Finite Group Databasebeta

← #12003700

Subgroups — #12003700

Order 1280.

604 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 121 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#10600297C212yesmaximal
3#10600213C211yesmaximal, characteristic
4#10598115C212yesmaximal
5#10598104C211yesmaximal, characteristic
6C2×C5×C22⋊Q8—21no—
7C22×C4⋊Dic5C2211yescharacteristic
8C22×#683—21no—
9C5×#398—22no—
10C5×#395—22no—
11C5×#380—21no—
12C5×#380C2212yes—
13C2×C5×#95C2211yescharacteristic
14C2×#3963—21no—
15C2×#3963C2211yescharacteristic
16C2×C22⋊#168C2212yes—
17C2×#3939—22no—
18#64749—22no—
19#10567—51nomaximal, Sylow
20C22×C5×Q8—21no—
21C23×C4×C5D411yescharacteristic
22C23×C4×C5D411yescharacteristic
23C23×C4×C5C2311yescharacteristic
24C23×Dic5—21no—
25C23×Dic5—21no—
26C5×C22⋊Q8—42no—
27C5×C22⋊Q8—42no—
28C2×C5×C4⋊C4—22no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4D412yes—
33C2×C5×C4⋊C4D412yes—
34C2×C5×C22⋊C4—22no—
35C2×C4⋊Dic5—22no—
36C2×C4⋊Dic5—42no—
37C2×#683—42no—
38C2×#683—42no—
39C2×#683—42no—
40C22×#168—22no—
41C5×#95—22no—
42C5×#95—22no—
43C5×#95—22no—
44#3963—21no—
45#3963—42no—
46#3963Q812yescomplemented
47C22⋊#168—22no—
48C22⋊#168Q814yescomplemented
49#3939—44no—
50#2659D511yescharacteristic
51#1852—52no—
52#1444—51no—
53#1294—52no—
54#1280—51no—
55C24×C5C2×D411yescharacteristic
56C2×C5×Q8—42no—
57C2×C5×Q8—81no—
58C2×C5×Q8—81no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5—21no—
63C22×C4×C5—22no—
64C22×C4×C5—22no—
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×C5D812yes—
72C22×C4×C5Q1612yes—
73C22×C4×C5C2×D412yes—
74C22×C4×C5C2×Q812yes—
75C22×C4×C5C2×Q811yescharacteristic
76C22×C4×C5#4111yescharacteristic
77C22×Dic5—22no—
78C22×Dic5—22no—
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—
91C5×C4⋊C4—42no—
92C5×C4⋊C4—42no—
93C5×C4⋊C4—42no—
94C5×C4⋊C4—44no—
95C5×C4⋊C4—81no—
96C5×C4⋊C4—81no—
97C5×C22⋊C4—42no—
98C5×C22⋊C4—42no—
99C4⋊Dic5—24no—
100C4⋊Dic5—42no—
101#683—48no—
102C2×#168—24no—
103C2×#168—42no—
104C2×#168—42no—
105C2×C22⋊Q8—21no—
106C22×C4⋊C4—51no—
107C22×C4⋊C4—101no—
108C2×#107—102no—
109C2×C22⋊C8—52no—
110#398—22no—
111#395—22no—
112#380—21no—
113#380C2×D512yes—
114C2×#95—51no—
115C2×#95—101no—
116C2×#95C2×D511yescharacteristic
117#340—102no—
118C23×C5—21no—
119C23×C5—21no—
120C23×C5—21no—
121C23×C5—21no—
122C23×C5#12011yescharacteristic
123C23×C5C22⋊Q811yescharacteristic
124C23×C5C4⋊Q811yescharacteristic
125C23×C5C2×D811yescharacteristic
126C23×C5C2×Q1611yescharacteristic
127C23×C5AGL(1,ℤ/8)11yescharacteristic
128C23×C5#13711yescharacteristic
129C5×Q8—84no—
130C2×C4×C5—22no—
131C2×C4×C5—22no—
132C2×C4×C5—22no—
133C2×C4×C5—22no—
134C2×C4×C5—42no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5—41no—
139C2×C4×C5—41no—
140C2×C4×C5—41no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—42no—
145C2×C4×C5—42no—
146C2×C4×C5—42no—
147C2×C4×C5—42no—
148C2×C4×C5—42no—
149C2×C4×C5—81no—
150C2×C4×C5—81no—
151C2×C4×C5C22⋊Q812yes—
152C2×C4×C5C4⋊Q812yes—
153C2×Dic5—24no—
154C2×Dic5—42no—
155C2×Dic5—42no—
156C2×Dic5—42no—
157C2×Dic5—42no—
158C2×Dic5—42no—
159C2×Dic5—42no—
160C2×Dic5—42no—
161C2×Dic5—42no—
162C2×Dic5—42no—
163C2×Dic5—81no—
164C2×Dic5—81no—
165C2×Dic5—81no—
166C2×Dic5—81no—
167#168—44no—
168C22×Q8—21no—
169C23×C4—101no—
170C23×C4—101no—
171C23×C4C22⋊D511yescharacteristic
172C23×C4C22⋊D511yescharacteristic
173C23×C4C22×D511yescharacteristic
174C22×C8—102no—
175C22⋊Q8—42no—
176C22⋊Q8—42no—
177C2×C4⋊C4—22no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4—102no—
182C2×C4⋊C4—202no—
183C2×C4⋊C4—202no—
184C2×C4⋊C4—202no—
185C2×C4⋊C4—202no—
186C2×C4⋊C4C22⋊D512yes—
187C2×C4⋊C4C22⋊D512yes—
188C2×C22⋊C4—22no—
189#107—204no—
190C22⋊C8—54no—
191C22⋊C8—102no—
192#95—22no—
193#95—22no—
194#95—22no—
195#95—52no—
196#95—101no—
197#95—202no—
198C22×C5—21no—
199C22×C5—21no—
200C22×C5—21no—
201C22×C5—21no—
202C22×C5—21no—
203C22×C5—21no—
204C22×C5—21no—
205C22×C5—21no—
206C22×C5—21no—
207C22×C5—21no—
208C22×C5—21no—
209C22×C5—21no—
210C22×C5#39511yescharacteristic
211C22×C5#44711yescharacteristic
212C22×C5#45111yescharacteristic
213C22×C5#45311yescharacteristic
214C22×C5#45611yescharacteristic
215C22×C5B(4,𝔽2)11yescharacteristic
216C22×C5#45811yescharacteristic
217C22×C5#47411yescharacteristic
218C22×C5#47711yescharacteristic
219C22×C5#50011yescharacteristic
220C22×C5#50111yescharacteristic
221C4×C5—22no—
222C4×C5—22no—
223C4×C5—42no—
224C4×C5—42no—
225C4×C5—82no—
226C4×C5—82no—
227Dic5—44no—
228Dic5—82no—
229C24C2×C22⋊D511yescharacteristic
230C2×Q8—42no—
231C2×Q8—81no—
232C2×Q8—81no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—22no—
238C22×C4—22no—
239C22×C4—41no—
240C22×C4—41no—
241C22×C4—41no—
242C22×C4—41no—
243C22×C4—41no—
244C22×C4—41no—
245C22×C4—102no—
246C22×C4—102no—
247C22×C4—102no—
248C22×C4—102no—
249C22×C4—201no—
250C22×C4—201no—
251C22×C4—201no—
252C22×C4—201no—
253C22×C4—201no—
254C22×C4—201no—
255C22×C4—201no—
256C22×C4—201no—
257C22×C4—201no—
258C22×C4—201no—
259C22×C4#68612yes—
260C22×C4#68912yes—
261C22×C4Q8×D511yescharacteristic
262C22×C4Q8×D512yes—
263C22×C4#71311yescharacteristic
264C22×C4C2×C22⋊D512yes—
265C2×C8—104no—
266C2×C8—202no—
267C2×C8—202no—
268C4⋊C4—42no—
269C4⋊C4—42no—
270C4⋊C4—42no—
271C4⋊C4—44no—
272C4⋊C4—81no—
273C4⋊C4—81no—
274C4⋊C4—104no—
275C4⋊C4—202no—
276C4⋊C4—208no—
277C22⋊C4—42no—
278C22⋊C4—42no—
279C2×C5—21no—
280C2×C5—21no—
281C2×C5—21no—
282C2×C5—21no—
283C2×C5#159511yescharacteristic
284C2×C5#160511yescharacteristic
285C2×C5#161011yescharacteristic
286C2×C5#161411yescharacteristic
287C2×C5#205711yescharacteristic
288C2×C5#206011yescharacteristic
289C2×C5#206211yescharacteristic
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23C2×#68611yescharacteristic
295C23#407811yescharacteristic
296C23#408811yescharacteristic
297C23C2×#68911yescharacteristic
298C23#409011yescharacteristic
299C23#409211yescharacteristic
300C23#409911yescharacteristic
301Q8—84no—
302C2×C4—22no—
303C2×C4—22no—
304C2×C4—22no—
305C2×C4—22no—
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—42no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—81no—
322C2×C4—81no—
323C2×C4—104no—
324C2×C4—202no—
325C2×C4—202no—
326C2×C4—202no—
327C2×C4—202no—
328C2×C4—202no—
329C2×C4—202no—
330C2×C4—202no—
331C2×C4—202no—
332C2×C4—202no—
333C2×C4—401no—
334C2×C4—401no—
335C2×C4—401no—
336C2×C4—401no—
337C2×C4#409012yes—
338C2×C4#409212yes—
339C8—204no—
340C5#1056711yescharacteristic, complemented, Sylow
341C22—21no—
342C22—21no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—21no—
353C22#6536711yescharacteristic
354C22#6536911yescharacteristic
355C22#6537611yescharacteristic
356C22#6538011yescharacteristic
357C22#6550611yescharacteristic
358C22#6551711yescharacteristic
359C22#6551811yescharacteristic
360C22#6553011yescharacteristic
361C22#6553211yescharacteristic
362C22#6553311yescharacteristic
363C22#6553511yescharacteristic
364C4—22no—
365C4—22no—
366C4—42no—
367C4—42no—
368C4—82no—
369C4—82no—
370C4—204no—
371C4—402no—
372C2—21no—
373C2—21no—
374C2—21no—
375C2—21no—
376C2#1060257511yescharacteristic
377C2#1060263811yescharacteristic
378C2#1060266711yescharacteristic
379C2#1060268411yescharacteristic
380C2#1060268811yescharacteristic
381C2#1060269311yescharacteristic
382C2#1060269711yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC23×C4×C5C23
FrattiniC23×C4C22×D5
FittingC5×#2659C2
socleC23×C5#120
prime radicalC24×C5C2×D4
hypercenter#2659D5
hypocenterC5#10567
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
46. #3963Q8semidirect
48. C22⋊#168Q8semidirect
340. C5#10567semidirect

Maximal subgroups

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

subgroupindex
C5×#26592
#106002972
#106002132
#105981152
#105981042
#105675