Finite Group Databasebeta

← C2×C3×#65841 #14482680

Subgroups — C2×C3×#65841 #14482680

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C212yesmaximal, complemented
2C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#4076C211yesmaximal, characteristic, complemented
4C2×C3×#4075C212yesmaximal, complemented
5C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
6C2×C3×#4042C212yesmaximal, complemented
7C3×#65841C2116yesmaximal, direct product factor
8C2×C3×#4041C211yesmaximal, characteristic, complemented
9C2×C3×#4040C212yesmaximal, complemented
10C2×C3×#4039C211yesmaximal, characteristic, complemented
11C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
12C2×C3×#4034C211yesmaximal, characteristic, complemented
13C2×#65841C311yesmaximal, characteristic, direct product factor, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2212yes—
16C22×C3×C22⋊D5C2212yes—
17C22×C3×C22⋊D5C2211yescharacteristic
18C2×C3×#709—216no—
19C2×C3×#709C22116yescomplemented
20C22×C3×D20C2211yescharacteristic
21C22×C3×D20C2212yes—
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2212yes—
24C22×C3×C4×D5C2212yes—
25C22×C3×Dic10C2212yes—
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×C5×C4⋊C4C2212yes—
29C2×C3×C5×C4⋊C4C2218yescomplemented
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C3×#4076C2218yescomplemented
32C3×#4075C22116yescomplemented
33C3×C4×C22⋊D5C2218yescomplemented
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2212yes—
36C2×C3×#685C2212yes—
37C2×C3×#685C2212yes—
38C2×C3×C4⋊Dic5C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2212yes—
41C2×C3×#683C2212yes—
42C2×C3×C4×Dic5C2211yescharacteristic
43C3×#4042C22116yescomplemented
44C3×#4041C2218yescomplemented
45C3×#4040C22116yescomplemented
46C3×#4039C2218yescomplemented
47C3×D5×C4⋊C4C2218yescomplemented
48C3×#4034C2218yescomplemented
49C2×C3×#547—51nomaximal, Hall
50C22×#709C2×C312yescomplemented
51C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
52C2×#4076C2×C311yescharacteristic, complemented
53C2×#4075C2×C312yescomplemented
54C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
55C2×#4042C2×C312yescomplemented
56#65841C2×C3116yesdirect product factor
57C2×#4041C2×C311yescharacteristic, complemented
58C2×#4040C2×C312yescomplemented
59C2×#4039C2×C311yescharacteristic, complemented
60C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
61C2×#4034C2×C311yescharacteristic, complemented
62C24×C3×C5C2311yescharacteristic
63C23×C3×D5C2312yes—
64C23×C3×D5C2311yescharacteristic
65C22×C3×C4×C5—28no—
66C22×C3×C4×C5—24no—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2318yes—
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2314yes—
72C22×C3×C4×C5C2311yescharacteristic
73C2×C3×C22⋊D5—28no—
74C2×C3×C22⋊D5D418yescomplemented
75C2×C3×C22⋊D5C2318yes—
76C2×C3×C22⋊D5C2314yes—
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2312yes—
80C22×C3×Dic5C2311yescharacteristic
81C3×#709—264no—
82C2×C3×D20—28no—
83C2×C3×D20—24no—
84C2×C3×D20C2318yes—
85C2×C3×D20C2314yes—
86C2×C3×C4×D5—28no—
87C2×C3×C4×D5—24no—
88C2×C3×C4×D5—28no—
89C2×C3×C4×D5C2318yes—
90C2×C3×C4×D5C2318yes—
91C2×C3×C4×D5C2314yes—
92C2×C3×Dic10—28no—
93C2×C3×Dic10C2318yes—
94C3×C5×C4⋊C4C2314yes—
95C3×C5×C4⋊C4C2314yes—
96C3×C5×C4⋊C4C2318yes—
97C3×C22⋊Dic5C2314yes—
98C3×#685C2318yes—
99C3×#685C2314yes—
100C3×#685C2318yes—
101C3×#685C2318yes—
102C3×C4⋊Dic5C2314yes—
103C3×#683C2318yes—
104C3×#683C2318yes—
105C3×#683C2314yes—
106C3×C4×Dic5C2314yes—
107C22×C3×#41—52no—
108C3×#547—516no—
109C2×C3×C4⋊Q8—51no—
110C2×C3×#123—52no—
111C2×C3×#123—52no—
112C2×C3×C22⋊Q8—52no—
113C2×C3×#121—51no—
114C2×C3×#121—51no—
115C2×C3×C4×D4—51no—
116C2×C3×C4×D4—51no—
117C22×C3×C4⋊C4—51no—
118C22×C3×C4⋊C4D511yescharacteristic, complemented
119C23×C4×C5C22×C311yescharacteristic
120C23×C4×C5C22×C312yes—
121C22×C22⋊D5C22×C312yes—
122C22×C22⋊D5C22×C311yescharacteristic
123C2×#709—216no—
124C2×#709C22×C3116yescomplemented
125C22×D20C22×C311yescharacteristic
126C22×D20C22×C312yes—
127C22×C4×D5C22×C312yes—
128C22×C4×D5C22×C311yescharacteristic
129C22×C4×D5C22×C312yes—
130C22×Dic10C22×C312yes—
131C2×C5×C4⋊C4C22×C311yescharacteristic
132C2×C5×C4⋊C4C22×C311yescharacteristic
133C2×C5×C4⋊C4C22×C312yes—
134C2×C5×C4⋊C4C22×C318yescomplemented
135C2×C22⋊Dic5C22×C311yescharacteristic
136#4076C22×C318yescomplemented
137#4075C22×C3116yescomplemented
138C4×C22⋊D5C22×C318yescomplemented
139C2×#685C22×C312yes—
140C2×#685C22×C311yescharacteristic
141C2×#685C22×C312yes—
142C2×#685C22×C312yes—
143C2×C4⋊Dic5C22×C311yescharacteristic
144C2×#683C22×C312yes—
145C2×#683C22×C312yes—
146C2×#683C22×C311yescharacteristic
147C2×C4×Dic5C22×C311yescharacteristic
148#4042C22×C3116yescomplemented
149#4041C22×C318yescomplemented
150#4040C22×C3116yescomplemented
151#4039C22×C318yescomplemented
152D5×C4⋊C4C22×C318yescomplemented
153#4034C22×C318yescomplemented
154C2×#547—51noSylow
155C23×C3×C5—22no—
156C23×C3×C5—22no—
157C23×C3×C5C2×D414yes—
158C23×C3×C5C2412yes—
159C23×C3×C5C2411yescharacteristic
160C22×C3×D5—22no—
161C22×C3×D5—22no—
162C22×C3×D5—24no—
163C22×C3×D5—24no—
164C22×C3×D5—24no—
165C22×C3×D5C2×D414yes—
166C22×C3×D5C2414yes—
167C22×C3×D5C2412yes—
168C2×C3×C4×C5—24no—
169C2×C3×C4×C5—24no—
170C2×C3×C4×C5—216no—
171C2×C3×C4×C5—22no—
172C2×C3×C4×C5—28no—
173C2×C3×C4×C5#4114yescomplemented
174C2×C3×C4×C5C2412yes—
175C2×C3×C4×C5C2414yes—
176C2×C3×C4×C5C2414yes—
177C2×C3×C4×C5C2412yes—
178C3×C22⋊D5—216no—
179C3×C22⋊D5C2×D4116yescomplemented
180C2×C3×Dic5—24no—
181C2×C3×Dic5—22no—
182C2×C3×Dic5—22no—
183C2×C3×Dic5C2×D414yes—
184C2×C3×Dic5C2412yes—
185C2×C3×Dic5C2412yes—
186C2×C3×Dic5C2414yes—
187C2×C3×Dic5C2412yes—
188C3×D20—216no—
189C3×D20—28no—
190C3×C4×D5—216no—
191C3×C4×D5—28no—
192C3×C4×D5—216no—
193C3×Dic10—216no—
194C2×C3×#41—516no—
195C2×C3×#41—1016no—
196C22×C3×Q8—52no—
197C22×C3×D4—51no—
198C22×C3×D4—52no—
199C22×C3×D4—52no—
200C22×C3×D4—51no—
201C23×C3×C4—52no—
202C23×C3×C4—52no—
203C23×C3×C4—51no—
204C23×C3×C4C2×D512yes—
205C23×C3×C4C2×D511yescharacteristic
206C3×C4⋊Q8—58no—
207C3×#123—516no—
208C3×#123—516no—
209C3×C22⋊Q8—516no—
210C3×#121—58no—
211C3×#121—58no—
212C3×C4×D4—58no—
213C3×C4×D4—58no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C4⋊C4—52no—
216C2×C3×C4⋊C4—51no—
217C2×C3×C4⋊C4—52no—
218C2×C3×C4⋊C4—58no—
219C2×C3×C4⋊C4C2×D511yescharacteristic
220C2×C3×C4⋊C4C2×D511yescharacteristic
221C2×C3×C4⋊C4C2×D512yes—
222C2×C3×C4⋊C4C2×D518yescomplemented
223C2×C3×C22⋊C4—51no—
224C2×C3×C22⋊C4—51no—
225C2×C3×C22⋊C4—52no—
226C2×C3×C22⋊C4—52no—
227C2×C3×C22⋊C4—52no—
228C2×C3×C42—51no—
229C24×C5C23×C311yescharacteristic
230C23×D5C23×C312yes—
231C23×D5C23×C311yescharacteristic
232C22×C4×C5—28no—
233C22×C4×C5—24no—
234C22×C4×C5C23×C312yes—
235C22×C4×C5C23×C312yes—
236C22×C4×C5C23×C311yescharacteristic
237C22×C4×C5C23×C318yes—
238C22×C4×C5C23×C314yes—
239C22×C4×C5C23×C311yescharacteristic
240C2×C22⋊D5—28no—
241C2×C22⋊D5C3×D418yescomplemented
242C2×C22⋊D5C23×C318yes—
243C2×C22⋊D5C23×C314yes—
244C22×Dic5C23×C311yescharacteristic
245C22×Dic5C23×C311yescharacteristic
246C22×Dic5C23×C312yes—
247C22×Dic5C23×C311yescharacteristic
248#709—264no—
249C2×D20—28no—
250C2×D20—24no—
251C2×D20C23×C318yes—
252C2×D20C23×C314yes—
253C2×C4×D5—28no—
254C2×C4×D5—24no—
255C2×C4×D5—28no—
256C2×C4×D5C23×C318yes—
257C2×C4×D5C23×C318yes—
258C2×C4×D5C23×C314yes—
259C2×Dic10—28no—
260C2×Dic10C23×C318yes—
261C5×C4⋊C4C23×C314yes—
262C5×C4⋊C4C23×C314yes—
263C5×C4⋊C4C23×C318yes—
264C22⋊Dic5C23×C314yes—
265#685C23×C318yes—
266#685C23×C314yes—
267#685C23×C318yes—
268#685C23×C318yes—
269C4⋊Dic5C23×C314yes—
270#683C23×C318yes—
271#683C23×C318yes—
272#683C23×C314yes—
273C4×Dic5C23×C314yes—
274C22×#41—52no—
275#547—516no—
276C2×C4⋊Q8—51no—
277C2×#123—52no—
278C2×#123—52no—
279C2×C22⋊Q8—52no—
280C2×#121—51no—
281C2×#121—51no—
282C2×C4×D4—51no—
283C2×C4×D4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4C3×D511yescharacteristic, complemented
286C22×C3×C5—28no—
287C22×C3×C5—22no—
288C22×C3×C5—22no—
289C22×C3×C5C22×D414yes—
290C22×C3×C5C22×D412yes—
291C22×C3×C5C2×#4112yes—
292C22×C3×C52−1+412yes—
293C22×C3×C5C2511yescharacteristic
294C2×C3×D5—28no—
295C2×C3×D5—22no—
296C2×C3×D5—22no—
297C2×C3×D5—24no—
298C2×C3×D5—24no—
299C2×C3×D5—24no—
300C2×C3×D5—48no—
301C2×C3×D5C22×D414yes—
302C3×C4×C5—24no—
303C3×C4×C5—24no—
304C3×C4×C5—22no—
305C3×C4×C5C2×#4114yescomplemented
306C3×Dic5—24no—
307C3×Dic5—22no—
308C3×Dic5—22no—
309C3×Dic5C22×D414yes—
310C24×C3—51no—
311C24×C3—52no—
312C24×C3C22×D511yescharacteristic
313C3×#41—1064no—
314C2×C3×Q8—58no—
315C2×C3×Q8—108no—
316C2×C3×D4—58no—
317C2×C3×D4—54no—
318C2×C3×D4—58no—
319C2×C3×D4—54no—
320C2×C3×D4—58no—
321C2×C3×D4—108no—
322C2×C3×D4—108no—
323C2×C3×D4—104no—
324C22×C3×C4—28no—
325C22×C3×C4—24no—
326C22×C3×C4—51no—
327C22×C3×C4—51no—
328C22×C3×C4—51no—
329C22×C3×C4—52no—
330C22×C3×C4—54no—
331C22×C3×C4—58no—
332C22×C3×C4—58no—
333C22×C3×C4—108no—
334C22×C3×C4—108no—
335C22×C3×C4—104no—
336C22×C3×C4C22×D514yes—
337C22×C3×C4C22×D518yes—
338C22×C3×C4C22×D511yescharacteristic
339C22×C3×C4C22×D512yes—
340C22×C3×C4C22×D512yes—
341C22×C3×C4C22×D511yescharacteristic
342C3×C4⋊C4—58no—
343C3×C4⋊C4—54no—
344C3×C4⋊C4—58no—
345C3×C4⋊C4—54no—
346C3×C4⋊C4C22×D514yes—
347C3×C4⋊C4C22×D514yes—
348C3×C4⋊C4C22×D518yes—
349C3×C22⋊C4—54no—
350C3×C22⋊C4—54no—
351C3×C22⋊C4—58no—
352C3×C22⋊C4—58no—
353C3×C22⋊C4—58no—
354C3×C42—54no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5C2×C3×D414yes—
358C23×C5C24×C312yes—
359C23×C5C24×C311yescharacteristic
360C22×D5—22no—
361C22×D5—22no—
362C22×D5—24no—
363C22×D5—24no—
364C22×D5—24no—
365C22×D5C2×C3×D414yes—
366C22×D5C24×C314yes—
367C22×D5C24×C312yes—
368C2×C4×C5—24no—
369C2×C4×C5—24no—
370C2×C4×C5—216no—
371C2×C4×C5—22no—
372C2×C4×C5—28no—
373C2×C4×C5C3×#4114yescomplemented
374C2×C4×C5C24×C312yes—
375C2×C4×C5C24×C314yes—
376C2×C4×C5C24×C314yes—
377C2×C4×C5C24×C312yes—
378C22⋊D5—216no—
379C22⋊D5C2×C3×D4116yescomplemented
380C2×Dic5—24no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5C2×C3×D414yes—
384C2×Dic5C24×C312yes—
385C2×Dic5C24×C312yes—
386C2×Dic5C24×C314yes—
387C2×Dic5C24×C312yes—
388D20—216no—
389D20—28no—
390C4×D5—216no—
391C4×D5—28no—
392C4×D5—216no—
393Dic10—216no—
394C2×#41—516no—
395C2×#41—1016no—
396C22×Q8—52no—
397C22×D4—51no—
398C22×D4—52no—
399C22×D4—51no—
400C22×D4—52no—
401C23×C4—51no—
402C23×C4—52no—
403C23×C4—52no—
404C23×C4C2×C3×D511yescharacteristic
405C23×C4C2×C3×D512yes—
406C4⋊Q8—58no—
407#123—516no—
408#123—516no—
409C22⋊Q8—516no—
410#121—58no—
411#121—58no—
412C4×D4—58no—
413C4×D4—58no—
414C2×C4⋊C4—51no—
415C2×C4⋊C4—52no—
416C2×C4⋊C4—51no—
417C2×C4⋊C4—52no—
418C2×C4⋊C4—58no—
419C2×C4⋊C4C2×C3×D511yescharacteristic
420C2×C4⋊C4C2×C3×D511yescharacteristic
421C2×C4⋊C4C2×C3×D512yes—
422C2×C4⋊C4C2×C3×D518yescomplemented
423C2×C22⋊C4—51no—
424C2×C22⋊C4—51no—
425C2×C22⋊C4—52no—
426C2×C22⋊C4—52no—
427C2×C22⋊C4—52no—
428C2×C42—51no—
429C2×C3×C5—24no—
430C2×C3×C5#54714yescomplemented
431C2×C3×C5C23×D411yescharacteristic
432C2×C3×C5C22×#4111yescharacteristic
433C2×C3×C5C2×2−1+411yescharacteristic
434C3×D5—24no—
435C3×D5—44no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—54no—
439C23×C3—52no—
440C23×C3—54no—
441C23×C3—102no—
442C23×C3—102no—
443C23×C3—104no—
444C23×C3—104no—
445C23×C3—104no—
446C23×C3D4×D514yes—
447C23×C3C23×D512yes—
448C23×C3C23×D511yescharacteristic
449C3×Q8—1016no—
450C3×D4—516no—
451C3×D4—1016no—
452C3×D4—1016no—
453C3×D4—108no—
454C2×C3×C4—22no—
455C2×C3×C4—24no—
456C2×C3×C4—24no—
457C2×C3×C4—216no—
458C2×C3×C4—28no—
459C2×C3×C4—54no—
460C2×C3×C4—52no—
461C2×C3×C4—52no—
462C2×C3×C4—52no—
463C2×C3×C4—54no—
464C2×C3×C4—1016no—
465C2×C3×C4—1016no—
466C2×C3×C4—102no—
467C2×C3×C4—104no—
468C2×C3×C4—102no—
469C2×C3×C4—108no—
470C2×C3×C4#70914yescomplemented
471C2×C3×C4C23×D512yes—
472C2×C3×C4C23×D514yes—
473C2×C3×C4C23×D514yes—
474C2×C3×C4C23×D512yes—
475C22×C5—22no—
476C22×C5—22no—
477C22×C5—28no—
478C22×C5C22×C3×D414yes—
479C22×C5C22×C3×D412yes—
480C22×C5C2×C3×#4112yes—
481C22×C5C3×2−1+412yes—
482C22×C5C25×C311yescharacteristic
483C2×D5—22no—
484C2×D5—22no—
485C2×D5—28no—
486C2×D5—24no—
487C2×D5—24no—
488C2×D5—24no—
489C2×D5—48no—
490C2×D5C22×C3×D414yes—
491C4×C5—24no—
492C4×C5—24no—
493C4×C5—22no—
494C4×C5C2×C3×#4114yescomplemented
495Dic5—24no—
496Dic5—22no—
497Dic5—22no—
498Dic5C22×C3×D414yes—
499C24—51no—
500C24—52no—
501C24C22×C3×D511yescharacteristic
502#41—1064no—
503C2×Q8—58no—
504C2×Q8—108no—
505C2×D4—58no—
506C2×D4—54no—
507C2×D4—58no—
508C2×D4—54no—
509C2×D4—58no—
510C2×D4—108no—
511C2×D4—108no—
512C2×D4—104no—
513C22×C4—28no—
514C22×C4—24no—
515C22×C4—51no—
516C22×C4—51no—
517C22×C4—51no—
518C22×C4—52no—
519C22×C4—54no—
520C22×C4—58no—
521C22×C4—58no—
522C22×C4—108no—
523C22×C4—108no—
524C22×C4—104no—
525C22×C4C22×C3×D511yescharacteristic
526C22×C4C22×C3×D512yes—
527C22×C4C22×C3×D512yes—
528C22×C4C22×C3×D514yes—
529C22×C4C22×C3×D518yes—
530C22×C4C22×C3×D511yescharacteristic
531C4⋊C4—54no—
532C4⋊C4—58no—
533C4⋊C4—54no—
534C4⋊C4—58no—
535C4⋊C4C22×C3×D514yes—
536C4⋊C4C22×C3×D514yes—
537C4⋊C4C22×C3×D518yes—
538C22⋊C4—54no—
539C22⋊C4—54no—
540C22⋊C4—58no—
541C22⋊C4—58no—
542C22⋊C4—58no—
543C42—54no—
544C3×C5C2×#54711yescharacteristic, complemented, Hall
545C22×C3—28no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—54no—
549C22×C3—108no—
550C22×C3—102no—
551C22×C3—102no—
552C22×C3—104no—
553C22×C3—104no—
554C22×C3—104no—
555C22×C3—208no—
556C22×C3C2×#70912yes—
557C22×C3C2×D4×D514yes—
558C22×C3C2×D4×D512yes—
559C22×C3#414712yes—
560C22×C3C24×D511yescharacteristic
561C3×C4—22no—
562C3×C4—24no—
563C3×C4—24no—
564C3×C4—54no—
565C3×C4—102no—
566C3×C4—104no—
567C3×C4—102no—
568C3×C4C2×#70914yescomplemented
569C2×C5—24no—
570C2×C5C3×#54714yescomplemented
571C2×C5C23×C3×D411yescharacteristic
572C2×C5C22×C3×#4111yescharacteristic
573C2×C5C2×C3×2−1+411yescharacteristic
574D5—24no—
575D5—44no—
576C23—22no—
577C23—22no—
578C23—54no—
579C23—52no—
580C23—54no—
581C23—102no—
582C23—102no—
583C23—104no—
584C23—104no—
585C23—104no—
586C23C3×D4×D514yes—
587C23C23×C3×D512yes—
588C23C23×C3×D511yescharacteristic
589Q8—1016no—
590D4—516no—
591D4—1016no—
592D4—1016no—
593D4—108no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—216no—
598C2×C4—28no—
599C2×C4—54no—
600C2×C4—52no—
601C2×C4—52no—
602C2×C4—52no—
603C2×C4—54no—
604C2×C4—1016no—
605C2×C4—1016no—
606C2×C4—102no—
607C2×C4—104no—
608C2×C4—102no—
609C2×C4—108no—
610C2×C4C3×#70914yescomplemented
611C2×C4C23×C3×D512yes—
612C2×C4C23×C3×D514yes—
613C2×C4C23×C3×D514yes—
614C2×C4C23×C3×D512yes—
615C2×C3—24no—
616C2×C3—104no—
617C2×C3—204no—
618C2×C3#6584114yesdirect product factor
619C2×C3C22×#70911yescharacteristic
620C2×C3C22×D4×D511yescharacteristic
621C2×C3C2×#414711yescharacteristic
622C5C2×C3×#54711yescharacteristic, complemented, Sylow
623C22—22no—
624C22—22no—
625C22—28no—
626C22—54no—
627C22—102no—
628C22—102no—
629C22—108no—
630C22—104no—
631C22—104no—
632C22—104no—
633C22—208no—
634C22C2×C3×#70912yes—
635C22C2×C3×D4×D514yes—
636C22C2×C3×D4×D512yes—
637C22C3×#414712yes—
638C22C24×C3×D511yescharacteristic
639C4—22no—
640C4—24no—
641C4—24no—
642C4—54no—
643C4—102no—
644C4—104no—
645C4—102no—
646C4C2×C3×#70914yescomplemented
647C3C2×#6584111yescharacteristic, direct product factor, Sylow
648C2—24no—
649C2—104no—
650C2—204no—
651C2C3×#6584114yesdirect product factor
652C2C22×C3×#70911yescharacteristic
653C2C22×C3×D4×D511yescharacteristic
654C2C2×C3×#414711yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC22×C3×C5×C4⋊C4C2
socleC23×C3×C5C24
hypercenterC22×C3×C4⋊C4D5
hypocenterC5C2×C3×#547
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C22×C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#709C2semidirect
2. C22×C3×C5×C4⋊C4C2semidirect
3. C2×C3×#4076C2semidirect
4. C2×C3×#4075C2semidirect
5. C2×C3×C4×C22⋊D5C2semidirect
6. C2×C3×#4042C2semidirect
7. C3×#65841C2direct (N × H)
8. C2×C3×#4041C2semidirect
9. C2×C3×#4040C2semidirect
10. C2×C3×#4039C2semidirect
11. C2×C3×D5×C4⋊C4C2semidirect
12. C2×C3×#4034C2semidirect
13. C2×#65841C3direct (N × H)
19. C2×C3×#709C22semidirect
29. C2×C3×C5×C4⋊C4C22semidirect
31. C3×#4076C22semidirect
32. C3×#4075C22semidirect
33. C3×C4×C22⋊D5C22semidirect
43. C3×#4042C22semidirect
44. C3×#4041C22semidirect
45. C3×#4040C22semidirect
46. C3×#4039C22semidirect
47. C3×D5×C4⋊C4C22semidirect
48. C3×#4034C22semidirect
50. C22×#709C2×C3semidirect
51. C22×C5×C4⋊C4C2×C3semidirect
52. C2×#4076C2×C3semidirect
53. C2×#4075C2×C3semidirect
54. C2×C4×C22⋊D5C2×C3semidirect
55. C2×#4042C2×C3semidirect
56. #65841C2×C3direct (N × H)
57. C2×#4041C2×C3semidirect
58. C2×#4040C2×C3semidirect
59. C2×#4039C2×C3semidirect
60. C2×D5×C4⋊C4C2×C3semidirect
61. C2×#4034C2×C3semidirect
74. C2×C3×C22⋊D5D4semidirect
118. C22×C3×C4⋊C4D5semidirect
124. C2×#709C22×C3semidirect
134. C2×C5×C4⋊C4C22×C3semidirect
136. #4076C22×C3semidirect
137. #4075C22×C3semidirect
138. C4×C22⋊D5C22×C3semidirect
148. #4042C22×C3semidirect
149. #4041C22×C3semidirect
150. #4040C22×C3semidirect
151. #4039C22×C3semidirect
152. D5×C4⋊C4C22×C3semidirect
153. #4034C22×C3semidirect
173. C2×C3×C4×C5#41semidirect
179. C3×C22⋊D5C2×D4semidirect
222. C2×C3×C4⋊C4C2×D5semidirect
241. C2×C22⋊D5C3×D4semidirect
285. C22×C4⋊C4C3×D5semidirect
305. C3×C4×C5C2×#41semidirect
373. C2×C4×C5C3×#41semidirect
379. C22⋊D5C2×C3×D4semidirect
422. C2×C4⋊C4C2×C3×D5semidirect
430. C2×C3×C5#547semidirect
470. C2×C3×C4#709semidirect
494. C4×C5C2×C3×#41semidirect
544. C3×C5C2×#547semidirect
568. C3×C4C2×#709semidirect
570. C2×C5C3×#547semidirect
610. C2×C4C3×#709semidirect
618. C2×C3#65841direct (N × H)
622. C5C2×C3×#547semidirect
646. C4C2×C3×#709semidirect
647. C3C2×#65841direct (N × H)
651. C2C3×#65841direct (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
C22×C3×C5×C4⋊C42
C2×C3×#40762
C2×C3×#40752
C2×C3×C4×C22⋊D52
C2×C3×#40422
C3×#658412
C2×C3×#40412
C2×C3×#40402
C2×C3×#40392
C2×C3×D5×C4⋊C42
C2×C3×#40342
C2×#658413
C2×C3×#5475