Finite Group Databasebeta

← C2×#10618616 #13007768

Subgroups — C2×#10618616 #13007768

Order 1280.

11534 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
1C22×#4149C211yesmaximal, characteristic, complemented
2C22×#4147C211yesmaximal, characteristic, complemented
3C2×C5×#548C211yesmaximal, characteristic, complemented
4C2×#66165C211yesmaximal, characteristic, complemented
5C2×#66151C211yesmaximal, characteristic, complemented
6#10618616C2132yesmaximal, direct product factor
7C2×#66010C213yesmaximal, complemented
8C2×D5×#124C213yesmaximal, complemented
9C2×#65964C213yesmaximal, complemented
10C2×#65962C213yesmaximal, complemented
11C2×#65946C213yesmaximal, complemented
12C2×#65941C213yesmaximal, complemented
13C2×#65910C211yesmaximal, characteristic, complemented
14C2×C4×#713C211yesmaximal, characteristic, complemented
15C2×#65884C213yesmaximal, complemented
16C2×#65882C213yesmaximal, complemented
17C22×C5×#41C2211yescharacteristic
18C23×C5×Q8C2211yescharacteristic, complemented
19C2×#4149—216no—
20C2×#4149C22116yescomplemented
21C2×#4147—216no—
22C2×#4147C22116yescomplemented
23C22×#713C2211yescharacteristic
24C22×#713C2211yescharacteristic
25C22×#713C2213yescomplemented
26C22×Q8×D5C2213yescomplemented
27C22×Q8×D5C2211yescharacteristic, complemented
28C22×D4×D5C2213yes—
29C22×D4×D5C2213yes—
30C22×#709C2213yes—
31C22×#709C2213yescomplemented
32C22×#709C2213yescomplemented
33C23×D20C2213yes—
34C5×#548C22116yescomplemented
35C2×C5×#124C2213yescomplemented
36C2×C5×C22⋊Q8C2213yescomplemented
37C2×C5×#121C2213yescomplemented
38C2×C4×C5×Q8C2211yescharacteristic, complemented
39C2×C4×C5×D4C2213yescomplemented
40#66165C22116yescomplemented
41#66151C22116yescomplemented
42C2×#4093C2213yescomplemented
43C2×#4092C2213yescomplemented
44C2×Q8×Dic5C2211yescharacteristic, complemented
45C2×#4086C2213yescomplemented
46C2×#4084C2213yescomplemented
47C2×#4084C2213yescomplemented
48C2×#4083C2216yescomplemented
49C2×#4082C2213yescomplemented
50C2×#4076C2213yescomplemented
51C2×C4×C22⋊D5C2213yescomplemented
52C2×C4×C22⋊D5C2213yescomplemented
53C2×#4070C2213yescomplemented
54#66010C22148yescomplemented
55D5×#124C22148yescomplemented
56#65964C22148yescomplemented
57#65962C22148yescomplemented
58#65946C22148yescomplemented
59#65941C22148yescomplemented
60#65910C22116yescomplemented
61C4×#713C22116yescomplemented
62#65884C22148yescomplemented
63#65882C22148yescomplemented
64C2×#4043C2213yescomplemented
65C2×#4041C2213yescomplemented
66C2×#4041C2213yescomplemented
67C2×#4040C2216yescomplemented
68C2×#4039C2213yescomplemented
69C2×#4038C2213yescomplemented
70C2×#4034C2213yescomplemented
71C2×#4031C2216yescomplemented
72C2×#4031C2211yescharacteristic, complemented
73C2×#4031C2213yescomplemented
74C2×#4030C2213yescomplemented
75C2×#4030C2213yescomplemented
76C2×#4029C2216yescomplemented
77C2×#4028C2216yescomplemented
78C2×D5×C22⋊C4C2216yescomplemented
79C2×D5×C22⋊C4C2216yescomplemented
80C2×#4021C2213yescomplemented
81C2×C4×D20C2213yescomplemented
82C2×C4×D20C2213yescomplemented
83C2×C42×D5C2213yescomplemented
84C2×#3500—51nomaximal, Sylow
85C24×D5C2316yes—
86C2×C5×#41—28no—
87C2×C5×#41C2318yes—
88C22×C5×Q8—28no—
89C22×C5×Q8C2313yes—
90C22×C5×Q8C2311yescharacteristic
91C22×C5×Q8C2318yescomplemented
92C22×C5×D4C2313yes—
93C22×C5×D4C2313yes—
94C23×C4×C5C2313yes—
95C23×C4×C5C2313yes—
96C22×C22⋊D5C2313yes—
97C22×C22⋊D5C2313yes—
98C22×C22⋊D5C2313yes—
99C22×C22⋊D5C2311yescharacteristic
100C22×C22⋊D5C2313yes—
101C22×C22⋊D5C2313yes—
102#4149—2128no—
103#4147—2128no—
104C2×#713—28no—
105C2×#713—224no—
106C2×#713D4116yescomplemented
107C2×#713C2318yes—
108C2×#713C2318yes—
109C2×#713C23124yescomplemented
110C2×Q8×D5—28no—
111C2×Q8×D5—224no—
112C2×Q8×D5C2318yescomplemented
113C2×Q8×D5C23124yescomplemented
114C2×D4×D5—224no—
115C2×D4×D5—224no—
116C2×D4×D5C23124yes—
117C2×D4×D5C23124yes—
118C2×#709—224no—
119C2×#709—224no—
120C2×#709—224no—
121C2×#709C23124yes—
122C2×#709C23124yescomplemented
123C2×#709C23124yescomplemented
124C22×D20—224no—
125C22×D20C2313yes—
126C22×D20C2313yes—
127C22×D20C2313yes—
128C22×D20C23124yes—
129C22×D20C2313yes—
130C22×D20C2313yes—
131C22×C4×D5C2313yes—
132C22×C4×D5C2313yes—
133C22×C4×D5C2316yes—
134C22×C4×D5C2313yes—
135C22×C4×D5C2313yes—
136C22×C4×D5C2313yes—
137C22×Dic10C2313yes—
138C22×Dic10C2313yes—
139C22×Dic10C2311yescharacteristic
140C5×#124C23124yescomplemented
141C5×C22⋊Q8C23124yescomplemented
142C5×#121C23124yescomplemented
143C4×C5×Q8C2318yescomplemented
144C4×C5×D4C23124yescomplemented
145C2×C5×C4⋊C4C2313yes—
146C2×C5×C4⋊C4C2313yes—
147C2×C5×C22⋊C4C2313yes—
148C2×C5×C22⋊C4C2316yes—
149C2×C5×C22⋊C4C2311yescharacteristic
150C2×C42×C5C2313yes—
151C2×C22⋊Dic5C2313yes—
152C2×C22⋊Dic5C2316yes—
153C2×C22⋊Dic5C2311yescharacteristic
154#4093C23124yescomplemented
155#4092C23124yescomplemented
156Q8×Dic5C2318yescomplemented
157#4086C23124yescomplemented
158#4084C23124yescomplemented
159#4084C23124yescomplemented
160#4083C23148yescomplemented
161#4082C23124yescomplemented
162#4076C23124yescomplemented
163C4×C22⋊D5C23124yescomplemented
164C4×C22⋊D5C23124yescomplemented
165C2×#685C2311yescharacteristic
166C2×#685C2313yes—
167C2×#685C2316yes—
168C2×#685C2316yes—
169C2×#685C2313yes—
170C2×#685C2316yes—
171C2×#685C2311yescharacteristic
172C2×C4⋊Dic5C2313yes—
173C2×C4⋊Dic5C2313yes—
174#4070C23124yescomplemented
175C2×#683C2313yes—
176C2×#683C2313yes—
177C2×C4×Dic5C2311yescharacteristic
178C2×C4×Dic5C2313yes—
179C2×C4×Dic5C2313yes—
180#4043C23124yescomplemented
181#4041C23124yescomplemented
182#4041C23124yescomplemented
183#4040C23148yescomplemented
184#4039C23124yescomplemented
185#4038C23124yescomplemented
186#4034C23124yescomplemented
187#4031C2318yescomplemented
188#4031C23124yescomplemented
189#4031C23148yescomplemented
190#4030C23124yescomplemented
191#4030C23124yescomplemented
192#4029C23148yescomplemented
193#4028C23148yescomplemented
194D5×C22⋊C4C23148yescomplemented
195D5×C22⋊C4C23148yescomplemented
196#4021C23124yescomplemented
197C4×D20C23124yescomplemented
198C4×D20C23124yescomplemented
199C42×D5C23124yescomplemented
200C22×2−1+4—51no—
201C22×H(5,𝔽2)—51no—
202#3500—532no—
203C2×#548—51no—
204C2×#548—51no—
205C2×#548—51no—
206C2×#548D511yescharacteristic, complemented
207C2×#546—53no—
208C2×#546—53no—
209C2×#546—53no—
210C2×#546—53no—
211C2×#536—53no—
212C2×#535—53no—
213C2×#532—53no—
214C22×#124—53no—
215C2×C4×#41—51no—
216C24×C5C2413yes—
217C24×C5C2411yescharacteristic
218C23×D5—224no—
219C23×D5—412no—
220C23×D5—412no—
221C23×D5C2411yescharacteristic
222C23×D5C2413yes—
223C23×D5C2413yes—
224C23×D5C24124yes—
225C5×#41—232no—
226C2×C5×Q8—232no—
227C2×C5×Q8—212no—
228C2×C5×Q8C2×D418yes—
229C2×C5×Q8C24112yes—
230C2×C5×Q8C2414yes—
231C2×C5×D4—212no—
232C2×C5×D4—46no—
233C2×C5×D4C24112yes—
234C2×C5×D4C24112yes—
235C22×C4×C5—212no—
236C22×C4×C5—212no—
237C22×C4×C5C2411yescharacteristic
238C22×C4×C5C2413yes—
239C22×C4×C5C2413yes—
240C22×C4×C5C2411yescharacteristic
241C22×C4×C5C24112yes—
242C22×C4×C5C24112yes—
243C22×C4×C5C2413yes—
244C2×C22⋊D5—212no—
245C2×C22⋊D5—212no—
246C2×C22⋊D5—24no—
247C2×C22⋊D5—212no—
248C2×C22⋊D5—46no—
249C2×C22⋊D5—46no—
250C2×C22⋊D5C24112yes—
251C2×C22⋊D5C24112yes—
252C2×C22⋊D5C24112yes—
253C2×C22⋊D5C2414yes—
254C2×C22⋊D5C24112yes—
255C2×C22⋊D5C24112yes—
256C22×Dic5C2411yescharacteristic
257C22×Dic5C2413yes—
258C22×Dic5C2413yes—
259C22×Dic5C2411yescharacteristic
260C22×Dic5C2411yescharacteristic
261#713—232no—
262#713—296no—
263#713C2×D4164yescomplemented
264Q8×D5—232no—
265Q8×D5—296no—
266D4×D5—296no—
267D4×D5—296no—
268#709—296no—
269#709—296no—
270#709—296no—
271C2×D20—212no—
272C2×D20—212no—
273C2×D20—212no—
274C2×D20—296no—
275C2×D20—46no—
276C2×D20C2×D4124yes—
277C2×D20C24112yes—
278C2×D20C24112yes—
279C2×D20C24112yes—
280C2×D20C24112yes—
281C2×D20C24112yes—
282C2×C4×D5—224no—
283C2×C4×D5—212no—
284C2×C4×D5—212no—
285C2×C4×D5—46no—
286C2×C4×D5—46no—
287C2×C4×D5C2×D4124yes—
288C2×C4×D5C24112yes—
289C2×C4×D5C24112yes—
290C2×C4×D5C24124yes—
291C2×C4×D5C24112yes—
292C2×C4×D5C24112yes—
293C2×C4×D5C24112yes—
294C2×Dic10—212no—
295C2×Dic10—24no—
296C2×Dic10—212no—
297C2×Dic10C2414yes—
298C2×Dic10C24112yes—
299C2×Dic10C24112yes—
300C5×C4⋊C4C24112yes—
301C5×C4⋊C4C24112yes—
302C5×C22⋊C4C2414yes—
303C5×C22⋊C4C24112yes—
304C5×C22⋊C4C24124yes—
305C42×C5C24112yes—
306C22⋊Dic5C24112yes—
307C22⋊Dic5C24124yes—
308C22⋊Dic5C2414yes—
309#685C2414yes—
310#685C24112yes—
311#685C24124yes—
312#685C24124yes—
313#685C24112yes—
314#685C24124yes—
315#685C2414yes—
316C4⋊Dic5C24112yes—
317C4⋊Dic5C24112yes—
318#683C24112yes—
319#683C24112yes—
320C4×Dic5C2414yes—
321C4×Dic5C24112yes—
322C4×Dic5C24112yes—
323C2×2−1+4—516no—
324C2×2−1+4—1016no—
325C2×H(5,𝔽2)—516no—
326C2×H(5,𝔽2)—1016no—
327C22×#41—51no—
328C22×#41—51no—
329C22×#41—53no—
330C22×#41—53no—
331C22×#41—53no—
332C22×#41—53no—
333C22×#41C2×D511yescharacteristic
334C23×Q8—53no—
335C23×Q8—51no—
336C23×Q8C2×D511yescharacteristic, complemented
337C23×D4—53no—
338C23×D4—53no—
339C23×D4—53no—
340#548—516no—
341#548—516no—
342#548—516no—
343#548C2×D5116yescomplemented
344#546—548no—
345#546—548no—
346#546—548no—
347#546—548no—
348#536—548no—
349#535—548no—
350#532—548no—
351C2×C4⋊Q8—53no—
352C2×#127—53no—
353C2×#124—53no—
354C2×#124—53no—
355C2×#124—548no—
356C2×#124—53no—
357C2×#124—56no—
358C2×#124—51no—
359C2×#124—53no—
360C2×#124C2×D513yescomplemented
361C2×#123—56no—
362C2×#123—56no—
363C2×C22⋊Q8—53no—
364C2×C22⋊Q8—53no—
365C2×C22⋊Q8—53no—
366C2×C22⋊Q8C2×D513yescomplemented
367C2×#121—53no—
368C2×#121—53no—
369C2×#121—53no—
370C2×#121—53no—
371C2×#121—53no—
372C2×#121—53no—
373C2×#121—53no—
374C2×#121C2×D513yescomplemented
375C2×#120—56no—
376C2×#120—56no—
377C4×#41—516no—
378C2×C4×Q8—51no—
379C2×C4×Q8C2×D511yescharacteristic, complemented
380C2×C4×D4—53no—
381C2×C4×D4—53no—
382C2×C4×D4—53no—
383C2×C4×D4—53no—
384C2×C4×D4—53no—
385C2×C4×D4C2×D513yescomplemented
386C2×#117—53no—
387C22×C22⋊C4—56no—
388C22×C22⋊C4—56no—
389C22×C42—53no—
390C23×C5—22no—
391C23×C5—26no—
392C23×C5—22no—
393C23×C5—26no—
394C23×C5—22no—
395C23×C5—26no—
396C23×C5C2516yes—
397C23×C5C2512yes—
398C23×C5C2511yescharacteristic
399C22×D5—26no—
400C22×D5—26no—
401C22×D5—22no—
402C22×D5—26no—
403C22×D5—22no—
404C22×D5—26no—
405C22×D5—22no—
406C22×D5—26no—
407C22×D5—248no—
408C22×D5—424no—
409C22×D5—424no—
410C22×D5—848no—
411C22×D5C22×D4112yes—
412C22×D5C2516yes—
413C22×D5C2512yes—
414C22×D5C2516yes—
415C5×Q8—224no—
416C5×Q8C22×D4116yes—
417C5×D4—224no—
418C5×D4—412no—
419C2×C4×C5—26no—
420C2×C4×C5—22no—
421C2×C4×C5—22no—
422C2×C4×C5—26no—
423C2×C4×C5—224no—
424C2×C4×C5—224no—
425C2×C4×C5C22×D4112yes—
426C2×C4×C5C2516yes—
427C2×C4×C5C2512yes—
428C2×C4×C5C2512yes—
429C2×C4×C5C2516yes—
430C2×C4×C5C2516yes—
431C22⋊D5—224no—
432C22⋊D5—224no—
433C22⋊D5—28no—
434C22⋊D5—224no—
435C22⋊D5—412no—
436C22⋊D5—412no—
437C2×Dic5—26no—
438C2×Dic5—22no—
439C2×Dic5—22no—
440C2×Dic5—26no—
441C2×Dic5C22×D414yes—
442C2×Dic5C2512yes—
443C2×Dic5C2516yes—
444C2×Dic5C2512yes—
445C2×Dic5C2516yes—
446C2×Dic5C2512yes—
447D20—224no—
448D20—224no—
449D20—224no—
450D20—412no—
451D20C22×D4148yes—
452C4×D5—248no—
453C4×D5—224no—
454C4×D5—224no—
455C4×D5—412no—
456C4×D5—412no—
457C4×D5C22×D4148yes—
458Dic10—224no—
459Dic10—28no—
460Dic10—224no—
461C25—56no—
4622−1+4—10128no—
463H(5,𝔽2)—10128no—
464C2×#41—28no—
465C2×#41—516no—
466C2×#41—58no—
467C2×#41—524no—
468C2×#41—58no—
469C2×#41—524no—
470C2×#41—524no—
471C2×#41—524no—
472C2×#41—1024no—
473C2×#41—1024no—
474C2×#41—1024no—
475C2×#41—1024no—
476C2×#41—108no—
477C2×#41C22×D518yes—
478C22×Q8—28no—
479C22×Q8—524no—
480C22×Q8—58no—
481C22×Q8—53no—
482C22×Q8—53no—
483C22×Q8—51no—
484C22×Q8—1024no—
485C22×Q8—108no—
486C22×Q8C22×D513yes—
487C22×Q8C22×D511yescharacteristic
488C22×Q8C22×D518yescomplemented
489C22×D4—53no—
490C22×D4—53no—
491C22×D4—53no—
492C22×D4—51no—
493C22×D4—53no—
494C22×D4—53no—
495C22×D4—524no—
496C22×D4—524no—
497C22×D4—53no—
498C22×D4—53no—
499C22×D4—53no—
500C22×D4—53no—
501C22×D4—524no—
502C22×D4—53no—
503C22×D4—1024no—
504C22×D4—1024no—
505C22×D4—1024no—
506C22×D4C22×D513yes—
507C22×D4C22×D513yes—
508C23×C4—53no—
509C23×C4—56no—
510C23×C4—53no—
511C23×C4—53no—
512C23×C4—53no—
513C23×C4—53no—
514C23×C4C22×D513yes—
515C23×C4C22×D513yes—
516C4⋊Q8—524no—
517#127—524no—
518#124—524no—
519#124—524no—
520#124—524no—
521#124—548no—
522#124—58no—
523#124—524no—
524#124C22×D5124yescomplemented
525#123—548no—
526#123—548no—
527C22⋊Q8—524no—
528C22⋊Q8—524no—
529C22⋊Q8—524no—
530C22⋊Q8C22×D5124yescomplemented
531#121—524no—
532#121—524no—
533#121—524no—
534#121—524no—
535#121—524no—
536#121—524no—
537#121—524no—
538#121C22×D5124yescomplemented
539#120—548no—
540#120—548no—
541C4×Q8—58no—
542C4×Q8C22×D518yescomplemented
543C4×D4—524no—
544C4×D4—524no—
545C4×D4—524no—
546C4×D4—524no—
547C4×D4—524no—
548C4×D4C22×D5124yescomplemented
549#117—524no—
550C2×C4⋊C4—53no—
551C2×C4⋊C4—53no—
552C2×C4⋊C4—53no—
553C2×C4⋊C4—53no—
554C2×C4⋊C4C22×D513yes—
555C2×C4⋊C4C22×D513yes—
556C2×C22⋊C4—53no—
557C2×C22⋊C4—56no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—53no—
560C2×C22⋊C4—53no—
561C2×C22⋊C4—56no—
562C2×C22⋊C4—56no—
563C2×C22⋊C4—56no—
564C2×C22⋊C4—51no—
565C2×C22⋊C4—51no—
566C2×C22⋊C4—548no—
567C2×C22⋊C4—548no—
568C2×C22⋊C4C22×D513yes—
569C2×C22⋊C4C22×D516yes—
570C2×C22⋊C4C22×D511yescharacteristic
571C2×C42—53no—
572C2×C42—53no—
573C2×C42—51no—
574C2×C42—524no—
575C2×C42C22×D513yes—
576C22×C5—22no—
577C22×C5—26no—
578C22×C5—22no—
579C22×C5—26no—
580C22×C5—22no—
581C22×C5—26no—
582C22×C5—412no—
583C22×C5—44no—
584C22×C5C23×D412yes—
585C22×C5#58512yes—
586C22×C5#58512yes—
587C22×C5C2611yescharacteristic
588C2×D5—26no—
589C2×D5—26no—
590C2×D5—224no—
591C2×D5—22no—
592C2×D5—26no—
593C2×D5—22no—
594C2×D5—26no—
595C2×D5—22no—
596C2×D5—26no—
597C2×D5—44no—
598C2×D5—412no—
599C2×D5—848no—
600C2×D5C23×D4112yes—
601C4×C5—26no—
602C4×C5—22no—
603C4×C5—22no—
604C4×C5—26no—
605C4×C5C23×D4112yes—
606Dic5—26no—
607Dic5—22no—
608Dic5—22no—
609Dic5—26no—
610Dic5C23×D414yes—
611C24—53no—
612C24—53no—
613C24—51no—
614C24—524no—
615C24—1024no—
616C24—2012no—
617C24—2012no—
618C24C23×D513yes—
619C24C23×D511yescharacteristic
620#41—232no—
621#41—564no—
622#41—1096no—
623#41—1096no—
624#41—1096no—
625#41—1096no—
626#41—1032no—
627C2×Q8—232no—
628C2×Q8—212no—
629C2×Q8—512no—
630C2×Q8—512no—
631C2×Q8—54no—
632C2×Q8—1012no—
633C2×Q8—104no—
634C2×Q8—1096no—
635C2×Q8—1032no—
636C2×Q8—1012no—
637C2×Q8D4×D518yes—
638C2×Q8C23×D5112yes—
639C2×Q8C23×D514yes—
640C2×D4—212no—
641C2×D4—46no—
642C2×D4—512no—
643C2×D4—512no—
644C2×D4—512no—
645C2×D4—54no—
646C2×D4—512no—
647C2×D4—512no—
648C2×D4—524no—
649C2×D4—512no—
650C2×D4—512no—
651C2×D4—512no—
652C2×D4—512no—
653C2×D4—512no—
654C2×D4—1096no—
655C2×D4—1012no—
656C2×D4—1012no—
657C2×D4—1096no—
658C2×D4—1012no—
659C2×D4—104no—
660C2×D4—1096no—
661C2×D4—1012no—
662C2×D4—1012no—
663C2×D4—1012no—
664C2×D4—206no—
665C2×D4—206no—
666C2×D4—206no—
667C2×D4C23×D5112yes—
668C2×D4C23×D5112yes—
669C22×C4—212no—
670C22×C4—212no—
671C22×C4—51no—
672C22×C4—524no—
673C22×C4—512no—
674C22×C4—51no—
675C22×C4—53no—
676C22×C4—53no—
677C22×C4—51no—
678C22×C4—524no—
679C22×C4—512no—
680C22×C4—512no—
681C22×C4—512no—
682C22×C4—512no—
683C22×C4—1024no—
684C22×C4—1012no—
685C22×C4—1012no—
686C22×C4—206no—
687C22×C4—206no—
688C22×C4C23×D5112yes—
689C22×C4C23×D5112yes—
690C22×C4C23×D511yescharacteristic
691C22×C4C23×D513yes—
692C22×C4C23×D513yes—
693C22×C4C23×D511yescharacteristic
694C22×C4C23×D513yes—
695C4⋊C4—512no—
696C4⋊C4—512no—
697C4⋊C4—512no—
698C4⋊C4—512no—
699C4⋊C4C23×D5112yes—
700C4⋊C4C23×D5112yes—
701C22⋊C4—512no—
702C22⋊C4—524no—
703C22⋊C4—54no—
704C22⋊C4—512no—
705C22⋊C4—512no—
706C22⋊C4—524no—
707C22⋊C4—524no—
708C22⋊C4—524no—
709C22⋊C4—54no—
710C22⋊C4—54no—
711C22⋊C4C23×D5112yes—
712C22⋊C4C23×D5124yes—
713C22⋊C4C23×D514yes—
714C42—54no—
715C42—512no—
716C42—512no—
717C42C23×D5112yes—
718C2×C5—46no—
719C2×C5—42no—
720C2×C5#350014yescomplemented
721C2×C5C24×D411yescharacteristic
722C2×C5C2×#58511yescharacteristic
723C2×C5C2×#58511yescharacteristic
724D5—212no—
725D5—42no—
726D5—46no—
727C23—22no—
728C23—26no—
729C23—22no—
730C23—26no—
731C23—22no—
732C23—26no—
733C23—512no—
734C23—56no—
735C23—56no—
736C23—52no—
737C23—1048no—
738C23—106no—
739C23—106no—
740C23—102no—
741C23—106no—
742C23—102no—
743C23—106no—
744C23—102no—
745C23—106no—
746C23—2024no—
747C23—2024no—
748C23—4048no—
749C23C24×D516yes—
750C23C24×D512yes—
751C23C24×D511yescharacteristic
752Q8—224no—
753Q8—1024no—
754Q8—108no—
755Q8—1024no—
756Q8C2×D4×D5116yes—
757D4—224no—
758D4—412no—
759D4—548no—
760D4—1024no—
761D4—1024no—
762D4—1024no—
763D4—108no—
764D4—1024no—
765D4—1024no—
766D4—1024no—
767D4—2012no—
768D4—2012no—
769D4—2012no—
770C2×C4—22no—
771C2×C4—26no—
772C2×C4—26no—
773C2×C4—22no—
774C2×C4—224no—
775C2×C4—224no—
776C2×C4—54no—
777C2×C4—52no—
778C2×C4—548no—
779C2×C4—52no—
780C2×C4—56no—
781C2×C4—56no—
782C2×C4—52no—
783C2×C4—1048no—
784C2×C4—102no—
785C2×C4—106no—
786C2×C4—102no—
787C2×C4—106no—
788C2×C4—1024no—
789C2×C4—1024no—
790C2×C4—2012no—
791C2×C4—2012no—
792C2×C4C2×D4×D5112yes—
793C2×C4C24×D512yes—
794C2×C4C24×D516yes—
795C2×C4C24×D516yes—
796C2×C4C24×D512yes—
797C2×C4C24×D516yes—
798C5C2×#350011yescharacteristic, complemented, Sylow
799C22—22no—
800C22—26no—
801C22—22no—
802C22—26no—
803C22—22no—
804C22—26no—
805C22—412no—
806C22—44no—
807C22—512no—
808C22—106no—
809C22—106no—
810C22—1024no—
811C22—102no—
812C22—106no—
813C22—102no—
814C22—106no—
815C22—102no—
816C22—106no—
817C22—2012no—
818C22—204no—
819C22—4048no—
820C22C22×D4×D512yes—
821C22#6628312yes—
822C22#6628712yes—
823C22C25×D511yescharacteristic
824C4—22no—
825C4—26no—
826C4—26no—
827C4—22no—
828C4—54no—
829C4—102no—
830C4—106no—
831C4—102no—
832C4—106no—
833C4C22×D4×D5112yes—
834C2—46no—
835C2—42no—
836C2—1012no—
837C2—206no—
838C2—202no—
839C2#1061861614yesdirect product factor
840C2C23×D4×D511yescharacteristic
841C2C2×#6628311yescharacteristic
842C2C2×#6628711yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#548C2
socleC23×C5C25
hypercenterC2×#548D5
hypocenterC5C2×#3500
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#4149C2semidirect
2. C22×#4147C2semidirect
3. C2×C5×#548C2semidirect
4. C2×#66165C2semidirect
5. C2×#66151C2semidirect
6. #10618616C2direct (N × H)
7. C2×#66010C2semidirect
8. C2×D5×#124C2semidirect
9. C2×#65964C2semidirect
10. C2×#65962C2semidirect
11. C2×#65946C2semidirect
12. C2×#65941C2semidirect
13. C2×#65910C2semidirect
14. C2×C4×#713C2semidirect
15. C2×#65884C2semidirect
16. C2×#65882C2semidirect
18. C23×C5×Q8C22semidirect
20. C2×#4149C22semidirect
22. C2×#4147C22semidirect
25. C22×#713C22semidirect
26. C22×Q8×D5C22semidirect
27. C22×Q8×D5C22semidirect
31. C22×#709C22semidirect
32. C22×#709C22semidirect
34. C5×#548C22semidirect
35. C2×C5×#124C22semidirect
36. C2×C5×C22⋊Q8C22semidirect
37. C2×C5×#121C22semidirect
38. C2×C4×C5×Q8C22semidirect
39. C2×C4×C5×D4C22semidirect
40. #66165C22semidirect
41. #66151C22semidirect
42. C2×#4093C22semidirect
43. C2×#4092C22semidirect
44. C2×Q8×Dic5C22semidirect
45. C2×#4086C22semidirect
46. C2×#4084C22semidirect
47. C2×#4084C22semidirect
48. C2×#4083C22semidirect
49. C2×#4082C22semidirect
50. C2×#4076C22semidirect
51. C2×C4×C22⋊D5C22semidirect
52. C2×C4×C22⋊D5C22semidirect
53. C2×#4070C22semidirect
54. #66010C22semidirect
55. D5×#124C22semidirect
56. #65964C22semidirect
57. #65962C22semidirect
58. #65946C22semidirect
59. #65941C22semidirect
60. #65910C22semidirect
61. C4×#713C22semidirect
62. #65884C22semidirect
63. #65882C22semidirect
64. C2×#4043C22semidirect
65. C2×#4041C22semidirect
66. C2×#4041C22semidirect
67. C2×#4040C22semidirect
68. C2×#4039C22semidirect
69. C2×#4038C22semidirect
70. C2×#4034C22semidirect
71. C2×#4031C22semidirect
72. C2×#4031C22semidirect
73. C2×#4031C22semidirect
74. C2×#4030C22semidirect
75. C2×#4030C22semidirect
76. C2×#4029C22semidirect
77. C2×#4028C22semidirect
78. C2×D5×C22⋊C4C22semidirect
79. C2×D5×C22⋊C4C22semidirect
80. C2×#4021C22semidirect
81. C2×C4×D20C22semidirect
82. C2×C4×D20C22semidirect
83. C2×C42×D5C22semidirect
91. C22×C5×Q8C23semidirect
106. C2×#713D4semidirect
109. C2×#713C23semidirect
112. C2×Q8×D5C23semidirect
113. C2×Q8×D5C23semidirect
122. C2×#709C23semidirect
123. C2×#709C23semidirect
140. C5×#124C23semidirect
141. C5×C22⋊Q8C23semidirect
142. C5×#121C23semidirect
143. C4×C5×Q8C23semidirect
144. C4×C5×D4C23semidirect
154. #4093C23semidirect
155. #4092C23semidirect
156. Q8×Dic5C23semidirect
157. #4086C23semidirect
158. #4084C23semidirect
159. #4084C23semidirect
160. #4083C23semidirect
161. #4082C23semidirect
162. #4076C23semidirect
163. C4×C22⋊D5C23semidirect
164. C4×C22⋊D5C23semidirect
174. #4070C23semidirect
180. #4043C23semidirect
181. #4041C23semidirect
182. #4041C23semidirect
183. #4040C23semidirect
184. #4039C23semidirect
185. #4038C23semidirect
186. #4034C23semidirect
187. #4031C23semidirect
188. #4031C23semidirect
189. #4031C23semidirect
190. #4030C23semidirect
191. #4030C23semidirect
192. #4029C23semidirect
193. #4028C23semidirect
194. D5×C22⋊C4C23semidirect
195. D5×C22⋊C4C23semidirect
196. #4021C23semidirect
197. C4×D20C23semidirect
198. C4×D20C23semidirect
199. C42×D5C23semidirect
206. C2×#548D5semidirect
263. #713C2×D4semidirect
336. C23×Q8C2×D5semidirect
343. #548C2×D5semidirect
360. C2×#124C2×D5semidirect
366. C2×C22⋊Q8C2×D5semidirect
374. C2×#121C2×D5semidirect
379. C2×C4×Q8C2×D5semidirect
385. C2×C4×D4C2×D5semidirect
488. C22×Q8C22×D5semidirect
524. #124C22×D5semidirect
530. C22⋊Q8C22×D5semidirect
538. #121C22×D5semidirect
542. C4×Q8C22×D5semidirect
548. C4×D4C22×D5semidirect
720. C2×C5#3500semidirect
798. C5C2×#3500semidirect
839. C2#10618616direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41492
C22×#41472
C2×C5×#5482
C2×#661652
C2×#661512
#106186162
C2×#660102
C2×D5×#1242
C2×#659642
C2×#659622
C2×#659462
C2×#659412
C2×#659102
C2×C4×#7132
C2×#658842
C2×#658822
C2×#35005