Finite Group Databasebeta

← #11998571

Subgroups — #11998571

Order 1280.

538 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65359C211yesmaximal, characteristic
2C5×#1982C211yesmaximal, characteristic
3C2×#64764C211yesmaximal, characteristic
4C2×#64702C211yesmaximal, characteristic, complemented
5C2×#64699C211yesmaximal, characteristic, complemented
6#10600279C211yesmaximal, characteristic, complemented
7C4⋊C4×#168C211yesmaximal, characteristic, complemented
8C2×C5×#127C2211yescharacteristic
9C2×#4015C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C5×#102—22no—
12C4×C5×C4⋊C4C2211yescharacteristic
13C2×#3964—21no—
14C2×#3964—21no—
15#65359—22no—
16#65359C414yescomplemented
17C2×#3942—22no—
18C2×C4⋊#168C2211yescharacteristic
19C2×C4⋊#168C2211yescharacteristic
20C2×C4×#168—21no—
21C2×C4×#168C2211yescharacteristic
22#64764—22no—
23#64744—21no—
24#64702—22no—
25#64699—22no—
26#9738—51nomaximal, Sylow
27C22×C5×D4—21no—
28C22×C5×D4—21no—
29C22×C5×D4—21no—
30C22×Dic10—21no—
31C22×C5×C8—21no—
32C5×#127—21no—
33C5×#127—21no—
34C5×#127—21no—
35C5×#127C2×C412yes—
36C2×C5×C4⋊C4D412yes—
37C2×C42×C5—21no—
38C2×C42×C5C2311yescharacteristic
39C2×C4⋊Dic5—21no—
40C2×C4⋊Dic5—21no—
41C22×#168—21no—
42C22×#168—21no—
43C22×#168D411yescharacteristic
44C22×#168D411yescharacteristic
45#4015—21no—
46#4015—21no—
47#4015—21no—
48#4015C2×C412yes—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×#102—44no—
52C5×#95—21no—
53#3964—24no—
54#3964—24no—
55#3942—44no—
56C4⋊#168—21no—
57C4⋊#168—21no—
58C4⋊#168—21no—
59C4⋊#168D412yes—
60C4×#168—42no—
61C4×#168C2×C412yes—
62C4×#168D412yes—
63C2×#486—51no—
64#1982D511yescharacteristic
65#1981—51no—
66C8×C4⋊C4—51no—
67C2×#335—51no—
68C2×#332—51no—
69C2×#331—51no—
70C24×C5—41no—
71C2×C5×D4—22no—
72C2×C5×D4—22no—
73C2×C5×D4—22no—
74C2×C5×D4—41no—
75C2×C5×D4—41no—
76C2×C5×D4—41no—
77C2×C5×D4—42no—
78C2×C5×D4—42no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—82no—
84C22×C4×C5—22no—
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5C2×D411yescharacteristic
87C22×C4×C5#4111yescharacteristic
88C22×Dic5—41no—
89C2×Dic10—22no—
90C2×Dic10—42no—
91C2×Dic10—42no—
92C2×Dic10—41no—
93C2×C5×C8—41no—
94C2×C5×C8—42no—
95C5×C4⋊C4—22no—
96C5×C4⋊C4D814yes—
97C42×C5—41no—
98C42×C5—41no—
99C42×C5C22×C411yescharacteristic
100C42×C5C2×D411yescharacteristic
101C42×C5C2×D411yescharacteristic
102C42×C5#4111yescharacteristic
103C4⋊Dic5—22no—
104C4⋊Dic5—22no—
105C4⋊Dic5—41no—
106C4⋊Dic5—41no—
107C2×#168—21no—
108C2×#168—21no—
109C2×#168—21no—
110C2×#168—21no—
111C2×#168—22no—
112C2×#168—41no—
113C2×#168—41no—
114C2×#168—41no—
115C2×#168—42no—
116C2×#168C22⋊C412yes—
117C2×#168C22⋊C412yes—
118C2×C4⋊Q8—51no—
119C2×#127C2×D511yescharacteristic
120#486—54no—
121#486—102no—
122C2×C4⋊C8—51no—
123C2×C4⋊C8—51no—
124C2×C4⋊C8C2×D511yescharacteristic
125C2×#103—102no—
126C2×#102—22no—
127C2×#102—101no—
128C2×#102—101no—
129C2×C4×C8—51no—
130C2×C4×C8—101no—
131C4×C4⋊C4C2×D511yescharacteristic
132#336—101no—
133#335—102no—
134#332—102no—
135#331—102no—
136C23×C5—42no—
137C23×C5—81no—
138C23×C5—81no—
139C23×C5—82no—
140C23×C5—82no—
141C23×C5#12111yescharacteristic
142C5×D4—42no—
143C5×D4—42no—
144C5×D4—44no—
145C5×D4—82no—
146C5×D4—82no—
147C5×D4—81no—
148C5×D4—81no—
149C5×D4—81no—
150C5×D4—81no—
151C2×C4×C5—22no—
152C2×C4×C5—24no—
153C2×C4×C5—42no—
154C2×C4×C5—42no—
155C2×C4×C5C2×C22⋊C411yescharacteristic
156C2×C4×C5C4×D411yescharacteristic
157C2×C4×C5C4×D411yescharacteristic
158C2×C4×C5#12111yescharacteristic
159C2×C4×C5#12411yescharacteristic
160C2×C4×C5#12711yescharacteristic
161C2×C4×C5C2×D812yes—
162C2×C4×C5#13512yes—
163C2×C4×C5#13511yescharacteristic
164C2×C4×C5#13511yescharacteristic
165C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C5#13711yescharacteristic
167C2×Dic5—42no—
168C2×Dic5—82no—
169Dic10—44no—
170Dic10—81no—
171Dic10—81no—
172C5×C8—81no—
173#168—22no—
174#168—22no—
175#168—42no—
176#168—81no—
177C22×Q8—101no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4—21no—
181C22×C8—21no—
182C22×C8—51no—
183C22×C8—51no—
184C22×C8—101no—
185C22×C8—101no—
186C4⋊Q8—52no—
187C4⋊Q8—101no—
188C4⋊Q8—101no—
189C4⋊Q8—101no—
190#127—21no—
191#127—21no—
192#127—21no—
193#127C4×D512yes—
194C2×C4⋊C4—101no—
195C2×C4⋊C4—101no—
196C2×C4⋊C4C22⋊D512yes—
197C2×C42—21no—
198C2×C42C22×D511yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—52no—
202C4⋊C8—101no—
203C4⋊C8—101no—
204C4⋊C8—101no—
205#103—204no—
206#102—44no—
207#102—104no—
208#102—104no—
209C4×C8—52no—
210C4×C8—52no—
211C4×C8—202no—
212#95—21no—
213C22×C5—82no—
214C22×C5—82no—
215C22×C5—82no—
216C22×C5—162no—
217C22×C5—162no—
218C22×C5#39011yescharacteristic
219C22×C5#46311yescharacteristic
220C22×C5#46411yescharacteristic
221C22×C5#46612yes—
222C22×C5#47112yes—
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—44no—
226C4×C5#41611yescharacteristic
227C4×C5#41711yescharacteristic
228C4×C5C4×D812yes—
229C4×C5#46311yescharacteristic
230C4×C5#46411yescharacteristic
231C4×C5#49311yescharacteristic
232C4×C5#49511yescharacteristic
233Dic5—82no—
234C24—41no—
235C2×Q8—102no—
236C2×Q8—201no—
237C2×Q8—202no—
238C2×Q8—202no—
239C2×D4—22no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4—42no—
243C2×D4—41no—
244C2×D4—41no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—42no—
250C2×D4—41no—
251C2×D4—82no—
252C22×C4—22no—
253C22×C4—201no—
254C22×C4D4×D511yescharacteristic
255C22×C4#71111yescharacteristic
256C22×C4C2×C22⋊D511yescharacteristic
257C2×C8—42no—
258C2×C8—41no—
259C2×C8—52no—
260C2×C8—52no—
261C2×C8—101no—
262C2×C8—101no—
263C2×C8—101no—
264C2×C8—101no—
265C2×C8—102no—
266C2×C8—201no—
267C2×C8—201no—
268C2×C8—202no—
269C2×C8—201no—
270C4⋊C4—22no—
271C4⋊C4—102no—
272C4⋊C4—102no—
273C4⋊C4—201no—
274C4⋊C4—201no—
275C4⋊C4#68614yes—
276C42—41no—
277C42—41no—
278C42C2×C4×D511yescharacteristic
279C42#70911yescharacteristic
280C42D4×D511yescharacteristic
281C42D4×D511yescharacteristic
282C2×C5—162no—
283C2×C5#168112yes—
284C2×C5#168212yes—
285C2×C5#197011yescharacteristic
286C2×C5#197711yescharacteristic
287C2×C5#198311yescharacteristic
288C23—42no—
289C23—82no—
290C23—81no—
291C23—81no—
292C23—82no—
293C23#408511yescharacteristic
294Q8—204no—
295Q8—401no—
296Q8—401no—
297D4—44no—
298D4—42no—
299D4—42no—
300D4—82no—
301D4—82no—
302D4—81no—
303D4—81no—
304D4—81no—
305D4—81no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—42no—
309C2×C4—42no—
310C2×C4—202no—
311C2×C4—402no—
312C2×C4D5×C22⋊C411yescharacteristic
313C2×C4#402711yescharacteristic
314C2×C4#403011yescharacteristic
315C2×C4#403111yescharacteristic
316C2×C4#405711yescharacteristic
317C2×C4#405811yescharacteristic
318C2×C4#406111yescharacteristic
319C2×C4#406211yescharacteristic
320C2×C4C4×C22⋊D511yescharacteristic
321C2×C4C2×#68612yes—
322C2×C4#408611yescharacteristic
323C2×C4#409612yes—
324C8—81no—
325C8—102no—
326C8—102no—
327C8—202no—
328C8—401no—
329C5#973811yescharacteristic, complemented, Sylow
330C22—82no—
331C22—82no—
332C22—82no—
333C22—162no—
334C22—162no—
335C22#6524611yescharacteristic
336C22#6532712yes—
337C22#6544211yescharacteristic
338C22#6545511yescharacteristic
339C22#6548912yes—
340C4—21no—
341C4—21no—
342C4—44no—
343C4—402no—
344C4#6505611yescharacteristic
345C4#6506011yescharacteristic
346C4#6506111yescharacteristic
347C4#6507611yescharacteristic
348C4C4×#68612yes—
349C4#6534811yescharacteristic
350C4#6536211yescharacteristic
351C2—162no—
352C2#1060044011yescharacteristic
353C2#1060095511yescharacteristic
354C2#1060110811yescharacteristic
355C2#1060180012yes—
356C2#1060181612yes—
subgroupG/H
centerC23#4085
commutatorC42×C5C22×C4
FrattiniC2×C42C22×D5
FittingC5×#1982C2
socleC23×C5#121
prime radicalC2×C5×#127C22
cosocleC2×C42×C5C23
hypercenter#1982D5
hypocenterC5#9738
LCSG ▷ C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1982

Complements

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

NH ≅ G/Ntype
4. C2×#64702C2semidirect
5. C2×#64699C2semidirect
6. #10600279C2semidirect
7. C4⋊C4×#168C2semidirect
16. #65359C4semidirect
329. C5#9738semidirect

Maximal subgroups

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

subgroupindex
C2×#653592
C5×#19822
C2×#647642
C2×#647022
C2×#646992
#106002792
C4⋊C4×#1682
#97385