Finite Group Databasebeta

← C2×#10604387 #13034414

Subgroups — C2×#10604387 #13034414

Order 1280.

1218 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65850C211yesmaximal, characteristic
2C22×#4005C212yesmaximal
3#10604387C218yesmaximal, direct product factor
4C2×#64867C214yesmaximal
5C23×Dic10C2211yescharacteristic
6C22×#704C2214yes—
7C2×C5×#117C411yescharacteristic
8C2×#4072C411yescharacteristic
9#65850—24no—
10#65850C414yes—
11#65850C2214yes—
12C2×#4033—22no—
13C2×#4023C412yes—
14C2×#4023C2212yes—
15C2×C4×Dic10—22no—
16C2×#4005—22no—
17C2×#4005—22no—
18C2×#4005—24no—
19C2×#4005C2218yes—
20#64867C22116yes—
21C2×#1830—51nomaximal, Sylow
22C23×C4×C5C2×C411yescharacteristic
23C23×Dic5C2×C411yescharacteristic
24C23×Dic5C2311yescharacteristic
25C22×Dic10—24no—
26C22×Dic10—24no—
27C22×Dic10C2×C412yes—
28C22×Dic10D412yes—
29C22×Dic10D412yes—
30C22×Dic10D414yes—
31C22×Dic10C2312yes—
32C2×#704—24no—
33C2×#704—24no—
34C2×#704—24no—
35C2×#704—24no—
36C2×#704—24no—
37C2×#704C2318yes—
38C22×#170—24no—
39C5×#117—22no—
40C5×#117C2×C414yes—
41C2×C5×C4⋊C4—21no—
42C2×C5×C22⋊C4C2×C412yes—
43C2×C42×C5—21no—
44C2×C22⋊Dic5C2×C412yes—
45#4072—22no—
46#4072C2×C414yes—
47C2×C4⋊Dic5—21no—
48C2×#683—22no—
49C2×#683—22no—
50C2×C4×Dic5—21no—
51C2×C4×Dic5—22no—
52C2×C4×Dic5—22no—
53#4033—28no—
54#4033—28no—
55#4023—24no—
56#4023—22no—
57#4023—22no—
58#4023C2×C418yes—
59#4023C2×C414yes—
60#4023C2314yes—
61C4×Dic10—28no—
62C4×Dic10—28no—
63#4005—28no—
64#4005—28no—
65C2×#519—51no—
66C22×#101—52no—
67#1830—58no—
68C2×#344—54no—
69C24×C5C22×C411yescharacteristic
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22⋊C412yes—
76C22×C4×C5C22×C412yes—
77C22×Dic5—22no—
78C22×Dic5—22no—
79C22×Dic5—22no—
80C22×Dic5C22⋊C412yes—
81C22×Dic5C22⋊C412yes—
82C22×Dic5C22×C412yes—
83C22×Dic5C22×C411yescharacteristic
84C22×Dic5C2×D412yes—
85C22×Dic5C2×D412yes—
86C22×Dic5#4114yes—
87C22×Dic5#4114yes—
88C22×Dic5C2411yescharacteristic
89C2×Dic10—28no—
90C2×Dic10—24no—
91C2×Dic10—24no—
92C2×Dic10—28no—
93C2×Dic10—24no—
94C2×Dic10—24no—
95C2×Dic10—28no—
96C2×Dic10—28no—
97C2×Dic10C22⋊C414yes—
98C2×Dic10C22⋊C414yes—
99C2×Dic10C2×D414yes—
100C2×Dic10C2×D414yes—
101#704—28no—
102#704—28no—
103#704—44no—
104#704—44no—
105C2×#170—28no—
106C2×#170—44no—
107C2×#170—44no—
108C5×C4⋊C4—24no—
109C5×C22⋊C4—22no—
110C5×C22⋊C4C22×C414yes—
111C42×C5—24no—
112C22⋊Dic5—22no—
113C22⋊Dic5C22×C414yes—
114C4⋊Dic5—24no—
115#683—28no—
116#683—24no—
117#683—24no—
118C4×Dic5—24no—
119C4×Dic5—28no—
120C4×Dic5—24no—
121C4×Dic5—24no—
122C23×Q8—51no—
123C22×M16—54no—
124#519—54no—
125#519—54no—
126#519—104no—
127C2×C4×Q8—102no—
128C2×C4×Q8—102no—
129C2×#117—51no—
130C2×#117—52no—
131C2×#117—52no—
132C2×#117AGL(1,𝔽5)11yescharacteristic
133C2×#101—58no—
134C2×#101—102no—
135C2×#101—102no—
136C2×#101—104no—
137#344—516no—
138C23×C5—42no—
139C23×C5C2×C22⋊C411yescharacteristic
140C23×C5C2×C22⋊C411yescharacteristic
141C23×C5#11712yes—
142C23×C5#11712yes—
143C23×C5C23×C411yescharacteristic
144C2×C4×C5—24no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—24no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—24no—
151C2×C4×C5—44no—
152C2×C4×C5C2×C22⋊C412yes—
153C2×C4×C5C2×C22⋊C412yes—
154C2×Dic5—24no—
155C2×Dic5—24no—
156C2×Dic5—22no—
157C2×Dic5—22no—
158C2×Dic5—24no—
159C2×Dic5—44no—
160C2×Dic5C2×C22⋊C414yes—
161C2×Dic5C2×C22⋊C412yes—
162C2×Dic5#11714yes—
163C2×Dic5#12314yes—
164C2×Dic5#12314yes—
165C2×Dic5#12314yes—
166C2×Dic5#12314yes—
167C2×Dic5C22×D412yes—
168C2×Dic5C2×#4114yes—
169Dic10—28no—
170Dic10—28no—
171Dic10—28no—
172Dic10—28no—
173#170—48no—
174C22×Q8—52no—
175C22×Q8—52no—
176C22×Q8—54no—
177C22×Q8—52no—
178C22×Q8—52no—
179C22×Q8—104no—
180C22×Q8—104no—
181C23×C4—51no—
182C23×C4—51no—
183C23×C4C2×AGL(1,𝔽5)11yescharacteristic
184C2×M16—58no—
185C2×M16—104no—
186C2×M16—104no—
187C2×M16—104no—
188C2×M16—104no—
189C2×M16—104no—
190C22×C8—104no—
191C4×Q8—108no—
192C4×Q8—108no—
193C4×Q8—108no—
194C4×Q8—108no—
195#117—22no—
196#117—54no—
197#117—54no—
198#117—54no—
199#117—58no—
200#117—102no—
201#117—102no—
202#117—104no—
203#117—102no—
204#117C2×AGL(1,𝔽5)14yes—
205C2×C4⋊C4—21no—
206C2×C4⋊C4—102no—
207C2×C4⋊C4—102no—
208C2×C4⋊C4—101no—
209C2×C22⋊C4—52no—
210C2×C22⋊C4C2×AGL(1,𝔽5)12yes—
211C2×C42—21no—
212C2×C42—102no—
213C2×C42—102no—
214C2×C42—101no—
215#101—108no—
216#101—108no—
217C22×C5—22no—
218C22×C5—24no—
219C22×C5—41no—
220C22×C5—42no—
221C22×C5—41no—
222C22×C5#38112yes—
223C22×C5#38111yescharacteristic
224C22×C5#38111yescharacteristic
225C22×C5C22×C22⋊C411yescharacteristic
226C22×C5C2×#11712yes—
227C4×C5—22no—
228C4×C5—22no—
229C4×C5—44no—
230Dic5—24no—
231Dic5—44no—
232Dic5#38114yes—
233Dic5C2×#12314yes—
234C24C22×AGL(1,𝔽5)11yescharacteristic
235C2×Q8—54no—
236C2×Q8—54no—
237C2×Q8—54no—
238C2×Q8—54no—
239C2×Q8—108no—
240C2×Q8—108no—
241C2×Q8—108no—
242C2×Q8—104no—
243C2×Q8—104no—
244C2×Q8—108no—
245C2×Q8—104no—
246C2×Q8—104no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—54no—
251C22×C4—54no—
252C22×C4—52no—
253C22×C4—52no—
254C22×C4—51no—
255C22×C4—51no—
256C22×C4—52no—
257C22×C4—52no—
258C22×C4—52no—
259C22×C4—102no—
260C22×C4—102no—
261C22×C4—102no—
262C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
263C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
264C22×C4C22⋊AGL(1,𝔽5)12yes—
265C22×C4C22×AGL(1,𝔽5)12yes—
266M16—108no—
267M16—108no—
268M16—204no—
269M16—204no—
270C2×C8—108no—
271C2×C8—204no—
272C2×C8—204no—
273C4⋊C4—24no—
274C4⋊C4—104no—
275C4⋊C4—104no—
276C4⋊C4—108no—
277C4⋊C4—104no—
278C22⋊C4—22no—
279C22⋊C4—54no—
280C22⋊C4—102no—
281C22⋊C4C22×AGL(1,𝔽5)14yes—
282C42—24no—
283C42—104no—
284C42—104no—
285C42—108no—
286C42—104no—
287C2×C5—21no—
288C2×C5—22no—
289C2×C5—21no—
290C2×C5—22no—
291C2×C5#183012yescomplemented
292C2×C5C2×#38111yescharacteristic
293C23—42no—
294C23#413012yes—
295C23#413012yes—
296C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
297C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
298C23C23×AGL(1,𝔽5)11yescharacteristic
299Q8—108no—
300Q8—108no—
301Q8—108no—
302Q8—108no—
303C2×C4—24no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—24no—
310C2×C4—44no—
311C2×C4—54no—
312C2×C4—54no—
313C2×C4—52no—
314C2×C4—52no—
315C2×C4—54no—
316C2×C4—54no—
317C2×C4—54no—
318C2×C4—54no—
319C2×C4—54no—
320C2×C4—104no—
321C2×C4—102no—
322C2×C4—104no—
323C2×C4—102no—
324C2×C4—104no—
325C2×C4—204no—
326C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
327C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
328C8—208no—
329C5C2×#183011yescharacteristic, complemented, Sylow
330C22—22no—
331C22—24no—
332C22—42no—
333C22—41no—
334C22—41no—
335C22#6576412yes—
336C22#6576411yescharacteristic
337C22#6576411yescharacteristic
338C22C2×#413012yes—
339C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
340C4—22no—
341C4—22no—
342C4—44no—
343C4—54no—
344C4—54no—
345C4—104no—
346C4—204no—
347C2—21no—
348C2—22no—
349C2—21no—
350C2—22no—
351C2#1060438712yesdirect product factor
352C2C2×#6576411yescharacteristic
subgroupG/H
centerC22#65764
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C5×#117C4
socleC22×C5#381
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenterC2×#117AGL(1,𝔽5)
hypocenterC5C2×#1830
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #10604387C2direct (N × H)
291. C2×C5#1830semidirect
329. C5C2×#1830semidirect
351. C2#10604387direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#658502
C22×#40052
#106043872
C2×#648672
C2×#18305