Finite Group Databasebeta

← C2×#10618857 #13007011

Subgroups — C2×#10618857 #13007011

Order 1280.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#554C211yesmaximal, characteristic, complemented
2#10618857C2132yesmaximal, direct product factor
3C2×#66056C211yesmaximal, characteristic, complemented
4C2×#66062C211yesmaximal, characteristic, complemented
5C2×#66031C212yesmaximal, complemented
6C2×#66019C212yesmaximal, complemented
7C2×#65980C214yesmaximal, complemented
8C2×#65975C212yesmaximal, complemented
9C2×#65959C214yesmaximal, complemented
10C2×#65959C212yesmaximal, complemented
11C2×#65912C211yesmaximal, characteristic, complemented
12C2×#65904C211yesmaximal, characteristic, complemented
13C2×#65895C212yesmaximal
14C2×#65891C211yesmaximal, characteristic
15C2×#65876C212yesmaximal, complemented
16C2×#65876C211yesmaximal, characteristic, complemented
17C2×#65847C212yesmaximal, complemented
18C2×#65834C212yesmaximal, complemented
19C5×#554C22116yescomplemented
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×#125C2212yes—
22C2×C5×C22⋊Q8C2212yes—
23C2×C5×C22⋊Q8C2214yes—
24C2×C4×C5×Q8C2211yescharacteristic
25C2×C4×C5×D4C2211yescharacteristic
26C2×C4×C5×D4C2212yes—
27C22×C5×C4⋊C4C2212yes—
28C2×#4092C2211yescharacteristic
29C2×#4092C2212yes—
30C2×Q8×Dic5C2212yes—
31C2×Q8×Dic5C2212yes—
32C2×#4090C2211yescharacteristic
33C2×#4090C2214yes—
34C2×#4084C2211yescharacteristic
35C2×#4082C2211yescharacteristic
36C2×#4082C2212yes—
37C2×#4075C2214yes—
38C2×C4×C22⋊D5C2212yes—
39C2×#4072C2212yes—
40C2×#4072C2212yes—
41C2×#4072C2214yes—
42C2×#4070C2214yes—
43C2×#4070C2214yes—
44C2×#4070C2212yes—
45#66062C22116yescomplemented
46#66056C22116yescomplemented
47#66031C22132yescomplemented
48#66019C22132yescomplemented
49#65980C22164yescomplemented
50#65975C22132yescomplemented
51#65959C22132yescomplemented
52#65959C22164yescomplemented
53#65912C22116yescomplemented
54#65904C22116yescomplemented
55#65895C22132yes—
56#65891C22116yes—
57#65876C22116yescomplemented
58#65876C22132yescomplemented
59#65847C22132yescomplemented
60C2×#4044C2214yes—
61C2×#4044C2214yes—
62C2×#4043C2211yescharacteristic
63C2×#4043C2211yescharacteristic
64C2×#4043C2212yes—
65C2×#4042C2212yes—
66C2×#4038C2212yes—
67#65834C22132yescomplemented
68C2×#4036C2214yes—
69C2×#4036C2212yes—
70C2×#4036C2212yes—
71C2×#4036C2214yes—
72C2×#4036C2214yes—
73C2×#4036C2211yescharacteristic
74C2×#4035C2212yes—
75C2×#4035C2214yes—
76C2×#4035C2214yes—
77C2×#4034C2211yescharacteristic
78C2×#4034C2212yes—
79C2×#4034C2214yes—
80C2×#4034C2212yes—
81C2×#4033C2212yes—
82C2×#4033C2214yes—
83C2×#4033C2212yes—
84C2×#4033C2212yes—
85C2×#4033C2212yes—
86C2×#4031C2214yes—
87C2×#4029C2212yes—
88C2×#4025C2212yes—
89C2×#4025C2214yes—
90C2×#4025C2214yes—
91C2×#4025C2214yes—
92C2×#4025C2214yes—
93C2×#4018C2212yes—
94C2×C42×D5C2211yescharacteristic
95C2×#4015C2212yes—
96C2×#4015C2211yescharacteristic
97C2×C4×Dic10C2212yes—
98C2×C4×Dic10C2211yescharacteristic
99C2×C4×Dic10C2211yescharacteristic
100C2×C4×Dic10C2212yes—
101C2×#3555—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×Q8C2312yes—
104C22×C5×D4C2311yescharacteristic
105C23×C4×C5C2312yes—
106C23×C4×C5C2314yes—
107C22×C22⋊D5C2312yes—
108C22×C4×D5C2311yescharacteristic
109C22×C4×D5C2311yescharacteristic
110C22×C4×D5C2311yescharacteristic
111C22×Dic10C2311yescharacteristic
112C22×Dic10C2312yes—
113C22×Dic10C2311yescharacteristic
114C22×Dic10C2312yes—
115C22×Dic10C2314yes—
116C5×C4⋊Q8C2318yes—
117C5×#125C23116yes—
118C5×C22⋊Q8C23116yes—
119C5×C22⋊Q8C23132yes—
120C4×C5×Q8C2318yes—
121C4×C5×D4C2318yes—
122C4×C5×D4C23116yes—
123C2×C5×C4⋊C4C2312yes—
124C2×C5×C4⋊C4C2311yescharacteristic
125C2×C5×C4⋊C4C2312yes—
126C2×C5×C4⋊C4C2314yes—
127C2×C5×C4⋊C4C2314yes—
128C2×C5×C4⋊C4C2311yescharacteristic
129C2×C5×C4⋊C4C2312yes—
130C2×C5×C4⋊C4C23116yes—
131C2×C5×C22⋊C4C2312yes—
132C2×C5×C22⋊C4C2314yes—
133C2×C42×C5C2311yescharacteristic
134C2×C42×C5C2312yes—
135C2×C22⋊Dic5C2312yes—
136C2×C22⋊Dic5C2314yes—
137C2×C22⋊Dic5C2312yes—
138C2×C22⋊Dic5C2312yes—
139C2×C22⋊Dic5C2314yes—
140#4092C23116yes—
141#4092C2318yes—
142Q8×Dic5C23116yes—
143Q8×Dic5C23116yes—
144#4090C23132yes—
145#4090C2318yes—
146#4084C2318yes—
147#4082C2318yes—
148#4082C23116yes—
149#4075C23132yes—
150C4×C22⋊D5C23116yes—
151C2×#685C2312yes—
152C2×#685C2312yes—
153C2×#685C2312yes—
154C2×#685C2314yes—
155#4072C23116yes—
156#4072C23116yes—
157#4072C23132yes—
158C2×C4⋊Dic5C2311yescharacteristic
159C2×C4⋊Dic5C2311yescharacteristic
160C2×C4⋊Dic5C2312yes—
161C2×C4⋊Dic5C2314yes—
162C2×C4⋊Dic5C2312yes—
163C2×C4⋊Dic5C2314yes—
164C2×C4⋊Dic5C2312yes—
165C2×C4⋊Dic5C2312yes—
166C2×C4⋊Dic5C2314yes—
167C2×C4⋊Dic5C2312yes—
168#4070C23132yes—
169#4070C23132yes—
170#4070C23116yes—
171C2×#683C2312yes—
172C2×#683C2312yes—
173C2×#683C2312yes—
174C2×#683C2312yes—
175C2×#683C2314yes—
176C2×#683C2312yes—
177C2×#683C2312yes—
178C2×#683C2312yes—
179C2×#683C2314yes—
180C2×#683C2314yes—
181C2×#683C2314yes—
182C2×#683C2314yes—
183C2×C4×Dic5C2311yescharacteristic
184C2×C4×Dic5C2312yes—
185C2×C4×Dic5C2314yes—
186C2×C4×Dic5C2312yes—
187C2×C4×Dic5C2311yescharacteristic
188C2×C4×Dic5C2311yescharacteristic
189C2×C4×Dic5C2314yes—
190C2×C4×Dic5C2314yes—
191C2×C4×Dic5C2314yes—
192#4044C23132yes—
193#4044C23132yes—
194#4043C23116yes—
195#4043C2318yes—
196#4043C2318yes—
197#4042C23116yes—
198#4038C23116yes—
199#4036C23116yes—
200#4036C23116yes—
201#4036C23132yes—
202#4036C2318yes—
203#4036C23132yes—
204#4036C23132yes—
205#4035C23132yes—
206#4035C23116yes—
207#4035C23132yes—
208#4034C23116yes—
209#4034C23116yes—
210#4034C2318yes—
211#4034C23132yes—
212#4033C23116yes—
213#4033C23116yes—
214#4033C23116yes—
215#4033C23116yes—
216#4033C23132yes—
217#4031C23132yes—
218#4029C23116yes—
219#4025C23132yes—
220#4025C23132yes—
221#4025C23132yes—
222#4025C23116yes—
223#4025C23132yes—
224#4018C23116yes—
225C42×D5C2318yes—
226#4015C2318yes—
227#4015C23116yes—
228C4×Dic10C2318yes—
229C4×Dic10C2318yes—
230C4×Dic10C23116yes—
231C4×Dic10C23116yes—
232#3555—532no—
233C2×#563—54no—
234C2×Q82—51no—
235C2×#557—52no—
236C2×#557—51no—
237C2×#556—52no—
238C2×#556—52no—
239C2×#556—51no—
240C2×#554D511yescharacteristic, complemented
241C2×#552—52no—
242C2×#544—52no—
243C2×#542—52no—
244C2×#541—52no—
245C2×#541—52no—
246C2×#541—54no—
247C2×#533—51no—
248C2×#533—51no—
249C2×#529—51no—
250C24×C5C2412yes—
251C23×D5C2411yescharacteristic
252C2×C5×Q8—24no—
253C2×C5×Q8—44no—
254C2×C5×Q8C2414yes—
255C2×C5×Q8C2418yes—
256C2×C5×D4—24no—
257C2×C5×D4C2414yes—
258C22×C4×C5—28no—
259C22×C4×C5—48no—
260C22×C4×C5C2412yes—
261C22×C4×C5C2411yescharacteristic
262C22×C4×C5C2412yes—
263C22×C4×C5C2412yes—
264C22×C4×C5C2414yes—
265C22×C4×C5C2418yes—
266C22×C4×C5C24116yes—
267C22×C4×C5C2411yescharacteristic
268C22×C4×C5C2411yescharacteristic
269C2×C22⋊D5—44no—
270C2×C22⋊D5C2418yes—
271C22×Dic5C2412yes—
272C22×Dic5C2411yescharacteristic
273C22×Dic5C2412yes—
274C22×Dic5C2414yes—
275C22×Dic5C2412yes—
276C22×Dic5C2411yescharacteristic
277C22×Dic5C2411yescharacteristic
278C22×Dic5C2412yes—
279C2×C4×D5—24no—
280C2×C4×D5—24no—
281C2×C4×D5—42no—
282C2×C4×D5C2414yes—
283C2×C4×D5C2414yes—
284C2×C4×D5C2414yes—
285C2×Dic10—24no—
286C2×Dic10—28no—
287C2×Dic10—24no—
288C2×Dic10—44no—
289C2×Dic10—48no—
290C2×Dic10C2414yes—
291C2×Dic10C2418yes—
292C2×Dic10C2414yes—
293C2×Dic10C2418yes—
294C2×Dic10C24116yes—
295C5×C4⋊C4C2414yes—
296C5×C4⋊C4C24116yes—
297C5×C4⋊C4C2418yes—
298C5×C4⋊C4C2414yes—
299C5×C4⋊C4C2418yes—
300C5×C4⋊C4C2418yes—
301C5×C4⋊C4C24116yes—
302C5×C22⋊C4C2418yes—
303C5×C22⋊C4C24116yes—
304C42×C5C2418yes—
305C42×C5C2414yes—
306C22⋊Dic5C2418yes—
307C22⋊Dic5C24116yes—
308C22⋊Dic5C2418yes—
309C22⋊Dic5C2418yes—
310C22⋊Dic5C24116yes—
311#685C2418yes—
312#685C2418yes—
313#685C2418yes—
314#685C24116yes—
315C4⋊Dic5C2414yes—
316C4⋊Dic5C2414yes—
317C4⋊Dic5C2418yes—
318C4⋊Dic5C24116yes—
319C4⋊Dic5C2418yes—
320C4⋊Dic5C24116yes—
321C4⋊Dic5C2418yes—
322C4⋊Dic5C2418yes—
323C4⋊Dic5C24116yes—
324C4⋊Dic5C2418yes—
325#683C2418yes—
326#683C2418yes—
327#683C2418yes—
328#683C2418yes—
329#683C24116yes—
330#683C2418yes—
331#683C2418yes—
332#683C2418yes—
333#683C24116yes—
334#683C24116yes—
335#683C24116yes—
336#683C24116yes—
337C4×Dic5C2414yes—
338C4×Dic5C2418yes—
339C4×Dic5C24116yes—
340C4×Dic5C2418yes—
341C4×Dic5C2414yes—
342C4×Dic5C2414yes—
343C4×Dic5C24116yes—
344C4×Dic5C24116yes—
345C4×Dic5C24116yes—
346#563—564no—
347Q82—516no—
348#557—532no—
349#557—516no—
350#556—532no—
351#556—532no—
352#556—516no—
353#554C2×D5116yescomplemented
354#552—532no—
355#544—532no—
356#542—532no—
357#541—532no—
358#541—532no—
359#541—564no—
360#533—516no—
361#533—516no—
362C2×C4⋊Q8—51no—
363C2×C4⋊Q8—54no—
364C2×C4⋊Q8—51no—
365C2×C4⋊Q8—52no—
366C2×C4⋊Q8—52no—
367C2×C4⋊Q8—54no—
368C2×C4⋊Q8—51no—
369C2×C4⋊Q8—52no—
370C2×C4⋊Q8C2×D511yescharacteristic
371#529—516no—
372C2×#126—54no—
373C2×#126—54no—
374C2×#126—52no—
375C2×#126—54no—
376C2×#126—54no—
377C2×#126—54no—
378C2×#126—54no—
379C2×#125—52no—
380C2×#125—54no—
381C2×#125—54no—
382C2×#125—51no—
383C2×#125—52no—
384C2×#125—54no—
385C2×#125—54no—
386C2×#125—54no—
387C2×#125—52no—
388C2×#125C2×D512yes—
389C2×#124—51no—
390C2×#124—52no—
391C2×#124—54no—
392C2×#123—54no—
393C2×#123—52no—
394C2×C22⋊Q8—51no—
395C2×C22⋊Q8—52no—
396C2×C22⋊Q8—54no—
397C2×C22⋊Q8—52no—
398C2×C22⋊Q8—54no—
399C2×C22⋊Q8—52no—
400C2×C22⋊Q8—51no—
401C2×C22⋊Q8—52no—
402C2×C22⋊Q8—51no—
403C2×C22⋊Q8C2×D512yes—
404C2×C22⋊Q8C2×D514yes—
405C2×#121—51no—
406C2×C4×Q8—52no—
407C2×C4×Q8—52no—
408C2×C4×Q8—52no—
409C2×C4×Q8—52no—
410C2×C4×Q8—54no—
411C2×C4×Q8—52no—
412C2×C4×Q8—52no—
413C2×C4×Q8—51no—
414C2×C4×Q8—52no—
415C2×C4×Q8—51no—
416C2×C4×Q8—52no—
417C2×C4×Q8C2×D511yescharacteristic
418C2×C4×D4—52no—
419C2×C4×D4C2×D511yescharacteristic
420C2×C4×D4C2×D512yes—
421C2×#117—52no—
422C2×#117—54no—
423C2×#117—52no—
424C2×#117—52no—
425C2×#117—52no—
426C22×C4⋊C4C2×D512yes—
427C22×C42—51no—
428C23×C5—24no—
429C23×C5—24no—
430C23×C5—24no—
431C23×C5C2514yes—
432C23×C5C2511yescharacteristic
433C22×D5—22no—
434C22×D5—22no—
435C22×D5—22no—
436C22×D5C2512yes—
437C5×Q8—28no—
438C5×Q8—48no—
439C5×D4—28no—
440C2×C4×C5—24no—
441C2×C4×C5—24no—
442C2×C4×C5—24no—
443C2×C4×C5—28no—
444C2×C4×C5—22no—
445C2×C4×C5—216no—
446C2×C4×C5—416no—
447C2×C4×C52−1+414yes—
448C2×C4×C52−1+414yes—
449C2×C4×C5C2514yes—
450C2×C4×C5C2514yes—
451C2×C4×C5C2518yes—
452C2×C4×C5C2512yes—
453C2×C4×C5C2514yes—
454C2×C4×C5C2512yes—
455C2×C4×C5C2512yes—
456C22⋊D5—48no—
457C2×Dic5—28no—
458C2×Dic5—24no—
459C2×Dic5—24no—
460C2×Dic5—22no—
461C2×Dic5—22no—
462C2×Dic5—24no—
463C2×Dic5—22no—
464C2×Dic5—24no—
465C2×Dic5C2512yes—
466C2×Dic5C2514yes—
467C2×Dic5C2514yes—
468C2×Dic5C2514yes—
469C2×Dic5C2518yes—
470C2×Dic5C2514yes—
471C2×Dic5C2512yes—
472C2×Dic5C2512yes—
473C4×D5—28no—
474C4×D5—28no—
475C4×D5—44no—
476Dic10—28no—
477Dic10—216no—
478Dic10—28no—
479Dic10—48no—
480Dic10—416no—
481C22×Q8—51no—
482C22×Q8—52no—
483C22×Q8—51no—
484C22×Q8—52no—
485C22×Q8—54no—
486C22×Q8C22×D511yescharacteristic
487C22×Q8C22×D512yes—
488C22×D4—52no—
489C22×D4C22×D511yescharacteristic
490C23×C4—51no—
491C23×C4—51no—
492C23×C4—51no—
493C23×C4C22×D512yes—
494C23×C4C22×D514yes—
495C4⋊Q8—58no—
496C4⋊Q8—532no—
497C4⋊Q8—58no—
498C4⋊Q8—516no—
499C4⋊Q8—516no—
500C4⋊Q8—532no—
501C4⋊Q8—58no—
502C4⋊Q8—516no—
503C4⋊Q8C22×D518yes—
504#126—532no—
505#126—532no—
506#126—516no—
507#126—532no—
508#126—532no—
509#126—532no—
510#126—532no—
511#125—58no—
512#125—516no—
513#125—516no—
514#125—532no—
515#125—532no—
516#125—532no—
517#125—532no—
518#125—532no—
519#125—516no—
520#125C22×D5116yes—
521#124—58no—
522#124—516no—
523#124—532no—
524#123—532no—
525#123—516no—
526C22⋊Q8—58no—
527C22⋊Q8—516no—
528C22⋊Q8—532no—
529C22⋊Q8—516no—
530C22⋊Q8—532no—
531C22⋊Q8—58no—
532C22⋊Q8—516no—
533C22⋊Q8—58no—
534C22⋊Q8—516no—
535C22⋊Q8C22×D5116yes—
536C22⋊Q8C22×D5132yes—
537#121—58no—
538C4×Q8—516no—
539C4×Q8—516no—
540C4×Q8—516no—
541C4×Q8—516no—
542C4×Q8—532no—
543C4×Q8—516no—
544C4×Q8—516no—
545C4×Q8—58no—
546C4×Q8—516no—
547C4×Q8—58no—
548C4×Q8—516no—
549C4×Q8C22×D518yes—
550C4×D4—516no—
551C4×D4C22×D518yes—
552C4×D4C22×D5116yes—
553#117—516no—
554#117—532no—
555#117—516no—
556#117—516no—
557#117—516no—
558C2×C4⋊C4—52no—
559C2×C4⋊C4—52no—
560C2×C4⋊C4—51no—
561C2×C4⋊C4—52no—
562C2×C4⋊C4—52no—
563C2×C4⋊C4—54no—
564C2×C4⋊C4—52no—
565C2×C4⋊C4—52no—
566C2×C4⋊C4—52no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—52no—
569C2×C4⋊C4—54no—
570C2×C4⋊C4—54no—
571C2×C4⋊C4—54no—
572C2×C4⋊C4—54no—
573C2×C4⋊C4—52no—
574C2×C4⋊C4—52no—
575C2×C4⋊C4—54no—
576C2×C4⋊C4—52no—
577C2×C4⋊C4—54no—
578C2×C4⋊C4—52no—
579C2×C4⋊C4—54no—
580C2×C4⋊C4C22×D511yescharacteristic
581C2×C4⋊C4C22×D512yes—
582C2×C4⋊C4C22×D514yes—
583C2×C4⋊C4C22×D5116yes—
584C2×C4⋊C4C22×D511yescharacteristic
585C2×C4⋊C4C22×D512yes—
586C2×C4⋊C4C22×D514yes—
587C2×C4⋊C4C22×D512yes—
588C2×C22⋊C4—52no—
589C2×C22⋊C4—52no—
590C2×C22⋊C4—52no—
591C2×C22⋊C4—54no—
592C2×C22⋊C4—54no—
593C2×C22⋊C4—52no—
594C2×C22⋊C4—54no—
595C2×C22⋊C4—52no—
596C2×C22⋊C4—52no—
597C2×C22⋊C4C22×D512yes—
598C2×C22⋊C4C22×D514yes—
599C2×C42—54no—
600C2×C42—51no—
601C2×C42—52no—
602C2×C42—52no—
603C2×C42—54no—
604C2×C42—54no—
605C2×C42—51no—
606C2×C42—54no—
607C2×C42—51no—
608C2×C42—58no—
609C2×C42C22×D512yes—
610C2×C42C22×D511yescharacteristic
611C22×C5—24no—
612C22×C5—24no—
613C22×C5—24no—
614C22×C5—48no—
615C22×C5C2×2−1+412yes—
616C22×C5C2×2−1+412yes—
617C22×C5#58512yes—
618C22×C5C2611yescharacteristic
619C2×D5—22no—
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—44no—
623C4×C5—24no—
624C4×C5—24no—
625C4×C5—24no—
626C4×C5—28no—
627C4×C5—22no—
628C4×C5C2×2−1+414yes—
629C4×C5C2×2−1+414yes—
630Dic5—28no—
631Dic5—24no—
632Dic5—24no—
633Dic5—22no—
634Dic5—22no—
635Dic5—24no—
636Dic5—22no—
637Dic5—24no—
638C24—51no—
639C24C23×D512yes—
640C2×Q8—24no—
641C2×Q8—44no—
642C2×Q8—54no—
643C2×Q8—58no—
644C2×Q8—54no—
645C2×Q8—58no—
646C2×Q8—516no—
647C2×Q8—108no—
648C2×Q8—104no—
649C2×Q8—104no—
650C2×Q8—204no—
651C2×Q8—208no—
652C2×Q8C23×D514yes—
653C2×Q8C23×D518yes—
654C2×D4—24no—
655C2×D4—58no—
656C2×D4—204no—
657C2×D4C23×D514yes—
658C22×C4—28no—
659C22×C4—48no—
660C22×C4—51no—
661C22×C4—54no—
662C22×C4—52no—
663C22×C4—52no—
664C22×C4—52no—
665C22×C4—52no—
666C22×C4—51no—
667C22×C4—51no—
668C22×C4—54no—
669C22×C4—54no—
670C22×C4—54no—
671C22×C4—104no—
672C22×C4—104no—
673C22×C4—202no—
674C22×C4C23×D518yes—
675C22×C4C23×D512yes—
676C22×C4C23×D512yes—
677C22×C4C23×D514yes—
678C22×C4C23×D511yescharacteristic
679C22×C4C23×D512yes—
680C22×C4C23×D5116yes—
681C22×C4C23×D511yescharacteristic
682C22×C4C23×D511yescharacteristic
683C4⋊C4—58no—
684C4⋊C4—58no—
685C4⋊C4—54no—
686C4⋊C4—58no—
687C4⋊C4—58no—
688C4⋊C4—516no—
689C4⋊C4—58no—
690C4⋊C4—58no—
691C4⋊C4—58no—
692C4⋊C4—54no—
693C4⋊C4—58no—
694C4⋊C4—516no—
695C4⋊C4—516no—
696C4⋊C4—516no—
697C4⋊C4—516no—
698C4⋊C4—58no—
699C4⋊C4—58no—
700C4⋊C4—516no—
701C4⋊C4—58no—
702C4⋊C4—516no—
703C4⋊C4—58no—
704C4⋊C4—516no—
705C4⋊C4C23×D514yes—
706C4⋊C4C23×D518yes—
707C4⋊C4C23×D5116yes—
708C4⋊C4C23×D514yes—
709C4⋊C4C23×D518yes—
710C4⋊C4C23×D5116yes—
711C4⋊C4C23×D518yes—
712C22⋊C4—58no—
713C22⋊C4—58no—
714C22⋊C4—58no—
715C22⋊C4—516no—
716C22⋊C4—516no—
717C22⋊C4—58no—
718C22⋊C4—516no—
719C22⋊C4—58no—
720C22⋊C4—58no—
721C22⋊C4C23×D518yes—
722C22⋊C4C23×D5116yes—
723C42—54no—
724C42—54no—
725C42—54no—
726C42—516no—
727C42—58no—
728C42—58no—
729C42—516no—
730C42—516no—
731C42—516no—
732C42C23×D514yes—
733C42C23×D518yes—
734C2×C5—44no—
735C2×C5#355514yescomplemented
736C2×C5C22×2−1+411yescharacteristic
737C2×C5C22×2−1+411yescharacteristic
738C2×C5C2×#58511yescharacteristic
739D5—42no—
740C23—24no—
741C23—24no—
742C23—24no—
743C23—52no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23C24×D514yes—
748C23C24×D511yescharacteristic
749Q8—28no—
750Q8—48no—
751Q8—1016no—
752Q8—108no—
753Q8—108no—
754Q8—208no—
755Q8—2016no—
756D4—28no—
757D4—208no—
758C2×C4—24no—
759C2×C4—24no—
760C2×C4—24no—
761C2×C4—28no—
762C2×C4—22no—
763C2×C4—216no—
764C2×C4—416no—
765C2×C4—52no—
766C2×C4—58no—
767C2×C4—54no—
768C2×C4—54no—
769C2×C4—54no—
770C2×C4—54no—
771C2×C4—52no—
772C2×C4—52no—
773C2×C4—102no—
774C2×C4—108no—
775C2×C4—104no—
776C2×C4—102no—
777C2×C4—104no—
778C2×C4—102no—
779C2×C4—104no—
780C2×C4—104no—
781C2×C4—108no—
782C2×C4—108no—
783C2×C4—204no—
784C2×C4#414714yes—
785C2×C4#415014yes—
786C2×C4C24×D514yes—
787C2×C4C24×D514yes—
788C2×C4C24×D518yes—
789C2×C4C24×D512yes—
790C2×C4C24×D514yes—
791C2×C4C24×D512yes—
792C2×C4C24×D512yes—
793C5C2×#355511yescharacteristic, complemented, Sylow
794C22—24no—
795C22—24no—
796C22—24no—
797C22—48no—
798C22—102no—
799C22—102no—
800C22—102no—
801C22—204no—
802C22C2×#414712yes—
803C22C2×#415012yes—
804C22#6628512yes—
805C22C25×D511yescharacteristic
806C4—24no—
807C4—24no—
808C4—24no—
809C4—28no—
810C4—22no—
811C4—102no—
812C4—108no—
813C4—104no—
814C4—102no—
815C4—104no—
816C4—102no—
817C4—104no—
818C4—104no—
819C4C2×#414714yes—
820C4C2×#415014yes—
821C2—44no—
822C2—202no—
823C2#1061885714yesdirect product factor
824C2C22×#414711yescharacteristic
825C2C22×#415011yescharacteristic
826C2C2×#6628511yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#554C2
socleC23×C5C25
prime radicalC2×#4084C22
hypercenterC2×#554D5
hypocenterC5C2×#3555
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. #10618857C2direct (N × H)
3. C2×#66056C2semidirect
4. C2×#66062C2semidirect
5. C2×#66031C2semidirect
6. C2×#66019C2semidirect
7. C2×#65980C2semidirect
8. C2×#65975C2semidirect
9. C2×#65959C2semidirect
10. C2×#65959C2semidirect
11. C2×#65912C2semidirect
12. C2×#65904C2semidirect
15. C2×#65876C2semidirect
16. C2×#65876C2semidirect
17. C2×#65847C2semidirect
18. C2×#65834C2semidirect
19. C5×#554C22semidirect
45. #66062C22semidirect
46. #66056C22semidirect
47. #66031C22semidirect
48. #66019C22semidirect
49. #65980C22semidirect
50. #65975C22semidirect
51. #65959C22semidirect
52. #65959C22semidirect
53. #65912C22semidirect
54. #65904C22semidirect
57. #65876C22semidirect
58. #65876C22semidirect
59. #65847C22semidirect
67. #65834C22semidirect
240. C2×#554D5semidirect
353. #554C2×D5semidirect
735. C2×C5#3555semidirect
793. C5C2×#3555semidirect
823. C2#10618857direct (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
#106188572
C2×#660562
C2×#660622
C2×#660312
C2×#660192
C2×#659802
C2×#659752
C2×#659592
C2×#659122
C2×#659042
C2×#658952
C2×#658912
C2×#658762
C2×#658472
C2×#658342
C2×#35555