Finite Group Databasebeta

← #12002650

Subgroups — #12002650

Order 1280.

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

normal subgroups only

This group has 576 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
1C5×#2659C211yesmaximal, characteristic
2#10602485C212yesmaximal
3C2×#64758C212yesmaximal
4#10600208C211yesmaximal, characteristic
5#10598104C211yesmaximal, characteristic
6C2×C5×C22⋊Q8C2212yes—
7C22×C4⋊Dic5C2211yescharacteristic
8C5×#398—22no—
9C5×#395—22no—
10C5×#380—21no—
11C5×#380—21no—
12C2×C5×#95C2211yescharacteristic
13C2×#3967—22no—
14C2×#3963—21no—
15C2×#3963—21no—
16C2×#3963C2211yescharacteristic
17C2×C22⋊#168C2212yes—
18#64758—24no—
19#64749—22no—
20#10407—51nomaximal, Sylow
21C22×C5×Q8D412yes—
22C23×C4×C5D411yescharacteristic
23C23×C4×C5D411yescharacteristic
24C23×C4×C5C2311yescharacteristic
25C23×Dic5—21no—
26C23×Dic5—21no—
27C5×C22⋊Q8—22no—
28C5×C22⋊Q8—22no—
29C5×C22⋊Q8—22no—
30C5×C22⋊Q8—22no—
31C2×C5×C4⋊C4—22no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4—21no—
36C2×C5×C4⋊C4D412yes—
37C2×C5×C22⋊C4—22no—
38C2×C4⋊Dic5—22no—
39C2×C4⋊Dic5—42no—
40C22×#168—22no—
41C5×#95—22no—
42C5×#95—22no—
43C5×#95—22no—
44#3967—44no—
45#3963—21no—
46#3963—42no—
47#3963—42no—
48#3963D412yes—
49C22⋊#168—22no—
50C22⋊#168—22no—
51#2659D511yescharacteristic
52#1872—52no—
53C2×#328—52no—
54#1442—51no—
55#1280—51no—
56C24×C5C2×D411yescharacteristic
57C2×C5×Q8—22no—
58C2×C5×Q8—22no—
59C2×C5×Q8—42no—
60C2×C5×Q8—42no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—22no—
66C22×C4×C5—22no—
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×C5SD1612yes—
74C22×C4×C5Q1612yes—
75C22×C4×C5C2×D411yescharacteristic
76C22×C4×C5C2×D412yes—
77C22×C4×C5#4112yes—
78C22×C4×C5#4111yescharacteristic
79C22×Dic5—22no—
80C22×Dic5—22no—
81C22×Dic5—41no—
82C22×Dic5—41no—
83C22×Dic5—41no—
84C22×Dic5—41no—
85C22×Dic5—41no—
86C22×Dic5—41no—
87C22×Dic5—41no—
88C22×Dic5—41no—
89C22×Dic5—41no—
90C22×Dic5—41no—
91C22×Dic5—41no—
92C22×Dic5—41no—
93C5×C4⋊C4—22no—
94C5×C4⋊C4—22no—
95C5×C4⋊C4—42no—
96C5×C4⋊C4—42no—
97C5×C4⋊C4—81no—
98C5×C4⋊C4—81no—
99C5×C4⋊C4—81no—
100C5×C4⋊C4—81no—
101C5×C22⋊C4—42no—
102C5×C22⋊C4—42no—
103C4⋊Dic5—24no—
104C4⋊Dic5—42no—
105C2×#168—42no—
106C2×#168—42no—
107C2×#168—42no—
108C2×C22⋊Q8C2×D512yes—
109C22×C4⋊C4—51no—
110C2×#103—102no—
111C2×C22⋊C8—52no—
112#398—22no—
113#395—22no—
114#380—21no—
115#380—21no—
116C2×#95—51no—
117C2×#95—101no—
118C2×#95—101no—
119C2×#95C2×D511yescharacteristic
120#340—102no—
121#328—104no—
122C23×C5—21no—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5#12011yescharacteristic
127C23×C5#12111yescharacteristic
128C23×C5#12411yescharacteristic
129C23×C5C2×SD1611yescharacteristic
130C23×C5C2×Q1611yescharacteristic
131C23×C5#13711yescharacteristic
132C23×C5#13711yescharacteristic
133C5×Q8—44no—
134C5×Q8—82no—
135C2×C4×C5—22no—
136C2×C4×C5—22no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
139C2×C4×C5—41no—
140C2×C4×C5—42no—
141C2×C4×C5—41no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—42no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—81no—
155C2×C4×C5—81no—
156C2×C4×C5#12112yes—
157C2×C4×C5#12312yes—
158C2×Dic5—42no—
159C2×Dic5—42no—
160C2×Dic5—42no—
161C2×Dic5—42no—
162C2×Dic5—42no—
163C2×Dic5—42no—
164C2×Dic5—81no—
165C2×Dic5—81no—
166C2×Dic5—81no—
167C2×Dic5—81no—
168C2×Dic5—81no—
169C2×Dic5—81no—
170C2×Dic5—81no—
171C2×Dic5—81no—
172#168—82no—
173C22×Q8C22⋊D512yes—
174C23×C4—101no—
175C23×C4—101no—
176C23×C4C22⋊D511yescharacteristic
177C23×C4C22⋊D511yescharacteristic
178C23×C4C22×D511yescharacteristic
179C22×C8—102no—
180C22⋊Q8—22no—
181C22⋊Q8—22no—
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C2×C4⋊C4—22no—
185C2×C4⋊C4—21no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—21no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—102no—
190C2×C4⋊C4—202no—
191C2×C4⋊C4C22⋊D512yes—
192C2×C22⋊C4—22no—
193#103—204no—
194C22⋊C8—102no—
195C22⋊C8—102no—
196#95—22no—
197#95—22no—
198#95—22no—
199#95—52no—
200#95—101no—
201#95—202no—
202#95—202no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5#39411yescharacteristic
216C22×C5#44811yescharacteristic
217C22×C5#45111yescharacteristic
218C22×C5#45411yescharacteristic
219C22×C5#45511yescharacteristic
220C22×C5B(4,𝔽2)11yescharacteristic
221C22×C5#45811yescharacteristic
222C22×C5#46111yescharacteristic
223C22×C5#46211yescharacteristic
224C22×C5#48711yescharacteristic
225C22×C5#49111yescharacteristic
226C4×C5—22no—
227C4×C5—22no—
228C4×C5—42no—
229C4×C5—42no—
230C4×C5—82no—
231C4×C5—82no—
232Dic5—82no—
233Dic5—82no—
234C24C2×C22⋊D511yescharacteristic
235C2×Q8—22no—
236C2×Q8—22no—
237C2×Q8—42no—
238C2×Q8—42no—
239C22×C4—21no—
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—21no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4—41no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—102no—
252C22×C4—102no—
253C22×C4—201no—
254C22×C4—201no—
255C22×C4—201no—
256C22×C4—201no—
257C22×C4—201no—
258C22×C4—201no—
259C22×C4—201no—
260C22×C4—201no—
261C22×C4—201no—
262C22×C4—201no—
263C22×C4—201no—
264C22×C4—201no—
265C22×C4#68812yes—
266C22×C4#68912yes—
267C22×C4D4×D511yescharacteristic
268C22×C4#71111yescharacteristic
269C22×C4#71112yes—
270C22×C4C2×C22⋊D512yes—
271C2×C8—202no—
272C2×C8—202no—
273C2×C8—202no—
274C4⋊C4—22no—
275C4⋊C4—22no—
276C4⋊C4—42no—
277C4⋊C4—42no—
278C4⋊C4—81no—
279C4⋊C4—81no—
280C4⋊C4—81no—
281C4⋊C4—81no—
282C4⋊C4—104no—
283C4⋊C4—202no—
284C22⋊C4—42no—
285C22⋊C4—42no—
286C2×C5—21no—
287C2×C5—21no—
288C2×C5—21no—
289C2×C5—21no—
290C2×C5#159911yescharacteristic
291C2×C5#160211yescharacteristic
292C2×C5#160811yescharacteristic
293C2×C5#161711yescharacteristic
294C2×C5#204011yescharacteristic
295C2×C5#204311yescharacteristic
296C2×C5#204411yescharacteristic
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23#408211yescharacteristic
302C23#408411yescharacteristic
303C23C2×#68811yescharacteristic
304C23#408811yescharacteristic
305C23#408811yescharacteristic
306C23C2×#68911yescharacteristic
307C23#409911yescharacteristic
308Q8—44no—
309Q8—82no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—41no—
315C2×C4—42no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—42no—
325C2×C4—42no—
326C2×C4—42no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—81no—
330C2×C4—81no—
331C2×C4—202no—
332C2×C4—202no—
333C2×C4—202no—
334C2×C4—202no—
335C2×C4—202no—
336C2×C4—202no—
337C2×C4—401no—
338C2×C4—401no—
339C2×C4—401no—
340C2×C4—401no—
341C2×C4—401no—
342C2×C4—401no—
343C2×C4—401no—
344C2×C4—401no—
345C2×C4#408112yes—
346C2×C4#408512yes—
347C8—402no—
348C5#1040711yescharacteristic, complemented, Sylow
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22#6537011yescharacteristic
362C22#6537111yescharacteristic
363C22#6537211yescharacteristic
364C22#6537911yescharacteristic
365C22#6551111yescharacteristic
366C22#6551611yescharacteristic
367C22#6551711yescharacteristic
368C22#6553111yescharacteristic
369C22#6553211yescharacteristic
370C22#6553311yescharacteristic
371C22#6553411yescharacteristic
372C4—22no—
373C4—22no—
374C4—42no—
375C4—42no—
376C4—82no—
377C4—82no—
378C4—402no—
379C4—402no—
380C2—21no—
381C2—21no—
382C2—21no—
383C2—21no—
384C2#1060257411yescharacteristic
385C2#1060264311yescharacteristic
386C2#1060267011yescharacteristic
387C2#1060268311yescharacteristic
388C2#1060268611yescharacteristic
389C2#1060269211yescharacteristic
390C2#1060269511yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#2659C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenter#2659D5
hypocenterC5#10407
LCSG ▷ C23×C4×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2659

Complements

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

NH ≅ G/Ntype
348. C5#10407semidirect

Maximal subgroups

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

subgroupindex
C5×#26592
#106024852
C2×#647582
#106002082
#105981042
#104075