Finite Group Databasebeta

← C3×#10614074 #14329449

Subgroups — C3×#10614074 #14329449

Order 1920.

1664 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×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×#4086C211yesmaximal, characteristic
3C2×C3×C4×C22⋊D5C212yesmaximal, complemented
4C2×C3×#4039C211yesmaximal, characteristic, complemented
5C3×#65510C211yesmaximal, characteristic, complemented
6C3×#65502C212yesmaximal, complemented
7C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C3×#65246C212yesmaximal, complemented
9C3×#65245C212yesmaximal, complemented
10C3×#65228C211yesmaximal, characteristic, complemented
11C3×C4×#683C211yesmaximal, characteristic, complemented
12#10614074C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2212yes—
15C22×C3×C22⋊D5C2212yes—
16C22×C3×C22⋊D5C2212yes—
17C22×C3×D20C2211yescharacteristic
18C22×C3×C4×D5C2212yes—
19C3×C4×C5×D4—24no—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2212yes—
22C2×C3×C42×C5C2211yescharacteristic
23C2×C3×C22⋊Dic5C2212yes—
24C2×C3×C22⋊Dic5C2212yes—
25C3×#4086C418yescomplemented
26C3×C4×C22⋊D5—28no—
27C2×C3×#685C2212yes—
28C2×C3×#685C2212yes—
29C2×C3×#685C2212yes—
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×C4×Dic5C2212yes—
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C3×#4039—24no—
37C3×#3963C2211yescharacteristic
38C3×#3963C2211yescharacteristic
39C3×#3963C2212yes—
40C3×#2366—51nomaximal, Hall
41C2×C4×C5×D4C2×C311yescharacteristic, complemented
42C2×#4086C2×C311yescharacteristic
43C2×C4×C22⋊D5C2×C312yescomplemented
44C2×#4039C2×C311yescharacteristic, complemented
45#65510C2×C311yescharacteristic, complemented
46#65502C2×C312yescomplemented
47C4⋊C4×Dic5C2×C311yescharacteristic, complemented
48#65246C2×C312yescomplemented
49#65245C2×C312yescomplemented
50#65228C2×C311yescharacteristic, complemented
51C4×#683C2×C311yescharacteristic, complemented
52C24×C3×C5C2312yes—
53C23×C3×D5C2312yes—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4C2×C414yescomplemented
57C22×C3×C4×C5—24no—
58C22×C3×C4×C5—24no—
59C22×C3×C4×C5—42no—
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2312yes—
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C2×C3×C22⋊D5—24no—
65C2×C3×C22⋊D5—24no—
66C2×C3×C22⋊D5—42no—
67C2×C3×C22⋊D5—42no—
68C2×C3×C22⋊D5C2×C418yescomplemented
69C2×C3×C22⋊D5C2×C418yescomplemented
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2312yes—
72C22×C3×Dic5C2311yescharacteristic
73C22×C3×Dic5C2311yescharacteristic
74C22×C3×Dic5C2311yescharacteristic
75C2×C3×D20—22no—
76C2×C3×D20—22no—
77C2×C3×D20C2×C414yescomplemented
78C2×C3×C4×D5—24no—
79C2×C3×C4×D5—24no—
80C2×C3×C4×D5—42no—
81C3×C5×C4⋊C4D414yescomplemented
82C3×C5×C22⋊C4—24no—
83C3×C42×C5—22no—
84C3×C22⋊Dic5—24no—
85C3×C22⋊Dic5—42no—
86C3×#685—24no—
87C3×#685—24no—
88C3×#685—42no—
89C3×C4⋊Dic5—22no—
90C3×#683—22no—
91C3×#683D414yescomplemented
92C3×C4×Dic5—22no—
93C3×C4×Dic5—24no—
94C3×C4×Dic5C2×C414yescomplemented
95C2×C3×#127—51no—
96C2×C3×C4×D4—52no—
97C2×C3×C4×D4—51no—
98C2×C3×C4×D4D511yescharacteristic, complemented
99C3×#390—51no—
100C3×#390—52no—
101C3×#390—51no—
102C3×#386—52no—
103C3×#386—52no—
104C3×C4×C4⋊C4—51no—
105C3×C4×C4⋊C4—51no—
106C22×C5×D4C22×C311yescharacteristic
107C23×C4×C5C22×C312yes—
108C22×C22⋊D5C22×C312yes—
109C22×C22⋊D5C22×C312yes—
110C22×D20C22×C311yescharacteristic
111C22×C4×D5C22×C312yes—
112C4×C5×D4—24no—
113C2×C5×C4⋊C4C22×C311yescharacteristic
114C2×C5×C22⋊C4C22×C312yes—
115C2×C42×C5C22×C311yescharacteristic
116C2×C22⋊Dic5C22×C312yes—
117C2×C22⋊Dic5C22×C312yes—
118#4086C3×C418yescomplemented
119C4×C22⋊D5—28no—
120C2×#685C22×C312yes—
121C2×#685C22×C312yes—
122C2×#685C22×C312yes—
123C2×C4⋊Dic5C22×C311yescharacteristic
124C2×#683C22×C311yescharacteristic
125C2×#683C22×C311yescharacteristic
126C2×C4×Dic5C22×C311yescharacteristic
127C2×C4×Dic5C22×C312yes—
128C2×C4×Dic5C22×C311yescharacteristic
129#4039—24no—
130#3963C22×C311yescharacteristic
131#3963C22×C311yescharacteristic
132#3963C22×C312yes—
133#2366—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—22no—
143C22×C3×D5—22no—
144C22×C3×D5—22no—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5C22×C414yes—
149C3×C5×D4—28no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—21no—
157C2×C3×C4×C5—48no—
158C2×C3×C4×C5C22×C412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2×D414yes—
161C2×C3×C4×C5C2×D412yes—
162C2×C3×C4×C5#4112yes—
163C3×C22⋊D5—216no—
164C3×C22⋊D5—48no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—21no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—21no—
175C2×C3×Dic5C22×C412yes—
176C2×C3×Dic5C22×C412yes—
177C2×C3×Dic5C2×D412yes—
178C2×C3×Dic5C2×D412yes—
179C2×C3×Dic5#4112yes—
180C3×D20—28no—
181C3×C4×D5—48no—
182C22×C3×D4—52no—
183C22×C3×D4—52no—
184C22×C3×D4—51no—
185C22×C3×D4C2×D511yescharacteristic
186C23×C3×C4—52no—
187C23×C3×C4C2×D512yes—
188C3×#127—58no—
189C3×C4×D4—24no—
190C3×C4×D4—108no—
191C3×C4×D4—104no—
192C2×C3×C4⋊C4—51no—
193C2×C3×C4⋊C4—51no—
194C2×C3×C4⋊C4—51no—
195C2×C3×C4⋊C4C2×D511yescharacteristic
196C2×C3×C22⋊C4—52no—
197C2×C3×C22⋊C4—52no—
198C2×C3×C22⋊C4—52no—
199C2×C3×C22⋊C4—52no—
200C2×C3×C22⋊C4—52no—
201C2×C3×C22⋊C4C2×D512yes—
202C2×C3×C42—51no—
203C2×C3×C42—52no—
204C2×C3×C42—51no—
205C2×C3×C42C2×D511yescharacteristic
206C3×#95—51no—
207C3×#95—51no—
208C3×#95—52no—
209C24×C5C23×C312yes—
210C23×D5C23×C312yes—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4C2×C3×C414yescomplemented
214C22×C4×C5—24no—
215C22×C4×C5—24no—
216C22×C4×C5—42no—
217C22×C4×C5C23×C311yescharacteristic
218C22×C4×C5C23×C311yescharacteristic
219C22×C4×C5C23×C312yes—
220C22×C4×C5C23×C311yescharacteristic
221C2×C22⋊D5—24no—
222C2×C22⋊D5—24no—
223C2×C22⋊D5—42no—
224C2×C22⋊D5—42no—
225C2×C22⋊D5C2×C3×C418yescomplemented
226C2×C22⋊D5C2×C3×C418yescomplemented
227C22×Dic5C23×C311yescharacteristic
228C22×Dic5C23×C312yes—
229C22×Dic5C23×C311yescharacteristic
230C22×Dic5C23×C311yescharacteristic
231C22×Dic5C23×C311yescharacteristic
232C2×D20—22no—
233C2×D20—22no—
234C2×D20C2×C3×C414yescomplemented
235C2×C4×D5—24no—
236C2×C4×D5—24no—
237C2×C4×D5—42no—
238C5×C4⋊C4C3×D414yescomplemented
239C5×C22⋊C4—24no—
240C42×C5—22no—
241C22⋊Dic5—24no—
242C22⋊Dic5—42no—
243#685—24no—
244#685—24no—
245#685—42no—
246C4⋊Dic5—22no—
247#683—22no—
248#683C3×D414yescomplemented
249C4×Dic5—22no—
250C4×Dic5—24no—
251C4×Dic5C2×C3×C414yescomplemented
252C2×#127—51no—
253C2×C4×D4—52no—
254C2×C4×D4—51no—
255C2×C4×D4C3×D511yescharacteristic, complemented
256#390—51no—
257#390—52no—
258#390—51no—
259#386—52no—
260#386—52no—
261C4×C4⋊C4—51no—
262C4×C4⋊C4—51no—
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×C5H(5,𝔽2)11yescharacteristic
276C22×C3×C5H(5,𝔽2)11yescharacteristic
277C2×C3×D5—24no—
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C3×C4×C5—24no—
285C3×C4×C5—22no—
286C3×C4×C5—41no—
287C3×C4×C5C4×D414yescomplemented
288C3×Dic5—22no—
289C3×Dic5—22no—
290C3×Dic5—42no—
291C3×Dic5—41no—
292C3×Dic5C4×D414yescomplemented
293C24×C3—52no—
294C24×C3C22×D512yes—
295C2×C3×D4—22no—
296C2×C3×D4—22no—
297C2×C3×D4—58no—
298C2×C3×D4—58no—
299C2×C3×D4—54no—
300C2×C3×D4—104no—
301C2×C3×D4—104no—
302C2×C3×D4—102no—
303C2×C3×D4—102no—
304C2×C3×D4—202no—
305C2×C3×D4—202no—
306C2×C3×D4C4×D514yescomplemented
307C22×C3×C4—24no—
308C22×C3×C4—24no—
309C22×C3×C4—42no—
310C22×C3×C4—51no—
311C22×C3×C4—51no—
312C22×C3×C4—51no—
313C22×C3×C4—52no—
314C22×C3×C4—51no—
315C22×C3×C4—104no—
316C22×C3×C4—104no—
317C22×C3×C4—202no—
318C22×C3×C4C22×D511yescharacteristic
319C22×C3×C4C22×D511yescharacteristic
320C22×C3×C4C22×D512yes—
321C22×C3×C4C22×D511yescharacteristic
322C3×C4⋊C4—54no—
323C3×C4⋊C4—102no—
324C3×C4⋊C4—102no—
325C3×C4⋊C4C22⋊D514yescomplemented
326C3×C22⋊C4—24no—
327C3×C22⋊C4—104no—
328C3×C22⋊C4—104no—
329C3×C22⋊C4—104no—
330C3×C22⋊C4—202no—
331C3×C22⋊C4—202no—
332C3×C42—22no—
333C3×C42—54no—
334C3×C42—104no—
335C3×C42—102no—
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—22no—
345C22×D5—22no—
346C22×D5—22no—
347C22×D5—22no—
348C22×D5—22no—
349C22×D5—22no—
350C22×D5C22×C3×C414yes—
351C5×D4—28no—
352C2×C4×C5—22no—
353C2×C4×C5—21no—
354C2×C4×C5—22no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—21no—
358C2×C4×C5—21no—
359C2×C4×C5—48no—
360C2×C4×C5C22×C3×C412yes—
361C2×C4×C5C2×C3×D412yes—
362C2×C4×C5C2×C3×D414yes—
363C2×C4×C5C2×C3×D412yes—
364C2×C4×C5C3×#4112yes—
365C22⋊D5—216no—
366C22⋊D5—48no—
367C2×Dic5—21no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—21no—
371C2×Dic5—21no—
372C2×Dic5—22no—
373C2×Dic5—21no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—21no—
377C2×Dic5C22×C3×C412yes—
378C2×Dic5C22×C3×C412yes—
379C2×Dic5C2×C3×D412yes—
380C2×Dic5C2×C3×D412yes—
381C2×Dic5C3×#4112yes—
382D20—28no—
383C4×D5—48no—
384C22×D4—52no—
385C22×D4—52no—
386C22×D4—51no—
387C22×D4C2×C3×D511yescharacteristic
388C23×C4—52no—
389C23×C4C2×C3×D512yes—
390#127—58no—
391C4×D4—24no—
392C4×D4—108no—
393C4×D4—104no—
394C2×C4⋊C4—51no—
395C2×C4⋊C4—51no—
396C2×C4⋊C4—51no—
397C2×C4⋊C4C2×C3×D511yescharacteristic
398C2×C22⋊C4—52no—
399C2×C22⋊C4—52no—
400C2×C22⋊C4—52no—
401C2×C22⋊C4—52no—
402C2×C22⋊C4—52no—
403C2×C22⋊C4C2×C3×D512yes—
404C2×C42—51no—
405C2×C42—52no—
406C2×C42—51no—
407C2×C42C2×C3×D511yescharacteristic
408#95—51no—
409#95—51no—
410#95—52no—
411C2×C3×C5—44no—
412C2×C3×C5C2×C4×D411yescharacteristic
413C2×C3×C5C2×C4×D411yescharacteristic
414C2×C3×C5#51811yescharacteristic
415C2×C3×C5D4211yescharacteristic
416C2×C3×C5#55011yescharacteristic
417C2×C3×C5#55011yescharacteristic
418C2×C3×C5#55911yescharacteristic
419C3×D5—44no—
420C23×C3—22no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—54no—
427C23×C3—102no—
428C23×C3—102no—
429C23×C3—102no—
430C23×C3—102no—
431C23×C3—102no—
432C23×C3—102no—
433C23×C3C2×C4×D514yes—
434C23×C3C23×D511yescharacteristic
435C3×D4—28no—
436C3×D4—1016no—
437C3×D4—108no—
438C3×D4—208no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—48no—
447C2×C3×C4—52no—
448C2×C3×C4—52no—
449C2×C3×C4—52no—
450C2×C3×C4—52no—
451C2×C3×C4—52no—
452C2×C3×C4—101no—
453C2×C3×C4—101no—
454C2×C3×C4—101no—
455C2×C3×C4—101no—
456C2×C3×C4—102no—
457C2×C3×C4—102no—
458C2×C3×C4—101no—
459C2×C3×C4—102no—
460C2×C3×C4—101no—
461C2×C3×C4—101no—
462C2×C3×C4—208no—
463C2×C3×C4C2×C4×D512yes—
464C2×C3×C4#70912yes—
465C2×C3×C4D4×D512yes—
466C2×C3×C4C2×C22⋊D514yes—
467C2×C3×C4C2×C22⋊D512yes—
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×C5C3×H(5,𝔽2)11yescharacteristic
481C22×C5C3×H(5,𝔽2)11yescharacteristic
482C2×D5—24no—
483C2×D5—24no—
484C2×D5—24no—
485C2×D5—42no—
486C2×D5—42no—
487C2×D5—42no—
488C2×D5—42no—
489C4×C5—24no—
490C4×C5—22no—
491C4×C5—41no—
492C4×C5C3×C4×D414yescomplemented
493Dic5—22no—
494Dic5—22no—
495Dic5—42no—
496Dic5—41no—
497Dic5C3×C4×D414yescomplemented
498C24—52no—
499C24C22×C3×D512yes—
500C2×D4—22no—
501C2×D4—22no—
502C2×D4—58no—
503C2×D4—58no—
504C2×D4—54no—
505C2×D4—104no—
506C2×D4—104no—
507C2×D4—102no—
508C2×D4—102no—
509C2×D4—202no—
510C2×D4—202no—
511C2×D4C3×C4×D514yescomplemented
512C22×C4—24no—
513C22×C4—24no—
514C22×C4—42no—
515C22×C4—51no—
516C22×C4—51no—
517C22×C4—51no—
518C22×C4—52no—
519C22×C4—51no—
520C22×C4—104no—
521C22×C4—104no—
522C22×C4—202no—
523C22×C4C22×C3×D511yescharacteristic
524C22×C4C22×C3×D511yescharacteristic
525C22×C4C22×C3×D512yes—
526C22×C4C22×C3×D511yescharacteristic
527C4⋊C4—54no—
528C4⋊C4—102no—
529C4⋊C4—102no—
530C4⋊C4C3×C22⋊D514yescomplemented
531C22⋊C4—24no—
532C22⋊C4—104no—
533C22⋊C4—104no—
534C22⋊C4—104no—
535C22⋊C4—202no—
536C22⋊C4—202no—
537C42—22no—
538C42—54no—
539C42—104no—
540C42—102no—
541C3×C5#236611yescharacteristic, 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—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×#70911yescharacteristic
558C22×C3C2×D4×D511yescharacteristic
559C22×C3#414411yescharacteristic
560C22×C3D5×#4111yescharacteristic
561C22×C3#414911yescharacteristic
562C22×C3C22×C22⋊D511yescharacteristic
563C3×C4—22no—
564C3×C4—24no—
565C3×C4—41no—
566C3×C4—54no—
567C3×C4—102no—
568C3×C4—102no—
569C3×C4—202no—
570C3×C4—201no—
571C3×C4C4×C22⋊D514yescomplemented
572C2×C5—44no—
573C2×C5C2×C3×C4×D411yescharacteristic
574C2×C5C2×C3×C4×D411yescharacteristic
575C2×C5C3×#51811yescharacteristic
576C2×C5C3×D4211yescharacteristic
577C2×C5C3×#55011yescharacteristic
578C2×C5C3×#55011yescharacteristic
579C2×C5C3×#55911yescharacteristic
580D5—44no—
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—22no—
586C23—22no—
587C23—54no—
588C23—102no—
589C23—102no—
590C23—102no—
591C23—102no—
592C23—102no—
593C23—102no—
594C23C2×C3×C4×D514yes—
595C23C23×C3×D511yescharacteristic
596D4—28no—
597D4—1016no—
598D4—108no—
599D4—208no—
600C2×C4—22no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—48no—
608C2×C4—52no—
609C2×C4—52no—
610C2×C4—52no—
611C2×C4—52no—
612C2×C4—52no—
613C2×C4—101no—
614C2×C4—101no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—102no—
618C2×C4—102no—
619C2×C4—101no—
620C2×C4—102no—
621C2×C4—101no—
622C2×C4—101no—
623C2×C4—208no—
624C2×C4C2×C3×C4×D512yes—
625C2×C4C3×#70912yes—
626C2×C4C3×D4×D512yes—
627C2×C4C2×C3×C22⋊D514yes—
628C2×C4C2×C3×C22⋊D512yes—
629C2×C3—44no—
630C2×C3—204no—
631C2×C3C4×D4×D511yescharacteristic
632C2×C3#6587911yescharacteristic
633C2×C3#6588711yescharacteristic
634C2×C3#6589311yescharacteristic
635C2×C3C2×C4×C22⋊D511yescharacteristic
636C2×C3D4×C22⋊D511yescharacteristic
637C2×C3#6616811yescharacteristic
638C5C3×#236611yescharacteristic, complemented, Sylow
639C22—24no—
640C22—24no—
641C22—24no—
642C22—42no—
643C22—42no—
644C22—42no—
645C22—42no—
646C22—104no—
647C22—104no—
648C22—104no—
649C22—202no—
650C22—202no—
651C22—202no—
652C22—202no—
653C22C22×C3×C4×D511yescharacteristic
654C22C2×C3×#70911yescharacteristic
655C22C2×C3×D4×D511yescharacteristic
656C22C3×#414411yescharacteristic
657C22C3×D5×#4111yescharacteristic
658C22C3×#414911yescharacteristic
659C22C22×C3×C22⋊D511yescharacteristic
660C4—22no—
661C4—24no—
662C4—41no—
663C4—54no—
664C4—102no—
665C4—102no—
666C4—202no—
667C4—201no—
668C4C3×C4×C22⋊D514yescomplemented
669C3#1061407411yescharacteristic, direct product factor, Sylow
670C2—44no—
671C2—204no—
672C2C3×C4×D4×D511yescharacteristic
673C2C3×#6587911yescharacteristic
674C2C3×#6588711yescharacteristic
675C2C3×#6589311yescharacteristic
676C2C2×C3×C4×C22⋊D511yescharacteristic
677C2C3×D4×C22⋊D511yescharacteristic
678C2C3×#6616811yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4086C2
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2366
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
3. C2×C3×C4×C22⋊D5C2semidirect
4. C2×C3×#4039C2semidirect
5. C3×#65510C2semidirect
6. C3×#65502C2semidirect
7. C3×C4⋊C4×Dic5C2semidirect
8. C3×#65246C2semidirect
9. C3×#65245C2semidirect
10. C3×#65228C2semidirect
11. C3×C4×#683C2semidirect
12. #10614074C3direct (N × H)
25. C3×#4086C4semidirect
41. C2×C4×C5×D4C2×C3semidirect
43. C2×C4×C22⋊D5C2×C3semidirect
44. C2×#4039C2×C3semidirect
45. #65510C2×C3semidirect
46. #65502C2×C3semidirect
47. C4⋊C4×Dic5C2×C3semidirect
48. #65246C2×C3semidirect
49. #65245C2×C3semidirect
50. #65228C2×C3semidirect
51. C4×#683C2×C3semidirect
56. C2×C3×C5×D4C2×C4semidirect
68. C2×C3×C22⋊D5C2×C4semidirect
69. C2×C3×C22⋊D5C2×C4semidirect
77. C2×C3×D20C2×C4semidirect
81. C3×C5×C4⋊C4D4semidirect
91. C3×#683D4semidirect
94. C3×C4×Dic5C2×C4semidirect
98. C2×C3×C4×D4D5semidirect
118. #4086C3×C4semidirect
213. C2×C5×D4C2×C3×C4semidirect
225. C2×C22⋊D5C2×C3×C4semidirect
226. C2×C22⋊D5C2×C3×C4semidirect
234. C2×D20C2×C3×C4semidirect
238. C5×C4⋊C4C3×D4semidirect
248. #683C3×D4semidirect
251. C4×Dic5C2×C3×C4semidirect
255. C2×C4×D4C3×D5semidirect
287. C3×C4×C5C4×D4semidirect
292. C3×Dic5C4×D4semidirect
306. C2×C3×D4C4×D5semidirect
325. C3×C4⋊C4C22⋊D5semidirect
492. C4×C5C3×C4×D4semidirect
497. Dic5C3×C4×D4semidirect
511. C2×D4C3×C4×D5semidirect
530. C4⋊C4C3×C22⋊D5semidirect
541. C3×C5#2366semidirect
571. C3×C4C4×C22⋊D5semidirect
638. C5C3×#2366semidirect
668. C4C3×C4×C22⋊D5semidirect
669. C3#10614074direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×C3×#40862
C2×C3×C4×C22⋊D52
C2×C3×#40392
C3×#655102
C3×#655022
C3×C4⋊C4×Dic52
C3×#652462
C3×#652452
C3×#652282
C3×C4×#6832
#106140743
C3×#23665