Finite Group Databasebeta

← C2×#10618930 #13006810

Subgroups — C2×#10618930 #13006810

Order 1280.

6554 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#557C211yesmaximal, characteristic, complemented
2#10618930C2132yesmaximal, direct product factor
3C2×#66069C212yesmaximal, complemented
4C2×#66063C211yesmaximal, characteristic, complemented
5C2×#66067C212yesmaximal, complemented
6C2×#66068C211yesmaximal, characteristic, complemented
7C2×#66034C212yesmaximal, complemented
8C2×#66029C211yesmaximal, characteristic, complemented
9C2×#66029C211yesmaximal, characteristic, complemented
10C2×#66027C212yesmaximal, complemented
11C2×#66023C211yesmaximal, characteristic, complemented
12C2×#66026C212yesmaximal, complemented
13C2×#66030C212yesmaximal, complemented
14C2×#66022C211yesmaximal, characteristic, complemented
15C2×#65913C211yesmaximal, characteristic, complemented
16C2×#65915C211yesmaximal, characteristic, complemented
17C2×#65915C211yesmaximal, characteristic, complemented
18C2×#65916C211yesmaximal, characteristic, complemented
19C2×#65916C211yesmaximal, characteristic, complemented
20C2×#65916C212yesmaximal, complemented
21C2×#65914C211yesmaximal, characteristic, complemented
22C2×#65914C211yesmaximal, characteristic, complemented
23C2×#65902C212yesmaximal, complemented
24C2×#65918C211yesmaximal, characteristic, complemented
25C5×#557C22116yescomplemented
26C2×C5×C4⋊Q8C2212yes—
27C2×C5×C4⋊Q8C2211yescharacteristic
28C2×C5×#125C2211yescharacteristic
29C2×C5×#125C2212yes—
30C2×C5×#125C2212yes—
31C2×C5×#125C2211yescharacteristic
32C2×C4×C5×Q8C2211yescharacteristic
33C2×C4×C5×Q8C2212yes—
34C2×C4×C5×Q8C2211yescharacteristic
35C2×C4×C5×Q8C2211yescharacteristic
36C2×C4×C5×Q8C2211yescharacteristic
37C2×#4093C2212yes—
38C2×#4093C2212yes—
39C2×#4093C2211yescharacteristic
40C2×#4093C2211yescharacteristic
41C2×#4092C2211yescharacteristic
42C2×#4092C2212yes—
43C2×#4092C2211yescharacteristic
44C2×#4092C2211yescharacteristic
45C2×#4092C2211yescharacteristic
46C2×#4092C2212yes—
47C2×#4090C2212yes—
48#66069C22132yescomplemented
49#66068C22116yescomplemented
50#66067C22132yescomplemented
51#66063C22116yescomplemented
52#66034C22132yescomplemented
53#66030C22132yescomplemented
54#66029C22116yescomplemented
55#66029C22116yescomplemented
56#66027C22132yescomplemented
57#66026C22132yescomplemented
58#66023C22116yescomplemented
59#66022C22116yescomplemented
60#65918C22116yescomplemented
61#65916C22132yescomplemented
62#65916C22116yescomplemented
63#65916C22116yescomplemented
64#65915C22116yescomplemented
65#65915C22116yescomplemented
66#65914C22116yescomplemented
67#65914C22116yescomplemented
68#65913C22116yescomplemented
69#65902C22132yescomplemented
70C2×#4044C2212yes—
71C2×#4044C2212yes—
72C2×#4044C2212yes—
73C2×#4044C2211yescharacteristic
74C2×#4044C2212yes—
75C2×#4044C2212yes—
76C2×#4044C2211yescharacteristic
77C2×#4043C2212yes—
78C2×#4042C2212yes—
79C2×#4042C2212yes—
80C2×#4042C2212yes—
81C2×#4042C2212yes—
82C2×#4042C2212yes—
83C2×#4042C2212yes—
84C2×#4042C2212yes—
85C2×#4042C2212yes—
86C2×#4041C2211yescharacteristic
87C2×#4041C2211yescharacteristic
88C2×#4041C2211yescharacteristic
89C2×#4041C2212yes—
90C2×#4041C2211yescharacteristic
91C2×#4041C2212yes—
92C2×#4041C2212yes—
93C2×#4040C2212yes—
94C2×#4040C2212yes—
95C2×#4040C2211yescharacteristic
96C2×#4040C2211yescharacteristic
97C2×#4040C2212yes—
98C2×#4040C2212yes—
99C2×#4040C2212yes—
100C2×#4040C2212yes—
101C2×#4040C2212yes—
102C2×#4039C2212yes—
103C2×#4039C2212yes—
104C2×#4038C2211yescharacteristic
105C2×#4038C2211yescharacteristic
106C2×#4038C2211yescharacteristic
107C2×#4038C2211yescharacteristic
108C2×#4038C2212yes—
109C2×D5×C4⋊C4C2211yescharacteristic
110C2×D5×C4⋊C4C2211yescharacteristic
111C2×D5×C4⋊C4C2212yes—
112C2×#4036C2211yescharacteristic
113C2×#4036C2211yescharacteristic
114C2×#4035C2212yes—
115C2×#4035C2212yes—
116C2×#4035C2212yes—
117C2×#4035C2212yes—
118C2×#4034C2211yescharacteristic
119C2×#4034C2211yescharacteristic
120C2×#4034C2212yes—
121C2×#4033C2212yes—
122C2×#4033C2212yes—
123C2×#4022C2212yes—
124C2×#4022C2212yes—
125C2×#4022C2212yes—
126C2×#4022C2212yes—
127C2×#4021C2212yes—
128C2×#4021C2212yes—
129C2×#4021C2212yes—
130C2×C4×D20C2211yescharacteristic
131C2×C4×D20C2212yes—
132C2×C4×D20C2211yescharacteristic
133C2×C4×D20C2211yescharacteristic
134C2×C4×D20C2211yescharacteristic
135C2×C4×D20C2211yescharacteristic
136C2×C4×D20C2211yescharacteristic
137C2×#4018C2212yes—
138C2×#4018C2212yes—
139C2×#4018C2211yescharacteristic
140C2×#4018C2211yescharacteristic
141C2×#4018C2212yes—
142C2×C42×D5C2211yescharacteristic
143C2×#4016C2211yescharacteristic
144C2×#4016C2211yescharacteristic
145C2×#4015C2211yescharacteristic
146C2×C4×Dic10C2212yes—
147C2×#3565—51nomaximal, Sylow
148C22×C5×Q8C2311yescharacteristic
149C22×C5×Q8C2312yes—
150C22×C5×Q8C2311yescharacteristic
151C22×D20C2311yescharacteristic
152C22×D20C2311yescharacteristic
153C22×D20C2311yescharacteristic
154C22×D20C2312yes—
155C22×D20C2311yescharacteristic
156C22×D20C2312yes—
157C22×D20C2312yes—
158C22×C4×D5C2311yescharacteristic
159C22×C4×D5C2311yescharacteristic
160C22×C4×D5C2311yescharacteristic
161C22×C4×D5C2311yescharacteristic
162C22×C4×D5C2311yescharacteristic
163C22×C4×D5C2312yes—
164C22×C4×D5C2312yes—
165C22×C4×D5C2312yes—
166C22×C4×D5C2312yes—
167C22×C4×D5C2312yes—
168C22×Dic10C2312yes—
169C22×Dic10C2312yes—
170C22×Dic10C2312yes—
171C5×C4⋊Q8C2318yes—
172C5×C4⋊Q8C23116yes—
173C5×#125C2318yes—
174C5×#125C2318yes—
175C5×#125C23116yes—
176C5×#125C23116yes—
177C4×C5×Q8C23116yes—
178C4×C5×Q8C2318yes—
179C4×C5×Q8C2318yes—
180C4×C5×Q8C2318yes—
181C4×C5×Q8C2318yes—
182C2×C5×C4⋊C4C2312yes—
183C2×C5×C4⋊C4C2312yes—
184C2×C5×C4⋊C4C2311yescharacteristic
185C2×C5×C4⋊C4C2311yescharacteristic
186C2×C5×C4⋊C4C2312yes—
187C2×C5×C4⋊C4C2312yes—
188C2×C5×C4⋊C4C2312yes—
189C2×C5×C4⋊C4C2312yes—
190C2×C5×C4⋊C4C2312yes—
191C2×C5×C4⋊C4C2311yescharacteristic
192C2×C5×C4⋊C4C2311yescharacteristic
193C2×C5×C4⋊C4C2311yescharacteristic
194C2×C5×C4⋊C4C2311yescharacteristic
195C2×C5×C4⋊C4C2312yes—
196C2×C42×C5C2312yes—
197C2×C42×C5C2311yescharacteristic
198C2×C42×C5C2311yescharacteristic
199C2×C42×C5C2311yescharacteristic
200C2×C42×C5C2312yes—
201C2×C42×C5C2312yes—
202#4093C2318yes—
203#4093C23116yes—
204#4093C23116yes—
205#4093C2318yes—
206#4092C23116yes—
207#4092C23116yes—
208#4092C2318yes—
209#4092C2318yes—
210#4092C2318yes—
211#4092C2318yes—
212#4090C23116yes—
213C2×#685C2311yescharacteristic
214C2×#685C2311yescharacteristic
215C2×#685C2312yes—
216C2×#685C2311yescharacteristic
217C2×#685C2311yescharacteristic
218C2×#685C2312yes—
219C2×#685C2312yes—
220C2×#685C2312yes—
221C2×#685C2311yescharacteristic
222C2×#685C2311yescharacteristic
223C2×#685C2312yes—
224C2×#685C2312yes—
225C2×#685C2312yes—
226C2×#685C2312yes—
227C2×#685C2311yescharacteristic
228C2×#685C2311yescharacteristic
229C2×#685C2311yescharacteristic
230C2×#685C2311yescharacteristic
231C2×#685C2312yes—
232C2×#685C2312yes—
233C2×#685C2312yes—
234C2×#685C2312yes—
235C2×#685C2312yes—
236C2×#685C2312yes—
237C2×#685C2312yes—
238C2×C4⋊Dic5C2311yescharacteristic
239C2×C4⋊Dic5C2311yescharacteristic
240C2×C4⋊Dic5C2311yescharacteristic
241C2×C4⋊Dic5C2312yes—
242C2×C4⋊Dic5C2311yescharacteristic
243C2×C4⋊Dic5C2312yes—
244C2×C4⋊Dic5C2311yescharacteristic
245C2×C4⋊Dic5C2311yescharacteristic
246C2×#683C2312yes—
247C2×#683C2312yes—
248C2×#683C2312yes—
249C2×#683C2312yes—
250C2×#683C2312yes—
251C2×#683C2312yes—
252C2×#683C2311yescharacteristic
253C2×#683C2312yes—
254C2×#683C2311yescharacteristic
255C2×#683C2311yescharacteristic
256C2×#683C2311yescharacteristic
257C2×#683C2312yes—
258C2×#683C2312yes—
259C2×#683C2312yes—
260C2×#683C2312yes—
261C2×#683C2312yes—
262C2×C4×Dic5C2312yes—
263C2×C4×Dic5C2312yes—
264C2×C4×Dic5C2311yescharacteristic
265C2×C4×Dic5C2311yescharacteristic
266C2×C4×Dic5C2311yescharacteristic
267C2×C4×Dic5C2312yes—
268C2×C4×Dic5C2312yes—
269#4044C23116yes—
270#4044C23116yes—
271#4044C23116yes—
272#4044C23116yes—
273#4044C2318yes—
274#4044C23116yes—
275#4044C2318yes—
276#4043C23116yes—
277#4042C23116yes—
278#4042C23116yes—
279#4042C23116yes—
280#4042C23116yes—
281#4042C23116yes—
282#4042C23116yes—
283#4042C23116yes—
284#4042C23116yes—
285#4041C23116yes—
286#4041C2318yes—
287#4041C2318yes—
288#4041C23116yes—
289#4041C2318yes—
290#4041C2318yes—
291#4041C23116yes—
292#4040C23116yes—
293#4040C23116yes—
294#4040C23116yes—
295#4040C23116yes—
296#4040C2318yes—
297#4040C2318yes—
298#4040C23116yes—
299#4040C23116yes—
300#4040C23116yes—
301#4039C23116yes—
302#4039C23116yes—
303#4038C2318yes—
304#4038C2318yes—
305#4038C2318yes—
306#4038C23116yes—
307#4038C2318yes—
308D5×C4⋊C4C2318yes—
309D5×C4⋊C4C23116yes—
310D5×C4⋊C4C2318yes—
311#4036C2318yes—
312#4036C2318yes—
313#4035C23116yes—
314#4035C23116yes—
315#4035C23116yes—
316#4035C23116yes—
317#4034C2318yes—
318#4034C2318yes—
319#4034C23116yes—
320#4033C23116yes—
321#4033C23116yes—
322#4022C23116yes—
323#4022C23116yes—
324#4022C23116yes—
325#4022C23116yes—
326#4021C23116yes—
327#4021C23116yes—
328#4021C23116yes—
329C4×D20C2318yes—
330C4×D20C2318yes—
331C4×D20C2318yes—
332C4×D20C2318yes—
333C4×D20C2318yes—
334C4×D20C23116yes—
335C4×D20C2318yes—
336#4018C2318yes—
337#4018C23116yes—
338#4018C23116yes—
339#4018C2318yes—
340#4018C23116yes—
341C42×D5C2318yes—
342#4016C2318yes—
343#4016C2318yes—
344#4015C2318yes—
345C4×Dic10C23116yes—
346#3565—532no—
347C2×#563—52no—
348C2×#562—52no—
349C2×#557D511yescharacteristic, complemented
350C2×#556—51no—
351C2×#556—52no—
352C2×#555—51no—
353C2×#554—51no—
354C2×#553—51no—
355C2×#553—51no—
356C2×#552—52no—
357C2×#552—51no—
358C2×#552—51no—
359C2×#544—51no—
360C2×#544—51no—
361C2×#542—52no—
362C2×#542—51no—
363C2×#542—51no—
364C2×#542—52no—
365C2×#541—52no—
366C2×#539—52no—
367C2×#533—51no—
368C2×#529—51no—
369C2×#529—51no—
370C23×D5C2411yescharacteristic
371C23×D5C2411yescharacteristic
372C23×D5C2411yescharacteristic
373C23×D5C2412yes—
374C2×C5×Q8—24no—
375C2×C5×Q8—44no—
376C2×C5×Q8—42no—
377C2×C5×Q8C2414yes—
378C2×C5×Q8C2418yes—
379C2×C5×Q8C2414yes—
380C22×C4×C5C2411yescharacteristic
381C22×C4×C5C2411yescharacteristic
382C22×C4×C5C2412yes—
383C22×C4×C5C2411yescharacteristic
384C22×C4×C5C2412yes—
385C22×C4×C5C2411yescharacteristic
386C22×C4×C5C2412yes—
387C22×C4×C5C2411yescharacteristic
388C22×C4×C5C2411yescharacteristic
389C22×C4×C5C2412yes—
390C22×C4×C5C2411yescharacteristic
391C22×Dic5C2411yescharacteristic
392C22×Dic5C2412yes—
393C22×Dic5C2411yescharacteristic
394C22×Dic5C2412yes—
395C22×Dic5C2412yes—
396C22×Dic5C2411yescharacteristic
397C22×Dic5C2411yescharacteristic
398C22×Dic5C2411yescharacteristic
399C2×D20—24no—
400C2×D20—42no—
401C2×D20—44no—
402C2×D20—44no—
403C2×D20—42no—
404C2×D20—42no—
405C2×D20—44no—
406C2×D20C2414yes—
407C2×D20C2414yes—
408C2×D20C2414yes—
409C2×D20C2414yes—
410C2×D20C2418yes—
411C2×D20C2418yes—
412C2×D20C2418yes—
413C2×C4×D5—24no—
414C2×C4×D5—24no—
415C2×C4×D5—24no—
416C2×C4×D5—42no—
417C2×C4×D5—44no—
418C2×C4×D5—42no—
419C2×C4×D5—44no—
420C2×C4×D5—44no—
421C2×C4×D5—44no—
422C2×C4×D5—44no—
423C2×C4×D5C2414yes—
424C2×C4×D5C2414yes—
425C2×C4×D5C2414yes—
426C2×C4×D5C2414yes—
427C2×C4×D5C2414yes—
428C2×C4×D5C2418yes—
429C2×C4×D5C2418yes—
430C2×C4×D5C2418yes—
431C2×C4×D5C2418yes—
432C2×C4×D5C2418yes—
433C2×Dic10—44no—
434C2×Dic10—44no—
435C2×Dic10—44no—
436C2×Dic10C2418yes—
437C2×Dic10C2418yes—
438C2×Dic10C2418yes—
439C5×C4⋊C4C2414yes—
440C5×C4⋊C4C2418yes—
441C5×C4⋊C4C2414yes—
442C5×C4⋊C4C2418yes—
443C5×C4⋊C4C2418yes—
444C5×C4⋊C4C2414yes—
445C5×C4⋊C4C2414yes—
446C5×C4⋊C4C2414yes—
447C5×C4⋊C4C2418yes—
448C5×C4⋊C4C2414yes—
449C5×C4⋊C4C2418yes—
450C5×C4⋊C4C2418yes—
451C5×C4⋊C4C2418yes—
452C5×C4⋊C4C2418yes—
453C42×C5C2418yes—
454C42×C5C2414yes—
455C42×C5C2414yes—
456C42×C5C2418yes—
457C42×C5C2414yes—
458C42×C5C2418yes—
459#685C2414yes—
460#685C2414yes—
461#685C2418yes—
462#685C2414yes—
463#685C2414yes—
464#685C2418yes—
465#685C2418yes—
466#685C2418yes—
467#685C2414yes—
468#685C2414yes—
469#685C2418yes—
470#685C2418yes—
471#685C2418yes—
472#685C2418yes—
473#685C2414yes—
474#685C2414yes—
475#685C2414yes—
476#685C2414yes—
477#685C2418yes—
478#685C2418yes—
479#685C2418yes—
480#685C2418yes—
481#685C2418yes—
482#685C2418yes—
483#685C2418yes—
484C4⋊Dic5C2414yes—
485C4⋊Dic5C2414yes—
486C4⋊Dic5C2414yes—
487C4⋊Dic5C2418yes—
488C4⋊Dic5C2414yes—
489C4⋊Dic5C2418yes—
490C4⋊Dic5C2414yes—
491C4⋊Dic5C2414yes—
492#683C2418yes—
493#683C2418yes—
494#683C2418yes—
495#683C2418yes—
496#683C2418yes—
497#683C2418yes—
498#683C2414yes—
499#683C2418yes—
500#683C2414yes—
501#683C2414yes—
502#683C2414yes—
503#683C2418yes—
504#683C2418yes—
505#683C2418yes—
506#683C2418yes—
507#683C2418yes—
508C4×Dic5C2418yes—
509C4×Dic5C2418yes—
510C4×Dic5C2414yes—
511C4×Dic5C2414yes—
512C4×Dic5C2414yes—
513C4×Dic5C2418yes—
514C4×Dic5C2418yes—
515#563—532no—
516#562—532no—
517#557C2×D5116yescomplemented
518#556—532no—
519#556—516no—
520#555—516no—
521#554—516no—
522#553—516no—
523#553—516no—
524#552—532no—
525#552—516no—
526#552—516no—
527#544—516no—
528#544—516no—
529#542—532no—
530#542—516no—
531#542—516no—
532#542—532no—
533#541—532no—
534#539—532no—
535#533—516no—
536C2×C4⋊Q8—52no—
537C2×C4⋊Q8—51no—
538C2×C4⋊Q8—51no—
539C2×C4⋊Q8—52no—
540C2×C4⋊Q8—51no—
541C2×C4⋊Q8C2×D512yes—
542C2×C4⋊Q8C2×D511yescharacteristic
543#529—516no—
544#529—516no—
545C2×#126—52no—
546C2×#126—51no—
547C2×#126—51no—
548C2×#126—52no—
549C2×#126—52no—
550C2×#126—52no—
551C2×#126—52no—
552C2×#126—52no—
553C2×#126—52no—
554C2×#126—52no—
555C2×#126—52no—
556C2×#125—52no—
557C2×#125—52no—
558C2×#125—52no—
559C2×#125—52no—
560C2×#125—51no—
561C2×#125—51no—
562C2×#125—51no—
563C2×#125—51no—
564C2×#125C2×D511yescharacteristic
565C2×#125C2×D512yes—
566C2×#125C2×D512yes—
567C2×#125C2×D511yescharacteristic
568C2×#124—51no—
569C2×#124—51no—
570C2×#124—52no—
571C2×#124—52no—
572C2×#124—52no—
573C2×#124—52no—
574C2×#124—52no—
575C2×#123—51no—
576C2×#123—51no—
577C2×#123—52no—
578C2×#123—52no—
579C2×#123—52no—
580C2×#123—52no—
581C2×#123—52no—
582C2×#123—52no—
583C2×#123—52no—
584C2×C22⋊Q8—51no—
585C2×C22⋊Q8—51no—
586C2×C22⋊Q8—52no—
587C2×C22⋊Q8—51no—
588C2×C22⋊Q8—51no—
589C2×C22⋊Q8—52no—
590C2×C22⋊Q8—52no—
591C2×C22⋊Q8—52no—
592C2×C22⋊Q8—52no—
593C2×C22⋊Q8—52no—
594C2×C22⋊Q8—52no—
595C2×C22⋊Q8—52no—
596C2×C22⋊Q8—52no—
597C2×C22⋊Q8—52no—
598C2×C22⋊Q8—52no—
599C2×#121—51no—
600C2×#121—51no—
601C2×#121—52no—
602C2×#121—51no—
603C2×#121—51no—
604C2×#121—52no—
605C2×#121—52no—
606C2×C4×Q8—52no—
607C2×C4×Q8—52no—
608C2×C4×Q8—52no—
609C2×C4×Q8C2×D511yescharacteristic
610C2×C4×Q8C2×D511yescharacteristic
611C2×C4×Q8C2×D511yescharacteristic
612C2×C4×Q8C2×D512yes—
613C2×C4×Q8C2×D511yescharacteristic
614C2×C4×D4—52no—
615C2×C4×D4—52no—
616C2×C4×D4—52no—
617C2×C4×D4—51no—
618C2×C4×D4—51no—
619C2×C4×D4—51no—
620C2×C4×D4—51no—
621C2×C4×D4—51no—
622C2×C4×D4—51no—
623C2×#117—51no—
624C2×#117—51no—
625C2×#117—52no—
626C2×#117—51no—
627C2×#117—51no—
628C2×#117—51no—
629C2×#117—51no—
630C2×#117—52no—
631C2×#117—52no—
632C2×#117—52no—
633C22×C4⋊C4—52no—
634C22×C4⋊C4—51no—
635C22×C4⋊C4—51no—
636C22×C42—51no—
637C23×C5C2511yescharacteristic
638C22×D5—22no—
639C22×D5—22no—
640C22×D5—22no—
641C22×D5—24no—
642C22×D5—22no—
643C22×D5—22no—
644C22×D5—24no—
645C22×D5—22no—
646C22×D5—24no—
647C22×D5—22no—
648C22×D5—22no—
649C22×D5—22no—
650C22×D5C2512yes—
651C22×D5C2512yes—
652C22×D5C2512yes—
653C22×D5C2514yes—
654C5×Q8—28no—
655C5×Q8—48no—
656C5×Q8—44no—
657C2×C4×C5—24no—
658C2×C4×C5—22no—
659C2×C4×C5—24no—
660C2×C4×C5—24no—
661C2×C4×C5—22no—
662C2×C4×C5—22no—
663C2×C4×C5—22no—
664C2×C4×C5—22no—
665C2×C4×C5—24no—
666C2×C4×C5—22no—
667C2×C4×C52−1+414yes—
668C2×C4×C5C2514yes—
669C2×C4×C5C2512yes—
670C2×C4×C5C2514yes—
671C2×C4×C5C2512yes—
672C2×C4×C5C2514yes—
673C2×C4×C5C2512yes—
674C2×C4×C5C2514yes—
675C2×C4×C5C2512yes—
676C2×C4×C5C2512yes—
677C2×C4×C5C2512yes—
678C2×C4×C5C2512yes—
679C2×Dic5—22no—
680C2×Dic5—22no—
681C2×Dic5—22no—
682C2×Dic5—22no—
683C2×Dic5—22no—
684C2×Dic5—24no—
685C2×Dic5—24no—
686C2×Dic5—24no—
687C2×Dic5C2512yes—
688C2×Dic5C2512yes—
689C2×Dic5C2512yes—
690C2×Dic5C2512yes—
691C2×Dic5C2514yes—
692C2×Dic5C2512yes—
693C2×Dic5C2514yes—
694C2×Dic5C2514yes—
695D20—28no—
696D20—44no—
697D20—48no—
698D20—48no—
699D20—44no—
700D20—44no—
701D20—48no—
702C4×D5—28no—
703C4×D5—28no—
704C4×D5—28no—
705C4×D5—44no—
706C4×D5—48no—
707C4×D5—44no—
708C4×D5—48no—
709C4×D5—48no—
710C4×D5—48no—
711C4×D5—48no—
712Dic10—48no—
713Dic10—48no—
714Dic10—48no—
715C22×Q8—52no—
716C22×Q8—52no—
717C22×Q8—52no—
718C22×Q8C22×D511yescharacteristic
719C22×Q8C22×D511yescharacteristic
720C22×Q8C22×D512yes—
721C22×D4—51no—
722C22×D4—51no—
723C22×D4—52no—
724C22×D4—51no—
725C22×D4—52no—
726C22×D4—52no—
727C22×D4—51no—
728C23×C4—51no—
729C23×C4—51no—
730C23×C4—51no—
731C23×C4—52no—
732C23×C4—52no—
733C23×C4—52no—
734C23×C4—52no—
735C23×C4—52no—
736C23×C4—51no—
737C23×C4—51no—
738C4⋊Q8—516no—
739C4⋊Q8—58no—
740C4⋊Q8—58no—
741C4⋊Q8—516no—
742C4⋊Q8—58no—
743C4⋊Q8C22×D5116yes—
744C4⋊Q8C22×D518yes—
745#126—516no—
746#126—58no—
747#126—58no—
748#126—516no—
749#126—516no—
750#126—516no—
751#126—516no—
752#126—516no—
753#126—516no—
754#126—516no—
755#126—516no—
756#125—58no—
757#125—58no—
758#125—516no—
759#125—516no—
760#125—516no—
761#125—516no—
762#125—58no—
763#125—58no—
764#125C22×D518yes—
765#125C22×D5116yes—
766#125C22×D5116yes—
767#125C22×D518yes—
768#124—58no—
769#124—58no—
770#124—516no—
771#124—516no—
772#124—516no—
773#124—516no—
774#124—516no—
775#123—58no—
776#123—58no—
777#123—516no—
778#123—516no—
779#123—516no—
780#123—516no—
781#123—516no—
782#123—516no—
783#123—516no—
784C22⋊Q8—58no—
785C22⋊Q8—58no—
786C22⋊Q8—516no—
787C22⋊Q8—58no—
788C22⋊Q8—58no—
789C22⋊Q8—516no—
790C22⋊Q8—516no—
791C22⋊Q8—516no—
792C22⋊Q8—516no—
793C22⋊Q8—516no—
794C22⋊Q8—516no—
795C22⋊Q8—516no—
796C22⋊Q8—516no—
797C22⋊Q8—516no—
798C22⋊Q8—516no—
799#121—58no—
800#121—58no—
801#121—516no—
802#121—58no—
803#121—58no—
804#121—516no—
805#121—516no—
806C4×Q8—516no—
807C4×Q8—516no—
808C4×Q8—516no—
809C4×Q8C22×D518yes—
810C4×Q8C22×D518yes—
811C4×Q8C22×D518yes—
812C4×Q8C22×D5116yes—
813C4×Q8C22×D518yes—
814C4×D4—516no—
815C4×D4—516no—
816C4×D4—516no—
817C4×D4—58no—
818C4×D4—58no—
819C4×D4—58no—
820C4×D4—58no—
821C4×D4—58no—
822C4×D4—58no—
823#117—58no—
824#117—58no—
825#117—516no—
826#117—58no—
827#117—58no—
828#117—58no—
829#117—58no—
830#117—516no—
831#117—516no—
832#117—516no—
833C2×C4⋊C4—51no—
834C2×C4⋊C4—51no—
835C2×C4⋊C4—52no—
836C2×C4⋊C4—52no—
837C2×C4⋊C4—52no—
838C2×C4⋊C4—52no—
839C2×C4⋊C4—52no—
840C2×C4⋊C4—51no—
841C2×C4⋊C4—51no—
842C2×C4⋊C4—52no—
843C2×C4⋊C4—51no—
844C2×C4⋊C4—52no—
845C2×C4⋊C4—51no—
846C2×C4⋊C4—52no—
847C2×C4⋊C4—52no—
848C2×C4⋊C4—51no—
849C2×C4⋊C4—51no—
850C2×C4⋊C4—51no—
851C2×C4⋊C4—52no—
852C2×C4⋊C4—51no—
853C2×C4⋊C4—52no—
854C2×C4⋊C4—52no—
855C2×C4⋊C4—52no—
856C2×C4⋊C4—52no—
857C2×C4⋊C4—516no—
858C2×C4⋊C4—58no—
859C2×C4⋊C4—58no—
860C2×C4⋊C4C22×D511yescharacteristic
861C2×C4⋊C4C22×D511yescharacteristic
862C2×C4⋊C4C22×D511yescharacteristic
863C2×C4⋊C4C22×D511yescharacteristic
864C2×C4⋊C4C22×D512yes—
865C2×C4⋊C4C22×D512yes—
866C2×C4⋊C4C22×D512yes—
867C2×C4⋊C4C22×D512yes—
868C2×C4⋊C4C22×D511yescharacteristic
869C2×C4⋊C4C22×D511yescharacteristic
870C2×C4⋊C4C22×D512yes—
871C2×C4⋊C4C22×D512yes—
872C2×C4⋊C4C22×D512yes—
873C2×C4⋊C4C22×D512yes—
874C2×C22⋊C4—52no—
875C2×C22⋊C4—51no—
876C2×C22⋊C4—51no—
877C2×C22⋊C4—51no—
878C2×C22⋊C4—52no—
879C2×C22⋊C4—52no—
880C2×C22⋊C4—52no—
881C2×C22⋊C4—52no—
882C2×C22⋊C4—51no—
883C2×C22⋊C4—52no—
884C2×C22⋊C4—51no—
885C2×C22⋊C4—51no—
886C2×C22⋊C4—52no—
887C2×C22⋊C4—52no—
888C2×C22⋊C4—52no—
889C2×C22⋊C4—51no—
890C2×C22⋊C4—51no—
891C2×C22⋊C4—52no—
892C2×C22⋊C4—52no—
893C2×C22⋊C4—52no—
894C2×C22⋊C4—52no—
895C2×C22⋊C4—51no—
896C2×C22⋊C4—52no—
897C2×C22⋊C4—51no—
898C2×C22⋊C4—52no—
899C2×C42—52no—
900C2×C42—52no—
901C2×C42—52no—
902C2×C42—51no—
903C2×C42—51no—
904C2×C42—52no—
905C2×C42—51no—
906C2×C42—58no—
907C2×C42C22×D512yes—
908C2×C42C22×D511yescharacteristic
909C2×C42C22×D511yescharacteristic
910C2×C42C22×D512yes—
911C2×C42C22×D511yescharacteristic
912C2×C42C22×D512yes—
913C22×C5C2×2−1+412yes—
914C22×C5#58512yes—
915C22×C5#58512yes—
916C22×C5C2611yescharacteristic
917C2×D5—22no—
918C2×D5—22no—
919C2×D5—22no—
920C2×D5—24no—
921C2×D5—22no—
922C2×D5—22no—
923C2×D5—24no—
924C2×D5—22no—
925C2×D5—24no—
926C2×D5—22no—
927C2×D5—22no—
928C2×D5—22no—
929C2×D5—44no—
930C2×D5—44no—
931C2×D5—44no—
932C2×D5—48no—
933C4×C5—24no—
934C4×C5—22no—
935C4×C5—24no—
936C4×C5—24no—
937C4×C5—22no—
938C4×C5—22no—
939C4×C5—22no—
940C4×C5—22no—
941C4×C5—24no—
942C4×C5—22no—
943C4×C5C2×2−1+414yes—
944Dic5—22no—
945Dic5—22no—
946Dic5—22no—
947Dic5—22no—
948Dic5—22no—
949Dic5—24no—
950Dic5—24no—
951Dic5—24no—
952C24—51no—
953C24—51no—
954C24—51no—
955C24—52no—
956C2×Q8—24no—
957C2×Q8—42no—
958C2×Q8—44no—
959C2×Q8—58no—
960C2×Q8—58no—
961C2×Q8—58no—
962C2×Q8—204no—
963C2×Q8—204no—
964C2×Q8—204no—
965C2×Q8C23×D514yes—
966C2×Q8C23×D514yes—
967C2×Q8C23×D518yes—
968C2×D4—54no—
969C2×D4—54no—
970C2×D4—58no—
971C2×D4—54no—
972C2×D4—58no—
973C2×D4—58no—
974C2×D4—54no—
975C2×D4—104no—
976C2×D4—202no—
977C2×D4—204no—
978C2×D4—204no—
979C2×D4—202no—
980C2×D4—204no—
981C2×D4—202no—
982C22×C4—51no—
983C22×C4—51no—
984C22×C4—51no—
985C22×C4—51no—
986C22×C4—52no—
987C22×C4—51no—
988C22×C4—52no—
989C22×C4—52no—
990C22×C4—54no—
991C22×C4—54no—
992C22×C4—54no—
993C22×C4—54no—
994C22×C4—54no—
995C22×C4—58no—
996C22×C4—58no—
997C22×C4—58no—
998C22×C4—58no—
999C22×C4—58no—
1000C22×C4—104no—
1001C22×C4—104no—
1002C22×C4—104no—
1003C22×C4—204no—
1004C22×C4—204no—
1005C22×C4—202no—
1006C22×C4—204no—
1007C22×C4—202no—
1008C22×C4—204no—
1009C22×C4—204no—
1010C22×C4C23×D512yes—
1011C22×C4C23×D511yescharacteristic
1012C22×C4C23×D512yes—
1013C22×C4C23×D511yescharacteristic
1014C22×C4C23×D512yes—
1015C22×C4C23×D512yes—
1016C22×C4C23×D511yescharacteristic
1017C22×C4C23×D511yescharacteristic
1018C22×C4C23×D511yescharacteristic
1019C22×C4C23×D511yescharacteristic
1020C22×C4C23×D511yescharacteristic
1021C4⋊C4—54no—
1022C4⋊C4—54no—
1023C4⋊C4—58no—
1024C4⋊C4—58no—
1025C4⋊C4—58no—
1026C4⋊C4—58no—
1027C4⋊C4—58no—
1028C4⋊C4—54no—
1029C4⋊C4—54no—
1030C4⋊C4—58no—
1031C4⋊C4—54no—
1032C4⋊C4—58no—
1033C4⋊C4—54no—
1034C4⋊C4—58no—
1035C4⋊C4—58no—
1036C4⋊C4—54no—
1037C4⋊C4—54no—
1038C4⋊C4—54no—
1039C4⋊C4—58no—
1040C4⋊C4—54no—
1041C4⋊C4—58no—
1042C4⋊C4—58no—
1043C4⋊C4—58no—
1044C4⋊C4—58no—
1045C4⋊C4C23×D514yes—
1046C4⋊C4C23×D514yes—
1047C4⋊C4C23×D514yes—
1048C4⋊C4C23×D514yes—
1049C4⋊C4C23×D518yes—
1050C4⋊C4C23×D518yes—
1051C4⋊C4C23×D518yes—
1052C4⋊C4C23×D518yes—
1053C4⋊C4C23×D514yes—
1054C4⋊C4C23×D514yes—
1055C4⋊C4C23×D518yes—
1056C4⋊C4C23×D518yes—
1057C4⋊C4C23×D518yes—
1058C4⋊C4C23×D518yes—
1059C22⋊C4—58no—
1060C22⋊C4—54no—
1061C22⋊C4—54no—
1062C22⋊C4—54no—
1063C22⋊C4—58no—
1064C22⋊C4—58no—
1065C22⋊C4—58no—
1066C22⋊C4—58no—
1067C22⋊C4—54no—
1068C22⋊C4—58no—
1069C22⋊C4—54no—
1070C22⋊C4—54no—
1071C22⋊C4—58no—
1072C22⋊C4—58no—
1073C22⋊C4—58no—
1074C22⋊C4—54no—
1075C22⋊C4—54no—
1076C22⋊C4—58no—
1077C22⋊C4—58no—
1078C22⋊C4—58no—
1079C22⋊C4—58no—
1080C22⋊C4—54no—
1081C22⋊C4—58no—
1082C22⋊C4—54no—
1083C22⋊C4—58no—
1084C42—54no—
1085C42—54no—
1086C42—54no—
1087C42—58no—
1088C42—58no—
1089C42—58no—
1090C42—58no—
1091C42C23×D514yes—
1092C42C23×D518yes—
1093C42C23×D514yes—
1094C42C23×D514yes—
1095C42C23×D518yes—
1096C42C23×D518yes—
1097C2×C5#356514yescomplemented
1098C2×C5C22×2−1+411yescharacteristic
1099C2×C5C2×#58511yescharacteristic
1100C2×C5C2×#58511yescharacteristic
1101D5—42no—
1102D5—42no—
1103D5—42no—
1104D5—44no—
1105C23—52no—
1106C23—52no—
1107C23—52no—
1108C23—54no—
1109C23—102no—
1110C23—102no—
1111C23—102no—
1112C23—104no—
1113C23—102no—
1114C23—102no—
1115C23—104no—
1116C23—102no—
1117C23—102no—
1118C23—104no—
1119C23—102no—
1120C23—102no—
1121C23C24×D511yescharacteristic
1122Q8—28no—
1123Q8—44no—
1124Q8—48no—
1125Q8—208no—
1126Q8—208no—
1127Q8—208no—
1128D4—108no—
1129D4—204no—
1130D4—208no—
1131D4—208no—
1132D4—204no—
1133D4—208no—
1134D4—204no—
1135C2×C4—24no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—22no—
1139C2×C4—24no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—24no—
1144C2×C4—22no—
1145C2×C4—52no—
1146C2×C4—52no—
1147C2×C4—52no—
1148C2×C4—52no—
1149C2×C4—52no—
1150C2×C4—54no—
1151C2×C4—54no—
1152C2×C4—54no—
1153C2×C4—102no—
1154C2×C4—102no—
1155C2×C4—102no—
1156C2×C4—104no—
1157C2×C4—102no—
1158C2×C4—104no—
1159C2×C4—104no—
1160C2×C4—102no—
1161C2×C4—108no—
1162C2×C4—108no—
1163C2×C4—108no—
1164C2×C4—208no—
1165C2×C4—208no—
1166C2×C4—204no—
1167C2×C4—208no—
1168C2×C4—204no—
1169C2×C4—208no—
1170C2×C4—208no—
1171C2×C4#414714yes—
1172C2×C4C24×D514yes—
1173C2×C4C24×D512yes—
1174C2×C4C24×D512yes—
1175C2×C4C24×D514yes—
1176C2×C4C24×D514yes—
1177C2×C4C24×D514yes—
1178C2×C4C24×D512yes—
1179C2×C4C24×D512yes—
1180C2×C4C24×D512yes—
1181C2×C4C24×D512yes—
1182C2×C4C24×D512yes—
1183C5C2×#356511yescharacteristic, complemented, Sylow
1184C22—102no—
1185C22—102no—
1186C22—102no—
1187C22—104no—
1188C22—102no—
1189C22—102no—
1190C22—104no—
1191C22—102no—
1192C22—102no—
1193C22—104no—
1194C22—102no—
1195C22—102no—
1196C22—204no—
1197C22—204no—
1198C22—204no—
1199C22—208no—
1200C22C2×#414712yes—
1201C22#6628312yes—
1202C22#6628712yes—
1203C22C25×D511yescharacteristic
1204C4—24no—
1205C4—22no—
1206C4—24no—
1207C4—22no—
1208C4—24no—
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—24no—
1213C4—22no—
1214C4—102no—
1215C4—102no—
1216C4—102no—
1217C4—104no—
1218C4—102no—
1219C4—104no—
1220C4—102no—
1221C4—104no—
1222C4C2×#414714yes—
1223C2—202no—
1224C2—202no—
1225C2—202no—
1226C2—204no—
1227C2#1061893014yesdirect product factor
1228C2C22×#414711yescharacteristic
1229C2C2×#6628311yescharacteristic
1230C2C2×#6628711yescharacteristic
subgroupG/H
centerC23C24×D5
commutator, cosocleC22×C5C26
FrattiniC22C25×D5
FittingC2×C5×#557C2
socleC23×C5C25
hypercenterC2×#557D5
hypocenterC5C2×#3565
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. #10618930C2direct (N × H)
3. C2×#66069C2semidirect
4. C2×#66063C2semidirect
5. C2×#66067C2semidirect
6. C2×#66068C2semidirect
7. C2×#66034C2semidirect
8. C2×#66029C2semidirect
9. C2×#66029C2semidirect
10. C2×#66027C2semidirect
11. C2×#66023C2semidirect
12. C2×#66026C2semidirect
13. C2×#66030C2semidirect
14. C2×#66022C2semidirect
15. C2×#65913C2semidirect
16. C2×#65915C2semidirect
17. C2×#65915C2semidirect
18. C2×#65916C2semidirect
19. C2×#65916C2semidirect
20. C2×#65916C2semidirect
21. C2×#65914C2semidirect
22. C2×#65914C2semidirect
23. C2×#65902C2semidirect
24. C2×#65918C2semidirect
25. C5×#557C22semidirect
48. #66069C22semidirect
49. #66068C22semidirect
50. #66067C22semidirect
51. #66063C22semidirect
52. #66034C22semidirect
53. #66030C22semidirect
54. #66029C22semidirect
55. #66029C22semidirect
56. #66027C22semidirect
57. #66026C22semidirect
58. #66023C22semidirect
59. #66022C22semidirect
60. #65918C22semidirect
61. #65916C22semidirect
62. #65916C22semidirect
63. #65916C22semidirect
64. #65915C22semidirect
65. #65915C22semidirect
66. #65914C22semidirect
67. #65914C22semidirect
68. #65913C22semidirect
69. #65902C22semidirect
349. C2×#557D5semidirect
517. #557C2×D5semidirect
1097. C2×C5#3565semidirect
1183. C5C2×#3565semidirect
1227. C2#10618930direct (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
#106189302
C2×#660692
C2×#660632
C2×#660672
C2×#660682
C2×#660342
C2×#660292
C2×#660272
C2×#660232
C2×#660262
C2×#660302
C2×#660222
C2×#659132
C2×#659152
C2×#659162
C2×#659142
C2×#659022
C2×#659182
C2×#35655