Finite Group Databasebeta

← #72230203

Subgroups — #72230203

Order 2880.

1268 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#3796C211yesmaximal, characteristic
2#13088724C211yesmaximal, characteristic, complemented
3D12×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
4Dic6×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C3⋊D3×C4⋊AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6C3×#91921C211yesmaximal, characteristic, complemented
7C3×ΓL(1,𝔽16)⋊Q8C211yesmaximal, characteristic, complemented
8#13088417C212yesmaximal, complemented
9AGL(1,𝔽5)×#626C212yesmaximal, complemented
10#13088408C212yesmaximal, complemented
11D3×Dic3⋊AGL(1,𝔽5)C212yesmaximal, complemented
12#11756854—31nomaximal
13#11756846—31nomaximal
14C2×D3×ΓL(1,𝔽16)C2212yes—
15C2×C3⋊D3×AGL(1,𝔽5)C2212yes—
16C2×C3×D3×AGL(1,𝔽5)C2212yes—
17#10624220C411yescharacteristic, complemented
18#10624196C411yescharacteristic, complemented
19#10624194C411yescharacteristic, complemented
20C5×#3796C411yescharacteristic, complemented
21C4×D5×C3⋊D3C2211yescharacteristic
22C3×D5×D12C2211yescharacteristic
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#10624056C412yescomplemented
29#10624055C412yescomplemented
30D5×#626C2212yes—
31D3×D5×Dic3C2212yes—
32#10623979C2211yescharacteristic
33#10623979C2211yescharacteristic
34#10623978C2211yescharacteristic
35#10623978C2211yescharacteristic
36Dic3⋊ΓL(1,𝔽16)C2212yes—
37(C2×D3)⋊ΓL(1,𝔽16)C2212yes—
38Dic3×ΓL(1,𝔽16)C2212yes—
39#10623965C2212yes—
40C3×Dic3⋊AGL(1,𝔽5)C2212yes—
41C3×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
42C3×Dic3×AGL(1,𝔽5)C2212yes—
43#10594361—51nomaximal, Hall
44D5×#239—31no—
45D5×#237—31no—
46Q8×ΓL(1,𝔽16)—31no—
47D4×ΓL(1,𝔽16)—31no—
48C3×Q8×AGL(1,𝔽5)—31no—
49C3×D4×AGL(1,𝔽5)—31no—
50#67⋊AGL(1,𝔽5)—32no—
51AGL(1,𝔽5)×#67—32no—
52C2×Dic3⋊AGL(1,𝔽5)—32no—
53#91923—32no—
54#91921—32no—
55#91921D311yescharacteristic, complemented
56D3×C4⋊AGL(1,𝔽5)—32no—
57D3×C4⋊AGL(1,𝔽5)—31no—
58D3×C4⋊AGL(1,𝔽5)—31no—
59D3×C4⋊AGL(1,𝔽5)—61no—
60AGL(1,𝔽5)×D12—32no—
61AGL(1,𝔽5)×D12—31no—
62#91909—31no—
63#91909—31no—
64#91909—32no—
65ΓL(1,𝔽16)⋊Q8D311yescharacteristic, complemented
66AGL(1,𝔽5)×Dic6—31no—
67C2×D5×C3⋊D3C2311yescharacteristic
68C2×C3×D3×D5C2312yes—
69C2×C3⋊ΓL(1,𝔽16)C2312yes—
70C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
71C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
72C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
73C2×C3×ΓL(1,𝔽16)C2311yescharacteristic
74C2×C32×AGL(1,𝔽5)C2312yes—
75D3×ΓL(1,𝔽16)—42no—
76C3⋊D3×AGL(1,𝔽5)—42no—
77C3×D3×AGL(1,𝔽5)—42no—
78C4×C3⋊D15C2×C411yescharacteristic, complemented
79C4×C5×C3⋊D3C2×C411yescharacteristic, complemented
80C3×D60C2×C411yescharacteristic, complemented
81C3×Dic30C2×C411yescharacteristic, complemented
82C3×C5×D12C2×C411yescharacteristic, complemented
83C3×C5×Dic6C2×C411yescharacteristic, complemented
84C32×C4×D5C2311yescharacteristic
85#67156C2×C412yescomplemented
86#67154C2×C412yescomplemented
87#67152C2×C412yescomplemented
88#67151C2×C412yescomplemented
89D3×Dic15C2×C412yescomplemented
90Dic3×D15C2×C412yescomplemented
91C5×#626C2×C412yescomplemented
92C5×D3×Dic3C2×C412yescomplemented
93#67137C2×C411yescharacteristic, complemented
94C3⋊D3×Dic5C2×C411yescharacteristic, complemented
95D5×C3⋊Dic3C2311yescharacteristic
96C3×#1204C2×C412yescomplemented
97C3×#1203C2×C412yescomplemented
98C3×D5×Dic3C2312yes—
99#66266—91noHall
100C2×#3796—51no—
101C4⋊C4×C3⋊D3—51no—
102C3×#893—51no—
103C3×#887—51no—
104C4×#626—52no—
105Dic3×D12—51no—
106#63881—52no—
107#63877—52no—
108D3×Dic3⋊C4—52no—
109#63874—51no—
110Dic3×Dic6—51no—
111C22×ΓL(1,𝔽16)—32no—
112C22×C3×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)—62no—
117C2×D3×AGL(1,𝔽5)C2×D312yes—
118#6821—31no—
119#6819—31no—
120C5×#239—31no—
121C5×#237—31no—
122C3×Q8×D5—31no—
123C3×D4×D5—31no—
124D5×#67—32no—
125#6780—32no—
126#6779—32no—
127C2×D5×Dic3—32no—
128D5×D12—32no—
129D5×D12C2×D311yescharacteristic
130C4×D3×D5—32no—
131C4×D3×D5—31no—
132C4×D3×D5—31no—
133C4×D3×D5—61no—
134#6769—31no—
135#6769—32no—
136#6768—31no—
137#6768—32no—
138#6766—31no—
139#6765—31no—
140D5×Dic6C2×D311yescharacteristic
141#6763—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)—32no—
147C4×ΓL(1,𝔽16)C2×D311yescharacteristic
148C4×ΓL(1,𝔽16)C2×D311yescharacteristic
149C3×C22⋊AGL(1,𝔽5)—32no—
150C3×C4⋊AGL(1,𝔽5)—21no—
151C3×C4⋊AGL(1,𝔽5)—32no—
152C3×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
153C3×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
154C3×C4×AGL(1,𝔽5)—32no—
155C3×C4×AGL(1,𝔽5)—31no—
156C3×C4×AGL(1,𝔽5)—31no—
157Dic3⋊AGL(1,𝔽5)—31no—
158Dic3⋊AGL(1,𝔽5)—31no—
159Dic3⋊AGL(1,𝔽5)—31no—
160Dic3⋊AGL(1,𝔽5)—31no—
161Dic3⋊AGL(1,𝔽5)—32no—
162Dic3⋊AGL(1,𝔽5)—32no—
163Dic3⋊AGL(1,𝔽5)—32no—
164Dic3⋊AGL(1,𝔽5)—62no—
165Dic3⋊AGL(1,𝔽5)C2×D312yes—
166(C2×D3)⋊AGL(1,𝔽5)—32no—
167(C2×D3)⋊AGL(1,𝔽5)—31no—
168(C2×D3)⋊AGL(1,𝔽5)—31no—
169(C2×D3)⋊AGL(1,𝔽5)—31no—
170(C2×D3)⋊AGL(1,𝔽5)—31no—
171(C2×D3)⋊AGL(1,𝔽5)C2×D312yes—
172Dic3×AGL(1,𝔽5)—32no—
173Dic3×AGL(1,𝔽5)C2×D312yes—
174#5574—151no—
175#5546—151no—
176C2×C3⋊D15C22×C411yescharacteristic
177C2×C5×C3⋊D3C22×C411yescharacteristic
178C2×C3×D15C22×C412yes—
179C2×C3×C5×D3C22×C412yes—
180C2×C32×D5C2411yescharacteristic
181D5×C3⋊D3—21no—
182D5×C3⋊D3—21no—
183C3×D3×D5—22no—
184C3×D3×D5—22no—
185C3⋊ΓL(1,𝔽16)—22no—
186C3×ΓL(1,𝔽16)—21no—
187C3×ΓL(1,𝔽16)—21no—
188C3×ΓL(1,𝔽16)—21no—
189C3×ΓL(1,𝔽16)—21no—
190C32×AGL(1,𝔽5)—22no—
191C32×C4×C5C22×C411yescharacteristic
192C3⋊Dic15C22×C411yescharacteristic
193C5×C3⋊Dic3C22×C411yescharacteristic
194C3×Dic15C22×C412yes—
195C3×C5×Dic3C22×C412yes—
196C32×Dic5C22×C411yescharacteristic
197D5×#41—91no—
198Q8×AGL(1,𝔽5)—31no—
199Q8×AGL(1,𝔽5)—91no—
200D4×AGL(1,𝔽5)—31no—
201D4×AGL(1,𝔽5)—91no—
202D4×AGL(1,𝔽5)—92no—
203D4×AGL(1,𝔽5)—92no—
204#4130—91no—
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×D12—51no—
211C2×C3×C4×D3—52no—
212C2×C3×Dic6—51no—
213C2×#626—52no—
214C2×D3×Dic3—52no—
215C2×D3×Dic3—52no—
216#3796—51no—
217#3796—51no—
218#3796—51no—
219#3796—52no—
220#3796—52no—
221#3796AGL(1,𝔽5)11yescharacteristic, complemented
222C32×C4⋊C4—51no—
223C4⋊(C3⋊Dic3)—51no—
224#3750—52no—
225C3×(C2×D3)⋊C4—52no—
226C3×Dic3⋊C4—52no—
227C3×C4×Dic3—51no—
228C3×C4×Dic3—52no—
229C3×C4×Dic3—51no—
230#3724—51no—
231#3724—51no—
232Dic3⋊Dic3—52no—
233#3722—51no—
234#3722—51no—
235(C2×D3)⋊Dic3—52no—
236Dic32—52no—
237C22×C3×D5—32no—
238C2×D3×D5—31no—
239C2×D3×D5—31no—
240C2×D3×D5—61no—
241C2×D3×D5C22×D312yes—
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×D311yescharacteristic
247C2×ΓL(1,𝔽16)C22×D311yescharacteristic
248C2×ΓL(1,𝔽16)C22×D311yescharacteristic
249C2×ΓL(1,𝔽16)C22×D311yescharacteristic
250C2×C3×AGL(1,𝔽5)—22no—
251C2×C3×AGL(1,𝔽5)—31no—
252C2×C3×AGL(1,𝔽5)—31no—
253C2×C3×AGL(1,𝔽5)—31no—
254C2×C3×AGL(1,𝔽5)—31no—
255C2×C3×AGL(1,𝔽5)—122no—
256C2×C3×AGL(1,𝔽5)C22×D312yes—
257C2×C3×AGL(1,𝔽5)C22×D312yes—
258D3×AGL(1,𝔽5)—42no—
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—
264C3×C5×Q8—31no—
265C3×C5×D4—31no—
266#1220—32no—
267C2×Dic15—32no—
268D60—32no—
269D60C4×D311yescharacteristic, complemented
270C4×D15—32no—
271C4×D15—31no—
272C4×D15—31no—
273C4×D15—61no—
274Dic30C4×D311yescharacteristic, complemented
275C5×#67—32no—
276C2×C5×Dic3—32no—
277C5×D12—32no—
278C5×D12C4×D311yescharacteristic, complemented
279C4×C5×D3—32no—
280C4×C5×D3—31no—
281C4×C5×D3—31no—
282C4×C5×D3—61no—
283C5×Dic6C4×D311yescharacteristic, complemented
284C3×C22⋊D5—32no—
285C3×D20—31no—
286C3×C4×D5—21no—
287C3×C4×D5—32no—
288C3×C4×D5C22×D311yescharacteristic
289C3×C4×D5C22×D311yescharacteristic
290C3×Dic10—31no—
291C3×Dic10—32no—
292#1204C4×D312yescomplemented
293#1203—32no—
294#1203—32no—
295#1203C4×D312yescomplemented
296#1202—32no—
297#1201—32no—
298#1200—32no—
299#1200—31no—
300#1200—31no—
301#1200—61no—
302D3×Dic5—32no—
303D3×Dic5—31no—
304D3×Dic5—31no—
305D3×Dic5—61no—
306D5×Dic3—31no—
307D5×Dic3—31no—
308D5×Dic3—32no—
309D5×Dic3—32no—
310D5×Dic3—61no—
311D5×Dic3C22×D312yes—
312C2×#239—151no—
313C2×#237—151no—
314C3×C4×Q8—151no—
315C3×C4×D4—151no—
316Q8×Dic3—151no—
317D4×Dic3—151no—
318C4×#67—152no—
319C2×Dic3⋊C4—152no—
320#893—51no—
321#893—152no—
322D3×C4⋊C4—151no—
323D3×C4⋊C4—151no—
324D3×C4⋊C4—152no—
325D3×C4⋊C4—301no—
326#887—51no—
327#67⋊C4—152no—
328#877—152no—
329C4×D12—152no—
330C4×D12—151no—
331#872—151no—
332#872—151no—
333#872—152no—
334C4×Dic6—151no—
335C2×C32×C5C23×C411yescharacteristic
336C3⋊D15—21no—
337C5×C3⋊D3—21no—
338C3×D15—22no—
339C3×C5×D3—22no—
340C32×D5H(5,𝔽2)11yescharacteristic
341C32×D52−1+411yescharacteristic
342C22×AGL(1,𝔽5)—32no—
343C22×AGL(1,𝔽5)—92no—
344C22×AGL(1,𝔽5)—92no—
345C5×#41—91no—
346#713—91no—
347Q8×D5—31no—
348#711—92no—
349#711—91no—
350D4×D5—31no—
351D4×D5—92no—
352#709—91no—
353#709—92no—
354C2×C4×D5—92no—
355C2×C4×D5—91no—
356C22⋊AGL(1,𝔽5)—32no—
357C22⋊AGL(1,𝔽5)—91no—
358C22⋊AGL(1,𝔽5)—91no—
359C22⋊AGL(1,𝔽5)—92no—
360C4⋊AGL(1,𝔽5)—32no—
361C4⋊AGL(1,𝔽5)—92no—
362C4⋊AGL(1,𝔽5)—91no—
363C4⋊AGL(1,𝔽5)—91no—
364C4⋊AGL(1,𝔽5)—92no—
365C4⋊AGL(1,𝔽5)—91no—
366C4⋊AGL(1,𝔽5)D3211yescharacteristic
367C4×AGL(1,𝔽5)—32no—
368C4×AGL(1,𝔽5)—31no—
369C4×AGL(1,𝔽5)—31no—
370C4×AGL(1,𝔽5)—92no—
371C22×C3⋊D3—51no—
372C22×C3×D3—52no—
373C2×C32×C4—51no—
374C2×C32×C4—52no—
375C2×C3⋊Dic3—51no—
376C2×C3⋊Dic3—52no—
377C4×C3⋊D3—51no—
378C4×C3⋊D3—51no—
379C4×C3⋊D3—51no—
380C4×C3⋊D3—202no—
381C4×C3⋊D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
382C2×C3×Dic3—52no—
383C2×C3×Dic3—51no—
384C2×C3×Dic3—51no—
385C2×C3×Dic3—51no—
386C2×C3×Dic3—51no—
387C3×D12—52no—
388C3×D12—51no—
389C3×D12C2×AGL(1,𝔽5)11yescharacteristic, complemented
390C3×C4×D3—202no—
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
398D3×Dic3—52no—
399D3×Dic3—52no—
400D3×Dic3—52no—
401D3×Dic3—202no—
402D3×Dic3C2×AGL(1,𝔽5)12yescomplemented
403#520—451noSylow
404C22×C3×C5—32no—
405C2×D15—31no—
406C2×D15—31no—
407C2×D15—61no—
408C2×D15C2×C4×D312yes—
409C2×C5×D3—31no—
410C2×C5×D3—31no—
411C2×C5×D3—61no—
412C2×C5×D3C2×C4×D312yes—
413C2×C3×D5—21no—
414C2×C3×D5—32no—
415C2×C3×D5—62no—
416C2×C3×D5—62no—
417C2×C3×D5C23×D311yescharacteristic
418C2×C3×D5C23×D311yescharacteristic
419D3×D5—22no—
420D3×D5—22no—
421D3×D5—61no—
422D3×D5—61no—
423D3×D5—61no—
424D3×D5—61no—
425D3×D5—61no—
426D3×D5—61no—
427D3×D5—61no—
428D3×D5—61no—
429ΓL(1,𝔽16)—21no—
430ΓL(1,𝔽16)—21no—
431ΓL(1,𝔽16)—21no—
432ΓL(1,𝔽16)—21no—
433ΓL(1,𝔽16)—62no—
434ΓL(1,𝔽16)—62no—
435ΓL(1,𝔽16)—122no—
436C3×AGL(1,𝔽5)—22no—
437C3×AGL(1,𝔽5)—22no—
438C3×AGL(1,𝔽5)—42no—
439C3×AGL(1,𝔽5)—61no—
440C3×AGL(1,𝔽5)—61no—
441C3×AGL(1,𝔽5)—61no—
442C3×AGL(1,𝔽5)—61no—
443C3×C4×C5—21no—
444C3×C4×C5—32no—
445C3×C4×C5C2×C4×D311yescharacteristic
446C3×C4×C5C2×C4×D311yescharacteristic
447Dic15—31no—
448Dic15—31no—
449Dic15—61no—
450Dic15C2×C4×D312yes—
451C3×Dic5—21no—
452C3×Dic5—32no—
453C3×Dic5C2×C4×D311yescharacteristic
454C3×Dic5C2×C4×D311yescharacteristic
455C5×Dic3—31no—
456C5×Dic3—31no—
457C5×Dic3—61no—
458C5×Dic3C2×C4×D312yes—
459C2×C3×Q8—151no—
460C2×C3×D4—151no—
461C22×C3×C4—152no—
462C2×#67—152no—
463C22×Dic3—152no—
464C22×Dic3—152no—
465#239—31no—
466#239—152no—
467#239—151no—
468#239—152no—
469#239—151no—
470#239—151no—
471#237—31no—
472#237—151no—
473#237—152no—
474#237—152no—
475#237—151no—
476#237—151no—
477C2×D12—51no—
478C2×D12—152no—
479C2×C4×D3—52no—
480C2×C4×D3—151no—
481C2×C4×D3—151no—
482C2×C4×D3—152no—
483C2×C4×D3—152no—
484C2×C4×D3—152no—
485C2×C4×D3—152no—
486C2×C4×D3—301no—
487C2×C4×D3—302no—
488C2×Dic6—51no—
489C3×C4⋊C4—51no—
490C3×C4⋊C4—51no—
491C3×C4⋊C4—101no—
492C3×C4⋊C4—152no—
493C3×C22⋊C4—152no—
494C3×C42—151no—
495C3×C42—151no—
496C3×C42—152no—
497#217—152no—
498(C2×D3)⋊C4—52no—
499(C2×D3)⋊C4—151no—
500(C2×D3)⋊C4—151no—
501(C2×D3)⋊C4—151no—
502(C2×D3)⋊C4—151no—
503(C2×D3)⋊C4—152no—
504C4⋊Dic3—152no—
505C4⋊Dic3—151no—
506C4⋊Dic3—151no—
507C4⋊Dic3—301no—
508Dic3⋊C4—52no—
509Dic3⋊C4—152no—
510Dic3⋊C4—151no—
511Dic3⋊C4—151no—
512Dic3⋊C4—151no—
513Dic3⋊C4—151no—
514Dic3⋊C4—152no—
515Dic3⋊C4—152no—
516Dic3⋊C4—302no—
517C4×Dic3—52no—
518C4×Dic3—51no—
519C4×Dic3—51no—
520C4×Dic3—152no—
521C4×Dic3—152no—
522C32×C5#52011yescharacteristic, complemented, Hall
523C22×D5—32no—
524C22×D5—91no—
525C2×AGL(1,𝔽5)—31no—
526C2×AGL(1,𝔽5)—31no—
527C2×AGL(1,𝔽5)—31no—
528C2×AGL(1,𝔽5)—31no—
529C2×AGL(1,𝔽5)—92no—
530C2×AGL(1,𝔽5)—122no—
531C2×AGL(1,𝔽5)—362no—
532C2×AGL(1,𝔽5)—362no—
533C2×AGL(1,𝔽5)C2×D3212yes—
534C5×Q8—31no—
535C5×D4—31no—
536C5×D4—92no—
537C2×C4×C5—92no—
538C2×C4×C5—91no—
539C22⋊D5—32no—
540C22⋊D5—92no—
541C22⋊D5—92no—
542C2×Dic5—92no—
543C2×Dic5—91no—
544D20—31no—
545D20—92no—
546C4×D5—32no—
547C4×D5—92no—
548C4×D5—92no—
549C4×D5—91no—
550C4×D5—91no—
551C4×D5—91no—
552C4×D5C2×D3211yescharacteristic
553Dic10—31no—
554Dic10—32no—
555C22×C32—51no—
556C2×C3⋊D3—51no—
557C2×C3⋊D3—101no—
558C2×C3⋊D3—101no—
559C2×C3⋊D3C22×AGL(1,𝔽5)11yescharacteristic
560C2×C3×D3—52no—
561C2×C3×D3—102no—
562C2×C3×D3—102no—
563C2×C3×D3C22×AGL(1,𝔽5)12yes—
564C32×C4—51no—
565C32×C4—102no—
566C32×C4C22×AGL(1,𝔽5)11yescharacteristic
567C3⋊Dic3—51no—
568C3⋊Dic3—102no—
569C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
570C3×Dic3—52no—
571C3×Dic3—101no—
572C3×Dic3—101no—
573C3×Dic3—101no—
574C3×Dic3—101no—
575C3×Dic3C22×AGL(1,𝔽5)12yes—
576C2×#41—451no—
577C4×Q8—151no—
578C4×Q8—451no—
579C4×D4—151no—
580C4×D4—452no—
581C4×D4—451no—
582C4×D4—452no—
583#117—451no—
584#117—452no—
585C2×C4⋊C4—451no—
586C2×C4⋊C4—452no—
587C2×C3×C5—21no—
588C2×C3×C5—62no—
589C2×C3×C5C22×C4×D311yescharacteristic
590C2×C3×C5C22×C4×D311yescharacteristic
591D15—22no—
592D15—61no—
593D15—61no—
594D15—61no—
595D15—61no—
596C3×D5—21no—
597C3×D5—21no—
598C3×D5—62no—
599C3×D5#100411yescharacteristic
600C3×D5#100711yescharacteristic
601C3×D5#100911yescharacteristic
602C3×D5#101011yescharacteristic
603C5×D3—22no—
604C5×D3—61no—
605C5×D3—61no—
606C5×D3—61no—
607C5×D3—61no—
608C23×C3—152no—
609C22×D3—52no—
610C22×D3—151no—
611C22×D3—151no—
612C22×D3—301no—
613C3×Q8—31no—
614C3×Q8—152no—
615C3×Q8—151no—
616C3×D4—31no—
617C3×D4—152no—
618C3×D4—151no—
619C2×C3×C4—51no—
620C2×C3×C4—51no—
621C2×C3×C4—52no—
622C2×C3×C4—52no—
623C2×C3×C4—101no—
624C2×C3×C4—102no—
625C2×C3×C4—152no—
626C2×C3×C4—151no—
627C2×C3×C4—151no—
628C2×C3×C4—151no—
629C2×C3×C4—151no—
630C2×C3×C4—602no—
631#67—32no—
632#67—152no—
633#67—152no—
634#67—152no—
635C2×Dic3—32no—
636C2×Dic3—52no—
637C2×Dic3—51no—
638C2×Dic3—51no—
639C2×Dic3—51no—
640C2×Dic3—51no—
641C2×Dic3—152no—
642C2×Dic3—151no—
643C2×Dic3—151no—
644C2×Dic3—152no—
645C2×Dic3—152no—
646C2×Dic3—152no—
647C2×Dic3—152no—
648C2×Dic3—301no—
649C2×Dic3—302no—
650C2×Dic3—602no—
651D12—32no—
652D12—52no—
653D12—51no—
654D12—152no—
655D12—152no—
656D12—152no—
657D12D3×AGL(1,𝔽5)11yescharacteristic, complemented
658C4×D3—32no—
659C4×D3—31no—
660C4×D3—31no—
661C4×D3—61no—
662C4×D3—151no—
663C4×D3—151no—
664C4×D3—152no—
665C4×D3—152no—
666C4×D3—151no—
667C4×D3—151no—
668C4×D3—152no—
669C4×D3—151no—
670C4×D3—151no—
671C4×D3—202no—
672C4×D3—301no—
673C4×D3—301no—
674C4×D3—301no—
675C4×D3—602no—
676C4×D3—602no—
677C4×D3—602no—
678C4×D3—602no—
679C4×D3—602no—
680Dic6—51no—
681Dic6—52no—
682Dic6D3×AGL(1,𝔽5)11yescharacteristic, complemented
683C22×C5—32no—
684C22×C5—91no—
685C2×D5—32no—
686C2×D5—62no—
687C2×D5—62no—
688C2×D5—91no—
689C2×D5—181no—
690C2×D5—181no—
691C2×D5C22×D3211yescharacteristic
692AGL(1,𝔽5)—22no—
693AGL(1,𝔽5)—61no—
694AGL(1,𝔽5)—61no—
695AGL(1,𝔽5)—61no—
696AGL(1,𝔽5)—61no—
697AGL(1,𝔽5)—182no—
698C4×C5—32no—
699C4×C5—91no—
700C4×C5C4×D3211yescharacteristic
701Dic5—32no—
702Dic5—91no—
703Dic5C4×D3211yescharacteristic
704C2×C32—51no—
705C2×C32—51no—
706C2×C32C23×AGL(1,𝔽5)11yescharacteristic
707C3⋊D3—21no—
708C3⋊D3—101no—
709C3×D3—22no—
710C3×D3—102no—
711#41—91no—
712#41—452no—
713#41—451no—
714#41—451no—
715#41—452no—
716#41—451no—
717C2×Q8—151no—
718C2×D4—151no—
719C2×D4—452no—
720C22×C4—152no—
721C22×C4—451no—
722C22×C4—452no—
723C22×C4—452no—
724C22×C4—452no—
725C4⋊C4—51no—
726C4⋊C4—152no—
727C4⋊C4—452no—
728C4⋊C4—451no—
729C4⋊C4—451no—
730C4⋊C4—452no—
731C4⋊C4—451no—
732C22⋊C4—152no—
733C22⋊C4—451no—
734C22⋊C4—451no—
735C22⋊C4—452no—
736C42—151no—
737C42—151no—
738C42—152no—
739C42—452no—
740C3×C5—21no—
741C3×C5#554611yescharacteristic, complemented
742C3×C5#557411yescharacteristic, complemented
743C22×C3—32no—
744C22×C3—51no—
745C22×C3—51no—
746C22×C3—101no—
747C22×C3—152no—
748C22×C3—302no—
749C22×C3—302no—
750C2×D3—31no—
751C2×D3—31no—
752C2×D3—52no—
753C2×D3—61no—
754C2×D3—102no—
755C2×D3—102no—
756C2×D3—151no—
757C2×D3—151no—
758C2×D3—301no—
759C2×D3—301no—
760C2×D3—301no—
761C2×D3—301no—
762C2×D3—301no—
763C2×D3—301no—
764C2×D3—301no—
765C2×D3—301no—
766C2×D3—301no—
767C2×D3C2×D3×AGL(1,𝔽5)12yes—
768C3×C4—21no—
769C3×C4—32no—
770C3×C4—51no—
771C3×C4—51no—
772C3×C4—101no—
773C3×C4—102no—
774C3×C4—102no—
775C3×C4—152no—
776C3×C4—202no—
777C3×C4—301no—
778C3×C4—301no—
779C3×C4—301no—
780C3×C4—301no—
781C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
782C3×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
783Dic3—31no—
784Dic3—31no—
785Dic3—52no—
786Dic3—61no—
787Dic3—101no—
788Dic3—101no—
789Dic3—101no—
790Dic3—101no—
791Dic3—151no—
792Dic3—151no—
793Dic3—301no—
794Dic3—302no—
795Dic3—302no—
796Dic3—602no—
797Dic3C2×D3×AGL(1,𝔽5)12yes—
798C2×C5—62no—
799C2×C5—181no—
800C2×C5C2×C4×D3211yescharacteristic
801D5—62no—
802D5—181no—
803D5#6431411yescharacteristic
804D5#6431511yescharacteristic
805C32#6626611yescharacteristic, complemented, Sylow
806C23—152no—
807C23—451no—
808Q8—31no—
809Q8—152no—
810Q8—151no—
811D4—31no—
812D4—92no—
813D4—152no—
814D4—151no—
815D4—452no—
816D4—452no—
817D4—452no—
818C2×C4—51no—
819C2×C4—52no—
820C2×C4—92no—
821C2×C4—91no—
822C2×C4—152no—
823C2×C4—151no—
824C2×C4—151no—
825C2×C4—151no—
826C2×C4—151no—
827C2×C4—452no—
828C2×C4—451no—
829C2×C4—451no—
830C2×C4—452no—
831C2×C4—451no—
832C2×C4—452no—
833C2×C4—451no—
834C2×C4—452no—
835C2×C4—602no—
836C2×C4—1802no—
837C2×C4—1802no—
838C2×C3—21no—
839C2×C3—51no—
840C2×C3—51no—
841C2×C3—51no—
842C2×C3—51no—
843C2×C3—62no—
844C2×C3—101no—
845C2×C3—101no—
846C2×C3—302no—
847C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
848C2×C3C22×D3×AGL(1,𝔽5)11yescharacteristic
849D3—22no—
850D3—61no—
851D3—61no—
852D3—61no—
853D3—61no—
854D3—102no—
855D3—301no—
856D3—301no—
857D3—301no—
858D3—301no—
859C5#1059436111yescharacteristic, complemented, Sylow
860C22—32no—
861C22—51no—
862C22—91no—
863C22—152no—
864C22—302no—
865C22—302no—
866C22—451no—
867C22—901no—
868C22—901no—
869C4—32no—
870C4—51no—
871C4—91no—
872C4—102no—
873C4—152no—
874C4—301no—
875C4—301no—
876C4—301no—
877C4—301no—
878C4—451no—
879C4—902no—
880C4D32×AGL(1,𝔽5)11yescharacteristic
881C3—21no—
882C3#1175684611yescharacteristic, complemented
883C3#1175685411yescharacteristic, complemented
884C2—51no—
885C2—51no—
886C2—62no—
887C2—181no—
888C2—302no—
889C2—901no—
890C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FittingC32×C4×C5C22×C4
prime radicalD5×#3796C2
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. #13088724C2semidirect
3. D12×ΓL(1,𝔽16)C2semidirect
4. Dic6×ΓL(1,𝔽16)C2semidirect
5. C3⋊D3×C4⋊AGL(1,𝔽5)C2semidirect
6. C3×#91921C2semidirect
7. C3×ΓL(1,𝔽16)⋊Q8C2semidirect
8. #13088417C2semidirect
9. AGL(1,𝔽5)×#626C2semidirect
10. #13088408C2semidirect
11. D3×Dic3⋊AGL(1,𝔽5)C2semidirect
17. #10624220C4semidirect
18. #10624196C4semidirect
19. #10624194C4semidirect
20. C5×#3796C4semidirect
28. #10624056C4semidirect
29. #10624055C4semidirect
55. #91921D3semidirect
65. ΓL(1,𝔽16)⋊Q8D3semidirect
78. C4×C3⋊D15C2×C4semidirect
79. C4×C5×C3⋊D3C2×C4semidirect
80. C3×D60C2×C4semidirect
81. C3×Dic30C2×C4semidirect
82. C3×C5×D12C2×C4semidirect
83. C3×C5×Dic6C2×C4semidirect
85. #67156C2×C4semidirect
86. #67154C2×C4semidirect
87. #67152C2×C4semidirect
88. #67151C2×C4semidirect
89. D3×Dic15C2×C4semidirect
90. Dic3×D15C2×C4semidirect
91. C5×#626C2×C4semidirect
92. C5×D3×Dic3C2×C4semidirect
93. #67137C2×C4semidirect
94. C3⋊D3×Dic5C2×C4semidirect
96. C3×#1204C2×C4semidirect
97. C3×#1203C2×C4semidirect
221. #3796AGL(1,𝔽5)semidirect
269. D60C4×D3semidirect
274. Dic30C4×D3semidirect
278. C5×D12C4×D3semidirect
283. C5×Dic6C4×D3semidirect
292. #1204C4×D3semidirect
295. #1203C4×D3semidirect
381. C4×C3⋊D3C2×AGL(1,𝔽5)semidirect
389. C3×D12C2×AGL(1,𝔽5)semidirect
393. C3×Dic6C2×AGL(1,𝔽5)semidirect
397. #626C2×AGL(1,𝔽5)semidirect
402. D3×Dic3C2×AGL(1,𝔽5)semidirect
522. C32×C5#520semidirect
657. D12D3×AGL(1,𝔽5)semidirect
682. Dic6D3×AGL(1,𝔽5)semidirect
741. C3×C5#5546semidirect
742. C3×C5#5574semidirect
805. C32#66266semidirect
859. C5#10594361semidirect
882. C3#11756846semidirect
883. C3#11756854semidirect

Maximal subgroups

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

subgroupindex
D5×#37962
#130887242
D12×ΓL(1,𝔽16)2
Dic6×ΓL(1,𝔽16)2
C3⋊D3×C4⋊AGL(1,𝔽5)2
C3×#919212
C3×ΓL(1,𝔽16)⋊Q82
#130884172
AGL(1,𝔽5)×#6262
#130884082
D3×Dic3⋊AGL(1,𝔽5)2
#117568543
#117568463
#105943615