Finite Group Databasebeta

← C2×#10618921 #13007739

Subgroups — C2×#10618921 #13007739

Order 1280.

7022 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
1C2×C5×#557C211yesmaximal, characteristic, complemented
2#10618921C2132yesmaximal, direct product factor
3C2×#66058C212yesmaximal
4C2×D5×C4⋊Q8C211yesmaximal, characteristic, complemented
5C2×#66055C212yesmaximal, complemented
6C2×#66066C211yesmaximal, characteristic, complemented
7C2×#66028C212yesmaximal, complemented
8C2×#66027C214yesmaximal, complemented
9C2×#66030C214yesmaximal, complemented
10C2×#66022C212yesmaximal, complemented
11C2×#65915C212yesmaximal, complemented
12C2×#65912C211yesmaximal, characteristic, complemented
13C2×#65912C212yesmaximal, complemented
14C2×#65906C212yesmaximal, complemented
15C2×#65901C211yesmaximal, characteristic, complemented
16C2×#65902C212yesmaximal, complemented
17C2×#65918C211yesmaximal, characteristic, complemented
18C2×C4×#713C211yesmaximal, characteristic
19C22×#713C2211yescharacteristic
20C22×Q8×D5C2212yes—
21C5×#557C22116yescomplemented
22C2×C5×C4⋊Q8C2211yescharacteristic
23C2×C5×C4⋊Q8C2212yes—
24C2×C5×#125C2212yes—
25C2×C5×#125C2214yes—
26C2×C4×C5×Q8C2211yescharacteristic
27C2×C4×C5×Q8C2211yescharacteristic
28C2×C4×C5×Q8C2212yes—
29C2×C4×C5×Q8C2212yes—
30C2×#4093C2212yes—
31C2×#4092C2212yes—
32C2×#4092C2211yescharacteristic
33C2×Q8×Dic5C2211yescharacteristic
34C2×Q8×Dic5C2212yes—
35C2×#4090C2212yes—
36C2×#4090C2212yes—
37C2×#4090C2211yescharacteristic
38#66066C22116yescomplemented
39#66058C22132yes—
40D5×C4⋊Q8C22116yescomplemented
41#66055C22132yescomplemented
42#66030C22164yescomplemented
43#66028C22132yescomplemented
44#66027C22164yescomplemented
45#66022C22132yescomplemented
46#65918C22116yescomplemented
47#65915C22132yescomplemented
48#65912C22132yescomplemented
49#65912C22116yescomplemented
50C4×#713C22116yes—
51#65906C22132yescomplemented
52#65902C22132yescomplemented
53#65901C22116yescomplemented
54C2×#4044C2214yes—
55C2×#4044C2214yes—
56C2×#4044C2214yes—
57C2×#4043C2211yescharacteristic
58C2×#4043C2212yes—
59C2×#4042C2214yes—
60C2×#4042C2214yes—
61C2×#4042C2212yes—
62C2×#4042C2214yes—
63C2×#4040C2214yes—
64C2×#4040C2214yes—
65C2×#4039C2211yescharacteristic
66C2×#4039C2212yes—
67C2×#4038C2211yescharacteristic
68C2×#4038C2212yes—
69C2×#4038C2212yes—
70C2×#4038C2214yes—
71C2×#4038C2212yes—
72C2×D5×C4⋊C4C2212yes—
73C2×D5×C4⋊C4C2212yes—
74C2×#4036C2214yes—
75C2×#4035C2214yes—
76C2×#4035C2212yes—
77C2×#4035C2214yes—
78C2×#4035C2214yes—
79C2×#4034C2211yescharacteristic
80C2×#4034C2212yes—
81C2×#4034C2212yes—
82C2×#4033C2212yes—
83C2×#4033C2214yes—
84C2×#4033C2214yes—
85C2×#4022C2214yes—
86C2×#4021C2212yes—
87C2×C4×D20C2211yescharacteristic
88C2×C4×D20C2212yes—
89C2×#4018C2214yes—
90C2×#4018C2212yes—
91C2×#4018C2214yes—
92C2×C42×D5C2212yes—
93C2×C42×D5C2211yescharacteristic
94C2×#4016C2212yes—
95C2×#4015C2211yescharacteristic
96C2×C4×Dic10C2212yes—
97C2×C4×Dic10C2212yes—
98C2×C4×Dic10C2212yes—
99C2×C4×Dic10C2211yescharacteristic
100C2×C4×Dic10C2214yes—
101C2×#3509—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×Q8C2312yes—
104C22×C5×Q8C2311yescharacteristic
105C2×#713—28no—
106C2×#713C2318yes—
107C2×Q8×D5—216no—
108C2×Q8×D5C23116yes—
109C22×D20C2311yescharacteristic
110C22×D20C2312yes—
111C22×C4×D5C2312yes—
112C22×C4×D5C2311yescharacteristic
113C22×C4×D5C2312yes—
114C22×C4×D5C2311yescharacteristic
115C22×C4×D5C2312yes—
116C22×C4×D5C2314yes—
117C22×C4×D5C2311yescharacteristic
118C22×Dic10C2311yescharacteristic
119C22×Dic10C2312yes—
120C22×Dic10C2312yes—
121C22×Dic10C2314yes—
122C5×C4⋊Q8C23116yes—
123C5×C4⋊Q8C2318yes—
124C5×#125C23116yes—
125C5×#125C23132yes—
126C4×C5×Q8C2318yes—
127C4×C5×Q8C23116yes—
128C4×C5×Q8C23116yes—
129C4×C5×Q8C2318yes—
130C2×C5×C4⋊C4C2311yescharacteristic
131C2×C5×C4⋊C4C2314yes—
132C2×C5×C4⋊C4C2314yes—
133C2×C5×C4⋊C4C2312yes—
134C2×C5×C4⋊C4C2312yes—
135C2×C5×C4⋊C4C2311yescharacteristic
136C2×C5×C4⋊C4C2312yes—
137C2×C5×C4⋊C4C2314yes—
138C2×C5×C4⋊C4C2312yes—
139C2×C42×C5C2312yes—
140C2×C42×C5C2311yescharacteristic
141C2×C42×C5C2312yes—
142C2×C42×C5C2314yes—
143#4093C23116yes—
144#4092C2318yes—
145#4092C23116yes—
146Q8×Dic5C2318yes—
147Q8×Dic5C23116yes—
148#4090C23116yes—
149#4090C23116yes—
150#4090C2318yes—
151C2×#685C2312yes—
152C2×#685C2312yes—
153C2×#685C2314yes—
154C2×#685C2312yes—
155C2×#685C2314yes—
156C2×#685C2312yes—
157C2×#685C2312yes—
158C2×#685C2314yes—
159C2×#685C2314yes—
160C2×C4⋊Dic5C2311yescharacteristic
161C2×C4⋊Dic5C2312yes—
162C2×C4⋊Dic5C2311yescharacteristic
163C2×C4⋊Dic5C2312yes—
164C2×C4⋊Dic5C2314yes—
165C2×C4⋊Dic5C2312yes—
166C2×C4⋊Dic5C2312yes—
167C2×#683C2314yes—
168C2×#683C2312yes—
169C2×#683C2312yes—
170C2×#683C2312yes—
171C2×#683C2312yes—
172C2×#683C2314yes—
173C2×#683C2314yes—
174C2×#683C2314yes—
175C2×#683C2312yes—
176C2×#683C2314yes—
177C2×#683C2314yes—
178C2×C4×Dic5C2312yes—
179C2×C4×Dic5C2311yescharacteristic
180C2×C4×Dic5C2314yes—
181C2×C4×Dic5C2312yes—
182C2×C4×Dic5C2314yes—
183C2×C4×Dic5C2311yescharacteristic
184C2×C4×Dic5C2312yes—
185C2×C4×Dic5C2311yescharacteristic
186C2×C4×Dic5C2314yes—
187#4044C23132yes—
188#4044C23132yes—
189#4044C23132yes—
190#4043C23116yes—
191#4043C2318yes—
192#4042C23132yes—
193#4042C23132yes—
194#4042C23132yes—
195#4042C23116yes—
196#4040C23132yes—
197#4040C23132yes—
198#4039C2318yes—
199#4039C23116yes—
200#4038C23116yes—
201#4038C2318yes—
202#4038C23132yes—
203#4038C23116yes—
204#4038C23116yes—
205D5×C4⋊C4C23116yes—
206D5×C4⋊C4C23116yes—
207#4036C23132yes—
208#4035C23132yes—
209#4035C23132yes—
210#4035C23132yes—
211#4035C23116yes—
212#4034C23116yes—
213#4034C23116yes—
214#4034C2318yes—
215#4033C23132yes—
216#4033C23116yes—
217#4033C23132yes—
218#4022C23132yes—
219#4021C23116yes—
220C4×D20C2318yes—
221C4×D20C23116yes—
222#4018C23116yes—
223#4018C23132yes—
224#4018C23132yes—
225C42×D5C2318yes—
226C42×D5C23116yes—
227#4016C23116yes—
228#4015C2318yes—
229C4×Dic10C23116yes—
230C4×Dic10C23116yes—
231C4×Dic10C2318yes—
232C4×Dic10C23116yes—
233C4×Dic10C23132yes—
234#3509—532no—
235C2×#557—52no—
236C2×#557—51no—
237C2×#557D511yescharacteristic, complemented
238C2×#556—51no—
239C2×#556—51no—
240C2×#556—52no—
241C2×#552—54no—
242C2×#552—52no—
243C2×#552—52no—
244C2×#541—54no—
245C2×#536—52no—
246C2×#533—52no—
247C2×#533—51no—
248C2×#533—52no—
249C22×C4⋊Q8—51no—
250C2×#519—52no—
251C2×C4×#41—51no—
252C23×D5C2412yes—
253C23×D5C2411yescharacteristic
254C2×C5×Q8—28no—
255C2×C5×Q8—24no—
256C2×C5×Q8—24no—
257C2×C5×Q8C2414yes—
258C2×C5×Q8C2418yes—
259C2×C5×Q8C2414yes—
260C22×C4×C5C2412yes—
261C22×C4×C5C2412yes—
262C22×C4×C5C2412yes—
263C22×C4×C5C2411yescharacteristic
264C22×C4×C5C2414yes—
265C22×C4×C5C2412yes—
266C22×C4×C5C2411yescharacteristic
267C22×C4×C5C2411yescharacteristic
268C22×Dic5C2414yes—
269C22×Dic5C2412yes—
270C22×Dic5C2412yes—
271C22×Dic5C2412yes—
272C22×Dic5C2411yescharacteristic
273C22×Dic5C2411yescharacteristic
274C22×Dic5C2411yescharacteristic
275#713—232no—
276Q8×D5—264no—
277C2×D20—28no—
278C2×D20—24no—
279C2×D20C2414yes—
280C2×D20C2418yes—
281C2×C4×D5—216no—
282C2×C4×D5—24no—
283C2×C4×D5—28no—
284C2×C4×D5—28no—
285C2×C4×D5—24no—
286C2×C4×D5—28no—
287C2×C4×D5#4118yes—
288C2×C4×D5C24116yes—
289C2×C4×D5C2418yes—
290C2×C4×D5C2418yes—
291C2×C4×D5C2414yes—
292C2×C4×D5C2418yes—
293C2×C4×D5C2414yes—
294C2×C4×D5C2414yes—
295C2×Dic10—28no—
296C2×Dic10—24no—
297C2×Dic10—216no—
298C2×Dic10—28no—
299C2×Dic10C2418yes—
300C2×Dic10C24116yes—
301C2×Dic10C2414yes—
302C2×Dic10C2418yes—
303C5×C4⋊C4C2414yes—
304C5×C4⋊C4C24116yes—
305C5×C4⋊C4C2414yes—
306C5×C4⋊C4C2418yes—
307C5×C4⋊C4C2418yes—
308C5×C4⋊C4C2418yes—
309C5×C4⋊C4C24116yes—
310C5×C4⋊C4C24116yes—
311C5×C4⋊C4C2418yes—
312C42×C5C2418yes—
313C42×C5C24116yes—
314C42×C5C2418yes—
315C42×C5C2414yes—
316#685C2418yes—
317#685C2418yes—
318#685C24116yes—
319#685C2418yes—
320#685C24116yes—
321#685C2418yes—
322#685C2418yes—
323#685C24116yes—
324#685C24116yes—
325C4⋊Dic5C2414yes—
326C4⋊Dic5C2418yes—
327C4⋊Dic5C2414yes—
328C4⋊Dic5C2418yes—
329C4⋊Dic5C24116yes—
330C4⋊Dic5C2418yes—
331C4⋊Dic5C2418yes—
332#683C24116yes—
333#683C2418yes—
334#683C2418yes—
335#683C2418yes—
336#683C2418yes—
337#683C24116yes—
338#683C24116yes—
339#683C24116yes—
340#683C2418yes—
341#683C24116yes—
342#683C24116yes—
343C4×Dic5C2418yes—
344C4×Dic5C2414yes—
345C4×Dic5C24116yes—
346C4×Dic5C2418yes—
347C4×Dic5C24116yes—
348C4×Dic5C2414yes—
349C4×Dic5C2418yes—
350C4×Dic5C2414yes—
351C4×Dic5C24116yes—
352C22×#41—51no—
353C23×Q8—52no—
354#557—532no—
355#557—516no—
356#557C2×D5116yescomplemented
357#556—516no—
358#556—532no—
359#556—516no—
360#552—564no—
361#552—532no—
362#552—532no—
363#541—564no—
364#536—532no—
365#533—532no—
366#533—516no—
367#533—532no—
368C2×C4⋊Q8—52no—
369C2×C4⋊Q8—51no—
370C2×C4⋊Q8—52no—
371C2×C4⋊Q8—516no—
372C2×C4⋊Q8—52no—
373C2×C4⋊Q8—52no—
374C2×C4⋊Q8—51no—
375C2×C4⋊Q8—51no—
376C2×C4⋊Q8C2×D511yescharacteristic
377C2×C4⋊Q8C2×D512yes—
378C2×#126—54no—
379C2×#126—54no—
380C2×#126—54no—
381C2×#126—54no—
382C2×#125—52no—
383C2×#125—54no—
384C2×#125—54no—
385C2×#125—54no—
386C2×#125—54no—
387C2×#125—52no—
388C2×#125C2×D512yes—
389C2×#125C2×D514yes—
390C2×#124—52no—
391C2×#124—52no—
392C2×#123—54no—
393C2×#123—54no—
394C2×C22⋊Q8—51no—
395C2×C22⋊Q8—52no—
396C2×C22⋊Q8—54no—
397C2×C22⋊Q8—54no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—54no—
400C2×C22⋊Q8—51no—
401C2×C22⋊Q8—52no—
402#519—532no—
403C4×#41—516no—
404C2×C4×Q8—51no—
405C2×C4×Q8—52no—
406C2×C4×Q8—54no—
407C2×C4×Q8—52no—
408C2×C4×Q8—54no—
409C2×C4×Q8—54no—
410C2×C4×Q8—52no—
411C2×C4×Q8—52no—
412C2×C4×Q8—51no—
413C2×C4×Q8—52no—
414C2×C4×Q8C2×D511yescharacteristic
415C2×C4×Q8C2×D512yes—
416C2×C4×Q8C2×D512yes—
417C2×C4×Q8C2×D511yescharacteristic
418C2×C4×D4—52no—
419C2×C4×D4—51no—
420C2×C4×D4—52no—
421C2×C4×D4—51no—
422C2×#117—51no—
423C2×#117—52no—
424C2×#117—54no—
425C2×#117—52no—
426C2×#117—52no—
427C2×#117—52no—
428C2×#117—54no—
429C2×#117—54no—
430C22×C4⋊C4—52no—
431C22×C4⋊C4—52no—
432C22×C42—51no—
433C22×C42—52no—
434C23×C5C2511yescharacteristic
435C22×D5—22no—
436C22×D5—22no—
437C22×D5—24no—
438C22×D5—24no—
439C22×D5—24no—
440C22×D5C2×#4114yes—
441C22×D5C2514yes—
442C22×D5C2512yes—
443C5×Q8—216no—
444C5×Q8—28no—
445C5×Q8—28no—
446C2×C4×C5—28no—
447C2×C4×C5—24no—
448C2×C4×C5—24no—
449C2×C4×C5—24no—
450C2×C4×C5—22no—
451C2×C4×C5—24no—
452C2×C4×C5C2×#4114yes—
453C2×C4×C52−1+414yes—
454C2×C4×C5C2514yes—
455C2×C4×C5C2514yes—
456C2×C4×C5C2514yes—
457C2×C4×C5C2512yes—
458C2×C4×C5C2518yes—
459C2×C4×C5C2514yes—
460C2×C4×C5C2512yes—
461C2×C4×C5C2512yes—
462C2×Dic5—28no—
463C2×Dic5—24no—
464C2×Dic5—24no—
465C2×Dic5—24no—
466C2×Dic5—22no—
467C2×Dic5C2×#4114yes—
468C2×Dic52−1+414yes—
469C2×Dic5C2514yes—
470C2×Dic5C2514yes—
471C2×Dic5C2514yes—
472C2×Dic5C2512yes—
473C2×Dic5C2518yes—
474C2×Dic5C2512yes—
475C2×Dic5C2512yes—
476D20—216no—
477D20—28no—
478C4×D5—232no—
479C4×D5—28no—
480C4×D5—216no—
481C4×D5—216no—
482C4×D5—28no—
483C4×D5—216no—
484C4×D5C2×#41116yes—
485Dic10—216no—
486Dic10—28no—
487Dic10—232no—
488Dic10—216no—
489C2×#41—58no—
490C2×#41—108no—
491C22×Q8—516no—
492C22×Q8—52no—
493C22×Q8—51no—
494C22×Q8—54no—
495C22×Q8—52no—
496C22×Q8—1016no—
497C22×Q8C22×D512yes—
498C22×Q8C22×D511yescharacteristic
499C22×Q8C22×D511yescharacteristic
500C22×D4—52no—
501C22×D4—51no—
502C23×C4—51no—
503C23×C4—54no—
504C23×C4—51no—
505C23×C4—51no—
506C23×C4—52no—
507C23×C4—52no—
508C23×C4—52no—
509C4⋊Q8—516no—
510C4⋊Q8—58no—
511C4⋊Q8—516no—
512C4⋊Q8—516no—
513C4⋊Q8—516no—
514C4⋊Q8—58no—
515C4⋊Q8—58no—
516C4⋊Q8C22×D518yes—
517C4⋊Q8C22×D5116yes—
518#126—532no—
519#126—532no—
520#126—532no—
521#126—532no—
522#125—516no—
523#125—532no—
524#125—532no—
525#125—532no—
526#125—532no—
527#125—516no—
528#125C22×D5116yes—
529#125C22×D5132yes—
530#124—516no—
531#124—516no—
532#123—532no—
533#123—532no—
534C22⋊Q8—58no—
535C22⋊Q8—516no—
536C22⋊Q8—532no—
537C22⋊Q8—532no—
538C22⋊Q8—516no—
539C22⋊Q8—58no—
540C22⋊Q8—532no—
541C22⋊Q8—516no—
542C4×Q8—58no—
543C4×Q8—516no—
544C4×Q8—532no—
545C4×Q8—516no—
546C4×Q8—532no—
547C4×Q8—532no—
548C4×Q8—516no—
549C4×Q8—516no—
550C4×Q8—516no—
551C4×Q8—58no—
552C4×Q8C22×D518yes—
553C4×Q8C22×D5116yes—
554C4×Q8C22×D5116yes—
555C4×Q8C22×D518yes—
556C4×D4—516no—
557C4×D4—58no—
558C4×D4—516no—
559C4×D4—58no—
560#117—58no—
561#117—516no—
562#117—532no—
563#117—516no—
564#117—516no—
565#117—516no—
566#117—532no—
567#117—532no—
568C2×C4⋊C4—54no—
569C2×C4⋊C4—52no—
570C2×C4⋊C4—54no—
571C2×C4⋊C4—52no—
572C2×C4⋊C4—52no—
573C2×C4⋊C4—51no—
574C2×C4⋊C4—51no—
575C2×C4⋊C4—52no—
576C2×C4⋊C4—52no—
577C2×C4⋊C4—52no—
578C2×C4⋊C4—54no—
579C2×C4⋊C4—54no—
580C2×C4⋊C4—54no—
581C2×C4⋊C4—54no—
582C2×C4⋊C4—54no—
583C2×C4⋊C4—52no—
584C2×C4⋊C4—52no—
585C2×C4⋊C4—52no—
586C2×C4⋊C4—516no—
587C2×C4⋊C4—516no—
588C2×C4⋊C4C22×D512yes—
589C2×C4⋊C4C22×D512yes—
590C2×C4⋊C4C22×D511yescharacteristic
591C2×C4⋊C4C22×D511yescharacteristic
592C2×C4⋊C4C22×D512yes—
593C2×C4⋊C4C22×D514yes—
594C2×C4⋊C4C22×D514yes—
595C2×C4⋊C4C22×D514yes—
596C2×C4⋊C4C22×D512yes—
597C2×C22⋊C4—52no—
598C2×C22⋊C4—52no—
599C2×C22⋊C4—52no—
600C2×C22⋊C4—52no—
601C2×C22⋊C4—52no—
602C2×C22⋊C4—54no—
603C2×C22⋊C4—54no—
604C2×C22⋊C4—54no—
605C2×C22⋊C4—54no—
606C2×C42—52no—
607C2×C42—54no—
608C2×C42—54no—
609C2×C42—54no—
610C2×C42—51no—
611C2×C42—52no—
612C2×C42—52no—
613C2×C42—51no—
614C2×C42—51no—
615C2×C42—58no—
616C2×C42—516no—
617C2×C42C22×D514yes—
618C2×C42C22×D512yes—
619C2×C42C22×D512yes—
620C2×C42C22×D511yescharacteristic
621C22×C5C22×#4112yes—
622C22×C5C2×2−1+412yes—
623C22×C5C2×2−1+412yes—
624C22×C5C2611yescharacteristic
625C2×D5—22no—
626C2×D5—22no—
627C2×D5—28no—
628C2×D5—24no—
629C2×D5—24no—
630C2×D5—24no—
631C2×D5—48no—
632C2×D5C22×#4114yes—
633C4×C5—28no—
634C4×C5—24no—
635C4×C5—24no—
636C4×C5—24no—
637C4×C5—22no—
638C4×C5—24no—
639C4×C5C22×#4114yes—
640C4×C5C2×2−1+414yes—
641Dic5—28no—
642Dic5—24no—
643Dic5—24no—
644Dic5—24no—
645Dic5—22no—
646Dic5C22×#4114yes—
647Dic5C2×2−1+414yes—
648C24—51no—
649C24—52no—
650#41—1032no—
651C2×Q8—24no—
652C2×Q8—28no—
653C2×Q8—24no—
654C2×Q8—58no—
655C2×Q8—54no—
656C2×Q8—516no—
657C2×Q8—58no—
658C2×Q8—1016no—
659C2×Q8—108no—
660C2×Q8—1064no—
661C2×Q8—104no—
662C2×Q8—108no—
663C2×Q8C23×D518yes—
664C2×Q8C23×D514yes—
665C2×Q8C23×D514yes—
666C2×D4—58no—
667C2×D4—54no—
668C2×D4—108no—
669C2×D4—104no—
670C22×C4—51no—
671C22×C4—51no—
672C22×C4—58no—
673C22×C4—54no—
674C22×C4—52no—
675C22×C4—52no—
676C22×C4—52no—
677C22×C4—51no—
678C22×C4—54no—
679C22×C4—54no—
680C22×C4—54no—
681C22×C4—58no—
682C22×C4—58no—
683C22×C4—58no—
684C22×C4—516no—
685C22×C4—108no—
686C22×C4—104no—
687C22×C4—108no—
688C22×C4—1016no—
689C22×C4—104no—
690C22×C4—108no—
691C22×C4C23×D512yes—
692C22×C4C23×D512yes—
693C22×C4C23×D511yescharacteristic
694C22×C4C23×D514yes—
695C22×C4C23×D512yes—
696C22×C4C23×D512yes—
697C22×C4C23×D511yescharacteristic
698C22×C4C23×D511yescharacteristic
699C4⋊C4—516no—
700C4⋊C4—58no—
701C4⋊C4—516no—
702C4⋊C4—58no—
703C4⋊C4—58no—
704C4⋊C4—54no—
705C4⋊C4—54no—
706C4⋊C4—58no—
707C4⋊C4—58no—
708C4⋊C4—58no—
709C4⋊C4—516no—
710C4⋊C4—516no—
711C4⋊C4—516no—
712C4⋊C4—516no—
713C4⋊C4—516no—
714C4⋊C4—58no—
715C4⋊C4—58no—
716C4⋊C4—58no—
717C4⋊C4C23×D518yes—
718C4⋊C4C23×D518yes—
719C4⋊C4C23×D514yes—
720C4⋊C4C23×D514yes—
721C4⋊C4C23×D518yes—
722C4⋊C4C23×D5116yes—
723C4⋊C4C23×D5116yes—
724C4⋊C4C23×D5116yes—
725C4⋊C4C23×D518yes—
726C22⋊C4—58no—
727C22⋊C4—58no—
728C22⋊C4—58no—
729C22⋊C4—58no—
730C22⋊C4—58no—
731C22⋊C4—516no—
732C22⋊C4—516no—
733C22⋊C4—516no—
734C22⋊C4—516no—
735C42—54no—
736C42—58no—
737C42—54no—
738C42—58no—
739C42—54no—
740C42—516no—
741C42—516no—
742C42—516no—
743C42—58no—
744C42C23×D518yes—
745C42C23×D514yes—
746C42C23×D5116yes—
747C42C23×D518yes—
748C2×C5#350914yescomplemented
749C2×C5C23×#4111yescharacteristic
750C2×C5C22×2−1+411yescharacteristic
751C2×C5C22×2−1+411yescharacteristic
752D5—24no—
753D5—44no—
754C23—54no—
755C23—52no—
756C23—54no—
757C23—102no—
758C23—102no—
759C23—104no—
760C23—104no—
761C23—104no—
762C23C24×D511yescharacteristic
763Q8—28no—
764Q8—216no—
765Q8—28no—
766Q8—1032no—
767Q8—1016no—
768Q8—108no—
769Q8—1016no—
770D4—1016no—
771D4—108no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—54no—
779C2×C4—54no—
780C2×C4—52no—
781C2×C4—52no—
782C2×C4—516no—
783C2×C4—54no—
784C2×C4—54no—
785C2×C4—54no—
786C2×C4—52no—
787C2×C4—58no—
788C2×C4—1016no—
789C2×C4—108no—
790C2×C4—1016no—
791C2×C4—1032no—
792C2×C4—104no—
793C2×C4—102no—
794C2×C4—104no—
795C2×C4—108no—
796C2×C4—104no—
797C2×C4—108no—
798C2×C4—1016no—
799C2×C4#414714yes—
800C2×C4D5×#4114yes—
801C2×C4C24×D514yes—
802C2×C4C24×D514yes—
803C2×C4C24×D512yes—
804C2×C4C24×D518yes—
805C2×C4C24×D514yes—
806C2×C4C24×D514yes—
807C2×C4C24×D512yes—
808C2×C4C24×D512yes—
809C5C2×#350911yescharacteristic, complemented, Sylow
810C22—54no—
811C22—102no—
812C22—108no—
813C22—102no—
814C22—104no—
815C22—104no—
816C22—104no—
817C22—208no—
818C22C2×#414712yes—
819C22C2×D5×#4112yes—
820C22D5×2−1+412yes—
821C22C25×D511yescharacteristic
822C4—24no—
823C4—24no—
824C4—28no—
825C4—24no—
826C4—22no—
827C4—24no—
828C4—54no—
829C4—54no—
830C4—104no—
831C4—102no—
832C4—104no—
833C4—108no—
834C4—104no—
835C4C2×#414714yes—
836C4C2×D5×#4114yes—
837C2—104no—
838C2—204no—
839C2#1061892114yesdirect product factor
840C2C22×#414711yescharacteristic
841C2C22×D5×#4111yescharacteristic
842C2C2×D5×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#557C2
socleC23×C5C25
prime radicalC22×#713C22
hypercenterC2×#557D5
hypocenterC5C2×#3509
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. #10618921C2direct (N × H)
4. C2×D5×C4⋊Q8C2semidirect
5. C2×#66055C2semidirect
6. C2×#66066C2semidirect
7. C2×#66028C2semidirect
8. C2×#66027C2semidirect
9. C2×#66030C2semidirect
10. C2×#66022C2semidirect
11. C2×#65915C2semidirect
12. C2×#65912C2semidirect
13. C2×#65912C2semidirect
14. C2×#65906C2semidirect
15. C2×#65901C2semidirect
16. C2×#65902C2semidirect
17. C2×#65918C2semidirect
21. C5×#557C22semidirect
38. #66066C22semidirect
40. D5×C4⋊Q8C22semidirect
41. #66055C22semidirect
42. #66030C22semidirect
43. #66028C22semidirect
44. #66027C22semidirect
45. #66022C22semidirect
46. #65918C22semidirect
47. #65915C22semidirect
48. #65912C22semidirect
49. #65912C22semidirect
51. #65906C22semidirect
52. #65902C22semidirect
53. #65901C22semidirect
237. C2×#557D5semidirect
356. #557C2×D5semidirect
748. C2×C5#3509semidirect
809. C5C2×#3509semidirect
839. C2#10618921direct (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
#106189212
C2×#660582
C2×D5×C4⋊Q82
C2×#660552
C2×#660662
C2×#660282
C2×#660272
C2×#660302
C2×#660222
C2×#659152
C2×#659122
C2×#659062
C2×#659012
C2×#659022
C2×#659182
C2×C4×#7132
C2×#35095