Finite Group Databasebeta

← C3×D5×#394 #14331517

Subgroups — C3×D5×#394 #14331517

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D4×D5C211yesmaximal, characteristic
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C212yesmaximal, complemented
4C2×C3×D5×C22⋊C4C212yesmaximal, complemented
5C3×C5×#394C211yesmaximal, characteristic, complemented
6C3×#65511C211yesmaximal, characteristic, complemented
7C3×#65280C211yesmaximal, characteristic, complemented
8C3×#65250C212yesmaximal, complemented
9C3×#65248C212yesmaximal, complemented
10C3×#64961C211yesmaximal, characteristic, complemented
11C3×D5×#95C211yesmaximal, characteristic, complemented
12D5×#394C311yesmaximal, characteristic, direct product factor, Hall
13C24×C3×D5C2212yes—
14C22×C3×C5×D4C2211yescharacteristic
15C22×C3×C22⋊D5C2212yes—
16C2×C3×D4×D5—28no—
17C2×C3×D4×D5—24no—
18C22×C3×D20C2211yescharacteristic
19C22×C3×C4×D5C2212yes—
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
24C2×C3×C5×C22⋊C4C2212yescomplemented
25C2×C3×C5×C22⋊C4C2212yescomplemented
26C2×C3×C22⋊Dic5C2212yescomplemented
27C2×C3×C22⋊Dic5C2212yescomplemented
28C2×C3×#685C2212yescomplemented
29C2×C3×#685C2212yescomplemented
30C2×C3×#685C2212yescomplemented
31C2×C3×#685C2212yescomplemented
32C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
33C2×C3×#683C2211yescharacteristic, complemented
34C2×C3×#683C2211yescharacteristic, complemented
35C3×D5×C4⋊C4—24no—
36C3×D5×C22⋊C4—28no—
37C3×D5×C22⋊C4—28no—
38C3×C5×#95C2211yescharacteristic, complemented
39C3×#3963C2211yescharacteristic, complemented
40C3×#3963C2212yescomplemented
41C2×C3×#394—51nomaximal, Hall
42C22×D4×D5C2×C311yescharacteristic
43C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
44C2×D5×C22⋊C4C2×C312yescomplemented
45C2×D5×C22⋊C4C2×C312yescomplemented
46C5×#394C2×C311yescharacteristic, complemented
47#65511C2×C311yescharacteristic, complemented
48#65280C2×C311yescharacteristic, complemented
49#65250C2×C312yescomplemented
50#65248C2×C312yescomplemented
51#64961C2×C311yescharacteristic, complemented
52D5×#95C2×C311yescharacteristic, complemented
53C24×C3×C5C2312yes—
54C23×C3×D5—24no—
55C23×C3×D5—24no—
56C23×C3×D5—24no—
57C23×C3×D5—24no—
58C23×C3×D5—24no—
59C23×C3×D5—24no—
60C23×C3×D5D418yes—
61C23×C3×D5C2312yes—
62C23×C3×D5C2311yescharacteristic
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4—22no—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C2×C3×C22⋊D5—24no—
70C2×C3×C22⋊D5—24no—
71C2×C3×C22⋊D5—24no—
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2311yescharacteristic
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C3×D4×D5—232no—
77C2×C3×D20—24no—
78C2×C3×D20—22no—
79C2×C3×C4×D5—24no—
80C2×C3×C4×D5—22no—
81C2×C3×C4×D5—22no—
82C2×C3×C4×D5—24no—
83C2×C3×C4×D5—24no—
84C2×C3×C4×D5—24no—
85C2×C3×C4×D5—22no—
86C2×C3×C4×D5—24no—
87C2×C3×C4×D5D414yes—
88C2×C3×C4×D5D414yescomplemented
89C3×C5×C4⋊C4—22no—
90C3×C5×C22⋊C4—24no—
91C3×C5×C22⋊C4—24no—
92C3×C22⋊Dic5—24no—
93C3×C22⋊Dic5—24no—
94C3×#685—24no—
95C3×#685—24no—
96C3×#685—24no—
97C3×#685—24no—
98C3×C4⋊Dic5—22no—
99C3×#683—22no—
100C3×#683—22no—
101C23×C3×D4—51no—
102C22×C3×C4⋊C4—51no—
103C22×C3×C22⋊C4—52no—
104C22×C3×C22⋊C4—52no—
105C3×#394—51no—
106C3×#394—51no—
107C3×#394—52no—
108C3×#394—52no—
109C3×#394—51no—
110C3×#394D511yescharacteristic, direct product factor
111C2×C3×#95—51no—
112C24×D5C22×C312yes—
113C22×C5×D4C22×C311yescharacteristic
114C22×C22⋊D5C22×C312yes—
115C2×D4×D5—28no—
116C2×D4×D5—24no—
117C22×D20C22×C311yescharacteristic
118C22×C4×D5C22×C311yescharacteristic
119C22×C4×D5C22×C312yes—
120C22×C4×D5C22×C311yescharacteristic
121C22×C4×D5C22×C311yescharacteristic
122C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
123C2×C5×C22⋊C4C22×C312yescomplemented
124C2×C5×C22⋊C4C22×C312yescomplemented
125C2×C22⋊Dic5C22×C312yescomplemented
126C2×C22⋊Dic5C22×C312yescomplemented
127C2×#685C22×C312yescomplemented
128C2×#685C22×C312yescomplemented
129C2×#685C22×C312yescomplemented
130C2×#685C22×C312yescomplemented
131C2×C4⋊Dic5C22×C311yescharacteristic, complemented
132C2×#683C22×C311yescharacteristic, complemented
133C2×#683C22×C311yescharacteristic, complemented
134D5×C4⋊C4—24no—
135D5×C22⋊C4—28no—
136D5×C22⋊C4—28no—
137C5×#95C22×C311yescharacteristic, complemented
138#3963C22×C311yescharacteristic, complemented
139#3963C22×C312yescomplemented
140C2×#394—51noSylow
141C23×C3×C5—22no—
142C23×C3×C5—22no—
143C23×C3×C5—22no—
144C23×C3×C5—22no—
145C23×C3×C5—22no—
146C23×C3×C5—22no—
147C23×C3×C5C2×D414yes—
148C23×C3×C5C2411yescharacteristic
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5—22no—
155C22×C3×D5—216no—
156C22×C3×D5—216no—
157C22×C3×D5—216no—
158C22×C3×D5—48no—
159C22×C3×D5—48no—
160C22×C3×D5—48no—
161C22×C3×D5—48no—
162C22×C3×D5C2×D414yes—
163C22×C3×D5C2×D414yes—
164C22×C3×D5C2×D412yes—
165C22×C3×D5C2×D412yes—
166C22×C3×D5#4112yes—
167C22×C3×D5#4114yes—
168C3×C5×D4—28no—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—22no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—22no—
174C2×C3×C4×C5—22no—
175C2×C3×C4×C5—22no—
176C2×C3×C4×C5—22no—
177C2×C3×C4×C5C2×D412yes—
178C2×C3×C4×C5C2×D412yescomplemented
179C3×C22⋊D5—216no—
180C2×C3×Dic5—21no—
181C2×C3×Dic5—22no—
182C2×C3×Dic5—21no—
183C2×C3×Dic5—21no—
184C2×C3×Dic5—22no—
185C2×C3×Dic5—22no—
186C2×C3×Dic5—22no—
187C2×C3×Dic5—22no—
188C2×C3×Dic5C2×D412yes—
189C2×C3×Dic5C2×D412yescomplemented
190C3×D20—28no—
191C3×C4×D5—28no—
192C3×C4×D5—28no—
193C3×C4×D5—44no—
194C3×C4×D5—48no—
195C25×C3—52no—
196C22×C3×D4—52no—
197C22×C3×D4—51no—
198C22×C3×D4—104no—
199C22×C3×D4—108no—
200C22×C3×D4C2×D511yescharacteristic
201C23×C3×C4—51no—
202C23×C3×C4—51no—
203C23×C3×C4—52no—
204C23×C3×C4—51no—
205C2×C3×C4⋊C4—51no—
206C2×C3×C4⋊C4—51no—
207C2×C3×C4⋊C4—51no—
208C2×C3×C4⋊C4—104no—
209C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
210C2×C3×C22⋊C4—52no—
211C2×C3×C22⋊C4—52no—
212C2×C3×C22⋊C4—52no—
213C2×C3×C22⋊C4—52no—
214C2×C3×C22⋊C4—52no—
215C2×C3×C22⋊C4—52no—
216C2×C3×C22⋊C4—108no—
217C2×C3×C22⋊C4—108no—
218C2×C3×C22⋊C4C2×D512yescomplemented
219C2×C3×C22⋊C4C2×D512yescomplemented
220C3×#95—52no—
221C3×#95—51no—
222C3×#95C2×D511yescharacteristic, complemented
223C24×C5C23×C312yes—
224C23×D5—24no—
225C23×D5—24no—
226C23×D5—24no—
227C23×D5—24no—
228C23×D5—24no—
229C23×D5—24no—
230C23×D5C3×D418yes—
231C23×D5C23×C312yes—
232C23×D5C23×C311yescharacteristic
233C2×C5×D4—24no—
234C2×C5×D4—22no—
235C22×C4×C5C23×C311yescharacteristic
236C22×C4×C5C23×C312yes—
237C22×C4×C5C23×C311yescharacteristic
238C22×C4×C5C23×C311yescharacteristic
239C2×C22⋊D5—24no—
240C2×C22⋊D5—24no—
241C2×C22⋊D5—24no—
242C22×Dic5C23×C312yes—
243C22×Dic5C23×C311yescharacteristic
244C22×Dic5C23×C311yescharacteristic
245C22×Dic5C23×C311yescharacteristic
246D4×D5—232no—
247C2×D20—24no—
248C2×D20—22no—
249C2×C4×D5—24no—
250C2×C4×D5—22no—
251C2×C4×D5—22no—
252C2×C4×D5—24no—
253C2×C4×D5—24no—
254C2×C4×D5—24no—
255C2×C4×D5—22no—
256C2×C4×D5—24no—
257C2×C4×D5C3×D414yes—
258C2×C4×D5C3×D414yescomplemented
259C5×C4⋊C4—22no—
260C5×C22⋊C4—24no—
261C5×C22⋊C4—24no—
262C22⋊Dic5—24no—
263C22⋊Dic5—24no—
264#685—24no—
265#685—24no—
266#685—24no—
267#685—24no—
268C4⋊Dic5—22no—
269#683—22no—
270#683—22no—
271C23×D4—51no—
272C22×C4⋊C4—51no—
273C22×C22⋊C4—52no—
274C22×C22⋊C4—52no—
275#394—51no—
276#394—51no—
277#394—52no—
278#394—52no—
279#394—51no—
280#394C3×D511yescharacteristic, direct product factor
281C2×#95—51no—
282C22×C3×C5—24no—
283C22×C3×C5—24no—
284C22×C3×C5—24no—
285C22×C3×C5—42no—
286C22×C3×C5—42no—
287C22×C3×C5—42no—
288C22×C3×C5—42no—
289C22×C3×C5C22×D412yes—
290C22×C3×C5C22×D411yescharacteristic
291C22×C3×C5C22×D411yescharacteristic
292C22×C3×C5C2×#4111yescharacteristic
293C22×C3×C5C2×#4112yes—
294C2×C3×D5—24no—
295C2×C3×D5—24no—
296C2×C3×D5—24no—
297C2×C3×D5—42no—
298C2×C3×D5—42no—
299C2×C3×D5—42no—
300C2×C3×D5—42no—
301C2×C3×D5—432no—
302C2×C3×D5#12014yes—
303C2×C3×D5#12114yes—
304C2×C3×D5#12118yes—
305C2×C3×D5#12318yes—
306C2×C3×D5#12414yes—
307C3×C4×C5—22no—
308C3×C4×C5—22no—
309C3×C4×C5—41no—
310C3×C4×C5—42no—
311C3×Dic5—22no—
312C3×Dic5—22no—
313C3×Dic5—41no—
314C3×Dic5—42no—
315C24×C3—51no—
316C24×C3—58no—
317C24×C3—52no—
318C24×C3—104no—
319C24×C3—104no—
320C24×C3—104no—
321C24×C3—104no—
322C24×C3—104no—
323C24×C3—104no—
324C24×C3C22×D512yes—
325C2×C3×D4—24no—
326C2×C3×D4—22no—
327C2×C3×D4—104no—
328C2×C3×D4—104no—
329C2×C3×D4—1032no—
330C2×C3×D4—104no—
331C2×C3×D4—104no—
332C2×C3×D4—102no—
333C22×C3×C4—51no—
334C22×C3×C4—51no—
335C22×C3×C4—54no—
336C22×C3×C4—54no—
337C22×C3×C4—52no—
338C22×C3×C4—51no—
339C22×C3×C4—102no—
340C22×C3×C4—102no—
341C22×C3×C4—104no—
342C22×C3×C4—104no—
343C22×C3×C4—104no—
344C22×C3×C4—104no—
345C22×C3×C4—102no—
346C22×C3×C4—104no—
347C22×C3×C4C22×D512yes—
348C22×C3×C4C22×D511yescharacteristic
349C22×C3×C4C22×D511yescharacteristic
350C22×C3×C4C22×D511yescharacteristic
351C3×C4⋊C4—22no—
352C3×C4⋊C4—102no—
353C3×C4⋊C4—102no—
354C3×C4⋊C4—102no—
355C3×C22⋊C4—24no—
356C3×C22⋊C4—24no—
357C3×C22⋊C4—104no—
358C3×C22⋊C4—104no—
359C3×C22⋊C4—104no—
360C3×C22⋊C4—104no—
361C3×C22⋊C4—104no—
362C3×C22⋊C4—104no—
363C23×C5—22no—
364C23×C5—22no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5—22no—
369C23×C5C2×C3×D414yes—
370C23×C5C24×C311yescharacteristic
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—216no—
378C22×D5—216no—
379C22×D5—216no—
380C22×D5—48no—
381C22×D5—48no—
382C22×D5—48no—
383C22×D5—48no—
384C22×D5C2×C3×D414yes—
385C22×D5C2×C3×D414yes—
386C22×D5C2×C3×D412yes—
387C22×D5C2×C3×D412yes—
388C22×D5C3×#4112yes—
389C22×D5C3×#4114yes—
390C5×D4—28no—
391C2×C4×C5—21no—
392C2×C4×C5—22no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5C2×C3×D412yes—
400C2×C4×C5C2×C3×D412yescomplemented
401C22⋊D5—216no—
402C2×Dic5—21no—
403C2×Dic5—22no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5—22no—
409C2×Dic5—22no—
410C2×Dic5C2×C3×D412yes—
411C2×Dic5C2×C3×D412yescomplemented
412D20—28no—
413C4×D5—28no—
414C4×D5—28no—
415C4×D5—44no—
416C4×D5—48no—
417C25—52no—
418C22×D4—52no—
419C22×D4—51no—
420C22×D4—104no—
421C22×D4—108no—
422C22×D4C2×C3×D511yescharacteristic
423C23×C4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—52no—
427C2×C4⋊C4—51no—
428C2×C4⋊C4—51no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—104no—
431C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
432C2×C22⋊C4—52no—
433C2×C22⋊C4—52no—
434C2×C22⋊C4—52no—
435C2×C22⋊C4—52no—
436C2×C22⋊C4—52no—
437C2×C22⋊C4—52no—
438C2×C22⋊C4—108no—
439C2×C22⋊C4—108no—
440C2×C22⋊C4C2×C3×D512yescomplemented
441C2×C22⋊C4C2×C3×D512yescomplemented
442#95—52no—
443#95—51no—
444#95C2×C3×D511yescharacteristic, complemented
445C2×C3×C5—44no—
446C2×C3×C5C2×#12011yescharacteristic
447C2×C3×C5C2×#12111yescharacteristic
448C2×C3×C5C2×#12112yes—
449C2×C3×C5C2×#12312yes—
450C2×C3×C5C2×#12411yescharacteristic
451C3×D5—44no—
452C3×D5#39418yesdirect product factor
453C23×C3—22no—
454C23×C3—22no—
455C23×C3—22no—
456C23×C3—22no—
457C23×C3—22no—
458C23×C3—22no—
459C23×C3—52no—
460C23×C3—52no—
461C23×C3—54no—
462C23×C3—52no—
463C23×C3—54no—
464C23×C3—54no—
465C23×C3—1016no—
466C23×C3—1016no—
467C23×C3—1016no—
468C23×C3—102no—
469C23×C3—102no—
470C23×C3—102no—
471C23×C3—102no—
472C23×C3—102no—
473C23×C3—102no—
474C23×C3—208no—
475C23×C3—208no—
476C23×C3—208no—
477C23×C3—208no—
478C23×C3D4×D514yes—
479C23×C3C23×D511yescharacteristic
480C3×D4—28no—
481C3×D4—108no—
482C3×D4—1016no—
483C2×C3×C4—21no—
484C2×C3×C4—22no—
485C2×C3×C4—21no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—21no—
490C2×C3×C4—22no—
491C2×C3×C4—52no—
492C2×C3×C4—52no—
493C2×C3×C4—108no—
494C2×C3×C4—108no—
495C2×C3×C4—101no—
496C2×C3×C4—102no—
497C2×C3×C4—101no—
498C2×C3×C4—102no—
499C2×C3×C4—102no—
500C2×C3×C4—102no—
501C2×C3×C4—101no—
502C2×C3×C4—102no—
503C2×C3×C4—204no—
504C2×C3×C4—208no—
505C2×C3×C4D4×D512yes—
506C2×C3×C4D4×D512yescomplemented
507C22×C5—24no—
508C22×C5—24no—
509C22×C5—24no—
510C22×C5—42no—
511C22×C5—42no—
512C22×C5—42no—
513C22×C5—42no—
514C22×C5C22×C3×D412yes—
515C22×C5C22×C3×D411yescharacteristic
516C22×C5C22×C3×D411yescharacteristic
517C22×C5C2×C3×#4111yescharacteristic
518C22×C5C2×C3×#4112yes—
519C2×D5—24no—
520C2×D5—24no—
521C2×D5—24no—
522C2×D5—42no—
523C2×D5—42no—
524C2×D5—42no—
525C2×D5—42no—
526C2×D5—432no—
527C2×D5C3×#12014yes—
528C2×D5C3×#12114yes—
529C2×D5C3×#12118yes—
530C2×D5C3×#12318yes—
531C2×D5C3×#12414yes—
532C4×C5—22no—
533C4×C5—22no—
534C4×C5—41no—
535C4×C5—42no—
536Dic5—22no—
537Dic5—22no—
538Dic5—41no—
539Dic5—42no—
540C24—51no—
541C24—58no—
542C24—52no—
543C24—104no—
544C24—104no—
545C24—104no—
546C24—104no—
547C24—104no—
548C24—104no—
549C24C22×C3×D512yes—
550C2×D4—24no—
551C2×D4—22no—
552C2×D4—104no—
553C2×D4—104no—
554C2×D4—1032no—
555C2×D4—104no—
556C2×D4—104no—
557C2×D4—102no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—54no—
561C22×C4—54no—
562C22×C4—52no—
563C22×C4—51no—
564C22×C4—102no—
565C22×C4—104no—
566C22×C4—102no—
567C22×C4—104no—
568C22×C4—104no—
569C22×C4—104no—
570C22×C4—102no—
571C22×C4—104no—
572C22×C4C22×C3×D512yes—
573C22×C4C22×C3×D511yescharacteristic
574C22×C4C22×C3×D511yescharacteristic
575C22×C4C22×C3×D511yescharacteristic
576C4⋊C4—22no—
577C4⋊C4—102no—
578C4⋊C4—102no—
579C4⋊C4—102no—
580C22⋊C4—24no—
581C22⋊C4—24no—
582C22⋊C4—104no—
583C22⋊C4—104no—
584C22⋊C4—104no—
585C22⋊C4—104no—
586C22⋊C4—104no—
587C22⋊C4—104no—
588C3×C5C2×#39411yescharacteristic, complemented, Hall
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—54no—
597C22×C3—54no—
598C22×C3—58no—
599C22×C3—58no—
600C22×C3—54no—
601C22×C3—104no—
602C22×C3—104no—
603C22×C3—104no—
604C22×C3—2032no—
605C22×C3—202no—
606C22×C3—202no—
607C22×C3—202no—
608C22×C3—202no—
609C22×C3C2×D4×D512yes—
610C22×C3C2×D4×D511yescharacteristic
611C22×C3C2×D4×D511yescharacteristic
612C22×C3D5×#4111yescharacteristic
613C22×C3D5×#4112yes—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—41no—
617C3×C4—42no—
618C3×C4—102no—
619C3×C4—102no—
620C3×C4—201no—
621C3×C4—202no—
622C2×C5—44no—
623C2×C5C2×C3×#12011yescharacteristic
624C2×C5C2×C3×#12111yescharacteristic
625C2×C5C2×C3×#12112yes—
626C2×C5C2×C3×#12312yes—
627C2×C5C2×C3×#12411yescharacteristic
628D5—44no—
629D5C3×#39418yesdirect product factor
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—52no—
637C23—52no—
638C23—54no—
639C23—52no—
640C23—54no—
641C23—54no—
642C23—1016no—
643C23—1016no—
644C23—1016no—
645C23—102no—
646C23—102no—
647C23—102no—
648C23—102no—
649C23—102no—
650C23—102no—
651C23—208no—
652C23—208no—
653C23—208no—
654C23—208no—
655C23C3×D4×D514yes—
656C23C23×C3×D511yescharacteristic
657D4—28no—
658D4—108no—
659D4—1016no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—22no—
668C2×C4—52no—
669C2×C4—52no—
670C2×C4—108no—
671C2×C4—108no—
672C2×C4—101no—
673C2×C4—102no—
674C2×C4—101no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—101no—
679C2×C4—102no—
680C2×C4—204no—
681C2×C4—208no—
682C2×C4C3×D4×D512yes—
683C2×C4C3×D4×D512yescomplemented
684C2×C3—44no—
685C2×C3—58no—
686C2×C3—204no—
687C2×C3D5×#12011yescharacteristic
688C2×C3D5×#12111yescharacteristic
689C2×C3D5×#12112yes—
690C2×C3D5×#12312yes—
691C2×C3D5×#12411yescharacteristic
692C5C2×C3×#39411yescharacteristic, complemented, Sylow
693C22—24no—
694C22—24no—
695C22—24no—
696C22—42no—
697C22—42no—
698C22—42no—
699C22—42no—
700C22—54no—
701C22—54no—
702C22—58no—
703C22—58no—
704C22—54no—
705C22—104no—
706C22—104no—
707C22—104no—
708C22—2032no—
709C22—202no—
710C22—202no—
711C22—202no—
712C22—202no—
713C22C2×C3×D4×D512yes—
714C22C2×C3×D4×D511yescharacteristic
715C22C2×C3×D4×D511yescharacteristic
716C22C3×D5×#4111yescharacteristic
717C22C3×D5×#4112yes—
718C4—22no—
719C4—22no—
720C4—41no—
721C4—42no—
722C4—102no—
723C4—102no—
724C4—201no—
725C4—202no—
726C3D5×#39411yescharacteristic, direct product factor, Sylow
727C2—44no—
728C2—58no—
729C2—204no—
730C2C3×D5×#12011yescharacteristic
731C2C3×D5×#12111yescharacteristic
732C2C3×D5×#12112yes—
733C2C3×D5×#12312yes—
734C2C3×D5×#12411yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC23×C5C24×C3
FrattiniC23C23×C3×D5
FittingC3×C5×#394C2
socleC23×C3×C5C24
prime radicalC22×C3×D4×D5C2
hypercenterC3×#394D5
hypocenterC5C2×C3×#394
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#394

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×C4⋊C4C2semidirect
3. C2×C3×D5×C22⋊C4C2semidirect
4. C2×C3×D5×C22⋊C4C2semidirect
5. C3×C5×#394C2semidirect
6. C3×#65511C2semidirect
7. C3×#65280C2semidirect
8. C3×#65250C2semidirect
9. C3×#65248C2semidirect
10. C3×#64961C2semidirect
11. C3×D5×#95C2semidirect
12. D5×#394C3direct (N × H)
23. C2×C3×C5×C4⋊C4C22semidirect
24. C2×C3×C5×C22⋊C4C22semidirect
25. C2×C3×C5×C22⋊C4C22semidirect
26. C2×C3×C22⋊Dic5C22semidirect
27. C2×C3×C22⋊Dic5C22semidirect
28. C2×C3×#685C22semidirect
29. C2×C3×#685C22semidirect
30. C2×C3×#685C22semidirect
31. C2×C3×#685C22semidirect
32. C2×C3×C4⋊Dic5C22semidirect
33. C2×C3×#683C22semidirect
34. C2×C3×#683C22semidirect
38. C3×C5×#95C22semidirect
39. C3×#3963C22semidirect
40. C3×#3963C22semidirect
43. C2×D5×C4⋊C4C2×C3semidirect
44. C2×D5×C22⋊C4C2×C3semidirect
45. C2×D5×C22⋊C4C2×C3semidirect
46. C5×#394C2×C3semidirect
47. #65511C2×C3semidirect
48. #65280C2×C3semidirect
49. #65250C2×C3semidirect
50. #65248C2×C3semidirect
51. #64961C2×C3semidirect
52. D5×#95C2×C3semidirect
88. C2×C3×C4×D5D4semidirect
110. C3×#394D5direct (N × H)
122. C2×C5×C4⋊C4C22×C3semidirect
123. C2×C5×C22⋊C4C22×C3semidirect
124. C2×C5×C22⋊C4C22×C3semidirect
125. C2×C22⋊Dic5C22×C3semidirect
126. C2×C22⋊Dic5C22×C3semidirect
127. C2×#685C22×C3semidirect
128. C2×#685C22×C3semidirect
129. C2×#685C22×C3semidirect
130. C2×#685C22×C3semidirect
131. C2×C4⋊Dic5C22×C3semidirect
132. C2×#683C22×C3semidirect
133. C2×#683C22×C3semidirect
137. C5×#95C22×C3semidirect
138. #3963C22×C3semidirect
139. #3963C22×C3semidirect
178. C2×C3×C4×C5C2×D4semidirect
189. C2×C3×Dic5C2×D4semidirect
209. C2×C3×C4⋊C4C2×D5semidirect
218. C2×C3×C22⋊C4C2×D5semidirect
219. C2×C3×C22⋊C4C2×D5semidirect
222. C3×#95C2×D5semidirect
258. C2×C4×D5C3×D4semidirect
280. #394C3×D5direct (N × H)
400. C2×C4×C5C2×C3×D4semidirect
411. C2×Dic5C2×C3×D4semidirect
431. C2×C4⋊C4C2×C3×D5semidirect
440. C2×C22⋊C4C2×C3×D5semidirect
441. C2×C22⋊C4C2×C3×D5semidirect
444. #95C2×C3×D5semidirect
452. C3×D5#394direct (N × H)
506. C2×C3×C4D4×D5semidirect
588. C3×C5C2×#394semidirect
629. D5C3×#394direct (N × H)
683. C2×C4C3×D4×D5semidirect
692. C5C2×C3×#394semidirect
726. C3D5×#394direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D4×D52
C2×C3×D5×C4⋊C42
C2×C3×D5×C22⋊C42
C3×C5×#3942
C3×#655112
C3×#652802
C3×#652502
C3×#652482
C3×#649612
C3×D5×#952
D5×#3943
C2×C3×#3945