Finite Group Databasebeta

← #11997161

Subgroups — #11997161

Order 1280.

454 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 105 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
1#10614211C211yesmaximal, characteristic
2#10610995C211yesmaximal, characteristic
3C5×#1487C211yesmaximal, characteristic
4#10602415C211yesmaximal, characteristic
5#10601321C211yesmaximal, characteristic
6#10598229C211yesmaximal, characteristic
7#10598204C211yesmaximal, characteristic
8C2×C4×C5×Q8C2211yescharacteristic
9C2×C4×Dic10C2211yescharacteristic
10C5×#431C2211yescharacteristic
11C5×#423C2211yescharacteristic
12#65518C412yes—
13C2×#3956—21no—
14#65271C412yes—
15#65267—22no—
16#65225C2211yescharacteristic
17#65218—21no—
18#65217—21no—
19#65214C2211yescharacteristic
20#65213C2211yescharacteristic
21#65120—22no—
22#65008—22no—
23#64968—22no—
24C5×Q8⋊C8—22no—
25#64774—21no—
26Q8⋊#168—22no—
27#9488—51nomaximal, Sylow
28C22×C5×Q8C2×C411yescharacteristic
29C22×Dic10D411yescharacteristic
30C2×C5×M16—21no—
31C4×C5×Q8—21no—
32C4×C5×Q8—21no—
33C4×C5×Q8—21no—
34C4×C5×Q8—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C42×C5—21no—
38C2×C42×C5C2311yescharacteristic
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5D411yescharacteristic
41C2×#683—22no—
42C2×#683C2×C412yes—
43C2×C4×Dic5D412yes—
44C2×#681—21no—
45C4×Dic10—21no—
46C4×Dic10—21no—
47C4×Dic10—21no—
48C4×Dic10—21no—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C22⋊C8—21no—
53C4×C5×C8D412yes—
54#3963—21no—
55#3963—22no—
56#3963—22no—
57#3963—22no—
58#3963C2×C412yes—
59C22⋊#168—21no—
60#3956—42no—
61#3947—24no—
62#3946—24no—
63C4⋊#168—21no—
64C4⋊#168—21no—
65C4⋊#168—21no—
66C4×#168D412yes—
67#2983—51no—
68#2581—51no—
69#1801—51no—
70#1487—51no—
71#1487D511yescharacteristic
72#1286—51no—
73#1286—51no—
74C2×C5×Q8—21no—
75C2×C5×Q8—21no—
76C2×C5×Q8—42no—
77C22×C4×C5—21no—
78C22×C4×C5—21no—
79C22×C4×C5C22×C411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C22×Dic5—22no—
83C22×Dic5C22⋊C412yes—
84C22×Dic5C22⋊C412yes—
85C2×Dic10—21no—
86C2×Dic10—21no—
87C2×Dic10—21no—
88C2×Dic10—21no—
89C2×Dic10—21no—
90C2×Dic10—21no—
91C5×M16—41no—
92C5×M16—41no—
93C2×C5×C8—22no—
94C2×C5×C8—41no—
95C5×C4⋊C4—21no—
96C5×C4⋊C4—21no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C42×C5—41no—
100C42×C5—41no—
101C42×C5C2×D411yescharacteristic
102C42×C5C2×D411yescharacteristic
103C42×C5#4111yescharacteristic
104C42×C5#4111yescharacteristic
105C4⋊Dic5—21no—
106C4⋊Dic5—21no—
107C4⋊Dic5—41no—
108C4⋊Dic5—41no—
109#683—22no—
110#683—22no—
111#683—44no—
112C4×Dic5—22no—
113C4×Dic5—22no—
114#681—41no—
115#681—41no—
116C2×#168—22no—
117C2×#168—41no—
118C2×C4×Q8—51no—
119C2×C4×Q8C2×D511yescharacteristic
120#446—102no—
121#446—102no—
122#432—102no—
123#431—51no—
124#431C2×D511yescharacteristic
125#423—51no—
126#423C2×D511yescharacteristic
127C2×#101—101no—
128#400—52no—
129#395—52no—
130#391—101no—
131#389—101no—
132#387—102no—
133#382—51no—
134#343—101no—
135Q8⋊C8—22no—
136Q8⋊C8—102no—
137C23×C5C2×C22⋊C411yescharacteristic
138C5×Q8—22no—
139C5×Q8—22no—
140C5×Q8—41no—
141C5×Q8—41no—
142C2×C4×C5—22no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—42no—
148C2×C4×C5—41no—
149C2×C4×C5C4×D411yescharacteristic
150C2×C4×C5C4×D411yescharacteristic
151C2×C4×C5#12011yescharacteristic
152C2×C4×C5#12111yescharacteristic
153C2×C4×C5#12111yescharacteristic
154C2×C4×C5#12311yescharacteristic
155C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C5#13711yescharacteristic
157C2×C4×C5#13711yescharacteristic
158C2×C4×C5#13711yescharacteristic
159C2×Dic5—22no—
160C2×Dic5—22no—
161C2×Dic5—22no—
162C2×Dic5—22no—
163C2×Dic5—42no—
164C2×Dic5—42no—
165C2×Dic5—42no—
166C2×Dic5—42no—
167Dic10—41no—
168Dic10—41no—
169Dic10—41no—
170Dic10—41no—
171C5×C8—42no—
172C5×C8—81no—
173#168—42no—
174#168—81no—
175C22×Q8—51no—
176C22×Q8C4×D511yescharacteristic
177C2×M16—21no—
178C2×M16—101no—
179C4×Q8—21no—
180C4×Q8—21no—
181C4×Q8—21no—
182C4×Q8—21no—
183C4×Q8—101no—
184C4×Q8—101no—
185C4×Q8—101no—
186C4×Q8—101no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—52no—
189C2×C4⋊C4—51no—
190C2×C4⋊C4—102no—
191C2×C4⋊C4—101no—
192C2×C4⋊C4C4×D511yescharacteristic
193C2×C42—21no—
194C2×C42—52no—
195C2×C42C22×D511yescharacteristic
196C4⋊C8—21no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—104no—
200C4⋊C8—101no—
201C4⋊C8—101no—
202C4⋊C8—101no—
203#101—202no—
204C22⋊C8—21no—
205C22⋊C8—101no—
206#97—104no—
207C4×C8—52no—
208C4×C8C22⋊D512yes—
209#95—52no—
210#95—102no—
211#95—102no—
212#95—102no—
213#95—101no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5#38611yescharacteristic
217C22×C5#41711yescharacteristic
218C22×C5#41911yescharacteristic
219C4×C5—21no—
220C4×C5—21no—
221C4×C5—21no—
222C4×C5—21no—
223C4×C5—42no—
224C4×C5—81no—
225C4×C5#46811yescharacteristic
226C4×C5#46811yescharacteristic
227C4×C5#47011yescharacteristic
228C4×C5#47011yescharacteristic
229Dic5—42no—
230Dic5—42no—
231Dic5—82no—
232C2×Q8—21no—
233C2×Q8—21no—
234C2×Q8—42no—
235C2×Q8—101no—
236C2×Q8—101no—
237C2×Q8—101no—
238C2×Q8—101no—
239C2×Q8—101no—
240C2×Q8—101no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—52no—
244C22×C4—52no—
245C22×C4—102no—
246C22×C4C2×C4×D511yescharacteristic
247C22×C4D4×D511yescharacteristic
248C22×C4D4×D511yescharacteristic
249M16—41no—
250M16—41no—
251M16—201no—
252M16—201no—
253C2×C8—22no—
254C2×C8—41no—
255C2×C8—102no—
256C2×C8—201no—
257C4⋊C4—21no—
258C4⋊C4—21no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—102no—
262C4⋊C4—101no—
263C4⋊C4—102no—
264C4⋊C4—101no—
265C4⋊C4—204no—
266C4⋊C4—201no—
267C4⋊C4—201no—
268C42—41no—
269C42—41no—
270C42—102no—
271C42—102no—
272C42#70911yescharacteristic
273C42D4×D511yescharacteristic
274C42#71111yescharacteristic
275C42C2×C22⋊D511yescharacteristic
276C2×C5—21no—
277C2×C5—21no—
278C2×C5#189111yescharacteristic
279C2×C5#189411yescharacteristic
280C2×C5#191211yescharacteristic
281C23D5×C22⋊C411yescharacteristic
282Q8—22no—
283Q8—22no—
284Q8—41no—
285Q8—41no—
286Q8—201no—
287Q8—201no—
288Q8—201no—
289Q8—201no—
290C2×C4—22no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4—42no—
296C2×C4—41no—
297C2×C4—102no—
298C2×C4—102no—
299C2×C4—102no—
300C2×C4—102no—
301C2×C4—202no—
302C2×C4—202no—
303C2×C4—202no—
304C2×C4—202no—
305C2×C4#402711yescharacteristic
306C2×C4#402911yescharacteristic
307C2×C4#403011yescharacteristic
308C2×C4#406011yescharacteristic
309C2×C4#406111yescharacteristic
310C2×C4#406411yescharacteristic
311C2×C4#406411yescharacteristic
312C2×C4C4×C22⋊D511yescharacteristic
313C2×C4#408311yescharacteristic
314C2×C4#408411yescharacteristic
315C8—42no—
316C8—81no—
317C8—202no—
318C8—401no—
319C5#948811yescharacteristic, complemented, Sylow
320C22—21no—
321C22—21no—
322C22#6509111yescharacteristic
323C22#6509211yescharacteristic
324C22#6524511yescharacteristic
325C4—21no—
326C4—21no—
327C4—21no—
328C4—21no—
329C4—42no—
330C4—81no—
331C4—202no—
332C4—202no—
333C4—402no—
334C4#6510111yescharacteristic
335C4#6510511yescharacteristic
336C4#6546311yescharacteristic
337C4#6547811yescharacteristic
338C2—21no—
339C2—21no—
340C2#1060078511yescharacteristic
341C2#1060106411yescharacteristic
342C2#1060120411yescharacteristic
subgroupG/H
centerC22#65245
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1487C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1487D5
hypocenterC5#9488
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
319. C5#9488semidirect

Maximal subgroups

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

subgroupindex
#106142112
#106109952
C5×#14872
#106024152
#106013212
#105982292
#105982042
#94885