Finite Group Databasebeta

← AGL(1,𝔽5)×#3805 #72230248

Subgroups — AGL(1,𝔽5)×#3805 #72230248

Order 2880.

1348 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D5×#3805C211yesmaximal, characteristic
2#13088735C211yesmaximal, characteristic, complemented
3#67⋊ΓL(1,𝔽16)C212yesmaximal, complemented
4C2×AGL(1,𝔽5)×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×AGL(1,𝔽5)×#67C212yesmaximal, complemented
6#13088420C211yesmaximal, characteristic, complemented
7AGL(1,𝔽5)×#627C211yesmaximal, characteristic, complemented
8#13088416C211yesmaximal, characteristic, complemented
9AGL(1,𝔽5)×#625C211yesmaximal, characteristic, complemented
10#13088410C212yesmaximal, complemented
11D3×Dic3×AGL(1,𝔽5)C212yesmaximal, complemented
12AGL(1,𝔽5)×#237—32nomaximal
13C22×C3⋊ΓL(1,𝔽16)C2211yescharacteristic
14C22×C32×AGL(1,𝔽5)C2211yescharacteristic
15C2×D3×ΓL(1,𝔽16)C2212yes—
16C2×C3×D3×AGL(1,𝔽5)C2212yes—
17#10624229C411yescharacteristic, complemented
18#10624208C412yescomplemented
19C5×#3805C411yescharacteristic, complemented
20C2×D5×C3⋊Dic3C2211yescharacteristic
21C3×D5×#67C2212yes—
22C3×#6763C2212yes—
23#10624047C411yescharacteristic, complemented
24#10624046C411yescharacteristic, complemented
25#10624045C412yescomplemented
26D5×#627C2211yescharacteristic
27D5×#625C2211yescharacteristic
28D3×D5×Dic3C2212yes—
29#10623979C2211yescharacteristic
30#10623979C2211yescharacteristic
31ΓL(1,𝔽16)⋊Dic3C2212yes—
32Dic3⋊ΓL(1,𝔽16)C2212yes—
33(C2×D3)⋊ΓL(1,𝔽16)C2212yes—
34Dic3×ΓL(1,𝔽16)C2212yes—
35AGL(1,𝔽5)×C3⋊Dic3C2211yescharacteristic
36AGL(1,𝔽5)×C3⋊Dic3C2211yescharacteristic
37AGL(1,𝔽5)×C3⋊Dic3C2211yescharacteristic
38AGL(1,𝔽5)×C3⋊Dic3C2211yescharacteristic
39C3×Dic3⋊AGL(1,𝔽5)C2212yes—
40C3×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
41C3×Dic3×AGL(1,𝔽5)C2212yes—
42C4×#3805—51nomaximal, Hall
43D5×#237—32no—
44D4×ΓL(1,𝔽16)—32no—
45C3×D4×AGL(1,𝔽5)—32no—
46#67⋊AGL(1,𝔽5)—32no—
47#67⋊AGL(1,𝔽5)—32no—
48AGL(1,𝔽5)×#67—32no—
49AGL(1,𝔽5)×#67D312yescomplemented
50#91923—32no—
51#91923—32no—
52C2×Dic3×AGL(1,𝔽5)—32no—
53C2×Dic3×AGL(1,𝔽5)—32no—
54C2×Dic3×AGL(1,𝔽5)—61no—
55C4×D3×AGL(1,𝔽5)—32no—
56ΓL(1,𝔽16)⋊Q8—32no—
57#91907—32no—
58AGL(1,𝔽5)×Dic6—32no—
59C22×C32×D5C2311yescharacteristic
60C2×C3×D3×D5C2312yes—
61C2×C3⋊ΓL(1,𝔽16)—22no—
62C2×C3⋊ΓL(1,𝔽16)C2311yescharacteristic
63C2×C3⋊ΓL(1,𝔽16)C2311yescharacteristic
64C2×C3×ΓL(1,𝔽16)C2312yes—
65C2×C3×ΓL(1,𝔽16)C2312yes—
66C2×C32×AGL(1,𝔽5)—22no—
67C2×C32×AGL(1,𝔽5)C2311yescharacteristic
68C2×C32×AGL(1,𝔽5)C2311yescharacteristic
69D3×ΓL(1,𝔽16)—24no—
70C3×D3×AGL(1,𝔽5)—24no—
71C2×C3⋊Dic15C2×C411yescharacteristic, complemented
72C2×C5×C3⋊Dic3C2×C411yescharacteristic, complemented
73C3×#1220C2×C412yescomplemented
74C3×C5×#67C2×C412yescomplemented
75#67158C2×C411yescharacteristic, complemented
76#67157C2×C411yescharacteristic, complemented
77#67154C2×C412yescomplemented
78#67153C2×C412yescomplemented
79#67150C2×C412yescomplemented
80D3×Dic15C2×C412yescomplemented
81Dic3×D15C2×C412yescomplemented
82C5×#627C2×C411yescharacteristic, complemented
83C5×#625C2×C411yescharacteristic, complemented
84C5×D3×Dic3C2×C412yescomplemented
85D5×C3⋊Dic3C2×C411yescharacteristic, complemented
86D5×C3⋊Dic3C2×C411yescharacteristic, complemented
87D5×C3⋊Dic3C2311yescharacteristic
88D5×C3⋊Dic3C2311yescharacteristic
89C3×#1202C2×C412yescomplemented
90C3×#1201C2×C412yescomplemented
91C3×D5×Dic3C2312yes—
92#41×AGL(1,𝔽5)—91noHall
93C2×#3805—51no—
94C2×C4×C3⋊Dic3—51no—
95C3×C4×#67—52no—
96#67⋊Dic3—52no—
97#63957—51no—
98C4×#627—51no—
99#63902—51no—
100C4×#625—51no—
101#63878—52no—
102C4×D3×Dic3—52no—
103#63838—51no—
104C22×ΓL(1,𝔽16)—32no—
105C22×ΓL(1,𝔽16)—32no—
106C22×ΓL(1,𝔽16)—61no—
107C22×C3×AGL(1,𝔽5)—21no—
108C22×C3×AGL(1,𝔽5)—32no—
109C22×C3×AGL(1,𝔽5)C2×D312yes—
110C2×D3×AGL(1,𝔽5)—32no—
111C2×D3×AGL(1,𝔽5)C2×D312yes—
112#6819—32no—
113C5×#237—32no—
114C3×D4×D5—32no—
115D5×#67—32no—
116D5×#67C2×D312yes—
117#6780—32no—
118#6780—32no—
119#6779—32no—
120#6779—32no—
121C2×D5×Dic3—32no—
122C2×D5×Dic3—32no—
123C2×D5×Dic3—61no—
124C4×D3×D5—32no—
125#6766—32no—
126#6765—32no—
127D5×Dic6—32no—
128#6763—32no—
129#6763C2×D312yes—
130C4⋊ΓL(1,𝔽16)—32no—
131C4×ΓL(1,𝔽16)—32no—
132C3×C22⋊AGL(1,𝔽5)—32no—
133C3×C22⋊AGL(1,𝔽5)—32no—
134C3×C4⋊AGL(1,𝔽5)—32no—
135C3×C4×AGL(1,𝔽5)—32no—
136Dic3⋊AGL(1,𝔽5)—32no—
137Dic3⋊AGL(1,𝔽5)—32no—
138Dic3⋊AGL(1,𝔽5)—32no—
139Dic3⋊AGL(1,𝔽5)C2×D312yes—
140(C2×D3)⋊AGL(1,𝔽5)—32no—
141(C2×D3)⋊AGL(1,𝔽5)C2×D312yes—
142Dic3×AGL(1,𝔽5)—32no—
143Dic3×AGL(1,𝔽5)—32no—
144Dic3×AGL(1,𝔽5)—32no—
145Dic3×AGL(1,𝔽5)—32no—
146Dic3×AGL(1,𝔽5)—32no—
147Dic3×AGL(1,𝔽5)—32no—
148Dic3×AGL(1,𝔽5)—32no—
149Dic3×AGL(1,𝔽5)—61no—
150Dic3×AGL(1,𝔽5)—61no—
151Dic3×AGL(1,𝔽5)—61no—
152Dic3×AGL(1,𝔽5)—61no—
153Dic3×AGL(1,𝔽5)C2×D312yes—
154C4×#237—152no—
155C22×C32×C5C22×C411yescharacteristic
156C2×C3×D15C22×C412yes—
157C2×C3×C5×D3C22×C412yes—
158C2×C32×D5—21no—
159C2×C32×D5—21no—
160C2×C32×D5C22×C411yescharacteristic
161C2×C32×D5C2411yescharacteristic
162C3×D3×D5—22no—
163C3×D3×D5—22no—
164C3⋊ΓL(1,𝔽16)—21no—
165C3⋊ΓL(1,𝔽16)#4112yescomplemented
166C3×ΓL(1,𝔽16)—22no—
167C3×ΓL(1,𝔽16)—22no—
168C32×AGL(1,𝔽5)—21no—
169C32×AGL(1,𝔽5)#4112yescomplemented
170C3⋊Dic15C22×C411yescharacteristic
171C3⋊Dic15C22×C411yescharacteristic
172C5×C3⋊Dic3C22×C411yescharacteristic
173C5×C3⋊Dic3C22×C411yescharacteristic
174C3×Dic15C22×C412yes—
175C3×C5×Dic3C22×C412yes—
176D5×#41—91no—
177Q8×AGL(1,𝔽5)—91no—
178Q8×AGL(1,𝔽5)—91no—
179D4×AGL(1,𝔽5)—32no—
180D4×AGL(1,𝔽5)—91no—
181D4×AGL(1,𝔽5)—92no—
182D4×AGL(1,𝔽5)—91no—
183#4130—92no—
184#4130—91no—
185C2×C4×AGL(1,𝔽5)—92no—
186C2×C4×AGL(1,𝔽5)—91no—
187C22×C32×C4—51no—
188C22×C3⋊Dic3—51no—
189C22×C3⋊Dic3—51no—
190C2×C3×#67—52no—
191C2×C3×C4×D3—52no—
192C2×#627—51no—
193C2×#625—51no—
194#3805—51no—
195#3805—52no—
196#3805—51no—
197#3805—51no—
198#3805—52no—
199#3805AGL(1,𝔽5)11yescharacteristic, direct product factor
200C2×D3×Dic3—52no—
201C2×D3×Dic3—52no—
202C4×C3⋊Dic3—51no—
203C4×C3⋊Dic3—51no—
204C4×C3⋊Dic3—51no—
205C4×C3⋊Dic3—51no—
206C3×#217—52no—
207C3×(C2×D3)⋊C4—52no—
208C3×Dic3⋊C4—52no—
209C3×C4×Dic3—52no—
210#3724—51no—
211#3724—51no—
212Dic3⋊Dic3—52no—
213(C2×D3)⋊Dic3—52no—
214Dic32—52no—
215Dic32—52no—
216C22×C3×D5—21no—
217C22×C3×D5—32no—
218C22×C3×D5C22×D312yes—
219C2×D3×D5C22×D312yes—
220C2×ΓL(1,𝔽16)—32no—
221C2×ΓL(1,𝔽16)—32no—
222C2×ΓL(1,𝔽16)—64no—
223C2×ΓL(1,𝔽16)—64no—
224C2×ΓL(1,𝔽16)—61no—
225C2×ΓL(1,𝔽16)—62no—
226C2×ΓL(1,𝔽16)—62no—
227C2×ΓL(1,𝔽16)—61no—
228C2×ΓL(1,𝔽16)C22×D312yes—
229C2×ΓL(1,𝔽16)C22×D312yes—
230C2×C3×AGL(1,𝔽5)—22no—
231C2×C3×AGL(1,𝔽5)—22no—
232C2×C3×AGL(1,𝔽5)—21no—
233C2×C3×AGL(1,𝔽5)—24no—
234C2×C3×AGL(1,𝔽5)—21no—
235C2×C3×AGL(1,𝔽5)—32no—
236C2×C3×AGL(1,𝔽5)—32no—
237C2×C3×AGL(1,𝔽5)—64no—
238C2×C3×AGL(1,𝔽5)C22×D312yes—
239C2×C3×AGL(1,𝔽5)C22×D312yes—
240D3×AGL(1,𝔽5)—24no—
241D3×AGL(1,𝔽5)—64no—
242C3×C5×D4—32no—
243#1220—32no—
244#1220C4×D312yescomplemented
245C2×Dic15—32no—
246C2×Dic15—32no—
247C2×Dic15—61no—
248C4×D15—32no—
249Dic30—32no—
250C5×#67—32no—
251C5×#67C4×D312yescomplemented
252C2×C5×Dic3—32no—
253C2×C5×Dic3—32no—
254C2×C5×Dic3—61no—
255C4×C5×D3—32no—
256C5×Dic6—32no—
257C3×C22⋊D5—32no—
258C3×C22⋊D5—32no—
259C3×D20—32no—
260C3×C4×D5—32no—
261#1204—32no—
262#1204—32no—
263#1202—32no—
264#1202C4×D312yescomplemented
265#1201—32no—
266#1201C4×D312yescomplemented
267#1200—32no—
268D3×Dic5—32no—
269D5×Dic3—32no—
270D5×Dic3—32no—
271D5×Dic3—32no—
272D5×Dic3—32no—
273D5×Dic3—32no—
274D5×Dic3—32no—
275D5×Dic3—61no—
276D5×Dic3—61no—
277D5×Dic3—61no—
278D5×Dic3—61no—
279D5×Dic3C22×D312yes—
280C2×#237—152no—
281C3×C4×D4—152no—
282D4×Dic3—152no—
283C4×#67—52no—
284C4×#67—152no—
285C2×C4×Dic3—152no—
286C2×C4×Dic3—152no—
287C2×C4×Dic3—301no—
288#892—152no—
289#887—152no—
290#67⋊C4—152no—
291#67⋊C4—152no—
292#877—152no—
293#877—152no—
294C42×D3—152no—
295C4×Dic6—152no—
296C2×C32×C5—21no—
297C2×C32×C5C23×C411yescharacteristic
298C3×D15—22no—
299C3×C5×D3—22no—
300C32×D5—21no—
301C32×D5C2×#4111yescharacteristic
302C32×D5C2×#4111yescharacteristic
303C22×AGL(1,𝔽5)—32no—
304C22×AGL(1,𝔽5)—92no—
305C22×AGL(1,𝔽5)—91no—
306C22×AGL(1,𝔽5)D3211yescharacteristic
307C5×#41—91no—
308#713—91no—
309Q8×D5—91no—
310#711—91no—
311#711—92no—
312D4×D5—32no—
313D4×D5—91no—
314#709—92no—
315#709—91no—
316C2×C4×D5—92no—
317C2×C4×D5—91no—
318C22⋊AGL(1,𝔽5)—32no—
319C22⋊AGL(1,𝔽5)—32no—
320C22⋊AGL(1,𝔽5)—92no—
321C4⋊AGL(1,𝔽5)—32no—
322C4⋊AGL(1,𝔽5)—92no—
323C4⋊AGL(1,𝔽5)—91no—
324C4⋊AGL(1,𝔽5)—91no—
325C4×AGL(1,𝔽5)—32no—
326C4×AGL(1,𝔽5)—92no—
327C4×AGL(1,𝔽5)—92no—
328C4×AGL(1,𝔽5)—91no—
329C4×AGL(1,𝔽5)—91no—
330C4×AGL(1,𝔽5)—91no—
331C4×AGL(1,𝔽5)—91no—
332C23×C32—51no—
333C22×C3×D3—52no—
334C2×C32×C4—51no—
335C2×C32×C4—51no—
336C2×C32×C4—102no—
337C2×C3⋊Dic3—51no—
338C2×C3⋊Dic3—51no—
339C2×C3⋊Dic3—51no—
340C2×C3⋊Dic3—51no—
341C2×C3⋊Dic3—51no—
342C2×C3⋊Dic3—51no—
343C2×C3⋊Dic3—51no—
344C2×C3⋊Dic3—102no—
345C2×C3⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic, complemented
346C3×#67—52no—
347C3×#67—52no—
348C3×#67—52no—
349C3×#67C2×AGL(1,𝔽5)12yescomplemented
350C2×C3×Dic3—52no—
351C2×C3×Dic3—52no—
352C2×C3×Dic3—52no—
353C3×C4×D3—104no—
354#627—51no—
355#627—52no—
356#627C2×AGL(1,𝔽5)11yescharacteristic, complemented
357#625—52no—
358#625—51no—
359#625C2×AGL(1,𝔽5)11yescharacteristic, complemented
360D3×Dic3—52no—
361D3×Dic3—52no—
362D3×Dic3—52no—
363D3×Dic3—104no—
364D3×Dic3C2×AGL(1,𝔽5)12yescomplemented
365C4×#41—451noSylow
366C22×C3×C5—21no—
367C22×C3×C5—32no—
368C22×C3×C5C2×C4×D312yes—
369C2×D15C2×C4×D312yes—
370C2×C5×D3C2×C4×D312yes—
371C2×C3×D5—21no—
372C2×C3×D5—21no—
373C2×C3×D5—21no—
374C2×C3×D5—21no—
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—21no—
378C2×C3×D5—21no—
379C2×C3×D5—32no—
380C2×C3×D5—62no—
381C2×C3×D5—62no—
382C2×C3×D5C2×C4×D312yes—
383C2×C3×D5C23×D312yes—
384D3×D5—22no—
385D3×D5—22no—
386ΓL(1,𝔽16)—22no—
387ΓL(1,𝔽16)—22no—
388ΓL(1,𝔽16)—34no—
389ΓL(1,𝔽16)—62no—
390ΓL(1,𝔽16)—61no—
391ΓL(1,𝔽16)—61no—
392ΓL(1,𝔽16)—62no—
393C3×AGL(1,𝔽5)—21no—
394C3×AGL(1,𝔽5)—21no—
395C3×AGL(1,𝔽5)—22no—
396C3×AGL(1,𝔽5)—22no—
397C3×AGL(1,𝔽5)—62no—
398C3×AGL(1,𝔽5)—62no—
399C3×AGL(1,𝔽5)#23714yescomplemented
400C3×C4×C5—32no—
401Dic15—32no—
402Dic15—32no—
403Dic15—61no—
404Dic15—61no—
405Dic15C2×C4×D312yes—
406C3×Dic5—32no—
407C5×Dic3—32no—
408C5×Dic3—32no—
409C5×Dic3—61no—
410C5×Dic3—61no—
411C5×Dic3C2×C4×D312yes—
412C2×C3×D4—152no—
413C22×C3×C4—52no—
414C22×C3×C4—101no—
415C22×C3×C4—152no—
416C2×#67—52no—
417C2×#67—152no—
418C22×Dic3—152no—
419C22×Dic3—152no—
420C22×Dic3—152no—
421C22×Dic3—152no—
422C22×Dic3—301no—
423C22×Dic3—301no—
424#237—32no—
425#237—152no—
426#237—152no—
427#237—152no—
428#237—152no—
429#237—152no—
430#237—152no—
431#237—152no—
432C2×C4×D3—52no—
433C2×C4×D3—152no—
434C2×C4×D3—152no—
435C2×Dic6—152no—
436C3×C4⋊C4—152no—
437C3×C22⋊C4—152no—
438C3×C22⋊C4—152no—
439C3×C42—152no—
440#217—52no—
441#217—152no—
442(C2×D3)⋊C4—52no—
443(C2×D3)⋊C4—152no—
444C4⋊Dic3—152no—
445Dic3⋊C4—52no—
446Dic3⋊C4—152no—
447Dic3⋊C4—152no—
448Dic3⋊C4—152no—
449C4×Dic3—52no—
450C4×Dic3—152no—
451C4×Dic3—152no—
452C4×Dic3—152no—
453C4×Dic3—152no—
454C4×Dic3—152no—
455C4×Dic3—152no—
456C4×Dic3—152no—
457C4×Dic3—152no—
458C4×Dic3—301no—
459C4×Dic3—301no—
460C4×Dic3—301no—
461C4×Dic3—301no—
462C32×C5C4×#4111yescharacteristic, complemented, Hall
463C22×D5—32no—
464C22×D5C2×D3211yescharacteristic
465C2×AGL(1,𝔽5)—22no—
466C2×AGL(1,𝔽5)—32no—
467C2×AGL(1,𝔽5)—32no—
468C2×AGL(1,𝔽5)—64no—
469C2×AGL(1,𝔽5)—91no—
470C2×AGL(1,𝔽5)—91no—
471C2×AGL(1,𝔽5)—184no—
472C2×AGL(1,𝔽5)—182no—
473C2×AGL(1,𝔽5)C2×D3211yescharacteristic
474C2×AGL(1,𝔽5)C2×D3211yescharacteristic
475C5×Q8—91no—
476C5×D4—32no—
477C5×D4—91no—
478C2×C4×C5—92no—
479C2×C4×C5—91no—
480C22⋊D5—32no—
481C22⋊D5—32no—
482C22⋊D5—92no—
483C2×Dic5—92no—
484C2×Dic5—91no—
485D20—32no—
486D20—91no—
487C4×D5—32no—
488C4×D5—92no—
489C4×D5—92no—
490C4×D5—91no—
491C4×D5—91no—
492C4×D5—91no—
493C4×D5—91no—
494Dic10—91no—
495Dic10—92no—
496C22×C32—51no—
497C22×C32—51no—
498C22×C32—101no—
499C22×C32—101no—
500C22×C32C22×AGL(1,𝔽5)11yescharacteristic
501C2×C3×D3—52no—
502C2×C3×D3—102no—
503C2×C3×D3—102no—
504C2×C3×D3C22×AGL(1,𝔽5)12yes—
505C32×C4—52no—
506C32×C4—101no—
507C3⋊Dic3—52no—
508C3⋊Dic3—51no—
509C3⋊Dic3—51no—
510C3⋊Dic3—101no—
511C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
512C3⋊Dic3C22×AGL(1,𝔽5)11yescharacteristic
513C3×Dic3—52no—
514C3×Dic3—102no—
515C3×Dic3—102no—
516C3×Dic3C22×AGL(1,𝔽5)12yes—
517C2×#41—451no—
518C4×Q8—451no—
519C4×Q8—451no—
520C4×D4—152no—
521C4×D4—451no—
522C4×D4—452no—
523C4×D4—451no—
524#117—451no—
525#117—452no—
526C2×C42—452no—
527C2×C42—451no—
528C2×C3×C5—21no—
529C2×C3×C5—21no—
530C2×C3×C5—22no—
531C2×C3×C5—21no—
532C2×C3×C5—62no—
533C2×C3×C5C22×C4×D312yes—
534D15—22no—
535C3×D5—21no—
536C3×D5—21no—
537C3×D5—22no—
538C3×D5—21no—
539C3×D5—21no—
540C3×D5—62no—
541C3×D5C2×#23712yes—
542C3×D5D3×#4112yes—
543C5×D3—22no—
544C23×C3—52no—
545C23×C3—101no—
546C23×C3—152no—
547C22×D3—52no—
548C3×D4—32no—
549C3×D4—152no—
550C3×D4—152no—
551C3×D4—152no—
552C2×C3×C4—52no—
553C2×C3×C4—52no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—104no—
557C2×C3×C4—102no—
558C2×C3×C4—102no—
559C2×C3×C4—152no—
560C2×C3×C4—152no—
561C2×C3×C4—152no—
562C2×C3×C4—304no—
563#67—32no—
564#67—52no—
565#67—52no—
566#67—52no—
567#67—152no—
568#67—152no—
569#67—152no—
570#67D3×AGL(1,𝔽5)12yescomplemented
571C2×Dic3—32no—
572C2×Dic3—32no—
573C2×Dic3—52no—
574C2×Dic3—52no—
575C2×Dic3—52no—
576C2×Dic3—61no—
577C2×Dic3—152no—
578C2×Dic3—152no—
579C2×Dic3—152no—
580C2×Dic3—152no—
581C2×Dic3—152no—
582C2×Dic3—152no—
583C2×Dic3—152no—
584C2×Dic3—152no—
585C2×Dic3—152no—
586C2×Dic3—152no—
587C2×Dic3—301no—
588C2×Dic3—301no—
589C2×Dic3—301no—
590C2×Dic3—301no—
591C2×Dic3—301no—
592C2×Dic3—301no—
593C2×Dic3—301no—
594C2×Dic3—304no—
595C2×Dic3—304no—
596C2×Dic3—302no—
597C2×Dic3—302no—
598C4×D3—32no—
599C4×D3—104no—
600C4×D3—152no—
601C4×D3—152no—
602C4×D3—152no—
603C4×D3—304no—
604Dic6—32no—
605Dic6—152no—
606Dic6—152no—
607Dic6—152no—
608C22×C5—32no—
609C22×C5C4×D3211yescharacteristic
610C2×D5—21no—
611C2×D5—21no—
612C2×D5—32no—
613C2×D5—62no—
614C2×D5—62no—
615C2×D5C4×D3211yescharacteristic
616C2×D5C22×D3211yescharacteristic
617AGL(1,𝔽5)—21no—
618AGL(1,𝔽5)—62no—
619AGL(1,𝔽5)—62no—
620AGL(1,𝔽5)—92no—
621AGL(1,𝔽5)—181no—
622AGL(1,𝔽5)#380512yesdirect product factor
623C4×C5—32no—
624C4×C5—91no—
625C4×C5—91no—
626Dic5—32no—
627Dic5—91no—
628Dic5—91no—
629C2×C32—21no—
630C2×C32—51no—
631C2×C32—51no—
632C2×C32—101no—
633C2×C32C23×AGL(1,𝔽5)11yescharacteristic
634C3×D3—22no—
635C3×D3—102no—
636#41—91no—
637#41—452no—
638#41—451no—
639#41—452no—
640#41—451no—
641#41—451no—
642C2×Q8—451no—
643C2×D4—152no—
644C2×D4—451no—
645C22×C4—51no—
646C22×C4—152no—
647C22×C4—452no—
648C22×C4—451no—
649C22×C4—452no—
650C22×C4—451no—
651C4⋊C4—152no—
652C4⋊C4—451no—
653C4⋊C4—451no—
654C4⋊C4—452no—
655C22⋊C4—152no—
656C22⋊C4—152no—
657C22⋊C4—452no—
658C42—152no—
659C42—451no—
660C42—451no—
661C42—451no—
662C42—451no—
663C42—452no—
664C42—452no—
665C3×C5—21no—
666C3×C5C4×#23712yescomplemented
667C22×C3—21no—
668C22×C3—32no—
669C22×C3—52no—
670C22×C3—52no—
671C22×C3—101no—
672C22×C3—101no—
673C22×C3—102no—
674C22×C3—102no—
675C22×C3—101no—
676C22×C3—101no—
677C22×C3—101no—
678C22×C3—101no—
679C22×C3—152no—
680C22×C3—302no—
681C22×C3—302no—
682C22×C3C2×D3×AGL(1,𝔽5)12yes—
683C2×D3—52no—
684C2×D3—102no—
685C2×D3—102no—
686C2×D3C2×D3×AGL(1,𝔽5)12yes—
687C3×C4—32no—
688C3×C4—54no—
689C3×C4—102no—
690C3×C4—102no—
691C3×C4—101no—
692C3×C4—101no—
693C3×C4—152no—
694C3×C4—302no—
695C3×C4—302no—
696Dic3—32no—
697Dic3—32no—
698Dic3—52no—
699Dic3—61no—
700Dic3—61no—
701Dic3—102no—
702Dic3—102no—
703Dic3—154no—
704Dic3—152no—
705Dic3—152no—
706Dic3—301no—
707Dic3—301no—
708Dic3—302no—
709Dic3—302no—
710Dic3—301no—
711Dic3—301no—
712Dic3C2×D3×AGL(1,𝔽5)12yes—
713C2×C5—21no—
714C2×C5—62no—
715C2×C5C2×C4×D3211yescharacteristic
716D5—21no—
717D5—62no—
718D5#6430611yescharacteristic
719D5C2×#380511yescharacteristic
720C32#41×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
721C23—51no—
722C23—152no—
723Q8—91no—
724Q8—452no—
725Q8—451no—
726D4—32no—
727D4—91no—
728D4—152no—
729D4—152no—
730D4—152no—
731D4—451no—
732D4—452no—
733C2×C4—51no—
734C2×C4—51no—
735C2×C4—92no—
736C2×C4—91no—
737C2×C4—102no—
738C2×C4—152no—
739C2×C4—152no—
740C2×C4—152no—
741C2×C4—304no—
742C2×C4—452no—
743C2×C4—452no—
744C2×C4—451no—
745C2×C4—451no—
746C2×C4—451no—
747C2×C4—451no—
748C2×C4—452no—
749C2×C4—451no—
750C2×C4—451no—
751C2×C4—451no—
752C2×C4—904no—
753C2×C4—902no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—22no—
757C2×C3—21no—
758C2×C3—52no—
759C2×C3—52no—
760C2×C3—62no—
761C2×C3—101no—
762C2×C3—101no—
763C2×C3—101no—
764C2×C3—101no—
765C2×C3—102no—
766C2×C3—302no—
767C2×C3C22×D3×AGL(1,𝔽5)12yes—
768D3—22no—
769D3—102no—
770C5C4×#380511yescharacteristic, complemented, Sylow
771C22—32no—
772C22—51no—
773C22—51no—
774C22—101no—
775C22—101no—
776C22—152no—
777C22—302no—
778C22—302no—
779C22D32×AGL(1,𝔽5)11yescharacteristic
780C4—32no—
781C4—52no—
782C4—91no—
783C4—91no—
784C4—101no—
785C4—152no—
786C4—302no—
787C4—302no—
788C4—452no—
789C4—451no—
790C4—451no—
791C4—901no—
792C3—21no—
793C3AGL(1,𝔽5)×#23712yescomplemented
794C2—21no—
795C2—51no—
796C2—51no—
797C2—62no—
798C2—101no—
799C2—302no—
800C2C2×D32×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC2C2×D32×AGL(1,𝔽5)
commutator, socleC2×C32×C5C23×C4
FittingC22×C32×C5C22×C4
prime radicalD5×#3805C2
cosocleC2×C32×D5C24
hypercenterC22D32×AGL(1,𝔽5)
hypocenterC32×C5C4×#41
LCSG ▷ C2×C32×C5 ▷ C32×C5
UCSC1 ◁ C2 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #13088735C2semidirect
3. #67⋊ΓL(1,𝔽16)C2semidirect
4. C2×AGL(1,𝔽5)×C3⋊Dic3C2semidirect
5. C3×AGL(1,𝔽5)×#67C2semidirect
6. #13088420C2semidirect
7. AGL(1,𝔽5)×#627C2semidirect
8. #13088416C2semidirect
9. AGL(1,𝔽5)×#625C2semidirect
10. #13088410C2semidirect
11. D3×Dic3×AGL(1,𝔽5)C2semidirect
17. #10624229C4semidirect
18. #10624208C4semidirect
19. C5×#3805C4semidirect
23. #10624047C4semidirect
24. #10624046C4semidirect
25. #10624045C4semidirect
49. AGL(1,𝔽5)×#67D3semidirect
71. C2×C3⋊Dic15C2×C4semidirect
72. C2×C5×C3⋊Dic3C2×C4semidirect
73. C3×#1220C2×C4semidirect
74. C3×C5×#67C2×C4semidirect
75. #67158C2×C4semidirect
76. #67157C2×C4semidirect
77. #67154C2×C4semidirect
78. #67153C2×C4semidirect
79. #67150C2×C4semidirect
80. D3×Dic15C2×C4semidirect
81. Dic3×D15C2×C4semidirect
82. C5×#627C2×C4semidirect
83. C5×#625C2×C4semidirect
84. C5×D3×Dic3C2×C4semidirect
85. D5×C3⋊Dic3C2×C4semidirect
86. D5×C3⋊Dic3C2×C4semidirect
89. C3×#1202C2×C4semidirect
90. C3×#1201C2×C4semidirect
165. C3⋊ΓL(1,𝔽16)#41semidirect
169. C32×AGL(1,𝔽5)#41semidirect
199. #3805AGL(1,𝔽5)direct (N × H)
244. #1220C4×D3semidirect
251. C5×#67C4×D3semidirect
264. #1202C4×D3semidirect
266. #1201C4×D3semidirect
345. C2×C3⋊Dic3C2×AGL(1,𝔽5)semidirect
349. C3×#67C2×AGL(1,𝔽5)semidirect
356. #627C2×AGL(1,𝔽5)semidirect
359. #625C2×AGL(1,𝔽5)semidirect
364. D3×Dic3C2×AGL(1,𝔽5)semidirect
399. C3×AGL(1,𝔽5)#237semidirect
462. C32×C5C4×#41semidirect
570. #67D3×AGL(1,𝔽5)semidirect
622. AGL(1,𝔽5)#3805direct (N × H)
666. C3×C5C4×#237semidirect
720. C32#41×AGL(1,𝔽5)semidirect
770. C5C4×#3805semidirect
793. C3AGL(1,𝔽5)×#237semidirect

Maximal subgroups

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

subgroupindex
D5×#38052
#130887352
#67⋊ΓL(1,𝔽16)2
C2×AGL(1,𝔽5)×C3⋊Dic32
C3×AGL(1,𝔽5)×#672
#130884202
AGL(1,𝔽5)×#6272
#130884162
AGL(1,𝔽5)×#6252
#130884102
D3×Dic3×AGL(1,𝔽5)2
AGL(1,𝔽5)×#2373
C4×#38055