Finite Group Databasebeta

← C2×#10604283 #13034387

Subgroups — C2×#10604283 #13034387

Order 1280.

1878 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#65765C211yesmaximal, characteristic
3C2×D5⋊(C22⋊C8)C211yesmaximal, characteristic
4C2×#64874C214yesmaximal, complemented
5#10604283C218yesmaximal, direct product factor
6C23×C4×D5—21no—
7C23×C4×D5C2211yescharacteristic
8C22×C22⋊AGL(1,𝔽5)—21no—
9C22×C4⋊AGL(1,𝔽5)C2212yes—
10C22×D5⋊C8C2212yes—
11C22×C5×C4⋊C4C411yescharacteristic, complemented
12C22×C4⋊Dic5C411yescharacteristic, complemented
13C22×#683—21no—
14C2×D5×C4⋊C4—21no—
15C2×D5×C4⋊C4—22no—
16C2×D5×C4⋊C4—21no—
17C2×D5×C4⋊C4—22no—
18C2×D5×C4⋊C4C412yescomplemented
19C2×D5×C4⋊C4C414yescomplemented
20C2×D5×C4⋊C4C2212yes—
21C2×D5×C4⋊C4C2214yes—
22C2×C22⋊#170—21no—
23#65765—22no—
24#65765C2214yes—
25C2×(C2×AGL(1,𝔽5))⋊C4—21no—
26D5⋊(C22⋊C8)—22no—
27D5⋊(C22⋊C8)C2214yes—
28C2×#4003—21no—
29#64874C22116yescomplemented
30C2×#1824—51nomaximal, Sylow
31C24×D5D411yescharacteristic
32C23×AGL(1,𝔽5)—22no—
33C23×C4×C5—21no—
34C23×C4×C5C2×C411yescharacteristic
35C23×Dic5—21no—
36C23×Dic5D411yescharacteristic
37C22×C4×D5—28no—
38C22×C4×D5—24no—
39C22×C4×D5—22no—
40C22×C4×D5—22no—
41C22×C4×D5—24no—
42C22×C4×D5—48no—
43C22×C4×D5C2×C411yescharacteristic
44C22×C4×D5C2×C412yes—
45C22×C4×D5D411yescharacteristic
46C22×C4×D5D412yes—
47C22×C4×D5D411yescharacteristic
48C22×C4×D5D412yes—
49C22×C4×D5C2312yes—
50C22×C4×D5C2311yescharacteristic
51C2×C22⋊AGL(1,𝔽5)—24no—
52C2×C22⋊AGL(1,𝔽5)—44no—
53C22×#170—22no—
54C2×C4⋊AGL(1,𝔽5)—28no—
55C2×C4⋊AGL(1,𝔽5)—22no—
56C2×C4⋊AGL(1,𝔽5)C2314yes—
57C2×D5⋊C8—28no—
58C2×D5⋊C8—22no—
59C2×D5⋊C8C2314yes—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—21no—
62C2×C5×C4⋊C4C2×C412yes—
63C2×C5×C4⋊C4C2×C414yescomplemented
64C2×C4⋊Dic5—22no—
65C2×C4⋊Dic5—21no—
66C2×C4⋊Dic5C2×C412yes—
67C2×C4⋊Dic5C2×C414yescomplemented
68C2×#683—24no—
69C2×#683—22no—
70C2×#683—22no—
71C2×#683—24no—
72D5×C4⋊C4—24no—
73D5×C4⋊C4—24no—
74D5×C4⋊C4—24no—
75D5×C4⋊C4—22no—
76D5×C4⋊C4—24no—
77D5×C4⋊C4—22no—
78D5×C4⋊C4—24no—
79D5×C4⋊C4C2×C414yes—
80D5×C4⋊C4C2×C418yescomplemented
81D5×C4⋊C4C2314yes—
82C22⋊#170—24no—
83(C2×AGL(1,𝔽5))⋊C4—24no—
84#4003—24no—
85C23×C4⋊C4—51no—
86C22×C22⋊C8—51no—
87C2×#380—51no—
88#1824—58no—
89C2×#340—54no—
90C24×C5C22⋊C411yescharacteristic
91C23×D5—24no—
92C23×D5—24no—
93C23×D5C22⋊C412yes—
94C23×D5C22⋊C411yescharacteristic
95C23×D5SD1614yes—
96C23×D5Q1614yes—
97C23×D5C2×D412yes—
98C23×D5C2×D411yescharacteristic
99C22×AGL(1,𝔽5)—24no—
100C22×AGL(1,𝔽5)—44no—
101C22×AGL(1,𝔽5)—44no—
102C22×AGL(1,𝔽5)—44no—
103C22×C4×C5—24no—
104C22×C4×C5—22no—
105C22×C4×C5—24no—
106C22×C4×C5—44no—
107C22×C4×C5C22⋊C412yes—
108C22×C4×C5C22⋊C411yescharacteristic
109C22×C4×C5C22×C412yes—
110C22×C4×C5C22×C411yescharacteristic
111C22×Dic5—24no—
112C22×Dic5—22no—
113C22×Dic5—24no—
114C22×Dic5—44no—
115C22×Dic5C22⋊C412yes—
116C22×Dic5C22⋊C411yescharacteristic
117C22×Dic5C2×D412yes—
118C22×Dic5C2×D411yescharacteristic
119C2×C4×D5—24no—
120C2×C4×D5—24no—
121C2×C4×D5—24no—
122C2×C4×D5—28no—
123C2×C4×D5—28no—
124C2×C4×D5—28no—
125C2×C4×D5—28no—
126C2×C4×D5—24no—
127C2×C4×D5—28no—
128C2×C4×D5—24no—
129C2×C4×D5—48no—
130C2×C4×D5—416no—
131C2×C4×D5—416no—
132C2×C4×D5—48no—
133C2×C4×D5C22⋊C412yes—
134C2×C4×D5C22⋊C412yes—
135C2×C4×D5C22⋊C412yes—
136C2×C4×D5C22×C412yes—
137C2×C4×D5C22×C411yescharacteristic
138C2×C4×D5C2×D412yes—
139C2×C4×D5C2×D412yes—
140C2×C4×D5C2×D411yescharacteristic
141C2×C4×D5C2×D411yescharacteristic
142C2×C4×D5#4118yes—
143C2×C4×D5C2411yescharacteristic
144C22⋊AGL(1,𝔽5)—48no—
145C2×#170—24no—
146C2×#170—44no—
147C4⋊AGL(1,𝔽5)—28no—
148C4⋊AGL(1,𝔽5)—44no—
149D5⋊C8—28no—
150D5⋊C8—44no—
151C5×C4⋊C4—22no—
152C5×C4⋊C4—24no—
153C5×C4⋊C4C22×C414yes—
154C4⋊Dic5—22no—
155C4⋊Dic5—24no—
156C4⋊Dic5C22×C414yes—
157#683—24no—
158#683—28no—
159#683—24no—
160C24×C4—51no—
161C24×C4—101no—
162C23×C8—52no—
163C22×C4⋊C4—51no—
164C22×C4⋊C4—52no—
165C22×C4⋊C4—52no—
166C22×C4⋊C4—54no—
167C22×C4⋊C4—54no—
168C22×C4⋊C4—52no—
169C22×C4⋊C4—101no—
170C22×C4⋊C4—102no—
171C22×C4⋊C4—102no—
172C22×C4⋊C4—101no—
173C22×C4⋊C4—101no—
174C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
175C22×C22⋊C4—101no—
176C2×C22⋊C8—54no—
177C2×C22⋊C8—101no—
178C2×C22⋊C8—101no—
179C2×C22⋊C8—102no—
180#380—54no—
181#380—102no—
182C2×#95—101no—
183#340—516no—
184C23×C5—22no—
185C23×C5—22no—
186C23×C5#10314yes—
187C23×C5C2×C22⋊C412yes—
188C23×C5C2×C22⋊C411yescharacteristic
189C22×D5—22no—
190C22×D5—22no—
191C22×D5—24no—
192C22×D5—24no—
193C22×D5—24no—
194C22×D5—24no—
195C22×D5—216no—
196C22×D5—216no—
197C22×D5#10314yes—
198C22×D5#10318yes—
199C22×D5C2×C22⋊C412yes—
200C22×D5C2×C22⋊C411yescharacteristic
201C22×D5#12314yes—
202C22×D5C2×SD1614yes—
203C22×D5C2×SD1612yes—
204C22×D5C2×Q1614yes—
205C22×D5C2×Q1612yes—
206C22×D5AGL(1,ℤ/8)14yes—
207C22×D5C22×D411yescharacteristic
208C2×AGL(1,𝔽5)—44no—
209C2×AGL(1,𝔽5)—44no—
210C2×AGL(1,𝔽5)—44no—
211C2×AGL(1,𝔽5)—88no—
212C2×C4×C5—22no—
213C2×C4×C5—24no—
214C2×C4×C5—24no—
215C2×C4×C5—24no—
216C2×C4×C5—48no—
217C2×C4×C5—44no—
218C2×C4×C5C2×C22⋊C412yes—
219C2×C4×C5C2×C22⋊C411yescharacteristic
220C2×C4×C5#11714yes—
221C2×C4×C5C23×C411yescharacteristic
222C2×Dic5—22no—
223C2×Dic5—24no—
224C2×Dic5—24no—
225C2×Dic5—24no—
226C2×Dic5—48no—
227C2×Dic5—44no—
228C2×Dic5C2×C22⋊C412yes—
229C2×Dic5C2×C22⋊C411yescharacteristic
230C2×Dic5#12314yes—
231C2×Dic5C22×D411yescharacteristic
232C4×D5—24no—
233C4×D5—24no—
234C4×D5—24no—
235C4×D5—24no—
236C4×D5—24no—
237C4×D5—24no—
238C4×D5—416no—
239C4×D5—48no—
240C4×D5—48no—
241C4×D5#11714yes—
242C4×D5#12314yes—
243C4×D5#12314yes—
244C4×D5C2×#4114yes—
245#170—44no—
246C25—51no—
247C23×C4—21no—
248C23×C4—51no—
249C23×C4—51no—
250C23×C4—51no—
251C23×C4—52no—
252C23×C4—51no—
253C23×C4—52no—
254C23×C4—52no—
255C23×C4—51no—
256C23×C4—52no—
257C23×C4—108no—
258C23×C4—104no—
259C23×C4—104no—
260C23×C4—102no—
261C23×C4—102no—
262C23×C4—101no—
263C23×C4—102no—
264C23×C4—208no—
265C23×C4C2×AGL(1,𝔽5)11yescharacteristic
266C22×C8—54no—
267C22×C8—108no—
268C22×C8—102no—
269C22×C8—102no—
270C2×C4⋊C4—22no—
271C2×C4⋊C4—21no—
272C2×C4⋊C4—52no—
273C2×C4⋊C4—54no—
274C2×C4⋊C4—54no—
275C2×C4⋊C4—54no—
276C2×C4⋊C4—58no—
277C2×C4⋊C4—54no—
278C2×C4⋊C4—102no—
279C2×C4⋊C4—102no—
280C2×C4⋊C4—104no—
281C2×C4⋊C4—104no—
282C2×C4⋊C4—104no—
283C2×C4⋊C4—104no—
284C2×C4⋊C4—104no—
285C2×C4⋊C4—104no—
286C2×C4⋊C4—104no—
287C2×C4⋊C4—102no—
288C2×C4⋊C4—102no—
289C2×C4⋊C4—102no—
290C2×C4⋊C4—101no—
291C2×C4⋊C4—108no—
292C2×C4⋊C4—102no—
293C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
294C2×C4⋊C4C2×AGL(1,𝔽5)14yescomplemented
295C2×C22⋊C4—104no—
296C2×C22⋊C4—204no—
297C22⋊C8—104no—
298C22⋊C8—104no—
299#95—104no—
300C22×C5—28no—
301C22×C5—22no—
302C22×C5—22no—
303C22×C5#38112yes—
304C22×C5C2×#10314yes—
305C22×C5C2×#10312yes—
306C22×C5#41812yes—
307C22×C5C22×C22⋊C411yescharacteristic
308C2×D5—28no—
309C2×D5—22no—
310C2×D5—22no—
311C2×D5—28no—
312C2×D5—28no—
313C2×D5—216no—
314C2×D5#38112yes—
315C2×D5C2×#10314yes—
316C2×D5C2×#10312yes—
317C2×D5#41812yes—
318C2×D5#48118yes—
319C2×D5#48418yes—
320C2×D5C2×#12312yes—
321C2×D5C22×SD1611yescharacteristic
322C2×D5C22×Q1611yescharacteristic
323C2×D5C2×AGL(1,ℤ/8)12yes—
324AGL(1,𝔽5)—84no—
325C4×C5—22no—
326C4×C5—44no—
327C4×C5#38112yes—
328C4×C5C2×#11712yes—
329Dic5—22no—
330Dic5—44no—
331Dic5#38112yes—
332Dic5C2×#12312yes—
333C24—51no—
334C24—52no—
335C24—52no—
336C24—51no—
337C24—54no—
338C24—54no—
339C24—104no—
340C24—104no—
341C24C22⋊AGL(1,𝔽5)11yescharacteristic
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—22no—
345C22×C4—44no—
346C22×C4—51no—
347C22×C4—58no—
348C22×C4—51no—
349C22×C4—51no—
350C22×C4—51no—
351C22×C4—51no—
352C22×C4—52no—
353C22×C4—52no—
354C22×C4—51no—
355C22×C4—52no—
356C22×C4—52no—
357C22×C4—52no—
358C22×C4—52no—
359C22×C4—52no—
360C22×C4—52no—
361C22×C4—104no—
362C22×C4—108no—
363C22×C4—108no—
364C22×C4—108no—
365C22×C4—108no—
366C22×C4—104no—
367C22×C4—104no—
368C22×C4—104no—
369C22×C4—108no—
370C22×C4—104no—
371C22×C4—104no—
372C22×C4—104no—
373C22×C4—102no—
374C22×C4—104no—
375C22×C4—208no—
376C22×C4—2016no—
377C22×C4—2016no—
378C22×C4—208no—
379C22×C4—204no—
380C22×C4—204no—
381C22×C4—204no—
382C22×C4—204no—
383C22×C4C22⋊AGL(1,𝔽5)12yes—
384C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
385C22×C4C22×AGL(1,𝔽5)12yes—
386C22×C4C22×AGL(1,𝔽5)11yescharacteristic
387C2×C8—104no—
388C2×C8—108no—
389C2×C8—204no—
390C2×C8—204no—
391C4⋊C4—22no—
392C4⋊C4—24no—
393C4⋊C4—54no—
394C4⋊C4—104no—
395C4⋊C4—104no—
396C4⋊C4—108no—
397C4⋊C4—108no—
398C4⋊C4—104no—
399C4⋊C4—102no—
400C4⋊C4—204no—
401C4⋊C4C22×AGL(1,𝔽5)14yes—
402C22⋊C4—208no—
403C2×C5—24no—
404C2×C5#182414yescomplemented
405C2×C5C2×#38111yescharacteristic
406C2×C5C22×#10311yescharacteristic
407C2×C5C2×#41811yescharacteristic
408D5—24no—
409D5#182414yescomplemented
410D5C2×#48112yes—
411D5C2×#48412yes—
412C23—22no—
413C23—22no—
414C23—51no—
415C23—51no—
416C23—54no—
417C23—54no—
418C23—52no—
419C23—52no—
420C23—52no—
421C23—54no—
422C23—58no—
423C23—54no—
424C23—54no—
425C23—104no—
426C23—104no—
427C23—104no—
428C23—104no—
429C23—1016no—
430C23—1016no—
431C23—102no—
432C23—102no—
433C23#400914yes—
434C23C2×C22⋊AGL(1,𝔽5)12yes—
435C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—48no—
441C2×C4—44no—
442C2×C4—51no—
443C2×C4—51no—
444C2×C4—54no—
445C2×C4—54no—
446C2×C4—54no—
447C2×C4—54no—
448C2×C4—54no—
449C2×C4—52no—
450C2×C4—104no—
451C2×C4—104no—
452C2×C4—104no—
453C2×C4—104no—
454C2×C4—104no—
455C2×C4—104no—
456C2×C4—102no—
457C2×C4—104no—
458C2×C4—104no—
459C2×C4—104no—
460C2×C4—208no—
461C2×C4—208no—
462C2×C4—2016no—
463C2×C4—208no—
464C2×C4—204no—
465C2×C4—204no—
466C2×C4—204no—
467C2×C4—204no—
468C2×C4—408no—
469C2×C4#413014yes—
470C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
471C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
472C2×C4C23×AGL(1,𝔽5)11yescharacteristic
473C8—204no—
474C5C2×#182411yescharacteristic, complemented, Sylow
475C22—22no—
476C22—22no—
477C22—28no—
478C22—52no—
479C22—52no—
480C22—52no—
481C22—52no—
482C22—51no—
483C22—51no—
484C22—52no—
485C22—58no—
486C22—58no—
487C22—54no—
488C22—108no—
489C22—108no—
490C22—1016no—
491C22—102no—
492C22—102no—
493C22—108no—
494C22#6576412yes—
495C22#6576712yes—
496C22C2×#400914yes—
497C22C2×#400912yes—
498C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
499C4—22no—
500C4—44no—
501C4—52no—
502C4—52no—
503C4—102no—
504C4—204no—
505C4—404no—
506C4#6576412yes—
507C4C2×#413012yes—
508C2—24no—
509C2—52no—
510C2—52no—
511C2—54no—
512C2—104no—
513C2#1060428314yesdirect product factor
514C2C2×#6576411yescharacteristic
515C2C2×#6576711yescharacteristic
516C2C22×#400911yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
prime radicalC24×D5D4
cosocleC2×C4×D5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C2×#1824
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×#64874C2semidirect
5. #10604283C2direct (N × H)
11. C22×C5×C4⋊C4C4semidirect
12. C22×C4⋊Dic5C4semidirect
18. C2×D5×C4⋊C4C4semidirect
19. C2×D5×C4⋊C4C4semidirect
29. #64874C22semidirect
63. C2×C5×C4⋊C4C2×C4semidirect
67. C2×C4⋊Dic5C2×C4semidirect
80. D5×C4⋊C4C2×C4semidirect
174. C22×C4⋊C4AGL(1,𝔽5)semidirect
294. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
404. C2×C5#1824semidirect
409. D5#1824semidirect
474. C5C2×#1824semidirect
513. C2#10604283direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×C4⋊C42
C2×#657652
C2×D5⋊(C22⋊C8)2
C2×#648742
#106042832
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