Finite Group Databasebeta

← #11996667

Subgroups — #11996667

Order 1280.

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

normal subgroups only

This group has 506 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#10614970C211yesmaximal, characteristic
2#10610994C211yesmaximal, characteristic
3C5×#1546C211yesmaximal, characteristic
4#10602566C211yesmaximal, characteristic
5#10601321C211yesmaximal, characteristic
6#10598237C211yesmaximal, characteristic
7#10598206C211yesmaximal, characteristic
8C2×C5×C4⋊Q8C2211yescharacteristic
9C2×#4090—21no—
10C2×C4×Dic10C2211yescharacteristic
11C5×#431C2211yescharacteristic
12C5×#423C2211yescharacteristic
13#65519—21no—
14C2×#3956—21no—
15#65269C414yes—
16#65262—22no—
17C4×C4⋊Dic5C2211yescharacteristic
18#65214C2211yescharacteristic
19#65213C2211yescharacteristic
20#65119—22no—
21#65007—22no—
22C8×Dic10—22no—
23C5×#332—22no—
24#64774—21no—
25#64767—22no—
26#9394—51nomaximal, Sylow
27C22×C5×Q8—21no—
28C22×Dic10D411yescharacteristic
29C2×C5×M16—21no—
30C5×C4⋊Q8—21no—
31C5×C4⋊Q8—21no—
32C5×C4⋊Q8—21no—
33C5×C4⋊Q8—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4C2×C412yes—
36C2×C42×C5C2311yescharacteristic
37#4090—42no—
38#4090—42no—
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5D411yescharacteristic
41C2×#683—24no—
42C2×#683C2×C412yes—
43C2×C4×Dic5—21no—
44C2×C4×Dic5D412yes—
45C2×#681—21no—
46C4×Dic10—21no—
47C4×Dic10—21no—
48C4×Dic10—21no—
49C4×Dic10—21no—
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8D412yes—
53C5×C22⋊C8—21no—
54C4×C5×C8—21no—
55#3963—24no—
56#3963C2×C412yes—
57C22⋊#168—21no—
58#3956—42no—
59#3946—24no—
60C8×Dic5—24no—
61C4⋊#168—21no—
62C4⋊#168—21no—
63C4⋊#168D412yes—
64C4×#168—21no—
65#2982—51no—
66#2546—51no—
67#1801—51no—
68#1546—51no—
69#1546D511yescharacteristic
70#1303—51no—
71#1303—51no—
72C2×C5×Q8—41no—
73C2×C5×Q8—41no—
74C2×C5×Q8—41no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C22×C4×C5—22no—
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×Dic10D812yes—
90C2×Dic10SD1612yes—
91C5×M16—41no—
92C5×M16—41no—
93C2×C5×C8—22no—
94C2×C5×C8—41no—
95C5×C4⋊C4—22no—
96C5×C4⋊C4—22no—
97C5×C4⋊C4—41no—
98C5×C4⋊C4—41no—
99C42×C5C2×D411yescharacteristic
100C42×C5C2×D411yescharacteristic
101C42×C5#4111yescharacteristic
102C42×C5#4111yescharacteristic
103C4⋊Dic5—24no—
104C4⋊Dic5—21no—
105C4⋊Dic5—21no—
106#683—22no—
107#683—22no—
108#683—48no—
109C4×Dic5—22no—
110C4×Dic5—22no—
111C4×Dic5—41no—
112C4×Dic5—41no—
113#681—41no—
114#681—41no—
115C2×#168—22no—
116C2×#168—41no—
117C2×C4⋊Q8—101no—
118C2×C4⋊Q8C2×D511yescharacteristic
119C2×C4×Q8—51no—
120C8×Q8—102no—
121C8×Q8—102no—
122#431—51no—
123#431—102no—
124#431C2×D511yescharacteristic
125#423—51no—
126#423C2×D511yescharacteristic
127C2×#101—101no—
128#398—54no—
129#391—101no—
130#389—102no—
131C4×C4⋊C4—51no—
132#343—101no—
133#332—22no—
134#332—102no—
135C23×C5C2×C22⋊C411yescharacteristic
136C5×Q8—81no—
137C5×Q8—81no—
138C5×Q8—81no—
139C5×Q8—81no—
140C2×C4×C5—22no—
141C2×C4×C5—41no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5C4×D411yescharacteristic
146C2×C4×C5C4×D411yescharacteristic
147C2×C4×C5#12011yescharacteristic
148C2×C4×C5#12111yescharacteristic
149C2×C4×C5#12111yescharacteristic
150C2×C4×C5#12311yescharacteristic
151C2×C4×C5C2×D811yescharacteristic
152C2×C4×C5C2×SD1611yescharacteristic
153C2×C4×C5#13511yescharacteristic
154C2×C4×C5#13511yescharacteristic
155C2×Dic5—22no—
156C2×Dic5—22no—
157C2×Dic5—24no—
158C2×Dic5—22no—
159C2×Dic5—42no—
160C2×Dic5—42no—
161C2×Dic5—42no—
162C2×Dic5#10214yes—
163Dic10—22no—
164Dic10—22no—
165Dic10—22no—
166Dic10—22no—
167C5×C8—42no—
168C5×C8—81no—
169#168—42no—
170#168—81no—
171C22×Q8—21no—
172C22×Q8—51no—
173C2×M16—21no—
174C2×M16—101no—
175C4⋊Q8—21no—
176C4⋊Q8—21no—
177C4⋊Q8—21no—
178C4⋊Q8—21no—
179C4⋊Q8—202no—
180C4⋊Q8—202no—
181C4×Q8—101no—
182C4×Q8—101no—
183C4×Q8—101no—
184C4×Q8—101no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—52no—
187C2×C4⋊C4—51no—
188C2×C4⋊C4—101no—
189C2×C4⋊C4—104no—
190C2×C4⋊C4C4×D512yes—
191C2×C42—52no—
192C2×C42—101no—
193C2×C42C22×D511yescharacteristic
194C4⋊C8—21no—
195C4⋊C8—21no—
196C4⋊C8—52no—
197C4⋊C8—104no—
198C4⋊C8—101no—
199C4⋊C8—101no—
200C4⋊C8C22⋊D512yes—
201#101—202no—
202C22⋊C8—21no—
203C22⋊C8—101no—
204C4×C8—21no—
205C4×C8—104no—
206C4×C8—101no—
207#95—52no—
208#95—104no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5#38611yescharacteristic
212C22×C5C2×#10211yescharacteristic
213C22×C5#41611yescharacteristic
214C4×C5—21no—
215C4×C5—21no—
216C4×C5—21no—
217C4×C5—82no—
218C4×C5#45612yes—
219C4×C5#46511yescharacteristic
220C4×C5#46511yescharacteristic
221C4×C5#46611yescharacteristic
222C4×C5#46611yescharacteristic
223Dic5—24no—
224Dic5—44no—
225Dic5—42no—
226C2×Q8—41no—
227C2×Q8—41no—
228C2×Q8—41no—
229C2×Q8—41no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8—52no—
233C2×Q8—52no—
234C2×Q8—101no—
235C2×Q8—101no—
236C2×Q8—101no—
237C2×Q8—101no—
238C22×C4—22no—
239C22×C4—52no—
240C22×C4—52no—
241C22×C4—102no—
242C22×C4C2×C4×D511yescharacteristic
243C22×C4D4×D511yescharacteristic
244C22×C4D4×D511yescharacteristic
245M16—41no—
246M16—41no—
247M16—201no—
248M16—201no—
249C2×C8—22no—
250C2×C8—41no—
251C2×C8—102no—
252C2×C8—201no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—41no—
256C4⋊C4—41no—
257C4⋊C4—104no—
258C4⋊C4—102no—
259C4⋊C4—101no—
260C4⋊C4—102no—
261C4⋊C4—101no—
262C4⋊C4—208no—
263C42—102no—
264C42—102no—
265C42—201no—
266C42—201no—
267C42#70911yescharacteristic
268C42D4×D511yescharacteristic
269C42#71111yescharacteristic
270C42C2×C22⋊D511yescharacteristic
271C2×C5—21no—
272C2×C5—21no—
273C2×C5#188611yescharacteristic
274C2×C5#189311yescharacteristic
275C2×C5#191511yescharacteristic
276C23D5×C22⋊C411yescharacteristic
277Q8—81no—
278Q8—81no—
279Q8—81no—
280Q8—81no—
281Q8—102no—
282Q8—102no—
283Q8—102no—
284Q8—102no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—42no—
289C2×C4—42no—
290C2×C4—54no—
291C2×C4—102no—
292C2×C4—102no—
293C2×C4—104no—
294C2×C4—102no—
295C2×C4—202no—
296C2×C4—202no—
297C2×C4—202no—
298C2×C4#402711yescharacteristic
299C2×C4#402911yescharacteristic
300C2×C4#403011yescharacteristic
301C2×C4D5×D811yescharacteristic
302C2×C4#405811yescharacteristic
303C2×C4D5×SD1611yescharacteristic
304C2×C4#406211yescharacteristic
305C2×C4C4×C22⋊D511yescharacteristic
306C2×C4#408311yescharacteristic
307C2×C4#408411yescharacteristic
308C8—42no—
309C8—81no—
310C8—202no—
311C8—401no—
312C5#939411yescharacteristic, complemented, Sylow
313C22—21no—
314C22—21no—
315C22D5×#10211yescharacteristic
316C22#6506111yescharacteristic
317C22#6524511yescharacteristic
318C4—21no—
319C4—21no—
320C4—21no—
321C4—82no—
322C4—104no—
323C4—204no—
324C4—202no—
325C4#6506411yescharacteristic
326C4#6506711yescharacteristic
327C4#6544611yescharacteristic
328C4#6546011yescharacteristic
329C4#6549412yes—
330C2—21no—
331C2—21no—
332C2#1060091711yescharacteristic
333C2#1060099511yescharacteristic
334C2#1060113811yescharacteristic
subgroupG/H
centerC22#65245
commutatorC22×C4×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1546C2
socleC22×C5#386
prime radicalC23×C5C2×C22⋊C4
cosocleC2×C42×C5C23
hypercenter#1546D5
hypocenterC5#9394
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
312. C5#9394semidirect

Maximal subgroups

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

subgroupindex
#106149702
#106109942
C5×#15462
#106025662
#106013212
#105982372
#105982062
#93945