Finite Group Databasebeta

← #13017409

Subgroups — #13017409

Order 1280.

1158 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 1158 conjugacy classes of subgroups — too many to draw. Only its 160 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
1C22×#4023C211yesmaximal, characteristic
2C2×#64933C212yesmaximal
3#10604902C212yesmaximal, complemented
4C2×#64914C212yesmaximal, complemented
5C24×Dic5C411yescharacteristic
6C22×C5×C22⋊C4C411yescharacteristic
7C22×C22⋊Dic5C2211yescharacteristic
8C22×#683C411yescharacteristic
9C22×#683C2211yescharacteristic
10C22×C4×Dic5C411yescharacteristic
11C22×C4×Dic5C2211yescharacteristic
12C2×#4023—24no—
13C2×#4023—24no—
14C2×#4023—24no—
15C2×C22⋊#170C2214yes—
16#64933—24no—
17#64918—24no—
18#64914—24no—
19#8300—51nomaximal, Sylow
20C25×C5C2×C411yescharacteristic
21C23×C4×C5C2×C411yescharacteristic
22C23×C4×C5C2×C411yescharacteristic
23C23×Dic5—22no—
24C23×Dic5—22no—
25C23×Dic5—22no—
26C23×Dic5—22no—
27C23×Dic5—22no—
28C23×Dic5—22no—
29C23×Dic5C814yescomplemented
30C23×Dic5C2×C411yescharacteristic
31C23×Dic5C2×C411yescharacteristic
32C23×Dic5C2×C411yescharacteristic
33C23×Dic5C2311yescharacteristic
34C22×#170—24no—
35C2×C5×C22⋊C4—22no—
36C2×C5×C22⋊C4—22no—
37C2×C5×C22⋊C4—22no—
38C2×C22⋊Dic5—22no—
39C2×C22⋊Dic5—22no—
40C2×C22⋊Dic5D414yes—
41C2×#683—22no—
42C2×#683—22no—
43C2×#683—22no—
44C2×#683—22no—
45C2×#683—22no—
46C2×#683D414yes—
47C2×C4×Dic5—22no—
48C2×C4×Dic5—22no—
49C2×C4×Dic5—22no—
50C2×C4×Dic5—22no—
51C2×C4×Dic5—22no—
52C2×C4×Dic5D414yes—
53#4023—232no—
54C22⋊#170—24no—
55C22⋊#170—24no—
56C22×#117—51no—
57#1817—52no—
58C2×#324—52no—
59C2×#323—52no—
60C24×C5—21no—
61C24×C5—21no—
62C24×C5—21no—
63C24×C5—21no—
64C24×C5—42no—
65C24×C5—42no—
66C24×C5C22⋊C412yes—
67C24×C5C2×C812yes—
68C24×C5M1612yes—
69C24×C5C22×C411yescharacteristic
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—21no—
73C22×C4×C5—21no—
74C22×C4×C5—42no—
75C22×C4×C5—42no—
76C22×C4×C5C22⋊C412yes—
77C22×C4×C5C22⋊C412yes—
78C22×Dic5—28no—
79C22×Dic5—28no—
80C22×Dic5—28no—
81C22×Dic5—28no—
82C22×Dic5—28no—
83C22×Dic5—21no—
84C22×Dic5—21no—
85C22×Dic5—21no—
86C22×Dic5—21no—
87C22×Dic5—21no—
88C22×Dic5—21no—
89C22×Dic5—21no—
90C22×Dic5—21no—
91C22×Dic5—28no—
92C22×Dic5—28no—
93C22×Dic5—21no—
94C22×Dic5—21no—
95C22×Dic5—42no—
96C22×Dic5—42no—
97C22×Dic5C22⋊C412yes—
98C22×Dic5C22⋊C412yes—
99C22×Dic5C22⋊C412yes—
100C22×Dic5C2×C812yes—
101C22×Dic5C2×C812yes—
102C22×Dic5M1612yes—
103C22×Dic5M1612yes—
104C22×Dic5C2×D412yes—
105C22×Dic5C2×D412yes—
106C22×Dic5C2×D412yes—
107C2×#170—48no—
108C2×#170—44no—
109C5×C22⋊C4—28no—
110C22⋊Dic5—28no—
111#683—28no—
112#683—28no—
113C4×Dic5—28no—
114C4×Dic5—28no—
115C24×C4—51no—
116C2×#117—104no—
117C2×#117—104no—
118C2×#117—104no—
119C22×C4⋊C4—51no—
120C22×C4⋊C4—51no—
121C22×C22⋊C4—51no—
122C22×C22⋊C4AGL(1,𝔽5)11yescharacteristic
123C22×C42—51no—
124C22×C42—51no—
125C2×C22⋊C8—54no—
126#336—104no—
127#324—104no—
128#323—104no—
129C23×C5—22no—
130C23×C5—22no—
131C23×C5—22no—
132C23×C5—22no—
133C23×C5—22no—
134C23×C5—22no—
135C23×C5—22no—
136C23×C5—22no—
137C23×C5—42no—
138C23×C5—42no—
139C23×C5—44no—
140C23×C5—44no—
141C23×C5—44no—
142C23×C5—44no—
143C23×C5—42no—
144C23×C5—42no—
145C23×C5—42no—
146C23×C5—42no—
147C23×C5C22⋊C814yes—
148C23×C5C2×C22⋊C411yescharacteristic
149C23×C5C2×C22⋊C411yescharacteristic
150C23×C5C2×C22⋊C411yescharacteristic
151C23×C5C22×C811yescharacteristic
152C23×C5C2×M1611yescharacteristic
153C23×C5C2×M1611yescharacteristic
154C23×C5C2×M1611yescharacteristic
155C2×C4×C5—22no—
156C2×C4×C5—22no—
157C2×C4×C5—24no—
158C2×C4×C5—42no—
159C2×C4×C5—42no—
160C2×C4×C5—42no—
161C2×C4×C5—42no—
162C2×C4×C5—42no—
163C2×Dic5—232no—
164C2×Dic5—22no—
165C2×Dic5—22no—
166C2×Dic5—22no—
167C2×Dic5—22no—
168C2×Dic5—22no—
169C2×Dic5—22no—
170C2×Dic5—22no—
171C2×Dic5—22no—
172C2×Dic5—22no—
173C2×Dic5—22no—
174C2×Dic5—22no—
175C2×Dic5—22no—
176C2×Dic5—24no—
177C2×Dic5—22no—
178C2×Dic5—42no—
179C2×Dic5—42no—
180C2×Dic5—42no—
181C2×Dic5—42no—
182C2×Dic5—42no—
183C2×Dic5C22⋊C814yes—
184C2×Dic5C22⋊C814yes—
185C2×Dic5#12014yes—
186#170—84no—
187C25C2×AGL(1,𝔽5)11yescharacteristic
188C23×C4—51no—
189C23×C4—51no—
190C23×C4—51no—
191C23×C4—54no—
192C23×C4—51no—
193C23×C4—102no—
194C23×C4—102no—
195C23×C4—102no—
196C23×C4—102no—
197C23×C4—102no—
198C23×C4—102no—
199C23×C4C2×AGL(1,𝔽5)11yescharacteristic
200C23×C4C2×AGL(1,𝔽5)11yescharacteristic
201C22×C8—104no—
202#117—1032no—
203C2×C4⋊C4—54no—
204C2×C4⋊C4—102no—
205C2×C4⋊C4—102no—
206C2×C4⋊C4—102no—
207C2×C4⋊C4—102no—
208C2×C4⋊C4—102no—
209C2×C22⋊C4—22no—
210C2×C22⋊C4—22no—
211C2×C22⋊C4—22no—
212C2×C22⋊C4—54no—
213C2×C22⋊C4—102no—
214C2×C22⋊C4—102no—
215C2×C42—54no—
216C2×C42—102no—
217C2×C42—102no—
218C2×C42—102no—
219C2×C42—102no—
220C2×C42—102no—
221C22⋊C8—104no—
222C22⋊C8—104no—
223C22×C5—22no—
224C22×C5—22no—
225C22×C5—22no—
226C22×C5—22no—
227C22×C5—21no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—24no—
232C22×C5—44no—
233C22×C5—44no—
234C22×C5—44no—
235C22×C5—44no—
236C22×C5—44no—
237C22×C5—44no—
238C22×C5—42no—
239C22×C5—42no—
240C22×C5#37911yescharacteristic
241C22×C5C2×C22⋊C811yescharacteristic
242C22×C5C2×C22⋊C811yescharacteristic
243C22×C5C2×C22⋊C811yescharacteristic
244C22×C5#40711yescharacteristic
245C22×C5#40711yescharacteristic
246C22×C5#40711yescharacteristic
247C22×C5#41012yes—
248C22×C5#41312yes—
249C4×C5—42no—
250C4×C5—42no—
251Dic5—24no—
252Dic5—24no—
253Dic5—24no—
254Dic5—42no—
255C24—21no—
256C24—21no—
257C24—21no—
258C24—21no—
259C24—42no—
260C24—42no—
261C24D5⋊C812yes—
262C24#70012yes—
263C24C22⋊AGL(1,𝔽5)12yes—
264C24C22×AGL(1,𝔽5)11yescharacteristic
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—42no—
270C22×C4—42no—
271C22×C4—52no—
272C22×C4—52no—
273C22×C4—52no—
274C22×C4—52no—
275C22×C4—52no—
276C22×C4—52no—
277C22×C4—52no—
278C22×C4—52no—
279C22×C4—52no—
280C22×C4—52no—
281C22×C4—108no—
282C22×C4—108no—
283C22×C4—108no—
284C22×C4—108no—
285C22×C4—108no—
286C22×C4—108no—
287C22×C4—101no—
288C22×C4—101no—
289C22×C4—101no—
290C22×C4—101no—
291C22×C4—101no—
292C22×C4—101no—
293C22×C4—101no—
294C22×C4—101no—
295C22×C4—108no—
296C22×C4—101no—
297C22×C4—101no—
298C22×C4—202no—
299C22×C4—202no—
300C22×C4C22⋊AGL(1,𝔽5)12yes—
301C22×C4C22⋊AGL(1,𝔽5)12yes—
302C2×C8—204no—
303C2×C8—208no—
304C4⋊C4—108no—
305C4⋊C4—108no—
306C22⋊C4—28no—
307C22⋊C4—108no—
308C42—108no—
309C42—108no—
310C2×C5—21no—
311C2×C5—21no—
312C2×C5—21no—
313C2×C5—21no—
314C2×C5—44no—
315C2×C5#145812yes—
316C2×C5#146412yes—
317C2×C5#177911yescharacteristic
318C2×C5#178211yescharacteristic
319C2×C5#178511yescharacteristic
320C23—22no—
321C23—22no—
322C23—22no—
323C23—22no—
324C23—22no—
325C23—22no—
326C23—22no—
327C23—22no—
328C23—44no—
329C23—44no—
330C23—42no—
331C23—42no—
332C23—42no—
333C23—42no—
334C23—44no—
335C23—44no—
336C23—42no—
337C23—42no—
338C23#400314yes—
339C23C2×D5⋊C811yescharacteristic
340C23C2×#70011yescharacteristic
341C23D5⋊M1611yescharacteristic
342C23D5⋊M1611yescharacteristic
343C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
344C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
345C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
346C2×C4—22no—
347C2×C4—22no—
348C2×C4—24no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—42no—
352C2×C4—42no—
353C2×C4—42no—
354C2×C4—54no—
355C2×C4—54no—
356C2×C4—54no—
357C2×C4—1032no—
358C2×C4—102no—
359C2×C4—102no—
360C2×C4—102no—
361C2×C4—102no—
362C2×C4—102no—
363C2×C4—102no—
364C2×C4—102no—
365C2×C4—102no—
366C2×C4—102no—
367C2×C4—102no—
368C2×C4—102no—
369C2×C4—102no—
370C2×C4—104no—
371C2×C4—102no—
372C2×C4—202no—
373C2×C4—202no—
374C2×C4—202no—
375C2×C4—202no—
376C2×C4—202no—
377C8—404no—
378C5#830011yescharacteristic, complemented, Sylow
379C22—21no—
380C22—21no—
381C22—21no—
382C22—21no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—24no—
388C22—44no—
389C22—44no—
390C22—44no—
391C22—44no—
392C22—42no—
393C22—42no—
394C22—44no—
395C22—44no—
396C22C2×#400311yescharacteristic
397C22D5⋊(C22⋊C8)11yescharacteristic
398C22D5⋊(C22⋊C8)11yescharacteristic
399C22#6575511yescharacteristic
400C22#6575611yescharacteristic
401C22#6575611yescharacteristic
402C22#6577112yes—
403C22#6577712yes—
404C22#6580011yescharacteristic
405C4—42no—
406C4—42no—
407C4—104no—
408C4—104no—
409C4—104no—
410C4—202no—
411C2—21no—
412C2—21no—
413C2—21no—
414C2—21no—
415C2—44no—
416C2#1060420012yes—
417C2#1060420312yes—
418C2#1060489811yescharacteristic
419C2#1060494211yescharacteristic
420C2#1060495111yescharacteristic
subgroupG/H
centerC23C2×C22⋊AGL(1,𝔽5)
commutatorC23×C5C22×C8
FrattiniC24C22×AGL(1,𝔽5)
FittingC22×C5×C22⋊C4C4
socleC23×C5C2×C22⋊C4
prime radicalC25×C5C2×C4
cosocleC23×Dic5C23
hypercenterC22×C22⋊C4AGL(1,𝔽5)
hypocenterC5#8300
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. #10604902C2semidirect
4. C2×#64914C2semidirect
29. C23×Dic5C8semidirect
378. C5#8300semidirect

Maximal subgroups

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

subgroupindex
C22×#40232
C2×#649332
#106049022
C2×#649142
#83005