Finite Group Databasebeta

← #13034481

Subgroups — #13034481

Order 1280.

1262 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#4033C211yesmaximal, characteristic
2#10617473C212yesmaximal
3#10604908C212yesmaximal
4#10604905C212yesmaximal
5#10604336C214yesmaximal, complemented
6#10604335C214yesmaximal, complemented
7C23×Dic10C2211yescharacteristic
8C22×C5×C4⋊C4C411yescharacteristic
9C22×#683C411yescharacteristic
10C22×#683C2211yescharacteristic
11C22×C4×Dic5C411yescharacteristic
12C22×C4×Dic5C411yescharacteristic
13C22×C4×Dic5C2211yescharacteristic
14C2×#4033—22no—
15C2×#4033—22no—
16C2×#4033—22no—
17C2×#4033—22no—
18C2×#4033C412yes—
19C2×#4033C412yes—
20C2×#4033C2212yes—
21C2×#4033C2212yes—
22#65798C2214yes—
23C2×#4005C2218yes—
24#65759—22no—
25#65758C2214yes—
26#65757—22no—
27#65754—22no—
28C4×#704C2214yes—
29#65748—22no—
30#64919C2218yes—
31#20727—51nomaximal, Sylow
32C23×C4×C5C2×C411yescharacteristic
33C23×C4×C5C2×C411yescharacteristic
34C23×C4×C5C2×C411yescharacteristic
35C23×Dic5C2×C411yescharacteristic
36C23×Dic5C2×C411yescharacteristic
37C23×Dic5C2×C411yescharacteristic
38C23×Dic5C2311yescharacteristic
39C22×Dic10—22no—
40C22×Dic10—22no—
41C22×Dic10—28no—
42C22×Dic10C2×C412yes—
43C22×Dic10C2312yes—
44C2×#704C2318yes—
45C2×C5×C4⋊C4—22no—
46C2×C5×C4⋊C4—22no—
47C2×C5×C4⋊C4C2×C412yes—
48C2×C5×C4⋊C4C2×C412yes—
49C2×#683—22no—
50C2×#683—22no—
51C2×#683—22no—
52C2×#683—22no—
53C2×#683C2×C412yes—
54C2×#683C2×C412yes—
55C2×#683C2×C412yes—
56C2×#683C2312yes—
57C2×C4×Dic5—21no—
58C2×C4×Dic5—21no—
59C2×C4×Dic5—21no—
60C2×C4×Dic5—21no—
61C2×C4×Dic5—21no—
62C2×C4×Dic5—21no—
63C2×C4×Dic5—21no—
64C2×C4×Dic5—21no—
65C2×C4×Dic5C2×C412yes—
66C2×C4×Dic5C2×C412yes—
67C2×C4×Dic5C2×C412yes—
68C2×C4×Dic5C2×C412yes—
69C2×C4×Dic5C2×C411yescharacteristic
70C2×C4×Dic5C2×C411yescharacteristic
71C2×C4×Dic5D412yes—
72C2×C4×Dic5D412yes—
73C2×C4×Dic5D412yes—
74C2×C4×Dic5D412yes—
75C2×C4×Dic5C2311yescharacteristic
76C2×C4×Dic5C2311yescharacteristic
77#4033—24no—
78#4033—24no—
79#4033—24no—
80#4033—24no—
81#4033—24no—
82#4033—24no—
83#4033—24no—
84#4033—24no—
85C22⋊#170—24no—
86C22⋊#170—24no—
87#4005—216no—
88#4004—24no—
89#4002—24no—
90C4⋊#170—24no—
91C4×#170—24no—
92C22×C4×Q8—51no—
93#2920—52no—
94#1821—52no—
95#1801—54no—
96#1784—52no—
97C4×#101—54no—
98C24×C5C22×C411yescharacteristic
99C22×C4×C5—21no—
100C22×C4×C5—21no—
101C22×C4×C5—24no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—42no—
105C22×C4×C5—42no—
106C22×C4×C5C22⋊C412yes—
107C22×C4×C5C22⋊C412yes—
108C22×C4×C5C22×C412yes—
109C22×C4×C5C22×C412yes—
110C22×C4×C5C22×C411yescharacteristic
111C22×C4×C5C22×C411yescharacteristic
112C22×Dic5—21no—
113C22×Dic5—21no—
114C22×Dic5—24no—
115C22×Dic5—24no—
116C22×Dic5—24no—
117C22×Dic5—21no—
118C22×Dic5—21no—
119C22×Dic5—42no—
120C22×Dic5C22⋊C411yescharacteristic
121C22×Dic5C22⋊C411yescharacteristic
122C22×Dic5C22⋊C411yescharacteristic
123C22×Dic5C22⋊C411yescharacteristic
124C22×Dic5C22×C411yescharacteristic
125C22×Dic5C22×C411yescharacteristic
126C22×Dic5C22×C411yescharacteristic
127C22×Dic5C22×C412yes—
128C22×Dic5C22×C412yes—
129C22×Dic5C2×D412yes—
130C22×Dic5C2×D412yes—
131C22×Dic5C2411yescharacteristic
132C2×Dic10—216no—
133C2×Dic10—216no—
134C2×Dic10—24no—
135C2×Dic10—24no—
136C2×Dic10—24no—
137C2×Dic10—24no—
138C2×Dic10—24no—
139C2×Dic10#4118yes—
140#704—216no—
141C2×#170—28no—
142C5×C4⋊C4—24no—
143C5×C4⋊C4—24no—
144#683—24no—
145#683—24no—
146#683—24no—
147#683—24no—
148C4×Dic5—22no—
149C4×Dic5—22no—
150C4×Dic5—22no—
151C4×Dic5—22no—
152C4×Dic5—22no—
153C4×Dic5—22no—
154C4×Dic5—22no—
155C4×Dic5—22no—
156C4×Dic5C22⋊C412yes—
157C4×Dic5C22⋊C412yes—
158C4×Dic5C22⋊C412yes—
159C4×Dic5C22⋊C412yes—
160C4×Dic5C2×D412yes—
161C4×Dic5C2×D412yes—
162C4×Dic5C2×D412yes—
163C4×Dic5C2×D412yes—
164C23×Q8—51no—
165C2×C4×Q8—52no—
166C2×C4×Q8—52no—
167C2×C4×Q8—52no—
168C2×C4×Q8—52no—
169C2×C4×Q8—102no—
170C2×C4×Q8—102no—
171C2×C4×Q8—102no—
172C2×C4×Q8—102no—
173C22×C4⋊C4—51no—
174C22×C4⋊C4—51no—
175C22×C4⋊C4AGL(1,𝔽5)11yescharacteristic
176C22×C42—51no—
177C22×C42—51no—
178C22×C42—51no—
179#432—102no—
180#432—102no—
181#431—102no—
182#431—102no—
183#423—54no—
184C2×#101—58no—
185#407—54no—
186C4×M16—54no—
187#343—58no—
188C23×C5—22no—
189C23×C5—22no—
190C23×C5—22no—
191C23×C5C2×C22⋊C411yescharacteristic
192C23×C5C2×C22⋊C411yescharacteristic
193C23×C5C23×C411yescharacteristic
194C2×C4×C5—24no—
195C2×C4×C5—24no—
196C2×C4×C5—22no—
197C2×C4×C5—22no—
198C2×C4×C5—24no—
199C2×C4×C5—22no—
200C2×C4×C5—42no—
201C2×C4×C5—41no—
202C2×C4×C5—41no—
203C2×C4×C5—42no—
204C2×C4×C5—42no—
205C2×C4×C5—42no—
206C2×C4×C5C2×C22⋊C412yes—
207C2×C4×C5C2×C22⋊C412yes—
208C2×C4×C5#11714yes—
209C2×Dic5—24no—
210C2×Dic5—24no—
211C2×Dic5—22no—
212C2×Dic5—22no—
213C2×Dic5—22no—
214C2×Dic5—22no—
215C2×Dic5—24no—
216C2×Dic5—24no—
217C2×Dic5—22no—
218C2×Dic5—22no—
219C2×Dic5—22no—
220C2×Dic5—22no—
221C2×Dic5—22no—
222C2×Dic5—42no—
223C2×Dic5—42no—
224C2×Dic5—42no—
225C2×Dic5#10114yescomplemented
226C2×Dic5C2×C22⋊C411yescharacteristic
227C2×Dic5C2×C22⋊C411yescharacteristic
228C2×Dic5C2×C22⋊C412yes—
229C2×Dic5C2×C22⋊C411yescharacteristic
230C2×Dic5C2×C22⋊C411yescharacteristic
231C2×Dic5#11714yes—
232C2×Dic5C22×D412yes—
233C2×Dic5C2×#4114yes—
234Dic10—216no—
235Dic10—216no—
236#170—48no—
237C22×Q8—52no—
238C22×Q8—52no—
239C22×Q8—102no—
240C22×Q8—102no—
241C22×Q8—108no—
242C23×C4—51no—
243C23×C4—51no—
244C23×C4—51no—
245C23×C4—51no—
246C23×C4C2×AGL(1,𝔽5)11yescharacteristic
247C23×C4C2×AGL(1,𝔽5)11yescharacteristic
248C23×C4C2×AGL(1,𝔽5)11yescharacteristic
249C2×M16—58no—
250C4×Q8—104no—
251C4×Q8—104no—
252C4×Q8—104no—
253C4×Q8—104no—
254C4×Q8—104no—
255C4×Q8—104no—
256C4×Q8—104no—
257C4×Q8—104no—
258C2×C4⋊C4—22no—
259C2×C4⋊C4—22no—
260C2×C4⋊C4—52no—
261C2×C4⋊C4—52no—
262C2×C4⋊C4—52no—
263C2×C4⋊C4—52no—
264C2×C4⋊C4—102no—
265C2×C4⋊C4—102no—
266C2×C4⋊C4—102no—
267C2×C4⋊C4—102no—
268C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
269C2×C4⋊C4C2×AGL(1,𝔽5)12yes—
270C2×C42—52no—
271C2×C42—52no—
272C2×C42—52no—
273C2×C42—52no—
274C2×C42—51no—
275C2×C42—51no—
276C2×C42—51no—
277C2×C42—51no—
278C2×C42—52no—
279C2×C42—52no—
280C2×C42—52no—
281C2×C42—52no—
282C2×C42—101no—
283C2×C42—101no—
284C2×C42—101no—
285C2×C42—101no—
286C2×C42—101no—
287C2×C42—101no—
288C2×C42—101no—
289C2×C42—101no—
290C4⋊C8—104no—
291C4⋊C8—104no—
292#101—1016no—
293C22⋊C8—104no—
294C22⋊C8—104no—
295#97—104no—
296C4×C8—104no—
297C22×C5—28no—
298C22×C5—21no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—21no—
302C22×C5—21no—
303C22×C5—21no—
304C22×C5C2×#10112yes—
305C22×C5#41312yes—
306C22×C5C22×C22⋊C411yescharacteristic
307C22×C5C2×#11712yes—
308C4×C5—22no—
309C4×C5—22no—
310C4×C5—24no—
311C4×C5—42no—
312Dic5—21no—
313Dic5—21no—
314Dic5—22no—
315Dic5—24no—
316Dic5—42no—
317Dic5C2×#10112yes—
318Dic5C2×#10112yes—
319Dic5#52514yes—
320C24C22×AGL(1,𝔽5)11yescharacteristic
321C2×Q8—58no—
322C2×Q8—104no—
323C2×Q8—104no—
324C2×Q8—104no—
325C2×Q8—104no—
326C2×Q8—1016no—
327C2×Q8—1016no—
328C2×Q8—104no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—24no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—42no—
335C22×C4—42no—
336C22×C4—51no—
337C22×C4—51no—
338C22×C4—52no—
339C22×C4—52no—
340C22×C4—51no—
341C22×C4—51no—
342C22×C4—51no—
343C22×C4—51no—
344C22×C4—51no—
345C22×C4—52no—
346C22×C4—51no—
347C22×C4—52no—
348C22×C4—104no—
349C22×C4—104no—
350C22×C4—104no—
351C22×C4—101no—
352C22×C4—101no—
353C22×C4—101no—
354C22×C4—101no—
355C22×C4—202no—
356C22×C4C22⋊AGL(1,𝔽5)12yes—
357C22×C4C22⋊AGL(1,𝔽5)12yes—
358C22×C4C22×AGL(1,𝔽5)12yes—
359C22×C4C22×AGL(1,𝔽5)12yes—
360C22×C4C22×AGL(1,𝔽5)11yescharacteristic
361C22×C4C22×AGL(1,𝔽5)11yescharacteristic
362M16—1016no—
363C2×C8—108no—
364C4⋊C4—24no—
365C4⋊C4—24no—
366C4⋊C4—104no—
367C4⋊C4—104no—
368C4⋊C4—104no—
369C4⋊C4—104no—
370C42—52no—
371C42—52no—
372C42—52no—
373C42—52no—
374C42—52no—
375C42—52no—
376C42—52no—
377C42—52no—
378C42—102no—
379C42—102no—
380C42—102no—
381C42—102no—
382C42—102no—
383C42—102no—
384C42—102no—
385C42—102no—
386C2×C5—22no—
387C2×C5—22no—
388C2×C5—22no—
389C2×C5#228011yescharacteristic
390C2×C5C22×#10111yescharacteristic
391C2×C5C2×#41311yescharacteristic
392C23—22no—
393C23—22no—
394C23—22no—
395C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
396C23C2×C22⋊AGL(1,𝔽5)11yescharacteristic
397C23C23×AGL(1,𝔽5)11yescharacteristic
398Q8—1016no—
399Q8—1016no—
400C2×C4—24no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—22no—
406C2×C4—42no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—54no—
413C2×C4—51no—
414C2×C4—51no—
415C2×C4—52no—
416C2×C4—54no—
417C2×C4—54no—
418C2×C4—51no—
419C2×C4—51no—
420C2×C4—52no—
421C2×C4—104no—
422C2×C4—104no—
423C2×C4—102no—
424C2×C4—102no—
425C2×C4—102no—
426C2×C4—102no—
427C2×C4—104no—
428C2×C4—104no—
429C2×C4—102no—
430C2×C4—102no—
431C2×C4—102no—
432C2×C4—102no—
433C2×C4—102no—
434C2×C4—202no—
435C2×C4—202no—
436C2×C4—202no—
437C2×C4#413014yes—
438C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
439C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
440C8—208no—
441C5#2072711yescharacteristic, complemented, Sylow
442C22—28no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22#6577712yes—
450C22D5⋊#10112yes—
451C22C2×#413012yes—
452C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
453C4—24no—
454C4—22no—
455C4—22no—
456C4—42no—
457C4—54no—
458C4—52no—
459C4—52no—
460C4—104no—
461C4—102no—
462C4—101no—
463C4—101no—
464C4—202no—
465C2—22no—
466C2—22no—
467C2—22no—
468C2#1061748011yescharacteristic
469C2C2×#6577711yescharacteristic
470C2C2×D5⋊#10111yescharacteristic
subgroupG/H
centerC22C22×C22⋊AGL(1,𝔽5)
commutatorC23×C5C23×C4
FrattiniC23C23×AGL(1,𝔽5)
FittingC22×C5×C4⋊C4C4
socleC22×C5C22×C22⋊C4
prime radicalC24×C5C22×C4
cosocleC22×Dic5C24
hypercenterC22×C4⋊C4AGL(1,𝔽5)
hypocenterC5#20727
LCSG ▷ C23×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #10604336C2semidirect
6. #10604335C2semidirect
225. C2×Dic5#101semidirect
441. C5#20727semidirect

Maximal subgroups

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

subgroupindex
C22×#40332
#106174732
#106049082
#106049052
#106043362
#106043352
#207275