Finite Group Databasebeta

← #12016181

Subgroups — #12016181

Order 1280.

488 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10615465C211yesmaximal, characteristic
2#10613738C211yesmaximal, characteristic, complemented
3C5×#2112C211yesmaximal, characteristic, complemented
4#10602756C211yesmaximal, characteristic, complemented
5#10602228C211yesmaximal, characteristic, complemented
6#10598305C211yesmaximal, characteristic, complemented
7#10598304C211yesmaximal, characteristic, complemented
8C23×C5×C8C2211yescharacteristic
9#66125C411yescharacteristic
10C2×#4047C2211yescharacteristic
11C2×C5×M32C2211yescharacteristic
12C2×C5×M32C2211yescharacteristic
13#65496C411yescharacteristic
14#65400—22no—
15#65399C411yescharacteristic
16C8×C22⋊D5—22no—
17#65391C411yescharacteristic
18#65390C2211yescharacteristic
19C2×#3944C2211yescharacteristic
20C2×#3944C2211yescharacteristic
21#65196—22no—
22D5×M32—22no—
23#65190—22no—
24C5×C22⋊C16—22no—
25C22⋊#672—22no—
26#64734—22no—
27#12981—51nomaximal, Sylow
28C23×C4×C5C2×C411yescharacteristic
29C2×#709C2×C411yescharacteristic
30C22×C5×C8—21no—
31C22×C5×C8—21no—
32C22×C5×C8—21no—
33C22×C5×C8—21no—
34C22×C5×C8—21no—
35C22×C5×C8—21no—
36C22×C5×C8C2×C411yescharacteristic
37C22×C5×C8C2311yescharacteristic
38#4099C812yes—
39#4076—21no—
40#4075C812yes—
41C4×C22⋊D5—22no—
42#4072C2×C411yescharacteristic
43#4070—21no—
44C2×#681C2×C411yescharacteristic
45C2×#681C2×C411yescharacteristic
46#4047—21no—
47#4047—21no—
48#4047—21no—
49#4047—21no—
50C2×#676D412yes—
51C2×C8×D5D412yes—
52C5×M32—21no—
53C5×M32—21no—
54C5×M32—21no—
55C5×M32—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—
65#3944—21no—
66#3944—21no—
67C2×#672—21no—
68C2×#672D412yescomplemented
69#3930—24no—
70D5×C16—24no—
71#3407—51no—
72#2929—51no—
73#2115—51no—
74#2112—51no—
75#2112D511yescharacteristic, complemented
76#1378—51no—
77#1378—51no—
78C24×C5C2×C811yescharacteristic
79C22×C4×C5—21no—
80C22×C4×C5—21no—
81C22×C4×C5—21no—
82C22×C4×C5—21no—
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5C2×C811yescharacteristic
86C22×C4×C5C22×C411yescharacteristic
87C2×C22⋊D5—22no—
88C2×C22⋊D5C2×C812yes—
89#709—21no—
90#709—21no—
91#709—21no—
92#709—21no—
93C2×D20M1611yescharacteristic
94C2×C4×D5C22⋊C412yes—
95C2×Dic10M1611yescharacteristic
96C2×C5×C8—21no—
97C2×C5×C8—21no—
98C2×C5×C8—21no—
99C2×C5×C8—41no—
100C2×C5×C8—41no—
101C2×C5×C8—41no—
102C2×C5×C8—41no—
103C2×C5×C8C2×D411yescharacteristic
104C2×C5×C8C2×D411yescharacteristic
105C2×C5×C8C2×D411yescharacteristic
106C2×C5×C8C2×D411yescharacteristic
107C2×C5×C8#4111yescharacteristic
108C2×C5×C8#4111yescharacteristic
109C22⋊Dic5—22no—
110C22⋊Dic5C2×C812yes—
111#685—22no—
112C4⋊Dic5—21no—
113#683—22no—
114C4×Dic5—21no—
115#681—21no—
116#681—21no—
117#681—21no—
118#681—21no—
119C2×#168—21no—
120C2×#168C22⋊C412yes—
121#676—22no—
122#676—22no—
123C8×D5—22no—
124C8×D5—22no—
125C5×C16—22no—
126C5×C16—41no—
127#672—22no—
128#672—41no—
129C2×#131—51no—
130C23×C8C2×D511yescharacteristic
131#525—51no—
132#504—102no—
133#504—102no—
134C2×M32—51no—
135C2×M32—51no—
136C2×M32—102no—
137C2×M32C2×D511yescharacteristic
138C2×M32C2×D511yescharacteristic
139#435—102no—
140C8×D4—102no—
141#424—51no—
142#408—51no—
143#407—51no—
144#405—51no—
145#349—102no—
146C22⋊C16—22no—
147C22⋊C16—102no—
148C23×C5—21no—
149C23×C5—21no—
150C23×C5—21no—
151C23×C5—42no—
152C23×C5C22×C811yescharacteristic
153C22×D5C22⋊C812yes—
154C2×C4×C5—21no—
155C2×C4×C5—21no—
156C2×C4×C5—21no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5C2×C22⋊C411yescharacteristic
162C2×C4×C5C4×D411yescharacteristic
163C2×C4×C5C4×D411yescharacteristic
164C2×C4×C5C2×M1611yescharacteristic
165C2×C4×C5#13111yescharacteristic
166C2×C4×C5#13111yescharacteristic
167C22⋊D5—22no—
168C22⋊D5—22no—
169C22⋊D5—44no—
170C2×Dic5—22no—
171C2×Dic5C22⋊C812yes—
172D20—21no—
173D20—21no—
174C4×D5—22no—
175C4×D5—22no—
176Dic10—21no—
177Dic10—21no—
178C5×C8—41no—
179C5×C8#12011yescharacteristic
180C5×C8#12111yescharacteristic
181C5×C8#12111yescharacteristic
182C5×C8#12311yescharacteristic
183#168—22no—
184#168—41no—
185C2×#41—51no—
186C23×C4C4×D511yescharacteristic
187#131—101no—
188#131—101no—
189#131—101no—
190#131—101no—
191C2×M16—51no—
192C2×M16—52no—
193C2×M16—51no—
194C22×C8—21no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—21no—
198C22×C8—21no—
199C22×C8—21no—
200C22×C8—52no—
201C22×C8C4×D511yescharacteristic
202C22×C8C22×D511yescharacteristic
203#123—52no—
204C22⋊Q8—101no—
205#121—101no—
206#120—52no—
207C4×D4—102no—
208#117—51no—
209M32—21no—
210M32—21no—
211M32—21no—
212M32—21no—
213M32—104no—
214M32—101no—
215M32—101no—
216M32—101no—
217M32—101no—
218C2×C16—21no—
219C2×C16—52no—
220C2×C16—104no—
221C2×C16—101no—
222C2×C16C22⋊D512yescomplemented
223C4⋊C8—102no—
224C22⋊C8—102no—
225C22⋊C8—102no—
226#97—101no—
227C4×C8—101no—
228C22×C5—22no—
229C22×C5—22no—
230C22×C5—22no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5—41no—
234C22×C5—41no—
235C22×C5—41no—
236C22×C5C2×C22⋊C811yescharacteristic
237C22×C5C8×D411yescharacteristic
238C22×C5C8×D411yescharacteristic
239C2×D5—22no—
240C2×D5—42no—
241C4×C5—41no—
242C4×C5#38611yescharacteristic
243C4×C5#40811yescharacteristic
244C4×C5#43511yescharacteristic
245C4×C5#43511yescharacteristic
246Dic5—22no—
247Dic5—42no—
248C24C8×D511yescharacteristic
249#41—101no—
250#41—101no—
251#41—101no—
252#41—101no—
253C2×Q8—51no—
254C2×D4—52no—
255C2×D4—51no—
256C2×D4—102no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—21no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—52no—
264C22×C4C8×D511yescharacteristic
265C22×C4C2×C4×D511yescharacteristic
266M16—101no—
267M16—101no—
268M16—102no—
269M16—102no—
270M16—101no—
271M16—101no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—41no—
276C2×C8—41no—
277C2×C8—41no—
278C2×C8—41no—
279C2×C8—52no—
280C2×C8—102no—
281C2×C8—102no—
282C2×C8—101no—
283C2×C8#70911yescharacteristic
284C2×C8D4×D511yescharacteristic
285C2×C8D4×D511yescharacteristic
286C2×C8D4×D511yescharacteristic
287C2×C8#71111yescharacteristic
288C2×C8C2×C22⋊D511yescharacteristic
289C4⋊C4—102no—
290C4⋊C4—101no—
291C22⋊C4—52no—
292C22⋊C4—102no—
293C22⋊C4—102no—
294C42—101no—
295C16—22no—
296C16—41no—
297C16—102no—
298C16—201no—
299C2×C5—21no—
300C2×C5—21no—
301C2×C5—21no—
302C2×C5—42no—
303C2×C5#186911yescharacteristic
304D5—42no—
305C23—21no—
306C23—21no—
307C23—21no—
308C23—42no—
309C23—52no—
310C23C2×C8×D511yescharacteristic
311Q8—101no—
312Q8—101no—
313D4—102no—
314D4—102no—
315D4—101no—
316D4—101no—
317D4—204no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—52no—
326C2×C4—102no—
327C2×C4—102no—
328C2×C4—102no—
329C2×C4D5×C22⋊C411yescharacteristic
330C2×C4#402711yescharacteristic
331C2×C4#404711yescharacteristic
332C2×C4D5×M1611yescharacteristic
333C2×C4#405311yescharacteristic
334C2×C4C4×C22⋊D511yescharacteristic
335C8—41no—
336C8—102no—
337C8—201no—
338C8#402911yescharacteristic
339C8#403011yescharacteristic
340C8#408311yescharacteristic
341C8#408411yescharacteristic
342C5#1298111yescharacteristic, complemented, Sylow
343C22—22no—
344C22—22no—
345C22—22no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—102no—
352C22—202no—
353C22D5×C22⋊C811yescharacteristic
354C22#6501411yescharacteristic
355C22C8×C22⋊D511yescharacteristic
356C4—41no—
357C4—102no—
358C4—202no—
359C4#6501611yescharacteristic
360C4#6501711yescharacteristic
361C4#6524511yescharacteristic
362C4#6541611yescharacteristic
363C2—21no—
364C2—21no—
365C2—21no—
366C2—42no—
367C2—202no—
368C2#1060075011yescharacteristic
subgroupG/H
centerC8#4083
commutatorC23×C5C22×C8
FrattiniC22×C8C22×D5
FittingC5×#2112C2
socleC2×C5#1869
prime radical#66125C4
cosocleC22×C5×C8C23
hypercenter#2112D5
hypocenterC5#12981
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C8 ◁ C22×C8 ◁ #2112

Complements

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

NH ≅ G/Ntype
2. #10613738C2semidirect
3. C5×#2112C2semidirect
4. #10602756C2semidirect
5. #10602228C2semidirect
6. #10598305C2semidirect
7. #10598304C2semidirect
57. C2×C5×C16D4semidirect
68. C2×#672D4semidirect
75. #2112D5semidirect
222. C2×C16C22⋊D5semidirect
342. C5#12981semidirect

Maximal subgroups

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

subgroupindex
#106154652
#106137382
C5×#21122
#106027562
#106022282
#105983052
#105983042
#129815