Finite Group Databasebeta

← C3×#10607695 #14321417

Subgroups — C3×#10607695 #14321417

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×#4041C211yesmaximal, characteristic
2C2×C3×#4039C211yesmaximal, characteristic, complemented
3C2×C3×#4039C212yesmaximal, complemented
4C2×C3×C42×D5C211yesmaximal, characteristic, complemented
5C3×C5×#389C211yesmaximal, characteristic, complemented
6C3×#65279C212yesmaximal, complemented
7C3×#65276C211yesmaximal, characteristic, complemented
8C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C3×#65228C211yesmaximal, characteristic, complemented
10C3×#64955C212yesmaximal, complemented
11C3×#64954C212yesmaximal, complemented
12#10607695C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×D20C2212yes—
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×C3×C4×D5C2212yes—
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2212yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×C3×#685C2212yes—
24C2×C3×#685C2212yes—
25C2×C3×#685C2212yes—
26C2×C3×#685C2212yes—
27C2×C3×#685C2212yes—
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4×Dic5C2211yescharacteristic
30C2×C3×C4×Dic5C2212yes—
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C3×#4041C418yescomplemented
34C3×#4039—28no—
35C3×#4039—24no—
36C3×C42×D5—24no—
37C3×C5×#95C2212yes—
38C3×#3963C2212yes—
39C3×#3963C2212yes—
40C3×C4×#121—51nomaximal, Hall
41C2×#4041C2×C311yescharacteristic
42C2×#4039C2×C311yescharacteristic, complemented
43C2×#4039C2×C312yescomplemented
44C2×C42×D5C2×C311yescharacteristic, complemented
45C5×#389C2×C311yescharacteristic, complemented
46#65279C2×C312yescomplemented
47#65276C2×C311yescharacteristic, complemented
48C4⋊C4×Dic5C2×C311yescharacteristic, complemented
49#65228C2×C311yescharacteristic, complemented
50#64955C2×C312yescomplemented
51#64954C2×C312yescomplemented
52C23×C3×D5C2312yes—
53C23×C3×D5C2311yescharacteristic
54C22×C3×C4×C5C2312yes—
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×Dic5C2312yes—
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C2×C3×D20—24no—
64C2×C3×D20—24no—
65C2×C3×D20—22no—
66C2×C3×D20—22no—
67C2×C3×D20C2×C418yescomplemented
68C2×C3×D20C2×C414yescomplemented
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5—22no—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—22no—
75C2×C3×C4×D5—22no—
76C2×C3×C4×D5—24no—
77C2×C3×C4×D5—24no—
78C2×C3×C4×D5—24no—
79C2×C3×C4×D5C2×C414yescomplemented
80C2×C3×C4×D5D414yescomplemented
81C3×C5×C4⋊C4—24no—
82C3×C5×C4⋊C4—22no—
83C3×C5×C4⋊C4C2×C414yescomplemented
84C3×C42×C5—22no—
85C3×#685—24no—
86C3×#685—24no—
87C3×#685—24no—
88C3×#685—24no—
89C3×#685C2×C418yescomplemented
90C3×C4⋊Dic5—22no—
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×#390—51no—
100C3×#389D511yescharacteristic, complemented
101C3×#388—52no—
102C3×#386—52no—
103C3×#380—51no—
104C3×C4×C4⋊C4—51no—
105C3×C4×C22⋊C4—52no—
106C22×D20C22×C312yes—
107C22×D20C22×C311yescharacteristic
108C22×C4×D5C22×C311yescharacteristic
109C22×C4×D5C22×C312yes—
110C22×C4×D5C22×C311yescharacteristic
111C22×C4×D5C22×C311yescharacteristic
112C2×C5×C4⋊C4C22×C311yescharacteristic
113C2×C5×C4⋊C4C22×C312yes—
114C2×C5×C4⋊C4C22×C311yescharacteristic
115C2×C42×C5C22×C311yescharacteristic
116C2×#685C22×C312yes—
117C2×#685C22×C312yes—
118C2×#685C22×C312yes—
119C2×#685C22×C312yes—
120C2×#685C22×C312yes—
121C2×C4⋊Dic5C22×C311yescharacteristic
122C2×C4×Dic5C22×C311yescharacteristic
123C2×C4×Dic5C22×C311yescharacteristic
124C2×C4×Dic5C22×C312yes—
125C2×C4×Dic5C22×C311yescharacteristic
126#4041C3×C418yescomplemented
127#4039—28no—
128#4039—24no—
129C42×D5—24no—
130C5×#95C22×C312yes—
131#3963C22×C312yes—
132#3963C22×C312yes—
133C4×#121—51noSylow
134C23×C3×C5C2411yescharacteristic
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5—21no—
138C22×C3×D5—21no—
139C22×C3×D5—22no—
140C22×C3×D5—22no—
141C22×C3×D5—22no—
142C22×C3×D5—22no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5C22×C414yes—
146C22×C3×D5C22×C412yes—
147C22×C3×D5C2×D412yes—
148C22×C3×D5#4112yes—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—22no—
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×C5—22no—
158C2×C3×C4×C5C22×C414yes—
159C2×C3×C4×C5C22×C412yes—
160C2×C3×C4×C5C2×D412yes—
161C2×C3×C4×C5C2×D412yes—
162C2×C3×C4×C5#4112yes—
163C2×C3×C4×C5#4112yes—
164C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
172C2×C3×Dic5C2×D412yes—
173C2×C3×Dic5C2×D412yes—
174C2×C3×Dic5C2×D412yes—
175C2×C3×Dic5#4112yes—
176C3×D20—216no—
177C3×D20—28no—
178C3×C4×D5—28no—
179C3×C4×D5—28no—
180C3×C4×D5—28no—
181C3×C4×D5—48no—
182C22×C3×D4—52no—
183C22×C3×D4—51no—
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⋊C4C2×D511yescharacteristic
193C2×C3×C4⋊C4C2×D512yes—
194C2×C3×C4⋊C4C2×D511yescharacteristic
195C2×C3×C22⋊C4—52no—
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C22⋊C4—52no—
199C2×C3×C22⋊C4—52no—
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×#95C2×D512yes—
209C23×D5C23×C312yes—
210C23×D5C23×C311yescharacteristic
211C22×C4×C5C23×C312yes—
212C22×C4×C5C23×C312yes—
213C22×C4×C5C23×C311yescharacteristic
214C22×C4×C5C23×C311yescharacteristic
215C22×C4×C5C23×C311yescharacteristic
216C22×Dic5C23×C312yes—
217C22×Dic5C23×C311yescharacteristic
218C22×Dic5C23×C311yescharacteristic
219C22×Dic5C23×C311yescharacteristic
220C2×D20—24no—
221C2×D20—24no—
222C2×D20—22no—
223C2×D20—22no—
224C2×D20C2×C3×C418yescomplemented
225C2×D20C2×C3×C414yescomplemented
226C2×C4×D5—22no—
227C2×C4×D5—22no—
228C2×C4×D5—22no—
229C2×C4×D5—22no—
230C2×C4×D5—22no—
231C2×C4×D5—22no—
232C2×C4×D5—22no—
233C2×C4×D5—24no—
234C2×C4×D5—24no—
235C2×C4×D5—24no—
236C2×C4×D5C2×C3×C414yescomplemented
237C2×C4×D5C3×D414yescomplemented
238C5×C4⋊C4—24no—
239C5×C4⋊C4—22no—
240C5×C4⋊C4C2×C3×C414yescomplemented
241C42×C5—22no—
242#685—24no—
243#685—24no—
244#685—24no—
245#685—24no—
246#685C2×C3×C418yescomplemented
247C4⋊Dic5—22no—
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#390—51no—
257#389C3×D511yescharacteristic, complemented
258#388—52no—
259#386—52no—
260#380—51no—
261C4×C4⋊C4—51no—
262C4×C22⋊C4—52no—
263C22×C3×C5C23×C411yescharacteristic
264C22×C3×C5C22×D411yescharacteristic
265C22×C3×C5C22×D411yescharacteristic
266C22×C3×C5C2×#4111yescharacteristic
267C22×C3×C5C2×#4111yescharacteristic
268C22×C3×C5C2×#4111yescharacteristic
269C22×C3×C5C2×#4111yescharacteristic
270C2×C3×D5—22no—
271C2×C3×D5—22no—
272C2×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5—22no—
275C2×C3×D5—22no—
276C2×C3×D5—24no—
277C2×C3×D5—24no—
278C2×C3×D5—24no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5C4×D414yescomplemented
284C3×C4×C5—24no—
285C3×C4×C5—22no—
286C3×C4×C5—22no—
287C3×C4×C5—42no—
288C3×C4×C5C4×D414yescomplemented
289C3×Dic5—22no—
290C3×Dic5—22no—
291C3×Dic5—42no—
292C3×Dic5#12114yescomplemented
293C24×C3—51no—
294C24×C3—52no—
295C2×C3×D4—58no—
296C2×C3×D4—54no—
297C2×C3×D4—104no—
298C2×C3×D4—104no—
299C2×C3×D4—102no—
300C2×C3×D4—102no—
301C22×C3×C4—51no—
302C22×C3×C4—51no—
303C22×C3×C4—51no—
304C22×C3×C4—54no—
305C22×C3×C4—54no—
306C22×C3×C4—52no—
307C22×C3×C4—102no—
308C22×C3×C4—102no—
309C22×C3×C4—102no—
310C22×C3×C4—104no—
311C22×C3×C4—104no—
312C22×C3×C4—104no—
313C22×C3×C4—102no—
314C22×C3×C4—102no—
315C22×C3×C4—102no—
316C22×C3×C4—102no—
317C22×C3×C4C22×D512yes—
318C22×C3×C4C22×D512yes—
319C22×C3×C4C22×D511yescharacteristic
320C22×C3×C4C22×D511yescharacteristic
321C22×C3×C4C22×D511yescharacteristic
322C3×C4⋊C4—24no—
323C3×C4⋊C4—22no—
324C3×C4⋊C4—102no—
325C3×C4⋊C4C4×D514yescomplemented
326C3×C22⋊C4—58no—
327C3×C22⋊C4—104no—
328C3×C22⋊C4—104no—
329C3×C22⋊C4—104no—
330C3×C22⋊C4—104no—
331C3×C42—22no—
332C3×C42—54no—
333C3×C42—102no—
334C3×C42—102no—
335C3×C42—104no—
336C23×C5C24×C311yescharacteristic
337C22×D5—21no—
338C22×D5—21no—
339C22×D5—21no—
340C22×D5—21no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5C22×C3×C414yes—
348C22×D5C22×C3×C412yes—
349C22×D5C2×C3×D412yes—
350C22×D5C3×#4112yes—
351C2×C4×C5—21no—
352C2×C4×C5—21no—
353C2×C4×C5—22no—
354C2×C4×C5—21no—
355C2×C4×C5—21no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5C22×C3×C414yes—
361C2×C4×C5C22×C3×C412yes—
362C2×C4×C5C2×C3×D412yes—
363C2×C4×C5C2×C3×D412yes—
364C2×C4×C5C3×#4112yes—
365C2×C4×C5C3×#4112yes—
366C2×Dic5—21no—
367C2×Dic5—21no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5C22×C3×C412yes—
374C2×Dic5C2×C3×D412yes—
375C2×Dic5C2×C3×D412yes—
376C2×Dic5C2×C3×D412yes—
377C2×Dic5C3×#4112yes—
378D20—216no—
379D20—28no—
380C4×D5—28no—
381C4×D5—28no—
382C4×D5—28no—
383C4×D5—48no—
384C22×D4—52no—
385C22×D4—51no—
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⋊C4C2×C3×D511yescharacteristic
395C2×C4⋊C4C2×C3×D512yes—
396C2×C4⋊C4C2×C3×D511yescharacteristic
397C2×C22⋊C4—52no—
398C2×C22⋊C4—52no—
399C2×C22⋊C4—52no—
400C2×C22⋊C4—52no—
401C2×C22⋊C4—52no—
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#95C2×C3×D512yes—
411C2×C3×C5C2×C4×D411yescharacteristic
412C2×C3×C5C2×C4×D411yescharacteristic
413C2×C3×C5C4×#4111yescharacteristic
414C2×C3×C5C2×#12111yescharacteristic
415C2×C3×C5#52511yescharacteristic
416C2×C3×C5#52911yescharacteristic
417C2×C3×C5#53211yescharacteristic
418C3×D5—24no—
419C3×D5—44no—
420C23×C3—52no—
421C23×C3—52no—
422C23×C3—52no—
423C23×C3—54no—
424C23×C3—101no—
425C23×C3—101no—
426C23×C3—101no—
427C23×C3—101no—
428C23×C3—102no—
429C23×C3—102no—
430C23×C3—102no—
431C23×C3—102no—
432C23×C3—102no—
433C23×C3—102no—
434C23×C3C23×D511yescharacteristic
435C3×D4—1016no—
436C3×D4—108no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—52no—
447C2×C3×C4—52no—
448C2×C3×C4—52no—
449C2×C3×C4—52no—
450C2×C3×C4—52no—
451C2×C3×C4—108no—
452C2×C3×C4—108no—
453C2×C3×C4—101no—
454C2×C3×C4—101no—
455C2×C3×C4—101no—
456C2×C3×C4—101no—
457C2×C3×C4—108no—
458C2×C3×C4—102no—
459C2×C3×C4—102no—
460C2×C3×C4—102no—
461C2×C3×C4—208no—
462C2×C3×C4C2×C4×D514yes—
463C2×C3×C4C2×C4×D512yes—
464C2×C3×C4D4×D512yes—
465C2×C3×C4D4×D512yes—
466C2×C3×C4#71312yes—
467C2×C3×C4#71312yes—
468C22×C5C23×C3×C411yescharacteristic
469C22×C5C22×C3×D411yescharacteristic
470C22×C5C22×C3×D411yescharacteristic
471C22×C5C2×C3×#4111yescharacteristic
472C22×C5C2×C3×#4111yescharacteristic
473C22×C5C2×C3×#4111yescharacteristic
474C22×C5C2×C3×#4111yescharacteristic
475C2×D5—22no—
476C2×D5—22no—
477C2×D5—22no—
478C2×D5—22no—
479C2×D5—22no—
480C2×D5—22no—
481C2×D5—24no—
482C2×D5—24no—
483C2×D5—24no—
484C2×D5—42no—
485C2×D5—42no—
486C2×D5—42no—
487C2×D5—42no—
488C2×D5C3×C4×D414yescomplemented
489C4×C5—24no—
490C4×C5—22no—
491C4×C5—22no—
492C4×C5—42no—
493C4×C5C3×C4×D414yescomplemented
494Dic5—22no—
495Dic5—22no—
496Dic5—42no—
497Dic5C3×#12114yescomplemented
498C24—51no—
499C24—52no—
500C2×D4—58no—
501C2×D4—54no—
502C2×D4—104no—
503C2×D4—104no—
504C2×D4—102no—
505C2×D4—102no—
506C22×C4—51no—
507C22×C4—51no—
508C22×C4—51no—
509C22×C4—54no—
510C22×C4—54no—
511C22×C4—52no—
512C22×C4—102no—
513C22×C4—102no—
514C22×C4—102no—
515C22×C4—104no—
516C22×C4—104no—
517C22×C4—104no—
518C22×C4—102no—
519C22×C4—102no—
520C22×C4—102no—
521C22×C4—102no—
522C22×C4C22×C3×D512yes—
523C22×C4C22×C3×D512yes—
524C22×C4C22×C3×D511yescharacteristic
525C22×C4C22×C3×D511yescharacteristic
526C22×C4C22×C3×D511yescharacteristic
527C4⋊C4—24no—
528C4⋊C4—22no—
529C4⋊C4—102no—
530C4⋊C4C3×C4×D514yescomplemented
531C22⋊C4—58no—
532C22⋊C4—104no—
533C22⋊C4—104no—
534C22⋊C4—104no—
535C22⋊C4—104no—
536C42—22no—
537C42—54no—
538C42—102no—
539C42—102no—
540C42—104no—
541C3×C5C4×#12111yescharacteristic, complemented, Hall
542C22×C3—54no—
543C22×C3—102no—
544C22×C3—102no—
545C22×C3—102no—
546C22×C3—102no—
547C22×C3—102no—
548C22×C3—102no—
549C22×C3—104no—
550C22×C3—104no—
551C22×C3—104no—
552C22×C3—202no—
553C22×C3—202no—
554C22×C3—202no—
555C22×C3—202no—
556C22×C3C22×C4×D511yescharacteristic
557C22×C3C2×D4×D511yescharacteristic
558C22×C3C2×D4×D511yescharacteristic
559C22×C3C2×#71311yescharacteristic
560C22×C3C2×#71311yescharacteristic
561C22×C3D5×#4111yescharacteristic
562C22×C3D5×#4111yescharacteristic
563C3×C4—24no—
564C3×C4—22no—
565C3×C4—22no—
566C3×C4—42no—
567C3×C4—54no—
568C3×C4—102no—
569C3×C4—102no—
570C3×C4—202no—
571C3×C4#403914yescomplemented
572C2×C5C2×C3×C4×D411yescharacteristic
573C2×C5C2×C3×C4×D411yescharacteristic
574C2×C5C3×C4×#4111yescharacteristic
575C2×C5C2×C3×#12111yescharacteristic
576C2×C5C3×#52511yescharacteristic
577C2×C5C3×#52911yescharacteristic
578C2×C5C3×#53211yescharacteristic
579D5—24no—
580D5—44no—
581C23—52no—
582C23—52no—
583C23—52no—
584C23—54no—
585C23—101no—
586C23—101no—
587C23—101no—
588C23—101no—
589C23—102no—
590C23—102no—
591C23—102no—
592C23—102no—
593C23—102no—
594C23—102no—
595C23C23×C3×D511yescharacteristic
596D4—1016no—
597D4—108no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—22no—
606C2×C4—22no—
607C2×C4—52no—
608C2×C4—52no—
609C2×C4—52no—
610C2×C4—52no—
611C2×C4—52no—
612C2×C4—108no—
613C2×C4—108no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—101no—
618C2×C4—108no—
619C2×C4—102no—
620C2×C4—102no—
621C2×C4—102no—
622C2×C4—208no—
623C2×C4C2×C3×C4×D514yes—
624C2×C4C2×C3×C4×D512yes—
625C2×C4C3×D4×D512yes—
626C2×C4C3×D4×D512yes—
627C2×C4C3×#71312yes—
628C2×C4C3×#71312yes—
629C2×C3—104no—
630C2×C3—204no—
631C2×C3C2×#403911yescharacteristic
632C2×C3C4×D4×D511yescharacteristic
633C2×C3C4×#71311yescharacteristic
634C2×C3D5×#12111yescharacteristic
635C2×C3#6596111yescharacteristic
636C2×C3#6602511yescharacteristic
637C2×C3#6605911yescharacteristic
638C5C3×C4×#12111yescharacteristic, complemented, Sylow
639C22—54no—
640C22—102no—
641C22—102no—
642C22—102no—
643C22—102no—
644C22—102no—
645C22—102no—
646C22—104no—
647C22—104no—
648C22—104no—
649C22—202no—
650C22—202no—
651C22—202no—
652C22—202no—
653C22C22×C3×C4×D511yescharacteristic
654C22C2×C3×D4×D511yescharacteristic
655C22C2×C3×D4×D511yescharacteristic
656C22C2×C3×#71311yescharacteristic
657C22C2×C3×#71311yescharacteristic
658C22C3×D5×#4111yescharacteristic
659C22C3×D5×#4111yescharacteristic
660C4—24no—
661C4—22no—
662C4—22no—
663C4—42no—
664C4—54no—
665C4—102no—
666C4—102no—
667C4—202no—
668C4C3×#403914yescomplemented
669C3#1060769511yescharacteristic, direct product factor, Sylow
670C2—104no—
671C2—204no—
672C2C2×C3×#403911yescharacteristic
673C2C3×C4×D4×D511yescharacteristic
674C2C3×C4×#71311yescharacteristic
675C2C3×D5×#12111yescharacteristic
676C2C3×#6596111yescharacteristic
677C2C3×#6602511yescharacteristic
678C2C3×#6605911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#389C2
socleC23×C3×C5C24
prime radicalC2×C3×#4041C2
cosocleC23×C5C24×C3
hypercenterC3×#389D5
hypocenterC5C3×C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#389

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4039C2semidirect
3. C2×C3×#4039C2semidirect
4. C2×C3×C42×D5C2semidirect
5. C3×C5×#389C2semidirect
6. C3×#65279C2semidirect
7. C3×#65276C2semidirect
8. C3×C4⋊C4×Dic5C2semidirect
9. C3×#65228C2semidirect
10. C3×#64955C2semidirect
11. C3×#64954C2semidirect
12. #10607695C3direct (N × H)
33. C3×#4041C4semidirect
42. C2×#4039C2×C3semidirect
43. C2×#4039C2×C3semidirect
44. C2×C42×D5C2×C3semidirect
45. C5×#389C2×C3semidirect
46. #65279C2×C3semidirect
47. #65276C2×C3semidirect
48. C4⋊C4×Dic5C2×C3semidirect
49. #65228C2×C3semidirect
50. #64955C2×C3semidirect
51. #64954C2×C3semidirect
67. C2×C3×D20C2×C4semidirect
68. C2×C3×D20C2×C4semidirect
79. C2×C3×C4×D5C2×C4semidirect
80. C2×C3×C4×D5D4semidirect
83. C3×C5×C4⋊C4C2×C4semidirect
89. C3×#685C2×C4semidirect
94. C3×C4×Dic5D4semidirect
100. C3×#389D5semidirect
126. #4041C3×C4semidirect
224. C2×D20C2×C3×C4semidirect
225. C2×D20C2×C3×C4semidirect
236. C2×C4×D5C2×C3×C4semidirect
237. C2×C4×D5C3×D4semidirect
240. C5×C4⋊C4C2×C3×C4semidirect
246. #685C2×C3×C4semidirect
251. C4×Dic5C3×D4semidirect
257. #389C3×D5semidirect
283. C2×C3×D5C4×D4semidirect
288. C3×C4×C5C4×D4semidirect
292. C3×Dic5#121semidirect
325. C3×C4⋊C4C4×D5semidirect
488. C2×D5C3×C4×D4semidirect
493. C4×C5C3×C4×D4semidirect
497. Dic5C3×#121semidirect
530. C4⋊C4C3×C4×D5semidirect
541. C3×C5C4×#121semidirect
571. C3×C4#4039semidirect
638. C5C3×C4×#121semidirect
668. C4C3×#4039semidirect
669. C3#10607695direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40412
C2×C3×#40392
C2×C3×C42×D52
C3×C5×#3892
C3×#652792
C3×#652762
C3×C4⋊C4×Dic52
C3×#652282
C3×#649552
C3×#649542
#106076953
C3×C4×#1215