Finite Group Databasebeta

← #13031161

Subgroups — #13031161

Order 1280.

1178 conjugacy classes of subgroups; only the 240 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 240 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×C4⋊Q8C211yesmaximal, characteristic
2#10617039C212yesmaximal
3#10604972C214yesmaximal, complemented
4#10604659C218yesmaximal, complemented
5C22×Q8×D5C412yes—
6C2×C5×C4⋊Q8C411yescharacteristic
7C2×#4090C2212yes—
8D5×C4⋊Q8—22no—
9D5×C4⋊Q8—22no—
10D5×C4⋊Q8C414yes—
11D5×C4⋊Q8C2214yes—
12C2×D5×C4⋊C4—22no—
13C2×#4034—22no—
14C2×C42×D5C2211yescharacteristic
15C2×#4015C411yescharacteristic
16#65757C2214yes—
17#65756—22no—
18#65754—22no—
19#65684—22no—
20#65682C2214yes—
21#65678C2214yes—
22C4×#700—22no—
23#64931C22116yescomplemented
24#17746—51nomaximal, Sylow
25C22×C5×Q8C2×C412yes—
26C2×Q8×D5—24no—
27C2×Q8×D5—48no—
28C2×Q8×D5C2×C418yes—
29C22×C4×D5—22no—
30C22×C4×D5C2×C411yescharacteristic
31C22×C4×D5D412yes—
32C22×Dic10—22no—
33C22×Dic10C2×C412yes—
34C2×#700—24no—
35C5×C4⋊Q8—21no—
36C5×C4⋊Q8—21no—
37C5×C4⋊Q8C2×C414yes—
38C2×C5×C4⋊C4—22no—
39C2×C42×C5C2×C411yescharacteristic
40#4090—24no—
41#4090C2×C414yes—
42#4090C2314yes—
43C2×C4⋊Dic5—22no—
44C2×#683—24no—
45C2×C4×Dic5D412yes—
46C2×C4×Dic5C2311yescharacteristic
47D5×C4⋊C4—24no—
48D5×C4⋊C4—24no—
49D5×C4⋊C4—24no—
50D5×C4⋊C4—24no—
51#4034—24no—
52#4034—24no—
53#4034—24no—
54#4034—24no—
55C42×D5C2×C412yes—
56C42×D5D412yes—
57C42×D5D412yes—
58C42×D5C2312yes—
59#4015—21no—
60#4015—21no—
61#4015C2×C414yes—
62C22⋊#170—24no—
63#4004—24no—
64#4004C2318yes—
65#4003—24no—
66#4002—24no—
67C4×#170—24no—
68C22×C4⋊Q8—51no—
69#2920—52no—
70#1558—54no—
71#1548—58no—
72C23×D5C22⋊C411yescharacteristic
73C2×C5×Q8—22no—
74C2×C5×Q8—44no—
75C2×C5×Q8C22×C414yes—
76C22×C4×C5—22no—
77C22×C4×C5C22⋊C412yes—
78C22×C4×C5C22×C411yescharacteristic
79C22×Dic5—22no—
80C22×Dic5C22⋊C411yescharacteristic
81C22×Dic5C2×D412yes—
82Q8×D5—416no—
83Q8×D5—416no—
84C2×C4×D5—24no—
85C2×C4×D5—28no—
86C2×C4×D5—28no—
87C2×C4×D5—48no—
88C2×C4×D5C22⋊C412yes—
89C2×C4×D5C22⋊C412yes—
90C2×C4×D5C22⋊C412yes—
91C2×C4×D5C22×C412yes—
92C2×C4×D5C2×D412yes—
93C2×C4×D5C2×D412yes—
94C2×Dic10—22no—
95C2×Dic10—28no—
96C2×Dic10—48no—
97C2×Dic10—44no—
98C2×Dic10C22×C414yes—
99C2×#170—28no—
100#700—48no—
101C5×C4⋊C4—24no—
102C5×C4⋊C4—24no—
103C42×C5C22⋊C411yescharacteristic
104C42×C5C22⋊C411yescharacteristic
105C42×C5C22×C412yes—
106C4⋊Dic5—24no—
107C4⋊Dic5—24no—
108#683—28no—
109#683—28no—
110C4×Dic5C22⋊C412yes—
111C4×Dic5C22⋊C412yes—
112C4×Dic5C22×C411yescharacteristic
113C4×Dic5C2×D412yes—
114C4×Dic5C2×D412yes—
115C4×Dic5C2×D412yes—
116C4×Dic5C2411yescharacteristic
117C23×Q8—52no—
118C2×C4⋊Q8—52no—
119C2×C4⋊Q8—54no—
120C2×C4⋊Q8—54no—
121C2×C4⋊Q8—51no—
122C2×C4⋊Q8—102no—
123C2×C4⋊Q8—102no—
124C2×C4⋊Q8—102no—
125C2×C4⋊Q8AGL(1,𝔽5)11yescharacteristic
126C22×C4⋊C4—102no—
127C22×C42—51no—
128#432—54no—
129#432—102no—
130#431—54no—
131#431—102no—
132#423—54no—
133#407—102no—
134C4×M16—102no—
135#333—516no—
136C23×C5C2×C22⋊C411yescharacteristic
137C22×D5—22no—
138C22×D5—24no—
139C22×D5C2×C22⋊C412yes—
140C5×Q8—44no—
141C5×Q8—44no—
142C2×C4×C5—22no—
143C2×C4×C5—24no—
144C2×C4×C5—24no—
145C2×C4×C5—44no—
146C2×C4×C5C2×C22⋊C412yes—
147C2×C4×C5C2×C22⋊C411yescharacteristic
148C2×C4×C5C2×C22⋊C412yes—
149C2×C4×C5C23×C411yescharacteristic
150C2×Dic5—24no—
151C2×Dic5—24no—
152C2×Dic5—44no—
153C2×Dic5#10014yes—
154C2×Dic5C2×C22⋊C412yes—
155C2×Dic5C2×C22⋊C412yes—
156C2×Dic5C22×D412yes—
157C4×D5—24no—
158C4×D5—24no—
159C4×D5—24no—
160C4×D5—24no—
161C4×D5—24no—
162C4×D5—416no—
163C4×D5#13718yes—
164Dic10—44no—
165Dic10—416no—
166Dic10—44no—
167#170—48no—
168C22×Q8—58no—
169C22×Q8—52no—
170C22×Q8—102no—
171C22×Q8—104no—
172C22×Q8—208no—
173C22×Q8C2×AGL(1,𝔽5)12yes—
174C23×C4—52no—
175C23×C4—51no—
176C23×C4—102no—
177C2×M16—104no—
178C4⋊Q8—21no—
179C4⋊Q8—21no—
180C4⋊Q8—54no—
181C4⋊Q8—54no—
182C4⋊Q8—54no—
183C4⋊Q8—104no—
184C4⋊Q8—104no—
185C4⋊Q8—104no—
186C4⋊Q8—104no—
187C4⋊Q8—104no—
188C4⋊Q8—101no—
189C4⋊Q8—101no—
190C4⋊Q8C2×AGL(1,𝔽5)14yes—
191C2×C4⋊C4—22no—
192C2×C4⋊C4—104no—
193C2×C4⋊C4—104no—
194C2×C4⋊C4—104no—
195C2×C4⋊C4—104no—
196C2×C4⋊C4—104no—
197C2×C4⋊C4—102no—
198C2×C42—52no—
199C2×C42—51no—
200C2×C42—52no—
201C2×C42—52no—
202C2×C42—52no—
203C2×C42—52no—
204C2×C42C2×AGL(1,𝔽5)11yescharacteristic
205C4⋊C8—58no—
206C4⋊C8—104no—
207C22⋊C8—104no—
208C22⋊C8—104no—
209#97—104no—
210C4×C8—104no—
211C22×C5—22no—
212C22×C5C2×#10012yes—
213C22×C5C22×C22⋊C411yescharacteristic
214C2×D5—28no—
215C2×D5—22no—
216C2×D5—22no—
217C2×D5#41914yes—
218C4×C5—21no—
219C4×C5—21no—
220C4×C5—22no—
221C4×C5—44no—
222C4×C5#41914yes—
223Dic5—22no—
224Dic5—44no—
225Dic5C2×#10014yes—
226Dic5C2×#13714yes—
227C24—51no—
228C2×Q8—22no—
229C2×Q8—44no—
230C2×Q8—54no—
231C2×Q8—108no—
232C2×Q8—102no—
233C2×Q8—204no—
234C2×Q8—208no—
235C2×Q8—2016no—
236C2×Q8—2016no—
237C2×Q8C22×AGL(1,𝔽5)14yes—
238C22×C4—22no—
239C22×C4—51no—
240C22×C4—52no—
241C22×C4—52no—
242C22×C4—52no—
243C22×C4—52no—
244C22×C4—52no—
245C22×C4—52no—
246C22×C4—52no—
247C22×C4—104no—
248C22×C4—108no—
249C22×C4—108no—
250C22×C4—102no—
251C22×C4—208no—
252C22×C4C22⋊AGL(1,𝔽5)12yes—
253C22×C4C22×AGL(1,𝔽5)11yescharacteristic
254M16—208no—
255C2×C8—108no—
256C4⋊C4—24no—
257C4⋊C4—24no—
258C4⋊C4—108no—
259C4⋊C4—108no—
260C4⋊C4—104no—
261C4⋊C4—104no—
262C42—52no—
263C42—52no—
264C42—52no—
265C42—52no—
266C42—52no—
267C42—51no—
268C42—51no—
269C42C22⋊AGL(1,𝔽5)11yescharacteristic
270C42C22⋊AGL(1,𝔽5)11yescharacteristic
271C42C22×AGL(1,𝔽5)12yes—
272C2×C5—22no—
273C2×C5C22×#10011yescharacteristic
274C2×C5C2×#41912yes—
275D5—24no—
276C23—52no—
277C23—104no—
278C23—102no—
279C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
280Q8—44no—
281Q8—44no—
282Q8—204no—
283Q8—204no—
284Q8—2016no—
285C2×C4—22no—
286C2×C4—24no—
287C2×C4—24no—
288C2×C4—44no—
289C2×C4—52no—
290C2×C4—52no—
291C2×C4—54no—
292C2×C4—58no—
293C2×C4—52no—
294C2×C4—104no—
295C2×C4—104no—
296C2×C4—104no—
297C2×C4—104no—
298C2×C4—104no—
299C2×C4—104no—
300C2×C4—104no—
301C2×C4—2016no—
302C2×C4—204no—
303C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
304C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
305C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
306C2×C4C23×AGL(1,𝔽5)11yescharacteristic
307C8—208no—
308C5#1774611yescharacteristic, complemented, Sylow
309C22—22no—
310C22—54no—
311C22—108no—
312C22—102no—
313C22—102no—
314C22D5⋊#10012yes—
315C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
316C4—21no—
317C4—21no—
318C4—22no—
319C4—44no—
320C4—54no—
321C4—54no—
322C4—102no—
323C4—204no—
324C4#6578214yes—
325C2—22no—
326C2—104no—
327C2C2×D5⋊#10011yescharacteristic
328C2C2×#6578212yes—
subgroupG/H
centerC22C22×C22⋊AGL(1,𝔽5)
commutatorC2×C4×C5C23×C4
FrattiniC2×C4C23×AGL(1,𝔽5)
FittingC2×C5×C4⋊Q8C4
socleC22×C5C22×C22⋊C4
prime radicalC23×D5C22⋊C4
cosocleC4×Dic5C24
hypercenterC2×C4⋊Q8AGL(1,𝔽5)
hypocenterC5#17746
LCSG ▷ C2×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #10604972C2semidirect
4. #10604659C2semidirect
23. #64931C22semidirect
308. C5#17746semidirect

Maximal subgroups

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

subgroupindex
C2×D5×C4⋊Q82
#106170392
#106049722
#106046592
#177465