Finite Group Databasebeta

← C2×#10618922 #13007417

Subgroups — C2×#10618922 #13007417

Order 1280.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#557C211yesmaximal, characteristic, complemented
2#10618922C2132yesmaximal, direct product factor
3C2×#66060C211yesmaximal, characteristic, complemented
4C2×#66060C212yesmaximal, complemented
5C2×#66065C212yesmaximal, complemented
6C2×#66062C211yesmaximal, characteristic, complemented
7C2×#66029C212yesmaximal, complemented
8C2×#66027C214yesmaximal, complemented
9C2×#66026C214yesmaximal, complemented
10C2×D5×#125C212yesmaximal, complemented
11C2×#65913C211yesmaximal, characteristic, complemented
12C2×#65913C211yesmaximal, characteristic, complemented
13C2×#65915C212yesmaximal, complemented
14C2×#65915C212yesmaximal, complemented
15C2×#65914C212yesmaximal, complemented
16C2×#65914C211yesmaximal, characteristic, complemented
17C2×#65908C212yesmaximal, complemented
18C2×C4×#713C211yesmaximal, characteristic, complemented
19C22×#713C2211yescharacteristic
20C22×#713C2212yes—
21C5×#557C22116yescomplemented
22C2×C5×C4⋊Q8C2211yescharacteristic
23C2×C5×C4⋊Q8C2212yes—
24C2×C5×#125C2212yes—
25C2×C5×#125C2214yes—
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×Q8C2212yes—
28C2×C4×C5×Q8C2212yes—
29C2×C4×C5×Q8C2211yescharacteristic
30C2×#4093C2211yescharacteristic
31C2×#4092C2212yes—
32C2×#4092C2212yes—
33C2×#4092C2212yes—
34C2×#4092C2211yescharacteristic
35C2×#4092C2212yes—
36C2×Q8×Dic5C2211yescharacteristic
37C2×Q8×Dic5C2212yes—
38#66065C22132yescomplemented
39#66062C22116yescomplemented
40#66060C22116yescomplemented
41#66060C22132yescomplemented
42#66029C22132yescomplemented
43#66027C22164yescomplemented
44#66026C22164yescomplemented
45D5×#125C22132yescomplemented
46#65915C22132yescomplemented
47#65915C22132yescomplemented
48#65914C22116yescomplemented
49#65914C22132yescomplemented
50#65913C22116yescomplemented
51#65913C22116yescomplemented
52#65908C22132yescomplemented
53C4×#713C22116yescomplemented
54C2×#4044C2214yes—
55C2×#4044C2212yes—
56C2×#4044C2214yes—
57C2×#4043C2212yes—
58C2×#4042C2214yes—
59C2×#4042C2214yes—
60C2×#4041C2212yes—
61C2×#4041C2214yes—
62C2×#4041C2211yescharacteristic
63C2×#4040C2214yes—
64C2×#4040C2214yes—
65C2×#4040C2214yes—
66C2×#4040C2212yes—
67C2×#4040C2214yes—
68C2×#4039C2211yescharacteristic
69C2×#4039C2212yes—
70C2×#4039C2214yes—
71C2×#4038C2211yescharacteristic
72C2×#4038C2212yes—
73C2×#4038C2212yes—
74C2×D5×C4⋊C4C2212yes—
75C2×D5×C4⋊C4C2214yes—
76C2×D5×C4⋊C4C2212yes—
77C2×D5×C4⋊C4C2214yes—
78C2×D5×C4⋊C4C2212yes—
79C2×#4036C2211yescharacteristic
80C2×#4036C2212yes—
81C2×#4035C2214yes—
82C2×#4035C2214yes—
83C2×#4035C2214yes—
84C2×#4033C2212yes—
85C2×#4022C2214yes—
86C2×C4×D20C2211yescharacteristic
87C2×C4×D20C2212yes—
88C2×C4×D20C2212yes—
89C2×C4×D20C2211yescharacteristic
90C2×C4×D20C2212yes—
91C2×C4×D20C2214yes—
92C2×C4×D20C2212yes—
93C2×#4018C2212yes—
94C2×#4018C2214yes—
95C2×#4018C2214yes—
96C2×C42×D5C2212yes—
97C2×C42×D5C2211yescharacteristic
98C2×#4016C2212yes—
99C2×#4016C2212yes—
100C2×#4015C2211yescharacteristic
101C2×#3515—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×Q8C2312yes—
104C22×C5×Q8C2311yescharacteristic
105C2×#713—28no—
106C2×#713—216no—
107C2×#713C2318yes—
108C2×#713C23116yes—
109C22×D20C2311yescharacteristic
110C22×D20C2312yes—
111C22×D20C2314yes—
112C22×D20C2312yes—
113C22×D20C2311yescharacteristic
114C22×C4×D5C2312yes—
115C22×C4×D5C2311yescharacteristic
116C22×C4×D5C2311yescharacteristic
117C22×C4×D5C2312yes—
118C22×C4×D5C2312yes—
119C22×C4×D5C2314yes—
120C22×C4×D5C2312yes—
121C22×C4×D5C2311yescharacteristic
122C22×C4×D5C2314yes—
123C22×C4×D5C2314yes—
124C22×Dic10C2312yes—
125C5×C4⋊Q8C2318yes—
126C5×C4⋊Q8C23116yes—
127C5×#125C23116yes—
128C5×#125C23132yes—
129C4×C5×Q8C2318yes—
130C4×C5×Q8C23116yes—
131C4×C5×Q8C2318yes—
132C4×C5×Q8C23116yes—
133C2×C5×C4⋊C4C2312yes—
134C2×C5×C4⋊C4C2314yes—
135C2×C5×C4⋊C4C2314yes—
136C2×C5×C4⋊C4C2314yes—
137C2×C5×C4⋊C4C2311yescharacteristic
138C2×C5×C4⋊C4C2312yes—
139C2×C5×C4⋊C4C2311yescharacteristic
140C2×C5×C4⋊C4C2312yes—
141C2×C5×C4⋊C4C2312yes—
142C2×C42×C5C2311yescharacteristic
143C2×C42×C5C2312yes—
144C2×C42×C5C2312yes—
145C2×C42×C5C2314yes—
146#4093C2318yes—
147#4092C23116yes—
148#4092C23116yes—
149#4092C23116yes—
150#4092C23116yes—
151#4092C2318yes—
152Q8×Dic5C23116yes—
153Q8×Dic5C2318yes—
154C2×#685C2312yes—
155C2×#685C2312yes—
156C2×#685C2314yes—
157C2×#685C2312yes—
158C2×#685C2312yes—
159C2×#685C2314yes—
160C2×#685C2312yes—
161C2×#685C2312yes—
162C2×#685C2312yes—
163C2×#685C2312yes—
164C2×#685C2314yes—
165C2×#685C2314yes—
166C2×C4⋊Dic5C2312yes—
167C2×C4⋊Dic5C2312yes—
168C2×C4⋊Dic5C2311yescharacteristic
169C2×C4⋊Dic5C2311yescharacteristic
170C2×C4⋊Dic5C2312yes—
171C2×C4⋊Dic5C2312yes—
172C2×C4⋊Dic5C2314yes—
173C2×#683C2314yes—
174C2×#683C2314yes—
175C2×#683C2314yes—
176C2×#683C2314yes—
177C2×#683C2312yes—
178C2×#683C2314yes—
179C2×#683C2312yes—
180C2×#683C2314yes—
181C2×C4×Dic5C2311yescharacteristic
182C2×C4×Dic5C2312yes—
183C2×C4×Dic5C2311yescharacteristic
184C2×C4×Dic5C2311yescharacteristic
185C2×C4×Dic5C2312yes—
186C2×C4×Dic5C2314yes—
187#4044C23132yes—
188#4044C23132yes—
189#4044C23116yes—
190#4043C23116yes—
191#4042C23132yes—
192#4042C23132yes—
193#4041C23116yes—
194#4041C23132yes—
195#4041C2318yes—
196#4040C23132yes—
197#4040C23132yes—
198#4040C23132yes—
199#4040C23116yes—
200#4040C23132yes—
201#4039C2318yes—
202#4039C23116yes—
203#4039C23132yes—
204#4038C23116yes—
205#4038C2318yes—
206#4038C23116yes—
207D5×C4⋊C4C23116yes—
208D5×C4⋊C4C23132yes—
209D5×C4⋊C4C23116yes—
210D5×C4⋊C4C23132yes—
211D5×C4⋊C4C23116yes—
212#4036C23116yes—
213#4036C2318yes—
214#4035C23132yes—
215#4035C23132yes—
216#4035C23132yes—
217#4033C23116yes—
218#4022C23132yes—
219C4×D20C2318yes—
220C4×D20C23116yes—
221C4×D20C2318yes—
222C4×D20C23116yes—
223C4×D20C23116yes—
224C4×D20C23132yes—
225C4×D20C23116yes—
226#4018C23116yes—
227#4018C23132yes—
228#4018C23132yes—
229C42×D5C2318yes—
230C42×D5C23116yes—
231#4016C23116yes—
232#4016C23116yes—
233#4015C2318yes—
234#3515—532no—
235C2×#557D511yescharacteristic, complemented
236C2×#554—51no—
237C2×#554—51no—
238C2×#553—52no—
239C2×#552—54no—
240C2×#552—52no—
241C2×#552—52no—
242C2×#547—51no—
243C2×#547—52no—
244C2×#541—52no—
245C2×#539—54no—
246C2×#533—51no—
247C2×#529—51no—
248C2×#529—52no—
249C22×#125—52no—
250C2×#520—52no—
251C2×C4×#41—51no—
252C23×D5C2411yescharacteristic
253C23×D5C2412yes—
254C23×D5C2412yes—
255C2×C5×Q8—24no—
256C2×C5×Q8—28no—
257C2×C5×Q8—24no—
258C2×C5×Q8C2414yes—
259C2×C5×Q8C2414yes—
260C2×C5×Q8C2418yes—
261C22×C4×C5C2412yes—
262C22×C4×C5C2412yes—
263C22×C4×C5C2411yescharacteristic
264C22×C4×C5C2412yes—
265C22×C4×C5C2412yes—
266C22×C4×C5C2414yes—
267C22×C4×C5C2411yescharacteristic
268C22×C4×C5C2411yescharacteristic
269C22×Dic5C2414yes—
270C22×Dic5C2411yescharacteristic
271C22×Dic5C2411yescharacteristic
272C22×Dic5C2412yes—
273C22×Dic5C2411yescharacteristic
274C22×Dic5C2412yes—
275#713—232no—
276#713—264no—
277C2×D20—28no—
278C2×D20—216no—
279C2×D20—24no—
280C2×D20—44no—
281C2×D20#4118yes—
282C2×D20C2418yes—
283C2×D20C24116yes—
284C2×D20C2414yes—
285C2×D20C2418yes—
286C2×D20C2414yes—
287C2×C4×D5—28no—
288C2×C4×D5—216no—
289C2×C4×D5—24no—
290C2×C4×D5—28no—
291C2×C4×D5—28no—
292C2×C4×D5—24no—
293C2×C4×D5—48no—
294C2×C4×D5—48no—
295C2×C4×D5—42no—
296C2×C4×D5—44no—
297C2×C4×D5C2414yes—
298C2×C4×D5C2418yes—
299C2×C4×D5C2418yes—
300C2×C4×D5C24116yes—
301C2×C4×D5C2418yes—
302C2×C4×D5C2414yes—
303C2×C4×D5C2418yes—
304C2×C4×D5C2414yes—
305C2×C4×D5C24116yes—
306C2×C4×D5C24116yes—
307C2×Dic10—44no—
308C2×Dic10C2418yes—
309C5×C4⋊C4C2414yes—
310C5×C4⋊C4C24116yes—
311C5×C4⋊C4C2414yes—
312C5×C4⋊C4C2418yes—
313C5×C4⋊C4C2418yes—
314C5×C4⋊C4C24116yes—
315C5×C4⋊C4C2418yes—
316C5×C4⋊C4C2418yes—
317C5×C4⋊C4C24116yes—
318C42×C5C2418yes—
319C42×C5C24116yes—
320C42×C5C2414yes—
321C42×C5C2418yes—
322#685C2418yes—
323#685C2418yes—
324#685C24116yes—
325#685C2418yes—
326#685C2418yes—
327#685C24116yes—
328#685C2418yes—
329#685C2418yes—
330#685C2418yes—
331#685C2418yes—
332#685C24116yes—
333#685C24116yes—
334C4⋊Dic5C2418yes—
335C4⋊Dic5C2418yes—
336C4⋊Dic5C2414yes—
337C4⋊Dic5C2414yes—
338C4⋊Dic5C2418yes—
339C4⋊Dic5C2418yes—
340C4⋊Dic5C24116yes—
341#683C24116yes—
342#683C24116yes—
343#683C24116yes—
344#683C24116yes—
345#683C2418yes—
346#683C24116yes—
347#683C2418yes—
348#683C24116yes—
349C4×Dic5C2414yes—
350C4×Dic5C2418yes—
351C4×Dic5C2414yes—
352C4×Dic5C2414yes—
353C4×Dic5C2418yes—
354C4×Dic5C24116yes—
355C22×#41—51no—
356C22×#41—52no—
357#557C2×D5116yescomplemented
358#554—516no—
359#554—516no—
360#553—532no—
361#552—564no—
362#552—532no—
363#552—532no—
364#547—516no—
365#547—532no—
366#541—532no—
367#539—564no—
368#533—516no—
369C2×C4⋊Q8—51no—
370C2×C4⋊Q8C2×D511yescharacteristic
371C2×C4⋊Q8C2×D512yes—
372#529—532no—
373#529—516no—
374C2×#126—54no—
375C2×#126—52no—
376C2×#126—54no—
377C2×#126—54no—
378C2×#125—532no—
379C2×#125—54no—
380C2×#125—54no—
381C2×#125—54no—
382C2×#125—51no—
383C2×#125—52no—
384C2×#125—52no—
385C2×#125—52no—
386C2×#125C2×D512yes—
387C2×#125C2×D514yes—
388C2×#124—51no—
389C2×#123—52no—
390C2×#123—54no—
391C2×#123—54no—
392C2×#123—54no—
393C2×#123—54no—
394C2×C22⋊Q8—51no—
395C2×C22⋊Q8—52no—
396C2×C22⋊Q8—52no—
397C2×C22⋊Q8—52no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—54no—
400C2×C22⋊Q8—54no—
401C2×C22⋊Q8—52no—
402C2×#121—52no—
403C2×#121—51no—
404C2×#121—54no—
405#520—532no—
406C4×#41—516no—
407C2×C4×Q8—51no—
408C2×C4×Q8—52no—
409C2×C4×Q8—52no—
410C2×C4×Q8C2×D511yescharacteristic
411C2×C4×Q8C2×D512yes—
412C2×C4×Q8C2×D512yes—
413C2×C4×Q8C2×D511yescharacteristic
414C2×C4×D4—51no—
415C2×C4×D4—52no—
416C2×C4×D4—54no—
417C2×C4×D4—51no—
418C2×C4×D4—52no—
419C2×C4×D4—54no—
420C2×C4×D4—52no—
421C2×C4×D4—52no—
422C2×C4×D4—51no—
423C2×C4×D4—52no—
424C2×#117—51no—
425C2×#117—52no—
426C2×#117—52no—
427C2×#117—52no—
428C2×#117—54no—
429C2×#117—54no—
430C22×C4⋊C4—54no—
431C22×C4⋊C4—52no—
432C22×C4⋊C4—52no—
433C22×C4⋊C4—54no—
434C22×C4⋊C4—52no—
435C22×C42—52no—
436C22×C42—51no—
437C23×C5C2511yescharacteristic
438C22×D5—24no—
439C22×D5—24no—
440C22×D5—22no—
441C22×D5—24no—
442C22×D5—22no—
443C22×D5—24no—
444C22×D5—24no—
445C22×D5—22no—
446C22×D5C2×#4118yes—
447C22×D5C2512yes—
448C22×D5C2514yes—
449C22×D5C2514yes—
450C5×Q8—28no—
451C5×Q8—216no—
452C5×Q8—28no—
453C2×C4×C5—24no—
454C2×C4×C5—28no—
455C2×C4×C5—24no—
456C2×C4×C5—22no—
457C2×C4×C5—24no—
458C2×C4×C5—24no—
459C2×C4×C5C2×#4114yes—
460C2×C4×C52−1+414yes—
461C2×C4×C5C2514yes—
462C2×C4×C5C2518yes—
463C2×C4×C5C2514yes—
464C2×C4×C5C2512yes—
465C2×C4×C5C2514yes—
466C2×C4×C5C2514yes—
467C2×C4×C5C2512yes—
468C2×C4×C5C2512yes—
469C2×Dic5—22no—
470C2×Dic5—24no—
471C2×Dic5—22no—
472C2×Dic5—24no—
473C2×Dic5—28no—
474C2×Dic5—22no—
475C2×Dic5C2512yes—
476C2×Dic5C2512yes—
477C2×Dic5C2512yes—
478C2×Dic5C2514yes—
479C2×Dic5C2518yes—
480C2×Dic5C2514yes—
481D20—216no—
482D20—232no—
483D20—28no—
484D20—48no—
485D20C2×#41116yes—
486C4×D5—216no—
487C4×D5—232no—
488C4×D5—28no—
489C4×D5—216no—
490C4×D5—216no—
491C4×D5—28no—
492C4×D5—416no—
493C4×D5—416no—
494C4×D5—44no—
495C4×D5—48no—
496Dic10—48no—
497C2×#41—58no—
498C2×#41—516no—
499C2×#41—108no—
500C2×#41—1016no—
501C22×Q8—52no—
502C22×Q8C22×D511yescharacteristic
503C22×Q8C22×D512yes—
504C22×Q8C22×D511yescharacteristic
505C22×D4—51no—
506C22×D4—51no—
507C22×D4—52no—
508C22×D4—54no—
509C22×D4—52no—
510C23×C4—54no—
511C23×C4—52no—
512C23×C4—52no—
513C23×C4—52no—
514C23×C4—51no—
515C23×C4—51no—
516C23×C4—54no—
517C23×C4—52no—
518C23×C4—54no—
519C23×C4—51no—
520C4⋊Q8—58no—
521C4⋊Q8C22×D518yes—
522C4⋊Q8C22×D5116yes—
523#126—532no—
524#126—516no—
525#126—532no—
526#126—532no—
527#125—58no—
528#125—516no—
529#125—532no—
530#125—532no—
531#125—532no—
532#125—516no—
533#125—516no—
534#125C22×D5116yes—
535#125C22×D5132yes—
536#124—58no—
537#123—516no—
538#123—532no—
539#123—532no—
540#123—532no—
541#123—532no—
542C22⋊Q8—58no—
543C22⋊Q8—516no—
544C22⋊Q8—516no—
545C22⋊Q8—516no—
546C22⋊Q8—516no—
547C22⋊Q8—516no—
548C22⋊Q8—532no—
549C22⋊Q8—532no—
550#121—516no—
551#121—58no—
552#121—532no—
553C4×Q8—58no—
554C4×Q8—516no—
555C4×Q8—516no—
556C4×Q8C22×D518yes—
557C4×Q8C22×D5116yes—
558C4×Q8C22×D5116yes—
559C4×Q8C22×D518yes—
560C4×D4—58no—
561C4×D4—516no—
562C4×D4—532no—
563C4×D4—58no—
564C4×D4—516no—
565C4×D4—532no—
566C4×D4—516no—
567C4×D4—516no—
568C4×D4—58no—
569C4×D4—516no—
570#117—58no—
571#117—516no—
572#117—516no—
573#117—516no—
574#117—532no—
575#117—532no—
576C2×C4⋊C4—54no—
577C2×C4⋊C4—52no—
578C2×C4⋊C4—51no—
579C2×C4⋊C4—52no—
580C2×C4⋊C4—52no—
581C2×C4⋊C4—54no—
582C2×C4⋊C4—52no—
583C2×C4⋊C4—54no—
584C2×C4⋊C4—54no—
585C2×C4⋊C4—54no—
586C2×C4⋊C4—54no—
587C2×C4⋊C4—52no—
588C2×C4⋊C4—51no—
589C2×C4⋊C4—52no—
590C2×C4⋊C4—54no—
591C2×C4⋊C4—532no—
592C2×C4⋊C4—516no—
593C2×C4⋊C4—516no—
594C2×C4⋊C4—532no—
595C2×C4⋊C4—516no—
596C2×C4⋊C4C22×D511yescharacteristic
597C2×C4⋊C4C22×D511yescharacteristic
598C2×C4⋊C4C22×D512yes—
599C2×C4⋊C4C22×D514yes—
600C2×C4⋊C4C22×D514yes—
601C2×C4⋊C4C22×D512yes—
602C2×C4⋊C4C22×D512yes—
603C2×C4⋊C4C22×D512yes—
604C2×C4⋊C4C22×D514yes—
605C2×C22⋊C4—52no—
606C2×C22⋊C4—52no—
607C2×C22⋊C4—52no—
608C2×C22⋊C4—52no—
609C2×C22⋊C4—54no—
610C2×C22⋊C4—52no—
611C2×C22⋊C4—52no—
612C2×C22⋊C4—54no—
613C2×C22⋊C4—54no—
614C2×C22⋊C4—54no—
615C2×C22⋊C4—52no—
616C2×C22⋊C4—52no—
617C2×C42—52no—
618C2×C42—51no—
619C2×C42—54no—
620C2×C42—51no—
621C2×C42—52no—
622C2×C42—51no—
623C2×C42—516no—
624C2×C42—58no—
625C2×C42C22×D514yes—
626C2×C42C22×D512yes—
627C2×C42C22×D512yes—
628C2×C42C22×D511yescharacteristic
629C22×C5C22×#4112yes—
630C22×C5C2×2−1+412yes—
631C22×C5#58512yes—
632C22×C5C2611yescharacteristic
633C2×D5—24no—
634C2×D5—24no—
635C2×D5—216no—
636C2×D5—22no—
637C2×D5—24no—
638C2×D5—22no—
639C2×D5—24no—
640C2×D5—24no—
641C2×D5—22no—
642C2×D5—44no—
643C2×D5—48no—
644C2×D5C22×#4118yes—
645C4×C5—24no—
646C4×C5—28no—
647C4×C5—24no—
648C4×C5—22no—
649C4×C5—24no—
650C4×C5—24no—
651C4×C5C22×#4114yes—
652C4×C5C2×2−1+414yes—
653Dic5—22no—
654Dic5—24no—
655Dic5—22no—
656Dic5—24no—
657Dic5—28no—
658Dic5—22no—
659C24—52no—
660C24—51no—
661C24—52no—
662#41—1032no—
663#41—1064no—
664C2×Q8—24no—
665C2×Q8—24no—
666C2×Q8—28no—
667C2×Q8—58no—
668C2×Q8—204no—
669C2×Q8C23×D514yes—
670C2×Q8C23×D518yes—
671C2×Q8C23×D514yes—
672C2×D4—58no—
673C2×D4—54no—
674C2×D4—54no—
675C2×D4—58no—
676C2×D4—516no—
677C2×D4—58no—
678C2×D4—108no—
679C2×D4—1016no—
680C2×D4—104no—
681C2×D4—204no—
682C22×C4—51no—
683C22×C4—51no—
684C22×C4—51no—
685C22×C4—52no—
686C22×C4—54no—
687C22×C4—52no—
688C22×C4—58no—
689C22×C4—58no—
690C22×C4—54no—
691C22×C4—54no—
692C22×C4—516no—
693C22×C4—58no—
694C22×C4—58no—
695C22×C4—54no—
696C22×C4—516no—
697C22×C4—516no—
698C22×C4—1016no—
699C22×C4—108no—
700C22×C4—108no—
701C22×C4—104no—
702C22×C4—108no—
703C22×C4—104no—
704C22×C4—204no—
705C22×C4—208no—
706C22×C4—208no—
707C22×C4—202no—
708C22×C4C23×D512yes—
709C22×C4C23×D511yescharacteristic
710C22×C4C23×D514yes—
711C22×C4C23×D512yes—
712C22×C4C23×D512yes—
713C22×C4C23×D512yes—
714C22×C4C23×D511yescharacteristic
715C22×C4C23×D511yescharacteristic
716C4⋊C4—516no—
717C4⋊C4—58no—
718C4⋊C4—54no—
719C4⋊C4—58no—
720C4⋊C4—58no—
721C4⋊C4—516no—
722C4⋊C4—58no—
723C4⋊C4—516no—
724C4⋊C4—516no—
725C4⋊C4—516no—
726C4⋊C4—516no—
727C4⋊C4—58no—
728C4⋊C4—54no—
729C4⋊C4—58no—
730C4⋊C4—516no—
731C4⋊C4C23×D514yes—
732C4⋊C4C23×D514yes—
733C4⋊C4C23×D518yes—
734C4⋊C4C23×D5116yes—
735C4⋊C4C23×D5116yes—
736C4⋊C4C23×D518yes—
737C4⋊C4C23×D518yes—
738C4⋊C4C23×D518yes—
739C4⋊C4C23×D5116yes—
740C22⋊C4—58no—
741C22⋊C4—58no—
742C22⋊C4—58no—
743C22⋊C4—58no—
744C22⋊C4—516no—
745C22⋊C4—58no—
746C22⋊C4—58no—
747C22⋊C4—516no—
748C22⋊C4—516no—
749C22⋊C4—516no—
750C22⋊C4—58no—
751C22⋊C4—58no—
752C42—54no—
753C42—58no—
754C42—54no—
755C42—54no—
756C42—58no—
757C42—516no—
758C42C23×D518yes—
759C42C23×D514yes—
760C42C23×D5116yes—
761C42C23×D518yes—
762C2×C5#351514yescomplemented
763C2×C5C23×#4111yescharacteristic
764C2×C5C22×2−1+411yescharacteristic
765C2×C5C2×#58511yescharacteristic
766D5—28no—
767D5—42no—
768D5—44no—
769C23—58no—
770C23—54no—
771C23—52no—
772C23—54no—
773C23—104no—
774C23—104no—
775C23—102no—
776C23—104no—
777C23—102no—
778C23—104no—
779C23—104no—
780C23—102no—
781C23C24×D511yescharacteristic
782Q8—28no—
783Q8—28no—
784Q8—216no—
785Q8—208no—
786D4—516no—
787D4—1016no—
788D4—1032no—
789D4—108no—
790D4—208no—
791C2×C4—24no—
792C2×C4—28no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—52no—
798C2×C4—52no—
799C2×C4—52no—
800C2×C4—54no—
801C2×C4—58no—
802C2×C4—54no—
803C2×C4—1016no—
804C2×C4—1032no—
805C2×C4—102no—
806C2×C4—104no—
807C2×C4—102no—
808C2×C4—104no—
809C2×C4—102no—
810C2×C4—108no—
811C2×C4—1016no—
812C2×C4—108no—
813C2×C4—108no—
814C2×C4—1016no—
815C2×C4—208no—
816C2×C4—2016no—
817C2×C4—2016no—
818C2×C4—204no—
819C2×C4#414714yes—
820C2×C4D5×#4114yes—
821C2×C4C24×D514yes—
822C2×C4C24×D512yes—
823C2×C4C24×D514yes—
824C2×C4C24×D518yes—
825C2×C4C24×D514yes—
826C2×C4C24×D514yes—
827C2×C4C24×D512yes—
828C2×C4C24×D512yes—
829C5C2×#351511yescharacteristic, complemented, Sylow
830C22—58no—
831C22—104no—
832C22—1016no—
833C22—104no—
834C22—102no—
835C22—104no—
836C22—102no—
837C22—104no—
838C22—104no—
839C22—102no—
840C22—204no—
841C22—208no—
842C22C2×#414712yes—
843C22C2×D5×#4112yes—
844C22#6628712yes—
845C22C25×D511yescharacteristic
846C4—24no—
847C4—24no—
848C4—28no—
849C4—24no—
850C4—24no—
851C4—22no—
852C4—102no—
853C4—104no—
854C4—102no—
855C4—104no—
856C4—102no—
857C4—108no—
858C4C2×#414714yes—
859C4C2×D5×#4114yes—
860C2—108no—
861C2—202no—
862C2—204no—
863C2#1061892214yesdirect product factor
864C2C22×#414711yescharacteristic
865C2C22×D5×#4111yescharacteristic
866C2C2×#6628711yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#557C2
socleC23×C5C25
hypercenterC2×#557D5
hypocenterC5C2×#3515
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. C2×C5×#557C2semidirect
2. #10618922C2direct (N × H)
3. C2×#66060C2semidirect
4. C2×#66060C2semidirect
5. C2×#66065C2semidirect
6. C2×#66062C2semidirect
7. C2×#66029C2semidirect
8. C2×#66027C2semidirect
9. C2×#66026C2semidirect
10. C2×D5×#125C2semidirect
11. C2×#65913C2semidirect
12. C2×#65913C2semidirect
13. C2×#65915C2semidirect
14. C2×#65915C2semidirect
15. C2×#65914C2semidirect
16. C2×#65914C2semidirect
17. C2×#65908C2semidirect
18. C2×C4×#713C2semidirect
21. C5×#557C22semidirect
38. #66065C22semidirect
39. #66062C22semidirect
40. #66060C22semidirect
41. #66060C22semidirect
42. #66029C22semidirect
43. #66027C22semidirect
44. #66026C22semidirect
45. D5×#125C22semidirect
46. #65915C22semidirect
47. #65915C22semidirect
48. #65914C22semidirect
49. #65914C22semidirect
50. #65913C22semidirect
51. #65913C22semidirect
52. #65908C22semidirect
53. C4×#713C22semidirect
235. C2×#557D5semidirect
357. #557C2×D5semidirect
762. C2×C5#3515semidirect
829. C5C2×#3515semidirect
863. C2#10618922direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5572
#106189222
C2×#660602
C2×#660652
C2×#660622
C2×#660292
C2×#660272
C2×#660262
C2×D5×#1252
C2×#659132
C2×#659152
C2×#659142
C2×#659082
C2×C4×#7132
C2×#35155