Finite Group Databasebeta

← #12016180

Subgroups — #12016180

Order 1280.

470 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#65433C211yesmaximal, characteristic
2C2×#65190C211yesmaximal, characteristic, complemented
3C5×#2113C211yesmaximal, characteristic, complemented
4C2×#64781C211yesmaximal, characteristic, complemented
5C2×#64735C211yesmaximal, characteristic, complemented
6#10598301C211yesmaximal, characteristic, complemented
7#10598295C211yesmaximal, characteristic, complemented
8C2×C5×#131C2211yescharacteristic
9C2×#4096C411yescharacteristic
10C2×#4047C2211yescharacteristic
11C2×C5×M32C2211yescharacteristic
12C22×C5×C16C2211yescharacteristic
13C2×#3969C411yescharacteristic
14#65433—22no—
15#65433—22no—
16C2×#3957C411yescharacteristic
17C2×#3954C411yescharacteristic
18C2×C8×Dic5C2211yescharacteristic
19C2×#3944C2211yescharacteristic
20C22×#672C2211yescharacteristic
21#65190—22no—
22#65190—22no—
23C2×#3930—21no—
24C2×D5×C16—21no—
25C5×C22⋊C16—21no—
26C5×C22⋊C16—21no—
27#64781—22no—
28#64735—22no—
29#12980—51nomaximal, Sylow
30C2×C5×#41C2×C411yescharacteristic
31C2×#709C2×C411yescharacteristic
32C5×#131—21no—
33C5×#131—21no—
34C5×#131—21no—
35C5×#131—21no—
36C2×C5×M16—21no—
37C2×C5×M16C2×C411yescharacteristic
38C22×C5×C8—21no—
39C22×C5×C8C2311yescharacteristic
40#4096—22no—
41#4096—22no—
42C2×#689C811yescharacteristic
43C2×#688C811yescharacteristic
44C2×#687C811yescharacteristic
45C2×#686C811yescharacteristic
46C2×C4×Dic5C2×C411yescharacteristic
47C2×#681C2×C411yescharacteristic
48C22×#168C2×C411yescharacteristic
49#4047—21no—
50#4047—21no—
51#4047D412yes—
52#4047D412yes—
53C2×#676—21no—
54C2×C8×D5—21no—
55C5×M32—21no—
56C5×M32—21no—
57C2×C5×C16—21no—
58C2×C5×C16—21no—
59C2×C5×C16—21no—
60C2×C5×C16D411yescharacteristic
61C2×C5×C16D411yescharacteristic
62#3969—22no—
63#3957—22no—
64#3954—22no—
65C8×Dic5—21no—
66C8×Dic5—21no—
67#3944—21no—
68#3944D412yes—
69C2×#672—21no—
70C2×#672—21no—
71C2×#672—21no—
72C2×#672—21no—
73#3930—24no—
74D5×C16—24no—
75C2×#504—51no—
76C2×#443—51no—
77C2×#350—51no—
78C2×#350—51no—
79#2113D511yescharacteristic, complemented
80#1376—51no—
81#1374—51no—
82C5×#41—21no—
83C5×#41—21no—
84C5×#41—21no—
85C5×#41—21no—
86C2×C5×Q8C2×C811yescharacteristic
87C2×C5×D4—21no—
88C2×C5×D4C2×C811yescharacteristic
89C22×C4×C5—21no—
90C22×C4×C5C22×C411yescharacteristic
91C2×C22⋊D5—21no—
92C22×Dic5—21no—
93#709—21no—
94#709—21no—
95#709C22⋊C412yes—
96#709M1612yes—
97C2×D20C2×C811yescharacteristic
98C2×C4×D5—21no—
99C2×Dic10C2×C811yescharacteristic
100C5×M16—21no—
101C5×M16—21no—
102C5×M16—41no—
103C5×M16—41no—
104C2×C5×C8—21no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8C2×D411yescharacteristic
108C2×C5×C8C2×D411yescharacteristic
109C2×C5×C8C2×D411yescharacteristic
110C2×C5×C8C2×D411yescharacteristic
111C2×C5×C8#4111yescharacteristic
112C2×C5×C8#4111yescharacteristic
113#689—22no—
114#688—22no—
115#687—22no—
116#686—22no—
117C4×Dic5—21no—
118C4×Dic5—21no—
119#681—21no—
120#681C22⋊C412yes—
121C2×#168—21no—
122C2×#168—21no—
123C2×#168—21no—
124C2×#168C2×C811yescharacteristic
125C2×#168C2×C811yescharacteristic
126#676—22no—
127#676—22no—
128C8×D5—22no—
129C8×D5—22no—
130C5×C16—21no—
131C5×C16—21no—
132C5×C16—41no—
133#672—22no—
134#672—41no—
135C2×#135—51no—
136C2×#131—51no—
137C2×#131C2×D511yescharacteristic
138#504—102no—
139#504—102no—
140C2×M32—51no—
141C2×M32—101no—
142C2×M32C2×D511yescharacteristic
143C22×C16—51no—
144C22×C16—101no—
145C22×C16C2×D511yescharacteristic
146#443—102no—
147#443—102no—
148C2×#108—51no—
149C2×#104—51no—
150C2×#104—51no—
151C2×C4×C8—51no—
152#350—102no—
153#350—102no—
154C22⋊C16—21no—
155C22⋊C16—21no—
156C23×C5—21no—
157C23×C5#13111yescharacteristic
158C22×D5—21no—
159C5×Q8—21no—
160C5×Q8—21no—
161C5×D4—21no—
162C5×D4—21no—
163C5×D4—41no—
164C5×D4—41no—
165C2×C4×C5—21no—
166C2×C4×C5—41no—
167C2×C4×C5—41no—
168C2×C4×C5C2×C22⋊C411yescharacteristic
169C2×C4×C5C4×D411yescharacteristic
170C2×C4×C5C4×D411yescharacteristic
171C2×C4×C5C22×C811yescharacteristic
172C2×C4×C5C2×M1611yescharacteristic
173C2×C4×C5#13111yescharacteristic
174C22⋊D5—22no—
175C22⋊D5—22no—
176C2×Dic5—21no—
177C2×Dic5—22no—
178C2×Dic5—41no—
179C2×Dic5—41no—
180D20—21no—
181D20C22⋊C812yes—
182C4×D5—22no—
183C4×D5—22no—
184Dic10—21no—
185Dic10C22⋊C812yes—
186C5×C8—41no—
187C5×C8#12011yescharacteristic
188C5×C8#12111yescharacteristic
189C5×C8#12111yescharacteristic
190C5×C8#12311yescharacteristic
191#168—22no—
192#168—21no—
193#168—21no—
194C2×#41—51no—
195C2×#41C4×D511yescharacteristic
196#135—102no—
197#135—102no—
198C2×Q16—51no—
199C2×SD16—51no—
200C2×SD16—51no—
201C2×D8—51no—
202#131—21no—
203#131—21no—
204#131—21no—
205#131—21no—
206#131—52no—
207#131—52no—
208#131—101no—
209#131—101no—
210C2×M16—21no—
211C2×M16—51no—
212C2×M16—101no—
213C2×M16C4×D511yescharacteristic
214C22×C8—21no—
215C22×C8—51no—
216C22×C8—101no—
217C22×C8C22×D511yescharacteristic
218C2×C42—51no—
219M32—21no—
220M32—21no—
221M32—52no—
222M32—104no—
223M32—101no—
224C2×C16—21no—
225C2×C16—21no—
226C2×C16—21no—
227C2×C16—104no—
228C2×C16—101no—
229C2×C16—101no—
230C2×C16—101no—
231C2×C16—101no—
232C2×C16C22⋊D511yescharacteristic
233C2×C16C22⋊D511yescharacteristic
234#108—102no—
235#104—102no—
236#104—102no—
237C4×C8—101no—
238C4×C8—101no—
239C22×C5—21no—
240C22×C5—21no—
241C22×C5—41no—
242C22×C5—41no—
243C22×C5—41no—
244C22×C5#40811yescharacteristic
245C22×C5C8×D411yescharacteristic
246C22×C5#43511yescharacteristic
247C2×D5—22no—
248C2×D5—41no—
249C2×D5—41no—
250C4×C5—41no—
251C4×C5#38611yescharacteristic
252C4×C5C2×C22⋊C811yescharacteristic
253C4×C5C8×D411yescharacteristic
254C4×C5#43511yescharacteristic
255Dic5—22no—
256Dic5—42no—
257#41—21no—
258#41—21no—
259#41—21no—
260#41—21no—
261#41—52no—
262#41—52no—
263#41—101no—
264#41—101no—
265C2×Q8—51no—
266C2×Q8C8×D511yescharacteristic
267C2×D4—21no—
268C2×D4—51no—
269C2×D4—101no—
270C2×D4C8×D511yescharacteristic
271C22×C4—21no—
272C22×C4—101no—
273C22×C4—101no—
274C22×C4C2×C4×D511yescharacteristic
275Q16—102no—
276SD16—102no—
277SD16—102no—
278D8—102no—
279M16—21no—
280M16—21no—
281M16—41no—
282M16—41no—
283M16—52no—
284M16—101no—
285M16—102no—
286M16—102no—
287C2×C8—21no—
288C2×C8—41no—
289C2×C8—41no—
290C2×C8—51no—
291C2×C8—51no—
292C2×C8—101no—
293C2×C8—101no—
294C2×C8—101no—
295C2×C8—102no—
296C2×C8—102no—
297C2×C8#70911yescharacteristic
298C2×C8D4×D511yescharacteristic
299C2×C8D4×D511yescharacteristic
300C2×C8D4×D511yescharacteristic
301C2×C8#71111yescharacteristic
302C2×C8C2×C22⋊D511yescharacteristic
303C42—101no—
304C42—101no—
305C16—21no—
306C16—21no—
307C16—41no—
308C16—102no—
309C16—201no—
310C2×C5—21no—
311C2×C5—21no—
312C2×C5—81no—
313C2×C5#186911yescharacteristic
314C2×C5#217011yescharacteristic
315C2×C5#217111yescharacteristic
316D5—42no—
317C23—21no—
318C23—101no—
319C23#404711yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—52no—
323Q8—101no—
324D4—21no—
325D4—21no—
326D4—41no—
327D4—41no—
328D4—52no—
329D4—102no—
330D4—102no—
331D4—101no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—101no—
336C2×C4—102no—
337C2×C4—102no—
338C2×C4—102no—
339C2×C4—201no—
340C2×C4—201no—
341C2×C4D5×C22⋊C411yescharacteristic
342C2×C4#402711yescharacteristic
343C2×C4C2×C8×D511yescharacteristic
344C2×C4D5×M1611yescharacteristic
345C2×C4#405311yescharacteristic
346C2×C4C4×C22⋊D511yescharacteristic
347C8—41no—
348C8—102no—
349C8—101no—
350C8—101no—
351C8#402911yescharacteristic
352C8#403011yescharacteristic
353C8#408311yescharacteristic
354C8#408411yescharacteristic
355C5#1298011yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—41no—
359C22—41no—
360C22—41no—
361C22—102no—
362C22—201no—
363C22—201no—
364C22#6501611yescharacteristic
365C22#6501711yescharacteristic
366C22C8×C22⋊D511yescharacteristic
367C4—41no—
368C4—102no—
369C4—202no—
370C4D5×C22⋊C811yescharacteristic
371C4#6501411yescharacteristic
372C4#6524511yescharacteristic
373C4#6541611yescharacteristic
374C2—21no—
375C2—21no—
376C2—81no—
377C2—202no—
378C2#1060075011yescharacteristic
379C2#1060224511yescharacteristic
380C2#1060224611yescharacteristic
subgroupG/H
centerC2×C8C2×C22⋊D5
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#2113C2
socleC22×C5C8×D4
prime radicalC2×#4096C4
cosocleC22×C5×C8C23
hypercenter#2113D5
hypocenterC5#12980
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×C16 ◁ #2113

Complements

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

NH ≅ G/Ntype
2. C2×#65190C2semidirect
3. C5×#2113C2semidirect
4. C2×#64781C2semidirect
5. C2×#64735C2semidirect
6. #10598301C2semidirect
7. #10598295C2semidirect
79. #2113D5semidirect
355. C5#12980semidirect

Maximal subgroups

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

subgroupindex
C2×#654332
C2×#651902
C5×#21132
C2×#647812
C2×#647352
#105983012
#105982952
#129805