Finite Group Databasebeta

← C2×#10601503 #12103298

Subgroups — C2×#10601503 #12103298

Order 1280.

1438 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic20C211yesmaximal, characteristic
2C22×C5×#108C211yesmaximal, characteristic
3C2×#65409C212yesmaximal
4C22×#3956C212yesmaximal
5C2×#65390C211yesmaximal, characteristic
6#10601503C218yesmaximal, direct product factor
7C23×Dic10C2212yes—
8C22×C5×M16C2212yes—
9C23×C5×C8C2211yescharacteristic
10C2×#4072C2211yescharacteristic
11C22×#681C2211yescharacteristic
12C22×Dic20—21no—
13C22×Dic20—21no—
14C22×Dic20—22no—
15C22×Dic20—24no—
16C22×Dic20C418yescomplemented
17C22×Dic20C2214yes—
18C2×C5×#108—24no—
19C2×C5×#108C2214yes—
20C2×#3956—28no—
21C2×#3956C2218yes—
22#65409—24no—
23#65409C2218yes—
24C2×#3948—24no—
25#65390—22no—
26#65390C2214yes—
27C2×#3947—21no—
28C2×C8×Dic5—21no—
29C2×#1979—51nomaximal, Sylow
30C23×C4×C5C2311yescharacteristic
31C23×Dic5—22no—
32C22×Dic10—22no—
33C22×Dic10—22no—
34C22×Dic10—24no—
35C22×Dic10—22no—
36C22×Dic10—22no—
37C22×Dic10—24no—
38C22×Dic10—24no—
39C22×Dic10—22no—
40C22×Dic10C2×C418yes—
41C22×Dic10C2314yes—
42C2×C5×M16—22no—
43C2×C5×M16—24no—
44C2×C5×M16—24no—
45C2×C5×M16C2314yes—
46C22×C5×C8—22no—
47C22×C5×C8C2×C414yes—
48C22×C5×C8D411yescharacteristic
49C22×C5×C8D411yescharacteristic
50C22×C5×C8D412yes—
51C22×C5×C8D414yes—
52C22×C5×C8C2312yes—
53C2×C22⋊Dic5—21no—
54#4072—21no—
55#4072—21no—
56#4072D412yes—
57#4072C2312yes—
58C2×C4⋊Dic5D412yes—
59C2×C4×Dic5—21no—
60C2×#681—21no—
61C2×#681—22no—
62C2×#681D414yes—
63C2×#681C2312yes—
64C22×#168—21no—
65C2×Dic20—28no—
66C2×Dic20—28no—
67C2×Dic20—216no—
68C2×Dic20—24no—
69C2×Dic20—24no—
70C2×Dic20—28no—
71C2×Dic20C2×C4116yescomplemented
72C5×#108—28no—
73#3956—216no—
74#3948—216no—
75#3947—24no—
76C8×Dic5—24no—
77C23×Q16—51no—
78C22×#108D511yescharacteristic
79C2×#419—52no—
80C22×#101—52no—
81C2×#405—51no—
82#1979—58no—
83C24×C5#4111yescharacteristic
84C22×C4×C5C22×C412yes—
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5C2×D411yescharacteristic
89C22×C4×C5C2×D412yes—
90C22×C4×C5C2×D412yes—
91C22×C4×C5#4111yescharacteristic
92C22×C4×C5#4112yes—
93C22×C4×C5C2411yescharacteristic
94C22×Dic5—28no—
95C22×Dic5—22no—
96C22×Dic5—24no—
97C22×Dic5—42no—
98C22×Dic5—42no—
99C22×Dic5—44no—
100C2×Dic10—28no—
101C2×Dic10—28no—
102C2×Dic10—28no—
103C2×Dic10—28no—
104C2×Dic10—24no—
105C2×Dic10—24no—
106C2×Dic10—24no—
107C2×Dic10—24no—
108C2×Dic10—28no—
109C2×Dic10—24no—
110C2×Dic10—44no—
111C2×Dic10—44no—
112C2×Dic10—42no—
113C2×Dic10—42no—
114C2×Dic10—44no—
115C2×Dic10—44no—
116C2×Dic10—44no—
117C2×Dic10C22×C418yes—
118C5×M16—24no—
119C5×M16—24no—
120C5×M16—44no—
121C2×C5×C8—24no—
122C2×C5×C8—44no—
123C2×C5×C8C22⋊C414yes—
124C2×C5×C8C22⋊C414yes—
125C2×C5×C8C22⋊C418yes—
126C2×C5×C8C22×C414yes—
127C2×C5×C8C2×D412yes—
128C2×C5×C8C2×D412yes—
129C2×C5×C8C2×D414yes—
130C22⋊Dic5—22no—
131C22⋊Dic5—22no—
132C4⋊Dic5—22no—
133C4⋊Dic5C2×D414yes—
134C4×Dic5—22no—
135C4×Dic5—22no—
136#681—24no—
137#681—22no—
138#681C2×D414yes—
139C2×#168—24no—
140C2×#168—22no—
141Dic20—216no—
142Dic20—216no—
143C23×Q8—52no—
144C22×Q16—58no—
145C22×Q16—54no—
146C22×Q16—101no—
147C22×Q16—101no—
148C22×Q16—102no—
149C22×Q16—104no—
150C22×M16—51no—
151C22×M16C2×D512yes—
152C23×C8C2×D511yescharacteristic
153C2×#117—51no—
154C2×#108—24no—
155C2×#108C2×D514yes—
156#419—58no—
157#419—104no—
158C2×#103—104no—
159C2×#101—58no—
160C2×#101—108no—
161#405—54no—
162#405—102no—
163C2×#97—101no—
164C2×C4×C8—101no—
165C23×C5—24no—
166C23×C5C4×D412yes—
167C23×C5#12111yescharacteristic
168C23×C5#12111yescharacteristic
169C23×C5#12412yes—
170C23×C5C2×#4111yescharacteristic
171C2×C4×C5C2×C22⋊C412yes—
172C2×C4×C5C2×C22⋊C412yes—
173C2×C4×C5C4×D412yes—
174C2×C4×C5C4×D412yes—
175C2×C4×C5C4×D412yes—
176C2×C4×C5#12112yes—
177C2×C4×C5#12112yes—
178C2×C4×C5#12111yescharacteristic
179C2×C4×C5#12111yescharacteristic
180C2×C4×C5#12412yes—
181C2×C4×C5#12712yes—
182C2×C4×C5#12712yes—
183C2×C4×C5C23×C411yescharacteristic
184C2×C4×C5C22×D411yescharacteristic
185C2×C4×C5C22×D411yescharacteristic
186C2×C4×C5C22×D411yescharacteristic
187C2×C4×C5C22×D411yescharacteristic
188C2×C4×C5C2×#4111yescharacteristic
189C2×Dic5—28no—
190C2×Dic5—24no—
191C2×Dic5—44no—
192C2×Dic5—44no—
193C2×Dic5—48no—
194C2×Dic5—48no—
195C2×Dic5—44no—
196Dic10—28no—
197Dic10—28no—
198Dic10—44no—
199Dic10—44no—
200Dic10—48no—
201Dic10—48no—
202C5×C8—44no—
203C5×C8C2×C22⋊C414yes—
204C5×C8C2×C22⋊C414yes—
205#168—24no—
206C22×Q8—58no—
207C22×Q8—54no—
208C22×Q8—104no—
209C22×Q8—102no—
210C22×Q8—102no—
211C22×Q8—102no—
212C22×Q8—102no—
213C22×Q8—102no—
214C22×Q8—104no—
215C22×Q8—104no—
216C23×C4—102no—
217C23×C4C22×D511yescharacteristic
218C2×Q16—516no—
219C2×Q16—108no—
220C2×Q16—108no—
221C2×Q16—1016no—
222C2×Q16—104no—
223C2×Q16—104no—
224C2×Q16—108no—
225C2×M16—22no—
226C2×M16—24no—
227C2×M16—24no—
228C2×M16—54no—
229C2×M16—52no—
230C2×M16—101no—
231C2×M16—102no—
232C2×M16C22×D514yes—
233C22×C8—22no—
234C22×C8—101no—
235C22×C8C4×D514yes—
236C22×C8D2011yescharacteristic
237C22×C8D2011yescharacteristic
238C22×C8D2012yes—
239C22×C8C22⋊D514yes—
240C22×C8C22×D512yes—
241#117—52no—
242#117—52no—
243#117—101no—
244#117—101no—
245C2×C4⋊C4—52no—
246C2×C22⋊C4—101no—
247C2×C42—101no—
248#108—28no—
249#103—1016no—
250#101—1016no—
251#97—104no—
252C4×C8—104no—
253C22×C5—24no—
254C22×C5—24no—
255C22×C5—22no—
256C22×C5—22no—
257C22×C5#39012yes—
258C22×C5#39012yes—
259C22×C5#47314yes—
260C22×C5C2×C4×D411yescharacteristic
261C22×C5C2×#12111yescharacteristic
262C22×C5C2×#12411yescharacteristic
263C4×C5#39012yes—
264C4×C5#39012yes—
265C4×C5C22×C22⋊C411yescharacteristic
266C4×C5C2×C4×D411yescharacteristic
267C4×C5C2×#12111yescharacteristic
268C4×C5C2×#12711yescharacteristic
269Dic5—48no—
270Dic5—44no—
271C24#71311yescharacteristic
272C2×Q8—58no—
273C2×Q8—104no—
274C2×Q8—108no—
275C2×Q8—104no—
276C2×Q8—104no—
277C2×Q8—104no—
278C2×Q8—104no—
279C2×Q8—108no—
280C2×Q8—108no—
281C2×Q8—108no—
282C2×Q8—108no—
283C2×Q8—202no—
284C2×Q8—202no—
285C2×Q8—204no—
286C2×Q8—204no—
287C2×Q8—204no—
288C2×Q8—204no—
289C2×Q8—204no—
290C22×C4—104no—
291C22×C4—108no—
292C22×C4—102no—
293C22×C4—202no—
294C22×C4—202no—
295C22×C4—204no—
296C22×C4C2×C4×D512yes—
297C22×C4C2×D2011yescharacteristic
298C22×C4C2×D2011yescharacteristic
299C22×C4D4×D511yescharacteristic
300C22×C4D4×D511yescharacteristic
301C22×C4D4×D512yes—
302C22×C4#71312yes—
303C22×C4#71311yescharacteristic
304C22×C4C2×C22⋊D512yes—
305C22×C4C23×D511yescharacteristic
306Q16—1016no—
307Q16—1016no—
308M16—24no—
309M16—24no—
310M16—44no—
311M16—54no—
312M16—102no—
313M16—104no—
314C2×C8—24no—
315C2×C8—44no—
316C2×C8—102no—
317C2×C8—104no—
318C2×C8#68514yes—
319C2×C8#68514yes—
320C2×C8#68518yes—
321C2×C8C2×C4×D514yes—
322C2×C8C2×D2012yes—
323C2×C8C2×D2012yes—
324C2×C8C2×C22⋊D514yes—
325C4⋊C4—54no—
326C4⋊C4—102no—
327C22⋊C4—102no—
328C22⋊C4—102no—
329C42—102no—
330C42—102no—
331C2×C5—21no—
332C2×C5—21no—
333C2×C5—22no—
334C2×C5#197914yescomplemented
335C2×C5C2×#39011yescharacteristic
336C2×C5C2×#47312yes—
337C23—24no—
338C23#403912yes—
339C23#404111yescharacteristic
340C23#404111yescharacteristic
341C23#409312yes—
342C23C2×#71311yescharacteristic
343Q8—108no—
344Q8—108no—
345Q8—204no—
346Q8—204no—
347Q8—208no—
348Q8—208no—
349C2×C4—108no—
350C2×C4—104no—
351C2×C4—204no—
352C2×C4—204no—
353C2×C4—204no—
354C2×C4—208no—
355C2×C4—208no—
356C2×C4#403912yes—
357C2×C4#403912yes—
358C2×C4#403912yes—
359C2×C4#404112yes—
360C2×C4#404112yes—
361C2×C4#404111yescharacteristic
362C2×C4#404111yescharacteristic
363C2×C4C2×#68512yes—
364C2×C4C2×#68512yes—
365C2×C4#408612yes—
366C2×C4#408612yes—
367C2×C4#409312yes—
368C2×C4C22×C4×D511yescharacteristic
369C2×C4C22×D2011yescharacteristic
370C2×C4C2×D4×D511yescharacteristic
371C2×C4C2×D4×D511yescharacteristic
372C2×C4C2×#71311yescharacteristic
373C2×C4C22×C22⋊D511yescharacteristic
374C8—44no—
375C8—104no—
376C8C2×#68514yes—
377C8C2×#68514yes—
378C5C2×#197911yescharacteristic, complemented, Sylow
379C22—24no—
380C22—24no—
381C22—22no—
382C22—22no—
383C22#6518514yes—
384C22#6527712yes—
385C22#6527712yes—
386C22C2×#403911yescharacteristic
387C22C2×#404111yescharacteristic
388C22C2×#409311yescharacteristic
389C4—204no—
390C4—208no—
391C4#6527712yes—
392C4#6527712yes—
393C4C2×#403911yescharacteristic
394C4C2×#404111yescharacteristic
395C4C22×#68511yescharacteristic
396C4C2×#408611yescharacteristic
397C2—21no—
398C2—21no—
399C2—22no—
400C2#1060150314yesdirect product factor
401C2C2×#6518512yes—
402C2C2×#6527711yescharacteristic
subgroupG/H
centerC23#4041
commutatorC2×C4×C5C23×C4
FrattiniC22×C4C23×D5
FittingC22×C5×#108C2
socleC23×C5#121
prime radicalC24×C5#41
cosocleC22×C4×C5C24
hypercenterC22×#108D5
hypocenterC5C2×#1979
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#108

Complements

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

NH ≅ G/Ntype
6. #10601503C2direct (N × H)
16. C22×Dic20C4semidirect
71. C2×Dic20C2×C4semidirect
334. C2×C5#1979semidirect
378. C5C2×#1979semidirect
400. C2#10601503direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic202
C22×C5×#1082
C2×#654092
C22×#39562
C2×#653902
#106015032
C2×#19795