Finite Group Databasebeta

← C3×#10613972 #14327679

Subgroups — C3×#10613972 #14327679

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
3C2×C3×#4038C211yesmaximal, characteristic, complemented
4C3×#65501C211yesmaximal, characteristic, complemented
5C3×#65276C211yesmaximal, characteristic, complemented
6C3×#65265C211yesmaximal, characteristic, complemented
7C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C3×#65246C212yesmaximal
9C3×#65233C212yesmaximal, complemented
10C3×#65229C212yesmaximal, complemented
11C3×C4×#683C212yesmaximal, complemented
12#10613972C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C3×C5×#117—24no—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2212yes—
20C2×C3×C42×C5C2212yes—
21C2×C3×C22⋊Dic5C2212yes—
22C2×C3×C22⋊Dic5C2211yescharacteristic
23C3×C4×C22⋊D5C418yescomplemented
24C2×C3×#685C2212yes—
25C2×C3×#685C2212yes—
26C2×C3×#685C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×#683C2212yes—
30C2×C3×#683C2212yes—
31C2×C3×#683C2211yescharacteristic
32C2×C3×C4×Dic5C2212yes—
33C2×C3×C4×Dic5C2212yes—
34C2×C3×C4×Dic5C2211yescharacteristic
35C3×#4038—24no—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2354—51nomaximal, Hall
40C2×C5×#117C2×C311yescharacteristic, complemented
41C2×C4×C22⋊D5C2×C311yescharacteristic
42C2×#4038C2×C311yescharacteristic, complemented
43#65501C2×C311yescharacteristic, complemented
44#65276C2×C311yescharacteristic, complemented
45#65265C2×C311yescharacteristic, complemented
46C4⋊C4×Dic5C2×C311yescharacteristic, complemented
47#65246C2×C312yes—
48#65233C2×C312yescomplemented
49#65229C2×C312yescomplemented
50C4×#683C2×C312yescomplemented
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yes—
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2312yes—
59C22×C3×C4×C5C2311yescharacteristic
60C2×C3×C22⋊D5—22no—
61C2×C3×C22⋊D5—22no—
62C2×C3×C22⋊D5C2×C414yes—
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2312yes—
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2311yescharacteristic
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5C2×C414yes—
71C3×C5×C4⋊C4—22no—
72C3×C5×C4⋊C4D414yescomplemented
73C3×C5×C22⋊C4—24no—
74C3×C42×C5—24no—
75C3×C22⋊Dic5—42no—
76C3×C22⋊Dic5C2×C414yes—
77C3×#685—24no—
78C3×#685—42no—
79C3×#685C2×C414yes—
80C3×C4⋊Dic5—22no—
81C3×C4⋊Dic5—22no—
82C3×#683—24no—
83C3×#683—42no—
84C3×#683C2×C414yes—
85C3×C4×Dic5—24no—
86C3×C4×Dic5—24no—
87C3×C4×Dic5C2×C414yes—
88C2×C3×C4×D4—51no—
89C2×C3×#117—51no—
90C2×C3×#117D511yescharacteristic, complemented
91C3×#390—52no—
92C3×#388—52no—
93C3×#388—52no—
94C3×#384—51no—
95C3×#380—51no—
96C3×#380—51no—
97C3×C4×C4⋊C4—51no—
98C3×C4×C4⋊C4—52no—
99C23×C4×C5C22×C311yescharacteristic
100C22×C22⋊D5C22×C311yescharacteristic
101C22×C4×D5C22×C311yescharacteristic
102C5×#117—24no—
103C2×C5×C4⋊C4C22×C311yescharacteristic
104C2×C5×C4⋊C4C22×C311yescharacteristic
105C2×C5×C22⋊C4C22×C312yes—
106C2×C42×C5C22×C312yes—
107C2×C22⋊Dic5C22×C312yes—
108C2×C22⋊Dic5C22×C311yescharacteristic
109C4×C22⋊D5C3×C418yescomplemented
110C2×#685C22×C312yes—
111C2×#685C22×C312yes—
112C2×#685C22×C311yescharacteristic
113C2×C4⋊Dic5C22×C311yescharacteristic
114C2×C4⋊Dic5C22×C311yescharacteristic
115C2×#683C22×C312yes—
116C2×#683C22×C312yes—
117C2×#683C22×C311yescharacteristic
118C2×C4×Dic5C22×C312yes—
119C2×C4×Dic5C22×C312yes—
120C2×C4×Dic5C22×C311yescharacteristic
121#4038—24no—
122#3963C22×C312yes—
123#3963C22×C312yes—
124#3963C22×C312yes—
125#2354—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×D5—21no—
139C22×C3×D5—21no—
140C22×C3×D5C22×C412yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—28no—
146C2×C3×C4×C5—22no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5C22×C412yes—
150C2×C3×C4×C5C22×C412yes—
151C2×C3×C4×C5C2×D414yes—
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—21no—
158C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
166C2×C3×Dic5C22×C412yes—
167C2×C3×Dic5C22×C412yes—
168C2×C3×Dic5#4112yes—
169C2×C3×Dic5#4112yes—
170C3×C4×D5—28no—
171C22×C3×D4—51no—
172C23×C3×C4—51no—
173C23×C3×C4C2×D511yescharacteristic
174C3×C4×D4—58no—
175C3×#117—24no—
176C3×#117—104no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C4⋊C4—52no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C4⋊C4—52no—
182C2×C3×C4⋊C4C2×D511yescharacteristic
183C2×C3×C4⋊C4C2×D511yescharacteristic
184C2×C3×C22⋊C4—51no—
185C2×C3×C22⋊C4—51no—
186C2×C3×C22⋊C4—52no—
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—
193C2×C3×C42C2×D512yes—
194C3×#95—52no—
195C3×#95—52no—
196C3×#95—52no—
197C24×C5C23×C311yescharacteristic
198C23×D5C23×C311yescharacteristic
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5C2×C3×C414yes—
202C22×C4×C5C23×C312yes—
203C22×C4×C5C23×C311yescharacteristic
204C22×C4×C5C23×C312yes—
205C22×C4×C5C23×C311yescharacteristic
206C2×C22⋊D5—22no—
207C2×C22⋊D5—22no—
208C2×C22⋊D5C2×C3×C414yes—
209C22×Dic5C23×C312yes—
210C22×Dic5C23×C312yes—
211C22×Dic5C23×C311yescharacteristic
212C22×Dic5C23×C311yescharacteristic
213C22×Dic5C23×C311yescharacteristic
214C2×C4×D5—22no—
215C2×C4×D5—22no—
216C2×C4×D5C2×C3×C414yes—
217C5×C4⋊C4—22no—
218C5×C4⋊C4C3×D414yescomplemented
219C5×C22⋊C4—24no—
220C42×C5—24no—
221C22⋊Dic5—42no—
222C22⋊Dic5C2×C3×C414yes—
223#685—24no—
224#685—42no—
225#685C2×C3×C414yes—
226C4⋊Dic5—22no—
227C4⋊Dic5—22no—
228#683—24no—
229#683—42no—
230#683C2×C3×C414yes—
231C4×Dic5—24no—
232C4×Dic5—24no—
233C4×Dic5C2×C3×C414yes—
234C2×C4×D4—51no—
235C2×#117—51no—
236C2×#117C3×D511yescharacteristic, complemented
237#390—52no—
238#388—52no—
239#388—52no—
240#384—51no—
241#380—51no—
242#380—51no—
243C4×C4⋊C4—51no—
244C4×C4⋊C4—52no—
245C22×C3×C5—22no—
246C22×C3×C5—22no—
247C22×C3×C5—22no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5—41no—
252C22×C3×C5C23×C411yescharacteristic
253C22×C3×C5C22×D411yescharacteristic
254C22×C3×C5C2×#4111yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5H(5,𝔽2)11yescharacteristic
258C22×C3×C52−1+411yescharacteristic
259C2×C3×D5—22no—
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—41no—
263C2×C3×D5—41no—
264C2×C3×D5—41no—
265C2×C3×D5—41no—
266C3×C4×C5—22no—
267C3×C4×C5—24no—
268C3×C4×C5—42no—
269C3×C4×C5C4×D414yes—
270C3×Dic5—22no—
271C3×Dic5—22no—
272C3×Dic5—42no—
273C3×Dic5—42no—
274C3×Dic5#11714yescomplemented
275C24×C3—51no—
276C24×C3C22×D511yescharacteristic
277C2×C3×D4—54no—
278C2×C3×D4—102no—
279C2×C3×D4—102no—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—51no—
283C22×C3×C4—51no—
284C22×C3×C4—51no—
285C22×C3×C4—54no—
286C22×C3×C4—52no—
287C22×C3×C4—52no—
288C22×C3×C4—102no—
289C22×C3×C4—102no—
290C22×C3×C4C4×D514yes—
291C22×C3×C4C22×D512yes—
292C22×C3×C4C22×D511yescharacteristic
293C22×C3×C4C22×D512yes—
294C22×C3×C4C22×D511yescharacteristic
295C3×C4⋊C4—22no—
296C3×C4⋊C4—54no—
297C3×C4⋊C4—104no—
298C3×C4⋊C4—102no—
299C3×C4⋊C4—102no—
300C3×C4⋊C4—202no—
301C3×C4⋊C4C22⋊D514yescomplemented
302C3×C22⋊C4—24no—
303C3×C22⋊C4—54no—
304C3×C22⋊C4—54no—
305C3×C22⋊C4—104no—
306C3×C22⋊C4—202no—
307C3×C22⋊C4—202no—
308C3×C42—24no—
309C3×C42—54no—
310C3×C42—104no—
311C3×C42—104no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5—21no—
316C23×C5—21no—
317C23×C5—21no—
318C23×C5C22×C3×C412yes—
319C23×C5C24×C311yescharacteristic
320C22×D5—21no—
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5—21no—
325C22×D5—21no—
326C22×D5C22×C3×C412yes—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—21no—
330C2×C4×C5—22no—
331C2×C4×C5—28no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—22no—
335C2×C4×C5C22×C3×C412yes—
336C2×C4×C5C22×C3×C412yes—
337C2×C4×C5C2×C3×D414yes—
338C2×C4×C5C2×C3×D412yes—
339C2×C4×C5C3×#4112yes—
340C22⋊D5—28no—
341C2×Dic5—21no—
342C2×Dic5—21no—
343C2×Dic5—21no—
344C2×Dic5—21no—
345C2×Dic5—22no—
346C2×Dic5—22no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5C22×C3×C412yes—
352C2×Dic5C22×C3×C412yes—
353C2×Dic5C22×C3×C412yes—
354C2×Dic5C3×#4112yes—
355C2×Dic5C3×#4112yes—
356C4×D5—28no—
357C22×D4—51no—
358C23×C4—51no—
359C23×C4C2×C3×D511yescharacteristic
360C4×D4—58no—
361#117—24no—
362#117—104no—
363C2×C4⋊C4—51no—
364C2×C4⋊C4—51no—
365C2×C4⋊C4—51no—
366C2×C4⋊C4—52no—
367C2×C4⋊C4—52no—
368C2×C4⋊C4C2×C3×D511yescharacteristic
369C2×C4⋊C4C2×C3×D511yescharacteristic
370C2×C22⋊C4—51no—
371C2×C22⋊C4—51no—
372C2×C22⋊C4—52no—
373C2×C22⋊C4—52no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4C2×C3×D512yes—
376C2×C42—51no—
377C2×C42—52no—
378C2×C42—52no—
379C2×C42C2×C3×D512yes—
380#95—52no—
381#95—52no—
382#95—52no—
383C2×C3×C5—42no—
384C2×C3×C5C2×#11711yescharacteristic
385C2×C3×C5C2×C4×D411yescharacteristic
386C2×C3×C5#52011yescharacteristic
387C2×C3×C5#54711yescharacteristic
388C2×C3×C5#55011yescharacteristic
389C2×C3×C5#55511yescharacteristic
390C2×C3×C5#55611yescharacteristic
391C3×D5—42no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—52no—
399C23×C3—101no—
400C23×C3—101no—
401C23×C3—101no—
402C23×C3—101no—
403C23×C3—101no—
404C23×C3—101no—
405C23×C3C2×C4×D512yes—
406C23×C3C23×D511yescharacteristic
407C3×D4—108no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—21no—
412C2×C3×C4—28no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—52no—
417C2×C3×C4—52no—
418C2×C3×C4—52no—
419C2×C3×C4—52no—
420C2×C3×C4—52no—
421C2×C3×C4—101no—
422C2×C3×C4—101no—
423C2×C3×C4—101no—
424C2×C3×C4—101no—
425C2×C3×C4—108no—
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×C4C2×C4×D512yes—
433C2×C3×C4C2×C4×D512yes—
434C2×C3×C4#70912yes—
435C2×C3×C4C2×C22⋊D514yes—
436C2×C3×C4C2×C22⋊D512yes—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—22no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5—41no—
444C22×C5C23×C3×C411yescharacteristic
445C22×C5C22×C3×D411yescharacteristic
446C22×C5C2×C3×#4111yescharacteristic
447C22×C5C2×C3×#4111yescharacteristic
448C22×C5C2×C3×#4111yescharacteristic
449C22×C5C3×H(5,𝔽2)11yescharacteristic
450C22×C5C3×2−1+411yescharacteristic
451C2×D5—22no—
452C2×D5—22no—
453C2×D5—22no—
454C2×D5—41no—
455C2×D5—41no—
456C2×D5—41no—
457C2×D5—41no—
458C4×C5—22no—
459C4×C5—24no—
460C4×C5—42no—
461C4×C5C3×C4×D414yes—
462Dic5—22no—
463Dic5—22no—
464Dic5—42no—
465Dic5—42no—
466Dic5C3×#11714yescomplemented
467C24—51no—
468C24C22×C3×D511yescharacteristic
469C2×D4—54no—
470C2×D4—102no—
471C2×D4—102no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—51no—
475C22×C4—51no—
476C22×C4—51no—
477C22×C4—54no—
478C22×C4—52no—
479C22×C4—52no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4C3×C4×D514yes—
483C22×C4C22×C3×D512yes—
484C22×C4C22×C3×D511yescharacteristic
485C22×C4C22×C3×D512yes—
486C22×C4C22×C3×D511yescharacteristic
487C4⋊C4—22no—
488C4⋊C4—54no—
489C4⋊C4—104no—
490C4⋊C4—102no—
491C4⋊C4—102no—
492C4⋊C4—202no—
493C4⋊C4C3×C22⋊D514yescomplemented
494C22⋊C4—24no—
495C22⋊C4—54no—
496C22⋊C4—54no—
497C22⋊C4—104no—
498C22⋊C4—202no—
499C22⋊C4—202no—
500C42—24no—
501C42—54no—
502C42—104no—
503C42—104no—
504C3×C5#235411yescharacteristic, complemented, Hall
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—41no—
512C22×C3—102no—
513C22×C3—102no—
514C22×C3—102no—
515C22×C3—201no—
516C22×C3—201no—
517C22×C3—201no—
518C22×C3—201no—
519C22×C3C22×C4×D511yescharacteristic
520C22×C3C2×#70911yescharacteristic
521C22×C3D5×#4111yescharacteristic
522C22×C3D5×#4111yescharacteristic
523C22×C3#414911yescharacteristic
524C22×C3#415011yescharacteristic
525C22×C3C22×C22⋊D511yescharacteristic
526C3×C4—22no—
527C3×C4—24no—
528C3×C4—42no—
529C3×C4—54no—
530C3×C4—102no—
531C3×C4—102no—
532C3×C4—202no—
533C3×C4—202no—
534C3×C4C4×C22⋊D514yes—
535C2×C5—42no—
536C2×C5C2×C3×#11711yescharacteristic
537C2×C5C2×C3×C4×D411yescharacteristic
538C2×C5C3×#52011yescharacteristic
539C2×C5C3×#54711yescharacteristic
540C2×C5C3×#55011yescharacteristic
541C2×C5C3×#55511yescharacteristic
542C2×C5C3×#55611yescharacteristic
543D5—42no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—52no—
551C23—101no—
552C23—101no—
553C23—101no—
554C23—101no—
555C23—101no—
556C23—101no—
557C23C2×C3×C4×D512yes—
558C23C23×C3×D511yescharacteristic
559D4—108no—
560C2×C4—21no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—28no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—52no—
569C2×C4—52no—
570C2×C4—52no—
571C2×C4—52no—
572C2×C4—52no—
573C2×C4—101no—
574C2×C4—101no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—108no—
578C2×C4—102no—
579C2×C4—102no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—102no—
584C2×C4C2×C3×C4×D512yes—
585C2×C4C2×C3×C4×D512yes—
586C2×C4C3×#70912yes—
587C2×C4C2×C3×C22⋊D514yes—
588C2×C4C2×C3×C22⋊D512yes—
589C2×C3—42no—
590C2×C3—202no—
591C2×C3D5×#11711yescharacteristic
592C2×C3#6585711yescharacteristic
593C2×C3#6586611yescharacteristic
594C2×C3#6586711yescharacteristic
595C2×C3C2×C4×C22⋊D511yescharacteristic
596C2×C3#6615811yescharacteristic
597C2×C3#6616811yescharacteristic
598C5C3×#235411yescharacteristic, complemented, Sylow
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—102no—
607C22—102no—
608C22—102no—
609C22—201no—
610C22—201no—
611C22—201no—
612C22—201no—
613C22C22×C3×C4×D511yescharacteristic
614C22C2×C3×#70911yescharacteristic
615C22C3×D5×#4111yescharacteristic
616C22C3×D5×#4111yescharacteristic
617C22C3×#414911yescharacteristic
618C22C3×#415011yescharacteristic
619C22C22×C3×C22⋊D511yescharacteristic
620C4—22no—
621C4—24no—
622C4—42no—
623C4—54no—
624C4—102no—
625C4—102no—
626C4—202no—
627C4—202no—
628C4C3×C4×C22⋊D514yes—
629C3#1061397211yescharacteristic, direct product factor, Sylow
630C2—42no—
631C2—202no—
632C2C3×D5×#11711yescharacteristic
633C2C3×#6585711yescharacteristic
634C2C3×#6586611yescharacteristic
635C2C3×#6586711yescharacteristic
636C2C2×C3×C4×C22⋊D511yescharacteristic
637C2C3×#6615811yescharacteristic
638C2C3×#6616811yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#2354
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#117C2semidirect
3. C2×C3×#4038C2semidirect
4. C3×#65501C2semidirect
5. C3×#65276C2semidirect
6. C3×#65265C2semidirect
7. C3×C4⋊C4×Dic5C2semidirect
9. C3×#65233C2semidirect
10. C3×#65229C2semidirect
11. C3×C4×#683C2semidirect
12. #10613972C3direct (N × H)
23. C3×C4×C22⋊D5C4semidirect
40. C2×C5×#117C2×C3semidirect
42. C2×#4038C2×C3semidirect
43. #65501C2×C3semidirect
44. #65276C2×C3semidirect
45. #65265C2×C3semidirect
46. C4⋊C4×Dic5C2×C3semidirect
48. #65233C2×C3semidirect
49. #65229C2×C3semidirect
50. C4×#683C2×C3semidirect
72. C3×C5×C4⋊C4D4semidirect
90. C2×C3×#117D5semidirect
109. C4×C22⋊D5C3×C4semidirect
218. C5×C4⋊C4C3×D4semidirect
236. C2×#117C3×D5semidirect
274. C3×Dic5#117semidirect
301. C3×C4⋊C4C22⋊D5semidirect
466. Dic5C3×#117semidirect
493. C4⋊C4C3×C22⋊D5semidirect
504. C3×C5#2354semidirect
598. C5C3×#2354semidirect
629. C3#10613972direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
C2×C3×C4×C22⋊D52
C2×C3×#40382
C3×#655012
C3×#652762
C3×#652652
C3×C4⋊C4×Dic52
C3×#652462
C3×#652332
C3×#652292
C3×C4×#6832
#106139723
C3×#23545