Finite Group Databasebeta

← C3×#10613967 #14323880

Subgroups — C3×#10613967 #14323880

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic, complemented
2C2×C3×#4076C211yesmaximal, characteristic
3C2×C3×C4×D20C211yesmaximal, characteristic, complemented
4C3×#65501C211yesmaximal, characteristic, complemented
5C3×#65279C212yesmaximal, complemented
6C3×#65278C212yesmaximal, complemented
7C3×#65246C212yesmaximal, complemented
8C3×#65245C212yesmaximal, complemented
9C3×#65228C211yesmaximal, characteristic, complemented
10C3×C4×C4⋊Dic5C211yesmaximal, characteristic, complemented
11C3×#65217C211yesmaximal, characteristic, complemented
12#10613967C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2212yes—
15C22×C3×D20C2211yescharacteristic
16C22×C3×C4×D5C2212yes—
17C3×C5×#117—24no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×C22⋊Dic5C2212yes—
25C3×#4076C418yescomplemented
26C2×C3×#685C2212yes—
27C2×C3×#685C2212yes—
28C2×C3×#685C2212yes—
29C2×C3×#685C2212yes—
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×#683C2212yes—
34C2×C3×C4×Dic5C2212yes—
35C3×C4×D20—24no—
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2324—51nomaximal, Hall
40C2×C5×#117C2×C311yescharacteristic, complemented
41C2×#4076C2×C311yescharacteristic
42C2×C4×D20C2×C311yescharacteristic, complemented
43#65501C2×C311yescharacteristic, complemented
44#65279C2×C312yescomplemented
45#65278C2×C312yescomplemented
46#65246C2×C312yescomplemented
47#65245C2×C312yescomplemented
48#65228C2×C311yescharacteristic, complemented
49C4×C4⋊Dic5C2×C311yescharacteristic, complemented
50#65217C2×C311yescharacteristic, complemented
51C24×C3×C5C2311yescharacteristic
52C23×C3×D5C2312yes—
53C22×C3×C4×C5—22no—
54C22×C3×C4×C5—22no—
55C22×C3×C4×C5C2×C414yescomplemented
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C2×C3×C22⋊D5—42no—
63C2×C3×C22⋊D5—42no—
64C2×C3×C22⋊D5C2×C418yescomplemented
65C22×C3×Dic5C2312yes—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68C2×C3×D20—22no—
69C2×C3×D20—22no—
70C2×C3×D20C2×C414yes—
71C2×C3×C4×D5—24no—
72C2×C3×C4×D5—42no—
73C2×C3×C4×D5—42no—
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C22⋊C4—22no—
77C3×C5×C22⋊C4—22no—
78C3×C42×C5—22no—
79C3×C42×C5D414yescomplemented
80C3×C22⋊Dic5—42no—
81C3×#685—24no—
82C3×#685—42no—
83C3×#685—42no—
84C3×#685C2×C418yescomplemented
85C3×C4⋊Dic5—22no—
86C3×C4⋊Dic5—22no—
87C3×C4⋊Dic5C2×C414yescomplemented
88C3×#683—42no—
89C3×C4×Dic5—42no—
90C2×C3×#121—51no—
91C2×C3×C4×D4—51no—
92C2×C3×#117D511yescharacteristic, complemented
93C3×#390—52no—
94C3×#390—51no—
95C3×#389—51no—
96C3×#388—52no—
97C3×#386—52no—
98C3×#385—52no—
99C3×#380—51no—
100C3×C4×C4⋊C4—51no—
101C23×C4×C5C22×C311yescharacteristic
102C22×C22⋊D5C22×C312yes—
103C22×D20C22×C311yescharacteristic
104C22×C4×D5C22×C312yes—
105C5×#117—24no—
106C2×C5×C4⋊C4C22×C311yescharacteristic
107C2×C5×C4⋊C4C22×C311yescharacteristic
108C2×C5×C22⋊C4C22×C311yescharacteristic
109C2×C5×C22⋊C4C22×C311yescharacteristic
110C2×C42×C5C22×C311yescharacteristic
111C2×C42×C5C22×C311yescharacteristic
112C2×C22⋊Dic5C22×C312yes—
113#4076C3×C418yescomplemented
114C2×#685C22×C312yes—
115C2×#685C22×C312yes—
116C2×#685C22×C312yes—
117C2×#685C22×C312yes—
118C2×C4⋊Dic5C22×C311yescharacteristic
119C2×C4⋊Dic5C22×C311yescharacteristic
120C2×C4⋊Dic5C22×C311yescharacteristic
121C2×#683C22×C312yes—
122C2×C4×Dic5C22×C312yes—
123C4×D20—24no—
124#3963C22×C312yes—
125#3963C22×C312yes—
126#3963C22×C312yes—
127#2324—51noSylow
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×C5C22×C412yes—
135C23×C3×C5C2411yescharacteristic
136C22×C3×D5—22no—
137C22×C3×D5—22no—
138C22×C3×D5—22no—
139C22×C3×D5—22no—
140C22×C3×D5—22no—
141C22×C3×D5—22no—
142C22×C3×D5C22×C414yes—
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—28no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C22×C412yes—
158C2×C3×C4×C5C2×D412yes—
159C2×C3×C4×C5C2×D412yes—
160C2×C3×C4×C5C2×D412yes—
161C2×C3×C4×C5#4112yes—
162C3×C22⋊D5—48no—
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—22no—
171C2×C3×Dic5C22×C414yes—
172C3×D20—28no—
173C3×C4×D5—48no—
174C22×C3×D4—52no—
175C22×C3×D4—51no—
176C23×C3×C4—52no—
177C23×C3×C4C2×D511yescharacteristic
178C3×#121—58no—
179C3×C4×D4—104no—
180C3×#117—24no—
181C2×C3×C4⋊C4—51no—
182C2×C3×C4⋊C4—51no—
183C2×C3×C4⋊C4—51no—
184C2×C3×C4⋊C4—52no—
185C2×C3×C4⋊C4C2×D511yescharacteristic
186C2×C3×C4⋊C4C2×D511yescharacteristic
187C2×C3×C22⋊C4—52no—
188C2×C3×C22⋊C4—52no—
189C2×C3×C22⋊C4—52no—
190C2×C3×C22⋊C4—52no—
191C2×C3×C22⋊C4—52no—
192C2×C3×C22⋊C4C2×D511yescharacteristic
193C2×C3×C22⋊C4C2×D511yescharacteristic
194C2×C3×C42—52no—
195C2×C3×C42C2×D511yescharacteristic
196C2×C3×C42C2×D511yescharacteristic
197C3×#95—52no—
198C3×#95—52no—
199C3×#95—52no—
200C24×C5C23×C311yescharacteristic
201C23×D5C23×C312yes—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5C2×C3×C414yescomplemented
205C22×C4×C5C23×C311yescharacteristic
206C22×C4×C5C23×C311yescharacteristic
207C22×C4×C5C23×C311yescharacteristic
208C22×C4×C5C23×C311yescharacteristic
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C311yescharacteristic
211C2×C22⋊D5—42no—
212C2×C22⋊D5—42no—
213C2×C22⋊D5C2×C3×C418yescomplemented
214C22×Dic5C23×C312yes—
215C22×Dic5C23×C312yes—
216C22×Dic5C23×C312yes—
217C2×D20—22no—
218C2×D20—22no—
219C2×D20C2×C3×C414yes—
220C2×C4×D5—24no—
221C2×C4×D5—42no—
222C2×C4×D5—42no—
223C5×C4⋊C4—22no—
224C5×C4⋊C4—22no—
225C5×C22⋊C4—22no—
226C5×C22⋊C4—22no—
227C42×C5—22no—
228C42×C5C3×D414yescomplemented
229C22⋊Dic5—42no—
230#685—24no—
231#685—42no—
232#685—42no—
233#685C2×C3×C418yescomplemented
234C4⋊Dic5—22no—
235C4⋊Dic5—22no—
236C4⋊Dic5C2×C3×C414yescomplemented
237#683—42no—
238C4×Dic5—42no—
239C2×#121—51no—
240C2×C4×D4—51no—
241C2×#117C3×D511yescharacteristic, complemented
242#390—52no—
243#390—51no—
244#389—51no—
245#388—52no—
246#386—52no—
247#385—52no—
248#380—51no—
249C4×C4⋊C4—51no—
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—41no—
254C22×C3×C5—41no—
255C22×C3×C5—41no—
256C22×C3×C5—41no—
257C22×C3×C5C23×C411yescharacteristic
258C22×C3×C5C22×D411yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C22×C3×C5H(5,𝔽2)11yescharacteristic
262C22×C3×C5H(5,𝔽2)11yescharacteristic
263C22×C3×C52−1+411yescharacteristic
264C2×C3×D5—24no—
265C2×C3×D5—24no—
266C2×C3×D5—24no—
267C2×C3×D5—42no—
268C2×C3×D5—42no—
269C2×C3×D5—42no—
270C2×C3×D5—42no—
271C3×C4×C5—22no—
272C3×C4×C5—22no—
273C3×C4×C5—22no—
274C3×C4×C5—41no—
275C3×C4×C5—41no—
276C3×C4×C5C4×D414yes—
277C3×Dic5—24no—
278C3×Dic5—42no—
279C3×Dic5—42no—
280C24×C3—52no—
281C24×C3C22×D511yescharacteristic
282C2×C3×D4—58no—
283C2×C3×D4—54no—
284C2×C3×D4—102no—
285C2×C3×D4—102no—
286C2×C3×D4—202no—
287C2×C3×D4—202no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—52no—
291C22×C3×C4—52no—
292C22×C3×C4—52no—
293C22×C3×C4—104no—
294C22×C3×C4—202no—
295C22×C3×C4—202no—
296C22×C3×C4C4×D514yescomplemented
297C22×C3×C4C22×D511yescharacteristic
298C22×C3×C4C22×D511yescharacteristic
299C22×C3×C4C22×D511yescharacteristic
300C22×C3×C4C22×D511yescharacteristic
301C22×C3×C4C22×D511yescharacteristic
302C22×C3×C4C22×D511yescharacteristic
303C3×C4⋊C4—22no—
304C3×C4⋊C4—22no—
305C3×C4⋊C4—54no—
306C3×C4⋊C4—102no—
307C3×C4⋊C4—102no—
308C3×C4⋊C4—202no—
309C3×C22⋊C4—22no—
310C3×C22⋊C4—22no—
311C3×C22⋊C4—58no—
312C3×C22⋊C4—104no—
313C3×C22⋊C4—202no—
314C3×C22⋊C4—202no—
315C3×C22⋊C4—202no—
316C3×C42—22no—
317C3×C42—202no—
318C3×C42C22⋊D514yescomplemented
319C23×C5—21no—
320C23×C5—21no—
321C23×C5—21no—
322C23×C5—21no—
323C23×C5—21no—
324C23×C5—21no—
325C23×C5C22×C3×C412yes—
326C23×C5C24×C311yescharacteristic
327C22×D5—22no—
328C22×D5—22no—
329C22×D5—22no—
330C22×D5—22no—
331C22×D5—22no—
332C22×D5—22no—
333C22×D5C22×C3×C414yes—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—21no—
340C2×C4×C5—28no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5C22×C3×C412yes—
348C2×C4×C5C22×C3×C412yes—
349C2×C4×C5C2×C3×D412yes—
350C2×C4×C5C2×C3×D412yes—
351C2×C4×C5C2×C3×D412yes—
352C2×C4×C5C3×#4112yes—
353C22⋊D5—48no—
354C2×Dic5—22no—
355C2×Dic5—22no—
356C2×Dic5—22no—
357C2×Dic5—22no—
358C2×Dic5—22no—
359C2×Dic5—22no—
360C2×Dic5—22no—
361C2×Dic5—22no—
362C2×Dic5C22×C3×C414yes—
363D20—28no—
364C4×D5—48no—
365C22×D4—52no—
366C22×D4—51no—
367C23×C4—52no—
368C23×C4C2×C3×D511yescharacteristic
369#121—58no—
370C4×D4—104no—
371#117—24no—
372C2×C4⋊C4—51no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—51no—
375C2×C4⋊C4—52no—
376C2×C4⋊C4C2×C3×D511yescharacteristic
377C2×C4⋊C4C2×C3×D511yescharacteristic
378C2×C22⋊C4—52no—
379C2×C22⋊C4—52no—
380C2×C22⋊C4—52no—
381C2×C22⋊C4—52no—
382C2×C22⋊C4—52no—
383C2×C22⋊C4C2×C3×D511yescharacteristic
384C2×C22⋊C4C2×C3×D511yescharacteristic
385C2×C42—52no—
386C2×C42C2×C3×D511yescharacteristic
387C2×C42C2×C3×D511yescharacteristic
388#95—52no—
389#95—52no—
390#95—52no—
391C2×C3×C5—42no—
392C2×C3×C5C2×C4×D411yescharacteristic
393C2×C3×C5#51811yescharacteristic
394C2×C3×C5#52011yescharacteristic
395C2×C3×C5#53511yescharacteristic
396C2×C3×C5#53711yescharacteristic
397C2×C3×C5#54011yescharacteristic
398C2×C3×C5#54211yescharacteristic
399C3×D5—44no—
400C23×C3—21no—
401C23×C3—21no—
402C23×C3—21no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—54no—
407C23×C3—102no—
408C23×C3—102no—
409C23×C3—102no—
410C23×C3—102no—
411C23×C3—102no—
412C23×C3—102no—
413C23×C3C2×C4×D512yes—
414C23×C3C23×D511yescharacteristic
415C3×D4—108no—
416C3×D4—208no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—28no—
424C2×C3×C4—21no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—54no—
431C2×C3×C4—102no—
432C2×C3×C4—102no—
433C2×C3×C4—102no—
434C2×C3×C4—102no—
435C2×C3×C4—102no—
436C2×C3×C4—102no—
437C2×C3×C4—102no—
438C2×C3×C4—102no—
439C2×C3×C4—208no—
440C2×C3×C4C2×C4×D512yes—
441C2×C3×C4C2×C4×D512yes—
442C2×C3×C4#70912yes—
443C2×C3×C4C2×C22⋊D512yes—
444C2×C3×C4C2×C22⋊D512yes—
445C2×C3×C4C2×C22⋊D512yes—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—22no—
449C22×C5—41no—
450C22×C5—41no—
451C22×C5—41no—
452C22×C5—41no—
453C22×C5C23×C3×C411yescharacteristic
454C22×C5C22×C3×D411yescharacteristic
455C22×C5C2×C3×#4111yescharacteristic
456C22×C5C3×H(5,𝔽2)11yescharacteristic
457C22×C5C3×H(5,𝔽2)11yescharacteristic
458C22×C5C3×H(5,𝔽2)11yescharacteristic
459C22×C5C3×2−1+411yescharacteristic
460C2×D5—24no—
461C2×D5—24no—
462C2×D5—24no—
463C2×D5—42no—
464C2×D5—42no—
465C2×D5—42no—
466C2×D5—42no—
467C4×C5—22no—
468C4×C5—22no—
469C4×C5—22no—
470C4×C5—41no—
471C4×C5—41no—
472C4×C5C3×C4×D414yes—
473Dic5—24no—
474Dic5—42no—
475Dic5—42no—
476C24—52no—
477C24C22×C3×D511yescharacteristic
478C2×D4—58no—
479C2×D4—54no—
480C2×D4—102no—
481C2×D4—102no—
482C2×D4—202no—
483C2×D4—202no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—52no—
487C22×C4—52no—
488C22×C4—52no—
489C22×C4—104no—
490C22×C4—202no—
491C22×C4—202no—
492C22×C4C3×C4×D514yescomplemented
493C22×C4C22×C3×D511yescharacteristic
494C22×C4C22×C3×D511yescharacteristic
495C22×C4C22×C3×D511yescharacteristic
496C22×C4C22×C3×D511yescharacteristic
497C22×C4C22×C3×D511yescharacteristic
498C22×C4C22×C3×D511yescharacteristic
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—54no—
502C4⋊C4—102no—
503C4⋊C4—102no—
504C4⋊C4—202no—
505C22⋊C4—22no—
506C22⋊C4—22no—
507C22⋊C4—58no—
508C22⋊C4—104no—
509C22⋊C4—202no—
510C22⋊C4—202no—
511C22⋊C4—202no—
512C42—22no—
513C42—202no—
514C42C3×C22⋊D514yescomplemented
515C3×C5#232411yescharacteristic, complemented, Hall
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—104no—
524C22×C3—104no—
525C22×C3—104no—
526C22×C3—202no—
527C22×C3—202no—
528C22×C3—202no—
529C22×C3—202no—
530C22×C3C22×C4×D511yescharacteristic
531C22×C3C2×#70911yescharacteristic
532C22×C3#414911yescharacteristic
533C22×C3#414911yescharacteristic
534C22×C3#414911yescharacteristic
535C22×C3#415011yescharacteristic
536C22×C3C22×C22⋊D511yescharacteristic
537C3×C4—22no—
538C3×C4—22no—
539C3×C4—22no—
540C3×C4—41no—
541C3×C4—41no—
542C3×C4—104no—
543C3×C4—202no—
544C3×C4—202no—
545C3×C4C4×C22⋊D514yes—
546C2×C5—42no—
547C2×C5C2×C3×C4×D411yescharacteristic
548C2×C5C3×#51811yescharacteristic
549C2×C5C3×#52011yescharacteristic
550C2×C5C3×#53511yescharacteristic
551C2×C5C3×#53711yescharacteristic
552C2×C5C3×#54011yescharacteristic
553C2×C5C3×#54211yescharacteristic
554D5—44no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—54no—
562C23—102no—
563C23—102no—
564C23—102no—
565C23—102no—
566C23—102no—
567C23—102no—
568C23C2×C3×C4×D512yes—
569C23C23×C3×D511yescharacteristic
570D4—108no—
571D4—208no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—28no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—54no—
586C2×C4—102no—
587C2×C4—102no—
588C2×C4—102no—
589C2×C4—102no—
590C2×C4—102no—
591C2×C4—102no—
592C2×C4—102no—
593C2×C4—102no—
594C2×C4—208no—
595C2×C4C2×C3×C4×D512yes—
596C2×C4C2×C3×C4×D512yes—
597C2×C4C3×#70912yes—
598C2×C4C2×C3×C22⋊D512yes—
599C2×C4C2×C3×C22⋊D512yes—
600C2×C4C2×C3×C22⋊D512yes—
601C2×C3—42no—
602C2×C3—204no—
603C2×C3#6585511yescharacteristic
604C2×C3#6585711yescharacteristic
605C2×C3#6586811yescharacteristic
606C2×C3#6586911yescharacteristic
607C2×C3C2×C4×C22⋊D511yescharacteristic
608C2×C3#6616411yescharacteristic
609C2×C3#6616711yescharacteristic
610C5C3×#232411yescharacteristic, complemented, Sylow
611C22—22no—
612C22—22no—
613C22—22no—
614C22—41no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—104no—
619C22—104no—
620C22—104no—
621C22—202no—
622C22—202no—
623C22—202no—
624C22—202no—
625C22C22×C3×C4×D511yescharacteristic
626C22C2×C3×#70911yescharacteristic
627C22C3×#414911yescharacteristic
628C22C3×#414911yescharacteristic
629C22C3×#414911yescharacteristic
630C22C3×#415011yescharacteristic
631C22C22×C3×C22⋊D511yescharacteristic
632C4—22no—
633C4—22no—
634C4—22no—
635C4—41no—
636C4—41no—
637C4—104no—
638C4—202no—
639C4—202no—
640C4C3×C4×C22⋊D514yes—
641C3#1061396711yescharacteristic, direct product factor, Sylow
642C2—42no—
643C2—204no—
644C2C3×#6585511yescharacteristic
645C2C3×#6585711yescharacteristic
646C2C3×#6586811yescharacteristic
647C2C3×#6586911yescharacteristic
648C2C2×C3×C4×C22⋊D511yescharacteristic
649C2C3×#6616411yescharacteristic
650C2C3×#6616711yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#117C2
socleC23×C3×C5C24
prime radicalC2×C3×#4076C2
cosocleC23×C5C24×C3
hypercenterC2×C3×#117D5
hypocenterC5C3×#2324
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×C4×D20C2semidirect
4. C3×#65501C2semidirect
5. C3×#65279C2semidirect
6. C3×#65278C2semidirect
7. C3×#65246C2semidirect
8. C3×#65245C2semidirect
9. C3×#65228C2semidirect
10. C3×C4×C4⋊Dic5C2semidirect
11. C3×#65217C2semidirect
12. #10613967C3direct (N × H)
25. C3×#4076C4semidirect
40. C2×C5×#117C2×C3semidirect
42. C2×C4×D20C2×C3semidirect
43. #65501C2×C3semidirect
44. #65279C2×C3semidirect
45. #65278C2×C3semidirect
46. #65246C2×C3semidirect
47. #65245C2×C3semidirect
48. #65228C2×C3semidirect
49. C4×C4⋊Dic5C2×C3semidirect
50. #65217C2×C3semidirect
55. C22×C3×C4×C5C2×C4semidirect
64. C2×C3×C22⋊D5C2×C4semidirect
79. C3×C42×C5D4semidirect
84. C3×#685C2×C4semidirect
87. C3×C4⋊Dic5C2×C4semidirect
92. C2×C3×#117D5semidirect
113. #4076C3×C4semidirect
204. C22×C4×C5C2×C3×C4semidirect
213. C2×C22⋊D5C2×C3×C4semidirect
228. C42×C5C3×D4semidirect
233. #685C2×C3×C4semidirect
236. C4⋊Dic5C2×C3×C4semidirect
241. C2×#117C3×D5semidirect
296. C22×C3×C4C4×D5semidirect
318. C3×C42C22⋊D5semidirect
492. C22×C4C3×C4×D5semidirect
514. C42C3×C22⋊D5semidirect
515. C3×C5#2324semidirect
610. C5C3×#2324semidirect
641. C3#10613967direct (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×#40762
C2×C3×C4×D202
C3×#655012
C3×#652792
C3×#652782
C3×#652462
C3×#652452
C3×#652282
C3×C4×C4⋊Dic52
C3×#652172
#106139673
C3×#23245