Finite Group Databasebeta

← C3×#10605294 #14321149

Subgroups — C3×#10605294 #14321149

Order 1920.

1872 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic
2C2×C3×#4018C211yesmaximal, characteristic, complemented
3C2×C3×C42×D5C211yesmaximal, characteristic, complemented
4C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
5C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
6C3×#65246C212yesmaximal, complemented
7C3×#65245C212yesmaximal, complemented
8C3×C4×#685C211yesmaximal, characteristic, complemented
9C3×C4×#685C211yesmaximal, characteristic, complemented
10C3×#64954C212yesmaximal, complemented
11C3×#64935C212yesmaximal, complemented
12#10605294C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C22⋊D5C2211yescharacteristic
16C2×C3×#709—24no—
17C2×C3×#709—24no—
18C2×C3×#709C418yescomplemented
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5C2212yes—
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×Dic10C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2212yes—
25C2×C3×C42×C5C2211yescharacteristic
26C2×C3×C42×C5C2211yescharacteristic
27C2×C3×C22⋊Dic5C2212yes—
28C2×C3×#685C2212yes—
29C2×C3×#685C2212yes—
30C2×C3×#685C2212yes—
31C2×C3×#683C2212yes—
32C2×C3×C4×Dic5C2212yes—
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C3×#4018—24no—
36C3×C42×D5—24no—
37C3×C5×#95C2212yes—
38C3×#3963C2212yes—
39C3×#3963C2212yes—
40C3×#3963C2212yes—
41C3×#2297—51nomaximal, Hall
42C22×#709C2×C311yescharacteristic
43C2×#4018C2×C311yescharacteristic, complemented
44C2×C42×D5C2×C311yescharacteristic, complemented
45C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
46C4×C22⋊Dic5C2×C311yescharacteristic, complemented
47#65246C2×C312yescomplemented
48#65245C2×C312yescomplemented
49C4×#685C2×C311yescharacteristic, complemented
50C4×#685C2×C311yescharacteristic, complemented
51#64954C2×C312yescomplemented
52#64935C2×C312yescomplemented
53C24×C3×C5C2311yescharacteristic
54C23×C3×D5C2311yescharacteristic
55C23×C3×D5C2311yescharacteristic
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5C2×C414yescomplemented
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C2×C3×C22⋊D5—22no—
64C2×C3×C22⋊D5—22no—
65C2×C3×C22⋊D5—22no—
66C2×C3×C22⋊D5—22no—
67C2×C3×C22⋊D5C2×C414yes—
68C2×C3×C22⋊D5C2×C414yescomplemented
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2312yes—
72C22×C3×Dic5C2311yescharacteristic
73C3×#709—232no—
74C2×C3×D20—22no—
75C2×C3×D20—22no—
76C2×C3×D20C2×C414yes—
77C2×C3×C4×D5—24no—
78C2×C3×C4×D5—22no—
79C2×C3×C4×D5—22no—
80C2×C3×C4×D5—24no—
81C2×C3×C4×D5—24no—
82C2×C3×C4×D5C2×C414yes—
83C2×C3×C4×D5C2×C414yescomplemented
84C2×C3×C4×D5D414yes—
85C2×C3×C4×D5D414yes—
86C2×C3×Dic10—22no—
87C2×C3×Dic10—22no—
88C2×C3×Dic10C2×C414yescomplemented
89C3×C5×C22⋊C4—24no—
90C3×C42×C5—22no—
91C3×C42×C5—22no—
92C3×C22⋊Dic5—24no—
93C3×#685—24no—
94C3×#685—24no—
95C3×#685—24no—
96C3×#683—24no—
97C3×C4×Dic5—22no—
98C3×C4×Dic5—22no—
99C3×C4×Dic5—24no—
100C22×C3×#41—51no—
101C2×C3×#117—51no—
102C22×C3×C42—51no—
103C3×#391—52no—
104C3×#390—52no—
105C3×#386—52no—
106C3×#386—52no—
107C3×C4×C22⋊C4—51no—
108C3×C4×C22⋊C4—51no—
109C3×C4×C22⋊C4—51no—
110C3×C4×C22⋊C4D511yescharacteristic, complemented
111C23×C4×C5C22×C311yescharacteristic
112C22×C22⋊D5C22×C311yescharacteristic
113C22×C22⋊D5C22×C311yescharacteristic
114C2×#709—24no—
115C2×#709—24no—
116C2×#709C3×C418yescomplemented
117C22×D20C22×C311yescharacteristic
118C22×C4×D5C22×C312yes—
119C22×C4×D5C22×C311yescharacteristic
120C22×C4×D5C22×C311yescharacteristic
121C22×Dic10C22×C311yescharacteristic
122C2×C5×C22⋊C4C22×C312yes—
123C2×C42×C5C22×C311yescharacteristic
124C2×C42×C5C22×C311yescharacteristic
125C2×C22⋊Dic5C22×C312yes—
126C2×#685C22×C312yes—
127C2×#685C22×C312yes—
128C2×#685C22×C312yes—
129C2×#683C22×C312yes—
130C2×C4×Dic5C22×C312yes—
131C2×C4×Dic5C22×C311yescharacteristic
132C2×C4×Dic5C22×C311yescharacteristic
133#4018—24no—
134C42×D5—24no—
135C5×#95C22×C312yes—
136#3963C22×C312yes—
137#3963C22×C312yes—
138#3963C22×C312yes—
139#2297—51noSylow
140C23×C3×C5—21no—
141C23×C3×C5—21no—
142C23×C3×C5—22no—
143C23×C3×C5—22no—
144C23×C3×C5C22×C412yes—
145C23×C3×C5C2411yescharacteristic
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—21no—
149C22×C3×D5—21no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5C22×C412yes—
153C22×C3×D5C22×C412yes—
154C22×C3×D5C2×D412yes—
155C22×C3×D5C2×D412yes—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—28no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5C22×C412yes—
165C2×C3×C4×C5C22×C412yes—
166C2×C3×C4×C5C2×D412yes—
167C2×C3×C4×C5C2×D412yes—
168C2×C3×C4×C5#4114yescomplemented
169C3×C22⋊D5—28no—
170C3×C22⋊D5—28no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—21no—
173C2×C3×Dic5—21no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—22no—
176C2×C3×Dic5—22no—
177C2×C3×Dic5—22no—
178C2×C3×Dic5C22×C412yes—
179C2×C3×Dic5C22×C412yes—
180C2×C3×Dic5C2×D412yes—
181C2×C3×Dic5C2×D412yes—
182C2×C3×Dic5#4114yescomplemented
183C3×D20—28no—
184C3×C4×D5—216no—
185C3×C4×D5—28no—
186C3×C4×D5C22⋊C4116yescomplemented
187C3×Dic10—28no—
188C2×C3×#41—58no—
189C2×C3×#41—104no—
190C2×C3×#41—104no—
191C22×C3×Q8—51no—
192C22×C3×D4—51no—
193C22×C3×D4—51no—
194C22×C3×D4—51no—
195C23×C3×C4—51no—
196C23×C3×C4—51no—
197C23×C3×C4—52no—
198C23×C3×C4C2×D511yescharacteristic
199C3×#117—104no—
200C2×C3×C4⋊C4—52no—
201C2×C3×C22⋊C4—52no—
202C2×C3×C22⋊C4—52no—
203C2×C3×C22⋊C4—52no—
204C2×C3×C22⋊C4—52no—
205C2×C3×C22⋊C4C2×D512yes—
206C2×C3×C42—52no—
207C2×C3×C42—51no—
208C2×C3×C42—51no—
209C2×C3×C42—104no—
210C2×C3×C42C2×D511yescharacteristic
211C2×C3×C42C2×D511yescharacteristic
212C3×#95—52no—
213C3×#95—52no—
214C3×#95—52no—
215C3×#95C2×D512yes—
216C24×C5C23×C311yescharacteristic
217C23×D5C23×C311yescharacteristic
218C23×D5C23×C311yescharacteristic
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5C2×C3×C414yescomplemented
222C22×C4×C5C23×C312yes—
223C22×C4×C5C23×C311yescharacteristic
224C22×C4×C5C23×C312yes—
225C22×C4×C5C23×C311yescharacteristic
226C2×C22⋊D5—22no—
227C2×C22⋊D5—22no—
228C2×C22⋊D5—22no—
229C2×C22⋊D5—22no—
230C2×C22⋊D5C2×C3×C414yes—
231C2×C22⋊D5C2×C3×C414yescomplemented
232C22×Dic5C23×C312yes—
233C22×Dic5C23×C311yescharacteristic
234C22×Dic5C23×C312yes—
235C22×Dic5C23×C311yescharacteristic
236#709—232no—
237C2×D20—22no—
238C2×D20—22no—
239C2×D20C2×C3×C414yes—
240C2×C4×D5—24no—
241C2×C4×D5—22no—
242C2×C4×D5—22no—
243C2×C4×D5—24no—
244C2×C4×D5—24no—
245C2×C4×D5C2×C3×C414yes—
246C2×C4×D5C2×C3×C414yescomplemented
247C2×C4×D5C3×D414yes—
248C2×C4×D5C3×D414yes—
249C2×Dic10—22no—
250C2×Dic10—22no—
251C2×Dic10C2×C3×C414yescomplemented
252C5×C22⋊C4—24no—
253C42×C5—22no—
254C42×C5—22no—
255C22⋊Dic5—24no—
256#685—24no—
257#685—24no—
258#685—24no—
259#683—24no—
260C4×Dic5—22no—
261C4×Dic5—22no—
262C4×Dic5—24no—
263C22×#41—51no—
264C2×#117—51no—
265C22×C42—51no—
266#391—52no—
267#390—52no—
268#386—52no—
269#386—52no—
270C4×C22⋊C4—51no—
271C4×C22⋊C4—51no—
272C4×C22⋊C4—51no—
273C4×C22⋊C4C3×D511yescharacteristic, complemented
274C22×C3×C5—22no—
275C22×C3×C5—22no—
276C22×C3×C5—22no—
277C22×C3×C5—42no—
278C22×C3×C5—42no—
279C22×C3×C5C23×C411yescharacteristic
280C22×C3×C5C22×D411yescharacteristic
281C22×C3×C5C22×D411yescharacteristic
282C22×C3×C5C2×#4112yes—
283C22×C3×C5C2×#4112yes—
284C2×C3×D5—22no—
285C2×C3×D5—22no—
286C2×C3×D5—24no—
287C2×C3×D5—24no—
288C2×C3×D5—22no—
289C2×C3×D5—22no—
290C2×C3×D5—22no—
291C2×C3×D5—42no—
292C2×C3×D5—42no—
293C2×C3×D5C2×C22⋊C414yes—
294C3×C4×C5—22no—
295C3×C4×C5—24no—
296C3×C4×C5—42no—
297C3×C4×C5C2×C22⋊C414yes—
298C3×Dic5—22no—
299C3×Dic5—24no—
300C3×Dic5—42no—
301C3×Dic5C2×C22⋊C414yes—
302C24×C3—51no—
303C24×C3—51no—
304C24×C3C22×D511yescharacteristic
305C3×#41—1032no—
306C2×C3×Q8—54no—
307C2×C3×Q8—102no—
308C2×C3×Q8—102no—
309C2×C3×D4—54no—
310C2×C3×D4—54no—
311C2×C3×D4—54no—
312C2×C3×D4—102no—
313C2×C3×D4—102no—
314C2×C3×D4—102no—
315C2×C3×D4—102no—
316C2×C3×D4—102no—
317C2×C3×D4—102no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—51no—
321C22×C3×C4—54no—
322C22×C3×C4—54no—
323C22×C3×C4—54no—
324C22×C3×C4—51no—
325C22×C3×C4—52no—
326C22×C3×C4—54no—
327C22×C3×C4—52no—
328C22×C3×C4—104no—
329C22×C3×C4—104no—
330C22×C3×C4—104no—
331C22×C3×C4—102no—
332C22×C3×C4—102no—
333C22×C3×C4C4×D514yescomplemented
334C22×C3×C4C22×D512yes—
335C22×C3×C4C22×D511yescharacteristic
336C22×C3×C4C22×D512yes—
337C22×C3×C4C22×D511yescharacteristic
338C3×C4⋊C4—104no—
339C3×C22⋊C4—24no—
340C3×C22⋊C4—104no—
341C3×C22⋊C4—104no—
342C3×C22⋊C4—104no—
343C3×C22⋊C4—104no—
344C3×C42—22no—
345C3×C42—22no—
346C3×C42—104no—
347C3×C42—102no—
348C3×C42—102no—
349C23×C5—21no—
350C23×C5—21no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5C22×C3×C412yes—
354C23×C5C24×C311yescharacteristic
355C22×D5—22no—
356C22×D5—22no—
357C22×D5—21no—
358C22×D5—21no—
359C22×D5—22no—
360C22×D5—22no—
361C22×D5C22×C3×C412yes—
362C22×D5C22×C3×C412yes—
363C22×D5C2×C3×D412yes—
364C22×D5C2×C3×D412yes—
365C2×C4×C5—22no—
366C2×C4×C5—21no—
367C2×C4×C5—21no—
368C2×C4×C5—22no—
369C2×C4×C5—28no—
370C2×C4×C5—22no—
371C2×C4×C5—22no—
372C2×C4×C5—22no—
373C2×C4×C5C22×C3×C412yes—
374C2×C4×C5C22×C3×C412yes—
375C2×C4×C5C2×C3×D412yes—
376C2×C4×C5C2×C3×D412yes—
377C2×C4×C5C3×#4114yescomplemented
378C22⋊D5—28no—
379C22⋊D5—28no—
380C2×Dic5—22no—
381C2×Dic5—21no—
382C2×Dic5—21no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5C22×C3×C412yes—
388C2×Dic5C22×C3×C412yes—
389C2×Dic5C2×C3×D412yes—
390C2×Dic5C2×C3×D412yes—
391C2×Dic5C3×#4114yescomplemented
392D20—28no—
393C4×D5—216no—
394C4×D5—28no—
395C4×D5C3×C22⋊C4116yescomplemented
396Dic10—28no—
397C2×#41—58no—
398C2×#41—104no—
399C2×#41—104no—
400C22×Q8—51no—
401C22×D4—51no—
402C22×D4—51no—
403C22×D4—51no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—52no—
407C23×C4C2×C3×D511yescharacteristic
408#117—104no—
409C2×C4⋊C4—52no—
410C2×C22⋊C4—52no—
411C2×C22⋊C4—52no—
412C2×C22⋊C4—52no—
413C2×C22⋊C4—52no—
414C2×C22⋊C4C2×C3×D512yes—
415C2×C42—51no—
416C2×C42—51no—
417C2×C42—52no—
418C2×C42—104no—
419C2×C42C2×C3×D511yescharacteristic
420C2×C42C2×C3×D511yescharacteristic
421#95—52no—
422#95—52no—
423#95—52no—
424#95C2×C3×D512yes—
425C2×C3×C5—42no—
426C2×C3×C5C22×C22⋊C411yescharacteristic
427C2×C3×C5C4×#4111yescharacteristic
428C2×C3×C5C4×#4111yescharacteristic
429C2×C3×C5#52512yes—
430C2×C3×C5#53212yes—
431C3×D5—24no—
432C3×D5—42no—
433C23×C3—22no—
434C23×C3—21no—
435C23×C3—21no—
436C23×C3—22no—
437C23×C3—52no—
438C23×C3—52no—
439C23×C3—52no—
440C23×C3—52no—
441C23×C3—102no—
442C23×C3—102no—
443C23×C3—102no—
444C23×C3—101no—
445C23×C3—101no—
446C23×C3—102no—
447C23×C3C2×C4×D512yes—
448C23×C3C23×D511yescharacteristic
449C3×Q8—108no—
450C3×D4—108no—
451C3×D4—108no—
452C3×D4—108no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—28no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—22no—
461C2×C3×C4—52no—
462C2×C3×C4—52no—
463C2×C3×C4—52no—
464C2×C3×C4—516no—
465C2×C3×C4—52no—
466C2×C3×C4—54no—
467C2×C3×C4—1016no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—101no—
471C2×C3×C4—101no—
472C2×C3×C4—108no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4C2×C4×D512yes—
477C2×C3×C4C2×C4×D512yes—
478C2×C3×C4#70914yescomplemented
479C2×C3×C4D4×D512yes—
480C2×C3×C4D4×D512yes—
481C22×C5—22no—
482C22×C5—22no—
483C22×C5—22no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5C23×C3×C411yescharacteristic
487C22×C5C22×C3×D411yescharacteristic
488C22×C5C22×C3×D411yescharacteristic
489C22×C5C2×C3×#4112yes—
490C22×C5C2×C3×#4112yes—
491C2×D5—22no—
492C2×D5—22no—
493C2×D5—24no—
494C2×D5—24no—
495C2×D5—22no—
496C2×D5—22no—
497C2×D5—22no—
498C2×D5—42no—
499C2×D5—42no—
500C2×D5C2×C3×C22⋊C414yes—
501C4×C5—22no—
502C4×C5—24no—
503C4×C5—42no—
504C4×C5C2×C3×C22⋊C414yes—
505Dic5—22no—
506Dic5—24no—
507Dic5—42no—
508Dic5C2×C3×C22⋊C414yes—
509C24—51no—
510C24—51no—
511C24C22×C3×D511yescharacteristic
512#41—1032no—
513C2×Q8—54no—
514C2×Q8—102no—
515C2×Q8—102no—
516C2×D4—54no—
517C2×D4—54no—
518C2×D4—54no—
519C2×D4—102no—
520C2×D4—102no—
521C2×D4—102no—
522C2×D4—102no—
523C2×D4—102no—
524C2×D4—102no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—51no—
528C22×C4—54no—
529C22×C4—54no—
530C22×C4—54no—
531C22×C4—51no—
532C22×C4—52no—
533C22×C4—54no—
534C22×C4—52no—
535C22×C4—104no—
536C22×C4—104no—
537C22×C4—104no—
538C22×C4—102no—
539C22×C4—102no—
540C22×C4C3×C4×D514yescomplemented
541C22×C4C22×C3×D512yes—
542C22×C4C22×C3×D511yescharacteristic
543C22×C4C22×C3×D512yes—
544C22×C4C22×C3×D511yescharacteristic
545C4⋊C4—104no—
546C22⋊C4—24no—
547C22⋊C4—104no—
548C22⋊C4—104no—
549C22⋊C4—104no—
550C22⋊C4—104no—
551C42—22no—
552C42—22no—
553C42—104no—
554C42—102no—
555C42—102no—
556C3×C5#229711yescharacteristic, complemented, Hall
557C22×C3—22no—
558C22×C3—22no—
559C22×C3—22no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—54no—
563C22×C3—102no—
564C22×C3—102no—
565C22×C3—104no—
566C22×C3—104no—
567C22×C3—102no—
568C22×C3—102no—
569C22×C3—102no—
570C22×C3—202no—
571C22×C3—202no—
572C22×C3C22×C4×D511yescharacteristic
573C22×C3C2×#70912yes—
574C22×C3C2×D4×D511yescharacteristic
575C22×C3C2×D4×D511yescharacteristic
576C22×C3D5×#4112yes—
577C3×C4—22no—
578C3×C4—24no—
579C3×C4—42no—
580C3×C4—54no—
581C3×C4—102no—
582C3×C4—104no—
583C3×C4—202no—
584C3×C4D5×C22⋊C414yes—
585C2×C5—42no—
586C2×C5C22×C3×C22⋊C411yescharacteristic
587C2×C5C3×C4×#4111yescharacteristic
588C2×C5C3×C4×#4111yescharacteristic
589C2×C5C3×#52512yes—
590C2×C5C3×#53212yes—
591D5—24no—
592D5—42no—
593C23—22no—
594C23—21no—
595C23—21no—
596C23—22no—
597C23—52no—
598C23—52no—
599C23—52no—
600C23—52no—
601C23—102no—
602C23—102no—
603C23—102no—
604C23—101no—
605C23—101no—
606C23—102no—
607C23C2×C3×C4×D512yes—
608C23C23×C3×D511yescharacteristic
609Q8—108no—
610D4—108no—
611D4—108no—
612D4—108no—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—28no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—52no—
622C2×C4—52no—
623C2×C4—52no—
624C2×C4—516no—
625C2×C4—52no—
626C2×C4—54no—
627C2×C4—1016no—
628C2×C4—102no—
629C2×C4—102no—
630C2×C4—101no—
631C2×C4—101no—
632C2×C4—108no—
633C2×C4—102no—
634C2×C4—102no—
635C2×C4—102no—
636C2×C4C2×C3×C4×D512yes—
637C2×C4C2×C3×C4×D512yes—
638C2×C4C3×#70914yescomplemented
639C2×C4C3×D4×D512yes—
640C2×C4C3×D4×D512yes—
641C2×C3—42no—
642C2×C3—104no—
643C2×C3—202no—
644C2×C3C4×#70911yescharacteristic
645C2×C3C2×D5×C22⋊C411yescharacteristic
646C2×C3#6585611yescharacteristic
647C2×C3#6588112yes—
648C2×C3#6588212yes—
649C5C3×#229711yescharacteristic, complemented, Sylow
650C22—22no—
651C22—22no—
652C22—22no—
653C22—42no—
654C22—42no—
655C22—54no—
656C22—102no—
657C22—104no—
658C22—104no—
659C22—102no—
660C22—102no—
661C22—102no—
662C22—102no—
663C22—202no—
664C22—202no—
665C22C22×C3×C4×D511yescharacteristic
666C22C2×C3×#70912yes—
667C22C2×C3×D4×D511yescharacteristic
668C22C2×C3×D4×D511yescharacteristic
669C22C3×D5×#4112yes—
670C4—24no—
671C4—22no—
672C4—42no—
673C4—54no—
674C4—104no—
675C4—102no—
676C4—202no—
677C4C3×D5×C22⋊C414yes—
678C3#1060529411yescharacteristic, direct product factor, Sylow
679C2—42no—
680C2—104no—
681C2—202no—
682C2C3×C4×#70911yescharacteristic
683C2C2×C3×D5×C22⋊C411yescharacteristic
684C2C3×#6585611yescharacteristic
685C2C3×#6588112yes—
686C2C3×#6588212yes—
subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC22×C3×#709C2
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2297
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4018C2semidirect
3. C2×C3×C42×D5C2semidirect
4. C3×C4×C5×C22⋊C4C2semidirect
5. C3×C4×C22⋊Dic5C2semidirect
6. C3×#65246C2semidirect
7. C3×#65245C2semidirect
8. C3×C4×#685C2semidirect
9. C3×C4×#685C2semidirect
10. C3×#64954C2semidirect
11. C3×#64935C2semidirect
12. #10605294C3direct (N × H)
18. C2×C3×#709C4semidirect
43. C2×#4018C2×C3semidirect
44. C2×C42×D5C2×C3semidirect
45. C4×C5×C22⋊C4C2×C3semidirect
46. C4×C22⋊Dic5C2×C3semidirect
47. #65246C2×C3semidirect
48. #65245C2×C3semidirect
49. C4×#685C2×C3semidirect
50. C4×#685C2×C3semidirect
51. #64954C2×C3semidirect
52. #64935C2×C3semidirect
58. C22×C3×C4×C5C2×C4semidirect
68. C2×C3×C22⋊D5C2×C4semidirect
83. C2×C3×C4×D5C2×C4semidirect
88. C2×C3×Dic10C2×C4semidirect
110. C3×C4×C22⋊C4D5semidirect
116. C2×#709C3×C4semidirect
168. C2×C3×C4×C5#41semidirect
182. C2×C3×Dic5#41semidirect
186. C3×C4×D5C22⋊C4semidirect
221. C22×C4×C5C2×C3×C4semidirect
231. C2×C22⋊D5C2×C3×C4semidirect
246. C2×C4×D5C2×C3×C4semidirect
251. C2×Dic10C2×C3×C4semidirect
273. C4×C22⋊C4C3×D5semidirect
333. C22×C3×C4C4×D5semidirect
377. C2×C4×C5C3×#41semidirect
391. C2×Dic5C3×#41semidirect
395. C4×D5C3×C22⋊C4semidirect
478. C2×C3×C4#709semidirect
540. C22×C4C3×C4×D5semidirect
556. C3×C5#2297semidirect
638. C2×C4C3×#709semidirect
649. C5C3×#2297semidirect
678. C3#10605294direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×C3×#40182
C2×C3×C42×D52
C3×C4×C5×C22⋊C42
C3×C4×C22⋊Dic52
C3×#652462
C3×#652452
C3×C4×#6852
C3×#649542
C3×#649352
#106052943
C3×#22975