Finite Group Databasebeta

← C2×#10613708 #12968955

Subgroups — C2×#10613708 #12968955

Order 1280.

1902 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66062C211yesmaximal, characteristic
2C2×D5×#125C211yesmaximal, characteristic
3C2×C5×#501C211yesmaximal, characteristic, complemented
4C2×#65369C211yesmaximal, characteristic, complemented
5C2×#65354C211yesmaximal, characteristic, complemented
6#10613708C2116yesmaximal, direct product factor
7C2×#65170C212yesmaximal
8C2×#65167C212yesmaximal, complemented
9C2×#65150C212yesmaximal
10C2×#65147C212yesmaximal, complemented
11C2×#64996C211yesmaximal, characteristic
12C2×#64991C211yesmaximal, characteristic, complemented
13C2×C5×C4⋊Q8C2211yescharacteristic
14C2×C5×#125C2211yescharacteristic
15C2×#4092—21no—
16C2×Q8×Dic5—21no—
17C22×#676C2212yes—
18#66062—24no—
19#66062C2218yes—
20D5×#125—24no—
21D5×#125C2218yes—
22C2×#4043—21no—
23C2×#4038C2212yes—
24C2×D5×C4⋊C4—21no—
25C2×D5×C4⋊C4—21no—
26C2×D5×C4⋊C4C2211yescharacteristic
27C2×D5×C4⋊C4C2211yescharacteristic
28C2×#4036C2211yescharacteristic
29C2×#4036C2211yescharacteristic
30C2×#4036C2212yes—
31C2×#4035—21no—
32C2×#4035—21no—
33C2×#4033—21no—
34C2×C42×D5C2211yescharacteristic
35C2×#4016C2211yescharacteristic
36C2×#4015C2211yescharacteristic
37C5×#501C2218yescomplemented
38C2×C5×#107C2212yes—
39C2×C5×#106C2212yes—
40C2×C5×#97C2211yescharacteristic
41C2×#3950C2212yes—
42C2×#3949C2212yes—
43C2×C8×Dic5C2212yes—
44#65369C2218yescomplemented
45#65354C2218yescomplemented
46C2×#3940C2212yes—
47C2×#3940C2212yes—
48C2×#3939C2212yes—
49C2×#3939C2212yes—
50C2×#3935C2211yescharacteristic
51#65170C22116yes—
52#65167C22116yescomplemented
53#65150C22116yes—
54#65147C22116yescomplemented
55#64996C2218yes—
56#64991C2218yescomplemented
57C2×#3166—51nomaximal, Sylow
58C22×C5×Q8—21no—
59C22×C4×D5—21no—
60C22×C4×D5—21no—
61C22×C4×D5D411yescharacteristic
62C22×C4×D5D411yescharacteristic
63C22×C4×D5C2311yescharacteristic
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⋊C4C2311yescharacteristic
74C2×C5×C4⋊C4C2311yescharacteristic
75C2×C5×C4⋊C4C2312yes—
76C2×C42×C5C2311yescharacteristic
77#4092—28no—
78Q8×Dic5—28no—
79C2×#685—22no—
80C2×C4⋊Dic5—21no—
81C2×C4⋊Dic5—21no—
82C2×C4⋊Dic5—21no—
83C2×C4⋊Dic5—22no—
84C2×C4⋊Dic5C2312yes—
85C2×C4⋊Dic5C2311yescharacteristic
86C2×C4⋊Dic5C2311yescharacteristic
87C2×#683—21no—
88C2×#683—21no—
89C2×#683—22no—
90C2×#683—21no—
91C2×#683—21no—
92C2×#683—21no—
93C2×#683—21no—
94C2×C4×Dic5—22no—
95C2×C4×Dic5D411yescharacteristic
96C2×C4×Dic5D411yescharacteristic
97C2×C4×Dic5C2311yescharacteristic
98C22×#168C2312yes—
99C2×#676Q8116yescomplemented
100C2×#676C2318yes—
101#4043—28no—
102#4038—24no—
103#4038C2318yes—
104D5×C4⋊C4—28no—
105D5×C4⋊C4—28no—
106D5×C4⋊C4—22no—
107D5×C4⋊C4—22no—
108D5×C4⋊C4C2314yes—
109D5×C4⋊C4C2314yes—
110#4036—24no—
111#4036—22no—
112#4036—22no—
113#4036C2318yes—
114#4036C2314yes—
115#4036C2314yes—
116#4035—28no—
117#4035—28no—
118#4033—28no—
119C42×D5D414yes—
120C42×D5C2314yes—
121#4016—22no—
122#4016C2314yes—
123#4015—22no—
124#4015C2314yes—
125C5×#107C2318yes—
126C5×#106C2318yes—
127C5×#97C2314yes—
128#3950C2318yes—
129#3949C2318yes—
130C8×Dic5C2318yes—
131#3940C2318yes—
132#3940C2318yes—
133#3939C2318yes—
134#3939C2318yes—
135#3935C2314yes—
136C2×#533—51no—
137C22×#125—51no—
138#3166—516no—
139C2×#501—51no—
140C2×#501—51no—
141C2×#501—51no—
142C2×#501D511yescharacteristic, complemented
143C2×#499—52no—
144C2×#499—52no—
145C2×#428—52no—
146C2×#428—52no—
147C2×C4×M16—51no—
148C23×D5C2×D411yescharacteristic
149C2×C5×Q8—24no—
150C2×C5×Q8—44no—
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—22no—
158C22×Dic5—21no—
159C22×Dic5—21no—
160C22×Dic5C2×D411yescharacteristic
161C22×Dic5C2×D411yescharacteristic
162C22×Dic5C2×D411yescharacteristic
163C2×C4×D5—24no—
164C2×C4×D5—24no—
165C2×C4×D5—42no—
166C2×C4×D5—42no—
167C2×C4×D5—44no—
168C2×C4×D5—44no—
169C2×C4×D5C2×D414yes—
170C2×C4×D5C2×D414yes—
171C2×C4×D5C2×D412yes—
172C2×C4×D5C2×Q818yes—
173C2×C4×D5C2412yes—
174C2×Dic10—24no—
175C2×Dic10—44no—
176C2×C5×C8C2×Q818yes—
177C2×C5×C8C2414yes—
178C5×C4⋊C4—24no—
179C5×C4⋊C4—24no—
180C5×C4⋊C4—24no—
181C5×C4⋊C4—21no—
182C5×C4⋊C4—21no—
183C5×C4⋊C4—22no—
184C5×C4⋊C4C2412yes—
185C5×C4⋊C4C2412yes—
186C5×C4⋊C4C2414yes—
187C42×C5C2×D412yes—
188C42×C5C2412yes—
189#685—28no—
190C4⋊Dic5—22no—
191C4⋊Dic5—24no—
192C4⋊Dic5—21no—
193C4⋊Dic5—21no—
194C4⋊Dic5—24no—
195C4⋊Dic5—24no—
196C4⋊Dic5—28no—
197C4⋊Dic5C2412yes—
198C4⋊Dic5C2414yes—
199C4⋊Dic5C2412yes—
200#683—24no—
201#683—24no—
202#683—28no—
203#683—24no—
204#683—24no—
205#683—24no—
206#683—24no—
207C4×Dic5—28no—
208C4×Dic5C2×D412yes—
209C4×Dic5C2×D414yes—
210C4×Dic5C2×D414yes—
211C4×Dic5C2412yes—
212C2×#168C2×Q818yes—
213C2×#168C2414yes—
214#676C2×Q8132yescomplemented
215C22×M16—52no—
216#533—58no—
217#533—104no—
218C2×C4⋊Q8—51no—
219C2×C4⋊Q8C2×D511yescharacteristic
220C2×#125—58no—
221C2×#125—51no—
222C2×#125—51no—
223C2×#125—52no—
224C2×#125—51no—
225C2×#125—101no—
226C2×#125—101no—
227C2×#125—104no—
228C2×#125C2×D511yescharacteristic
229C2×C22⋊Q8—101no—
230C2×C22⋊Q8—101no—
231C2×C4×Q8—101no—
232C2×C4×Q8—101no—
233C2×#117—52no—
234C22×C4⋊C4—51no—
235C22×C4⋊C4—51no—
236C22×C4⋊C4—101no—
237C22×C4⋊C4—101no—
238C22×C42—51no—
239#501—58no—
240#501—58no—
241#501—58no—
242#501C2×D518yescomplemented
243#499—516no—
244#499—516no—
245#428—516no—
246#428—516no—
247C2×#107—52no—
248C2×#107—52no—
249C2×#107—52no—
250C2×#107C2×D512yes—
251C2×#106—52no—
252C2×#106—52no—
253C2×#106—52no—
254C2×#106C2×D512yes—
255C4×M16—58no—
256C2×#97—51no—
257C2×#97C2×D511yescharacteristic
258C2×C4×C8—52no—
259C23×C5C22×D411yescharacteristic
260C22×D5—22no—
261C22×D5—22no—
262C22×D5C4⋊Q814yes—
263C22×D5C22×D412yes—
264C5×Q8—48no—
265C2×C4×C5—22no—
266C2×C4×C5—22no—
267C2×C4×C5—24no—
268C2×C4×C5—22no—
269C2×C4×C5—22no—
270C2×C4×C5—42no—
271C2×C4×C5—42no—
272C2×C4×C5—44no—
273C2×C4×C5C22×D412yes—
274C2×C4×C5C22×D412yes—
275C2×C4×C5C22×D411yescharacteristic
276C2×C4×C5C22×Q814yes—
277C2×C4×C5C2511yescharacteristic
278C2×Dic5—22no—
279C2×Dic5—22no—
280C2×Dic5—24no—
281C2×Dic5—22no—
282C2×Dic5—22no—
283C2×Dic5—44no—
284C2×Dic5—42no—
285C2×Dic5—42no—
286C2×Dic5C4⋊Q814yes—
287C2×Dic5C22×D412yes—
288C2×Dic5C22×D412yes—
289C2×Dic5C22×D412yes—
290C4×D5—44no—
291C4×D5—44no—
292C4×D5—48no—
293C4×D5—48no—
294C4×D5C4⋊Q818yes—
295C4×D5C22×Q818yes—
296Dic10—48no—
297C5×C8C22×Q818yes—
298#168C22×Q818yes—
299C22×Q8—21no—
300C22×Q8—101no—
301C23×C4—51no—
302C23×C4—51no—
303C23×C4—51no—
304C23×C4—101no—
305C23×C4—101no—
306C2×M16—516no—
307C2×M16—58no—
308C22×C8—52no—
309C22×C8C22×D512yes—
310C4⋊Q8—22no—
311C4⋊Q8—54no—
312C4⋊Q8—102no—
313C4⋊Q8C22×D514yes—
314#125—22no—
315#125—54no—
316#125—54no—
317#125—58no—
318#125—54no—
319#125—108no—
320#125—108no—
321#125—102no—
322#125—102no—
323#125—104no—
324#125—102no—
325#125C22×D514yes—
326C22⋊Q8—108no—
327C22⋊Q8—108no—
328C4×Q8—108no—
329C4×Q8—108no—
330#117—58no—
331#117—104no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—51no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—52no—
338C2×C4⋊C4—54no—
339C2×C4⋊C4—54no—
340C2×C4⋊C4—102no—
341C2×C4⋊C4—102no—
342C2×C4⋊C4—108no—
343C2×C4⋊C4—108no—
344C2×C4⋊C4—101no—
345C2×C4⋊C4—101no—
346C2×C4⋊C4—101no—
347C2×C4⋊C4—101no—
348C2×C4⋊C4—101no—
349C2×C4⋊C4—101no—
350C2×C4⋊C4—102no—
351C2×C4⋊C4—102no—
352C2×C4⋊C4—101no—
353C2×C4⋊C4—101no—
354C2×C4⋊C4—101no—
355C2×C4⋊C4C22×D511yescharacteristic
356C2×C4⋊C4C22×D511yescharacteristic
357C2×C4⋊C4C22×D512yes—
358C2×C22⋊C4—102no—
359C2×C42—51no—
360C2×C42—51no—
361C2×C42—51no—
362C2×C42—54no—
363C2×C42—54no—
364C2×C42—102no—
365C2×C42C22×D511yescharacteristic
366#107—58no—
367#107—58no—
368#107—58no—
369#107C22×D518yes—
370#106—58no—
371#106—58no—
372#106—58no—
373#106C22×D518yes—
374#97—54no—
375#97C22×D514yes—
376C4×C8—58no—
377C22×C5C2×C4⋊Q812yes—
378C22×C5#57512yes—
379C22×C5#57512yes—
380C22×C5C23×D411yescharacteristic
381C2×D5—28no—
382C2×D5—22no—
383C2×D5—22no—
384C2×D5C2×C4⋊Q814yes—
385C4×C5—22no—
386C4×C5—22no—
387C4×C5—42no—
388C4×C5—42no—
389C4×C5—44no—
390C4×C5C2×C4⋊Q812yes—
391C4×C5C23×Q812yes—
392Dic5—22no—
393Dic5—22no—
394Dic5—44no—
395Dic5—42no—
396Dic5—42no—
397Dic5C2×C4⋊Q814yes—
398C24—51no—
399C2×Q8—24no—
400C2×Q8—44no—
401C2×Q8—104no—
402C2×Q8—204no—
403C22×C4—22no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—51no—
407C22×C4—52no—
408C22×C4—58no—
409C22×C4—52no—
410C22×C4—51no—
411C22×C4—51no—
412C22×C4—54no—
413C22×C4—54no—
414C22×C4—104no—
415C22×C4—104no—
416C22×C4—102no—
417C22×C4—101no—
418C22×C4—101no—
419C22×C4—202no—
420C22×C4—202no—
421C22×C4—204no—
422C22×C4—204no—
423C22×C4D4×D511yescharacteristic
424C22×C4D4×D511yescharacteristic
425C22×C4C23×D511yescharacteristic
426M16—532no—
427C2×C8—58no—
428C2×C8—54no—
429C2×C8Q8×D518yes—
430C2×C8C23×D514yes—
431C4⋊C4—24no—
432C4⋊C4—24no—
433C4⋊C4—24no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—22no—
437C4⋊C4—52no—
438C4⋊C4—52no—
439C4⋊C4—54no—
440C4⋊C4—104no—
441C4⋊C4—104no—
442C4⋊C4—104no—
443C4⋊C4—104no—
444C4⋊C4—104no—
445C4⋊C4—104no—
446C4⋊C4—108no—
447C4⋊C4—108no—
448C4⋊C4—101no—
449C4⋊C4—101no—
450C4⋊C4—102no—
451C4⋊C4—104no—
452C4⋊C4—104no—
453C4⋊C4—104no—
454C4⋊C4C23×D512yes—
455C4⋊C4C23×D514yes—
456C4⋊C4C23×D512yes—
457C22⋊C4—108no—
458C42—54no—
459C42—54no—
460C42—52no—
461C42—52no—
462C42—108no—
463C42D4×D512yes—
464C42C23×D512yes—
465C2×C5#316614yescomplemented
466C2×C5C22×C4⋊Q811yescharacteristic
467C2×C5C2×#57511yescharacteristic
468C2×C5C2×#57511yescharacteristic
469D5—24no—
470C23—54no—
471C23—52no—
472C23—102no—
473C23—102no—
474C23C2×D4×D511yescharacteristic
475Q8—48no—
476Q8—208no—
477C2×C4—22no—
478C2×C4—22no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—42no—
485C2×C4—54no—
486C2×C4—52no—
487C2×C4—58no—
488C2×C4—58no—
489C2×C4—52no—
490C2×C4—52no—
491C2×C4—102no—
492C2×C4—102no—
493C2×C4—104no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—204no—
497C2×C4—204no—
498C2×C4—208no—
499C2×C4—208no—
500C2×C4—202no—
501C2×C4—202no—
502C2×C4—204no—
503C2×C4C2×D4×D512yes—
504C2×C4C2×D4×D512yes—
505C2×C4C2×D4×D511yescharacteristic
506C2×C4C2×Q8×D514yes—
507C2×C4C24×D511yescharacteristic
508C8—58no—
509C8C2×Q8×D518yes—
510C5C2×#316611yescharacteristic, complemented, Sylow
511C22—54no—
512C22—108no—
513C22—102no—
514C22—102no—
515C22D5×C4⋊Q812yes—
516C22#6610712yes—
517C22#6611112yes—
518C22C22×D4×D511yescharacteristic
519C4—22no—
520C4—22no—
521C4—42no—
522C4—44no—
523C4—42no—
524C4—54no—
525C4—102no—
526C4—102no—
527C4—202no—
528C4—202no—
529C4—204no—
530C4D5×C4⋊Q812yes—
531C4C22×Q8×D512yes—
532C2—104no—
533C2#1061370814yesdirect product factor
534C2C2×D5×C4⋊Q811yescharacteristic
535C2C2×#6610711yescharacteristic
536C2C2×#6611111yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#501C2
socleC23×C5C22×D4
prime radicalC23×D5C2×D4
hypercenterC2×#501D5
hypocenterC5C2×#3166
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
3. C2×C5×#501C2semidirect
4. C2×#65369C2semidirect
5. C2×#65354C2semidirect
6. #10613708C2direct (N × H)
8. C2×#65167C2semidirect
10. C2×#65147C2semidirect
12. C2×#64991C2semidirect
37. C5×#501C22semidirect
44. #65369C22semidirect
45. #65354C22semidirect
52. #65167C22semidirect
54. #65147C22semidirect
56. #64991C22semidirect
99. C2×#676Q8semidirect
142. C2×#501D5semidirect
214. #676C2×Q8semidirect
242. #501C2×D5semidirect
465. C2×C5#3166semidirect
510. C5C2×#3166semidirect
533. C2#10613708direct (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×D5×#1252
C2×C5×#5012
C2×#653692
C2×#653542
#106137082
C2×#651702
C2×#651672
C2×#651502
C2×#651472
C2×#649962
C2×#649912
C2×#31665