Finite Group Databasebeta

← #14280024

Subgroups — #14280024

Order 1920.

1656 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
2C22×(C2×D3)⋊AGL(1,𝔽5)C212yesmaximal
3C2×D5×(C2×D3)⋊C4C211yesmaximal, characteristic
4C2×C3×(C2×AGL(1,𝔽5))⋊C4C211yesmaximal, characteristic, complemented
5C2×(C2×AGL(1,𝔽5))⋊Dic3C212yesmaximal, complemented
6#10604253—31nomaximal, Hall
7C23×D3×D5C2211yescharacteristic
8C23×ΓL(1,𝔽16)C2212yes—
9C23×C3×AGL(1,𝔽5)C2212yes—
10C22×C3×C4×D5C2211yescharacteristic
11C22×D5×Dic3C2211yescharacteristic
12C2×C4×ΓL(1,𝔽16)—24no—
13C2×C4×ΓL(1,𝔽16)—22no—
14C2×(C2×D3)⋊AGL(1,𝔽5)—24no—
15C2×(C2×D3)⋊AGL(1,𝔽5)—24no—
16C2×(C2×D3)⋊AGL(1,𝔽5)C418yescomplemented
17C2×#6714C411yescharacteristic, complemented
18C2×C5×(C2×D3)⋊C4C411yescharacteristic, complemented
19C2×#6667C411yescharacteristic, complemented
20C2×(C2×D3)⋊Dic5C411yescharacteristic, complemented
21D5×(C2×D3)⋊C4—22no—
22D5×(C2×D3)⋊C4—22no—
23C3×(C2×AGL(1,𝔽5))⋊C4—22no—
24(C2×AGL(1,𝔽5))⋊Dic3—24no—
25#69408—51nomaximal, Hall
26C22×C22⋊AGL(1,𝔽5)—32no—
27C22×C4×AGL(1,𝔽5)—31no—
28C2×D5×C22⋊C4—31no—
29C2×(C2×AGL(1,𝔽5))⋊C4—32no—
30C2×(C2×AGL(1,𝔽5))⋊C4D311yescharacteristic, complemented
31C23×D15C2×C411yescharacteristic
32C23×C5×D3C2×C411yescharacteristic
33C23×C3×D5C2311yescharacteristic
34C22×D3×D5—22no—
35C22×D3×D5—22no—
36C22×D3×D5—21no—
37C22×D3×D5—21no—
38C22×D3×D5—22no—
39C22×D3×D5—22no—
40C22×D3×D5—22no—
41C22×D3×D5C2×C414yes—
42C22×ΓL(1,𝔽16)—22no—
43C22×ΓL(1,𝔽16)—22no—
44C22×ΓL(1,𝔽16)—22no—
45C22×ΓL(1,𝔽16)—22no—
46C22×ΓL(1,𝔽16)C2×C414yes—
47C22×ΓL(1,𝔽16)D414yes—
48C22×ΓL(1,𝔽16)D414yes—
49C22×C3×AGL(1,𝔽5)—22no—
50C22×C3×AGL(1,𝔽5)—22no—
51C22×C3×AGL(1,𝔽5)—22no—
52C22×C3×AGL(1,𝔽5)—22no—
53C22×C3×AGL(1,𝔽5)—22no—
54C22×C3×AGL(1,𝔽5)—22no—
55C22×C3×AGL(1,𝔽5)C2×C414yes—
56C22×C3×C4×C5C2×C411yescharacteristic
57C22×Dic15C2×C411yescharacteristic
58C22×C5×Dic3C2×C411yescharacteristic
59C22×C3×Dic5C2×C411yescharacteristic
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5D412yes—
63C2×C3×C4×D5D412yes—
64C2×D5×Dic3—22no—
65C2×D5×Dic3—21no—
66C2×D5×Dic3—21no—
67C2×D5×Dic3—22no—
68C4×ΓL(1,𝔽16)—28no—
69(C2×D3)⋊AGL(1,𝔽5)—216no—
70#6714—22no—
71C5×(C2×D3)⋊C4—22no—
72#6667—22no—
73(C2×D3)⋊Dic5—22no—
74C22×(C2×D3)⋊C4—52no—
75C22×(C2×D3)⋊C4—51no—
76C22×C4×Dic3—51no—
77C2×C3×#95—51no—
78C2×C3⋊#95—52no—
79C24×D5—31no—
80C23×AGL(1,𝔽5)—32no—
81C23×AGL(1,𝔽5)C2×D312yes—
82C22×C4×D5—31no—
83C22×C4×D5C2×D311yescharacteristic
84C2×C22⋊AGL(1,𝔽5)—38no—
85C2×C22⋊AGL(1,𝔽5)—64no—
86C2×C22⋊AGL(1,𝔽5)—64no—
87C2×C4×AGL(1,𝔽5)—64no—
88C2×C4×AGL(1,𝔽5)—62no—
89C2×C5×C22⋊C4—31no—
90C2×C22⋊Dic5—31no—
91C2×#685—31no—
92C2×#685—31no—
93D5×C22⋊C4—62no—
94D5×C22⋊C4—62no—
95(C2×AGL(1,𝔽5))⋊C4—22no—
96(C2×AGL(1,𝔽5))⋊C4—64no—
97#1437—151noSylow
98C23×C3×C5C22×C411yescharacteristic
99C22×D15—21no—
100C22×D15—21no—
101C22×D15—22no—
102C22×D15—22no—
103C22×D15C4212yescomplemented
104C22×C5×D3—21no—
105C22×C5×D3—21no—
106C22×C5×D3—22no—
107C22×C5×D3—22no—
108C22×C5×D3C4212yescomplemented
109C22×C3×D5C22×C412yes—
110C22×C3×D5C2×D412yes—
111C22×C3×D5C2×D412yes—
112C22×C3×D5C2×D411yescharacteristic
113C22×C3×D5C2×D411yescharacteristic
114C22×C3×D5#4112yes—
115C22×C3×D5#4112yes—
116C22×C3×D5#4112yes—
117C2×D3×D5—24no—
118C2×D3×D5—24no—
119C2×D3×D5—24no—
120C2×D3×D5—24no—
121C2×D3×D5—24no—
122C2×D3×D5—24no—
123C2×D3×D5—41no—
124C2×D3×D5—42no—
125C2×D3×D5—42no—
126C2×D3×D5—42no—
127C2×D3×D5—42no—
128C2×D3×D5—41no—
129C2×D3×D5—41no—
130C2×D3×D5—42no—
131C2×D3×D5—42no—
132C2×D3×D5—41no—
133C2×ΓL(1,𝔽16)—24no—
134C2×ΓL(1,𝔽16)—24no—
135C2×ΓL(1,𝔽16)—24no—
136C2×ΓL(1,𝔽16)—24no—
137C2×ΓL(1,𝔽16)—24no—
138C2×ΓL(1,𝔽16)—24no—
139C2×ΓL(1,𝔽16)C22⋊C418yescomplemented
140C2×C3×AGL(1,𝔽5)—24no—
141C2×C3×AGL(1,𝔽5)—24no—
142C2×C3×AGL(1,𝔽5)—24no—
143C2×C3×AGL(1,𝔽5)—42no—
144C2×C3×AGL(1,𝔽5)—42no—
145C2×C3×AGL(1,𝔽5)—42no—
146C2×C3×AGL(1,𝔽5)—42no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5C22⋊C412yescomplemented
149C2×Dic15—21no—
150C2×Dic15—22no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22⋊C412yescomplemented
155C3×C4×D5—22no—
156C3×C4×D5—24no—
157C3×C4×D5—22no—
158D5×Dic3—42no—
159D5×Dic3—41no—
160D5×Dic3—41no—
161C24×D3—51no—
162C23×C3×C4—51no—
163C23×C3×C4—52no—
164C23×Dic3—52no—
165C23×Dic3—51no—
166C2×(C2×D3)⋊C4—58no—
167C2×(C2×D3)⋊C4—51no—
168C2×(C2×D3)⋊C4—51no—
169C2×(C2×D3)⋊C4—51no—
170C2×(C2×D3)⋊C4—102no—
171C2×(C2×D3)⋊C4—102no—
172C2×(C2×D3)⋊C4—104no—
173C2×(C2×D3)⋊C4—104no—
174C2×(C2×D3)⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
175C2×C4×Dic3—104no—
176C2×C4×Dic3—102no—
177C3×#95—102no—
178C3⋊#95—104no—
179C24×C5—31no—
180C23×D5—31no—
181C23×D5—34no—
182C23×D5—61no—
183C23×D5—62no—
184C23×D5—62no—
185C23×D5—62no—
186C23×D5—62no—
187C23×D5—62no—
188C23×D5—61no—
189C23×D5C22×D311yescharacteristic
190C22×AGL(1,𝔽5)—22no—
191C22×AGL(1,𝔽5)—22no—
192C22×AGL(1,𝔽5)—22no—
193C22×AGL(1,𝔽5)—22no—
194C22×AGL(1,𝔽5)—22no—
195C22×AGL(1,𝔽5)—22no—
196C22×AGL(1,𝔽5)—34no—
197C22×AGL(1,𝔽5)—34no—
198C22×AGL(1,𝔽5)—34no—
199C22×AGL(1,𝔽5)—62no—
200C22×AGL(1,𝔽5)—62no—
201C22×AGL(1,𝔽5)—62no—
202C22×AGL(1,𝔽5)—62no—
203C22×AGL(1,𝔽5)C4×D314yes—
204C22×C4×C5—31no—
205C22×C4×C5C4×D311yescharacteristic
206C22×Dic5—31no—
207C22×Dic5C4×D311yescharacteristic
208C2×C4×D5—22no—
209C2×C4×D5—22no—
210C2×C4×D5—61no—
211C2×C4×D5—62no—
212C2×C4×D5—62no—
213C2×C4×D5—61no—
214C2×C4×D5D1212yes—
215C2×C4×D5#6712yes—
216C22⋊AGL(1,𝔽5)—616no—
217C4×AGL(1,𝔽5)—68no—
218C5×C22⋊C4—62no—
219C22⋊Dic5—62no—
220#685—62no—
221#685—62no—
222C22×C22⋊C4—151no—
223C22×C22⋊C4—152no—
224C22×C42—151no—
225C2×#95—51no—
226C2×#95—152no—
227C22×C3×C5C2×C4211yescharacteristic
228C22×C3×C5C2×C22⋊C411yescharacteristic
229C22×C3×C5#11711yescharacteristic
230C22×C3×C5C4×D412yes—
231C22×C3×C5C4×D412yes—
232C2×D15—24no—
233C2×D15—22no—
234C2×D15—41no—
235C2×D15—42no—
236C2×D15—41no—
237C2×C5×D3—24no—
238C2×C5×D3—22no—
239C2×C5×D3—41no—
240C2×C5×D3—42no—
241C2×C5×D3—41no—
242C2×C3×D5C2×C22⋊C412yes—
243C2×C3×D5#11712yes—
244C2×C3×D5C4×D412yes—
245C2×C3×D5C4×D412yes—
246C2×C3×D5C4×D412yes—
247C2×C3×D5C4×D412yes—
248C2×C3×D5#12011yescharacteristic
249C2×C3×D5#12112yes—
250C2×C3×D5#12112yes—
251C2×C3×D5#12112yes—
252C2×C3×D5#12311yescharacteristic
253C2×C3×D5#12312yes—
254C2×C3×D5#12412yes—
255C2×C3×D5#12411yescharacteristic
256C2×C3×D5#12612yes—
257C2×C3×D5#12711yescharacteristic
258D3×D5—44no—
259D3×D5—44no—
260D3×D5—44no—
261D3×D5—44no—
262ΓL(1,𝔽16)—28no—
263C3×AGL(1,𝔽5)—44no—
264C3×C4×C5—22no—
265Dic15—41no—
266C3×Dic5—22no—
267C5×Dic3—41no—
268C24×C3—51no—
269C23×D3—51no—
270C23×D3—54no—
271C23×D3—102no—
272C23×D3—102no—
273C23×D3—101no—
274C23×D3—101no—
275C23×D3—102no—
276C23×D3—102no—
277C23×D3—102no—
278C23×D3C2×AGL(1,𝔽5)11yescharacteristic
279C22×C3×C4—51no—
280C22×C3×C4—52no—
281C22×C3×C4—52no—
282C22×C3×C4—54no—
283C22×C3×C4—102no—
284C22×C3×C4—102no—
285C22×C3×C4—102no—
286C22×C3×C4—102no—
287C22×C3×C4—102no—
288C22×C3×C4—102no—
289C22×C3×C4—102no—
290C22×C3×C4—102no—
291C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
292C22×Dic3—54no—
293C22×Dic3—54no—
294C22×Dic3—54no—
295C22×Dic3—51no—
296C22×Dic3—102no—
297C22×Dic3—101no—
298C22×Dic3—101no—
299C22×Dic3—102no—
300C22×Dic3—102no—
301C22×Dic3—102no—
302C22×Dic3—102no—
303C22×Dic3—102no—
304C22×Dic3C2×AGL(1,𝔽5)11yescharacteristic
305(C2×D3)⋊C4—22no—
306(C2×D3)⋊C4—102no—
307(C2×D3)⋊C4—1016no—
308(C2×D3)⋊C4—102no—
309(C2×D3)⋊C4—102no—
310C4×Dic3—108no—
311C23×C5—32no—
312C23×C5—61no—
313C23×C5—62no—
314C23×C5—62no—
315C23×C5—61no—
316C23×C5C2×C4×D311yescharacteristic
317C22×D5—32no—
318C22×D5—61no—
319C22×D5—62no—
320C22×D5—62no—
321C22×D5—61no—
322C22×D5—64no—
323C22×D5—64no—
324C22×D5—64no—
325C22×D5—64no—
326C22×D5—64no—
327C22×D5—64no—
328C22×D5—121no—
329C22×D5—122no—
330C22×D5—122no—
331C22×D5—121no—
332C22×D5—122no—
333C22×D5—122no—
334C22×D5—122no—
335C22×D5—122no—
336C22×D5—121no—
337C22×D5—121no—
338C22×D5C2×C4×D312yes—
339C22×D5C2×D1211yescharacteristic
340C22×D5#23512yes—
341C22×D5D3×D412yes—
342C22×D5D3×D412yes—
343C22×D5#23712yes—
344C22×D5#23912yes—
345C22×D5C2×#6711yescharacteristic
346C2×AGL(1,𝔽5)—24no—
347C2×AGL(1,𝔽5)—24no—
348C2×AGL(1,𝔽5)—24no—
349C2×AGL(1,𝔽5)—38no—
350C2×AGL(1,𝔽5)—42no—
351C2×AGL(1,𝔽5)—42no—
352C2×AGL(1,𝔽5)—42no—
353C2×AGL(1,𝔽5)—42no—
354C2×AGL(1,𝔽5)—64no—
355C2×AGL(1,𝔽5)—64no—
356C2×AGL(1,𝔽5)—64no—
357C2×AGL(1,𝔽5)—64no—
358C2×AGL(1,𝔽5)—64no—
359C2×AGL(1,𝔽5)—64no—
360C2×C4×C5—22no—
361C2×C4×C5—62no—
362C2×C4×C5—61no—
363C2×C4×C5(C2×D3)⋊C412yescomplemented
364C2×Dic5—22no—
365C2×Dic5—62no—
366C2×Dic5—61no—
367C2×Dic5(C2×D3)⋊C412yescomplemented
368C4×D5—22no—
369C4×D5—22no—
370C4×D5—24no—
371C4×D5—122no—
372C4×D5—121no—
373C4×D5—121no—
374C25—151no—
375C23×C4—51no—
376C23×C4—52no—
377C23×C4—151no—
378C23×C4—152no—
379C2×C22⋊C4—31no—
380C2×C22⋊C4—151no—
381C2×C22⋊C4—151no—
382C2×C22⋊C4—158no—
383C2×C22⋊C4—151no—
384C2×C22⋊C4—302no—
385C2×C22⋊C4—302no—
386C2×C22⋊C4—304no—
387C2×C22⋊C4—304no—
388C2×C42—302no—
389C2×C42—304no—
390#95—102no—
391#95—304no—
392C2×C3×C5C4×C22⋊C412yes—
393C2×C3×C5C4×C22⋊C411yescharacteristic
394C2×C3×C5#38611yescharacteristic
395C2×C3×C5#38812yes—
396C2×C3×C5#39011yescharacteristic
397D15—42no—
398C3×D5#38612yes—
399C3×D5#38812yes—
400C3×D5#38812yes—
401C3×D5#39012yes—
402C5×D3—42no—
403C23×C3—52no—
404C23×C3—52no—
405C23×C3—52no—
406C23×C3—52no—
407C23×C3—52no—
408C23×C3—52no—
409C23×C3—51no—
410C23×C3—51no—
411C23×C3C22×AGL(1,𝔽5)11yescharacteristic
412C22×D3—21no—
413C22×D3—22no—
414C22×D3—22no—
415C22×D3—21no—
416C22×D3—52no—
417C22×D3—104no—
418C22×D3—104no—
419C22×D3—104no—
420C22×D3—104no—
421C22×D3—104no—
422C22×D3—104no—
423C22×D3—101no—
424C22×D3—102no—
425C22×D3—102no—
426C22×D3—101no—
427C22×D3—202no—
428C22×D3—202no—
429C22×D3—202no—
430C22×D3—202no—
431C22×D3—201no—
432C22×D3—202no—
433C22×D3—201no—
434C22×D3—202no—
435C22×D3—201no—
436C22×D3—201no—
437C22×D3C4×AGL(1,𝔽5)12yescomplemented
438C2×C3×C4—22no—
439C2×C3×C4—52no—
440C2×C3×C4—102no—
441C2×C3×C4—104no—
442C2×C3×C4—102no—
443C2×C3×C4—102no—
444C2×C3×C4—104no—
445C2×C3×C4—104no—
446C2×C3×C4—104no—
447C2×C3×C4—202no—
448C2×C3×C4—202no—
449C2×C3×C4—202no—
450C2×C3×C4—202no—
451C2×C3×C4C22⋊AGL(1,𝔽5)12yescomplemented
452C2×Dic3—22no—
453C2×Dic3—21no—
454C2×Dic3—58no—
455C2×Dic3—104no—
456C2×Dic3—104no—
457C2×Dic3—104no—
458C2×Dic3—104no—
459C2×Dic3—104no—
460C2×Dic3—104no—
461C2×Dic3—102no—
462C2×Dic3—101no—
463C2×Dic3—202no—
464C2×Dic3—201no—
465C2×Dic3—201no—
466C22×C5—64no—
467C22×C5—62no—
468C22×C5—122no—
469C22×C5—121no—
470C22×C5—121no—
471C22×C5C42×D311yescharacteristic
472C22×C5#87211yescharacteristic
473C22×C5#67⋊C412yes—
474C22×C5#89312yes—
475C22×C5C2×(C2×D3)⋊C411yescharacteristic
476C2×D5—64no—
477C2×D5—62no—
478C2×D5—122no—
479C2×D5—121no—
480C2×D5—121no—
481C2×D5—124no—
482C2×D5—124no—
483C2×D5—124no—
484C2×D5—124no—
485C2×D5C4×D1212yes—
486C2×D5D3×C22⋊C412yes—
487C2×D5#67⋊C412yes—
488C2×D5#88211yescharacteristic
489C2×D5#88412yes—
490C2×D5#88512yes—
491C2×D5#88611yescharacteristic
492C2×D5#89212yes—
493C2×D5#89312yes—
494C2×D5#89412yes—
495C2×D5#89512yes—
496C2×D5#89812yes—
497C2×D5C4×#6712yes—
498C2×D5#93912yes—
499C2×D5#94011yescharacteristic
500C2×D5#94711yescharacteristic
501AGL(1,𝔽5)—44no—
502AGL(1,𝔽5)—68no—
503C4×C5—22no—
504C4×C5—121no—
505Dic5—22no—
506Dic5—121no—
507C24—31no—
508C24—51no—
509C24—154no—
510C24—151no—
511C24—302no—
512C24—301no—
513C24—301no—
514C24—302no—
515C24—302no—
516C24—302no—
517C24—302no—
518C22×C4—31no—
519C22×C4—51no—
520C22×C4—52no—
521C22×C4—52no—
522C22×C4—54no—
523C22×C4—102no—
524C22×C4—102no—
525C22×C4—102no—
526C22×C4—102no—
527C22×C4—102no—
528C22×C4—102no—
529C22×C4—102no—
530C22×C4—102no—
531C22×C4—154no—
532C22×C4—154no—
533C22×C4—154no—
534C22×C4—151no—
535C22×C4—302no—
536C22×C4—301no—
537C22×C4—301no—
538C22×C4—302no—
539C22×C4—302no—
540C22×C4—302no—
541C22×C4—302no—
542C22×C4—302no—
543C22×C4D3×AGL(1,𝔽5)11yescharacteristic
544C22⋊C4—62no—
545C22⋊C4—302no—
546C22⋊C4—302no—
547C22⋊C4—3016no—
548C22⋊C4—302no—
549C42—308no—
550C3×C5#143711yescharacteristic, complemented, Hall
551C22×C3—52no—
552C22×C3—52no—
553C22×C3—52no—
554C22×C3—52no—
555C22×C3—52no—
556C22×C3—52no—
557C22×C3—52no—
558C22×C3—52no—
559C22×C3—52no—
560C22×C3—52no—
561C22×C3—51no—
562C22×C3—52no—
563C22×C3—51no—
564C22×C3—52no—
565C22×C3—51no—
566C22×C3—51no—
567C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
568C22×C3#413011yescharacteristic
569C22×C3D4×AGL(1,𝔽5)12yes—
570C22×C3D4×AGL(1,𝔽5)12yes—
571C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
572C2×D3—24no—
573C2×D3—22no—
574C2×D3—42no—
575C2×D3—41no—
576C2×D3—41no—
577C2×D3—104no—
578C2×D3—102no—
579C2×D3—204no—
580C2×D3—204no—
581C2×D3—204no—
582C2×D3—204no—
583C2×D3—202no—
584C2×D3—201no—
585C2×D3—201no—
586C3×C4—22no—
587C3×C4—102no—
588C3×C4—204no—
589Dic3—41no—
590Dic3—108no—
591Dic3—201no—
592C2×C5—122no—
593C2×C5#466612yes—
594C2×C5#466912yes—
595C2×C5C4×(C2×D3)⋊C411yescharacteristic
596C2×C5#495811yescharacteristic
597C2×C5#498811yescharacteristic
598D5—122no—
599D5#466512yes—
600D5#467012yes—
601D5#495712yes—
602D5#499012yes—
603C23—32no—
604C23—52no—
605C23—52no—
606C23—52no—
607C23—52no—
608C23—51no—
609C23—51no—
610C23—52no—
611C23—52no—
612C23—61no—
613C23—62no—
614C23—61no—
615C23—62no—
616C23—152no—
617C23—304no—
618C23—304no—
619C23—304no—
620C23—304no—
621C23—304no—
622C23—304no—
623C23—301no—
624C23—302no—
625C23—301no—
626C23—302no—
627C23—602no—
628C23—601no—
629C23—601no—
630C23—602no—
631C23—602no—
632C23—602no—
633C23—602no—
634C23—601no—
635C23—602no—
636C23—601no—
637C23C2×D3×AGL(1,𝔽5)11yescharacteristic
638C2×C4—22no—
639C2×C4—52no—
640C2×C4—62no—
641C2×C4—61no—
642C2×C4—102no—
643C2×C4—104no—
644C2×C4—102no—
645C2×C4—102no—
646C2×C4—104no—
647C2×C4—104no—
648C2×C4—104no—
649C2×C4—158no—
650C2×C4—202no—
651C2×C4—202no—
652C2×C4—202no—
653C2×C4—202no—
654C2×C4—304no—
655C2×C4—304no—
656C2×C4—304no—
657C2×C4—304no—
658C2×C4—304no—
659C2×C4—304no—
660C2×C4—302no—
661C2×C4—301no—
662C2×C4—601no—
663C2×C4—602no—
664C2×C4—601no—
665C2×C4(C2×D3)⋊AGL(1,𝔽5)12yescomplemented
666C2×C3—52no—
667C2×C3—52no—
668C2×C3—52no—
669C2×C3—52no—
670C2×C3C22⋊C4×AGL(1,𝔽5)12yes—
671C2×C3#6570012yes—
672C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
673C2×C3#6577911yescharacteristic
674C2×C3#6578011yescharacteristic
675D3—42no—
676D3—202no—
677C5#6940811yescharacteristic, complemented, Sylow
678C22—52no—
679C22—51no—
680C22—51no—
681C22—52no—
682C22—52no—
683C22—52no—
684C22—52no—
685C22—52no—
686C22—52no—
687C22—51no—
688C22—52no—
689C22—51no—
690C22—52no—
691C22—52no—
692C22—52no—
693C22—52no—
694C22—62no—
695C22—64no—
696C22—121no—
697C22—122no—
698C22—121no—
699C22—302no—
700C22—304no—
701C22—604no—
702C22—604no—
703C22—604no—
704C22—604no—
705C22—601no—
706C22—602no—
707C22—601no—
708C22#9190911yescharacteristic
709C22C4×D3×AGL(1,𝔽5)11yescharacteristic
710C22#9192112yes—
711C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
712C22#67⋊AGL(1,𝔽5)12yes—
713C4—22no—
714C4—102no—
715C4—121no—
716C4—204no—
717C4—308no—
718C4—601no—
719C3#1060425311yescharacteristic, complemented, Sylow
720C2—52no—
721C2—52no—
722C2—52no—
723C2—52no—
724C2—122no—
725C2—602no—
726C2C4×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
727C2#1175185612yes—
728C2#1175185711yescharacteristic
729C2#1175193112yes—
730C2#1175202611yescharacteristic
subgroupG/H
center, FrattiniC23C2×D3×AGL(1,𝔽5)
commutatorC22×C3×C5C2×C42
FittingC22×C3×C4×C5C2×C4
socleC23×C3×C5C22×C4
prime radicalC23×D3×D5C22
cosocleC23×C3×D5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1437
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×ΓL(1,𝔽16)C2semidirect
4. C2×C3×(C2×AGL(1,𝔽5))⋊C4C2semidirect
5. C2×(C2×AGL(1,𝔽5))⋊Dic3C2semidirect
16. C2×(C2×D3)⋊AGL(1,𝔽5)C4semidirect
17. C2×#6714C4semidirect
18. C2×C5×(C2×D3)⋊C4C4semidirect
19. C2×#6667C4semidirect
20. C2×(C2×D3)⋊Dic5C4semidirect
30. C2×(C2×AGL(1,𝔽5))⋊C4D3semidirect
103. C22×D15C42semidirect
108. C22×C5×D3C42semidirect
139. C2×ΓL(1,𝔽16)C22⋊C4semidirect
148. C2×C3×C4×C5C22⋊C4semidirect
154. C2×C3×Dic5C22⋊C4semidirect
174. C2×(C2×D3)⋊C4AGL(1,𝔽5)semidirect
363. C2×C4×C5(C2×D3)⋊C4semidirect
367. C2×Dic5(C2×D3)⋊C4semidirect
437. C22×D3C4×AGL(1,𝔽5)semidirect
451. C2×C3×C4C22⋊AGL(1,𝔽5)semidirect
550. C3×C5#1437semidirect
665. C2×C4(C2×D3)⋊AGL(1,𝔽5)semidirect
677. C5#69408semidirect
719. C3#10604253semidirect

Maximal subgroups

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

subgroupindex
C22×C4×ΓL(1,𝔽16)2
C22×(C2×D3)⋊AGL(1,𝔽5)2
C2×D5×(C2×D3)⋊C42
C2×C3×(C2×AGL(1,𝔽5))⋊C42
C2×(C2×AGL(1,𝔽5))⋊Dic32
#106042533
#694085