Finite Group Databasebeta

← C3×#10605743 #14327319

Subgroups — C3×#10605743 #14327319

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×C22⋊D5C211yesmaximal, characteristic
2C2×C3×#4072C211yesmaximal, characteristic, complemented
3C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×C5×#380C211yesmaximal, characteristic, complemented
5C3×#65276C211yesmaximal, characteristic, complemented
6C3×#65266C211yesmaximal, characteristic, complemented
7C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C3×#65245C212yesmaximal
9C3×#65233C212yesmaximal, complemented
10C3×#64955C212yesmaximal, complemented
11C3×#64941C212yesmaximal, complemented
12#10605743C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2212yes—
16C22×C3×C4×D5C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2212yes—
20C2×C3×C22⋊Dic5C2212yes—
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C3×C4×C22⋊D5C418yescomplemented
23C2×C3×#685C2212yes—
24C2×C3×#685C2211yescharacteristic
25C3×#4072—24no—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×#683C2212yes—
29C2×C3×#683C2211yescharacteristic
30C2×C3×C4×Dic5C2212yes—
31C2×C3×C4×Dic5C2212yes—
32C2×C3×C4×Dic5C2211yescharacteristic
33C3×D5×C4⋊C4—24no—
34C3×C5×#95C2212yes—
35C3×#3963C2212yes—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2352—51nomaximal, Hall
40C2×C4×C22⋊D5C2×C311yescharacteristic
41C2×#4072C2×C311yescharacteristic, complemented
42C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
43C5×#380C2×C311yescharacteristic, complemented
44#65276C2×C311yescharacteristic, complemented
45#65266C2×C311yescharacteristic, complemented
46C4⋊C4×Dic5C2×C311yescharacteristic, complemented
47#65245C2×C312yes—
48#65233C2×C312yescomplemented
49#64955C2×C312yescomplemented
50#64941C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5—22no—
62C2×C3×C22⋊D5C2×C414yes—
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2312yes—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5—24no—
71C2×C3×C4×D5—24no—
72C2×C3×C4×D5—42no—
73C2×C3×C4×D5C2×C414yes—
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C22⋊C4—42no—
77C3×C22⋊Dic5—24no—
78C3×C22⋊Dic5C2×C414yescomplemented
79C3×#685—24no—
80C3×#685C2×C414yes—
81C3×C4⋊Dic5—22no—
82C3×C4⋊Dic5D414yescomplemented
83C3×#683—24no—
84C3×#683C2×C414yescomplemented
85C3×C4×Dic5—24no—
86C3×C4×Dic5—42no—
87C3×C4×Dic5C2×C414yescomplemented
88C2×C3×C4×D4—51no—
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×#380D511yescharacteristic, complemented
97C3×C4×C4⋊C4—51no—
98C3×C4×C22⋊C4—52no—
99C23×C4×C5C22×C311yescharacteristic
100C22×C22⋊D5C22×C311yescharacteristic
101C22×C4×D5C22×C312yes—
102C22×C4×D5C22×C311yescharacteristic
103C2×C5×C4⋊C4C22×C311yescharacteristic
104C2×C5×C4⋊C4C22×C311yescharacteristic
105C2×C5×C22⋊C4C22×C312yes—
106C2×C22⋊Dic5C22×C312yes—
107C2×C22⋊Dic5C22×C311yescharacteristic
108C4×C22⋊D5C3×C418yescomplemented
109C2×#685C22×C312yes—
110C2×#685C22×C311yescharacteristic
111#4072—24no—
112C2×C4⋊Dic5C22×C311yescharacteristic
113C2×C4⋊Dic5C22×C311yescharacteristic
114C2×#683C22×C312yes—
115C2×#683C22×C311yescharacteristic
116C2×C4×Dic5C22×C312yes—
117C2×C4×Dic5C22×C312yes—
118C2×C4×Dic5C22×C311yescharacteristic
119D5×C4⋊C4—24no—
120C5×#95C22×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×C5C22×C412yes—
133C23×C3×C5C2411yescharacteristic
134C22×C3×D5—21no—
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5—21no—
138C22×C3×D5C22×C412yes—
139C22×C3×D5#4112yes—
140C22×C3×D5#4112yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—28no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D412yes—
153C2×C3×C4×C5#4112yes—
154C3×C22⋊D5—28no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—21no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5—21no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—21no—
163C2×C3×Dic5—22no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—22no—
166C2×C3×Dic5C22×C412yes—
167C2×C3×Dic5C22×C412yes—
168C2×C3×Dic5C22×C412yes—
169C2×C3×Dic5C2×D414yes—
170C3×C4×D5—28no—
171C3×C4×D5—48no—
172C22×C3×D4—51no—
173C23×C3×C4—51no—
174C23×C3×C4—52no—
175C23×C3×C4C2×D511yescharacteristic
176C3×C4×D4—58no—
177C3×#117—104no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C4⋊C4—51no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C4⋊C4—52no—
182C2×C3×C4⋊C4—104no—
183C2×C3×C4⋊C4C2×D511yescharacteristic
184C2×C3×C4⋊C4C2×D511yescharacteristic
185C2×C3×C22⋊C4—51no—
186C2×C3×C22⋊C4—51no—
187C2×C3×C22⋊C4—52no—
188C2×C3×C22⋊C4—52no—
189C2×C3×C22⋊C4C2×D512yes—
190C2×C3×C42—51no—
191C2×C3×C42—52no—
192C2×C3×C42—52no—
193C3×#95—52no—
194C3×#95—52no—
195C3×#95—52no—
196C3×#95—52no—
197C3×#95C2×D512yes—
198C24×C5C23×C311yescharacteristic
199C23×D5C23×C311yescharacteristic
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5C2×C3×C414yescomplemented
203C22×C4×C5C23×C312yes—
204C22×C4×C5C23×C312yes—
205C22×C4×C5C23×C311yescharacteristic
206C22×C4×C5C23×C311yescharacteristic
207C2×C22⋊D5—22no—
208C2×C22⋊D5—22no—
209C2×C22⋊D5C2×C3×C414yes—
210C22×Dic5C23×C312yes—
211C22×Dic5C23×C311yescharacteristic
212C22×Dic5C23×C311yescharacteristic
213C22×Dic5C23×C311yescharacteristic
214C22×Dic5C23×C312yes—
215C2×C4×D5—22no—
216C2×C4×D5—22no—
217C2×C4×D5—24no—
218C2×C4×D5—24no—
219C2×C4×D5—42no—
220C2×C4×D5C2×C3×C414yes—
221C5×C4⋊C4—22no—
222C5×C4⋊C4—22no—
223C5×C22⋊C4—42no—
224C22⋊Dic5—24no—
225C22⋊Dic5C2×C3×C414yescomplemented
226#685—24no—
227#685C2×C3×C414yes—
228C4⋊Dic5—22no—
229C4⋊Dic5C3×D414yescomplemented
230#683—24no—
231#683C2×C3×C414yescomplemented
232C4×Dic5—24no—
233C4×Dic5—42no—
234C4×Dic5C2×C3×C414yescomplemented
235C2×C4×D4—51no—
236C2×#117—51no—
237C22×C4⋊C4—51no—
238#388—52no—
239#387—52no—
240#386—52no—
241#382—51no—
242#380—51no—
243#380C3×D511yescharacteristic, complemented
244C4×C4⋊C4—51no—
245C4×C22⋊C4—52no—
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—22no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5—41no—
252C22×C3×C5—41no—
253C22×C3×C5C23×C411yescharacteristic
254C22×C3×C5C22×D411yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5H(5,𝔽2)11yescharacteristic
259C22×C3×C52−1+411yescharacteristic
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—22no—
263C2×C3×D5—22no—
264C2×C3×D5—22no—
265C2×C3×D5—22no—
266C2×C3×D5#11714yescomplemented
267C3×C4×C5—22no—
268C3×C4×C5—42no—
269C3×C4×C5—42no—
270C3×C4×C5C4×D414yes—
271C3×Dic5—22no—
272C3×Dic5—22no—
273C3×Dic5—22no—
274C3×Dic5—24no—
275C3×Dic5—42no—
276C24×C3—51no—
277C24×C3C22×D511yescharacteristic
278C2×C3×D4—54no—
279C2×C3×D4—102no—
280C2×C3×D4—102no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—51no—
284C22×C3×C4—51no—
285C22×C3×C4—51no—
286C22×C3×C4—52no—
287C22×C3×C4—54no—
288C22×C3×C4—52no—
289C22×C3×C4—104no—
290C22×C3×C4—104no—
291C22×C3×C4—102no—
292C22×C3×C4—102no—
293C22×C3×C4—202no—
294C22×C3×C4C4×D514yescomplemented
295C22×C3×C4C22×D512yes—
296C22×C3×C4C22×D512yes—
297C22×C3×C4C22×D511yescharacteristic
298C22×C3×C4C22×D511yescharacteristic
299C3×C4⋊C4—22no—
300C3×C4⋊C4—22no—
301C3×C4⋊C4—54no—
302C3×C4⋊C4—54no—
303C3×C4⋊C4—104no—
304C3×C4⋊C4—102no—
305C3×C22⋊C4—42no—
306C3×C22⋊C4—54no—
307C3×C22⋊C4—54no—
308C3×C22⋊C4—104no—
309C3×C22⋊C4—104no—
310C3×C42—54no—
311C3×C42—104no—
312C3×C42—202no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5—21no—
319C23×C5C22×C3×C412yes—
320C23×C5C24×C311yescharacteristic
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5—21no—
325C22×D5C22×C3×C412yes—
326C22×D5C3×#4112yes—
327C22×D5C3×#4112yes—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—28no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5—22no—
336C2×C4×C5—22no—
337C2×C4×C5C22×C3×C412yes—
338C2×C4×C5C22×C3×C412yes—
339C2×C4×C5C2×C3×D412yes—
340C2×C4×C5C3×#4112yes—
341C22⋊D5—28no—
342C2×Dic5—21no—
343C2×Dic5—21no—
344C2×Dic5—22no—
345C2×Dic5—21no—
346C2×Dic5—21no—
347C2×Dic5—21no—
348C2×Dic5—22no—
349C2×Dic5—21no—
350C2×Dic5—22no—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5C22×C3×C412yes—
354C2×Dic5C22×C3×C412yes—
355C2×Dic5C22×C3×C412yes—
356C2×Dic5C2×C3×D414yes—
357C4×D5—28no—
358C4×D5—48no—
359C22×D4—51no—
360C23×C4—51no—
361C23×C4—52no—
362C23×C4C2×C3×D511yescharacteristic
363C4×D4—58no—
364#117—104no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—51no—
367C2×C4⋊C4—52no—
368C2×C4⋊C4—51no—
369C2×C4⋊C4—104no—
370C2×C4⋊C4C2×C3×D511yescharacteristic
371C2×C4⋊C4C2×C3×D511yescharacteristic
372C2×C22⋊C4—51no—
373C2×C22⋊C4—51no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4—52no—
376C2×C22⋊C4C2×C3×D512yes—
377C2×C42—51no—
378C2×C42—52no—
379C2×C42—52no—
380#95—52no—
381#95—52no—
382#95—52no—
383#95—52no—
384#95C2×C3×D512yes—
385C2×C3×C5—42no—
386C2×C3×C5C2×#11711yescharacteristic
387C2×C3×C5C2×C4×D411yescharacteristic
388C2×C3×C5#52011yescharacteristic
389C2×C3×C5#54611yescharacteristic
390C2×C3×C5#54811yescharacteristic
391C2×C3×C5#55211yescharacteristic
392C2×C3×C5#55311yescharacteristic
393C3×D5—24no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—52no—
401C23×C3—52no—
402C23×C3—52no—
403C23×C3—101no—
404C23×C3—101no—
405C23×C3—101no—
406C23×C3—101no—
407C23×C3C2×C4×D512yes—
408C23×C3C23×D511yescharacteristic
409C3×D4—108no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—28no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—52no—
420C2×C3×C4—52no—
421C2×C3×C4—52no—
422C2×C3×C4—54no—
423C2×C3×C4—101no—
424C2×C3×C4—101no—
425C2×C3×C4—101no—
426C2×C3×C4—102no—
427C2×C3×C4—101no—
428C2×C3×C4—102no—
429C2×C3×C4—101no—
430C2×C3×C4—101no—
431C2×C3×C4—108no—
432C2×C3×C4—102no—
433C2×C3×C4—102no—
434C2×C3×C4—102no—
435C2×C3×C4—208no—
436C2×C3×C4C2×C4×D512yes—
437C2×C3×C4C2×C4×D512yes—
438C2×C3×C4D4×D512yes—
439C2×C3×C4#71112yes—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—22no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5C23×C3×C411yescharacteristic
448C22×C5C22×C3×D411yescharacteristic
449C22×C5C2×C3×#4111yescharacteristic
450C22×C5C2×C3×#4111yescharacteristic
451C22×C5C2×C3×#4111yescharacteristic
452C22×C5C3×H(5,𝔽2)11yescharacteristic
453C22×C5C3×2−1+411yescharacteristic
454C2×D5—22no—
455C2×D5—22no—
456C2×D5—22no—
457C2×D5—22no—
458C2×D5—22no—
459C2×D5—22no—
460C2×D5C3×#11714yescomplemented
461C4×C5—22no—
462C4×C5—42no—
463C4×C5—42no—
464C4×C5C3×C4×D414yes—
465Dic5—22no—
466Dic5—22no—
467Dic5—22no—
468Dic5—24no—
469Dic5—42no—
470C24—51no—
471C24C22×C3×D511yescharacteristic
472C2×D4—54no—
473C2×D4—102no—
474C2×D4—102no—
475C22×C4—22no—
476C22×C4—22no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—51no—
480C22×C4—52no—
481C22×C4—54no—
482C22×C4—52no—
483C22×C4—104no—
484C22×C4—104no—
485C22×C4—102no—
486C22×C4—102no—
487C22×C4—202no—
488C22×C4C3×C4×D514yescomplemented
489C22×C4C22×C3×D512yes—
490C22×C4C22×C3×D512yes—
491C22×C4C22×C3×D511yescharacteristic
492C22×C4C22×C3×D511yescharacteristic
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—54no—
496C4⋊C4—54no—
497C4⋊C4—104no—
498C4⋊C4—102no—
499C22⋊C4—42no—
500C22⋊C4—54no—
501C22⋊C4—54no—
502C22⋊C4—104no—
503C22⋊C4—104no—
504C42—54no—
505C42—104no—
506C42—202no—
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—54no—
516C22×C3—102no—
517C22×C3—102no—
518C22×C3—102no—
519C22×C3—102no—
520C22×C3—102no—
521C22×C3—102no—
522C22×C3C22×C4×D511yescharacteristic
523C22×C3C2×D4×D511yescharacteristic
524C22×C3C2×#71111yescharacteristic
525C22×C3#414411yescharacteristic
526C22×C3#414711yescharacteristic
527C22×C3D5×#4111yescharacteristic
528C22×C3D5×#4111yescharacteristic
529C3×C4—22no—
530C3×C4—42no—
531C3×C4—42no—
532C3×C4—102no—
533C3×C4—102no—
534C3×C4—102no—
535C3×C4—104no—
536C3×C4—202no—
537C3×C4#402714yes—
538C2×C5—42no—
539C2×C5C2×C3×#11711yescharacteristic
540C2×C5C2×C3×C4×D411yescharacteristic
541C2×C5C3×#52011yescharacteristic
542C2×C5C3×#54611yescharacteristic
543C2×C5C3×#54811yescharacteristic
544C2×C5C3×#55211yescharacteristic
545C2×C5C3×#55311yescharacteristic
546D5—24no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—52no—
554C23—52no—
555C23—52no—
556C23—101no—
557C23—101no—
558C23—101no—
559C23—101no—
560C23C2×C3×C4×D512yes—
561C23C23×C3×D511yescharacteristic
562D4—108no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—28no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—52no—
573C2×C4—52no—
574C2×C4—52no—
575C2×C4—54no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—102no—
580C2×C4—101no—
581C2×C4—102no—
582C2×C4—101no—
583C2×C4—101no—
584C2×C4—108no—
585C2×C4—102no—
586C2×C4—102no—
587C2×C4—102no—
588C2×C4—208no—
589C2×C4C2×C3×C4×D512yes—
590C2×C4C2×C3×C4×D512yes—
591C2×C4C3×D4×D512yes—
592C2×C4C3×#71112yes—
593C2×C3—42no—
594C2×C3—104no—
595C2×C3C2×#402711yescharacteristic
596C2×C3#6583811yescharacteristic
597C2×C3D5×#11711yescharacteristic
598C2×C3#6594611yescharacteristic
599C2×C3#6594811yescharacteristic
600C2×C3#6596711yescharacteristic
601C2×C3#6597311yescharacteristic
602C5C3×#235211yescharacteristic, complemented, Sylow
603C22—22no—
604C22—22no—
605C22—22no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—54no—
611C22—102no—
612C22—102no—
613C22—102no—
614C22—102no—
615C22—102no—
616C22—102no—
617C22C22×C3×C4×D511yescharacteristic
618C22C2×C3×D4×D511yescharacteristic
619C22C2×C3×#71111yescharacteristic
620C22C3×#414411yescharacteristic
621C22C3×#414711yescharacteristic
622C22C3×D5×#4111yescharacteristic
623C22C3×D5×#4111yescharacteristic
624C4—22no—
625C4—42no—
626C4—42no—
627C4—102no—
628C4—104no—
629C4—102no—
630C4—102no—
631C4—202no—
632C4C3×#402714yes—
633C3#1060574311yescharacteristic, direct product factor, Sylow
634C2—42no—
635C2—104no—
636C2C2×C3×#402711yescharacteristic
637C2C3×#6583811yescharacteristic
638C2C3×D5×#11711yescharacteristic
639C2C3×#6594611yescharacteristic
640C2C3×#6594811yescharacteristic
641C2C3×#6596711yescharacteristic
642C2C3×#6597311yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#380C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#380D5
hypocenterC5C3×#2352
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4072C2semidirect
3. C2×C3×D5×C4⋊C4C2semidirect
4. C3×C5×#380C2semidirect
5. C3×#65276C2semidirect
6. C3×#65266C2semidirect
7. C3×C4⋊C4×Dic5C2semidirect
9. C3×#65233C2semidirect
10. C3×#64955C2semidirect
11. C3×#64941C2semidirect
12. #10605743C3direct (N × H)
22. C3×C4×C22⋊D5C4semidirect
41. C2×#4072C2×C3semidirect
42. C2×D5×C4⋊C4C2×C3semidirect
43. C5×#380C2×C3semidirect
44. #65276C2×C3semidirect
45. #65266C2×C3semidirect
46. C4⋊C4×Dic5C2×C3semidirect
48. #65233C2×C3semidirect
49. #64955C2×C3semidirect
50. #64941C2×C3semidirect
55. C22×C3×C4×C5C2×C4semidirect
78. C3×C22⋊Dic5C2×C4semidirect
82. C3×C4⋊Dic5D4semidirect
84. C3×#683C2×C4semidirect
87. C3×C4×Dic5C2×C4semidirect
96. C3×#380D5semidirect
108. C4×C22⋊D5C3×C4semidirect
202. C22×C4×C5C2×C3×C4semidirect
225. C22⋊Dic5C2×C3×C4semidirect
229. C4⋊Dic5C3×D4semidirect
231. #683C2×C3×C4semidirect
234. C4×Dic5C2×C3×C4semidirect
243. #380C3×D5semidirect
266. C2×C3×D5#117semidirect
294. C22×C3×C4C4×D5semidirect
460. C2×D5C3×#117semidirect
488. C22×C4C3×C4×D5semidirect
507. C3×C5#2352semidirect
602. C5C3×#2352semidirect
633. C3#10605743direct (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×C22⋊D52
C2×C3×#40722
C2×C3×D5×C4⋊C42
C3×C5×#3802
C3×#652762
C3×#652662
C3×C4⋊C4×Dic52
C3×#652452
C3×#652332
C3×#649552
C3×#649412
#106057433
C3×#23525