Finite Group Databasebeta

← #13007850

Subgroups — #13007850

Order 1280.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66283C212yesmaximal, complemented
2C5×#3449C211yesmaximal, characteristic, complemented
3C2×#66166C212yesmaximal, complemented
4#10618283C214yesmaximal, complemented
5#10618268C214yesmaximal, complemented
6#10618242C214yesmaximal, complemented
7#10618241C214yesmaximal, complemented
8#10618218C214yesmaximal, complemented
9#10618217C214yesmaximal, complemented
10#10618199C218yesmaximal, complemented
11#10618136C214yesmaximal, complemented
12D5×#532C214yesmaximal, complemented
13#10617938C2116yesmaximal, complemented
14#10617636C211yesmaximal, characteristic, complemented
15C2×#65856C211yesmaximal, characteristic, complemented
16C22×C5×#41C2212yescomplemented
17#66283—232no—
18C2×#4150C2214yescomplemented
19C2×#4150C2214yescomplemented
20C2×#4149C2214yescomplemented
21C2×#4149C2214yescomplemented
22C2×D5×#41C2218yescomplemented
23C2×D5×#41C2218yescomplemented
24C2×#4147C2214yescomplemented
25C2×#4144C2218yescomplemented
26C2×#4144C2214yescomplemented
27C22×#709C2211yescharacteristic
28C22×#709C2212yescomplemented
29C22×#709C2218yescomplemented
30C5×#537C2214yescomplemented
31C5×#536C2214yescomplemented
32C5×#535C2214yescomplemented
33C5×#534C2214yescomplemented
34C5×#532C2214yescomplemented
35C5×#525C2218yescomplemented
36C2×C5×#117C2211yescharacteristic, complemented
37#66166C2214yescomplemented
38#66166C2214yescomplemented
39#66166C2218yescomplemented
40#66166C2214yescomplemented
41#66166C2214yescomplemented
42#66166C2218yescomplemented
43C2×#4093C2212yescomplemented
44C2×#4090C2212yescomplemented
45C2×#4086C2212yescomplemented
46C2×#4085C2218yescomplemented
47C2×#4082C2212yescomplemented
48C2×C4×C22⋊D5C2218yescomplemented
49C22×C4×Dic5C2211yescharacteristic, complemented
50#66059C2214yescomplemented
51#66058C2218yescomplemented
52D5×C4⋊Q8C2214yescomplemented
53#66050C2214yescomplemented
54#66049C2218yescomplemented
55D5×#127C2214yescomplemented
56#66009C2218yescomplemented
57#66008C2218yescomplemented
58D5×#124C2218yescomplemented
59#66002C2218yescomplemented
60#65989C22132yescomplemented
61#65988C22132yescomplemented
62#65967C22116yescomplemented
63#65966C22116yescomplemented
64#65965C22116yescomplemented
65#65964C22116yescomplemented
66#65946C22116yescomplemented
67#65943C22116yescomplemented
68#65939C22116yescomplemented
69D5×#121C22116yescomplemented
70#65933C22116yescomplemented
71#65932C22116yescomplemented
72#65931C22116yescomplemented
73#65930C22116yescomplemented
74#65925C22132yescomplemented
75#65924C22132yescomplemented
76#65882C22116yescomplemented
77#65881C22132yescomplemented
78C4×D4×D5C22116yescomplemented
79#65860C2214yescomplemented
80#65859C2214yescomplemented
81#65858C2218yescomplemented
82#65856C2218yescomplemented
83#65856C2214yescomplemented
84#65856C2214yescomplemented
85#65844C2214yescomplemented
86C2×#4039C2212yescomplemented
87C2×#4033C2212yescomplemented
88#65827C2214yescomplemented
89C2×#4027C2214yescomplemented
90#65811C2214yescomplemented
91C2×#4018C2212yescomplemented
92C2×C42×D5C2212yescomplemented
93#62812—51nomaximal, Sylow
94C2×C5×#41—216no—
95C2×C5×#41C2314yes—
96C2×C5×#41C2314yes—
97C2×C5×#41C2314yes—
98C2×C5×#41C2314yes—
99C22×C5×Q8C2312yes—
100C22×C5×D4C2312yes—
101C22×C5×D4C2314yes—
102C23×C4×C5C2314yes—
103C23×C4×C5C2311yescharacteristic
104C22×C22⋊D5C2314yes—
105C22×C22⋊D5C23116yes—
106C22×C22⋊D5C2318yes—
107C22×C22⋊D5C2312yes—
108C23×Dic5C2312yes—
109#4150—232no—
110#4150—232no—
111#4149—232no—
112#4149—232no—
113D5×#41—264no—
114D5×#41—264no—
115#4147—232no—
116C2×#713C2318yes—
117C2×#713C2318yes—
118C2×Q8×D5C2318yes—
119C2×Q8×D5C2318yes—
120#4144—264no—
121#4144—232no—
122C2×#711C2318yes—
123C2×#711C23116yes—
124C2×#711C23116yes—
125C2×#711C2318yes—
126C2×D4×D5C2318yes—
127C2×D4×D5C23116yes—
128C2×D4×D5C23116yes—
129C2×D4×D5C2318yes—
130C2×D4×D5C23116yes—
131C2×#709—216no—
132C2×#709—264no—
133C2×#709D4116yescomplemented
134C2×#709C2314yes—
135C2×#709C2314yes—
136C2×#709C2314yes—
137C2×#709C2314yes—
138C2×#709C23116yes—
139C2×#709C2318yes—
140C2×#709C2318yes—
141C2×#709C23116yes—
142C2×#709C2314yes—
143C2×#709C2314yes—
144C22×D20C2312yes—
145C22×D20C2318yes—
146C22×D20C2311yescharacteristic
147C22×C4×D5C2314yes—
148C22×C4×D5C23116yes—
149C22×C4×D5C2314yes—
150C22×C4×D5C2312yes—
151C22×Dic10C2312yes—
152C22×Dic10C2318yes—
153C22×Dic10C2311yescharacteristic
154C5×C4⋊Q8C2314yes—
155C5×#127C2314yes—
156C5×#124C2318yes—
157C5×#123C23116yes—
158C5×C22⋊Q8C23116yes—
159C5×#121C23116yes—
160C5×#121C23116yes—
161C5×#120C23116yes—
162C4×C5×D4C23116yes—
163C5×#117C2314yes—
164C5×#117C2314yes—
165C2×C5×C4⋊C4C2312yes—
166C2×C5×C22⋊C4C2312yes—
167C2×C42×C5C2312yes—
168C2×C22⋊Dic5C2318yes—
169#4093C2314yes—
170#4093C2314yes—
171#4093C2318yes—
172#4090C2314yes—
173#4090C2314yes—
174#4090C2318yes—
175#4086C2314yes—
176#4086C23116yes—
177#4086C2314yes—
178#4086C2318yes—
179#4085C23132yes—
180#4085C23116yes—
181#4085C23116yes—
182#4085C23116yes—
183#4085C23116yes—
184#4084C23116yes—
185#4083C23132yes—
186#4082C2314yes—
187#4082C2314yes—
188#4082C2318yes—
189D4×Dic5C23116yes—
190#4076C23116yes—
191C4×C22⋊D5C23116yes—
192C4×C22⋊D5C23116yes—
193C4×C22⋊D5C23116yes—
194C4×C22⋊D5C23116yes—
195C2×#685C2314yes—
196C2×#685C2318yes—
197C2×#683C2314yes—
198C2×#683C2318yes—
199C2×C4×Dic5C2311yescharacteristic
200C2×C4×Dic5C2314yes—
201C2×C4×Dic5C2311yescharacteristic
202C2×C4×Dic5C2312yes—
203C2×C4×Dic5C2314yes—
204C2×C4×Dic5C2312yes—
205C2×C4×Dic5C2312yes—
206#4043C23116yes—
207#4042C23132yes—
208#4041C23116yes—
209#4041C23116yes—
210#4040C23132yes—
211#4039C23116yes—
212#4039C2318yes—
213#4039C2318yes—
214D5×C4⋊C4C23116yes—
215#4034C23116yes—
216#4033C2318yes—
217#4033C2318yes—
218#4032C23116yes—
219#4031C23132yes—
220#4030C23132yes—
221#4030C23132yes—
222#4029C23132yes—
223#4028C23116yes—
224#4028C23132yes—
225#4027C23116yes—
226#4027C23116yes—
227#4027C23132yes—
228D5×C22⋊C4C23132yes—
229#4024C23132yes—
230#4021C2318yes—
231#4020C2314yes—
232C4×D20C23116yes—
233#4018C2318yes—
234#4018C2318yes—
235C42×D5C2314yes—
236C42×D5C2314yes—
237C42×D5C2318yes—
238#4015C2314yes—
239C2×#585—52no—
240#3500—54no—
241#3500—54no—
242#3499—54no—
243#3498—54no—
244#3497—54no—
245#3496—54no—
246#3496—58no—
247D4×#41—516no—
248#3449—54no—
249#3449—51no—
250#3449D511yescharacteristic, complemented
251C2×#532—52no—
252C2×#532—54no—
253C2×C4×#41—51no—
254C24×C5C2414yes—
255C24×C5C2411yescharacteristic
256C23×D5C24116yes—
257C23×D5C2414yes—
258C23×D5C2412yes—
259C5×#41—216no—
260C5×#41—216no—
261C5×#41—216no—
262C5×#41—216no—
263C2×C5×Q8—28no—
264C2×C5×Q8C2414yes—
265C2×C5×Q8C2414yes—
266C2×C5×D4—216no—
267C2×C5×D4—28no—
268C2×C5×D4C2418yes—
269C2×C5×D4C2414yes—
270C2×C5×D4C2418yes—
271C2×C5×D4C2414yes—
272C2×C5×D4C24116yes—
273C22×C4×C5—216no—
274C22×C4×C5C2×D418yescomplemented
275C22×C4×C5C2418yes—
276C22×C4×C5C2418yes—
277C22×C4×C5C2414yes—
278C22×C4×C5C2414yes—
279C22×C4×C5C2411yescharacteristic
280C22×C4×C5C2411yescharacteristic
281C22×C4×C5C2412yes—
282C22×C4×C5C2412yes—
283C2×C22⋊D5—216no—
284C2×C22⋊D5—264no—
285C2×C22⋊D5—416no—
286C2×C22⋊D5C2×D4116yescomplemented
287C2×C22⋊D5C2418yes—
288C2×C22⋊D5C24116yes—
289C2×C22⋊D5C24116yes—
290C2×C22⋊D5C2418yes—
291C2×C22⋊D5C24116yes—
292C2×C22⋊D5C24116yes—
293C2×C22⋊D5C2418yes—
294C22×Dic5—44no—
295C22×Dic5C2414yes—
296C22×Dic5C24116yes—
297C22×Dic5C2412yes—
298C22×Dic5C2414yes—
299C22×Dic5C2414yes—
300C22×Dic5C2412yes—
301C22×Dic5C2412yes—
302#713—232no—
303#713—232no—
304Q8×D5—232no—
305Q8×D5—232no—
306#711—264no—
307#711—264no—
308#711—232no—
309#711—232no—
310D4×D5—264no—
311D4×D5—264no—
312D4×D5—232no—
313D4×D5—232no—
314D4×D5—432no—
315#709—216no—
316#709—216no—
317#709—216no—
318#709—216no—
319#709—264no—
320#709—232no—
321#709—264no—
322#709—232no—
323#709C2×D4132yescomplemented
324#709C2×D4132yescomplemented
325C2×D20—28no—
326C2×D20—232no—
327C2×D20C2×D418yescomplemented
328C2×D20C2414yes—
329C2×D20C2414yes—
330C2×D20C24116yes—
331C2×D20C24116yes—
332C2×D20C2414yes—
333C2×C4×D5—216no—
334C2×C4×D5—264no—
335C2×C4×D5—48no—
336C2×C4×D5C2×D4116yescomplemented
337C2×C4×D5C2418yes—
338C2×C4×D5C24116yes—
339C2×C4×D5C24116yes—
340C2×C4×D5C2418yes—
341C2×C4×D5C2418yes—
342C2×C4×D5C2418yes—
343C2×C4×D5C2414yes—
344C2×C4×D5C2414yes—
345C2×Dic10—28no—
346C2×Dic10—232no—
347C2×Dic10C2×D418yescomplemented
348C2×Dic10C2414yes—
349C2×Dic10C2414yes—
350C2×Dic10C24116yes—
351C2×Dic10C2414yes—
352C5×C4⋊C4C2418yes—
353C5×C4⋊C4C24116yes—
354C5×C22⋊C4C2418yes—
355C5×C22⋊C4C24132yes—
356C42×C5C2414yes—
357C42×C5C2414yes—
358C22⋊Dic5C24116yes—
359C22⋊Dic5C24116yes—
360#685C24116yes—
361#685C24132yes—
362#685C24116yes—
363#685C24116yes—
364C4⋊Dic5C24116yes—
365#683C24116yes—
366#683C24116yes—
367#683C24116yes—
368C4×Dic5C2412yes—
369C4×Dic5C2411yescharacteristic
370C4×Dic5C2411yescharacteristic
371C4×Dic5C2418yes—
372C4×Dic5C2418yes—
373C4×Dic5C2412yes—
374C4×Dic5C2412yes—
375C4×Dic5C2414yes—
376C4×Dic5C2414yes—
377#585—1032no—
378C2×2−1+4—54no—
379C2×2−1+4—54no—
380C2×2−1+4—54no—
381C2×H(5,𝔽2)—54no—
382C2×H(5,𝔽2)—54no—
383C2×H(5,𝔽2)—58no—
384C2×H(5,𝔽2)—54no—
385C22×#41—58no—
386C22×#41—58no—
387C22×#41—51no—
388C22×#41—52no—
389C22×#41—58no—
390C22×#41C2×D512yescomplemented
391#550—516no—
392D4×Q8—516no—
393#548—516no—
394#548—516no—
395#547—532no—
396#547—516no—
397#546—532no—
398#546—516no—
399#546—516no—
400#546—532no—
401D42—516no—
402D42—532no—
403#537—516no—
404#537—54no—
405#537C2×D514yescomplemented
406#536—58no—
407#536—58no—
408#536—54no—
409#536C2×D514yescomplemented
410#535—58no—
411#535—58no—
412#535—54no—
413#535C2×D514yescomplemented
414#534—516no—
415#534—54no—
416#534C2×D514yescomplemented
417#532—54no—
418#532—54no—
419#532—58no—
420#532—58no—
421#532—54no—
422#532—54no—
423#532—54no—
424#532—54no—
425#532—58no—
426#532—516no—
427#532—516no—
428#532—54no—
429#532C2×D514yescomplemented
430C2×C4⋊Q8—52no—
431C2×C4⋊Q8—54no—
432C2×#127—52no—
433C2×#127—54no—
434C2×#124—52no—
435C2×#124—52no—
436C2×#124—58no—
437#525—532no—
438#525—58no—
439#525C2×D518yescomplemented
440C2×#121—58no—
441C2×#121—516no—
442C4×#41—58no—
443C4×#41—54no—
444C4×#41—54no—
445C2×C4×Q8—52no—
446C2×C4×D4—58no—
447C2×C4×D4—516no—
448C2×C4×D4—52no—
449C2×C4×D4—54no—
450C2×#117—52no—
451C2×#117C2×D511yescharacteristic, complemented
452C22×C42—51no—
453C22×C42—52no—
454C23×C5—28no—
455C23×C5—42no—
456C23×C5—48no—
457C23×C5C22×D414yes—
458C23×C5C2518yes—
459C23×C5C2512yes—
460C23×C5C2511yescharacteristic
461C22×D5—28no—
462C22×D5—232no—
463C22×D5—44no—
464C22×D5—432no—
465C22×D5—48no—
466C22×D5C22×D418yes—
467C22×D5C2518yes—
468C22×D5C2514yes—
469C5×Q8—28no—
470C5×Q8—28no—
471C5×D4—216no—
472C5×D4—216no—
473C5×D4—28no—
474C5×D4—28no—
475C5×D4—416no—
476C2×C4×C5—28no—
477C2×C4×C5—216no—
478C2×C4×C5—216no—
479C2×C4×C5—44no—
480C2×C4×C5C22×D418yes—
481C2×C4×C5C22×D414yes—
482C2×C4×C5C22×D418yes—
483C2×C4×C5C22×D414yes—
484C2×C4×C5C2518yes—
485C2×C4×C5C2518yes—
486C2×C4×C5C2511yescharacteristic
487C2×C4×C5C2512yes—
488C2×C4×C5C2511yescharacteristic
489C22⋊D5—216no—
490C22⋊D5—216no—
491C22⋊D5—232no—
492C22⋊D5—232no—
493C22⋊D5—232no—
494C22⋊D5—416no—
495C22⋊D5C22×D4132yes—
496C2×Dic5—28no—
497C2×Dic5—232no—
498C2×Dic5—24no—
499C2×Dic5—28no—
500C2×Dic5—44no—
501C2×Dic5—42no—
502C2×Dic5C22×D418yes—
503C2×Dic5C2512yes—
504C2×Dic5C2514yes—
505C2×Dic5C2518yes—
506C2×Dic5C2514yes—
507C2×Dic5C2512yes—
508D20—232no—
509D20—28no—
510D20—28no—
511D20—416no—
512D20C22×D4116yes—
513C4×D5—232no—
514C4×D5—216no—
515C4×D5—216no—
516C4×D5—232no—
517C4×D5—216no—
518C4×D5—48no—
519C4×D5C22×D4116yes—
520C4×D5C22×D4116yes—
521Dic10—28no—
522Dic10—28no—
523Dic10—232no—
524Dic10C22×D4116yes—
5252−1+4—1032no—
5262−1+4—1032no—
5272−1+4—1032no—
528H(5,𝔽2)—1064no—
529H(5,𝔽2)—1032no—
530H(5,𝔽2)—1032no—
531H(5,𝔽2)—1032no—
532C2×#41—216no—
533C2×#41—58no—
534C2×#41—58no—
535C2×#41—58no—
536C2×#41—516no—
537C2×#41—516no—
538C2×#41—58no—
539C2×#41—516no—
540C2×#41—54no—
541C2×#41—54no—
542C2×#41—516no—
543C2×#41—54no—
544C2×#41—54no—
545C2×#41—54no—
546C2×#41—54no—
547C2×#41—58no—
548C2×#41—516no—
549C2×#41—58no—
550C2×#41—1064no—
551C2×#41—1064no—
552C2×#41—1064no—
553C2×#41—1016no—
554C2×#41C22×D514yes—
555C2×#41C22×D514yes—
556C2×#41C22×D514yes—
557C2×#41C22×D514yes—
558C22×Q8—58no—
559C22×Q8—58no—
560C22×Q8—51no—
561C22×Q8—52no—
562C22×Q8—58no—
563C22×Q8C22×D512yes—
564C22×D4—52no—
565C22×D4—54no—
566C22×D4—516no—
567C22×D4—58no—
568C22×D4—516no—
569C22×D4—58no—
570C22×D4—516no—
571C22×D4—58no—
572C22×D4—516no—
573C22×D4—51no—
574C22×D4—52no—
575C22×D4—58no—
576C22×D4C22×D514yes—
577C22×D4C22×D512yes—
578C23×C4—52no—
579C23×C4—52no—
580C23×C4—516no—
581C23×C4—54no—
582C23×C4—54no—
583C23×C4C22×D514yes—
584C23×C4C22×D511yescharacteristic
585C4⋊Q8—54no—
586C4⋊Q8—54no—
587C4⋊Q8—58no—
588C4⋊Q8—516no—
589C4⋊Q8—54no—
590C4⋊Q8C22×D514yes—
591#127—54no—
592#127—54no—
593#127—516no—
594#127—58no—
595#127—54no—
596#127C22×D514yes—
597#124—54no—
598#124—54no—
599#124—58no—
600#124—54no—
601#124—54no—
602#124—58no—
603#124—532no—
604#124—58no—
605#124C22×D518yes—
606#123—532no—
607#123—532no—
608#123—516no—
609#123C22×D5116yes—
610C22⋊Q8—532no—
611C22⋊Q8—516no—
612C22⋊Q8—532no—
613C22⋊Q8C22×D5116yes—
614#121—516no—
615#121—516no—
616#121—516no—
617#121—516no—
618#121—516no—
619#121—532no—
620#121—516no—
621#121—516no—
622#121—516no—
623#121—532no—
624#121—532no—
625#121C22×D5116yes—
626#121C22×D5116yes—
627#120—532no—
628#120—532no—
629#120—516no—
630#120C22×D5116yes—
631C4×Q8—58no—
632C4×Q8—58no—
633C4×D4—516no—
634C4×D4—516no—
635C4×D4—516no—
636C4×D4—516no—
637C4×D4—516no—
638C4×D4—58no—
639C4×D4—58no—
640C4×D4—516no—
641C4×D4—516no—
642C4×D4—516no—
643C4×D4—532no—
644C4×D4—516no—
645C4×D4C22×D5116yes—
646#117—58no—
647#117—58no—
648#117C22×D514yes—
649#117C22×D514yes—
650C2×C4⋊C4—54no—
651C2×C4⋊C4—58no—
652C2×C4⋊C4—516no—
653C2×C4⋊C4C22×D512yes—
654C2×C22⋊C4—58no—
655C2×C22⋊C4—54no—
656C2×C22⋊C4—58no—
657C2×C22⋊C4—532no—
658C2×C22⋊C4C22×D512yes—
659C2×C42—51no—
660C2×C42—54no—
661C2×C42—54no—
662C2×C42—52no—
663C2×C42—52no—
664C2×C42—52no—
665C2×C42—51no—
666C2×C42—58no—
667C2×C42—54no—
668C2×C42—54no—
669C2×C42C22×D512yes—
670C22×C5—22no—
671C22×C5—24no—
672C22×C5—28no—
673C22×C5—216no—
674C22×C5—44no—
675C22×C5—88no—
676C22×C5C23×D414yes—
677C22×C5C23×D412yes—
678C22×C5C2611yescharacteristic
679C2×D5—28no—
680C2×D5—28no—
681C2×D5—216no—
682C2×D5—48no—
683C2×D5—832no—
684C2×D5—88no—
685C2×D5C23×D418yes—
686C4×C5—28no—
687C4×C5—28no—
688C4×C5C23×D412yes—
689C4×C5C23×D414yes—
690C4×C5C23×D412yes—
691Dic5—28no—
692Dic5—22no—
693Dic5—24no—
694Dic5C23×D418yes—
695Dic5#58514yescomplemented
696C24—52no—
697C24—516no—
698C24—54no—
699C24C23×D514yes—
700C24C23×D511yescharacteristic
701#41—216no—
702#41—216no—
703#41—216no—
704#41—216no—
705#41—532no—
706#41—532no—
707#41—1064no—
708#41—1064no—
709#41—1032no—
710#41—1032no—
711#41—1064no—
712#41—1032no—
713#41—1032no—
714#41—1064no—
715#41—1032no—
716#41—1032no—
717#41—1016no—
718#41—1016no—
719#41—1016no—
720#41—1016no—
721C2×Q8—28no—
722C2×Q8—58no—
723C2×Q8—54no—
724C2×Q8—516no—
725C2×Q8—54no—
726C2×Q8—54no—
727C2×Q8—1032no—
728C2×Q8—1032no—
729C2×Q8—1032no—
730C2×Q8—108no—
731C2×Q8C23×D514yes—
732C2×Q8C23×D514yes—
733C2×D4—216no—
734C2×D4—28no—
735C2×D4—516no—
736C2×D4—58no—
737C2×D4—516no—
738C2×D4—516no—
739C2×D4—58no—
740C2×D4—58no—
741C2×D4—516no—
742C2×D4—516no—
743C2×D4—58no—
744C2×D4—54no—
745C2×D4—516no—
746C2×D4—54no—
747C2×D4—54no—
748C2×D4—516no—
749C2×D4—1032no—
750C2×D4—1032no—
751C2×D4—1064no—
752C2×D4—1032no—
753C2×D4—1064no—
754C2×D4—1064no—
755C2×D4—1016no—
756C2×D4—108no—
757C2×D4—2032no—
758C2×D4—2016no—
759C2×D4C23×D518yes—
760C2×D4C23×D518yes—
761C2×D4C23×D514yes—
762C2×D4C23×D514yes—
763C2×D4C23×D5116yes—
764C22×C4—216no—
765C22×C4—52no—
766C22×C4—516no—
767C22×C4—54no—
768C22×C4—54no—
769C22×C4—52no—
770C22×C4—54no—
771C22×C4—54no—
772C22×C4—516no—
773C22×C4—54no—
774C22×C4—52no—
775C22×C4—58no—
776C22×C4—516no—
777C22×C4—516no—
778C22×C4—58no—
779C22×C4—58no—
780C22×C4—58no—
781C22×C4—1064no—
782C22×C4—1016no—
783C22×C4—208no—
784C22×C4—204no—
785C22×C4D4×D518yescomplemented
786C22×C4C23×D514yes—
787C22×C4C23×D518yes—
788C22×C4C23×D518yes—
789C22×C4C23×D514yes—
790C22×C4C23×D511yescharacteristic
791C22×C4C23×D512yes—
792C22×C4C23×D511yescharacteristic
793C22×C4C23×D512yes—
794C4⋊C4—516no—
795C4⋊C4—516no—
796C4⋊C4—516no—
797C4⋊C4—516no—
798C4⋊C4C23×D5116yes—
799C4⋊C4C23×D518yes—
800C22⋊C4—516no—
801C22⋊C4—516no—
802C22⋊C4—516no—
803C22⋊C4—516no—
804C22⋊C4—516no—
805C22⋊C4—532no—
806C22⋊C4C23×D5132yes—
807C22⋊C4C23×D518yes—
808C42—51no—
809C42—51no—
810C42—52no—
811C42—58no—
812C42—54no—
813C42—58no—
814C42—54no—
815C42—52no—
816C42—52no—
817C42C23×D514yes—
818C42C23×D514yes—
819C2×C5—22no—
820C2×C5—24no—
821C2×C5—48no—
822C2×C5C24×D411yescharacteristic
823C2×C5C2×#58512yes—
824D5—28no—
825D5—48no—
826C23—28no—
827C23—42no—
828C23—48no—
829C23—54no—
830C23—58no—
831C23—58no—
832C23—1032no—
833C23—108no—
834C23—204no—
835C23—208no—
836C23—2032no—
837C23C2×D4×D514yes—
838C23C24×D518yes—
839C23C24×D512yes—
840C23C24×D511yescharacteristic
841Q8—28no—
842Q8—28no—
843Q8—516no—
844Q8—1032no—
845Q8—108no—
846Q8—108no—
847D4—216no—
848D4—216no—
849D4—28no—
850D4—28no—
851D4—416no—
852D4—532no—
853D4—516no—
854D4—1032no—
855D4—1032no—
856D4—1032no—
857D4—1032no—
858D4—1016no—
859D4—1016no—
860D4—108no—
861D4—108no—
862D4—2016no—
863D4—2016no—
864C2×C4—28no—
865C2×C4—216no—
866C2×C4—216no—
867C2×C4—44no—
868C2×C4—58no—
869C2×C4—52no—
870C2×C4—54no—
871C2×C4—516no—
872C2×C4—516no—
873C2×C4—52no—
874C2×C4—54no—
875C2×C4—58no—
876C2×C4—1032no—
877C2×C4—1016no—
878C2×C4—1032no—
879C2×C4—1032no—
880C2×C4—104no—
881C2×C4—108no—
882C2×C4—108no—
883C2×C4—1016no—
884C2×C4—1016no—
885C2×C4—208no—
886C2×C4—204no—
887C2×C4—202no—
888C2×C4C2×D4×D518yes—
889C2×C4C2×D4×D514yes—
890C2×C4C2×D4×D518yes—
891C2×C4C2×D4×D514yes—
892C2×C4C24×D518yes—
893C2×C4C24×D518yes—
894C2×C4C24×D511yescharacteristic
895C2×C4C24×D512yes—
896C2×C4C24×D511yescharacteristic
897C5#6281211yescharacteristic, complemented, Sylow
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—58no—
904C22—88no—
905C22—108no—
906C22—108no—
907C22—1016no—
908C22—208no—
909C22—408no—
910C22—4032no—
911C22C22×D4×D514yes—
912C22C22×D4×D512yes—
913C22C25×D511yescharacteristic
914C4—28no—
915C4—28no—
916C4—58no—
917C4—54no—
918C4—108no—
919C4—102no—
920C4—104no—
921C4C22×D4×D512yes—
922C4C22×D4×D514yes—
923C4C22×D4×D512yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—108no—
928C2—208no—
929C2C23×D4×D511yescharacteristic
930C2D5×#58512yes—
subgroupG/H
centerC2×C4C24×D5
commutator, socle, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC5×#3449C2
hypercenter#3449D5
hypocenterC5#62812
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#66283C2semidirect
2. C5×#3449C2semidirect
3. C2×#66166C2semidirect
4. #10618283C2semidirect
5. #10618268C2semidirect
6. #10618242C2semidirect
7. #10618241C2semidirect
8. #10618218C2semidirect
9. #10618217C2semidirect
10. #10618199C2semidirect
11. #10618136C2semidirect
12. D5×#532C2semidirect
13. #10617938C2semidirect
14. #10617636C2semidirect
15. C2×#65856C2semidirect
16. C22×C5×#41C22semidirect
18. C2×#4150C22semidirect
19. C2×#4150C22semidirect
20. C2×#4149C22semidirect
21. C2×#4149C22semidirect
22. C2×D5×#41C22semidirect
23. C2×D5×#41C22semidirect
24. C2×#4147C22semidirect
25. C2×#4144C22semidirect
26. C2×#4144C22semidirect
28. C22×#709C22semidirect
29. C22×#709C22semidirect
30. C5×#537C22semidirect
31. C5×#536C22semidirect
32. C5×#535C22semidirect
33. C5×#534C22semidirect
34. C5×#532C22semidirect
35. C5×#525C22semidirect
36. C2×C5×#117C22semidirect
37. #66166C22semidirect
38. #66166C22semidirect
39. #66166C22semidirect
40. #66166C22semidirect
41. #66166C22semidirect
42. #66166C22semidirect
43. C2×#4093C22semidirect
44. C2×#4090C22semidirect
45. C2×#4086C22semidirect
46. C2×#4085C22semidirect
47. C2×#4082C22semidirect
48. C2×C4×C22⋊D5C22semidirect
49. C22×C4×Dic5C22semidirect
50. #66059C22semidirect
51. #66058C22semidirect
52. D5×C4⋊Q8C22semidirect
53. #66050C22semidirect
54. #66049C22semidirect
55. D5×#127C22semidirect
56. #66009C22semidirect
57. #66008C22semidirect
58. D5×#124C22semidirect
59. #66002C22semidirect
60. #65989C22semidirect
61. #65988C22semidirect
62. #65967C22semidirect
63. #65966C22semidirect
64. #65965C22semidirect
65. #65964C22semidirect
66. #65946C22semidirect
67. #65943C22semidirect
68. #65939C22semidirect
69. D5×#121C22semidirect
70. #65933C22semidirect
71. #65932C22semidirect
72. #65931C22semidirect
73. #65930C22semidirect
74. #65925C22semidirect
75. #65924C22semidirect
76. #65882C22semidirect
77. #65881C22semidirect
78. C4×D4×D5C22semidirect
79. #65860C22semidirect
80. #65859C22semidirect
81. #65858C22semidirect
82. #65856C22semidirect
83. #65856C22semidirect
84. #65856C22semidirect
85. #65844C22semidirect
86. C2×#4039C22semidirect
87. C2×#4033C22semidirect
88. #65827C22semidirect
89. C2×#4027C22semidirect
90. #65811C22semidirect
91. C2×#4018C22semidirect
92. C2×C42×D5C22semidirect
133. C2×#709D4semidirect
250. #3449D5semidirect
274. C22×C4×C5C2×D4semidirect
286. C2×C22⋊D5C2×D4semidirect
323. #709C2×D4semidirect
324. #709C2×D4semidirect
327. C2×D20C2×D4semidirect
336. C2×C4×D5C2×D4semidirect
347. C2×Dic10C2×D4semidirect
390. C22×#41C2×D5semidirect
405. #537C2×D5semidirect
409. #536C2×D5semidirect
413. #535C2×D5semidirect
416. #534C2×D5semidirect
429. #532C2×D5semidirect
439. #525C2×D5semidirect
451. C2×#117C2×D5semidirect
695. Dic5#585semidirect
785. C22×C4D4×D5semidirect
897. C5#62812semidirect

Maximal subgroups

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

subgroupindex
C2×#662832
C5×#34492
C2×#661662
#106182832
#106182682
#106182422
#106182412
#106182182
#106182172
#106181992
#106181362
D5×#5322
#106179382
#106176362
C2×#658562
#628125