Finite Group Databasebeta

← #13007132

Subgroups — #13007132

Order 1280.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3550C211yesmaximal, characteristic, complemented
2#10619032C214yesmaximal, complemented
3#10619016C214yesmaximal, complemented
4#10618967C212yesmaximal, complemented
5#10618951C212yesmaximal, complemented
6#10618948C212yesmaximal, complemented
7#10618941C212yesmaximal, complemented
8#10618910C214yesmaximal, complemented
9#10618880C214yesmaximal, complemented
10#10618664C214yesmaximal, complemented
11D4×#713C214yesmaximal, complemented
12#10618464C218yesmaximal, complemented
13#10618425C218yesmaximal, complemented
14#10618251C214yesmaximal, complemented
15#10618239C214yesmaximal, complemented
16#10618189C212yesmaximal, complemented
17#10618158C212yesmaximal, complemented
18#10618153C211yesmaximal, characteristic, complemented
19D5×#532C211yesmaximal, characteristic, complemented
20C2×D5×#41C2212yescomplemented
21C22×#713C2214yescomplemented
22C5×#563C2214yescomplemented
23C5×#559C2212yescomplemented
24C5×Q82C2212yescomplemented
25C5×#556C2214yescomplemented
26C5×D4×Q8C2214yescomplemented
27C5×#542C2218yescomplemented
28C5×#536C2214yescomplemented
29C5×#533C2212yescomplemented
30C5×#532C2211yescharacteristic
31#66166C2212yescomplemented
32#66164C2214yescomplemented
33#66151C2218yescomplemented
34#66150C2214yescomplemented
35#66069C2218yescomplemented
36#66068C2218yescomplemented
37#66068C2212yescomplemented
38#66068C2218yescomplemented
39#66063C2218yescomplemented
40#66062C2212yescomplemented
41#66062C2212yescomplemented
42#66060C2214yescomplemented
43#66060C2214yescomplemented
44#66060C2218yescomplemented
45#66059C2212yes—
46#66059C2218yescomplemented
47#66059C2211yescharacteristic, complemented
48#66059C2212yescomplemented
49#66059C2218yescomplemented
50#66058C2218yescomplemented
51D5×C4⋊Q8C2211yescharacteristic, complemented
52#66051C2212yescomplemented
53#66050C2211yescharacteristic
54D5×#127C2211yescharacteristic
55#66045C22116yescomplemented
56#66040C22116yescomplemented
57#66039C22116yescomplemented
58#66038C22116yescomplemented
59#66034C2218yescomplemented
60#66025C2214yescomplemented
61#66025C2214yescomplemented
62#66017C2214yescomplemented
63#66014C2218yescomplemented
64#66012C22116yescomplemented
65#66010C2218yescomplemented
66#66010C2218yescomplemented
67#66008C2218yescomplemented
68#66008C2218yescomplemented
69D5×#124C2212yescomplemented
70#66002C2212yescomplemented
71#66002C2218yescomplemented
72#66000C2218yescomplemented
73#65997C22116yescomplemented
74#65993C2218yescomplemented
75#65990C2218yescomplemented
76#65990C2218yescomplemented
77#65987C2218yescomplemented
78#65987C2218yescomplemented
79#65981C22116yescomplemented
80#65974C22116yescomplemented
81#65973C2218yescomplemented
82#65964C2218yescomplemented
83#65964C22116yescomplemented
84#65963C2218yescomplemented
85#65963C2218yescomplemented
86#65963C2218yescomplemented
87#65961C2218yescomplemented
88#65961C22116yescomplemented
89#65961C2214yescomplemented
90#65961C2214yescomplemented
91#65958C2214yescomplemented
92#65958C2214yescomplemented
93#65941C2218yescomplemented
94D5×#121C2214yescomplemented
95#65930C2214yescomplemented
96#65916C2218yescomplemented
97#65915C2218yescomplemented
98#65914C2214yescomplemented
99#65914C2214yescomplemented
100#65913C2214yescomplemented
101#65913C2214yescomplemented
102#65911C2214yescomplemented
103#65911C2218yescomplemented
104#65911C2214yescomplemented
105C4×#713C2214yescomplemented
106C4×#713C2218yescomplemented
107C4×#713C2214yescomplemented
108#65897C2214yescomplemented
109#65896C2218yescomplemented
110#65892C2218yescomplemented
111D4×D20C2214yescomplemented
112D4×D20C2218yescomplemented
113#65882C2214yescomplemented
114C4×D4×D5C2214yescomplemented
115C4×D4×D5C2218yescomplemented
116#65869C2218yescomplemented
117#65864C2218yescomplemented
118#65859C2214yescomplemented
119#65858C2214yescomplemented
120#65856C2214yescomplemented
121D5×#117C2214yescomplemented
122#65811C2211yescharacteristic, complemented
123#65811C2212yescomplemented
124C2×C42×D5C2211yescharacteristic, complemented
125#62759—51nomaximal, Sylow
126C2×C5×#41C2312yes—
127C22×C5×Q8C2314yes—
128D5×#41—48no—
129C2×#713—416no—
130C2×#713C2314yes—
131C2×#713C2318yes—
132C2×#713C2312yes—
133C2×#713C2318yes—
134C2×#713C2314yes—
135C2×#713C2318yes—
136C2×#713C2318yes—
137C2×Q8×D5C2312yes—
138C2×#711C2312yes—
139C2×#711C2314yes—
140C2×D4×D5C2314yes—
141C2×D4×D5C2312yes—
142C2×D4×D5C2318yes—
143C2×D4×D5C2314yes—
144C2×#709C2314yes—
145C2×#709C2312yes—
146C2×#709C2314yes—
147C22×D20C2314yes—
148C22×D20C2318yes—
149C22×C4×D5C2311yescharacteristic
150C22×C4×D5C2314yes—
151C22×C4×D5C2312yes—
152C22×C4×D5C2318yes—
153C5×C4⋊Q8C2311yescharacteristic
154C5×C4⋊Q8C2318yes—
155C5×C4⋊Q8C2312yes—
156C5×C4⋊Q8C2312yes—
157C5×C4⋊Q8C2318yes—
158C5×#127C2311yescharacteristic
159C5×#126C23116yes—
160C5×#125C2314yes—
161C5×#124C2312yes—
162C5×#124C2318yes—
163C5×#124C2318yes—
164C5×#123C2318yes—
165C5×#123C2318yes—
166C5×C22⋊Q8C2314yes—
167C5×C22⋊Q8C2314yes—
168C5×C22⋊Q8C2318yes—
169C5×C22⋊Q8C23116yes—
170C5×#121C2314yes—
171C4×C5×Q8C2314yes—
172C4×C5×Q8C2314yes—
173C4×C5×Q8C2318yes—
174C4×C5×D4C2314yes—
175C4×C5×D4C2318yes—
176C5×#117C2314yes—
177C5×#117C2314yes—
178C2×C42×C5C2311yescharacteristic
179#4093C2318yes—
180#4093C2314yes—
181#4093C2312yes—
182#4093C2318yes—
183#4093C23116yes—
184#4093C2314yes—
185#4092C23116yes—
186#4092C2318yes—
187#4092C2318yes—
188#4092C2314yes—
189#4092C2314yes—
190Q8×Dic5C2314yes—
191Q8×Dic5C2314yes—
192#4090C2312yes—
193#4090C2318yes—
194#4086C2314yes—
195#4086C2312yes—
196#4086C2318yes—
197#4085C2318yes—
198#4084C2314yes—
199#4084C2318yes—
200#4083C2318yes—
201#4083C2318yes—
202#4082C2312yes—
203D4×Dic5C2314yes—
204#4076C2314yes—
205#4076C2314yes—
206#4076C2314yes—
207#4076C2318yes—
208#4076C23116yes—
209#4075C2318yes—
210#4075C2318yes—
211C4×C22⋊D5C2318yes—
212C4×C22⋊D5C23116yes—
213#4072C2314yes—
214C2×C4×Dic5C2312yes—
215C2×C4×Dic5C2311yescharacteristic
216#4044C2318yes—
217#4044C2318yes—
218#4043C2314yes—
219#4043C2314yes—
220#4042C23116yes—
221#4042C23116yes—
222#4042C23116yes—
223#4041C2314yes—
224#4041C2314yes—
225#4041C2318yes—
226#4041C2318yes—
227#4041C2314yes—
228#4041C23116yes—
229#4041C23116yes—
230#4041C23116yes—
231#4041C2314yes—
232#4041C2314yes—
233#4041C2318yes—
234#4041C23116yes—
235#4040C2318yes—
236#4040C23116yes—
237#4040C23116yes—
238#4040C23116yes—
239#4040C23116yes—
240#4040C2318yes—
241#4039C2314yes—
242#4039C2314yes—
243#4039C2314yes—
244#4039C23116yes—
245#4039C2318yes—
246#4039C2314yes—
247#4039C2314yes—
248#4039C2318yes—
249#4038C2314yes—
250#4038C2314yes—
251#4038C2318yes—
252#4038C2318yes—
253#4038C23116yes—
254#4038C2318yes—
255D5×C4⋊C4C2314yes—
256D5×C4⋊C4C2318yes—
257D5×C4⋊C4C2318yes—
258#4036C2314yes—
259#4036C2314yes—
260#4035C23116yes—
261#4034C2314yes—
262#4033C2314yes—
263#4033C2314yes—
264#4032C2318yes—
265#4031C2318yes—
266#4031C23116yes—
267#4030C23116yes—
268#4030C23116yes—
269#4030C23116yes—
270#4030C2318yes—
271#4030C23116yes—
272#4030C23116yes—
273#4029C23116yes—
274#4029C23116yes—
275#4028C2318yes—
276#4028C2318yes—
277#4028C2318yes—
278#4028C23116yes—
279#4028C23116yes—
280#4028C23116yes—
281#4027C2318yes—
282#4027C2318yes—
283#4027C2318yes—
284#4027C23116yes—
285D5×C22⋊C4C2318yes—
286D5×C22⋊C4C2318yes—
287D5×C22⋊C4C23116yes—
288#4025C23116yes—
289#4023C2318yes—
290#4022C23116yes—
291#4021C2318yes—
292#4021C2312yes—
293#4021C2314yes—
294#4020C2311yescharacteristic
295#4020C2312yes—
296#4020C2318yes—
297#4020C2318yes—
298C4×D20C2314yes—
299C4×D20C2314yes—
300C4×D20C2314yes—
301C4×D20C2318yes—
302C4×D20C2318yes—
303C4×D20C2318yes—
304C4×D20C23116yes—
305C4×D20C2318yes—
306#4018C2318yes—
307#4018C2318yes—
308C42×D5C2311yescharacteristic
309C42×D5C2311yescharacteristic
310C42×D5C2312yes—
311C42×D5C2312yes—
312C42×D5C2318yes—
313C42×D5C2318yes—
314C42×D5C2311yescharacteristic
315C42×D5C2311yescharacteristic
316#4016C2318yes—
317#4015C2311yescharacteristic
318#4015C2312yes—
319#3551—54no—
320#3550D511yescharacteristic, complemented
321#3549—51no—
322#3548—52no—
323#3547—54no—
324#3546—54no—
325#3545—54no—
326#3544—52no—
327#3543—52no—
328#3542—58no—
329#3529—54no—
330#3483—52no—
331#3481—52no—
332#3475—54no—
333D4×#41—54no—
334#3460—58no—
335#3449—54no—
336#3444—52no—
337C2×#532—51no—
338C23×D5C2411yescharacteristic
339C23×D5C2414yes—
340C23×D5C2418yes—
341C5×#41—44no—
342C2×C5×Q8—48no—
343C2×C5×Q8C2414yes—
344C2×C5×Q8C2414yes—
345C2×C5×Q8C2418yes—
346C2×C5×Q8C2412yes—
347C2×C5×D4C2414yes—
348C2×C5×D4C2414yes—
349C2×C5×D4C2412yes—
350C22×C4×C5C2412yes—
351C22×C4×C5C2411yescharacteristic
352C22×C4×C5C2414yes—
353C22×C4×C5C2418yes—
354C2×C22⋊D5C2414yes—
355C2×C22⋊D5C2414yes—
356C2×C22⋊D5C2414yes—
357C2×C22⋊D5C2418yes—
358C2×C22⋊D5C2418yes—
359C2×C22⋊D5C24116yes—
360C22×Dic5C2414yes—
361C22×Dic5C2411yescharacteristic
362C22×Dic5C2412yes—
363#713—216no—
364#713—416no—
365#713—44no—
366#713—416no—
367#713—416no—
368#713—48no—
369#713—416no—
370Q8×D5—44no—
371#711—44no—
372#711—48no—
373D4×D5—48no—
374D4×D5—416no—
375D4×D5—44no—
376D4×D5—48no—
377#709—48no—
378#709—48no—
379#709—44no—
380C2×D20—48no—
381C2×D20—416no—
382C2×D20C2414yes—
383C2×D20C2418yes—
384C2×D20C2414yes—
385C2×D20C2414yes—
386C2×D20C2418yes—
387C2×D20C24116yes—
388C2×D20C2414yes—
389C2×D20C2412yes—
390C2×D20C2414yes—
391C2×D20C2418yes—
392C2×D20C24116yes—
393C2×C4×D5—216no—
394C2×C4×D5—24no—
395C2×C4×D5—416no—
396C2×C4×D5—44no—
397C2×C4×D5C2418yes—
398C2×C4×D5C2411yescharacteristic
399C2×C4×D5C2414yes—
400C2×C4×D5C2411yescharacteristic
401C2×C4×D5C2412yes—
402C2×C4×D5C2414yes—
403C2×C4×D5C2411yescharacteristic
404C2×C4×D5C2414yes—
405C2×C4×D5C2412yes—
406C2×C4×D5C2418yes—
407C2×C4×D5C24116yes—
408C2×C4×D5C2412yes—
409C2×C4×D5C2412yes—
410C2×C4×D5C2418yes—
411C2×C4×D5C24116yes—
412C2×C4×D5C2411yescharacteristic
413C2×Dic10C2412yes—
414C2×Dic10C2414yes—
415C2×Dic10C2414yes—
416C5×C4⋊C4C2414yes—
417C5×C4⋊C4C2414yes—
418C5×C4⋊C4C2414yes—
419C5×C4⋊C4C2414yes—
420C5×C4⋊C4C2414yes—
421C5×C4⋊C4C2418yes—
422C5×C4⋊C4C24116yes—
423C5×C4⋊C4C2418yes—
424C5×C22⋊C4C2418yes—
425C5×C22⋊C4C2418yes—
426C5×C22⋊C4C2418yes—
427C5×C22⋊C4C24116yes—
428C42×C5C2412yes—
429C42×C5C2411yescharacteristic
430C42×C5C2411yescharacteristic
431C42×C5C2418yes—
432C42×C5C2418yes—
433C22⋊Dic5C2418yes—
434C22⋊Dic5C2418yes—
435#685C2418yes—
436#685C2418yes—
437#685C2418yes—
438#685C2418yes—
439#685C24116yes—
440#685C2418yes—
441#685C2418yes—
442#685C2418yes—
443#685C2418yes—
444#685C24116yes—
445#685C2418yes—
446#685C24116yes—
447#685C2418yes—
448C4⋊Dic5C2414yes—
449C4⋊Dic5C2414yes—
450C4⋊Dic5C2414yes—
451C4⋊Dic5C2418yes—
452C4⋊Dic5C2418yes—
453#683C24116yes—
454#683C24116yes—
455#683C2418yes—
456#683C2418yes—
457#683C2418yes—
458C4×Dic5C2412yes—
459C4×Dic5C2418yes—
460C4×Dic5C2412yes—
461C4×Dic5C2412yes—
462C4×Dic5C2412yes—
463C4×Dic5C2412yes—
464C4×Dic5C2411yescharacteristic
465C4×Dic5C2411yescharacteristic
466C4×Dic5C2418yes—
467C4×Dic5C2418yes—
468C22×#41—52no—
469C22×#41—54no—
470#563—58no—
471#563C2×D514yescomplemented
472#562—58no—
473#562—516no—
474H(3,𝔽4)—54no—
475#560—516no—
476#560—58no—
477#559C2×D512yescomplemented
478Q82C2×D512yescomplemented
479#556C2×D514yescomplemented
480#555—58no—
481#555—52no—
482#555—58no—
483#555—54no—
484#554—54no—
485#554—54no—
486#553—58no—
487#553—58no—
488#552—58no—
489#552—58no—
490#551—516no—
491#551—58no—
492#550—54no—
493#550—58no—
494#550—54no—
495D4×Q8C2×D514yescomplemented
496#548—58no—
497#547—58no—
498#547—54no—
499#547—54no—
500#546—58no—
501#546—58no—
502#546—516no—
503#546—58no—
504D42—52no—
505D42—58no—
506D42—54no—
507#544—58no—
508#542—516no—
509#542—58no—
510#542C2×D518yescomplemented
511#540—516no—
512#540—58no—
513#540—58no—
514#538—516no—
515#538—516no—
516#537—58no—
517#537—58no—
518#537—58no—
519#536—54no—
520#536—58no—
521#536C2×D514yescomplemented
522#535—54no—
523#535—58no—
524#535—58no—
525#535—58no—
526#535—54no—
527#534—58no—
528#534—58no—
529#533—52no—
530#533—52no—
531#533C2×D512yescomplemented
532#532—52no—
533#532—52no—
534#532—51no—
535#532—52no—
536#532—58no—
537#532—58no—
538#532—51no—
539#532—52no—
540#532—58no—
541#532—54no—
542#532—54no—
543#532—51no—
544#532—52no—
545#532C2×D511yescharacteristic
546C2×C4⋊Q8—51no—
547C2×#127—51no—
548#529—516no—
549#529—54no—
550#529—54no—
551#529—58no—
552#529—54no—
553#529—54no—
554#529—54no—
555#529—54no—
556C2×#124—52no—
557#525—58no—
558#525—58no—
559#525—54no—
560#525—54no—
561#525—58no—
562#525—516no—
563#525—54no—
564C2×#121—54no—
565C4×#41—54no—
566C4×#41—54no—
567C4×#41—58no—
568C4×#41—54no—
569C2×C4×D4—54no—
570C2×C4×D4—58no—
571C2×#117—54no—
572C22×C42—51no—
573C23×C5C2514yes—
574C23×C5C2511yescharacteristic
575C22×D5—22no—
576C22×D5—28no—
577C22×D5—42no—
578C22×D5—48no—
579C22×D5—48no—
580C22×D5—416no—
581C22×D5C2518yes—
582C22×D5C2514yes—
583C22×D5C2511yescharacteristic
584C22×D5C2511yescharacteristic
585C5×Q8—28no—
586C5×Q8—28no—
587C5×Q8—42no—
588C5×Q8—48no—
589C5×D4—28no—
590C5×D4—42no—
591C5×D4—44no—
592C2×C4×C5—28no—
593C2×C4×C5—22no—
594C2×C4×C5—24no—
595C2×C4×C5—48no—
596C2×C4×C5C2514yes—
597C2×C4×C5C2512yes—
598C2×C4×C5C2511yescharacteristic
599C2×C4×C5C2518yes—
600C2×C4×C5C2518yes—
601C2×C4×C5C2511yescharacteristic
602C2×C4×C5C2512yes—
603C22⋊D5—44no—
604C22⋊D5—44no—
605C22⋊D5—44no—
606C22⋊D5—48no—
607C22⋊D5—416no—
608C22⋊D5—48no—
609C2×Dic5—28no—
610C2×Dic5—22no—
611C2×Dic5—42no—
612C2×Dic5C2512yes—
613C2×Dic5C2512yes—
614C2×Dic5C2511yescharacteristic
615C2×Dic5C2518yes—
616C2×Dic5C2514yes—
617C2×Dic5C2511yescharacteristic
618D20—216no—
619D20—28no—
620D20—28no—
621D20—28no—
622D20—48no—
623D20—416no—
624D20—44no—
625D20—42no—
626D20—44no—
627D20—48no—
628D20—416no—
629C4×D5—22no—
630C4×D5—28no—
631C4×D5—22no—
632C4×D5—28no—
633C4×D5—24no—
634C4×D5—24no—
635C4×D5—216no—
636C4×D5—22no—
637C4×D5—28no—
638C4×D5—216no—
639C4×D5—42no—
640C4×D5—42no—
641C4×D5—416no—
642C4×D5—416no—
643C4×D5—48no—
644C4×D5H(5,𝔽2)14yes—
645Dic10—44no—
646Dic10—44no—
647Dic10—42no—
648C2×#41—54no—
649C2×#41—54no—
650C2×#41—58no—
651C2×#41—58no—
652C2×#41—52no—
653C2×#41—58no—
654C2×#41—58no—
655C2×#41—52no—
656C2×#41—54no—
657C2×#41—54no—
658C2×#41—54no—
659C2×#41—52no—
660C2×#41—208no—
661C2×#41—2016no—
662C2×#41C22×D512yes—
663C22×Q8—52no—
664C22×Q8C22×D514yes—
665C22×D4—54no—
666C22×D4—58no—
667C22×D4—54no—
668C22×D4—52no—
669C22×D4—58no—
670C22×D4—54no—
671C23×C4—54no—
672C23×C4—51no—
673C23×C4—58no—
674C23×C4—52no—
675C4⋊Q8—52no—
676C4⋊Q8—58no—
677C4⋊Q8—54no—
678C4⋊Q8—51no—
679C4⋊Q8—52no—
680C4⋊Q8C22×D511yescharacteristic
681C4⋊Q8C22×D512yes—
682C4⋊Q8C22×D512yes—
683C4⋊Q8C22×D518yes—
684C4⋊Q8C22×D518yes—
685#127—54no—
686#127—52no—
687#127—58no—
688#127—51no—
689#127—52no—
690#127—58no—
691#127—58no—
692#127C22×D511yescharacteristic
693#126—58no—
694#126—58no—
695#126—516no—
696#126—516no—
697#126C22×D5116yes—
698#125—54no—
699#125—54no—
700#125—516no—
701#125—58no—
702#125C22×D514yes—
703#124—52no—
704#124—54no—
705#124—54no—
706#124—58no—
707#124—58no—
708#124—516no—
709#124—52no—
710#124—58no—
711#124—516no—
712#124—52no—
713#124—54no—
714#124—58no—
715#124C22×D512yes—
716#124C22×D518yes—
717#124C22×D518yes—
718#123—58no—
719#123—58no—
720#123—58no—
721#123—58no—
722#123—516no—
723#123—516no—
724#123—516no—
725#123—516no—
726#123—58no—
727#123—516no—
728#123—516no—
729#123C22×D518yes—
730#123C22×D518yes—
731C22⋊Q8—54no—
732C22⋊Q8—54no—
733C22⋊Q8—58no—
734C22⋊Q8—516no—
735C22⋊Q8—58no—
736C22⋊Q8—54no—
737C22⋊Q8—54no—
738C22⋊Q8—516no—
739C22⋊Q8—516no—
740C22⋊Q8—516no—
741C22⋊Q8C22×D514yes—
742C22⋊Q8C22×D514yes—
743C22⋊Q8C22×D518yes—
744C22⋊Q8C22×D5116yes—
745#121—58no—
746#121—54no—
747#121—58no—
748#121—54no—
749#121—54no—
750#121—54no—
751#121—58no—
752#121—516no—
753#121—54no—
754#121—54no—
755#121—54no—
756#121—54no—
757#121—54no—
758#121—58no—
759#121—516no—
760#121—516no—
761#121—516no—
762#121—58no—
763#121—58no—
764#121—516no—
765#121—58no—
766#121—516no—
767#121—516no—
768#121—516no—
769#121—516no—
770#121—516no—
771#121C22×D514yes—
772#120—58no—
773#120—58no—
774#120—58no—
775#120—58no—
776#120—516no—
777#120—58no—
778#120—516no—
779#120—516no—
780C4×Q8—54no—
781C4×Q8—54no—
782C4×Q8—54no—
783C4×Q8—54no—
784C4×Q8C22×D514yes—
785C4×Q8C22×D514yes—
786C4×Q8C22×D518yes—
787C4×D4—54no—
788C4×D4—58no—
789C4×D4—516no—
790C4×D4—54no—
791C4×D4—54no—
792C4×D4—54no—
793C4×D4—58no—
794C4×D4—516no—
795C4×D4—58no—
796C4×D4—54no—
797C4×D4—54no—
798C4×D4—516no—
799C4×D4—58no—
800C4×D4—58no—
801C4×D4—58no—
802C4×D4—54no—
803C4×D4—58no—
804C4×D4—58no—
805C4×D4—58no—
806C4×D4—54no—
807C4×D4—54no—
808C4×D4—516no—
809C4×D4—58no—
810C4×D4C22×D514yes—
811C4×D4C22×D518yes—
812#117—54no—
813#117—54no—
814#117—58no—
815#117—54no—
816#117—58no—
817#117—58no—
818#117—516no—
819#117—58no—
820#117—58no—
821#117—58no—
822#117C22×D514yes—
823#117C22×D514yes—
824C2×C4⋊C4—58no—
825C2×C4⋊C4—54no—
826C2×C4⋊C4—58no—
827C2×C22⋊C4—58no—
828C2×C22⋊C4—58no—
829C2×C22⋊C4—516no—
830C2×C42—52no—
831C2×C42—51no—
832C2×C42—58no—
833C2×C42—52no—
834C2×C42—58no—
835C2×C42—51no—
836C2×C42—51no—
837C2×C42—51no—
838C2×C42—51no—
839C2×C42—52no—
840C2×C42C22×D511yescharacteristic
841C22×C5—21no—
842C22×C5—24no—
843C22×C5—22no—
844C22×C5—28no—
845C22×C5C2611yescharacteristic
846C2×D5—22no—
847C2×D5—24no—
848C2×D5—21no—
849C2×D5—28no—
850C2×D5—22no—
851C2×D5—28no—
852C2×D5—28no—
853C2×D5—28no—
854C2×D5—44no—
855C2×D5—88no—
856C2×D5—816no—
857C2×D5C2×H(5,𝔽2)12yes—
858C4×C5—21no—
859C4×C5—24no—
860C4×C5—28no—
861C4×C5—22no—
862C4×C5—28no—
863C4×C5C2×H(5,𝔽2)12yes—
864C4×C5#58514yes—
865Dic5—21no—
866Dic5—24no—
867Dic5—28no—
868Dic5—22no—
869Dic5—22no—
870Dic5C2×H(5,𝔽2)12yes—
871C24—54no—
872C24—51no—
873C24—58no—
874#41—44no—
875#41—1016no—
876#41—208no—
877#41—204no—
878#41—208no—
879#41—204no—
880#41—208no—
881#41—204no—
882#41—2016no—
883#41—2016no—
884#41—2016no—
885#41—208no—
886#41—2016no—
887C2×Q8—48no—
888C2×Q8—54no—
889C2×Q8—52no—
890C2×Q8—54no—
891C2×Q8—204no—
892C2×Q8C23×D514yes—
893C2×Q8C23×D514yes—
894C2×Q8C23×D518yes—
895C2×Q8C23×D512yes—
896C2×D4—516no—
897C2×D4—58no—
898C2×D4—58no—
899C2×D4—54no—
900C2×D4—54no—
901C2×D4—54no—
902C2×D4—54no—
903C2×D4—54no—
904C2×D4—58no—
905C2×D4—54no—
906C2×D4—54no—
907C2×D4—58no—
908C2×D4—516no—
909C2×D4—58no—
910C2×D4—516no—
911C2×D4—52no—
912C2×D4—54no—
913C2×D4—208no—
914C2×D4—2016no—
915C2×D4—208no—
916C2×D4—2016no—
917C2×D4—204no—
918C2×D4—208no—
919C2×D4C23×D514yes—
920C2×D4C23×D512yes—
921C2×D4C23×D514yes—
922C22×C4—51no—
923C22×C4—51no—
924C22×C4—54no—
925C22×C4—52no—
926C22×C4—52no—
927C22×C4—52no—
928C22×C4—51no—
929C22×C4—54no—
930C22×C4—51no—
931C22×C4—51no—
932C22×C4—58no—
933C22×C4—58no—
934C22×C4—54no—
935C22×C4—54no—
936C22×C4—52no—
937C22×C4—52no—
938C22×C4—58no—
939C22×C4—516no—
940C22×C4—516no—
941C22×C4—1016no—
942C22×C4—104no—
943C22×C4—204no—
944C22×C4—2016no—
945C22×C4C23×D512yes—
946C22×C4C23×D511yescharacteristic
947C22×C4C23×D514yes—
948C22×C4C23×D518yes—
949C4⋊C4—54no—
950C4⋊C4—54no—
951C4⋊C4—516no—
952C4⋊C4—58no—
953C4⋊C4—516no—
954C4⋊C4—54no—
955C4⋊C4—58no—
956C4⋊C4—58no—
957C4⋊C4—58no—
958C4⋊C4—58no—
959C4⋊C4C23×D514yes—
960C4⋊C4C23×D514yes—
961C4⋊C4C23×D514yes—
962C4⋊C4C23×D518yes—
963C4⋊C4C23×D518yes—
964C4⋊C4C23×D5116yes—
965C4⋊C4C23×D514yes—
966C4⋊C4C23×D514yes—
967C22⋊C4—58no—
968C22⋊C4—58no—
969C22⋊C4—58no—
970C22⋊C4—58no—
971C22⋊C4—58no—
972C22⋊C4—516no—
973C22⋊C4—58no—
974C22⋊C4—58no—
975C22⋊C4—58no—
976C22⋊C4—516no—
977C22⋊C4—58no—
978C22⋊C4—58no—
979C22⋊C4—58no—
980C22⋊C4—58no—
981C22⋊C4—516no—
982C22⋊C4C23×D518yes—
983C22⋊C4C23×D5116yes—
984C22⋊C4C23×D518yes—
985C22⋊C4C23×D518yes—
986C42—52no—
987C42—51no—
988C42—58no—
989C42—52no—
990C42—52no—
991C42—52no—
992C42—52no—
993C42—51no—
994C42—58no—
995C42—58no—
996C42C23×D512yes—
997C42C23×D511yescharacteristic
998C42C23×D511yescharacteristic
999C42C23×D518yes—
1000C42C23×D518yes—
1001C2×C5—41no—
1002C2×C5—44no—
1003C2×C5C22×H(5,𝔽2)11yescharacteristic
1004C2×C5C2×#58512yes—
1005D5—22no—
1006D5—41no—
1007D5—44no—
1008D5—48no—
1009C23—51no—
1010C23—58no—
1011C23—51no—
1012C23—54no—
1013C23—102no—
1014C23—108no—
1015C23—202no—
1016C23—208no—
1017C23—208no—
1018C23—2016no—
1019C23C24×D514yes—
1020C23C24×D511yescharacteristic
1021Q8—28no—
1022Q8—28no—
1023Q8—48no—
1024Q8—42no—
1025Q8—202no—
1026Q8—204no—
1027Q8—204no—
1028D4—28no—
1029D4—42no—
1030D4—44no—
1031D4—1016no—
1032D4—108no—
1033D4—108no—
1034D4—108no—
1035D4—202no—
1036D4—204no—
1037D4—208no—
1038D4—2016no—
1039D4—204no—
1040D4—208no—
1041D4—2016no—
1042D4—204no—
1043D4—204no—
1044D4—204no—
1045D4—208no—
1046D4—2016no—
1047D4—208no—
1048C2×C4—28no—
1049C2×C4—22no—
1050C2×C4—24no—
1051C2×C4—48no—
1052C2×C4—51no—
1053C2×C4—54no—
1054C2×C4—52no—
1055C2×C4—58no—
1056C2×C4—52no—
1057C2×C4—51no—
1058C2×C4—54no—
1059C2×C4—102no—
1060C2×C4—108no—
1061C2×C4—1016no—
1062C2×C4—102no—
1063C2×C4—108no—
1064C2×C4—108no—
1065C2×C4—102no—
1066C2×C4—108no—
1067C2×C4—102no—
1068C2×C4—104no—
1069C2×C4—104no—
1070C2×C4—1016no—
1071C2×C4—2016no—
1072C2×C4—202no—
1073C2×C4—202no—
1074C2×C4—208no—
1075C2×C4—2016no—
1076C2×C4—202no—
1077C2×C4C24×D512yes—
1078C2×C4C24×D511yescharacteristic
1079C2×C4C24×D514yes—
1080C2×C4C24×D518yes—
1081C2×C4C24×D518yes—
1082C2×C4C24×D511yescharacteristic
1083C2×C4C24×D512yes—
1084C5#6275911yescharacteristic, complemented, Sylow
1085C22—24no—
1086C22—21no—
1087C22—22no—
1088C22—28no—
1089C22—52no—
1090C22—102no—
1091C22—101no—
1092C22—104no—
1093C22—108no—
1094C22—102no—
1095C22—108no—
1096C22—108no—
1097C22—108no—
1098C22—204no—
1099C22—408no—
1100C22—4016no—
1101C22C25×D511yescharacteristic
1102C4—21no—
1103C4—24no—
1104C4—28no—
1105C4—22no—
1106C4—28no—
1107C4—52no—
1108C4—104no—
1109C4—101no—
1110C4—102no—
1111C4—102no—
1112C4—108no—
1113C4D5×H(5,𝔽2)12yes—
1114C4#6628714yes—
1115C2—41no—
1116C2—44no—
1117C2—102no—
1118C2—201no—
1119C2—208no—
1120C2—204no—
1121C2C2×D5×H(5,𝔽2)11yescharacteristic
1122C2C2×#6628712yes—
subgroupG/H
center, FrattiniC22C25×D5
commutator, socle, cosocleC22×C5C26
FittingC5×#3550C2
hypercenter#3550D5
hypocenterC5#62759
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. C5×#3550C2semidirect
2. #10619032C2semidirect
3. #10619016C2semidirect
4. #10618967C2semidirect
5. #10618951C2semidirect
6. #10618948C2semidirect
7. #10618941C2semidirect
8. #10618910C2semidirect
9. #10618880C2semidirect
10. #10618664C2semidirect
11. D4×#713C2semidirect
12. #10618464C2semidirect
13. #10618425C2semidirect
14. #10618251C2semidirect
15. #10618239C2semidirect
16. #10618189C2semidirect
17. #10618158C2semidirect
18. #10618153C2semidirect
19. D5×#532C2semidirect
20. C2×D5×#41C22semidirect
21. C22×#713C22semidirect
22. C5×#563C22semidirect
23. C5×#559C22semidirect
24. C5×Q82C22semidirect
25. C5×#556C22semidirect
26. C5×D4×Q8C22semidirect
27. C5×#542C22semidirect
28. C5×#536C22semidirect
29. C5×#533C22semidirect
31. #66166C22semidirect
32. #66164C22semidirect
33. #66151C22semidirect
34. #66150C22semidirect
35. #66069C22semidirect
36. #66068C22semidirect
37. #66068C22semidirect
38. #66068C22semidirect
39. #66063C22semidirect
40. #66062C22semidirect
41. #66062C22semidirect
42. #66060C22semidirect
43. #66060C22semidirect
44. #66060C22semidirect
46. #66059C22semidirect
47. #66059C22semidirect
48. #66059C22semidirect
49. #66059C22semidirect
50. #66058C22semidirect
51. D5×C4⋊Q8C22semidirect
52. #66051C22semidirect
55. #66045C22semidirect
56. #66040C22semidirect
57. #66039C22semidirect
58. #66038C22semidirect
59. #66034C22semidirect
60. #66025C22semidirect
61. #66025C22semidirect
62. #66017C22semidirect
63. #66014C22semidirect
64. #66012C22semidirect
65. #66010C22semidirect
66. #66010C22semidirect
67. #66008C22semidirect
68. #66008C22semidirect
69. D5×#124C22semidirect
70. #66002C22semidirect
71. #66002C22semidirect
72. #66000C22semidirect
73. #65997C22semidirect
74. #65993C22semidirect
75. #65990C22semidirect
76. #65990C22semidirect
77. #65987C22semidirect
78. #65987C22semidirect
79. #65981C22semidirect
80. #65974C22semidirect
81. #65973C22semidirect
82. #65964C22semidirect
83. #65964C22semidirect
84. #65963C22semidirect
85. #65963C22semidirect
86. #65963C22semidirect
87. #65961C22semidirect
88. #65961C22semidirect
89. #65961C22semidirect
90. #65961C22semidirect
91. #65958C22semidirect
92. #65958C22semidirect
93. #65941C22semidirect
94. D5×#121C22semidirect
95. #65930C22semidirect
96. #65916C22semidirect
97. #65915C22semidirect
98. #65914C22semidirect
99. #65914C22semidirect
100. #65913C22semidirect
101. #65913C22semidirect
102. #65911C22semidirect
103. #65911C22semidirect
104. #65911C22semidirect
105. C4×#713C22semidirect
106. C4×#713C22semidirect
107. C4×#713C22semidirect
108. #65897C22semidirect
109. #65896C22semidirect
110. #65892C22semidirect
111. D4×D20C22semidirect
112. D4×D20C22semidirect
113. #65882C22semidirect
114. C4×D4×D5C22semidirect
115. C4×D4×D5C22semidirect
116. #65869C22semidirect
117. #65864C22semidirect
118. #65859C22semidirect
119. #65858C22semidirect
120. #65856C22semidirect
121. D5×#117C22semidirect
122. #65811C22semidirect
123. #65811C22semidirect
124. C2×C42×D5C22semidirect
320. #3550D5semidirect
471. #563C2×D5semidirect
477. #559C2×D5semidirect
478. Q82C2×D5semidirect
479. #556C2×D5semidirect
495. D4×Q8C2×D5semidirect
510. #542C2×D5semidirect
521. #536C2×D5semidirect
531. #533C2×D5semidirect
1084. C5#62759semidirect

Maximal subgroups

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

subgroupindex
C5×#35502
#106190322
#106190162
#106189672
#106189512
#106189482
#106189412
#106189102
#106188802
#106186642
D4×#7132
#106184642
#106184252
#106182512
#106182392
#106181892
#106181582
#106181532
D5×#5322
#627595