Finite Group Databasebeta

← #11992639

Subgroups — #11992639

Order 1280.

830 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 830 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#65501C211yesmaximal, characteristic
2C5×#1779C211yesmaximal, characteristic
3#10602919C211yesmaximal, characteristic
4#10598165C214yesmaximal, complemented
5C24×C4×C5C2211yescharacteristic
6C22×C22⋊Dic5C412yes—
7C22×C4⋊Dic5C411yescharacteristic
8C22×C4⋊Dic5C411yescharacteristic
9C2×C5×C22⋊C8—21no—
10C2×C5×C22⋊C8—21no—
11C2×C5×C22⋊C8C2212yes—
12#65501—21no—
13#65501—21no—
14#65501—21no—
15#65501—21no—
16C2×#3963C2212yes—
17C2×C22⋊#168—21no—
18C2×C22⋊#168—21no—
19C2×C22⋊#168C2212yes—
20#8704—51nomaximal, Sylow
21C25×C5C2×C411yescharacteristic
22C23×C4×C5—24no—
23C23×C4×C5—42no—
24C23×C4×C5—42no—
25C23×C4×C5C2×C411yescharacteristic
26C23×C4×C5D411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C23×C4×C5D411yescharacteristic
30C23×C4×C5C2311yescharacteristic
31C23×Dic5C2×C412yes—
32C23×Dic5C2×C412yes—
33C22×C5×C8—22no—
34C2×C22⋊Dic5—22no—
35C2×C22⋊Dic5—22no—
36C2×C22⋊Dic5—44no—
37C2×C4⋊Dic5—21no—
38C2×C4⋊Dic5—21no—
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5—21no—
41C2×C4⋊Dic5—42no—
42C2×C4⋊Dic5—42no—
43C22×#168—22no—
44C5×C22⋊C8—24no—
45C5×C22⋊C8—42no—
46C5×C22⋊C8—42no—
47#3963—22no—
48#3963—22no—
49C22⋊#168—24no—
50C22⋊#168—42no—
51C22⋊#168—42no—
52C2×#380—51no—
53#1779—51no—
54#1779D511yescharacteristic
55#1280—54no—
56C24×C5—22no—
57C24×C5—22no—
58C24×C5—22no—
59C24×C5—22no—
60C24×C5—22no—
61C24×C5—41no—
62C24×C5—41no—
63C24×C5C22⋊C411yescharacteristic
64C24×C5C22⋊C411yescharacteristic
65C24×C5C22×C411yescharacteristic
66C22×C4×C5—22no—
67C22×C4×C5—22no—
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—22no—
74C22×C4×C5—22no—
75C22×C4×C5—22no—
76C22×C4×C5—22no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—41no—
83C22×C4×C5—416no—
84C22×C4×C5C22⋊C411yescharacteristic
85C22×C4×C5C22⋊C411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5C2×D411yescharacteristic
88C22×C4×C5#4114yes—
89C22×Dic5—22no—
90C22×Dic5—22no—
91C22×Dic5—24no—
92C22×Dic5—24no—
93C22×Dic5—42no—
94C22×Dic5—42no—
95C22×Dic5—42no—
96C22×Dic5—42no—
97C2×C5×C8—42no—
98C2×C5×C8—42no—
99C2×C5×C8—42no—
100C22⋊Dic5—44no—
101C22⋊Dic5—44no—
102C4⋊Dic5—42no—
103C4⋊Dic5—42no—
104C4⋊Dic5—42no—
105C4⋊Dic5—42no—
106C2×#168—42no—
107C2×#168—42no—
108C2×#168—42no—
109C24×C4C2×D511yescharacteristic
110C22×C4⋊C4—51no—
111C22×C4⋊C4—51no—
112C22×C22⋊C4—52no—
113C2×C22⋊C8—21no—
114C2×C22⋊C8—21no—
115C2×C22⋊C8—52no—
116C2×C22⋊C8—101no—
117C2×C22⋊C8—101no—
118C2×C22⋊C8C2×D512yes—
119#380—101no—
120#380—101no—
121#380—101no—
122#380—101no—
123C2×#95—52no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—28no—
129C23×C5—21no—
130C23×C5—21no—
131C23×C5—21no—
132C23×C5—21no—
133C23×C5—21no—
134C23×C5—21no—
135C23×C5—21no—
136C23×C5—21no—
137C23×C5—21no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—44no—
142C23×C5—44no—
143C23×C5—44no—
144C23×C5—44no—
145C23×C5—44no—
146C23×C5—44no—
147C23×C5#10012yes—
148C23×C5#10112yes—
149C23×C5C2×C22⋊C411yescharacteristic
150C23×C5#11712yes—
151C23×C5#13112yes—
152C23×C5#13112yes—
153C2×C4×C5—28no—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—21no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—44no—
163C2×C4×C5—44no—
164C2×C4×C5—44no—
165C2×C4×C5—44no—
166C2×C4×C5—44no—
167C2×C4×C5#9912yes—
168C2×C4×C5#9912yes—
169C2×C4×C5#12312yes—
170C2×C4×C5#12312yes—
171C2×Dic5—42no—
172C2×Dic5—42no—
173C2×Dic5—42no—
174C2×Dic5—42no—
175C2×Dic5—42no—
176C2×Dic5—42no—
177C2×Dic5—84no—
178C2×Dic5—84no—
179C5×C8—82no—
180#168—82no—
181C25C4×D511yescharacteristic
182C23×C4—24no—
183C23×C4—42no—
184C23×C4—42no—
185C23×C4—52no—
186C23×C4—52no—
187C23×C4C4×D511yescharacteristic
188C23×C4D2011yescharacteristic
189C23×C4D2011yescharacteristic
190C23×C4C22⋊D511yescharacteristic
191C23×C4C22⋊D511yescharacteristic
192C23×C4C22×D511yescharacteristic
193C22×C8—22no—
194C22×C8—102no—
195C2×C4⋊C4—101no—
196C2×C4⋊C4—101no—
197C2×C4⋊C4—101no—
198C2×C4⋊C4—101no—
199C2×C4⋊C4—202no—
200C2×C4⋊C4—202no—
201C2×C22⋊C4—102no—
202C2×C22⋊C4—102no—
203C2×C22⋊C4—204no—
204C22⋊C8—24no—
205C22⋊C8—42no—
206C22⋊C8—42no—
207C22⋊C8—104no—
208C22⋊C8—202no—
209C22⋊C8—202no—
210#95—102no—
211#95—102no—
212C22×C5—22no—
213C22×C5—22no—
214C22×C5—22no—
215C22×C5—22no—
216C22×C5—22no—
217C22×C5—22no—
218C22×C5—22no—
219C22×C5—22no—
220C22×C5—22no—
221C22×C5—22no—
222C22×C5—22no—
223C22×C5—22no—
224C22×C5—416no—
225C22×C5—41no—
226C22×C5—41no—
227C22×C5—41no—
228C22×C5—41no—
229C22×C5—41no—
230C22×C5—41no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5#38111yescharacteristic
234C22×C5#40811yescharacteristic
235C22×C5#40811yescharacteristic
236C22×C5C2×#9911yescharacteristic
237C22×C5C2×#9911yescharacteristic
238C22×C5C2×#10011yescharacteristic
239C22×C5C2×#10111yescharacteristic
240C22×C5#43314yes—
241C4×C5—22no—
242C4×C5—22no—
243C4×C5—22no—
244C4×C5—22no—
245Dic5—82no—
246Dic5—82no—
247C24—22no—
248C24—22no—
249C24—22no—
250C24—22no—
251C24—22no—
252C24—41no—
253C24—41no—
254C24#68511yescharacteristic
255C24#68511yescharacteristic
256C24C2×C4×D511yescharacteristic
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—22no—
260C22×C4—22no—
261C22×C4—22no—
262C22×C4—22no—
263C22×C4—22no—
264C22×C4—22no—
265C22×C4—22no—
266C22×C4—22no—
267C22×C4—22no—
268C22×C4—41no—
269C22×C4—41no—
270C22×C4—41no—
271C22×C4—41no—
272C22×C4—41no—
273C22×C4—41no—
274C22×C4—416no—
275C22×C4—102no—
276C22×C4—102no—
277C22×C4—104no—
278C22×C4—104no—
279C22×C4—202no—
280C22×C4—202no—
281C22×C4—202no—
282C22×C4—202no—
283C22×C4#68511yescharacteristic
284C22×C4#68511yescharacteristic
285C22×C4C2×D2011yescharacteristic
286C22×C4#71114yes—
287C22×C4C2×C22⋊D511yescharacteristic
288C2×C8—42no—
289C2×C8—42no—
290C2×C8—42no—
291C2×C8—202no—
292C2×C8—202no—
293C2×C8—202no—
294C4⋊C4—202no—
295C4⋊C4—202no—
296C4⋊C4—202no—
297C4⋊C4—202no—
298C22⋊C4—204no—
299C22⋊C4—204no—
300C2×C5—24no—
301C2×C5—42no—
302C2×C5—42no—
303C2×C5#147111yescharacteristic
304C2×C5#147111yescharacteristic
305C2×C5#147211yescharacteristic
306C2×C5#147211yescharacteristic
307C2×C5#181811yescharacteristic
308C2×C5#181911yescharacteristic
309C2×C5#182111yescharacteristic
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—28no—
315C23—21no—
316C23—21no—
317C23—21no—
318C23—21no—
319C23—21no—
320C23—21no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—44no—
328C23—44no—
329C23—44no—
330C23—44no—
331C23—44no—
332C23—44no—
333C23#395512yes—
334C23#395612yes—
335C23#402312yes—
336C23#404712yes—
337C23#405312yes—
338C23C2×#68511yescharacteristic
339C2×C4—28no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—44no—
349C2×C4—44no—
350C2×C4—44no—
351C2×C4—44no—
352C2×C4—44no—
353C2×C4—202no—
354C2×C4—202no—
355C2×C4—202no—
356C2×C4—202no—
357C2×C4—202no—
358C2×C4—202no—
359C2×C4—404no—
360C2×C4—404no—
361C2×C4#393812yes—
362C2×C4#393812yes—
363C2×C4#403212yes—
364C2×C4#408112yes—
365C8—82no—
366C8—402no—
367C5#870411yescharacteristic, complemented, Sylow
368C22—22no—
369C22—22no—
370C22—22no—
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—22no—
376C22—22no—
377C22—22no—
378C22—22no—
379C22—22no—
380C22—416no—
381C22—41no—
382C22—41no—
383C22—41no—
384C22—41no—
385C22—41no—
386C22—41no—
387C22—41no—
388C22—41no—
389C22#6500914yes—
390C22#6523211yescharacteristic
391C22C2×#393811yescharacteristic
392C22C2×#393811yescharacteristic
393C22#6539911yescharacteristic
394C22#6541811yescharacteristic
395C22C2×#395511yescharacteristic
396C22C2×#395611yescharacteristic
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—402no—
402C4—402no—
403C2—24no—
404C2—42no—
405C2—42no—
406C2#1060028811yescharacteristic
407C2#1060070411yescharacteristic
408C2#1060071411yescharacteristic
409C2#1060071611yescharacteristic
410C2#1060076311yescharacteristic
411C2#1060076511yescharacteristic
412C2#1060076611yescharacteristic
subgroupG/H
centerC23C2×#685
commutatorC24×C5C22×C4
FrattiniC23×C4C22×D5
FittingC5×#1779C2
socleC23×C5C2×C22⋊C4
prime radicalC25×C5C2×C4
cosocleC23×C4×C5C23
hypercenter#1779D5
hypocenterC5#8704
LCSG ▷ C24×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C24×C4 ◁ #1779

Complements

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

NH ≅ G/Ntype
4. #10598165C2semidirect
367. C5#8704semidirect

Maximal subgroups

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

subgroupindex
C2×#655012
C5×#17792
#106029192
#105981652
#87045