Finite Group Databasebeta

← C2×#10618831 #13007408

Subgroups — C2×#10618831 #13007408

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×#554C211yesmaximal, characteristic, complemented
2#10618831C2132yesmaximal, direct product factor
3C2×#66064C211yesmaximal, characteristic, complemented
4C2×#66062C211yesmaximal, characteristic, complemented
5C2×#66028C212yesmaximal, complemented
6C2×#66031C212yesmaximal, complemented
7C2×#65976C214yesmaximal, complemented
8C2×#65976C212yesmaximal, complemented
9C2×#65979C214yesmaximal, complemented
10C2×#65958C212yesmaximal, complemented
11C2×#65914C211yesmaximal, characteristic, complemented
12C2×#65904C211yesmaximal, characteristic, complemented
13C2×#65889C212yesmaximal, complemented
14C2×#65889C211yesmaximal, characteristic, complemented
15C2×#65880C212yesmaximal, complemented
16C2×C4×#711C211yesmaximal, characteristic, complemented
17C2×#65848C212yesmaximal, complemented
18C22×#4036C212yesmaximal, complemented
19C22×#711C2211yescharacteristic
20C22×#711C2212yes—
21C5×#554C22116yescomplemented
22C2×C5×C4⋊Q8C2211yescharacteristic
23C2×C5×#125C2212yes—
24C2×C5×C22⋊Q8C2212yes—
25C2×C5×C22⋊Q8C2214yes—
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×D4C2211yescharacteristic
28C2×C4×C5×D4C2212yes—
29C22×C5×C4⋊C4C2212yes—
30C2×#4093C2211yescharacteristic
31C2×#4092C2214yes—
32C2×#4092C2212yes—
33C2×#4092C2211yescharacteristic
34C2×Q8×Dic5C2212yes—
35C2×Q8×Dic5C2212yes—
36C2×D4×Dic5C2211yescharacteristic
37C2×#4076C2212yes—
38C2×#4076C2214yes—
39C2×C4×C22⋊D5C2212yes—
40C2×C4×C22⋊D5C2214yes—
41C22×C4⋊Dic5C2214yes—
42C22×C4⋊Dic5C2212yes—
43C22×#683C2214yes—
44C22×C4×Dic5C2212yes—
45#66064C22116yescomplemented
46#66062C22116yescomplemented
47#66031C22132yescomplemented
48#66028C22132yescomplemented
49#65979C22164yescomplemented
50#65976C22132yescomplemented
51#65976C22164yescomplemented
52#65958C22132yescomplemented
53#65914C22116yescomplemented
54#65904C22116yescomplemented
55#65889C22116yescomplemented
56#65889C22132yescomplemented
57#65880C22132yescomplemented
58C4×#711C22116yescomplemented
59#65848C22132yescomplemented
60C2×#4044C2214yes—
61C2×#4044C2214yes—
62C2×#4044C2212yes—
63C2×#4044C2214yes—
64C2×#4043C2212yes—
65C2×#4043C2212yes—
66C2×#4043C2212yes—
67C2×#4041C2211yescharacteristic
68C2×#4040C2212yes—
69C2×#4040C2214yes—
70C2×#4039C2212yes—
71C2×#4038C2214yes—
72C2×#4038C2212yes—
73C2×#4038C2211yescharacteristic
74C2×D5×C4⋊C4C2212yes—
75C2×#4036C2212yes—
76C2×#4036C2211yescharacteristic
77C2×#4036C2212yes—
78C2×#4036C2214yes—
79C2×#4036C2214yes—
80C2×#4036C2212yes—
81C2×#4036C2214yes—
82C2×#4036C2214yes—
83C2×#4036C22132yescomplemented
84C2×#4033C2211yescharacteristic
85C2×#4033C2212yes—
86C2×#4032C2214yes—
87C2×#4032C2214yes—
88C2×#4032C2214yes—
89C2×#4027C2214yes—
90C2×#4027C2212yes—
91C2×#4023C2212yes—
92C2×#4023C2214yes—
93C2×C4×D20C2211yescharacteristic
94C2×C4×D20C2212yes—
95C2×#4018C2212yes—
96C2×C42×D5C2211yescharacteristic
97C2×#4015C2212yes—
98C2×#4015C2211yescharacteristic
99C2×C4×Dic10C2211yescharacteristic
100C2×C4×Dic10C2212yes—
101C2×#3515—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×Q8C2312yes—
104C22×C5×D4C2311yescharacteristic
105C23×C4×C5C2312yes—
106C23×C4×C5C2314yes—
107C22×C22⋊D5C2314yes—
108C22×C22⋊D5C2312yes—
109C23×Dic5C2312yes—
110C23×Dic5C2314yes—
111C23×Dic5C2312yes—
112C2×#711—28no—
113C2×#711—216no—
114C2×#711C2318yes—
115C2×#711C23116yes—
116C22×D20C2311yescharacteristic
117C22×D20C2312yes—
118C22×C4×D5C2311yescharacteristic
119C22×C4×D5C2311yescharacteristic
120C22×C4×D5C2312yes—
121C22×C4×D5C2311yescharacteristic
122C22×C4×D5C2314yes—
123C22×Dic10C2311yescharacteristic
124C22×Dic10C2312yes—
125C5×C4⋊Q8C2318yes—
126C5×#125C23116yes—
127C5×C22⋊Q8C23116yes—
128C5×C22⋊Q8C23132yes—
129C4×C5×Q8C2318yes—
130C4×C5×D4C2318yes—
131C4×C5×D4C23116yes—
132C2×C5×C4⋊C4C2312yes—
133C2×C5×C4⋊C4C2311yescharacteristic
134C2×C5×C4⋊C4C2311yescharacteristic
135C2×C5×C4⋊C4C2312yes—
136C2×C5×C4⋊C4C2314yes—
137C2×C5×C4⋊C4C2312yes—
138C2×C5×C4⋊C4C2314yes—
139C2×C5×C4⋊C4C23116yes—
140C2×C5×C22⋊C4C2314yes—
141C2×C5×C22⋊C4C2312yes—
142C2×C42×C5C2311yescharacteristic
143C2×C42×C5C2312yes—
144C2×C22⋊Dic5C2312yes—
145#4093C2318yes—
146#4092C23116yes—
147#4092C23132yes—
148#4092C2318yes—
149Q8×Dic5C23116yes—
150Q8×Dic5C23116yes—
151D4×Dic5C2318yes—
152#4076C23116yes—
153#4076C23132yes—
154C4×C22⋊D5C23116yes—
155C4×C22⋊D5C23132yes—
156C2×#685C2312yes—
157C2×#685C2312yes—
158C2×#685C2312yes—
159C2×#685C2312yes—
160C2×#685C2312yes—
161C2×#685C2312yes—
162C2×#685C2314yes—
163C2×#685C2314yes—
164C2×#685C2314yes—
165C2×C4⋊Dic5C2311yescharacteristic
166C2×C4⋊Dic5C2314yes—
167C2×C4⋊Dic5C2312yes—
168C2×C4⋊Dic5C2314yes—
169C2×C4⋊Dic5C2312yes—
170C2×C4⋊Dic5C2312yes—
171C2×C4⋊Dic5C2311yescharacteristic
172C2×C4⋊Dic5C2314yes—
173C2×C4⋊Dic5C2314yes—
174C2×C4⋊Dic5C2314yes—
175C2×C4⋊Dic5C23132yes—
176C2×C4⋊Dic5C23116yes—
177C2×#683C2312yes—
178C2×#683C2314yes—
179C2×#683C2312yes—
180C2×#683C2312yes—
181C2×#683C2312yes—
182C2×#683C2314yes—
183C2×#683C2314yes—
184C2×#683C23132yes—
185C2×C4×Dic5C2314yes—
186C2×C4×Dic5C2312yes—
187C2×C4×Dic5C2311yescharacteristic
188C2×C4×Dic5C2311yescharacteristic
189C2×C4×Dic5C2311yescharacteristic
190C2×C4×Dic5C2314yes—
191C2×C4×Dic5C2312yes—
192C2×C4×Dic5C2312yes—
193C2×C4×Dic5C23116yes—
194#4044C23132yes—
195#4044C23116yes—
196#4044C23132yes—
197#4044C23132yes—
198#4043C23116yes—
199#4043C23116yes—
200#4043C23116yes—
201#4041C2318yes—
202#4040C23132yes—
203#4040C23116yes—
204#4039C23116yes—
205#4038C23116yes—
206#4038C2318yes—
207#4038C23132yes—
208D5×C4⋊C4C23116yes—
209#4036C23116yes—
210#4036C23116yes—
211#4036C2318yes—
212#4036C23116yes—
213#4036C23132yes—
214#4036C23132yes—
215#4036C23132yes—
216#4036C23132yes—
217#4033C23116yes—
218#4033C2318yes—
219#4032C23132yes—
220#4032C23132yes—
221#4032C23132yes—
222#4027C23116yes—
223#4027C23132yes—
224#4023C23116yes—
225#4023C23132yes—
226C4×D20C2318yes—
227C4×D20C23116yes—
228#4018C23116yes—
229C42×D5C2318yes—
230#4015C2318yes—
231#4015C23116yes—
232C4×Dic10C2318yes—
233C4×Dic10C23116yes—
234#3515—532no—
235C2×#557—51no—
236C2×#554—51no—
237C2×#554D511yescharacteristic, complemented
238C2×#553—52no—
239C2×#552—52no—
240C2×#552—54no—
241C2×#552—52no—
242C2×#547—52no—
243C2×#547—51no—
244C2×#541—52no—
245C2×#539—54no—
246C2×#533—51no—
247C2×#529—52no—
248C2×#529—51no—
249C22×#125—52no—
250C2×#520—52no—
251C2×C4×#41—51no—
252C24×C5C2412yes—
253C23×D5C2411yescharacteristic
254C23×D5C2412yes—
255C2×C5×Q8—24no—
256C2×C5×Q8—44no—
257C2×C5×Q8C2414yes—
258C2×C5×Q8C2418yes—
259C2×C5×D4#4118yes—
260C2×C5×D4C2414yes—
261C22×C4×C5—28no—
262C22×C4×C5—48no—
263C22×C4×C5C2412yes—
264C22×C4×C5C2411yescharacteristic
265C22×C4×C5C2412yes—
266C22×C4×C5C2412yes—
267C22×C4×C5C2414yes—
268C22×C4×C5C2418yes—
269C22×C4×C5C24116yes—
270C22×C4×C5C2411yescharacteristic
271C22×C4×C5C2411yescharacteristic
272C2×C22⋊D5—28no—
273C2×C22⋊D5—216no—
274C2×C22⋊D5C2418yes—
275C2×C22⋊D5C24116yes—
276C22×Dic5—28no—
277C22×Dic5—216no—
278C22×Dic5—44no—
279C22×Dic5C2411yescharacteristic
280C22×Dic5C2412yes—
281C22×Dic5C2412yes—
282C22×Dic5C2414yes—
283C22×Dic5C2411yescharacteristic
284C22×Dic5C2411yescharacteristic
285C22×Dic5C2412yes—
286C22×Dic5C2418yes—
287C22×Dic5C24116yes—
288C22×Dic5C2418yes—
289#711—232no—
290#711—264no—
291C2×D20—24no—
292C2×D20—44no—
293C2×D20C2414yes—
294C2×D20C2418yes—
295C2×C4×D5—24no—
296C2×C4×D5—28no—
297C2×C4×D5—24no—
298C2×C4×D5—48no—
299C2×C4×D5—42no—
300C2×C4×D5C2414yes—
301C2×C4×D5C2418yes—
302C2×C4×D5C2414yes—
303C2×C4×D5C2414yes—
304C2×C4×D5C24116yes—
305C2×Dic10—24no—
306C2×Dic10—28no—
307C2×Dic10C2414yes—
308C2×Dic10C2418yes—
309C5×C4⋊C4C2414yes—
310C5×C4⋊C4C24116yes—
311C5×C4⋊C4C2418yes—
312C5×C4⋊C4C2414yes—
313C5×C4⋊C4C2418yes—
314C5×C4⋊C4C2418yes—
315C5×C4⋊C4C24116yes—
316C5×C22⋊C4C24116yes—
317C5×C22⋊C4C2418yes—
318C42×C5C2418yes—
319C42×C5C2414yes—
320C22⋊Dic5C2418yes—
321#685C2418yes—
322#685C2418yes—
323#685C2418yes—
324#685C2418yes—
325#685C2418yes—
326#685C2418yes—
327#685C24116yes—
328#685C24116yes—
329#685C24116yes—
330C4⋊Dic5C2414yes—
331C4⋊Dic5C24116yes—
332C4⋊Dic5C2418yes—
333C4⋊Dic5C24116yes—
334C4⋊Dic5C2418yes—
335C4⋊Dic5C2418yes—
336C4⋊Dic5C2414yes—
337C4⋊Dic5C24116yes—
338C4⋊Dic5C24116yes—
339C4⋊Dic5C24116yes—
340#683C2418yes—
341#683C24116yes—
342#683C2418yes—
343#683C2418yes—
344#683C2418yes—
345#683C24116yes—
346#683C24116yes—
347C4×Dic5C24116yes—
348C4×Dic5C2418yes—
349C4×Dic5C2414yes—
350C4×Dic5C2414yes—
351C4×Dic5C2414yes—
352C4×Dic5C24116yes—
353C4×Dic5C2418yes—
354C4×Dic5C2418yes—
355C22×#41—51no—
356C22×#41—52no—
357#557—516no—
358#554—516no—
359#554C2×D5116yescomplemented
360#553—532no—
361#552—532no—
362#552—564no—
363#552—532no—
364#547—532no—
365#547—516no—
366#541—532no—
367#539—564no—
368#533—516no—
369C2×C4⋊Q8—51no—
370C2×C4⋊Q8—52no—
371C2×C4⋊Q8C2×D511yescharacteristic
372#529—532no—
373#529—516no—
374C2×#126—54no—
375C2×#126—52no—
376C2×#126—54no—
377C2×#126—54no—
378C2×#125—51no—
379C2×#125—52no—
380C2×#125—54no—
381C2×#125—54no—
382C2×#125—52no—
383C2×#125—52no—
384C2×#125—54no—
385C2×#125—54no—
386C2×#125—532no—
387C2×#125C2×D512yes—
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—54no—
397C2×C22⋊Q8—52no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—52no—
400C2×C22⋊Q8C2×D512yes—
401C2×C22⋊Q8C2×D514yes—
402C2×#121—52no—
403C2×#121—54no—
404C2×#121—51no—
405#520—532no—
406C4×#41—516no—
407C2×C4×Q8—52no—
408C2×C4×Q8—52no—
409C2×C4×Q8—51no—
410C2×C4×Q8—52no—
411C2×C4×Q8—51no—
412C2×C4×Q8—52no—
413C2×C4×Q8C2×D511yescharacteristic
414C2×C4×D4—51no—
415C2×C4×D4—52no—
416C2×C4×D4—54no—
417C2×C4×D4—52no—
418C2×C4×D4—52no—
419C2×C4×D4—54no—
420C2×C4×D4—52no—
421C2×C4×D4—51no—
422C2×C4×D4C2×D511yescharacteristic
423C2×C4×D4C2×D512yes—
424C2×#117—51no—
425C2×#117—54no—
426C2×#117—52no—
427C2×#117—52no—
428C2×#117—54no—
429C2×#117—52no—
430C22×C4⋊C4—54no—
431C22×C4⋊C4—52no—
432C22×C4⋊C4—54no—
433C22×C4⋊C4—52no—
434C22×C4⋊C4C2×D512yes—
435C22×C42—52no—
436C22×C42—51no—
437C23×C5—24no—
438C23×C5—24no—
439C23×C5C2×#4118yes—
440C23×C5C2514yes—
441C23×C5C2511yescharacteristic
442C22×D5—22no—
443C22×D5—24no—
444C22×D5—22no—
445C22×D5—24no—
446C22×D5—24no—
447C22×D5—22no—
448C22×D5C2512yes—
449C22×D5C2514yes—
450C5×Q8—28no—
451C5×Q8—48no—
452C5×D4C2×#41116yes—
453C2×C4×C5—24no—
454C2×C4×C5—24no—
455C2×C4×C5—28no—
456C2×C4×C5—22no—
457C2×C4×C5—24no—
458C2×C4×C5—216no—
459C2×C4×C5—416no—
460C2×C4×C5C2×#4114yes—
461C2×C4×C52−1+414yes—
462C2×C4×C5C2514yes—
463C2×C4×C5C2514yes—
464C2×C4×C5C2512yes—
465C2×C4×C5C2518yes—
466C2×C4×C5C2514yes—
467C2×C4×C5C2512yes—
468C2×C4×C5C2512yes—
469C22⋊D5—216no—
470C22⋊D5—232no—
471C2×Dic5—24no—
472C2×Dic5—28no—
473C2×Dic5—22no—
474C2×Dic5—24no—
475C2×Dic5—216no—
476C2×Dic5—232no—
477C2×Dic5—22no—
478C2×Dic5—24no—
479C2×Dic5—22no—
480C2×Dic5—48no—
481C2×Dic5C2512yes—
482C2×Dic5C2512yes—
483C2×Dic5C2514yes—
484C2×Dic5C2512yes—
485C2×Dic5C2518yes—
486C2×Dic5C2514yes—
487C2×Dic5C2514yes—
488D20—28no—
489D20—48no—
490C4×D5—28no—
491C4×D5—216no—
492C4×D5—28no—
493C4×D5—416no—
494C4×D5—44no—
495Dic10—28no—
496Dic10—216no—
497C2×#41—58no—
498C2×#41—516no—
499C2×#41—108no—
500C2×#41—1016no—
501C22×Q8—51no—
502C22×Q8—52no—
503C22×Q8C22×D511yescharacteristic
504C22×Q8C22×D512yes—
505C22×D4—52no—
506C22×D4—54no—
507C22×D4—51no—
508C22×D4—52no—
509C22×D4C22×D511yescharacteristic
510C23×C4—54no—
511C23×C4—52no—
512C23×C4—52no—
513C23×C4—52no—
514C23×C4—51no—
515C23×C4—51no—
516C23×C4—54no—
517C23×C4—51no—
518C23×C4C22×D512yes—
519C23×C4C22×D514yes—
520C4⋊Q8—58no—
521C4⋊Q8—516no—
522C4⋊Q8C22×D518yes—
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—516no—
532#125—516no—
533#125—532no—
534#125—532no—
535#125C22×D5116yes—
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—532no—
545C22⋊Q8—516no—
546C22⋊Q8—516no—
547C22⋊Q8—516no—
548C22⋊Q8C22×D5116yes—
549C22⋊Q8C22×D5132yes—
550#121—516no—
551#121—532no—
552#121—58no—
553C4×Q8—516no—
554C4×Q8—516no—
555C4×Q8—58no—
556C4×Q8—516no—
557C4×Q8—58no—
558C4×Q8—516no—
559C4×Q8C22×D518yes—
560C4×D4—58no—
561C4×D4—516no—
562C4×D4—532no—
563C4×D4—516no—
564C4×D4—516no—
565C4×D4—532no—
566C4×D4—516no—
567C4×D4—58no—
568C4×D4C22×D518yes—
569C4×D4C22×D5116yes—
570#117—58no—
571#117—532no—
572#117—516no—
573#117—516no—
574#117—532no—
575#117—516no—
576C2×C4⋊C4—51no—
577C2×C4⋊C4—54no—
578C2×C4⋊C4—52no—
579C2×C4⋊C4—51no—
580C2×C4⋊C4—52no—
581C2×C4⋊C4—52no—
582C2×C4⋊C4—54no—
583C2×C4⋊C4—54no—
584C2×C4⋊C4—54no—
585C2×C4⋊C4—532no—
586C2×C4⋊C4—54no—
587C2×C4⋊C4—54no—
588C2×C4⋊C4—54no—
589C2×C4⋊C4—516no—
590C2×C4⋊C4—532no—
591C2×C4⋊C4—52no—
592C2×C4⋊C4—52no—
593C2×C4⋊C4—52no—
594C2×C4⋊C4—52no—
595C2×C4⋊C4—54no—
596C2×C4⋊C4—516no—
597C2×C4⋊C4C22×D512yes—
598C2×C4⋊C4C22×D511yescharacteristic
599C2×C4⋊C4C22×D512yes—
600C2×C4⋊C4C22×D514yes—
601C2×C4⋊C4C22×D5116yes—
602C2×C4⋊C4C22×D511yescharacteristic
603C2×C4⋊C4C22×D514yes—
604C2×C4⋊C4C22×D512yes—
605C2×C22⋊C4—52no—
606C2×C22⋊C4—52no—
607C2×C22⋊C4—52no—
608C2×C22⋊C4—52no—
609C2×C22⋊C4—52no—
610C2×C22⋊C4—54no—
611C2×C22⋊C4—54no—
612C2×C22⋊C4—54no—
613C2×C22⋊C4—52no—
614C2×C22⋊C4—52no—
615C2×C22⋊C4C22×D514yes—
616C2×C22⋊C4C22×D512yes—
617C2×C42—52no—
618C2×C42—51no—
619C2×C42—54no—
620C2×C42—54no—
621C2×C42—51no—
622C2×C42—52no—
623C2×C42—52no—
624C2×C42—516no—
625C2×C42—51no—
626C2×C42—58no—
627C2×C42C22×D512yes—
628C2×C42C22×D511yescharacteristic
629C22×C5—24no—
630C22×C5—24no—
631C22×C5—216no—
632C22×C5C22×#4118yes—
633C22×C5C22×#4112yes—
634C22×C5C2×2−1+412yes—
635C22×C5#58512yes—
636C22×C5C2611yescharacteristic
637C2×D5—22no—
638C2×D5—24no—
639C2×D5—22no—
640C2×D5—24no—
641C2×D5—24no—
642C2×D5—22no—
643C2×D5—44no—
644C2×D5—48no—
645C4×C5—24no—
646C4×C5—24no—
647C4×C5—28no—
648C4×C5—22no—
649C4×C5—24no—
650C4×C5C22×#4114yes—
651C4×C5C2×2−1+414yes—
652Dic5—24no—
653Dic5—28no—
654Dic5—22no—
655Dic5—24no—
656Dic5—22no—
657Dic5—24no—
658Dic5—22no—
659C24—51no—
660C24—52no—
661C24C23×D512yes—
662#41—1032no—
663#41—1064no—
664C2×Q8—24no—
665C2×Q8—44no—
666C2×Q8—54no—
667C2×Q8—58no—
668C2×Q8—104no—
669C2×Q8—108no—
670C2×Q8C23×D514yes—
671C2×Q8C23×D518yes—
672C2×D4—58no—
673C2×D4—516no—
674C2×D4—54no—
675C2×D4—58no—
676C2×D4—108no—
677C2×D4—1016no—
678C2×D4—104no—
679C2×D4—204no—
680C2×D4#71318yes—
681C2×D4C23×D514yes—
682C22×C4—28no—
683C22×C4—48no—
684C22×C4—58no—
685C22×C4—516no—
686C22×C4—51no—
687C22×C4—51no—
688C22×C4—52no—
689C22×C4—51no—
690C22×C4—54no—
691C22×C4—52no—
692C22×C4—52no—
693C22×C4—58no—
694C22×C4—54no—
695C22×C4—54no—
696C22×C4—58no—
697C22×C4—54no—
698C22×C4—516no—
699C22×C4—1016no—
700C22×C4—108no—
701C22×C4—108no—
702C22×C4—104no—
703C22×C4—104no—
704C22×C4—208no—
705C22×C4—202no—
706C22×C4—204no—
707C22×C4C23×D518yes—
708C22×C4C23×D512yes—
709C22×C4C23×D512yes—
710C22×C4C23×D511yescharacteristic
711C22×C4C23×D514yes—
712C22×C4C23×D512yes—
713C22×C4C23×D5116yes—
714C22×C4C23×D511yescharacteristic
715C22×C4C23×D511yescharacteristic
716C4⋊C4—54no—
717C4⋊C4—516no—
718C4⋊C4—58no—
719C4⋊C4—54no—
720C4⋊C4—58no—
721C4⋊C4—58no—
722C4⋊C4—516no—
723C4⋊C4—516no—
724C4⋊C4—516no—
725C4⋊C4—516no—
726C4⋊C4—516no—
727C4⋊C4—516no—
728C4⋊C4—58no—
729C4⋊C4—58no—
730C4⋊C4—58no—
731C4⋊C4—58no—
732C4⋊C4—516no—
733C4⋊C4C23×D518yes—
734C4⋊C4C23×D514yes—
735C4⋊C4C23×D518yes—
736C4⋊C4C23×D5116yes—
737C4⋊C4C23×D514yes—
738C4⋊C4C23×D5116yes—
739C4⋊C4C23×D518yes—
740C22⋊C4—58no—
741C22⋊C4—58no—
742C22⋊C4—58no—
743C22⋊C4—58no—
744C22⋊C4—58no—
745C22⋊C4—516no—
746C22⋊C4—516no—
747C22⋊C4—516no—
748C22⋊C4—58no—
749C22⋊C4—58no—
750C22⋊C4C23×D5116yes—
751C22⋊C4C23×D518yes—
752C42—54no—
753C42—58no—
754C42—54no—
755C42—54no—
756C42—58no—
757C42—58no—
758C42—516no—
759C42—516no—
760C42C23×D514yes—
761C42C23×D518yes—
762C2×C5—28no—
763C2×C5#351514yescomplemented
764C2×C5C23×#4111yescharacteristic
765C2×C5C22×2−1+411yescharacteristic
766C2×C5C2×#58511yescharacteristic
767D5—42no—
768D5—44no—
769C23—24no—
770C23—24no—
771C23—52no—
772C23—54no—
773C23—102no—
774C23—104no—
775C23—102no—
776C23—104no—
777C23—104no—
778C23—102no—
779C23C2×#71318yes—
780C23C24×D514yes—
781C23C24×D511yescharacteristic
782Q8—28no—
783Q8—48no—
784Q8—108no—
785Q8—1016no—
786D4—1016no—
787D4—1032no—
788D4—108no—
789D4—208no—
790D4C2×#713116yes—
791C2×C4—24no—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—28no—
795C2×C4—22no—
796C2×C4—216no—
797C2×C4—416no—
798C2×C4—52no—
799C2×C4—52no—
800C2×C4—52no—
801C2×C4—54no—
802C2×C4—54no—
803C2×C4—58no—
804C2×C4—54no—
805C2×C4—102no—
806C2×C4—104no—
807C2×C4—108no—
808C2×C4—104no—
809C2×C4—1016no—
810C2×C4—1032no—
811C2×C4—102no—
812C2×C4—104no—
813C2×C4—102no—
814C2×C4—108no—
815C2×C4—1016no—
816C2×C4—108no—
817C2×C4—2016no—
818C2×C4—204no—
819C2×C4—208no—
820C2×C4C2×#71314yes—
821C2×C4#415014yes—
822C2×C4C24×D514yes—
823C2×C4C24×D514yes—
824C2×C4C24×D512yes—
825C2×C4C24×D518yes—
826C2×C4C24×D514yes—
827C2×C4C24×D512yes—
828C2×C4C24×D512yes—
829C5C2×#351511yescharacteristic, complemented, Sylow
830C22—24no—
831C22—24no—
832C22—216no—
833C22—102no—
834C22—104no—
835C22—102no—
836C22—104no—
837C22—104no—
838C22—102no—
839C22—204no—
840C22—208no—
841C22C22×#71318yes—
842C22C22×#71312yes—
843C22C2×#415012yes—
844C22#6628512yes—
845C22C25×D511yescharacteristic
846C4—24no—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—22no—
851C4—102no—
852C4—104no—
853C4—104no—
854C4—108no—
855C4—102no—
856C4—104no—
857C4—102no—
858C4C22×#71314yes—
859C4C2×#415014yes—
860C2—28no—
861C2—202no—
862C2—204no—
863C2#1061883114yesdirect product factor
864C2C23×#71311yescharacteristic
865C2C22×#415011yescharacteristic
866C2C2×#6628511yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#554C2
socleC23×C5C25
hypercenterC2×#554D5
hypocenterC5C2×#3515
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. #10618831C2direct (N × H)
3. C2×#66064C2semidirect
4. C2×#66062C2semidirect
5. C2×#66028C2semidirect
6. C2×#66031C2semidirect
7. C2×#65976C2semidirect
8. C2×#65976C2semidirect
9. C2×#65979C2semidirect
10. C2×#65958C2semidirect
11. C2×#65914C2semidirect
12. C2×#65904C2semidirect
13. C2×#65889C2semidirect
14. C2×#65889C2semidirect
15. C2×#65880C2semidirect
16. C2×C4×#711C2semidirect
17. C2×#65848C2semidirect
18. C22×#4036C2semidirect
21. C5×#554C22semidirect
45. #66064C22semidirect
46. #66062C22semidirect
47. #66031C22semidirect
48. #66028C22semidirect
49. #65979C22semidirect
50. #65976C22semidirect
51. #65976C22semidirect
52. #65958C22semidirect
53. #65914C22semidirect
54. #65904C22semidirect
55. #65889C22semidirect
56. #65889C22semidirect
57. #65880C22semidirect
58. C4×#711C22semidirect
59. #65848C22semidirect
83. C2×#4036C22semidirect
237. C2×#554D5semidirect
359. #554C2×D5semidirect
763. C2×C5#3515semidirect
829. C5C2×#3515semidirect
863. C2#10618831direct (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
#106188312
C2×#660642
C2×#660622
C2×#660282
C2×#660312
C2×#659762
C2×#659792
C2×#659582
C2×#659142
C2×#659042
C2×#658892
C2×#658802
C2×C4×#7112
C2×#658482
C22×#40362
C2×#35155