Finite Group Databasebeta

← C2×#10604292 #13029228

Subgroups — C2×#10604292 #13029228

Order 1280.

1718 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#65756C212yesmaximal
3C2×#64914C212yesmaximal, complemented
4C2×#64913C212yesmaximal, complemented
5#10604292C218yesmaximal, direct product factor
6C23×C4×D5C411yescharacteristic
7C23×C4×D5C411yescharacteristic
8C23×C4×D5C2211yescharacteristic
9C22×#700—22no—
10C22×C5×C4⋊C4C411yescharacteristic
11C22×C4⋊Dic5C2211yescharacteristic
12C22×#683C411yescharacteristic
13C22×#683C2211yescharacteristic
14C2×D5×C4⋊C4—22no—
15C2×D5×C4⋊C4—22no—
16C2×D5×C4⋊C4—24no—
17C2×D5×C4⋊C4C414yes—
18C2×D5×C4⋊C4C2214yes—
19C2×C22⋊#170C2214yes—
20#65756—24no—
21#65756C2218yes—
22C2×#4003—22no—
23#64914C2218yescomplemented
24#64913C2218yescomplemented
25C2×#1463—51nomaximal, Sylow
26C24×D5C2×C411yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×Dic5C2×C411yescharacteristic
31C23×Dic5C2×C411yescharacteristic
32C23×Dic5C2311yescharacteristic
33C22×C4×D5—22no—
34C22×C4×D5—21no—
35C22×C4×D5—21no—
36C22×C4×D5—24no—
37C22×C4×D5—24no—
38C22×C4×D5—22no—
39C22×C4×D5—21no—
40C22×C4×D5—21no—
41C22×C4×D5—44no—
42C22×C4×D5—44no—
43C22×C4×D5C2×C414yes—
44C22×C4×D5C2×C414yes—
45C22×C4×D5C2×C412yes—
46C22×C4×D5D412yes—
47C22×C4×D5D412yes—
48C22×C4×D5D414yes—
49C22×C4×D5C2312yes—
50C22×#170—24no—
51C2×#700—28no—
52C2×#700—48no—
53C2×C5×C4⋊C4—22no—
54C2×C5×C4⋊C4—22no—
55C2×C5×C4⋊C4C2×C414yes—
56C2×C4⋊Dic5—22no—
57C2×C4⋊Dic5—22no—
58C2×C4⋊Dic5C2×C412yes—
59C2×C4⋊Dic5C2312yes—
60C2×#683—22no—
61C2×#683—22no—
62C2×#683—22no—
63C2×#683—22no—
64C2×#683C2×C412yes—
65C2×#683C2×C414yes—
66C2×#683C2312yes—
67D5×C4⋊C4—28no—
68D5×C4⋊C4—28no—
69D5×C4⋊C4—28no—
70D5×C4⋊C4—28no—
71C22⋊#170—24no—
72C22⋊#170C2318yes—
73#4003—28no—
74C23×C4⋊C4—51no—
75C2×#407—52no—
76#1463—58no—
77C2×#324—52no—
78C2×#324—52no—
79C24×C5C22×C411yescharacteristic
80C23×D5—22no—
81C23×D5—22no—
82C23×D5—24no—
83C23×D5—24no—
84C23×D5C22⋊C412yes—
85C23×D5C22⋊C411yescharacteristic
86C23×D5C22⋊C411yescharacteristic
87C23×D5C22×C412yes—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—22no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—42no—
94C22×C4×C5—42no—
95C22×C4×C5C22⋊C412yes—
96C22×C4×C5C22⋊C412yes—
97C22×C4×C5M1614yescomplemented
98C22×C4×C5C22×C412yes—
99C22×C4×C5C22×C412yes—
100C22×C4×C5C22×C412yes—
101C22×Dic5—21no—
102C22×Dic5—21no—
103C22×Dic5—22no—
104C22×Dic5—21no—
105C22×Dic5—21no—
106C22×Dic5—42no—
107C22×Dic5—42no—
108C22×Dic5M1614yescomplemented
109C22×Dic5C22×C412yes—
110C22×Dic5C22×C412yes—
111C22×Dic5C22×C411yescharacteristic
112C22×Dic5C2×D412yes—
113C22×Dic5C2×D412yes—
114C22×Dic5C2411yescharacteristic
115C2×C4×D5—216no—
116C2×C4×D5—28no—
117C2×C4×D5—28no—
118C2×C4×D5—28no—
119C2×C4×D5—24no—
120C2×C4×D5—24no—
121C2×C4×D5—28no—
122C2×C4×D5—28no—
123C2×C4×D5—24no—
124C2×C4×D5—24no—
125C2×C4×D5—44no—
126C2×C4×D5—48no—
127C2×C4×D5—44no—
128C2×C4×D5—44no—
129C2×C4×D5—44no—
130C2×C4×D5—48no—
131C2×C4×D5—44no—
132C2×C4×D5—48no—
133C2×C4×D5C22⋊C414yes—
134C2×C4×D5C22⋊C414yes—
135C2×C4×D5C2×D414yes—
136C2×C4×D5C2×D414yes—
137C2×#170—28no—
138C2×#170—48no—
139#700—416no—
140C5×C4⋊C4—28no—
141C4⋊Dic5—24no—
142C4⋊Dic5—24no—
143#683—28no—
144#683—24no—
145#683—24no—
146C24×C4—51no—
147C24×C4—51no—
148C24×C4—51no—
149C22×M16—102no—
150C22×C4⋊C4—51no—
151C22×C4⋊C4—51no—
152C22×C4⋊C4—51no—
153C22×C4⋊C4—54no—
154C22×C4⋊C4—54no—
155C22×C4⋊C4—102no—
156C22×C4⋊C4—102no—
157C22×C4⋊C4—104no—
158C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
159#407—58no—
160#407—104no—
161C2×C22⋊C8—54no—
162C2×C22⋊C8—102no—
163#324—58no—
164#324—58no—
165C23×C5—22no—
166C23×C5—22no—
167C23×C5C2×C22⋊C411yescharacteristic
168C23×C5C2×C22⋊C411yescharacteristic
169C23×C5C2×M1612yes—
170C23×C5C2×M1612yes—
171C23×C5C23×C411yescharacteristic
172C22×D5—216no—
173C22×D5—216no—
174C22×D5—22no—
175C22×D5—22no—
176C22×D5—24no—
177C22×D5—22no—
178C22×D5—22no—
179C22×D5—22no—
180C22×D5—22no—
181C22×D5—24no—
182C22×D5—24no—
183C22×D5—24no—
184C22×D5—24no—
185C22×D5#9914yes—
186C22×D5#10114yes—
187C22×D5C2×C22⋊C412yes—
188C22×D5C2×C22⋊C412yes—
189C2×C4×C5—22no—
190C2×C4×C5—22no—
191C2×C4×C5—24no—
192C2×C4×C5—24no—
193C2×C4×C5—24no—
194C2×C4×C5—22no—
195C2×C4×C5—42no—
196C2×C4×C5—42no—
197C2×C4×C5—42no—
198C2×C4×C5—42no—
199C2×C4×C5—42no—
200C2×C4×C5C2×C22⋊C414yes—
201C2×C4×C5C2×M1614yescomplemented
202C2×Dic5—22no—
203C2×Dic5—22no—
204C2×Dic5—24no—
205C2×Dic5—24no—
206C2×Dic5—24no—
207C2×Dic5—22no—
208C2×Dic5—41no—
209C2×Dic5—42no—
210C2×Dic5—41no—
211C2×Dic5—42no—
212C2×Dic5—42no—
213C2×Dic5—42no—
214C2×Dic5C2×C22⋊C412yes—
215C2×Dic5C2×M1614yescomplemented
216C2×Dic5C22×D412yes—
217C4×D5—216no—
218C4×D5—216no—
219C4×D5—28no—
220C4×D5—28no—
221C4×D5—44no—
222C4×D5—44no—
223C4×D5—48no—
224C4×D5—48no—
225#170—48no—
226C25—51no—
227C23×C4—51no—
228C23×C4—51no—
229C23×C4—52no—
230C23×C4—52no—
231C23×C4—54no—
232C23×C4—52no—
233C23×C4—52no—
234C23×C4—51no—
235C23×C4—54no—
236C23×C4—54no—
237C23×C4—104no—
238C23×C4—102no—
239C23×C4—101no—
240C23×C4—101no—
241C23×C4—102no—
242C23×C4—101no—
243C23×C4—101no—
244C23×C4—104no—
245C23×C4—204no—
246C23×C4—204no—
247C23×C4C2×AGL(1,𝔽5)11yescharacteristic
248C23×C4C2×AGL(1,𝔽5)11yescharacteristic
249C23×C4C2×AGL(1,𝔽5)11yescharacteristic
250C2×M16—108no—
251C2×M16—208no—
252C22×C8—104no—
253C2×C4⋊C4—22no—
254C2×C4⋊C4—22no—
255C2×C4⋊C4—52no—
256C2×C4⋊C4—52no—
257C2×C4⋊C4—52no—
258C2×C4⋊C4—54no—
259C2×C4⋊C4—52no—
260C2×C4⋊C4—108no—
261C2×C4⋊C4—108no—
262C2×C4⋊C4—108no—
263C2×C4⋊C4—108no—
264C2×C4⋊C4—102no—
265C2×C4⋊C4—102no—
266C2×C4⋊C4—102no—
267C2×C4⋊C4—102no—
268C2×C4⋊C4—102no—
269C2×C4⋊C4—102no—
270C2×C4⋊C4C2×AGL(1,𝔽5)14yes—
271C22⋊C8—58no—
272C22⋊C8—104no—
273C22⋊C8—108no—
274C22×C5—21no—
275C22×C5—21no—
276C22×C5—21no—
277C22×C5—21no—
278C22×C5—24no—
279C22×C5—24no—
280C22×C5#40712yes—
281C22×C5#40712yes—
282C22×C5C2×#9912yes—
283C22×C5C2×#10112yes—
284C22×C5C22×C22⋊C411yescharacteristic
285C22×C5C22×M1611yescharacteristic
286C22×C5C22×M1611yescharacteristic
287C2×D5—28no—
288C2×D5—28no—
289C2×D5—216no—
290C2×D5—22no—
291C2×D5—22no—
292C2×D5—22no—
293C2×D5—22no—
294C2×D5—28no—
295C2×D5—28no—
296C2×D5C2×#9914yes—
297C2×D5C2×#10114yes—
298C4×C5—24no—
299C4×C5—24no—
300C4×C5—42no—
301Dic5—24no—
302Dic5—22no—
303Dic5—22no—
304Dic5—42no—
305C24—51no—
306C24—51no—
307C24—52no—
308C24—52no—
309C24—104no—
310C24—104no—
311C24—102no—
312C24—102no—
313C24C22×AGL(1,𝔽5)11yescharacteristic
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—42no—
320C22×C4—42no—
321C22×C4—54no—
322C22×C4—52no—
323C22×C4—52no—
324C22×C4—52no—
325C22×C4—51no—
326C22×C4—51no—
327C22×C4—54no—
328C22×C4—54no—
329C22×C4—54no—
330C22×C4—54no—
331C22×C4—52no—
332C22×C4—108no—
333C22×C4—104no—
334C22×C4—104no—
335C22×C4—108no—
336C22×C4—1016no—
337C22×C4—108no—
338C22×C4—108no—
339C22×C4—104no—
340C22×C4—104no—
341C22×C4—102no—
342C22×C4—101no—
343C22×C4—101no—
344C22×C4—108no—
345C22×C4—101no—
346C22×C4—101no—
347C22×C4—204no—
348C22×C4—208no—
349C22×C4—204no—
350C22×C4—204no—
351C22×C4—204no—
352C22×C4—208no—
353C22×C4—204no—
354C22×C4—208no—
355C22×C4—202no—
356C22×C4—202no—
357C22×C4#70014yescomplemented
358C22×C4C22⋊AGL(1,𝔽5)12yes—
359C22×C4C22⋊AGL(1,𝔽5)12yes—
360C22×C4C22×AGL(1,𝔽5)12yes—
361C22×C4C22×AGL(1,𝔽5)12yes—
362C22×C4C22×AGL(1,𝔽5)12yes—
363M16—2016no—
364C2×C8—108no—
365C2×C8—208no—
366C4⋊C4—28no—
367C4⋊C4—104no—
368C4⋊C4—104no—
369C4⋊C4—104no—
370C4⋊C4—104no—
371C4⋊C4—108no—
372C2×C5—21no—
373C2×C5—21no—
374C2×C5—22no—
375C2×C5#146314yescomplemented
376C2×C5C2×#40711yescharacteristic
377C2×C5C22×#9911yescharacteristic
378C2×C5C22×#10111yescharacteristic
379D5—24no—
380D5—24no—
381C23—22no—
382C23—22no—
383C23—52no—
384C23—52no—
385C23—54no—
386C23—54no—
387C23—104no—
388C23—104no—
389C23—104no—
390C23—104no—
391C23—1016no—
392C23—1016no—
393C23—102no—
394C23—102no—
395C23—104no—
396C23—102no—
397C23—102no—
398C23—102no—
399C23—102no—
400C23C2×#70012yes—
401C23D5⋊M1612yes—
402C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
403C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
404C23C23×AGL(1,𝔽5)11yescharacteristic
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—54no—
417C2×C4—52no—
418C2×C4—52no—
419C2×C4—108no—
420C2×C4—108no—
421C2×C4—1016no—
422C2×C4—1016no—
423C2×C4—102no—
424C2×C4—104no—
425C2×C4—104no—
426C2×C4—102no—
427C2×C4—104no—
428C2×C4—102no—
429C2×C4—204no—
430C2×C4—204no—
431C2×C4—208no—
432C2×C4—208no—
433C2×C4—201no—
434C2×C4—202no—
435C2×C4—201no—
436C2×C4—202no—
437C2×C4—202no—
438C2×C4—202no—
439C2×C4C2×#70014yescomplemented
440C2×C4C2×C22⋊AGL(1,𝔽5)14yes—
441C8—208no—
442C5C2×#146311yescharacteristic, complemented, Sylow
443C22—24no—
444C22—24no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—54no—
450C22—54no—
451C22—108no—
452C22—108no—
453C22—1016no—
454C22—108no—
455C22—108no—
456C22—102no—
457C22—102no—
458C22—102no—
459C22—102no—
460C22#6575612yes—
461C22#6575612yes—
462C22D5⋊#9912yes—
463C22D5⋊#10112yes—
464C22C22×#70011yescharacteristic
465C22C2×D5⋊M1611yescharacteristic
466C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
467C4—24no—
468C4—24no—
469C4—42no—
470C4—104no—
471C4—102no—
472C4—102no—
473C4—202no—
474C2—21no—
475C2—21no—
476C2—22no—
477C2—104no—
478C2—104no—
479C2#1060429214yesdirect product factor
480C2C2×#6575611yescharacteristic
481C2C2×D5⋊#9911yescharacteristic
482C2C2×D5⋊#10111yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC23×C5C2×C22⋊C4
prime radicalC24×D5C2×C4
cosocleC22×Dic5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5C2×#1463
LCSG ▷ C23×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
3. C2×#64914C2semidirect
4. C2×#64913C2semidirect
5. #10604292C2direct (N × H)
23. #64914C22semidirect
24. #64913C22semidirect
97. C22×C4×C5M16semidirect
108. C22×Dic5M16semidirect
201. C2×C4×C5C2×M16semidirect
215. C2×Dic5C2×M16semidirect
357. C22×C4#700semidirect
375. C2×C5#1463semidirect
439. C2×C4C2×#700semidirect
442. C5C2×#1463semidirect
479. C2#10604292direct (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×#657562
C2×#649142
C2×#649132
#106042922
C2×#14635