Finite Group Databasebeta

← #12016179

Subgroups — #12016179

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×C5×#443C211yesmaximal, characteristic
2C2×#65429C211yesmaximal, characteristic, complemented
3C2×#64781C211yesmaximal, characteristic, complemented
4C2×#64781C211yesmaximal, characteristic, complemented
5#10602797C211yesmaximal, characteristic, complemented
6#10598149C211yesmaximal, characteristic, complemented
7#10598148C211yesmaximal, characteristic, complemented
8C2×C5×#135C411yescharacteristic
9C2×C5×#131C2211yescharacteristic
10C2×C5×#131C2211yescharacteristic
11C5×#443—22no—
12C5×#443—22no—
13C2×C5×#108C411yescharacteristic
14C2×C5×#104C411yescharacteristic
15C2×C5×#104C411yescharacteristic
16C2×C4×C5×C8C2211yescharacteristic
17#65429—22no—
18#65429—22no—
19C2×#3944—21no—
20C2×#3944C2211yescharacteristic
21C2×#3944C2211yescharacteristic
22C22×#672—21no—
23C22×#672C2211yescharacteristic
24C22×#672C2211yescharacteristic
25#64781—22no—
26#64781—22no—
27C22⋊#672—21no—
28C22⋊#672—21no—
29#12980—51nomaximal, Sylow
30C2×C5×#41C2×C411yescharacteristic
31C2×C5×#41C2×C411yescharacteristic
32C5×#135—22no—
33C5×#135—22no—
34C2×C5×Q16C811yescharacteristic
35C2×C5×SD16C811yescharacteristic
36C2×C5×SD16C811yescharacteristic
37C2×C5×D8C811yescharacteristic
38C5×#131—21no—
39C5×#131—21no—
40C5×#131—21no—
41C5×#131—21no—
42C5×#131—21no—
43C5×#131—21no—
44C5×#131D412yes—
45C5×#131D412yes—
46C2×C5×M16—21no—
47C2×C5×M16—21no—
48C2×C5×M16C2×C411yescharacteristic
49C2×C5×M16C2×C411yescharacteristic
50C22×C5×C8—21no—
51C22×C5×C8—21no—
52C22×C5×C8C2×C411yescharacteristic
53C22×C5×C8C2311yescharacteristic
54C2×C42×C5C2×C411yescharacteristic
55C5×#108—22no—
56C5×#104—22no—
57C5×#104—22no—
58C4×C5×C8—21no—
59C4×C5×C8—21no—
60#3944—24no—
61#3944—21no—
62#3944—21no—
63#3944—21no—
64#3944D412yes—
65C2×#672—24no—
66C2×#672—21no—
67C2×#672—21no—
68C2×#672—21no—
69C2×#672—21no—
70C2×#672—21no—
71C2×#672—21no—
72C2×#672—21no—
73C2×#672D411yescharacteristic
74C2×#672D411yescharacteristic
75C2×#504—51no—
76C2×#443D511yescharacteristic
77C2×#350—51no—
78C2×#350—51no—
79#2113—51no—
80#1376—51no—
81#1374—51no—
82C5×#41—21no—
83C5×#41—21no—
84C5×#41—21no—
85C5×#41—21no—
86C5×#41—21no—
87C5×#41—21no—
88C5×#41C22⋊C412yes—
89C5×#41M1612yes—
90C2×C5×Q8C2×C811yescharacteristic
91C2×C5×Q8C2×C811yescharacteristic
92C2×C5×D4—21no—
93C2×C5×D4—21no—
94C2×C5×D4C2×C811yescharacteristic
95C2×C5×D4C2×C811yescharacteristic
96C22×C4×C5—21no—
97C22×C4×C5—21no—
98C22×C4×C5—21no—
99C22×C4×C5C22×C411yescharacteristic
100C5×Q16—22no—
101C5×SD16—22no—
102C5×SD16—22no—
103C5×D8—22no—
104C5×M16—21no—
105C5×M16—22no—
106C5×M16—22no—
107C5×M16—21no—
108C5×M16—21no—
109C5×M16—41no—
110C5×M16—41no—
111C5×M16C22⋊C412yes—
112C2×C5×C8—21no—
113C2×C5×C8—21no—
114C2×C5×C8—21no—
115C2×C5×C8—22no—
116C2×C5×C8—22no—
117C2×C5×C8—21no—
118C2×C5×C8—41no—
119C2×C5×C8—41no—
120C2×C5×C8C2×C811yescharacteristic
121C2×C5×C8C2×C811yescharacteristic
122C2×C5×C8C2×D411yescharacteristic
123C2×C5×C8C2×D411yescharacteristic
124C2×C5×C8C2×D411yescharacteristic
125C2×C5×C8C2×D411yescharacteristic
126C2×C5×C8#4111yescharacteristic
127C2×C5×C8#4111yescharacteristic
128C42×C5—21no—
129C42×C5—21no—
130#672—21no—
131#672—22no—
132#672—21no—
133#672—41no—
134#672—41no—
135C2×#135Dic511yescharacteristic
136C2×#131C2×D511yescharacteristic
137C2×#131C2×D511yescharacteristic
138#504—102no—
139#504—102no—
140C2×M32—51no—
141C2×M32—51no—
142C2×M32—101no—
143C22×C16—51no—
144C22×C16—51no—
145C22×C16—101no—
146#443—22no—
147#443—22no—
148C2×#108Dic511yescharacteristic
149C2×#104Dic511yescharacteristic
150C2×#104Dic511yescharacteristic
151C2×C4×C8C2×D511yescharacteristic
152#350—102no—
153#350—102no—
154C22⋊C16—101no—
155C22⋊C16—101no—
156C23×C5—21no—
157C23×C5—21no—
158C23×C5#13111yescharacteristic
159C5×Q8—21no—
160C5×Q8—21no—
161C5×Q8—21no—
162C5×Q8C22⋊C812yes—
163C5×D4—22no—
164C5×D4—22no—
165C5×D4—21no—
166C5×D4—21no—
167C5×D4—21no—
168C5×D4—41no—
169C5×D4—41no—
170C5×D4C22⋊C812yes—
171C2×C4×C5—21no—
172C2×C4×C5—22no—
173C2×C4×C5—22no—
174C2×C4×C5—22no—
175C2×C4×C5—21no—
176C2×C4×C5—41no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—41no—
180C2×C4×C5C2×C22⋊C411yescharacteristic
181C2×C4×C5C4×D411yescharacteristic
182C2×C4×C5C4×D411yescharacteristic
183C2×C4×C5C22×C811yescharacteristic
184C2×C4×C5C2×M1611yescharacteristic
185C2×C4×C5#13111yescharacteristic
186C5×C8—22no—
187C5×C8—21no—
188C5×C8—21no—
189C5×C8—41no—
190C5×C8#12011yescharacteristic
191C5×C8#12111yescharacteristic
192C5×C8#12111yescharacteristic
193C5×C8#12311yescharacteristic
194C2×#41C2×Dic511yescharacteristic
195C2×#41C2×Dic511yescharacteristic
196#135—22no—
197#135—22no—
198C2×Q16#16811yescharacteristic
199C2×SD16#16811yescharacteristic
200C2×SD16#16811yescharacteristic
201C2×D8#16811yescharacteristic
202#131—21no—
203#131—21no—
204#131—21no—
205#131—21no—
206#131—21no—
207#131—21no—
208#131C22⋊D512yes—
209#131C22⋊D512yes—
210C2×M16—21no—
211C2×M16—21no—
212C2×M16C2×Dic511yescharacteristic
213C2×M16C2×Dic511yescharacteristic
214C22×C8—21no—
215C22×C8—21no—
216C22×C8C2×Dic511yescharacteristic
217C22×C8C22×D511yescharacteristic
218C2×C42C2×Dic511yescharacteristic
219M32—52no—
220M32—104no—
221M32—101no—
222M32—101no—
223M32—101no—
224C2×C16—51no—
225C2×C16—51no—
226C2×C16—104no—
227C2×C16—101no—
228C2×C16—101no—
229C2×C16—101no—
230C2×C16—101no—
231C2×C16—101no—
232C2×C16—101no—
233C2×C16—101no—
234#108—22no—
235#104—22no—
236#104—22no—
237C4×C8—21no—
238C4×C8—21no—
239C22×C5—21no—
240C22×C5—21no—
241C22×C5—22no—
242C22×C5—41no—
243C22×C5—41no—
244C22×C5—41no—
245C22×C5—41no—
246C22×C5—41no—
247C22×C5#40811yescharacteristic
248C22×C5C8×D411yescharacteristic
249C22×C5#43511yescharacteristic
250C4×C5—22no—
251C4×C5—42no—
252C4×C5—41no—
253C4×C5#38611yescharacteristic
254C4×C5C2×C22⋊C811yescharacteristic
255C4×C5C8×D411yescharacteristic
256C4×C5#43511yescharacteristic
257#41—21no—
258#41—21no—
259#41—21no—
260#41—21no—
261#41—21no—
262#41—21no—
263#41#68112yes—
264#41C22⋊Dic512yes—
265C2×Q8C2×#16811yescharacteristic
266C2×Q8C2×#16811yescharacteristic
267C2×D4—21no—
268C2×D4—21no—
269C2×D4C2×#16811yescharacteristic
270C2×D4C2×#16811yescharacteristic
271C22×C4—21no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4C22×Dic511yescharacteristic
275Q16—22no—
276SD16—22no—
277SD16—22no—
278D8—22no—
279M16—21no—
280M16—22no—
281M16—22no—
282M16—21no—
283M16—21no—
284M16—41no—
285M16—41no—
286M16C22⋊Dic512yes—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—22no—
291C2×C8—22no—
292C2×C8—21no—
293C2×C8—41no—
294C2×C8—41no—
295C2×C8C2×#16811yescharacteristic
296C2×C8C2×#16811yescharacteristic
297C2×C8D4×D511yescharacteristic
298C2×C8D4×D511yescharacteristic
299C2×C8#71111yescharacteristic
300C2×C8#71111yescharacteristic
301C2×C8C2×C22⋊D511yescharacteristic
302C2×C8C2×C22⋊D511yescharacteristic
303C42—21no—
304C42—21no—
305C16—101no—
306C16—101no—
307C16—102no—
308C16—201no—
309C16—201no—
310C2×C5—21no—
311C2×C5—21no—
312C2×C5—42no—
313C2×C5—81no—
314C2×C5#186911yescharacteristic
315C2×C5#217011yescharacteristic
316C2×C5#217111yescharacteristic
317C23—21no—
318C23—21no—
319C23#409411yescharacteristic
320Q8—21no—
321Q8—21no—
322Q8—21no—
323Q8C22⋊#16812yes—
324D4—22no—
325D4—22no—
326D4—21no—
327D4—21no—
328D4—21no—
329D4—41no—
330D4—41no—
331D4C22⋊#16812yes—
332C2×C4—21no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—22no—
336C2×C4—21no—
337C2×C4—41no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—41no—
341C2×C4C22×#16811yescharacteristic
342C2×C4C2×#68111yescharacteristic
343C2×C4D4×Dic511yescharacteristic
344C2×C4D4×Dic511yescharacteristic
345C2×C4#409411yescharacteristic
346C2×C4C2×C22⋊Dic511yescharacteristic
347C8—21no—
348C8—21no—
349C8—22no—
350C8—41no—
351C8#408111yescharacteristic
352C8#408311yescharacteristic
353C8#408511yescharacteristic
354C8#408511yescharacteristic
355C5#1298011yescharacteristic, complemented, Sylow
356C22—21no—
357C22—21no—
358C22—22no—
359C22—41no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22D4×#16811yescharacteristic
365C22#6530011yescharacteristic
366C22#6552311yescharacteristic
367C4—22no—
368C4—42no—
369C4—41no—
370C4D4×#16811yescharacteristic
371C4#6530011yescharacteristic
372C4C2×C22⋊#16811yescharacteristic
373C4#6550911yescharacteristic
374C2—21no—
375C2—21no—
376C2—42no—
377C2—81no—
378C2#1060171611yescharacteristic
379C2#1060171711yescharacteristic
380C2#1060240311yescharacteristic
subgroupG/H
centerC2×C8D4×D5
commutatorC2×C4×C5C22×C8
FrattiniC22×C8C22×D5
FittingC2×C5×#443C2
socleC22×C5C8×D4
prime radicalC2×C5×#135C4
cosocleC22×C5×C8C23
hypercenterC2×#443D5
hypocenterC5#12980
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C2×#443

Complements

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

NH ≅ G/Ntype
2. C2×#65429C2semidirect
3. C2×#64781C2semidirect
4. C2×#64781C2semidirect
5. #10602797C2semidirect
6. #10598149C2semidirect
7. #10598148C2semidirect
355. C5#12980semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#4432
C2×#654292
C2×#647812
#106027972
#105981492
#105981482
#129805