Finite Group Databasebeta

← C3×#10614066 #14327340

Subgroups — C3×#10614066 #14327340

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×C3×#4072C211yesmaximal, characteristic, complemented
3C22×C3×C4⋊Dic5C211yesmaximal, characteristic, complemented
4C3×#65509C212yesmaximal
5C3×#65501C211yesmaximal, characteristic, complemented
6C3×#65501C211yesmaximal, characteristic, complemented
7C3×#65270C212yesmaximal, complemented
8C3×#65240C212yesmaximal, complemented
9C3×C22⋊C4×Dic5C212yesmaximal, complemented
10C3×#65225C211yesmaximal, characteristic, complemented
11C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
12#10614066C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×Dic5C2212yes—
17C3×C4×C5×D4C418yescomplemented
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×C3×C22⋊Dic5C2212yes—
23C2×C3×C22⋊Dic5C2212yes—
24C2×C3×C22⋊Dic5C2212yes—
25C3×#4072—24no—
26C2×C3×C4⋊Dic5—24no—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4⋊Dic5C2212yes—
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2212yes—
33C2×C3×C4×Dic5C2212yes—
34C3×#3963C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2352—51nomaximal, Hall
40C2×C4×C5×D4C2×C311yescharacteristic
41C2×#4072C2×C311yescharacteristic, complemented
42C22×C4⋊Dic5C2×C311yescharacteristic, complemented
43#65509C2×C312yes—
44#65501C2×C311yescharacteristic, complemented
45#65501C2×C311yescharacteristic, complemented
46#65270C2×C312yescomplemented
47#65240C2×C312yescomplemented
48C22⋊C4×Dic5C2×C312yescomplemented
49#65225C2×C311yescharacteristic, complemented
50C4×C4⋊Dic5C2×C311yescharacteristic, complemented
51C24×C3×C5C2311yescharacteristic
52C24×C3×C5C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5C2×C414yes—
61C22×C3×C4×C5C2×C414yescomplemented
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2311yescharacteristic
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×Dic5—24no—
68C22×C3×Dic5—24no—
69C22×C3×Dic5—42no—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2312yes—
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2312yes—
74C3×C5×C4⋊C4C2×C414yescomplemented
75C3×C5×C22⋊C4C2×C414yes—
76C3×C5×C22⋊C4C2×C414yescomplemented
77C3×C42×C5C2×C414yescomplemented
78C3×C22⋊Dic5—24no—
79C3×C22⋊Dic5—24no—
80C3×C22⋊Dic5—42no—
81C3×C4⋊Dic5—22no—
82C3×C4⋊Dic5—22no—
83C3×C4⋊Dic5—22no—
84C3×C4⋊Dic5—24no—
85C3×C4⋊Dic5D414yescomplemented
86C3×C4×Dic5—24no—
87C3×C4×Dic5—42no—
88C2×C3×C4×D4D511yescharacteristic
89C2×C3×#117—51no—
90C22×C3×C4⋊C4—51no—
91C3×#388—52no—
92C3×#387—52no—
93C3×#386—52no—
94C3×#382—51no—
95C3×#380—51no—
96C3×#380—51no—
97C3×C4×C4⋊C4—51no—
98C3×C4×C22⋊C4—52no—
99C22×C5×D4C22×C311yescharacteristic
100C23×C4×C5C22×C311yescharacteristic
101C23×C4×C5C22×C311yescharacteristic
102C23×Dic5C22×C312yes—
103C4×C5×D4C3×C418yescomplemented
104C2×C5×C4⋊C4C22×C311yescharacteristic
105C2×C5×C22⋊C4C22×C311yescharacteristic
106C2×C5×C22⋊C4C22×C311yescharacteristic
107C2×C42×C5C22×C311yescharacteristic
108C2×C22⋊Dic5C22×C312yes—
109C2×C22⋊Dic5C22×C312yes—
110C2×C22⋊Dic5C22×C312yes—
111#4072—24no—
112C2×C4⋊Dic5—24no—
113C2×C4⋊Dic5C22×C311yescharacteristic
114C2×C4⋊Dic5C22×C312yes—
115C2×C4⋊Dic5C22×C311yescharacteristic
116C2×C4⋊Dic5C22×C311yescharacteristic
117C2×C4⋊Dic5C22×C311yescharacteristic
118C2×C4×Dic5C22×C312yes—
119C2×C4×Dic5C22×C312yes—
120#3963C22×C312yes—
121#3963C22×C312yes—
122#3963C22×C312yes—
123#3963C22×C312yes—
124#3963C22×C312yes—
125#2352—51noSylow
126C23×C3×C5—21no—
127C23×C3×C5—21no—
128C23×C3×C5—21no—
129C23×C3×C5—21no—
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5C22×C412yes—
137C23×C3×C5C22×C412yes—
138C23×C3×C5#4112yes—
139C23×C3×C5#4112yes—
140C23×C3×C5C2411yescharacteristic
141C3×C5×D4—28no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—28no—
151C2×C3×C4×C5—28no—
152C2×C3×C4×C5C22×C412yes—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C22×C412yes—
155C2×C3×C4×C5C22×C412yes—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C2×D412yes—
158C2×C3×C4×C5#4112yes—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—48no—
171C2×C3×Dic5C2×D414yes—
172C22×C3×D4C2×D511yescharacteristic
173C23×C3×C4—52no—
174C23×C3×C4C2×D511yescharacteristic
175C23×C3×C4C2×D511yescharacteristic
176C3×C4×D4Dic518yescomplemented
177C3×#117—104no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C4⋊C4—51no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C4⋊C4—51no—
182C2×C3×C4⋊C4—52no—
183C2×C3×C4⋊C4—104no—
184C2×C3×C4⋊C4C2×D511yescharacteristic
185C2×C3×C22⋊C4—52no—
186C2×C3×C22⋊C4—52no—
187C2×C3×C22⋊C4—52no—
188C2×C3×C22⋊C4C2×D511yescharacteristic
189C2×C3×C22⋊C4C2×D511yescharacteristic
190C2×C3×C42—52no—
191C2×C3×C42—52no—
192C2×C3×C42C2×D511yescharacteristic
193C3×#95—52no—
194C3×#95—52no—
195C3×#95—52no—
196C3×#95—52no—
197C3×#95—52no—
198C24×C5C23×C311yescharacteristic
199C24×C5C23×C311yescharacteristic
200C2×C5×D4—22no—
201C2×C5×D4—22no—
202C2×C5×D4C2×C3×C414yes—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5C2×C3×C414yes—
208C22×C4×C5C2×C3×C414yescomplemented
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C311yescharacteristic
211C22×C4×C5C23×C311yescharacteristic
212C22×C4×C5C23×C311yescharacteristic
213C22×C4×C5C23×C311yescharacteristic
214C22×Dic5—24no—
215C22×Dic5—24no—
216C22×Dic5—42no—
217C22×Dic5C23×C312yes—
218C22×Dic5C23×C312yes—
219C22×Dic5C23×C312yes—
220C22×Dic5C23×C312yes—
221C5×C4⋊C4C2×C3×C414yescomplemented
222C5×C22⋊C4C2×C3×C414yes—
223C5×C22⋊C4C2×C3×C414yescomplemented
224C42×C5C2×C3×C414yescomplemented
225C22⋊Dic5—24no—
226C22⋊Dic5—24no—
227C22⋊Dic5—42no—
228C4⋊Dic5—22no—
229C4⋊Dic5—22no—
230C4⋊Dic5—22no—
231C4⋊Dic5—24no—
232C4⋊Dic5C3×D414yescomplemented
233C4×Dic5—24no—
234C4×Dic5—42no—
235C2×C4×D4C3×D511yescharacteristic
236C2×#117—51no—
237C22×C4⋊C4—51no—
238#388—52no—
239#387—52no—
240#386—52no—
241#382—51no—
242#380—51no—
243#380—51no—
244C4×C4⋊C4—51no—
245C4×C22⋊C4—52no—
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—22no—
249C22×C3×C5—22no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—22no—
255C22×C3×C5—41no—
256C22×C3×C5—41no—
257C22×C3×C5—41no—
258C22×C3×C5—41no—
259C22×C3×C5#11714yescomplemented
260C22×C3×C5C23×C411yescharacteristic
261C22×C3×C5C22×D411yescharacteristic
262C22×C3×C5C2×#4111yescharacteristic
263C22×C3×C5C2×#4111yescharacteristic
264C22×C3×C5C2×#4111yescharacteristic
265C22×C3×C5H(5,𝔽2)11yescharacteristic
266C22×C3×C52−1+411yescharacteristic
267C3×C4×C5—22no—
268C3×C4×C5—22no—
269C3×C4×C5—22no—
270C3×C4×C5—22no—
271C3×C4×C5C4×D414yes—
272C3×Dic5—24no—
273C3×Dic5—42no—
274C3×Dic5—42no—
275C3×Dic5—42no—
276C24×C3C22×D511yescharacteristic
277C24×C3C22×D511yescharacteristic
278C2×C3×D4—22no—
279C2×C3×D4—22no—
280C2×C3×D4C2×Dic514yes—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—52no—
286C22×C3×C4—52no—
287C22×C3×C4—52no—
288C22×C3×C4—52no—
289C22×C3×C4—104no—
290C22×C3×C4—104no—
291C22×C3×C4—202no—
292C22×C3×C4C2×Dic514yes—
293C22×C3×C4C2×Dic514yescomplemented
294C22×C3×C4C22×D511yescharacteristic
295C22×C3×C4C22×D511yescharacteristic
296C22×C3×C4C22×D511yescharacteristic
297C22×C3×C4C22×D511yescharacteristic
298C22×C3×C4C22×D511yescharacteristic
299C3×C4⋊C4—54no—
300C3×C4⋊C4—104no—
301C3×C4⋊C4—102no—
302C3×C4⋊C4—102no—
303C3×C4⋊C4—102no—
304C3×C4⋊C4C2×Dic514yescomplemented
305C3×C22⋊C4—104no—
306C3×C22⋊C4—104no—
307C3×C22⋊C4—202no—
308C3×C22⋊C4C2×Dic514yes—
309C3×C22⋊C4C2×Dic514yescomplemented
310C3×C42—104no—
311C3×C42—202no—
312C3×C42C2×Dic514yescomplemented
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5C22×C3×C412yes—
324C23×C5C22×C3×C412yes—
325C23×C5C3×#4112yes—
326C23×C5C3×#4112yes—
327C23×C5C24×C311yescharacteristic
328C5×D4—28no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—21no—
333C2×C4×C5—21no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—28no—
338C2×C4×C5—28no—
339C2×C4×C5C22×C3×C412yes—
340C2×C4×C5C22×C3×C412yes—
341C2×C4×C5C22×C3×C412yes—
342C2×C4×C5C22×C3×C412yes—
343C2×C4×C5C22×C3×C412yes—
344C2×C4×C5C2×C3×D412yes—
345C2×C4×C5C3×#4112yes—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—48no—
358C2×Dic5C2×C3×D414yes—
359C22×D4C2×C3×D511yescharacteristic
360C23×C4—52no—
361C23×C4C2×C3×D511yescharacteristic
362C23×C4C2×C3×D511yescharacteristic
363C4×D4C3×Dic518yescomplemented
364#117—104no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—52no—
368C2×C4⋊C4—51no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4—104no—
371C2×C4⋊C4C2×C3×D511yescharacteristic
372C2×C22⋊C4—52no—
373C2×C22⋊C4—52no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4C2×C3×D511yescharacteristic
376C2×C22⋊C4C2×C3×D511yescharacteristic
377C2×C42—52no—
378C2×C42—52no—
379C2×C42C2×C3×D511yescharacteristic
380#95—52no—
381#95—52no—
382#95—52no—
383#95—52no—
384#95—52no—
385C2×C3×C5—24no—
386C2×C3×C5—42no—
387C2×C3×C5C2×#11711yescharacteristic
388C2×C3×C5C2×C4×D411yescharacteristic
389C2×C3×C5#52011yescharacteristic
390C2×C3×C5#54611yescharacteristic
391C2×C3×C5#54811yescharacteristic
392C2×C3×C5#55211yescharacteristic
393C2×C3×C5#55311yescharacteristic
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3#70912yes—
405C23×C3#70912yes—
406C23×C3C22×Dic512yes—
407C23×C3C22×Dic512yes—
408C23×C3C23×D511yescharacteristic
409C3×D4—28no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—28no—
419C2×C3×C4—28no—
420C2×C3×C4—54no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4—102no—
424C2×C3×C4—102no—
425C2×C3×C4—102no—
426C2×C3×C4—102no—
427C2×C3×C4—102no—
428C2×C3×C4—102no—
429C2×C3×C4—102no—
430C2×C3×C4—102no—
431C2×C3×C4—102no—
432C2×C3×C4—208no—
433C2×C3×C4D4×D512yes—
434C2×C3×C4#71112yes—
435C2×C3×C4C22×Dic512yes—
436C2×C3×C4C22×Dic512yes—
437C2×C3×C4C22×Dic512yes—
438C2×C3×C4C22×Dic512yes—
439C2×C3×C4C22×Dic512yes—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—22no—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5C3×#11714yescomplemented
454C22×C5C23×C3×C411yescharacteristic
455C22×C5C22×C3×D411yescharacteristic
456C22×C5C2×C3×#4111yescharacteristic
457C22×C5C2×C3×#4111yescharacteristic
458C22×C5C2×C3×#4111yescharacteristic
459C22×C5C3×H(5,𝔽2)11yescharacteristic
460C22×C5C3×2−1+411yescharacteristic
461C4×C5—22no—
462C4×C5—22no—
463C4×C5—22no—
464C4×C5—22no—
465C4×C5C3×C4×D414yes—
466Dic5—24no—
467Dic5—42no—
468Dic5—42no—
469Dic5—42no—
470C24C22×C3×D511yescharacteristic
471C24C22×C3×D511yescharacteristic
472C2×D4—22no—
473C2×D4—22no—
474C2×D4C2×C3×Dic514yes—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—52no—
480C22×C4—52no—
481C22×C4—52no—
482C22×C4—52no—
483C22×C4—104no—
484C22×C4—104no—
485C22×C4—202no—
486C22×C4C2×C3×Dic514yes—
487C22×C4C2×C3×Dic514yescomplemented
488C22×C4C22×C3×D511yescharacteristic
489C22×C4C22×C3×D511yescharacteristic
490C22×C4C22×C3×D511yescharacteristic
491C22×C4C22×C3×D511yescharacteristic
492C22×C4C22×C3×D511yescharacteristic
493C4⋊C4—54no—
494C4⋊C4—104no—
495C4⋊C4—102no—
496C4⋊C4—102no—
497C4⋊C4—102no—
498C4⋊C4C2×C3×Dic514yescomplemented
499C22⋊C4—104no—
500C22⋊C4—104no—
501C22⋊C4—202no—
502C22⋊C4C2×C3×Dic514yes—
503C22⋊C4C2×C3×Dic514yescomplemented
504C42—104no—
505C42—202no—
506C42C2×C3×Dic514yescomplemented
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3#407214yescomplemented
522C22×C3C2×#70911yescharacteristic
523C22×C3C2×#70911yescharacteristic
524C22×C3C2×D4×D511yescharacteristic
525C22×C3C2×#71111yescharacteristic
526C22×C3#414911yescharacteristic
527C22×C3#415011yescharacteristic
528C22×C3C23×Dic511yescharacteristic
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—104no—
534C3×C4—202no—
535C3×C4—202no—
536C3×C4—202no—
537C3×C4D4×Dic514yes—
538C2×C5—24no—
539C2×C5—42no—
540C2×C5C2×C3×#11711yescharacteristic
541C2×C5C2×C3×C4×D411yescharacteristic
542C2×C5C3×#52011yescharacteristic
543C2×C5C3×#54611yescharacteristic
544C2×C5C3×#54811yescharacteristic
545C2×C5C3×#55211yescharacteristic
546C2×C5C3×#55311yescharacteristic
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23C3×#70912yes—
558C23C3×#70912yes—
559C23C22×C3×Dic512yes—
560C23C22×C3×Dic512yes—
561C23C23×C3×D511yescharacteristic
562D4—28no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—54no—
574C2×C4—102no—
575C2×C4—102no—
576C2×C4—102no—
577C2×C4—102no—
578C2×C4—102no—
579C2×C4—102no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4—102no—
585C2×C4—208no—
586C2×C4C3×D4×D512yes—
587C2×C4C3×#71112yes—
588C2×C4C22×C3×Dic512yes—
589C2×C4C22×C3×Dic512yes—
590C2×C4C22×C3×Dic512yes—
591C2×C4C22×C3×Dic512yes—
592C2×C4C22×C3×Dic512yes—
593C2×C3—24no—
594C2×C3—42no—
595C2×C3#6587511yescharacteristic
596C2×C3#6588411yescharacteristic
597C2×C3#6588611yescharacteristic
598C2×C3#6589911yescharacteristic
599C2×C3C2×#407211yescharacteristic
600C2×C3C2×D4×Dic511yescharacteristic
601C2×C3#6616111yescharacteristic
602C5C3×#235211yescharacteristic, complemented, Sylow
603C22—22no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—41no—
613C22—41no—
614C22—41no—
615C22—41no—
616C22C3×#407214yescomplemented
617C22C2×C3×#70911yescharacteristic
618C22C2×C3×#70911yescharacteristic
619C22C2×C3×D4×D511yescharacteristic
620C22C2×C3×#71111yescharacteristic
621C22C3×#414911yescharacteristic
622C22C3×#415011yescharacteristic
623C22C23×C3×Dic511yescharacteristic
624C4—22no—
625C4—22no—
626C4—22no—
627C4—22no—
628C4—104no—
629C4—202no—
630C4—202no—
631C4—202no—
632C4C3×D4×Dic514yes—
633C3#1061406611yescharacteristic, direct product factor, Sylow
634C2—24no—
635C2—42no—
636C2C3×#6587511yescharacteristic
637C2C3×#6588411yescharacteristic
638C2C3×#6588611yescharacteristic
639C2C3×#6589911yescharacteristic
640C2C2×C3×#407211yescharacteristic
641C2C2×C3×D4×Dic511yescharacteristic
642C2C3×#6616111yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2352
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
2. C2×C3×#4072C2semidirect
3. C22×C3×C4⋊Dic5C2semidirect
5. C3×#65501C2semidirect
6. C3×#65501C2semidirect
7. C3×#65270C2semidirect
8. C3×#65240C2semidirect
9. C3×C22⋊C4×Dic5C2semidirect
10. C3×#65225C2semidirect
11. C3×C4×C4⋊Dic5C2semidirect
12. #10614066C3direct (N × H)
17. C3×C4×C5×D4C4semidirect
41. C2×#4072C2×C3semidirect
42. C22×C4⋊Dic5C2×C3semidirect
44. #65501C2×C3semidirect
45. #65501C2×C3semidirect
46. #65270C2×C3semidirect
47. #65240C2×C3semidirect
48. C22⋊C4×Dic5C2×C3semidirect
49. #65225C2×C3semidirect
50. C4×C4⋊Dic5C2×C3semidirect
61. C22×C3×C4×C5C2×C4semidirect
74. C3×C5×C4⋊C4C2×C4semidirect
76. C3×C5×C22⋊C4C2×C4semidirect
77. C3×C42×C5C2×C4semidirect
85. C3×C4⋊Dic5D4semidirect
103. C4×C5×D4C3×C4semidirect
176. C3×C4×D4Dic5semidirect
208. C22×C4×C5C2×C3×C4semidirect
221. C5×C4⋊C4C2×C3×C4semidirect
223. C5×C22⋊C4C2×C3×C4semidirect
224. C42×C5C2×C3×C4semidirect
232. C4⋊Dic5C3×D4semidirect
259. C22×C3×C5#117semidirect
293. C22×C3×C4C2×Dic5semidirect
304. C3×C4⋊C4C2×Dic5semidirect
309. C3×C22⋊C4C2×Dic5semidirect
312. C3×C42C2×Dic5semidirect
363. C4×D4C3×Dic5semidirect
453. C22×C5C3×#117semidirect
487. C22×C4C2×C3×Dic5semidirect
498. C4⋊C4C2×C3×Dic5semidirect
503. C22⋊C4C2×C3×Dic5semidirect
506. C42C2×C3×Dic5semidirect
507. C3×C5#2352semidirect
521. C22×C3#4072semidirect
602. C5C3×#2352semidirect
616. C22C3×#4072semidirect
633. C3#10614066direct (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×#40722
C22×C3×C4⋊Dic52
C3×#655092
C3×#655012
C3×#652702
C3×#652402
C3×C22⋊C4×Dic52
C3×#652252
C3×C4×C4⋊Dic52
#106140663
C3×#23525