Finite Group Databasebeta

← C3×#10602343 #14280027

Subgroups — C3×#10602343 #14280027

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊D5C211yesmaximal, characteristic
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C22×C3×#685C212yesmaximal, complemented
5C2×C3×#3963C212yesmaximal, complemented
6#10602343C311yesmaximal, characteristic, direct product factor, Hall
7C25×C3×C5C2211yescharacteristic
8C24×C3×D5C2211yescharacteristic
9C23×C3×C4×C5C2212yes—
10C22×C3×C22⋊D5—22no—
11C22×C3×C22⋊D5—22no—
12C22×C3×C22⋊D5—24no—
13C22×C3×C22⋊D5—24no—
14C22×C3×C22⋊D5C414yescomplemented
15C23×C3×Dic5C2212yes—
16C23×C3×Dic5C2211yescharacteristic
17C2×C3×C5×C22⋊C4—22no—
18C2×C3×C5×C22⋊C4—24no—
19C2×C3×C22⋊Dic5—22no—
20C2×C3×C22⋊Dic5—24no—
21C2×C3×#685—24no—
22C2×C3×#685—24no—
23C2×C3×#685—24no—
24C3×#3963—24no—
25C3×#1438—51nomaximal, Hall
26C23×C22⋊D5C2×C311yescharacteristic
27C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
28C22×C22⋊Dic5C2×C311yescharacteristic, complemented
29C22×#685C2×C312yescomplemented
30C2×#3963C2×C312yescomplemented
31C24×C3×C5—22no—
32C24×C3×C5—22no—
33C24×C3×C5—22no—
34C24×C3×C5—22no—
35C24×C3×C5—22no—
36C24×C3×C5—22no—
37C24×C3×C5C2×C412yes—
38C24×C3×C5D412yes—
39C24×C3×C5D412yes—
40C24×C3×C5C2311yescharacteristic
41C23×C3×D5—21no—
42C23×C3×D5—21no—
43C23×C3×D5—22no—
44C23×C3×D5—22no—
45C23×C3×D5—22no—
46C23×C3×D5—22no—
47C23×C3×D5—22no—
48C23×C3×D5C2×C412yes—
49C23×C3×D5D414yes—
50C22×C3×C4×C5—22no—
51C22×C3×C4×C5—22no—
52C22×C3×C4×C5—22no—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5D414yescomplemented
57C2×C3×C22⋊D5—216no—
58C2×C3×C22⋊D5—216no—
59C2×C3×C22⋊D5—28no—
60C2×C3×C22⋊D5—28no—
61C2×C3×C22⋊D5—28no—
62C22×C3×Dic5—21no—
63C22×C3×Dic5—22no—
64C22×C3×Dic5—21no—
65C22×C3×Dic5—22no—
66C22×C3×Dic5—22no—
67C22×C3×Dic5—22no—
68C22×C3×Dic5—22no—
69C22×C3×Dic5—22no—
70C22×C3×Dic5—22no—
71C22×C3×Dic5C2×C412yes—
72C22×C3×Dic5D414yes—
73C22×C3×Dic5D414yescomplemented
74C3×C5×C22⋊C4—28no—
75C3×C22⋊Dic5—28no—
76C3×#685—216no—
77C23×C3×D4—51no—
78C22×C3×C22⋊C4—52no—
79C22×C3×C22⋊C4—51no—
80C22×C3×C22⋊C4D511yescharacteristic, complemented
81C2×C3×#95—52no—
82C25×C5C22×C311yescharacteristic
83C24×D5C22×C311yescharacteristic
84C23×C4×C5C22×C312yes—
85C22×C22⋊D5—22no—
86C22×C22⋊D5—22no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5C3×C414yescomplemented
90C23×Dic5C22×C312yes—
91C23×Dic5C22×C311yescharacteristic
92C2×C5×C22⋊C4—22no—
93C2×C5×C22⋊C4—24no—
94C2×C22⋊Dic5—22no—
95C2×C22⋊Dic5—24no—
96C2×#685—24no—
97C2×#685—24no—
98C2×#685—24no—
99#3963—24no—
100#1438—51noSylow
101C23×C3×C5—22no—
102C23×C3×C5—22no—
103C23×C3×C5—24no—
104C23×C3×C5—24no—
105C23×C3×C5—22no—
106C23×C3×C5—22no—
107C23×C3×C5—24no—
108C23×C3×C5—24no—
109C23×C3×C5—24no—
110C23×C3×C5—24no—
111C23×C3×C5—22no—
112C23×C3×C5—22no—
113C23×C3×C5—42no—
114C23×C3×C5—42no—
115C23×C3×C5—42no—
116C23×C3×C5—42no—
117C23×C3×C5—42no—
118C23×C3×C5—42no—
119C23×C3×C5—42no—
120C23×C3×C5—42no—
121C23×C3×C5C22⋊C414yescomplemented
122C23×C3×C5C22×C411yescharacteristic
123C23×C3×C5C2×D411yescharacteristic
124C23×C3×C5C2×D412yes—
125C23×C3×C5C2×D411yescharacteristic
126C23×C3×C5C2×D412yes—
127C23×C3×C5C2×D412yes—
128C23×C3×C5C2×D412yes—
129C23×C3×C5#4112yes—
130C23×C3×C5#4112yes—
131C22×C3×D5—22no—
132C22×C3×D5—22no—
133C22×C3×D5—24no—
134C22×C3×D5—24no—
135C22×C3×D5—24no—
136C22×C3×D5—24no—
137C22×C3×D5—24no—
138C22×C3×D5—24no—
139C22×C3×D5—24no—
140C22×C3×D5—24no—
141C22×C3×D5—41no—
142C22×C3×D5—41no—
143C22×C3×D5—42no—
144C22×C3×D5—42no—
145C22×C3×D5—42no—
146C22×C3×D5—42no—
147C22×C3×D5—41no—
148C22×C3×D5—41no—
149C22×C3×D5—42no—
150C22×C3×D5—42no—
151C22×C3×D5C22⋊C414yescomplemented
152C2×C3×C4×C5—24no—
153C2×C3×C4×C5—24no—
154C2×C3×C4×C5—24no—
155C2×C3×C4×C5—42no—
156C2×C3×C4×C5—42no—
157C2×C3×C4×C5—42no—
158C2×C3×C4×C5—42no—
159C3×C22⋊D5—232no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—24no—
163C2×C3×Dic5—24no—
164C2×C3×Dic5—24no—
165C2×C3×Dic5—24no—
166C2×C3×Dic5—24no—
167C2×C3×Dic5—42no—
168C2×C3×Dic5—42no—
169C2×C3×Dic5—42no—
170C2×C3×Dic5—42no—
171C2×C3×Dic5C22⋊C414yescomplemented
172C25×C3—51no—
173C25×C3C2×D511yescharacteristic
174C22×C3×D4—54no—
175C22×C3×D4—104no—
176C22×C3×D4—104no—
177C22×C3×D4—102no—
178C22×C3×D4—102no—
179C23×C3×C4—51no—
180C23×C3×C4—52no—
181C23×C3×C4C2×D512yes—
182C2×C3×C22⋊C4—22no—
183C2×C3×C22⋊C4—24no—
184C2×C3×C22⋊C4—104no—
185C2×C3×C22⋊C4—104no—
186C2×C3×C22⋊C4—104no—
187C2×C3×C22⋊C4—102no—
188C2×C3×C22⋊C4—104no—
189C3×#95—104no—
190C24×C5—22no—
191C24×C5—22no—
192C24×C5—22no—
193C24×C5—22no—
194C24×C5—22no—
195C24×C5—22no—
196C24×C5C2×C3×C412yes—
197C24×C5C3×D412yes—
198C24×C5C3×D412yes—
199C24×C5C23×C311yescharacteristic
200C23×D5—21no—
201C23×D5—22no—
202C23×D5—21no—
203C23×D5—22no—
204C23×D5—22no—
205C23×D5—22no—
206C23×D5—22no—
207C23×D5C2×C3×C412yes—
208C23×D5C3×D414yes—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5C3×D414yescomplemented
216C2×C22⋊D5—216no—
217C2×C22⋊D5—216no—
218C2×C22⋊D5—28no—
219C2×C22⋊D5—28no—
220C2×C22⋊D5—28no—
221C22×Dic5—21no—
222C22×Dic5—22no—
223C22×Dic5—21no—
224C22×Dic5—22no—
225C22×Dic5—22no—
226C22×Dic5—22no—
227C22×Dic5—22no—
228C22×Dic5—22no—
229C22×Dic5—22no—
230C22×Dic5C2×C3×C412yes—
231C22×Dic5C3×D414yes—
232C22×Dic5C3×D414yescomplemented
233C5×C22⋊C4—28no—
234C22⋊Dic5—28no—
235#685—216no—
236C23×D4—51no—
237C22×C22⋊C4—51no—
238C22×C22⋊C4—52no—
239C22×C22⋊C4C3×D511yescharacteristic, complemented
240C2×#95—52no—
241C22×C3×C5—24no—
242C22×C3×C5—24no—
243C22×C3×C5—24no—
244C22×C3×C5—44no—
245C22×C3×C5—44no—
246C22×C3×C5—44no—
247C22×C3×C5—44no—
248C22×C3×C5—44no—
249C22×C3×C5—44no—
250C22×C3×C5C2×C22⋊C411yescharacteristic
251C22×C3×C5C2×C22⋊C411yescharacteristic
252C22×C3×C5C2×C22⋊C411yescharacteristic
253C22×C3×C5C4×D412yes—
254C22×C3×C5C4×D412yes—
255C22×C3×C5#12011yescharacteristic
256C22×C3×C5#12012yes—
257C22×C3×C5#12011yescharacteristic
258C22×C3×C5#12012yes—
259C22×C3×C5#12012yes—
260C22×C3×C5#12112yes—
261C22×C3×C5#12112yes—
262C22×C3×C5#12112yes—
263C22×C3×C5#12112yes—
264C22×C3×C5#12112yes—
265C22×C3×C5#12112yes—
266C22×C3×C5#12312yes—
267C22×C3×C5#12311yescharacteristic
268C22×C3×C5#12311yescharacteristic
269C22×C3×C5#12412yes—
270C22×C3×C5#12712yes—
271C2×C3×D5—24no—
272C2×C3×D5—28no—
273C2×C3×D5—42no—
274C2×C3×D5—42no—
275C2×C3×D5—44no—
276C2×C3×D5—44no—
277C2×C3×D5—44no—
278C2×C3×D5—44no—
279C2×C3×D5—44no—
280C3×C4×C5—44no—
281C3×Dic5—24no—
282C3×Dic5—44no—
283C24×C3—22no—
284C24×C3—22no—
285C24×C3—22no—
286C24×C3—22no—
287C24×C3—22no—
288C24×C3—22no—
289C24×C3—52no—
290C24×C3—54no—
291C24×C3—101no—
292C24×C3—102no—
293C24×C3—102no—
294C24×C3—102no—
295C24×C3—102no—
296C24×C3—102no—
297C24×C3—101no—
298C24×C3C4×D512yes—
299C24×C3D2012yes—
300C24×C3C22⋊D512yes—
301C24×C3C22×D511yescharacteristic
302C2×C3×D4—108no—
303C2×C3×D4—108no—
304C2×C3×D4—1016no—
305C2×C3×D4—1016no—
306C2×C3×D4—108no—
307C22×C3×C4—22no—
308C22×C3×C4—22no—
309C22×C3×C4—22no—
310C22×C3×C4—22no—
311C22×C3×C4—22no—
312C22×C3×C4—22no—
313C22×C3×C4—52no—
314C22×C3×C4—54no—
315C22×C3×C4—54no—
316C22×C3×C4—101no—
317C22×C3×C4—102no—
318C22×C3×C4—101no—
319C22×C3×C4—102no—
320C22×C3×C4—102no—
321C22×C3×C4—102no—
322C22×C3×C4—102no—
323C22×C3×C4—102no—
324C22×C3×C4—102no—
325C22×C3×C4C22⋊D514yescomplemented
326C3×C22⋊C4—28no—
327C3×C22⋊C4—1016no—
328C3×C22⋊C4—108no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—24no—
332C23×C5—24no—
333C23×C5—22no—
334C23×C5—22no—
335C23×C5—24no—
336C23×C5—24no—
337C23×C5—24no—
338C23×C5—24no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—42no—
342C23×C5—42no—
343C23×C5—42no—
344C23×C5—42no—
345C23×C5—42no—
346C23×C5—42no—
347C23×C5—42no—
348C23×C5—42no—
349C23×C5C3×C22⋊C414yescomplemented
350C23×C5C22×C3×C411yescharacteristic
351C23×C5C2×C3×D411yescharacteristic
352C23×C5C2×C3×D412yes—
353C23×C5C2×C3×D412yes—
354C23×C5C2×C3×D412yes—
355C23×C5C2×C3×D411yescharacteristic
356C23×C5C2×C3×D412yes—
357C23×C5C3×#4112yes—
358C23×C5C3×#4112yes—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5—24no—
362C22×D5—24no—
363C22×D5—24no—
364C22×D5—24no—
365C22×D5—24no—
366C22×D5—24no—
367C22×D5—24no—
368C22×D5—24no—
369C22×D5—41no—
370C22×D5—41no—
371C22×D5—42no—
372C22×D5—42no—
373C22×D5—42no—
374C22×D5—42no—
375C22×D5—41no—
376C22×D5—41no—
377C22×D5—42no—
378C22×D5—42no—
379C22×D5C3×C22⋊C414yescomplemented
380C2×C4×C5—24no—
381C2×C4×C5—24no—
382C2×C4×C5—24no—
383C2×C4×C5—42no—
384C2×C4×C5—42no—
385C2×C4×C5—42no—
386C2×C4×C5—42no—
387C22⋊D5—232no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—24no—
391C2×Dic5—24no—
392C2×Dic5—24no—
393C2×Dic5—24no—
394C2×Dic5—24no—
395C2×Dic5—42no—
396C2×Dic5—42no—
397C2×Dic5—42no—
398C2×Dic5—42no—
399C2×Dic5C3×C22⋊C414yescomplemented
400C25—51no—
401C25C2×C3×D511yescharacteristic
402C22×D4—54no—
403C22×D4—104no—
404C22×D4—104no—
405C22×D4—102no—
406C22×D4—102no—
407C23×C4—51no—
408C23×C4—52no—
409C23×C4C2×C3×D512yes—
410C2×C22⋊C4—22no—
411C2×C22⋊C4—24no—
412C2×C22⋊C4—104no—
413C2×C22⋊C4—104no—
414C2×C22⋊C4—104no—
415C2×C22⋊C4—102no—
416C2×C22⋊C4—104no—
417#95—104no—
418C2×C3×C5—44no—
419C2×C3×C5#37911yescharacteristic
420C2×C3×C5#38612yes—
421C2×C3×C5#38611yescharacteristic
422C2×C3×C5#38611yescharacteristic
423C2×C3×C5#39012yes—
424C2×C3×C5#39212yes—
425C2×C3×C5#39212yes—
426C2×C3×C5#39412yes—
427C2×C3×C5#39412yes—
428C3×D5—44no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—24no—
433C23×C3—22no—
434C23×C3—24no—
435C23×C3—22no—
436C23×C3—24no—
437C23×C3—22no—
438C23×C3—24no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—42no—
442C23×C3—42no—
443C23×C3—42no—
444C23×C3—42no—
445C23×C3—42no—
446C23×C3—42no—
447C23×C3—42no—
448C23×C3—42no—
449C23×C3—54no—
450C23×C3—102no—
451C23×C3—104no—
452C23×C3—104no—
453C23×C3—104no—
454C23×C3—104no—
455C23×C3—102no—
456C23×C3—104no—
457C23×C3—104no—
458C23×C3—104no—
459C23×C3—104no—
460C23×C3—201no—
461C23×C3—201no—
462C23×C3—202no—
463C23×C3—202no—
464C23×C3—201no—
465C23×C3—201no—
466C23×C3—202no—
467C23×C3—202no—
468C23×C3—202no—
469C23×C3—202no—
470C23×C3#68514yescomplemented
471C23×C3C2×C4×D511yescharacteristic
472C23×C3C2×D2011yescharacteristic
473C23×C3#70912yes—
474C23×C3D4×D512yes—
475C23×C3D4×D512yes—
476C23×C3D4×D512yes—
477C23×C3#71112yes—
478C23×C3C2×C22⋊D511yescharacteristic
479C23×C3C2×C22⋊D512yes—
480C3×D4—1032no—
481C2×C3×C4—24no—
482C2×C3×C4—24no—
483C2×C3×C4—24no—
484C2×C3×C4—42no—
485C2×C3×C4—42no—
486C2×C3×C4—42no—
487C2×C3×C4—42no—
488C2×C3×C4—54no—
489C2×C3×C4—102no—
490C2×C3×C4—104no—
491C2×C3×C4—102no—
492C2×C3×C4—104no—
493C2×C3×C4—104no—
494C2×C3×C4—104no—
495C2×C3×C4—104no—
496C2×C3×C4—202no—
497C2×C3×C4—202no—
498C2×C3×C4—202no—
499C2×C3×C4—202no—
500C22×C5—24no—
501C22×C5—24no—
502C22×C5—24no—
503C22×C5—44no—
504C22×C5—44no—
505C22×C5—44no—
506C22×C5—44no—
507C22×C5—44no—
508C22×C5—44no—
509C22×C5C2×C3×C22⋊C411yescharacteristic
510C22×C5C2×C3×C22⋊C411yescharacteristic
511C22×C5C2×C3×C22⋊C411yescharacteristic
512C22×C5C3×C4×D412yes—
513C22×C5C3×C4×D412yes—
514C22×C5C3×#12012yes—
515C22×C5C3×#12012yes—
516C22×C5C3×#12011yescharacteristic
517C22×C5C3×#12012yes—
518C22×C5C3×#12011yescharacteristic
519C22×C5C3×#12112yes—
520C22×C5C3×#12112yes—
521C22×C5C3×#12112yes—
522C22×C5C3×#12112yes—
523C22×C5C3×#12112yes—
524C22×C5C3×#12112yes—
525C22×C5C3×#12312yes—
526C22×C5C3×#12311yescharacteristic
527C22×C5C3×#12311yescharacteristic
528C22×C5C3×#12412yes—
529C22×C5C3×#12712yes—
530C2×D5—24no—
531C2×D5—28no—
532C2×D5—42no—
533C2×D5—42no—
534C2×D5—44no—
535C2×D5—44no—
536C2×D5—44no—
537C2×D5—44no—
538C2×D5—44no—
539C4×C5—44no—
540Dic5—24no—
541Dic5—44no—
542C24—22no—
543C24—22no—
544C24—22no—
545C24—22no—
546C24—22no—
547C24—22no—
548C24—52no—
549C24—54no—
550C24—101no—
551C24—102no—
552C24—102no—
553C24—102no—
554C24—102no—
555C24—102no—
556C24—101no—
557C24C3×C4×D512yes—
558C24C3×D2012yes—
559C24C3×C22⋊D512yes—
560C24C22×C3×D511yescharacteristic
561C2×D4—108no—
562C2×D4—108no—
563C2×D4—1016no—
564C2×D4—1016no—
565C2×D4—108no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—52no—
573C22×C4—54no—
574C22×C4—54no—
575C22×C4—101no—
576C22×C4—102no—
577C22×C4—101no—
578C22×C4—102no—
579C22×C4—102no—
580C22×C4—102no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4—102no—
584C22×C4C3×C22⋊D514yescomplemented
585C22⋊C4—28no—
586C22⋊C4—1016no—
587C22⋊C4—108no—
588C3×C5#143811yescharacteristic, complemented, Hall
589C22×C3—24no—
590C22×C3—24no—
591C22×C3—24no—
592C22×C3—44no—
593C22×C3—44no—
594C22×C3—44no—
595C22×C3—44no—
596C22×C3—44no—
597C22×C3—44no—
598C22×C3—104no—
599C22×C3—108no—
600C22×C3—204no—
601C22×C3—202no—
602C22×C3—202no—
603C22×C3—204no—
604C22×C3—204no—
605C22×C3—204no—
606C22×C3—204no—
607C22×C3D5×C22⋊C411yescharacteristic
608C22×C3D5×C22⋊C411yescharacteristic
609C22×C3#402712yes—
610C22×C3#402812yes—
611C22×C3#402811yescharacteristic
612C22×C3#402912yes—
613C22×C3#403012yes—
614C22×C3#403012yes—
615C22×C3#403112yes—
616C22×C3#403211yescharacteristic
617C22×C3C2×#68511yescharacteristic
618C22×C3C4×C22⋊D512yes—
619C22×C3#407511yescharacteristic
620C22×C3#407612yes—
621C22×C3#408312yes—
622C22×C3#408312yes—
623C22×C3#408412yes—
624C22×C3#408512yes—
625C22×C3#408512yes—
626C22×C3#408612yes—
627C22×C3#409911yescharacteristic
628C3×C4—44no—
629C3×C4—104no—
630C3×C4—204no—
631C2×C5—44no—
632C2×C5C3×#37911yescharacteristic
633C2×C5C3×#38612yes—
634C2×C5C3×#38611yescharacteristic
635C2×C5C3×#38611yescharacteristic
636C2×C5C3×#39012yes—
637C2×C5C3×#39212yes—
638C2×C5C3×#39212yes—
639C2×C5C3×#39412yes—
640C2×C5C3×#39412yes—
641D5—44no—
642C23—24no—
643C23—24no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—24no—
648C23—22no—
649C23—24no—
650C23—22no—
651C23—24no—
652C23—22no—
653C23—24no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—54no—
663C23—104no—
664C23—104no—
665C23—104no—
666C23—102no—
667C23—104no—
668C23—104no—
669C23—104no—
670C23—104no—
671C23—102no—
672C23—104no—
673C23—202no—
674C23—202no—
675C23—202no—
676C23—201no—
677C23—201no—
678C23—202no—
679C23—202no—
680C23—201no—
681C23—201no—
682C23—202no—
683C23C3×#68514yescomplemented
684C23C2×C3×C4×D511yescharacteristic
685C23C2×C3×D2011yescharacteristic
686C23C3×#70912yes—
687C23C3×D4×D512yes—
688C23C3×D4×D512yes—
689C23C3×D4×D512yes—
690C23C3×#71112yes—
691C23C2×C3×C22⋊D511yescharacteristic
692C23C2×C3×C22⋊D512yes—
693D4—1032no—
694C2×C4—24no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—54no—
702C2×C4—104no—
703C2×C4—102no—
704C2×C4—104no—
705C2×C4—102no—
706C2×C4—104no—
707C2×C4—104no—
708C2×C4—104no—
709C2×C4—202no—
710C2×C4—202no—
711C2×C4—202no—
712C2×C4—202no—
713C2×C3—44no—
714C2×C3—204no—
715C2×C3#6524411yescharacteristic
716C2×C3#6524512yes—
717C2×C3#6524612yes—
718C2×C3#6524711yescharacteristic
719C2×C3#6524812yes—
720C2×C3#6524912yes—
721C2×C3#6525012yes—
722C2×C3#6550211yescharacteristic
723C2×C3#6551212yes—
724C5C3×#143811yescharacteristic, complemented, Sylow
725C22—24no—
726C22—24no—
727C22—24no—
728C22—44no—
729C22—44no—
730C22—44no—
731C22—44no—
732C22—44no—
733C22—44no—
734C22—104no—
735C22—108no—
736C22—204no—
737C22—202no—
738C22—202no—
739C22—204no—
740C22—204no—
741C22—204no—
742C22—204no—
743C22C3×D5×C22⋊C411yescharacteristic
744C22C3×D5×C22⋊C411yescharacteristic
745C22C3×#402712yes—
746C22C3×#402812yes—
747C22C3×#402811yescharacteristic
748C22C3×#402912yes—
749C22C3×#403012yes—
750C22C3×#403012yes—
751C22C3×#403112yes—
752C22C3×#403211yescharacteristic
753C22C2×C3×#68511yescharacteristic
754C22C3×C4×C22⋊D512yes—
755C22C3×#407511yescharacteristic
756C22C3×#407612yes—
757C22C3×#408312yes—
758C22C3×#408312yes—
759C22C3×#408412yes—
760C22C3×#408512yes—
761C22C3×#408512yes—
762C22C3×#408612yes—
763C22C3×#409911yescharacteristic
764C4—44no—
765C4—104no—
766C4—204no—
767C3#1060234311yescharacteristic, direct product factor, Sylow
768C2—44no—
769C2—204no—
770C2C3×#6524411yescharacteristic
771C2C3×#6524512yes—
772C2C3×#6524612yes—
773C2C3×#6524711yescharacteristic
774C2C3×#6524812yes—
775C2C3×#6524912yes—
776C2C3×#6525012yes—
777C2C3×#6550211yescharacteristic
778C2C3×#6551212yes—
subgroupG/H
centerC24×C3C22×D5
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×C3×C22⋊D5C2
cosocleC24×C5C23×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C3×#1438
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×C22⋊C4C2semidirect
3. C22×C3×C22⋊Dic5C2semidirect
4. C22×C3×#685C2semidirect
5. C2×C3×#3963C2semidirect
6. #10602343C3direct (N × H)
14. C22×C3×C22⋊D5C4semidirect
27. C22×C5×C22⋊C4C2×C3semidirect
28. C22×C22⋊Dic5C2×C3semidirect
29. C22×#685C2×C3semidirect
30. C2×#3963C2×C3semidirect
56. C22×C3×C4×C5D4semidirect
73. C22×C3×Dic5D4semidirect
80. C22×C3×C22⋊C4D5semidirect
89. C22×C22⋊D5C3×C4semidirect
121. C23×C3×C5C22⋊C4semidirect
151. C22×C3×D5C22⋊C4semidirect
171. C2×C3×Dic5C22⋊C4semidirect
215. C22×C4×C5C3×D4semidirect
232. C22×Dic5C3×D4semidirect
239. C22×C22⋊C4C3×D5semidirect
325. C22×C3×C4C22⋊D5semidirect
349. C23×C5C3×C22⋊C4semidirect
379. C22×D5C3×C22⋊C4semidirect
399. C2×Dic5C3×C22⋊C4semidirect
470. C23×C3#685semidirect
584. C22×C4C3×C22⋊D5semidirect
588. C3×C5#1438semidirect
683. C23C3×#685semidirect
724. C5C3×#1438semidirect
767. C3#10602343direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊D52
C22×C3×C5×C22⋊C42
C22×C3×C22⋊Dic52
C22×C3×#6852
C2×C3×#39632
#106023433
C3×#14385