Finite Group Databasebeta

← C3×C5×#2407 #14275441

Subgroups — C3×C5×#2407 #14275441

Order 1920.

1816 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic, complemented
2C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×C5×#121C211yesmaximal, characteristic, complemented
4C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
5C3×C5×#394C212yesmaximal, complemented
6C3×C5×#392C212yesmaximal, complemented
7C3×C5×#391C211yesmaximal, characteristic, complemented
8C3×C5×#390C211yesmaximal, characteristic, complemented
9C3×C5×#386C212yesmaximal, complemented
10C3×C5×#385C212yesmaximal, complemented
11C3×C5×#380C211yesmaximal, characteristic, complemented
12C5×#2407C311yesmaximal, characteristic, direct product factor, Hall
13C2×C3×C5×#41—24no—
14C2×C3×C5×#41—24no—
15C2×C3×C5×#41—24no—
16C22×C3×C5×Q8C2211yescharacteristic
17C22×C3×C5×D4C2211yescharacteristic
18C22×C3×C5×D4C2212yes—
19C22×C3×C5×D4C2212yes—
20C22×C3×C5×D4C2211yescharacteristic
21C23×C3×C4×C5C2211yescharacteristic
22C23×C3×C4×C5C2212yes—
23C23×C3×C4×C5C2211yescharacteristic
24C3×C5×C22⋊Q8—24no—
25C3×C5×#121—24no—
26C3×C4×C5×D4—24no—
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×C5×C4⋊C4C2211yescharacteristic
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2212yes—
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2212yes—
34C2×C3×C5×C22⋊C4C2212yes—
35C2×C3×C5×C22⋊C4C2212yes—
36C2×C3×C5×C22⋊C4C2212yes—
37C2×C3×C5×C22⋊C4C2212yes—
38C2×C3×C42×C5C2211yescharacteristic
39C3×C5×#95C2212yes—
40C3×C5×#95C2212yes—
41C3×C5×#95C2212yes—
42C3×#2407C511yesmaximal, characteristic, direct product factor, Hall
43C22×C5×#41C2×C311yescharacteristic, complemented
44C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
45C2×C5×#121C2×C311yescharacteristic, complemented
46C2×C4×C5×D4C2×C311yescharacteristic, complemented
47C5×#394C2×C312yescomplemented
48C5×#392C2×C312yescomplemented
49C5×#391C2×C311yescharacteristic, complemented
50C5×#390C2×C311yescharacteristic, complemented
51C5×#386C2×C312yescomplemented
52C5×#385C2×C312yescomplemented
53C5×#380C2×C311yescharacteristic, complemented
54C24×C3×C5C2312yes—
55C24×C3×C5C2311yescharacteristic
56C24×C3×C5C2311yescharacteristic
57C3×C5×#41—232no—
58C2×C3×C5×Q8—22no—
59C2×C3×C5×Q8—22no—
60C2×C3×C5×Q8D414yescomplemented
61C2×C3×C5×D4—22no—
62C2×C3×C5×D4—24no—
63C2×C3×C5×D4—24no—
64C2×C3×C5×D4—22no—
65C2×C3×C5×D4—24no—
66C2×C3×C5×D4—24no—
67C2×C3×C5×D4—24no—
68C2×C3×C5×D4—22no—
69C2×C3×C5×D4—22no—
70C2×C3×C5×D4—22no—
71C2×C3×C5×D4—42no—
72C2×C3×C5×D4D414yescomplemented
73C22×C3×C4×C5—24no—
74C22×C3×C4×C5—24no—
75C22×C3×C4×C5—24no—
76C22×C3×C4×C5—22no—
77C22×C3×C4×C5—22no—
78C22×C3×C4×C5—22no—
79C22×C3×C4×C5—22no—
80C22×C3×C4×C5—22no—
81C22×C3×C4×C5D414yescomplemented
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2312yes—
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2312yes—
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2312yes—
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C3×C5×C4⋊C4—22no—
91C3×C5×C4⋊C4—22no—
92C3×C5×C4⋊C4—22no—
93C3×C5×C4⋊C4—24no—
94C3×C5×C22⋊C4—22no—
95C3×C5×C22⋊C4—24no—
96C3×C5×C22⋊C4—22no—
97C3×C5×C22⋊C4—24no—
98C3×C5×C22⋊C4—24no—
99C3×C5×C22⋊C4—42no—
100C3×C5×C22⋊C4—42no—
101C3×C42×C5—22no—
102C22×C3×#41C2×C511yescharacteristic, complemented
103C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
104C2×C3×#121C2×C511yescharacteristic, complemented
105C2×C3×C4×D4C2×C511yescharacteristic, complemented
106C3×#394C2×C512yescomplemented
107C3×#392C2×C512yescomplemented
108C3×#391C2×C511yescharacteristic, complemented
109C3×#390C2×C511yescharacteristic, complemented
110C3×#386C2×C512yescomplemented
111C3×#385C2×C512yescomplemented
112C3×#380C2×C511yescharacteristic, complemented
113C2×C5×#41—24no—
114C2×C5×#41—24no—
115C2×C5×#41—24no—
116C22×C5×Q8C22×C311yescharacteristic
117C22×C5×D4C22×C311yescharacteristic
118C22×C5×D4C22×C312yes—
119C22×C5×D4C22×C312yes—
120C22×C5×D4C22×C311yescharacteristic
121C23×C4×C5C22×C312yes—
122C23×C4×C5C22×C311yescharacteristic
123C23×C4×C5C22×C311yescharacteristic
124C5×C22⋊Q8—24no—
125C5×#121—24no—
126C4×C5×D4—24no—
127C2×C5×C4⋊C4C22×C311yescharacteristic
128C2×C5×C4⋊C4C22×C311yescharacteristic
129C2×C5×C4⋊C4C22×C311yescharacteristic
130C2×C5×C4⋊C4C22×C312yes—
131C2×C5×C22⋊C4C22×C312yes—
132C2×C5×C22⋊C4C22×C312yes—
133C2×C5×C22⋊C4C22×C311yescharacteristic
134C2×C5×C22⋊C4C22×C312yes—
135C2×C5×C22⋊C4C22×C311yescharacteristic
136C2×C5×C22⋊C4C22×C312yes—
137C2×C5×C22⋊C4C22×C312yes—
138C2×C42×C5C22×C311yescharacteristic
139C5×#95C22×C312yes—
140C5×#95C22×C312yes—
141C5×#95C22×C312yes—
142#2407C3×C511yescharacteristic, direct product factor, Sylow
143C23×C3×C5—21no—
144C23×C3×C5—21no—
145C23×C3×C5—22no—
146C23×C3×C5—21no—
147C23×C3×C5—22no—
148C23×C3×C5—21no—
149C23×C3×C5—21no—
150C23×C3×C5—22no—
151C23×C3×C5—21no—
152C23×C3×C5—21no—
153C23×C3×C5—21no—
154C23×C3×C5—22no—
155C23×C3×C5—21no—
156C23×C3×C5—22no—
157C23×C3×C5—21no—
158C23×C3×C5—21no—
159C23×C3×C5—22no—
160C23×C3×C5—21no—
161C23×C3×C5C2×D414yes—
162C23×C3×C5C2×D412yes—
163C23×C3×C5#4112yescomplemented
164C23×C3×C5C2411yescharacteristic
165C3×C5×Q8—28no—
166C3×C5×D4—28no—
167C3×C5×D4—216no—
168C3×C5×D4—28no—
169C3×C5×D4—48no—
170C2×C3×C4×C5—216no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—22no—
175C2×C3×C4×C5—22no—
176C2×C3×C4×C5—21no—
177C2×C3×C4×C5—28no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—22no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—22no—
185C2×C3×C4×C5—22no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—22no—
188C2×C3×C4×C5—22no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—44no—
191C2×C3×C4×C5C2×D412yes—
192C2×C3×C4×C5C2×D414yes—
193C2×C3×C4×C5C2×D412yes—
194C2×C3×C4×C5C2×D412yes—
195C2×C3×C4×C5C2×D412yes—
196C2×C3×C4×C5#4112yescomplemented
197C2×C3×#41—24no—
198C2×C3×#41—24no—
199C2×C3×#41—24no—
200C22×C3×Q8C22×C511yescharacteristic
201C22×C3×D4C22×C512yes—
202C22×C3×D4C22×C511yescharacteristic
203C22×C3×D4C22×C512yes—
204C22×C3×D4C22×C511yescharacteristic
205C23×C3×C4C22×C512yes—
206C23×C3×C4C22×C511yescharacteristic
207C23×C3×C4C22×C511yescharacteristic
208C3×C22⋊Q8—24no—
209C3×#121—24no—
210C3×C4×D4—24no—
211C2×C3×C4⋊C4C22×C511yescharacteristic
212C2×C3×C4⋊C4C22×C511yescharacteristic
213C2×C3×C4⋊C4C22×C511yescharacteristic
214C2×C3×C4⋊C4C22×C512yes—
215C2×C3×C22⋊C4C22×C512yes—
216C2×C3×C22⋊C4C22×C512yes—
217C2×C3×C22⋊C4C22×C511yescharacteristic
218C2×C3×C22⋊C4C22×C512yes—
219C2×C3×C22⋊C4C22×C511yescharacteristic
220C2×C3×C22⋊C4C22×C512yes—
221C2×C3×C22⋊C4C22×C512yes—
222C2×C3×C42C22×C511yescharacteristic
223C3×#95C22×C512yes—
224C3×#95C22×C512yes—
225C3×#95C22×C512yes—
226C24×C5C23×C312yes—
227C24×C5C23×C311yescharacteristic
228C24×C5C23×C311yescharacteristic
229C5×#41—232no—
230C2×C5×Q8—22no—
231C2×C5×Q8—22no—
232C2×C5×Q8C3×D414yescomplemented
233C2×C5×D4—22no—
234C2×C5×D4—24no—
235C2×C5×D4—24no—
236C2×C5×D4—22no—
237C2×C5×D4—24no—
238C2×C5×D4—24no—
239C2×C5×D4—24no—
240C2×C5×D4—22no—
241C2×C5×D4—22no—
242C2×C5×D4—22no—
243C2×C5×D4—42no—
244C2×C5×D4C3×D414yescomplemented
245C22×C4×C5—24no—
246C22×C4×C5—24no—
247C22×C4×C5—24no—
248C22×C4×C5—22no—
249C22×C4×C5—22no—
250C22×C4×C5—22no—
251C22×C4×C5—22no—
252C22×C4×C5—22no—
253C22×C4×C5C3×D414yescomplemented
254C22×C4×C5C23×C311yescharacteristic
255C22×C4×C5C23×C312yes—
256C22×C4×C5C23×C311yescharacteristic
257C22×C4×C5C23×C312yes—
258C22×C4×C5C23×C311yescharacteristic
259C22×C4×C5C23×C312yes—
260C22×C4×C5C23×C311yescharacteristic
261C22×C4×C5C23×C311yescharacteristic
262C5×C4⋊C4—22no—
263C5×C4⋊C4—22no—
264C5×C4⋊C4—22no—
265C5×C4⋊C4—24no—
266C5×C22⋊C4—22no—
267C5×C22⋊C4—24no—
268C5×C22⋊C4—22no—
269C5×C22⋊C4—24no—
270C5×C22⋊C4—24no—
271C5×C22⋊C4—42no—
272C5×C22⋊C4—42no—
273C42×C5—22no—
274C22×#41C2×C3×C511yescharacteristic, complemented
275C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
276C2×#121C2×C3×C511yescharacteristic, complemented
277C2×C4×D4C2×C3×C511yescharacteristic, complemented
278#394C2×C3×C512yescomplemented
279#392C2×C3×C512yescomplemented
280#391C2×C3×C511yescharacteristic, complemented
281#390C2×C3×C511yescharacteristic, complemented
282#386C2×C3×C512yescomplemented
283#385C2×C3×C512yescomplemented
284#380C2×C3×C511yescharacteristic, complemented
285C22×C3×C5—24no—
286C22×C3×C5—22no—
287C22×C3×C5—22no—
288C22×C3×C5—22no—
289C22×C3×C5—22no—
290C22×C3×C5—22no—
291C22×C3×C5—24no—
292C22×C3×C5—24no—
293C22×C3×C5—22no—
294C22×C3×C5—41no—
295C22×C3×C5—42no—
296C22×C3×C5—41no—
297C22×C3×C5—42no—
298C22×C3×C5—41no—
299C22×C3×C5—41no—
300C22×C3×C5—41no—
301C22×C3×C5—41no—
302C22×C3×C5—42no—
303C22×C3×C5—41no—
304C22×C3×C5—42no—
305C22×C3×C5—41no—
306C22×C3×C5C22×D411yescharacteristic
307C22×C3×C5C22×D411yescharacteristic
308C22×C3×C5C22×D411yescharacteristic
309C22×C3×C5C2×#4111yescharacteristic
310C22×C3×C5C2×#4111yescharacteristic
311C22×C3×C5H(5,𝔽2)11yescharacteristic
312C22×C3×C52−1+411yescharacteristic
313C3×C4×C5—22no—
314C3×C4×C5—24no—
315C3×C4×C5—22no—
316C3×C4×C5—41no—
317C3×C4×C5—41no—
318C3×C4×C5—42no—
319C3×C4×C5—42no—
320C3×C4×C5#12014yes—
321C24×C3C23×C512yes—
322C24×C3C23×C511yescharacteristic
323C24×C3C23×C511yescharacteristic
324C3×#41—232no—
325C2×C3×Q8—22no—
326C2×C3×Q8—22no—
327C2×C3×Q8C5×D414yescomplemented
328C2×C3×D4—22no—
329C2×C3×D4—24no—
330C2×C3×D4—24no—
331C2×C3×D4—22no—
332C2×C3×D4—24no—
333C2×C3×D4—24no—
334C2×C3×D4—24no—
335C2×C3×D4—22no—
336C2×C3×D4—22no—
337C2×C3×D4—22no—
338C2×C3×D4—42no—
339C2×C3×D4C5×D414yescomplemented
340C22×C3×C4—24no—
341C22×C3×C4—24no—
342C22×C3×C4—24no—
343C22×C3×C4—22no—
344C22×C3×C4—22no—
345C22×C3×C4—22no—
346C22×C3×C4—22no—
347C22×C3×C4—22no—
348C22×C3×C4C5×D414yescomplemented
349C22×C3×C4C23×C512yes—
350C22×C3×C4C23×C511yescharacteristic
351C22×C3×C4C23×C512yes—
352C22×C3×C4C23×C511yescharacteristic
353C22×C3×C4C23×C511yescharacteristic
354C22×C3×C4C23×C512yes—
355C22×C3×C4C23×C511yescharacteristic
356C22×C3×C4C23×C511yescharacteristic
357C3×C4⋊C4—22no—
358C3×C4⋊C4—22no—
359C3×C4⋊C4—22no—
360C3×C4⋊C4—24no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—24no—
363C3×C22⋊C4—22no—
364C3×C22⋊C4—24no—
365C3×C22⋊C4—24no—
366C3×C22⋊C4—42no—
367C3×C22⋊C4—42no—
368C3×C42—22no—
369C23×C5—21no—
370C23×C5—21no—
371C23×C5—22no—
372C23×C5—21no—
373C23×C5—22no—
374C23×C5—21no—
375C23×C5—21no—
376C23×C5—22no—
377C23×C5—21no—
378C23×C5—21no—
379C23×C5—21no—
380C23×C5—22no—
381C23×C5—21no—
382C23×C5—22no—
383C23×C5—21no—
384C23×C5—21no—
385C23×C5—22no—
386C23×C5—21no—
387C23×C5C2×C3×D414yes—
388C23×C5C2×C3×D412yes—
389C23×C5C3×#4112yescomplemented
390C23×C5C24×C311yescharacteristic
391C5×Q8—28no—
392C5×D4—28no—
393C5×D4—216no—
394C5×D4—28no—
395C5×D4—48no—
396C2×C4×C5—216no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—21no—
403C2×C4×C5—28no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—22no—
407C2×C4×C5—21no—
408C2×C4×C5—22no—
409C2×C4×C5—21no—
410C2×C4×C5—22no—
411C2×C4×C5—22no—
412C2×C4×C5—21no—
413C2×C4×C5—22no—
414C2×C4×C5—22no—
415C2×C4×C5—21no—
416C2×C4×C5—44no—
417C2×C4×C5C2×C3×D412yes—
418C2×C4×C5C2×C3×D414yes—
419C2×C4×C5C2×C3×D412yes—
420C2×C4×C5C2×C3×D412yes—
421C2×C4×C5C2×C3×D412yes—
422C2×C4×C5C3×#4112yescomplemented
423C2×#41—24no—
424C2×#41—24no—
425C2×#41—24no—
426C22×Q8C22×C3×C511yescharacteristic
427C22×D4C22×C3×C511yescharacteristic
428C22×D4C22×C3×C512yes—
429C22×D4C22×C3×C512yes—
430C22×D4C22×C3×C511yescharacteristic
431C23×C4C22×C3×C511yescharacteristic
432C23×C4C22×C3×C512yes—
433C23×C4C22×C3×C511yescharacteristic
434C22⋊Q8—24no—
435#121—24no—
436C4×D4—24no—
437C2×C4⋊C4C22×C3×C511yescharacteristic
438C2×C4⋊C4C22×C3×C511yescharacteristic
439C2×C4⋊C4C22×C3×C511yescharacteristic
440C2×C4⋊C4C22×C3×C512yes—
441C2×C22⋊C4C22×C3×C511yescharacteristic
442C2×C22⋊C4C22×C3×C511yescharacteristic
443C2×C22⋊C4C22×C3×C512yes—
444C2×C22⋊C4C22×C3×C512yes—
445C2×C22⋊C4C22×C3×C512yes—
446C2×C22⋊C4C22×C3×C512yes—
447C2×C22⋊C4C22×C3×C512yes—
448C2×C42C22×C3×C511yescharacteristic
449#95C22×C3×C512yes—
450#95C22×C3×C512yes—
451#95C22×C3×C512yes—
452C2×C3×C5—42no—
453C2×C3×C5—44no—
454C2×C3×C5—42no—
455C2×C3×C5C2×#12011yescharacteristic
456C2×C3×C5#52511yescharacteristic
457C2×C3×C5#53711yescharacteristic
458C2×C3×C5#54611yescharacteristic
459C2×C3×C5#54711yescharacteristic
460C2×C3×C5#54811yescharacteristic
461C2×C3×C5#55011yescharacteristic
462C23×C3—21no—
463C23×C3—21no—
464C23×C3—22no—
465C23×C3—21no—
466C23×C3—22no—
467C23×C3—21no—
468C23×C3—21no—
469C23×C3—22no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—22no—
474C23×C3—21no—
475C23×C3—22no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—22no—
479C23×C3—21no—
480C23×C3C2×C5×D414yes—
481C23×C3C2×C5×D412yes—
482C23×C3C5×#4112yescomplemented
483C23×C3C24×C511yescharacteristic
484C3×Q8—28no—
485C3×D4—28no—
486C3×D4—216no—
487C3×D4—28no—
488C3×D4—48no—
489C2×C3×C4—216no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—22no—
494C2×C3×C4—22no—
495C2×C3×C4—21no—
496C2×C3×C4—28no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—22no—
500C2×C3×C4—21no—
501C2×C3×C4—22no—
502C2×C3×C4—21no—
503C2×C3×C4—22no—
504C2×C3×C4—22no—
505C2×C3×C4—21no—
506C2×C3×C4—22no—
507C2×C3×C4—22no—
508C2×C3×C4—21no—
509C2×C3×C4—44no—
510C2×C3×C4C2×C5×D412yes—
511C2×C3×C4C2×C5×D414yes—
512C2×C3×C4C2×C5×D412yes—
513C2×C3×C4C2×C5×D412yes—
514C2×C3×C4C2×C5×D412yes—
515C2×C3×C4C5×#4112yescomplemented
516C22×C5—24no—
517C22×C5—22no—
518C22×C5—22no—
519C22×C5—22no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—24no—
523C22×C5—24no—
524C22×C5—22no—
525C22×C5—41no—
526C22×C5—42no—
527C22×C5—41no—
528C22×C5—42no—
529C22×C5—41no—
530C22×C5—41no—
531C22×C5—41no—
532C22×C5—41no—
533C22×C5—42no—
534C22×C5—41no—
535C22×C5—42no—
536C22×C5—41no—
537C22×C5C22×C3×D411yescharacteristic
538C22×C5C22×C3×D411yescharacteristic
539C22×C5C22×C3×D411yescharacteristic
540C22×C5C2×C3×#4111yescharacteristic
541C22×C5C2×C3×#4111yescharacteristic
542C22×C5C3×H(5,𝔽2)11yescharacteristic
543C22×C5C3×2−1+411yescharacteristic
544C4×C5—22no—
545C4×C5—24no—
546C4×C5—22no—
547C4×C5—41no—
548C4×C5—41no—
549C4×C5—42no—
550C4×C5—42no—
551C4×C5C3×#12014yes—
552C24C23×C3×C512yes—
553C24C23×C3×C511yescharacteristic
554C24C23×C3×C511yescharacteristic
555#41—232no—
556C2×Q8—22no—
557C2×Q8—22no—
558C2×Q8C3×C5×D414yescomplemented
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—22no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—42no—
570C2×D4C3×C5×D414yescomplemented
571C22×C4—24no—
572C22×C4—24no—
573C22×C4—24no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4C3×C5×D414yescomplemented
580C22×C4C23×C3×C512yes—
581C22×C4C23×C3×C511yescharacteristic
582C22×C4C23×C3×C512yes—
583C22×C4C23×C3×C511yescharacteristic
584C22×C4C23×C3×C511yescharacteristic
585C22×C4C23×C3×C512yes—
586C22×C4C23×C3×C511yescharacteristic
587C22×C4C23×C3×C511yescharacteristic
588C4⋊C4—22no—
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—24no—
592C22⋊C4—22no—
593C22⋊C4—24no—
594C22⋊C4—22no—
595C22⋊C4—24no—
596C22⋊C4—24no—
597C22⋊C4—42no—
598C22⋊C4—42no—
599C42—22no—
600C3×C5#240711yescharacteristic, direct product factor, Hall
601C22×C3—24no—
602C22×C3—22no—
603C22×C3—22no—
604C22×C3—22no—
605C22×C3—22no—
606C22×C3—22no—
607C22×C3—24no—
608C22×C3—24no—
609C22×C3—22no—
610C22×C3—41no—
611C22×C3—42no—
612C22×C3—41no—
613C22×C3—42no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—42no—
619C22×C3—41no—
620C22×C3—42no—
621C22×C3—41no—
622C22×C3C22×C5×D411yescharacteristic
623C22×C3C22×C5×D411yescharacteristic
624C22×C3C22×C5×D411yescharacteristic
625C22×C3C2×C5×#4111yescharacteristic
626C22×C3C2×C5×#4111yescharacteristic
627C22×C3C5×H(5,𝔽2)11yescharacteristic
628C22×C3C5×2−1+411yescharacteristic
629C3×C4—22no—
630C3×C4—24no—
631C3×C4—22no—
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—42no—
635C3×C4—42no—
636C3×C4C5×#12014yes—
637C2×C5—42no—
638C2×C5—44no—
639C2×C5—42no—
640C2×C5C2×C3×#12011yescharacteristic
641C2×C5C3×#52511yescharacteristic
642C2×C5C3×#53711yescharacteristic
643C2×C5C3×#54611yescharacteristic
644C2×C5C3×#54711yescharacteristic
645C2×C5C3×#54811yescharacteristic
646C2×C5C3×#55011yescharacteristic
647C23—21no—
648C23—21no—
649C23—22no—
650C23—21no—
651C23—22no—
652C23—21no—
653C23—21no—
654C23—22no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—21no—
660C23—22no—
661C23—21no—
662C23—21no—
663C23—22no—
664C23—21no—
665C23C2×C3×C5×D414yes—
666C23C2×C3×C5×D412yes—
667C23C3×C5×#4112yescomplemented
668C23C24×C3×C511yescharacteristic
669Q8—28no—
670D4—216no—
671D4—28no—
672D4—28no—
673D4—48no—
674C2×C4—216no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—21no—
681C2×C4—28no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—44no—
695C2×C4C2×C3×C5×D412yes—
696C2×C4C2×C3×C5×D414yes—
697C2×C4C2×C3×C5×D412yes—
698C2×C4C2×C3×C5×D412yes—
699C2×C4C2×C3×C5×D412yes—
700C2×C4C3×C5×#4112yescomplemented
701C2×C3—42no—
702C2×C3—44no—
703C2×C3—42no—
704C2×C3C2×C5×#12011yescharacteristic
705C2×C3C5×#52511yescharacteristic
706C2×C3C5×#53711yescharacteristic
707C2×C3C5×#54611yescharacteristic
708C2×C3C5×#54711yescharacteristic
709C2×C3C5×#54811yescharacteristic
710C2×C3C5×#55011yescharacteristic
711C5C3×#240711yescharacteristic, direct product factor, Sylow
712C22—24no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—22no—
721C22—41no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—41no—
733C22C22×C3×C5×D411yescharacteristic
734C22C22×C3×C5×D411yescharacteristic
735C22C22×C3×C5×D411yescharacteristic
736C22C2×C3×C5×#4111yescharacteristic
737C22C2×C3×C5×#4111yescharacteristic
738C22C3×C5×H(5,𝔽2)11yescharacteristic
739C22C3×C5×2−1+411yescharacteristic
740C4—22no—
741C4—24no—
742C4—22no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—42no—
747C4C3×C5×#12014yes—
748C3C5×#240711yescharacteristic, direct product factor, Sylow
749C2—42no—
750C2—44no—
751C2—42no—
752C2C2×C3×C5×#12011yescharacteristic
753C2C3×C5×#52511yescharacteristic
754C2C3×C5×#53711yescharacteristic
755C2C3×C5×#54611yescharacteristic
756C2C3×C5×#54711yescharacteristic
757C2C3×C5×#54811yescharacteristic
758C2C3×C5×#55011yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C5×#41C2semidirect
2. C2×C3×C5×C22⋊Q8C2semidirect
3. C2×C3×C5×#121C2semidirect
4. C2×C3×C4×C5×D4C2semidirect
5. C3×C5×#394C2semidirect
6. C3×C5×#392C2semidirect
7. C3×C5×#391C2semidirect
8. C3×C5×#390C2semidirect
9. C3×C5×#386C2semidirect
10. C3×C5×#385C2semidirect
11. C3×C5×#380C2semidirect
12. C5×#2407C3direct (N × H)
42. C3×#2407C5direct (N × H)
43. C22×C5×#41C2×C3semidirect
44. C2×C5×C22⋊Q8C2×C3semidirect
45. C2×C5×#121C2×C3semidirect
46. C2×C4×C5×D4C2×C3semidirect
47. C5×#394C2×C3semidirect
48. C5×#392C2×C3semidirect
49. C5×#391C2×C3semidirect
50. C5×#390C2×C3semidirect
51. C5×#386C2×C3semidirect
52. C5×#385C2×C3semidirect
53. C5×#380C2×C3semidirect
60. C2×C3×C5×Q8D4semidirect
72. C2×C3×C5×D4D4semidirect
81. C22×C3×C4×C5D4semidirect
102. C22×C3×#41C2×C5semidirect
103. C2×C3×C22⋊Q8C2×C5semidirect
104. C2×C3×#121C2×C5semidirect
105. C2×C3×C4×D4C2×C5semidirect
106. C3×#394C2×C5semidirect
107. C3×#392C2×C5semidirect
108. C3×#391C2×C5semidirect
109. C3×#390C2×C5semidirect
110. C3×#386C2×C5semidirect
111. C3×#385C2×C5semidirect
112. C3×#380C2×C5semidirect
142. #2407C3×C5direct (N × H)
163. C23×C3×C5#41semidirect
196. C2×C3×C4×C5#41semidirect
232. C2×C5×Q8C3×D4semidirect
244. C2×C5×D4C3×D4semidirect
253. C22×C4×C5C3×D4semidirect
274. C22×#41C2×C3×C5semidirect
275. C2×C22⋊Q8C2×C3×C5semidirect
276. C2×#121C2×C3×C5semidirect
277. C2×C4×D4C2×C3×C5semidirect
278. #394C2×C3×C5semidirect
279. #392C2×C3×C5semidirect
280. #391C2×C3×C5semidirect
281. #390C2×C3×C5semidirect
282. #386C2×C3×C5semidirect
283. #385C2×C3×C5semidirect
284. #380C2×C3×C5semidirect
327. C2×C3×Q8C5×D4semidirect
339. C2×C3×D4C5×D4semidirect
348. C22×C3×C4C5×D4semidirect
389. C23×C5C3×#41semidirect
422. C2×C4×C5C3×#41semidirect
482. C23×C3C5×#41semidirect
515. C2×C3×C4C5×#41semidirect
558. C2×Q8C3×C5×D4semidirect
570. C2×D4C3×C5×D4semidirect
579. C22×C4C3×C5×D4semidirect
600. C3×C5#2407direct (N × H)
667. C23C3×C5×#41semidirect
700. C2×C4C3×C5×#41semidirect
711. C5C3×#2407direct (N × H)
748. C3C5×#2407direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C2×C3×C5×C22⋊Q82
C2×C3×C5×#1212
C2×C3×C4×C5×D42
C3×C5×#3942
C3×C5×#3922
C3×C5×#3912
C3×C5×#3902
C3×C5×#3862
C3×C5×#3852
C3×C5×#3802
C5×#24073
C3×#24075