Finite Group Databasebeta

← D5×#3230 #12971344

Subgroups — D5×#3230 #12971344

Order 1280.

2006 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#533C211yesmaximal, characteristic
2C2×D5×C4⋊Q8C211yesmaximal, characteristic
3C5×#3230C211yesmaximal, characteristic, complemented
4#10615055C211yesmaximal, characteristic, complemented
5#10614955C211yesmaximal, characteristic, complemented
6#10613674C212yesmaximal, complemented
7D5×#500C212yesmaximal, complemented
8#10613339C212yesmaximal, complemented
9D5×#487C212yesmaximal, complemented
10D5×#484C214yesmaximal
11#10613189C214yesmaximal, complemented
12#10612843C214yesmaximal, complemented
13D5×#477C214yesmaximal, complemented
14D5×#431C211yesmaximal, characteristic
15#10611003C211yesmaximal, characteristic, complemented
16C22×Q8×D5—21no—
17C5×#533C2211yescharacteristic
18C2×C5×C4⋊Q8C2211yescharacteristic
19C2×#4090—21no—
20#66062C2211yescharacteristic
21#66062C2211yescharacteristic
22D5×C4⋊Q8—21no—
23D5×C4⋊Q8—21no—
24D5×C4⋊Q8—21no—
25D5×C4⋊Q8—21no—
26D5×C4⋊Q8C2211yescharacteristic
27D5×C4⋊Q8C2212yes—
28D5×C4⋊Q8C2212yes—
29D5×C4⋊Q8C2212yes—
30D5×C4⋊Q8C2212yes—
31D5×C4⋊Q8C2211yescharacteristic
32#66022—21no—
33D5×#125—21no—
34D5×C22⋊Q8—21no—
35D5×C22⋊Q8C2212yes—
36#65956—21no—
37#65956C2212yes—
38#65912—21no—
39#65912C2212yes—
40C4×Q8×D5—21no—
41C4×Q8×D5C2212yes—
42D5×#117—21no—
43#65851—21no—
44C2×D5×C4⋊C4—21no—
45C2×D5×C4⋊C4C2212yes—
46C2×#4034—21no—
47C2×#4034C2212yes—
48C2×C42×D5C2211yescharacteristic
49#65804C2211yescharacteristic
50C2×#4015C2211yescharacteristic
51C5×#500C2212yescomplemented
52C5×#487C2212yescomplemented
53C5×#484C2214yes—
54C5×#477C2214yescomplemented
55C5×#431C2211yescharacteristic
56#65382C2212yescomplemented
57#65380C2214yescomplemented
58#65370C2212yescomplemented
59#65367C2212yescomplemented
60#65367C2212yescomplemented
61#65333C2214yes—
62#65310C2214yescomplemented
63#65259C2214yes—
64#65214C2211yescharacteristic
65#65173C2218yes—
66D5×#107C2218yes—
67#65164C2218yescomplemented
68#65163C2218yescomplemented
69#65139C2214yescomplemented
70#65122C2212yes—
71D5×C4⋊C8C2212yes—
72#65098C2218yes—
73D5×#103C2218yes—
74#65083C2218yescomplemented
75#65081C2218yescomplemented
76D5×C22⋊C8C2212yes—
77#65011C2214yes—
78#65007C2212yes—
79#64974C2212yes—
80C4×C8×D5C2212yes—
81#64971C2212yescomplemented
82#64970C2212yescomplemented
83C2×#3230—51nomaximal, Sylow
84C22×C5×Q8—21no—
85C2×Q8×D5—22no—
86C2×Q8×D5—22no—
87C2×Q8×D5—22no—
88C2×Q8×D5—22no—
89C2×Q8×D5—21no—
90C2×Q8×D5—48no—
91C2×Q8×D5C2312yes—
92C22×C4×D5—22no—
93C22×C4×D5D411yescharacteristic
94C22×C4×D5D411yescharacteristic
95C22×C4×D5C2311yescharacteristic
96C22×Dic10—21no—
97C22×Dic10—22no—
98C5×C4⋊Q8—21no—
99C5×C4⋊Q8—21no—
100C5×C4⋊Q8C2311yescharacteristic
101C5×C4⋊Q8C2312yes—
102C5×C4⋊Q8C2312yes—
103C5×C4⋊Q8C2311yescharacteristic
104C5×#125—21no—
105C5×C22⋊Q8—21no—
106C5×C22⋊Q8C2312yes—
107C4×C5×Q8—21no—
108C4×C5×Q8C2312yes—
109C5×#117—21no—
110C2×C5×C4⋊C4—21no—
111C2×C5×C4⋊C4C2312yes—
112C2×C42×C5C2311yescharacteristic
113#4092—21no—
114#4092C2312yes—
115Q8×Dic5—21no—
116Q8×Dic5C2312yes—
117#4090—22no—
118#4090—22no—
119#4090—22no—
120#4090—22no—
121#4090—21no—
122#4090C2312yes—
123#4072—21no—
124C2×C4⋊Dic5—21no—
125C2×C4⋊Dic5C2312yes—
126#4070—21no—
127#4070C2312yes—
128C2×#683—22no—
129C2×#683—22no—
130C2×C4×Dic5D411yescharacteristic
131C2×C4×Dic5D411yescharacteristic
132C2×C4×Dic5C2311yescharacteristic
133C2×C8×D5C2314yes—
134#4043—21no—
135#4043C2312yes—
136#4042—22no—
137#4042—22no—
138#4038—21no—
139#4038—21no—
140D5×C4⋊C4—22no—
141D5×C4⋊C4—22no—
142D5×C4⋊C4—22no—
143D5×C4⋊C4—22no—
144D5×C4⋊C4—22no—
145D5×C4⋊C4—22no—
146D5×C4⋊C4—21no—
147D5×C4⋊C4—21no—
148D5×C4⋊C4—21no—
149D5×C4⋊C4—22no—
150D5×C4⋊C4—22no—
151D5×C4⋊C4C2314yes—
152D5×C4⋊C4C2314yes—
153D5×C4⋊C4C2312yes—
154#4036—21no—
155#4036—21no—
156#4035—22no—
157#4035—22no—
158#4034—22no—
159#4034—22no—
160#4034—22no—
161#4034—22no—
162#4034—22no—
163#4034—22no—
164#4034—21no—
165#4034—21no—
166#4034—21no—
167#4034C2314yes—
168#4034C2314yes—
169#4034C2312yes—
170#4033—21no—
171#4033—22no—
172#4033—22no—
173#4033C2312yes—
174D5×C22⋊C4—22no—
175#4024—22no—
176#4024—22no—
177#4023—22no—
178#4018—22no—
179C42×D5—22no—
180C42×D5D411yescharacteristic
181C42×D5D411yescharacteristic
182C42×D5D411yescharacteristic
183C42×D5D411yescharacteristic
184C42×D5C2311yescharacteristic
185C42×D5C2311yescharacteristic
186C42×D5C2311yescharacteristic
187C42×D5C2311yescharacteristic
188#4016—21no—
189#4015—21no—
190#4015—21no—
191#4015C2311yescharacteristic
192#4015C2312yes—
193#4015C2312yes—
194#4015C2311yescharacteristic
195C4×Dic10—21no—
196C4×Dic10—22no—
197C4×Dic10—22no—
198C4×Dic10C2312yes—
199C5×#107C2318yes—
200C5×C4⋊C8C2312yes—
201C5×#103C2318yes—
202C5×C22⋊C8C2312yes—
203C4×C5×C8C2312yes—
204#3967C2318yes—
205C22⋊#168C2312yes—
206#3952C2314yes—
207#3950C2318yes—
208#3948C2318yes—
209#3946C2314yes—
210C8×Dic5C2314yes—
211#3942C2318yes—
212#3939C2318yes—
213#3939C2318yes—
214C4⋊#168C2312yes—
215C4×#168C2312yes—
216C2×#533—51no—
217C22×C4⋊Q8—51no—
218#3230—52no—
219#3230—52no—
220#3230—54no—
221#3230—54no—
222#3230—51no—
223#3230—51no—
224#3230—51no—
225#3230D511yescharacteristic, direct product factor
226C2×#500—52no—
227C2×#487—52no—
228C2×#484—54no—
229C2×#477—54no—
230C2×#431—51no—
231C23×D5C2×D411yescharacteristic
232C2×C5×Q8—21no—
233C2×C5×Q8—22no—
234C2×C5×Q8—22no—
235C2×C5×Q8—44no—
236C2×C5×Q8C2412yes—
237C22×C4×C5—22no—
238C22×C4×C5C2×D411yescharacteristic
239C22×C4×C5C2×D411yescharacteristic
240C22×C4×C5C2411yescharacteristic
241C22×Dic5—22no—
242C22×Dic5C2×D411yescharacteristic
243C22×Dic5C2×D411yescharacteristic
244C22×Dic5C2×D411yescharacteristic
245Q8×D5—28no—
246Q8×D5—48no—
247Q8×D5—48no—
248Q8×D5—48no—
249Q8×D5—44no—
250Q8×D5—48no—
251C2×C4×D5—24no—
252C2×C4×D5—24no—
253C2×C4×D5—24no—
254C2×C4×D5—24no—
255C2×C4×D5—22no—
256C2×C4×D5—22no—
257C2×C4×D5—48no—
258C2×C4×D5Q1618yes—
259C2×C4×D5C2×D411yescharacteristic
260C2×C4×D5C2×D411yescharacteristic
261C2×C4×D5C2×D411yescharacteristic
262C2×C4×D5C2×D411yescharacteristic
263C2×C4×D5C2×D411yescharacteristic
264C2×C4×D5C2×D411yescharacteristic
265C2×C4×D5C2×D411yescharacteristic
266C2×C4×D5C2×D411yescharacteristic
267C2×C4×D5C2×D411yescharacteristic
268C2×C4×D5C2×D411yescharacteristic
269C2×C4×D5C2411yescharacteristic
270C2×C4×D5C2411yescharacteristic
271C2×Dic10—22no—
272C2×Dic10—22no—
273C2×Dic10—21no—
274C2×Dic10—24no—
275C2×Dic10—24no—
276C2×Dic10—22no—
277C2×Dic10—22no—
278C2×Dic10—48no—
279C2×Dic10—44no—
280C2×Dic10C2412yes—
281C2×C5×C8C2414yes—
282C5×C4⋊C4—22no—
283C5×C4⋊C4—22no—
284C5×C4⋊C4—22no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—21no—
288C5×C4⋊C4—22no—
289C5×C4⋊C4—22no—
290C5×C4⋊C4C2414yes—
291C5×C4⋊C4C2412yes—
292C5×C22⋊C4—22no—
293C42×C5—22no—
294C42×C5C2×D411yescharacteristic
295C42×C5C2×D411yescharacteristic
296C42×C5C2411yescharacteristic
297C42×C5C2411yescharacteristic
298C22⋊Dic5—22no—
299#685—22no—
300#685—22no—
301C4⋊Dic5—21no—
302C4⋊Dic5—22no—
303C4⋊Dic5—22no—
304C4⋊Dic5—22no—
305C4⋊Dic5—21no—
306C4⋊Dic5—21no—
307C4⋊Dic5—22no—
308C4⋊Dic5—22no—
309C4⋊Dic5C2412yes—
310C4⋊Dic5C2414yes—
311#683—22no—
312#683—22no—
313#683—22no—
314#683—22no—
315#683—22no—
316#683—22no—
317#683—22no—
318#683—22no—
319#683—24no—
320#683—24no—
321#683—24no—
322#683—24no—
323C4×Dic5—22no—
324C4×Dic5—22no—
325C4×Dic5—22no—
326C4×Dic5C2×D411yescharacteristic
327C4×Dic5C2×D411yescharacteristic
328C4×Dic5C2×D411yescharacteristic
329C4×Dic5C2×D411yescharacteristic
330C4×Dic5C2×D411yescharacteristic
331C4×Dic5C2×D411yescharacteristic
332C4×Dic5C2×D411yescharacteristic
333C4×Dic5C2×D411yescharacteristic
334C4×Dic5C2×D411yescharacteristic
335C4×Dic5C2×D411yescharacteristic
336C4×Dic5C2411yescharacteristic
337C4×Dic5C2411yescharacteristic
338C2×#168C2414yes—
339C8×D5—28no—
340C23×Q8—101no—
341#533—51no—
342#533—51no—
343#533—52no—
344#533—52no—
345#533—51no—
346#533—101no—
347#533—101no—
348#533—101no—
349#533—101no—
350#533C2×D511yescharacteristic
351C2×C4⋊Q8—52no—
352C2×C4⋊Q8—52no—
353C2×C4⋊Q8—51no—
354C2×C4⋊Q8—52no—
355C2×C4⋊Q8—52no—
356C2×C4⋊Q8—52no—
357C2×C4⋊Q8—51no—
358C2×C4⋊Q8—51no—
359C2×C4⋊Q8—101no—
360C2×C4⋊Q8—101no—
361C2×C4⋊Q8—101no—
362C2×C4⋊Q8—101no—
363C2×C4⋊Q8—101no—
364C2×C4⋊Q8—101no—
365C2×C4⋊Q8C2×D511yescharacteristic
366C2×#125—101no—
367C2×C22⋊Q8—52no—
368C2×C22⋊Q8—101no—
369C2×C4×Q8—52no—
370C2×C4×Q8—101no—
371C2×#117—101no—
372C22×C4⋊C4—52no—
373C22×C4⋊C4—101no—
374C22×C42—51no—
375#500—52no—
376#500—52no—
377#500—58no—
378#500—52no—
379#500C2×D512yescomplemented
380#487—52no—
381#487—52no—
382#487—58no—
383#487—52no—
384#487C2×D512yescomplemented
385#484—54no—
386#484—54no—
387#484—58no—
388#484—58no—
389#484—54no—
390#484C2×D514yes—
391#477—54no—
392#477—54no—
393#477—58no—
394#477—54no—
395#477—58no—
396#477C2×D514yescomplemented
397#431—51no—
398#431—52no—
399#431—52no—
400#431—52no—
401#431C2×D511yescharacteristic
402C2×#107—58no—
403C2×C4⋊C8—52no—
404C2×#103—58no—
405C2×C22⋊C8—52no—
406C2×C4×C8—52no—
407C23×C5C22×D411yescharacteristic
408C22×D5—22no—
409C22×D5—22no—
410C22×D5C2×Q1614yes—
411C22×D5C22×D411yescharacteristic
412C22×D5C22×D411yescharacteristic
413C5×Q8—24no—
414C5×Q8—44no—
415C5×Q8—44no—
416C5×Q8—42no—
417C2×C4×C5—22no—
418C2×C4×C5—22no—
419C2×C4×C5—22no—
420C2×C4×C5—22no—
421C2×C4×C5—24no—
422C2×C4×C5—44no—
423C2×C4×C5C2×Q1614yes—
424C2×C4×C5C22×D411yescharacteristic
425C2×C4×C5C22×D411yescharacteristic
426C2×C4×C5C22×D411yescharacteristic
427C2×C4×C5C22×D411yescharacteristic
428C2×C4×C5C22×D411yescharacteristic
429C2×C4×C5C2511yescharacteristic
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—24no—
435C2×Dic5—44no—
436C2×Dic5C2×Q1614yes—
437C2×Dic5C22×D411yescharacteristic
438C2×Dic5C22×D411yescharacteristic
439C2×Dic5C22×D411yescharacteristic
440C2×Dic5C22×D411yescharacteristic
441C2×Dic5C22×D411yescharacteristic
442C2×Dic5C22×D411yescharacteristic
443C4×D5—22no—
444C4×D5—22no—
445C4×D5—22no—
446C4×D5—22no—
447C4×D5—22no—
448C4×D5—22no—
449C4×D5—48no—
450C4×D5—44no—
451C4×D5—48no—
452C4×D5—44no—
453C4×D5C2×Q1614yes—
454C4×D5C2×Q1614yes—
455C4×D5C2×Q1614yes—
456C4×D5C2×Q1614yes—
457C4×D5AGL(1,ℤ/8)14yes—
458C4×D52−1+414yes—
459Dic10—24no—
460Dic10—48no—
461Dic10—44no—
462Dic10—44no—
463Dic10—42no—
464Dic10—44no—
465Dic10—48no—
466Dic10—44no—
467C5×C8—24no—
468#168—24no—
469C22×Q8—21no—
470C22×Q8—52no—
471C22×Q8—102no—
472C22×Q8—101no—
473C22×Q8—102no—
474C22×Q8—102no—
475C22×Q8—102no—
476C22×Q8—102no—
477C22×Q8—101no—
478C22×Q8—208no—
479C23×C4—51no—
480C23×C4—51no—
481C23×C4—51no—
482C23×C4—102no—
483C22×C8—54no—
484C4⋊Q8—21no—
485C4⋊Q8—21no—
486C4⋊Q8—54no—
487C4⋊Q8—54no—
488C4⋊Q8—52no—
489C4⋊Q8—52no—
490C4⋊Q8—52no—
491C4⋊Q8—52no—
492C4⋊Q8—51no—
493C4⋊Q8—51no—
494C4⋊Q8—102no—
495C4⋊Q8—102no—
496C4⋊Q8—102no—
497C4⋊Q8—102no—
498C4⋊Q8—102no—
499C4⋊Q8—102no—
500C4⋊Q8—101no—
501C4⋊Q8—101no—
502C4⋊Q8—101no—
503C4⋊Q8—102no—
504C4⋊Q8—102no—
505C4⋊Q8—102no—
506C4⋊Q8—102no—
507C4⋊Q8—101no—
508C4⋊Q8—101no—
509C4⋊Q8—101no—
510C4⋊Q8C22×D511yescharacteristic
511C4⋊Q8C22×D512yes—
512C4⋊Q8C22×D512yes—
513C4⋊Q8C22×D511yescharacteristic
514#125—21no—
515#125—102no—
516#125—102no—
517#125—101no—
518#125—101no—
519#125—101no—
520C22⋊Q8—21no—
521C22⋊Q8—52no—
522C22⋊Q8—52no—
523C22⋊Q8—52no—
524C22⋊Q8—102no—
525C22⋊Q8—102no—
526C22⋊Q8—102no—
527C22⋊Q8—102no—
528C22⋊Q8—101no—
529C22⋊Q8—101no—
530C22⋊Q8—101no—
531C22⋊Q8C22×D512yes—
532C4×Q8—21no—
533C4×Q8—52no—
534C4×Q8—52no—
535C4×Q8—52no—
536C4×Q8—102no—
537C4×Q8—102no—
538C4×Q8—102no—
539C4×Q8—101no—
540C4×Q8—102no—
541C4×Q8—101no—
542C4×Q8—101no—
543C4×Q8C22×D512yes—
544#117—21no—
545#117—102no—
546#117—102no—
547#117—101no—
548#117—101no—
549#117—101no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—52no—
552C2×C4⋊C4—54no—
553C2×C4⋊C4—54no—
554C2×C4⋊C4—52no—
555C2×C4⋊C4—102no—
556C2×C4⋊C4—102no—
557C2×C4⋊C4—102no—
558C2×C4⋊C4—102no—
559C2×C4⋊C4—102no—
560C2×C4⋊C4—102no—
561C2×C4⋊C4—101no—
562C2×C4⋊C4—101no—
563C2×C4⋊C4—102no—
564C2×C4⋊C4—102no—
565C2×C4⋊C4—101no—
566C2×C4⋊C4—102no—
567C2×C4⋊C4—102no—
568C2×C4⋊C4—101no—
569C2×C4⋊C4C22×D512yes—
570C2×C22⋊C4—102no—
571C2×C42—51no—
572C2×C42—51no—
573C2×C42—51no—
574C2×C42—51no—
575C2×C42—51no—
576C2×C42—51no—
577C2×C42—51no—
578C2×C42—51no—
579C2×C42—51no—
580C2×C42—51no—
581C2×C42—51no—
582C2×C42—102no—
583C2×C42C22×D511yescharacteristic
584#107—58no—
585#107—58no—
586#107—58no—
587#107C22×D518yes—
588C4⋊C8—54no—
589C4⋊C8—52no—
590C4⋊C8C22×D512yes—
591#103—58no—
592#103—58no—
593#103—58no—
594#103C22×D518yes—
595C22⋊C8—52no—
596C22⋊C8—54no—
597C22⋊C8C22×D512yes—
598C4×C8—54no—
599C4×C8—52no—
600C4×C8C22×D512yes—
601C22×C5—21no—
602C22×C5—21no—
603C22×C5C22×Q1612yes—
604C22×C5C23×D411yescharacteristic
605C2×D5—21no—
606C2×D5—21no—
607C2×D5—28no—
608C2×D5#53612yes—
609C2×D5C22×Q1612yes—
610C2×D5C22×Q1612yes—
611C2×D5C2×AGL(1,ℤ/8)12yes—
612C4×C5—21no—
613C4×C5—21no—
614C4×C5—42no—
615C4×C5—44no—
616C4×C5—42no—
617C4×C5C22×Q1612yes—
618C4×C5C22×Q1612yes—
619C4×C5C2×AGL(1,ℤ/8)12yes—
620C4×C5C2×2−1+412yes—
621Dic5—21no—
622Dic5—21no—
623Dic5—42no—
624Dic5—44no—
625Dic5—42no—
626Dic5#53612yes—
627Dic5C22×Q1612yes—
628Dic5C22×Q1612yes—
629Dic5C2×AGL(1,ℤ/8)12yes—
630C24—51no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—44no—
635C2×Q8—52no—
636C2×Q8—102no—
637C2×Q8—102no—
638C2×Q8—104no—
639C2×Q8—104no—
640C2×Q8—108no—
641C2×Q8—101no—
642C2×Q8—102no—
643C2×Q8—102no—
644C2×Q8—204no—
645C2×Q8—208no—
646C2×Q8—208no—
647C2×Q8—204no—
648C2×Q8—208no—
649C2×Q8—208no—
650C2×Q8—208no—
651C2×Q8C23×D512yes—
652C22×C4—22no—
653C22×C4—51no—
654C22×C4—51no—
655C22×C4—51no—
656C22×C4—51no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—51no—
660C22×C4—58no—
661C22×C4—51no—
662C22×C4—51no—
663C22×C4—51no—
664C22×C4—51no—
665C22×C4—51no—
666C22×C4—51no—
667C22×C4—51no—
668C22×C4—51no—
669C22×C4—104no—
670C22×C4—104no—
671C22×C4—102no—
672C22×C4—102no—
673C22×C4—104no—
674C22×C4—104no—
675C22×C4—102no—
676C22×C4—208no—
677C22×C4D4×D511yescharacteristic
678C22×C4D4×D511yescharacteristic
679C22×C4C23×D511yescharacteristic
680C2×C8—54no—
681C2×C8—108no—
682C2×C8C23×D514yes—
683C4⋊C4—22no—
684C4⋊C4—22no—
685C4⋊C4—22no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—22no—
690C4⋊C4—22no—
691C4⋊C4—54no—
692C4⋊C4—52no—
693C4⋊C4—104no—
694C4⋊C4—104no—
695C4⋊C4—102no—
696C4⋊C4—104no—
697C4⋊C4—104no—
698C4⋊C4—102no—
699C4⋊C4—102no—
700C4⋊C4—102no—
701C4⋊C4—102no—
702C4⋊C4—102no—
703C4⋊C4—102no—
704C4⋊C4—102no—
705C4⋊C4—102no—
706C4⋊C4—102no—
707C4⋊C4—102no—
708C4⋊C4—101no—
709C4⋊C4—101no—
710C4⋊C4—102no—
711C4⋊C4—102no—
712C4⋊C4—101no—
713C4⋊C4C23×D514yes—
714C4⋊C4C23×D512yes—
715C22⋊C4—22no—
716C22⋊C4—102no—
717C22⋊C4—102no—
718C22⋊C4—102no—
719C42—22no—
720C42—51no—
721C42—51no—
722C42—51no—
723C42—51no—
724C42—51no—
725C42—51no—
726C42—51no—
727C42—51no—
728C42—51no—
729C42—51no—
730C42—51no—
731C42—51no—
732C42—102no—
733C42—102no—
734C42—102no—
735C42D4×D511yescharacteristic
736C42D4×D511yescharacteristic
737C42C23×D511yescharacteristic
738C42C23×D511yescharacteristic
739C2×C5—22no—
740C2×C5C2×#53611yescharacteristic
741C2×C5C23×Q1611yescharacteristic
742C2×C5C22×AGL(1,ℤ/8)11yescharacteristic
743D5—22no—
744D5#323014yesdirect product factor
745C23—51no—
746C23—54no—
747C23—51no—
748C23—102no—
749C23—102no—
750C23C2×D4×D511yescharacteristic
751Q8—24no—
752Q8—44no—
753Q8—44no—
754Q8—42no—
755Q8—104no—
756Q8—204no—
757Q8—204no—
758Q8—208no—
759Q8—204no—
760Q8—208no—
761Q8—204no—
762Q8—202no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—44no—
769C2×C4—54no—
770C2×C4—51no—
771C2×C4—51no—
772C2×C4—51no—
773C2×C4—51no—
774C2×C4—54no—
775C2×C4—54no—
776C2×C4—54no—
777C2×C4—54no—
778C2×C4—54no—
779C2×C4—54no—
780C2×C4—51no—
781C2×C4—51no—
782C2×C4—102no—
783C2×C4—102no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—104no—
793C2×C4—208no—
794C2×C4—204no—
795C2×C4—204no—
796C2×C4—208no—
797C2×C4—204no—
798C2×C4D5×Q1614yes—
799C2×C4C2×D4×D511yescharacteristic
800C2×C4C2×D4×D511yescharacteristic
801C2×C4C2×D4×D511yescharacteristic
802C2×C4C2×D4×D511yescharacteristic
803C2×C4C2×D4×D511yescharacteristic
804C2×C4C24×D511yescharacteristic
805C8—24no—
806C8—104no—
807C5C2×#323011yescharacteristic, complemented, Sylow
808C22—21no—
809C22—21no—
810C22—52no—
811C22—52no—
812C22—52no—
813C22—52no—
814C22—108no—
815C22—101no—
816C22—101no—
817C22C2×D5×Q1612yes—
818C22C22×D4×D511yescharacteristic
819C4—21no—
820C4—21no—
821C4—42no—
822C4—44no—
823C4—42no—
824C4—52no—
825C4—52no—
826C4—52no—
827C4—52no—
828C4—101no—
829C4—101no—
830C4—202no—
831C4—204no—
832C4—202no—
833C4C2×D5×Q1612yes—
834C4C2×D5×Q1612yes—
835C4D5×AGL(1,ℤ/8)12yes—
836C4D5×2−1+412yes—
837C2—22no—
838C2—54no—
839C2—102no—
840C2D5×#53611yescharacteristic
841C2C22×D5×Q1611yescharacteristic
842C2C2×D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C22×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC5×#3230C2
socleC22×C5C23×D4
prime radicalC23×D5C2×D4
hypercenter#3230D5
hypocenterC5C2×#3230
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
3. C5×#3230C2semidirect
4. #10615055C2semidirect
5. #10614955C2semidirect
6. #10613674C2semidirect
7. D5×#500C2semidirect
8. #10613339C2semidirect
9. D5×#487C2semidirect
11. #10613189C2semidirect
12. #10612843C2semidirect
13. D5×#477C2semidirect
15. #10611003C2semidirect
51. C5×#500C22semidirect
52. C5×#487C22semidirect
54. C5×#477C22semidirect
56. #65382C22semidirect
57. #65380C22semidirect
58. #65370C22semidirect
59. #65367C22semidirect
60. #65367C22semidirect
62. #65310C22semidirect
67. #65164C22semidirect
68. #65163C22semidirect
69. #65139C22semidirect
74. #65083C22semidirect
75. #65081C22semidirect
81. #64971C22semidirect
82. #64970C22semidirect
225. #3230D5direct (N × H)
379. #500C2×D5semidirect
384. #487C2×D5semidirect
396. #477C2×D5semidirect
744. D5#3230direct (N × H)
807. C5C2×#3230semidirect

Maximal subgroups

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

subgroupindex
D5×#5332
C2×D5×C4⋊Q82
C5×#32302
#106150552
#106149552
#106136742
D5×#5002
#106133392
D5×#4872
D5×#4842
#106131892
#106128432
D5×#4772
D5×#4312
#106110032
C2×#32305