Finite Group Databasebeta

← #14280011

Subgroups — #14280011

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×#6763C212yesmaximal
2C22×C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
4C2×#91235C212yesmaximal, complemented
5C2×#91235C211yesmaximal, characteristic, complemented
6#10604253—31nomaximal, Hall
7C24×C3×D5C2211yescharacteristic
8C23×ΓL(1,𝔽16)C2212yes—
9C23×ΓL(1,𝔽16)C2212yes—
10C22×C3×C4×D5C2211yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C2×#6763—24no—
13C2×#6763—24no—
14C2×#6763C418yescomplemented
15C2×C4×ΓL(1,𝔽16)—24no—
16C2×C4×ΓL(1,𝔽16)—22no—
17C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
18C2×C3×C22⋊Dic5C411yescharacteristic, complemented
19C2×C3×#685C411yescharacteristic, complemented
20C2×C3×#685C411yescharacteristic, complemented
21C3×D5×C22⋊C4—22no—
22C3×D5×C22⋊C4—22no—
23#91235—24no—
24#91235—22no—
25#71545—51nomaximal, Hall
26C22×C22⋊AGL(1,𝔽5)—32no—
27C22×C4×AGL(1,𝔽5)—31no—
28C2×D5×C22⋊C4D311yescharacteristic
29C2×(C2×AGL(1,𝔽5))⋊C4—32no—
30C2×(C2×AGL(1,𝔽5))⋊C4—31no—
31C24×C3×C5C2×C411yescharacteristic
32C23×C3×D5—22no—
33C23×C3×D5—22no—
34C23×C3×D5—21no—
35C23×C3×D5—21no—
36C23×C3×D5—22no—
37C23×C3×D5—22no—
38C23×C3×D5—22no—
39C23×C3×D5C2×C414yes—
40C23×C3×D5C2×C411yescharacteristic
41C23×C3×D5C2311yescharacteristic
42C22×ΓL(1,𝔽16)—22no—
43C22×ΓL(1,𝔽16)—22no—
44C22×ΓL(1,𝔽16)—22no—
45C22×ΓL(1,𝔽16)—22no—
46C22×ΓL(1,𝔽16)—22no—
47C22×ΓL(1,𝔽16)—22no—
48C22×ΓL(1,𝔽16)—22no—
49C22×ΓL(1,𝔽16)—22no—
50C22×ΓL(1,𝔽16)—22no—
51C22×ΓL(1,𝔽16)—22no—
52C22×ΓL(1,𝔽16)C2×C414yes—
53C22×ΓL(1,𝔽16)C2×C414yes—
54C22×ΓL(1,𝔽16)D414yes—
55C22×ΓL(1,𝔽16)D414yes—
56C22×C3×C4×C5C2×C411yescharacteristic
57C22×C3×C4×C5C2×C411yescharacteristic
58C22×C3×Dic5C2×C411yescharacteristic
59C22×C3×Dic5C2×C411yescharacteristic
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×C4×D5—22no—
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5—21no—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5D412yes—
67C2×C3×C4×D5D412yes—
68#6763—216no—
69C4×ΓL(1,𝔽16)—28no—
70C3×C5×C22⋊C4—22no—
71C3×C22⋊Dic5—22no—
72C3×#685—22no—
73C3×#685—22no—
74C22×C3×C22⋊C4—51no—
75C22×#217—52no—
76C22×C4×Dic3—51no—
77C2×C3⋊#95—52no—
78C2×C3⋊#95—51no—
79C24×D5C2×D311yescharacteristic
80C23×AGL(1,𝔽5)—32no—
81C23×AGL(1,𝔽5)—32no—
82C22×C4×D5C2×D311yescharacteristic
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⋊C4Dic311yescharacteristic, complemented
90C2×C22⋊Dic5Dic311yescharacteristic, complemented
91C2×#685Dic311yescharacteristic, complemented
92C2×#685Dic311yescharacteristic, complemented
93D5×C22⋊C4—22no—
94D5×C22⋊C4—22no—
95(C2×AGL(1,𝔽5))⋊C4—64no—
96(C2×AGL(1,𝔽5))⋊C4—62no—
97#1437—151noSylow
98C23×C3×C5—21no—
99C23×C3×C5—21no—
100C23×C3×C5—22no—
101C23×C3×C5—22no—
102C23×C3×C5C4212yescomplemented
103C23×C3×C5C22×C411yescharacteristic
104C22×C3×D5—21no—
105C22×C3×D5—21no—
106C22×C3×D5—22no—
107C22×C3×D5—22no—
108C22×C3×D5—24no—
109C22×C3×D5—24no—
110C22×C3×D5—24no—
111C22×C3×D5—24no—
112C22×C3×D5—24no—
113C22×C3×D5—24no—
114C22×C3×D5—41no—
115C22×C3×D5—42no—
116C22×C3×D5—42no—
117C22×C3×D5—42no—
118C22×C3×D5—41no—
119C22×C3×D5—42no—
120C22×C3×D5—42no—
121C22×C3×D5—41no—
122C22×C3×D5—42no—
123C22×C3×D5—41no—
124C22×C3×D5C4212yescomplemented
125C22×C3×D5C22×C412yes—
126C22×C3×D5C2×D412yes—
127C22×C3×D5C2×D412yes—
128C22×C3×D5C2×D411yescharacteristic
129C22×C3×D5C2×D411yescharacteristic
130C22×C3×D5#4112yes—
131C22×C3×D5#4112yes—
132C22×C3×D5#4112yes—
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)—24no—
140C2×ΓL(1,𝔽16)—24no—
141C2×ΓL(1,𝔽16)—24no—
142C2×ΓL(1,𝔽16)—42no—
143C2×ΓL(1,𝔽16)—42no—
144C2×ΓL(1,𝔽16)—42no—
145C2×ΓL(1,𝔽16)—42no—
146C2×ΓL(1,𝔽16)C22⋊C418yescomplemented
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C22⋊C412yescomplemented
151C2×C3×Dic5—22no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5C22⋊C412yescomplemented
155C3×C4×D5—22no—
156C3×C4×D5—24no—
157C3×C4×D5—22no—
158C3×C4×D5—42no—
159C3×C4×D5—41no—
160C3×C4×D5—41no—
161C25×C3—51no—
162C23×C3×C4—51no—
163C23×C3×C4—51no—
164C23×Dic3—52no—
165C23×Dic3—52no—
166C2×C3×C22⋊C4—51no—
167C2×C3×C22⋊C4—51no—
168C2×C3×C22⋊C4—51no—
169C2×C3×C22⋊C4—102no—
170C2×C3×C22⋊C4—102no—
171C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
172C2×#217—58no—
173C2×#217—104no—
174C2×#217—104no—
175C2×C4×Dic3—104no—
176C2×C4×Dic3—102no—
177C3⋊#95—104no—
178C3⋊#95—102no—
179C24×C5C2×Dic311yescharacteristic
180C23×D5—22no—
181C23×D5—22no—
182C23×D5—22no—
183C23×D5—22no—
184C23×D5—22no—
185C23×D5—21no—
186C23×D5—21no—
187C23×D5C4×D314yes—
188C23×D5C2×Dic311yescharacteristic
189C23×D5C22×D311yescharacteristic
190C22×AGL(1,𝔽5)—34no—
191C22×AGL(1,𝔽5)—34no—
192C22×AGL(1,𝔽5)—34no—
193C22×AGL(1,𝔽5)—34no—
194C22×AGL(1,𝔽5)—62no—
195C22×AGL(1,𝔽5)—62no—
196C22×AGL(1,𝔽5)—62no—
197C22×AGL(1,𝔽5)—62no—
198C22×AGL(1,𝔽5)—62no—
199C22×AGL(1,𝔽5)—62no—
200C22×AGL(1,𝔽5)—62no—
201C22×AGL(1,𝔽5)—62no—
202C22×AGL(1,𝔽5)—62no—
203C22×AGL(1,𝔽5)—62no—
204C22×C4×C5C2×Dic311yescharacteristic
205C22×C4×C5C2×Dic311yescharacteristic
206C22×Dic5C2×Dic311yescharacteristic
207C22×Dic5C2×Dic311yescharacteristic
208C2×C4×D5—22no—
209C2×C4×D5—22no—
210C2×C4×D5—22no—
211C2×C4×D5—22no—
212C2×C4×D5—21no—
213C2×C4×D5—21no—
214C2×C4×D5#6712yes—
215C2×C4×D5#6712yes—
216C22⋊AGL(1,𝔽5)—616no—
217C4×AGL(1,𝔽5)—68no—
218C5×C22⋊C4—22no—
219C22⋊Dic5—22no—
220#685—22no—
221#685—22no—
222C22×C22⋊C4—51no—
223C22×C22⋊C4—152no—
224C22×C42—151no—
225C2×#95—151no—
226C2×#95—152no—
227C22×C3×C5—24no—
228C22×C3×C5—22no—
229C22×C3×C5—41no—
230C22×C3×C5—42no—
231C22×C3×C5—41no—
232C22×C3×C5C2×C4211yescharacteristic
233C22×C3×C5C2×C22⋊C411yescharacteristic
234C22×C3×C5#11711yescharacteristic
235C22×C3×C5C4×D412yes—
236C22×C3×C5C4×D412yes—
237C2×C3×D5—24no—
238C2×C3×D5—22no—
239C2×C3×D5—41no—
240C2×C3×D5—42no—
241C2×C3×D5—41no—
242C2×C3×D5—44no—
243C2×C3×D5—44no—
244C2×C3×D5—44no—
245C2×C3×D5—44no—
246C2×C3×D5C2×C22⋊C412yes—
247C2×C3×D5#11712yes—
248C2×C3×D5C4×D412yes—
249C2×C3×D5C4×D412yes—
250C2×C3×D5C4×D412yes—
251C2×C3×D5C4×D412yes—
252C2×C3×D5#12011yescharacteristic
253C2×C3×D5#12112yes—
254C2×C3×D5#12112yes—
255C2×C3×D5#12112yes—
256C2×C3×D5#12312yes—
257C2×C3×D5#12311yescharacteristic
258C2×C3×D5#12412yes—
259C2×C3×D5#12411yescharacteristic
260C2×C3×D5#12612yes—
261C2×C3×D5#12711yescharacteristic
262ΓL(1,𝔽16)—28no—
263ΓL(1,𝔽16)—44no—
264C3×C4×C5—22no—
265C3×C4×C5—41no—
266C3×Dic5—22no—
267C3×Dic5—41no—
268C24×C3—51no—
269C24×C3—54no—
270C24×C3—51no—
271C24×C3—102no—
272C24×C3—102no—
273C24×C3—101no—
274C24×C3—101no—
275C24×C3—102no—
276C24×C3—102no—
277C24×C3—102no—
278C24×C3C2×AGL(1,𝔽5)11yescharacteristic
279C22×C3×C4—51no—
280C22×C3×C4—52no—
281C22×C3×C4—52no—
282C22×C3×C4—51no—
283C22×C3×C4—102no—
284C22×C3×C4—102no—
285C22×C3×C4—102no—
286C22×C3×C4—101no—
287C22×C3×C4—101no—
288C22×C3×C4—102no—
289C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
290C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
291C22×Dic3—54no—
292C22×Dic3—54no—
293C22×Dic3—54no—
294C22×Dic3—54no—
295C22×Dic3—102no—
296C22×Dic3—102no—
297C22×Dic3—102no—
298C22×Dic3—102no—
299C22×Dic3—102no—
300C22×Dic3—102no—
301C22×Dic3—102no—
302C22×Dic3—102no—
303C22×Dic3—102no—
304C22×Dic3—102no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—102no—
307C3×C22⋊C4—102no—
308C3×C22⋊C4—102no—
309#217—1016no—
310C4×Dic3—108no—
311C23×C5—21no—
312C23×C5—22no—
313C23×C5—22no—
314C23×C5—21no—
315C23×C5C4×Dic312yescomplemented
316C23×C5C22×Dic311yescharacteristic
317C22×D5—21no—
318C22×D5—22no—
319C22×D5—22no—
320C22×D5—21no—
321C22×D5—24no—
322C22×D5—24no—
323C22×D5—24no—
324C22×D5—24no—
325C22×D5—24no—
326C22×D5—24no—
327C22×D5—42no—
328C22×D5—42no—
329C22×D5—42no—
330C22×D5—42no—
331C22×D5—41no—
332C22×D5—41no—
333C22×D5—41no—
334C22×D5—42no—
335C22×D5—42no—
336C22×D5—41no—
337C22×D5C4×Dic312yescomplemented
338C22×D5C2×C4×D312yes—
339C22×D5#23512yes—
340C22×D5D3×D412yes—
341C22×D5D3×D412yes—
342C22×D5#23712yes—
343C22×D5#23712yes—
344C22×D5C2×#6711yescharacteristic
345C22×D5C2×#6711yescharacteristic
346C2×AGL(1,𝔽5)—38no—
347C2×AGL(1,𝔽5)—64no—
348C2×AGL(1,𝔽5)—64no—
349C2×AGL(1,𝔽5)—64no—
350C2×AGL(1,𝔽5)—64no—
351C2×AGL(1,𝔽5)—64no—
352C2×AGL(1,𝔽5)—64no—
353C2×AGL(1,𝔽5)—64no—
354C2×AGL(1,𝔽5)—64no—
355C2×AGL(1,𝔽5)—64no—
356C2×AGL(1,𝔽5)—122no—
357C2×AGL(1,𝔽5)—122no—
358C2×AGL(1,𝔽5)—122no—
359C2×AGL(1,𝔽5)—122no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—21no—
363C2×C4×C5#21712yescomplemented
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—21no—
367C2×Dic5#21712yescomplemented
368C4×D5—22no—
369C4×D5—22no—
370C4×D5—24no—
371C4×D5—41no—
372C4×D5—42no—
373C4×D5—41no—
374C25—51no—
375C23×C4—51no—
376C23×C4—51no—
377C23×C4—152no—
378C23×C4—152no—
379C2×C22⋊C4—51no—
380C2×C22⋊C4—51no—
381C2×C22⋊C4—51no—
382C2×C22⋊C4—102no—
383C2×C22⋊C4—102no—
384C2×C22⋊C4—158no—
385C2×C22⋊C4—304no—
386C2×C22⋊C4—304no—
387C2×C22⋊C4ΓL(1,𝔽16)11yescharacteristic, complemented
388C2×C42—302no—
389C2×C42—304no—
390#95—302no—
391#95—304no—
392C2×C3×C5—42no—
393C2×C3×C5C4×C22⋊C412yes—
394C2×C3×C5C4×C22⋊C411yescharacteristic
395C2×C3×C5#38611yescharacteristic
396C2×C3×C5#38812yes—
397C2×C3×C5#39011yescharacteristic
398C3×D5—42no—
399C3×D5#38612yes—
400C3×D5#38812yes—
401C3×D5#38812yes—
402C3×D5#39012yes—
403C23×C3—21no—
404C23×C3—22no—
405C23×C3—22no—
406C23×C3—21no—
407C23×C3—52no—
408C23×C3—52no—
409C23×C3—52no—
410C23×C3—52no—
411C23×C3—52no—
412C23×C3—52no—
413C23×C3—51no—
414C23×C3—51no—
415C23×C3—52no—
416C23×C3—104no—
417C23×C3—104no—
418C23×C3—104no—
419C23×C3—104no—
420C23×C3—104no—
421C23×C3—104no—
422C23×C3—101no—
423C23×C3—102no—
424C23×C3—102no—
425C23×C3—101no—
426C23×C3—202no—
427C23×C3—202no—
428C23×C3—202no—
429C23×C3—202no—
430C23×C3—201no—
431C23×C3—202no—
432C23×C3—201no—
433C23×C3—202no—
434C23×C3—201no—
435C23×C3—201no—
436C23×C3C4×AGL(1,𝔽5)12yescomplemented
437C23×C3C22×AGL(1,𝔽5)11yescharacteristic
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—52no—
442C2×C3×C4—102no—
443C2×C3×C4—104no—
444C2×C3×C4—102no—
445C2×C3×C4—102no—
446C2×C3×C4—102no—
447C2×C3×C4—101no—
448C2×C3×C4—202no—
449C2×C3×C4—201no—
450C2×C3×C4—201no—
451C2×C3×C4C22⋊AGL(1,𝔽5)12yescomplemented
452C2×Dic3—58no—
453C2×Dic3—104no—
454C2×Dic3—104no—
455C2×Dic3—104no—
456C2×Dic3—104no—
457C2×Dic3—104no—
458C2×Dic3—104no—
459C2×Dic3—104no—
460C2×Dic3—104no—
461C2×Dic3—104no—
462C2×Dic3—202no—
463C2×Dic3—202no—
464C2×Dic3—202no—
465C2×Dic3—202no—
466C22×C5—24no—
467C22×C5—22no—
468C22×C5—42no—
469C22×C5—41no—
470C22×C5—41no—
471C22×C5C2×C4×Dic311yescharacteristic
472C22×C5#92611yescharacteristic
473C22×C5D4×Dic312yes—
474C22×C5D4×Dic312yes—
475C22×C5C2×#21711yescharacteristic
476C2×D5—24no—
477C2×D5—22no—
478C2×D5—42no—
479C2×D5—41no—
480C2×D5—41no—
481C2×D5—44no—
482C2×D5—44no—
483C2×D5—44no—
484C2×D5—44no—
485C2×D5#87712yes—
486C2×D5#87912yes—
487C2×D5D3×C22⋊C412yes—
488C2×D5#67⋊C412yes—
489C2×D5#67⋊C412yes—
490C2×D5#88312yes—
491C2×D5#88412yes—
492C2×D5#88512yes—
493C2×D5C4×#6712yes—
494C2×D5C4×#6712yes—
495C2×D5#93511yescharacteristic
496C2×D5#93611yescharacteristic
497C2×D5#93711yescharacteristic
498C2×D5#93812yes—
499C2×D5#93912yes—
500C2×D5#94011yescharacteristic
501AGL(1,𝔽5)—68no—
502AGL(1,𝔽5)—124no—
503C4×C5—22no—
504C4×C5—41no—
505Dic5—22no—
506Dic5—41no—
507C24—51no—
508C24—54no—
509C24—51no—
510C24—101no—
511C24—101no—
512C24—102no—
513C24—102no—
514C24—102no—
515C24—102no—
516C24—102no—
517C24C2×ΓL(1,𝔽16)11yescharacteristic
518C22×C4—51no—
519C22×C4—52no—
520C22×C4—52no—
521C22×C4—51no—
522C22×C4—102no—
523C22×C4—102no—
524C22×C4—102no—
525C22×C4—101no—
526C22×C4—101no—
527C22×C4—102no—
528C22×C4—154no—
529C22×C4—154no—
530C22×C4—154no—
531C22×C4—154no—
532C22×C4—302no—
533C22×C4—302no—
534C22×C4—302no—
535C22×C4—302no—
536C22×C4—302no—
537C22×C4—302no—
538C22×C4—302no—
539C22×C4—302no—
540C22×C4—302no—
541C22×C4—302no—
542C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
543C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
544C22⋊C4—22no—
545C22⋊C4—102no—
546C22⋊C4—102no—
547C22⋊C4—102no—
548C22⋊C4—3016no—
549C42—308no—
550C3×C5#143711yescharacteristic, complemented, Hall
551C22×C3—24no—
552C22×C3—22no—
553C22×C3—42no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—52no—
557C22×C3—52no—
558C22×C3—52no—
559C22×C3—52no—
560C22×C3—52no—
561C22×C3—52no—
562C22×C3—52no—
563C22×C3—52no—
564C22×C3—52no—
565C22×C3—52no—
566C22×C3—51no—
567C22×C3—52no—
568C22×C3—51no—
569C22×C3—52no—
570C22×C3—51no—
571C22×C3—51no—
572C22×C3—104no—
573C22×C3—102no—
574C22×C3—204no—
575C22×C3—204no—
576C22×C3—204no—
577C22×C3—204no—
578C22×C3—202no—
579C22×C3—201no—
580C22×C3—201no—
581C22×C3C2×C4×AGL(1,𝔽5)11yescharacteristic
582C22×C3#413011yescharacteristic
583C22×C3D4×AGL(1,𝔽5)12yes—
584C22×C3D4×AGL(1,𝔽5)12yes—
585C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
586C3×C4—22no—
587C3×C4—41no—
588C3×C4—102no—
589C3×C4—201no—
590Dic3—108no—
591Dic3—204no—
592C2×C5—42no—
593C2×C5Dic3×C22⋊C412yes—
594C2×C5#495112yes—
595C2×C5C4×#21711yescharacteristic
596C2×C5#522011yescharacteristic
597C2×C5#522111yescharacteristic
598D5—42no—
599D5#494412yes—
600D5#494512yes—
601D5#495612yes—
602D5#495712yes—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—52no—
608C23—52no—
609C23—52no—
610C23—52no—
611C23—52no—
612C23—52no—
613C23—51no—
614C23—51no—
615C23—52no—
616C23—104no—
617C23—104no—
618C23—104no—
619C23—104no—
620C23—104no—
621C23—104no—
622C23—101no—
623C23—102no—
624C23—102no—
625C23—101no—
626C23—202no—
627C23—202no—
628C23—202no—
629C23—202no—
630C23—201no—
631C23—202no—
632C23—201no—
633C23—202no—
634C23—201no—
635C23—201no—
636C23C4×ΓL(1,𝔽16)12yescomplemented
637C23C22×ΓL(1,𝔽16)11yescharacteristic
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—21no—
641C2×C4—52no—
642C2×C4—102no—
643C2×C4—104no—
644C2×C4—102no—
645C2×C4—102no—
646C2×C4—102no—
647C2×C4—101no—
648C2×C4—158no—
649C2×C4—202no—
650C2×C4—201no—
651C2×C4—201no—
652C2×C4—304no—
653C2×C4—304no—
654C2×C4—304no—
655C2×C4—304no—
656C2×C4—304no—
657C2×C4—304no—
658C2×C4—304no—
659C2×C4—304no—
660C2×C4—304no—
661C2×C4—602no—
662C2×C4—602no—
663C2×C4—602no—
664C2×C4—602no—
665C2×C4#676312yescomplemented
666C2×C3—42no—
667C2×C3—52no—
668C2×C3—52no—
669C2×C3—52no—
670C2×C3—52no—
671C2×C3—202no—
672C2×C3C22⋊C4×AGL(1,𝔽5)12yes—
673C2×C3#6570012yes—
674C2×C3C4×C22⋊AGL(1,𝔽5)11yescharacteristic
675C2×C3#6577911yescharacteristic
676C2×C3#6578011yescharacteristic
677C5#7154511yescharacteristic, complemented, Sylow
678C22—24no—
679C22—22no—
680C22—42no—
681C22—41no—
682C22—41no—
683C22—52no—
684C22—52no—
685C22—52no—
686C22—52no—
687C22—52no—
688C22—52no—
689C22—52no—
690C22—52no—
691C22—52no—
692C22—52no—
693C22—51no—
694C22—52no—
695C22—51no—
696C22—52no—
697C22—51no—
698C22—51no—
699C22—104no—
700C22—102no—
701C22—204no—
702C22—204no—
703C22—204no—
704C22—204no—
705C22—202no—
706C22—201no—
707C22—201no—
708C22C2×C4×ΓL(1,𝔽16)11yescharacteristic
709C22#9198911yescharacteristic
710C22D4×ΓL(1,𝔽16)12yes—
711C22D4×ΓL(1,𝔽16)12yes—
712C22C2×#676311yescharacteristic
713C4—22no—
714C4—41no—
715C4—102no—
716C4—201no—
717C4—308no—
718C4—604no—
719C3#1060425311yescharacteristic, complemented, Sylow
720C2—42no—
721C2—52no—
722C2—52no—
723C2—52no—
724C2—52no—
725C2—202no—
726C2C22⋊C4×ΓL(1,𝔽16)12yes—
727C2#1175235912yes—
728C2C4×#676311yescharacteristic
729C2#1175243811yescharacteristic
730C2#1175243911yescharacteristic
subgroupG/H
center, FrattiniC23C22×ΓL(1,𝔽16)
commutatorC22×C3×C5C2×C42
FittingC2×C3×C5×C22⋊C4C4
socleC23×C3×C5C22×C4
prime radicalC24×C3×D5C22
cosocleC23×C3×D5C23
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1437
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×ΓL(1,𝔽16)C2semidirect
4. C2×#91235C2semidirect
5. C2×#91235C2semidirect
14. C2×#6763C4semidirect
17. C2×C3×C5×C22⋊C4C4semidirect
18. C2×C3×C22⋊Dic5C4semidirect
19. C2×C3×#685C4semidirect
20. C2×C3×#685C4semidirect
89. C2×C5×C22⋊C4Dic3semidirect
90. C2×C22⋊Dic5Dic3semidirect
91. C2×#685Dic3semidirect
92. C2×#685Dic3semidirect
102. C23×C3×C5C42semidirect
124. C22×C3×D5C42semidirect
146. C2×ΓL(1,𝔽16)C22⋊C4semidirect
150. C2×C3×C4×C5C22⋊C4semidirect
154. C2×C3×Dic5C22⋊C4semidirect
171. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
315. C23×C5C4×Dic3semidirect
337. C22×D5C4×Dic3semidirect
363. C2×C4×C5#217semidirect
367. C2×Dic5#217semidirect
387. C2×C22⋊C4ΓL(1,𝔽16)semidirect
436. C23×C3C4×AGL(1,𝔽5)semidirect
451. C2×C3×C4C22⋊AGL(1,𝔽5)semidirect
550. C3×C5#1437semidirect
636. C23C4×ΓL(1,𝔽16)semidirect
665. C2×C4#6763semidirect
677. C5#71545semidirect
719. C3#10604253semidirect

Maximal subgroups

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

subgroupindex
C22×#67632
C22×C4×ΓL(1,𝔽16)2
C2×C3×D5×C22⋊C42
C2×#912352
#106042533
#715455