Finite Group Databasebeta

← C2×#10604073 #13035129

Subgroups — C2×#10604073 #13035129

Order 1280.

1086 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65712C211yesmaximal, characteristic
2C2×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic
3C2×D5×#107C211yesmaximal, characteristic
4C2×#64893C211yesmaximal, characteristic
5C2×(C2×AGL(1,𝔽5))⋊C8C211yesmaximal, characteristic
6C2×#64874C211yesmaximal, characteristic
7C2×#64874C211yesmaximal, characteristic
8#10604073C218yesmaximal, direct product factor
9C22×C4⋊AGL(1,𝔽5)—21no—
10C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
11C22×C4⋊AGL(1,𝔽5)C2211yescharacteristic
12C22×C4×AGL(1,𝔽5)—21no—
13C22×C4×AGL(1,𝔽5)C2211yescharacteristic
14C22×D5⋊C8C2211yescharacteristic
15C22×C8×D5C2211yescharacteristic
16C2×D5×C4⋊C4C2211yescharacteristic
17C2×D5×C4⋊C4C2211yescharacteristic
18C2×(C2×AGL(1,𝔽5))⋊C4—21no—
19C2×(C2×AGL(1,𝔽5))⋊C4—21no—
20#65712—22no—
21#65712C2214yes—
22C4⋊C4×AGL(1,𝔽5)—22no—
23C4⋊C4×AGL(1,𝔽5)C2214yes—
24C2×C5×#107C411yescharacteristic, complemented
25C2×#3950C411yescharacteristic, complemented
26C2×#3939C411yescharacteristic, complemented
27C2×#3939C411yescharacteristic, complemented
28D5×#107C414yescomplemented
29D5×#107C2214yes—
30#64893C2214yes—
31(C2×AGL(1,𝔽5))⋊C8C2214yes—
32#64874C2214yes—
33#64874C2214yes—
34C2×#1918—51nomaximal, Sylow
35C23×AGL(1,𝔽5)—21no—
36C23×AGL(1,𝔽5)—21no—
37C23×AGL(1,𝔽5)D411yescharacteristic
38C23×AGL(1,𝔽5)D411yescharacteristic
39C22×C4×D5—21no—
40C22×C4×D5—21no—
41C22×C4×D5C2311yescharacteristic
42C22×#170—21no—
43C2×C4⋊AGL(1,𝔽5)—21no—
44C2×C4⋊AGL(1,𝔽5)—22no—
45C2×C4⋊AGL(1,𝔽5)—22no—
46C2×C4⋊AGL(1,𝔽5)—22no—
47C2×C4⋊AGL(1,𝔽5)—24no—
48C2×C4⋊AGL(1,𝔽5)—21no—
49C2×C4⋊AGL(1,𝔽5)—44no—
50C2×C4⋊AGL(1,𝔽5)Q814yes—
51C2×C4⋊AGL(1,𝔽5)C2312yes—
52C2×C4⋊AGL(1,𝔽5)C2312yes—
53C2×C4×AGL(1,𝔽5)—22no—
54C2×C4×AGL(1,𝔽5)—22no—
55C2×C4×AGL(1,𝔽5)—24no—
56C2×C4×AGL(1,𝔽5)—44no—
57C2×C4×AGL(1,𝔽5)D412yes—
58C2×C4×AGL(1,𝔽5)C2312yes—
59C2×D5⋊C8—22no—
60C2×D5⋊C8—22no—
61C2×D5⋊C8—21no—
62C2×D5⋊C8C2312yes—
63C22×C5×C8C2×C411yescharacteristic
64C2×C5×C4⋊C4C2×C411yescharacteristic
65C2×C5×C4⋊C4C2×C411yescharacteristic
66C2×C4⋊Dic5C2×C411yescharacteristic
67C2×C4⋊Dic5C2×C411yescharacteristic
68C2×#683—21no—
69C2×#683—21no—
70C22×#168C2×C411yescharacteristic
71C2×C8×D5—22no—
72C2×C8×D5—22no—
73C2×C8×D5C2×C412yes—
74C2×C8×D5C2312yes—
75D5×C4⋊C4—21no—
76D5×C4⋊C4—21no—
77D5×C4⋊C4—21no—
78D5×C4⋊C4—21no—
79D5×C4⋊C4C2×C412yes—
80D5×C4⋊C4C2×C412yes—
81D5×C4⋊C4C2312yes—
82D5×C4⋊C4C2312yes—
83(C2×AGL(1,𝔽5))⋊C4—24no—
84(C2×AGL(1,𝔽5))⋊C4—24no—
85C5×#107C2×C414yescomplemented
86#3950C2×C414yescomplemented
87#3939C2×C414yescomplemented
88#3939C2×C414yescomplemented
89C22×#107—51no—
90C2×#389—51no—
91C2×C4×C4⋊C4—51no—
92#1918—58no—
93C2×#340—51no—
94C2×#340—51no—
95C2×#340—51no—
96C2×#336—51no—
97C23×D5C2×D411yescharacteristic
98C22×AGL(1,𝔽5)—22no—
99C22×AGL(1,𝔽5)—22no—
100C22×AGL(1,𝔽5)—24no—
101C22×AGL(1,𝔽5)—22no—
102C22×AGL(1,𝔽5)—22no—
103C22×AGL(1,𝔽5)—22no—
104C22×AGL(1,𝔽5)—22no—
105C22×AGL(1,𝔽5)—22no—
106C22×AGL(1,𝔽5)—42no—
107C22×AGL(1,𝔽5)—42no—
108C22×AGL(1,𝔽5)—42no—
109C22×AGL(1,𝔽5)—42no—
110C22×AGL(1,𝔽5)—42no—
111C22×AGL(1,𝔽5)D814yes—
112C22×AGL(1,𝔽5)C2×D412yes—
113C22×AGL(1,𝔽5)C2×D412yes—
114C22×C4×C5—21no—
115C22×C4×C5—21no—
116C22×C4×C5C22×C411yescharacteristic
117C22×Dic5—21no—
118C22×Dic5—21no—
119C22×Dic5#4111yescharacteristic
120C2×C4×D5—22no—
121C2×C4×D5—22no—
122C2×C4×D5—22no—
123C2×C4×D5—22no—
124C2×C4×D5—42no—
125C2×C4×D5—42no—
126C2×C4×D5—42no—
127C2×C4×D5—42no—
128C2×C4×D5C22×C411yescharacteristic
129C2×C4×D5C2×D411yescharacteristic
130C2×C4×D5C2×Q812yes—
131C2×C4×D5#4112yes—
132C2×C4×D5#4112yes—
133C2×C4×D5#4112yes—
134C2×C4×D5#4111yescharacteristic
135C2×C4×D5C2411yescharacteristic
136C2×#170—22no—
137C2×#170—42no—
138C4⋊AGL(1,𝔽5)—24no—
139C4⋊AGL(1,𝔽5)—22no—
140C4⋊AGL(1,𝔽5)—22no—
141C4⋊AGL(1,𝔽5)—22no—
142C4⋊AGL(1,𝔽5)—48no—
143C4⋊AGL(1,𝔽5)—42no—
144C4⋊AGL(1,𝔽5)C2×Q814yes—
145C4×AGL(1,𝔽5)—24no—
146C4×AGL(1,𝔽5)—22no—
147C4×AGL(1,𝔽5)—22no—
148C4×AGL(1,𝔽5)—48no—
149D5⋊C8—22no—
150D5⋊C8—22no—
151D5⋊C8—42no—
152C2×C5×C8—22no—
153C2×C5×C8C22×C412yes—
154C5×C4⋊C4—21no—
155C5×C4⋊C4—21no—
156C5×C4⋊C4C22×C412yes—
157C5×C4⋊C4C22×C412yes—
158C4⋊Dic5—21no—
159C4⋊Dic5—21no—
160C4⋊Dic5C22×C412yes—
161C4⋊Dic5C22×C412yes—
162#683—22no—
163#683—22no—
164#683—22no—
165#683—22no—
166C2×#168—22no—
167C2×#168C22×C412yes—
168C8×D5—24no—
169C8×D5—22no—
170C8×D5—22no—
171C23×C8—51no—
172C23×C8—51no—
173C22×C4⋊C4—51no—
174C22×C4⋊C4—51no—
175C22×C4⋊C4—51no—
176C22×C4⋊C4—51no—
177C22×C4⋊C4—101no—
178C22×C42—51no—
179C22×C42—101no—
180C2×#107—51no—
181C2×#107—51no—
182C2×#107—51no—
183C2×#107—54no—
184C2×#107—54no—
185C2×#107AGL(1,𝔽5)11yescharacteristic, complemented
186#389—54no—
187#389—102no—
188C4×C4⋊C4—54no—
189C4×C4⋊C4—102no—
190C2×#95—101no—
191C2×#95—101no—
192#340—54no—
193#340—54no—
194#340—54no—
195#336—54no—
196C23×C5C4×D411yescharacteristic
197C22×D5C4×D411yescharacteristic
198C22×D5C22⋊Q812yes—
199C22×D5#12312yes—
200C22×D5C2×D812yes—
201C22×D5#13512yes—
202C22×D5#13712yes—
203C22×D5#13712yes—
204C22×D5C22×D411yescharacteristic
205C2×AGL(1,𝔽5)—22no—
206C2×AGL(1,𝔽5)—22no—
207C2×AGL(1,𝔽5)—28no—
208C2×AGL(1,𝔽5)—24no—
209C2×AGL(1,𝔽5)—22no—
210C2×AGL(1,𝔽5)—22no—
211C2×AGL(1,𝔽5)—22no—
212C2×AGL(1,𝔽5)—42no—
213C2×AGL(1,𝔽5)—42no—
214C2×AGL(1,𝔽5)—48no—
215C2×AGL(1,𝔽5)—44no—
216C2×AGL(1,𝔽5)—42no—
217C2×AGL(1,𝔽5)—42no—
218C2×AGL(1,𝔽5)—42no—
219C2×AGL(1,𝔽5)—84no—
220C2×AGL(1,𝔽5)C2×D814yes—
221C2×C4×C5—22no—
222C2×C4×C5—22no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5#11712yes—
226C2×C4×C5C4×D411yescharacteristic
227C2×C4×C5C4×Q812yes—
228C2×C4×C5C23×C411yescharacteristic
229C2×Dic5—22no—
230C2×Dic5—22no—
231C2×Dic5—42no—
232C2×Dic5—42no—
233C2×Dic5C4×D411yescharacteristic
234C2×Dic5#12512yes—
235C2×Dic5#12612yes—
236C2×Dic5C2×#4111yescharacteristic
237C4×D5—42no—
238C4×D5—42no—
239C4×D5—42no—
240C4×D5—42no—
241C4×D5—44no—
242C4×D5—44no—
243C4×D5#11712yes—
244C4×D5C4×Q812yes—
245C4×D5C22⋊Q812yes—
246C4×D5#12312yes—
247C4×D5#12512yes—
248C4×D5#12612yes—
249C4×D5C22×Q811yescharacteristic
250C4×D5C2×#4111yescharacteristic
251C4×D5C2×#4111yescharacteristic
252C4×D5C2×#4111yescharacteristic
253#170—42no—
254C5×C8—22no—
255#168—22no—
256C23×C4—51no—
257C23×C4—51no—
258C23×C4—51no—
259C23×C4—101no—
260C23×C4—101no—
261C23×C4—101no—
262C23×C4—101no—
263C22×C8—51no—
264C22×C8—52no—
265C22×C8—52no—
266C22×C8—52no—
267C22×C8—102no—
268C22×C8—102no—
269C22×C8—102no—
270C22×C8—102no—
271C22×C8—101no—
272C22×C8—101no—
273C22×C8C2×AGL(1,𝔽5)11yescharacteristic
274C2×C4⋊C4—54no—
275C2×C4⋊C4—52no—
276C2×C4⋊C4—51no—
277C2×C4⋊C4—51no—
278C2×C4⋊C4—52no—
279C2×C4⋊C4—52no—
280C2×C4⋊C4—52no—
281C2×C4⋊C4—52no—
282C2×C4⋊C4—52no—
283C2×C4⋊C4—101no—
284C2×C4⋊C4—101no—
285C2×C4⋊C4—101no—
286C2×C4⋊C4—101no—
287C2×C4⋊C4—101no—
288C2×C4⋊C4—101no—
289C2×C4⋊C4—102no—
290C2×C4⋊C4—101no—
291C2×C4⋊C4—102no—
292C2×C4⋊C4—102no—
293C2×C4⋊C4—101no—
294C2×C4⋊C4—104no—
295C2×C4⋊C4—204no—
296C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
297C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
298C2×C42—52no—
299C2×C42—52no—
300C2×C42—102no—
301C2×C42—102no—
302C2×C42—104no—
303C2×C42—204no—
304#107—54no—
305#107—54no—
306#107—54no—
307#107C2×AGL(1,𝔽5)14yescomplemented
308#95—104no—
309#95—104no—
310C22×C5#38712yes—
311C22×C5C4×D812yes—
312C22×C5#44112yes—
313C22×C5C2×C4×D411yescharacteristic
314C2×D5#38712yes—
315C2×D5C4×D812yes—
316C2×D5#44112yes—
317C2×D5#47414yes—
318C2×D5#47914yes—
319C2×D5#48014yes—
320C2×D5#48514yes—
321C2×D5C2×C22⋊Q811yescharacteristic
322C2×D5C2×#12311yescharacteristic
323C2×D5C22×D811yescharacteristic
324C2×D5C2×#13511yescharacteristic
325C2×D5C2×#13711yescharacteristic
326C2×D5C2×#13711yescharacteristic
327AGL(1,𝔽5)—24no—
328AGL(1,𝔽5)—42no—
329AGL(1,𝔽5)—44no—
330AGL(1,𝔽5)—82no—
331C4×C5—42no—
332C4×C5—42no—
333C4×C5#38712yes—
334C4×C5C2×#11711yescharacteristic
335C4×C5C2×C4×Q811yescharacteristic
336Dic5—42no—
337Dic5—42no—
338Dic5#38712yes—
339Dic5C2×#12511yescharacteristic
340Dic5C2×#12611yescharacteristic
341C24—51no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—51no—
345C22×C4—52no—
346C22×C4—52no—
347C22×C4—51no—
348C22×C4—51no—
349C22×C4—52no—
350C22×C4—52no—
351C22×C4—51no—
352C22×C4—51no—
353C22×C4—52no—
354C22×C4—54no—
355C22×C4—52no—
356C22×C4—102no—
357C22×C4—102no—
358C22×C4—102no—
359C22×C4—102no—
360C22×C4—102no—
361C22×C4—102no—
362C22×C4—102no—
363C22×C4—102no—
364C22×C4—104no—
365C22×C4—102no—
366C22×C4—102no—
367C22×C4—101no—
368C22×C4—101no—
369C22×C4—102no—
370C22×C4—202no—
371C22×C4—202no—
372C22×C4—202no—
373C22×C4—202no—
374C22×C4—202no—
375C22×C4—202no—
376C22×C4—202no—
377C22×C4—202no—
378C22×C4—202no—
379C22×C4C22×AGL(1,𝔽5)11yescharacteristic
380C2×C8—22no—
381C2×C8—52no—
382C2×C8—102no—
383C2×C8—102no—
384C2×C8—104no—
385C2×C8—102no—
386C2×C8—102no—
387C2×C8—102no—
388C2×C8—102no—
389C2×C8—202no—
390C2×C8—202no—
391C2×C8C22×AGL(1,𝔽5)12yes—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—54no—
395C4⋊C4—52no—
396C4⋊C4—52no—
397C4⋊C4—102no—
398C4⋊C4—102no—
399C4⋊C4—102no—
400C4⋊C4—102no—
401C4⋊C4—104no—
402C4⋊C4—102no—
403C4⋊C4—102no—
404C4⋊C4—102no—
405C4⋊C4—101no—
406C4⋊C4—101no—
407C4⋊C4—202no—
408C4⋊C4—208no—
409C4⋊C4C22×AGL(1,𝔽5)12yes—
410C4⋊C4C22×AGL(1,𝔽5)12yes—
411C42—104no—
412C42—102no—
413C42—102no—
414C42—208no—
415C2×C5#191814yescomplemented
416C2×C5C2×#38711yescharacteristic
417C2×C5C2×C4×D811yescharacteristic
418C2×C5C2×#44111yescharacteristic
419D5#191814yescomplemented
420D5C2×#47411yescharacteristic
421D5C2×#47911yescharacteristic
422D5C2×#48011yescharacteristic
423D5C2×#48511yescharacteristic
424C23—52no—
425C23—52no—
426C23—52no—
427C23—52no—
428C23—52no—
429C23—52no—
430C23—51no—
431C23—51no—
432C23D4×AGL(1,𝔽5)11yescharacteristic
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—52no—
438C2×C4—52no—
439C2×C4—51no—
440C2×C4—51no—
441C2×C4—52no—
442C2×C4—52no—
443C2×C4—52no—
444C2×C4—52no—
445C2×C4—51no—
446C2×C4—51no—
447C2×C4—52no—
448C2×C4—51no—
449C2×C4—51no—
450C2×C4—52no—
451C2×C4—54no—
452C2×C4—102no—
453C2×C4—108no—
454C2×C4—102no—
455C2×C4—102no—
456C2×C4—104no—
457C2×C4—102no—
458C2×C4—102no—
459C2×C4—102no—
460C2×C4—102no—
461C2×C4—202no—
462C2×C4—202no—
463C2×C4—202no—
464C2×C4—202no—
465C2×C4—204no—
466C2×C4—204no—
467C2×C4—202no—
468C2×C4—204no—
469C2×C4—208no—
470C2×C4—202no—
471C2×C4—202no—
472C2×C4—202no—
473C2×C4—202no—
474C2×C4—202no—
475C2×C4—202no—
476C2×C4—404no—
477C2×C4#413012yes—
478C2×C4D4×AGL(1,𝔽5)11yescharacteristic
479C2×C4Q8×AGL(1,𝔽5)12yes—
480C2×C4C23×AGL(1,𝔽5)11yescharacteristic
481C8—22no—
482C8—102no—
483C8—202no—
484C5C2×#191811yescharacteristic, complemented, Sylow
485C22—51no—
486C22—51no—
487C22—52no—
488C22—54no—
489C22—54no—
490C22—54no—
491C22—54no—
492C22—51no—
493C22—51no—
494C22—52no—
495C22—51no—
496C22—51no—
497C22—52no—
498C22#6571112yes—
499C22D8×AGL(1,𝔽5)12yes—
500C22#6573912yes—
501C22C2×D4×AGL(1,𝔽5)11yescharacteristic
502C4—42no—
503C4—42no—
504C4—51no—
505C4—51no—
506C4—52no—
507C4—104no—
508C4—202no—
509C4—204no—
510C4—202no—
511C4—202no—
512C4—402no—
513C4#6571112yes—
514C4C2×#413011yescharacteristic
515C4C2×Q8×AGL(1,𝔽5)11yescharacteristic
516C2—51no—
517C2—51no—
518C2—51no—
519C2—51no—
520C2—54no—
521C2#1060407314yesdirect product factor
522C2C2×#6571111yescharacteristic
523C2C2×D8×AGL(1,𝔽5)11yescharacteristic
524C2C2×#6573911yescharacteristic
subgroupG/H
centerC23D4×AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×#107C4
socleC23×C5C4×D4
prime radicalC23×D5C2×D4
cosocleC2×C4×D5C24
hypercenterC2×#107AGL(1,𝔽5)
hypocenterC5C2×#1918
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
8. #10604073C2direct (N × H)
24. C2×C5×#107C4semidirect
25. C2×#3950C4semidirect
26. C2×#3939C4semidirect
27. C2×#3939C4semidirect
28. D5×#107C4semidirect
85. C5×#107C2×C4semidirect
86. #3950C2×C4semidirect
87. #3939C2×C4semidirect
88. #3939C2×C4semidirect
185. C2×#107AGL(1,𝔽5)semidirect
307. #107C2×AGL(1,𝔽5)semidirect
415. C2×C5#1918semidirect
419. D5#1918semidirect
484. C5C2×#1918semidirect
521. C2#10604073direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#657122
C2×C4⋊C4×AGL(1,𝔽5)2
C2×D5×#1072
C2×#648932
C2×(C2×AGL(1,𝔽5))⋊C82
C2×#648742
#106040732
C2×#19185