Finite Group Databasebeta

← C2×#10611440 #12979849

Subgroups — C2×#10611440 #12979849

Order 1280.

1746 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65903C212yesmaximal
2C2×C4×C5×Q16C211yesmaximal, characteristic
3C2×#65473C212yesmaximal
4C2×#65311C212yesmaximal
5#10611440C2116yesmaximal, direct product factor
6C2×#65165C212yesmaximal
7C2×#65085C212yesmaximal
8C2×#65083C212yesmaximal
9C2×#64968C211yesmaximal, characteristic
10C2×#64972C211yesmaximal, characteristic
11C22×C5×Q16C2211yescharacteristic
12C2×C4×C5×Q8C2212yes—
13C2×Q8×Dic5C2212yes—
14C2×Q8×Dic5C2212yes—
15#65903—28no—
16#65903C22116yes—
17C2×#4036—22no—
18C2×#4036C2212yes—
19C2×#4034—22no—
20C2×#4034C2212yes—
21C2×#4016—22no—
22C2×#4016C2212yes—
23C2×C4×Dic10—22no—
24C2×C4×Dic10C2211yescharacteristic
25C4×C5×Q16C2218yes—
26C2×C5×#107C2211yescharacteristic
27C2×C5×#103C2212yes—
28C2×C4×C5×C8C2211yescharacteristic
29C2×#3967C2212yes—
30C2×#3967C2212yes—
31#65473C22116yes—
32C2×#3950C2211yescharacteristic
33C2×#3950C2211yescharacteristic
34C2×#3949C2212yes—
35C2×#3947C2212yes—
36C2×#3946C2212yes—
37#65311C22116yes—
38C2×#3940C2212yes—
39C2×#3939C2212yes—
40C2×C4⋊#168C2211yescharacteristic
41#65165C22116yes—
42#65085C22116yes—
43#65083C22116yes—
44#64972C2218yes—
45#64968C2218yes—
46C2×#3390—51nomaximal, Sylow
47C22×C5×Q8C2312yes—
48C22×Dic10—22no—
49C22×Dic10D411yescharacteristic
50C2×C5×Q16Q818yescomplemented
51C2×C5×Q16C2314yes—
52C22×C5×C8C2311yescharacteristic
53C22×C5×C8C2311yescharacteristic
54C4×C5×Q8—24no—
55C4×C5×Q8C2318yes—
56C2×C5×C4⋊C4—22no—
57C2×C5×C4⋊C4C2312yes—
58C2×C42×C5—22no—
59C2×C42×C5C2311yescharacteristic
60Q8×Dic5—24no—
61Q8×Dic5—24no—
62Q8×Dic5C2318yes—
63Q8×Dic5C2318yes—
64C2×C4⋊Dic5—22no—
65C2×C4⋊Dic5—22no—
66C2×C4⋊Dic5—22no—
67C2×C4⋊Dic5D411yescharacteristic
68C2×C4⋊Dic5C2312yes—
69C2×C4⋊Dic5C2312yes—
70C2×#683—22no—
71C2×#683—22no—
72C2×#683—22no—
73C2×#683—22no—
74C2×#683D412yes—
75C2×C4×Dic5—22no—
76C2×C4×Dic5—22no—
77C2×C4×Dic5C2312yes—
78C22×#168C2312yes—
79#4036—216no—
80#4036—24no—
81#4036C2318yes—
82#4034—216no—
83#4034—24no—
84#4034C2318yes—
85#4016—24no—
86#4016—216no—
87#4016C2318yes—
88C4×Dic10—216no—
89C4×Dic10D414yes—
90C4×Dic10C2314yes—
91C5×#107C2314yes—
92C5×#103C2318yes—
93C4×C5×C8C2314yes—
94#3967C2318yes—
95#3967C2318yes—
96#3950C2314yes—
97#3950C2314yes—
98#3949C2318yes—
99#3947C2318yes—
100#3946C2318yes—
101#3940C2318yes—
102#3939C2318yes—
103C4⋊#168C2314yes—
104C2×#557—52no—
105#3390—516no—
106C2×#501—52no—
107C2×#499—51no—
108C2×#479—52no—
109C2×#479—52no—
110C2×#477—52no—
111C2×#446—51no—
112C2×#441—52no—
113C2×C4×Q16D511yescharacteristic
114C2×C5×Q8—22no—
115C2×C5×Q8—24no—
116C2×C5×Q8C2×Q818yes—
117C2×C5×Q8C2414yes—
118C22×C4×C5—22no—
119C22×C4×C5—22no—
120C22×C4×C5C2×D411yescharacteristic
121C22×C4×C5C2×D411yescharacteristic
122C22×C4×C5C2411yescharacteristic
123C22×Dic5—22no—
124C22×Dic5—22no—
125C22×Dic5C2×D412yes—
126C22×Dic5C2×D412yes—
127C2×Dic10—28no—
128C2×Dic10—42no—
129C2×Dic10—48no—
130C2×Dic10C2×D414yes—
131C5×Q16C2×Q8116yescomplemented
132C2×C5×C8—22no—
133C2×C5×C8C2×Q814yes—
134C2×C5×C8C2412yes—
135C2×C5×C8C2412yes—
136C5×C4⋊C4—28no—
137C5×C4⋊C4—22no—
138C5×C4⋊C4C2414yes—
139C42×C5—28no—
140C42×C5C2×D412yes—
141C42×C5C2412yes—
142C4⋊Dic5—22no—
143C4⋊Dic5—22no—
144C4⋊Dic5—28no—
145C4⋊Dic5—28no—
146C4⋊Dic5—28no—
147C4⋊Dic5C2×D414yes—
148C4⋊Dic5C2414yes—
149C4⋊Dic5C2414yes—
150#683—28no—
151#683—28no—
152#683—28no—
153#683—28no—
154#683C2×D418yes—
155C4×Dic5—28no—
156C4×Dic5—28no—
157C4×Dic5C2×D414yes—
158C4×Dic5C2414yes—
159C2×#168—24no—
160C2×#168C2414yes—
161C22×Q16C2×D511yescharacteristic
162#557—516no—
163#557—108no—
164C2×C4⋊Q8—52no—
165C2×C4⋊Q8—102no—
166C2×#125—52no—
167C2×#125—52no—
168C2×#125—102no—
169C2×#125—102no—
170C2×C4×Q8—51no—
171C2×C4×Q8—52no—
172C2×C4×Q8—52no—
173C2×C4×Q8—102no—
174C2×C4×Q8C2×D512yes—
175#501—516no—
176#499—58no—
177#479—516no—
178#479—516no—
179#477—516no—
180#446—58no—
181#441—516no—
182C4×Q16C2×D518yes—
183C2×#107—51no—
184C2×#107—51no—
185C2×#107—52no—
186C2×#107C2×D511yescharacteristic
187C2×#106—52no—
188C2×#106—52no—
189C2×C4⋊C8—52no—
190C2×C4⋊C8—51no—
191C2×#103—52no—
192C2×#103—52no—
193C2×#103C2×D512yes—
194C2×#97—52no—
195C2×C4×C8C2×D511yescharacteristic
196C23×C5C22×D411yescharacteristic
197C5×Q8—28no—
198C5×Q8—24no—
199C5×Q8C22×Q818yes—
200C2×C4×C5—28no—
201C2×C4×C5—22no—
202C2×C4×C5—22no—
203C2×C4×C5—24no—
204C2×C4×C5—24no—
205C2×C4×C5—44no—
206C2×C4×C5C22×D412yes—
207C2×C4×C5C22×D412yes—
208C2×C4×C5C22×D411yescharacteristic
209C2×C4×C5C22×Q812yes—
210C2×C4×C52−1+412yes—
211C2×C4×C5C2511yescharacteristic
212C2×Dic5—24no—
213C2×Dic5—24no—
214C2×Dic5—24no—
215C2×Dic5—24no—
216C2×Dic5—44no—
217C2×Dic5—44no—
218C2×Dic5C22×D414yes—
219C2×Dic5C22×D414yes—
220Dic10—44no—
221Dic10—416no—
222C5×C8—22no—
223C5×C8C22×Q814yes—
224#168—24no—
225C22×Q8—51no—
226C22×Q8—102no—
227C22×Q8C22×D512yes—
228C2×Q16Dic1018yescomplemented
229C2×Q16C22×D514yes—
230C22×C8—52no—
231C22×C8C22×D511yescharacteristic
232C22×C8C22×D511yescharacteristic
233C4⋊Q8—58no—
234C4⋊Q8—104no—
235C4⋊Q8—1016no—
236#125—58no—
237#125—58no—
238#125—1016no—
239#125—104no—
240#125—1016no—
241#125—104no—
242C4×Q8—24no—
243C4×Q8—54no—
244C4×Q8—54no—
245C4×Q8—58no—
246C4×Q8—58no—
247C4×Q8—1016no—
248C4×Q8—104no—
249C4×Q8—104no—
250C4×Q8C22×D518yes—
251C2×C4⋊C4—22no—
252C2×C4⋊C4—52no—
253C2×C4⋊C4—51no—
254C2×C4⋊C4—52no—
255C2×C4⋊C4—52no—
256C2×C4⋊C4—102no—
257C2×C4⋊C4—102no—
258C2×C4⋊C4—102no—
259C2×C4⋊C4—102no—
260C2×C4⋊C4—102no—
261C2×C4⋊C4—102no—
262C2×C4⋊C4—102no—
263C2×C4⋊C4C22×D512yes—
264C2×C42—22no—
265C2×C42—52no—
266C2×C42—102no—
267C2×C42—102no—
268C2×C42C22×D511yescharacteristic
269#107—54no—
270#107—54no—
271#107—58no—
272#107C22×D514yes—
273#106—58no—
274#106—58no—
275C4⋊C8—58no—
276C4⋊C8—54no—
277#103—58no—
278#103—58no—
279#103C22×D518yes—
280#97—58no—
281C4×C8C22×D514yes—
282C22×C5D4×Q812yes—
283C22×C5#57512yes—
284C22×C5#57812yes—
285C22×C5C23×D411yescharacteristic
286C4×C5—28no—
287C4×C5—22no—
288C4×C5—22no—
289C4×C5—44no—
290C4×C5D4×Q812yes—
291C4×C5C23×Q811yescharacteristic
292C4×C5C2×2−1+411yescharacteristic
293Dic5—24no—
294Dic5—24no—
295Dic5—44no—
296Dic5—44no—
297C2×Q8—22no—
298C2×Q8—24no—
299C2×Q8—54no—
300C2×Q8—108no—
301C2×Q8—202no—
302C2×Q8—208no—
303C2×Q8C2×Dic1018yes—
304C2×Q8C23×D514yes—
305C22×C4—22no—
306C22×C4—22no—
307C22×C4—52no—
308C22×C4—52no—
309C22×C4—102no—
310C22×C4—102no—
311C22×C4D4×D511yescharacteristic
312C22×C4D4×D511yescharacteristic
313C22×C4C23×D511yescharacteristic
314Q16C2×Dic10116yescomplemented
315C2×C8—22no—
316C2×C8—54no—
317C2×C8—104no—
318C2×C8C2×Dic1014yes—
319C2×C8C23×D512yes—
320C2×C8C23×D512yes—
321C4⋊C4—28no—
322C4⋊C4—22no—
323C4⋊C4—58no—
324C4⋊C4—54no—
325C4⋊C4—54no—
326C4⋊C4—54no—
327C4⋊C4—108no—
328C4⋊C4—108no—
329C4⋊C4—108no—
330C4⋊C4—108no—
331C4⋊C4—108no—
332C4⋊C4—102no—
333C4⋊C4—102no—
334C4⋊C4—108no—
335C4⋊C4—108no—
336C4⋊C4C23×D514yes—
337C42—28no—
338C42—54no—
339C42—54no—
340C42—108no—
341C42—108no—
342C42D4×D512yes—
343C42C23×D512yes—
344C2×C5#339014yescomplemented
345C2×C5C2×D4×Q811yescharacteristic
346C2×C5C2×#57511yescharacteristic
347C2×C5C2×#57811yescharacteristic
348C23C2×D4×D511yescharacteristic
349Q8—28no—
350Q8—24no—
351Q8—204no—
352Q8—2016no—
353Q8C22×Dic1018yes—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—28no—
357C2×C4—24no—
358C2×C4—24no—
359C2×C4—44no—
360C2×C4—54no—
361C2×C4—54no—
362C2×C4—104no—
363C2×C4—104no—
364C2×C4—104no—
365C2×C4—104no—
366C2×C4—204no—
367C2×C4—204no—
368C2×C4C22×Dic1012yes—
369C2×C4C2×D4×D512yes—
370C2×C4C2×D4×D512yes—
371C2×C4C2×D4×D511yescharacteristic
372C2×C4#415012yes—
373C2×C4C24×D511yescharacteristic
374C8—22no—
375C8—104no—
376C8C22×Dic1014yes—
377C5C2×#339011yescharacteristic, complemented, Sylow
378C22D4×Dic1012yes—
379C22#6610012yes—
380C22#6610212yes—
381C22C22×D4×D511yescharacteristic
382C4—28no—
383C4—22no—
384C4—22no—
385C4—44no—
386C4—104no—
387C4—104no—
388C4—204no—
389C4—204no—
390C4D4×Dic1012yes—
391C4C23×Dic1011yescharacteristic
392C4C2×#415011yescharacteristic
393C2#1061144014yesdirect product factor
394C2C2×D4×Dic1011yescharacteristic
395C2C2×#6610011yescharacteristic
396C2C2×#6610211yescharacteristic
subgroupG/H
centerC23C2×D4×D5
commutator, cosocleC2×C4×C5C25
FrattiniC2×C4C24×D5
FittingC2×C4×C5×Q16C2
socle, prime radicalC23×C5C22×D4
hypercenterC2×C4×Q16D5
hypocenterC5C2×#3390
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
5. #10611440C2direct (N × H)
50. C2×C5×Q16Q8semidirect
131. C5×Q16C2×Q8semidirect
228. C2×Q16Dic10semidirect
314. Q16C2×Dic10semidirect
344. C2×C5#3390semidirect
377. C5C2×#3390semidirect
393. C2#10611440direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#659032
C2×C4×C5×Q162
C2×#654732
C2×#653112
#106114402
C2×#651652
C2×#650852
C2×#650832
C2×#649682
C2×#649722
C2×#33905