Finite Group Databasebeta

← #11994329

Subgroups — #11994329

Order 1280.

812 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 147 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
1C5×#2315C211yesmaximal, characteristic
2C2×#65238C211yesmaximal, characteristic
3C2×#64745C211yesmaximal, characteristic
4#10600295C212yesmaximal, complemented
5#10598115C212yesmaximal, complemented
6C22×C5×C22⋊C4—21no—
7C22×C5×C22⋊C4C2211yescharacteristic
8C22×C22⋊Dic5—21no—
9C22×C4⋊Dic5C2211yescharacteristic
10C22×#683—21no—
11C5×#385—24no—
12C5×#380—21no—
13C5×#380C2212yes—
14C2×#3963C2211yescharacteristic
15C2×C22⋊#168C2212yes—
16#65238—22no—
17#65238C414yescomplemented
18#64749—24no—
19#64745—22no—
20#9021—51nomaximal, Sylow
21C25×C5D411yescharacteristic
22C23×C4×C5—22no—
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C23×Dic5—21no—
26C23×Dic5—21no—
27C2×C5×C4⋊C4—22no—
28C2×C5×C4⋊C4D414yes—
29C2×C5×C22⋊C4—22no—
30C2×C5×C22⋊C4—22no—
31C2×C5×C22⋊C4—22no—
32C2×C5×C22⋊C4—22no—
33C2×C5×C22⋊C4—42no—
34C2×C5×C22⋊C4—42no—
35C2×C5×C22⋊C4C2×C412yes—
36C2×C5×C22⋊C4D412yes—
37C2×C22⋊Dic5—24no—
38C2×C22⋊Dic5—44no—
39C2×C4⋊Dic5—22no—
40C2×C4⋊Dic5—22no—
41C2×C4⋊Dic5—21no—
42C2×C4⋊Dic5C2×C412yescomplemented
43C2×#683—24no—
44C2×#683—44no—
45C22×#168—22no—
46C5×#95—22no—
47C5×#95—22no—
48#3963—21no—
49#3963C2×C412yescomplemented
50C22⋊#168—22no—
51C22⋊#168—22no—
52C2×#399—51no—
53#2315D511yescharacteristic
54#1824—52no—
55C2×#323—51no—
56#1294—52no—
57C24×C5—21no—
58C24×C5—21no—
59C24×C5—21no—
60C24×C5—21no—
61C24×C5—42no—
62C24×C5—42no—
63C24×C5C22⋊C412yes—
64C24×C5SD1612yes—
65C24×C5Q1612yes—
66C24×C5C2×D411yescharacteristic
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—24no—
70C22×C4×C5—42no—
71C22×C4×C5—42no—
72C22×C4×C5—44no—
73C22×C4×C5—82no—
74C22×C4×C5—82no—
75C22×C4×C5C22⋊C412yes—
76C22×C4×C5C22×C411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D412yes—
79C22×C4×C5#4112yes—
80C22×Dic5—24no—
81C22×Dic5—22no—
82C22×Dic5—22no—
83C22×Dic5—42no—
84C22×Dic5—41no—
85C22×Dic5—41no—
86C22×Dic5—42no—
87C22×Dic5—42no—
88C22×Dic5—41no—
89C22×Dic5—41no—
90C5×C4⋊C4—44no—
91C5×C4⋊C4—82no—
92C5×C22⋊C4—24no—
93C5×C22⋊C4—24no—
94C5×C22⋊C4—44no—
95C5×C22⋊C4—42no—
96C5×C22⋊C4—42no—
97C22⋊Dic5—48no—
98C4⋊Dic5—24no—
99C4⋊Dic5—42no—
100#683—48no—
101C2×#168—44no—
102C2×#168—42no—
103C22×C4⋊C4—51no—
104C22×C4⋊C4—101no—
105C22×C22⋊C4—21no—
106C22×C22⋊C4—101no—
107C22×C22⋊C4C2×D511yescharacteristic
108C2×C22⋊C8—52no—
109#399—54no—
110#399—102no—
111#385—24no—
112#380—21no—
113#380C2×D512yes—
114C2×#95—51no—
115#340—104no—
116#323—102no—
117C23×C5—22no—
118C23×C5—22no—
119C23×C5—22no—
120C23×C5—22no—
121C23×C5—22no—
122C23×C5—22no—
123C23×C5—22no—
124C23×C5—22no—
125C23×C5—42no—
126C23×C5—42no—
127C23×C5—44no—
128C23×C5—44no—
129C23×C5—42no—
130C23×C5—42no—
131C23×C5—82no—
132C23×C5—82no—
133C23×C5—81no—
134C23×C5—81no—
135C23×C5#10314yes—
136C23×C5C2×C22⋊C411yescharacteristic
137C23×C5#12011yescharacteristic
138C23×C5#12311yescharacteristic
139C23×C5C2×SD1611yescharacteristic
140C23×C5C2×Q1611yescharacteristic
141C23×C5AGL(1,ℤ/8)11yescharacteristic
142C23×C5#13711yescharacteristic
143C2×C4×C5—24no—
144C2×C4×C5—22no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—44no—
151C2×C4×C5—44no—
152C2×C4×C5—44no—
153C2×C4×C5—81no—
154C2×C4×C5—88no—
155C2×C4×C5C4×D412yes—
156C2×C4×C5#12112yes—
157C2×Dic5—24no—
158C2×Dic5—44no—
159C2×Dic5—44no—
160C2×Dic5—42no—
161C2×Dic5—42no—
162C2×Dic5—42no—
163C2×Dic5—42no—
164C2×Dic5—42no—
165C2×Dic5—82no—
166C2×Dic5—82no—
167#168—82no—
168C25C22⋊D511yescharacteristic
169C23×C4—22no—
170C23×C4—101no—
171C23×C4—101no—
172C23×C4C22⋊D511yescharacteristic
173C23×C4C22×D511yescharacteristic
174C22×C8—102no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—52no—
177C2×C4⋊C4—102no—
178C2×C4⋊C4—102no—
179C2×C4⋊C4—104no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—204no—
182C2×C4⋊C4C22⋊D514yes—
183C2×C22⋊C4—22no—
184C2×C22⋊C4—22no—
185C2×C22⋊C4—22no—
186C2×C22⋊C4—22no—
187C2×C22⋊C4—42no—
188C2×C22⋊C4—42no—
189C2×C22⋊C4—104no—
190C2×C22⋊C4—204no—
191C2×C22⋊C4C4×D512yes—
192C2×C22⋊C4D2012yes—
193C22⋊C8—102no—
194C22⋊C8—102no—
195#95—22no—
196#95—22no—
197#95—52no—
198#95—101no—
199C22×C5—22no—
200C22×C5—22no—
201C22×C5—22no—
202C22×C5—22no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—24no—
208C22×C5—44no—
209C22×C5—44no—
210C22×C5—44no—
211C22×C5—42no—
212C22×C5—42no—
213C22×C5—82no—
214C22×C5—82no—
215C22×C5—82no—
216C22×C5#38611yescharacteristic
217C22×C5C2×#10311yescharacteristic
218C22×C5#41711yescharacteristic
219C22×C5#45011yescharacteristic
220C22×C5#45111yescharacteristic
221C22×C5#45312yes—
222C22×C5#45812yes—
223C22×C5#48311yescharacteristic
224C22×C5#48411yescharacteristic
225C4×C5—22no—
226C4×C5—22no—
227C4×C5—42no—
228C4×C5—84no—
229Dic5—44no—
230Dic5—82no—
231C24—21no—
232C24—21no—
233C24—21no—
234C24—21no—
235C24—42no—
236C24—42no—
237C24#68512yes—
238C24#68712yes—
239C24#68912yes—
240C24C2×C22⋊D511yescharacteristic
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—24no—
244C22×C4—42no—
245C22×C4—42no—
246C22×C4—44no—
247C22×C4—82no—
248C22×C4—82no—
249C22×C4—104no—
250C22×C4—102no—
251C22×C4—102no—
252C22×C4—202no—
253C22×C4—201no—
254C22×C4—201no—
255C22×C4—202no—
256C22×C4—202no—
257C22×C4—201no—
258C22×C4—201no—
259C22×C4#68512yes—
260C22×C4C2×C4×D511yescharacteristic
261C22×C4C2×D2011yescharacteristic
262C22×C4#70912yes—
263C22×C4C2×C22⋊D512yes—
264C2×C8—204no—
265C2×C8—202no—
266C4⋊C4—44no—
267C4⋊C4—82no—
268C4⋊C4—104no—
269C4⋊C4—208no—
270C4⋊C4—202no—
271C22⋊C4—24no—
272C22⋊C4—24no—
273C22⋊C4—44no—
274C22⋊C4—42no—
275C22⋊C4—42no—
276C22⋊C4—208no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—44no—
282C2×C5#161312yes—
283C2×C5#161412yes—
284C2×C5#187211yescharacteristic
285C2×C5#188711yescharacteristic
286C2×C5#189011yescharacteristic
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—22no—
295C23—42no—
296C23—42no—
297C23—44no—
298C23—44no—
299C23—42no—
300C23—42no—
301C23—82no—
302C23—82no—
303C23—81no—
304C23—81no—
305C23#394214yes—
306C23C2×#68511yescharacteristic
307C23#407511yescharacteristic
308C23#407811yescharacteristic
309C23C2×#68711yescharacteristic
310C23#408811yescharacteristic
311C23C2×#68911yescharacteristic
312C23#409911yescharacteristic
313C2×C4—24no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—81no—
324C2×C4—88no—
325C2×C4—104no—
326C2×C4—204no—
327C2×C4—204no—
328C2×C4—202no—
329C2×C4—202no—
330C2×C4—202no—
331C2×C4—202no—
332C2×C4—202no—
333C2×C4—402no—
334C2×C4—402no—
335C2×C4C4×C22⋊D512yes—
336C2×C4#407612yes—
337C8—402no—
338C5#902111yescharacteristic, complemented, Sylow
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—24no—
348C22—44no—
349C22—44no—
350C22—44no—
351C22—42no—
352C22—42no—
353C22—82no—
354C22—82no—
355C22—82no—
356C22#6525511yescharacteristic
357C22C2×#394211yescharacteristic
358C22#6525911yescharacteristic
359C22#6526011yescharacteristic
360C22#6550211yescharacteristic
361C22#6550711yescharacteristic
362C22#6551711yescharacteristic
363C22#6553012yes—
364C22#6553212yes—
365C4—22no—
366C4—22no—
367C4—42no—
368C4—84no—
369C4—204no—
370C4—402no—
371C2—21no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—44no—
376C2#1060235211yescharacteristic
377C2#1060244311yescharacteristic
378C2#1060244811yescharacteristic
379C2#1060263712yes—
380C2#1060268412yes—
subgroupG/H
centerC23#4099
commutatorC22×C4×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#2315C2
socleC23×C5#120
prime radicalC25×C5D4
cosocleC23×C4×C5C23
hypercenter#2315D5
hypocenterC5#9021
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2315

Complements

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

NH ≅ G/Ntype
4. #10600295C2semidirect
5. #10598115C2semidirect
17. #65238C4semidirect
42. C2×C4⋊Dic5C2×C4semidirect
49. #3963C2×C4semidirect
338. C5#9021semidirect

Maximal subgroups

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

subgroupindex
C5×#23152
C2×#652382
C2×#647452
#106002952
#105981152
#90215