Finite Group Databasebeta

← #12015567

Subgroups — #12015567

Order 1280.

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

normal subgroups only

This group has 642 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#10615817C211yesmaximal, characteristic
2C5×#1785C211yesmaximal, characteristic
3#10602930C211yesmaximal, characteristic
4#10598190C214yesmaximal, complemented
5C22×C5×#41C2211yescharacteristic
6C2×#4072C411yescharacteristic
7C22×C4×Dic5C411yescharacteristic
8C2×C5×#101C2212yes—
9C2×C5×#100—21no—
10C5×#407—21no—
11#65519C2212yes—
12C2×#3968C2212yes—
13#65510C412yes—
14#65509—21no—
15#65509—21no—
16C2×#3965—21no—
17C4×C22⋊Dic5—21no—
18C4×C22⋊Dic5—21no—
19#65496—21no—
20#12861—51nomaximal, Sylow
21C2×C5×#41—24no—
22C2×C5×#41—42no—
23C2×C5×#41—42no—
24C22×C5×Q8C2311yescharacteristic
25C22×C5×D4C2×C411yescharacteristic
26C22×C5×D4D411yescharacteristic
27C22×C5×D4D411yescharacteristic
28C23×C4×C5C2×C411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C23×Dic5—21no—
32C2×C5×M16—22no—
33C2×C22⋊Dic5—21no—
34C2×C22⋊Dic5—22no—
35C2×C22⋊Dic5—22no—
36#4072—42no—
37C2×C4⋊Dic5C2×C412yes—
38C2×C4×Dic5—21no—
39C2×C4×Dic5—21no—
40C2×C4×Dic5—42no—
41C2×C4×Dic5C2×C412yes—
42C2×#681—22no—
43C5×#101—24no—
44C5×#100—42no—
45C5×C22⋊C8—42no—
46#3968—24no—
47#3965—42no—
48#3963—22no—
49#3963—22no—
50C22⋊#168—42no—
51#2297—51no—
52#1785—51no—
53#1785D511yescharacteristic
54#1394—54no—
55C24×C5C22⋊C411yescharacteristic
56C24×C5C22⋊C411yescharacteristic
57C24×C5C22⋊C411yescharacteristic
58C5×#41—416no—
59C2×C5×Q8—41no—
60C2×C5×Q8—41no—
61C2×C5×Q8#4114yes—
62C2×C5×D4—22no—
63C2×C5×D4—22no—
64C2×C5×D4—22no—
65C2×C5×D4—22no—
66C2×C5×D4—22no—
67C2×C5×D4—41no—
68C2×C5×D4—41no—
69C2×C5×D4—41no—
70C2×C5×D4—41no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—22no—
76C22×C4×C5—22no—
77C22×C4×C5—22no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5C22⋊C411yescharacteristic
81C22×C4×C5C22×C411yescharacteristic
82C22×C4×C5C2×D411yescharacteristic
83C22×C4×C5C2×D411yescharacteristic
84C22×Dic5—22no—
85C22×Dic5—22no—
86C22×Dic5—44no—
87C22×Dic5—42no—
88C5×M16—42no—
89C5×M16—42no—
90C2×C5×C8—42no—
91C22⋊Dic5—44no—
92C22⋊Dic5—44no—
93C22⋊Dic5—42no—
94C4⋊Dic5—42no—
95C4×Dic5—42no—
96C4×Dic5—42no—
97C4×Dic5—42no—
98#681—42no—
99#681—42no—
100C2×#168—42no—
101C22×#41C2×D511yescharacteristic
102C2×#117—51no—
103C22×C42—51no—
104C2×#101—52no—
105C2×#101C2×D512yes—
106C2×#100—21no—
107C2×#100—101no—
108#407—21no—
109#407—101no—
110#391—52no—
111#390—52no—
112#386—101no—
113#386—101no—
114C4×C22⋊C4—101no—
115C4×C22⋊C4—101no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5—21no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—42no—
125C23×C5—42no—
126C23×C5—42no—
127C23×C5#9912yes—
128C23×C5C2×C22⋊C411yescharacteristic
129C5×Q8—44no—
130C5×D4—44no—
131C5×D4—44no—
132C5×D4—44no—
133C2×C4×C5—28no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—44no—
143C2×C4×C5—44no—
144C2×C4×C5#9912yes—
145C2×C4×C5#11712yes—
146C2×C4×C5#12312yes—
147C2×C4×C5#12312yes—
148C2×Dic5—24no—
149C2×Dic5—42no—
150C2×Dic5—48no—
151C2×Dic5—42no—
152C2×Dic5—42no—
153C2×Dic5—42no—
154C2×Dic5—42no—
155C5×C8—82no—
156#168—82no—
157C2×#41—24no—
158C2×#41—42no—
159C2×#41—42no—
160C22×Q8C22×D511yescharacteristic
161C22×D4C4×D511yescharacteristic
162C22×D4D2011yescharacteristic
163C22×D4C22⋊D511yescharacteristic
164C23×C4—101no—
165C23×C4C4×D511yescharacteristic
166C23×C4D2011yescharacteristic
167C23×C4C22⋊D511yescharacteristic
168C2×M16—22no—
169C2×M16—102no—
170#117—202no—
171C2×C4⋊C4—52no—
172C2×C22⋊C4—101no—
173C2×C22⋊C4—102no—
174C2×C22⋊C4—102no—
175C2×C42—52no—
176C2×C42—101no—
177C2×C42—101no—
178C2×C42—202no—
179#101—24no—
180#101—104no—
181#100—42no—
182#100—202no—
183C22⋊C8—42no—
184C22⋊C8—202no—
185#95—102no—
186#95—102no—
187C22×C5—22no—
188C22×C5—22no—
189C22×C5—42no—
190C22×C5—42no—
191C22×C5—42no—
192C22×C5—42no—
193C22×C5—42no—
194C22×C5—41no—
195C22×C5—41no—
196C22×C5—42no—
197C22×C5—42no—
198C22×C5—81no—
199C22×C5—81no—
200C22×C5#38111yescharacteristic
201C22×C5C2×#9911yescharacteristic
202C22×C5C2×#9911yescharacteristic
203C4×C5—22no—
204C4×C5—22no—
205C4×C5—22no—
206C4×C5—22no—
207Dic5—44no—
208Dic5—82no—
209C24#68511yescharacteristic
210C24#68511yescharacteristic
211C24#68511yescharacteristic
212#41—416no—
213C2×Q8—41no—
214C2×Q8—41no—
215C2×Q8#71114yes—
216C2×D4—22no—
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—22no—
220C2×D4—22no—
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—41no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—22no—
230C22×C4—22no—
231C22×C4—22no—
232C22×C4—41no—
233C22×C4—41no—
234C22×C4—102no—
235C22×C4—102no—
236C22×C4—204no—
237C22×C4—202no—
238C22×C4#68511yescharacteristic
239C22×C4C2×C4×D511yescharacteristic
240C22×C4C2×D2011yescharacteristic
241C22×C4C2×C22⋊D511yescharacteristic
242M16—42no—
243M16—42no—
244M16—202no—
245M16—202no—
246C2×C8—42no—
247C2×C8—202no—
248C4⋊C4—202no—
249C22⋊C4—204no—
250C22⋊C4—204no—
251C22⋊C4—202no—
252C42—202no—
253C42—202no—
254C42—202no—
255C2×C5—21no—
256C2×C5—21no—
257C2×C5—42no—
258C2×C5—81no—
259C2×C5—81no—
260C2×C5#181911yescharacteristic
261C2×C5#213212yes—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—21no—
266C23—21no—
267C23—21no—
268C23—21no—
269C23—21no—
270C23—42no—
271C23—42no—
272C23—42no—
273C23#393812yes—
274C23C2×#68511yescharacteristic
275Q8—44no—
276D4—44no—
277D4—44no—
278D4—44no—
279C2×C4—28no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—44no—
289C2×C4—44no—
290C2×C4—104no—
291C2×C4—202no—
292C2×C4—208no—
293C2×C4—202no—
294C2×C4—202no—
295C2×C4—202no—
296C2×C4—202no—
297C2×C4#393812yes—
298C2×C4#402312yes—
299C2×C4#403212yes—
300C2×C4#408112yes—
301C8—82no—
302C8—402no—
303C5#1286111yescharacteristic, complemented, Sylow
304C22—22no—
305C22—22no—
306C22—42no—
307C22—42no—
308C22—42no—
309C22—42no—
310C22—42no—
311C22—41no—
312C22—41no—
313C22—42no—
314C22—42no—
315C22—81no—
316C22—81no—
317C22#6523211yescharacteristic
318C22C2×#393811yescharacteristic
319C22C2×#393811yescharacteristic
320C4—22no—
321C4—22no—
322C4—22no—
323C4—22no—
324C4—204no—
325C4—402no—
326C2—21no—
327C2—21no—
328C2—42no—
329C2—81no—
330C2—81no—
331C2#1060028811yescharacteristic
332C2#1060094112yes—
subgroupG/H
centerC22C2×#3938
commutatorC22×C4×C5C22×C4
FrattiniC22×Q8C22×D5
FittingC5×#1785C2
socleC22×C5C2×#99
prime radicalC22×C5×#41C22
cosocleC22×C5×Q8C23
hypercenter#1785D5
hypocenterC5#12861
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ #1785

Complements

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

NH ≅ G/Ntype
4. #10598190C2semidirect
303. C5#12861semidirect

Maximal subgroups

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

subgroupindex
#106158172
C5×#17852
#106029302
#105981902
#128615