Finite Group Databasebeta

← #12010444

Subgroups — #12010444

Order 1280.

440 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 99 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#10614105C211yesmaximal, characteristic
2C5×#1800C211yesmaximal, characteristic
3#10602393C211yesmaximal, characteristic
4#10597987C214yesmaximal, complemented
5C2×C4×C5×D4C2211yescharacteristic
6C22×C4⋊Dic5C411yescharacteristic
7C5×#423—21no—
8C2×C5×#100—21no—
9#65509—21no—
10#65501—21no—
11#65501C411yescharacteristic
12C2×C22⋊#168—21no—
13#65275C2212yes—
14#65238C412yes—
15#65235—21no—
16#65217—21no—
17C5×#343C2212yes—
18#64748C2212yes—
19#64745—21no—
20#11903—51nomaximal, Sylow
21C22×C5×D4D411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×Dic5—21no—
25C2×C5×M16—22no—
26C4×C5×D4—41no—
27C4×C5×D4—41no—
28C2×C5×C4⋊C4C2311yescharacteristic
29C2×C5×C22⋊C4C2×C411yescharacteristic
30C2×C5×C22⋊C4D411yescharacteristic
31C2×C42×C5D411yescharacteristic
32C2×C22⋊Dic5—21no—
33C2×C22⋊Dic5—22no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—21no—
36C2×C4⋊Dic5—41no—
37C2×C4⋊Dic5—41no—
38C2×C4⋊Dic5C2×C412yes—
39C2×#683—22no—
40C22×#168—41no—
41C5×C4⋊C8—41no—
42C5×C4⋊C8—41no—
43C5×#100—42no—
44#3963—22no—
45#3963—22no—
46#3963C2×C412yes—
47C22⋊#168—22no—
48C22⋊#168—41no—
49#2487—51no—
50#1800D511yescharacteristic
51#1459—51no—
52#1353—54no—
53C24×C5C22⋊C411yescharacteristic
54C24×C5C22⋊C411yescharacteristic
55C2×C5×D4—41no—
56C2×C5×D4—41no—
57C2×C5×D4SD1612yes—
58C2×C5×D4Q1612yes—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—42no—
64C22×C4×C5—42no—
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22⋊C411yescharacteristic
67C22×C4×C5C22×C411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C22×C4×C5C2×D411yescharacteristic
70C22×Dic5—22no—
71C22×Dic5—22no—
72C22×Dic5—42no—
73C22×Dic5—82no—
74C5×M16—42no—
75C5×M16—42no—
76C2×C5×C8—42no—
77C5×C4⋊C4—41no—
78C5×C22⋊C4—41no—
79C5×C22⋊C4—41no—
80C42×C5—21no—
81C42×C5—21no—
82C22⋊Dic5—42no—
83C22⋊Dic5—82no—
84C4⋊Dic5—42no—
85C4⋊Dic5—41no—
86C4⋊Dic5—41no—
87C4⋊Dic5—42no—
88#683—82no—
89C2×#168—42no—
90C2×#168—82no—
91C2×C4×D4C2×D511yescharacteristic
92C22×C4⋊C4—51no—
93#423—21no—
94C2×#100—21no—
95C2×C22⋊C8—101no—
96#400—52no—
97#399—52no—
98#389—101no—
99#386—101no—
100#385—101no—
101#380—51no—
102#380—101no—
103#343C2×D512yes—
104#324—52no—
105#323—101no—
106C23×C5—21no—
107C23×C5—21no—
108C23×C5—21no—
109C23×C5—21no—
110C23×C5—41no—
111C23×C5—41no—
112C23×C5—41no—
113C23×C5—41no—
114C23×C5#10312yes—
115C23×C5#10312yes—
116C23×C5C2×C22⋊C411yescharacteristic
117C5×D4—42no—
118C5×D4—42no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—22no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—42no—
126C2×C4×C5—42no—
127C2×C4×C5—42no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—81no—
132C2×C4×C5#9911yescharacteristic
133C2×C4×C5#9911yescharacteristic
134C2×C4×C5C2×SD1611yescharacteristic
135C2×C4×C5C2×Q1611yescharacteristic
136C2×Dic5—42no—
137C2×Dic5—42no—
138C2×Dic5—42no—
139C2×Dic5—42no—
140C2×Dic5—42no—
141C2×Dic5—42no—
142C2×Dic5—84no—
143C5×C8—82no—
144#168—82no—
145C22×D4C22⋊D511yescharacteristic
146C23×C4—101no—
147C23×C4C4×D511yescharacteristic
148C23×C4D2011yescharacteristic
149C2×M16—22no—
150C22×C8—201no—
151C4×D4—41no—
152C4×D4—41no—
153C2×C4⋊C4—52no—
154C2×C4⋊C4—101no—
155C2×C4⋊C4—101no—
156C2×C4⋊C4—102no—
157C2×C4⋊C4—201no—
158C2×C4⋊C4—201no—
159C2×C4⋊C4C22×D511yescharacteristic
160C2×C22⋊C4—101no—
161C2×C22⋊C4—102no—
162C2×C22⋊C4C4×D511yescharacteristic
163C2×C22⋊C4D2011yescharacteristic
164C2×C42C22⋊D511yescharacteristic
165C4⋊C8—41no—
166C4⋊C8—41no—
167#100—42no—
168C22⋊C8—102no—
169C22⋊C8—201no—
170#95—52no—
171#95—102no—
172#95—102no—
173C22×C5—21no—
174C22×C5—21no—
175C22×C5—22no—
176C22×C5—22no—
177C22×C5—42no—
178C22×C5—42no—
179C22×C5—42no—
180C22×C5—41no—
181C22×C5—41no—
182C22×C5—41no—
183C22×C5—41no—
184C22×C5—81no—
185C22×C5C2×#9911yescharacteristic
186C22×C5C2×#10311yescharacteristic
187C22×C5#42111yescharacteristic
188C4×C5—21no—
189C4×C5—21no—
190C4×C5—21no—
191C4×C5—41no—
192C4×C5—41no—
193C4×C5—41no—
194C4×C5#35212yes—
195Dic5—82no—
196Dic5—82no—
197C24#68511yescharacteristic
198C24#68511yescharacteristic
199C2×D4—41no—
200C2×D4—41no—
201C2×D4#68712yes—
202C2×D4#68912yes—
203C22×C4—21no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—42no—
208C22×C4—42no—
209C22×C4—102no—
210C22×C4—102no—
211C22×C4—202no—
212C22×C4—402no—
213C22×C4#68511yescharacteristic
214C22×C4#68511yescharacteristic
215C22×C4C2×C4×D511yescharacteristic
216C22×C4C2×D2011yescharacteristic
217C22×C4C2×C22⋊D511yescharacteristic
218M16—42no—
219M16—42no—
220C2×C8—42no—
221C2×C8—202no—
222C2×C8—402no—
223C4⋊C4—41no—
224C4⋊C4—202no—
225C4⋊C4—202no—
226C4⋊C4—201no—
227C4⋊C4—201no—
228C4⋊C4—402no—
229C22⋊C4—41no—
230C22⋊C4—41no—
231C22⋊C4—202no—
232C22⋊C4—402no—
233C42—21no—
234C42—21no—
235C2×C5—21no—
236C2×C5—21no—
237C2×C5—42no—
238C2×C5—42no—
239C2×C5#152011yescharacteristic
240C2×C5C2×#35211yescharacteristic
241C2×C5#213411yescharacteristic
242C23—21no—
243C23—21no—
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23—41no—
249C23—41no—
250C23#394212yes—
251C23#394212yes—
252C23C2×#68511yescharacteristic
253D4—42no—
254D4—42no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—22no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—81no—
268C2×C4—202no—
269C2×C4—202no—
270C2×C4—202no—
271C2×C4—202no—
272C2×C4—202no—
273C2×C4—202no—
274C2×C4—404no—
275C2×C4#393811yescharacteristic
276C2×C4#393811yescharacteristic
277C2×C4C2×#68711yescharacteristic
278C2×C4C2×#68911yescharacteristic
279C8—82no—
280C8—402no—
281C5#1190311yescharacteristic, complemented, Sylow
282C22—21no—
283C22—21no—
284C22—22no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—42no—
289C22—41no—
290C22—41no—
291C22—41no—
292C22—41no—
293C22—81no—
294C22C2×#393811yescharacteristic
295C22C2×#394211yescharacteristic
296C22#6529411yescharacteristic
297C4—21no—
298C4—21no—
299C4—21no—
300C4—41no—
301C4—41no—
302C4—41no—
303C4—402no—
304C4—402no—
305C4#6469612yes—
306C2—21no—
307C2—21no—
308C2—42no—
309C2—42no—
310C2#1060030311yescharacteristic
311C2C2×#6469611yescharacteristic
312C2#1060094211yescharacteristic
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC2×C4⋊C4C22×D5
FittingC5×#1800C2
socleC22×C5C2×#99
prime radicalC22×C5×D4D4
cosocleC2×C5×C4⋊C4C23
hypercenter#1800D5
hypocenterC5#11903
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1800

Complements

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

NH ≅ G/Ntype
4. #10597987C2semidirect
281. C5#11903semidirect

Maximal subgroups

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

subgroupindex
#106141052
C5×#18002
#106023932
#105979872
#119035