Finite Group Databasebeta

← C2×#10618837 #13007506

Subgroups — C2×#10618837 #13007506

Order 1280.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic, complemented
2#10618837C2132yesmaximal, direct product factor
3C2×#66056C211yesmaximal, characteristic, complemented
4C2×#66059C211yesmaximal, characteristic, complemented
5C2×#66024C212yesmaximal, complemented
6C2×#66025C212yesmaximal, complemented
7C2×#65967C212yesmaximal, complemented
8C2×#65965C214yesmaximal, complemented
9C2×#65974C214yesmaximal, complemented
10C2×#65977C212yesmaximal, complemented
11C2×C4×Q8×D5C211yesmaximal, characteristic, complemented
12C2×#65919C211yesmaximal, characteristic, complemented
13C2×#65882C212yesmaximal, complemented
14C2×#65891C211yesmaximal, characteristic, complemented
15C2×#65893C212yesmaximal, complemented
16C2×#65887C211yesmaximal, characteristic, complemented
17C2×#65841C212yesmaximal, complemented
18C2×#65838C212yesmaximal, complemented
19C22×#713C2212yes—
20C22×Q8×D5C2211yescharacteristic
21C22×#709C2212yes—
22C22×#709C2214yes—
23C5×#554C22116yescomplemented
24C2×C5×C4⋊Q8C2211yescharacteristic
25C2×C5×#125C2212yes—
26C2×C5×C22⋊Q8C2212yes—
27C2×C5×C22⋊Q8C2214yes—
28C2×C4×C5×Q8C2211yescharacteristic
29C2×C4×C5×D4C2211yescharacteristic
30C2×C4×C5×D4C2212yes—
31C22×C5×C4⋊C4C2212yes—
32C2×#4093C2212yes—
33C2×#4093C2212yes—
34C2×Q8×Dic5C2211yescharacteristic
35C2×#4090C2214yes—
36C2×#4086C2212yes—
37C2×#4084C2211yescharacteristic
38C2×#4082C2211yescharacteristic
39C2×#4076C2212yes—
40C2×#4075C2214yes—
41C2×C4×C22⋊D5C2214yes—
42C2×C4×C22⋊D5C2214yes—
43C2×C4×C22⋊D5C2212yes—
44C2×#4072C2212yes—
45#66059C22116yescomplemented
46#66056C22116yescomplemented
47#66025C22132yescomplemented
48#66024C22132yescomplemented
49#65977C22132yescomplemented
50#65974C22164yescomplemented
51#65967C22132yescomplemented
52#65965C22164yescomplemented
53#65919C22116yescomplemented
54C4×Q8×D5C22116yescomplemented
55#65893C22132yescomplemented
56#65891C22116yescomplemented
57#65887C22116yescomplemented
58#65882C22132yescomplemented
59C2×#4044C2214yes—
60C2×#4043C2214yes—
61C2×#4043C2211yescharacteristic
62C2×#4042C2214yes—
63C2×#4042C2214yes—
64#65841C22132yescomplemented
65C2×#4041C2212yes—
66C2×#4041C2212yes—
67C2×#4040C2214yes—
68C2×#4040C2214yes—
69#65838C22132yescomplemented
70C2×#4039C2212yes—
71C2×#4039C2212yes—
72C2×#4039C2214yes—
73C2×#4039C2212yes—
74C2×#4039C2212yes—
75C2×#4038C2214yes—
76C2×D5×C4⋊C4C2214yes—
77C2×D5×C4⋊C4C2211yescharacteristic
78C2×D5×C4⋊C4C2212yes—
79C2×#4036C2211yescharacteristic
80C2×#4034C2212yes—
81C2×#4034C2212yes—
82C2×#4033C2212yes—
83C2×#4033C2211yescharacteristic
84C2×#4033C2212yes—
85C2×#4033C2212yes—
86C2×#4031C2214yes—
87C2×#4031C2214yes—
88C2×#4030C2214yes—
89C2×#4030C2214yes—
90C2×#4029C2214yes—
91C2×#4029C2212yes—
92C2×#4025C2212yes—
93C2×#4021C2212yes—
94C2×#4020C2211yescharacteristic
95C2×C4×D20C2212yes—
96C2×C42×D5C2211yescharacteristic
97C2×C42×D5C2212yes—
98C2×C4×Dic10C2211yescharacteristic
99C2×C4×Dic10C2212yes—
100C2×C4×Dic10C2211yescharacteristic
101C2×#3522—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×Q8C2312yes—
104C22×C5×D4C2311yescharacteristic
105C23×C4×C5C2312yes—
106C23×C4×C5C2314yes—
107C22×C22⋊D5C2312yes—
108C22×C22⋊D5C2314yes—
109C22×C22⋊D5C2314yes—
110C2×#713—48no—
111C2×#713C23116yes—
112C2×Q8×D5—28no—
113C2×Q8×D5C2318yes—
114C2×#709—216no—
115C2×#709—416no—
116C2×#709C23116yes—
117C2×#709C23132yes—
118C22×D20C2312yes—
119C22×D20C2312yes—
120C22×D20C2314yes—
121C22×D20C2312yes—
122C22×C4×D5C2311yescharacteristic
123C22×C4×D5C2311yescharacteristic
124C22×C4×D5C2312yes—
125C22×C4×D5C2312yes—
126C22×C4×D5C2311yescharacteristic
127C22×C4×D5C2314yes—
128C22×C4×D5C2314yes—
129C22×C4×D5C2314yes—
130C22×Dic10C2311yescharacteristic
131C22×Dic10C2312yes—
132C22×Dic10C2314yes—
133C22×Dic10C2311yescharacteristic
134C5×C4⋊Q8C2318yes—
135C5×#125C23116yes—
136C5×C22⋊Q8C23132yes—
137C5×C22⋊Q8C23116yes—
138C4×C5×Q8C2318yes—
139C4×C5×D4C23116yes—
140C4×C5×D4C2318yes—
141C2×C5×C4⋊C4C2312yes—
142C2×C5×C4⋊C4C2312yes—
143C2×C5×C4⋊C4C2311yescharacteristic
144C2×C5×C4⋊C4C2312yes—
145C2×C5×C4⋊C4C2311yescharacteristic
146C2×C5×C4⋊C4C2314yes—
147C2×C5×C4⋊C4C2314yes—
148C2×C5×C4⋊C4C23116yes—
149C2×C5×C22⋊C4C2312yes—
150C2×C5×C22⋊C4C2314yes—
151C2×C42×C5C2311yescharacteristic
152C2×C42×C5C2312yes—
153C2×C22⋊Dic5C2312yes—
154C2×C22⋊Dic5C2312yes—
155C2×C22⋊Dic5C2312yes—
156#4093C23116yes—
157#4093C23116yes—
158Q8×Dic5C2318yes—
159#4090C23132yes—
160#4086C23116yes—
161#4084C2318yes—
162#4082C2318yes—
163#4076C23116yes—
164#4075C23132yes—
165C4×C22⋊D5C23132yes—
166C4×C22⋊D5C23132yes—
167C4×C22⋊D5C23116yes—
168C2×#685C2314yes—
169C2×#685C2314yes—
170C2×#685C2314yes—
171C2×#685C2312yes—
172C2×#685C2314yes—
173C2×#685C2314yes—
174C2×#685C2314yes—
175#4072C23116yes—
176C2×C4⋊Dic5C2311yescharacteristic
177C2×C4⋊Dic5C2312yes—
178C2×C4⋊Dic5C2311yescharacteristic
179C2×C4⋊Dic5C2312yes—
180C2×C4⋊Dic5C2312yes—
181C2×#683C2312yes—
182C2×#683C2312yes—
183C2×#683C2312yes—
184C2×#683C2312yes—
185C2×#683C2312yes—
186C2×#683C2314yes—
187C2×#683C2314yes—
188C2×C4×Dic5C2312yes—
189C2×C4×Dic5C2311yescharacteristic
190C2×C4×Dic5C2312yes—
191C2×C4×Dic5C2311yescharacteristic
192C2×C4×Dic5C2312yes—
193C2×C4×Dic5C2312yes—
194C2×C4×Dic5C2311yescharacteristic
195C2×C4×Dic5C2314yes—
196#4044C23132yes—
197#4043C2318yes—
198#4043C23132yes—
199#4042C23132yes—
200#4042C23132yes—
201#4041C23116yes—
202#4041C23116yes—
203#4040C23132yes—
204#4040C23132yes—
205#4039C23116yes—
206#4039C23116yes—
207#4039C23116yes—
208#4039C23116yes—
209#4039C23132yes—
210#4038C23132yes—
211D5×C4⋊C4C23132yes—
212D5×C4⋊C4C2318yes—
213D5×C4⋊C4C23116yes—
214#4036C2318yes—
215#4034C23116yes—
216#4034C23116yes—
217#4033C23116yes—
218#4033C23116yes—
219#4033C2318yes—
220#4033C23116yes—
221#4031C23132yes—
222#4031C23132yes—
223#4030C23132yes—
224#4030C23132yes—
225#4029C23116yes—
226#4029C23132yes—
227#4025C23116yes—
228#4021C23116yes—
229#4020C2318yes—
230C4×D20C23116yes—
231C42×D5C2318yes—
232C42×D5C23116yes—
233C4×Dic10C2318yes—
234C4×Dic10C2318yes—
235C4×Dic10C23116yes—
236#3522—532no—
237C2×#559—51no—
238C2×#559—52no—
239C2×Q82—51no—
240C2×#554—52no—
241C2×#554D511yescharacteristic, complemented
242C2×#550—51no—
243C2×#548—52no—
244C2×#547—54no—
245C2×#547—52no—
246C2×#542—52no—
247C2×#542—54no—
248C2×#532—51no—
249C2×#532—52no—
250C2×#529—52no—
251C2×#529—51no—
252C2×#520—52no—
253C22×C4×Q8—51no—
254C24×C5C2412yes—
255C23×D5C2414yes—
256C23×D5C2411yescharacteristic
257C2×C5×Q8—24no—
258C2×C5×Q8—44no—
259C2×C5×Q8C2414yes—
260C2×C5×Q8C2418yes—
261C2×C5×D4—24no—
262C2×C5×D4C2414yes—
263C22×C4×C5—28no—
264C22×C4×C5—48no—
265C22×C4×C5C2412yes—
266C22×C4×C5C2411yescharacteristic
267C22×C4×C5C2412yes—
268C22×C4×C5C2412yes—
269C22×C4×C5C2414yes—
270C22×C4×C5C2418yes—
271C22×C4×C5C24116yes—
272C22×C4×C5C2411yescharacteristic
273C22×C4×C5C2411yescharacteristic
274C2×C22⋊D5—28no—
275C2×C22⋊D5—216no—
276C2×C22⋊D5—48no—
277C2×C22⋊D5C2418yes—
278C2×C22⋊D5C24116yes—
279C2×C22⋊D5C24116yes—
280C22×Dic5C2411yescharacteristic
281C22×Dic5C2412yes—
282C22×Dic5C2411yescharacteristic
283C22×Dic5C2411yescharacteristic
284C22×Dic5C2412yes—
285C22×Dic5C2412yes—
286C22×Dic5C2412yes—
287#713—432no—
288Q8×D5—232no—
289#709—264no—
290#709—464no—
291C2×D20—216no—
292C2×D20—28no—
293C2×D20—28no—
294C2×D20—44no—
295C2×D20C24116yes—
296C2×D20C2418yes—
297C2×D20C2418yes—
298C2×D20C2418yes—
299C2×C4×D5—28no—
300C2×C4×D5—24no—
301C2×C4×D5—24no—
302C2×C4×D5—24no—
303C2×C4×D5—216no—
304C2×C4×D5—28no—
305C2×C4×D5—48no—
306C2×C4×D5—48no—
307C2×C4×D5C2418yes—
308C2×C4×D5C24116yes—
309C2×C4×D5C2418yes—
310C2×C4×D5C2414yes—
311C2×C4×D5C2414yes—
312C2×C4×D5C2414yes—
313C2×C4×D5C24116yes—
314C2×C4×D5C24116yes—
315C2×Dic10—24no—
316C2×Dic10—28no—
317C2×Dic10—48no—
318C2×Dic10#4118yescomplemented
319C2×Dic10C2418yes—
320C2×Dic10C2414yes—
321C2×Dic10C24116yes—
322C2×Dic10C2414yes—
323C5×C4⋊C4C2414yes—
324C5×C4⋊C4C24116yes—
325C5×C4⋊C4C2418yes—
326C5×C4⋊C4C2414yes—
327C5×C4⋊C4C2418yes—
328C5×C4⋊C4C2418yes—
329C5×C4⋊C4C24116yes—
330C5×C22⋊C4C2418yes—
331C5×C22⋊C4C24116yes—
332C42×C5C2418yes—
333C42×C5C2414yes—
334C22⋊Dic5C2418yes—
335C22⋊Dic5C2418yes—
336C22⋊Dic5C2418yes—
337#685C24116yes—
338#685C24116yes—
339#685C24116yes—
340#685C2418yes—
341#685C24116yes—
342#685C24116yes—
343#685C24116yes—
344C4⋊Dic5C2414yes—
345C4⋊Dic5C2418yes—
346C4⋊Dic5C2414yes—
347C4⋊Dic5C2418yes—
348C4⋊Dic5C2418yes—
349#683C2418yes—
350#683C2418yes—
351#683C2418yes—
352#683C2418yes—
353#683C2418yes—
354#683C24116yes—
355#683C24116yes—
356C4×Dic5C2418yes—
357C4×Dic5C2414yes—
358C4×Dic5C2418yes—
359C4×Dic5C2414yes—
360C4×Dic5C2418yes—
361C4×Dic5C2418yes—
362C4×Dic5C2414yes—
363C4×Dic5C24116yes—
364C22×#41—52no—
365C22×#41—52no—
366C22×#41—54no—
367C23×Q8—51no—
368#559—516no—
369#559—532no—
370Q82—516no—
371#554—532no—
372#554C2×D5116yescomplemented
373#550—516no—
374#548—532no—
375#547—564no—
376#547—532no—
377#542—564no—
378#542—532no—
379#532—516no—
380#532—532no—
381C2×C4⋊Q8—54no—
382C2×C4⋊Q8—52no—
383C2×C4⋊Q8—52no—
384C2×C4⋊Q8C2×D511yescharacteristic
385C2×#127—52no—
386C2×#127—51no—
387#529—532no—
388#529—516no—
389C2×#126—54no—
390C2×#126—52no—
391C2×#125—51no—
392C2×#125C2×D512yes—
393C2×#124—52no—
394C2×#124—52no—
395C2×#124—51no—
396C2×#124—54no—
397C2×#124—54no—
398C2×#124—52no—
399C2×#123—54no—
400C2×#123—54no—
401C2×#123—54no—
402C2×#123—52no—
403C2×#123—54no—
404C2×C22⋊Q8—54no—
405C2×C22⋊Q8—54no—
406C2×C22⋊Q8—51no—
407C2×C22⋊Q8—54no—
408C2×C22⋊Q8C2×D514yes—
409C2×C22⋊Q8C2×D512yes—
410C2×#121—51no—
411C2×#121—52no—
412C2×#121—52no—
413C2×#121—52no—
414C2×#121—54no—
415C2×#121—54no—
416#520—532no—
417C2×C4×Q8—51no—
418C2×C4×Q8—516no—
419C2×C4×Q8—51no—
420C2×C4×Q8—52no—
421C2×C4×Q8—52no—
422C2×C4×Q8—52no—
423C2×C4×Q8—51no—
424C2×C4×Q8—52no—
425C2×C4×Q8—51no—
426C2×C4×Q8C2×D511yescharacteristic
427C2×C4×D4—54no—
428C2×C4×D4—54no—
429C2×C4×D4—52no—
430C2×C4×D4—52no—
431C2×C4×D4—52no—
432C2×C4×D4—54no—
433C2×C4×D4—52no—
434C2×C4×D4—52no—
435C2×C4×D4—52no—
436C2×C4×D4C2×D511yescharacteristic
437C2×C4×D4C2×D512yes—
438C2×#117—52no—
439C2×#117—54no—
440C22×C4⋊C4—52no—
441C22×C4⋊C4—51no—
442C22×C4⋊C4—54no—
443C22×C4⋊C4C2×D512yes—
444C22×C42—51no—
445C22×C42—52no—
446C23×C5—24no—
447C23×C5—24no—
448C23×C5—24no—
449C23×C5C2514yes—
450C23×C5C2511yescharacteristic
451C22×D5—22no—
452C22×D5—22no—
453C22×D5—28no—
454C22×D5—28no—
455C22×D5—28no—
456C22×D5H(5,𝔽2)14yes—
457C22×D5C2518yes—
458C22×D5C2512yes—
459C5×Q8—28no—
460C5×Q8—48no—
461C5×D4—28no—
462C2×C4×C5—24no—
463C2×C4×C5—24no—
464C2×C4×C5—28no—
465C2×C4×C5—24no—
466C2×C4×C5—22no—
467C2×C4×C5—216no—
468C2×C4×C5—416no—
469C2×C4×C5C2×#4114yes—
470C2×C4×C52−1+414yes—
471C2×C4×C5C2512yes—
472C2×C4×C5C2514yes—
473C2×C4×C5C2518yes—
474C2×C4×C5C2514yes—
475C2×C4×C5C2514yes—
476C2×C4×C5C2512yes—
477C2×C4×C5C2512yes—
478C22⋊D5—216no—
479C22⋊D5—232no—
480C22⋊D5—416no—
481C2×Dic5—22no—
482C2×Dic5—24no—
483C2×Dic5—24no—
484C2×Dic5—22no—
485C2×Dic5—24no—
486C2×Dic5—22no—
487C2×Dic5C2×#4118yes—
488C2×Dic5C2512yes—
489C2×Dic5C2514yes—
490C2×Dic5C2514yes—
491C2×Dic5C2512yes—
492C2×Dic5C2512yes—
493C2×Dic5C2514yes—
494C2×Dic5C2514yes—
495D20—232no—
496D20—216no—
497D20—216no—
498D20—48no—
499C4×D5—216no—
500C4×D5—28no—
501C4×D5—28no—
502C4×D5—28no—
503C4×D5—232no—
504C4×D5—216no—
505C4×D5—416no—
506C4×D5—416no—
507Dic10—28no—
508Dic10—216no—
509Dic10—416no—
510Dic10C2×#41116yescomplemented
511C2×#41—516no—
512C2×#41—516no—
513C2×#41—532no—
514C2×#41—1016no—
515C2×#41—2016no—
516C2×#41—208no—
517C22×Q8—58no—
518C22×Q8—51no—
519C22×Q8—51no—
520C22×Q8—52no—
521C22×Q8—54no—
522C22×Q8—108no—
523C22×Q8C22×D511yescharacteristic
524C22×Q8C22×D512yes—
525C22×D4—54no—
526C22×D4—52no—
527C22×D4—54no—
528C22×D4—52no—
529C22×D4—52no—
530C22×D4—54no—
531C22×D4—52no—
532C22×D4C22×D511yescharacteristic
533C23×C4—51no—
534C23×C4—52no—
535C23×C4—54no—
536C23×C4—52no—
537C23×C4—51no—
538C23×C4—51no—
539C23×C4—54no—
540C23×C4—54no—
541C23×C4C22×D512yes—
542C23×C4C22×D514yes—
543C4⋊Q8—532no—
544C4⋊Q8—516no—
545C4⋊Q8—516no—
546C4⋊Q8C22×D518yes—
547#127—516no—
548#127—58no—
549#126—532no—
550#126—516no—
551#125—58no—
552#125C22×D5116yes—
553#124—516no—
554#124—516no—
555#124—58no—
556#124—532no—
557#124—532no—
558#124—516no—
559#123—532no—
560#123—532no—
561#123—532no—
562#123—516no—
563#123—532no—
564C22⋊Q8—58no—
565C22⋊Q8—532no—
566C22⋊Q8—532no—
567C22⋊Q8—532no—
568C22⋊Q8C22×D5132yes—
569C22⋊Q8C22×D5116yes—
570#121—58no—
571#121—516no—
572#121—516no—
573#121—516no—
574#121—532no—
575#121—532no—
576C4×Q8—58no—
577C4×Q8—58no—
578C4×Q8—516no—
579C4×Q8—516no—
580C4×Q8—516no—
581C4×Q8—58no—
582C4×Q8—516no—
583C4×Q8—58no—
584C4×Q8C22×D518yes—
585C4×D4—532no—
586C4×D4—532no—
587C4×D4—516no—
588C4×D4—516no—
589C4×D4—516no—
590C4×D4—532no—
591C4×D4—516no—
592C4×D4—516no—
593C4×D4—516no—
594C4×D4C22×D518yes—
595C4×D4C22×D5116yes—
596#117—516no—
597#117—532no—
598C2×C4⋊C4—52no—
599C2×C4⋊C4—52no—
600C2×C4⋊C4—54no—
601C2×C4⋊C4—52no—
602C2×C4⋊C4—51no—
603C2×C4⋊C4—52no—
604C2×C4⋊C4—52no—
605C2×C4⋊C4—52no—
606C2×C4⋊C4—51no—
607C2×C4⋊C4—52no—
608C2×C4⋊C4—54no—
609C2×C4⋊C4—52no—
610C2×C4⋊C4—516no—
611C2×C4⋊C4—58no—
612C2×C4⋊C4—532no—
613C2×C4⋊C4C22×D511yescharacteristic
614C2×C4⋊C4C22×D514yes—
615C2×C4⋊C4C22×D512yes—
616C2×C4⋊C4C22×D512yes—
617C2×C4⋊C4C22×D5116yes—
618C2×C4⋊C4C22×D511yescharacteristic
619C2×C4⋊C4C22×D512yes—
620C2×C4⋊C4C22×D514yes—
621C2×C22⋊C4—52no—
622C2×C22⋊C4—52no—
623C2×C22⋊C4—52no—
624C2×C22⋊C4—54no—
625C2×C22⋊C4—54no—
626C2×C22⋊C4—52no—
627C2×C22⋊C4—54no—
628C2×C22⋊C4—54no—
629C2×C22⋊C4—54no—
630C2×C22⋊C4—54no—
631C2×C22⋊C4C22×D512yes—
632C2×C22⋊C4C22×D514yes—
633C2×C42—52no—
634C2×C42—51no—
635C2×C42—54no—
636C2×C42—52no—
637C2×C42—51no—
638C2×C42—52no—
639C2×C42—51no—
640C2×C42—52no—
641C2×C42—58no—
642C2×C42—516no—
643C2×C42C22×D512yes—
644C2×C42C22×D511yescharacteristic
645C22×C5—24no—
646C22×C5—24no—
647C22×C5—24no—
648C22×C5—48no—
649C22×C5C22×#4112yes—
650C22×C5C2×H(5,𝔽2)12yes—
651C22×C5C2×2−1+412yes—
652C22×C5C2611yescharacteristic
653C2×D5—22no—
654C2×D5—22no—
655C2×D5—28no—
656C2×D5—28no—
657C2×D5—28no—
658C2×D5—28no—
659C2×D5—416no—
660C2×D5C2×H(5,𝔽2)14yes—
661C4×C5—24no—
662C4×C5—24no—
663C4×C5—28no—
664C4×C5—24no—
665C4×C5—22no—
666C4×C5C22×#4114yes—
667C4×C5C2×2−1+414yes—
668Dic5—22no—
669Dic5—24no—
670Dic5—24no—
671Dic5—22no—
672Dic5—24no—
673Dic5—22no—
674Dic5C22×#4118yes—
675C24—51no—
676C24—54no—
677C24C23×D512yes—
678#41—1064no—
679#41—2064no—
680#41—2032no—
681C2×Q8—24no—
682C2×Q8—44no—
683C2×Q8—58no—
684C2×Q8—54no—
685C2×Q8—54no—
686C2×Q8—58no—
687C2×Q8—516no—
688C2×Q8—108no—
689C2×Q8—1032no—
690C2×Q8—104no—
691C2×Q8—208no—
692C2×Q8C23×D514yes—
693C2×Q8C23×D518yes—
694C2×D4—24no—
695C2×D4—516no—
696C2×D4—58no—
697C2×D4—516no—
698C2×D4—58no—
699C2×D4—58no—
700C2×D4—516no—
701C2×D4—58no—
702C2×D4—1016no—
703C2×D4—1016no—
704C2×D4—108no—
705C2×D4—108no—
706C2×D4—108no—
707C2×D4—204no—
708C2×D4—208no—
709C2×D4C23×D514yes—
710C22×C4—28no—
711C22×C4—48no—
712C22×C4—52no—
713C22×C4—51no—
714C22×C4—52no—
715C22×C4—51no—
716C22×C4—51no—
717C22×C4—52no—
718C22×C4—52no—
719C22×C4—54no—
720C22×C4—54no—
721C22×C4—58no—
722C22×C4—58no—
723C22×C4—54no—
724C22×C4—516no—
725C22×C4—516no—
726C22×C4—516no—
727C22×C4—108no—
728C22×C4—1016no—
729C22×C4—108no—
730C22×C4—104no—
731C22×C4—104no—
732C22×C4—104no—
733C22×C4—208no—
734C22×C4—208no—
735C22×C4C23×D518yes—
736C22×C4C23×D512yes—
737C22×C4C23×D512yes—
738C22×C4C23×D511yescharacteristic
739C22×C4C23×D514yes—
740C22×C4C23×D512yes—
741C22×C4C23×D5116yes—
742C22×C4C23×D511yescharacteristic
743C22×C4C23×D511yescharacteristic
744C4⋊C4—58no—
745C4⋊C4—58no—
746C4⋊C4—516no—
747C4⋊C4—58no—
748C4⋊C4—54no—
749C4⋊C4—58no—
750C4⋊C4—58no—
751C4⋊C4—58no—
752C4⋊C4—54no—
753C4⋊C4—58no—
754C4⋊C4—516no—
755C4⋊C4—58no—
756C4⋊C4C23×D514yes—
757C4⋊C4C23×D5116yes—
758C4⋊C4C23×D518yes—
759C4⋊C4C23×D518yes—
760C4⋊C4C23×D514yes—
761C4⋊C4C23×D518yes—
762C4⋊C4C23×D5116yes—
763C22⋊C4—58no—
764C22⋊C4—58no—
765C22⋊C4—58no—
766C22⋊C4—516no—
767C22⋊C4—516no—
768C22⋊C4—58no—
769C22⋊C4—516no—
770C22⋊C4—516no—
771C22⋊C4—516no—
772C22⋊C4—516no—
773C22⋊C4C23×D518yes—
774C22⋊C4C23×D5116yes—
775C42—58no—
776C42—54no—
777C42—54no—
778C42—58no—
779C42—54no—
780C42—58no—
781C42—516no—
782C42—58no—
783C42C23×D518yes—
784C42C23×D514yes—
785C2×C5—44no—
786C2×C5#352214yescomplemented
787C2×C5C23×#4111yescharacteristic
788C2×C5C22×H(5,𝔽2)11yescharacteristic
789C2×C5C22×2−1+411yescharacteristic
790D5—24no—
791D5—48no—
792C23—24no—
793C23—24no—
794C23—24no—
795C23—54no—
796C23—52no—
797C23—58no—
798C23—102no—
799C23—102no—
800C23—108no—
801C23—108no—
802C23—108no—
803C23C24×D514yes—
804C23C24×D511yescharacteristic
805Q8—28no—
806Q8—48no—
807Q8—516no—
808Q8—1016no—
809Q8—108no—
810Q8—2016no—
811D4—28no—
812D4—1032no—
813D4—1032no—
814D4—1016no—
815D4—1016no—
816D4—1016no—
817D4—208no—
818D4—2016no—
819C2×C4—24no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—28no—
823C2×C4—22no—
824C2×C4—216no—
825C2×C4—416no—
826C2×C4—58no—
827C2×C4—54no—
828C2×C4—52no—
829C2×C4—54no—
830C2×C4—52no—
831C2×C4—52no—
832C2×C4—54no—
833C2×C4—54no—
834C2×C4—1016no—
835C2×C4—1032no—
836C2×C4—1016no—
837C2×C4—108no—
838C2×C4—102no—
839C2×C4—104no—
840C2×C4—102no—
841C2×C4—102no—
842C2×C4—104no—
843C2×C4—104no—
844C2×C4—108no—
845C2×C4—108no—
846C2×C4—2016no—
847C2×C4—2016no—
848C2×C4#414714yes—
849C2×C4D5×#4114yes—
850C2×C4C24×D514yes—
851C2×C4C24×D514yes—
852C2×C4C24×D512yes—
853C2×C4C24×D518yes—
854C2×C4C24×D514yes—
855C2×C4C24×D512yes—
856C2×C4C24×D512yes—
857C5C2×#352211yescharacteristic, complemented, Sylow
858C22—24no—
859C22—24no—
860C22—24no—
861C22—48no—
862C22—54no—
863C22—102no—
864C22—102no—
865C22—108no—
866C22—108no—
867C22—108no—
868C22—108no—
869C22—2016no—
870C22C2×#414712yes—
871C22C2×D5×#4112yes—
872C22D5×H(5,𝔽2)12yes—
873C22C25×D511yescharacteristic
874C4—24no—
875C4—24no—
876C4—24no—
877C4—28no—
878C4—22no—
879C4—58no—
880C4—102no—
881C4—104no—
882C4—102no—
883C4—102no—
884C4—104no—
885C4—104no—
886C4C2×#414714yes—
887C4C2×D5×#4114yes—
888C2—44no—
889C2—104no—
890C2—208no—
891C2#1061883714yesdirect product factor
892C2C22×#414711yescharacteristic
893C2C22×D5×#4111yescharacteristic
894C2C2×D5×H(5,𝔽2)11yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#554C2
socleC23×C5C25
hypercenterC2×#554D5
hypocenterC5C2×#3522
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×C5×#554C2semidirect
2. #10618837C2direct (N × H)
3. C2×#66056C2semidirect
4. C2×#66059C2semidirect
5. C2×#66024C2semidirect
6. C2×#66025C2semidirect
7. C2×#65967C2semidirect
8. C2×#65965C2semidirect
9. C2×#65974C2semidirect
10. C2×#65977C2semidirect
11. C2×C4×Q8×D5C2semidirect
12. C2×#65919C2semidirect
13. C2×#65882C2semidirect
14. C2×#65891C2semidirect
15. C2×#65893C2semidirect
16. C2×#65887C2semidirect
17. C2×#65841C2semidirect
18. C2×#65838C2semidirect
23. C5×#554C22semidirect
45. #66059C22semidirect
46. #66056C22semidirect
47. #66025C22semidirect
48. #66024C22semidirect
49. #65977C22semidirect
50. #65974C22semidirect
51. #65967C22semidirect
52. #65965C22semidirect
53. #65919C22semidirect
54. C4×Q8×D5C22semidirect
55. #65893C22semidirect
56. #65891C22semidirect
57. #65887C22semidirect
58. #65882C22semidirect
64. #65841C22semidirect
69. #65838C22semidirect
241. C2×#554D5semidirect
318. C2×Dic10#41semidirect
372. #554C2×D5semidirect
510. Dic10C2×#41semidirect
786. C2×C5#3522semidirect
857. C5C2×#3522semidirect
891. C2#10618837direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5542
#106188372
C2×#660562
C2×#660592
C2×#660242
C2×#660252
C2×#659672
C2×#659652
C2×#659742
C2×#659772
C2×C4×Q8×D52
C2×#659192
C2×#658822
C2×#658912
C2×#658932
C2×#658872
C2×#658412
C2×#658382
C2×#35225