Finite Group Databasebeta

← D5×#3548 #13007089

Subgroups — D5×#3548 #13007089

Order 1280.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3548C211yesmaximal, characteristic, complemented
2D5×#562C214yesmaximal, complemented
3#10619000C214yesmaximal, complemented
4D5×#554C214yesmaximal, complemented
5#10618840C214yesmaximal, complemented
6D5×#550C214yesmaximal, complemented
7#10618681C214yesmaximal, complemented
8D5×#547C214yesmaximal, complemented
9#10618594C214yesmaximal, complemented
10D5×#540C214yesmaximal, complemented
11#10618377C214yesmaximal, complemented
12D5×#537C218yesmaximal, complemented
13#10618275C218yesmaximal, complemented
14#10618189C211yesmaximal, characteristic, complemented
15D5×#533C211yesmaximal, characteristic, complemented
16#10618152C212yesmaximal, complemented
17D5×#532C212yesmaximal, complemented
18C2×D5×#41C2214yes—
19C2×D5×#41C2218yes—
20C5×#562C2214yescomplemented
21C5×#554C2214yescomplemented
22C5×#550C2214yescomplemented
23C5×#547C2214yescomplemented
24C5×#540C2214yescomplemented
25C5×#537C2218yescomplemented
26C5×#533C2211yescharacteristic, complemented
27C5×#532C2212yescomplemented
28#66168C2218yescomplemented
29#66167C2218yescomplemented
30#66167C2218yescomplemented
31#66166C2214yescomplemented
32#66158C2218yescomplemented
33#66064C2214yescomplemented
34#66062C2212yescomplemented
35#66060C2214yescomplemented
36#66059C2212yescomplemented
37D5×C4⋊Q8C2212yes—
38D5×C4⋊Q8C2212yes—
39#66053C2214yescomplemented
40#66052C2218yescomplemented
41#66052C2214yescomplemented
42#66050C2212yescomplemented
43D5×#127C2214yes—
44D5×#127C2212yes—
45#66034C2214yescomplemented
46#66032C2214yescomplemented
47#66024C2218yescomplemented
48#66022C2212yescomplemented
49D5×#125C2214yes—
50D5×#125C2212yes—
51#66018C2218yescomplemented
52D5×#124C2214yes—
53#66002C2214yescomplemented
54#66001C22116yescomplemented
55#65997C22116yescomplemented
56#65989C22116yescomplemented
57D5×#123C22116yes—
58#65981C22116yescomplemented
59#65970C22116yescomplemented
60#65969C2218yescomplemented
61#65965C2218yescomplemented
62#65963C2218yescomplemented
63#65963C22116yescomplemented
64#65963C2218yescomplemented
65D5×C22⋊Q8C2214yes—
66D5×C22⋊Q8C22116yes—
67D5×C22⋊Q8C2218yes—
68#65956C2214yescomplemented
69#65955C22116yescomplemented
70#65953C2218yescomplemented
71#65949C22116yescomplemented
72#65945C2218yescomplemented
73#65942C22116yescomplemented
74#65942C2218yescomplemented
75#65942C2218yescomplemented
76D5×#121C2214yes—
77D5×#121C22116yes—
78D5×#121C2214yes—
79D5×#121C22116yes—
80D5×#121C2218yes—
81#65933C22116yescomplemented
82#65933C2218yescomplemented
83#65931C22116yescomplemented
84#65931C22116yescomplemented
85#65930C2214yescomplemented
86#65930C2214yescomplemented
87#65913C2214yescomplemented
88#65912C2214yescomplemented
89#65911C2214yescomplemented
90C4×Q8×D5C2214yes—
91#65896C2218yescomplemented
92#65889C2214yescomplemented
93#65887C2218yescomplemented
94#65887C2214yescomplemented
95#65885C2214yescomplemented
96#65882C2214yescomplemented
97#65882C2214yescomplemented
98C4×D4×D5C2218yes—
99C4×D4×D5C2214yes—
100C4×D4×D5C2214yes—
101#65877C2214yescomplemented
102#65873C2218yescomplemented
103#65869C2214yescomplemented
104D5×#117C2212yes—
105#65851C2212yescomplemented
106#65845C2218yescomplemented
107#65844C2218yescomplemented
108#65841C2218yescomplemented
109C2×D5×C4⋊C4C2218yes—
110#65811C2212yescomplemented
111C2×C42×D5C2211yescharacteristic
112#65804C2211yescharacteristic, complemented
113C2×#3548—51nomaximal, Sylow
114C2×C5×#41C2318yes—
115C2×C5×#41C2314yes—
116D5×#41—416no—
117D5×#41—432no—
118C2×#713C2314yes—
119C2×#713C2318yes—
120C2×Q8×D5C2314yes—
121C2×Q8×D5C2314yes—
122C2×#711C2314yes—
123C2×#711C2318yes—
124C2×#711C23116yes—
125C2×#711C2318yes—
126C2×D4×D5C2314yes—
127C2×D4×D5C2314yes—
128C2×D4×D5C23116yes—
129C2×D4×D5C2314yes—
130C2×D4×D5C2318yes—
131C2×#709C2314yes—
132C2×#709C23116yes—
133C2×#709C2318yes—
134C2×#709C2318yes—
135C22×C4×D5C2311yescharacteristic
136C22×C4×D5C2312yes—
137C22×C4×D5C2318yes—
138C22×C4×D5C23116yes—
139C5×C4⋊Q8C2312yes—
140C5×C4⋊Q8C2312yes—
141C5×#127C2312yes—
142C5×#127C2314yes—
143C5×#125C2312yes—
144C5×#125C2314yes—
145C5×#124C2314yes—
146C5×#123C23116yes—
147C5×C22⋊Q8C2314yes—
148C5×C22⋊Q8C2318yes—
149C5×C22⋊Q8C23116yes—
150C5×#121C2314yes—
151C5×#121C2314yes—
152C5×#121C23116yes—
153C5×#121C23116yes—
154C5×#121C2318yes—
155C4×C5×Q8C2314yes—
156C4×C5×D4C2318yes—
157C4×C5×D4C2314yes—
158C4×C5×D4C2314yes—
159C5×#117C2312yes—
160C2×C5×C4⋊C4C2318yes—
161C2×C42×C5C2311yescharacteristic
162#4093C2314yes—
163#4092C2318yes—
164#4092C2314yes—
165#4092C23116yes—
166Q8×Dic5C2314yes—
167#4090C2314yes—
168#4090C2314yes—
169#4086C2314yes—
170#4086C2318yes—
171#4086C2314yes—
172#4086C2314yes—
173#4086C23116yes—
174#4085C23116yes—
175#4085C23116yes—
176#4085C23116yes—
177#4085C23116yes—
178#4085C2318yes—
179#4085C2318yes—
180#4085C23116yes—
181#4084C2314yes—
182#4084C2314yes—
183#4084C2318yes—
184#4084C23116yes—
185#4084C23116yes—
186#4082C2314yes—
187#4081C23116yes—
188D4×Dic5C2314yes—
189D4×Dic5C2314yes—
190D4×Dic5C2318yes—
191#4076C2314yes—
192#4076C2314yes—
193#4076C2318yes—
194#4076C23116yes—
195#4076C23116yes—
196#4075C23116yes—
197C4×C22⋊D5C2318yes—
198C4×C22⋊D5C2318yes—
199C4×C22⋊D5C23116yes—
200#4072C2312yes—
201C2×C4⋊Dic5C2318yes—
202#4070C2314yes—
203#4070C23116yes—
204#4070C2318yes—
205C2×#683C23116yes—
206C2×C4×Dic5C2311yescharacteristic
207C2×C4×Dic5C2312yes—
208#4043C2314yes—
209#4043C2318yes—
210#4043C23116yes—
211#4042C23116yes—
212#4042C23116yes—
213#4042C2318yes—
214#4042C23116yes—
215#4041C2314yes—
216#4041C2314yes—
217#4041C2318yes—
218#4041C23116yes—
219#4041C23116yes—
220#4040C23116yes—
221#4040C23116yes—
222#4039C2314yes—
223#4039C2314yes—
224#4039C2318yes—
225#4038C2314yes—
226D5×C4⋊C4C2314yes—
227D5×C4⋊C4C2314yes—
228D5×C4⋊C4C2314yes—
229D5×C4⋊C4C2314yes—
230D5×C4⋊C4C2318yes—
231D5×C4⋊C4C2318yes—
232D5×C4⋊C4C23116yes—
233D5×C4⋊C4C23116yes—
234D5×C4⋊C4C2318yes—
235#4036C2314yes—
236#4036C2318yes—
237#4035C23116yes—
238#4035C2318yes—
239#4034C2314yes—
240#4034C2314yes—
241#4034C2314yes—
242#4034C2314yes—
243#4033C2314yes—
244#4033C2318yes—
245#4032C23116yes—
246#4031C2318yes—
247#4031C2318yes—
248#4030C23116yes—
249#4030C2318yes—
250#4030C2318yes—
251#4030C23116yes—
252#4030C23116yes—
253#4030C23116yes—
254#4030C23116yes—
255#4029C23116yes—
256#4029C23116yes—
257#4027C2318yes—
258#4027C2318yes—
259#4027C23116yes—
260D5×C22⋊C4C2314yes—
261D5×C22⋊C4C23116yes—
262D5×C22⋊C4C2318yes—
263D5×C22⋊C4C2318yes—
264#4024C2318yes—
265#4024C23116yes—
266#4024C23116yes—
267#4024C23116yes—
268#4023C2314yes—
269#4021C2314yes—
270#4020C2312yes—
271#4020C2314yes—
272C4×D20C2314yes—
273C4×D20C2318yes—
274C4×D20C2314yes—
275#4018C2314yes—
276C42×D5C2312yes—
277C42×D5C2314yes—
278C42×D5C2312yes—
279C42×D5C2311yescharacteristic
280C42×D5C2311yescharacteristic
281C42×D5C2311yescharacteristic
282C42×D5C2311yescharacteristic
283#4016C2314yes—
284#4016C2312yes—
285#4015C2312yes—
286#4015C2312yes—
287C4×Dic10C2314yes—
288C4×Dic10C2318yes—
289#3548—54no—
290#3548—54no—
291#3548—54no—
292#3548—54no—
293#3548—54no—
294#3548—58no—
295#3548—51no—
296#3548—52no—
297#3548D511yescharacteristic, direct product factor
298C2×#562—54no—
299C2×#554—54no—
300C2×#550—54no—
301C2×#547—54no—
302C2×#540—54no—
303C2×#537—58no—
304C2×#533—51no—
305C2×#532—52no—
306C23×D5C2411yescharacteristic
307C23×D5C2418yes—
308C5×#41—48no—
309C5×#41—416no—
310C2×C5×Q8C2414yes—
311C2×C5×Q8C2414yes—
312C2×C5×D4C2414yes—
313C2×C5×D4C2414yes—
314C2×C5×D4C2418yes—
315C2×C5×D4C24116yes—
316C2×C5×D4C2414yes—
317C22×C4×C5C2411yescharacteristic
318C22×C4×C5C2412yes—
319C22×C4×C5C2418yes—
320C22×C4×C5C24116yes—
321C2×C22⋊D5C2418yes—
322C2×C22⋊D5C2418yes—
323C2×C22⋊D5C24116yes—
324C2×C22⋊D5C2418yes—
325C2×C22⋊D5C2418yes—
326C2×C22⋊D5C24116yes—
327C2×C22⋊D5C2418yes—
328C22×Dic5C2412yes—
329C22×Dic5C2418yes—
330C22×Dic5C2411yescharacteristic
331C22×Dic5C24116yes—
332#713—48no—
333#713—416no—
334Q8×D5—216no—
335Q8×D5—48no—
336#711—416no—
337#711—432no—
338#711—416no—
339#711—48no—
340D4×D5—216no—
341D4×D5—216no—
342D4×D5—416no—
343D4×D5—48no—
344D4×D5—432no—
345#709—432no—
346#709—416no—
347#709—416no—
348#709—48no—
349C2×D20C2414yes—
350C2×D20C2414yes—
351C2×D20C2414yes—
352C2×D20C24116yes—
353C2×D20C2418yes—
354C2×C4×D5—232no—
355C2×C4×D5—28no—
356C2×C4×D5—24no—
357C2×C4×D5—432no—
358C2×C4×D5C2418yes—
359C2×C4×D5C2418yes—
360C2×C4×D5C2412yes—
361C2×C4×D5C2418yes—
362C2×C4×D5C2418yes—
363C2×C4×D5C2412yes—
364C2×C4×D5C2412yes—
365C2×C4×D5C2411yescharacteristic
366C2×C4×D5C2411yescharacteristic
367C2×C4×D5C2411yescharacteristic
368C2×C4×D5C24116yes—
369C2×C4×D5C24116yes—
370C2×C4×D5C2412yes—
371C2×C4×D5C2411yescharacteristic
372C2×Dic10C2414yes—
373C2×Dic10C2418yes—
374C2×Dic10C2414yes—
375C2×Dic10C2418yes—
376C5×C4⋊C4C2414yes—
377C5×C4⋊C4C2414yes—
378C5×C4⋊C4C24116yes—
379C5×C4⋊C4C2414yes—
380C5×C4⋊C4C2414yes—
381C5×C4⋊C4C2418yes—
382C5×C22⋊C4C2414yes—
383C5×C22⋊C4C24116yes—
384C5×C22⋊C4C2418yes—
385C5×C22⋊C4C2418yes—
386C42×C5C2411yescharacteristic
387C42×C5C2412yes—
388C42×C5C2411yescharacteristic
389C42×C5C2414yes—
390C22⋊Dic5C2414yes—
391C22⋊Dic5C24116yes—
392C22⋊Dic5C2418yes—
393C22⋊Dic5C2418yes—
394#685C2418yes—
395#685C2418yes—
396#685C2418yes—
397#685C24116yes—
398#685C2418yes—
399#685C2418yes—
400#685C24116yes—
401C4⋊Dic5C2414yes—
402C4⋊Dic5C2418yes—
403C4⋊Dic5C2414yes—
404C4⋊Dic5C2414yes—
405C4⋊Dic5C2414yes—
406C4⋊Dic5C24116yes—
407#683C2418yes—
408#683C2418yes—
409#683C2418yes—
410#683C24116yes—
411#683C2418yes—
412#683C2418yes—
413#683C24116yes—
414#683C2418yes—
415C4×Dic5C2412yes—
416C4×Dic5C2414yes—
417C4×Dic5C2411yescharacteristic
418C4×Dic5C2412yes—
419C4×Dic5C2411yescharacteristic
420C4×Dic5C2412yes—
421C4×Dic5C2412yes—
422C4×Dic5C2412yes—
423C4×Dic5C2418yes—
424C22×#41—54no—
425C22×#41—58no—
426#562—54no—
427#562—58no—
428#562—516no—
429#562—516no—
430#562—516no—
431#562C2×D514yescomplemented
432#554—54no—
433#554—58no—
434#554—58no—
435#554—516no—
436#554—54no—
437#554—58no—
438#554—54no—
439#554—58no—
440#554C2×D514yescomplemented
441#550—58no—
442#550—58no—
443#550—54no—
444#550—58no—
445#550—516no—
446#550—54no—
447#550—58no—
448#550—54no—
449#550C2×D514yescomplemented
450#547—58no—
451#547—54no—
452#547—516no—
453#547—58no—
454#547—58no—
455#547—54no—
456#547—54no—
457#547—58no—
458#547C2×D514yescomplemented
459#540—54no—
460#540—54no—
461#540—516no—
462#540—516no—
463#540—58no—
464#540—58no—
465#540—54no—
466#540C2×D514yescomplemented
467#537—58no—
468#537—58no—
469#537—58no—
470#537—516no—
471#537—58no—
472#537—516no—
473#537—516no—
474#537—58no—
475#537—516no—
476#537—58no—
477#537—58no—
478#537C2×D518yescomplemented
479#533—52no—
480#533—52no—
481#533—54no—
482#533—54no—
483#533—52no—
484#533—51no—
485#533C2×D511yescharacteristic, complemented
486#532—54no—
487#532—52no—
488#532—52no—
489#532—54no—
490#532—54no—
491#532—54no—
492#532—54no—
493#532—54no—
494#532—52no—
495#532C2×D512yescomplemented
496C2×C4⋊Q8—52no—
497C2×C4⋊Q8—52no—
498C2×#127—52no—
499C2×#127—54no—
500C2×#125—52no—
501C2×#125—54no—
502C2×#124—54no—
503C2×#123—516no—
504C2×C22⋊Q8—54no—
505C2×C22⋊Q8—58no—
506C2×C22⋊Q8—516no—
507C2×#121—54no—
508C2×#121—54no—
509C2×#121—516no—
510C2×#121—58no—
511C2×#121—516no—
512C2×C4×Q8—54no—
513C2×C4×D4—54no—
514C2×C4×D4—54no—
515C2×C4×D4—58no—
516C2×#117—52no—
517C22×C4⋊C4—58no—
518C22×C42—51no—
519C23×C5C2511yescharacteristic
520C23×C5C2518yes—
521C22×D5—24no—
522C22×D5—216no—
523C22×D5—216no—
524C22×D5—22no—
525C22×D5—216no—
526C22×D5C2511yescharacteristic
527C22×D5C2518yes—
528C22×D5C2511yescharacteristic
529C5×Q8—28no—
530C5×Q8—44no—
531C5×D4—28no—
532C5×D4—28no—
533C5×D4—416no—
534C5×D4—44no—
535C5×D4—48no—
536C2×C4×C5—24no—
537C2×C4×C5—216no—
538C2×C4×C5—22no—
539C2×C4×C5—416no—
540C2×C4×C5C2512yes—
541C2×C4×C5C2511yescharacteristic
542C2×C4×C5C2518yes—
543C2×C4×C5C2518yes—
544C2×C4×C5C2512yes—
545C2×C4×C5C2511yescharacteristic
546C22⋊D5—216no—
547C22⋊D5—216no—
548C22⋊D5—416no—
549C22⋊D5—416no—
550C22⋊D5—48no—
551C22⋊D5—48no—
552C22⋊D5—48no—
553C2×Dic5—24no—
554C2×Dic5—216no—
555C2×Dic5—22no—
556C2×Dic5—416no—
557C2×Dic5C2511yescharacteristic
558C2×Dic5C2512yes—
559C2×Dic5C2518yes—
560C2×Dic5C2518yes—
561C2×Dic5C2512yes—
562C2×Dic5C2511yescharacteristic
563D20—28no—
564D20—28no—
565D20—416no—
566D20—44no—
567D20—48no—
568C4×D5—216no—
569C4×D5—24no—
570C4×D5—216no—
571C4×D5—22no—
572C4×D5—24no—
573C4×D5—216no—
574C4×D5—22no—
575C4×D5—216no—
576C4×D5—24no—
577C4×D5—22no—
578C4×D5—416no—
579C4×D5—416no—
580C4×D5H(5,𝔽2)18yes—
581C4×D52−1+414yes—
582Dic10—28no—
583Dic10—216no—
584Dic10—48no—
585Dic10—44no—
586C2×#41—54no—
587C2×#41—58no—
588C2×#41—58no—
589C2×#41—54no—
590C2×#41—516no—
591C2×#41—58no—
592C2×#41—58no—
593C2×#41—54no—
594C2×#41—516no—
595C2×#41—58no—
596C2×#41—2016no—
597C2×#41—2032no—
598C2×#41C22×D514yes—
599C2×#41C22×D518yes—
600C22×Q8—54no—
601C22×Q8—54no—
602C22×D4—54no—
603C22×D4—54no—
604C22×D4—58no—
605C22×D4—516no—
606C22×D4—54no—
607C23×C4—58no—
608C23×C4—51no—
609C23×C4—52no—
610C23×C4—516no—
611C4⋊Q8—54no—
612C4⋊Q8—54no—
613C4⋊Q8—54no—
614C4⋊Q8—54no—
615C4⋊Q8—54no—
616C4⋊Q8—54no—
617C4⋊Q8—52no—
618C4⋊Q8—52no—
619C4⋊Q8C22×D512yes—
620C4⋊Q8C22×D512yes—
621#127—54no—
622#127—54no—
623#127—54no—
624#127—516no—
625#127—58no—
626#127—52no—
627#127—54no—
628#127C22×D512yes—
629#127C22×D514yes—
630#125—58no—
631#125—54no—
632#125—516no—
633#125—58no—
634#125—52no—
635#125—54no—
636#125C22×D512yes—
637#125C22×D514yes—
638#124—54no—
639#124—54no—
640#124—58no—
641#124—58no—
642#124—54no—
643#124C22×D514yes—
644#123—516no—
645#123—516no—
646#123—516no—
647#123—516no—
648#123—516no—
649#123—516no—
650#123—516no—
651#123C22×D5116yes—
652C22⋊Q8—54no—
653C22⋊Q8—58no—
654C22⋊Q8—516no—
655C22⋊Q8—54no—
656C22⋊Q8—58no—
657C22⋊Q8—516no—
658C22⋊Q8—58no—
659C22⋊Q8—54no—
660C22⋊Q8—516no—
661C22⋊Q8—58no—
662C22⋊Q8—516no—
663C22⋊Q8—516no—
664C22⋊Q8—516no—
665C22⋊Q8—58no—
666C22⋊Q8—516no—
667C22⋊Q8—516no—
668C22⋊Q8—516no—
669C22⋊Q8C22×D514yes—
670C22⋊Q8C22×D518yes—
671C22⋊Q8C22×D5116yes—
672#121—54no—
673#121—58no—
674#121—54no—
675#121—58no—
676#121—516no—
677#121—516no—
678#121—516no—
679#121—58no—
680#121—516no—
681#121—516no—
682#121—516no—
683#121—516no—
684#121—54no—
685#121—54no—
686#121—516no—
687#121—58no—
688#121—516no—
689#121—54no—
690#121—54no—
691#121—516no—
692#121—58no—
693#121—516no—
694#121—58no—
695#121—58no—
696#121—516no—
697#121—516no—
698#121—516no—
699#121—516no—
700#121—516no—
701#121C22×D514yes—
702#121C22×D514yes—
703#121C22×D5116yes—
704#121C22×D518yes—
705#121C22×D5116yes—
706C4×Q8—54no—
707C4×Q8—58no—
708C4×Q8—54no—
709C4×Q8—58no—
710C4×Q8—54no—
711C4×Q8C22×D514yes—
712C4×D4—54no—
713C4×D4—54no—
714C4×D4—58no—
715C4×D4—58no—
716C4×D4—58no—
717C4×D4—516no—
718C4×D4—54no—
719C4×D4—54no—
720C4×D4—58no—
721C4×D4—58no—
722C4×D4—58no—
723C4×D4—516no—
724C4×D4—54no—
725C4×D4—54no—
726C4×D4—58no—
727C4×D4C22×D514yes—
728C4×D4C22×D514yes—
729C4×D4C22×D518yes—
730#117—52no—
731#117—54no—
732#117—54no—
733#117—54no—
734#117C22×D512yes—
735C2×C4⋊C4—516no—
736C2×C4⋊C4—58no—
737C2×C4⋊C4—54no—
738C2×C4⋊C4—54no—
739C2×C4⋊C4—516no—
740C2×C4⋊C4—516no—
741C2×C4⋊C4—58no—
742C2×C4⋊C4—58no—
743C2×C4⋊C4—54no—
744C2×C4⋊C4—54no—
745C2×C4⋊C4—58no—
746C2×C4⋊C4C22×D518yes—
747C2×C22⋊C4—54no—
748C2×C22⋊C4—516no—
749C2×C22⋊C4—58no—
750C2×C22⋊C4—58no—
751C2×C42—52no—
752C2×C42—51no—
753C2×C42—54no—
754C2×C42—51no—
755C2×C42—52no—
756C2×C42—51no—
757C2×C42—51no—
758C2×C42—52no—
759C2×C42—51no—
760C2×C42C22×D511yescharacteristic
761C22×C5—22no—
762C22×C5—28no—
763C22×C5—28no—
764C22×C5—21no—
765C22×C5—28no—
766C22×C5C2611yescharacteristic
767C2×D5—22no—
768C2×D5—28no—
769C2×D5—28no—
770C2×D5—21no—
771C2×D5—28no—
772C2×D5—44no—
773C2×D5—432no—
774C2×D5C2×H(5,𝔽2)14yes—
775C2×D5C2×2−1+412yes—
776C4×C5—28no—
777C4×C5—22no—
778C4×C5—28no—
779C4×C5—21no—
780C4×C5C2×H(5,𝔽2)14yes—
781C4×C5C2×2−1+412yes—
782Dic5—28no—
783Dic5—22no—
784Dic5—28no—
785Dic5—21no—
786Dic5C2×H(5,𝔽2)14yes—
787Dic5C2×2−1+412yes—
788C24—51no—
789C24—58no—
790#41—48no—
791#41—416no—
792#41—2016no—
793#41—208no—
794#41—2016no—
795#41—2032no—
796#41—2016no—
797#41—208no—
798#41—208no—
799#41—2016no—
800#41—2032no—
801#41—2016no—
802C2×Q8—58no—
803C2×Q8—54no—
804C2×Q8—58no—
805C2×Q8—54no—
806C2×Q8—1016no—
807C2×Q8—208no—
808C2×Q8C23×D514yes—
809C2×Q8C23×D514yes—
810C2×D4—58no—
811C2×D4—58no—
812C2×D4—58no—
813C2×D4—58no—
814C2×D4—516no—
815C2×D4—516no—
816C2×D4—58no—
817C2×D4—54no—
818C2×D4—54no—
819C2×D4—58no—
820C2×D4—516no—
821C2×D4—54no—
822C2×D4—1016no—
823C2×D4—1016no—
824C2×D4—2016no—
825C2×D4—208no—
826C2×D4—2032no—
827C2×D4C23×D514yes—
828C2×D4C23×D514yes—
829C2×D4C23×D518yes—
830C2×D4C23×D5116yes—
831C2×D4C23×D514yes—
832C22×C4—51no—
833C22×C4—52no—
834C22×C4—51no—
835C22×C4—52no—
836C22×C4—58no—
837C22×C4—516no—
838C22×C4—51no—
839C22×C4—52no—
840C22×C4—51no—
841C22×C4—51no—
842C22×C4—52no—
843C22×C4—52no—
844C22×C4—58no—
845C22×C4—58no—
846C22×C4—58no—
847C22×C4—58no—
848C22×C4—516no—
849C22×C4—516no—
850C22×C4—1032no—
851C22×C4—108no—
852C22×C4—104no—
853C22×C4—2032no—
854C22×C4C23×D511yescharacteristic
855C22×C4C23×D512yes—
856C22×C4C23×D518yes—
857C22×C4C23×D5116yes—
858C4⋊C4—58no—
859C4⋊C4—54no—
860C4⋊C4—58no—
861C4⋊C4—54no—
862C4⋊C4—516no—
863C4⋊C4—516no—
864C4⋊C4—516no—
865C4⋊C4—58no—
866C4⋊C4—54no—
867C4⋊C4—58no—
868C4⋊C4—54no—
869C4⋊C4—58no—
870C4⋊C4—58no—
871C4⋊C4—58no—
872C4⋊C4C23×D514yes—
873C4⋊C4C23×D514yes—
874C4⋊C4C23×D5116yes—
875C4⋊C4C23×D514yes—
876C4⋊C4C23×D514yes—
877C4⋊C4C23×D518yes—
878C22⋊C4—54no—
879C22⋊C4—516no—
880C22⋊C4—58no—
881C22⋊C4—58no—
882C22⋊C4—58no—
883C22⋊C4—516no—
884C22⋊C4—516no—
885C22⋊C4—58no—
886C22⋊C4—58no—
887C22⋊C4—58no—
888C22⋊C4—58no—
889C22⋊C4C23×D514yes—
890C22⋊C4C23×D5116yes—
891C22⋊C4C23×D518yes—
892C22⋊C4C23×D518yes—
893C42—51no—
894C42—52no—
895C42—52no—
896C42—52no—
897C42—52no—
898C42—52no—
899C42—51no—
900C42—58no—
901C42—54no—
902C42C23×D511yescharacteristic
903C42C23×D512yes—
904C42C23×D511yescharacteristic
905C42C23×D514yes—
906C2×C5—41no—
907C2×C5—48no—
908C2×C5C22×H(5,𝔽2)12yes—
909C2×C5C22×2−1+411yescharacteristic
910D5—41no—
911D5—48no—
912D5#354814yesdirect product factor
913C23—51no—
914C23—51no—
915C23—58no—
916C23—104no—
917C23—1016no—
918C23—102no—
919C23—1016no—
920C23—1016no—
921C23C24×D511yescharacteristic
922C23C24×D518yes—
923Q8—28no—
924Q8—44no—
925Q8—1016no—
926Q8—108no—
927Q8—208no—
928Q8—204no—
929D4—28no—
930D4—28no—
931D4—48no—
932D4—44no—
933D4—416no—
934D4—1016no—
935D4—1016no—
936D4—108no—
937D4—108no—
938D4—208no—
939D4—204no—
940D4—2016no—
941D4—208no—
942D4—208no—
943D4—208no—
944D4—2016no—
945D4—2016no—
946C2×C4—216no—
947C2×C4—24no—
948C2×C4—22no—
949C2×C4—416no—
950C2×C4—51no—
951C2×C4—52no—
952C2×C4—58no—
953C2×C4—54no—
954C2×C4—51no—
955C2×C4—52no—
956C2×C4—58no—
957C2×C4—58no—
958C2×C4—1016no—
959C2×C4—104no—
960C2×C4—102no—
961C2×C4—1016no—
962C2×C4—104no—
963C2×C4—102no—
964C2×C4—1016no—
965C2×C4—1016no—
966C2×C4—104no—
967C2×C4—102no—
968C2×C4—1016no—
969C2×C4—104no—
970C2×C4—102no—
971C2×C4—2016no—
972C2×C4—2016no—
973C2×C4—2016no—
974C2×C4C24×D511yescharacteristic
975C2×C4C24×D512yes—
976C2×C4C24×D518yes—
977C2×C4C24×D518yes—
978C2×C4C24×D512yes—
979C2×C4C24×D511yescharacteristic
980C5C2×#354811yescharacteristic, complemented, Sylow
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—54no—
987C22—52no—
988C22—102no—
989C22—108no—
990C22—108no—
991C22—101no—
992C22—108no—
993C22—204no—
994C22—2032no—
995C22C25×D511yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—54no—
1001C4—52no—
1002C4—108no—
1003C4—102no—
1004C4—108no—
1005C4—101no—
1006C4D5×H(5,𝔽2)14yes—
1007C4D5×2−1+412yes—
1008C2—41no—
1009C2—48no—
1010C2—54no—
1011C2—201no—
1012C2—208no—
1013C2C2×D5×H(5,𝔽2)12yes—
1014C2C2×D5×2−1+411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3548C2
hypercenter#3548D5
hypocenterC5C2×#3548
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. C5×#3548C2semidirect
2. D5×#562C2semidirect
3. #10619000C2semidirect
4. D5×#554C2semidirect
5. #10618840C2semidirect
6. D5×#550C2semidirect
7. #10618681C2semidirect
8. D5×#547C2semidirect
9. #10618594C2semidirect
10. D5×#540C2semidirect
11. #10618377C2semidirect
12. D5×#537C2semidirect
13. #10618275C2semidirect
14. #10618189C2semidirect
15. D5×#533C2semidirect
16. #10618152C2semidirect
17. D5×#532C2semidirect
20. C5×#562C22semidirect
21. C5×#554C22semidirect
22. C5×#550C22semidirect
23. C5×#547C22semidirect
24. C5×#540C22semidirect
25. C5×#537C22semidirect
26. C5×#533C22semidirect
27. C5×#532C22semidirect
28. #66168C22semidirect
29. #66167C22semidirect
30. #66167C22semidirect
31. #66166C22semidirect
32. #66158C22semidirect
33. #66064C22semidirect
34. #66062C22semidirect
35. #66060C22semidirect
36. #66059C22semidirect
39. #66053C22semidirect
40. #66052C22semidirect
41. #66052C22semidirect
42. #66050C22semidirect
45. #66034C22semidirect
46. #66032C22semidirect
47. #66024C22semidirect
48. #66022C22semidirect
51. #66018C22semidirect
53. #66002C22semidirect
54. #66001C22semidirect
55. #65997C22semidirect
56. #65989C22semidirect
58. #65981C22semidirect
59. #65970C22semidirect
60. #65969C22semidirect
61. #65965C22semidirect
62. #65963C22semidirect
63. #65963C22semidirect
64. #65963C22semidirect
68. #65956C22semidirect
69. #65955C22semidirect
70. #65953C22semidirect
71. #65949C22semidirect
72. #65945C22semidirect
73. #65942C22semidirect
74. #65942C22semidirect
75. #65942C22semidirect
81. #65933C22semidirect
82. #65933C22semidirect
83. #65931C22semidirect
84. #65931C22semidirect
85. #65930C22semidirect
86. #65930C22semidirect
87. #65913C22semidirect
88. #65912C22semidirect
89. #65911C22semidirect
91. #65896C22semidirect
92. #65889C22semidirect
93. #65887C22semidirect
94. #65887C22semidirect
95. #65885C22semidirect
96. #65882C22semidirect
97. #65882C22semidirect
101. #65877C22semidirect
102. #65873C22semidirect
103. #65869C22semidirect
105. #65851C22semidirect
106. #65845C22semidirect
107. #65844C22semidirect
108. #65841C22semidirect
110. #65811C22semidirect
112. #65804C22semidirect
297. #3548D5direct (N × H)
431. #562C2×D5semidirect
440. #554C2×D5semidirect
449. #550C2×D5semidirect
458. #547C2×D5semidirect
466. #540C2×D5semidirect
478. #537C2×D5semidirect
485. #533C2×D5semidirect
495. #532C2×D5semidirect
912. D5#3548direct (N × H)
980. C5C2×#3548semidirect

Maximal subgroups

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

subgroupindex
C5×#35482
D5×#5622
#106190002
D5×#5542
#106188402
D5×#5502
#106186812
D5×#5472
#106185942
D5×#5402
#106183772
D5×#5372
#106182752
#106181892
D5×#5332
#106181522
D5×#5322
C2×#35485