Finite Group Databasebeta

← #12002645

Subgroups — #12002645

Order 1280.

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

normal subgroups only

This group has 620 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#10600213C211yesmaximal, characteristic
5#10598104C211yesmaximal, characteristic
6C2×C5×C22⋊Q8C2212yes—
7C22×C4⋊Dic5C2211yescharacteristic
8C22×#683—21no—
9C5×#398—22no—
10C5×#395—22no—
11C5×#380—21no—
12C5×#380—21no—
13C2×C5×#95C2211yescharacteristic
14C2×#3967—22no—
15C2×#3963—21no—
16C2×#3963C2211yescharacteristic
17C2×C22⋊#168C2212yes—
18#64758—24no—
19#64749—22no—
20#10406—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—
40C2×#683—42no—
41C2×#683—42no—
42C2×#683—42no—
43C22×#168—22no—
44C5×#95—22no—
45C5×#95—22no—
46C5×#95—22no—
47#3967—44no—
48#3963—21no—
49#3963—42no—
50#3963D412yes—
51C22⋊#168—22no—
52C22⋊#168—22no—
53#2659D511yescharacteristic
54#1872—52no—
55C2×#328—52no—
56#1444—51no—
57#1280—51no—
58C24×C5C2×D411yescharacteristic
59C2×C5×Q8—22no—
60C2×C5×Q8—22no—
61C2×C5×Q8—42no—
62C2×C5×Q8—42no—
63C22×C4×C5—21no—
64C22×C4×C5—21no—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—22no—
68C22×C4×C5—22no—
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×C5SD1612yes—
76C22×C4×C5Q1612yes—
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D412yes—
79C22×C4×C5#4112yes—
80C22×C4×C5#4111yescharacteristic
81C22×Dic5—22no—
82C22×Dic5—22no—
83C22×Dic5—22no—
84C22×Dic5—22no—
85C22×Dic5—41no—
86C22×Dic5—41no—
87C22×Dic5—41no—
88C22×Dic5—41no—
89C22×Dic5—41no—
90C22×Dic5—41no—
91C22×Dic5—41no—
92C22×Dic5—41no—
93C22×Dic5—41no—
94C22×Dic5—41no—
95C5×C4⋊C4—22no—
96C5×C4⋊C4—22no—
97C5×C4⋊C4—42no—
98C5×C4⋊C4—42no—
99C5×C4⋊C4—81no—
100C5×C4⋊C4—81no—
101C5×C4⋊C4—81no—
102C5×C4⋊C4—81no—
103C5×C22⋊C4—42no—
104C5×C22⋊C4—42no—
105C4⋊Dic5—24no—
106C4⋊Dic5—42no—
107#683—48no—
108C2×#168—42no—
109C2×#168—42no—
110C2×#168—42no—
111C2×C22⋊Q8C2×D512yes—
112C22×C4⋊C4—51no—
113C22×C4⋊C4—101no—
114C2×#103—102no—
115C2×C22⋊C8—52no—
116#398—22no—
117#395—22no—
118#380—21no—
119#380—21no—
120C2×#95—51no—
121C2×#95—101no—
122C2×#95C2×D511yescharacteristic
123#340—102no—
124#328—104no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5#12011yescharacteristic
130C23×C5#12111yescharacteristic
131C23×C5#12411yescharacteristic
132C23×C5C2×SD1611yescharacteristic
133C23×C5C2×Q1611yescharacteristic
134C23×C5#13711yescharacteristic
135C23×C5#13711yescharacteristic
136C5×Q8—44no—
137C5×Q8—82no—
138C2×C4×C5—22no—
139C2×C4×C5—22no—
140C2×C4×C5—22no—
141C2×C4×C5—22no—
142C2×C4×C5—41no—
143C2×C4×C5—42no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—42no—
150C2×C4×C5—42no—
151C2×C4×C5—42no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5—42no—
156C2×C4×C5—42no—
157C2×C4×C5—81no—
158C2×C4×C5—81no—
159C2×C4×C5#12112yes—
160C2×C4×C5#12312yes—
161C2×Dic5—24no—
162C2×Dic5—42no—
163C2×Dic5—42no—
164C2×Dic5—42no—
165C2×Dic5—42no—
166C2×Dic5—42no—
167C2×Dic5—42no—
168C2×Dic5—42no—
169C2×Dic5—42no—
170C2×Dic5—42no—
171C2×Dic5—81no—
172C2×Dic5—81no—
173C2×Dic5—81no—
174C2×Dic5—81no—
175#168—82no—
176C22×Q8C22⋊D512yes—
177C23×C4—101no—
178C23×C4—101no—
179C23×C4C22⋊D511yescharacteristic
180C23×C4C22⋊D511yescharacteristic
181C23×C4C22×D511yescharacteristic
182C22×C8—102no—
183C22⋊Q8—22no—
184C22⋊Q8—22no—
185C22⋊Q8—22no—
186C22⋊Q8—22no—
187C2×C4⋊C4—22no—
188C2×C4⋊C4—21no—
189C2×C4⋊C4—21no—
190C2×C4⋊C4—21no—
191C2×C4⋊C4—21no—
192C2×C4⋊C4—102no—
193C2×C4⋊C4—202no—
194C2×C4⋊C4—202no—
195C2×C4⋊C4—202no—
196C2×C4⋊C4—202no—
197C2×C4⋊C4C22⋊D512yes—
198C2×C22⋊C4—22no—
199#103—204no—
200C22⋊C8—102no—
201C22⋊C8—102no—
202#95—22no—
203#95—22no—
204#95—22no—
205#95—52no—
206#95—101no—
207#95—202no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—21no—
216C22×C5—21no—
217C22×C5—21no—
218C22×C5—21no—
219C22×C5—21no—
220C22×C5#39411yescharacteristic
221C22×C5#44811yescharacteristic
222C22×C5#45111yescharacteristic
223C22×C5#45311yescharacteristic
224C22×C5#45611yescharacteristic
225C22×C5B(4,𝔽2)11yescharacteristic
226C22×C5#45811yescharacteristic
227C22×C5#46111yescharacteristic
228C22×C5#46211yescharacteristic
229C22×C5#48711yescharacteristic
230C22×C5#49111yescharacteristic
231C4×C5—22no—
232C4×C5—22no—
233C4×C5—42no—
234C4×C5—42no—
235C4×C5—82no—
236C4×C5—82no—
237Dic5—44no—
238Dic5—82no—
239C24C2×C22⋊D511yescharacteristic
240C2×Q8—22no—
241C2×Q8—22no—
242C2×Q8—42no—
243C2×Q8—42no—
244C22×C4—21no—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—22no—
249C22×C4—22no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4—41no—
254C22×C4—41no—
255C22×C4—41no—
256C22×C4—102no—
257C22×C4—102no—
258C22×C4—102no—
259C22×C4—102no—
260C22×C4—201no—
261C22×C4—201no—
262C22×C4—201no—
263C22×C4—201no—
264C22×C4—201no—
265C22×C4—201no—
266C22×C4—201no—
267C22×C4—201no—
268C22×C4—201no—
269C22×C4—201no—
270C22×C4#68812yes—
271C22×C4#68912yes—
272C22×C4D4×D511yescharacteristic
273C22×C4#71111yescharacteristic
274C22×C4#71112yes—
275C22×C4C2×C22⋊D512yes—
276C2×C8—202no—
277C2×C8—202no—
278C2×C8—202no—
279C4⋊C4—22no—
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—42no—
283C4⋊C4—81no—
284C4⋊C4—81no—
285C4⋊C4—81no—
286C4⋊C4—81no—
287C4⋊C4—104no—
288C4⋊C4—202no—
289C4⋊C4—208no—
290C22⋊C4—42no—
291C22⋊C4—42no—
292C2×C5—21no—
293C2×C5—21no—
294C2×C5—21no—
295C2×C5—21no—
296C2×C5#159611yescharacteristic
297C2×C5#160511yescharacteristic
298C2×C5#161111yescharacteristic
299C2×C5#161411yescharacteristic
300C2×C5#203911yescharacteristic
301C2×C5#204311yescharacteristic
302C2×C5#204411yescharacteristic
303C23—21no—
304C23—21no—
305C23—21no—
306C23—21no—
307C23#408211yescharacteristic
308C23#408411yescharacteristic
309C23C2×#68811yescharacteristic
310C23#408811yescharacteristic
311C23#408811yescharacteristic
312C23C2×#68911yescharacteristic
313C23#409911yescharacteristic
314Q8—44no—
315Q8—82no—
316C2×C4—22no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—22no—
320C2×C4—41no—
321C2×C4—42no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—42no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—42no—
333C2×C4—42no—
334C2×C4—42no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—104no—
338C2×C4—202no—
339C2×C4—202no—
340C2×C4—202no—
341C2×C4—202no—
342C2×C4—202no—
343C2×C4—202no—
344C2×C4—202no—
345C2×C4—202no—
346C2×C4—202no—
347C2×C4—401no—
348C2×C4—401no—
349C2×C4—401no—
350C2×C4—401no—
351C2×C4#408112yes—
352C2×C4#408512yes—
353C8—402no—
354C5#1040611yescharacteristic, complemented, Sylow
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—21no—
361C22—21no—
362C22—21no—
363C22—21no—
364C22—21no—
365C22—21no—
366C22—21no—
367C22#6537011yescharacteristic
368C22#6537111yescharacteristic
369C22#6537211yescharacteristic
370C22#6537911yescharacteristic
371C22#6551111yescharacteristic
372C22#6551611yescharacteristic
373C22#6551711yescharacteristic
374C22#6553011yescharacteristic
375C22#6553211yescharacteristic
376C22#6553311yescharacteristic
377C22#6553511yescharacteristic
378C4—22no—
379C4—22no—
380C4—42no—
381C4—42no—
382C4—82no—
383C4—82no—
384C4—204no—
385C4—402no—
386C2—21no—
387C2—21no—
388C2—21no—
389C2—21no—
390C2#1060257411yescharacteristic
391C2#1060264311yescharacteristic
392C2#1060266911yescharacteristic
393C2#1060268411yescharacteristic
394C2#1060268511yescharacteristic
395C2#1060269111yescharacteristic
396C2#1060269711yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#2659C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenter#2659D5
hypocenterC5#10406
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
354. C5#10406semidirect

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
#106002132
#105981042
#104065