Finite Group Databasebeta

← C2×#10604186 #13034528

Subgroups — C2×#10604186 #13034528

Order 1280.

1246 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4004C212yesmaximal
2C2×C42×Dic5C211yesmaximal, characteristic
3C2×#64918C212yesmaximal
4C2×#64918C212yesmaximal
5#10604186C218yesmaximal, direct product factor
6C23×#170C2214yes—
7C22×C42×C5C411yescharacteristic
8C22×C4×Dic5C411yescharacteristic
9C22×C4×Dic5C411yescharacteristic
10C22×C4×Dic5C411yescharacteristic
11C22×C4×Dic5C2211yescharacteristic
12C22×C4×Dic5C2211yescharacteristic
13C22×C4×Dic5C2211yescharacteristic
14C2×#4004—28no—
15C2×#4004C2218yes—
16C42×Dic5C414yes—
17C42×Dic5C2214yes—
18#64918C2218yes—
19#64918C2218yes—
20C2×#1831—51nomaximal, Sylow
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5C2×C411yescharacteristic
24C23×Dic5C2×C411yescharacteristic
25C23×Dic5C2×C411yescharacteristic
26C23×Dic5C2×C411yescharacteristic
27C23×Dic5C2311yescharacteristic
28C22×#170—28no—
29C22×#170—28no—
30C22×#170—28no—
31C22×#170C2318yes—
32C2×C42×C5—24no—
33C2×C42×C5C2×C414yes—
34C2×C4×Dic5—24no—
35C2×C4×Dic5—24no—
36C2×C4×Dic5—24no—
37C2×C4×Dic5—24no—
38C2×C4×Dic5C818yescomplemented
39C2×C4×Dic5C2×C414yes—
40C2×C4×Dic5C2×C414yes—
41C2×C4×Dic5C2×C412yes—
42C2×C4×Dic5C2×C412yes—
43C2×C4×Dic5C2×C412yes—
44C2×C4×Dic5C2×C414yes—
45C2×C4×Dic5D414yes—
46C2×C4×Dic5Q814yes—
47C2×C4×Dic5C2312yes—
48C2×C4×Dic5C2312yes—
49C2×C4×Dic5C2312yes—
50#4004—216no—
51C22×C4⋊C8—52no—
52C2×C43—51no—
53#1831—58no—
54C2×#336—52no—
55C2×#336—52no—
56C24×C5C22×C411yescharacteristic
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5—22no—
63C22×C4×C5C4⋊C414yes—
64C22×C4×C5C2×C814yes—
65C22×C4×C5M1614yes—
66C22×C4×C5C22×C412yes—
67C22×C4×C5C22×C412yes—
68C22×C4×C5C22×C412yes—
69C22×Dic5—22no—
70C22×Dic5—22no—
71C22×Dic5—22no—
72C22×Dic5—22no—
73C22×Dic5C4⋊C414yes—
74C22×Dic5C2×C814yes—
75C22×Dic5C2×C814yes—
76C22×Dic5M1614yes—
77C22×Dic5M1614yes—
78C22×Dic5C22×C412yes—
79C22×Dic5C22×C412yes—
80C22×Dic5C22×C411yescharacteristic
81C22×Dic5C22×C412yes—
82C22×Dic5C2×D412yes—
83C22×Dic5C2×Q812yes—
84C22×Dic5#4114yes—
85C22×Dic5#4114yes—
86C22×Dic5C2411yescharacteristic
87C2×#170—28no—
88C2×#170—28no—
89C2×#170—28no—
90C2×#170—416no—
91C42×C5—28no—
92C4×Dic5—24no—
93C4×Dic5—24no—
94C4×Dic5—28no—
95C4×Dic5—28no—
96C4×Dic5—24no—
97C4×Dic5—24no—
98C4×Dic5C4⋊C418yes—
99C4×Dic5C2×C8116yescomplemented
100C4×Dic5C2×D414yes—
101C4×Dic5C2×Q814yes—
102C23×C8—54no—
103C22×C42—51no—
104C22×C42—51no—
105C22×C42—51no—
106C22×C42—51no—
107C22×C42—51no—
108C22×C42—51no—
109C22×C42AGL(1,𝔽5)11yescharacteristic
110C2×C4⋊C8—58no—
111C2×C4⋊C8—108no—
112C43—54no—
113C43—54no—
114#336—58no—
115#336—58no—
116C23×C5C2×C4⋊C412yes—
117C23×C5#11712yes—
118C23×C5#11712yes—
119C23×C5C22×C812yes—
120C23×C5C2×M1612yes—
121C23×C5C2×M1612yes—
122C23×C5C2×M1612yes—
123C23×C5C23×C411yescharacteristic
124C2×C4×C5—22no—
125C2×C4×C5—22no—
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—28no—
131C2×C4×C5—28no—
132C2×C4×C5—28no—
133C2×C4×C5C2×C4⋊C414yes—
134C2×C4×C5C22×C814yes—
135C2×C4×C5C2×M1614yes—
136C2×Dic5—22no—
137C2×Dic5—22no—
138C2×Dic5—22no—
139C2×Dic5—22no—
140C2×Dic5—28no—
141C2×Dic5—28no—
142C2×Dic5C4⋊C8116yes—
143C2×Dic5C2×C4⋊C412yes—
144C2×Dic5C2×C4⋊C414yes—
145C2×Dic5#11712yes—
146C2×Dic5#11712yes—
147C2×Dic5#12418yes—
148C2×Dic5#12518yes—
149C2×Dic5C22×C814yes—
150C2×Dic5C22×C814yes—
151C2×Dic5C2×M1614yes—
152C2×Dic5C2×M1614yes—
153C2×Dic5C22×D411yescharacteristic
154C2×Dic5C22×Q811yescharacteristic
155C2×Dic5C2×#4112yes—
156C2×Dic5C2×#4112yes—
157#170—48no—
158C23×C4—51no—
159C23×C4—51no—
160C23×C4—51no—
161C23×C4—51no—
162C23×C4C2×AGL(1,𝔽5)11yescharacteristic
163C23×C4C2×AGL(1,𝔽5)11yescharacteristic
164C23×C4C2×AGL(1,𝔽5)11yescharacteristic
165C22×C8—58no—
166C22×C8—108no—
167C22×C8—108no—
168C22×C8—108no—
169C2×C42—24no—
170C2×C42—58no—
171C2×C42—54no—
172C2×C42—54no—
173C2×C42—52no—
174C2×C42—54no—
175C2×C42—52no—
176C2×C42—52no—
177C2×C42—52no—
178C2×C42—52no—
179C2×C42—54no—
180C2×C42—52no—
181C2×C42—54no—
182C2×C42—104no—
183C2×C42—104no—
184C2×C42—104no—
185C2×C42—104no—
186C2×C42C2×AGL(1,𝔽5)14yes—
187C4⋊C8—1016no—
188C22×C5#38214yes—
189C22×C5C2×C4⋊C814yes—
190C22×C5#42314yes—
191C22×C5#43114yes—
192C22×C5#43114yes—
193C22×C5#43214yes—
194C22×C5#43214yes—
195C22×C5C22×C4⋊C411yescharacteristic
196C22×C5C2×#11711yescharacteristic
197C22×C5C2×#11711yescharacteristic
198C22×C5C23×C811yescharacteristic
199C22×C5C22×M1611yescharacteristic
200C22×C5C22×M1611yescharacteristic
201C22×C5C22×M1611yescharacteristic
202C4×C5—24no—
203C4×C5—24no—
204C4×C5—24no—
205Dic5—24no—
206Dic5—24no—
207Dic5#38214yes—
208Dic5C2×C4⋊C818yes—
209Dic5C2×#12412yes—
210Dic5C2×#12512yes—
211C24C22×AGL(1,𝔽5)11yescharacteristic
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—22no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—54no—
219C22×C4—54no—
220C22×C4—52no—
221C22×C4—54no—
222C22×C4—52no—
223C22×C4—54no—
224C22×C4—54no—
225C22×C4—51no—
226C22×C4—52no—
227C22×C4—51no—
228C22×C4—54no—
229C22×C4—54no—
230C22×C4—52no—
231C22×C4—52no—
232C22×C4—102no—
233C22×C4—102no—
234C22×C4—102no—
235C22×C4—102no—
236C22×C4D5⋊C814yes—
237C22×C4C4⋊AGL(1,𝔽5)14yes—
238C22×C4#70414yes—
239C22×C4C22×AGL(1,𝔽5)12yes—
240C22×C4C22×AGL(1,𝔽5)12yes—
241C22×C4C22×AGL(1,𝔽5)12yes—
242C2×C8—108no—
243C2×C8—108no—
244C2×C8—108no—
245C2×C8—2016no—
246C42—28no—
247C42—516no—
248C42—54no—
249C42—58no—
250C42—54no—
251C42—108no—
252C42—108no—
253C42—104no—
254C42—104no—
255C42—104no—
256C42—104no—
257C2×C5#183118yescomplemented
258C2×C5C2×#38211yescharacteristic
259C2×C5C22×C4⋊C811yescharacteristic
260C2×C5C2×#42311yescharacteristic
261C2×C5C2×#43111yescharacteristic
262C2×C5C2×#43111yescharacteristic
263C2×C5C2×#43211yescharacteristic
264C2×C5C2×#43211yescharacteristic
265C23C2×D5⋊C812yes—
266C23D5⋊M1612yes—
267C23D5⋊M1612yes—
268C23C2×C4⋊AGL(1,𝔽5)12yes—
269C23#413012yes—
270C23#413012yes—
271C23C2×#70412yes—
272C23C23×AGL(1,𝔽5)11yescharacteristic
273C2×C4—22no—
274C2×C4—22no—
275C2×C4—22no—
276C2×C4—22no—
277C2×C4—28no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—28no—
281C2×C4—28no—
282C2×C4—516no—
283C2×C4—58no—
284C2×C4—58no—
285C2×C4—54no—
286C2×C4—54no—
287C2×C4—51no—
288C2×C4—54no—
289C2×C4—52no—
290C2×C4—51no—
291C2×C4—52no—
292C2×C4—52no—
293C2×C4—52no—
294C2×C4—52no—
295C2×C4—54no—
296C2×C4—54no—
297C2×C4—108no—
298C2×C4—108no—
299C2×C4—102no—
300C2×C4—102no—
301C2×C4—102no—
302C2×C4—102no—
303C2×C4C2×D5⋊C814yes—
304C2×C4C2×C4⋊AGL(1,𝔽5)14yes—
305C2×C4C2×#70414yes—
306C8—208no—
307C5C2×#183111yescharacteristic, complemented, Sylow
308C22#6567814yes—
309C22D5⋊(C4⋊C8)14yes—
310C22#6568414yes—
311C22#6568914yes—
312C22#6575414yes—
313C22#6575714yes—
314C22#6575814yes—
315C22C22×D5⋊C811yescharacteristic
316C22C2×D5⋊M1611yescharacteristic
317C22C2×D5⋊M1611yescharacteristic
318C22C22×C4⋊AGL(1,𝔽5)11yescharacteristic
319C22C2×#413011yescharacteristic
320C22C2×#413011yescharacteristic
321C22C22×#70411yescharacteristic
322C4—24no—
323C4—24no—
324C4—24no—
325C4—58no—
326C4—52no—
327C4—52no—
328C4—54no—
329C4—104no—
330C4—104no—
331C2#1060418618yesdirect product factor
332C2C2×D5⋊(C4⋊C8)11yescharacteristic
333C2C2×#6567811yescharacteristic
334C2C2×#6568411yescharacteristic
335C2C2×#6568911yescharacteristic
336C2C2×#6575811yescharacteristic
337C2C2×#6575411yescharacteristic
338C2C2×#6575711yescharacteristic
subgroupG/H
centerC24C22×AGL(1,𝔽5)
commutatorC22×C5C23×C8
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C42×C5C4
socle, prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenterC22×C42AGL(1,𝔽5)
hypocenterC5C2×#1831
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
5. #10604186C2direct (N × H)
38. C2×C4×Dic5C8semidirect
99. C4×Dic5C2×C8semidirect
257. C2×C5#1831semidirect
307. C5C2×#1831semidirect
331. C2#10604186direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#40042
C2×C42×Dic52
C2×#649182
#106041862
C2×#18315