Finite Group Databasebeta

← C2×C3×#65945 #14482677

Subgroups — C2×C3×#65945 #14482677

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×#711C212yesmaximal, complemented
2C2×C3×C5×#121C211yesmaximal, characteristic, complemented
3C2×C3×#4084C211yesmaximal, characteristic, complemented
4C2×C3×#4081C212yesmaximal, complemented
5C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
6C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
7C22×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
8C3×#65945C2116yesmaximal, direct product factor
9C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#4034C211yesmaximal, characteristic, complemented
11C2×C3×#4029C212yesmaximal, complemented
12C2×C3×#4024C212yesmaximal, complemented
13C2×#65945C311yesmaximal, characteristic, direct product factor, Hall
14C22×C3×C5×D4C2211yescharacteristic
15C22×C3×C5×D4C2212yes—
16C23×C3×C4×C5C2211yescharacteristic
17C22×C3×C22⋊D5C2212yes—
18C22×C3×C22⋊D5C2211yescharacteristic
19C23×C3×Dic5C2212yes—
20C23×C3×Dic5C2212yes—
21C2×C3×#711—216no—
22C2×C3×#711C22116yescomplemented
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2212yes—
25C22×C3×Dic10C2212yes—
26C3×C5×#121C2218yescomplemented
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2212yes—
31C2×C3×C22⋊Dic5C2212yes—
32C3×#4084C2218yescomplemented
33C3×#4081C22116yescomplemented
34C3×D4×Dic5C2218yescomplemented
35C3×C4×C22⋊D5C2218yescomplemented
36C2×C3×#685C2211yescharacteristic
37C2×C3×C4⋊Dic5C2211yescharacteristic
38C2×C3×C4⋊Dic5C2211yescharacteristic
39C2×C3×C4⋊Dic5C2212yes—
40C2×C3×C4⋊Dic5C2218yescomplemented
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2212yes—
43C2×C3×#683C2212yes—
44C2×C3×C4×Dic5C2211yescharacteristic
45C3×D5×C4⋊C4C2218yescomplemented
46C3×#4034C2218yescomplemented
47C3×#4029C22116yescomplemented
48C3×#4024C22116yescomplemented
49C2×C3×#547—51nomaximal, Hall
50C22×#711C2×C312yescomplemented
51C2×C5×#121C2×C311yescharacteristic, complemented
52C2×#4084C2×C311yescharacteristic, complemented
53C2×#4081C2×C312yescomplemented
54C2×D4×Dic5C2×C311yescharacteristic, complemented
55C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
56C22×C4⋊Dic5C2×C311yescharacteristic, complemented
57#65945C2×C3116yesdirect product factor
58C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
59C2×#4034C2×C311yescharacteristic, complemented
60C2×#4029C2×C312yescomplemented
61C2×#4024C2×C312yescomplemented
62C24×C3×C5C2312yes—
63C24×C3×C5C2311yescharacteristic
64C23×C3×D5C2311yescharacteristic
65C2×C3×C5×D4—28no—
66C2×C3×C5×D4—24no—
67C2×C3×C5×D4C2314yes—
68C2×C3×C5×D4C2318yes—
69C22×C3×C4×C5—24no—
70C22×C3×C4×C5C2312yes—
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2314yes—
73C22×C3×C4×C5C2311yescharacteristic
74C2×C3×C22⋊D5—28no—
75C2×C3×C22⋊D5D418yescomplemented
76C2×C3×C22⋊D5C2318yes—
77C2×C3×C22⋊D5C2314yes—
78C22×C3×Dic5—28no—
79C22×C3×Dic5—28no—
80C22×C3×Dic5C2318yes—
81C22×C3×Dic5C2318yes—
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2312yes—
85C22×C3×Dic5C2312yes—
86C22×C3×Dic5C2311yescharacteristic
87C3×#711—264no—
88C2×C3×C4×D5—28no—
89C2×C3×C4×D5—24no—
90C2×C3×C4×D5C2314yes—
91C2×C3×C4×D5C2318yes—
92C2×C3×Dic10—28no—
93C2×C3×Dic10C2318yes—
94C3×C5×C4⋊C4C2314yes—
95C3×C5×C22⋊C4C2318yes—
96C3×C22⋊Dic5C2318yes—
97C3×C22⋊Dic5C2314yes—
98C3×C22⋊Dic5C2318yes—
99C3×#685C2314yes—
100C3×C4⋊Dic5C2314yes—
101C3×C4⋊Dic5C2314yes—
102C3×C4⋊Dic5C2318yes—
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×#121D511yescharacteristic, complemented
115C2×C3×C4×D4—51no—
116C2×C3×C4×D4—51no—
117C22×C3×C4⋊C4—51no—
118C22×C3×C4⋊C4—51no—
119C22×C5×D4C22×C311yescharacteristic
120C22×C5×D4C22×C312yes—
121C23×C4×C5C22×C311yescharacteristic
122C22×C22⋊D5C22×C312yes—
123C22×C22⋊D5C22×C311yescharacteristic
124C23×Dic5C22×C312yes—
125C23×Dic5C22×C312yes—
126C2×#711—216no—
127C2×#711C22×C3116yescomplemented
128C22×C4×D5C22×C312yes—
129C22×C4×D5C22×C311yescharacteristic
130C22×Dic10C22×C312yes—
131C5×#121C22×C318yescomplemented
132C2×C5×C4⋊C4C22×C311yescharacteristic
133C2×C5×C22⋊C4C22×C312yes—
134C2×C22⋊Dic5C22×C312yes—
135C2×C22⋊Dic5C22×C312yes—
136C2×C22⋊Dic5C22×C311yescharacteristic
137#4084C22×C318yescomplemented
138#4081C22×C3116yescomplemented
139D4×Dic5C22×C318yescomplemented
140C4×C22⋊D5C22×C318yescomplemented
141C2×#685C22×C311yescharacteristic
142C2×C4⋊Dic5C22×C312yes—
143C2×C4⋊Dic5C22×C311yescharacteristic
144C2×C4⋊Dic5C22×C311yescharacteristic
145C2×C4⋊Dic5C22×C318yescomplemented
146C2×#683C22×C311yescharacteristic
147C2×#683C22×C312yes—
148C2×#683C22×C312yes—
149C2×C4×Dic5C22×C311yescharacteristic
150D5×C4⋊C4C22×C318yescomplemented
151#4034C22×C318yescomplemented
152#4029C22×C3116yescomplemented
153#4024C22×C3116yescomplemented
154C2×#547—51noSylow
155C23×C3×C5—22no—
156C23×C3×C5—22no—
157C23×C3×C5—24no—
158C23×C3×C5—24no—
159C23×C3×C5—24no—
160C23×C3×C5C2×D414yes—
161C23×C3×C5C2414yes—
162C23×C3×C5C2412yes—
163C23×C3×C5C2411yescharacteristic
164C22×C3×D5—22no—
165C22×C3×D5—22no—
166C22×C3×D5C2×D414yes—
167C22×C3×D5C2412yes—
168C3×C5×D4—216no—
169C3×C5×D4—28no—
170C2×C3×C4×C5—24no—
171C2×C3×C4×C5—22no—
172C2×C3×C4×C5—28no—
173C2×C3×C4×C5#4114yescomplemented
174C2×C3×C4×C5C2414yes—
175C2×C3×C4×C5C2412yes—
176C2×C3×C4×C5C2412yes—
177C3×C22⋊D5—216no—
178C3×C22⋊D5C2×D4116yescomplemented
179C2×C3×Dic5—24no—
180C2×C3×Dic5—24no—
181C2×C3×Dic5—216no—
182C2×C3×Dic5—22no—
183C2×C3×Dic5—22no—
184C2×C3×Dic5—216no—
185C2×C3×Dic5C2×D414yes—
186C2×C3×Dic5C2412yes—
187C2×C3×Dic5C2412yes—
188C2×C3×Dic5C2414yes—
189C2×C3×Dic5C2414yes—
190C2×C3×Dic5C2412yes—
191C3×C4×D5—216no—
192C3×C4×D5—28no—
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×D4C2×D512yes—
200C22×C3×D4C2×D511yescharacteristic
201C23×C3×C4—52no—
202C23×C3×C4—52no—
203C23×C3×C4—52no—
204C23×C3×C4—51no—
205C23×C3×C4C2×D511yescharacteristic
206C3×C4⋊Q8—58no—
207C3×#123—516no—
208C3×#123—516no—
209C3×C22⋊Q8—516no—
210C3×#121—58no—
211C3×#121C2×D518yescomplemented
212C3×C4×D4—58no—
213C3×C4×D4—58no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C4⋊C4—51no—
216C2×C3×C4⋊C4—52no—
217C2×C3×C4⋊C4—52no—
218C2×C3×C4⋊C4—58no—
219C2×C3×C4⋊C4—51no—
220C2×C3×C4⋊C4—52no—
221C2×C3×C4⋊C4—58no—
222C2×C3×C4⋊C4C2×D511yescharacteristic
223C2×C3×C22⋊C4—51no—
224C2×C3×C22⋊C4—52no—
225C2×C3×C22⋊C4—52no—
226C2×C3×C22⋊C4—51no—
227C2×C3×C22⋊C4C2×D512yes—
228C2×C3×C42—51no—
229C24×C5C23×C312yes—
230C24×C5C23×C311yescharacteristic
231C23×D5C23×C311yescharacteristic
232C2×C5×D4—28no—
233C2×C5×D4—24no—
234C2×C5×D4C23×C318yes—
235C2×C5×D4C23×C314yes—
236C22×C4×C5—24no—
237C22×C4×C5C23×C311yescharacteristic
238C22×C4×C5C23×C312yes—
239C22×C4×C5C23×C314yes—
240C22×C4×C5C23×C311yescharacteristic
241C2×C22⋊D5—28no—
242C2×C22⋊D5C3×D418yescomplemented
243C2×C22⋊D5C23×C318yes—
244C2×C22⋊D5C23×C314yes—
245C22×Dic5—28no—
246C22×Dic5—28no—
247C22×Dic5C23×C311yescharacteristic
248C22×Dic5C23×C311yescharacteristic
249C22×Dic5C23×C312yes—
250C22×Dic5C23×C312yes—
251C22×Dic5C23×C318yes—
252C22×Dic5C23×C318yes—
253C22×Dic5C23×C311yescharacteristic
254#711—264no—
255C2×C4×D5—28no—
256C2×C4×D5—24no—
257C2×C4×D5C23×C318yes—
258C2×C4×D5C23×C314yes—
259C2×Dic10—28no—
260C2×Dic10C23×C318yes—
261C5×C4⋊C4C23×C314yes—
262C5×C22⋊C4C23×C318yes—
263C22⋊Dic5C23×C318yes—
264C22⋊Dic5C23×C318yes—
265C22⋊Dic5C23×C314yes—
266#685C23×C314yes—
267C4⋊Dic5C23×C318yes—
268C4⋊Dic5C23×C314yes—
269C4⋊Dic5C23×C314yes—
270#683C23×C314yes—
271#683C23×C318yes—
272#683C23×C318yes—
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×#121C3×D511yescharacteristic, complemented
282C2×C4×D4—51no—
283C2×C4×D4—51no—
284C22×C4⋊C4—51no—
285C22×C4⋊C4—51no—
286C22×C3×C5—28no—
287C22×C3×C5—22no—
288C22×C3×C5—22no—
289C22×C3×C5—24no—
290C22×C3×C5—24no—
291C22×C3×C5—24no—
292C22×C3×C5—48no—
293C22×C3×C5C22×D414yes—
294C22×C3×C5C22×D412yes—
295C22×C3×C5C2×#4112yes—
296C22×C3×C52−1+412yes—
297C22×C3×C5C2511yescharacteristic
298C2×C3×D5—28no—
299C2×C3×D5—22no—
300C2×C3×D5—22no—
301C2×C3×D5C22×D414yes—
302C3×C4×C5—24no—
303C3×C4×C5—22no—
304C3×C4×C5C2×#4114yescomplemented
305C3×Dic5—24no—
306C3×Dic5—24no—
307C3×Dic5—22no—
308C3×Dic5—22no—
309C3×Dic5C22×D414yes—
310C24×C3—51no—
311C24×C3C22×D512yes—
312C24×C3C22×D511yescharacteristic
313C3×#41—1064no—
314C2×C3×Q8—58no—
315C2×C3×Q8—108no—
316C2×C3×D4—28no—
317C2×C3×D4—24no—
318C2×C3×D4—58no—
319C2×C3×D4—54no—
320C2×C3×D4—58no—
321C2×C3×D4—108no—
322C2×C3×D4C22×D514yes—
323C2×C3×D4C22×D518yes—
324C22×C3×C4—24no—
325C22×C3×C4—51no—
326C22×C3×C4—58no—
327C22×C3×C4—58no—
328C22×C3×C4—51no—
329C22×C3×C4—51no—
330C22×C3×C4—52no—
331C22×C3×C4—52no—
332C22×C3×C4—54no—
333C22×C3×C4—58no—
334C22×C3×C4—108no—
335C22×C3×C4—108no—
336C22×C3×C4—108no—
337C22×C3×C4—104no—
338C22×C3×C4C22×D514yes—
339C22×C3×C4C22×D511yescharacteristic
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⋊C4—54no—
347C3×C4⋊C4—58no—
348C3×C4⋊C4C22×D514yes—
349C3×C22⋊C4—54no—
350C3×C22⋊C4—58no—
351C3×C22⋊C4—58no—
352C3×C22⋊C4—54no—
353C3×C22⋊C4C22×D518yes—
354C3×C42—54no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—24no—
358C23×C5—24no—
359C23×C5—24no—
360C23×C5C2×C3×D414yes—
361C23×C5C24×C314yes—
362C23×C5C24×C312yes—
363C23×C5C24×C311yescharacteristic
364C22×D5—22no—
365C22×D5—22no—
366C22×D5C2×C3×D414yes—
367C22×D5C24×C312yes—
368C5×D4—216no—
369C5×D4—28no—
370C2×C4×C5—24no—
371C2×C4×C5—22no—
372C2×C4×C5—28no—
373C2×C4×C5C3×#4114yescomplemented
374C2×C4×C5C24×C314yes—
375C2×C4×C5C24×C312yes—
376C2×C4×C5C24×C312yes—
377C22⋊D5—216no—
378C22⋊D5C2×C3×D4116yescomplemented
379C2×Dic5—24no—
380C2×Dic5—24no—
381C2×Dic5—216no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—216no—
385C2×Dic5C2×C3×D414yes—
386C2×Dic5C24×C312yes—
387C2×Dic5C24×C312yes—
388C2×Dic5C24×C314yes—
389C2×Dic5C24×C314yes—
390C2×Dic5C24×C312yes—
391C4×D5—216no—
392C4×D5—28no—
393Dic10—216no—
394C2×#41—516no—
395C2×#41—1016no—
396C22×Q8—52no—
397C22×D4—51no—
398C22×D4—52no—
399C22×D4C2×C3×D511yescharacteristic
400C22×D4C2×C3×D512yes—
401C23×C4—52no—
402C23×C4—52no—
403C23×C4—51no—
404C23×C4—52no—
405C23×C4C2×C3×D511yescharacteristic
406C4⋊Q8—58no—
407#123—516no—
408#123—516no—
409C22⋊Q8—516no—
410#121—58no—
411#121C2×C3×D518yescomplemented
412C4×D4—58no—
413C4×D4—58no—
414C2×C4⋊C4—51no—
415C2×C4⋊C4—51no—
416C2×C4⋊C4—52no—
417C2×C4⋊C4—52no—
418C2×C4⋊C4—58no—
419C2×C4⋊C4—51no—
420C2×C4⋊C4—52no—
421C2×C4⋊C4—58no—
422C2×C4⋊C4C2×C3×D511yescharacteristic
423C2×C22⋊C4—51no—
424C2×C22⋊C4—52no—
425C2×C22⋊C4—52no—
426C2×C22⋊C4—51no—
427C2×C22⋊C4C2×C3×D512yes—
428C2×C42—51no—
429C2×C3×C5—24no—
430C2×C3×C5—44no—
431C2×C3×C5#54714yescomplemented
432C2×C3×C5C23×D411yescharacteristic
433C2×C3×C5C22×#4111yescharacteristic
434C2×C3×C5C2×2−1+411yescharacteristic
435C3×D5—24no—
436C23×C3—22no—
437C23×C3—22no—
438C23×C3—24no—
439C23×C3—24no—
440C23×C3—24no—
441C23×C3—54no—
442C23×C3—52no—
443C23×C3—102no—
444C23×C3—102no—
445C23×C3D4×D514yes—
446C23×C3C23×D514yes—
447C23×C3C23×D512yes—
448C23×C3C23×D511yescharacteristic
449C3×Q8—1016no—
450C3×D4—216no—
451C3×D4—28no—
452C3×D4—516no—
453C3×D4—1016no—
454C2×C3×C4—24no—
455C2×C3×C4—22no—
456C2×C3×C4—28no—
457C2×C3×C4—54no—
458C2×C3×C4—52no—
459C2×C3×C4—52no—
460C2×C3×C4—52no—
461C2×C3×C4—54no—
462C2×C3×C4—54no—
463C2×C3×C4—1016no—
464C2×C3×C4—1016no—
465C2×C3×C4—104no—
466C2×C3×C4—104no—
467C2×C3×C4—1016no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—108no—
471C2×C3×C4#71114yescomplemented
472C2×C3×C4C23×D512yes—
473C2×C3×C4C23×D514yes—
474C2×C3×C4C23×D512yes—
475C22×C5—22no—
476C22×C5—22no—
477C22×C5—28no—
478C22×C5—24no—
479C22×C5—24no—
480C22×C5—24no—
481C22×C5—48no—
482C22×C5C22×C3×D414yes—
483C22×C5C22×C3×D412yes—
484C22×C5C2×C3×#4112yes—
485C22×C5C3×2−1+412yes—
486C22×C5C25×C311yescharacteristic
487C2×D5—22no—
488C2×D5—22no—
489C2×D5—28no—
490C2×D5C22×C3×D414yes—
491C4×C5—24no—
492C4×C5—22no—
493C4×C5C2×C3×#4114yescomplemented
494Dic5—24no—
495Dic5—24no—
496Dic5—22no—
497Dic5—22no—
498Dic5C22×C3×D414yes—
499C24—51no—
500C24C22×C3×D512yes—
501C24C22×C3×D511yescharacteristic
502#41—1064no—
503C2×Q8—58no—
504C2×Q8—108no—
505C2×D4—28no—
506C2×D4—24no—
507C2×D4—58no—
508C2×D4—54no—
509C2×D4—58no—
510C2×D4—108no—
511C2×D4C22×C3×D514yes—
512C2×D4C22×C3×D518yes—
513C22×C4—24no—
514C22×C4—51no—
515C22×C4—51no—
516C22×C4—51no—
517C22×C4—52no—
518C22×C4—52no—
519C22×C4—58no—
520C22×C4—58no—
521C22×C4—54no—
522C22×C4—58no—
523C22×C4—108no—
524C22×C4—108no—
525C22×C4—108no—
526C22×C4—104no—
527C22×C4C22×C3×D511yescharacteristic
528C22×C4C22×C3×D512yes—
529C22×C4C22×C3×D514yes—
530C22×C4C22×C3×D511yescharacteristic
531C4⋊C4—54no—
532C4⋊C4—54no—
533C4⋊C4—58no—
534C4⋊C4—58no—
535C4⋊C4—54no—
536C4⋊C4—58no—
537C4⋊C4C22×C3×D514yes—
538C22⋊C4—54no—
539C22⋊C4—58no—
540C22⋊C4—58no—
541C22⋊C4—54no—
542C22⋊C4C22×C3×D518yes—
543C42—54no—
544C3×C5C2×#54711yescharacteristic, complemented, Hall
545C22×C3—28no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—24no—
549C22×C3—24no—
550C22×C3—24no—
551C22×C3—48no—
552C22×C3—54no—
553C22×C3—108no—
554C22×C3—102no—
555C22×C3—102no—
556C22×C3C2×D4×D514yes—
557C22×C3C2×D4×D512yes—
558C22×C3C2×#71112yes—
559C22×C3#415012yes—
560C22×C3C24×D511yescharacteristic
561C3×C4—24no—
562C3×C4—22no—
563C3×C4—54no—
564C3×C4—104no—
565C3×C4—104no—
566C3×C4—102no—
567C3×C4—102no—
568C3×C4C2×#71114yescomplemented
569C2×C5—24no—
570C2×C5—44no—
571C2×C5C3×#54714yescomplemented
572C2×C5C23×C3×D411yescharacteristic
573C2×C5C22×C3×#4111yescharacteristic
574C2×C5C2×C3×2−1+411yescharacteristic
575D5—24no—
576C23—22no—
577C23—22no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—54no—
582C23—52no—
583C23—102no—
584C23—102no—
585C23C3×D4×D514yes—
586C23C23×C3×D514yes—
587C23C23×C3×D512yes—
588C23C23×C3×D511yescharacteristic
589Q8—1016no—
590D4—216no—
591D4—28no—
592D4—516no—
593D4—1016no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—28no—
597C2×C4—54no—
598C2×C4—52no—
599C2×C4—52no—
600C2×C4—52no—
601C2×C4—54no—
602C2×C4—54no—
603C2×C4—1016no—
604C2×C4—1016no—
605C2×C4—104no—
606C2×C4—104no—
607C2×C4—1016no—
608C2×C4—102no—
609C2×C4—102no—
610C2×C4—108no—
611C2×C4C3×#71114yescomplemented
612C2×C4C23×C3×D512yes—
613C2×C4C23×C3×D514yes—
614C2×C4C23×C3×D512yes—
615C2×C3—24no—
616C2×C3—44no—
617C2×C3—104no—
618C2×C3#6594514yesdirect product factor
619C2×C3C22×D4×D511yescharacteristic
620C2×C3C22×#71111yescharacteristic
621C2×C3C2×#415011yescharacteristic
622C5C2×C3×#54711yescharacteristic, complemented, Sylow
623C22—22no—
624C22—22no—
625C22—28no—
626C22—24no—
627C22—24no—
628C22—24no—
629C22—48no—
630C22—54no—
631C22—102no—
632C22—102no—
633C22—108no—
634C22C2×C3×D4×D514yes—
635C22C2×C3×D4×D512yes—
636C22C2×C3×#71112yes—
637C22C3×#415012yes—
638C22C24×C3×D511yescharacteristic
639C4—24no—
640C4—22no—
641C4—54no—
642C4—104no—
643C4—104no—
644C4—102no—
645C4—102no—
646C4C2×C3×#71114yescomplemented
647C3C2×#6594511yescharacteristic, direct product factor, Sylow
648C2—24no—
649C2—44no—
650C2—104no—
651C2C3×#6594514yesdirect product factor
652C2C22×C3×D4×D511yescharacteristic
653C2C22×C3×#71111yescharacteristic
654C2C2×C3×#415011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#121C2
socleC23×C3×C5C24
hypercenterC2×C3×#121D5
hypocenterC5C2×C3×#547
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#121

Complements

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

NH ≅ G/Ntype
1. C22×C3×#711C2semidirect
2. C2×C3×C5×#121C2semidirect
3. C2×C3×#4084C2semidirect
4. C2×C3×#4081C2semidirect
5. C2×C3×D4×Dic5C2semidirect
6. C2×C3×C4×C22⋊D5C2semidirect
7. C22×C3×C4⋊Dic5C2semidirect
8. C3×#65945C2direct (N × H)
9. C2×C3×D5×C4⋊C4C2semidirect
10. C2×C3×#4034C2semidirect
11. C2×C3×#4029C2semidirect
12. C2×C3×#4024C2semidirect
13. C2×#65945C3direct (N × H)
22. C2×C3×#711C22semidirect
26. C3×C5×#121C22semidirect
32. C3×#4084C22semidirect
33. C3×#4081C22semidirect
34. C3×D4×Dic5C22semidirect
35. C3×C4×C22⋊D5C22semidirect
40. C2×C3×C4⋊Dic5C22semidirect
45. C3×D5×C4⋊C4C22semidirect
46. C3×#4034C22semidirect
47. C3×#4029C22semidirect
48. C3×#4024C22semidirect
50. C22×#711C2×C3semidirect
51. C2×C5×#121C2×C3semidirect
52. C2×#4084C2×C3semidirect
53. C2×#4081C2×C3semidirect
54. C2×D4×Dic5C2×C3semidirect
55. C2×C4×C22⋊D5C2×C3semidirect
56. C22×C4⋊Dic5C2×C3semidirect
57. #65945C2×C3direct (N × H)
58. C2×D5×C4⋊C4C2×C3semidirect
59. C2×#4034C2×C3semidirect
60. C2×#4029C2×C3semidirect
61. C2×#4024C2×C3semidirect
75. C2×C3×C22⋊D5D4semidirect
114. C2×C3×#121D5semidirect
127. C2×#711C22×C3semidirect
131. C5×#121C22×C3semidirect
137. #4084C22×C3semidirect
138. #4081C22×C3semidirect
139. D4×Dic5C22×C3semidirect
140. C4×C22⋊D5C22×C3semidirect
145. C2×C4⋊Dic5C22×C3semidirect
150. D5×C4⋊C4C22×C3semidirect
151. #4034C22×C3semidirect
152. #4029C22×C3semidirect
153. #4024C22×C3semidirect
173. C2×C3×C4×C5#41semidirect
178. C3×C22⋊D5C2×D4semidirect
211. C3×#121C2×D5semidirect
242. C2×C22⋊D5C3×D4semidirect
281. C2×#121C3×D5semidirect
304. C3×C4×C5C2×#41semidirect
373. C2×C4×C5C3×#41semidirect
378. C22⋊D5C2×C3×D4semidirect
411. #121C2×C3×D5semidirect
431. C2×C3×C5#547semidirect
471. C2×C3×C4#711semidirect
493. C4×C5C2×C3×#41semidirect
544. C3×C5C2×#547semidirect
568. C3×C4C2×#711semidirect
571. C2×C5C3×#547semidirect
611. C2×C4C3×#711semidirect
618. C2×C3#65945direct (N × H)
622. C5C2×C3×#547semidirect
646. C4C2×C3×#711semidirect
647. C3C2×#65945direct (N × H)
651. C2C3×#65945direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7112
C2×C3×C5×#1212
C2×C3×#40842
C2×C3×#40812
C2×C3×D4×Dic52
C2×C3×C4×C22⋊D52
C22×C3×C4⋊Dic52
C3×#659452
C2×C3×D5×C4⋊C42
C2×C3×#40342
C2×C3×#40292
C2×C3×#40242
C2×#659453
C2×C3×#5475