Finite Group Databasebeta

← #72230179

Subgroups — #72230179

Order 2880.

1334 conjugacy classes of subgroups.

The subgroup lattice has 886 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#3799C211yesmaximal, characteristic
2#13088732C211yesmaximal, characteristic, complemented
3C4×D3×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
4#13088693C211yesmaximal, characteristic, complemented
5#13088675C211yesmaximal, characteristic, complemented
6C3×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic, complemented
7C3×#91907C211yesmaximal, characteristic, complemented
8#13088417C212yesmaximal, complemented
9#13088415C212yesmaximal, complemented
10#13088409C212yesmaximal, complemented
11AGL(1,𝔽5)×#624C212yesmaximal, complemented
12AGL(1,𝔽5)×#239—31nomaximal
13#11756835—31nomaximal
14C2×ΓL(1,𝔽16)⋊D3C2212yes—
15C2×D3×ΓL(1,𝔽16)C2211yescharacteristic
16C2×D3×ΓL(1,𝔽16)C2211yescharacteristic
17C2×C3⋊D3×AGL(1,𝔽5)C2212yes—
18#10624224C411yescharacteristic, complemented
19#10624201C411yescharacteristic, complemented
20#10624197C411yescharacteristic, complemented
21C5×#3799C411yescharacteristic, complemented
22D5×C4⋊(C3⋊D3)C2211yescharacteristic
23C3×C4×D3×D5C2211yescharacteristic
24C3×D5×Dic6C2211yescharacteristic
25C4×C3⋊ΓL(1,𝔽16)C2211yescharacteristic
26C3×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
27C3×C4×ΓL(1,𝔽16)C2211yescharacteristic
28C32×C4⋊AGL(1,𝔽5)C2211yescharacteristic
29#10624054C412yescomplemented
30#10624051C412yescomplemented
31D5×#626C2212yes—
32D5×#624C2212yes—
33#10623978C2212yes—
34Dic3⋊ΓL(1,𝔽16)C2212yes—
35Dic3×ΓL(1,𝔽16)C2211yescharacteristic
36Dic3×ΓL(1,𝔽16)C2212yes—
37Dic3×ΓL(1,𝔽16)C2211yescharacteristic
38(C2×AGL(1,𝔽5))⋊(C3⋊D3)C2212yes—
39C3×Dic3⋊AGL(1,𝔽5)C2212yes—
40C3×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
41C3×Dic3×AGL(1,𝔽5)C2212yes—
42C3×Dic3×AGL(1,𝔽5)C2212yes—
43#10594362—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—31no—
54#91921—31no—
55#91921—32no—
56#91921—61no—
57AGL(1,𝔽5)×D12—31no—
58AGL(1,𝔽5)×D12—32no—
59C4×D3×AGL(1,𝔽5)—31no—
60C4×D3×AGL(1,𝔽5)—32no—
61C4×D3×AGL(1,𝔽5)—32no—
62#91909—32no—
63ΓL(1,𝔽16)⋊Q8—31no—
64ΓL(1,𝔽16)⋊Q8D311yescharacteristic, complemented
65#91907—32no—
66#91907D311yescharacteristic, complemented
67C2×D5×C3⋊D3C2312yes—
68C2×C3×D3×D5C2311yescharacteristic
69C2×C3⋊ΓL(1,𝔽16)C2311yescharacteristic
70C2×C3⋊ΓL(1,𝔽16)C2311yescharacteristic
71C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
72C2×C3×ΓL(1,𝔽16)C2312yes—
73C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
74C2×C32×AGL(1,𝔽5)C2312yes—
75ΓL(1,𝔽16)⋊D3—24no—
76D3×ΓL(1,𝔽16)—22no—
77D3×ΓL(1,𝔽16)—22no—
78C3⋊D3×AGL(1,𝔽5)—24no—
79C4⋊(C3⋊D15)C2×C411yescharacteristic, complemented
80C5×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
81C3×C4×D15C2×C411yescharacteristic, complemented
82C3×Dic30C2×C411yescharacteristic, complemented
83C3×C4×C5×D3C2×C411yescharacteristic, complemented
84C3×C5×Dic6C2×C411yescharacteristic, complemented
85C32×C4×D5C2311yescharacteristic
86#67156C2×C412yescomplemented
87#67155C2×C412yescomplemented
88#67152C2×C412yescomplemented
89#67151C2×C412yescomplemented
90#67149C2×C412yescomplemented
91#67149C2×C412yescomplemented
92C5×#626C2×C412yescomplemented
93C5×#624C2×C412yescomplemented
94#67140C2×C412yescomplemented
95C3×#1204C2×C412yescomplemented
96C3×#1200C2×C411yescharacteristic, complemented
97C3×D3×Dic5C2×C411yescharacteristic, complemented
98C3×D5×Dic3C2311yescharacteristic
99C3×D5×Dic3C2312yes—
100#41×AGL(1,𝔽5)—91noHall
101C2×#3799—51no—
102#64102—51no—
103C3×#892—51no—
104C3×#887—51no—
105#63894—51no—
106C4×#624—52no—
107#63881—52no—
108#63880—52no—
109C4×D3×Dic3—51no—
110#63843—51no—
111#63836—52no—
112C22×ΓL(1,𝔽16)—31no—
113C22×ΓL(1,𝔽16)—31no—
114C2×D3×AGL(1,𝔽5)—31no—
115C2×D3×AGL(1,𝔽5)—31no—
116C2×D3×AGL(1,𝔽5)—32no—
117C2×D3×AGL(1,𝔽5)—32no—
118C2×D3×AGL(1,𝔽5)—32no—
119C2×D3×AGL(1,𝔽5)—32no—
120C2×D3×AGL(1,𝔽5)—62no—
121#6821—31no—
122#6817—31no—
123C5×#239—31no—
124C5×#235—31no—
125C3×Q8×D5—31no—
126C2×C3×C4×D5—31no—
127D5×#67—32no—
128#6782—32no—
129D5×D12—32no—
130D5×D12—31no—
131D5×D12—31no—
132D5×D12—61no—
133C4×D3×D5—32no—
134C4×D3×D5—32no—
135C4×D3×D5C2×D311yescharacteristic
136#6773—31no—
137#6772—31no—
138#6771—32no—
139#6769—31no—
140#6769—32no—
141#6768—31no—
142#6768—32no—
143D5×Dic6C2×D311yescharacteristic
144C4⋊ΓL(1,𝔽16)—32no—
145C4⋊ΓL(1,𝔽16)C2×D311yescharacteristic
146C4×ΓL(1,𝔽16)—31no—
147C4×ΓL(1,𝔽16)—31no—
148C4×ΓL(1,𝔽16)—32no—
149C4×ΓL(1,𝔽16)—31no—
150C4×ΓL(1,𝔽16)—31no—
151C4×ΓL(1,𝔽16)—61no—
152C4×ΓL(1,𝔽16)C2×D311yescharacteristic
153C3×C22⋊AGL(1,𝔽5)—32no—
154C3×C4⋊AGL(1,𝔽5)—21no—
155C3×C4⋊AGL(1,𝔽5)—32no—
156C3×C4⋊AGL(1,𝔽5)—31no—
157C3×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
158C3×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
159C3×C4×AGL(1,𝔽5)—32no—
160C3×C4×AGL(1,𝔽5)—32no—
161C3×C4×AGL(1,𝔽5)—31no—
162Dic3⋊AGL(1,𝔽5)—32no—
163Dic3⋊AGL(1,𝔽5)C2×D312yes—
164(C2×D3)⋊AGL(1,𝔽5)—32no—
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)—62no—
169(C2×D3)⋊AGL(1,𝔽5)C2×D312yes—
170Dic3×AGL(1,𝔽5)—31no—
171Dic3×AGL(1,𝔽5)—32no—
172Dic3×AGL(1,𝔽5)—31no—
173Dic3×AGL(1,𝔽5)C2×D312yes—
174Dic3×AGL(1,𝔽5)C2×D312yes—
175C4×#239—151no—
176#5522—151no—
177C2×C3⋊D15C22×C412yes—
178C2×C5×C3⋊D3C22×C412yes—
179C2×C3×D15C22×C411yescharacteristic
180C2×C3×C5×D3C22×C411yescharacteristic
181C2×C32×D5C2411yescharacteristic
182D5×C3⋊D3—22no—
183D5×C3⋊D3—22no—
184C3×D3×D5—21no—
185C3×D3×D5—21no—
186C3⋊ΓL(1,𝔽16)—21no—
187C3⋊ΓL(1,𝔽16)#4112yescomplemented
188C3×ΓL(1,𝔽16)—21no—
189C3×ΓL(1,𝔽16)—22no—
190C3×ΓL(1,𝔽16)#4112yescomplemented
191C32×AGL(1,𝔽5)—22no—
192C32×C4×C5C22×C411yescharacteristic
193C3×Dic15C22×C411yescharacteristic
194C3×Dic15C22×C412yes—
195C3×C5×Dic3C22×C411yescharacteristic
196C3×C5×Dic3C22×C412yes—
197C32×Dic5C22×C411yescharacteristic
198D5×#41—91no—
199Q8×AGL(1,𝔽5)—31no—
200Q8×AGL(1,𝔽5)—91no—
201D4×AGL(1,𝔽5)—91no—
202D4×AGL(1,𝔽5)—92no—
203D4×AGL(1,𝔽5)—92no—
204D4×AGL(1,𝔽5)—91no—
205#4130—31no—
206#4130—92no—
207C2×C4×AGL(1,𝔽5)—92no—
208C2×C4×AGL(1,𝔽5)—91no—
209C2×C4⋊(C3⋊D3)—51no—
210C2×C4×C3⋊D3—52no—
211C2×C3×C4×D3—51no—
212C2×C3×Dic6—51no—
213C2×#626—52no—
214C2×#624—52no—
215C2×#624—52no—
216C2×D3×Dic3—51no—
217C2×D3×Dic3—51no—
218#3799—51no—
219#3799—51no—
220#3799—51no—
221#3799—52no—
222#3799—52no—
223#3799AGL(1,𝔽5)11yescharacteristic, complemented
224C32×C4⋊C4—51no—
225#3752—52no—
226C4×C3⋊Dic3—51no—
227C3×(C2×D3)⋊C4—52no—
228C3×C4⋊Dic3—51no—
229C3×Dic3⋊C4—52no—
230C3×C4×Dic3—51no—
231C3×C4×Dic3—52no—
232C3×C4×Dic3—52no—
233Dic3⋊Dic3—52no—
234#3722—52no—
235Dic32—51no—
236Dic32—52no—
237Dic32—51no—
238C22×C3×D5—31no—
239C2×D3×D5—32no—
240C2×D3×D5—32no—
241C2×D3×D5—62no—
242C2×D3×D5C22×D311yescharacteristic
243C2×ΓL(1,𝔽16)—31no—
244C2×ΓL(1,𝔽16)—31no—
245C2×ΓL(1,𝔽16)—31no—
246C2×ΓL(1,𝔽16)—31no—
247C2×ΓL(1,𝔽16)—62no—
248C2×ΓL(1,𝔽16)—61no—
249C2×ΓL(1,𝔽16)—62no—
250C2×ΓL(1,𝔽16)—61no—
251C2×ΓL(1,𝔽16)C22×D312yes—
252C2×ΓL(1,𝔽16)C22×D311yescharacteristic
253C2×ΓL(1,𝔽16)C22×D311yescharacteristic
254C2×C3×AGL(1,𝔽5)—22no—
255C2×C3×AGL(1,𝔽5)—31no—
256C2×C3×AGL(1,𝔽5)—31no—
257C2×C3×AGL(1,𝔽5)—32no—
258C2×C3×AGL(1,𝔽5)C22×D312yes—
259C2×C3×AGL(1,𝔽5)C22×D312yes—
260D3×AGL(1,𝔽5)—64no—
261D3×AGL(1,𝔽5)—64no—
262D3×AGL(1,𝔽5)—64no—
263D3×AGL(1,𝔽5)—62no—
264D3×AGL(1,𝔽5)—62no—
265D3×AGL(1,𝔽5)—64no—
266D3×AGL(1,𝔽5)—124no—
267C3×C5×Q8—31no—
268C2×C3×C4×C5—31no—
269#1220—32no—
270D60—32no—
271D60—31no—
272D60—31no—
273D60—61no—
274C4×D15—32no—
275C4×D15—32no—
276C4×D15C4×D311yescharacteristic, complemented
277Dic30C4×D311yescharacteristic, complemented
278C5×#67—32no—
279C5×D12—32no—
280C5×D12—31no—
281C5×D12—31no—
282C5×D12—61no—
283C4×C5×D3—32no—
284C4×C5×D3—32no—
285C4×C5×D3C4×D311yescharacteristic, complemented
286C5×Dic6C4×D311yescharacteristic, complemented
287C2×C3×Dic5—31no—
288C3×C4×D5—21no—
289C3×C4×D5—31no—
290C3×C4×D5—32no—
291C3×C4×D5—31no—
292C3×C4×D5—31no—
293C3×C4×D5C22×D311yescharacteristic
294C3×C4×D5C22×D311yescharacteristic
295C3×Dic10—31no—
296C3×Dic10—32no—
297#1204C4×D312yescomplemented
298#1203—32no—
299#1203—32no—
300#1203—32no—
301#1203—32no—
302#1203—62no—
303#1202—32no—
304#1201—32no—
305#1200—32no—
306#1200—32no—
307#1200C4×D311yescharacteristic, complemented
308D3×Dic5—32no—
309D3×Dic5—32no—
310D3×Dic5C4×D311yescharacteristic, complemented
311D5×Dic3C22×D311yescharacteristic
312D5×Dic3C22×D312yes—
313C2×#239—151no—
314C2×#235—151no—
315C3×C4×Q8—151no—
316C3×#117—151no—
317Q8×Dic3—151no—
318C2×C4×Dic3—151no—
319#893—151no—
320#893—152no—
321#893—151no—
322#893—151no—
323#893—301no—
324#892—51no—
325#892—152no—
326#887—51no—
327#887—151no—
328#67⋊C4—152no—
329#67⋊C4—152no—
330C4×D12—151no—
331C4×D12—152no—
332#872—152no—
333C42×D3—152no—
334C42×D3—152no—
335C42×D3—151no—
336C2×C32×C5C23×C411yescharacteristic
337C3⋊D15—22no—
338C5×C3⋊D3—22no—
339C3×D15—21no—
340C3×C5×D3—21no—
341C32×D5C2×#4111yescharacteristic
342C32×D5C2×#4111yescharacteristic
343C22×AGL(1,𝔽5)—92no—
344C22×AGL(1,𝔽5)—91no—
345C22×AGL(1,𝔽5)—91no—
346C22×AGL(1,𝔽5)—92no—
347C5×#41—91no—
348#713—91no—
349Q8×D5—31no—
350#711—91no—
351#711—92no—
352D4×D5—92no—
353D4×D5—91no—
354#709—92no—
355#709—91no—
356C2×C4×D5—31no—
357C2×C4×D5—92no—
358C22⋊AGL(1,𝔽5)—32no—
359C22⋊AGL(1,𝔽5)—92no—
360C22⋊AGL(1,𝔽5)—92no—
361C4⋊AGL(1,𝔽5)—32no—
362C4⋊AGL(1,𝔽5)—31no—
363C4⋊AGL(1,𝔽5)—92no—
364C4⋊AGL(1,𝔽5)D3211yescharacteristic
365C4×AGL(1,𝔽5)—32no—
366C4×AGL(1,𝔽5)—32no—
367C4×AGL(1,𝔽5)—31no—
368C4×AGL(1,𝔽5)—91no—
369C4×AGL(1,𝔽5)—91no—
370C4×AGL(1,𝔽5)—92no—
371C4×AGL(1,𝔽5)—91no—
372C22×C3⋊D3—52no—
373C22×C3×D3—51no—
374C2×C32×C4—51no—
375C2×C32×C4—52no—
376C2×C3⋊Dic3—51no—
377C2×C3⋊Dic3—51no—
378C4⋊(C3⋊D3)—52no—
379C4⋊(C3⋊D3)—51no—
380C4⋊(C3⋊D3)C2×AGL(1,𝔽5)11yescharacteristic, complemented
381C4×C3⋊D3—104no—
382C2×C3×Dic3—51no—
383C2×C3×Dic3—51no—
384C2×C3×Dic3—52no—
385C2×C3×Dic3—51no—
386C2×C3×Dic3—52no—
387C3×C4×D3—51no—
388C3×C4×D3—51no—
389C3×C4×D3—51no—
390C3×C4×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
391C3×Dic6—51no—
392C3×Dic6—52no—
393C3×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
394#626—52no—
395#626—52no—
396#626—52no—
397#626C2×AGL(1,𝔽5)12yescomplemented
398#624—52no—
399#624—52no—
400#624—52no—
401#624—104no—
402#624C2×AGL(1,𝔽5)12yescomplemented
403D3×Dic3—102no—
404D3×Dic3—102no—
405C4×#41—451noSylow
406C22×C3×C5—31no—
407C2×D15—32no—
408C2×D15—32no—
409C2×D15—62no—
410C2×D15C2×C4×D311yescharacteristic
411C2×C5×D3—32no—
412C2×C5×D3—32no—
413C2×C5×D3—62no—
414C2×C5×D3C2×C4×D311yescharacteristic
415C2×C3×D5—21no—
416C2×C3×D5—31no—
417C2×C3×D5—61no—
418C2×C3×D5—61no—
419C2×C3×D5C23×D311yescharacteristic
420C2×C3×D5C23×D311yescharacteristic
421D3×D5—21no—
422D3×D5—21no—
423D3×D5—62no—
424D3×D5—62no—
425D3×D5—62no—
426D3×D5—62no—
427D3×D5—122no—
428D3×D5—122no—
429ΓL(1,𝔽16)—22no—
430ΓL(1,𝔽16)—21no—
431ΓL(1,𝔽16)—32no—
432ΓL(1,𝔽16)—32no—
433ΓL(1,𝔽16)—62no—
434ΓL(1,𝔽16)—61no—
435ΓL(1,𝔽16)—61no—
436ΓL(1,𝔽16)—121no—
437ΓL(1,𝔽16)#23912yescomplemented
438C3×AGL(1,𝔽5)—22no—
439C3×AGL(1,𝔽5)—22no—
440C3×AGL(1,𝔽5)—32no—
441C3×AGL(1,𝔽5)—42no—
442C3×AGL(1,𝔽5)—62no—
443C3×AGL(1,𝔽5)—61no—
444C3×C4×C5—21no—
445C3×C4×C5—32no—
446C3×C4×C5—31no—
447C3×C4×C5C2×C4×D311yescharacteristic
448C3×C4×C5C2×C4×D311yescharacteristic
449Dic15C2×C4×D311yescharacteristic
450Dic15C2×C4×D312yes—
451C3×Dic5—21no—
452C3×Dic5—31no—
453C3×Dic5—32no—
454C3×Dic5C2×C4×D311yescharacteristic
455C3×Dic5C2×C4×D311yescharacteristic
456C5×Dic3C2×C4×D311yescharacteristic
457C5×Dic3C2×C4×D312yes—
458C2×C3×Q8—151no—
459C22×C3×C4—151no—
460C2×#67—152no—
461C22×Dic3—151no—
462C22×Dic3—151no—
463#239—31no—
464#239—152no—
465#239—152no—
466#239—151no—
467#239—151no—
468#239—151no—
469#235—31no—
470#235—152no—
471#235—151no—
472#235—152no—
473#235—151no—
474#235—151no—
475C2×D12—151no—
476C2×D12—151no—
477C2×D12—152no—
478C2×D12—301no—
479C2×C4×D3—51no—
480C2×C4×D3—152no—
481C2×C4×D3—152no—
482C2×C4×D3—152no—
483C2×C4×D3—152no—
484C2×C4×D3—152no—
485C2×C4×D3—152no—
486C2×C4×D3—151no—
487C2×C4×D3—151no—
488C2×C4×D3—302no—
489C2×Dic6—51no—
490C3×C4⋊C4—51no—
491C3×C4⋊C4—51no—
492C3×C4⋊C4—101no—
493C3×C4⋊C4—151no—
494C3×C4⋊C4—152no—
495C3×C22⋊C4—152no—
496C3×C42—152no—
497C3×C42—151no—
498C3×C42—152no—
499(C2×D3)⋊C4—52no—
500(C2×D3)⋊C4—152no—
501(C2×D3)⋊C4—152no—
502(C2×D3)⋊C4—152no—
503(C2×D3)⋊C4—152no—
504(C2×D3)⋊C4—302no—
505C4⋊Dic3—51no—
506C4⋊Dic3—152no—
507Dic3⋊C4—52no—
508Dic3⋊C4—152no—
509C4×Dic3—52no—
510C4×Dic3—52no—
511C4×Dic3—51no—
512C4×Dic3—151no—
513C4×Dic3—152no—
514C4×Dic3—151no—
515C4×Dic3—151no—
516C4×Dic3—152no—
517C4×Dic3—151no—
518C4×Dic3—151no—
519C4×Dic3—151no—
520C4×Dic3—301no—
521C32×C5C4×#4111yescharacteristic, complemented, Hall
522C22×D5—31no—
523C22×D5—92no—
524C2×AGL(1,𝔽5)—31no—
525C2×AGL(1,𝔽5)—31no—
526C2×AGL(1,𝔽5)—32no—
527C2×AGL(1,𝔽5)—91no—
528C2×AGL(1,𝔽5)—91no—
529C2×AGL(1,𝔽5)—184no—
530C2×AGL(1,𝔽5)—184no—
531C2×AGL(1,𝔽5)—182no—
532C2×AGL(1,𝔽5)—182no—
533C2×AGL(1,𝔽5)C2×D3212yes—
534C5×Q8—31no—
535C5×D4—92no—
536C5×D4—91no—
537C2×C4×C5—31no—
538C2×C4×C5—92no—
539C22⋊D5—92no—
540C22⋊D5—92no—
541C22⋊D5—92no—
542C2×Dic5—31no—
543C2×Dic5—92no—
544D20—92no—
545D20—91no—
546C4×D5—31no—
547C4×D5—32no—
548C4×D5—31no—
549C4×D5—31no—
550C4×D5—92no—
551C4×D5—92no—
552C4×D5C2×D3211yescharacteristic
553Dic10—31no—
554Dic10—32no—
555C22×C32—51no—
556C2×C3⋊D3—52no—
557C2×C3⋊D3—102no—
558C2×C3⋊D3—102no—
559C2×C3⋊D3C22×AGL(1,𝔽5)12yes—
560C2×C3×D3—51no—
561C2×C3×D3—101no—
562C2×C3×D3—101no—
563C2×C3×D3C22×AGL(1,𝔽5)11yescharacteristic
564C32×C4—51no—
565C32×C4—102no—
566C32×C4C22×AGL(1,𝔽5)11yescharacteristic
567C3⋊Dic3—52no—
568C3⋊Dic3—101no—
569C3×Dic3—52no—
570C3×Dic3—51no—
571C3×Dic3—52no—
572C3×Dic3—101no—
573C3×Dic3—102no—
574C3×Dic3C22×AGL(1,𝔽5)11yescharacteristic
575C3×Dic3C22×AGL(1,𝔽5)12yes—
576C2×#41—451no—
577C4×Q8—151no—
578C4×Q8—451no—
579C4×D4—452no—
580C4×D4—451no—
581C4×D4—452no—
582C4×D4—451no—
583#117—151no—
584#117—452no—
585C2×C42—452no—
586C2×C42—451no—
587C2×C3×C5—21no—
588C2×C3×C5—61no—
589C2×C3×C5C22×C4×D311yescharacteristic
590C2×C3×C5C22×C4×D311yescharacteristic
591D15—21no—
592D15—62no—
593D15—62no—
594D15—122no—
595C3×D5—21no—
596C3×D5—21no—
597C3×D5—61no—
598C3×D5C2×#23911yescharacteristic
599C3×D5D3×#4111yescharacteristic
600C3×D5D3×#4111yescharacteristic
601C3×D5D3×#4111yescharacteristic
602C5×D3—21no—
603C5×D3—62no—
604C5×D3—62no—
605C5×D3—122no—
606C23×C3—151no—
607C22×D3—51no—
608C22×D3—152no—
609C22×D3—152no—
610C22×D3—302no—
611C3×Q8—31no—
612C3×Q8—152no—
613C3×Q8—151no—
614C2×C3×C4—31no—
615C2×C3×C4—51no—
616C2×C3×C4—51no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—101no—
620C2×C3×C4—102no—
621C2×C3×C4—151no—
622C2×C3×C4—151no—
623C2×C3×C4—152no—
624C2×C3×C4—151no—
625C2×C3×C4—151no—
626C2×C3×C4—151no—
627C2×C3×C4—152no—
628C2×C3×C4—151no—
629#67—32no—
630#67—152no—
631#67—152no—
632#67—152no—
633C2×Dic3—51no—
634C2×Dic3—51no—
635C2×Dic3—52no—
636C2×Dic3—51no—
637C2×Dic3—52no—
638C2×Dic3—151no—
639C2×Dic3—151no—
640C2×Dic3—151no—
641C2×Dic3—151no—
642C2×Dic3—301no—
643C2×Dic3—301no—
644C2×Dic3—302no—
645C2×Dic3—302no—
646D12—32no—
647D12—31no—
648D12—31no—
649D12—61no—
650D12—152no—
651D12—152no—
652D12—152no—
653D12—152no—
654D12—152no—
655D12—151no—
656D12—151no—
657D12—301no—
658D12—302no—
659C4×D3—32no—
660C4×D3—32no—
661C4×D3—51no—
662C4×D3—51no—
663C4×D3—51no—
664C4×D3—152no—
665C4×D3—152no—
666C4×D3—152no—
667C4×D3—152no—
668C4×D3—152no—
669C4×D3—152no—
670C4×D3—304no—
671C4×D3—304no—
672C4×D3—304no—
673C4×D3—304no—
674C4×D3—302no—
675C4×D3—302no—
676C4×D3—604no—
677C4×D3D3×AGL(1,𝔽5)11yescharacteristic, complemented
678Dic6—51no—
679Dic6—52no—
680Dic6D3×AGL(1,𝔽5)11yescharacteristic, complemented
681C22×C5—31no—
682C22×C5—92no—
683C2×D5—31no—
684C2×D5—61no—
685C2×D5—61no—
686C2×D5—92no—
687C2×D5—182no—
688C2×D5—182no—
689C2×D5C22×D3211yescharacteristic
690AGL(1,𝔽5)—22no—
691AGL(1,𝔽5)—32no—
692AGL(1,𝔽5)—61no—
693AGL(1,𝔽5)—62no—
694AGL(1,𝔽5)—92no—
695AGL(1,𝔽5)—181no—
696C4×C5—32no—
697C4×C5—31no—
698C4×C5C4×D3211yescharacteristic
699Dic5—32no—
700Dic5—31no—
701Dic5C4×D3211yescharacteristic
702C2×C32—51no—
703C2×C32—51no—
704C2×C32C23×AGL(1,𝔽5)11yescharacteristic
705C3⋊D3—22no—
706C3⋊D3—102no—
707C3×D3—21no—
708C3×D3—101no—
709#41—91no—
710#41—451no—
711#41—452no—
712#41—452no—
713#41—451no—
714#41—451no—
715C2×Q8—151no—
716C2×D4—451no—
717C2×D4—452no—
718C22×C4—151no—
719C22×C4—452no—
720C22×C4—452no—
721C22×C4—452no—
722C22×C4—451no—
723C22×C4—451no—
724C4⋊C4—51no—
725C4⋊C4—151no—
726C4⋊C4—152no—
727C4⋊C4—452no—
728C22⋊C4—152no—
729C22⋊C4—452no—
730C22⋊C4—452no—
731C42—152no—
732C42—151no—
733C42—152no—
734C42—451no—
735C42—451no—
736C42—451no—
737C42—452no—
738C3×C5—21no—
739C3×C5#552211yescharacteristic, complemented
740C3×C5C4×#23911yescharacteristic, complemented
741C22×C3—31no—
742C22×C3—51no—
743C22×C3—51no—
744C22×C3—101no—
745C22×C3—151no—
746C22×C3—301no—
747C22×C3—301no—
748C2×D3—32no—
749C2×D3—32no—
750C2×D3—51no—
751C2×D3—62no—
752C2×D3—101no—
753C2×D3—101no—
754C2×D3—152no—
755C2×D3—152no—
756C2×D3—302no—
757C2×D3—302no—
758C2×D3—302no—
759C2×D3—302no—
760C2×D3—302no—
761C2×D3—602no—
762C2×D3—602no—
763C2×D3C2×D3×AGL(1,𝔽5)11yescharacteristic
764C3×C4—21no—
765C3×C4—31no—
766C3×C4—32no—
767C3×C4—51no—
768C3×C4—51no—
769C3×C4—101no—
770C3×C4—102no—
771C3×C4—102no—
772C3×C4—152no—
773C3×C4—151no—
774C3×C4—152no—
775C3×C4—202no—
776C3×C4—301no—
777C3×C4—302no—
778C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
779C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
780Dic3—52no—
781Dic3—52no—
782Dic3—51no—
783Dic3—102no—
784Dic3—101no—
785Dic3—152no—
786Dic3—152no—
787Dic3—302no—
788Dic3—301no—
789Dic3—301no—
790Dic3—601no—
791Dic3C2×D3×AGL(1,𝔽5)12yes—
792Dic3C2×D3×AGL(1,𝔽5)11yescharacteristic
793C2×C5—61no—
794C2×C5—182no—
795C2×C5C2×C4×D3211yescharacteristic
796D5—61no—
797D5—182no—
798D5#6431211yescharacteristic
799D5D3×#23911yescharacteristic
800C32#41×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
801C23—151no—
802C23—452no—
803Q8—31no—
804Q8—152no—
805Q8—151no—
806D4—92no—
807D4—91no—
808D4—452no—
809D4—452no—
810D4—452no—
811D4—452no—
812D4—451no—
813C2×C4—31no—
814C2×C4—51no—
815C2×C4—52no—
816C2×C4—92no—
817C2×C4—151no—
818C2×C4—151no—
819C2×C4—152no—
820C2×C4—151no—
821C2×C4—151no—
822C2×C4—151no—
823C2×C4—152no—
824C2×C4—151no—
825C2×C4—452no—
826C2×C4—452no—
827C2×C4—452no—
828C2×C4—451no—
829C2×C4—451no—
830C2×C4—904no—
831C2×C4—904no—
832C2×C4—902no—
833C2×C4—902no—
834C2×C3—21no—
835C2×C3—51no—
836C2×C3—51no—
837C2×C3—51no—
838C2×C3—51no—
839C2×C3—61no—
840C2×C3—101no—
841C2×C3—101no—
842C2×C3—301no—
843C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
844C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
845D3—21no—
846D3—62no—
847D3—62no—
848D3—101no—
849D3—122no—
850D3—302no—
851D3—302no—
852D3—602no—
853C5#1059436211yescharacteristic, complemented, Sylow
854C22—31no—
855C22—51no—
856C22—92no—
857C22—151no—
858C22—301no—
859C22—301no—
860C22—452no—
861C22—902no—
862C22—902no—
863C4—31no—
864C4—32no—
865C4—51no—
866C4—102no—
867C4—152no—
868C4—151no—
869C4—152no—
870C4—301no—
871C4—302no—
872C4—452no—
873C4—901no—
874C4D32×AGL(1,𝔽5)11yescharacteristic
875C3—21no—
876C3#1175683511yescharacteristic, complemented
877C3AGL(1,𝔽5)×#23911yescharacteristic, complemented
878C2—51no—
879C2—51no—
880C2—61no—
881C2—182no—
882C2—301no—
883C2—902no—
884C2C2×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×C5C4×#41
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. C4×D3×ΓL(1,𝔽16)C2semidirect
4. #13088693C2semidirect
5. #13088675C2semidirect
6. C3×ΓL(1,𝔽16)⋊Q8C2semidirect
7. C3×#91907C2semidirect
8. #13088417C2semidirect
9. #13088415C2semidirect
10. #13088409C2semidirect
11. AGL(1,𝔽5)×#624C2semidirect
18. #10624224C4semidirect
19. #10624201C4semidirect
20. #10624197C4semidirect
21. C5×#3799C4semidirect
29. #10624054C4semidirect
30. #10624051C4semidirect
64. ΓL(1,𝔽16)⋊Q8D3semidirect
66. #91907D3semidirect
79. C4⋊(C3⋊D15)C2×C4semidirect
80. C5×C4⋊(C3⋊D3)C2×C4semidirect
81. C3×C4×D15C2×C4semidirect
82. C3×Dic30C2×C4semidirect
83. C3×C4×C5×D3C2×C4semidirect
84. C3×C5×Dic6C2×C4semidirect
86. #67156C2×C4semidirect
87. #67155C2×C4semidirect
88. #67152C2×C4semidirect
89. #67151C2×C4semidirect
90. #67149C2×C4semidirect
91. #67149C2×C4semidirect
92. C5×#626C2×C4semidirect
93. C5×#624C2×C4semidirect
94. #67140C2×C4semidirect
95. C3×#1204C2×C4semidirect
96. C3×#1200C2×C4semidirect
97. C3×D3×Dic5C2×C4semidirect
187. C3⋊ΓL(1,𝔽16)#41semidirect
190. C3×ΓL(1,𝔽16)#41semidirect
223. #3799AGL(1,𝔽5)semidirect
276. C4×D15C4×D3semidirect
277. Dic30C4×D3semidirect
285. C4×C5×D3C4×D3semidirect
286. C5×Dic6C4×D3semidirect
297. #1204C4×D3semidirect
307. #1200C4×D3semidirect
310. D3×Dic5C4×D3semidirect
380. C4⋊(C3⋊D3)C2×AGL(1,𝔽5)semidirect
390. C3×C4×D3C2×AGL(1,𝔽5)semidirect
393. C3×Dic6C2×AGL(1,𝔽5)semidirect
397. #626C2×AGL(1,𝔽5)semidirect
402. #624C2×AGL(1,𝔽5)semidirect
437. ΓL(1,𝔽16)#239semidirect
521. C32×C5C4×#41semidirect
677. C4×D3D3×AGL(1,𝔽5)semidirect
680. Dic6D3×AGL(1,𝔽5)semidirect
739. C3×C5#5522semidirect
740. C3×C5C4×#239semidirect
800. C32#41×AGL(1,𝔽5)semidirect
853. C5#10594362semidirect
876. C3#11756835semidirect
877. C3AGL(1,𝔽5)×#239semidirect

Maximal subgroups

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

subgroupindex
D5×#37992
#130887322
C4×D3×ΓL(1,𝔽16)2
#130886932
#130886752
C3×ΓL(1,𝔽16)⋊Q82
C3×#919072
#130884172
#130884152
#130884092
AGL(1,𝔽5)×#6242
AGL(1,𝔽5)×#2393
#117568353
#105943625