24no—
188C2×C4×D5—24no—
189C2×C4×D5—24no—
190C2×C4×D5—24no—
191C2×C4×D5—24no—
192C2×C4×D5—44no—
193C2×C4×D5—42no—
194C2×C4×D5—44no—
195C2×C4×D5—42no—
196C2×C4×D5—44no—
197C2×C4×D5—42no—
198C2×C4×D5—48no—
199C2×C4×D5—48no—
200C2×C4×D5C2×D412yes—
201C2×C4×D5C2×D412yes—
202C2×C4×D5C2×D411yescharacteristic
203C2×C4×D5C2×D411yescharacteristic
204C2×C4×D5C2×D412yes—
205C2×C4×D5C2×D412yes—
206C2×C4×D5C2×D412yes—
207C2×C4×D5C2412yes—
208C2×C4×D5C2411yescharacteristic
209C2×C4×D5C2411yescharacteristic
210C2×Dic10—22no—
211C2×Dic10—24no—
212C2×Dic10—24no—
213C2×Dic10—44no—
214C2×Dic10—48no—
215C2×Dic10C2414yes—
216C5×Q16—44no—
217C5×M16—42no—
218C2×C5×C8C2414yes—
219C5×C4⋊C4—24no—
220C5×C4⋊C4—24no—
221C5×C4⋊C4—22no—
222C5×C4⋊C4C2414yes—
223C5×C22⋊C4—24no—
224C5×C22⋊C4—24no—
225C22⋊Dic5—24no—
226C22⋊Dic5—24no—
227#689—48no—
228#685—24no—
229#685—24no—
230#685—24no—
231#685—24no—
232C4⋊Dic5—22no—
233C4⋊Dic5—24no—
234C4⋊Dic5—24no—
235C4⋊Dic5C2414yes—
236#683—24no—
237#683—24no—
238#683—24no—
239#683—24no—
240#683—24no—
241#683—24no—
242#681—42no—
243C2×#168C2414yes—
244Dic20—44no—
245#676—44no—
246C8×D5—28no—
247C23×Q8—52no—
248C24×C4—51no—
249C22×Q16—54no—
250C22×M16—52no—
251C2×C22⋊Q8—52no—
252C2×C22⋊Q8—52no—
253C2×C22⋊Q8—54no—
254C2×C22⋊Q8—54no—
255C2×C22⋊Q8—54no—
256C2×C22⋊Q8—54no—
257C2×C22⋊Q8—52no—
258C2×C22⋊Q8—102no—
259C2×C22⋊Q8—102no—
260C2×C22⋊Q8—102no—
261C2×C22⋊Q8—102no—
262C2×C22⋊Q8—102no—
263C2×C22⋊Q8—102no—
264C2×C22⋊Q8C2×D512yes—
265C22×C4⋊C4—52no—
266C22×C4⋊C4—102no—
267C22×C22⋊C4—102no—
268#483—54no—
269#483—54no—
270#483—58no—
271#483—58no—
272#483—54no—
273#483C2×D514yescomplemented
274#470—54no—
275#470—54no—
276#470—58no—
277#470—54no—
278#470—58no—
279#470C2×D514yescomplemented
280#451—54no—
281#451—58no—
282#451—54no—
283#451—58no—
284#451—54no—
285#451C2×D514yescomplemented
286C2×#106—54no—
287C2×#103—58no—
288#407—51no—
289#407—52no—
290#407—54no—
291#407C2×D511yescharacteristic
292C2×C22⋊C8—54no—
293C23×C5—24no—
294C23×C5—41no—
295C23×C5C22×D411yescharacteristic
296C23×C5C22×D412yes—
297C22×D5—24no—
298C22×D5—24no—
299C22×D5—24no—
300C22×D5—22no—
301C22×D5—24no—
302C22×D5—24no—
303C22×D5—24no—
304C22×D5—41no—
305C22×D5—42no—
306C22×D5—416no—
307C22×D5#13718yes—
308C22×D5C22×D411yescharacteristic
309C22×D5C22×D412yes—
310C22×D5C22×D411yescharacteristic
311C5×Q8—28no—
312C5×Q8—44no—
313C2×C4×C5—22no—
314C2×C4×C5—24no—
315C2×C4×C5—24no—
316C2×C4×C5—24no—
317C2×C4×C5—41no—
318C2×C4×C5—42no—
319C2×C4×C5—44no—
320C2×C4×C5—44no—
321C2×C4×C5C22×D411yescharacteristic
322C2×C4×C5C22×D412yes—
323C2×C4×C5C2511yescharacteristic
324C2×Dic5—24no—
325C2×Dic5—22no—
326C2×Dic5—24no—
327C2×Dic5—24no—
328C2×Dic5—41no—
329C2×Dic5—42no—
330C2×Dic5—44no—
331C2×Dic5—44no—
332C2×Dic5C22×D411yescharacteristic
333C2×Dic5C22×D412yes—
334C2×Dic5C22×D411yescharacteristic
335C4×D5—22no—
336C4×D5—24no—
337C4×D5—22no—
338C4×D5—24no—
339C4×D5—22no—
340C4×D5—24no—
341C4×D5—42no—
342C4×D5—42no—
343C4×D5—42no—
344C4×D5—48no—
345C4×D5—48no—
346C4×D5—48no—
347C4×D5—48no—
348C4×D5H(5,𝔽2)14yes—
349Dic10—28no—
350Dic10—48no—
351Dic10—44no—
352Dic10—48no—
353C5×C8—24no—
354#168—24no—
355C25—51no—
356C22×Q8—54no—
357C22×Q8—54no—
358C22×Q8—52no—
359C22×Q8—102no—
360C22×Q8—102no—
361C22×Q8—102no—
362C22×Q8—208no—
363C22×Q8C22×D512yes—
364C23×C4—51no—
365C23×C4—52no—
366C23×C4—51no—
367C23×C4—52no—
368C23×C4—52no—
369C23×C4—51no—
370C23×C4—51no—
371C23×C4—52no—
372C23×C4—51no—
373C23×C4—102no—
374C23×C4—102no—
375C23×C4—204no—
376C23×C4C22×D511yescharacteristic
377C2×Q16—58no—
378C2×Q16—54no—
379C2×Q16—208no—
380C2×Q16C22×D514yescomplemented
381C2×M16—52no—
382C2×M16—54no—
383C2×M16—204no—
384C2×M16C22×D512yes—
385C22×C8—54no—
386C22⋊Q8—22no—
387C22⋊Q8—22no—
388C22⋊Q8—54no—
389C22⋊Q8—54no—
390C22⋊Q8—54no—
391C22⋊Q8—54no—
392C22⋊Q8—54no—
393C22⋊Q8—54no—
394C22⋊Q8—104no—
395C22⋊Q8—104no—
396C22⋊Q8—104no—
397C22⋊Q8—104no—
398C22⋊Q8—104no—
399C22⋊Q8—104no—
400C22⋊Q8—104no—
401C22⋊Q8—104no—
402C22⋊Q8—102no—
403C22⋊Q8—102no—
404C22⋊Q8—102no—
405C22⋊Q8—102no—
406C22⋊Q8—102no—
407C22⋊Q8—102no—
408C22⋊Q8C22×D514yes—
409C22⋊Q8C22×D514yes—
410C2×C4⋊C4—22no—
411C2×C4⋊C4—52no—
412C2×C4⋊C4—54no—
413C2×C4⋊C4—54no—
414C2×C4⋊C4—102no—
415C2×C4⋊C4—102no—
416C2×C4⋊C4—104no—
417C2×C4⋊C4—104no—
418C2×C4⋊C4—104no—
419C2×C4⋊C4—104no—
420C2×C4⋊C4—102no—
421C2×C4⋊C4—102no—
422C2×C4⋊C4—102no—
423C2×C4⋊C4—102no—
424C2×C4⋊C4C22×D512yes—
425C2×C22⋊C4—22no—
426C2×C22⋊C4—104no—
427C2×C22⋊C4—104no—
428C2×C22⋊C4—104no—
429C2×C22⋊C4—104no—
430C2×C22⋊C4—102no—
431C2×C22⋊C4—102no—
432C2×C22⋊C4—102no—
433#106—54no—
434#106—58no—
435#106C22×D514yescomplemented
436#103—58no—
437#103—58no—
438#103—58no—
439#103C22×D518yescomplemented
440C22⋊C8—54no—
441C22⋊C8—58no—
442C22⋊C8C22×D514yes—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—21no—
446C22×C5—22no—
447C22×C5—44no—
448C22×C5C2×#13714yes—
449C22×C5C23×D411yescharacteristic
450C2×D5—22no—
451C2×D5—22no—
452C2×D5—216no—
453C2×D5—21no—
454C2×D5—22no—
455C2×D5—44no—
456C2×D5—48no—
457C2×D5—44no—
458C2×D5#53412yes—
459C2×D5C2×#13714yes—
460C2×D5C2×#13714yes—
461C4×C5—22no—
462C4×C5—21no—
463C4×C5—44no—
464C4×C5—44no—
465C4×C5C2×H(5,𝔽2)12yes—
466Dic5—22no—
467Dic5—21no—
468Dic5—44no—
469Dic5—44no—
470Dic5#53412yes—
471C24—52no—
472C24—51no—
473C24—51no—
474C24—52no—
475C24—108no—
476C24—202no—
477C24D4×D511yescharacteristic
478C2×Q8—22no—
479C2×Q8—44no—
480C2×Q8—54no—
481C2×Q8—104no—
482C2×Q8—104no—
483C2×Q8—1016no—
484C2×Q8—102no—
485C2×Q8—204no—
486C2×Q8—208no—
487C2×Q8—208no—
488C2×Q8—208no—
489C2×Q8—208no—
490C2×Q8C23×D514yes—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—42no—
494C22×C4—51no—
495C22×C4—52no—
496C22×C4—51no—
497C22×C4—52no—
498C22×C4—51no—
499C22×C4—51no—
500C22×C4—52no—
501C22×C4—52no—
502C22×C4—51no—
503C22×C4—52no—
504C22×C4—51no—
505C22×C4—52no—
506C22×C4—52no—
507C22×C4—52no—
508C22×C4—104no—
509C22×C4—108no—
510C22×C4—104no—
511C22×C4—104no—
512C22×C4—104no—
513C22×C4—104no—
514C22×C4—102no—
515C22×C4—102no—
516C22×C4—202no—
517C22×C4—204no—
518C22×C4—202no—
519C22×C4—204no—
520C22×C4—202no—
521C22×C4—204no—
522C22×C4—208no—
523C22×C4—208no—
524C22×C4—202no—
525C22×C4D4×D512yes—
526C22×C4D4×D511yescharacteristic
527C22×C4C23×D512yes—
528C22×C4C23×D511yescharacteristic
529Q16—44no—
530Q16—204no—
531Q16—208no—
532M16—42no—
533M16—204no—
534M16—202no—
535C2×C8—54no—
536C2×C8—108no—
537C2×C8C23×D514yes—
538C4⋊C4—24no—
539C4⋊C4—24no—
540C4⋊C4—22no—
541C4⋊C4—54no—
542C4⋊C4—104no—
543C4⋊C4—104no—
544C4⋊C4—104no—
545C4⋊C4—104no—
546C4⋊C4—104no—
547C4⋊C4—104no—
548C4⋊C4—102no—
549C4⋊C4—104no—
550C4⋊C4—104no—
551C4⋊C4C23×D514yes—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C22⋊C4—104no—
555C22⋊C4—104no—
556C22⋊C4—104no—
557C22⋊C4—104no—
558C22⋊C4—104no—
559C22⋊C4—104no—
560C2×C5—24no—
561C2×C5—41no—
562C2×C5C2×#53411yescharacteristic
563C2×C5C22×#13712yes—
564D5—24no—
565D5—41no—
566D5#319514yesdirect product factor
567C23—24no—
568C23—41no—
569C23—51no—
570C23—58no—
571C23—52no—
572C23—51no—
573C23—104no—
574C23—104no—
575C23—102no—
576C23—104no—
577C23—104no—
578C23—104no—
579C23—104no—
580C23—202no—
581C23—201no—
582C23—2016no—
583C23C2×D4×D511yescharacteristic
584C23C2×D4×D512yes—
585Q8—28no—
586Q8—44no—
587Q8—108no—
588Q8—204no—
589Q8—208no—
590Q8—208no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—41no—
596C2×C4—42no—
597C2×C4—44no—
598C2×C4—44no—
599C2×C4—51no—
600C2×C4—54no—
601C2×C4—51no—
602C2×C4—52no—
603C2×C4—104no—
604C2×C4—102no—
605C2×C4—104no—
606C2×C4—102no—
607C2×C4—104no—
608C2×C4—102no—
609C2×C4—102no—
610C2×C4—104no—
611C2×C4—104no—
612C2×C4—104no—
613C2×C4—202no—
614C2×C4—202no—
615C2×C4—202no—
616C2×C4—208no—
617C2×C4—208no—
618C2×C4—208no—
619C2×C4—208no—
620C2×C4—201no—
621C2×C4—202no—
622C2×C4—204no—
623C2×C4—204no—
624C2×C4C2×D4×D511yescharacteristic
625C2×C4C2×D4×D512yes—
626C2×C4C24×D511yescharacteristic
627C8—24no—
628C8—104no—
629C5C2×#319511yescharacteristic, complemented, Sylow
630C22—22no—
631C22—22no—
632C22—21no—
633C22—22no—
634C22—44no—
635C22—52no—
636C22—54no—
637C22—54no—
638C22—1016no—
639C22—102no—
640C22—102no—
641C22—101no—
642C22—102no—
643C22—208no—
644C22—204no—
645C22—204no—
646C22D5×#13714yes—
647C22C22×D4×D511yescharacteristic
648C4—22no—
649C4—21no—
650C4—44no—
651C4—44no—
652C4—52no—
653C4—102no—
654C4—101no—
655C4—204no—
656C4—204no—
657C4D5×H(5,𝔽2)12yes—
658C2—24no—
659C2—41no—
660C2—54no—
661C2—104no—
662C2—201no—
663C2D5×#53411yescharacteristic
664C2C2×D5×#13712yes—
subgroupG/H
centerC22C22×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3195C2
socleC22×C5C23×D4
prime radicalC24×D5D4
hypercenter#3195D5
hypocenterC5C2×#3195
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3195

Complements

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

NH ≅ G/Ntype
2. C5×#3195C2semidirect
3. #10614473C2semidirect
4. #10613180C2semidirect
5. D5×#483C2semidirect
6. #10612639C2semidirect
7. D5×#470C2semidirect
8. #10611920C2semidirect
9. D5×#451C2semidirect
10. #10610377C2semidirect
17. C2×D5×Q16C22semidirect
33. C5×#483C22semidirect
34. C5×#470C22semidirect
35. C5×#451C22semidirect
37. #65517C22semidirect
39. #65478C22semidirect
40. #65475C22semidirect
41. #65426C22semidirect
43. #65341C22semidirect
44. #65339C22semidirect
45. #65332C22semidirect
46. #65260C22semidirect
47. #65157C22semidirect
48. #65151C22semidirect
49. D5×#106C22semidirect
50. #65105C22semidirect
51. #65097C22semidirect
52. #65094C22semidirect
53. D5×#103C22semidirect
54. #65028C22semidirect
57. #65010C22semidirect
81. C2×C5×Q16C23semidirect
95. C2×#689C23semidirect
110. C2×Dic20C23semidirect
137. C5×#106C23semidirect
138. C5×#103C23semidirect
140. #3967C23semidirect
143. #3949C23semidirect
144. #3948C23semidirect
145. #3942C23semidirect
146. #3940C23semidirect
153. #3195D5direct (N × H)
273. #483C2×D5semidirect
279. #470C2×D5semidirect
285. #451C2×D5semidirect
380. C2×Q16C22×D5semidirect
435. #106C22×D5semidirect
439. #103C22×D5semidirect
566. D5#3195direct (N × H)
629. C5C2×#3195semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C22⋊Q82
C5×#31952
#106144732
#106131802
D5×#4832
#106126392
D5×#4702
#106119202
D5×#4512
#106103772
D5×#4072
C2×#31955