Finite Group Databasebeta

← #13018226

Subgroups — #13018226

Order 1280.

476 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C4×#4034C211yesmaximal, characteristic
2C2×#64873C212yesmaximal
3#10604186C211yesmaximal, characteristic
4#10604186C211yesmaximal, characteristic
5#10598725C212yesmaximal
6C2×#4034C2211yescharacteristic
7C2×C4×Dic10—21no—
8C2×#4004C2212yes—
9C2×#4004C2212yes—
10C4×C5×C4⋊C4C411yescharacteristic
11#65274C411yescharacteristic
12#65265C2211yescharacteristic
13#65262C411yescharacteristic
14C4×C4⋊Dic5C411yescharacteristic
15C4×#683—21no—
16C42×Dic5C2211yescharacteristic
17#64936—21no—
18#64935—21no—
19#64918—21no—
20#64918—21no—
21#64918—21no—
22#64918—21no—
23#64873—24no—
24#8593—51nomaximal, Sylow
25C22×Dic10—21no—
26C22×#170—22no—
27C22×#170—22no—
28C2×C5×C4⋊C4C2×C411yescharacteristic
29C2×C5×C4⋊C4C2×C411yescharacteristic
30C2×C42×C5—21no—
31C2×C42×C5C2×C411yescharacteristic
32C2×C4⋊Dic5—21no—
33C2×C4⋊Dic5C2×C411yescharacteristic
34C2×C4⋊Dic5C2×C411yescharacteristic
35C2×#683—21no—
36C2×#683—21no—
37C2×#683—21no—
38C2×#683—21no—
39C2×C4×Dic5—21no—
40C2×C4×Dic5C2×C411yescharacteristic
41C2×C4×Dic5D411yescharacteristic
42C2×C4×Dic5D411yescharacteristic
43C2×C4×Dic5D411yescharacteristic
44C2×C4×Dic5D411yescharacteristic
45C2×C4×Dic5C2311yescharacteristic
46#4034—21no—
47#4034—21no—
48#4034D412yes—
49#4034Q812yes—
50C4×Dic10—44no—
51#4004—22no—
52#4004—22no—
53#4004—22no—
54#4004—22no—
55C5×#95—21no—
56#3963—21no—
57#3963—21no—
58#3963—21no—
59C4×C4⋊Q8—51no—
60#1831—51no—
61#1831—51no—
62C2×#332—52no—
63#1296—52no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22⋊C411yescharacteristic
68C22×C4×C5C22×C411yescharacteristic
69C22×Dic5—21no—
70C22×Dic5—21no—
71C22×Dic5C22⋊C411yescharacteristic
72C22×Dic5C22⋊C411yescharacteristic
73C22×Dic5C2×D411yescharacteristic
74C22×Dic5C2×D411yescharacteristic
75C2×Dic10—22no—
76C2×Dic10—22no—
77C2×Dic10—42no—
78C2×Dic10—42no—
79C2×#170—42no—
80C2×#170—42no—
81C2×#170—42no—
82C2×#170—42no—
83C2×#170—42no—
84C2×#170—42no—
85C5×C4⋊C4—21no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4C4⋊C412yes—
88C42×C5—22no—
89C42×C5—42no—
90C4⋊Dic5—21no—
91C4⋊Dic5—42no—
92C4⋊Dic5—41no—
93C4⋊Dic5C4⋊C412yes—
94#683—22no—
95#683—22no—
96#683—42no—
97#683—42no—
98#683—42no—
99C4×Dic5—22no—
100C4×Dic5—22no—
101C4×Dic5—22no—
102C4×Dic5—22no—
103C4×Dic5—41no—
104C4×Dic5—42no—
105C4×Dic5C2×D411yescharacteristic
106C4×Dic5C2×Q811yescharacteristic
107C4×Dic5#4111yescharacteristic
108C4×Dic5#4111yescharacteristic
109C2×C4⋊Q8—51no—
110C2×C4×Q8—101no—
111C2×C4⋊C8—52no—
112C2×C4⋊C8—52no—
113#391—101no—
114#389—51no—
115#389—51no—
116#389—101no—
117#384—51no—
118C4×C4⋊C4—51no—
119C4×C4⋊C4—101no—
120C4×C4⋊C4AGL(1,𝔽5)11yescharacteristic
121C43—51no—
122#336—101no—
123#336—101no—
124#336—101no—
125#336—101no—
126#332—104no—
127C23×C5C2×C22⋊C411yescharacteristic
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—22no—
133C2×C4×C5—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5#10112yes—
142C2×C4×C5C2×C4⋊C411yescharacteristic
143C2×C4×C5#11711yescharacteristic
144C2×Dic5—22no—
145C2×Dic5—21no—
146C2×Dic5—21no—
147C2×Dic5—21no—
148C2×Dic5—21no—
149C2×Dic5—21no—
150C2×Dic5—21no—
151C2×Dic5—41no—
152C2×Dic5—41no—
153C2×Dic5—41no—
154C2×Dic5—41no—
155C2×Dic5—41no—
156C2×Dic5#12111yescharacteristic
157C2×Dic5#12111yescharacteristic
158C2×Dic5C22⋊Q811yescharacteristic
159C2×Dic5C22⋊Q811yescharacteristic
160C2×Dic5#13512yes—
161C2×Dic5#13512yes—
162C2×Dic5AGL(1,ℤ/8)12yes—
163C2×Dic5#13712yes—
164Dic10—44no—
165Dic10—44no—
166#170—82no—
167#170—82no—
168C22×Q8—101no—
169C22×C8—102no—
170C22×C8—102no—
171C4⋊Q8—52no—
172C4⋊Q8—52no—
173C4⋊Q8—101no—
174C4⋊Q8—101no—
175C4×Q8—204no—
176C2×C4⋊C4—51no—
177C2×C4⋊C4—51no—
178C2×C4⋊C4—101no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—101no—
182C2×C4⋊C4—101no—
183C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
184C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
185C2×C42—21no—
186C2×C42—51no—
187C2×C42—51no—
188C2×C42—51no—
189C2×C42—51no—
190C2×C42—51no—
191C2×C42—51no—
192C2×C42—101no—
193C2×C42C2×AGL(1,𝔽5)11yescharacteristic
194C4⋊C8—102no—
195C4⋊C8—102no—
196C4⋊C8—102no—
197C4⋊C8—102no—
198#95—21no—
199#95—101no—
200#95—101no—
201#95—101no—
202C22×C5#38011yescharacteristic
203C22×C5C2×#10111yescharacteristic
204C22×C5#41311yescharacteristic
205C22×C5#41611yescharacteristic
206C22×C5#41611yescharacteristic
207C22×C5#41811yescharacteristic
208C22×C5#41911yescharacteristic
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—22no—
212C4×C5—41no—
213C4×C5—42no—
214C4×C5—81no—
215Dic5—42no—
216Dic5—41no—
217Dic5—41no—
218Dic5—81no—
219Dic5#46312yes—
220Dic5#46412yes—
221Dic5#47812yes—
222Dic5#47912yes—
223C2×Q8—102no—
224C2×Q8—102no—
225C2×Q8—202no—
226C2×Q8—202no—
227C22×C4—21no—
228C22×C4—21no—
229C22×C4—51no—
230C22×C4—51no—
231C22×C4—51no—
232C22×C4—51no—
233C22×C4—101no—
234C22×C4—101no—
235C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
236C22×C4C22⋊AGL(1,𝔽5)11yescharacteristic
237C22×C4C22×AGL(1,𝔽5)11yescharacteristic
238C2×C8—202no—
239C2×C8—202no—
240C2×C8—202no—
241C2×C8—202no—
242C2×C8—202no—
243C2×C8—202no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—52no—
247C4⋊C4—102no—
248C4⋊C4—102no—
249C4⋊C4—101no—
250C4⋊C4—201no—
251C4⋊C4—202no—
252C4⋊C4—202no—
253C4⋊C4—202no—
254C4⋊C4—202no—
255C4⋊C4C4⋊AGL(1,𝔽5)12yes—
256C42—22no—
257C42—42no—
258C42—51no—
259C42—51no—
260C42—51no—
261C42—51no—
262C42—102no—
263C42—102no—
264C42—102no—
265C42—102no—
266C42—201no—
267C42—202no—
268C2×C5#154411yescharacteristic
269C2×C5#155311yescharacteristic
270C2×C5#155411yescharacteristic
271C2×C5#155611yescharacteristic
272C2×C5#180111yescharacteristic
273C2×C5#180411yescharacteristic
274C2×C5#180511yescharacteristic
275C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
276Q8—204no—
277Q8—204no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—52no—
292C2×C4—52no—
293C2×C4—51no—
294C2×C4—51no—
295C2×C4—51no—
296C2×C4—51no—
297C2×C4—52no—
298C2×C4—52no—
299C2×C4—101no—
300C2×C4—101no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—102no—
304C2×C4—101no—
305C2×C4—101no—
306C2×C4—201no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4—201no—
311C2×C4#400512yes—
312C2×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
313C2×C4#413011yescharacteristic
314C8—402no—
315C8—402no—
316C5#859311yescharacteristic, complemented, Sylow
317C22C2×#400511yescharacteristic
318C22#6576111yescharacteristic
319C22#6576511yescharacteristic
320C22#6576711yescharacteristic
321C22#6578211yescharacteristic
322C22#6579411yescharacteristic
323C22#6579411yescharacteristic
324C4—21no—
325C4—21no—
326C4—22no—
327C4—41no—
328C4—42no—
329C4—52no—
330C4—52no—
331C4—52no—
332C4—52no—
333C4—81no—
334C4—201no—
335C4—202no—
336C4—201no—
337C4—401no—
338C2#1060419411yescharacteristic
339C2#1060427911yescharacteristic
340C2#1060436311yescharacteristic
341C2#1060441011yescharacteristic
342C2#1060441811yescharacteristic
343C2#1060444511yescharacteristic
344C2#1060445211yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC22×C4×C5C22×C4
FrattiniC22×C4C22×AGL(1,𝔽5)
FittingC4×C5×C4⋊C4C4
socle, prime radicalC23×C5C2×C22⋊C4
cosocleC2×C4×Dic5C23
hypercenterC4×C4⋊C4AGL(1,𝔽5)
hypocenterC5#8593
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
316. C5#8593semidirect

Maximal subgroups

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

subgroupindex
C4×#40342
C2×#648732
#106041862
#105987252
#85935