Finite Group Databasebeta

← #12003708

Subgroups — #12003708

Order 1280.

560 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 560 conjugacy classes of subgroups — too many to draw. Only its 119 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#10605092C211yesmaximal, characteristic
2C5×#1442C211yesmaximal, characteristic
3#10602349C212yesmaximal
4#10598104C211yesmaximal, characteristic
5#10598103C212yesmaximal
6C22×C5×C4⋊C4C2211yescharacteristic
7C2×#4070—21no—
8C2×C5×#95—21no—
9C2×C5×#95—21no—
10C2×C5×#95C2211yescharacteristic
11C2×C5×#95C2211yescharacteristic
12#65501—21no—
13#65501C2212yes—
14C2×C22⋊#168C2212yes—
15C2×#3940—22no—
16#64950—22no—
17#64945—22no—
18#64749—22no—
19#10568—51nomaximal, Sylow
20C23×C4×C5—21no—
21C23×C4×C5—21no—
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C22×Dic10—21no—
26C2×C5×C4⋊C4—22no—
27C2×C5×C4⋊C4—42no—
28C2×C22⋊Dic5—22no—
29C2×C4⋊Dic5—21no—
30C2×C4⋊Dic5—21no—
31C2×C4⋊Dic5—21no—
32C2×C4⋊Dic5D412yes—
33C2×C4⋊Dic5D412yes—
34#4070—42no—
35#4070—42no—
36C2×#683—22no—
37C22×#168—22no—
38C5×#95—22no—
39C5×#95—21no—
40C5×#95—42no—
41C5×#95—42no—
42C5×#95Q812yescomplemented
43#3963—22no—
44#3963—22no—
45C22⋊#168—22no—
46C22⋊#168Q814yescomplemented
47#3940—44no—
48#2659—51no—
49#1853—52no—
50#1442D511yescharacteristic
51#1294—52no—
52#1280—51no—
53C24×C5C2×D411yescharacteristic
54C22×C4×C5—21no—
55C22×C4×C5—21no—
56C22×C4×C5—21no—
57C22×C4×C5—21no—
58C22×C4×C5—22no—
59C22×C4×C5—22no—
60C22×C4×C5—41no—
61C22×C4×C5—41no—
62C22×C4×C5—41no—
63C22×C4×C5—41no—
64C22×C4×C5—41no—
65C22×C4×C5—41no—
66C22×C4×C5—41no—
67C22×C4×C5—41no—
68C22×C4×C5—41no—
69C22×C4×C5—41no—
70C22×C4×C5—41no—
71C22×C4×C5—41no—
72C22×C4×C5—41no—
73C22×C4×C5—41no—
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5SD1612yes—
79C22×C4×C5SD1612yes—
80C22×C4×C5C2×D412yes—
81C22×C4×C5C2×Q811yescharacteristic
82C22×C4×C5C2×Q812yes—
83C22×C4×C5#4111yescharacteristic
84C22×Dic5—22no—
85C22×Dic5—22no—
86C2×Dic10—42no—
87C2×Dic10—81no—
88C2×Dic10—81no—
89C5×C4⋊C4—24no—
90C5×C4⋊C4—42no—
91C22⋊Dic5—42no—
92C22⋊Dic5—42no—
93C4⋊Dic5—42no—
94C4⋊Dic5—42no—
95C4⋊Dic5—42no—
96C4⋊Dic5—81no—
97C4⋊Dic5—81no—
98#683—44no—
99C2×#168—24no—
100C2×#168—42no—
101C2×#168—42no—
102C2×C22⋊Q8—101no—
103C22×C4⋊C4C2×D511yescharacteristic
104C2×#106—102no—
105C2×C22⋊C8—52no—
106#398—102no—
107#395—102no—
108#380—52no—
109#380—101no—
110C2×#95—21no—
111C2×#95—21no—
112C2×#95C2×D511yescharacteristic
113C2×#95C2×D511yescharacteristic
114#340—102no—
115C23×C5—21no—
116C23×C5—21no—
117C23×C5—21no—
118C23×C5—21no—
119C23×C5#12011yescharacteristic
120C23×C5C22⋊Q811yescharacteristic
121C23×C5C4⋊Q811yescharacteristic
122C23×C5C2×SD1611yescharacteristic
123C23×C5C2×SD1611yescharacteristic
124C23×C5AGL(1,ℤ/8)11yescharacteristic
125C23×C5#13711yescharacteristic
126C2×C4×C5—22no—
127C2×C4×C5—22no—
128C2×C4×C5—22no—
129C2×C4×C5—22no—
130C2×C4×C5—41no—
131C2×C4×C5—42no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—42no—
138C2×C4×C5—42no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5—81no—
146C2×C4×C5—81no—
147C2×C4×C5—81no—
148C2×C4×C5—81no—
149C2×C4×C5—81no—
150C2×C4×C5—81no—
151C2×C4×C5—81no—
152C2×C4×C5—81no—
153C2×C4×C5—81no—
154C2×C4×C5—81no—
155C2×C4×C5C22⋊Q812yes—
156C2×C4×C5C4⋊Q812yes—
157C2×Dic5—42no—
158C2×Dic5—42no—
159C2×Dic5—42no—
160C2×Dic5—42no—
161C2×Dic5—42no—
162C2×Dic5—42no—
163Dic10—84no—
164#168—44no—
165C22×Q8—101no—
166C23×C4—21no—
167C23×C4—21no—
168C23×C4C22⋊D511yescharacteristic
169C23×C4C22⋊D511yescharacteristic
170C23×C4C22×D511yescharacteristic
171C22×C8—102no—
172C22⋊Q8—202no—
173C22⋊Q8—202no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—42no—
176C2×C4⋊C4—52no—
177C2×C4⋊C4—52no—
178C2×C4⋊C4—102no—
179C2×C4⋊C4—101no—
180C2×C4⋊C4—101no—
181C2×C4⋊C4—101no—
182C2×C22⋊C4—102no—
183#106—204no—
184C22⋊C8—54no—
185C22⋊C8—102no—
186#95—21no—
187#95—22no—
188#95—42no—
189#95—42no—
190#95—102no—
191#95—102no—
192#95Dic1012yescomplemented
193C22×C5—21no—
194C22×C5—21no—
195C22×C5—21no—
196C22×C5—21no—
197C22×C5—21no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5#39511yescharacteristic
206C22×C5#44811yescharacteristic
207C22×C5#45011yescharacteristic
208C22×C5#45411yescharacteristic
209C22×C5#45511yescharacteristic
210C22×C5B(4,𝔽2)11yescharacteristic
211C22×C5#45811yescharacteristic
212C22×C5#47511yescharacteristic
213C22×C5#47611yescharacteristic
214C22×C5#49811yescharacteristic
215C22×C5#50111yescharacteristic
216C4×C5—22no—
217C4×C5—22no—
218C4×C5—42no—
219C4×C5—42no—
220C4×C5—82no—
221C4×C5—82no—
222Dic5—82no—
223Dic5—82no—
224C24C2×C22⋊D511yescharacteristic
225C2×Q8—202no—
226C2×Q8—401no—
227C2×Q8—401no—
228C22×C4—21no—
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—22no—
233C22×C4—22no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4—41no—
238C22×C4—41no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—102no—
253C22×C4—102no—
254C22×C4#68712yes—
255C22×C4#68812yes—
256C22×C4C2×Dic1011yescharacteristic
257C22×C4#70911yescharacteristic
258C22×C4D4×D512yes—
259C22×C4Q8×D512yes—
260C2×C8—104no—
261C2×C8—202no—
262C2×C8—202no—
263C4⋊C4—24no—
264C4⋊C4—42no—
265C4⋊C4—202no—
266C4⋊C4—202no—
267C4⋊C4—204no—
268C4⋊C4—202no—
269C4⋊C4—401no—
270C4⋊C4—401no—
271C22⋊C4—202no—
272C22⋊C4—202no—
273C2×C5—21no—
274C2×C5—21no—
275C2×C5—21no—
276C2×C5—21no—
277C2×C5#159911yescharacteristic
278C2×C5#160111yescharacteristic
279C2×C5#160811yescharacteristic
280C2×C5#161611yescharacteristic
281C2×C5#205811yescharacteristic
282C2×C5#206111yescharacteristic
283C2×C5#206211yescharacteristic
284C23—21no—
285C23—21no—
286C23—21no—
287C23—21no—
288C23#407011yescharacteristic
289C23C2×#68711yescharacteristic
290C23#408311yescharacteristic
291C23C2×#68811yescharacteristic
292C23#409011yescharacteristic
293C23#409511yescharacteristic
294C23#409711yescharacteristic
295Q8—404no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—22no—
300C2×C4—41no—
301C2×C4—41no—
302C2×C4—42no—
303C2×C4—41no—
304C2×C4—41no—
305C2×C4—41no—
306C2×C4—41no—
307C2×C4—42no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—42no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—81no—
324C2×C4—81no—
325C2×C4—202no—
326C2×C4—202no—
327C2×C4—202no—
328C2×C4—202no—
329C2×C4—202no—
330C2×C4—202no—
331C2×C4#403412yes—
332C2×C4#404212yes—
333C8—204no—
334C5#1056811yescharacteristic, complemented, Sylow
335C22—21no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22#6526811yescharacteristic
348C22#6529711yescharacteristic
349C22#6530911yescharacteristic
350C22#6532111yescharacteristic
351C22#6532911yescharacteristic
352C22#6533511yescharacteristic
353C22#6534211yescharacteristic
354C22#6535011yescharacteristic
355C22#6535111yescharacteristic
356C22#6535411yescharacteristic
357C22#6536811yescharacteristic
358C4—22no—
359C4—22no—
360C4—42no—
361C4—42no—
362C4—82no—
363C4—82no—
364C4—402no—
365C4—402no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2#1060033611yescharacteristic
371C2#1060038711yescharacteristic
372C2#1060039811yescharacteristic
373C2#1060049211yescharacteristic
374C2#1060049711yescharacteristic
375C2#1060050311yescharacteristic
376C2#1060051111yescharacteristic
subgroupG/H
centerC23#4083
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#1442C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenter#1442D5
hypocenterC5#10568
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1442

Complements

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

NH ≅ G/Ntype
42. C5×#95Q8semidirect
46. C22⋊#168Q8semidirect
192. #95Dic10semidirect
334. C5#10568semidirect

Maximal subgroups

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

subgroupindex
#106050922
C5×#14422
#106023492
#105981042
#105981032
#105685