Finite Group Databasebeta

← D5⋊#4720 #14413896

Subgroups — D5⋊#4720 #14413896

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#926C211yesmaximal, characteristic
2D5⋊#830C211yesmaximal, characteristic
3C3×D5⋊(C22⋊C8)C211yesmaximal, characteristic
4#11751990C212yesmaximal, complemented
5#11751989C212yesmaximal, complemented
6D5⋊(Dic3⋊C8)C211yesmaximal, characteristic, complemented
7D5⋊(Dic3⋊C8)C211yesmaximal, characteristic, complemented
8#11751788C211yesmaximal, characteristic, complemented
9#11751770C212yesmaximal, complemented
10#11751769C212yesmaximal, complemented
11Dic3×D5⋊C8C211yesmaximal, characteristic, complemented
12D5⋊#433—31nomaximal, Hall
13C22×C3×C4×D5C2211yescharacteristic
14C2×D5⋊(C3⋊C8)C2211yescharacteristic
15C2×D5⋊(C3⋊C8)C2211yescharacteristic
16C2×C3×D5⋊C8C2211yescharacteristic
17C2×C3×D5⋊C8C2211yescharacteristic
18#91815C411yescharacteristic
19C5×#926C411yescharacteristic
20D5×#217C411yescharacteristic
21D5×#217C411yescharacteristic
22#91528C2211yescharacteristic
23#91528C2211yescharacteristic
24D5×C4⋊Dic3C411yescharacteristic
25D5×C4⋊Dic3C411yescharacteristic
26C4×D5×Dic3C2211yescharacteristic
27C4×D5×Dic3C2211yescharacteristic
28#91358C2211yescharacteristic
29#91358C2211yescharacteristic
30#91357C411yescharacteristic
31#91357C411yescharacteristic
32#91241C2212yes—
33#91232C2212yes—
34C3×C22⋊#170C2212yes—
35C3×#4003C2212yes—
36#91177C2212yescomplemented
37#91177C2212yescomplemented
38Dic3⋊#170C2212yescomplemented
39Dic3⋊#170C2212yescomplemented
40#91169C2212yescomplemented
41#91169C2212yescomplemented
42Dic3×#170C2212yescomplemented
43Dic3×#170C2212yescomplemented
44C2×#4720—51nomaximal, Hall
45D5×#117—31no—
46D5⋊(C22⋊C8)—31no—
47D5⋊(C22⋊C8)D311yescharacteristic
48#65706—32no—
49#65706—32no—
50#65697—32no—
51#65697—32no—
52D5⋊(C4⋊C8)—31no—
53D5⋊(C4⋊C8)—31no—
54#65676—31no—
55C4×D5⋊C8—31no—
56C23×C3×D5C2×C411yescharacteristic
57C22×C3×C4×C5C2×C411yescharacteristic
58C22×C3×Dic5C2311yescharacteristic
59C2×C3×C4×D5—22no—
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5C2×C411yescharacteristic
62C2×C3×C4×D5C2×C411yescharacteristic
63C2×C3×C4×D5C2311yescharacteristic
64C2×C3×C4×D5C2311yescharacteristic
65C2×D5×Dic3C2×C411yescharacteristic
66C2×D5×Dic3C2×C411yescharacteristic
67C2×D5×Dic3C2×C411yescharacteristic
68C2×D5×Dic3C2×C411yescharacteristic
69C2×C3⋊#170C2312yes—
70C2×C3⋊#170C2312yes—
71D5⋊(C3⋊C8)—22no—
72D5⋊(C3⋊C8)—22no—
73C2×C3×#170C2312yes—
74C2×C3×#170C2312yes—
75C3×D5⋊C8—22no—
76C3×D5⋊C8—22no—
77#6719C2×C411yescharacteristic
78#6719C2×C411yescharacteristic
79C4⋊Dic15C2×C411yescharacteristic
80C4⋊Dic15C2×C411yescharacteristic
81C4×Dic15C2×C411yescharacteristic
82C4×Dic15C2×C411yescharacteristic
83C5×#217C2×C411yescharacteristic
84C5×#217C2×C411yescharacteristic
85C5×C4⋊Dic3C2×C411yescharacteristic
86C5×C4⋊Dic3C2×C411yescharacteristic
87C4×C5×Dic3C2×C411yescharacteristic
88C4×C5×Dic3C2×C411yescharacteristic
89#6668C2×C411yescharacteristic
90#6668C2×C411yescharacteristic
91#6668C2×C411yescharacteristic
92#6668C2×C411yescharacteristic
93#6665C2×C411yescharacteristic
94#6665C2×C411yescharacteristic
95#6665C2×C411yescharacteristic
96#6665C2×C411yescharacteristic
97Dic3×Dic5C2311yescharacteristic
98Dic3×Dic5C2311yescharacteristic
99Dic3×Dic5C2311yescharacteristic
100Dic3×Dic5C2311yescharacteristic
101C2×#926—51no—
102C2×C3×C22⋊C8—51no—
103C2×#830—51no—
104C2×#815—51no—
105C2×Dic3⋊C8—51no—
106C2×Dic3⋊C8—51no—
107C2×C8×Dic3—51no—
108#4720—52no—
109#4720—52no—
110#4720—52no—
111#4720—52no—
112C22×C4×D5C2×D311yescharacteristic
113C2×D5⋊C8—31no—
114C2×D5⋊C8—31no—
115C2×D5⋊C8C2×D311yescharacteristic
116C2×D5⋊C8C2×D311yescharacteristic
117C5×#117—31no—
118#4072—31no—
119#4038—31no—
120#4038—31no—
121D5×C4⋊C4—31no—
122D5×C4⋊C4—31no—
123D5×C22⋊C4—31no—
124D5×C22⋊C4—31no—
125#4023—31no—
126#4023—31no—
127#4018—31no—
128#4018—31no—
129C42×D5—31no—
130C42×D5—31no—
131C22⋊#170—32no—
132C22⋊#170C2×D312yes—
133#4004—32no—
134#4004—32no—
135#4003—32no—
136#4003C2×D312yes—
137#4002—32no—
138#4002—32no—
139C4⋊#170—32no—
140C4⋊#170—32no—
141C4×#170—32no—
142C4×#170—32no—
143C2×#433—151noSylow
144C23×C3×C5C22×C411yescharacteristic
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5C22×C411yescharacteristic
149C22×C3×D5C22×C411yescharacteristic
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5C22×C411yescharacteristic
152C2×C3×C4×C5C22×C411yescharacteristic
153C2×Dic15C22×C411yescharacteristic
154C2×Dic15C22×C411yescharacteristic
155C2×Dic15C22×C411yescharacteristic
156C2×Dic15C22×C411yescharacteristic
157C2×C5×Dic3C22×C411yescharacteristic
158C2×C5×Dic3C22×C411yescharacteristic
159C2×C5×Dic3C22×C411yescharacteristic
160C2×C5×Dic3C22×C411yescharacteristic
161C2×C3×Dic5—21no—
162C2×C3×Dic5—21no—
163C2×C3×Dic5C22×C411yescharacteristic
164C2×C3×Dic5C2411yescharacteristic
165C3×C4×D5—22no—
166C3×C4×D5—22no—
167C3×C4×D5—21no—
168C3×C4×D5—21no—
169C3×C4×D5#4112yes—
170C3×C4×D5#4112yes—
171D5×Dic3—22no—
172D5×Dic3—22no—
173D5×Dic3—22no—
174D5×Dic3—22no—
175C3⋊#170—22no—
176C3⋊#170—22no—
177C3×#170—22no—
178C3×#170—22no—
179C23×C3×C4—51no—
180C22×C3×C8—51no—
181C22×C3×C8—51no—
182C2×#217—51no—
183C2×#217—51no—
184#926—51no—
185#926—51no—
186#926—51no—
187#926—51no—
188#926—51no—
189#926—51no—
190#926—51no—
191#926AGL(1,𝔽5)11yescharacteristic
192C2×C4⋊Dic3—51no—
193C2×C4⋊Dic3—51no—
194C2×C4×Dic3—51no—
195C2×C4×Dic3—51no—
196C22×C3⋊C8—51no—
197C22×C3⋊C8—51no—
198C3×C22⋊C8—52no—
199C3×C22⋊C8—52no—
200#830—52no—
201#830—52no—
202#815—52no—
203#815—52no—
204Dic3⋊C8—52no—
205Dic3⋊C8—52no—
206Dic3⋊C8—52no—
207Dic3⋊C8—52no—
208C8×Dic3—52no—
209C8×Dic3—52no—
210C23×D5C4×D311yescharacteristic
211C22×C4×C5C4×D311yescharacteristic
212C22×Dic5C22×D311yescharacteristic
213C2×C4×D5—22no—
214C2×C4×D5—22no—
215C2×C4×D5—31no—
216C2×C4×D5—31no—
217C2×C4×D5—31no—
218C2×C4×D5—31no—
219C2×C4×D5C4×D311yescharacteristic
220C2×C4×D5C4×D311yescharacteristic
221C2×C4×D5C22×D311yescharacteristic
222C2×C4×D5C22×D311yescharacteristic
223C2×#170—32no—
224C2×#170—32no—
225C2×#170C22×D312yes—
226C2×#170C22×D312yes—
227D5⋊C8—22no—
228D5⋊C8—22no—
229D5⋊C8—62no—
230D5⋊C8—62no—
231C5×C4⋊C4—31no—
232C5×C4⋊C4—31no—
233C5×C22⋊C4—31no—
234C5×C22⋊C4—31no—
235C42×C5—31no—
236C42×C5—31no—
237C22⋊Dic5—31no—
238C22⋊Dic5—31no—
239#685—31no—
240#685—31no—
241#685—31no—
242#685—31no—
243C4⋊Dic5—31no—
244C4⋊Dic5—31no—
245#683—31no—
246#683—31no—
247#683—31no—
248#683—31no—
249C4×Dic5—31no—
250C4×Dic5—31no—
251C4×Dic5—31no—
252C4×Dic5—31no—
253C4×Dic5—31no—
254C4×Dic5—31no—
255C2×#117—151no—
256#433—152no—
257#433—152no—
258#433—152no—
259#433—152no—
260C2×C4⋊C8—151no—
261C2×C4⋊C8—151no—
262C2×C22⋊C8—51no—
263C2×C22⋊C8—151no—
264C2×#97—151no—
265C2×C4×C8—151no—
266C22×C3×C5—21no—
267C22×C3×C5—21no—
268C22×C3×C5—21no—
269C22×C3×C5C23×C411yescharacteristic
270C2×C3×D5—21no—
271C2×C3×D5—21no—
272C2×C3×D5—21no—
273C2×C3×D5—44no—
274C2×C3×D5#11712yes—
275C2×C3×D5#13112yes—
276C2×C3×D5#13112yes—
277C3×C4×C5—21no—
278C3×C4×C5#11712yes—
279Dic15—21no—
280Dic15—21no—
281Dic15—21no—
282Dic15—21no—
283C3×Dic5—21no—
284C3×Dic5C2×#4111yescharacteristic
285C3×Dic5C2×#4111yescharacteristic
286C5×Dic3—21no—
287C5×Dic3—21no—
288C5×Dic3—21no—
289C5×Dic3—21no—
290C24×C3—51no—
291C22×C3×C4—51no—
292C22×C3×C4—51no—
293C22×C3×C4—51no—
294C22×C3×C4—51no—
295C22×C3×C4—51no—
296C22×C3×C4—102no—
297C22×C3×C4—102no—
298C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
299C22×Dic3—51no—
300C22×Dic3—51no—
301C22×Dic3—51no—
302C22×Dic3—51no—
303C2×C3×C8—52no—
304C2×C3×C8—52no—
305C2×C3×C8—102no—
306C2×C3×C8—102no—
307#217—51no—
308#217—51no—
309#217—51no—
310#217—51no—
311#217—51no—
312#217—51no—
313#217C2×AGL(1,𝔽5)11yescharacteristic
314#217C2×AGL(1,𝔽5)11yescharacteristic
315C4⋊Dic3—51no—
316C4⋊Dic3—51no—
317C4⋊Dic3—51no—
318C4⋊Dic3—51no—
319C4⋊Dic3—51no—
320C4⋊Dic3—51no—
321C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
322C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
323C4×Dic3—51no—
324C4×Dic3—51no—
325C4×Dic3—51no—
326C4×Dic3—51no—
327C4×Dic3—51no—
328C4×Dic3—51no—
329C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
330C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
331C2×C3⋊C8—52no—
332C2×C3⋊C8—52no—
333C2×C3⋊C8—102no—
334C2×C3⋊C8—102no—
335C23×C5C2×C4×D311yescharacteristic
336C22×D5—22no—
337C22×D5—22no—
338C22×D5—22no—
339C22×D5C2×C4×D311yescharacteristic
340C22×D5C2×C4×D311yescharacteristic
341C2×C4×C5—22no—
342C2×C4×C5—31no—
343C2×C4×C5—31no—
344C2×C4×C5—31no—
345C2×C4×C5—31no—
346C2×C4×C5C2×C4×D311yescharacteristic
347C2×C4×C5C2×C4×D311yescharacteristic
348C2×Dic5—21no—
349C2×Dic5—21no—
350C2×Dic5—31no—
351C2×Dic5—31no—
352C2×Dic5—31no—
353C2×Dic5—31no—
354C2×Dic5C2×C4×D311yescharacteristic
355C2×Dic5C23×D311yescharacteristic
356C4×D5—22no—
357C4×D5—22no—
358C4×D5—21no—
359C4×D5—21no—
360C4×D5—62no—
361C4×D5—62no—
362C4×D5—62no—
363C4×D5—62no—
364C4×D5#23712yes—
365C4×D5#23712yes—
366#170—22no—
367#170—22no—
368#170—62no—
369#170—62no—
370C23×C4—51no—
371C22×C8—51no—
372C22×C8—51no—
373C22×C8—151no—
374C22×C8—151no—
375#117—31no—
376#117—151no—
377#117—151no—
378#117—151no—
379#117—151no—
380#117—151no—
381#117—151no—
382#117—151no—
383C2×C4⋊C4—151no—
384C2×C4⋊C4—151no—
385C2×C22⋊C4—151no—
386C2×C22⋊C4—151no—
387C2×C42—151no—
388C2×C42—151no—
389C4⋊C8—152no—
390C4⋊C8—152no—
391C4⋊C8—152no—
392C4⋊C8—152no—
393C22⋊C8—52no—
394C22⋊C8—52no—
395C22⋊C8—152no—
396C22⋊C8—152no—
397#97—152no—
398#97—152no—
399C4×C8—152no—
400C4×C8—152no—
401C2×C3×C5—41no—
402C2×C3×C5C2×#11711yescharacteristic
403C2×C3×C5C2×#13111yescharacteristic
404C2×C3×C5C2×#13111yescharacteristic
405C3×D5—41no—
406C3×D5#43314yescomplemented
407C23×C3—51no—
408C23×C3—51no—
409C23×C3—102no—
410C23×C3—102no—
411C23×C3—102no—
412C23×C3C22×AGL(1,𝔽5)11yescharacteristic
413C2×C3×C4—22no—
414C2×C3×C4—51no—
415C2×C3×C4—52no—
416C2×C3×C4—52no—
417C2×C3×C4—51no—
418C2×C3×C4—101no—
419C2×C3×C4—101no—
420C2×C3×C4—102no—
421C2×C3×C4—101no—
422C2×C3×C4—101no—
423C2×C3×C4—102no—
424C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
425C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
426C2×Dic3—51no—
427C2×Dic3—51no—
428C2×Dic3—51no—
429C2×Dic3—51no—
430C2×Dic3—102no—
431C2×Dic3—102no—
432C2×Dic3—102no—
433C2×Dic3—102no—
434C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
435C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
436C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
437C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
438C3×C8—102no—
439C3×C8—102no—
440C3⋊C8—102no—
441C3⋊C8—102no—
442C22×C5—21no—
443C22×C5—21no—
444C22×C5—21no—
445C22×C5C22×C4×D311yescharacteristic
446C2×D5—21no—
447C2×D5—21no—
448C2×D5—21no—
449C2×D5—44no—
450C2×D5#87712yes—
451C2×D5#90112yes—
452C2×D5#90712yes—
453C4×C5—21no—
454C4×C5—61no—
455C4×C5—61no—
456C4×C5—61no—
457C4×C5—61no—
458C4×C5#87712yes—
459Dic5—21no—
460Dic5—61no—
461Dic5—61no—
462Dic5—61no—
463Dic5—61no—
464Dic5C2×#23711yescharacteristic
465Dic5C2×#23711yescharacteristic
466C24—51no—
467C22×C4—51no—
468C22×C4—51no—
469C22×C4—51no—
470C22×C4—51no—
471C22×C4—51no—
472C22×C4—102no—
473C22×C4—102no—
474C22×C4—151no—
475C22×C4—151no—
476C22×C4—151no—
477C22×C4—151no—
478C22×C4D3×AGL(1,𝔽5)11yescharacteristic
479C2×C8—52no—
480C2×C8—52no—
481C2×C8—102no—
482C2×C8—102no—
483C2×C8—152no—
484C2×C8—152no—
485C2×C8—302no—
486C2×C8—302no—
487C4⋊C4—31no—
488C4⋊C4—31no—
489C4⋊C4—151no—
490C4⋊C4—151no—
491C4⋊C4—151no—
492C4⋊C4—151no—
493C4⋊C4—151no—
494C4⋊C4—151no—
495C22⋊C4—31no—
496C22⋊C4—31no—
497C22⋊C4—151no—
498C22⋊C4—151no—
499C22⋊C4—151no—
500C22⋊C4—151no—
501C22⋊C4—151no—
502C22⋊C4—151no—
503C42—31no—
504C42—31no—
505C42—151no—
506C42—151no—
507C42—151no—
508C42—151no—
509C42—151no—
510C42—151no—
511C3×C5C2×#43311yescharacteristic, complemented, Hall
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—52no—
516C22×C3—52no—
517C22×C3—52no—
518C22×C3—101no—
519C22×C3—101no—
520C22×C3—101no—
521C22×C3—204no—
522C22×C3C23×AGL(1,𝔽5)11yescharacteristic
523C3×C4—21no—
524C3×C4—51no—
525C3×C4—51no—
526C3×C4—101no—
527C3×C4#413012yes—
528Dic3—21no—
529Dic3—21no—
530Dic3—21no—
531Dic3—21no—
532Dic3—101no—
533Dic3—101no—
534Dic3—101no—
535Dic3—101no—
536C2×C5—41no—
537C2×C5C2×#87711yescharacteristic
538C2×C5C2×#90111yescharacteristic
539C2×C5C2×#90711yescharacteristic
540D5—41no—
541D5#472014yescomplemented
542C23—51no—
543C23—51no—
544C23—102no—
545C23—102no—
546C23—102no—
547C23C2×D3×AGL(1,𝔽5)11yescharacteristic
548C2×C4—22no—
549C2×C4—31no—
550C2×C4—31no—
551C2×C4—31no—
552C2×C4—31no—
553C2×C4—51no—
554C2×C4—52no—
555C2×C4—52no—
556C2×C4—51no—
557C2×C4—101no—
558C2×C4—101no—
559C2×C4—102no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—102no—
563C2×C4—151no—
564C2×C4—151no—
565C2×C4—151no—
566C2×C4—151no—
567C2×C4—302no—
568C2×C4—302no—
569C2×C4—302no—
570C2×C4—302no—
571C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
572C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
573C8—102no—
574C8—102no—
575C8—302no—
576C8—302no—
577C2×C3—41no—
578C2×C3—54no—
579C2×C3—201no—
580C2×C3C2×#413011yescharacteristic
581C2×C3D5⋊#13111yescharacteristic
582C2×C3D5⋊#13111yescharacteristic
583C5C2×#472011yescharacteristic, complemented, Sylow
584C22—21no—
585C22—21no—
586C22—21no—
587C22—52no—
588C22—52no—
589C22—52no—
590C22—101no—
591C22—101no—
592C22—101no—
593C22—204no—
594C22C22×D3×AGL(1,𝔽5)11yescharacteristic
595C4—21no—
596C4—51no—
597C4—51no—
598C4—61no—
599C4—61no—
600C4—61no—
601C4—61no—
602C4—101no—
603C4—301no—
604C4—301no—
605C4—301no—
606C4—301no—
607C4#9192312yes—
608C3D5⋊#43311yescharacteristic, complemented, Sylow
609C2—41no—
610C2—54no—
611C2—201no—
612C2D5⋊#90111yescharacteristic
613C2D5⋊#90711yescharacteristic
614C2C2×#9192311yescharacteristic
subgroupG/H
centerC2×C4C2×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FrattiniC22C22×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
prime radicalC23×C3×D5C2×C4
cosocleC2×C3×Dic5C24
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#433
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #11751990C2semidirect
5. #11751989C2semidirect
6. D5⋊(Dic3⋊C8)C2semidirect
7. D5⋊(Dic3⋊C8)C2semidirect
8. #11751788C2semidirect
9. #11751770C2semidirect
10. #11751769C2semidirect
11. Dic3×D5⋊C8C2semidirect
36. #91177C22semidirect
37. #91177C22semidirect
38. Dic3⋊#170C22semidirect
39. Dic3⋊#170C22semidirect
40. #91169C22semidirect
41. #91169C22semidirect
42. Dic3×#170C22semidirect
43. Dic3×#170C22semidirect
406. C3×D5#433semidirect
511. C3×C5C2×#433semidirect
541. D5#4720semidirect
583. C5C2×#4720semidirect
608. C3D5⋊#433semidirect

Maximal subgroups

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

subgroupindex
D5×#9262
D5⋊#8302
C3×D5⋊(C22⋊C8)2
#117519902
#117519892
D5⋊(Dic3⋊C8)2
#117517882
#117517702
#117517692
Dic3×D5⋊C82
D5⋊#4333
C2×#47205