Finite Group Databasebeta

← C3×C5×#2427 #14275461

Subgroups — C3×C5×#2427 #14275461

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#124C211yesmaximal, characteristic, complemented
2C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×C5×#121C211yesmaximal, characteristic
4C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
5C3×C5×#397C212yesmaximal, complemented
6C3×C5×#394C212yesmaximal, complemented
7C3×C5×#391C211yesmaximal, characteristic, complemented
8C3×C5×#389C211yesmaximal, characteristic, complemented
9C3×C5×#386C212yesmaximal, complemented
10C3×C5×#380C212yesmaximal, complemented
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2427C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C22×C3×C5×D4C2212yes—
15C22×C3×C5×D4C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C23×C3×C4×C5C2212yes—
18C3×C5×#124—24no—
19C3×C5×C22⋊Q8—24no—
20C3×C5×#121—24no—
21C3×C4×C5×D4—24no—
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2212yes—
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2212yes—
30C2×C3×C5×C22⋊C4C2212yes—
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C42×C5C2211yescharacteristic
34C2×C3×C42×C5C2211yescharacteristic
35C3×C5×#95C2211yescharacteristic
36C3×C5×#95C2211yescharacteristic
37C3×C5×#95C2212yes—
38C3×C5×#95C2212yes—
39C3×C5×#95C2212yes—
40C3×#2427C511yesmaximal, characteristic, direct product factor, Hall
41C2×C5×#124C2×C311yescharacteristic, complemented
42C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
43C2×C5×#121C2×C311yescharacteristic
44C2×C4×C5×D4C2×C311yescharacteristic, complemented
45C5×#397C2×C312yescomplemented
46C5×#394C2×C312yescomplemented
47C5×#391C2×C311yescharacteristic, complemented
48C5×#389C2×C311yescharacteristic, complemented
49C5×#386C2×C312yescomplemented
50C5×#380C2×C312yescomplemented
51C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
52C24×C3×C5C2312yes—
53C24×C3×C5C2311yescharacteristic
54C2×C3×C5×Q8—22no—
55C2×C3×C5×Q8—22no—
56C2×C3×C5×Q8—22no—
57C2×C3×C5×D4—24no—
58C2×C3×C5×D4—24no—
59C2×C3×C5×D4—22no—
60C2×C3×C5×D4—22no—
61C2×C3×C5×D4—42no—
62C2×C3×C5×D4D414yes—
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5—22no—
65C22×C3×C4×C5—22no—
66C22×C3×C4×C5—24no—
67C22×C3×C4×C5—22no—
68C22×C3×C4×C5—42no—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2312yes—
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2312yes—
75C22×C3×C4×C5C2312yes—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C3×C5×C4⋊C4—22no—
79C3×C5×C4⋊C4—24no—
80C3×C5×C4⋊C4—42no—
81C3×C5×C4⋊C4D414yescomplemented
82C3×C5×C22⋊C4—24no—
83C3×C5×C22⋊C4—24no—
84C3×C5×C22⋊C4—24no—
85C3×C5×C22⋊C4—22no—
86C3×C5×C22⋊C4—24no—
87C3×C5×C22⋊C4—24no—
88C3×C5×C22⋊C4—22no—
89C3×C42×C5—22no—
90C3×C42×C5—22no—
91C2×C3×#124C2×C511yescharacteristic, complemented
92C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
93C2×C3×#121C2×C511yescharacteristic
94C2×C3×C4×D4C2×C511yescharacteristic, complemented
95C3×#397C2×C512yescomplemented
96C3×#394C2×C512yescomplemented
97C3×#391C2×C511yescharacteristic, complemented
98C3×#389C2×C511yescharacteristic, complemented
99C3×#386C2×C512yescomplemented
100C3×#380C2×C512yescomplemented
101C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
102C22×C5×Q8C22×C311yescharacteristic
103C22×C5×D4C22×C312yes—
104C22×C5×D4C22×C311yescharacteristic
105C23×C4×C5C22×C311yescharacteristic
106C23×C4×C5C22×C312yes—
107C5×#124—24no—
108C5×C22⋊Q8—24no—
109C5×#121—24no—
110C4×C5×D4—24no—
111C2×C5×C4⋊C4C22×C312yes—
112C2×C5×C4⋊C4C22×C311yescharacteristic
113C2×C5×C4⋊C4C22×C312yes—
114C2×C5×C4⋊C4C22×C311yescharacteristic
115C2×C5×C22⋊C4C22×C311yescharacteristic
116C2×C5×C22⋊C4C22×C311yescharacteristic
117C2×C5×C22⋊C4C22×C312yes—
118C2×C5×C22⋊C4C22×C312yes—
119C2×C5×C22⋊C4C22×C312yes—
120C2×C5×C22⋊C4C22×C312yes—
121C2×C5×C22⋊C4C22×C312yes—
122C2×C42×C5C22×C311yescharacteristic
123C2×C42×C5C22×C311yescharacteristic
124C5×#95C22×C311yescharacteristic
125C5×#95C22×C311yescharacteristic
126C5×#95C22×C312yes—
127C5×#95C22×C312yes—
128C5×#95C22×C312yes—
129#2427C3×C511yescharacteristic, direct product factor, Sylow
130C23×C3×C5—21no—
131C23×C3×C5—22no—
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—22no—
136C23×C3×C5—22no—
137C23×C3×C5—22no—
138C23×C3×C5—22no—
139C23×C3×C5—21no—
140C23×C3×C5—22no—
141C23×C3×C5—21no—
142C23×C3×C5C2×D414yes—
143C23×C3×C5#4112yes—
144C23×C3×C5C2411yescharacteristic
145C3×C5×Q8—44no—
146C3×C5×D4—28no—
147C3×C5×D4—48no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
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×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—21no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—21no—
162C2×C3×C4×C5—21no—
163C2×C3×C4×C5—21no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—21no—
167C2×C3×C4×C5—22no—
168C2×C3×C4×C5—21no—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—48no—
171C2×C3×C4×C5—44no—
172C2×C3×C4×C5C2×D414yes—
173C2×C3×C4×C5C2×D412yes—
174C2×C3×C4×C5C2×D412yes—
175C2×C3×C4×C5#4112yes—
176C2×C3×C4×C5#4112yes—
177C22×C3×Q8C22×C511yescharacteristic
178C22×C3×D4C22×C512yes—
179C22×C3×D4C22×C511yescharacteristic
180C23×C3×C4C22×C511yescharacteristic
181C23×C3×C4C22×C512yes—
182C3×#124—24no—
183C3×C22⋊Q8—24no—
184C3×#121—24no—
185C3×C4×D4—24no—
186C2×C3×C4⋊C4C22×C512yes—
187C2×C3×C4⋊C4C22×C511yescharacteristic
188C2×C3×C4⋊C4C22×C512yes—
189C2×C3×C4⋊C4C22×C511yescharacteristic
190C2×C3×C22⋊C4C22×C511yescharacteristic
191C2×C3×C22⋊C4C22×C511yescharacteristic
192C2×C3×C22⋊C4C22×C512yes—
193C2×C3×C22⋊C4C22×C512yes—
194C2×C3×C22⋊C4C22×C512yes—
195C2×C3×C22⋊C4C22×C512yes—
196C2×C3×C22⋊C4C22×C512yes—
197C2×C3×C42C22×C511yescharacteristic
198C2×C3×C42C22×C511yescharacteristic
199C3×#95C22×C511yescharacteristic
200C3×#95C22×C511yescharacteristic
201C3×#95C22×C512yes—
202C3×#95C22×C512yes—
203C3×#95C22×C512yes—
204C24×C5C23×C312yes—
205C24×C5C23×C311yescharacteristic
206C2×C5×Q8—22no—
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×D4—24no—
210C2×C5×D4—24no—
211C2×C5×D4—22no—
212C2×C5×D4—22no—
213C2×C5×D4—42no—
214C2×C5×D4C3×D414yes—
215C22×C4×C5—24no—
216C22×C4×C5—22no—
217C22×C4×C5—22no—
218C22×C4×C5—24no—
219C22×C4×C5—22no—
220C22×C4×C5—42no—
221C22×C4×C5C23×C311yescharacteristic
222C22×C4×C5C23×C311yescharacteristic
223C22×C4×C5C23×C311yescharacteristic
224C22×C4×C5C23×C312yes—
225C22×C4×C5C23×C311yescharacteristic
226C22×C4×C5C23×C312yes—
227C22×C4×C5C23×C312yes—
228C22×C4×C5C23×C311yescharacteristic
229C22×C4×C5C23×C311yescharacteristic
230C5×C4⋊C4—22no—
231C5×C4⋊C4—24no—
232C5×C4⋊C4—42no—
233C5×C4⋊C4C3×D414yescomplemented
234C5×C22⋊C4—24no—
235C5×C22⋊C4—24no—
236C5×C22⋊C4—24no—
237C5×C22⋊C4—22no—
238C5×C22⋊C4—24no—
239C5×C22⋊C4—24no—
240C5×C22⋊C4—22no—
241C42×C5—22no—
242C42×C5—22no—
243C2×#124C2×C3×C511yescharacteristic, complemented
244C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
245C2×#121C2×C3×C511yescharacteristic
246C2×C4×D4C2×C3×C511yescharacteristic, complemented
247#397C2×C3×C512yescomplemented
248#394C2×C3×C512yescomplemented
249#391C2×C3×C511yescharacteristic, complemented
250#389C2×C3×C511yescharacteristic, complemented
251#386C2×C3×C512yescomplemented
252#380C2×C3×C512yescomplemented
253C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
254C22×C3×C5—24no—
255C22×C3×C5—22no—
256C22×C3×C5—22no—
257C22×C3×C5—24no—
258C22×C3×C5—24no—
259C22×C3×C5—22no—
260C22×C3×C5—41no—
261C22×C3×C5—42no—
262C22×C3×C5—41no—
263C22×C3×C5—42no—
264C22×C3×C5—42no—
265C22×C3×C5—41no—
266C22×C3×C5—41no—
267C22×C3×C5—42no—
268C22×C3×C5C22×D411yescharacteristic
269C22×C3×C5C22×D411yescharacteristic
270C22×C3×C5C2×#4111yescharacteristic
271C22×C3×C5C2×#4111yescharacteristic
272C22×C3×C5C2×#4111yescharacteristic
273C22×C3×C5H(5,𝔽2)11yescharacteristic
274C22×C3×C52−1+411yescharacteristic
275C3×C4×C5—22no—
276C3×C4×C5—24no—
277C3×C4×C5—41no—
278C3×C4×C5—42no—
279C3×C4×C5—41no—
280C3×C4×C5—42no—
281C3×C4×C5—41no—
282C3×C4×C5—41no—
283C3×C4×C5#12114yes—
284C24×C3C23×C512yes—
285C24×C3C23×C511yescharacteristic
286C2×C3×Q8—22no—
287C2×C3×Q8—22no—
288C2×C3×Q8—22no—
289C2×C3×D4—24no—
290C2×C3×D4—24no—
291C2×C3×D4—22no—
292C2×C3×D4—22no—
293C2×C3×D4—42no—
294C2×C3×D4C5×D414yes—
295C22×C3×C4—24no—
296C22×C3×C4—22no—
297C22×C3×C4—22no—
298C22×C3×C4—24no—
299C22×C3×C4—22no—
300C22×C3×C4—42no—
301C22×C3×C4C23×C511yescharacteristic
302C22×C3×C4C23×C511yescharacteristic
303C22×C3×C4C23×C512yes—
304C22×C3×C4C23×C512yes—
305C22×C3×C4C23×C511yescharacteristic
306C22×C3×C4C23×C511yescharacteristic
307C22×C3×C4C23×C512yes—
308C22×C3×C4C23×C511yescharacteristic
309C22×C3×C4C23×C511yescharacteristic
310C3×C4⋊C4—22no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—42no—
313C3×C4⋊C4C5×D414yescomplemented
314C3×C22⋊C4—24no—
315C3×C22⋊C4—24no—
316C3×C22⋊C4—24no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—24no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—22no—
321C3×C42—22no—
322C3×C42—22no—
323C23×C5—21no—
324C23×C5—22no—
325C23×C5—21no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—22no—
329C23×C5—22no—
330C23×C5—22no—
331C23×C5—22no—
332C23×C5—21no—
333C23×C5—22no—
334C23×C5—21no—
335C23×C5C2×C3×D414yes—
336C23×C5C3×#4112yes—
337C23×C5C24×C311yescharacteristic
338C5×Q8—44no—
339C5×D4—28no—
340C5×D4—48no—
341C2×C4×C5—21no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—21no—
347C2×C4×C5—21no—
348C2×C4×C5—21no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—21no—
353C2×C4×C5—21no—
354C2×C4×C5—21no—
355C2×C4×C5—21no—
356C2×C4×C5—21no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—21no—
360C2×C4×C5—22no—
361C2×C4×C5—21no—
362C2×C4×C5—21no—
363C2×C4×C5—48no—
364C2×C4×C5—44no—
365C2×C4×C5C2×C3×D414yes—
366C2×C4×C5C2×C3×D412yes—
367C2×C4×C5C2×C3×D412yes—
368C2×C4×C5C3×#4112yes—
369C2×C4×C5C3×#4112yes—
370C22×Q8C22×C3×C511yescharacteristic
371C22×D4C22×C3×C512yes—
372C22×D4C22×C3×C511yescharacteristic
373C23×C4C22×C3×C511yescharacteristic
374C23×C4C22×C3×C512yes—
375#124—24no—
376C22⋊Q8—24no—
377#121—24no—
378C4×D4—24no—
379C2×C4⋊C4C22×C3×C511yescharacteristic
380C2×C4⋊C4C22×C3×C512yes—
381C2×C4⋊C4C22×C3×C512yes—
382C2×C4⋊C4C22×C3×C511yescharacteristic
383C2×C22⋊C4C22×C3×C512yes—
384C2×C22⋊C4C22×C3×C512yes—
385C2×C22⋊C4C22×C3×C512yes—
386C2×C22⋊C4C22×C3×C512yes—
387C2×C22⋊C4C22×C3×C512yes—
388C2×C22⋊C4C22×C3×C511yescharacteristic
389C2×C22⋊C4C22×C3×C511yescharacteristic
390C2×C42C22×C3×C511yescharacteristic
391C2×C42C22×C3×C511yescharacteristic
392#95C22×C3×C511yescharacteristic
393#95C22×C3×C511yescharacteristic
394#95C22×C3×C512yes—
395#95C22×C3×C512yes—
396#95C22×C3×C512yes—
397C2×C3×C5—44no—
398C2×C3×C5—42no—
399C2×C3×C5C2×#12111yescharacteristic
400C2×C3×C5#52911yescharacteristic
401C2×C3×C5#54211yescharacteristic
402C2×C3×C5#54611yescharacteristic
403C2×C3×C5#54611yescharacteristic
404C2×C3×C5#54711yescharacteristic
405C2×C3×C5#54811yescharacteristic
406C23×C3—21no—
407C23×C3—22no—
408C23×C3—21no—
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—22no—
412C23×C3—22no—
413C23×C3—22no—
414C23×C3—22no—
415C23×C3—21no—
416C23×C3—22no—
417C23×C3—21no—
418C23×C3C2×C5×D414yes—
419C23×C3C5×#4112yes—
420C23×C3C24×C511yescharacteristic
421C3×Q8—44no—
422C3×D4—28no—
423C3×D4—48no—
424C2×C3×C4—21no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—21no—
443C2×C3×C4—22no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—48no—
447C2×C3×C4—44no—
448C2×C3×C4C2×C5×D414yes—
449C2×C3×C4C2×C5×D412yes—
450C2×C3×C4C2×C5×D412yes—
451C2×C3×C4C5×#4112yes—
452C2×C3×C4C5×#4112yes—
453C22×C5—24no—
454C22×C5—22no—
455C22×C5—22no—
456C22×C5—24no—
457C22×C5—24no—
458C22×C5—22no—
459C22×C5—41no—
460C22×C5—42no—
461C22×C5—41no—
462C22×C5—42no—
463C22×C5—42no—
464C22×C5—41no—
465C22×C5—41no—
466C22×C5—42no—
467C22×C5C22×C3×D411yescharacteristic
468C22×C5C22×C3×D411yescharacteristic
469C22×C5C2×C3×#4111yescharacteristic
470C22×C5C2×C3×#4111yescharacteristic
471C22×C5C2×C3×#4111yescharacteristic
472C22×C5C3×H(5,𝔽2)11yescharacteristic
473C22×C5C3×2−1+411yescharacteristic
474C4×C5—22no—
475C4×C5—24no—
476C4×C5—41no—
477C4×C5—42no—
478C4×C5—41no—
479C4×C5—42no—
480C4×C5—41no—
481C4×C5—41no—
482C4×C5C3×#12114yes—
483C24C23×C3×C512yes—
484C24C23×C3×C511yescharacteristic
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×D4—24no—
489C2×D4—24no—
490C2×D4—22no—
491C2×D4—22no—
492C2×D4—42no—
493C2×D4C3×C5×D414yes—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—42no—
500C22×C4C23×C3×C511yescharacteristic
501C22×C4C23×C3×C511yescharacteristic
502C22×C4C23×C3×C512yes—
503C22×C4C23×C3×C512yes—
504C22×C4C23×C3×C511yescharacteristic
505C22×C4C23×C3×C511yescharacteristic
506C22×C4C23×C3×C512yes—
507C22×C4C23×C3×C511yescharacteristic
508C22×C4C23×C3×C511yescharacteristic
509C4⋊C4—22no—
510C4⋊C4—24no—
511C4⋊C4—42no—
512C4⋊C4C3×C5×D414yescomplemented
513C22⋊C4—24no—
514C22⋊C4—24no—
515C22⋊C4—24no—
516C22⋊C4—22no—
517C22⋊C4—24no—
518C22⋊C4—24no—
519C22⋊C4—22no—
520C42—22no—
521C42—22no—
522C3×C5#242711yescharacteristic, direct product factor, Hall
523C22×C3—24no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—24no—
527C22×C3—24no—
528C22×C3—22no—
529C22×C3—41no—
530C22×C3—42no—
531C22×C3—41no—
532C22×C3—42no—
533C22×C3—42no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—42no—
537C22×C3C22×C5×D411yescharacteristic
538C22×C3C22×C5×D411yescharacteristic
539C22×C3C2×C5×#4111yescharacteristic
540C22×C3C2×C5×#4111yescharacteristic
541C22×C3C2×C5×#4111yescharacteristic
542C22×C3C5×H(5,𝔽2)11yescharacteristic
543C22×C3C5×2−1+411yescharacteristic
544C3×C4—22no—
545C3×C4—24no—
546C3×C4—41no—
547C3×C4—42no—
548C3×C4—41no—
549C3×C4—42no—
550C3×C4—41no—
551C3×C4—41no—
552C3×C4C5×#12114yes—
553C2×C5—44no—
554C2×C5—42no—
555C2×C5C2×C3×#12111yescharacteristic
556C2×C5C3×#52911yescharacteristic
557C2×C5C3×#54211yescharacteristic
558C2×C5C3×#54611yescharacteristic
559C2×C5C3×#54611yescharacteristic
560C2×C5C3×#54711yescharacteristic
561C2×C5C3×#54811yescharacteristic
562C23—21no—
563C23—22no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—22no—
568C23—22no—
569C23—22no—
570C23—22no—
571C23—21no—
572C23—22no—
573C23—21no—
574C23C2×C3×C5×D414yes—
575C23C3×C5×#4112yes—
576C23C24×C3×C511yescharacteristic
577Q8—44no—
578D4—28no—
579D4—48no—
580C2×C4—21no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—48no—
603C2×C4—44no—
604C2×C4C2×C3×C5×D414yes—
605C2×C4C2×C3×C5×D412yes—
606C2×C4C2×C3×C5×D412yes—
607C2×C4C3×C5×#4112yes—
608C2×C4C3×C5×#4112yes—
609C2×C3—44no—
610C2×C3—42no—
611C2×C3C2×C5×#12111yescharacteristic
612C2×C3C5×#52911yescharacteristic
613C2×C3C5×#54211yescharacteristic
614C2×C3C5×#54611yescharacteristic
615C2×C3C5×#54611yescharacteristic
616C2×C3C5×#54711yescharacteristic
617C2×C3C5×#54811yescharacteristic
618C5C3×#242711yescharacteristic, direct product factor, Sylow
619C22—24no—
620C22—22no—
621C22—22no—
622C22—24no—
623C22—24no—
624C22—22no—
625C22—41no—
626C22—42no—
627C22—41no—
628C22—42no—
629C22—42no—
630C22—41no—
631C22—41no—
632C22—42no—
633C22C22×C3×C5×D411yescharacteristic
634C22C22×C3×C5×D411yescharacteristic
635C22C2×C3×C5×#4111yescharacteristic
636C22C2×C3×C5×#4111yescharacteristic
637C22C2×C3×C5×#4111yescharacteristic
638C22C3×C5×H(5,𝔽2)11yescharacteristic
639C22C3×C5×2−1+411yescharacteristic
640C4—22no—
641C4—24no—
642C4—41no—
643C4—42no—
644C4—42no—
645C4—41no—
646C4—41no—
647C4—41no—
648C4C3×C5×#12114yes—
649C3C5×#242711yescharacteristic, direct product factor, Sylow
650C2—44no—
651C2—42no—
652C2C2×C3×C5×#12111yescharacteristic
653C2C3×C5×#52911yescharacteristic
654C2C3×C5×#54211yescharacteristic
655C2C3×C5×#54611yescharacteristic
656C2C3×C5×#54611yescharacteristic
657C2C3×C5×#54711yescharacteristic
658C2C3×C5×#54811yescharacteristic
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC2×C3×C5×#121C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#124C2semidirect
2. C2×C3×C5×C22⋊Q8C2semidirect
4. C2×C3×C4×C5×D4C2semidirect
5. C3×C5×#397C2semidirect
6. C3×C5×#394C2semidirect
7. C3×C5×#391C2semidirect
8. C3×C5×#389C2semidirect
9. C3×C5×#386C2semidirect
10. C3×C5×#380C2semidirect
11. C3×C4×C5×C22⋊C4C2semidirect
12. C5×#2427C3direct (N × H)
40. C3×#2427C5direct (N × H)
41. C2×C5×#124C2×C3semidirect
42. C2×C5×C22⋊Q8C2×C3semidirect
44. C2×C4×C5×D4C2×C3semidirect
45. C5×#397C2×C3semidirect
46. C5×#394C2×C3semidirect
47. C5×#391C2×C3semidirect
48. C5×#389C2×C3semidirect
49. C5×#386C2×C3semidirect
50. C5×#380C2×C3semidirect
51. C4×C5×C22⋊C4C2×C3semidirect
81. C3×C5×C4⋊C4D4semidirect
91. C2×C3×#124C2×C5semidirect
92. C2×C3×C22⋊Q8C2×C5semidirect
94. C2×C3×C4×D4C2×C5semidirect
95. C3×#397C2×C5semidirect
96. C3×#394C2×C5semidirect
97. C3×#391C2×C5semidirect
98. C3×#389C2×C5semidirect
99. C3×#386C2×C5semidirect
100. C3×#380C2×C5semidirect
101. C3×C4×C22⋊C4C2×C5semidirect
129. #2427C3×C5direct (N × H)
233. C5×C4⋊C4C3×D4semidirect
243. C2×#124C2×C3×C5semidirect
244. C2×C22⋊Q8C2×C3×C5semidirect
246. C2×C4×D4C2×C3×C5semidirect
247. #397C2×C3×C5semidirect
248. #394C2×C3×C5semidirect
249. #391C2×C3×C5semidirect
250. #389C2×C3×C5semidirect
251. #386C2×C3×C5semidirect
252. #380C2×C3×C5semidirect
253. C4×C22⋊C4C2×C3×C5semidirect
313. C3×C4⋊C4C5×D4semidirect
512. C4⋊C4C3×C5×D4semidirect
522. C3×C5#2427direct (N × H)
618. C5C3×#2427direct (N × H)
649. C3C5×#2427direct (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×#1242
C2×C3×C5×C22⋊Q82
C2×C3×C5×#1212
C2×C3×C4×C5×D42
C3×C5×#3972
C3×C5×#3942
C3×C5×#3912
C3×C5×#3892
C3×C5×#3862
C3×C5×#3802
C3×C4×C5×C22⋊C42
C5×#24273
C3×#24275