Finite Group Databasebeta

← #12016196

Subgroups — #12016196

Order 1280.

488 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615525C211yesmaximal, characteristic
2C22×#3930C211yesmaximal, characteristic, complemented
3C2×C5×#350C211yesmaximal, characteristic, complemented
4C2×#64781C211yesmaximal, characteristic, complemented
5#10602224C211yesmaximal, characteristic, complemented
6#10598306C211yesmaximal, characteristic, complemented
7#10598296C211yesmaximal, characteristic, complemented
8C2×C5×#131C2211yescharacteristic
9#66162C411yescharacteristic
10C22×C8×D5C2211yescharacteristic
11C2×C5×M32C2211yescharacteristic
12C22×C5×C16C2211yescharacteristic
13#65523C411yescharacteristic
14#65416—22no—
15#65415C411yescharacteristic
16#65408C411yescharacteristic
17C8×C22⋊D5—22no—
18#65390C2211yescharacteristic
19C2×#3944C2211yescharacteristic
20C22×#672C2211yescharacteristic
21C2×#3930—22no—
22C2×#3930—22no—
23C2×#3930—22no—
24C5×#350—22no—
25#64781—22no—
26#64727—22no—
27#12984—51nomaximal, Sylow
28C2×C5×#41C2×C411yescharacteristic
29C22×C4×D5C2×C411yescharacteristic
30C5×#131—21no—
31C5×#131—21no—
32C5×#131—21no—
33C5×#131—21no—
34C2×C5×M16—21no—
35C2×C5×M16C2×C411yescharacteristic
36C22×C5×C8—21no—
37C22×C5×C8C2311yescharacteristic
38#4092C812yes—
39#4084C812yes—
40#4083—21no—
41#4081—21no—
42C4×C22⋊D5—22no—
43#4072C2×C411yescharacteristic
44C2×#681C2×C411yescharacteristic
45C22×#168C2×C411yescharacteristic
46C2×C8×D5—21no—
47C2×C8×D5—21no—
48C2×C8×D5—21no—
49C2×C8×D5—21no—
50C2×C8×D5D412yes—
51C2×C8×D5D412yes—
52C5×M32—21no—
53C5×M32—21no—
54C2×C5×C16—21no—
55C2×C5×C16—21no—
56C2×C5×C16—21no—
57C2×C5×C16D412yescomplemented
58C22⋊#168—22no—
59#3952—22no—
60#3947—21no—
61#3946—22no—
62C8×Dic5—21no—
63#3944—21no—
64#3944—21no—
65C2×#672—21no—
66C2×#672—21no—
67C2×#672—21no—
68C2×#672D412yescomplemented
69#3930—28no—
70C22×M32—51no—
71#2929—51no—
72C2×#350—51no—
73C2×#350D511yescharacteristic, complemented
74#2112—51no—
75#1379—51no—
76#1379—51no—
77C23×D5M1611yescharacteristic
78C5×#41—21no—
79C5×#41—21no—
80C5×#41—21no—
81C5×#41—21no—
82C2×C5×Q8C2×C811yescharacteristic
83C2×C5×D4—21no—
84C2×C5×D4C2×C811yescharacteristic
85C22×C4×C5—21no—
86C22×C4×C5C22×C411yescharacteristic
87C2×C22⋊D5—22no—
88C22×Dic5M1611yescharacteristic
89C2×C4×D5—21no—
90C2×C4×D5—21no—
91C2×C4×D5—21no—
92C2×C4×D5—21no—
93C2×C4×D5C22⋊C412yes—
94C2×C4×D5C2×C812yes—
95C5×M16—21no—
96C5×M16—21no—
97C5×M16—41no—
98C5×M16—41no—
99C2×C5×C8—21no—
100C2×C5×C8—41no—
101C2×C5×C8—41no—
102C2×C5×C8C2×D411yescharacteristic
103C2×C5×C8C2×D411yescharacteristic
104C2×C5×C8C2×D411yescharacteristic
105C2×C5×C8C2×D411yescharacteristic
106C2×C5×C8#4111yescharacteristic
107C2×C5×C8#4111yescharacteristic
108C22⋊Dic5—21no—
109C22⋊Dic5—22no—
110#685—22no—
111C4⋊Dic5C2×C812yes—
112#683—22no—
113C4×Dic5—21no—
114#681—21no—
115#681—21no—
116C2×#168—21no—
117C2×#168—21no—
118C2×#168—21no—
119C2×#168C22⋊C412yes—
120C8×D5—22no—
121C8×D5—22no—
122C8×D5—22no—
123C8×D5—22no—
124C5×C16—22no—
125C5×C16—41no—
126#672—22no—
127#672—41no—
128C2×#131C2×D511yescharacteristic
129C23×C8—51no—
130#525—51no—
131C2×M32—51no—
132C2×M32—102no—
133C2×M32—102no—
134C2×M32—102no—
135C2×M32C2×D511yescharacteristic
136C22×C16—51no—
137C22×C16C2×D511yescharacteristic
138#435—102no—
139C8×D4—102no—
140#424—51no—
141#408—51no—
142#407—51no—
143#405—51no—
144#350—22no—
145#350—102no—
146C22⋊C16—102no—
147C23×C5—21no—
148C23×C5C2×M1611yescharacteristic
149C22×D5—21no—
150C22×D5—21no—
151C22×D5—42no—
152C22×D5C22⋊C812yes—
153C5×Q8—21no—
154C5×Q8—21no—
155C5×D4—21no—
156C5×D4—21no—
157C5×D4—41no—
158C5×D4—41no—
159C2×C4×C5—21no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5C2×C22⋊C411yescharacteristic
163C2×C4×C5C4×D411yescharacteristic
164C2×C4×C5C4×D411yescharacteristic
165C2×C4×C5C22×C811yescharacteristic
166C2×C4×C5#13111yescharacteristic
167C2×C4×C5#13111yescharacteristic
168C22⋊D5—44no—
169C2×Dic5—21no—
170C2×Dic5—21no—
171C2×Dic5—22no—
172C2×Dic5C22⋊C812yes—
173C4×D5—22no—
174C4×D5—22no—
175C4×D5—22no—
176C4×D5—22no—
177C5×C8—41no—
178C5×C8#12011yescharacteristic
179C5×C8#12111yescharacteristic
180C5×C8#12111yescharacteristic
181C5×C8#12311yescharacteristic
182#168—22no—
183#168—41no—
184C2×#41C4×D511yescharacteristic
185C23×C4—51no—
186#131—21no—
187#131—21no—
188#131—21no—
189#131—21no—
190C2×M16—21no—
191C2×M16—51no—
192C2×M16C4×D511yescharacteristic
193C22×C8—21no—
194C22×C8—51no—
195C22×C8—52no—
196C22×C8—52no—
197C22×C8—101no—
198C22×C8—101no—
199C22×C8—101no—
200C22×C8—101no—
201C22×C8C22×D511yescharacteristic
202#123—101no—
203C22⋊Q8—52no—
204#121—52no—
205#120—101no—
206C4×D4—102no—
207#117—51no—
208M32—21no—
209M32—21no—
210M32—108no—
211M32—101no—
212M32—101no—
213C2×C16—21no—
214C2×C16—21no—
215C2×C16—21no—
216C2×C16—52no—
217C2×C16—101no—
218C2×C16—101no—
219C2×C16—101no—
220C2×C16C22⋊D512yescomplemented
221C4⋊C8—102no—
222C22⋊C8—102no—
223C22⋊C8—102no—
224#97—101no—
225C4×C8—101no—
226C22×C5—22no—
227C22×C5—42no—
228C22×C5—41no—
229C22×C5C2×C22⋊C811yescharacteristic
230C22×C5#43511yescharacteristic
231C22×C5#43511yescharacteristic
232C2×D5—22no—
233C2×D5—22no—
234C2×D5—22no—
235C2×D5—42no—
236C2×D5—42no—
237C4×C5—41no—
238C4×C5#38611yescharacteristic
239C4×C5#40811yescharacteristic
240C4×C5C8×D411yescharacteristic
241C4×C5C8×D411yescharacteristic
242Dic5—22no—
243Dic5—42no—
244C24—51no—
245#41—21no—
246#41—21no—
247#41—21no—
248#41—21no—
249C2×Q8C8×D511yescharacteristic
250C2×D4—21no—
251C2×D4—102no—
252C2×D4C8×D511yescharacteristic
253C22×C4—21no—
254C22×C4—51no—
255C22×C4—52no—
256C22×C4—52no—
257C22×C4—101no—
258C22×C4—101no—
259C22×C4—101no—
260C22×C4—101no—
261C22×C4C2×C4×D511yescharacteristic
262M16—21no—
263M16—21no—
264M16—41no—
265M16—41no—
266M16—101no—
267M16—101no—
268C2×C8—21no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8—52no—
272C2×C8—101no—
273C2×C8—101no—
274C2×C8—102no—
275C2×C8—102no—
276C2×C8—102no—
277C2×C8—102no—
278C2×C8—101no—
279C2×C8#70911yescharacteristic
280C2×C8D4×D511yescharacteristic
281C2×C8D4×D511yescharacteristic
282C2×C8D4×D511yescharacteristic
283C2×C8#71111yescharacteristic
284C2×C8C2×C22⋊D511yescharacteristic
285C4⋊C4—52no—
286C4⋊C4—102no—
287C22⋊C4—102no—
288C22⋊C4—102no—
289C22⋊C4—101no—
290C42—101no—
291C16—22no—
292C16—41no—
293C16—102no—
294C16—201no—
295C2×C5—21no—
296C2×C5—21no—
297C2×C5—81no—
298C2×C5#186911yescharacteristic
299C2×C5#211712yes—
300D5—42no—
301C23—21no—
302C23—52no—
303C23—101no—
304C23—101no—
305C23—202no—
306C23D5×M1611yescharacteristic
307Q8—21no—
308Q8—21no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—41no—
313D4—204no—
314C2×C4—21no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—52no—
318C2×C4—101no—
319C2×C4—101no—
320C2×C4—102no—
321C2×C4—102no—
322C2×C4—102no—
323C2×C4—102no—
324C2×C4—102no—
325C2×C4D5×C22⋊C411yescharacteristic
326C2×C4#402711yescharacteristic
327C2×C4C2×C8×D511yescharacteristic
328C2×C4#404711yescharacteristic
329C2×C4#405311yescharacteristic
330C2×C4C4×C22⋊D511yescharacteristic
331C8—41no—
332C8—102no—
333C8—201no—
334C8#402911yescharacteristic
335C8#403011yescharacteristic
336C8#408311yescharacteristic
337C8#408411yescharacteristic
338C5#1298411yescharacteristic, complemented, Sylow
339C22—22no—
340C22—41no—
341C22—42no—
342C22—102no—
343C22—102no—
344C22—102no—
345C22—202no—
346C22—202no—
347C22D5×C22⋊C811yescharacteristic
348C22#6501711yescharacteristic
349C22#6541611yescharacteristic
350C4—41no—
351C4—102no—
352C4—202no—
353C4#6501411yescharacteristic
354C4#6501611yescharacteristic
355C4#6524511yescharacteristic
356C4C8×C22⋊D511yescharacteristic
357C2—21no—
358C2—21no—
359C2—81no—
360C2—202no—
361C2#1059991812yes—
362C2#1060075011yescharacteristic
subgroupG/H
centerC2×C8D4×D5
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC2×C5×#350C2
socleC22×C5C2×C22⋊C8
prime radical#66162C4
cosocleC22×C5×C8C23
hypercenterC2×#350D5
hypocenterC5#12984
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#350

Complements

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

NH ≅ G/Ntype
2. C22×#3930C2semidirect
3. C2×C5×#350C2semidirect
4. C2×#64781C2semidirect
5. #10602224C2semidirect
6. #10598306C2semidirect
7. #10598296C2semidirect
57. C2×C5×C16D4semidirect
68. C2×#672D4semidirect
73. C2×#350D5semidirect
220. C2×C16C22⋊D5semidirect
338. C5#12984semidirect

Maximal subgroups

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

subgroupindex
#106155252
C22×#39302
C2×C5×#3502
C2×#647812
#106022242
#105983062
#105982962
#129845