Finite Group Databasebeta

← #72230170

Subgroups — #72230170

Order 2880.

1270 conjugacy classes of subgroups.

The subgroup lattice has 882 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#3799C211yesmaximal, characteristic
2#13088732C211yesmaximal, characteristic, complemented
3D3×C4⋊ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
4Dic6×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
5AGL(1,𝔽5)×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
6C3×#91909C211yesmaximal, characteristic, complemented
7C3×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic, complemented
8#13088417C212yesmaximal, complemented
9#13088415C212yesmaximal, complemented
10#13088409C212yesmaximal, complemented
11#13088407C212yesmaximal, complemented
12#11756854—31nomaximal
13#11756838—31nomaximal
14C2×ΓL(1,𝔽16)⋊D3C2212yes—
15C2×D3×ΓL(1,𝔽16)C2212yes—
16C2×C3⋊D3×AGL(1,𝔽5)C2212yes—
17#10624224C411yescharacteristic, complemented
18#10624201C411yescharacteristic, complemented
19#10624197C411yescharacteristic, complemented
20C5×#3799C411yescharacteristic, complemented
21D5×C4⋊(C3⋊D3)C2211yescharacteristic
22C3×C4×D3×D5C2211yescharacteristic
23C3×D5×Dic6C2211yescharacteristic
24C4⋊(C3⋊ΓL(1,𝔽16))C2211yescharacteristic
25C3×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
26C3×C4×ΓL(1,𝔽16)C2211yescharacteristic
27C32×C4×AGL(1,𝔽5)C2211yescharacteristic
28#10624054C412yescomplemented
29#10624051C412yescomplemented
30D5×#626C2212yes—
31D5×#624C2212yes—
32#10623978C2212yes—
33Dic3⋊ΓL(1,𝔽16)C2212yes—
34Dic3⋊ΓL(1,𝔽16)C2212yes—
35Dic3×ΓL(1,𝔽16)C2212yes—
36(C2×AGL(1,𝔽5))⋊(C3⋊D3)C2212yes—
37C3×Dic3⋊AGL(1,𝔽5)C2212yes—
38C3×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
39C3×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
40C3×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
41C3×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
42C3×Dic3×AGL(1,𝔽5)C2212yes—
43#10593890—51nomaximal, Hall
44D5×#239—31no—
45D5×#235—31no—
46Q8×ΓL(1,𝔽16)—31no—
47C2×C4⋊ΓL(1,𝔽16)—31no—
48C3×Q8×AGL(1,𝔽5)—31no—
49C3×#4130—31no—
50#67⋊AGL(1,𝔽5)—32no—
51#67⋊AGL(1,𝔽5)—32no—
52#91921—31no—
53#91921—32no—
54D3×C4⋊AGL(1,𝔽5)—31no—
55D3×C4⋊AGL(1,𝔽5)—32no—
56D3×C4⋊AGL(1,𝔽5)—32no—
57AGL(1,𝔽5)×D12—31no—
58AGL(1,𝔽5)×D12—31no—
59AGL(1,𝔽5)×D12—31no—
60AGL(1,𝔽5)×D12—32no—
61AGL(1,𝔽5)×D12—61no—
62#91909—32no—
63#91909D311yescharacteristic, complemented
64#91907—32no—
65AGL(1,𝔽5)×Dic6—31no—
66AGL(1,𝔽5)×Dic6D311yescharacteristic, complemented
67C2×D5×C3⋊D3C2312yes—
68C2×C3×D3×D5C2311yescharacteristic
69C2×C3⋊ΓL(1,𝔽16)C2312yes—
70C2×C3×ΓL(1,𝔽16)C2312yes—
71C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
72C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
73C2×C32×AGL(1,𝔽5)C2311yescharacteristic
74C2×C32×AGL(1,𝔽5)C2311yescharacteristic
75ΓL(1,𝔽16)⋊D3—42no—
76D3×ΓL(1,𝔽16)—42no—
77C3⋊D3×AGL(1,𝔽5)—42no—
78C4⋊(C3⋊D15)C2×C411yescharacteristic, complemented
79C5×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
80C3×C4×D15C2×C411yescharacteristic, complemented
81C3×Dic30C2×C411yescharacteristic, complemented
82C3×C4×C5×D3C2×C411yescharacteristic, complemented
83C3×C5×Dic6C2×C411yescharacteristic, complemented
84C32×C4×D5C2311yescharacteristic
85#67156C2×C412yescomplemented
86#67155C2×C412yescomplemented
87#67152C2×C412yescomplemented
88#67151C2×C412yescomplemented
89#67149C2×C412yescomplemented
90#67149C2×C412yescomplemented
91C5×#626C2×C412yescomplemented
92C5×#624C2×C412yescomplemented
93#67140C2×C412yescomplemented
94C3×#1204C2×C412yescomplemented
95C3×#1200C2×C411yescharacteristic, complemented
96C3×D3×Dic5C2×C411yescharacteristic, complemented
97C3×D5×Dic3C2311yescharacteristic
98C3×D5×Dic3C2312yes—
99#66266—91noHall
100C2×#3799—51no—
101C4×C4⋊(C3⋊D3)—51no—
102C3×#872—51no—
103C3×C4×Dic6—51no—
104#63894—51no—
105D3×C4⋊Dic3—51no—
106#63883—52no—
107#63881—52no—
108#63880—52no—
109Dic3×Dic6—51no—
110#63836—52no—
111C22×ΓL(1,𝔽16)—32no—
112C2×D3×AGL(1,𝔽5)—32no—
113C2×D3×AGL(1,𝔽5)—32no—
114C2×D3×AGL(1,𝔽5)—32no—
115C2×D3×AGL(1,𝔽5)—32no—
116C2×D3×AGL(1,𝔽5)—32no—
117C2×D3×AGL(1,𝔽5)—62no—
118#6821—31no—
119#6817—31no—
120C5×#239—31no—
121C5×#235—31no—
122C3×Q8×D5—31no—
123C2×C3×C4×D5—31no—
124D5×#67—32no—
125#6782—32no—
126D5×D12—32no—
127D5×D12—31no—
128D5×D12—31no—
129D5×D12—61no—
130C4×D3×D5—32no—
131C4×D3×D5—32no—
132C4×D3×D5C2×D311yescharacteristic
133#6773—31no—
134#6772—31no—
135#6771—32no—
136#6769—31no—
137#6769—32no—
138#6768—31no—
139#6768—32no—
140D5×Dic6C2×D311yescharacteristic
141C4⋊ΓL(1,𝔽16)—32no—
142C4⋊ΓL(1,𝔽16)—32no—
143C4⋊ΓL(1,𝔽16)—31no—
144C4⋊ΓL(1,𝔽16)—31no—
145C4⋊ΓL(1,𝔽16)—61no—
146C4⋊ΓL(1,𝔽16)C2×D311yescharacteristic
147C4×ΓL(1,𝔽16)—32no—
148C4×ΓL(1,𝔽16)C2×D311yescharacteristic
149C3×C22⋊AGL(1,𝔽5)—31no—
150C3×C22⋊AGL(1,𝔽5)—31no—
151C3×C4⋊AGL(1,𝔽5)—31no—
152C3×C4⋊AGL(1,𝔽5)—31no—
153C3×C4⋊AGL(1,𝔽5)—32no—
154C3×C4⋊AGL(1,𝔽5)—31no—
155C3×C4×AGL(1,𝔽5)—21no—
156C3×C4×AGL(1,𝔽5)—32no—
157C3×C4×AGL(1,𝔽5)—31no—
158C3×C4×AGL(1,𝔽5)C2×D311yescharacteristic
159C3×C4×AGL(1,𝔽5)C2×D311yescharacteristic
160Dic3⋊AGL(1,𝔽5)—32no—
161Dic3⋊AGL(1,𝔽5)—32no—
162Dic3⋊AGL(1,𝔽5)C2×D312yes—
163Dic3⋊AGL(1,𝔽5)C2×D311yescharacteristic
164Dic3⋊AGL(1,𝔽5)C2×D311yescharacteristic
165(C2×D3)⋊AGL(1,𝔽5)—32no—
166(C2×D3)⋊AGL(1,𝔽5)—32no—
167(C2×D3)⋊AGL(1,𝔽5)—32no—
168(C2×D3)⋊AGL(1,𝔽5)—32no—
169(C2×D3)⋊AGL(1,𝔽5)—62no—
170(C2×D3)⋊AGL(1,𝔽5)C2×D311yescharacteristic
171(C2×D3)⋊AGL(1,𝔽5)C2×D311yescharacteristic
172Dic3×AGL(1,𝔽5)—32no—
173Dic3×AGL(1,𝔽5)C2×D312yes—
174#5574—151no—
175#5523—151no—
176C2×C3⋊D15C22×C412yes—
177C2×C5×C3⋊D3C22×C412yes—
178C2×C3×D15C22×C411yescharacteristic
179C2×C3×C5×D3C22×C411yescharacteristic
180C2×C32×D5C2411yescharacteristic
181D5×C3⋊D3—22no—
182D5×C3⋊D3—22no—
183C3×D3×D5—21no—
184C3×D3×D5—21no—
185C3⋊ΓL(1,𝔽16)—22no—
186C3×ΓL(1,𝔽16)—22no—
187C3×ΓL(1,𝔽16)—21no—
188C3×ΓL(1,𝔽16)—21no—
189C32×AGL(1,𝔽5)—21no—
190C32×AGL(1,𝔽5)—21no—
191C32×C4×C5C22×C411yescharacteristic
192C3×Dic15C22×C411yescharacteristic
193C3×Dic15C22×C412yes—
194C3×C5×Dic3C22×C411yescharacteristic
195C3×C5×Dic3C22×C412yes—
196C32×Dic5C22×C411yescharacteristic
197D5×#41—91no—
198Q8×AGL(1,𝔽5)—31no—
199Q8×AGL(1,𝔽5)—91no—
200D4×AGL(1,𝔽5)—91no—
201D4×AGL(1,𝔽5)—92no—
202D4×AGL(1,𝔽5)—92no—
203D4×AGL(1,𝔽5)—91no—
204#4130—31no—
205#4130—92no—
206C2×C4⋊AGL(1,𝔽5)—92no—
207C2×C4⋊AGL(1,𝔽5)—91no—
208C2×C4⋊(C3⋊D3)—51no—
209C2×C4×C3⋊D3—52no—
210C2×C3×C4×D3—51no—
211C2×C3×Dic6—51no—
212C2×#626—52no—
213C2×#624—52no—
214C2×#624—52no—
215C2×D3×Dic3—52no—
216#3799—51no—
217#3799—51no—
218#3799—51no—
219#3799—52no—
220#3799—52no—
221#3799AGL(1,𝔽5)11yescharacteristic, complemented
222C32×C42—51no—
223#3752—52no—
224C4⋊(C3⋊Dic3)—51no—
225C3×(C2×D3)⋊C4—51no—
226C3×(C2×D3)⋊C4—51no—
227C3×C4⋊Dic3—51no—
228C3×Dic3⋊C4—51no—
229C3×Dic3⋊C4—52no—
230C3×Dic3⋊C4—51no—
231C3×C4×Dic3—51no—
232C3×C4×Dic3—52no—
233Dic3⋊Dic3—52no—
234Dic3⋊Dic3—52no—
235#3722—52no—
236Dic32—52no—
237C22×C3×D5—31no—
238C2×D3×D5—32no—
239C2×D3×D5—32no—
240C2×D3×D5—62no—
241C2×D3×D5C22×D311yescharacteristic
242C2×ΓL(1,𝔽16)—32no—
243C2×ΓL(1,𝔽16)—32no—
244C2×ΓL(1,𝔽16)—62no—
245C2×ΓL(1,𝔽16)—122no—
246C2×ΓL(1,𝔽16)C22×D312yes—
247C2×ΓL(1,𝔽16)C22×D311yescharacteristic
248C2×ΓL(1,𝔽16)C22×D311yescharacteristic
249C2×C3×AGL(1,𝔽5)—21no—
250C2×C3×AGL(1,𝔽5)—21no—
251C2×C3×AGL(1,𝔽5)—31no—
252C2×C3×AGL(1,𝔽5)—32no—
253C2×C3×AGL(1,𝔽5)—31no—
254C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
255C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
256C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
257C2×C3×AGL(1,𝔽5)C22×D311yescharacteristic
258D3×AGL(1,𝔽5)—122no—
259D3×AGL(1,𝔽5)—122no—
260D3×AGL(1,𝔽5)—122no—
261D3×AGL(1,𝔽5)—122no—
262D3×AGL(1,𝔽5)—122no—
263D3×AGL(1,𝔽5)—122no—
264D3×AGL(1,𝔽5)—122no—
265C3×C5×Q8—31no—
266C2×C3×C4×C5—31no—
267#1220—32no—
268D60—32no—
269D60—31no—
270D60—31no—
271D60—61no—
272C4×D15—32no—
273C4×D15—32no—
274C4×D15C4×D311yescharacteristic, complemented
275Dic30C4×D311yescharacteristic, complemented
276C5×#67—32no—
277C5×D12—32no—
278C5×D12—31no—
279C5×D12—31no—
280C5×D12—61no—
281C4×C5×D3—32no—
282C4×C5×D3—32no—
283C4×C5×D3C4×D311yescharacteristic, complemented
284C5×Dic6C4×D311yescharacteristic, complemented
285C2×C3×Dic5—31no—
286C3×C4×D5—21no—
287C3×C4×D5—32no—
288C3×C4×D5—31no—
289C3×C4×D5—31no—
290C3×C4×D5—31no—
291C3×C4×D5C22×D311yescharacteristic
292C3×C4×D5C22×D311yescharacteristic
293C3×Dic10—31no—
294C3×Dic10—32no—
295#1204C4×D312yescomplemented
296#1203—32no—
297#1203—32no—
298#1203—32no—
299#1203—32no—
300#1203—62no—
301#1202—32no—
302#1201—32no—
303#1200—32no—
304#1200—32no—
305#1200C4×D311yescharacteristic, complemented
306D3×Dic5—32no—
307D3×Dic5—32no—
308D3×Dic5C4×D311yescharacteristic, complemented
309D5×Dic3C22×D312yes—
310D5×Dic3C22×D311yescharacteristic
311C2×#239—151no—
312C2×#235—151no—
313C3×C4×Q8—151no—
314C3×#117—151no—
315Q8×Dic3—151no—
316C2×C4⋊Dic3—151no—
317#893—151no—
318#893—152no—
319#892—152no—
320D3×C4⋊C4—152no—
321D3×C4⋊C4—152no—
322D3×C4⋊C4—151no—
323#67⋊C4—152no—
324#67⋊C4—152no—
325C4×D12—151no—
326C4×D12—152no—
327C4×D12—151no—
328C4×D12—151no—
329C4×D12—301no—
330#872—51no—
331#872—152no—
332C4×Dic6—51no—
333C4×Dic6—151no—
334C2×C32×C5C23×C411yescharacteristic
335C3⋊D15—22no—
336C5×C3⋊D3—22no—
337C3×D15—21no—
338C3×C5×D3—21no—
339C32×D5H(5,𝔽2)11yescharacteristic
340C32×D52−1+411yescharacteristic
341C22×AGL(1,𝔽5)—92no—
342C22×AGL(1,𝔽5)—92no—
343C22×AGL(1,𝔽5)—92no—
344C5×#41—91no—
345#713—91no—
346Q8×D5—31no—
347#711—91no—
348#711—92no—
349D4×D5—92no—
350D4×D5—91no—
351#709—92no—
352#709—91no—
353C2×C4×D5—31no—
354C2×C4×D5—92no—
355C22⋊AGL(1,𝔽5)—31no—
356C22⋊AGL(1,𝔽5)—31no—
357C22⋊AGL(1,𝔽5)—92no—
358C22⋊AGL(1,𝔽5)—92no—
359C4⋊AGL(1,𝔽5)—31no—
360C4⋊AGL(1,𝔽5)—32no—
361C4⋊AGL(1,𝔽5)—31no—
362C4⋊AGL(1,𝔽5)—31no—
363C4⋊AGL(1,𝔽5)—92no—
364C4⋊AGL(1,𝔽5)—92no—
365C4⋊AGL(1,𝔽5)—91no—
366C4×AGL(1,𝔽5)—32no—
367C4×AGL(1,𝔽5)—31no—
368C4×AGL(1,𝔽5)—92no—
369C4×AGL(1,𝔽5)D3211yescharacteristic
370C22×C3⋊D3—52no—
371C22×C3×D3—51no—
372C2×C32×C4—51no—
373C2×C32×C4—51no—
374C2×C32×C4—51no—
375C2×C3⋊Dic3—52no—
376C4⋊(C3⋊D3)—52no—
377C4⋊(C3⋊D3)—51no—
378C4⋊(C3⋊D3)C2×AGL(1,𝔽5)11yescharacteristic, complemented
379C4×C3⋊D3—202no—
380C2×C3×Dic3—52no—
381C2×C3×Dic3—51no—
382C2×C3×Dic3—51no—
383C2×C3×Dic3—52no—
384C2×C3×Dic3—51no—
385C3×C4×D3—51no—
386C3×C4×D3—51no—
387C3×C4×D3—51no—
388C3×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
389C3×Dic6—51no—
390C3×Dic6—52no—
391C3×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
392#626—52no—
393#626—52no—
394#626—52no—
395#626C2×AGL(1,𝔽5)12yescomplemented
396#624—52no—
397#624—52no—
398#624—52no—
399#624—202no—
400#624C2×AGL(1,𝔽5)12yescomplemented
401D3×Dic3—202no—
402#520—451noSylow
403C22×C3×C5—31no—
404C2×D15—32no—
405C2×D15—32no—
406C2×D15—62no—
407C2×D15C2×C4×D311yescharacteristic
408C2×C5×D3—32no—
409C2×C5×D3—32no—
410C2×C5×D3—62no—
411C2×C5×D3C2×C4×D311yescharacteristic
412C2×C3×D5—21no—
413C2×C3×D5—31no—
414C2×C3×D5—61no—
415C2×C3×D5—61no—
416C2×C3×D5C23×D311yescharacteristic
417C2×C3×D5C23×D311yescharacteristic
418D3×D5—21no—
419D3×D5—21no—
420D3×D5—62no—
421D3×D5—62no—
422D3×D5—62no—
423D3×D5—62no—
424D3×D5—122no—
425D3×D5—122no—
426ΓL(1,𝔽16)—21no—
427ΓL(1,𝔽16)—22no—
428ΓL(1,𝔽16)—21no—
429ΓL(1,𝔽16)—62no—
430ΓL(1,𝔽16)—62no—
431ΓL(1,𝔽16)—122no—
432C3×AGL(1,𝔽5)—21no—
433C3×AGL(1,𝔽5)—21no—
434C3×AGL(1,𝔽5)—21no—
435C3×AGL(1,𝔽5)—21no—
436C3×AGL(1,𝔽5)—21no—
437C3×AGL(1,𝔽5)—21no—
438C3×AGL(1,𝔽5)—41no—
439C3×AGL(1,𝔽5)—61no—
440C3×AGL(1,𝔽5)—62no—
441C3×AGL(1,𝔽5)—61no—
442C3×C4×C5—21no—
443C3×C4×C5—32no—
444C3×C4×C5—31no—
445C3×C4×C5C2×C4×D311yescharacteristic
446C3×C4×C5C2×C4×D311yescharacteristic
447Dic15C2×C4×D311yescharacteristic
448Dic15C2×C4×D312yes—
449C3×Dic5—21no—
450C3×Dic5—31no—
451C3×Dic5—32no—
452C3×Dic5C2×C4×D311yescharacteristic
453C3×Dic5C2×C4×D311yescharacteristic
454C5×Dic3C2×C4×D311yescharacteristic
455C5×Dic3C2×C4×D312yes—
456C2×C3×Q8—151no—
457C22×C3×C4—151no—
458C2×#67—152no—
459C22×Dic3—152no—
460#239—31no—
461#239—152no—
462#239—152no—
463#239—151no—
464#239—151no—
465#239—151no—
466#235—31no—
467#235—152no—
468#235—151no—
469#235—152no—
470#235—151no—
471#235—151no—
472C2×D12—151no—
473C2×D12—151no—
474C2×D12—152no—
475C2×D12—301no—
476C2×C4×D3—51no—
477C2×C4×D3—152no—
478C2×C4×D3—152no—
479C2×C4×D3—152no—
480C2×C4×D3—152no—
481C2×C4×D3—152no—
482C2×C4×D3—152no—
483C2×C4×D3—152no—
484C2×C4×D3—302no—
485C2×Dic6—51no—
486C3×C4⋊C4—151no—
487C3×C4⋊C4—152no—
488C3×C4⋊C4—151no—
489C3×C4⋊C4—151no—
490C3×C22⋊C4—151no—
491C3×C22⋊C4—151no—
492C3×C42—51no—
493C3×C42—51no—
494C3×C42—101no—
495C3×C42—151no—
496C3×C42—152no—
497(C2×D3)⋊C4—51no—
498(C2×D3)⋊C4—51no—
499(C2×D3)⋊C4—152no—
500(C2×D3)⋊C4—152no—
501(C2×D3)⋊C4—152no—
502(C2×D3)⋊C4—152no—
503(C2×D3)⋊C4—302no—
504C4⋊Dic3—51no—
505C4⋊Dic3—152no—
506C4⋊Dic3—152no—
507C4⋊Dic3—151no—
508C4⋊Dic3—151no—
509C4⋊Dic3—301no—
510Dic3⋊C4—52no—
511Dic3⋊C4—51no—
512Dic3⋊C4—51no—
513Dic3⋊C4—152no—
514Dic3⋊C4—152no—
515C4×Dic3—52no—
516C4×Dic3—51no—
517C4×Dic3—152no—
518C4×Dic3—152no—
519C32×C5#52011yescharacteristic, complemented, Hall
520C22×D5—31no—
521C22×D5—92no—
522C2×AGL(1,𝔽5)—31no—
523C2×AGL(1,𝔽5)—32no—
524C2×AGL(1,𝔽5)—31no—
525C2×AGL(1,𝔽5)—92no—
526C2×AGL(1,𝔽5)—362no—
527C2×AGL(1,𝔽5)—362no—
528C2×AGL(1,𝔽5)—362no—
529C2×AGL(1,𝔽5)C2×D3211yescharacteristic
530C2×AGL(1,𝔽5)C2×D3211yescharacteristic
531C5×Q8—31no—
532C5×D4—92no—
533C5×D4—91no—
534C2×C4×C5—31no—
535C2×C4×C5—92no—
536C22⋊D5—92no—
537C22⋊D5—92no—
538C22⋊D5—92no—
539C2×Dic5—31no—
540C2×Dic5—92no—
541D20—92no—
542D20—91no—
543C4×D5—32no—
544C4×D5—31no—
545C4×D5—31no—
546C4×D5—31no—
547C4×D5—92no—
548C4×D5—92no—
549C4×D5C2×D3211yescharacteristic
550Dic10—31no—
551Dic10—32no—
552C22×C32—51no—
553C2×C3⋊D3—52no—
554C2×C3⋊D3—102no—
555C2×C3⋊D3—102no—
556C2×C3⋊D3C22×AGL(1,𝔽5)12yes—
557C2×C3×D3—51no—
558C2×C3×D3—101no—
559C2×C3×D3—101no—
560C2×C3×D3C22×AGL(1,𝔽5)11yescharacteristic
561C32×C4—51no—
562C32×C4—101no—
563C32×C4—101no—
564C32×C4C22×AGL(1,𝔽5)11yescharacteristic
565C3⋊Dic3—102no—
566C3×Dic3—51no—
567C3×Dic3—52no—
568C3×Dic3—102no—
569C3×Dic3—101no—
570C3×Dic3—101no—
571C3×Dic3C22×AGL(1,𝔽5)11yescharacteristic
572C3×Dic3C22×AGL(1,𝔽5)12yes—
573C2×#41—451no—
574C4×Q8—151no—
575C4×Q8—451no—
576C4×D4—451no—
577C4×D4—452no—
578C4×D4—451no—
579C4×D4—452no—
580#117—151no—
581#117—452no—
582C2×C4⋊C4—452no—
583C2×C4⋊C4—451no—
584C2×C3×C5—21no—
585C2×C3×C5—61no—
586C2×C3×C5C22×C4×D311yescharacteristic
587C2×C3×C5C22×C4×D311yescharacteristic
588D15—21no—
589D15—62no—
590D15—62no—
591D15—122no—
592C3×D5—21no—
593C3×D5—21no—
594C3×D5—61no—
595C3×D5#100711yescharacteristic
596C3×D5#100911yescharacteristic
597C3×D5#100911yescharacteristic
598C3×D5#101011yescharacteristic
599C5×D3—21no—
600C5×D3—62no—
601C5×D3—62no—
602C5×D3—122no—
603C23×C3—151no—
604C22×D3—51no—
605C22×D3—152no—
606C22×D3—152no—
607C22×D3—302no—
608C3×Q8—31no—
609C3×Q8—152no—
610C3×Q8—151no—
611C2×C3×C4—31no—
612C2×C3×C4—51no—
613C2×C3×C4—51no—
614C2×C3×C4—51no—
615C2×C3×C4—51no—
616C2×C3×C4—51no—
617C2×C3×C4—51no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—151no—
622C2×C3×C4—152no—
623C2×C3×C4—151no—
624C2×C3×C4—151no—
625C2×C3×C4—151no—
626C2×C3×C4—151no—
627C2×C3×C4—151no—
628C2×C3×C4—152no—
629#67—32no—
630#67—152no—
631#67—152no—
632#67—152no—
633C2×Dic3—52no—
634C2×Dic3—51no—
635C2×Dic3—51no—
636C2×Dic3—52no—
637C2×Dic3—51no—
638C2×Dic3—152no—
639C2×Dic3—152no—
640C2×Dic3—302no—
641C2×Dic3—602no—
642D12—32no—
643D12—31no—
644D12—31no—
645D12—61no—
646D12—152no—
647D12—152no—
648D12—152no—
649D12—152no—
650D12—152no—
651D12—151no—
652D12—151no—
653D12—301no—
654D12—302no—
655C4×D3—32no—
656C4×D3—32no—
657C4×D3—51no—
658C4×D3—51no—
659C4×D3—51no—
660C4×D3—152no—
661C4×D3—152no—
662C4×D3—152no—
663C4×D3—152no—
664C4×D3—152no—
665C4×D3—152no—
666C4×D3—602no—
667C4×D3—602no—
668C4×D3—602no—
669C4×D3—602no—
670C4×D3—602no—
671C4×D3—602no—
672C4×D3—602no—
673C4×D3D3×AGL(1,𝔽5)11yescharacteristic, complemented
674Dic6—51no—
675Dic6—52no—
676Dic6D3×AGL(1,𝔽5)11yescharacteristic, complemented
677C22×C5—31no—
678C22×C5—92no—
679C2×D5—31no—
680C2×D5—61no—
681C2×D5—61no—
682C2×D5—92no—
683C2×D5—182no—
684C2×D5—182no—
685C2×D5C22×D3211yescharacteristic
686AGL(1,𝔽5)—21no—
687AGL(1,𝔽5)—21no—
688AGL(1,𝔽5)—61no—
689AGL(1,𝔽5)—61no—
690AGL(1,𝔽5)—62no—
691AGL(1,𝔽5)—182no—
692C4×C5—32no—
693C4×C5—31no—
694C4×C5C4×D3211yescharacteristic
695Dic5—32no—
696Dic5—31no—
697Dic5C4×D3211yescharacteristic
698C2×C32—51no—
699C2×C32—51no—
700C2×C32C23×AGL(1,𝔽5)11yescharacteristic
701C3⋊D3—22no—
702C3⋊D3—102no—
703C3×D3—21no—
704C3×D3—101no—
705#41—91no—
706#41—451no—
707#41—452no—
708#41—452no—
709#41—451no—
710#41—451no—
711C2×Q8—151no—
712C2×D4—451no—
713C2×D4—452no—
714C22×C4—151no—
715C22×C4—452no—
716C22×C4—452no—
717C22×C4—452no—
718C22×C4—452no—
719C4⋊C4—151no—
720C4⋊C4—152no—
721C4⋊C4—151no—
722C4⋊C4—151no—
723C4⋊C4—451no—
724C4⋊C4—452no—
725C4⋊C4—452no—
726C22⋊C4—151no—
727C22⋊C4—151no—
728C22⋊C4—452no—
729C22⋊C4—452no—
730C42—51no—
731C42—151no—
732C42—152no—
733C42—452no—
734C3×C5—21no—
735C3×C5#552311yescharacteristic, complemented
736C3×C5#557411yescharacteristic, complemented
737C22×C3—31no—
738C22×C3—51no—
739C22×C3—51no—
740C22×C3—101no—
741C22×C3—151no—
742C22×C3—301no—
743C22×C3—301no—
744C2×D3—32no—
745C2×D3—32no—
746C2×D3—51no—
747C2×D3—62no—
748C2×D3—101no—
749C2×D3—101no—
750C2×D3—152no—
751C2×D3—152no—
752C2×D3—302no—
753C2×D3—302no—
754C2×D3—302no—
755C2×D3—302no—
756C2×D3—302no—
757C2×D3—602no—
758C2×D3—602no—
759C2×D3C2×D3×AGL(1,𝔽5)11yescharacteristic
760C3×C4—21no—
761C3×C4—31no—
762C3×C4—32no—
763C3×C4—51no—
764C3×C4—51no—
765C3×C4—101no—
766C3×C4—101no—
767C3×C4—101no—
768C3×C4—101no—
769C3×C4—101no—
770C3×C4—101no—
771C3×C4—101no—
772C3×C4—151no—
773C3×C4—152no—
774C3×C4—201no—
775C3×C4—302no—
776C3×C4—301no—
777C3×C4—301no—
778C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
779C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
780Dic3—52no—
781Dic3—51no—
782Dic3—101no—
783Dic3—102no—
784Dic3—101no—
785Dic3—302no—
786Dic3—302no—
787Dic3—602no—
788Dic3C2×D3×AGL(1,𝔽5)12yes—
789Dic3C2×D3×AGL(1,𝔽5)11yescharacteristic
790C2×C5—61no—
791C2×C5—182no—
792C2×C5C2×C4×D3211yescharacteristic
793D5—61no—
794D5—182no—
795D5#6429711yescharacteristic
796D5#6430811yescharacteristic
797C32#6626611yescharacteristic, complemented, Sylow
798C23—151no—
799C23—452no—
800Q8—31no—
801Q8—152no—
802Q8—151no—
803D4—92no—
804D4—91no—
805D4—452no—
806D4—452no—
807D4—452no—
808D4—452no—
809D4—451no—
810C2×C4—31no—
811C2×C4—51no—
812C2×C4—51no—
813C2×C4—51no—
814C2×C4—92no—
815C2×C4—151no—
816C2×C4—152no—
817C2×C4—151no—
818C2×C4—151no—
819C2×C4—151no—
820C2×C4—151no—
821C2×C4—151no—
822C2×C4—152no—
823C2×C4—452no—
824C2×C4—452no—
825C2×C4—452no—
826C2×C4—452no—
827C2×C4—1802no—
828C2×C4—1802no—
829C2×C4—1802no—
830C2×C3—21no—
831C2×C3—51no—
832C2×C3—51no—
833C2×C3—51no—
834C2×C3—51no—
835C2×C3—61no—
836C2×C3—101no—
837C2×C3—101no—
838C2×C3—301no—
839C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
840C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
841D3—21no—
842D3—62no—
843D3—62no—
844D3—101no—
845D3—122no—
846D3—302no—
847D3—302no—
848D3—602no—
849C5#1059389011yescharacteristic, complemented, Sylow
850C22—31no—
851C22—51no—
852C22—92no—
853C22—151no—
854C22—301no—
855C22—301no—
856C22—452no—
857C22—902no—
858C22—902no—
859C4—31no—
860C4—32no—
861C4—51no—
862C4—101no—
863C4—101no—
864C4—151no—
865C4—152no—
866C4—301no—
867C4—302no—
868C4—301no—
869C4—902no—
870C4D32×AGL(1,𝔽5)11yescharacteristic
871C3—21no—
872C3#1175683811yescharacteristic, complemented
873C3#1175685411yescharacteristic, complemented
874C2—51no—
875C2—51no—
876C2—61no—
877C2—182no—
878C2—301no—
879C2—902no—
880C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FittingC32×C4×C5C22×C4
prime radicalD5×#3799C2
cosocleC2×C32×D5C24
hypercenterC4D32×AGL(1,𝔽5)
hypocenterC32×C5#520
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C4

Complements

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

NH ≅ G/Ntype
2. #13088732C2semidirect
3. D3×C4⋊ΓL(1,𝔽16)C2semidirect
4. Dic6×ΓL(1,𝔽16)C2semidirect
5. AGL(1,𝔽5)×C4⋊(C3⋊D3)C2semidirect
6. C3×#91909C2semidirect
7. C3×AGL(1,𝔽5)×Dic6C2semidirect
8. #13088417C2semidirect
9. #13088415C2semidirect
10. #13088409C2semidirect
11. #13088407C2semidirect
17. #10624224C4semidirect
18. #10624201C4semidirect
19. #10624197C4semidirect
20. C5×#3799C4semidirect
28. #10624054C4semidirect
29. #10624051C4semidirect
63. #91909D3semidirect
66. AGL(1,𝔽5)×Dic6D3semidirect
78. C4⋊(C3⋊D15)C2×C4semidirect
79. C5×C4⋊(C3⋊D3)C2×C4semidirect
80. C3×C4×D15C2×C4semidirect
81. C3×Dic30C2×C4semidirect
82. C3×C4×C5×D3C2×C4semidirect
83. C3×C5×Dic6C2×C4semidirect
85. #67156C2×C4semidirect
86. #67155C2×C4semidirect
87. #67152C2×C4semidirect
88. #67151C2×C4semidirect
89. #67149C2×C4semidirect
90. #67149C2×C4semidirect
91. C5×#626C2×C4semidirect
92. C5×#624C2×C4semidirect
93. #67140C2×C4semidirect
94. C3×#1204C2×C4semidirect
95. C3×#1200C2×C4semidirect
96. C3×D3×Dic5C2×C4semidirect
221. #3799AGL(1,𝔽5)semidirect
274. C4×D15C4×D3semidirect
275. Dic30C4×D3semidirect
283. C4×C5×D3C4×D3semidirect
284. C5×Dic6C4×D3semidirect
295. #1204C4×D3semidirect
305. #1200C4×D3semidirect
308. D3×Dic5C4×D3semidirect
378. C4⋊(C3⋊D3)C2×AGL(1,𝔽5)semidirect
388. C3×C4×D3C2×AGL(1,𝔽5)semidirect
391. C3×Dic6C2×AGL(1,𝔽5)semidirect
395. #626C2×AGL(1,𝔽5)semidirect
400. #624C2×AGL(1,𝔽5)semidirect
519. C32×C5#520semidirect
673. C4×D3D3×AGL(1,𝔽5)semidirect
676. Dic6D3×AGL(1,𝔽5)semidirect
735. C3×C5#5523semidirect
736. C3×C5#5574semidirect
797. C32#66266semidirect
849. C5#10593890semidirect
872. C3#11756838semidirect
873. C3#11756854semidirect

Maximal subgroups

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

subgroupindex
D5×#37992
#130887322
D3×C4⋊ΓL(1,𝔽16)2
Dic6×ΓL(1,𝔽16)2
AGL(1,𝔽5)×C4⋊(C3⋊D3)2
C3×#919092
C3×AGL(1,𝔽5)×Dic62
#130884172
#130884152
#130884092
#130884072
#117568543
#117568383
#105938905