Finite Group Databasebeta

← C3×#10608022 #14321441

Subgroups — C3×#10608022 #14321441

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4084C211yesmaximal, characteristic
2C2×C3×D4×Dic5C211yesmaximal, characteristic, complemented
3C2×C3×#4027C212yesmaximal, complemented
4C2×C3×C42×D5C211yesmaximal, characteristic, complemented
5C3×C5×#390C211yesmaximal, characteristic, complemented
6C3×#65276C211yesmaximal, characteristic, complemented
7C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C3×#65245C212yesmaximal, complemented
9C3×#65234C212yesmaximal, complemented
10C3×C22⋊C4×Dic5C212yesmaximal, complemented
11C3×#65217C211yesmaximal, characteristic, complemented
12#10608022C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C22×C3×C22⋊D5C2212yes—
15C23×C3×Dic5C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2212yes—
21C2×C3×C5×C22⋊C4C2212yes—
22C2×C3×C42×C5C2211yescharacteristic
23C2×C3×C22⋊Dic5C2212yes—
24C2×C3×C22⋊Dic5C2212yes—
25C3×#4084C418yescomplemented
26C3×D4×Dic5—24no—
27C2×C3×#685C2212yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×#683C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2212yes—
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C3×#4027—28no—
36C3×C42×D5—24no—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#3963C2212yes—
40C3×C4×#121—51nomaximal, Hall
41C2×#4084C2×C311yescharacteristic
42C2×D4×Dic5C2×C311yescharacteristic, complemented
43C2×#4027C2×C312yescomplemented
44C2×C42×D5C2×C311yescharacteristic, complemented
45C5×#390C2×C311yescharacteristic, complemented
46#65276C2×C311yescharacteristic, complemented
47C4⋊C4×Dic5C2×C311yescharacteristic, complemented
48#65245C2×C312yescomplemented
49#65234C2×C312yescomplemented
50C22⋊C4×Dic5C2×C312yescomplemented
51#65217C2×C311yescharacteristic, complemented
52C24×C3×C5C2312yes—
53C23×C3×D5C2311yescharacteristic
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4C2×C414yescomplemented
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C2×C3×C22⋊D5—24no—
62C2×C3×C22⋊D5—24no—
63C2×C3×C22⋊D5C2×C418yescomplemented
64C22×C3×Dic5—24no—
65C22×C3×Dic5—24no—
66C22×C3×Dic5—24no—
67C22×C3×Dic5C2312yes—
68C22×C3×Dic5C2311yescharacteristic
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5—22no—
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5—22no—
79C2×C3×C4×D5C2×C414yescomplemented
80C2×C3×C4×D5D414yescomplemented
81C3×C5×C4⋊C4—22no—
82C3×C5×C22⋊C4—24no—
83C3×C5×C22⋊C4—24no—
84C3×C42×C5—22no—
85C3×C22⋊Dic5—24no—
86C3×C22⋊Dic5C2×C418yescomplemented
87C3×#685—24no—
88C3×C4⋊Dic5—22no—
89C3×C4⋊Dic5C2×C414yescomplemented
90C3×#683—24no—
91C3×C4×Dic5—22no—
92C3×C4×Dic5—22no—
93C3×C4×Dic5—24no—
94C3×C4×Dic5D414yescomplemented
95C2×C3×#121—51no—
96C2×C3×C4×D4—51no—
97C2×C3×C4×D4—52no—
98C22×C3×C42—51no—
99C3×#390D511yescharacteristic, complemented
100C3×#389—51no—
101C3×#388—52no—
102C3×#386—52no—
103C3×#380—51no—
104C3×C4×C4⋊C4—51no—
105C3×C4×C22⋊C4—52no—
106C22×C5×D4C22×C311yescharacteristic
107C22×C22⋊D5C22×C312yes—
108C23×Dic5C22×C312yes—
109C22×C4×D5C22×C311yescharacteristic
110C22×C4×D5C22×C311yescharacteristic
111C22×C4×D5C22×C311yescharacteristic
112C2×C5×C4⋊C4C22×C311yescharacteristic
113C2×C5×C22⋊C4C22×C312yes—
114C2×C5×C22⋊C4C22×C312yes—
115C2×C42×C5C22×C311yescharacteristic
116C2×C22⋊Dic5C22×C312yes—
117C2×C22⋊Dic5C22×C312yes—
118#4084C3×C418yescomplemented
119D4×Dic5—24no—
120C2×#685C22×C312yes—
121C2×C4⋊Dic5C22×C311yescharacteristic
122C2×C4⋊Dic5C22×C311yescharacteristic
123C2×#683C22×C312yes—
124C2×C4×Dic5C22×C311yescharacteristic
125C2×C4×Dic5C22×C311yescharacteristic
126C2×C4×Dic5C22×C312yes—
127C2×C4×Dic5C22×C311yescharacteristic
128#4027—28no—
129C42×D5—24no—
130#3963C22×C312yes—
131#3963C22×C312yes—
132#3963C22×C312yes—
133C4×#121—51noSylow
134C23×C3×C5—22no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—22no—
140C23×C3×C5C22×C414yes—
141C23×C3×C5C2411yescharacteristic
142C22×C3×D5—21no—
143C22×C3×D5—21no—
144C22×C3×D5—21no—
145C22×C3×D5—21no—
146C22×C3×D5C22×C412yes—
147C22×C3×D5C2×D412yes—
148C22×C3×D5#4112yes—
149C3×C5×D4—28no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5C22×C412yes—
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5#4112yes—
161C2×C3×C4×C5#4112yes—
162C3×C22⋊D5—216no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—48no—
173C2×C3×Dic5C22×C414yes—
174C2×C3×Dic5C22×C412yes—
175C2×C3×Dic5C2×D412yes—
176C2×C3×Dic5C2×D412yes—
177C2×C3×Dic5C2×D412yes—
178C2×C3×Dic5#4112yes—
179C3×C4×D5—28no—
180C3×C4×D5—28no—
181C3×C4×D5—28no—
182C22×C3×D4—52no—
183C22×C3×D4C2×D511yescharacteristic
184C23×C3×C4—51no—
185C23×C3×C4—51no—
186C23×C3×C4—52no—
187C23×C3×C4—51no—
188C3×#121—58no—
189C3×C4×D4—104no—
190C3×C4×D4—108no—
191C2×C3×C4⋊C4—51no—
192C2×C3×C4⋊C4—51no—
193C2×C3×C4⋊C4—52no—
194C2×C3×C4⋊C4C2×D511yescharacteristic
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C22⋊C4C2×D512yes—
199C2×C3×C22⋊C4C2×D512yes—
200C2×C3×C42—51no—
201C2×C3×C42—51no—
202C2×C3×C42—52no—
203C2×C3×C42—51no—
204C2×C3×C42—104no—
205C2×C3×C42C2×D511yescharacteristic
206C3×#95—52no—
207C3×#95—52no—
208C3×#95—52no—
209C24×C5C23×C312yes—
210C23×D5C23×C311yescharacteristic
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4C2×C3×C414yescomplemented
214C22×C4×C5C23×C312yes—
215C22×C4×C5C23×C311yescharacteristic
216C22×C4×C5C23×C311yescharacteristic
217C22×C4×C5C23×C311yescharacteristic
218C2×C22⋊D5—24no—
219C2×C22⋊D5—24no—
220C2×C22⋊D5C2×C3×C418yescomplemented
221C22×Dic5—24no—
222C22×Dic5—24no—
223C22×Dic5—24no—
224C22×Dic5C23×C312yes—
225C22×Dic5C23×C311yescharacteristic
226C22×Dic5C23×C312yes—
227C22×Dic5C23×C311yescharacteristic
228C22×Dic5C23×C311yescharacteristic
229C2×C4×D5—22no—
230C2×C4×D5—22no—
231C2×C4×D5—22no—
232C2×C4×D5—22no—
233C2×C4×D5—22no—
234C2×C4×D5—22no—
235C2×C4×D5—22no—
236C2×C4×D5C2×C3×C414yescomplemented
237C2×C4×D5C3×D414yescomplemented
238C5×C4⋊C4—22no—
239C5×C22⋊C4—24no—
240C5×C22⋊C4—24no—
241C42×C5—22no—
242C22⋊Dic5—24no—
243C22⋊Dic5C2×C3×C418yescomplemented
244#685—24no—
245C4⋊Dic5—22no—
246C4⋊Dic5C2×C3×C414yescomplemented
247#683—24no—
248C4×Dic5—22no—
249C4×Dic5—22no—
250C4×Dic5—24no—
251C4×Dic5C3×D414yescomplemented
252C2×#121—51no—
253C2×C4×D4—51no—
254C2×C4×D4—52no—
255C22×C42—51no—
256#390C3×D511yescharacteristic, complemented
257#389—51no—
258#388—52no—
259#386—52no—
260#380—51no—
261C4×C4⋊C4—51no—
262C4×C22⋊C4—52no—
263C22×C3×C5—24no—
264C22×C3×C5—24no—
265C22×C3×C5—24no—
266C22×C3×C5—42no—
267C22×C3×C5—42no—
268C22×C3×C5—42no—
269C22×C3×C5—42no—
270C22×C3×C5C23×C411yescharacteristic
271C22×C3×C5C22×D411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C2×#4111yescharacteristic
274C22×C3×C5C2×#4111yescharacteristic
275C22×C3×C5C2×#4111yescharacteristic
276C22×C3×C5C2×#4111yescharacteristic
277C2×C3×D5—22no—
278C2×C3×D5—22no—
279C2×C3×D5—22no—
280C2×C3×D5—22no—
281C2×C3×D5—22no—
282C2×C3×D5—22no—
283C2×C3×D5C4×D414yescomplemented
284C3×C4×C5—22no—
285C3×C4×C5—22no—
286C3×C4×C5—42no—
287C3×C4×C5C4×D414yescomplemented
288C3×Dic5—22no—
289C3×Dic5—24no—
290C3×Dic5—22no—
291C3×Dic5—42no—
292C3×Dic5#12114yescomplemented
293C24×C3—51no—
294C24×C3C22×D512yes—
295C2×C3×D4—22no—
296C2×C3×D4—22no—
297C2×C3×D4—58no—
298C2×C3×D4—104no—
299C2×C3×D4—104no—
300C2×C3×D4C4×D514yescomplemented
301C22×C3×C4—51no—
302C22×C3×C4—51no—
303C22×C3×C4—51no—
304C22×C3×C4—52no—
305C22×C3×C4—54no—
306C22×C3×C4—54no—
307C22×C3×C4—52no—
308C22×C3×C4—102no—
309C22×C3×C4—102no—
310C22×C3×C4—102no—
311C22×C3×C4—102no—
312C22×C3×C4—104no—
313C22×C3×C4—104no—
314C22×C3×C4—104no—
315C22×C3×C4—102no—
316C22×C3×C4—102no—
317C22×C3×C4—102no—
318C22×C3×C4C22×D512yes—
319C22×C3×C4C22×D511yescharacteristic
320C22×C3×C4C22×D511yescharacteristic
321C22×C3×C4C22×D511yescharacteristic
322C3×C4⋊C4—22no—
323C3×C4⋊C4—54no—
324C3×C4⋊C4—104no—
325C3×C4⋊C4—102no—
326C3×C22⋊C4—24no—
327C3×C22⋊C4—24no—
328C3×C22⋊C4—58no—
329C3×C22⋊C4—104no—
330C3×C22⋊C4—104no—
331C3×C42—22no—
332C3×C42—54no—
333C3×C42—102no—
334C3×C42—102no—
335C3×C42—104no—
336C23×C5—22no—
337C23×C5—22no—
338C23×C5—22no—
339C23×C5—22no—
340C23×C5—22no—
341C23×C5—22no—
342C23×C5C22×C3×C414yes—
343C23×C5C24×C311yescharacteristic
344C22×D5—21no—
345C22×D5—21no—
346C22×D5—21no—
347C22×D5—21no—
348C22×D5C22×C3×C412yes—
349C22×D5C2×C3×D412yes—
350C22×D5C3×#4112yes—
351C5×D4—28no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—21no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5C22×C3×C412yes—
360C2×C4×C5C2×C3×D412yes—
361C2×C4×C5C2×C3×D412yes—
362C2×C4×C5C3×#4112yes—
363C2×C4×C5C3×#4112yes—
364C22⋊D5—216no—
365C2×Dic5—21no—
366C2×Dic5—22no—
367C2×Dic5—21no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—48no—
375C2×Dic5C22×C3×C414yes—
376C2×Dic5C22×C3×C412yes—
377C2×Dic5C2×C3×D412yes—
378C2×Dic5C2×C3×D412yes—
379C2×Dic5C2×C3×D412yes—
380C2×Dic5C3×#4112yes—
381C4×D5—28no—
382C4×D5—28no—
383C4×D5—28no—
384C22×D4—52no—
385C22×D4C2×C3×D511yescharacteristic
386C23×C4—51no—
387C23×C4—51no—
388C23×C4—52no—
389C23×C4—51no—
390#121—58no—
391C4×D4—104no—
392C4×D4—108no—
393C2×C4⋊C4—51no—
394C2×C4⋊C4—51no—
395C2×C4⋊C4—52no—
396C2×C4⋊C4C2×C3×D511yescharacteristic
397C2×C22⋊C4—52no—
398C2×C22⋊C4—52no—
399C2×C22⋊C4—52no—
400C2×C22⋊C4C2×C3×D512yes—
401C2×C22⋊C4C2×C3×D512yes—
402C2×C42—51no—
403C2×C42—52no—
404C2×C42—51no—
405C2×C42—51no—
406C2×C42—104no—
407C2×C42C2×C3×D511yescharacteristic
408#95—52no—
409#95—52no—
410#95—52no—
411C2×C3×C5—44no—
412C2×C3×C5C2×C4×D411yescharacteristic
413C2×C3×C5C2×C4×D411yescharacteristic
414C2×C3×C5C4×#4111yescharacteristic
415C2×C3×C5C2×#12111yescharacteristic
416C2×C3×C5#52511yescharacteristic
417C2×C3×C5#52911yescharacteristic
418C2×C3×C5#53211yescharacteristic
419C3×D5—24no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—52no—
427C23×C3—52no—
428C23×C3—52no—
429C23×C3—101no—
430C23×C3—101no—
431C23×C3—101no—
432C23×C3—101no—
433C23×C3C2×C4×D514yes—
434C23×C3C23×D511yescharacteristic
435C3×D4—28no—
436C3×D4—1016no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—52no—
445C2×C3×C4—52no—
446C2×C3×C4—52no—
447C2×C3×C4—52no—
448C2×C3×C4—54no—
449C2×C3×C4—52no—
450C2×C3×C4—108no—
451C2×C3×C4—108no—
452C2×C3×C4—101no—
453C2×C3×C4—102no—
454C2×C3×C4—101no—
455C2×C3×C4—101no—
456C2×C3×C4—101no—
457C2×C3×C4—102no—
458C2×C3×C4—108no—
459C2×C3×C4—102no—
460C2×C3×C4—102no—
461C2×C3×C4—102no—
462C2×C3×C4—208no—
463C2×C3×C4C2×C4×D512yes—
464C2×C3×C4D4×D512yes—
465C2×C3×C4D4×D512yes—
466C2×C3×C4#71112yes—
467C2×C3×C4#71112yes—
468C22×C5—24no—
469C22×C5—24no—
470C22×C5—24no—
471C22×C5—42no—
472C22×C5—42no—
473C22×C5—42no—
474C22×C5—42no—
475C22×C5C23×C3×C411yescharacteristic
476C22×C5C22×C3×D411yescharacteristic
477C22×C5C22×C3×D411yescharacteristic
478C22×C5C2×C3×#4111yescharacteristic
479C22×C5C2×C3×#4111yescharacteristic
480C22×C5C2×C3×#4111yescharacteristic
481C22×C5C2×C3×#4111yescharacteristic
482C2×D5—22no—
483C2×D5—22no—
484C2×D5—22no—
485C2×D5—22no—
486C2×D5—22no—
487C2×D5—22no—
488C2×D5C3×C4×D414yescomplemented
489C4×C5—22no—
490C4×C5—22no—
491C4×C5—42no—
492C4×C5C3×C4×D414yescomplemented
493Dic5—22no—
494Dic5—24no—
495Dic5—22no—
496Dic5—42no—
497Dic5C3×#12114yescomplemented
498C24—51no—
499C24C22×C3×D512yes—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—58no—
503C2×D4—104no—
504C2×D4—104no—
505C2×D4C3×C4×D514yescomplemented
506C22×C4—51no—
507C22×C4—51no—
508C22×C4—51no—
509C22×C4—52no—
510C22×C4—54no—
511C22×C4—54no—
512C22×C4—52no—
513C22×C4—102no—
514C22×C4—102no—
515C22×C4—102no—
516C22×C4—102no—
517C22×C4—104no—
518C22×C4—104no—
519C22×C4—104no—
520C22×C4—102no—
521C22×C4—102no—
522C22×C4—102no—
523C22×C4C22×C3×D512yes—
524C22×C4C22×C3×D511yescharacteristic
525C22×C4C22×C3×D511yescharacteristic
526C22×C4C22×C3×D511yescharacteristic
527C4⋊C4—22no—
528C4⋊C4—54no—
529C4⋊C4—104no—
530C4⋊C4—102no—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—58no—
534C22⋊C4—104no—
535C22⋊C4—104no—
536C42—22no—
537C42—54no—
538C42—102no—
539C42—102no—
540C42—104no—
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3—24no—
543C22×C3—24no—
544C22×C3—24no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—54no—
550C22×C3—102no—
551C22×C3—102no—
552C22×C3—102no—
553C22×C3—102no—
554C22×C3—102no—
555C22×C3—102no—
556C22×C3C22×C4×D511yescharacteristic
557C22×C3C2×D4×D511yescharacteristic
558C22×C3C2×D4×D511yescharacteristic
559C22×C3C2×#71111yescharacteristic
560C22×C3C2×#71111yescharacteristic
561C22×C3D5×#4111yescharacteristic
562C22×C3D5×#4111yescharacteristic
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—42no—
566C3×C4—54no—
567C3×C4—102no—
568C3×C4—104no—
569C3×C4—102no—
570C3×C4—202no—
571C3×C4#402714yescomplemented
572C2×C5—44no—
573C2×C5C2×C3×C4×D411yescharacteristic
574C2×C5C2×C3×C4×D411yescharacteristic
575C2×C5C3×C4×#4111yescharacteristic
576C2×C5C2×C3×#12111yescharacteristic
577C2×C5C3×#52511yescharacteristic
578C2×C5C3×#52911yescharacteristic
579C2×C5C3×#53211yescharacteristic
580D5—24no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—52no—
588C23—52no—
589C23—52no—
590C23—101no—
591C23—101no—
592C23—101no—
593C23—101no—
594C23C2×C3×C4×D514yes—
595C23C23×C3×D511yescharacteristic
596D4—28no—
597D4—1016no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—52no—
606C2×C4—52no—
607C2×C4—52no—
608C2×C4—52no—
609C2×C4—54no—
610C2×C4—52no—
611C2×C4—108no—
612C2×C4—108no—
613C2×C4—101no—
614C2×C4—102no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—101no—
618C2×C4—102no—
619C2×C4—108no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—102no—
623C2×C4—208no—
624C2×C4C2×C3×C4×D512yes—
625C2×C4C3×D4×D512yes—
626C2×C4C3×D4×D512yes—
627C2×C4C3×#71112yes—
628C2×C4C3×#71112yes—
629C2×C3—44no—
630C2×C3—104no—
631C2×C3C2×#402711yescharacteristic
632C2×C3C4×#71111yescharacteristic
633C2×C3C4×D4×D511yescharacteristic
634C2×C3D5×#12111yescharacteristic
635C2×C3#6594011yescharacteristic
636C2×C3#6601411yescharacteristic
637C2×C3#6605011yescharacteristic
638C5C3×C4×#12111yescharacteristic, complemented, Sylow
639C22—24no—
640C22—24no—
641C22—24no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—54no—
647C22—102no—
648C22—102no—
649C22—102no—
650C22—102no—
651C22—102no—
652C22—102no—
653C22C22×C3×C4×D511yescharacteristic
654C22C2×C3×D4×D511yescharacteristic
655C22C2×C3×D4×D511yescharacteristic
656C22C2×C3×#71111yescharacteristic
657C22C2×C3×#71111yescharacteristic
658C22C3×D5×#4111yescharacteristic
659C22C3×D5×#4111yescharacteristic
660C4—22no—
661C4—22no—
662C4—42no—
663C4—54no—
664C4—104no—
665C4—102no—
666C4—102no—
667C4—202no—
668C4C3×#402714yescomplemented
669C3#1060802211yescharacteristic, direct product factor, Sylow
670C2—44no—
671C2—104no—
672C2C2×C3×#402711yescharacteristic
673C2C3×C4×#71111yescharacteristic
674C2C3×C4×D4×D511yescharacteristic
675C2C3×D5×#12111yescharacteristic
676C2C3×#6594011yescharacteristic
677C2C3×#6601411yescharacteristic
678C2C3×#6605011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#390C2
socleC23×C3×C5C24
prime radicalC2×C3×#4084C2
cosocleC23×C5C24×C3
hypercenterC3×#390D5
hypocenterC5C3×C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C2×C3×D4×Dic5C2semidirect
3. C2×C3×#4027C2semidirect
4. C2×C3×C42×D5C2semidirect
5. C3×C5×#390C2semidirect
6. C3×#65276C2semidirect
7. C3×C4⋊C4×Dic5C2semidirect
8. C3×#65245C2semidirect
9. C3×#65234C2semidirect
10. C3×C22⋊C4×Dic5C2semidirect
11. C3×#65217C2semidirect
12. #10608022C3direct (N × H)
25. C3×#4084C4semidirect
42. C2×D4×Dic5C2×C3semidirect
43. C2×#4027C2×C3semidirect
44. C2×C42×D5C2×C3semidirect
45. C5×#390C2×C3semidirect
46. #65276C2×C3semidirect
47. C4⋊C4×Dic5C2×C3semidirect
48. #65245C2×C3semidirect
49. #65234C2×C3semidirect
50. C22⋊C4×Dic5C2×C3semidirect
51. #65217C2×C3semidirect
56. C2×C3×C5×D4C2×C4semidirect
63. C2×C3×C22⋊D5C2×C4semidirect
79. C2×C3×C4×D5C2×C4semidirect
80. C2×C3×C4×D5D4semidirect
86. C3×C22⋊Dic5C2×C4semidirect
89. C3×C4⋊Dic5C2×C4semidirect
94. C3×C4×Dic5D4semidirect
99. C3×#390D5semidirect
118. #4084C3×C4semidirect
213. C2×C5×D4C2×C3×C4semidirect
220. C2×C22⋊D5C2×C3×C4semidirect
236. C2×C4×D5C2×C3×C4semidirect
237. C2×C4×D5C3×D4semidirect
243. C22⋊Dic5C2×C3×C4semidirect
246. C4⋊Dic5C2×C3×C4semidirect
251. C4×Dic5C3×D4semidirect
256. #390C3×D5semidirect
283. C2×C3×D5C4×D4semidirect
287. C3×C4×C5C4×D4semidirect
292. C3×Dic5#121semidirect
300. C2×C3×D4C4×D5semidirect
488. C2×D5C3×C4×D4semidirect
492. C4×C5C3×C4×D4semidirect
497. Dic5C3×#121semidirect
505. C2×D4C3×C4×D5semidirect
541. C3×C5C4×#121semidirect
571. C3×C4#4027semidirect
638. C5C3×C4×#121semidirect
668. C4C3×#4027semidirect
669. C3#10608022direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40842
C2×C3×D4×Dic52
C2×C3×#40272
C2×C3×C42×D52
C3×C5×#3902
C3×#652762
C3×C4⋊C4×Dic52
C3×#652452
C3×#652342
C3×C22⋊C4×Dic52
C3×#652172
#106080223
C3×C4×#1215