Finite Group Databasebeta

← C2×#10599428 #12128031

Subgroups — C2×#10599428 #12128031

Order 1280.

1366 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3953C212yesmaximal
2C2×#65228C211yesmaximal, characteristic
3C2×#65224C211yesmaximal, characteristic, complemented
4C2×C5×#336C211yesmaximal, characteristic, complemented
5C2×#64771C212yesmaximal, complemented
6#10599428C218yesmaximal, direct product factor
7C23×D20C2211yescharacteristic
8C23×C5×C8C2212yes—
9C22×C42×C5C2211yescharacteristic
10C22×#685—21no—
11C22×#685—21no—
12C22×C4⋊Dic5—21no—
13C22×C4⋊Dic5—21no—
14C22×C4⋊Dic5C2211yescharacteristic
15C22×C4⋊Dic5C2212yes—
16C2×#3953—28no—
17C2×#3953C2218yes—
18#65228—22no—
19#65228C2214yes—
20#65224—22no—
21#65224C2214yescomplemented
22C5×#336C2214yescomplemented
23#64771C2218yescomplemented
24C2×#2071—51nomaximal, Sylow
25C24×D5—21no—
26C23×C4×C5D411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C23×C4×C5C2311yescharacteristic
29C23×Dic5—22no—
30C23×Dic5—21no—
31C22×D20—24no—
32C22×D20—24no—
33C22×D20—21no—
34C22×D20—22no—
35C22×D20D414yes—
36C22×D20C2312yes—
37C22×C5×C8—24no—
38C22×C5×C8—24no—
39C22×C5×C8—24no—
40C22×C5×C8C2314yes—
41C2×C42×C5—24no—
42C2×C42×C5D412yes—
43C2×C42×C5C2312yes—
44C2×#685—24no—
45C2×#685—24no—
46C2×#685—44no—
47C2×#685—44no—
48C2×C4⋊Dic5—24no—
49C2×C4⋊Dic5—24no—
50C2×C4⋊Dic5—24no—
51C2×C4⋊Dic5—24no—
52C2×C4⋊Dic5—24no—
53C2×C4⋊Dic5—22no—
54C2×C4⋊Dic5—21no—
55C2×C4⋊Dic5—44no—
56C2×C4⋊Dic5—44no—
57C2×C4⋊Dic5C2312yes—
58C2×C4⋊Dic5C2314yes—
59#3953—216no—
60C22×#102—52no—
61C2×#390—51no—
62C2×#384—51no—
63#2071—58no—
64C2×#340—52no—
65C2×#336D511yescharacteristic, complemented
66C24×C5C2×D411yescharacteristic
67C23×D5—24no—
68C23×D5—22no—
69C23×D5—42no—
70C23×D5—42no—
71C23×D5—42no—
72C23×D5—42no—
73C23×D5—42no—
74C23×D5—42no—
75C22×C4×C5—22no—
76C22×C4×C5—22no—
77C22×C4×C5—22no—
78C22×C4×C5—22no—
79C22×C4×C5D814yes—
80C22×C4×C5SD1614yes—
81C22×C4×C5C2×D412yes—
82C22×C4×C5C2×D412yes—
83C22×C4×C5C2×D411yescharacteristic
84C22×C4×C5C2×D412yes—
85C22×C4×C5#4114yes—
86C22×C4×C5#4114yes—
87C22×C4×C5#4112yes—
88C22×C4×C5C2411yescharacteristic
89C22×Dic5—24no—
90C22×Dic5—22no—
91C22×Dic5—44no—
92C22×Dic5—42no—
93C22×Dic5—44no—
94C22×Dic5—42no—
95C22×Dic5—42no—
96C22×Dic5—44no—
97C2×D20—216no—
98C2×D20—24no—
99C2×D20—24no—
100C2×D20—24no—
101C2×D20—22no—
102C2×D20—42no—
103C2×D20—42no—
104C2×D20—48no—
105C2×D20C2×D414yes—
106C2×C5×C8—24no—
107C2×C5×C8—24no—
108C2×C5×C8—24no—
109C2×C5×C8—48no—
110C42×C5—24no—
111C42×C5—24no—
112#685—48no—
113#685—48no—
114C4⋊Dic5—24no—
115C4⋊Dic5—24no—
116C4⋊Dic5—24no—
117C4⋊Dic5—48no—
118C4⋊Dic5—44no—
119C4⋊Dic5—42no—
120C4⋊Dic5—48no—
121C23×D4—51no—
122C23×C8C2×D512yes—
123C22×C4⋊C4—52no—
124C22×C4⋊C4—51no—
125C22×C4⋊C4—101no—
126C22×C4⋊C4—101no—
127C22×C22⋊C4—101no—
128C22×C22⋊C4—101no—
129C22×C42C2×D511yescharacteristic
130C2×#102—58no—
131C2×#102—108no—
132#390—54no—
133#390—102no—
134#384—54no—
135#384—102no—
136#340—58no—
137#336C2×D514yescomplemented
138C23×C5#12112yes—
139C23×C5#12312yes—
140C23×C5#12412yes—
141C23×C5C2×D812yes—
142C23×C5C2×SD1612yes—
143C23×C5AGL(1,ℤ/8)12yes—
144C23×C5#13712yes—
145C23×C5C22×D411yescharacteristic
146C22×D5—24no—
147C22×D5—42no—
148C22×D5—42no—
149C22×D5—42no—
150C22×D5—42no—
151C22×D5—42no—
152C22×D5—42no—
153C22×D5—48no—
154C22×D5—48no—
155C22×D5—48no—
156C22×D5—84no—
157C22×D5—84no—
158C22×D5—84no—
159C22×D5—84no—
160C2×C4×C5—22no—
161C2×C4×C5—22no—
162C2×C4×C5—22no—
163C2×C4×C5—22no—
164C2×C4×C5—28no—
165C2×C4×C5—28no—
166C2×C4×C5#12112yes—
167C2×C4×C5#12318yes—
168C2×C4×C5#12312yes—
169C2×C4×C5#12412yes—
170C2×C4×C5#12618yes—
171C2×C4×C5C2×D814yes—
172C2×C4×C5C2×SD1614yes—
173C2×C4×C5C22×D411yescharacteristic
174C2×C4×C5C2×#4112yes—
175C2×C4×C5C2×#4112yes—
176C2×C4×C5C2×#4111yescharacteristic
177C2×Dic5—44no—
178C2×Dic5—42no—
179C2×Dic5—44no—
180C2×Dic5—42no—
181C2×Dic5—42no—
182C2×Dic5—44no—
183C2×Dic5—88no—
184C2×Dic5—84no—
185D20—28no—
186D20—44no—
187D20—48no—
188C5×C8—44no—
189C25—101no—
190C22×D4—54no—
191C22×D4—52no—
192C22×D4—101no—
193C22×D4—104no—
194C22×D4—104no—
195C22×D4—102no—
196C23×C4—101no—
197C23×C4—102no—
198C23×C4D2011yescharacteristic
199C23×C4D2011yescharacteristic
200C23×C4C22×D511yescharacteristic
201C22×C8—24no—
202C22×C8—24no—
203C22×C8—24no—
204C22×C8C22×D514yes—
205C2×C4⋊C4—52no—
206C2×C4⋊C4—54no—
207C2×C4⋊C4—104no—
208C2×C4⋊C4—104no—
209C2×C4⋊C4—104no—
210C2×C4⋊C4—102no—
211C2×C4⋊C4—101no—
212C2×C4⋊C4—104no—
213C2×C4⋊C4—104no—
214C2×C4⋊C4—204no—
215C2×C4⋊C4—204no—
216C2×C22⋊C4—104no—
217C2×C22⋊C4—104no—
218C2×C22⋊C4—204no—
219C2×C22⋊C4—204no—
220C2×C42—24no—
221C2×C42D2012yes—
222C2×C42C22×D512yes—
223#102—1016no—
224C22×C5#39714yes—
225C22×C5#45914yes—
226C22×C5#46114yes—
227C22×C5#48014yes—
228C22×C5#48114yes—
229C22×C5#48614yes—
230C22×C5#48914yes—
231C22×C5C2×#12111yescharacteristic
232C22×C5C2×#12311yescharacteristic
233C22×C5C2×#12411yescharacteristic
234C22×C5C22×D811yescharacteristic
235C22×C5C22×SD1611yescharacteristic
236C22×C5C2×AGL(1,ℤ/8)11yescharacteristic
237C22×C5C2×#13711yescharacteristic
238C2×D5—44no—
239C2×D5—44no—
240C2×D5—44no—
241C2×D5—82no—
242C2×D5—82no—
243C2×D5—816no—
244C2×D5—82no—
245C2×D5—82no—
246C4×C5—24no—
247C4×C5—24no—
248C4×C5#39714yes—
249C4×C5C2×#12312yes—
250C4×C5C2×#12612yes—
251Dic5—82no—
252Dic5—84no—
253C24—102no—
254C24—104no—
255C24—202no—
256C24—202no—
257C24—202no—
258C24—202no—
259C24—202no—
260C24—202no—
261C24C2×D2011yescharacteristic
262C2×D4—54no—
263C2×D4—104no—
264C2×D4—104no—
265C2×D4—102no—
266C2×D4—1016no—
267C2×D4—104no—
268C2×D4—202no—
269C2×D4—202no—
270C2×D4—208no—
271C22×C4—22no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—22no—
275C22×C4—102no—
276C22×C4—104no—
277C22×C4—202no—
278C22×C4—204no—
279C22×C4—202no—
280C22×C4—202no—
281C22×C4—204no—
282C22×C4—204no—
283C22×C4#67714yes—
284C22×C4D4014yes—
285C22×C4C2×D2012yes—
286C22×C4C2×D2012yes—
287C22×C4C2×D2011yescharacteristic
288C22×C4#70914yes—
289C22×C4D4×D512yes—
290C22×C4#71114yes—
291C22×C4#71312yes—
292C22×C4C23×D511yescharacteristic
293C2×C8—24no—
294C2×C8—24no—
295C2×C8—24no—
296C2×C8—48no—
297C4⋊C4—104no—
298C4⋊C4—104no—
299C4⋊C4—104no—
300C4⋊C4—208no—
301C4⋊C4—202no—
302C4⋊C4—204no—
303C4⋊C4—208no—
304C22⋊C4—208no—
305C22⋊C4—208no—
306C42—24no—
307C42—24no—
308C2×C5#207118yescomplemented
309C2×C5C2×#39711yescharacteristic
310C2×C5C2×#45911yescharacteristic
311C2×C5C2×#46111yescharacteristic
312C2×C5C2×#48011yescharacteristic
313C2×C5C2×#48111yescharacteristic
314C2×C5C2×#48611yescharacteristic
315C2×C5C2×#48911yescharacteristic
316D5—84no—
317C23—104no—
318C23—202no—
319C23—202no—
320C23—202no—
321C23—202no—
322C23—202no—
323C23—202no—
324C23—208no—
325C23—208no—
326C23—208no—
327C23—404no—
328C23—404no—
329C23—404no—
330C23—404no—
331C23#402112yes—
332C23#403212yes—
333C23#404112yes—
334C23C2×#67712yes—
335C23C2×D4012yes—
336C23#405412yes—
337C23#405512yes—
338C23C22×D2011yescharacteristic
339D4—108no—
340D4—204no—
341D4—208no—
342C2×C4—28no—
343C2×C4—28no—
344C2×C4—22no—
345C2×C4—22no—
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—202no—
349C2×C4—202no—
350C2×C4—202no—
351C2×C4—204no—
352C2×C4—204no—
353C2×C4—204no—
354C2×C4—408no—
355C2×C4—404no—
356C2×C4#402112yes—
357C2×C4#402918yes—
358C2×C4#403212yes—
359C2×C4#404112yes—
360C2×C4#404418yes—
361C2×C4C2×#67714yes—
362C2×C4C2×D4014yes—
363C2×C4C2×#70912yes—
364C2×C4C2×D4×D511yescharacteristic
365C2×C4C2×#71112yes—
366C2×C4C2×#71311yescharacteristic
367C8—44no—
368C5C2×#207111yescharacteristic, complemented, Sylow
369C22—204no—
370C22—204no—
371C22—204no—
372C22—4016no—
373C22—402no—
374C22—402no—
375C22—402no—
376C22—402no—
377C22#6496314yes—
378C22#6498314yes—
379C22#6500314yes—
380C22#6502414yes—
381C22#6502514yes—
382C22#6513014yes—
383C22#6513214yes—
384C22C2×#402111yescharacteristic
385C22C2×#403211yescharacteristic
386C22C2×#404111yescharacteristic
387C22C22×#67711yescharacteristic
388C22C22×D4011yescharacteristic
389C22C2×#405411yescharacteristic
390C22C2×#405511yescharacteristic
391C4—24no—
392C4—24no—
393C4—402no—
394C4—404no—
395C4#6496314yes—
396C4C2×#402912yes—
397C4C2×#404412yes—
398C2—404no—
399C2#1059942818yesdirect product factor
400C2C2×#6496311yescharacteristic
401C2C2×#6498311yescharacteristic
402C2C2×#6500311yescharacteristic
403C2C2×#6502511yescharacteristic
404C2C2×#6502411yescharacteristic
405C2C2×#6513211yescharacteristic
406C2C2×#6513011yescharacteristic
subgroupG/H
centerC24C2×D20
commutator, cosocleC22×C4×C5C24
FrattiniC22×C4C23×D5
FittingC2×C5×#336C2
socleC24×C5C2×D4
prime radicalC23×D20C22
hypercenterC2×#336D5
hypocenterC5C2×#2071
LCSG ▷ C22×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
3. C2×#65224C2semidirect
4. C2×C5×#336C2semidirect
5. C2×#64771C2semidirect
6. #10599428C2direct (N × H)
21. #65224C22semidirect
22. C5×#336C22semidirect
23. #64771C22semidirect
65. C2×#336D5semidirect
137. #336C2×D5semidirect
308. C2×C5#2071semidirect
368. C5C2×#2071semidirect
399. C2#10599428direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#39532
C2×#652282
C2×#652242
C2×C5×#3362
C2×#647712
#105994282
C2×#20715