Finite Group Databasebeta

← C2×#10613471 #12968599

Subgroups — C2×#10613471 #12968599

Order 1280.

2182 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66059C211yesmaximal, characteristic
2C2×D5×#125C211yesmaximal, characteristic, complemented
3C2×C5×#491C211yesmaximal, characteristic, complemented
4C2×#65371C211yesmaximal, characteristic, complemented
5C2×#65356C211yesmaximal, characteristic, complemented
6#10613471C2116yesmaximal, direct product factor
7C2×#65092C214yesmaximal, complemented
8C2×#65089C214yesmaximal, complemented
9C2×#65002C211yesmaximal, characteristic, complemented
10C2×#64996C211yesmaximal, characteristic, complemented
11C22×#713C2212yes—
12C2×C5×C4⋊Q8C2211yescharacteristic
13C2×C5×#125C2211yescharacteristic
14C2×#4093C2212yes—
15C22×#676C2212yes—
16#66059—24no—
17#66059C2218yes—
18D5×#125—24no—
19D5×#125C2218yescomplemented
20C2×#4041—22no—
21C2×#4039—22no—
22C2×D5×C4⋊C4—22no—
23C2×D5×C4⋊C4C2212yes—
24C2×#4036C2212yes—
25C2×#4035—22no—
26C2×#4020C2211yescharacteristic
27C2×C42×D5C2211yescharacteristic
28C2×#4016C2211yescharacteristic
29C5×#491C2218yescomplemented
30C2×C5×#103C2214yes—
31C2×C5×#97C2211yescharacteristic
32C2×#3967C2214yes—
33C2×#3953C2214yes—
34C2×C8×Dic5C2212yes—
35#65371C2218yescomplemented
36#65356C2218yescomplemented
37C2×#3941C2214yes—
38C2×#3935C2211yescharacteristic
39#65092C22132yescomplemented
40#65089C22132yescomplemented
41#65002C2218yescomplemented
42#64996C2218yescomplemented
43C2×#3142—51nomaximal, Sylow
44C22×C5×Q8C2312yes—
45C2×#713—24no—
46C2×#713—216no—
47C2×#713C2318yes—
48C22×D20—22no—
49C22×D20—22no—
50C22×D20C2312yes—
51C22×C4×D5—22no—
52C22×C4×D5—22no—
53C22×C4×D5D412yes—
54C22×C4×D5C2311yescharacteristic
55C22×C5×C8C2312yes—
56C5×C4⋊Q8—22no—
57C5×C4⋊Q8C2314yes—
58C5×#125—22no—
59C5×#125C2314yes—
60C2×C5×C4⋊C4—22no—
61C2×C5×C4⋊C4—22no—
62C2×C5×C4⋊C4C2312yes—
63C2×C42×C5C2311yescharacteristic
64#4093—24no—
65#4093C2318yes—
66C2×#685—24no—
67C2×C4⋊Dic5—22no—
68C2×C4⋊Dic5C2312yes—
69C2×#683—22no—
70C2×#683—22no—
71C2×#683—22no—
72C2×C4×Dic5D412yes—
73C2×C4×Dic5C2311yescharacteristic
74C22×#168C2312yes—
75C2×#676—28no—
76C2×#676C2318yes—
77#4041—216no—
78#4039—216no—
79D5×C4⋊C4—216no—
80D5×C4⋊C4—24no—
81D5×C4⋊C4C2318yes—
82#4036—24no—
83#4036C2318yes—
84#4035—216no—
85#4020—22no—
86#4020C2314yes—
87C42×D5D414yes—
88C42×D5C2314yes—
89#4016—22no—
90#4016C2314yes—
91C5×#103C23116yes—
92C5×#97C2314yes—
93#3967C23116yes—
94#3953C23116yes—
95C8×Dic5C2318yes—
96#3941C23116yes—
97#3935C2314yes—
98C2×#532—51no—
99C22×#125—51no—
100#3142—516no—
101C2×#491—51no—
102C2×#491D511yescharacteristic, complemented
103C2×#490—51no—
104C2×#490—51no—
105C2×#488—54no—
106C2×#417—54no—
107C2×C4×M16—51no—
108C23×D5—22no—
109C23×D5C2×D411yescharacteristic
110C2×C5×Q8—22no—
111C2×C5×Q8—28no—
112C2×C5×Q8C2414yes—
113C22×C4×C5—22no—
114C22×C4×C5—22no—
115C22×C4×C5C2×D412yes—
116C22×C4×C5C2411yescharacteristic
117C22×Dic5—22no—
118C22×Dic5C2×D412yes—
119C22×Dic5C2×D411yescharacteristic
120#713—232no—
121#713—416no—
122C2×D20—28no—
123C2×D20—28no—
124C2×D20—28no—
125C2×D20—22no—
126C2×D20—48no—
127C2×D20—48no—
128C2×D20C2414yes—
129C2×C4×D5—28no—
130C2×C4×D5—28no—
131C2×C4×D5—44no—
132C2×C4×D5—48no—
133C2×C4×D5—48no—
134C2×C4×D5C2×D418yes—
135C2×C4×D5C2×D412yes—
136C2×C4×D5#4118yes—
137C2×C4×D5C2412yes—
138C2×C5×C8—24no—
139C2×C5×C8C2414yes—
140C5×C4⋊C4—28no—
141C5×C4⋊C4—28no—
142C5×C4⋊C4—22no—
143C5×C4⋊C4C2414yes—
144C42×C5C2×D412yes—
145C42×C5C2412yes—
146#685—216no—
147C4⋊Dic5—22no—
148C4⋊Dic5—28no—
149C4⋊Dic5C2414yes—
150#683—28no—
151#683—28no—
152#683—28no—
153C4×Dic5C2×D412yes—
154C4×Dic5C2×D418yes—
155C4×Dic5C2412yes—
156C2×#168—24no—
157C2×#168C2414yes—
158#676—216no—
159C22×#41—52no—
160C22×M16—52no—
161#532—58no—
162#532—104no—
163C2×C4⋊Q8C2×D511yescharacteristic
164C2×#127—51no—
165C2×#125—58no—
166C2×#125—52no—
167C2×#125—51no—
168C2×#125—102no—
169C2×#125—104no—
170C2×#125C2×D511yescharacteristic
171C2×#124—52no—
172C2×#121—102no—
173C2×C4×D4—102no—
174C22×C4⋊C4—52no—
175C22×C4⋊C4—102no—
176C22×C42—51no—
177#491—58no—
178#491C2×D518yescomplemented
179#490—58no—
180#490—58no—
181#488—532no—
182#417—532no—
183C2×#103—54no—
184C2×#103C2×D514yes—
185C2×#102—54no—
186C2×#102—54no—
187C4×M16—58no—
188C2×#97—51no—
189C2×#97C2×D511yescharacteristic
190C2×C4×C8—52no—
191C23×C5C22×D411yescharacteristic
192C22×D5—24no—
193C22×D5—24no—
194C22×D5—44no—
195C22×D5—48no—
196C22×D5#12414yes—
197C22×D5C22×D412yes—
198C5×Q8—28no—
199C5×Q8—44no—
200C2×C4×C5—24no—
201C2×C4×C5—24no—
202C2×C4×C5—24no—
203C2×C4×C5—44no—
204C2×C4×C5—44no—
205C2×C4×C5C22×D414yes—
206C2×C4×C5C22×D411yescharacteristic
207C2×C4×C5C2×#4114yes—
208C2×C4×C5C2511yescharacteristic
209C2×Dic5—24no—
210C2×Dic5—24no—
211C2×Dic5—44no—
212C2×Dic5#12414yes—
213C2×Dic5C22×D414yes—
214C2×Dic5C22×D412yes—
215D20—28no—
216D20—416no—
217D20—416no—
218D20—44no—
219C4×D5—48no—
220C4×D5—416no—
221C4×D5—416no—
222C4×D5#12418yes—
223C4×D5C2×#4118yes—
224C5×C8—24no—
225#168—24no—
226C2×#41—58no—
227C2×#41—104no—
228C2×#41—1016no—
229C22×Q8C22×D512yes—
230C22×D4—52no—
231C22×D4—102no—
232C22×D4—102no—
233C23×C4—51no—
234C23×C4—52no—
235C23×C4—102no—
236C23×C4—102no—
237C2×M16—58no—
238C2×M16—108no—
239C22×C8—52no—
240C22×C8C22×D512yes—
241C4⋊Q8—22no—
242C4⋊Q8C22×D514yes—
243#127—54no—
244#127—102no—
245#125—22no—
246#125—58no—
247#125—54no—
248#125—1016no—
249#125—104no—
250#125—102no—
251#125C22×D514yes—
252#124—58no—
253#124—104no—
254#121—1016no—
255C4×D4—1016no—
256C2×C4⋊C4—22no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—52no—
259C2×C4⋊C4—58no—
260C2×C4⋊C4—104no—
261C2×C4⋊C4—1016no—
262C2×C4⋊C4—102no—
263C2×C4⋊C4—102no—
264C2×C4⋊C4—102no—
265C2×C4⋊C4—102no—
266C2×C4⋊C4C22×D512yes—
267C2×C22⋊C4—104no—
268C2×C42—52no—
269C2×C42—51no—
270C2×C42—54no—
271C2×C42—54no—
272C2×C42C22×D511yescharacteristic
273#103—516no—
274#103C22×D5116yes—
275#102—516no—
276#102—516no—
277#97—54no—
278#97C22×D514yes—
279C4×C8—58no—
280C22×C5C2×#12412yes—
281C22×C5#57514yes—
282C22×C5C23×D411yescharacteristic
283C2×D5—28no—
284C2×D5—24no—
285C2×D5—44no—
286C2×D5—48no—
287C2×D5—88no—
288C2×D5C2×#12414yes—
289C4×C5—24no—
290C4×C5—44no—
291C4×C5—44no—
292C4×C5C2×#12412yes—
293C4×C5C22×#4112yes—
294Dic5—24no—
295Dic5—44no—
296Dic5C2×#12414yes—
297C24—51no—
298C24—102no—
299#41—1032no—
300#41—2016no—
301C2×Q8—22no—
302C2×Q8—28no—
303C2×Q8C23×D514yes—
304C2×D4—54no—
305C2×D4—108no—
306C2×D4—108no—
307C2×D4—102no—
308C2×D4—108no—
309C2×D4—208no—
310C2×D4—208no—
311C22×C4—22no—
312C22×C4—22no—
313C22×C4—51no—
314C22×C4—52no—
315C22×C4—58no—
316C22×C4—52no—
317C22×C4—52no—
318C22×C4—58no—
319C22×C4—108no—
320C22×C4—108no—
321C22×C4—102no—
322C22×C4—204no—
323C22×C4—208no—
324C22×C4—208no—
325C22×C4D4×D512yes—
326C22×C4C23×D511yescharacteristic
327M16—1016no—
328C2×C8—24no—
329C2×C8—54no—
330C2×C8—104no—
331C2×C8C23×D514yes—
332C4⋊C4—28no—
333C4⋊C4—28no—
334C4⋊C4—22no—
335C4⋊C4—54no—
336C4⋊C4—108no—
337C4⋊C4—108no—
338C4⋊C4—108no—
339C4⋊C4—102no—
340C4⋊C4—108no—
341C4⋊C4C23×D514yes—
342C22⋊C4—1016no—
343C42—58no—
344C42—52no—
345C42—52no—
346C42D4×D512yes—
347C42C23×D512yes—
348C2×C5#314214yescomplemented
349C2×C5C22×#12411yescharacteristic
350C2×C5C2×#57512yes—
351D5—24no—
352D5—84no—
353C23—54no—
354C23—52no—
355C23—104no—
356C23—104no—
357C23—208no—
358C23—204no—
359C23C2×D4×D511yescharacteristic
360Q8—28no—
361Q8—44no—
362D4—108no—
363D4—2016no—
364D4—2016no—
365D4—204no—
366C2×C4—24no—
367C2×C4—24no—
368C2×C4—24no—
369C2×C4—44no—
370C2×C4—44no—
371C2×C4—54no—
372C2×C4—52no—
373C2×C4—58no—
374C2×C4—58no—
375C2×C4—54no—
376C2×C4—104no—
377C2×C4—104no—
378C2×C4—208no—
379C2×C4—2016no—
380C2×C4—2016no—
381C2×C4—204no—
382C2×C4C2×D4×D514yes—
383C2×C4C2×D4×D511yescharacteristic
384C2×C4D5×#4114yes—
385C2×C4C24×D511yescharacteristic
386C8—24no—
387C8—104no—
388C5C2×#314211yescharacteristic, complemented, Sylow
389C22—54no—
390C22—104no—
391C22—108no—
392C22—204no—
393C22—208no—
394C22—408no—
395C22D5×#12412yes—
396C22#6611114yes—
397C22C22×D4×D511yescharacteristic
398C4—24no—
399C4—44no—
400C4—44no—
401C4—54no—
402C4—104no—
403C4—204no—
404C4D5×#12412yes—
405C4C2×D5×#4112yes—
406C2—104no—
407C2—404no—
408C2#1061347114yesdirect product factor
409C2C2×D5×#12411yescharacteristic
410C2C2×#6611112yes—
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C5×#491C2
socleC23×C5C22×D4
prime radicalC2×#66059C2
hypercenterC2×#491D5
hypocenterC5C2×#3142
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
2. C2×D5×#125C2semidirect
3. C2×C5×#491C2semidirect
4. C2×#65371C2semidirect
5. C2×#65356C2semidirect
6. #10613471C2direct (N × H)
7. C2×#65092C2semidirect
8. C2×#65089C2semidirect
9. C2×#65002C2semidirect
10. C2×#64996C2semidirect
19. D5×#125C22semidirect
29. C5×#491C22semidirect
35. #65371C22semidirect
36. #65356C22semidirect
39. #65092C22semidirect
40. #65089C22semidirect
41. #65002C22semidirect
42. #64996C22semidirect
102. C2×#491D5semidirect
178. #491C2×D5semidirect
348. C2×C5#3142semidirect
388. C5C2×#3142semidirect
408. C2#10613471direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#660592
C2×D5×#1252
C2×C5×#4912
C2×#653712
C2×#653562
#106134712
C2×#650922
C2×#650892
C2×#650022
C2×#649962
C2×#31425