Finite Group Databasebeta

← AGL(1,𝔽5)×#896 #14321921

Subgroups — AGL(1,𝔽5)×#896 #14321921

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×AGL(1,𝔽5)C211yesmaximal, characteristic
2C2×AGL(1,𝔽5)×Dic6C211yesmaximal, characteristic, complemented
3D5×#896C211yesmaximal, characteristic
4#11752370C211yesmaximal, characteristic, complemented
5C3×C4⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
6#11751934C211yesmaximal, characteristic
7#11751932C211yesmaximal, characteristic
8AGL(1,𝔽5)×(C2×D3)⋊C4C211yesmaximal, characteristic
9AGL(1,𝔽5)×(C2×D3)⋊C4C211yesmaximal, characteristic
10#11751854C211yesmaximal, characteristic
11#11751842C211yesmaximal, characteristic, complemented
12#11751837C211yesmaximal, characteristic, complemented
13AGL(1,𝔽5)×Dic3⋊C4C211yesmaximal, characteristic, complemented
14AGL(1,𝔽5)×Dic3⋊C4C211yesmaximal, characteristic, complemented
15#11751747C211yesmaximal, characteristic, complemented
16AGL(1,𝔽5)×C22⋊Q8—31nomaximal, Hall
17C22×D3×AGL(1,𝔽5)C2211yescharacteristic
18C22×D3×AGL(1,𝔽5)C2211yescharacteristic
19C2×C4×D3×D5C2211yescharacteristic
20C2×D5×Dic6C2211yescharacteristic
21C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
22C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
23C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
24C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
25C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
26C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
27C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
28C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
29C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
30C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
31C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
32C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic
33C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
34C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
35C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
36C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic
37C4×D3×AGL(1,𝔽5)—24no—
38AGL(1,𝔽5)×Dic6—24no—
39#91785C411yescharacteristic, complemented
40C5×#896C411yescharacteristic, complemented
41C3×D5×C4⋊C4C2211yescharacteristic
42D5×(C2×D3)⋊C4C2211yescharacteristic
43D5×(C2×D3)⋊C4C2211yescharacteristic
44#91436C411yescharacteristic, complemented
45#91432C411yescharacteristic, complemented
46#91429C411yescharacteristic, complemented
47#91424C411yescharacteristic, complemented
48D5×Dic3⋊C4C2211yescharacteristic
49D5×Dic3⋊C4C2211yescharacteristic
50#91377C411yescharacteristic, complemented
51#91352C411yescharacteristic, complemented
52#91235C2211yescharacteristic
53#91235C2211yescharacteristic
54#91235C2211yescharacteristic
55#91235C2211yescharacteristic
56C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
57C3×(C2×AGL(1,𝔽5))⋊C4C2211yescharacteristic
58(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
59(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
60(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
61(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
62C4×#896—51nomaximal, Hall
63C2×Q8×AGL(1,𝔽5)—31no—
64C22×C4×AGL(1,𝔽5)—31no—
65D5×C22⋊Q8—31no—
66(C2×AGL(1,𝔽5))⋊Q8—31no—
67#65765—31no—
68#65712—31no—
69#65711—31no—
70#65711—31no—
71C4⋊C4×AGL(1,𝔽5)—31no—
72C4⋊C4×AGL(1,𝔽5)—31no—
73C4⋊C4×AGL(1,𝔽5)D311yescharacteristic, complemented
74#65699—31no—
75#65699—31no—
76C22⋊C4×AGL(1,𝔽5)—31no—
77C22⋊C4×AGL(1,𝔽5)—31no—
78C22×D3×D5C2311yescharacteristic
79C22×ΓL(1,𝔽16)C2311yescharacteristic
80C22×ΓL(1,𝔽16)C2311yescharacteristic
81C22×ΓL(1,𝔽16)C2311yescharacteristic
82C22×ΓL(1,𝔽16)C2311yescharacteristic
83C22×C3×AGL(1,𝔽5)C2311yescharacteristic
84C22×C3×AGL(1,𝔽5)C2311yescharacteristic
85C22×C3×AGL(1,𝔽5)C2311yescharacteristic
86C22×C3×AGL(1,𝔽5)C2311yescharacteristic
87C2×D3×AGL(1,𝔽5)—22no—
88C2×D3×AGL(1,𝔽5)—22no—
89C2×D3×AGL(1,𝔽5)—22no—
90C2×D3×AGL(1,𝔽5)—22no—
91C2×D3×AGL(1,𝔽5)—22no—
92C2×D3×AGL(1,𝔽5)Q814yescomplemented
93C2×C4×D15C2×C411yescharacteristic
94C2×Dic30C2×C411yescharacteristic, complemented
95C2×C4×C5×D3C2×C411yescharacteristic
96C2×C5×Dic6C2×C411yescharacteristic, complemented
97C2×C3×C4×D5C2311yescharacteristic
98C2×C3×C4×D5C2311yescharacteristic
99C2×C3×C4×D5C2311yescharacteristic
100C2×#1204C2×C411yescharacteristic, complemented
101C2×#1204C2×C411yescharacteristic, complemented
102C2×#1200C2×C411yescharacteristic
103C2×D3×Dic5C2×C411yescharacteristic
104C2×D5×Dic3C2311yescharacteristic
105C2×D5×Dic3C2311yescharacteristic
106C2×D5×Dic3C2311yescharacteristic
107C4×D3×D5—22no—
108C4×D3×D5—22no—
109D5×Dic6—22no—
110D5×Dic6—22no—
111C4⋊ΓL(1,𝔽16)—22no—
112C4×ΓL(1,𝔽16)—22no—
113C3×C4⋊AGL(1,𝔽5)—22no—
114C3×C4×AGL(1,𝔽5)—22no—
115C3×C4×AGL(1,𝔽5)—22no—
116C3×C4×AGL(1,𝔽5)—22no—
117Dic3⋊AGL(1,𝔽5)—22no—
118Dic3⋊AGL(1,𝔽5)—22no—
119Dic3⋊AGL(1,𝔽5)—22no—
120Dic3⋊AGL(1,𝔽5)—22no—
121(C2×D3)⋊AGL(1,𝔽5)—22no—
122(C2×D3)⋊AGL(1,𝔽5)—22no—
123Dic3×AGL(1,𝔽5)—22no—
124Dic3×AGL(1,𝔽5)—22no—
125Dic3×AGL(1,𝔽5)—22no—
126Dic3×AGL(1,𝔽5)D414yes—
127C3×C5×C4⋊C4C2×C411yescharacteristic, complemented
128#6714C2×C411yescharacteristic
129#6714C2×C411yescharacteristic
130#6712C2×C411yescharacteristic, complemented
131#6712C2×C411yescharacteristic, complemented
132C5×(C2×D3)⋊C4C2×C411yescharacteristic
133C5×(C2×D3)⋊C4C2×C411yescharacteristic
134C5×Dic3⋊C4C2×C411yescharacteristic, complemented
135C5×Dic3⋊C4C2×C411yescharacteristic, complemented
136C3×C4⋊Dic5C2×C411yescharacteristic, complemented
137C3×#683C2×C411yescharacteristic, complemented
138C3×#683C2×C411yescharacteristic, complemented
139Dic3⋊Dic5C2×C411yescharacteristic, complemented
140Dic3⋊Dic5C2×C411yescharacteristic, complemented
141#6669C2×C411yescharacteristic, complemented
142#6669C2×C411yescharacteristic, complemented
143#6667C2×C411yescharacteristic
144#6667C2×C411yescharacteristic
145(C2×D3)⋊Dic5C2×C411yescharacteristic
146(C2×D3)⋊Dic5C2×C411yescharacteristic
147C2×#896—51no—
148C2×C42×D3—51no—
149C2×C4×Dic6—51no—
150C3×C4×C4⋊C4—51no—
151#4989—51no—
152#4980—51no—
153#4976—51no—
154C4×(C2×D3)⋊C4—51no—
155C4×(C2×D3)⋊C4—51no—
156C4×Dic3⋊C4—51no—
157C4×Dic3⋊C4—51no—
158#4668—51no—
159#4667—51no—
160#4652—51no—
161#4646—51no—
162C23×AGL(1,𝔽5)—31no—
163C23×AGL(1,𝔽5)—31no—
164C2×Q8×D5—31no—
165C22×C4×D5—31no—
166C2×C22⋊AGL(1,𝔽5)—31no—
167C2×C22⋊AGL(1,𝔽5)—31no—
168Q8×AGL(1,𝔽5)—64no—
169C2×C4⋊AGL(1,𝔽5)—31no—
170C2×C4⋊AGL(1,𝔽5)—31no—
171C2×C4⋊AGL(1,𝔽5)—31no—
172C2×C4⋊AGL(1,𝔽5)—31no—
173C2×C4⋊AGL(1,𝔽5)—31no—
174C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
175C2×C4×AGL(1,𝔽5)—31no—
176C2×C4×AGL(1,𝔽5)—31no—
177C2×C4×AGL(1,𝔽5)—31no—
178C2×C4×AGL(1,𝔽5)—31no—
179C2×C4×AGL(1,𝔽5)—31no—
180C2×C4×AGL(1,𝔽5)—64no—
181C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
182C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
183C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
184C5×C22⋊Q8—31no—
185#4092—31no—
186#4070—31no—
187#4043—31no—
188#4042—31no—
189#4042—31no—
190D5×C4⋊C4—31no—
191D5×C4⋊C4—31no—
192D5×C4⋊C4C2×D311yescharacteristic
193D5×C22⋊C4—31no—
194D5×C22⋊C4—31no—
195#4024—31no—
196#4024—31no—
197(C2×AGL(1,𝔽5))⋊C4—31no—
198(C2×AGL(1,𝔽5))⋊C4—31no—
199(C2×AGL(1,𝔽5))⋊C4—31no—
200(C2×AGL(1,𝔽5))⋊C4—31no—
201(C2×AGL(1,𝔽5))⋊C4—31no—
202(C2×AGL(1,𝔽5))⋊C4—31no—
203(C2×AGL(1,𝔽5))⋊C4—31no—
204(C2×AGL(1,𝔽5))⋊C4—31no—
205(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
206(C2×AGL(1,𝔽5))⋊C4C2×D311yescharacteristic
207C4×C22⋊Q8—151noSylow
208C22×D15C22×C411yescharacteristic
209C22×C5×D3C22×C411yescharacteristic
210C22×C3×D5C2411yescharacteristic
211C2×D3×D5—21no—
212C2×D3×D5—21no—
213C2×D3×D5—21no—
214C2×D3×D5—21no—
215C2×D3×D5C2×Q812yes—
216C2×D3×D5#4112yes—
217C2×ΓL(1,𝔽16)—21no—
218C2×ΓL(1,𝔽16)—21no—
219C2×ΓL(1,𝔽16)—21no—
220C2×ΓL(1,𝔽16)—21no—
221C2×ΓL(1,𝔽16)—21no—
222C2×ΓL(1,𝔽16)—21no—
223C2×ΓL(1,𝔽16)—21no—
224C2×ΓL(1,𝔽16)—21no—
225C2×ΓL(1,𝔽16)—21no—
226C2×ΓL(1,𝔽16)—21no—
227C2×ΓL(1,𝔽16)C2×D412yes—
228C2×ΓL(1,𝔽16)C2×Q812yes—
229C2×C3×AGL(1,𝔽5)—21no—
230C2×C3×AGL(1,𝔽5)—21no—
231C2×C3×AGL(1,𝔽5)—21no—
232C2×C3×AGL(1,𝔽5)—21no—
233C2×C3×AGL(1,𝔽5)—21no—
234C2×C3×AGL(1,𝔽5)—21no—
235C2×C3×AGL(1,𝔽5)—21no—
236C2×C3×AGL(1,𝔽5)—21no—
237C2×C3×AGL(1,𝔽5)C2×D412yes—
238C2×C3×AGL(1,𝔽5)C2×Q812yes—
239C2×C3×AGL(1,𝔽5)#4112yes—
240C2×C3×AGL(1,𝔽5)#4112yes—
241D3×AGL(1,𝔽5)—28no—
242D3×AGL(1,𝔽5)—28no—
243C2×C3×C4×C5C22×C411yescharacteristic
244C2×C3×C4×C5C22×C411yescharacteristic
245C2×C3×C4×C5C22×C411yescharacteristic
246C2×Dic15C22×C411yescharacteristic
247C2×Dic15C22×C411yescharacteristic
248C2×Dic15C22×C411yescharacteristic
249C4×D15—22no—
250Dic30—22no—
251C2×C5×Dic3C22×C411yescharacteristic
252C2×C5×Dic3C22×C411yescharacteristic
253C2×C5×Dic3C22×C411yescharacteristic
254C4×C5×D3—22no—
255C5×Dic6—22no—
256C2×C3×Dic5C22×C411yescharacteristic
257C2×C3×Dic5C22×C411yescharacteristic
258C2×C3×Dic5C22×C411yescharacteristic
259C3×C4×D5—21no—
260C3×C4×D5—21no—
261C3×C4×D5—21no—
262C3×C4×D5—21no—
263C3×C4×D5—21no—
264C3×C4×D5—21no—
265#1204—22no—
266#1204—22no—
267#1200—22no—
268D3×Dic5—22no—
269D5×Dic3—21no—
270D5×Dic3—21no—
271D5×Dic3—21no—
272D5×Dic3—21no—
273D5×Dic3C2×D412yes—
274D5×Dic3#4112yes—
275C22×C4×D3—51no—
276C22×C4×D3—51no—
277C22×C4×D3—51no—
278C22×Dic6—51no—
279C2×C3×C4⋊C4—51no—
280C2×C3×C4⋊C4—51no—
281C2×C3×C42—51no—
282C2×C3×C42—51no—
283C2×C3×C42—51no—
284C2×(C2×D3)⋊C4—51no—
285C2×(C2×D3)⋊C4—51no—
286C2×(C2×D3)⋊C4—51no—
287C2×(C2×D3)⋊C4—51no—
288C2×C4⋊Dic3—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×Dic3⋊C4—51no—
293C2×Dic3⋊C4—51no—
294C2×Dic3⋊C4—51no—
295C2×C4×Dic3—51no—
296C2×C4×Dic3—51no—
297C2×C4×Dic3—51no—
298C2×C4×Dic3—51no—
299C2×C4×Dic3—51no—
300#896—51no—
301#896—51no—
302#896—51no—
303#896—51no—
304#896—51no—
305#896—51no—
306#896—51no—
307#896AGL(1,𝔽5)11yescharacteristic, direct product factor
308C42×D3—104no—
309C4×Dic6—104no—
310C3×#95—51no—
311C3×#95—51no—
312C3⋊#95—51no—
313C3⋊#95—51no—
314C3⋊#95—51no—
315C3⋊#95—51no—
316C3⋊#95—51no—
317C3⋊#95—51no—
318C3⋊#95—51no—
319C3⋊#95—51no—
320C23×D5—31no—
321C22×AGL(1,𝔽5)—31no—
322C22×AGL(1,𝔽5)—31no—
323C22×AGL(1,𝔽5)—34no—
324C22×AGL(1,𝔽5)—31no—
325C22×AGL(1,𝔽5)—31no—
326C22×AGL(1,𝔽5)—62no—
327C22×AGL(1,𝔽5)—62no—
328C22×AGL(1,𝔽5)—62no—
329C22×AGL(1,𝔽5)—62no—
330C22×AGL(1,𝔽5)—62no—
331C22×AGL(1,𝔽5)C22×D311yescharacteristic
332C22×AGL(1,𝔽5)C22×D311yescharacteristic
333C22×AGL(1,𝔽5)C22×D311yescharacteristic
334C22×AGL(1,𝔽5)C22×D311yescharacteristic
335C2×C5×Q8—31no—
336C22×C4×C5—31no—
337C22×Dic5—31no—
338Q8×D5—62no—
339Q8×D5—62no—
340C2×C4×D5—31no—
341C2×C4×D5—31no—
342C2×C4×D5—31no—
343C2×C4×D5—31no—
344C2×C4×D5—31no—
345C2×C4×D5—62no—
346C2×C4×D5—62no—
347C2×C4×D5C22×D311yescharacteristic
348C2×C4×D5C22×D311yescharacteristic
349C2×C4×D5C22×D311yescharacteristic
350C2×Dic10—31no—
351C2×Dic10—31no—
352C2×Dic10—31no—
353C22⋊AGL(1,𝔽5)—62no—
354C22⋊AGL(1,𝔽5)—62no—
355C4⋊AGL(1,𝔽5)—22no—
356C4⋊AGL(1,𝔽5)—62no—
357C4⋊AGL(1,𝔽5)—62no—
358C4⋊AGL(1,𝔽5)—62no—
359C4⋊AGL(1,𝔽5)—62no—
360C4⋊AGL(1,𝔽5)—62no—
361C4×AGL(1,𝔽5)—22no—
362C4×AGL(1,𝔽5)—22no—
363C4×AGL(1,𝔽5)—22no—
364C4×AGL(1,𝔽5)—34no—
365C4×AGL(1,𝔽5)—62no—
366C4×AGL(1,𝔽5)—62no—
367C4×AGL(1,𝔽5)—62no—
368C4×AGL(1,𝔽5)—62no—
369C5×C4⋊C4—31no—
370C5×C4⋊C4—31no—
371C5×C4⋊C4C4×D311yescharacteristic, complemented
372C5×C22⋊C4—31no—
373C5×C22⋊C4—31no—
374C22⋊Dic5—31no—
375C22⋊Dic5—31no—
376#685—31no—
377#685—31no—
378#685—31no—
379#685—31no—
380C4⋊Dic5—31no—
381C4⋊Dic5—31no—
382C4⋊Dic5C4×D311yescharacteristic, complemented
383#683—31no—
384#683—31no—
385#683—31no—
386#683—31no—
387#683C4×D311yescharacteristic, complemented
388#683C4×D311yescharacteristic, complemented
389C2×C22⋊Q8—151no—
390C2×C4×Q8—151no—
391C22×C42—151no—
392#391—151no—
393#389—151no—
394#387—151no—
395#387—151no—
396#385—151no—
397#385—151no—
398#380—151no—
399C4×C4⋊C4—51no—
400C4×C4⋊C4—151no—
401C4×C4⋊C4—151no—
402C4×C22⋊C4—151no—
403C4×C22⋊C4—151no—
404C22×C3×C5C23×C411yescharacteristic
405C2×D15—21no—
406C2×D15—21no—
407C2×D15C4×Q812yescomplemented
408C2×C5×D3—21no—
409C2×C5×D3—21no—
410C2×C5×D3C4×Q812yescomplemented
411C2×C3×D5C22×D411yescharacteristic
412C2×C3×D5C22×Q811yescharacteristic
413C2×C3×D5C2×#4111yescharacteristic
414C2×C3×D5C2×#4111yescharacteristic
415C2×C3×D5C2×#4111yescharacteristic
416C2×C3×D5C2×#4111yescharacteristic
417D3×D5—22no—
418D3×D5—22no—
419D3×D5—22no—
420D3×D5—22no—
421ΓL(1,𝔽16)—22no—
422ΓL(1,𝔽16)—22no—
423ΓL(1,𝔽16)—41no—
424ΓL(1,𝔽16)—41no—
425C3×AGL(1,𝔽5)—22no—
426C3×AGL(1,𝔽5)—41no—
427C3×AGL(1,𝔽5)—41no—
428C3×AGL(1,𝔽5)C22⋊Q814yescomplemented
429C3×C4×C5—21no—
430C3×C4×C5—21no—
431C3×C4×C5—21no—
432Dic15—21no—
433Dic15—21no—
434Dic15C4×D412yes—
435C3×Dic5—21no—
436C3×Dic5—21no—
437C3×Dic5—21no—
438C5×Dic3—21no—
439C5×Dic3—21no—
440C5×Dic3C4×D412yes—
441C23×D3—51no—
442C22×C3×C4—51no—
443C22×C3×C4—51no—
444C22×C3×C4—51no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4—51no—
448C22×C3×C4—51no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—51no—
452C22×Dic3—51no—
453C22×Dic3—51no—
454C22×Dic3—51no—
455C22×Dic3—51no—
456C2×C4×D3—54no—
457C2×C4×D3—51no—
458C2×C4×D3—51no—
459C2×C4×D3—51no—
460C2×C4×D3—102no—
461C2×C4×D3—102no—
462C2×C4×D3—102no—
463C2×C4×D3—102no—
464C2×C4×D3—102no—
465C2×C4×D3—102no—
466C2×C4×D3—102no—
467C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
468C2×Dic6—51no—
469C2×Dic6—51no—
470C2×Dic6—51no—
471C2×Dic6—102no—
472C2×Dic6—102no—
473C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
474C3×C4⋊C4—51no—
475C3×C4⋊C4—51no—
476C3×C4⋊C4—51no—
477C3×C4⋊C4—102no—
478C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
479C3×C42—102no—
480C3×C42—102no—
481C3×C42—102no—
482(C2×D3)⋊C4—51no—
483(C2×D3)⋊C4—51no—
484(C2×D3)⋊C4—51no—
485(C2×D3)⋊C4—51no—
486(C2×D3)⋊C4—51no—
487(C2×D3)⋊C4—51no—
488(C2×D3)⋊C4—102no—
489(C2×D3)⋊C4—102no—
490(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
491(C2×D3)⋊C4C2×AGL(1,𝔽5)11yescharacteristic
492C4⋊Dic3—102no—
493Dic3⋊C4—51no—
494Dic3⋊C4—51no—
495Dic3⋊C4—51no—
496Dic3⋊C4—51no—
497Dic3⋊C4—51no—
498Dic3⋊C4—51no—
499Dic3⋊C4—102no—
500Dic3⋊C4—102no—
501Dic3⋊C4—102no—
502Dic3⋊C4—102no—
503Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
504Dic3⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
505C4×Dic3—54no—
506C4×Dic3—102no—
507C4×Dic3—102no—
508C4×Dic3—102no—
509C4×Dic3—102no—
510C23×C5—31no—
511C22×D5—31no—
512C22×D5—32no—
513C22×D5—32no—
514C22×D5—61no—
515C22×D5—61no—
516C22×D5—61no—
517C22×D5—61no—
518C22×D5C23×D311yescharacteristic
519C2×AGL(1,𝔽5)—21no—
520C2×AGL(1,𝔽5)—21no—
521C2×AGL(1,𝔽5)—21no—
522C2×AGL(1,𝔽5)—21no—
523C2×AGL(1,𝔽5)—21no—
524C2×AGL(1,𝔽5)—21no—
525C2×AGL(1,𝔽5)—21no—
526C2×AGL(1,𝔽5)—21no—
527C2×AGL(1,𝔽5)—32no—
528C2×AGL(1,𝔽5)—32no—
529C2×AGL(1,𝔽5)—68no—
530C2×AGL(1,𝔽5)—61no—
531C2×AGL(1,𝔽5)—61no—
532C2×AGL(1,𝔽5)—61no—
533C2×AGL(1,𝔽5)—61no—
534C2×AGL(1,𝔽5)—68no—
535C2×AGL(1,𝔽5)—61no—
536C2×AGL(1,𝔽5)—61no—
537C2×AGL(1,𝔽5)—61no—
538C2×AGL(1,𝔽5)—61no—
539C2×AGL(1,𝔽5)—61no—
540C2×AGL(1,𝔽5)—61no—
541C2×AGL(1,𝔽5)#23512yes—
542C2×AGL(1,𝔽5)#23512yes—
543C2×AGL(1,𝔽5)D3×D412yes—
544C2×AGL(1,𝔽5)D3×Q812yes—
545C5×Q8—62no—
546C2×C4×C5—31no—
547C2×C4×C5—31no—
548C2×C4×C5—31no—
549C2×C4×C5—62no—
550C2×C4×C5C2×C4×D311yescharacteristic
551C2×C4×C5C2×C4×D311yescharacteristic
552C2×C4×C5C2×C4×D311yescharacteristic
553C2×Dic5—31no—
554C2×Dic5—31no—
555C2×Dic5—31no—
556C2×Dic5—62no—
557C2×Dic5C2×C4×D311yescharacteristic
558C2×Dic5C2×C4×D311yescharacteristic
559C2×Dic5C2×C4×D311yescharacteristic
560C4×D5—21no—
561C4×D5—21no—
562C4×D5—21no—
563C4×D5—21no—
564C4×D5—21no—
565C4×D5—21no—
566C4×D5—32no—
567C4×D5—32no—
568C4×D5—62no—
569C4×D5—62no—
570C4×D5—61no—
571C4×D5—61no—
572C4×D5—61no—
573C4×D5—61no—
574Dic10—62no—
575Dic10—62no—
576Dic10—62no—
577C22×Q8—151no—
578C23×C4—151no—
579C23×C4—151no—
580C23×C4—151no—
581C22⋊Q8—31no—
582C22⋊Q8—151no—
583C22⋊Q8—151no—
584C22⋊Q8—151no—
585C22⋊Q8—151no—
586C22⋊Q8—151no—
587C22⋊Q8—151no—
588C22⋊Q8—151no—
589C4×Q8—304no—
590C2×C4⋊C4—51no—
591C2×C4⋊C4—51no—
592C2×C4⋊C4—151no—
593C2×C4⋊C4—151no—
594C2×C4⋊C4—151no—
595C2×C4⋊C4—151no—
596C2×C4⋊C4—151no—
597C2×C4⋊C4—151no—
598C2×C4⋊C4—151no—
599C2×C22⋊C4—151no—
600C2×C22⋊C4—151no—
601C2×C22⋊C4—151no—
602C2×C22⋊C4—151no—
603C2×C42—51no—
604C2×C42—51no—
605C2×C42—51no—
606C2×C42—151no—
607C2×C42—151no—
608C2×C42—151no—
609C2×C42—151no—
610C2×C42—151no—
611C2×C42—304no—
612#95—51no—
613#95—51no—
614#95—151no—
615#95—151no—
616#95—151no—
617#95—151no—
618#95—151no—
619#95—151no—
620#95—151no—
621#95—151no—
622C2×C3×C5C2×C4×D411yescharacteristic
623C2×C3×C5C2×C4×Q811yescharacteristic
624C2×C3×C5C4×#4111yescharacteristic
625D15—22no—
626C3×D5C2×C22⋊Q811yescharacteristic
627C3×D5#52511yescharacteristic
628C3×D5#52911yescharacteristic
629C3×D5#53311yescharacteristic
630C5×D3—22no—
631C23×C3—51no—
632C22×D3—51no—
633C22×D3—52no—
634C22×D3—52no—
635C22×D3—101no—
636C22×D3—101no—
637C22×D3—101no—
638C22×D3—101no—
639C22×D3C22×AGL(1,𝔽5)11yescharacteristic
640C2×C3×C4—52no—
641C2×C3×C4—52no—
642C2×C3×C4—52no—
643C2×C3×C4—52no—
644C2×C3×C4—51no—
645C2×C3×C4—51no—
646C2×C3×C4—51no—
647C2×C3×C4—101no—
648C2×C3×C4—101no—
649C2×C3×C4—101no—
650C2×C3×C4—101no—
651C2×C3×C4—101no—
652C2×C3×C4—101no—
653C2×C3×C4—101no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—101no—
660C2×C3×C4—101no—
661C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
662C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
663C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
664C2×Dic3—51no—
665C2×Dic3—52no—
666C2×Dic3—52no—
667C2×Dic3—52no—
668C2×Dic3—52no—
669C2×Dic3—51no—
670C2×Dic3—51no—
671C2×Dic3—101no—
672C2×Dic3—101no—
673C2×Dic3—101no—
674C2×Dic3—101no—
675C2×Dic3—101no—
676C2×Dic3—101no—
677C2×Dic3—101no—
678C2×Dic3—101no—
679C2×Dic3—101no—
680C2×Dic3—101no—
681C2×Dic3—101no—
682C2×Dic3—101no—
683C2×Dic3—101no—
684C2×Dic3—101no—
685C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
686C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
687C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
688C4×D3—22no—
689C4×D3—102no—
690C4×D3—102no—
691C4×D3—108no—
692C4×D3—108no—
693C4×D3—102no—
694Dic6—22no—
695Dic6—102no—
696Dic6—102no—
697Dic6—102no—
698C22×C5—32no—
699C22×C5—61no—
700C22×C5—61no—
701C22×C5C22×C4×D311yescharacteristic
702C2×D5—32no—
703C2×D5—61no—
704C2×D5—61no—
705C2×D5—62no—
706C2×D5—62no—
707C2×D5—62no—
708C2×D5—62no—
709C2×D5C2×#23511yescharacteristic
710C2×D5C2×#23511yescharacteristic
711C2×D5C2×D3×D411yescharacteristic
712C2×D5C2×D3×Q811yescharacteristic
713C2×D5D3×#4111yescharacteristic
714C2×D5D3×#4111yescharacteristic
715AGL(1,𝔽5)—22no—
716AGL(1,𝔽5)—41no—
717AGL(1,𝔽5)—41no—
718AGL(1,𝔽5)—62no—
719AGL(1,𝔽5)—62no—
720AGL(1,𝔽5)—121no—
721AGL(1,𝔽5)—121no—
722AGL(1,𝔽5)#89614yesdirect product factor
723C4×C5—21no—
724C4×C5—21no—
725C4×C5—21no—
726C4×C5—32no—
727C4×C5—61no—
728C4×C5—61no—
729Dic5—21no—
730Dic5—21no—
731Dic5—21no—
732Dic5—32no—
733Dic5—61no—
734Dic5—61no—
735C24—151no—
736C2×Q8—31no—
737C2×Q8—151no—
738C2×Q8—151no—
739C2×Q8—151no—
740C2×Q8—302no—
741C2×Q8—302no—
742C22×C4—31no—
743C22×C4—51no—
744C22×C4—51no—
745C22×C4—51no—
746C22×C4—51no—
747C22×C4—51no—
748C22×C4—51no—
749C22×C4—51no—
750C22×C4—151no—
751C22×C4—151no—
752C22×C4—151no—
753C22×C4—151no—
754C22×C4—151no—
755C22×C4—154no—
756C22×C4—151no—
757C22×C4—151no—
758C22×C4—151no—
759C22×C4—151no—
760C22×C4—151no—
761C22×C4—302no—
762C22×C4—302no—
763C22×C4—302no—
764C22×C4—302no—
765C22×C4—302no—
766C22×C4—302no—
767C22×C4—302no—
768C4⋊C4—31no—
769C4⋊C4—31no—
770C4⋊C4—51no—
771C4⋊C4—51no—
772C4⋊C4—51no—
773C4⋊C4—102no—
774C4⋊C4—151no—
775C4⋊C4—151no—
776C4⋊C4—151no—
777C4⋊C4—151no—
778C4⋊C4—151no—
779C4⋊C4—151no—
780C4⋊C4—302no—
781C4⋊C4—302no—
782C4⋊C4—302no—
783C4⋊C4—302no—
784C4⋊C4—302no—
785C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
786C22⋊C4—31no—
787C22⋊C4—31no—
788C22⋊C4—151no—
789C22⋊C4—151no—
790C22⋊C4—151no—
791C22⋊C4—151no—
792C22⋊C4—151no—
793C22⋊C4—151no—
794C22⋊C4—302no—
795C22⋊C4—302no—
796C42—102no—
797C42—102no—
798C42—102no—
799C42—154no—
800C42—302no—
801C42—302no—
802C42—302no—
803C42—302no—
804C3×C5C4×C22⋊Q811yescharacteristic, complemented, Hall
805C22×C3—51no—
806C22×C3—51no—
807C22×C3—51no—
808C22×C3—51no—
809C22×C3—51no—
810C22×C3—51no—
811C22×C3C23×AGL(1,𝔽5)11yescharacteristic
812C2×D3—21no—
813C2×D3—21no—
814C2×D3—52no—
815C2×D3—102no—
816C2×D3—102no—
817C2×D3—102no—
818C2×D3—102no—
819C2×D3—101no—
820C2×D3—101no—
821C2×D3Q8×AGL(1,𝔽5)12yescomplemented
822C3×C4—21no—
823C3×C4—21no—
824C3×C4—21no—
825C3×C4—54no—
826C3×C4—102no—
827C3×C4—101no—
828C3×C4—101no—
829C3×C4—101no—
830C3×C4—201no—
831C3×C4—201no—
832Dic3—21no—
833Dic3—21no—
834Dic3—52no—
835Dic3—102no—
836Dic3—102no—
837Dic3—101no—
838Dic3—101no—
839Dic3—201no—
840Dic3—201no—
841Dic3D4×AGL(1,𝔽5)12yes—
842C2×C5—62no—
843C2×C5C4×#23511yescharacteristic
844C2×C5C4×D3×D411yescharacteristic
845C2×C5C4×D3×Q811yescharacteristic
846D5—62no—
847D5C2×#89611yescharacteristic
848D5#552811yescharacteristic
849D5#554711yescharacteristic
850D5#557811yescharacteristic
851C23—31no—
852C23—51no—
853C23—152no—
854C23—152no—
855C23—151no—
856C23—301no—
857C23—301no—
858C23—301no—
859C23—301no—
860Q8—62no—
861Q8—302no—
862Q8—302no—
863Q8—302no—
864C2×C4—31no—
865C2×C4—31no—
866C2×C4—31no—
867C2×C4—52no—
868C2×C4—52no—
869C2×C4—52no—
870C2×C4—52no—
871C2×C4—51no—
872C2×C4—51no—
873C2×C4—51no—
874C2×C4—62no—
875C2×C4—101no—
876C2×C4—101no—
877C2×C4—101no—
878C2×C4—101no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—101no—
886C2×C4—101no—
887C2×C4—101no—
888C2×C4—101no—
889C2×C4—152no—
890C2×C4—152no—
891C2×C4—151no—
892C2×C4—152no—
893C2×C4—152no—
894C2×C4—151no—
895C2×C4—151no—
896C2×C4—302no—
897C2×C4—302no—
898C2×C4—308no—
899C2×C4—301no—
900C2×C4—301no—
901C2×C4—301no—
902C2×C4—301no—
903C2×C4—302no—
904C2×C4—308no—
905C2×C4—301no—
906C2×C4—301no—
907C2×C4—301no—
908C2×C4—301no—
909C2×C4—301no—
910C2×C4—301no—
911C2×C4—301no—
912C2×C4—301no—
913C2×C4—301no—
914C2×C4—301no—
915C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
916C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
917C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
918C2×C3—51no—
919C2×C3—51no—
920C2×C3—51no—
921C2×C3—51no—
922C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
923C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
924C2×C3#41×AGL(1,𝔽5)11yescharacteristic
925D3—22no—
926D3—102no—
927C5C4×#89611yescharacteristic, complemented, Sylow
928C22—32no—
929C22—51no—
930C22—51no—
931C22—51no—
932C22—51no—
933C22—51no—
934C22—51no—
935C22—61no—
936C22—61no—
937C22—152no—
938C22—302no—
939C22—302no—
940C22—302no—
941C22—302no—
942C22—301no—
943C22—301no—
944C22C22×D3×AGL(1,𝔽5)11yescharacteristic
945C4—21no—
946C4—21no—
947C4—21no—
948C4—32no—
949C4—54no—
950C4—61no—
951C4—61no—
952C4—102no—
953C4—101no—
954C4—101no—
955C4—101no—
956C4—152no—
957C4—201no—
958C4—201no—
959C4—302no—
960C4—302no—
961C4—301no—
962C4—301no—
963C4—601no—
964C4—601no—
965C3AGL(1,𝔽5)×C22⋊Q811yescharacteristic, complemented, Sylow
966C2—51no—
967C2—51no—
968C2—51no—
969C2—51no—
970C2—62no—
971C2—302no—
972C2AGL(1,𝔽5)×#23511yescharacteristic
973C2D3×D4×AGL(1,𝔽5)11yescharacteristic
974C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C4⋊C4C2×C4
prime radicalC22×D3×D5C23
cosocleC22×C3×D5C24
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×C22⋊Q8
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×AGL(1,𝔽5)×Dic6C2semidirect
4. #11752370C2semidirect
5. C3×C4⋊C4×AGL(1,𝔽5)C2semidirect
11. #11751842C2semidirect
12. #11751837C2semidirect
13. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
14. AGL(1,𝔽5)×Dic3⋊C4C2semidirect
15. #11751747C2semidirect
39. #91785C4semidirect
40. C5×#896C4semidirect
44. #91436C4semidirect
45. #91432C4semidirect
46. #91429C4semidirect
47. #91424C4semidirect
50. #91377C4semidirect
51. #91352C4semidirect
73. C4⋊C4×AGL(1,𝔽5)D3semidirect
92. C2×D3×AGL(1,𝔽5)Q8semidirect
94. C2×Dic30C2×C4semidirect
96. C2×C5×Dic6C2×C4semidirect
100. C2×#1204C2×C4semidirect
101. C2×#1204C2×C4semidirect
127. C3×C5×C4⋊C4C2×C4semidirect
130. #6712C2×C4semidirect
131. #6712C2×C4semidirect
134. C5×Dic3⋊C4C2×C4semidirect
135. C5×Dic3⋊C4C2×C4semidirect
136. C3×C4⋊Dic5C2×C4semidirect
137. C3×#683C2×C4semidirect
138. C3×#683C2×C4semidirect
139. Dic3⋊Dic5C2×C4semidirect
140. Dic3⋊Dic5C2×C4semidirect
141. #6669C2×C4semidirect
142. #6669C2×C4semidirect
307. #896AGL(1,𝔽5)direct (N × H)
371. C5×C4⋊C4C4×D3semidirect
382. C4⋊Dic5C4×D3semidirect
387. #683C4×D3semidirect
388. #683C4×D3semidirect
407. C2×D15C4×Q8semidirect
410. C2×C5×D3C4×Q8semidirect
428. C3×AGL(1,𝔽5)C22⋊Q8semidirect
473. C2×Dic6C2×AGL(1,𝔽5)semidirect
478. C3×C4⋊C4C2×AGL(1,𝔽5)semidirect
503. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
504. Dic3⋊C4C2×AGL(1,𝔽5)semidirect
722. AGL(1,𝔽5)#896direct (N × H)
785. C4⋊C4D3×AGL(1,𝔽5)semidirect
804. C3×C5C4×C22⋊Q8semidirect
821. C2×D3Q8×AGL(1,𝔽5)semidirect
927. C5C4×#896semidirect
965. C3AGL(1,𝔽5)×C22⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×D3×AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×Dic62
D5×#8962
#117523702
C3×C4⋊C4×AGL(1,𝔽5)2
#117519342
#117519322
AGL(1,𝔽5)×(C2×D3)⋊C42
#117518542
#117518422
#117518372
AGL(1,𝔽5)×Dic3⋊C42
#117517472
AGL(1,𝔽5)×C22⋊Q83
C4×#8965