Finite Group Databasebeta

← C2×C3×#65965 #14482683

Subgroups — C2×C3×#65965 #14482683

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#713C211yesmaximal, characteristic, complemented
2C22×C3×#709C211yesmaximal, characteristic, complemented
3C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C3×#4090C211yesmaximal, characteristic, complemented
5C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
6C3×#65965C2116yesmaximal, direct product factor
7C2×C3×#4043C211yesmaximal, characteristic, complemented
8C2×C3×#4040C212yesmaximal, complemented
9C2×C3×#4039C211yesmaximal, characteristic, complemented
10C2×C3×D5×C4⋊C4C212yesmaximal, complemented
11C2×C3×#4030C212yesmaximal, complemented
12C2×C3×#4029C212yesmaximal, complemented
13C2×#65965C311yesmaximal, characteristic, direct product factor, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C22×C3×C22⋊D5C2211yescharacteristic
17C22×C3×C22⋊D5C2212yes—
18C2×C3×#713—28no—
19C2×C3×#713C2218yescomplemented
20C2×C3×#709—28no—
21C2×C3×#709C2218yescomplemented
22C22×C3×D20C2212yes—
23C22×C3×D20C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×C3×C4×D5C2212yes—
26C22×C3×C4×D5C2212yes—
27C22×C3×C4×D5C2212yes—
28C22×C3×Dic10C2211yescharacteristic
29C3×C5×C22⋊Q8C2218yescomplemented
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C3×C5×C4⋊C4C2212yes—
32C2×C3×C5×C22⋊C4C2212yes—
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C3×#4090C2218yescomplemented
35C3×C4×C22⋊D5C2218yescomplemented
36C2×C3×#685C2212yes—
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2212yes—
39C2×C3×C4⋊Dic5C2212yes—
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2212yes—
42C2×C3×#683C2212yes—
43C2×C3×C4×Dic5C2211yescharacteristic
44C3×#4043C2218yescomplemented
45C3×#4040C22116yescomplemented
46C3×#4039C2218yescomplemented
47C3×D5×C4⋊C4C22116yescomplemented
48C3×#4030C22116yescomplemented
49C3×#4029C22116yescomplemented
50C2×C3×#547—51nomaximal, Hall
51C22×#713C2×C311yescharacteristic, complemented
52C22×#709C2×C311yescharacteristic, complemented
53C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
54C2×#4090C2×C311yescharacteristic, complemented
55C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
56#65965C2×C3116yesdirect product factor
57C2×#4043C2×C311yescharacteristic, complemented
58C2×#4040C2×C312yescomplemented
59C2×#4039C2×C311yescharacteristic, complemented
60C2×D5×C4⋊C4C2×C312yescomplemented
61C2×#4030C2×C312yescomplemented
62C2×#4029C2×C312yescomplemented
63C24×C3×C5C2311yescharacteristic
64C23×C3×D5C2311yescharacteristic
65C23×C3×D5C2312yes—
66C2×C3×C5×Q8—24no—
67C2×C3×C5×Q8C2314yes—
68C22×C3×C4×C5—24no—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2312yes—
71C22×C3×C4×C5C2312yes—
72C22×C3×C4×C5C2314yes—
73C22×C3×C4×C5C2311yescharacteristic
74C2×C3×C22⋊D5—28no—
75C2×C3×C22⋊D5—24no—
76C2×C3×C22⋊D5C2318yes—
77C2×C3×C22⋊D5C2314yes—
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2311yescharacteristic
82C3×#713—232no—
83C3×#709—232no—
84C2×C3×D20—28no—
85C2×C3×D20D418yescomplemented
86C2×C3×D20C2318yes—
87C2×C3×D20C2314yes—
88C2×C3×C4×D5—28no—
89C2×C3×C4×D5—28no—
90C2×C3×C4×D5—24no—
91C2×C3×C4×D5—28no—
92C2×C3×C4×D5C2318yes—
93C2×C3×C4×D5C2318yes—
94C2×C3×C4×D5C2314yes—
95C2×C3×C4×D5C2318yes—
96C2×C3×Dic10—24no—
97C2×C3×Dic10C2314yes—
98C3×C5×C4⋊C4C2318yes—
99C3×C5×C4⋊C4C2314yes—
100C3×C5×C22⋊C4C2318yes—
101C3×C22⋊Dic5C2314yes—
102C3×#685C2318yes—
103C3×#685C2318yes—
104C3×#685C2314yes—
105C3×C4⋊Dic5C2318yes—
106C3×#683C2318yes—
107C3×#683C2318yes—
108C3×#683C2314yes—
109C3×C4×Dic5C2314yes—
110C22×C3×#41—51no—
111C22×C3×#41—51no—
112C3×#547—516no—
113C2×C3×C4⋊Q8—51no—
114C2×C3×#123—52no—
115C2×C3×#123—52no—
116C2×C3×C22⋊Q8—51no—
117C2×C3×C22⋊Q8D511yescharacteristic, complemented
118C2×C3×#121—52no—
119C2×C3×C4×D4—51no—
120C2×C3×C4×D4—51no—
121C22×C3×C4⋊C4—52no—
122C22×C5×Q8C22×C311yescharacteristic
123C23×C4×C5C22×C311yescharacteristic
124C22×C22⋊D5C22×C312yes—
125C22×C22⋊D5C22×C311yescharacteristic
126C2×#713—28no—
127C2×#713C22×C318yescomplemented
128C2×#709—28no—
129C2×#709C22×C318yescomplemented
130C22×D20C22×C312yes—
131C22×D20C22×C311yescharacteristic
132C22×C4×D5C22×C312yes—
133C22×C4×D5C22×C312yes—
134C22×C4×D5C22×C312yes—
135C22×C4×D5C22×C311yescharacteristic
136C22×Dic10C22×C311yescharacteristic
137C5×C22⋊Q8C22×C318yescomplemented
138C2×C5×C4⋊C4C22×C312yes—
139C2×C5×C4⋊C4C22×C311yescharacteristic
140C2×C5×C22⋊C4C22×C312yes—
141C2×C22⋊Dic5C22×C311yescharacteristic
142#4090C22×C318yescomplemented
143C4×C22⋊D5C22×C318yescomplemented
144C2×#685C22×C312yes—
145C2×#685C22×C312yes—
146C2×#685C22×C311yescharacteristic
147C2×C4⋊Dic5C22×C312yes—
148C2×#683C22×C312yes—
149C2×#683C22×C312yes—
150C2×#683C22×C311yescharacteristic
151C2×C4×Dic5C22×C311yescharacteristic
152#4043C22×C318yescomplemented
153#4040C22×C3116yescomplemented
154#4039C22×C318yescomplemented
155D5×C4⋊C4C22×C3116yescomplemented
156#4030C22×C3116yescomplemented
157#4029C22×C3116yescomplemented
158C2×#547—51noSylow
159C23×C3×C5—22no—
160C23×C3×C5—22no—
161C23×C3×C5—22no—
162C23×C3×C5C2412yes—
163C23×C3×C5C2411yescharacteristic
164C22×C3×D5—24no—
165C22×C3×D5—24no—
166C22×C3×D5—22no—
167C22×C3×D5—22no—
168C22×C3×D5—22no—
169C22×C3×D5C2×D418yes—
170C22×C3×D5C2412yes—
171C22×C3×D5C2414yes—
172C3×C5×Q8—28no—
173C2×C3×C4×C5—22no—
174C2×C3×C4×C5—24no—
175C2×C3×C4×C5—24no—
176C2×C3×C4×C5—28no—
177C2×C3×C4×C5C2×D414yes—
178C2×C3×C4×C5C2414yes—
179C2×C3×C4×C5C2412yes—
180C2×C3×C4×C5C2414yes—
181C2×C3×C4×C5C2412yes—
182C3×C22⋊D5—216no—
183C3×C22⋊D5—28no—
184C2×C3×Dic5—24no—
185C2×C3×Dic5—22no—
186C2×C3×Dic5—22no—
187C2×C3×Dic5#4114yescomplemented
188C2×C3×Dic5C2412yes—
189C2×C3×Dic5C2414yes—
190C2×C3×Dic5C2412yes—
191C2×C3×Dic5C2412yes—
192C3×D20—216no—
193C3×D20C2×D4116yescomplemented
194C3×C4×D5—216no—
195C3×C4×D5—216no—
196C3×C4×D5—28no—
197C3×C4×D5—216no—
198C3×Dic10—28no—
199C2×C3×#41—58no—
200C2×C3×#41—58no—
201C2×C3×#41—108no—
202C2×C3×#41—108no—
203C22×C3×Q8—51no—
204C22×C3×Q8C2×D511yescharacteristic
205C22×C3×D4—52no—
206C22×C3×D4—51no—
207C22×C3×D4—51no—
208C22×C3×D4—52no—
209C23×C3×C4—52no—
210C23×C3×C4—52no—
211C23×C3×C4—51no—
212C23×C3×C4—52no—
213C23×C3×C4C2×D511yescharacteristic
214C3×C4⋊Q8—58no—
215C3×#123—516no—
216C3×#123—516no—
217C3×C22⋊Q8—58no—
218C3×C22⋊Q8C2×D518yescomplemented
219C3×#121—516no—
220C3×C4×D4—58no—
221C3×C4×D4—58no—
222C2×C3×C4⋊C4—51no—
223C2×C3×C4⋊C4—52no—
224C2×C3×C4⋊C4—52no—
225C2×C3×C4⋊C4—52no—
226C2×C3×C4⋊C4—516no—
227C2×C3×C4⋊C4C2×D512yes—
228C2×C3×C4⋊C4C2×D511yescharacteristic
229C2×C3×C22⋊C4—51no—
230C2×C3×C22⋊C4—52no—
231C2×C3×C22⋊C4—51no—
232C2×C3×C22⋊C4—52no—
233C2×C3×C22⋊C4C2×D512yes—
234C2×C3×C42—51no—
235C24×C5C23×C311yescharacteristic
236C23×D5C23×C311yescharacteristic
237C23×D5C23×C312yes—
238C2×C5×Q8—24no—
239C2×C5×Q8C23×C314yes—
240C22×C4×C5—24no—
241C22×C4×C5C23×C312yes—
242C22×C4×C5C23×C312yes—
243C22×C4×C5C23×C311yescharacteristic
244C22×C4×C5C23×C314yes—
245C22×C4×C5C23×C311yescharacteristic
246C2×C22⋊D5—28no—
247C2×C22⋊D5—24no—
248C2×C22⋊D5C23×C318yes—
249C2×C22⋊D5C23×C314yes—
250C22×Dic5C23×C311yescharacteristic
251C22×Dic5C23×C311yescharacteristic
252C22×Dic5C23×C312yes—
253C22×Dic5C23×C311yescharacteristic
254#713—232no—
255#709—232no—
256C2×D20—28no—
257C2×D20C3×D418yescomplemented
258C2×D20C23×C318yes—
259C2×D20C23×C314yes—
260C2×C4×D5—28no—
261C2×C4×D5—28no—
262C2×C4×D5—24no—
263C2×C4×D5—28no—
264C2×C4×D5C23×C318yes—
265C2×C4×D5C23×C318yes—
266C2×C4×D5C23×C314yes—
267C2×C4×D5C23×C318yes—
268C2×Dic10—24no—
269C2×Dic10C23×C314yes—
270C5×C4⋊C4C23×C318yes—
271C5×C4⋊C4C23×C314yes—
272C5×C22⋊C4C23×C318yes—
273C22⋊Dic5C23×C314yes—
274#685C23×C318yes—
275#685C23×C318yes—
276#685C23×C314yes—
277C4⋊Dic5C23×C318yes—
278#683C23×C318yes—
279#683C23×C318yes—
280#683C23×C314yes—
281C4×Dic5C23×C314yes—
282C22×#41—51no—
283C22×#41—51no—
284#547—516no—
285C2×C4⋊Q8—51no—
286C2×#123—52no—
287C2×#123—52no—
288C2×C22⋊Q8—51no—
289C2×C22⋊Q8C3×D511yescharacteristic, complemented
290C2×#121—52no—
291C2×C4×D4—51no—
292C2×C4×D4—51no—
293C22×C4⋊C4—52no—
294C22×C3×C5—22no—
295C22×C3×C5—22no—
296C22×C3×C5—22no—
297C22×C3×C5—44no—
298C22×C3×C5C22×D412yes—
299C22×C3×C5C2×#4112yes—
300C22×C3×C52−1+412yes—
301C22×C3×C5C2511yescharacteristic
302C2×C3×D5—216no—
303C2×C3×D5—24no—
304C2×C3×D5—24no—
305C2×C3×D5—22no—
306C2×C3×D5—22no—
307C2×C3×D5—22no—
308C2×C3×D5—44no—
309C2×C3×D5C22×D418yes—
310C3×C4×C5—22no—
311C3×C4×C5—24no—
312C3×C4×C5—24no—
313C3×C4×C5C22×D414yes—
314C3×Dic5—24no—
315C3×Dic5—22no—
316C3×Dic5—22no—
317C3×Dic5C2×#4114yescomplemented
318C24×C3—52no—
319C24×C3—51no—
320C24×C3C22×D511yescharacteristic
321C3×#41—1032no—
322C3×#41—1032no—
323C2×C3×Q8—24no—
324C2×C3×Q8—54no—
325C2×C3×Q8—104no—
326C2×C3×Q8C22×D514yes—
327C2×C3×D4—54no—
328C2×C3×D4—58no—
329C2×C3×D4—58no—
330C2×C3×D4—54no—
331C2×C3×D4—58no—
332C2×C3×D4—108no—
333C2×C3×D4—104no—
334C2×C3×D4—108no—
335C22×C3×C4—24no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4—51no—
339C22×C3×C4—52no—
340C22×C3×C4—58no—
341C22×C3×C4—58no—
342C22×C3×C4—58no—
343C22×C3×C4—54no—
344C22×C3×C4—108no—
345C22×C3×C4—108no—
346C22×C3×C4—108no—
347C22×C3×C4—104no—
348C22×C3×C4C22×D514yes—
349C22×C3×C4C22×D512yes—
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D512yes—
352C22×C3×C4C22×D511yescharacteristic
353C3×C4⋊C4—54no—
354C3×C4⋊C4—58no—
355C3×C4⋊C4—58no—
356C3×C4⋊C4—58no—
357C3×C4⋊C4C22×D518yes—
358C3×C4⋊C4C22×D514yes—
359C3×C22⋊C4—54no—
360C3×C22⋊C4—58no—
361C3×C22⋊C4—54no—
362C3×C22⋊C4—58no—
363C3×C22⋊C4C22×D518yes—
364C3×C42—54no—
365C23×C5—22no—
366C23×C5—22no—
367C23×C5—22no—
368C23×C5C24×C312yes—
369C23×C5C24×C311yescharacteristic
370C22×D5—24no—
371C22×D5—24no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5C2×C3×D418yes—
376C22×D5C24×C312yes—
377C22×D5C24×C314yes—
378C5×Q8—28no—
379C2×C4×C5—22no—
380C2×C4×C5—24no—
381C2×C4×C5—24no—
382C2×C4×C5—28no—
383C2×C4×C5C2×C3×D414yes—
384C2×C4×C5C24×C314yes—
385C2×C4×C5C24×C312yes—
386C2×C4×C5C24×C314yes—
387C2×C4×C5C24×C312yes—
388C22⋊D5—216no—
389C22⋊D5—28no—
390C2×Dic5—24no—
391C2×Dic5—22no—
392C2×Dic5—22no—
393C2×Dic5C3×#4114yescomplemented
394C2×Dic5C24×C312yes—
395C2×Dic5C24×C314yes—
396C2×Dic5C24×C312yes—
397C2×Dic5C24×C312yes—
398D20—216no—
399D20C2×C3×D4116yescomplemented
400C4×D5—216no—
401C4×D5—216no—
402C4×D5—28no—
403C4×D5—216no—
404Dic10—28no—
405C2×#41—58no—
406C2×#41—58no—
407C2×#41—108no—
408C2×#41—108no—
409C22×Q8—51no—
410C22×Q8C2×C3×D511yescharacteristic
411C22×D4—51no—
412C22×D4—52no—
413C22×D4—51no—
414C22×D4—52no—
415C23×C4—52no—
416C23×C4—52no—
417C23×C4—52no—
418C23×C4—51no—
419C23×C4C2×C3×D511yescharacteristic
420C4⋊Q8—58no—
421#123—516no—
422#123—516no—
423C22⋊Q8—58no—
424C22⋊Q8C2×C3×D518yescomplemented
425#121—516no—
426C4×D4—58no—
427C4×D4—58no—
428C2×C4⋊C4—51no—
429C2×C4⋊C4—52no—
430C2×C4⋊C4—52no—
431C2×C4⋊C4—52no—
432C2×C4⋊C4—516no—
433C2×C4⋊C4C2×C3×D512yes—
434C2×C4⋊C4C2×C3×D511yescharacteristic
435C2×C22⋊C4—51no—
436C2×C22⋊C4—52no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—52no—
439C2×C22⋊C4C2×C3×D512yes—
440C2×C42—51no—
441C2×C3×C5—42no—
442C2×C3×C5#54714yescomplemented
443C2×C3×C5C23×D411yescharacteristic
444C2×C3×C5C22×#4111yescharacteristic
445C2×C3×C5C2×2−1+411yescharacteristic
446C3×D5—28no—
447C3×D5—42no—
448C23×C3—22no—
449C23×C3—22no—
450C23×C3—22no—
451C23×C3—58no—
452C23×C3—54no—
453C23×C3—52no—
454C23×C3—104no—
455C23×C3—104no—
456C23×C3—102no—
457C23×C3—102no—
458C23×C3—102no—
459C23×C3C23×D512yes—
460C23×C3C23×D511yescharacteristic
461C3×Q8—28no—
462C3×Q8—108no—
463C3×D4—516no—
464C3×D4—1016no—
465C3×D4—108no—
466C3×D4—1016no—
467C2×C3×C4—22no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—28no—
471C2×C3×C4—54no—
472C2×C3×C4—52no—
473C2×C3×C4—52no—
474C2×C3×C4—52no—
475C2×C3×C4—54no—
476C2×C3×C4—1016no—
477C2×C3×C4—1016no—
478C2×C3×C4—1016no—
479C2×C3×C4—102no—
480C2×C3×C4—104no—
481C2×C3×C4—102no—
482C2×C3×C4—108no—
483C2×C3×C4D4×D514yes—
484C2×C3×C4C23×D514yes—
485C2×C3×C4C23×D512yes—
486C2×C3×C4C23×D514yes—
487C2×C3×C4C23×D512yes—
488C22×C5—22no—
489C22×C5—22no—
490C22×C5—22no—
491C22×C5—44no—
492C22×C5C22×C3×D412yes—
493C22×C5C2×C3×#4112yes—
494C22×C5C3×2−1+412yes—
495C22×C5C25×C311yescharacteristic
496C2×D5—24no—
497C2×D5—24no—
498C2×D5—216no—
499C2×D5—22no—
500C2×D5—22no—
501C2×D5—22no—
502C2×D5—44no—
503C2×D5C22×C3×D418yes—
504C4×C5—22no—
505C4×C5—24no—
506C4×C5—24no—
507C4×C5C22×C3×D414yes—
508Dic5—24no—
509Dic5—22no—
510Dic5—22no—
511Dic5C2×C3×#4114yescomplemented
512C24—52no—
513C24—51no—
514C24C22×C3×D511yescharacteristic
515#41—1032no—
516#41—1032no—
517C2×Q8—24no—
518C2×Q8—54no—
519C2×Q8—104no—
520C2×Q8C22×C3×D514yes—
521C2×D4—54no—
522C2×D4—58no—
523C2×D4—58no—
524C2×D4—54no—
525C2×D4—58no—
526C2×D4—108no—
527C2×D4—104no—
528C2×D4—108no—
529C22×C4—24no—
530C22×C4—51no—
531C22×C4—51no—
532C22×C4—51no—
533C22×C4—52no—
534C22×C4—58no—
535C22×C4—58no—
536C22×C4—58no—
537C22×C4—54no—
538C22×C4—108no—
539C22×C4—108no—
540C22×C4—108no—
541C22×C4—104no—
542C22×C4C22×C3×D512yes—
543C22×C4C22×C3×D511yescharacteristic
544C22×C4C22×C3×D512yes—
545C22×C4C22×C3×D514yes—
546C22×C4C22×C3×D511yescharacteristic
547C4⋊C4—54no—
548C4⋊C4—58no—
549C4⋊C4—58no—
550C4⋊C4—58no—
551C4⋊C4C22×C3×D518yes—
552C4⋊C4C22×C3×D514yes—
553C22⋊C4—54no—
554C22⋊C4—58no—
555C22⋊C4—54no—
556C22⋊C4—58no—
557C22⋊C4C22×C3×D518yes—
558C42—54no—
559C3×C5C2×#54711yescharacteristic, complemented, Hall
560C22×C3—22no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—44no—
564C22×C3—58no—
565C22×C3—1016no—
566C22×C3—104no—
567C22×C3—104no—
568C22×C3—102no—
569C22×C3—102no—
570C22×C3—102no—
571C22×C3—204no—
572C22×C3C2×D4×D512yes—
573C22×C3#414712yes—
574C22×C3D5×#4112yes—
575C22×C3C24×D511yescharacteristic
576C3×C4—22no—
577C3×C4—24no—
578C3×C4—24no—
579C3×C4—54no—
580C3×C4—102no—
581C3×C4—104no—
582C3×C4—102no—
583C3×C4C2×D4×D514yes—
584C2×C5—42no—
585C2×C5C3×#54714yescomplemented
586C2×C5C23×C3×D411yescharacteristic
587C2×C5C22×C3×#4111yescharacteristic
588C2×C5C2×C3×2−1+411yescharacteristic
589D5—28no—
590D5—42no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—58no—
595C23—54no—
596C23—52no—
597C23—104no—
598C23—104no—
599C23—102no—
600C23—102no—
601C23—102no—
602C23C23×C3×D512yes—
603C23C23×C3×D511yescharacteristic
604Q8—28no—
605Q8—108no—
606D4—516no—
607D4—1016no—
608D4—108no—
609D4—1016no—
610C2×C4—22no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—28no—
614C2×C4—54no—
615C2×C4—52no—
616C2×C4—52no—
617C2×C4—52no—
618C2×C4—54no—
619C2×C4—1016no—
620C2×C4—1016no—
621C2×C4—1016no—
622C2×C4—102no—
623C2×C4—104no—
624C2×C4—102no—
625C2×C4—108no—
626C2×C4C3×D4×D514yes—
627C2×C4C23×C3×D514yes—
628C2×C4C23×C3×D512yes—
629C2×C4C23×C3×D514yes—
630C2×C4C23×C3×D512yes—
631C2×C3—42no—
632C2×C3—108no—
633C2×C3—202no—
634C2×C3#6596514yesdirect product factor
635C2×C3C22×D4×D511yescharacteristic
636C2×C3C2×#414711yescharacteristic
637C2×C3C2×D5×#4111yescharacteristic
638C5C2×C3×#54711yescharacteristic, complemented, Sylow
639C22—22no—
640C22—22no—
641C22—22no—
642C22—44no—
643C22—58no—
644C22—104no—
645C22—104no—
646C22—1016no—
647C22—102no—
648C22—102no—
649C22—102no—
650C22—204no—
651C22C2×C3×D4×D512yes—
652C22C3×#414712yes—
653C22C3×D5×#4112yes—
654C22C24×C3×D511yescharacteristic
655C4—22no—
656C4—24no—
657C4—24no—
658C4—54no—
659C4—102no—
660C4—104no—
661C4—102no—
662C4C2×C3×D4×D514yes—
663C3C2×#6596511yescharacteristic, direct product factor, Sylow
664C2—42no—
665C2—108no—
666C2—202no—
667C2C3×#6596514yesdirect product factor
668C2C22×C3×D4×D511yescharacteristic
669C2C2×C3×#414711yescharacteristic
670C2C2×C3×D5×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×C22⋊Q8C2
socleC23×C3×C5C24
hypercenterC2×C3×C22⋊Q8D5
hypocenterC5C2×C3×#547
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#713C2semidirect
2. C22×C3×#709C2semidirect
3. C2×C3×C5×C22⋊Q8C2semidirect
4. C2×C3×#4090C2semidirect
5. C2×C3×C4×C22⋊D5C2semidirect
6. C3×#65965C2direct (N × H)
7. C2×C3×#4043C2semidirect
8. C2×C3×#4040C2semidirect
9. C2×C3×#4039C2semidirect
10. C2×C3×D5×C4⋊C4C2semidirect
11. C2×C3×#4030C2semidirect
12. C2×C3×#4029C2semidirect
13. C2×#65965C3direct (N × H)
19. C2×C3×#713C22semidirect
21. C2×C3×#709C22semidirect
29. C3×C5×C22⋊Q8C22semidirect
34. C3×#4090C22semidirect
35. C3×C4×C22⋊D5C22semidirect
44. C3×#4043C22semidirect
45. C3×#4040C22semidirect
46. C3×#4039C22semidirect
47. C3×D5×C4⋊C4C22semidirect
48. C3×#4030C22semidirect
49. C3×#4029C22semidirect
51. C22×#713C2×C3semidirect
52. C22×#709C2×C3semidirect
53. C2×C5×C22⋊Q8C2×C3semidirect
54. C2×#4090C2×C3semidirect
55. C2×C4×C22⋊D5C2×C3semidirect
56. #65965C2×C3direct (N × H)
57. C2×#4043C2×C3semidirect
58. C2×#4040C2×C3semidirect
59. C2×#4039C2×C3semidirect
60. C2×D5×C4⋊C4C2×C3semidirect
61. C2×#4030C2×C3semidirect
62. C2×#4029C2×C3semidirect
85. C2×C3×D20D4semidirect
117. C2×C3×C22⋊Q8D5semidirect
127. C2×#713C22×C3semidirect
129. C2×#709C22×C3semidirect
137. C5×C22⋊Q8C22×C3semidirect
142. #4090C22×C3semidirect
143. C4×C22⋊D5C22×C3semidirect
152. #4043C22×C3semidirect
153. #4040C22×C3semidirect
154. #4039C22×C3semidirect
155. D5×C4⋊C4C22×C3semidirect
156. #4030C22×C3semidirect
157. #4029C22×C3semidirect
187. C2×C3×Dic5#41semidirect
193. C3×D20C2×D4semidirect
218. C3×C22⋊Q8C2×D5semidirect
257. C2×D20C3×D4semidirect
289. C2×C22⋊Q8C3×D5semidirect
317. C3×Dic5C2×#41semidirect
393. C2×Dic5C3×#41semidirect
399. D20C2×C3×D4semidirect
424. C22⋊Q8C2×C3×D5semidirect
442. C2×C3×C5#547semidirect
511. Dic5C2×C3×#41semidirect
559. C3×C5C2×#547semidirect
585. C2×C5C3×#547semidirect
634. C2×C3#65965direct (N × H)
638. C5C2×C3×#547semidirect
663. C3C2×#65965direct (N × H)
667. C2C3×#65965direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7132
C22×C3×#7092
C2×C3×C5×C22⋊Q82
C2×C3×#40902
C2×C3×C4×C22⋊D52
C3×#659652
C2×C3×#40432
C2×C3×#40402
C2×C3×#40392
C2×C3×D5×C4⋊C42
C2×C3×#40302
C2×C3×#40292
C2×#659653
C2×C3×#5475