Finite Group Databasebeta

← C2×#10613477 #12971447

Subgroups — C2×#10613477 #12971447

Order 1280.

1758 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66062C211yesmaximal, characteristic
2C2×#66022C211yesmaximal, characteristic
3C2×C5×#491C211yesmaximal, characteristic, complemented
4C2×#65371C211yesmaximal, characteristic, complemented
5C2×#65354C211yesmaximal, characteristic, complemented
6#10613477C2116yesmaximal, direct product factor
7C2×#65104C212yesmaximal
8C2×#65103C212yesmaximal
9C2×#65083C212yesmaximal, complemented
10C2×#65080C212yesmaximal, complemented
11C2×#64994C211yesmaximal, characteristic
12C2×#64991C211yesmaximal, characteristic, complemented
13C2×C5×C4⋊Q8C2211yescharacteristic
14C2×C5×#125C2211yescharacteristic
15C2×#4092C2212yes—
16C2×Q8×Dic5C2212yes—
17#66062—24no—
18#66062C2218yes—
19#66022—24no—
20#66022C2218yes—
21C2×#4043—21no—
22C2×#4042—21no—
23C2×#4042—21no—
24C2×#4038—21no—
25C2×#4038C2211yescharacteristic
26C2×#4038C2211yescharacteristic
27C2×#4036—21no—
28C2×#4034C2211yescharacteristic
29C2×#4034C2211yescharacteristic
30C2×#4033—21no—
31C2×#4033—21no—
32C2×#4033—21no—
33C2×C42×D5C2211yescharacteristic
34C2×#4016C2211yescharacteristic
35C2×#4015C2211yescharacteristic
36C5×#491C2218yescomplemented
37C2×C5×#103C2212yes—
38C2×C5×#103C2212yes—
39C2×C5×#97C2211yescharacteristic
40C2×#3967C2212yes—
41C2×#3967C2212yes—
42C2×#3952C2212yes—
43C2×#3950C2212yes—
44C2×#3949C2212yes—
45C2×#3946C2212yes—
46#65371C2218yescomplemented
47#65354C2218yescomplemented
48C2×#3940C2212yes—
49C2×#3939C2212yes—
50C2×#3935C2211yescharacteristic
51#65104C22116yes—
52#65103C22116yes—
53#65083C22116yescomplemented
54#65080C22116yescomplemented
55#64994C2218yes—
56#64991C2218yescomplemented
57C2×#3237—51nomaximal, Sylow
58C22×C5×Q8C2312yes—
59C22×C4×D5D411yescharacteristic
60C22×C4×D5D411yescharacteristic
61C22×C4×D5C2311yescharacteristic
62C22×Dic10—21no—
63C22×Dic10—21no—
64C22×Dic10—21no—
65C22×C5×C8C2312yes—
66C5×C4⋊Q8—22no—
67C5×C4⋊Q8C2314yes—
68C5×#125—22no—
69C5×#125C2314yes—
70C2×C5×C4⋊C4—21no—
71C2×C5×C4⋊C4—21no—
72C2×C5×C4⋊C4—21no—
73C2×C5×C4⋊C4—21no—
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2311yescharacteristic
76C2×C42×C5C2311yescharacteristic
77#4092—24no—
78#4092C2318yes—
79Q8×Dic5—24no—
80Q8×Dic5C2318yes—
81C2×#685—22no—
82C2×#685—21no—
83C2×#685—21no—
84C2×C4⋊Dic5—21no—
85C2×C4⋊Dic5—22no—
86C2×C4⋊Dic5C2312yes—
87C2×C4⋊Dic5C2311yescharacteristic
88C2×C4⋊Dic5C2311yescharacteristic
89C2×#683—21no—
90C2×#683—21no—
91C2×#683—21no—
92C2×#683—21no—
93C2×#683—22no—
94C2×C4×Dic5—21no—
95C2×C4×Dic5—21no—
96C2×C4×Dic5—22no—
97C2×C4×Dic5D411yescharacteristic
98C2×C4×Dic5D411yescharacteristic
99C2×C4×Dic5C2311yescharacteristic
100C22×#168C2312yes—
101#4043—28no—
102#4042—28no—
103#4042—28no—
104#4038—28no—
105#4038—22no—
106#4038—22no—
107#4038C2314yes—
108#4038C2314yes—
109#4036—28no—
110#4034—22no—
111#4034—22no—
112#4034C2314yes—
113#4034C2314yes—
114#4033—28no—
115#4033—28no—
116#4033—28no—
117C42×D5D414yes—
118C42×D5C2314yes—
119#4016—22no—
120#4016C2314yes—
121#4015—22no—
122#4015C2314yes—
123C5×#103C2318yes—
124C5×#103C2318yes—
125C5×#97C2314yes—
126#3967C2318yes—
127#3967C2318yes—
128#3952C2318yes—
129#3950C2318yes—
130#3949C2318yes—
131#3946C2318yes—
132#3940C2318yes—
133#3939C2318yes—
134#3935C2314yes—
135C2×#533—51no—
136C2×#533—51no—
137#3237—516no—
138C2×#501—51no—
139C2×#501—51no—
140C2×#491—51no—
141C2×#491D511yescharacteristic, complemented
142C2×#485—52no—
143C2×#485—52no—
144C2×#477—52no—
145C2×#475—52no—
146C2×#432—51no—
147C23×D5C2×D411yescharacteristic
148C2×C5×Q8—22no—
149C2×C5×Q8—28no—
150C2×C5×Q8C2414yes—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—22no—
154C22×C4×C5C2×D411yescharacteristic
155C22×C4×C5C2×D411yescharacteristic
156C22×C4×C5C2411yescharacteristic
157C22×Dic5—21no—
158C22×Dic5—21no—
159C22×Dic5—22no—
160C22×Dic5C2×D411yescharacteristic
161C22×Dic5C2×D411yescharacteristic
162C22×Dic5C2×D411yescharacteristic
163C2×C4×D5—24no—
164C2×C4×D5—24no—
165C2×C4×D5—42no—
166C2×C4×D5C2×D414yes—
167C2×C4×D5C2×D412yes—
168C2×C4×D5C2×D414yes—
169C2×C4×D5C2412yes—
170C2×Dic10—24no—
171C2×Dic10—24no—
172C2×Dic10—24no—
173C2×Dic10—44no—
174C2×Dic10—44no—
175C2×Dic10—44no—
176C2×C5×C8—24no—
177C2×C5×C8C2414yes—
178C5×C4⋊C4—24no—
179C5×C4⋊C4—24no—
180C5×C4⋊C4—24no—
181C5×C4⋊C4—24no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4C2412yes—
185C5×C4⋊C4C2412yes—
186C42×C5C2×D412yes—
187C42×C5C2412yes—
188#685—28no—
189#685—24no—
190#685—24no—
191C4⋊Dic5—22no—
192C4⋊Dic5—24no—
193C4⋊Dic5—21no—
194C4⋊Dic5—21no—
195C4⋊Dic5—28no—
196C4⋊Dic5C2414yes—
197C4⋊Dic5C2412yes—
198C4⋊Dic5C2412yes—
199#683—24no—
200#683—24no—
201#683—24no—
202#683—24no—
203#683—28no—
204C4×Dic5—24no—
205C4×Dic5—24no—
206C4×Dic5—28no—
207C4×Dic5C2×D412yes—
208C4×Dic5C2×D414yes—
209C4×Dic5C2×D414yes—
210C4×Dic5C2412yes—
211C2×#168—24no—
212C2×#168C2414yes—
213#533—58no—
214#533—58no—
215#533—104no—
216#533—104no—
217C2×C4⋊Q8—51no—
218C2×C4⋊Q8—51no—
219C2×C4⋊Q8—51no—
220C2×C4⋊Q8C2×D511yescharacteristic
221C2×#125—51no—
222C2×#125—101no—
223C2×#125C2×D511yescharacteristic
224C2×C22⋊Q8—52no—
225C2×C22⋊Q8—101no—
226C2×C22⋊Q8—101no—
227C2×C22⋊Q8—101no—
228C2×C4×Q8—52no—
229C2×C4×Q8—101no—
230C2×C4×Q8—101no—
231C2×C4×Q8—101no—
232C2×#117—51no—
233C2×#117—51no—
234C2×#117—101no—
235C22×C42—51no—
236#501—58no—
237#501—58no—
238#491—58no—
239#491C2×D518yescomplemented
240#485—516no—
241#485—516no—
242#477—516no—
243#475—516no—
244#432—58no—
245C2×#107—52no—
246C2×#107—52no—
247C2×#106—52no—
248C2×#106—52no—
249C2×C4⋊C8—52no—
250C2×#103—52no—
251C2×#103—52no—
252C2×#103C2×D512yes—
253C2×#103C2×D512yes—
254C2×C22⋊C8—52no—
255C2×#97—51no—
256C2×#97C2×D511yescharacteristic
257C23×C5C22×D411yescharacteristic
258C22×D5—22no—
259C22×D5—22no—
260C22×D5—22no—
261C22×D5C22×D412yes—
262C5×Q8—28no—
263C5×Q8—44no—
264C2×C4×C5—22no—
265C2×C4×C5—22no—
266C2×C4×C5—24no—
267C2×C4×C5—22no—
268C2×C4×C5—22no—
269C2×C4×C5—44no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5C22×D412yes—
273C2×C4×C5C22×D412yes—
274C2×C4×C5C22×D411yescharacteristic
275C2×C4×C52−1+414yes—
276C2×C4×C5C2511yescharacteristic
277C2×Dic5—22no—
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—22no—
281C2×Dic5—24no—
282C2×Dic5—42no—
283C2×Dic5—42no—
284C2×Dic5—44no—
285C2×Dic5#13714yes—
286C2×Dic5C22×D412yes—
287C2×Dic5C22×D412yes—
288C2×Dic5C22×D412yes—
289C4×D5—24no—
290C4×D5—24no—
291C4×D5—28no—
292C4×D5—44no—
293Dic10—48no—
294Dic10—48no—
295Dic10—48no—
296C5×C8—24no—
297#168—24no—
298C22×Q8—101no—
299C22×Q8—101no—
300C22×Q8—101no—
301C22×Q8C22×D512yes—
302C23×C4—51no—
303C23×C4—51no—
304C23×C4—51no—
305C22×C8—52no—
306C22×C8C22×D512yes—
307C4⋊Q8—22no—
308C4⋊Q8—54no—
309C4⋊Q8—54no—
310C4⋊Q8—54no—
311C4⋊Q8—102no—
312C4⋊Q8—102no—
313C4⋊Q8—102no—
314C4⋊Q8C22×D514yes—
315#125—22no—
316#125—54no—
317#125—108no—
318#125—102no—
319#125C22×D514yes—
320C22⋊Q8—58no—
321C22⋊Q8—108no—
322C22⋊Q8—108no—
323C22⋊Q8—108no—
324C22⋊Q8—104no—
325C4×Q8—58no—
326C4×Q8—108no—
327C4×Q8—108no—
328C4×Q8—108no—
329C4×Q8—104no—
330#117—54no—
331#117—54no—
332#117—102no—
333#117—102no—
334#117—108no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—21no—
337C2×C4⋊C4—21no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—51no—
340C2×C4⋊C4—51no—
341C2×C4⋊C4—52no—
342C2×C4⋊C4—102no—
343C2×C4⋊C4—102no—
344C2×C4⋊C4—101no—
345C2×C4⋊C4—101no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—101no—
349C2×C4⋊C4C22×D511yescharacteristic
350C2×C4⋊C4C22×D511yescharacteristic
351C2×C22⋊C4—101no—
352C2×C22⋊C4—101no—
353C2×C22⋊C4—102no—
354C2×C42—51no—
355C2×C42—51no—
356C2×C42—51no—
357C2×C42—54no—
358C2×C42—54no—
359C2×C42—101no—
360C2×C42—101no—
361C2×C42—102no—
362C2×C42C22×D511yescharacteristic
363#107—58no—
364#107—58no—
365#106—58no—
366#106—58no—
367C4⋊C8—58no—
368#103—58no—
369#103—58no—
370#103C22×D518yes—
371#103C22×D518yes—
372C22⋊C8—58no—
373#97—54no—
374#97C22×D514yes—
375C22×C5#53612yes—
376C22×C5C2×#13712yes—
377C22×C5#57512yes—
378C22×C5C23×D411yescharacteristic
379C2×D5—22no—
380C2×D5—22no—
381C2×D5—22no—
382C2×D5—44no—
383C4×C5—22no—
384C4×C5—22no—
385C4×C5—44no—
386C4×C5—42no—
387C4×C5—42no—
388C4×C5#53612yes—
389C4×C5C2×2−1+412yes—
390Dic5—22no—
391Dic5—22no—
392Dic5—42no—
393Dic5—42no—
394Dic5—44no—
395Dic5C2×#13714yes—
396C24—51no—
397C2×Q8—22no—
398C2×Q8—28no—
399C2×Q8—104no—
400C2×Q8—104no—
401C2×Q8—104no—
402C2×Q8—204no—
403C2×Q8—204no—
404C2×Q8—204no—
405C2×Q8C23×D514yes—
406C22×C4—22no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—51no—
410C22×C4—51no—
411C22×C4—51no—
412C22×C4—54no—
413C22×C4—52no—
414C22×C4—52no—
415C22×C4—54no—
416C22×C4—104no—
417C22×C4—104no—
418C22×C4—101no—
419C22×C4—101no—
420C22×C4—102no—
421C22×C4—202no—
422C22×C4D4×D511yescharacteristic
423C22×C4D4×D511yescharacteristic
424C22×C4C23×D511yescharacteristic
425C2×C8—24no—
426C2×C8—54no—
427C2×C8—104no—
428C2×C8C23×D514yes—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—52no—
436C4⋊C4—52no—
437C4⋊C4—54no—
438C4⋊C4—108no—
439C4⋊C4—108no—
440C4⋊C4—104no—
441C4⋊C4—104no—
442C4⋊C4—101no—
443C4⋊C4—101no—
444C4⋊C4—102no—
445C4⋊C4—104no—
446C4⋊C4—104no—
447C4⋊C4—104no—
448C4⋊C4C23×D512yes—
449C4⋊C4C23×D512yes—
450C22⋊C4—104no—
451C22⋊C4—104no—
452C22⋊C4—108no—
453C42—54no—
454C42—54no—
455C42—52no—
456C42—52no—
457C42—104no—
458C42—104no—
459C42—108no—
460C42D4×D512yes—
461C42C23×D512yes—
462C2×C5#323714yescomplemented
463C2×C5C2×#53611yescharacteristic
464C2×C5C22×#13711yescharacteristic
465C2×C5C2×#57511yescharacteristic
466D5—42no—
467C23—52no—
468C23—102no—
469C23—102no—
470C23—102no—
471C23C2×D4×D511yescharacteristic
472Q8—28no—
473Q8—44no—
474Q8—208no—
475Q8—208no—
476Q8—208no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—54no—
486C2×C4—52no—
487C2×C4—52no—
488C2×C4—52no—
489C2×C4—108no—
490C2×C4—102no—
491C2×C4—102no—
492C2×C4—104no—
493C2×C4—104no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—104no—
497C2×C4—204no—
498C2×C4—202no—
499C2×C4—204no—
500C2×C4—202no—
501C2×C4C2×D4×D512yes—
502C2×C4C2×D4×D512yes—
503C2×C4C2×D4×D511yescharacteristic
504C2×C4#415014yes—
505C2×C4C24×D511yescharacteristic
506C8—24no—
507C8—104no—
508C5C2×#323711yescharacteristic, complemented, Sylow
509C22—102no—
510C22—102no—
511C22—102no—
512C22—204no—
513C22#6600912yes—
514C22D5×#13712yes—
515C22#6611112yes—
516C22C22×D4×D511yescharacteristic
517C4—22no—
518C4—22no—
519C4—44no—
520C4—42no—
521C4—42no—
522C4—54no—
523C4—102no—
524C4—102no—
525C4—202no—
526C4—204no—
527C4—202no—
528C4#6600912yes—
529C4C2×#415012yes—
530C2—202no—
531C2#1061347714yesdirect product factor
532C2C2×#6600911yescharacteristic
533C2C2×D5×#13711yescharacteristic
534C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#491C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#491D5
hypocenterC5C2×#3237
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#491

Complements

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

NH ≅ G/Ntype
3. C2×C5×#491C2semidirect
4. C2×#65371C2semidirect
5. C2×#65354C2semidirect
6. #10613477C2direct (N × H)
9. C2×#65083C2semidirect
10. C2×#65080C2semidirect
12. C2×#64991C2semidirect
36. C5×#491C22semidirect
46. #65371C22semidirect
47. #65354C22semidirect
53. #65083C22semidirect
54. #65080C22semidirect
56. #64991C22semidirect
141. C2×#491D5semidirect
239. #491C2×D5semidirect
462. C2×C5#3237semidirect
508. C5C2×#3237semidirect
531. C2#10613477direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660622
C2×#660222
C2×C5×#4912
C2×#653712
C2×#653542
#106134772
C2×#651042
C2×#651032
C2×#650832
C2×#650802
C2×#649942
C2×#649912
C2×#32375