Finite Group Databasebeta

← #12016676

Subgroups — #12016676

Order 1280.

506 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3930C211yesmaximal, characteristic
2C2×#65176C211yesmaximal, characteristic
3C2×#64723C211yesmaximal, characteristic, complemented
4#10601423C211yesmaximal, characteristic
5C2×#64712C211yesmaximal, characteristic, complemented
6C5×#1380C211yesmaximal, characteristic, complemented
7#10598213C211yesmaximal, characteristic, complemented
8C22×Dic20C2211yescharacteristic
9C22×C8×D5C2211yescharacteristic
10C2×#4043—21no—
11C22×C5×C16C2211yescharacteristic
12C2×C5×#107C2211yescharacteristic
13C2×C5×#107C2211yescharacteristic
14C2×#3950C2211yescharacteristic
15C22×#672C2211yescharacteristic
16#65276—21no—
17C2×#3942—21no—
18C2×#3930—22no—
19C2×#3930—22no—
20C2×#3930—22no—
21#65176—22no—
22#65176C414yescomplemented
23#64749—21no—
24#64723—22no—
25#64712—22no—
26#13062—51nomaximal, Sylow
27C22×C4×D5D411yescharacteristic
28C22×Dic10—21no—
29C22×C5×C8C2311yescharacteristic
30C2×C5×C4⋊C4—21no—
31C2×C5×C4⋊C4—21no—
32C2×#685—41no—
33C2×#685—41no—
34C2×C4⋊Dic5—21no—
35C2×C4⋊Dic5—41no—
36C22×#168D411yescharacteristic
37C2×Dic20—21no—
38C2×Dic20—21no—
39C2×Dic20—21no—
40C2×Dic20—21no—
41C2×Dic20—21no—
42C2×Dic20C2×C412yes—
43C2×C8×D5—21no—
44C2×C8×D5—21no—
45C2×C8×D5—21no—
46C2×C8×D5—21no—
47C2×C8×D5C2×C412yes—
48C2×C8×D5D412yes—
49#4043—24no—
50#4043—42no—
51C2×C5×C16—21no—
52C2×C5×C16—21no—
53C2×C5×C16D412yes—
54C5×#107—21no—
55C5×#107—21no—
56C5×#107—21no—
57C5×#107C2×C412yes—
58#3963—41no—
59#3950—21no—
60#3950—21no—
61C2×#672—21no—
62C2×#672—21no—
63C2×#672D412yes—
64#3942—24no—
65#3930—28no—
66C22×M32—51no—
67C2×#467—51no—
68C2×#358—51no—
69C2×#358—51no—
70#1808—51no—
71#1380—51no—
72#1380D511yescharacteristic, complemented
73C23×D5D811yescharacteristic
74C22×C4×C5—41no—
75C22×C4×C5—41no—
76C22×C4×C5C2×D411yescharacteristic
77C22×Dic5—41no—
78C22×Dic5—41no—
79C22×Dic5D811yescharacteristic
80C2×C4×D5—21no—
81C2×C4×D5—21no—
82C2×C4×D5—21no—
83C2×C4×D5—21no—
84C2×C4×D5C22⋊C412yes—
85C2×C4×D5SD1612yes—
86C2×Dic10—22no—
87C2×Dic10—41no—
88C2×Dic10—41no—
89C2×Dic10—41no—
90C2×Dic10—41no—
91C2×Dic10—41no—
92C2×C5×C8C22×C411yescharacteristic
93C2×C5×C8C2×D411yescharacteristic
94C2×C5×C8C2×D411yescharacteristic
95C2×C5×C8C2×D411yescharacteristic
96C2×C5×C8#4111yescharacteristic
97C2×C5×C8#4111yescharacteristic
98C5×C4⋊C4—22no—
99C5×C4⋊C4—41no—
100C5×C4⋊C4—41no—
101C5×C4⋊C4—41no—
102#685—44no—
103#685—82no—
104C4⋊Dic5—44no—
105C4⋊Dic5—41no—
106C4⋊Dic5—41no—
107C2×#168—21no—
108C2×#168—21no—
109C2×#168C22⋊C412yes—
110Dic20—22no—
111Dic20—22no—
112Dic20—41no—
113Dic20—41no—
114C8×D5—22no—
115C8×D5—22no—
116C8×D5—22no—
117C8×D5—22no—
118C5×C16—22no—
119#672—22no—
120C22×Q16—51no—
121C23×C8—51no—
122C2×C22⋊Q8—101no—
123C2×M32—102no—
124C2×M32—102no—
125C2×M32—102no—
126C22×C16—51no—
127C22×C16C2×D511yescharacteristic
128#467—54no—
129#467—102no—
130C2×#107—51no—
131C2×#107C2×D511yescharacteristic
132C2×#107C2×D511yescharacteristic
133C2×#103—101no—
134#380—101no—
135#358—102no—
136#358—102no—
137#340—101no—
138C23×C5C2×D811yescharacteristic
139C22×D5—21no—
140C22×D5—21no—
141C22×D5—21no—
142C22×D5—21no—
143C22×D5—21no—
144C22×D5—21no—
145C22×D5#10212yes—
146C2×C4×C5—42no—
147C2×C4×C5—81no—
148C2×C4×C5—81no—
149C2×C4×C5—81no—
150C2×C4×C5—81no—
151C2×C4×C5—81no—
152C2×C4×C5C2×C22⋊C411yescharacteristic
153C2×C4×C5#12111yescharacteristic
154C2×C4×C5#12111yescharacteristic
155C2×C4×C5C2×SD1611yescharacteristic
156C2×C4×C5#13511yescharacteristic
157C2×C4×C5#13511yescharacteristic
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—42no—
161C2×Dic5—81no—
162C2×Dic5—81no—
163C2×Dic5—81no—
164C2×Dic5—81no—
165C2×Dic5—81no—
166C2×Dic5#10212yes—
167C4×D5—22no—
168C4×D5—22no—
169C4×D5—22no—
170C4×D5—22no—
171Dic10—42no—
172Dic10—42no—
173Dic10—81no—
174Dic10—81no—
175C5×C8C4×D411yescharacteristic
176C5×C8C4×D411yescharacteristic
177C5×C8#12011yescharacteristic
178C5×C8#12311yescharacteristic
179#168—22no—
180C22×Q8—101no—
181C23×C4—51no—
182C2×Q16—52no—
183C2×Q16—101no—
184C2×Q16—101no—
185C2×Q16—101no—
186C2×Q16—101no—
187C2×Q16—101no—
188C22×C8—51no—
189C22×C8—52no—
190C22×C8—52no—
191C22×C8—101no—
192C22×C8—101no—
193C22×C8—101no—
194C22×C8—101no—
195C22×C8C22×D511yescharacteristic
196C22⋊Q8—104no—
197C22⋊Q8—202no—
198C2×C4⋊C4—21no—
199C2×C4⋊C4—21no—
200C2×C4⋊C4—101no—
201C2×C4⋊C4—201no—
202C2×C22⋊C4—201no—
203C2×C22⋊C4—201no—
204M32—108no—
205C2×C16—21no—
206C2×C16—21no—
207C2×C16—52no—
208C2×C16—101no—
209C2×C16—101no—
210C2×C16D2012yes—
211#107—21no—
212#107—21no—
213#107—21no—
214#107—101no—
215#107—101no—
216#107C4×D512yes—
217#103—104no—
218#95—201no—
219C22×C5C2×#10211yescharacteristic
220C22×C5#46611yescharacteristic
221C22×C5#46611yescharacteristic
222C22×C5#50911yescharacteristic
223C22×C5#51011yescharacteristic
224C22×C5#51011yescharacteristic
225C22×C5#51011yescharacteristic
226C2×D5—22no—
227C2×D5—22no—
228C2×D5—22no—
229C2×D5—41no—
230C2×D5—41no—
231C2×D5—41no—
232C2×D5—41no—
233C4×C5—82no—
234C4×C5—161no—
235C4×C5#38611yescharacteristic
236C4×C5#41611yescharacteristic
237C4×C5#46511yescharacteristic
238C4×C5#46511yescharacteristic
239Dic5—22no—
240Dic5—82no—
241Dic5—161no—
242C24—51no—
243C2×Q8—102no—
244C2×Q8—201no—
245C2×Q8—201no—
246C2×Q8—201no—
247C2×Q8—201no—
248C2×Q8—201no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—51no—
252C22×C4—52no—
253C22×C4—52no—
254C22×C4—101no—
255C22×C4—101no—
256C22×C4—101no—
257C22×C4—101no—
258C22×C4—201no—
259C22×C4—201no—
260C22×C4D4×D511yescharacteristic
261Q16—102no—
262Q16—102no—
263Q16—201no—
264Q16—201no—
265C2×C8—52no—
266C2×C8—101no—
267C2×C8—101no—
268C2×C8—102no—
269C2×C8—102no—
270C2×C8—102no—
271C2×C8—102no—
272C2×C8C2×C4×D511yescharacteristic
273C2×C8C2×D2011yescharacteristic
274C2×C8#70911yescharacteristic
275C2×C8D4×D511yescharacteristic
276C2×C8D4×D511yescharacteristic
277C2×C8#71311yescharacteristic
278C4⋊C4—22no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C4⋊C4—41no—
282C4⋊C4—204no—
283C4⋊C4—201no—
284C4⋊C4—201no—
285C22⋊C4—204no—
286C22⋊C4—402no—
287C16—22no—
288C16—102no—
289C2×C5#189311yescharacteristic
290C2×C5#213911yescharacteristic
291C2×C5#214111yescharacteristic
292C2×C5#221911yescharacteristic
293C2×C5#221911yescharacteristic
294C2×C5#222011yescharacteristic
295C2×C5#222011yescharacteristic
296D5—42no—
297C23—52no—
298C23—101no—
299C23—101no—
300C23—101no—
301C23—101no—
302C23—101no—
303C23—101no—
304C23D5×D811yescharacteristic
305Q8—202no—
306Q8—202no—
307Q8—401no—
308Q8—401no—
309C2×C4—42no—
310C2×C4—52no—
311C2×C4—81no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—101no—
317C2×C4—101no—
318C2×C4—102no—
319C2×C4—102no—
320C2×C4—102no—
321C2×C4—102no—
322C2×C4—202no—
323C2×C4—401no—
324C2×C4—401no—
325C2×C4—401no—
326C2×C4—401no—
327C2×C4—401no—
328C2×C4D5×C22⋊C411yescharacteristic
329C2×C4#403011yescharacteristic
330C2×C4#404111yescharacteristic
331C2×C4D5×SD1611yescharacteristic
332C2×C4#406211yescharacteristic
333C2×C4#406511yescharacteristic
334C8—102no—
335C8C4×D2011yescharacteristic
336C8#402811yescharacteristic
337C8#403911yescharacteristic
338C8#404011yescharacteristic
339C5#1306211yescharacteristic, complemented, Sylow
340C22—102no—
341C22—102no—
342C22—102no—
343C22—201no—
344C22—201no—
345C22—201no—
346C22—201no—
347C22D5×#10211yescharacteristic
348C22#6506411yescharacteristic
349C22#6517211yescharacteristic
350C22#6520011yescharacteristic
351C22#6520411yescharacteristic
352C22#6520411yescharacteristic
353C22#6520711yescharacteristic
354C4—82no—
355C4—102no—
356C4—161no—
357C4—402no—
358C4—801no—
359C4#6495411yescharacteristic
360C4#6509311yescharacteristic
361C4#6509611yescharacteristic
362C4#6515311yescharacteristic
363C2—202no—
364C2#1059967611yescharacteristic
365C2#1059998211yescharacteristic
366C2#1059999111yescharacteristic
367C2#1060001511yescharacteristic
368C2#1060002211yescharacteristic
369C2#1060012211yescharacteristic
370C2#1060014211yescharacteristic
subgroupG/H
centerC23D5×D8
commutatorC2×C5×C8C22×C4
FrattiniC22×C8C22×D5
FittingC5×#1380C2
socleC23×C5C2×D8
prime radicalC23×D5D8
cosocleC22×C5×C8C23
hypercenter#1380D5
hypocenterC5#13062
LCSG ▷ C2×C5×C8 ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ #1380

Complements

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

NH ≅ G/Ntype
3. C2×#64723C2semidirect
5. C2×#64712C2semidirect
6. C5×#1380C2semidirect
7. #10598213C2semidirect
22. #65176C4semidirect
72. #1380D5semidirect
339. C5#13062semidirect

Maximal subgroups

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

subgroupindex
C22×#39302
C2×#651762
C2×#647232
#106014232
C2×#647122
C5×#13802
#105982132
#130625