Finite Group Databasebeta

← AGL(1,𝔽5)×#882 #14321406

Subgroups — AGL(1,𝔽5)×#882 #14321406

Order 1920.

2448 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
2C2×AGL(1,𝔽5)×#67C211yesmaximal, characteristic, complemented
3C2×AGL(1,𝔽5)×D12C212yesmaximal, complemented
4D5×#882C211yesmaximal, characteristic
5#11752358C211yesmaximal, characteristic, complemented
6C3×C22⋊C4×AGL(1,𝔽5)C211yesmaximal, characteristic, complemented
7#11752026C211yesmaximal, characteristic, complemented
8#11752025C211yesmaximal, characteristic, complemented
9#11751934C212yesmaximal, complemented
10#11751933C212yesmaximal, complemented
11AGL(1,𝔽5)×(C2×D3)⋊C4C212yesmaximal, complemented
12AGL(1,𝔽5)×#120—31nomaximal, Hall
13C23×D3×D5C2211yescharacteristic
14C23×ΓL(1,𝔽16)C2211yescharacteristic
15C23×C3×AGL(1,𝔽5)C2211yescharacteristic
16C22×D3×AGL(1,𝔽5)—24no—
17C22×D3×AGL(1,𝔽5)—28no—
18C22×D3×AGL(1,𝔽5)C2212yes—
19C22×D3×AGL(1,𝔽5)C2212yes—
20C22×D3×AGL(1,𝔽5)C2211yescharacteristic, complemented
21C2×D5×#67C2211yescharacteristic
22C2×D5×D12C2212yes—
23C2×#6763C2211yescharacteristic
24C2×C4⋊ΓL(1,𝔽16)C2212yescomplemented
25C2×C3×C22⋊AGL(1,𝔽5)C2211yescharacteristic
26C2×C3×C4×AGL(1,𝔽5)C2212yescomplemented
27AGL(1,𝔽5)×#67—24no—
28C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
29C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
30C2×(C2×D3)⋊AGL(1,𝔽5)C2212yes—
31C2×(C2×D3)⋊AGL(1,𝔽5)C2212yescomplemented
32C2×(C2×D3)⋊AGL(1,𝔽5)C2211yescharacteristic, complemented
33C2×Dic3×AGL(1,𝔽5)C2211yescharacteristic, complemented
34AGL(1,𝔽5)×D12—28no—
35#91771C411yescharacteristic, complemented
36C5×#882C411yescharacteristic, complemented
37C3×D5×C22⋊C4C2211yescharacteristic
38#91573C411yescharacteristic, complemented
39#91570C411yescharacteristic, complemented
40#91476C412yescomplemented
41#91475C412yescomplemented
42D5×(C2×D3)⋊C4C2212yes—
43#91235C2212yescomplemented
44C3×(C2×AGL(1,𝔽5))⋊C4C2212yescomplemented
45(C2×AGL(1,𝔽5))⋊Dic3C2212yescomplemented
46C4×#882—51nomaximal, Hall
47C24×AGL(1,𝔽5)—31no—
48C2×D4×AGL(1,𝔽5)—31no—
49C2×D4×AGL(1,𝔽5)—32no—
50D5×#120—31no—
51#65800—31no—
52#65779—32no—
53#65779—31no—
54#65699—31no—
55#65699—32no—
56C22⋊C4×AGL(1,𝔽5)—32no—
57C22⋊C4×AGL(1,𝔽5)D311yescharacteristic, complemented
58C23×D15C2×C411yescharacteristic, complemented
59C23×C5×D3C2×C411yescharacteristic, complemented
60C23×C3×D5C2311yescharacteristic
61C22×D3×D5—22no—
62C22×D3×D5—22no—
63C22×D3×D5—24no—
64C22×D3×D5—24no—
65C22×D3×D5C2×C412yescomplemented
66C22×D3×D5C2311yescharacteristic
67C22×D3×D5C2312yes—
68C22×ΓL(1,𝔽16)—22no—
69C22×ΓL(1,𝔽16)—24no—
70C22×ΓL(1,𝔽16)C2311yescharacteristic
71C22×ΓL(1,𝔽16)C2311yescharacteristic
72C22×ΓL(1,𝔽16)C2312yes—
73C22×C3×AGL(1,𝔽5)—24no—
74C22×C3×AGL(1,𝔽5)D414yescomplemented
75C22×C3×AGL(1,𝔽5)C2312yes—
76C22×C3×AGL(1,𝔽5)C2311yescharacteristic
77C22×C3×AGL(1,𝔽5)C2311yescharacteristic
78C2×D3×AGL(1,𝔽5)—232no—
79C2×D3×AGL(1,𝔽5)—24no—
80C2×D3×AGL(1,𝔽5)—24no—
81C2×D3×AGL(1,𝔽5)—24no—
82C2×D3×AGL(1,𝔽5)—24no—
83C2×D3×AGL(1,𝔽5)—24no—
84C2×D3×AGL(1,𝔽5)—24no—
85C2×D3×AGL(1,𝔽5)—22no—
86C2×D3×AGL(1,𝔽5)D418yescomplemented
87C2×#1220C2×C411yescharacteristic, complemented
88C2×D60C2×C412yescomplemented
89C2×C5×#67C2×C411yescharacteristic, complemented
90C2×C5×D12C2×C412yescomplemented
91C2×C3×C4×D5C2312yes—
92D5×#67—22no—
93D5×#67—22no—
94C2×#1203C2×C412yescomplemented
95C2×#1203C2×C412yescomplemented
96C2×#1202C2×C411yescharacteristic, complemented
97C2×#1201C2×C411yescharacteristic, complemented
98C2×D5×Dic3C2311yescharacteristic
99D5×D12—24no—
100D5×D12—24no—
101#6763—22no—
102C4⋊ΓL(1,𝔽16)—24no—
103C3×C22⋊AGL(1,𝔽5)—22no—
104C3×C4×AGL(1,𝔽5)—24no—
105Dic3⋊AGL(1,𝔽5)—22no—
106(C2×D3)⋊AGL(1,𝔽5)—24no—
107(C2×D3)⋊AGL(1,𝔽5)—24no—
108(C2×D3)⋊AGL(1,𝔽5)—24no—
109(C2×D3)⋊AGL(1,𝔽5)—22no—
110Dic3×AGL(1,𝔽5)—22no—
111C3×C5×C22⋊C4C2×C411yescharacteristic, complemented
112#6714C2×C412yescomplemented
113C5×(C2×D3)⋊C4C2×C412yescomplemented
114C3×C22⋊Dic5C2×C411yescharacteristic, complemented
115C3×#685C2×C412yescomplemented
116#6667C2×C412yescomplemented
117(C2×D3)⋊Dic5C2×C412yescomplemented
118C23×C4×D3—51no—
119C2×C4×#67—51no—
120C2×#882—51no—
121C2×C4×D12—52no—
122C3×C4×C22⋊C4—51no—
123#4958—51no—
124#4955—51no—
125#4950—51no—
126C4×(C2×D3)⋊C4—52no—
127#4668—52no—
128#4665—52no—
129C24×D5—31no—
130C23×AGL(1,𝔽5)—32no—
131C23×AGL(1,𝔽5)—31no—
132C23×AGL(1,𝔽5)—32no—
133C23×AGL(1,𝔽5)—31no—
134C23×AGL(1,𝔽5)—68no—
135C23×AGL(1,𝔽5)—64no—
136C23×AGL(1,𝔽5)C2×D311yescharacteristic
137C2×D4×D5—31no—
138C2×D4×D5—32no—
139C2×C22⋊AGL(1,𝔽5)—31no—
140C2×C22⋊AGL(1,𝔽5)—32no—
141C2×C22⋊AGL(1,𝔽5)—32no—
142C2×C22⋊AGL(1,𝔽5)—32no—
143C2×C22⋊AGL(1,𝔽5)—31no—
144C2×C22⋊AGL(1,𝔽5)C2×D311yescharacteristic
145D4×AGL(1,𝔽5)—68no—
146D4×AGL(1,𝔽5)—64no—
147C2×C4⋊AGL(1,𝔽5)—31no—
148C2×C4⋊AGL(1,𝔽5)—32no—
149C2×C4×AGL(1,𝔽5)—31no—
150C2×C4×AGL(1,𝔽5)C2×D312yescomplemented
151C5×#120—31no—
152#4099—31no—
153#4083—31no—
154#4083—32no—
155#4028—31no—
156#4028—32no—
157D5×C22⋊C4—32no—
158D5×C22⋊C4C2×D311yescharacteristic
159(C2×AGL(1,𝔽5))⋊C4—32no—
160(C2×AGL(1,𝔽5))⋊C4—32no—
161(C2×AGL(1,𝔽5))⋊C4C2×D312yescomplemented
162C4×#120—151noSylow
163C23×C3×C5C22×C411yescharacteristic
164C22×D15—22no—
165C22×D15—24no—
166C22×D15C22×C412yes—
167C22×D15C22×C411yescharacteristic, complemented
168C22×C5×D3—22no—
169C22×C5×D3—24no—
170C22×C5×D3C22×C412yes—
171C22×C5×D3C22×C411yescharacteristic, complemented
172C22×C3×D5—22no—
173C22×C3×D5—22no—
174C22×C3×D5C22×C411yescharacteristic
175C22×C3×D5C2×D412yes—
176C22×C3×D5#4112yes—
177C22×C3×D5C2411yescharacteristic
178C2×D3×D5—28no—
179C2×D3×D5—216no—
180C2×D3×D5—28no—
181C2×D3×D5—24no—
182C2×D3×D5—24no—
183C2×D3×D5—24no—
184C2×D3×D5—22no—
185C2×D3×D5—22no—
186C2×D3×D5—22no—
187C2×D3×D5—22no—
188C2×D3×D5—22no—
189C2×D3×D5—21no—
190C2×D3×D5—22no—
191C2×D3×D5—21no—
192C2×D3×D5C2×D414yes—
193C2×D3×D5#4114yes—
194C2×ΓL(1,𝔽16)—28no—
195C2×ΓL(1,𝔽16)—22no—
196C2×ΓL(1,𝔽16)—22no—
197C2×ΓL(1,𝔽16)—21no—
198C2×ΓL(1,𝔽16)—22no—
199C2×ΓL(1,𝔽16)—21no—
200C2×ΓL(1,𝔽16)—22no—
201C2×ΓL(1,𝔽16)C2×D414yes—
202C2×C3×AGL(1,𝔽5)—22no—
203C2×C3×AGL(1,𝔽5)—28no—
204C2×C3×AGL(1,𝔽5)—22no—
205C2×C3×AGL(1,𝔽5)—22no—
206C2×C3×AGL(1,𝔽5)—22no—
207C2×C3×AGL(1,𝔽5)C2×D412yes—
208C2×C3×AGL(1,𝔽5)C2×D412yes—
209C2×C3×AGL(1,𝔽5)C2×D414yes—
210D3×AGL(1,𝔽5)—216no—
211D3×AGL(1,𝔽5)—216no—
212D3×AGL(1,𝔽5)—44no—
213C2×C3×C4×C5C22×C412yescomplemented
214#1220—22no—
215C2×Dic15C22×C411yescharacteristic, complemented
216D60—24no—
217C5×#67—22no—
218C2×C5×Dic3C22×C411yescharacteristic, complemented
219C5×D12—24no—
220C2×C3×Dic5C22×C412yescomplemented
221C3×C4×D5—22no—
222C3×C4×D5—22no—
223#1203—24no—
224#1203—24no—
225#1202—22no—
226#1201—22no—
227D5×Dic3—21no—
228D5×Dic3—21no—
229C24×D3—51no—
230C23×C3×C4—51no—
231C22×#67—51no—
232C23×Dic3—51no—
233C22×D12—52no—
234C22×C4×D3—52no—
235C22×C4×D3—52no—
236C22×C4×D3—51no—
237C22×C4×D3—108no—
238C22×C4×D3—104no—
239C2×C3×C22⋊C4—51no—
240C2×C3×C22⋊C4—51no—
241C2×C3×C42—52no—
242C2×#217—51no—
243C4×#67—104no—
244C2×(C2×D3)⋊C4—52no—
245C2×(C2×D3)⋊C4—52no—
246C2×(C2×D3)⋊C4—52no—
247C2×(C2×D3)⋊C4—51no—
248C2×(C2×D3)⋊C4—52no—
249C2×C4⋊Dic3—52no—
250C2×Dic3⋊C4—51no—
251C2×C4×Dic3—51no—
252#882—51no—
253#882—51no—
254#882—52no—
255#882—51no—
256#882—52no—
257#882AGL(1,𝔽5)11yescharacteristic, direct product factor
258C4×D12—108no—
259C3×#95—52no—
260C3⋊#95—52no—
261C3⋊#95—52no—
262C24×C5—31no—
263C23×D5—32no—
264C23×D5—31no—
265C23×D5—32no—
266C23×D5—31no—
267C23×D5—64no—
268C23×D5—64no—
269C23×D5—62no—
270C23×D5—62no—
271C23×D5C22×D311yescharacteristic
272C22×AGL(1,𝔽5)—24no—
273C22×AGL(1,𝔽5)—32no—
274C22×AGL(1,𝔽5)—38no—
275C22×AGL(1,𝔽5)—31no—
276C22×AGL(1,𝔽5)—31no—
277C22×AGL(1,𝔽5)—64no—
278C22×AGL(1,𝔽5)—64no—
279C22×AGL(1,𝔽5)—632no—
280C22×AGL(1,𝔽5)—64no—
281C22×AGL(1,𝔽5)—62no—
282C22×AGL(1,𝔽5)—64no—
283C22×AGL(1,𝔽5)—64no—
284C22×AGL(1,𝔽5)—64no—
285C22×AGL(1,𝔽5)—62no—
286C22×AGL(1,𝔽5)—64no—
287C22×AGL(1,𝔽5)D1214yescomplemented
288C22×AGL(1,𝔽5)C22×D312yes—
289C22×AGL(1,𝔽5)C22×D311yescharacteristic
290C22×AGL(1,𝔽5)C22×D311yescharacteristic
291C2×C5×D4—31no—
292C2×C5×D4—32no—
293C2×C22⋊D5—31no—
294C2×C22⋊D5—31no—
295C2×C22⋊D5—32no—
296C2×C22⋊D5—32no—
297D4×D5—64no—
298D4×D5—64no—
299D4×D5—62no—
300D4×D5—62no—
301C2×D20—31no—
302C2×D20—32no—
303C2×C4×D5—31no—
304C2×C4×D5C22×D312yes—
305C22⋊AGL(1,𝔽5)—22no—
306C22⋊AGL(1,𝔽5)—64no—
307C22⋊AGL(1,𝔽5)—64no—
308C22⋊AGL(1,𝔽5)—64no—
309C22⋊AGL(1,𝔽5)—62no—
310C22⋊AGL(1,𝔽5)—62no—
311C4⋊AGL(1,𝔽5)—64no—
312C4⋊AGL(1,𝔽5)—62no—
313C4×AGL(1,𝔽5)—24no—
314C4×AGL(1,𝔽5)—62no—
315C5×C22⋊C4—32no—
316C5×C22⋊C4C4×D311yescharacteristic, complemented
317C22⋊Dic5—32no—
318C22⋊Dic5C4×D311yescharacteristic, complemented
319#685—32no—
320#685—32no—
321#685C4×D312yescomplemented
322C24×C4—151no—
323C2×#120—151no—
324C2×C4×D4—152no—
325C2×C4×D4—151no—
326#386—152no—
327#386—151no—
328#385—152no—
329#385—151no—
330#379—151no—
331C4×C22⋊C4—51no—
332C4×C22⋊C4—152no—
333C22×C3×C5—22no—
334C22×C3×C5C4×D412yescomplemented
335C22×C3×C5C23×C411yescharacteristic
336C2×D15—28no—
337C2×D15—22no—
338C2×D15—22no—
339C2×D15—21no—
340C2×D15—22no—
341C2×D15C4×D414yescomplemented
342C2×C5×D3—28no—
343C2×C5×D3—22no—
344C2×C5×D3—22no—
345C2×C5×D3—21no—
346C2×C5×D3—22no—
347C2×C5×D3C4×D414yescomplemented
348C2×C3×D5—22no—
349C2×C3×D5—22no—
350C2×C3×D5—22no—
351C2×C3×D5—24no—
352C2×C3×D5C4×D412yescomplemented
353C2×C3×D5C22×D411yescharacteristic
354C2×C3×D5C22×D412yes—
355C2×C3×D5C2×#4111yescharacteristic
356C2×C3×D5C2×#4112yes—
357D3×D5—216no—
358D3×D5—24no—
359D3×D5—24no—
360D3×D5—24no—
361D3×D5—24no—
362D3×D5—41no—
363D3×D5—41no—
364D3×D5—42no—
365ΓL(1,𝔽16)—24no—
366ΓL(1,𝔽16)—41no—
367ΓL(1,𝔽16)—41no—
368C3×AGL(1,𝔽5)—22no—
369C3×AGL(1,𝔽5)—42no—
370C3×AGL(1,𝔽5)#12014yescomplemented
371C3×C4×C5—22no—
372Dic15—21no—
373C3×Dic5—22no—
374C5×Dic3—21no—
375C24×C3—51no—
376C23×D3—52no—
377C23×D3—51no—
378C23×D3—52no—
379C23×D3—51no—
380C23×D3—104no—
381C23×D3—104no—
382C23×D3—102no—
383C23×D3—102no—
384C23×D3C2×AGL(1,𝔽5)11yescharacteristic, complemented
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—54no—
388C22×C3×C4—52no—
389C22×C3×C4—52no—
390C22×C3×C4—104no—
391C2×#67—51no—
392C2×#67—51no—
393C2×#67—51no—
394C2×#67—102no—
395C2×#67—102no—
396C2×#67C2×AGL(1,𝔽5)11yescharacteristic, complemented
397C22×Dic3—52no—
398C22×Dic3—51no—
399C22×Dic3—51no—
400C22×Dic3—51no—
401C22×Dic3—104no—
402C22×Dic3—102no—
403C2×D12—52no—
404C2×D12—52no—
405C2×D12—52no—
406C2×D12—104no—
407C2×D12—104no—
408C2×D12C2×AGL(1,𝔽5)12yescomplemented
409C2×C4×D3—58no—
410C2×C4×D3—104no—
411C2×C4×D3—104no—
412C2×C4×D3—104no—
413C2×C4×D3—104no—
414C2×C4×D3—104no—
415C2×C4×D3—1032no—
416C2×C4×D3—104no—
417C2×C4×D3—102no—
418C3×C22⋊C4—51no—
419C3×C22⋊C4—52no—
420C3×C22⋊C4—102no—
421C3×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
422C3×C42—104no—
423#217—102no—
424(C2×D3)⋊C4—52no—
425(C2×D3)⋊C4—52no—
426(C2×D3)⋊C4—52no—
427(C2×D3)⋊C4—104no—
428(C2×D3)⋊C4—102no—
429(C2×D3)⋊C4—104no—
430(C2×D3)⋊C4—104no—
431(C2×D3)⋊C4C2×AGL(1,𝔽5)12yescomplemented
432C4⋊Dic3—104no—
433Dic3⋊C4—102no—
434C4×Dic3—102no—
435C23×C5—32no—
436C23×C5—31no—
437C23×C5—64no—
438C23×C5—62no—
439C23×C5C2×C4×D311yescharacteristic
440C22×D5—22no—
441C22×D5—22no—
442C22×D5—32no—
443C22×D5—34no—
444C22×D5—34no—
445C22×D5—31no—
446C22×D5—64no—
447C22×D5—64no—
448C22×D5—68no—
449C22×D5—68no—
450C22×D5—616no—
451C22×D5—64no—
452C22×D5—62no—
453C22×D5—64no—
454C22×D5—62no—
455C22×D5—62no—
456C22×D5—62no—
457C22×D5—62no—
458C22×D5—61no—
459C22×D5—61no—
460C22×D5—62no—
461C22×D5—62no—
462C22×D5C2×C4×D311yescharacteristic
463C22×D5C2×D1212yes—
464C22×D5#23512yes—
465C22×D5C23×D311yescharacteristic
466C2×AGL(1,𝔽5)—22no—
467C2×AGL(1,𝔽5)—28no—
468C2×AGL(1,𝔽5)—22no—
469C2×AGL(1,𝔽5)—22no—
470C2×AGL(1,𝔽5)—22no—
471C2×AGL(1,𝔽5)—34no—
472C2×AGL(1,𝔽5)—616no—
473C2×AGL(1,𝔽5)—68no—
474C2×AGL(1,𝔽5)—62no—
475C2×AGL(1,𝔽5)—62no—
476C2×AGL(1,𝔽5)—616no—
477C2×AGL(1,𝔽5)—61no—
478C2×AGL(1,𝔽5)—61no—
479C2×AGL(1,𝔽5)—62no—
480C2×AGL(1,𝔽5)—62no—
481C2×AGL(1,𝔽5)—124no—
482C2×AGL(1,𝔽5)C2×D1212yes—
483C2×AGL(1,𝔽5)C2×D1212yes—
484C2×AGL(1,𝔽5)D3×D414yes—
485C5×D4—64no—
486C5×D4—62no—
487C2×C4×C5—31no—
488C2×C4×C5C2×C4×D312yescomplemented
489C22⋊D5—64no—
490C22⋊D5—64no—
491C22⋊D5—62no—
492C22⋊D5—62no—
493C2×Dic5—31no—
494C2×Dic5C2×C4×D312yescomplemented
495D20—64no—
496D20—62no—
497C4×D5—22no—
498C4×D5—22no—
499C4×D5—61no—
500C4×D5—61no—
501C25—151no—
502C22×D4—152no—
503C22×D4—151no—
504C23×C4—51no—
505C23×C4—152no—
506C23×C4—151no—
507C23×C4—152no—
508C23×C4—151no—
509C23×C4—304no—
510C23×C4—308no—
511#120—31no—
512#120—152no—
513#120—151no—
514#120—152no—
515#120—151no—
516#120—151no—
517C4×D4—308no—
518C4×D4—304no—
519C2×C4⋊C4—151no—
520C2×C4⋊C4—152no—
521C2×C22⋊C4—51no—
522C2×C22⋊C4—51no—
523C2×C22⋊C4—152no—
524C2×C22⋊C4—152no—
525C2×C22⋊C4—151no—
526C2×C22⋊C4—152no—
527C2×C22⋊C4—152no—
528C2×C22⋊C4—151no—
529C2×C42—52no—
530C2×C42—151no—
531#95—52no—
532#95—152no—
533#95—152no—
534C2×C3×C5—22no—
535C2×C3×C5C2×C4×D411yescharacteristic
536C2×C3×C5C2×C4×D412yes—
537D15—24no—
538D15—41no—
539C3×D5—22no—
540C3×D5C2×#12011yescharacteristic
541C3×D5#52511yescharacteristic
542C3×D5#52512yes—
543C5×D3—24no—
544C5×D3—41no—
545C23×C3—51no—
546C23×C3—52no—
547C23×C3—52no—
548C23×C3—51no—
549C23×C3—102no—
550C23×C3—102no—
551C23×C3C22×AGL(1,𝔽5)11yescharacteristic
552C22×D3—22no—
553C22×D3—24no—
554C22×D3—52no—
555C22×D3—54no—
556C22×D3—54no—
557C22×D3—51no—
558C22×D3—104no—
559C22×D3—102no—
560C22×D3—102no—
561C22×D3—102no—
562C22×D3—102no—
563C22×D3—104no—
564C22×D3—108no—
565C22×D3—1016no—
566C22×D3—108no—
567C22×D3—102no—
568C22×D3—101no—
569C22×D3—102no—
570C22×D3—101no—
571C22×D3—104no—
572C22×D3—102no—
573C22×D3—104no—
574C22×D3C22×AGL(1,𝔽5)12yes—
575C22×D3C22×AGL(1,𝔽5)11yescharacteristic, complemented
576C2×C3×C4—52no—
577C2×C3×C4—54no—
578C2×C3×C4—52no—
579C2×C3×C4—52no—
580C2×C3×C4—102no—
581C2×C3×C4—102no—
582C2×C3×C4—108no—
583C2×C3×C4—102no—
584C2×C3×C4—102no—
585C2×C3×C4—102no—
586C2×C3×C4—102no—
587C2×C3×C4C22×AGL(1,𝔽5)12yescomplemented
588#67—22no—
589#67—102no—
590#67—102no—
591#67—102no—
592C2×Dic3—54no—
593C2×Dic3—51no—
594C2×Dic3—101no—
595C2×Dic3—101no—
596C2×Dic3—102no—
597C2×Dic3—102no—
598C2×Dic3—108no—
599C2×Dic3—101no—
600C2×Dic3—101no—
601C2×Dic3—102no—
602C2×Dic3—102no—
603C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic, complemented
604D12—24no—
605D12—104no—
606D12—104no—
607D12—104no—
608C4×D3—1016no—
609C4×D3—1016no—
610C4×D3—204no—
611C22×C5—22no—
612C22×C5—34no—
613C22×C5—68no—
614C22×C5—62no—
615C22×C5—62no—
616C22×C5—61no—
617C22×C5—62no—
618C22×C5C4×D1212yescomplemented
619C22×C5C22×C4×D311yescharacteristic
620C2×D5—22no—
621C2×D5—22no—
622C2×D5—22no—
623C2×D5—24no—
624C2×D5—34no—
625C2×D5—616no—
626C2×D5—68no—
627C2×D5—62no—
628C2×D5—62no—
629C2×D5—64no—
630C2×D5—64no—
631C2×D5—64no—
632C2×D5—64no—
633C2×D5—61no—
634C2×D5—62no—
635C2×D5—121no—
636C2×D5—121no—
637C2×D5—122no—
638C2×D5C4×D1212yescomplemented
639C2×D5C22×D1211yescharacteristic
640C2×D5C2×#23511yescharacteristic
641C2×D5C2×D3×D412yes—
642C2×D5D3×#4112yes—
643AGL(1,𝔽5)—22no—
644AGL(1,𝔽5)—42no—
645AGL(1,𝔽5)—64no—
646AGL(1,𝔽5)—121no—
647AGL(1,𝔽5)—121no—
648AGL(1,𝔽5)#88214yesdirect product factor
649C4×C5—22no—
650C4×C5—61no—
651Dic5—22no—
652Dic5—61no—
653C24—31no—
654C24—51no—
655C24—152no—
656C24—151no—
657C24—152no—
658C24—151no—
659C24—302no—
660C24—302no—
661C24—304no—
662C24—304no—
663C2×D4—31no—
664C2×D4—32no—
665C2×D4—151no—
666C2×D4—152no—
667C2×D4—152no—
668C2×D4—151no—
669C2×D4—151no—
670C2×D4—152no—
671C2×D4—304no—
672C2×D4—304no—
673C2×D4—302no—
674C2×D4—302no—
675C22×C4—51no—
676C22×C4—51no—
677C22×C4—54no—
678C22×C4—52no—
679C22×C4—52no—
680C22×C4—104no—
681C22×C4—151no—
682C22×C4—158no—
683C22×C4—152no—
684C22×C4—151no—
685C22×C4—151no—
686C22×C4—304no—
687C22×C4—304no—
688C22×C4—304no—
689C22×C4—304no—
690C22×C4—302no—
691C22×C4—304no—
692C22×C4—304no—
693C22×C4—3032no—
694C22×C4—304no—
695C22×C4—302no—
696C4⋊C4—302no—
697C4⋊C4—304no—
698C22⋊C4—32no—
699C22⋊C4—51no—
700C22⋊C4—52no—
701C22⋊C4—102no—
702C22⋊C4—152no—
703C22⋊C4—152no—
704C22⋊C4—152no—
705C22⋊C4—302no—
706C22⋊C4—304no—
707C22⋊C4—304no—
708C22⋊C4—304no—
709C22⋊C4—302no—
710C22⋊C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
711C42—104no—
712C42—302no—
713C3×C5C4×#12011yescharacteristic, complemented, Hall
714C22×C3—22no—
715C22×C3—52no—
716C22×C3—51no—
717C22×C3—52no—
718C22×C3—51no—
719C22×C3—52no—
720C22×C3—102no—
721C22×C3—102no—
722C22×C3—104no—
723C22×C3—102no—
724C22×C3D4×AGL(1,𝔽5)12yescomplemented
725C22×C3C23×AGL(1,𝔽5)11yescharacteristic
726C2×D3—28no—
727C2×D3—22no—
728C2×D3—22no—
729C2×D3—22no—
730C2×D3—21no—
731C2×D3—54no—
732C2×D3—104no—
733C2×D3—104no—
734C2×D3—104no—
735C2×D3—104no—
736C2×D3—1016no—
737C2×D3—108no—
738C2×D3—102no—
739C2×D3—102no—
740C2×D3—102no—
741C2×D3—101no—
742C2×D3—201no—
743C2×D3—201no—
744C2×D3—202no—
745C2×D3D4×AGL(1,𝔽5)14yescomplemented
746C3×C4—22no—
747C3×C4—54no—
748C3×C4—102no—
749C3×C4—102no—
750C3×C4—202no—
751Dic3—21no—
752Dic3—104no—
753Dic3—101no—
754Dic3—201no—
755Dic3—201no—
756C2×C5—22no—
757C2×C5—64no—
758C2×C5—121no—
759C2×C5C2×C4×D1211yescharacteristic
760C2×C5C4×D3×D412yes—
761D5—22no—
762D5—64no—
763D5—121no—
764D5C2×#88211yescharacteristic
765D5#552411yescharacteristic
766D5#554712yes—
767C23—32no—
768C23—31no—
769C23—51no—
770C23—52no—
771C23—52no—
772C23—51no—
773C23—64no—
774C23—62no—
775C23—102no—
776C23—102no—
777C23—154no—
778C23—154no—
779C23—152no—
780C23—151no—
781C23—304no—
782C23—304no—
783C23—302no—
784C23—302no—
785C23—302no—
786C23—302no—
787C23—304no—
788C23—301no—
789C23—302no—
790C23—301no—
791C23—302no—
792C23—304no—
793C23—308no—
794C23—308no—
795C23—3016no—
796C23—302no—
797C23C2×D3×AGL(1,𝔽5)11yescharacteristic
798D4—64no—
799D4—62no—
800D4—304no—
801D4—302no—
802D4—304no—
803D4—304no—
804D4—302no—
805D4—302no—
806C2×C4—31no—
807C2×C4—54no—
808C2×C4—52no—
809C2×C4—52no—
810C2×C4—52no—
811C2×C4—102no—
812C2×C4—102no—
813C2×C4—108no—
814C2×C4—102no—
815C2×C4—102no—
816C2×C4—102no—
817C2×C4—102no—
818C2×C4—154no—
819C2×C4—151no—
820C2×C4—3016no—
821C2×C4—301no—
822C2×C4—301no—
823C2×C4—3016no—
824C2×C4—302no—
825C2×C4—302no—
826C2×C4—308no—
827C2×C4—301no—
828C2×C4—301no—
829C2×C4—302no—
830C2×C4—302no—
831C2×C4—604no—
832C2×C4C2×D3×AGL(1,𝔽5)12yescomplemented
833C2×C3—22no—
834C2×C3—51no—
835C2×C3—51no—
836C2×C3—52no—
837C2×C3—102no—
838C2×C3C2×D4×AGL(1,𝔽5)11yescharacteristic
839C2×C3C2×D4×AGL(1,𝔽5)12yes—
840D3—24no—
841D3—41no—
842D3—104no—
843D3—201no—
844C5C4×#88211yescharacteristic, complemented, Sylow
845C22—22no—
846C22—34no—
847C22—51no—
848C22—51no—
849C22—52no—
850C22—52no—
851C22—52no—
852C22—68no—
853C22—62no—
854C22—62no—
855C22—61no—
856C22—62no—
857C22—102no—
858C22—104no—
859C22—102no—
860C22—102no—
861C22—154no—
862C22—308no—
863C22—304no—
864C22—304no—
865C22—304no—
866C22—304no—
867C22—3016no—
868C22—302no—
869C22—302no—
870C22—301no—
871C22—302no—
872C22—601no—
873C22—602no—
874C22—601no—
875C22AGL(1,𝔽5)×D1212yescomplemented
876C22C22×D3×AGL(1,𝔽5)11yescharacteristic
877C4—22no—
878C4—54no—
879C4—61no—
880C4—102no—
881C4—102no—
882C4—202no—
883C4—304no—
884C4—301no—
885C4—601no—
886C4—601no—
887C3AGL(1,𝔽5)×#12011yescharacteristic, complemented, Sylow
888C2—22no—
889C2—51no—
890C2—52no—
891C2—51no—
892C2—64no—
893C2—102no—
894C2—121no—
895C2—304no—
896C2—601no—
897C2C2×AGL(1,𝔽5)×D1211yescharacteristic
898C2D3×D4×AGL(1,𝔽5)12yes—
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC3×C5×C22⋊C4C2×C4
prime radicalD5×#882C2
cosocleC22×C3×D5C24
hypercenterC22⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5C4×#120
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C23×D3×AGL(1,𝔽5)C2semidirect
2. C2×AGL(1,𝔽5)×#67C2semidirect
3. C2×AGL(1,𝔽5)×D12C2semidirect
5. #11752358C2semidirect
6. C3×C22⋊C4×AGL(1,𝔽5)C2semidirect
7. #11752026C2semidirect
8. #11752025C2semidirect
9. #11751934C2semidirect
10. #11751933C2semidirect
11. AGL(1,𝔽5)×(C2×D3)⋊C4C2semidirect
20. C22×D3×AGL(1,𝔽5)C22semidirect
24. C2×C4⋊ΓL(1,𝔽16)C22semidirect
26. C2×C3×C4×AGL(1,𝔽5)C22semidirect
28. C2×Dic3⋊AGL(1,𝔽5)C22semidirect
31. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
32. C2×(C2×D3)⋊AGL(1,𝔽5)C22semidirect
33. C2×Dic3×AGL(1,𝔽5)C22semidirect
35. #91771C4semidirect
36. C5×#882C4semidirect
38. #91573C4semidirect
39. #91570C4semidirect
40. #91476C4semidirect
41. #91475C4semidirect
43. #91235C22semidirect
44. C3×(C2×AGL(1,𝔽5))⋊C4C22semidirect
45. (C2×AGL(1,𝔽5))⋊Dic3C22semidirect
57. C22⋊C4×AGL(1,𝔽5)D3semidirect
58. C23×D15C2×C4semidirect
59. C23×C5×D3C2×C4semidirect
65. C22×D3×D5C2×C4semidirect
74. C22×C3×AGL(1,𝔽5)D4semidirect
86. C2×D3×AGL(1,𝔽5)D4semidirect
87. C2×#1220C2×C4semidirect
88. C2×D60C2×C4semidirect
89. C2×C5×#67C2×C4semidirect
90. C2×C5×D12C2×C4semidirect
94. C2×#1203C2×C4semidirect
95. C2×#1203C2×C4semidirect
96. C2×#1202C2×C4semidirect
97. C2×#1201C2×C4semidirect
111. C3×C5×C22⋊C4C2×C4semidirect
112. #6714C2×C4semidirect
113. C5×(C2×D3)⋊C4C2×C4semidirect
114. C3×C22⋊Dic5C2×C4semidirect
115. C3×#685C2×C4semidirect
116. #6667C2×C4semidirect
117. (C2×D3)⋊Dic5C2×C4semidirect
150. C2×C4×AGL(1,𝔽5)C2×D3semidirect
161. (C2×AGL(1,𝔽5))⋊C4C2×D3semidirect
167. C22×D15C22×C4semidirect
171. C22×C5×D3C22×C4semidirect
213. C2×C3×C4×C5C22×C4semidirect
215. C2×Dic15C22×C4semidirect
218. C2×C5×Dic3C22×C4semidirect
220. C2×C3×Dic5C22×C4semidirect
257. #882AGL(1,𝔽5)direct (N × H)
287. C22×AGL(1,𝔽5)D12semidirect
316. C5×C22⋊C4C4×D3semidirect
318. C22⋊Dic5C4×D3semidirect
321. #685C4×D3semidirect
334. C22×C3×C5C4×D4semidirect
341. C2×D15C4×D4semidirect
347. C2×C5×D3C4×D4semidirect
352. C2×C3×D5C4×D4semidirect
370. C3×AGL(1,𝔽5)#120semidirect
384. C23×D3C2×AGL(1,𝔽5)semidirect
396. C2×#67C2×AGL(1,𝔽5)semidirect
408. C2×D12C2×AGL(1,𝔽5)semidirect
421. C3×C22⋊C4C2×AGL(1,𝔽5)semidirect
431. (C2×D3)⋊C4C2×AGL(1,𝔽5)semidirect
488. C2×C4×C5C2×C4×D3semidirect
494. C2×Dic5C2×C4×D3semidirect
575. C22×D3C22×AGL(1,𝔽5)semidirect
587. C2×C3×C4C22×AGL(1,𝔽5)semidirect
603. C2×Dic3C22×AGL(1,𝔽5)semidirect
618. C22×C5C4×D12semidirect
638. C2×D5C4×D12semidirect
648. AGL(1,𝔽5)#882direct (N × H)
710. C22⋊C4D3×AGL(1,𝔽5)semidirect
713. C3×C5C4×#120semidirect
724. C22×C3D4×AGL(1,𝔽5)semidirect
745. C2×D3D4×AGL(1,𝔽5)semidirect
832. C2×C4C2×D3×AGL(1,𝔽5)semidirect
844. C5C4×#882semidirect
875. C22AGL(1,𝔽5)×D12semidirect
887. C3AGL(1,𝔽5)×#120semidirect

Maximal subgroups

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

subgroupindex
C23×D3×AGL(1,𝔽5)2
C2×AGL(1,𝔽5)×#672
C2×AGL(1,𝔽5)×D122
D5×#8822
#117523582
C3×C22⋊C4×AGL(1,𝔽5)2
#117520262
#117520252
#117519342
#117519332
AGL(1,𝔽5)×(C2×D3)⋊C42
AGL(1,𝔽5)×#1203
C4×#8825