Finite Group Databasebeta

← C3×C5×#2485 #14275519

Subgroups — C3×C5×#2485 #14275519

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic
2C2×C3×C5×#117C211yesmaximal, characteristic, complemented
3C3×C5×#397C212yesmaximal, complemented
4C3×C5×#394C212yesmaximal
5C3×C5×#389C211yesmaximal, characteristic, complemented
6C3×C5×#389C211yesmaximal, characteristic, complemented
7C3×C5×#388C212yesmaximal, complemented
8C3×C5×#387C212yesmaximal, complemented
9C3×C5×#380C211yesmaximal, characteristic, complemented
10C3×C5×#380C211yesmaximal, characteristic, complemented
11C3×C5×#380C211yesmaximal, characteristic, complemented
12C5×#2485C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C3×C4×C5×D4—24no—
17C3×C5×#117—24no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2212yes—
25C2×C3×C5×C22⋊C4C2212yes—
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C5×C22⋊C4C2212yes—
31C2×C3×C42×C5C2212yes—
32C2×C3×C42×C5C2211yescharacteristic
33C3×C5×#95C2212yes—
34C3×C5×#95C2212yes—
35C3×C5×#95C2212yes—
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×#2485C511yesmaximal, characteristic, direct product factor, Hall
39C2×C4×C5×D4C2×C311yescharacteristic
40C2×C5×#117C2×C311yescharacteristic, complemented
41C5×#397C2×C312yescomplemented
42C5×#394C2×C312yes—
43C5×#389C2×C311yescharacteristic, complemented
44C5×#389C2×C311yescharacteristic, complemented
45C5×#388C2×C312yescomplemented
46C5×#387C2×C312yescomplemented
47C5×#380C2×C311yescharacteristic, complemented
48C5×#380C2×C311yescharacteristic, complemented
49C5×#380C2×C311yescharacteristic, complemented
50C24×C3×C5C2311yescharacteristic
51C24×C3×C5C2311yescharacteristic
52C2×C3×C5×D4—22no—
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C22×C3×C4×C5—22no—
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5—22no—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5D414yes—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2312yes—
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2312yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2311yescharacteristic
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2311yescharacteristic
70C3×C5×C4⋊C4—22no—
71C3×C5×C4⋊C4—22no—
72C3×C5×C4⋊C4—22no—
73C3×C5×C4⋊C4—24no—
74C3×C5×C4⋊C4—22no—
75C3×C5×C4⋊C4—22no—
76C3×C5×C4⋊C4—42no—
77C3×C5×C22⋊C4—24no—
78C3×C5×C22⋊C4—22no—
79C3×C5×C22⋊C4—24no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—42no—
82C3×C5×C22⋊C4—42no—
83C3×C42×C5—24no—
84C3×C42×C5—22no—
85C2×C3×C4×D4C2×C511yescharacteristic
86C2×C3×#117C2×C511yescharacteristic, complemented
87C3×#397C2×C512yescomplemented
88C3×#394C2×C512yes—
89C3×#389C2×C511yescharacteristic, complemented
90C3×#389C2×C511yescharacteristic, complemented
91C3×#388C2×C512yescomplemented
92C3×#387C2×C512yescomplemented
93C3×#380C2×C511yescharacteristic, complemented
94C3×#380C2×C511yescharacteristic, complemented
95C3×#380C2×C511yescharacteristic, complemented
96C22×C5×D4C22×C311yescharacteristic
97C23×C4×C5C22×C311yescharacteristic
98C23×C4×C5C22×C311yescharacteristic
99C4×C5×D4—24no—
100C5×#117—24no—
101C2×C5×C4⋊C4C22×C311yescharacteristic
102C2×C5×C4⋊C4C22×C311yescharacteristic
103C2×C5×C4⋊C4C22×C311yescharacteristic
104C2×C5×C4⋊C4C22×C311yescharacteristic
105C2×C5×C4⋊C4C22×C311yescharacteristic
106C2×C5×C4⋊C4C22×C312yes—
107C2×C5×C4⋊C4C22×C312yes—
108C2×C5×C22⋊C4C22×C312yes—
109C2×C5×C22⋊C4C22×C311yescharacteristic
110C2×C5×C22⋊C4C22×C312yes—
111C2×C5×C22⋊C4C22×C311yescharacteristic
112C2×C5×C22⋊C4C22×C312yes—
113C2×C5×C22⋊C4C22×C312yes—
114C2×C42×C5C22×C312yes—
115C2×C42×C5C22×C311yescharacteristic
116C5×#95C22×C312yes—
117C5×#95C22×C312yes—
118C5×#95C22×C312yes—
119C5×#95C22×C312yes—
120C5×#95C22×C312yes—
121#2485C3×C511yescharacteristic, direct product factor, Sylow
122C23×C3×C5—21no—
123C23×C3×C5—21no—
124C23×C3×C5—21no—
125C23×C3×C5—21no—
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×C5C2×D412yes—
135C23×C3×C5#4112yes—
136C23×C3×C5C2411yescharacteristic
137C3×C5×D4—28no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—28no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—22no—
148C2×C3×C4×C5—22no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—21no—
154C2×C3×C4×C5—21no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—21no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—44no—
162C2×C3×C4×C5C2×D412yes—
163C2×C3×C4×C5C2×D412yes—
164C2×C3×C4×C5#4112yes—
165C2×C3×C4×C5#4112yes—
166C2×C3×C4×C5#4112yes—
167C22×C3×D4C22×C511yescharacteristic
168C23×C3×C4C22×C511yescharacteristic
169C23×C3×C4C22×C511yescharacteristic
170C3×C4×D4—24no—
171C3×#117—24no—
172C2×C3×C4⋊C4C22×C511yescharacteristic
173C2×C3×C4⋊C4C22×C511yescharacteristic
174C2×C3×C4⋊C4C22×C511yescharacteristic
175C2×C3×C4⋊C4C22×C511yescharacteristic
176C2×C3×C4⋊C4C22×C511yescharacteristic
177C2×C3×C4⋊C4C22×C512yes—
178C2×C3×C4⋊C4C22×C512yes—
179C2×C3×C22⋊C4C22×C512yes—
180C2×C3×C22⋊C4C22×C511yescharacteristic
181C2×C3×C22⋊C4C22×C512yes—
182C2×C3×C22⋊C4C22×C511yescharacteristic
183C2×C3×C22⋊C4C22×C512yes—
184C2×C3×C22⋊C4C22×C512yes—
185C2×C3×C42C22×C512yes—
186C2×C3×C42C22×C511yescharacteristic
187C3×#95C22×C512yes—
188C3×#95C22×C512yes—
189C3×#95C22×C512yes—
190C3×#95C22×C512yes—
191C3×#95C22×C512yes—
192C24×C5C23×C311yescharacteristic
193C24×C5C23×C311yescharacteristic
194C2×C5×D4—22no—
195C2×C5×D4—22no—
196C2×C5×D4—22no—
197C22×C4×C5—22no—
198C22×C4×C5—22no—
199C22×C4×C5—22no—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5C3×D414yes—
203C22×C4×C5C23×C311yescharacteristic
204C22×C4×C5C23×C312yes—
205C22×C4×C5C23×C312yes—
206C22×C4×C5C23×C312yes—
207C22×C4×C5C23×C312yes—
208C22×C4×C5C23×C311yescharacteristic
209C22×C4×C5C23×C311yescharacteristic
210C22×C4×C5C23×C311yescharacteristic
211C22×C4×C5C23×C311yescharacteristic
212C5×C4⋊C4—22no—
213C5×C4⋊C4—22no—
214C5×C4⋊C4—22no—
215C5×C4⋊C4—24no—
216C5×C4⋊C4—22no—
217C5×C4⋊C4—22no—
218C5×C4⋊C4—42no—
219C5×C22⋊C4—24no—
220C5×C22⋊C4—22no—
221C5×C22⋊C4—24no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—42no—
225C42×C5—24no—
226C42×C5—22no—
227C2×C4×D4C2×C3×C511yescharacteristic
228C2×#117C2×C3×C511yescharacteristic, complemented
229#397C2×C3×C512yescomplemented
230#394C2×C3×C512yes—
231#389C2×C3×C511yescharacteristic, complemented
232#389C2×C3×C511yescharacteristic, complemented
233#388C2×C3×C512yescomplemented
234#387C2×C3×C512yescomplemented
235#380C2×C3×C511yescharacteristic, complemented
236#380C2×C3×C511yescharacteristic, complemented
237#380C2×C3×C511yescharacteristic, complemented
238C22×C3×C5—22no—
239C22×C3×C5—22no—
240C22×C3×C5—22no—
241C22×C3×C5—22no—
242C22×C3×C5—22no—
243C22×C3×C5—22no—
244C22×C3×C5—41no—
245C22×C3×C5—41no—
246C22×C3×C5—41no—
247C22×C3×C5—41no—
248C22×C3×C5—41no—
249C22×C3×C5—41no—
250C22×C3×C5—41no—
251C22×C3×C5—41no—
252C22×C3×C5C22×D411yescharacteristic
253C22×C3×C5C2×#4111yescharacteristic
254C22×C3×C5C2×#4111yescharacteristic
255C22×C3×C5C2×#4111yescharacteristic
256C22×C3×C5C2×#4111yescharacteristic
257C22×C3×C5H(5,𝔽2)11yescharacteristic
258C22×C3×C52−1+411yescharacteristic
259C3×C4×C5—22no—
260C3×C4×C5—22no—
261C3×C4×C5—41no—
262C3×C4×C5—42no—
263C3×C4×C5—41no—
264C3×C4×C5—42no—
265C3×C4×C5—42no—
266C3×C4×C5—42no—
267C3×C4×C5#12314yes—
268C24×C3C23×C511yescharacteristic
269C24×C3C23×C511yescharacteristic
270C2×C3×D4—22no—
271C2×C3×D4—22no—
272C2×C3×D4—22no—
273C22×C3×C4—22no—
274C22×C3×C4—22no—
275C22×C3×C4—22no—
276C22×C3×C4—22no—
277C22×C3×C4—22no—
278C22×C3×C4C5×D414yes—
279C22×C3×C4C23×C511yescharacteristic
280C22×C3×C4C23×C512yes—
281C22×C3×C4C23×C512yes—
282C22×C3×C4C23×C511yescharacteristic
283C22×C3×C4C23×C512yes—
284C22×C3×C4C23×C512yes—
285C22×C3×C4C23×C511yescharacteristic
286C22×C3×C4C23×C511yescharacteristic
287C22×C3×C4C23×C511yescharacteristic
288C3×C4⋊C4—22no—
289C3×C4⋊C4—22no—
290C3×C4⋊C4—22no—
291C3×C4⋊C4—24no—
292C3×C4⋊C4—22no—
293C3×C4⋊C4—22no—
294C3×C4⋊C4—42no—
295C3×C22⋊C4—24no—
296C3×C22⋊C4—22no—
297C3×C22⋊C4—24no—
298C3×C22⋊C4—22no—
299C3×C22⋊C4—42no—
300C3×C22⋊C4—42no—
301C3×C42—24no—
302C3×C42—22no—
303C23×C5—21no—
304C23×C5—21no—
305C23×C5—21no—
306C23×C5—21no—
307C23×C5—21no—
308C23×C5—21no—
309C23×C5—21no—
310C23×C5—21no—
311C23×C5—21no—
312C23×C5—21no—
313C23×C5—21no—
314C23×C5—21no—
315C23×C5C2×C3×D412yes—
316C23×C5C3×#4112yes—
317C23×C5C24×C311yescharacteristic
318C5×D4—28no—
319C2×C4×C5—21no—
320C2×C4×C5—21no—
321C2×C4×C5—21no—
322C2×C4×C5—21no—
323C2×C4×C5—28no—
324C2×C4×C5—21no—
325C2×C4×C5—22no—
326C2×C4×C5—22no—
327C2×C4×C5—21no—
328C2×C4×C5—22no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—22no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—22no—
337C2×C4×C5—22no—
338C2×C4×C5—22no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—22no—
342C2×C4×C5—44no—
343C2×C4×C5C2×C3×D412yes—
344C2×C4×C5C2×C3×D412yes—
345C2×C4×C5C3×#4112yes—
346C2×C4×C5C3×#4112yes—
347C2×C4×C5C3×#4112yes—
348C22×D4C22×C3×C511yescharacteristic
349C23×C4C22×C3×C511yescharacteristic
350C23×C4C22×C3×C511yescharacteristic
351C4×D4—24no—
352#117—24no—
353C2×C4⋊C4C22×C3×C511yescharacteristic
354C2×C4⋊C4C22×C3×C511yescharacteristic
355C2×C4⋊C4C22×C3×C511yescharacteristic
356C2×C4⋊C4C22×C3×C511yescharacteristic
357C2×C4⋊C4C22×C3×C511yescharacteristic
358C2×C4⋊C4C22×C3×C512yes—
359C2×C4⋊C4C22×C3×C512yes—
360C2×C22⋊C4C22×C3×C512yes—
361C2×C22⋊C4C22×C3×C511yescharacteristic
362C2×C22⋊C4C22×C3×C511yescharacteristic
363C2×C22⋊C4C22×C3×C512yes—
364C2×C22⋊C4C22×C3×C512yes—
365C2×C22⋊C4C22×C3×C512yes—
366C2×C42C22×C3×C512yes—
367C2×C42C22×C3×C511yescharacteristic
368#95C22×C3×C512yes—
369#95C22×C3×C512yes—
370#95C22×C3×C512yes—
371#95C22×C3×C512yes—
372#95C22×C3×C512yes—
373C2×C3×C5—42no—
374C2×C3×C5—42no—
375C2×C3×C5C2×#12311yescharacteristic
376C2×C3×C5#52511yescharacteristic
377C2×C3×C5#53711yescharacteristic
378C2×C3×C5#55211yescharacteristic
379C2×C3×C5#55311yescharacteristic
380C2×C3×C5#55511yescharacteristic
381C2×C3×C5#55611yescharacteristic
382C23×C3—21no—
383C23×C3—21no—
384C23×C3—21no—
385C23×C3—21no—
386C23×C3—21no—
387C23×C3—21no—
388C23×C3—21no—
389C23×C3—21no—
390C23×C3—21no—
391C23×C3—21no—
392C23×C3—21no—
393C23×C3—21no—
394C23×C3C2×C5×D412yes—
395C23×C3C5×#4112yes—
396C23×C3C24×C511yescharacteristic
397C3×D4—28no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—28no—
403C2×C3×C4—21no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—44no—
422C2×C3×C4C2×C5×D412yes—
423C2×C3×C4C2×C5×D412yes—
424C2×C3×C4C5×#4112yes—
425C2×C3×C4C5×#4112yes—
426C2×C3×C4C5×#4112yes—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—22no—
430C22×C5—22no—
431C22×C5—22no—
432C22×C5—22no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5C22×C3×D411yescharacteristic
442C22×C5C2×C3×#4111yescharacteristic
443C22×C5C2×C3×#4111yescharacteristic
444C22×C5C2×C3×#4111yescharacteristic
445C22×C5C2×C3×#4111yescharacteristic
446C22×C5C3×H(5,𝔽2)11yescharacteristic
447C22×C5C3×2−1+411yescharacteristic
448C4×C5—22no—
449C4×C5—22no—
450C4×C5—41no—
451C4×C5—42no—
452C4×C5—41no—
453C4×C5—42no—
454C4×C5—42no—
455C4×C5—42no—
456C4×C5C3×#12314yes—
457C24C23×C3×C511yescharacteristic
458C24C23×C3×C511yescharacteristic
459C2×D4—22no—
460C2×D4—22no—
461C2×D4—22no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4C3×C5×D414yes—
468C22×C4C23×C3×C511yescharacteristic
469C22×C4C23×C3×C512yes—
470C22×C4C23×C3×C512yes—
471C22×C4C23×C3×C511yescharacteristic
472C22×C4C23×C3×C512yes—
473C22×C4C23×C3×C512yes—
474C22×C4C23×C3×C511yescharacteristic
475C22×C4C23×C3×C511yescharacteristic
476C22×C4C23×C3×C511yescharacteristic
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—42no—
484C22⋊C4—24no—
485C22⋊C4—22no—
486C22⋊C4—24no—
487C22⋊C4—22no—
488C22⋊C4—42no—
489C22⋊C4—42no—
490C42—24no—
491C42—22no—
492C3×C5#248511yescharacteristic, direct product factor, Hall
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—41no—
505C22×C3—41no—
506C22×C3—41no—
507C22×C3C22×C5×D411yescharacteristic
508C22×C3C2×C5×#4111yescharacteristic
509C22×C3C2×C5×#4111yescharacteristic
510C22×C3C2×C5×#4111yescharacteristic
511C22×C3C2×C5×#4111yescharacteristic
512C22×C3C5×H(5,𝔽2)11yescharacteristic
513C22×C3C5×2−1+411yescharacteristic
514C3×C4—22no—
515C3×C4—22no—
516C3×C4—41no—
517C3×C4—42no—
518C3×C4—41no—
519C3×C4—42no—
520C3×C4—42no—
521C3×C4—42no—
522C3×C4C5×#12314yes—
523C2×C5—42no—
524C2×C5—42no—
525C2×C5C2×C3×#12311yescharacteristic
526C2×C5C3×#52511yescharacteristic
527C2×C5C3×#53711yescharacteristic
528C2×C5C3×#55211yescharacteristic
529C2×C5C3×#55311yescharacteristic
530C2×C5C3×#55511yescharacteristic
531C2×C5C3×#55611yescharacteristic
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23C2×C3×C5×D412yes—
545C23C3×C5×#4112yes—
546C23C24×C3×C511yescharacteristic
547D4—28no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—28no—
553C2×C4—21no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—44no—
572C2×C4C2×C3×C5×D412yes—
573C2×C4C2×C3×C5×D412yes—
574C2×C4C3×C5×#4112yes—
575C2×C4C3×C5×#4112yes—
576C2×C4C3×C5×#4112yes—
577C2×C3—42no—
578C2×C3—42no—
579C2×C3C2×C5×#12311yescharacteristic
580C2×C3C5×#52511yescharacteristic
581C2×C3C5×#53711yescharacteristic
582C2×C3C5×#55211yescharacteristic
583C2×C3C5×#55311yescharacteristic
584C2×C3C5×#55511yescharacteristic
585C2×C3C5×#55611yescharacteristic
586C5C3×#248511yescharacteristic, direct product factor, Sylow
587C22—22no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—22no—
592C22—22no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22C22×C3×C5×D411yescharacteristic
602C22C2×C3×C5×#4111yescharacteristic
603C22C2×C3×C5×#4111yescharacteristic
604C22C2×C3×C5×#4111yescharacteristic
605C22C2×C3×C5×#4111yescharacteristic
606C22C3×C5×H(5,𝔽2)11yescharacteristic
607C22C3×C5×2−1+411yescharacteristic
608C4—22no—
609C4—22no—
610C4—41no—
611C4—42no—
612C4—41no—
613C4—42no—
614C4—42no—
615C4—42no—
616C4C3×C5×#12314yes—
617C3C5×#248511yescharacteristic, direct product factor, Sylow
618C2—42no—
619C2—42no—
620C2C2×C3×C5×#12311yescharacteristic
621C2C3×C5×#52511yescharacteristic
622C2C3×C5×#53711yescharacteristic
623C2C3×C5×#55211yescharacteristic
624C2C3×C5×#55311yescharacteristic
625C2C3×C5×#55511yescharacteristic
626C2C3×C5×#55611yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC22×C3×C5×D4C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#117C2semidirect
3. C3×C5×#397C2semidirect
5. C3×C5×#389C2semidirect
6. C3×C5×#389C2semidirect
7. C3×C5×#388C2semidirect
8. C3×C5×#387C2semidirect
9. C3×C5×#380C2semidirect
10. C3×C5×#380C2semidirect
11. C3×C5×#380C2semidirect
12. C5×#2485C3direct (N × H)
38. C3×#2485C5direct (N × H)
40. C2×C5×#117C2×C3semidirect
41. C5×#397C2×C3semidirect
43. C5×#389C2×C3semidirect
44. C5×#389C2×C3semidirect
45. C5×#388C2×C3semidirect
46. C5×#387C2×C3semidirect
47. C5×#380C2×C3semidirect
48. C5×#380C2×C3semidirect
49. C5×#380C2×C3semidirect
86. C2×C3×#117C2×C5semidirect
87. C3×#397C2×C5semidirect
89. C3×#389C2×C5semidirect
90. C3×#389C2×C5semidirect
91. C3×#388C2×C5semidirect
92. C3×#387C2×C5semidirect
93. C3×#380C2×C5semidirect
94. C3×#380C2×C5semidirect
95. C3×#380C2×C5semidirect
121. #2485C3×C5direct (N × H)
228. C2×#117C2×C3×C5semidirect
229. #397C2×C3×C5semidirect
231. #389C2×C3×C5semidirect
232. #389C2×C3×C5semidirect
233. #388C2×C3×C5semidirect
234. #387C2×C3×C5semidirect
235. #380C2×C3×C5semidirect
236. #380C2×C3×C5semidirect
237. #380C2×C3×C5semidirect
492. C3×C5#2485direct (N × H)
586. C5C3×#2485direct (N × H)
617. C3C5×#2485direct (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×C5×#1172
C3×C5×#3972
C3×C5×#3942
C3×C5×#3892
C3×C5×#3882
C3×C5×#3872
C3×C5×#3802
C5×#24853
C3×#24855