Finite Group Databasebeta

← #11996662

Subgroups — #11996662

Order 1280.

558 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 558 conjugacy classes of subgroups — too many to draw. Only its 117 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#10614971C211yesmaximal, characteristic
2#10611017C211yesmaximal, characteristic
3C5×#1546C211yesmaximal, characteristic, complemented
4#10602566C211yesmaximal, characteristic, complemented
5#10601320C211yesmaximal, characteristic
6#10598237C211yesmaximal, characteristic, complemented
7#10598206C211yesmaximal, characteristic, complemented
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×#4093—21no—
10C2×C4×D20C2211yescharacteristic
11C5×#431C2211yescharacteristic
12C5×#423C2211yescharacteristic
13#65519—21no—
14C2×#3955—21no—
15#65282C414yes—
16#65276—22no—
17C4×C4⋊Dic5C2211yescharacteristic
18#65214C2211yescharacteristic
19#65213C2211yescharacteristic
20#65123—22no—
21D5×C22⋊C8—22no—
22C8×D20—22no—
23C5×#332—22no—
24#64774—21no—
25#64767—22no—
26#9393—51nomaximal, Sylow
27C22×C5×Q8—21no—
28C22×D20D411yescharacteristic
29C22×C4×D5D412yes—
30C2×C5×M16—21no—
31C5×C4⋊Q8—21no—
32C5×C4⋊Q8—21no—
33C5×C4⋊Q8—21no—
34C5×C4⋊Q8—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4C2×C412yes—
37C2×C42×C5C2311yescharacteristic
38#4093—42no—
39#4093—42no—
40C2×#685—24no—
41C2×#685C2×C412yes—
42C2×C4⋊Dic5—21no—
43C2×C4⋊Dic5D411yescharacteristic
44C2×C4×Dic5—21no—
45C2×#681—21no—
46C2×C8×D5—24no—
47C4×D20—21no—
48C4×D20—21no—
49C4×D20—21no—
50C4×D20—21no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8D412yes—
54C5×C22⋊C8—21no—
55C4×C5×C8—21no—
56#3963—24no—
57#3963C2×C412yes—
58C22⋊#168—21no—
59#3955—42no—
60#3952—24no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168D412yes—
64C4×#168—21no—
65#2972—51no—
66#2547—51no—
67#1800—51no—
68#1546—51no—
69#1546D511yescharacteristic, complemented
70#1303—51no—
71#1303—51no—
72C23×D5C22⋊C412yes—
73C2×C5×Q8—41no—
74C2×C5×Q8—41no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C2×C5×Q8—41no—
79C22×C4×C5—22no—
80C22×C4×C5C22×C411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C22×C4×C5C2×D411yescharacteristic
83C22×Dic5—22no—
84C22×Dic5C22⋊C412yes—
85C2×D20—21no—
86C2×D20—21no—
87C2×D20—21no—
88C2×D20—21no—
89C2×D20D812yes—
90C2×D20SD1612yes—
91C2×C4×D5—22no—
92C2×C4×D5—22no—
93C2×C4×D5—44no—
94C5×M16—41no—
95C5×M16—41no—
96C2×C5×C8—22no—
97C2×C5×C8—41no—
98C5×C4⋊C4—22no—
99C5×C4⋊C4—22no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—41no—
102C42×C5C2×D411yescharacteristic
103C42×C5C2×D411yescharacteristic
104C42×C5#4111yescharacteristic
105C42×C5#4111yescharacteristic
106#685—22no—
107#685—22no—
108#685—48no—
109C4⋊Dic5—21no—
110C4⋊Dic5—21no—
111C4⋊Dic5—42no—
112C4×Dic5—41no—
113C4×Dic5—41no—
114#681—41no—
115#681—41no—
116C2×#168—22no—
117C2×#168—41no—
118C8×D5—84no—
119C2×C4⋊Q8C2×D511yescharacteristic
120C2×#124—101no—
121C2×C4×D4—51no—
122C8×D4—102no—
123C8×D4—102no—
124#431—51no—
125#431C2×D511yescharacteristic
126#423—51no—
127#423C2×D511yescharacteristic
128C2×#100—101no—
129C2×C22⋊C8—102no—
130#397—54no—
131#391—101no—
132#380—102no—
133C4×C4⋊C4—51no—
134#343—101no—
135#332—22no—
136#332—102no—
137C23×C5C2×C22⋊C411yescharacteristic
138C22×D5—22no—
139C22×D5—22no—
140C22×D5—42no—
141C22×D5—42no—
142C22×D5#10214yes—
143C5×Q8—81no—
144C5×Q8—81no—
145C5×Q8—81no—
146C5×Q8—81no—
147C2×C4×C5—22no—
148C2×C4×C5—41no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5C4×D411yescharacteristic
153C2×C4×C5C4×D411yescharacteristic
154C2×C4×C5#12011yescharacteristic
155C2×C4×C5#12111yescharacteristic
156C2×C4×C5#12111yescharacteristic
157C2×C4×C5#12311yescharacteristic
158C2×C4×C5C2×D811yescharacteristic
159C2×C4×C5C2×SD1611yescharacteristic
160C2×C4×C5#13511yescharacteristic
161C2×C4×C5#13511yescharacteristic
162C2×Dic5—22no—
163C2×Dic5—42no—
164C2×Dic5—42no—
165C2×Dic5—42no—
166C2×Dic5—42no—
167D20—22no—
168D20—22no—
169D20—22no—
170D20—22no—
171C4×D5—44no—
172C4×D5—82no—
173C5×C8—42no—
174C5×C8—81no—
175#168—42no—
176#168—81no—
177C22×Q8—21no—
178C22×D4—51no—
179C23×C4—52no—
180C2×M16—21no—
181C2×M16—101no—
182C22×C8—104no—
183C4⋊Q8—21no—
184C4⋊Q8—21no—
185C4⋊Q8—21no—
186C4⋊Q8—21no—
187#124—202no—
188#124—202no—
189C4×D4—101no—
190C4×D4—101no—
191C4×D4—101no—
192C4×D4—101no—
193C2×C4⋊C4—21no—
194C2×C4⋊C4—51no—
195C2×C4⋊C4—101no—
196C2×C4⋊C4C4×D512yes—
197C2×C22⋊C4—52no—
198C2×C22⋊C4—104no—
199C2×C42—101no—
200C2×C42C22×D511yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—52no—
204C4⋊C8—101no—
205C4⋊C8—101no—
206C4⋊C8C22⋊D512yes—
207#100—202no—
208C22⋊C8—21no—
209C22⋊C8—104no—
210C22⋊C8—101no—
211C4×C8—21no—
212C4×C8—101no—
213#95—52no—
214#95—104no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5#38611yescharacteristic
218C22×C5C2×#10211yescharacteristic
219C22×C5#41611yescharacteristic
220C2×D5—24no—
221C2×D5—42no—
222C2×D5—42no—
223C2×D5—44no—
224C2×D5—82no—
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—21no—
228C4×C5—82no—
229C4×C5#45512yes—
230C4×C5#46511yescharacteristic
231C4×C5#46511yescharacteristic
232C4×C5#46611yescharacteristic
233C4×C5#46611yescharacteristic
234Dic5—42no—
235Dic5—82no—
236C24—52no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×D4—52no—
244C2×D4—52no—
245C2×D4—101no—
246C2×D4—101no—
247C2×D4—101no—
248C2×D4—101no—
249C22×C4—22no—
250C22×C4—52no—
251C22×C4—102no—
252C22×C4—102no—
253C22×C4—102no—
254C22×C4—204no—
255C22×C4C2×C4×D511yescharacteristic
256C22×C4D4×D511yescharacteristic
257C22×C4D4×D511yescharacteristic
258M16—41no—
259M16—41no—
260M16—201no—
261M16—201no—
262C2×C8—22no—
263C2×C8—41no—
264C2×C8—102no—
265C2×C8—201no—
266C2×C8—404no—
267C4⋊C4—22no—
268C4⋊C4—22no—
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—101no—
272C4⋊C4—101no—
273C4⋊C4—202no—
274C22⋊C4—102no—
275C22⋊C4—102no—
276C22⋊C4—208no—
277C42—201no—
278C42—201no—
279C42#70911yescharacteristic
280C42D4×D511yescharacteristic
281C42#71111yescharacteristic
282C42C2×C22⋊D511yescharacteristic
283C2×C5—21no—
284C2×C5—21no—
285C2×C5#188511yescharacteristic
286C2×C5#189311yescharacteristic
287C2×C5#191511yescharacteristic
288D5—44no—
289C23—54no—
290C23—102no—
291C23—102no—
292C23—202no—
293C23—202no—
294C23D5×C22⋊C411yescharacteristic
295Q8—81no—
296Q8—81no—
297Q8—81no—
298Q8—81no—
299D4—102no—
300D4—102no—
301D4—102no—
302D4—102no—
303C2×C4—22no—
304C2×C4—41no—
305C2×C4—42no—
306C2×C4—42no—
307C2×C4—42no—
308C2×C4—102no—
309C2×C4—204no—
310C2×C4—202no—
311C2×C4—202no—
312C2×C4—202no—
313C2×C4—202no—
314C2×C4—402no—
315C2×C4#402711yescharacteristic
316C2×C4#402911yescharacteristic
317C2×C4#403011yescharacteristic
318C2×C4D5×D811yescharacteristic
319C2×C4#405811yescharacteristic
320C2×C4D5×SD1611yescharacteristic
321C2×C4#406211yescharacteristic
322C2×C4C4×C22⋊D511yescharacteristic
323C2×C4#408311yescharacteristic
324C2×C4#408411yescharacteristic
325C8—42no—
326C8—81no—
327C8—202no—
328C8—401no—
329C5#939311yescharacteristic, complemented, Sylow
330C22—21no—
331C22—21no—
332C22—104no—
333C22—204no—
334C22—202no—
335C22—202no—
336C22—402no—
337C22D5×#10211yescharacteristic
338C22#6506111yescharacteristic
339C22#6524511yescharacteristic
340C4—21no—
341C4—21no—
342C4—21no—
343C4—82no—
344C4—202no—
345C4—402no—
346C4#6506411yescharacteristic
347C4#6506711yescharacteristic
348C4#6544611yescharacteristic
349C4#6546011yescharacteristic
350C4#6549112yes—
351C2—21no—
352C2—21no—
353C2—204no—
354C2#1060091711yescharacteristic
355C2#1060099511yescharacteristic
356C2#1060113611yescharacteristic
subgroupG/H
centerC22#65245
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1546C2
socleC22×C5#386
prime radicalC22×D20D4
cosocleC2×C42×C5C23
hypercenter#1546D5
hypocenterC5#9393
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1546

Complements

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

NH ≅ G/Ntype
3. C5×#1546C2semidirect
4. #10602566C2semidirect
6. #10598237C2semidirect
7. #10598206C2semidirect
69. #1546D5semidirect
329. C5#9393semidirect

Maximal subgroups

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

subgroupindex
#106149712
#106110172
C5×#15462
#106025662
#106013202
#105982372
#105982062
#93935