Finite Group Databasebeta

← C2×#10618750 #13007006

Subgroups — C2×#10618750 #13007006

Order 1280.

6446 conjugacy classes of subgroups.

The subgroup lattice has 1200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#552C211yesmaximal, characteristic, complemented
2#10618750C2132yesmaximal, direct product factor
3C2×#66046C212yesmaximal, complemented
4C2×#66035C212yesmaximal, complemented
5C2×#66023C211yesmaximal, characteristic, complemented
6C2×#66019C212yesmaximal, complemented
7C2×#66019C211yesmaximal, characteristic, complemented
8C2×#66030C212yesmaximal, complemented
9C2×#65985C212yesmaximal, complemented
10C2×#65996C212yesmaximal
11C2×#65973C211yesmaximal, characteristic, complemented
12C2×#65975C211yesmaximal, characteristic, complemented
13C2×#65959C211yesmaximal, characteristic, complemented
14C2×#65956C211yesmaximal, characteristic, complemented
15C2×#65917C211yesmaximal, characteristic, complemented
16C2×Q8×Dic10C211yesmaximal, characteristic, complemented
17C2×#65876C211yesmaximal, characteristic, complemented
18C2×#65872C211yesmaximal, characteristic
19C2×#65867C212yesmaximal, complemented
20C2×#65867C211yesmaximal, characteristic, complemented
21C2×#65852C212yesmaximal, complemented
22C2×#65851C211yesmaximal, characteristic, complemented
23C2×#65845C211yesmaximal, characteristic, complemented
24C2×#65834C211yesmaximal, characteristic, complemented
25C5×#552C22116yescomplemented
26C2×C5×#126C2212yes—
27C2×C5×#125C2212yes—
28C2×C5×#125C2211yescharacteristic
29C2×C5×#123C2212yes—
30C2×C5×C22⋊Q8C2211yescharacteristic
31C2×C5×C22⋊Q8C2211yescharacteristic
32C2×C4×C5×Q8C2211yescharacteristic
33C2×C4×C5×D4C2211yescharacteristic
34C2×C5×#117C2211yescharacteristic
35C2×C5×#117C2212yes—
36C22×C5×C4⋊C4C2211yescharacteristic
37C2×#4092C2211yescharacteristic
38C2×Q8×Dic5C2211yescharacteristic
39C2×Q8×Dic5C2211yescharacteristic
40C2×#4090C2211yescharacteristic
41C2×#4085C2211yescharacteristic
42C2×#4082C2212yes—
43C2×#4081C2211yescharacteristic
44C2×C4×C22⋊D5C2211yescharacteristic
45C2×C4×C22⋊D5C2212yes—
46C2×C4×C22⋊D5C2211yescharacteristic
47C2×#4072C2211yescharacteristic
48C2×#4072C2211yescharacteristic
49C2×#4072C2211yescharacteristic
50C2×#4070C2211yescharacteristic
51C2×#4070C2212yes—
52C2×#4070C2212yes—
53C2×#4070C2211yescharacteristic
54C2×#4070C2212yes—
55C22×C4×Dic5C2211yescharacteristic
56#66046C22132yescomplemented
57#66035C22132yescomplemented
58#66030C22132yescomplemented
59#66023C22116yescomplemented
60#66019C22116yescomplemented
61#66019C22132yescomplemented
62#65996C22132yes—
63#65985C22132yescomplemented
64#65975C22116yescomplemented
65#65973C22116yescomplemented
66#65959C22116yescomplemented
67#65956C22116yescomplemented
68#65917C22116yescomplemented
69Q8×Dic10C22116yescomplemented
70#65876C22116yescomplemented
71#65872C22116yes—
72#65867C22116yescomplemented
73#65867C22132yescomplemented
74#65852C22132yescomplemented
75#65851C22116yescomplemented
76C2×#4044C2212yes—
77C2×#4044C2212yes—
78C2×#4044C2211yescharacteristic
79#65845C22116yescomplemented
80C2×#4043C2211yescharacteristic
81C2×#4043C2212yes—
82C2×#4042C2212yes—
83C2×#4042C2212yes—
84C2×#4038C2211yescharacteristic
85C2×#4038C2212yes—
86C2×D5×C4⋊C4C2211yescharacteristic
87#65834C22116yescomplemented
88C2×#4036C2211yescharacteristic
89C2×#4036C2211yescharacteristic
90C2×#4036C2212yes—
91C2×#4036C2211yescharacteristic
92C2×#4036C2212yes—
93C2×#4035C2212yes—
94C2×#4035C2212yes—
95C2×#4035C2212yes—
96C2×#4035C2212yes—
97C2×#4035C2212yes—
98C2×#4035C2212yes—
99C2×#4035C2212yes—
100C2×#4035C2212yes—
101C2×#4035C2211yescharacteristic
102C2×#4034C2211yescharacteristic
103C2×#4034C2211yescharacteristic
104C2×#4034C2212yes—
105C2×#4034C2211yescharacteristic
106C2×#4034C2211yescharacteristic
107C2×#4034C2212yes—
108C2×#4034C2212yes—
109C2×#4034C2212yes—
110C2×#4034C2212yes—
111C2×#4033C2211yescharacteristic
112C2×#4033C2212yes—
113C2×#4033C2211yescharacteristic
114C2×#4033C2212yes—
115C2×#4033C2212yes—
116C2×#4033C2212yes—
117C2×#4032C2211yescharacteristic
118C2×#4031C2212yes—
119C2×#4031C2212yes—
120C2×#4031C2211yescharacteristic
121C2×#4029C2212yes—
122C2×#4025C2212yes—
123C2×#4025C2212yes—
124C2×#4025C2212yes—
125C2×#4025C2211yescharacteristic
126C2×#4025C2212yes—
127C2×#4025C2212yes—
128C2×#4025C2212yes—
129C2×#4025C2212yes—
130C2×#4024C2212yes—
131C2×#4024C2212yes—
132C2×#4024C2212yes—
133C2×#4024C2211yescharacteristic
134C2×#4023C2212yes—
135C2×#4022C2212yes—
136C2×#4022C2212yes—
137C2×#4018C2211yescharacteristic
138C2×#4016C2212yes—
139C2×#4015C2212yes—
140C2×#4015C2211yescharacteristic
141C2×C4×Dic10C2212yes—
142C2×C4×Dic10C2212yes—
143C2×C4×Dic10C2212yes—
144C2×C4×Dic10C2212yes—
145C2×C4×Dic10C2211yescharacteristic
146C2×C4×Dic10C2211yescharacteristic
147C2×#3555—51nomaximal, Sylow
148C22×C5×Q8C2311yescharacteristic
149C22×C5×D4C2311yescharacteristic
150C23×C4×C5C2311yescharacteristic
151C23×C4×C5C2311yescharacteristic
152C23×C4×C5C2312yes—
153C22×C22⋊D5C2311yescharacteristic
154C22×C22⋊D5C2311yescharacteristic
155C23×Dic5C2311yescharacteristic
156C23×Dic5C2311yescharacteristic
157C22×C4×D5C2311yescharacteristic
158C22×C4×D5C2312yes—
159C22×Dic10C2311yescharacteristic
160C22×Dic10C2312yes—
161C22×Dic10C2311yescharacteristic
162C22×Dic10C2312yes—
163C22×Dic10C2312yes—
164C22×Dic10C2312yes—
165C22×Dic10C2312yes—
166C5×#126C23116yes—
167C5×#125C2318yes—
168C5×#125C23116yes—
169C5×#123C23116yes—
170C5×C22⋊Q8C2318yes—
171C5×C22⋊Q8C2318yes—
172C4×C5×Q8C2318yes—
173C4×C5×D4C2318yes—
174C5×#117C2318yes—
175C5×#117C23116yes—
176C2×C5×C4⋊C4C2311yescharacteristic
177C2×C5×C4⋊C4C2312yes—
178C2×C5×C4⋊C4C2311yescharacteristic
179C2×C5×C4⋊C4C2311yescharacteristic
180C2×C5×C4⋊C4C2312yes—
181C2×C5×C4⋊C4C2312yes—
182C2×C5×C4⋊C4C2312yes—
183C2×C5×C4⋊C4C2311yescharacteristic
184C2×C5×C4⋊C4C2312yes—
185C2×C5×C4⋊C4C2312yes—
186C2×C5×C4⋊C4C2318yes—
187C2×C5×C22⋊C4C2312yes—
188C2×C5×C22⋊C4C2312yes—
189C2×C5×C22⋊C4C2311yescharacteristic
190C2×C5×C22⋊C4C2311yescharacteristic
191C2×C5×C22⋊C4C2312yes—
192C2×C42×C5C2312yes—
193C2×C42×C5C2311yescharacteristic
194C2×C42×C5C2312yes—
195C2×C22⋊Dic5C2312yes—
196C2×C22⋊Dic5C2312yes—
197C2×C22⋊Dic5C2311yescharacteristic
198C2×C22⋊Dic5C2311yescharacteristic
199C2×C22⋊Dic5C2311yescharacteristic
200C2×C22⋊Dic5C2312yes—
201C2×C22⋊Dic5C2311yescharacteristic
202C2×C22⋊Dic5C2312yes—
203#4092C2318yes—
204Q8×Dic5C2318yes—
205Q8×Dic5C2318yes—
206#4090C2318yes—
207#4085C2318yes—
208#4082C23116yes—
209#4081C2318yes—
210C4×C22⋊D5C23116yes—
211C4×C22⋊D5C2318yes—
212C4×C22⋊D5C2318yes—
213C2×#685C2311yescharacteristic
214C2×#685C2311yescharacteristic
215C2×#685C2311yescharacteristic
216C2×#685C2312yes—
217C2×#685C2312yes—
218C2×#685C2312yes—
219C2×#685C2311yescharacteristic
220#4072C2318yes—
221#4072C2318yes—
222#4072C2318yes—
223C2×C4⋊Dic5C2312yes—
224C2×C4⋊Dic5C2311yescharacteristic
225C2×C4⋊Dic5C2312yes—
226C2×C4⋊Dic5C2312yes—
227C2×C4⋊Dic5C2312yes—
228C2×C4⋊Dic5C2311yescharacteristic
229C2×C4⋊Dic5C2312yes—
230C2×C4⋊Dic5C2312yes—
231C2×C4⋊Dic5C2311yescharacteristic
232C2×C4⋊Dic5C2311yescharacteristic
233C2×C4⋊Dic5C2311yescharacteristic
234C2×C4⋊Dic5C2312yes—
235C2×C4⋊Dic5C2311yescharacteristic
236#4070C23116yes—
237#4070C23116yes—
238#4070C23116yes—
239#4070C2318yes—
240#4070C2318yes—
241C2×#683C2312yes—
242C2×#683C2311yescharacteristic
243C2×#683C2312yes—
244C2×#683C2312yes—
245C2×#683C2312yes—
246C2×#683C2312yes—
247C2×#683C2312yes—
248C2×#683C2312yes—
249C2×#683C2311yescharacteristic
250C2×#683C2311yescharacteristic
251C2×#683C2311yescharacteristic
252C2×#683C2312yes—
253C2×#683C2312yes—
254C2×#683C2311yescharacteristic
255C2×#683C2312yes—
256C2×#683C2312yes—
257C2×#683C2312yes—
258C2×#683C2311yescharacteristic
259C2×#683C2312yes—
260C2×#683C2312yes—
261C2×#683C2312yes—
262C2×#683C2312yes—
263C2×C4×Dic5C2312yes—
264C2×C4×Dic5C2311yescharacteristic
265C2×C4×Dic5C2311yescharacteristic
266C2×C4×Dic5C2312yes—
267C2×C4×Dic5C2312yes—
268C2×C4×Dic5C2312yes—
269C2×C4×Dic5C2312yes—
270C2×C4×Dic5C2312yes—
271C2×C4×Dic5C2311yescharacteristic
272C2×C4×Dic5C2311yescharacteristic
273C2×C4×Dic5C2311yescharacteristic
274C2×C4×Dic5C2312yes—
275C2×C4×Dic5C2312yes—
276C2×C4×Dic5C2318yes—
277#4044C2318yes—
278#4044C23116yes—
279#4044C23116yes—
280#4043C2318yes—
281#4043C23116yes—
282#4042C23116yes—
283#4042C23116yes—
284#4038C23116yes—
285#4038C2318yes—
286D5×C4⋊C4C2318yes—
287#4036C2318yes—
288#4036C2318yes—
289#4036C23116yes—
290#4036C2318yes—
291#4036C23116yes—
292#4035C23116yes—
293#4035C23116yes—
294#4035C23116yes—
295#4035C23116yes—
296#4035C23116yes—
297#4035C2318yes—
298#4035C23116yes—
299#4035C23116yes—
300#4035C23116yes—
301#4034C2318yes—
302#4034C2318yes—
303#4034C23116yes—
304#4034C2318yes—
305#4034C2318yes—
306#4034C23116yes—
307#4034C23116yes—
308#4034C23116yes—
309#4034C23116yes—
310#4033C2318yes—
311#4033C23116yes—
312#4033C2318yes—
313#4033C23116yes—
314#4033C23116yes—
315#4033C23116yes—
316#4032C2318yes—
317#4031C2318yes—
318#4031C23116yes—
319#4031C23116yes—
320#4029C23116yes—
321#4025C2318yes—
322#4025C23116yes—
323#4025C23116yes—
324#4025C23116yes—
325#4025C23116yes—
326#4025C23116yes—
327#4025C23116yes—
328#4025C23116yes—
329#4024C23116yes—
330#4024C23116yes—
331#4024C2318yes—
332#4024C23116yes—
333#4023C23116yes—
334#4022C23116yes—
335#4022C23116yes—
336#4018C2318yes—
337#4016C23116yes—
338#4015C23116yes—
339#4015C2318yes—
340C4×Dic10C23116yes—
341C4×Dic10C23116yes—
342C4×Dic10C23116yes—
343C4×Dic10C23116yes—
344C4×Dic10C2318yes—
345C4×Dic10C2318yes—
346#3555—532no—
347C2×#563—52no—
348C2×#563—52no—
349C2×Q82—51no—
350C2×#557—51no—
351C2×#557—52no—
352C2×#556—51no—
353C2×#556—51no—
354C2×#556—52no—
355C2×#556—51no—
356C2×#554—51no—
357C2×#552—51no—
358C2×#552D511yescharacteristic, complemented
359C2×#544—51no—
360C2×#544—51no—
361C2×#542—52no—
362C2×#541—52no—
363C2×#541—52no—
364C2×#541—51no—
365C2×#541—51no—
366C2×#541—52no—
367C2×#533—51no—
368C2×#533—51no—
369C2×#529—51no—
370C24×C5C2411yescharacteristic
371C24×C5C2411yescharacteristic
372C23×D5C2411yescharacteristic
373C2×C5×Q8—24no—
374C2×C5×Q8C2414yes—
375C2×C5×D4—42no—
376C2×C5×D4C2414yes—
377C22×C4×C5—24no—
378C22×C4×C5—24no—
379C22×C4×C5—44no—
380C22×C4×C5C2411yescharacteristic
381C22×C4×C5C2412yes—
382C22×C4×C5C2411yescharacteristic
383C22×C4×C5C2412yes—
384C22×C4×C5C2412yes—
385C22×C4×C5C2411yescharacteristic
386C22×C4×C5C2412yes—
387C22×C4×C5C2411yescharacteristic
388C22×C4×C5C2414yes—
389C22×C4×C5C2414yes—
390C22×C4×C5C2418yes—
391C22×C4×C5C2411yescharacteristic
392C2×C22⋊D5—24no—
393C2×C22⋊D5—42no—
394C2×C22⋊D5C2414yes—
395C2×C22⋊D5C2414yes—
396C22×Dic5—24no—
397C22×Dic5—42no—
398C22×Dic5C2412yes—
399C22×Dic5C2412yes—
400C22×Dic5C2412yes—
401C22×Dic5C2412yes—
402C22×Dic5C2411yescharacteristic
403C22×Dic5C2411yescharacteristic
404C22×Dic5C2411yescharacteristic
405C22×Dic5C2411yescharacteristic
406C22×Dic5C2411yescharacteristic
407C22×Dic5C2411yescharacteristic
408C22×Dic5C2414yes—
409C22×Dic5C2414yes—
410C22×Dic5C2411yescharacteristic
411C2×C4×D5—24no—
412C2×C4×D5—44no—
413C2×C4×D5C2414yes—
414C2×C4×D5C2418yes—
415C2×Dic10—24no—
416C2×Dic10—24no—
417C2×Dic10—28no—
418C2×Dic10—44no—
419C2×Dic10—44no—
420C2×Dic10—44no—
421C2×Dic10—44no—
422C2×Dic10C2414yes—
423C2×Dic10C2418yes—
424C2×Dic10C2414yes—
425C2×Dic10C2418yes—
426C2×Dic10C2418yes—
427C2×Dic10C2418yes—
428C2×Dic10C2418yes—
429C5×C4⋊C4C2414yes—
430C5×C4⋊C4C2414yes—
431C5×C4⋊C4C2418yes—
432C5×C4⋊C4C2414yes—
433C5×C4⋊C4C2418yes—
434C5×C4⋊C4C2418yes—
435C5×C4⋊C4C2414yes—
436C5×C4⋊C4C2418yes—
437C5×C4⋊C4C2418yes—
438C5×C4⋊C4C2418yes—
439C5×C22⋊C4C2414yes—
440C5×C22⋊C4C2418yes—
441C5×C22⋊C4C2418yes—
442C5×C22⋊C4C2414yes—
443C5×C22⋊C4C2418yes—
444C42×C5C2418yes—
445C42×C5C2418yes—
446C42×C5C2414yes—
447C22⋊Dic5C2418yes—
448C22⋊Dic5C2418yes—
449C22⋊Dic5C2414yes—
450C22⋊Dic5C2414yes—
451C22⋊Dic5C2414yes—
452C22⋊Dic5C2418yes—
453C22⋊Dic5C2414yes—
454C22⋊Dic5C2418yes—
455#685C2414yes—
456#685C2414yes—
457#685C2414yes—
458#685C2418yes—
459#685C2418yes—
460#685C2418yes—
461#685C2414yes—
462C4⋊Dic5C2418yes—
463C4⋊Dic5C2414yes—
464C4⋊Dic5C2418yes—
465C4⋊Dic5C2418yes—
466C4⋊Dic5C2418yes—
467C4⋊Dic5C2414yes—
468C4⋊Dic5C2418yes—
469C4⋊Dic5C2418yes—
470C4⋊Dic5C2414yes—
471C4⋊Dic5C2414yes—
472C4⋊Dic5C2414yes—
473C4⋊Dic5C2418yes—
474C4⋊Dic5C2414yes—
475#683C2418yes—
476#683C2414yes—
477#683C2418yes—
478#683C2418yes—
479#683C2418yes—
480#683C2418yes—
481#683C2418yes—
482#683C2418yes—
483#683C2414yes—
484#683C2414yes—
485#683C2414yes—
486#683C2418yes—
487#683C2418yes—
488#683C2414yes—
489#683C2418yes—
490#683C2418yes—
491#683C2418yes—
492#683C2414yes—
493#683C2418yes—
494#683C2418yes—
495#683C2418yes—
496#683C2418yes—
497C4×Dic5C2418yes—
498C4×Dic5C2414yes—
499C4×Dic5C2414yes—
500C4×Dic5C2418yes—
501C4×Dic5C2418yes—
502C4×Dic5C2418yes—
503C4×Dic5C2418yes—
504C4×Dic5C2418yes—
505C4×Dic5C2414yes—
506C4×Dic5C2414yes—
507C4×Dic5C2414yes—
508C4×Dic5C2418yes—
509C4×Dic5C2418yes—
510#563—532no—
511#563—532no—
512Q82—516no—
513#557—516no—
514#557—532no—
515#556—516no—
516#556—516no—
517#556—532no—
518#556—516no—
519#554—516no—
520#552—516no—
521#552C2×D5116yescomplemented
522#544—516no—
523#544—516no—
524#542—532no—
525#541—532no—
526#541—532no—
527#541—516no—
528#541—516no—
529#541—532no—
530#533—516no—
531#533—516no—
532C2×C4⋊Q8—51no—
533C2×C4⋊Q8—51no—
534C2×C4⋊Q8—51no—
535C2×C4⋊Q8—51no—
536C2×C4⋊Q8—52no—
537C2×C4⋊Q8—52no—
538C2×C4⋊Q8—52no—
539C2×C4⋊Q8—51no—
540C2×C4⋊Q8—52no—
541C2×C4⋊Q8—52no—
542C2×C4⋊Q8—52no—
543C2×C4⋊Q8—51no—
544#529—516no—
545C2×#126—51no—
546C2×#126—52no—
547C2×#126—52no—
548C2×#126—51no—
549C2×#126—52no—
550C2×#126—52no—
551C2×#126—52no—
552C2×#126—52no—
553C2×#126—52no—
554C2×#126—52no—
555C2×#126—52no—
556C2×#126—52no—
557C2×#126—52no—
558C2×#126C2×D512yes—
559C2×#125—51no—
560C2×#125—52no—
561C2×#125—52no—
562C2×#125—52no—
563C2×#125—52no—
564C2×#125—52no—
565C2×#125—52no—
566C2×#125—52no—
567C2×#125—52no—
568C2×#125—51no—
569C2×#125—51no—
570C2×#125—52no—
571C2×#125—52no—
572C2×#125—51no—
573C2×#125—52no—
574C2×#125C2×D512yes—
575C2×#125C2×D511yescharacteristic
576C2×#124—52no—
577C2×#124—51no—
578C2×#124—52no—
579C2×#124—52no—
580C2×#123—51no—
581C2×#123—52no—
582C2×#123—51no—
583C2×#123C2×D512yes—
584C2×C22⋊Q8—51no—
585C2×C22⋊Q8—51no—
586C2×C22⋊Q8—52no—
587C2×C22⋊Q8—51no—
588C2×C22⋊Q8—52no—
589C2×C22⋊Q8—52no—
590C2×C22⋊Q8—52no—
591C2×C22⋊Q8—52no—
592C2×C22⋊Q8—51no—
593C2×C22⋊Q8—52no—
594C2×C22⋊Q8—51no—
595C2×C22⋊Q8—52no—
596C2×C22⋊Q8—52no—
597C2×C22⋊Q8—52no—
598C2×C22⋊Q8C2×D511yescharacteristic
599C2×C22⋊Q8C2×D511yescharacteristic
600C2×#121—51no—
601C2×C4×Q8—51no—
602C2×C4×Q8—51no—
603C2×C4×Q8—51no—
604C2×C4×Q8—52no—
605C2×C4×Q8—52no—
606C2×C4×Q8—51no—
607C2×C4×Q8—52no—
608C2×C4×Q8—52no—
609C2×C4×Q8—51no—
610C2×C4×Q8—52no—
611C2×C4×Q8—52no—
612C2×C4×Q8—52no—
613C2×C4×Q8—51no—
614C2×C4×Q8—52no—
615C2×C4×Q8C2×D511yescharacteristic
616C2×C4×D4—51no—
617C2×C4×D4—51no—
618C2×C4×D4—52no—
619C2×C4×D4C2×D511yescharacteristic
620C2×#117—51no—
621C2×#117—51no—
622C2×#117—51no—
623C2×#117—52no—
624C2×#117—51no—
625C2×#117—52no—
626C2×#117—51no—
627C2×#117C2×D511yescharacteristic
628C2×#117C2×D512yes—
629C22×C4⋊C4—51no—
630C22×C4⋊C4C2×D511yescharacteristic
631C22×C42—51no—
632C23×C5—22no—
633C23×C5—22no—
634C23×C5—22no—
635C23×C5—22no—
636C23×C5—22no—
637C23×C5—22no—
638C23×C5C2512yes—
639C23×C5C2512yes—
640C23×C5C2511yescharacteristic
641C22×D5—22no—
642C22×D5—22no—
643C22×D5—22no—
644C22×D5C2512yes—
645C5×Q8—28no—
646C5×D4—44no—
647C2×C4×C5—22no—
648C2×C4×C5—24no—
649C2×C4×C5—22no—
650C2×C4×C5—22no—
651C2×C4×C5—24no—
652C2×C4×C5—24no—
653C2×C4×C5—22no—
654C2×C4×C5—24no—
655C2×C4×C5—28no—
656C2×C4×C5—28no—
657C2×C4×C5—48no—
658C2×C4×C52−1+414yes—
659C2×C4×C5C2512yes—
660C2×C4×C5C2514yes—
661C2×C4×C5C2512yes—
662C2×C4×C5C2514yes—
663C2×C4×C5C2512yes—
664C2×C4×C5C2514yes—
665C2×C4×C5C2512yes—
666C2×C4×C5C2514yes—
667C2×C4×C5C2512yes—
668C22⋊D5—28no—
669C22⋊D5—44no—
670C2×Dic5—24no—
671C2×Dic5—22no—
672C2×Dic5—24no—
673C2×Dic5—22no—
674C2×Dic5—22no—
675C2×Dic5—24no—
676C2×Dic5—24no—
677C2×Dic5—22no—
678C2×Dic5—22no—
679C2×Dic5—22no—
680C2×Dic5—28no—
681C2×Dic5—44no—
682C2×Dic52−1+414yes—
683C2×Dic5C2514yes—
684C2×Dic5C2514yes—
685C2×Dic5C2512yes—
686C2×Dic5C2512yes—
687C2×Dic5C2514yes—
688C2×Dic5C2512yes—
689C2×Dic5C2512yes—
690C2×Dic5C2512yes—
691C2×Dic5C2512yes—
692C2×Dic5C2514yes—
693C2×Dic5C2512yes—
694C4×D5—28no—
695C4×D5—48no—
696Dic10—28no—
697Dic10—28no—
698Dic10—216no—
699Dic10—48no—
700Dic10—48no—
701Dic10—48no—
702Dic10—48no—
703C22×Q8—51no—
704C22×Q8—52no—
705C22×Q8—51no—
706C22×Q8—52no—
707C22×Q8—52no—
708C22×Q8—52no—
709C22×Q8—52no—
710C22×Q8C22×D511yescharacteristic
711C22×D4—51no—
712C22×D4—51no—
713C22×D4C22×D511yescharacteristic
714C23×C4—51no—
715C23×C4—51no—
716C23×C4—51no—
717C23×C4—52no—
718C23×C4C22×D511yescharacteristic
719C23×C4C22×D511yescharacteristic
720C23×C4C22×D512yes—
721C4⋊Q8—58no—
722C4⋊Q8—58no—
723C4⋊Q8—58no—
724C4⋊Q8—58no—
725C4⋊Q8—516no—
726C4⋊Q8—516no—
727C4⋊Q8—516no—
728C4⋊Q8—58no—
729C4⋊Q8—516no—
730C4⋊Q8—516no—
731C4⋊Q8—516no—
732C4⋊Q8—58no—
733#126—58no—
734#126—516no—
735#126—516no—
736#126—58no—
737#126—516no—
738#126—516no—
739#126—516no—
740#126—516no—
741#126—516no—
742#126—516no—
743#126—516no—
744#126—516no—
745#126—516no—
746#126C22×D5116yes—
747#125—58no—
748#125—516no—
749#125—58no—
750#125—58no—
751#125—516no—
752#125—516no—
753#125—516no—
754#125—516no—
755#125—516no—
756#125—516no—
757#125—516no—
758#125—516no—
759#125—516no—
760#125—58no—
761#125—516no—
762#125C22×D5116yes—
763#125C22×D518yes—
764#124—516no—
765#124—58no—
766#124—516no—
767#124—516no—
768#123—58no—
769#123—58no—
770#123—516no—
771#123C22×D5116yes—
772C22⋊Q8—58no—
773C22⋊Q8—58no—
774C22⋊Q8—516no—
775C22⋊Q8—58no—
776C22⋊Q8—516no—
777C22⋊Q8—516no—
778C22⋊Q8—516no—
779C22⋊Q8—58no—
780C22⋊Q8—516no—
781C22⋊Q8—516no—
782C22⋊Q8—58no—
783C22⋊Q8—516no—
784C22⋊Q8—516no—
785C22⋊Q8—516no—
786C22⋊Q8C22×D518yes—
787C22⋊Q8C22×D518yes—
788#121—58no—
789C4×Q8—58no—
790C4×Q8—58no—
791C4×Q8—58no—
792C4×Q8—516no—
793C4×Q8—516no—
794C4×Q8—58no—
795C4×Q8—516no—
796C4×Q8—516no—
797C4×Q8—58no—
798C4×Q8—516no—
799C4×Q8—516no—
800C4×Q8—516no—
801C4×Q8—58no—
802C4×Q8—516no—
803C4×Q8C22×D518yes—
804C4×D4—58no—
805C4×D4—58no—
806C4×D4—516no—
807C4×D4C22×D518yes—
808#117—58no—
809#117—58no—
810#117—58no—
811#117—516no—
812#117—58no—
813#117—516no—
814#117—58no—
815#117C22×D518yes—
816#117C22×D5116yes—
817C2×C4⋊C4—51no—
818C2×C4⋊C4—52no—
819C2×C4⋊C4—51no—
820C2×C4⋊C4—51no—
821C2×C4⋊C4—52no—
822C2×C4⋊C4—51no—
823C2×C4⋊C4—51no—
824C2×C4⋊C4—52no—
825C2×C4⋊C4—51no—
826C2×C4⋊C4—51no—
827C2×C4⋊C4—52no—
828C2×C4⋊C4—51no—
829C2×C4⋊C4—52no—
830C2×C4⋊C4—51no—
831C2×C4⋊C4—51no—
832C2×C4⋊C4—52no—
833C2×C4⋊C4—52no—
834C2×C4⋊C4—52no—
835C2×C4⋊C4—52no—
836C2×C4⋊C4—52no—
837C2×C4⋊C4—52no—
838C2×C4⋊C4—52no—
839C2×C4⋊C4—52no—
840C2×C4⋊C4—52no—
841C2×C4⋊C4—52no—
842C2×C4⋊C4—52no—
843C2×C4⋊C4—52no—
844C2×C4⋊C4—52no—
845C2×C4⋊C4—52no—
846C2×C4⋊C4—52no—
847C2×C4⋊C4—51no—
848C2×C4⋊C4—52no—
849C2×C4⋊C4—51no—
850C2×C4⋊C4—52no—
851C2×C4⋊C4—52no—
852C2×C4⋊C4—58no—
853C2×C4⋊C4C22×D511yescharacteristic
854C2×C4⋊C4C22×D511yescharacteristic
855C2×C4⋊C4C22×D512yes—
856C2×C4⋊C4C22×D518yes—
857C2×C4⋊C4C22×D512yes—
858C2×C4⋊C4C22×D511yescharacteristic
859C2×C4⋊C4C22×D512yes—
860C2×C4⋊C4C22×D511yescharacteristic
861C2×C4⋊C4C22×D512yes—
862C2×C4⋊C4C22×D512yes—
863C2×C4⋊C4C22×D512yes—
864C2×C22⋊C4—51no—
865C2×C22⋊C4—51no—
866C2×C22⋊C4—52no—
867C2×C22⋊C4—52no—
868C2×C22⋊C4—52no—
869C2×C22⋊C4—51no—
870C2×C22⋊C4—52no—
871C2×C22⋊C4—51no—
872C2×C22⋊C4—51no—
873C2×C22⋊C4—51no—
874C2×C22⋊C4—51no—
875C2×C22⋊C4—52no—
876C2×C22⋊C4—52no—
877C2×C22⋊C4—51no—
878C2×C22⋊C4—52no—
879C2×C22⋊C4C22×D512yes—
880C2×C22⋊C4C22×D511yescharacteristic
881C2×C22⋊C4C22×D512yes—
882C2×C22⋊C4C22×D512yes—
883C2×C22⋊C4C22×D511yescharacteristic
884C2×C42—52no—
885C2×C42—51no—
886C2×C42—52no—
887C2×C42—51no—
888C2×C42—52no—
889C2×C42—52no—
890C2×C42—52no—
891C2×C42—52no—
892C2×C42—51no—
893C2×C42—51no—
894C2×C42—52no—
895C2×C42—52no—
896C2×C42—51no—
897C2×C42—58no—
898C2×C42C22×D511yescharacteristic
899C2×C42C22×D512yes—
900C2×C42C22×D512yes—
901C22×C5—22no—
902C22×C5—22no—
903C22×C5—22no—
904C22×C5—22no—
905C22×C5—22no—
906C22×C5—22no—
907C22×C5—44no—
908C22×C5—44no—
909C22×C5C2×2−1+412yes—
910C22×C5C2×2−1+412yes—
911C22×C5#58512yes—
912C22×C5C2611yescharacteristic
913C2×D5—22no—
914C2×D5—22no—
915C2×D5—22no—
916C2×D5—44no—
917C4×C5—24no—
918C4×C5—22no—
919C4×C5—22no—
920C4×C5—22no—
921C4×C5—24no—
922C4×C5—24no—
923C4×C5—22no—
924C4×C5—24no—
925C4×C5C2×2−1+414yes—
926Dic5—24no—
927Dic5—22no—
928Dic5—24no—
929Dic5—22no—
930Dic5—22no—
931Dic5—24no—
932Dic5—24no—
933Dic5—22no—
934Dic5—22no—
935Dic5—22no—
936Dic5C2×2−1+414yes—
937C24—51no—
938C24C23×D511yescharacteristic
939C24C23×D511yescharacteristic
940C2×Q8—24no—
941C2×Q8—54no—
942C2×Q8—58no—
943C2×Q8—54no—
944C2×Q8—58no—
945C2×Q8—58no—
946C2×Q8—58no—
947C2×Q8—58no—
948C2×Q8—108no—
949C2×Q8—104no—
950C2×Q8—104no—
951C2×Q8—204no—
952C2×Q8—204no—
953C2×Q8—204no—
954C2×Q8—204no—
955C2×Q8C23×D514yes—
956C2×D4—42no—
957C2×D4—54no—
958C2×D4—54no—
959C2×D4—104no—
960C2×D4—202no—
961C2×D4C23×D514yes—
962C22×C4—24no—
963C22×C4—24no—
964C22×C4—44no—
965C22×C4—51no—
966C22×C4—54no—
967C22×C4—52no—
968C22×C4—52no—
969C22×C4—51no—
970C22×C4—52no—
971C22×C4—51no—
972C22×C4—51no—
973C22×C4—51no—
974C22×C4—52no—
975C22×C4—51no—
976C22×C4—51no—
977C22×C4—54no—
978C22×C4—54no—
979C22×C4—58no—
980C22×C4—104no—
981C22×C4—104no—
982C22×C4—204no—
983C22×C4—202no—
984C22×C4C23×D514yes—
985C22×C4C23×D514yes—
986C22×C4C23×D511yescharacteristic
987C22×C4C23×D512yes—
988C22×C4C23×D512yes—
989C22×C4C23×D511yescharacteristic
990C22×C4C23×D511yescharacteristic
991C22×C4C23×D512yes—
992C22×C4C23×D511yescharacteristic
993C22×C4C23×D512yes—
994C22×C4C23×D518yes—
995C22×C4C23×D511yescharacteristic
996C4⋊C4—54no—
997C4⋊C4—58no—
998C4⋊C4—54no—
999C4⋊C4—54no—
1000C4⋊C4—58no—
1001C4⋊C4—54no—
1002C4⋊C4—54no—
1003C4⋊C4—58no—
1004C4⋊C4—54no—
1005C4⋊C4—54no—
1006C4⋊C4—58no—
1007C4⋊C4—54no—
1008C4⋊C4—58no—
1009C4⋊C4—54no—
1010C4⋊C4—54no—
1011C4⋊C4—58no—
1012C4⋊C4—58no—
1013C4⋊C4—58no—
1014C4⋊C4—58no—
1015C4⋊C4—58no—
1016C4⋊C4—58no—
1017C4⋊C4—58no—
1018C4⋊C4—58no—
1019C4⋊C4—58no—
1020C4⋊C4—58no—
1021C4⋊C4—58no—
1022C4⋊C4—58no—
1023C4⋊C4—58no—
1024C4⋊C4—58no—
1025C4⋊C4—58no—
1026C4⋊C4—54no—
1027C4⋊C4—58no—
1028C4⋊C4—54no—
1029C4⋊C4—58no—
1030C4⋊C4—58no—
1031C4⋊C4C23×D514yes—
1032C4⋊C4C23×D514yes—
1033C4⋊C4C23×D518yes—
1034C4⋊C4C23×D518yes—
1035C4⋊C4C23×D514yes—
1036C4⋊C4C23×D518yes—
1037C4⋊C4C23×D514yes—
1038C4⋊C4C23×D518yes—
1039C4⋊C4C23×D518yes—
1040C4⋊C4C23×D518yes—
1041C22⋊C4—54no—
1042C22⋊C4—54no—
1043C22⋊C4—58no—
1044C22⋊C4—58no—
1045C22⋊C4—58no—
1046C22⋊C4—54no—
1047C22⋊C4—58no—
1048C22⋊C4—54no—
1049C22⋊C4—54no—
1050C22⋊C4—54no—
1051C22⋊C4—54no—
1052C22⋊C4—58no—
1053C22⋊C4—58no—
1054C22⋊C4—54no—
1055C22⋊C4—58no—
1056C22⋊C4C23×D518yes—
1057C22⋊C4C23×D514yes—
1058C22⋊C4C23×D518yes—
1059C22⋊C4C23×D518yes—
1060C22⋊C4C23×D514yes—
1061C42—54no—
1062C42—54no—
1063C42—54no—
1064C42—54no—
1065C42—58no—
1066C42—58no—
1067C42—54no—
1068C42—58no—
1069C42—58no—
1070C42—58no—
1071C42—58no—
1072C42—58no—
1073C42—58no—
1074C42C23×D514yes—
1075C42C23×D518yes—
1076C42C23×D518yes—
1077C2×C5—42no—
1078C2×C5—42no—
1079C2×C5#355514yescomplemented
1080C2×C5C22×2−1+411yescharacteristic
1081C2×C5C22×2−1+411yescharacteristic
1082C2×C5C2×#58511yescharacteristic
1083D5—42no—
1084C23—22no—
1085C23—22no—
1086C23—22no—
1087C23—22no—
1088C23—22no—
1089C23—22no—
1090C23—52no—
1091C23—102no—
1092C23—102no—
1093C23—102no—
1094C23C24×D512yes—
1095C23C24×D512yes—
1096C23C24×D511yescharacteristic
1097Q8—28no—
1098Q8—1016no—
1099Q8—108no—
1100Q8—108no—
1101Q8—208no—
1102Q8—208no—
1103Q8—208no—
1104Q8—208no—
1105D4—44no—
1106D4—108no—
1107D4—204no—
1108C2×C4—22no—
1109C2×C4—22no—
1110C2×C4—24no—
1111C2×C4—24no—
1112C2×C4—24no—
1113C2×C4—22no—
1114C2×C4—24no—
1115C2×C4—22no—
1116C2×C4—28no—
1117C2×C4—28no—
1118C2×C4—48no—
1119C2×C4—54no—
1120C2×C4—52no—
1121C2×C4—54no—
1122C2×C4—54no—
1123C2×C4—52no—
1124C2×C4—54no—
1125C2×C4—52no—
1126C2×C4—52no—
1127C2×C4—52no—
1128C2×C4—52no—
1129C2×C4—52no—
1130C2×C4—54no—
1131C2×C4—108no—
1132C2×C4—102no—
1133C2×C4—104no—
1134C2×C4—104no—
1135C2×C4—102no—
1136C2×C4—102no—
1137C2×C4—102no—
1138C2×C4—104no—
1139C2×C4—102no—
1140C2×C4—104no—
1141C2×C4—102no—
1142C2×C4—108no—
1143C2×C4—208no—
1144C2×C4—204no—
1145C2×C4#415014yes—
1146C2×C4C24×D512yes—
1147C2×C4C24×D514yes—
1148C2×C4C24×D514yes—
1149C2×C4C24×D512yes—
1150C2×C4C24×D512yes—
1151C2×C4C24×D514yes—
1152C2×C4C24×D512yes—
1153C2×C4C24×D514yes—
1154C2×C4C24×D512yes—
1155C5C2×#355511yescharacteristic, complemented, Sylow
1156C22—22no—
1157C22—22no—
1158C22—22no—
1159C22—22no—
1160C22—22no—
1161C22—22no—
1162C22—44no—
1163C22—44no—
1164C22—102no—
1165C22—102no—
1166C22—102no—
1167C22—204no—
1168C22C2×#415012yes—
1169C22#6628312yes—
1170C22D5×2−1+412yes—
1171C22C25×D511yescharacteristic
1172C4—22no—
1173C4—22no—
1174C4—24no—
1175C4—24no—
1176C4—24no—
1177C4—22no—
1178C4—24no—
1179C4—22no—
1180C4—54no—
1181C4—102no—
1182C4—104no—
1183C4—104no—
1184C4—102no—
1185C4—102no—
1186C4—102no—
1187C4—104no—
1188C4—102no—
1189C4—104no—
1190C4—102no—
1191C4C2×#415014yes—
1192C2—42no—
1193C2—42no—
1194C2—202no—
1195C2#1061875014yesdirect product factor
1196C2C22×#415011yescharacteristic
1197C2C2×#6628311yescharacteristic
1198C2C2×D5×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#552C2
socleC23×C5C25
prime radicalC2×#4085C22
hypercenterC2×#552D5
hypocenterC5C2×#3555
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×C5×#552C2semidirect
2. #10618750C2direct (N × H)
3. C2×#66046C2semidirect
4. C2×#66035C2semidirect
5. C2×#66023C2semidirect
6. C2×#66019C2semidirect
7. C2×#66019C2semidirect
8. C2×#66030C2semidirect
9. C2×#65985C2semidirect
11. C2×#65973C2semidirect
12. C2×#65975C2semidirect
13. C2×#65959C2semidirect
14. C2×#65956C2semidirect
15. C2×#65917C2semidirect
16. C2×Q8×Dic10C2semidirect
17. C2×#65876C2semidirect
19. C2×#65867C2semidirect
20. C2×#65867C2semidirect
21. C2×#65852C2semidirect
22. C2×#65851C2semidirect
23. C2×#65845C2semidirect
24. C2×#65834C2semidirect
25. C5×#552C22semidirect
56. #66046C22semidirect
57. #66035C22semidirect
58. #66030C22semidirect
59. #66023C22semidirect
60. #66019C22semidirect
61. #66019C22semidirect
63. #65985C22semidirect
64. #65975C22semidirect
65. #65973C22semidirect
66. #65959C22semidirect
67. #65956C22semidirect
68. #65917C22semidirect
69. Q8×Dic10C22semidirect
70. #65876C22semidirect
72. #65867C22semidirect
73. #65867C22semidirect
74. #65852C22semidirect
75. #65851C22semidirect
79. #65845C22semidirect
87. #65834C22semidirect
358. C2×#552D5semidirect
521. #552C2×D5semidirect
1079. C2×C5#3555semidirect
1155. C5C2×#3555semidirect
1195. C2#10618750direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5522
#106187502
C2×#660462
C2×#660352
C2×#660232
C2×#660192
C2×#660302
C2×#659852
C2×#659962
C2×#659732
C2×#659752
C2×#659592
C2×#659562
C2×#659172
C2×Q8×Dic102
C2×#658762
C2×#658722
C2×#658672
C2×#658522
C2×#658512
C2×#658452
C2×#658342
C2×#35555