Finite Group Databasebeta

← C2×#10618928 #13007135

Subgroups — C2×#10618928 #13007135

Order 1280.

6338 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#557C211yesmaximal, characteristic, complemented
2#10618928C2132yesmaximal, direct product factor
3C2×#66065C212yesmaximal
4C2×#66055C211yesmaximal, characteristic, complemented
5C2×#66055C212yesmaximal, complemented
6C2×#66062C211yesmaximal, characteristic
7C2×#66031C212yesmaximal
8C2×C5⋊#564C214yesmaximal, complemented
9C2×#66019C212yesmaximal, complemented
10C2×#66030C214yesmaximal
11C2×#65917C212yesmaximal
12C2×#65917C212yesmaximal
13C2×#65912C211yesmaximal, characteristic
14C2×#65912C211yesmaximal, characteristic
15C2×#65903C212yesmaximal, complemented
16C2×#65901C212yesmaximal, complemented
17C2×#65901C211yesmaximal, characteristic, complemented
18C2×#65904C211yesmaximal, characteristic, complemented
19C5×#557C22116yescomplemented
20C2×C5×C4⋊Q8C2211yescharacteristic
21C2×C5×C4⋊Q8C2212yes—
22C2×C5×#125C2214yes—
23C2×C5×#125C2212yes—
24C2×C4×C5×Q8C2211yescharacteristic
25C2×C4×C5×Q8C2211yescharacteristic
26C2×C4×C5×Q8C2212yes—
27C2×C4×C5×Q8C2212yes—
28C2×#4092C2211yescharacteristic
29C2×#4092C2211yescharacteristic
30C2×#4092C2212yes—
31C2×Q8×Dic5C2212yes—
32C2×Q8×Dic5C2212yes—
33C2×Q8×Dic5C2212yes—
34C2×#4090C2211yescharacteristic
35C2×#4090C2212yes—
36C2×#4090C2211yescharacteristic
37C2×#4090C2212yes—
38#66065C22132yes—
39#66062C22116yes—
40#66055C22116yescomplemented
41#66055C22132yescomplemented
42#66031C22132yes—
43#66030C22164yes—
44C5⋊#564C22164yescomplemented
45#66019C22132yescomplemented
46#65917C22132yes—
47#65917C22132yes—
48#65912C22116yes—
49#65912C22116yes—
50#65904C22116yescomplemented
51#65903C22132yescomplemented
52#65901C22116yescomplemented
53#65901C22132yescomplemented
54C2×#4044C2214yes—
55C2×#4044C2214yes—
56C2×#4044C2214yes—
57C2×#4043C2211yescharacteristic
58C2×#4043C2211yescharacteristic
59C2×#4043C2212yes—
60C2×#4042C2212yes—
61C2×#4042C2212yes—
62C2×#4038C2212yes—
63C2×#4036C2212yes—
64C2×#4036C2214yes—
65C2×#4036C2214yes—
66C2×#4036C2212yes—
67C2×#4036C2212yes—
68C2×#4036C2214yes—
69C2×#4035C2214yes—
70C2×#4035C2214yes—
71C2×#4035C2214yes—
72C2×#4035C2212yes—
73C2×#4035C2212yes—
74C2×#4035C2214yes—
75C2×#4035C2214yes—
76C2×#4035C2214yes—
77C2×#4035C2214yes—
78C2×#4034C2211yescharacteristic
79C2×#4034C2214yes—
80C2×#4034C2211yescharacteristic
81C2×#4033C2212yes—
82C2×#4033C2212yes—
83C2×#4033C2212yes—
84C2×#4033C2214yes—
85C2×#4022C2214yes—
86C2×#4018C2212yes—
87C2×#4018C2212yes—
88C2×C42×D5C2211yescharacteristic
89C2×#4016C2212yes—
90C2×#4016C2214yes—
91C2×#4016C2214yes—
92C2×#4015C2212yes—
93C2×#4015C2211yescharacteristic
94C2×C4×Dic10C2211yescharacteristic
95C2×C4×Dic10C2212yes—
96C2×C4×Dic10C2214yes—
97C2×C4×Dic10C2212yes—
98C2×C4×Dic10C2211yescharacteristic
99C2×C4×Dic10C2212yes—
100C2×C4×Dic10C2212yes—
101C2×#3556—51nomaximal, Sylow
102C22×C5×Q8C2311yescharacteristic
103C22×C5×Q8C2311yescharacteristic
104C22×C5×Q8C2312yes—
105C22×C4×D5C2311yescharacteristic
106C22×C4×D5C2311yescharacteristic
107C22×C4×D5C2311yescharacteristic
108C22×Dic10C2312yes—
109C22×Dic10C2311yescharacteristic
110C22×Dic10C2311yescharacteristic
111C22×Dic10C2312yes—
112C22×Dic10C2312yes—
113C5×C4⋊Q8C2318yes—
114C5×C4⋊Q8C23116yes—
115C5×#125C23116yes—
116C5×#125C23132yes—
117C4×C5×Q8C2318yes—
118C4×C5×Q8C23116yes—
119C4×C5×Q8C23116yes—
120C4×C5×Q8C2318yes—
121C2×C5×C4⋊C4C2311yescharacteristic
122C2×C5×C4⋊C4C2312yes—
123C2×C5×C4⋊C4C2314yes—
124C2×C5×C4⋊C4C2314yes—
125C2×C5×C4⋊C4C2311yescharacteristic
126C2×C5×C4⋊C4C2312yes—
127C2×C5×C4⋊C4C2314yes—
128C2×C5×C4⋊C4C2312yes—
129C2×C5×C4⋊C4C2312yes—
130C2×C42×C5C2311yescharacteristic
131C2×C42×C5C2312yes—
132C2×C42×C5C2312yes—
133C2×C42×C5C2314yes—
134#4092C23116yes—
135#4092C2318yes—
136#4092C2318yes—
137Q8×Dic5C23116yes—
138Q8×Dic5C23116yes—
139Q8×Dic5C23116yes—
140#4090C2318yes—
141#4090C23116yes—
142#4090C2318yes—
143#4090C23116yes—
144C2×#685C2312yes—
145C2×#685C2312yes—
146C2×#685C2312yes—
147C2×#685C2312yes—
148C2×#685C2314yes—
149C2×C4⋊Dic5C2311yescharacteristic
150C2×C4⋊Dic5C2314yes—
151C2×C4⋊Dic5C2312yes—
152C2×C4⋊Dic5C2311yescharacteristic
153C2×C4⋊Dic5C2312yes—
154C2×C4⋊Dic5C2312yes—
155C2×C4⋊Dic5C2312yes—
156C2×C4⋊Dic5C2314yes—
157C2×C4⋊Dic5C2314yes—
158C2×C4⋊Dic5C2314yes—
159C2×#683C2312yes—
160C2×#683C2312yes—
161C2×#683C2314yes—
162C2×#683C2314yes—
163C2×#683C2314yes—
164C2×#683C2312yes—
165C2×#683C2312yes—
166C2×#683C2312yes—
167C2×#683C2312yes—
168C2×#683C2312yes—
169C2×#683C2312yes—
170C2×#683C2314yes—
171C2×#683C2314yes—
172C2×#683C2314yes—
173C2×#683C2312yes—
174C2×#683C2312yes—
175C2×#683C2314yes—
176C2×C4×Dic5C2311yescharacteristic
177C2×C4×Dic5C2311yescharacteristic
178C2×C4×Dic5C2312yes—
179C2×C4×Dic5C2312yes—
180C2×C4×Dic5C2314yes—
181C2×C4×Dic5C2314yes—
182C2×C4×Dic5C2314yes—
183C2×C4×Dic5C2314yes—
184C2×C4×Dic5C2311yescharacteristic
185#4044C23132yes—
186#4044C23132yes—
187#4044C23132yes—
188#4043C23116yes—
189#4043C2318yes—
190#4043C2318yes—
191#4042C23116yes—
192#4042C23116yes—
193#4038C23116yes—
194#4036C23116yes—
195#4036C23132yes—
196#4036C23116yes—
197#4036C23116yes—
198#4036C23132yes—
199#4036C23132yes—
200#4035C23132yes—
201#4035C23132yes—
202#4035C23132yes—
203#4035C23132yes—
204#4035C23132yes—
205#4035C23132yes—
206#4035C23116yes—
207#4035C23116yes—
208#4035C23132yes—
209#4034C2318yes—
210#4034C23132yes—
211#4034C2318yes—
212#4033C23116yes—
213#4033C23132yes—
214#4033C23116yes—
215#4033C23116yes—
216#4022C23132yes—
217#4018C23116yes—
218#4018C23116yes—
219C42×D5C2318yes—
220#4016C23116yes—
221#4016C23132yes—
222#4016C23132yes—
223#4015C2318yes—
224#4015C23116yes—
225C4×Dic10C2318yes—
226C4×Dic10C23116yes—
227C4×Dic10C23116yes—
228C4×Dic10C2318yes—
229C4×Dic10C23132yes—
230C4×Dic10C23116yes—
231C4×Dic10C23116yes—
232#3556—532no—
233C2×#564—54no—
234C2×#557—52no—
235C2×#557—51no—
236C2×#557—52no—
237C2×#557—51no—
238C2×#557—52no—
239C2×#557—51no—
240C2×#557—52no—
241C2×#557D511yescharacteristic, complemented
242C2×#541—52no—
243C2×#541—54no—
244C2×#541—52no—
245C2×#541—52no—
246C2×#541—52no—
247C2×#533—51no—
248C2×#533—51no—
249C2×#533—51no—
250C23×D5C2411yescharacteristic
251C2×C5×Q8—24no—
252C2×C5×Q8—24no—
253C2×C5×Q8—28no—
254C2×C5×Q8C2414yes—
255C2×C5×Q8C2418yes—
256C2×C5×Q8C2414yes—
257C22×C4×C5C2412yes—
258C22×C4×C5C2412yes—
259C22×C4×C5C2412yes—
260C22×C4×C5C2411yescharacteristic
261C22×C4×C5C2412yes—
262C22×C4×C5C2414yes—
263C22×C4×C5C2411yescharacteristic
264C22×C4×C5C2411yescharacteristic
265C22×Dic5C2412yes—
266C22×Dic5C2412yes—
267C22×Dic5C2412yes—
268C22×Dic5C2412yes—
269C22×Dic5C2414yes—
270C22×Dic5C2411yescharacteristic
271C22×Dic5C2411yescharacteristic
272C22×Dic5C2411yescharacteristic
273C2×C4×D5—24no—
274C2×C4×D5—24no—
275C2×C4×D5—24no—
276C2×C4×D5C2414yes—
277C2×C4×D5C2414yes—
278C2×C4×D5C2414yes—
279C2×Dic10—24no—
280C2×Dic10—28no—
281C2×Dic10—24no—
282C2×Dic10—28no—
283C2×Dic10—28no—
284C2×Dic10C2418yes—
285C2×Dic10C2414yes—
286C2×Dic10C2414yes—
287C2×Dic10C2418yes—
288C2×Dic10C2418yes—
289C5×C4⋊C4C2414yes—
290C5×C4⋊C4C2414yes—
291C5×C4⋊C4C24116yes—
292C5×C4⋊C4C2418yes—
293C5×C4⋊C4C2418yes—
294C5×C4⋊C4C2418yes—
295C5×C4⋊C4C24116yes—
296C5×C4⋊C4C24116yes—
297C5×C4⋊C4C2418yes—
298C42×C5C2418yes—
299C42×C5C24116yes—
300C42×C5C2414yes—
301C42×C5C2418yes—
302#685C2418yes—
303#685C2418yes—
304#685C2418yes—
305#685C2418yes—
306#685C24116yes—
307C4⋊Dic5C2414yes—
308C4⋊Dic5C24116yes—
309C4⋊Dic5C2418yes—
310C4⋊Dic5C2414yes—
311C4⋊Dic5C2418yes—
312C4⋊Dic5C2418yes—
313C4⋊Dic5C2418yes—
314C4⋊Dic5C24116yes—
315C4⋊Dic5C24116yes—
316C4⋊Dic5C24116yes—
317#683C2418yes—
318#683C2418yes—
319#683C24116yes—
320#683C24116yes—
321#683C24116yes—
322#683C2418yes—
323#683C2418yes—
324#683C2418yes—
325#683C2418yes—
326#683C2418yes—
327#683C2418yes—
328#683C24116yes—
329#683C24116yes—
330#683C24116yes—
331#683C2418yes—
332#683C2418yes—
333#683C24116yes—
334C4×Dic5C2414yes—
335C4×Dic5C2414yes—
336C4×Dic5C2418yes—
337C4×Dic5C2418yes—
338C4×Dic5C24116yes—
339C4×Dic5C24116yes—
340C4×Dic5C24116yes—
341C4×Dic5C24116yes—
342C4×Dic5C2414yes—
343#564—564no—
344#557—532no—
345#557—516no—
346#557—532no—
347#557—532no—
348#557—516no—
349#557—532no—
350#557—516no—
351#557C2×D5116yescomplemented
352#541—532no—
353#541—564no—
354#541—532no—
355#541—532no—
356#541—532no—
357#533—516no—
358#533—516no—
359#533—516no—
360C2×C4⋊Q8—51no—
361C2×C4⋊Q8—51no—
362C2×C4⋊Q8—52no—
363C2×C4⋊Q8—52no—
364C2×C4⋊Q8—51no—
365C2×C4⋊Q8—51no—
366C2×C4⋊Q8—54no—
367C2×C4⋊Q8—51no—
368C2×C4⋊Q8—52no—
369C2×C4⋊Q8C2×D511yescharacteristic
370C2×C4⋊Q8C2×D512yes—
371C2×#126—54no—
372C2×#126—54no—
373C2×#126—54no—
374C2×#126—54no—
375C2×#125—52no—
376C2×#125—52no—
377C2×#125—54no—
378C2×#125—54no—
379C2×#125—54no—
380C2×#125—54no—
381C2×#125—54no—
382C2×#125—54no—
383C2×#125—54no—
384C2×#125—52no—
385C2×#125—52no—
386C2×#125—52no—
387C2×#125—54no—
388C2×#125—54no—
389C2×#125—54no—
390C2×#125—52no—
391C2×#125—54no—
392C2×#125—54no—
393C2×#125C2×D512yes—
394C2×#125C2×D514yes—
395C2×C22⋊Q8—51no—
396C2×C22⋊Q8—52no—
397C2×C22⋊Q8—51no—
398C2×C22⋊Q8—52no—
399C2×C22⋊Q8—52no—
400C2×C22⋊Q8—52no—
401C2×C22⋊Q8—51no—
402C2×C22⋊Q8—51no—
403C2×C4×Q8—52no—
404C2×C4×Q8—52no—
405C2×C4×Q8—52no—
406C2×C4×Q8—52no—
407C2×C4×Q8—54no—
408C2×C4×Q8—52no—
409C2×C4×Q8—52no—
410C2×C4×Q8—51no—
411C2×C4×Q8—51no—
412C2×C4×Q8—52no—
413C2×C4×Q8—52no—
414C2×C4×Q8—54no—
415C2×C4×Q8—52no—
416C2×C4×Q8—52no—
417C2×C4×Q8C2×D511yescharacteristic
418C2×C4×Q8C2×D511yescharacteristic
419C2×C4×Q8C2×D512yes—
420C2×C4×Q8C2×D512yes—
421C2×#117—52no—
422C2×#117—52no—
423C2×#117—52no—
424C22×C42—51no—
425C23×C5C2511yescharacteristic
426C22×D5—22no—
427C22×D5—22no—
428C22×D5—22no—
429C22×D5C2512yes—
430C5×Q8—28no—
431C5×Q8—216no—
432C5×Q8—28no—
433C2×C4×C5—24no—
434C2×C4×C5—24no—
435C2×C4×C5—22no—
436C2×C4×C5—24no—
437C2×C4×C5—24no—
438C2×C4×C5—28no—
439C2×C4×C52−1+414yes—
440C2×C4×C52−1+414yes—
441C2×C4×C5C2518yes—
442C2×C4×C5C2514yes—
443C2×C4×C5C2514yes—
444C2×C4×C5C2512yes—
445C2×C4×C5C2514yes—
446C2×C4×C5C2514yes—
447C2×C4×C5C2512yes—
448C2×C4×C5C2512yes—
449C2×Dic5—24no—
450C2×Dic5—28no—
451C2×Dic5—24no—
452C2×Dic5—24no—
453C2×Dic5—24no—
454C2×Dic5—22no—
455C2×Dic5—22no—
456C2×Dic52−1+414yes—
457C2×Dic5C2514yes—
458C2×Dic5C2514yes—
459C2×Dic5C2514yes—
460C2×Dic5C2514yes—
461C2×Dic5C2518yes—
462C2×Dic5C2512yes—
463C2×Dic5C2512yes—
464C2×Dic5C2512yes—
465C4×D5—28no—
466C4×D5—28no—
467C4×D5—28no—
468Dic10—28no—
469Dic10—216no—
470Dic10—28no—
471Dic10—216no—
472Dic10—216no—
473C22×Q8—52no—
474C22×Q8—52no—
475C22×Q8—52no—
476C22×Q8—51no—
477C22×Q8—51no—
478C22×Q8C22×D512yes—
479C22×Q8C22×D511yescharacteristic
480C22×Q8C22×D511yescharacteristic
481C23×C4—51no—
482C23×C4—51no—
483C23×C4—51no—
484C4⋊Q8—58no—
485C4⋊Q8—58no—
486C4⋊Q8—516no—
487C4⋊Q8—516no—
488C4⋊Q8—58no—
489C4⋊Q8—58no—
490C4⋊Q8—532no—
491C4⋊Q8—58no—
492C4⋊Q8—516no—
493C4⋊Q8C22×D518yes—
494C4⋊Q8C22×D5116yes—
495#126—532no—
496#126—532no—
497#126—532no—
498#126—532no—
499#125—516no—
500#125—516no—
501#125—516no—
502#125—532no—
503#125—516no—
504#125—516no—
505#125—532no—
506#125—532no—
507#125—532no—
508#125—532no—
509#125—532no—
510#125—532no—
511#125—532no—
512#125—532no—
513#125—532no—
514#125—516no—
515#125—532no—
516#125—532no—
517#125C22×D5116yes—
518#125C22×D5132yes—
519C22⋊Q8—516no—
520C22⋊Q8—58no—
521C22⋊Q8—58no—
522C22⋊Q8—516no—
523C22⋊Q8—516no—
524C22⋊Q8—516no—
525C22⋊Q8—58no—
526C22⋊Q8—58no—
527C4×Q8—516no—
528C4×Q8—516no—
529C4×Q8—516no—
530C4×Q8—516no—
531C4×Q8—532no—
532C4×Q8—516no—
533C4×Q8—516no—
534C4×Q8—516no—
535C4×Q8—516no—
536C4×Q8—58no—
537C4×Q8—58no—
538C4×Q8—532no—
539C4×Q8—516no—
540C4×Q8—516no—
541C4×Q8C22×D518yes—
542C4×Q8C22×D518yes—
543C4×Q8C22×D5116yes—
544C4×Q8C22×D5116yes—
545#117—516no—
546#117—516no—
547#117—516no—
548C2×C4⋊C4—52no—
549C2×C4⋊C4—52no—
550C2×C4⋊C4—52no—
551C2×C4⋊C4—52no—
552C2×C4⋊C4—52no—
553C2×C4⋊C4—52no—
554C2×C4⋊C4—52no—
555C2×C4⋊C4—51no—
556C2×C4⋊C4—52no—
557C2×C4⋊C4—51no—
558C2×C4⋊C4—52no—
559C2×C4⋊C4—52no—
560C2×C4⋊C4—54no—
561C2×C4⋊C4—52no—
562C2×C4⋊C4—52no—
563C2×C4⋊C4—54no—
564C2×C4⋊C4—52no—
565C2×C4⋊C4—52no—
566C2×C4⋊C4—54no—
567C2×C4⋊C4—54no—
568C2×C4⋊C4—54no—
569C2×C4⋊C4—54no—
570C2×C4⋊C4—54no—
571C2×C4⋊C4—54no—
572C2×C4⋊C4—54no—
573C2×C4⋊C4—54no—
574C2×C4⋊C4—54no—
575C2×C4⋊C4C22×D512yes—
576C2×C4⋊C4C22×D512yes—
577C2×C4⋊C4C22×D511yescharacteristic
578C2×C4⋊C4C22×D514yes—
579C2×C4⋊C4C22×D511yescharacteristic
580C2×C4⋊C4C22×D512yes—
581C2×C4⋊C4C22×D512yes—
582C2×C4⋊C4C22×D514yes—
583C2×C4⋊C4C22×D514yes—
584C2×C22⋊C4—54no—
585C2×C22⋊C4—52no—
586C2×C22⋊C4—52no—
587C2×C22⋊C4—52no—
588C2×C22⋊C4—52no—
589C2×C42—54no—
590C2×C42—52no—
591C2×C42—52no—
592C2×C42—51no—
593C2×C42—51no—
594C2×C42—54no—
595C2×C42—54no—
596C2×C42—54no—
597C2×C42—51no—
598C2×C42—58no—
599C2×C42C22×D512yes—
600C2×C42C22×D512yes—
601C2×C42C22×D511yescharacteristic
602C2×C42C22×D514yes—
603C22×C5C2×2−1+412yes—
604C22×C5C2×2−1+412yes—
605C22×C5C2×2−1+412yes—
606C22×C5C2611yescharacteristic
607C2×D5—22no—
608C2×D5—22no—
609C2×D5—22no—
610C2×D5—44no—
611C4×C5—24no—
612C4×C5—24no—
613C4×C5—22no—
614C4×C5—24no—
615C4×C5—28no—
616C4×C5—24no—
617C4×C5C2×2−1+414yes—
618C4×C5C2×2−1+414yes—
619Dic5—24no—
620Dic5—28no—
621Dic5—24no—
622Dic5—24no—
623Dic5—24no—
624Dic5—22no—
625Dic5—22no—
626Dic5C2×2−1+414yes—
627C24—51no—
628C2×Q8—24no—
629C2×Q8—28no—
630C2×Q8—24no—
631C2×Q8—58no—
632C2×Q8—58no—
633C2×Q8—58no—
634C2×Q8—54no—
635C2×Q8—54no—
636C2×Q8—108no—
637C2×Q8—108no—
638C2×Q8—108no—
639C2×Q8—104no—
640C2×Q8—104no—
641C2×Q8C23×D518yes—
642C2×Q8C23×D514yes—
643C2×Q8C23×D514yes—
644C22×C4—51no—
645C22×C4—52no—
646C22×C4—54no—
647C22×C4—52no—
648C22×C4—52no—
649C22×C4—52no—
650C22×C4—51no—
651C22×C4—51no—
652C22×C4—54no—
653C22×C4—54no—
654C22×C4—54no—
655C22×C4—104no—
656C22×C4—104no—
657C22×C4—104no—
658C22×C4C23×D514yes—
659C22×C4C23×D512yes—
660C22×C4C23×D512yes—
661C22×C4C23×D511yescharacteristic
662C22×C4C23×D512yes—
663C22×C4C23×D512yes—
664C22×C4C23×D511yescharacteristic
665C22×C4C23×D511yescharacteristic
666C4⋊C4—58no—
667C4⋊C4—58no—
668C4⋊C4—58no—
669C4⋊C4—58no—
670C4⋊C4—58no—
671C4⋊C4—58no—
672C4⋊C4—58no—
673C4⋊C4—54no—
674C4⋊C4—58no—
675C4⋊C4—54no—
676C4⋊C4—58no—
677C4⋊C4—58no—
678C4⋊C4—516no—
679C4⋊C4—58no—
680C4⋊C4—58no—
681C4⋊C4—516no—
682C4⋊C4—58no—
683C4⋊C4—58no—
684C4⋊C4—516no—
685C4⋊C4—516no—
686C4⋊C4—516no—
687C4⋊C4—516no—
688C4⋊C4—516no—
689C4⋊C4—516no—
690C4⋊C4—516no—
691C4⋊C4—516no—
692C4⋊C4—516no—
693C4⋊C4C23×D518yes—
694C4⋊C4C23×D518yes—
695C4⋊C4C23×D514yes—
696C4⋊C4C23×D5116yes—
697C4⋊C4C23×D514yes—
698C4⋊C4C23×D518yes—
699C4⋊C4C23×D518yes—
700C4⋊C4C23×D5116yes—
701C4⋊C4C23×D5116yes—
702C22⋊C4—516no—
703C22⋊C4—58no—
704C22⋊C4—58no—
705C22⋊C4—58no—
706C22⋊C4—58no—
707C42—54no—
708C42—54no—
709C42—54no—
710C42—516no—
711C42—58no—
712C42—58no—
713C42—516no—
714C42—516no—
715C42—516no—
716C42C23×D514yes—
717C42C23×D518yes—
718C42C23×D518yes—
719C42C23×D5116yes—
720C2×C5#355614yescomplemented
721C2×C5C22×2−1+411yescharacteristic
722C2×C5C22×2−1+411yescharacteristic
723C2×C5C22×2−1+411yescharacteristic
724D5—42no—
725C23—52no—
726C23—102no—
727C23—102no—
728C23—102no—
729C23C24×D511yescharacteristic
730Q8—28no—
731Q8—216no—
732Q8—28no—
733Q8—1016no—
734Q8—1016no—
735Q8—1016no—
736Q8—108no—
737Q8—108no—
738C2×C4—24no—
739C2×C4—28no—
740C2×C4—24no—
741C2×C4—22no—
742C2×C4—24no—
743C2×C4—24no—
744C2×C4—54no—
745C2×C4—52no—
746C2×C4—54no—
747C2×C4—58no—
748C2×C4—54no—
749C2×C4—54no—
750C2×C4—54no—
751C2×C4—52no—
752C2×C4—52no—
753C2×C4—108no—
754C2×C4—102no—
755C2×C4—104no—
756C2×C4—108no—
757C2×C4—102no—
758C2×C4—104no—
759C2×C4—104no—
760C2×C4—104no—
761C2×C4—108no—
762C2×C4—108no—
763C2×C4#414714yes—
764C2×C4#415014yes—
765C2×C4C24×D518yes—
766C2×C4C24×D514yes—
767C2×C4C24×D514yes—
768C2×C4C24×D512yes—
769C2×C4C24×D514yes—
770C2×C4C24×D514yes—
771C2×C4C24×D512yes—
772C2×C4C24×D512yes—
773C5C2×#355611yescharacteristic, complemented, Sylow
774C22—102no—
775C22—102no—
776C22—102no—
777C22—204no—
778C22C2×#414712yes—
779C22C2×#415012yes—
780C22D5×2−1+412yes—
781C22C25×D511yescharacteristic
782C4—24no—
783C4—28no—
784C4—24no—
785C4—22no—
786C4—24no—
787C4—24no—
788C4—54no—
789C4—102no—
790C4—104no—
791C4—108no—
792C4—102no—
793C4—104no—
794C4—104no—
795C4—104no—
796C4C2×#414714yes—
797C4C2×#415014yes—
798C2—202no—
799C2#1061892814yesdirect product factor
800C2C22×#414711yescharacteristic
801C2C22×#415011yescharacteristic
802C2C2×D5×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#557C2
socleC23×C5C25
prime radicalC23×D5C24
hypercenterC2×#557D5
hypocenterC5C2×#3556
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. #10618928C2direct (N × H)
4. C2×#66055C2semidirect
5. C2×#66055C2semidirect
8. C2×C5⋊#564C2semidirect
9. C2×#66019C2semidirect
15. C2×#65903C2semidirect
16. C2×#65901C2semidirect
17. C2×#65901C2semidirect
18. C2×#65904C2semidirect
19. C5×#557C22semidirect
40. #66055C22semidirect
41. #66055C22semidirect
44. C5⋊#564C22semidirect
45. #66019C22semidirect
50. #65904C22semidirect
51. #65903C22semidirect
52. #65901C22semidirect
53. #65901C22semidirect
241. C2×#557D5semidirect
351. #557C2×D5semidirect
720. C2×C5#3556semidirect
773. C5C2×#3556semidirect
799. C2#10618928direct (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
#106189282
C2×#660652
C2×#660552
C2×#660622
C2×#660312
C2×C5⋊#5642
C2×#660192
C2×#660302
C2×#659172
C2×#659122
C2×#659032
C2×#659012
C2×#659042
C2×#35565