Finite Group Databasebeta

← C2×#10604337 #13034374

Subgroups — C2×#10604337 #13034374

Order 1280.

1734 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×C4⋊C4C211yesmaximal, characteristic
2C2×#65755C212yesmaximal
3C2×#64919C214yesmaximal, complemented
4#10604337C218yesmaximal, direct product factor
5C23×C4×D5C412yes—
6C23×C4×D5C2211yescharacteristic
7C22×#704C2214yes—
8C22×C5×C4⋊C4C411yescharacteristic
9C22×C4⋊Dic5C411yescharacteristic
10C22×#683C2212yes—
11C2×D5×C4⋊C4—22no—
12C2×D5×C4⋊C4—22no—
13C2×D5×C4⋊C4—24no—
14C2×D5×C4⋊C4C414yes—
15C2×D5×C4⋊C4C2214yes—
16#65755—24no—
17#65755C2218yes—
18C2×#4003—22no—
19C2×#4003—22no—
20#64919C22116yescomplemented
21C2×#1821—51nomaximal, Sylow
22C24×D5C2×C411yescharacteristic
23C23×C4×C5C2×C412yes—
24C23×C4×C5C2×C411yescharacteristic
25C23×Dic5C2×C412yes—
26C23×Dic5C2311yescharacteristic
27C22×C4×D5—28no—
28C22×C4×D5—24no—
29C22×C4×D5—22no—
30C22×C4×D5—22no—
31C22×C4×D5—48no—
32C22×C4×D5C2×C412yes—
33C22×C4×D5C2×C418yes—
34C22×C4×D5D412yes—
35C22×C4×D5D412yes—
36C22×C4×D5D414yes—
37C22×C4×D5C2312yes—
38C2×#704—24no—
39C2×#704—216no—
40C2×#704C2318yes—
41C22×#170—24no—
42C2×C5×C4⋊C4—22no—
43C2×C5×C4⋊C4—22no—
44C2×C5×C4⋊C4C2×C414yes—
45C2×C4⋊Dic5—22no—
46C2×C4⋊Dic5—22no—
47C2×C4⋊Dic5C2×C414yes—
48C2×#683—24no—
49C2×#683—24no—
50C2×#683C2×C414yes—
51C2×#683C2314yes—
52D5×C4⋊C4—28no—
53D5×C4⋊C4—28no—
54D5×C4⋊C4—28no—
55D5×C4⋊C4—28no—
56#4003—28no—
57#4003—28no—
58C23×C4⋊C4—51no—
59C2×#407—52no—
60#1821—58no—
61C2×#343—54no—
62C24×C5C22×C411yescharacteristic
63C23×D5—24no—
64C23×D5—24no—
65C23×D5—24no—
66C23×D5C22⋊C412yes—
67C23×D5C22⋊C411yescharacteristic
68C23×D5C22⋊C411yescharacteristic
69C23×D5C22×C412yes—
70C22×C4×C5—24no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—44no—
74C22×C4×C5C22⋊C412yes—
75C22×C4×C5C22⋊C412yes—
76C22×C4×C5C22×C412yes—
77C22×C4×C5C22×C414yes—
78C22×Dic5—22no—
79C22×Dic5—22no—
80C22×Dic5—44no—
81C22×Dic5C22×C414yes—
82C22×Dic5C22×C411yescharacteristic
83C22×Dic5C2×D412yes—
84C22×Dic5C2×D412yes—
85C22×Dic5#4118yes—
86C22×Dic5C2411yescharacteristic
87C2×C4×D5—28no—
88C2×C4×D5—28no—
89C2×C4×D5—28no—
90C2×C4×D5—216no—
91C2×C4×D5—28no—
92C2×C4×D5—28no—
93C2×C4×D5—28no—
94C2×C4×D5—48no—
95C2×C4×D5—416no—
96C2×C4×D5—48no—
97C2×C4×D5—416no—
98C2×C4×D5C22⋊C414yes—
99C2×C4×D5C22⋊C414yes—
100C2×C4×D5C2×D414yes—
101C2×C4×D5C2×D414yes—
102#704—216no—
103#704—48no—
104C2×#170—28no—
105C2×#170—48no—
106C5×C4⋊C4—28no—
107C4⋊Dic5—28no—
108#683—28no—
109#683—28no—
110C24×C4—51no—
111C24×C4—52no—
112C22×M16—54no—
113C22×C4⋊C4—52no—
114C22×C4⋊C4—51no—
115C22×C4⋊C4—54no—
116C22×C4⋊C4—54no—
117C22×C4⋊C4—102no—
118C22×C4⋊C4—102no—
119C22×C4⋊C4—104no—
120C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
121#407—58no—
122#407—104no—
123C2×C22⋊C8—102no—
124C2×C22⋊C8—102no—
125#343—516no—
126C23×C5—22no—
127C23×C5—22no—
128C23×C5C2×C22⋊C411yescharacteristic
129C23×C5C2×C22⋊C411yescharacteristic
130C23×C5#11714yes—
131C23×C5C23×C411yescharacteristic
132C22×D5—232no—
133C22×D5—24no—
134C22×D5—24no—
135C22×D5—22no—
136C22×D5—22no—
137C22×D5—22no—
138C22×D5—22no—
139C22×D5—24no—
140C22×D5—24no—
141C22×D5—24no—
142C22×D5—24no—
143C22×D5#10014yes—
144C22×D5#10114yes—
145C22×D5C2×C22⋊C412yes—
146C22×D5C2×C22⋊C412yes—
147C2×C4×C5—24no—
148C2×C4×C5—24no—
149C2×C4×C5—24no—
150C2×C4×C5—24no—
151C2×C4×C5—44no—
152C2×C4×C5—44no—
153C2×C4×C5—44no—
154C2×C4×C5C2×C22⋊C414yes—
155C2×Dic5—24no—
156C2×Dic5—44no—
157C2×Dic5—44no—
158C2×Dic5—44no—
159C2×Dic5C2×C22⋊C412yes—
160C2×Dic5#11714yes—
161C2×Dic5#12318yes—
162C2×Dic5#12318yes—
163C2×Dic5C22×D412yes—
164C2×Dic5C2×#4114yes—
165C4×D5—28no—
166C4×D5—28no—
167C4×D5—28no—
168C4×D5—28no—
169C4×D5—416no—
170C4×D5—416no—
171#170—48no—
172C25—51no—
173C23×C4—51no—
174C23×C4—52no—
175C23×C4—52no—
176C23×C4—54no—
177C23×C4—52no—
178C23×C4—52no—
179C23×C4—52no—
180C23×C4—58no—
181C23×C4—108no—
182C23×C4—104no—
183C23×C4—102no—
184C23×C4—102no—
185C23×C4—208no—
186C23×C4C2×AGL(1,𝔽5)12yes—
187C23×C4C2×AGL(1,𝔽5)11yescharacteristic
188C2×M16—58no—
189C2×M16—104no—
190C2×M16—1016no—
191C22×C8—104no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—54no—
195C2×C4⋊C4—54no—
196C2×C4⋊C4—54no—
197C2×C4⋊C4—108no—
198C2×C4⋊C4—108no—
199C2×C4⋊C4—108no—
200C2×C4⋊C4—108no—
201C2×C4⋊C4—104no—
202C2×C4⋊C4—104no—
203C2×C4⋊C4—102no—
204C2×C4⋊C4—102no—
205C2×C4⋊C4C2×AGL(1,𝔽5)14yes—
206C22⋊C8—108no—
207C22⋊C8—108no—
208C22×C5—28no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5#38112yes—
214C22×C5#38112yes—
215C22×C5C2×#10012yes—
216C22×C5C2×#10112yes—
217C22×C5C22×C22⋊C411yescharacteristic
218C22×C5C2×#11712yes—
219C2×D5—216no—
220C2×D5—216no—
221C2×D5—28no—
222C2×D5—28no—
223C2×D5—22no—
224C2×D5—22no—
225C2×D5—22no—
226C2×D5—22no—
227C2×D5C2×#10014yes—
228C2×D5C2×#10114yes—
229C4×C5—24no—
230C4×C5—44no—
231Dic5—44no—
232Dic5#38114yes—
233Dic5C2×#12314yes—
234C24—51no—
235C24—51no—
236C24—52no—
237C24—52no—
238C24—104no—
239C24—104no—
240C24—104no—
241C24C22×AGL(1,𝔽5)11yescharacteristic
242C22×C4—24no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—44no—
246C22×C4—58no—
247C22×C4—52no—
248C22×C4—52no—
249C22×C4—51no—
250C22×C4—51no—
251C22×C4—54no—
252C22×C4—54no—
253C22×C4—54no—
254C22×C4—54no—
255C22×C4—54no—
256C22×C4—108no—
257C22×C4—108no—
258C22×C4—108no—
259C22×C4—108no—
260C22×C4—1016no—
261C22×C4—108no—
262C22×C4—108no—
263C22×C4—102no—
264C22×C4—102no—
265C22×C4—208no—
266C22×C4—2016no—
267C22×C4—208no—
268C22×C4—2016no—
269C22×C4—204no—
270C22×C4C22⋊AGL(1,𝔽5)12yes—
271C22×C4C22⋊AGL(1,𝔽5)12yes—
272C22×C4C22×AGL(1,𝔽5)12yes—
273C22×C4C22×AGL(1,𝔽5)14yes—
274M16—1016no—
275M16—208no—
276C2×C8—108no—
277C2×C8—208no—
278C4⋊C4—28no—
279C4⋊C4—108no—
280C4⋊C4—108no—
281C4⋊C4—108no—
282C2×C5—22no—
283C2×C5—22no—
284C2×C5#182114yescomplemented
285C2×C5C2×#38111yescharacteristic
286C2×C5C22×#10011yescharacteristic
287C2×C5C22×#10111yescharacteristic
288D5—24no—
289D5—24no—
290C23—22no—
291C23—22no—
292C23—52no—
293C23—52no—
294C23—54no—
295C23—54no—
296C23—104no—
297C23—104no—
298C23—104no—
299C23—104no—
300C23—1032no—
301C23—104no—
302C23—104no—
303C23—102no—
304C23—102no—
305C23—102no—
306C23—102no—
307C23#413014yes—
308C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
309C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
310C23C23×AGL(1,𝔽5)11yescharacteristic
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—44no—
316C2×C4—44no—
317C2×C4—44no—
318C2×C4—54no—
319C2×C4—54no—
320C2×C4—52no—
321C2×C4—52no—
322C2×C4—58no—
323C2×C4—58no—
324C2×C4—108no—
325C2×C4—108no—
326C2×C4—108no—
327C2×C4—108no—
328C2×C4—104no—
329C2×C4—2016no—
330C2×C4—2016no—
331C2×C4—204no—
332C2×C4—204no—
333C2×C4—204no—
334C2×C4C2×C22⋊AGL(1,𝔽5)14yes—
335C8—208no—
336C5C2×#182111yescharacteristic, complemented, Sylow
337C22—28no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—54no—
343C22—54no—
344C22—1016no—
345C22—1016no—
346C22—108no—
347C22—108no—
348C22—102no—
349C22—102no—
350C22—102no—
351C22—102no—
352C22#6576412yes—
353C22#6576412yes—
354C22D5⋊#10012yes—
355C22D5⋊#10112yes—
356C22C2×#413012yes—
357C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
358C4—24no—
359C4—44no—
360C4—54no—
361C4—54no—
362C4—204no—
363C2—22no—
364C2—22no—
365C2—104no—
366C2—104no—
367C2#1060433714yesdirect product factor
368C2C2×#6576411yescharacteristic
369C2C2×D5⋊#10011yescharacteristic
370C2C2×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×#1821
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×#64919C2semidirect
4. #10604337C2direct (N × H)
20. #64919C22semidirect
284. C2×C5#1821semidirect
336. C5C2×#1821semidirect
367. C2#10604337direct (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×#657552
C2×#649192
#106043372
C2×#18215