Finite Group Databasebeta

← C3×C5×#2342 #14275376

Subgroups — C3×C5×#2342 #14275376

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#117C211yesmaximal, characteristic, complemented
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
3C22×C3×C5×C22⋊C4C211yesmaximal, characteristic
4C3×C5×#388C212yesmaximal, complemented
5C3×C5×#388C212yesmaximal, complemented
6C3×C5×#385C212yesmaximal, complemented
7C3×C5×#381C211yesmaximal, characteristic, complemented
8C3×C5×#380C211yesmaximal, characteristic, complemented
9C3×C5×#379C211yesmaximal, characteristic
10C3×C4×C5×C22⋊C4C212yesmaximal, complemented
11C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
12C5×#2342C311yesmaximal, characteristic, direct product factor, Hall
13C25×C3×C5C2211yescharacteristic
14C23×C3×C4×C5C2212yes—
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2211yescharacteristic
17C3×C5×#117—24no—
18C2×C3×C5×C4⋊C4C2212yescomplemented
19C2×C3×C5×C4⋊C4C2212yescomplemented
20C2×C3×C5×C22⋊C4—24no—
21C2×C3×C5×C22⋊C4C418yescomplemented
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2212yes—
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2212yes—
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C42×C5C2212yescomplemented
34C2×C3×C42×C5C2212yescomplemented
35C3×C5×#95C2212yescomplemented
36C3×C5×#95C2212yescomplemented
37C3×C5×#95C2212yescomplemented
38C3×C5×#95C2212yescomplemented
39C3×#2342C511yesmaximal, characteristic, direct product factor, Hall
40C2×C5×#117C2×C311yescharacteristic, complemented
41C22×C5×C22⋊C4C2×C311yescharacteristic
42C22×C5×C22⋊C4C2×C311yescharacteristic
43C5×#388C2×C312yescomplemented
44C5×#388C2×C312yescomplemented
45C5×#385C2×C312yescomplemented
46C5×#381C2×C311yescharacteristic, complemented
47C5×#380C2×C311yescharacteristic, complemented
48C5×#379C2×C311yescharacteristic
49C4×C5×C22⋊C4C2×C312yescomplemented
50C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
51C24×C3×C5—22no—
52C24×C3×C5—24no—
53C24×C3×C5—22no—
54C24×C3×C5—42no—
55C24×C3×C5C2×C414yes—
56C24×C3×C5C2311yescharacteristic
57C24×C3×C5C2311yescharacteristic
58C24×C3×C5C2311yescharacteristic
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—24no—
62C22×C3×C4×C5—24no—
63C22×C3×C4×C5—42no—
64C22×C3×C4×C5—42no—
65C22×C3×C4×C5C2×C414yescomplemented
66C22×C3×C4×C5C2×C414yescomplemented
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2312yes—
69C22×C3×C4×C5C2312yes—
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2312yes—
75C3×C5×C4⋊C4—24no—
76C3×C5×C4⋊C4—42no—
77C3×C5×C22⋊C4—22no—
78C3×C5×C22⋊C4—22no—
79C3×C5×C22⋊C4—24no—
80C3×C5×C22⋊C4—22no—
81C3×C5×C22⋊C4—24no—
82C3×C5×C22⋊C4—42no—
83C3×C5×C22⋊C4C2×C414yes—
84C3×C5×C22⋊C4C2×C414yes—
85C3×C5×C22⋊C4C2×C414yescomplemented
86C3×C5×C22⋊C4C2×C414yescomplemented
87C3×C5×C22⋊C4D414yes—
88C3×C42×C5—24no—
89C3×C42×C5—42no—
90C2×C3×#117C2×C511yescharacteristic, complemented
91C22×C3×C22⋊C4C2×C511yescharacteristic
92C22×C3×C22⋊C4C2×C511yescharacteristic
93C3×#388C2×C512yescomplemented
94C3×#388C2×C512yescomplemented
95C3×#385C2×C512yescomplemented
96C3×#381C2×C511yescharacteristic, complemented
97C3×#380C2×C511yescharacteristic, complemented
98C3×#379C2×C511yescharacteristic
99C3×C4×C22⋊C4C2×C512yescomplemented
100C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
101C25×C5C22×C311yescharacteristic
102C23×C4×C5C22×C312yes—
103C23×C4×C5C22×C311yescharacteristic
104C23×C4×C5C22×C311yescharacteristic
105C5×#117—24no—
106C2×C5×C4⋊C4C22×C312yescomplemented
107C2×C5×C4⋊C4C22×C312yescomplemented
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4C3×C418yescomplemented
110C2×C5×C22⋊C4C22×C311yescharacteristic
111C2×C5×C22⋊C4C22×C312yes—
112C2×C5×C22⋊C4C22×C311yescharacteristic
113C2×C5×C22⋊C4C22×C311yescharacteristic
114C2×C5×C22⋊C4C22×C312yes—
115C2×C5×C22⋊C4C22×C312yes—
116C2×C5×C22⋊C4C22×C311yescharacteristic
117C2×C5×C22⋊C4C22×C311yescharacteristic
118C2×C5×C22⋊C4C22×C311yescharacteristic
119C2×C5×C22⋊C4C22×C311yescharacteristic
120C2×C5×C22⋊C4C22×C311yescharacteristic
121C2×C42×C5C22×C312yescomplemented
122C2×C42×C5C22×C312yescomplemented
123C5×#95C22×C312yescomplemented
124C5×#95C22×C312yescomplemented
125C5×#95C22×C312yescomplemented
126C5×#95C22×C312yescomplemented
127#2342C3×C511yescharacteristic, direct product factor, Sylow
128C23×C3×C5—21no—
129C23×C3×C5—22no—
130C23×C3×C5—21no—
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5—28no—
134C23×C3×C5—28no—
135C23×C3×C5—21no—
136C23×C3×C5—22no—
137C23×C3×C5—21no—
138C23×C3×C5—22no—
139C23×C3×C5—44no—
140C23×C3×C5—48no—
141C23×C3×C5—48no—
142C23×C3×C5C22×C412yes—
143C23×C3×C5C22×C412yes—
144C23×C3×C5C22×C412yes—
145C23×C3×C5C2×D412yes—
146C23×C3×C5#4114yes—
147C23×C3×C5#4112yes—
148C23×C3×C5C2411yescharacteristic
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—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—22no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5—44no—
168C2×C3×C4×C5—48no—
169C2×C3×C4×C5C22×C412yes—
170C2×C3×C4×C5C22×C412yes—
171C2×C3×C4×C5C22×C412yes—
172C2×C3×C4×C5C22×C412yes—
173C2×C3×C4×C5C2×D414yes—
174C25×C3C22×C511yescharacteristic
175C23×C3×C4C22×C512yes—
176C23×C3×C4C22×C511yescharacteristic
177C23×C3×C4C22×C511yescharacteristic
178C3×#117—24no—
179C2×C3×C4⋊C4C22×C512yescomplemented
180C2×C3×C4⋊C4C22×C512yescomplemented
181C2×C3×C22⋊C4—24no—
182C2×C3×C22⋊C4C4×C518yescomplemented
183C2×C3×C22⋊C4C22×C511yescharacteristic
184C2×C3×C22⋊C4C22×C512yes—
185C2×C3×C22⋊C4C22×C511yescharacteristic
186C2×C3×C22⋊C4C22×C511yescharacteristic
187C2×C3×C22⋊C4C22×C512yes—
188C2×C3×C22⋊C4C22×C512yes—
189C2×C3×C22⋊C4C22×C511yescharacteristic
190C2×C3×C22⋊C4C22×C511yescharacteristic
191C2×C3×C22⋊C4C22×C511yescharacteristic
192C2×C3×C22⋊C4C22×C511yescharacteristic
193C2×C3×C22⋊C4C22×C511yescharacteristic
194C2×C3×C42C22×C512yescomplemented
195C2×C3×C42C22×C512yescomplemented
196C3×#95C22×C512yescomplemented
197C3×#95C22×C512yescomplemented
198C3×#95C22×C512yescomplemented
199C3×#95C22×C512yescomplemented
200C24×C5—22no—
201C24×C5—24no—
202C24×C5—22no—
203C24×C5—42no—
204C24×C5C2×C3×C414yes—
205C24×C5C23×C311yescharacteristic
206C24×C5C23×C311yescharacteristic
207C24×C5C23×C311yescharacteristic
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—24no—
211C22×C4×C5—24no—
212C22×C4×C5—42no—
213C22×C4×C5—42no—
214C22×C4×C5C2×C3×C414yescomplemented
215C22×C4×C5C2×C3×C414yescomplemented
216C22×C4×C5C23×C312yes—
217C22×C4×C5C23×C312yes—
218C22×C4×C5C23×C312yes—
219C22×C4×C5C23×C311yescharacteristic
220C22×C4×C5C23×C311yescharacteristic
221C22×C4×C5C23×C311yescharacteristic
222C22×C4×C5C23×C311yescharacteristic
223C22×C4×C5C23×C312yes—
224C5×C4⋊C4—24no—
225C5×C4⋊C4—42no—
226C5×C22⋊C4—22no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4—24no—
229C5×C22⋊C4—22no—
230C5×C22⋊C4—24no—
231C5×C22⋊C4—42no—
232C5×C22⋊C4C2×C3×C414yes—
233C5×C22⋊C4C2×C3×C414yes—
234C5×C22⋊C4C2×C3×C414yescomplemented
235C5×C22⋊C4C2×C3×C414yescomplemented
236C5×C22⋊C4C3×D414yes—
237C42×C5—24no—
238C42×C5—42no—
239C2×#117C2×C3×C511yescharacteristic, complemented
240C22×C22⋊C4C2×C3×C511yescharacteristic
241C22×C22⋊C4C2×C3×C511yescharacteristic
242#388C2×C3×C512yescomplemented
243#388C2×C3×C512yescomplemented
244#385C2×C3×C512yescomplemented
245#381C2×C3×C511yescharacteristic, complemented
246#380C2×C3×C511yescharacteristic, complemented
247#379C2×C3×C511yescharacteristic
248C4×C22⋊C4C2×C3×C512yescomplemented
249C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
250C22×C3×C5—22no—
251C22×C3×C5—22no—
252C22×C3×C5—22no—
253C22×C3×C5—22no—
254C22×C3×C5—24no—
255C22×C3×C5—24no—
256C22×C3×C5—24no—
257C22×C3×C5—24no—
258C22×C3×C5—22no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—416no—
262C22×C3×C5—42no—
263C22×C3×C5—42no—
264C22×C3×C5#11714yescomplemented
265C22×C3×C5C4×D414yes—
266C22×C3×C5C23×C411yescharacteristic
267C22×C3×C5C22×D411yescharacteristic
268C22×C3×C5C2×#4112yes—
269C22×C3×C5C2×#4111yescharacteristic
270C22×C3×C5H(5,𝔽2)12yes—
271C3×C4×C5—22no—
272C3×C4×C5—22no—
273C3×C4×C5—22no—
274C3×C4×C5—22no—
275C3×C4×C5—24no—
276C3×C4×C5—42no—
277C3×C4×C5—42no—
278C3×C4×C5—42no—
279C24×C3—22no—
280C24×C3—24no—
281C24×C3—22no—
282C24×C3—42no—
283C24×C3C2×C4×C514yes—
284C24×C3C23×C511yescharacteristic
285C24×C3C23×C511yescharacteristic
286C24×C3C23×C511yescharacteristic
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—24no—
290C22×C3×C4—24no—
291C22×C3×C4—42no—
292C22×C3×C4—42no—
293C22×C3×C4C2×C4×C514yescomplemented
294C22×C3×C4C2×C4×C514yescomplemented
295C22×C3×C4C23×C512yes—
296C22×C3×C4C23×C512yes—
297C22×C3×C4C23×C512yes—
298C22×C3×C4C23×C511yescharacteristic
299C22×C3×C4C23×C511yescharacteristic
300C22×C3×C4C23×C511yescharacteristic
301C22×C3×C4C23×C511yescharacteristic
302C22×C3×C4C23×C512yes—
303C3×C4⋊C4—24no—
304C3×C4⋊C4—42no—
305C3×C22⋊C4—22no—
306C3×C22⋊C4—22no—
307C3×C22⋊C4—24no—
308C3×C22⋊C4—22no—
309C3×C22⋊C4—24no—
310C3×C22⋊C4—42no—
311C3×C22⋊C4C2×C4×C514yes—
312C3×C22⋊C4C2×C4×C514yes—
313C3×C22⋊C4C2×C4×C514yescomplemented
314C3×C22⋊C4C2×C4×C514yescomplemented
315C3×C22⋊C4C5×D414yes—
316C3×C42—24no—
317C3×C42—42no—
318C23×C5—21no—
319C23×C5—22no—
320C23×C5—21no—
321C23×C5—22no—
322C23×C5—22no—
323C23×C5—28no—
324C23×C5—28no—
325C23×C5—21no—
326C23×C5—22no—
327C23×C5—21no—
328C23×C5—22no—
329C23×C5—44no—
330C23×C5—48no—
331C23×C5—48no—
332C23×C5C22×C3×C412yes—
333C23×C5C22×C3×C412yes—
334C23×C5C22×C3×C412yes—
335C23×C5C2×C3×D412yes—
336C23×C5C3×#4114yes—
337C23×C5C3×#4112yes—
338C23×C5C24×C311yescharacteristic
339C2×C4×C5—28no—
340C2×C4×C5—21no—
341C2×C4×C5—21no—
342C2×C4×C5—21no—
343C2×C4×C5—21no—
344C2×C4×C5—22no—
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—44no—
358C2×C4×C5—48no—
359C2×C4×C5C22×C3×C412yes—
360C2×C4×C5C22×C3×C412yes—
361C2×C4×C5C22×C3×C412yes—
362C2×C4×C5C22×C3×C412yes—
363C2×C4×C5C2×C3×D414yes—
364C25C22×C3×C511yescharacteristic
365C23×C4C22×C3×C512yes—
366C23×C4C22×C3×C511yescharacteristic
367C23×C4C22×C3×C511yescharacteristic
368#117—24no—
369C2×C4⋊C4C22×C3×C512yescomplemented
370C2×C4⋊C4C22×C3×C512yescomplemented
371C2×C22⋊C4—24no—
372C2×C22⋊C4C3×C4×C518yescomplemented
373C2×C22⋊C4C22×C3×C511yescharacteristic
374C2×C22⋊C4C22×C3×C512yes—
375C2×C22⋊C4C22×C3×C511yescharacteristic
376C2×C22⋊C4C22×C3×C511yescharacteristic
377C2×C22⋊C4C22×C3×C512yes—
378C2×C22⋊C4C22×C3×C512yes—
379C2×C22⋊C4C22×C3×C511yescharacteristic
380C2×C22⋊C4C22×C3×C511yescharacteristic
381C2×C22⋊C4C22×C3×C511yescharacteristic
382C2×C22⋊C4C22×C3×C511yescharacteristic
383C2×C22⋊C4C22×C3×C511yescharacteristic
384C2×C42C22×C3×C512yescomplemented
385C2×C42C22×C3×C512yescomplemented
386#95C22×C3×C512yescomplemented
387#95C22×C3×C512yescomplemented
388#95C22×C3×C512yescomplemented
389#95C22×C3×C512yescomplemented
390C2×C3×C5—24no—
391C2×C3×C5—24no—
392C2×C3×C5—42no—
393C2×C3×C5C2×#11711yescharacteristic
394C2×C3×C5C2×C4×D411yescharacteristic
395C2×C3×C5#51811yescharacteristic
396C2×C3×C5#54612yes—
397C2×C3×C5#55112yes—
398C23×C3—21no—
399C23×C3—22no—
400C23×C3—21no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3—28no—
404C23×C3—28no—
405C23×C3—21no—
406C23×C3—22no—
407C23×C3—21no—
408C23×C3—22no—
409C23×C3—44no—
410C23×C3—48no—
411C23×C3—48no—
412C23×C3C22×C4×C512yes—
413C23×C3C22×C4×C512yes—
414C23×C3C22×C4×C512yes—
415C23×C3C2×C5×D412yes—
416C23×C3C5×#4114yes—
417C23×C3C5×#4112yes—
418C23×C3C24×C511yescharacteristic
419C2×C3×C4—28no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—21no—
424C2×C3×C4—22no—
425C2×C3×C4—22no—
426C2×C3×C4—22no—
427C2×C3×C4—22no—
428C2×C3×C4—22no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—22no—
432C2×C3×C4—22no—
433C2×C3×C4—22no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—44no—
438C2×C3×C4—48no—
439C2×C3×C4C22×C4×C512yes—
440C2×C3×C4C22×C4×C512yes—
441C2×C3×C4C22×C4×C512yes—
442C2×C3×C4C22×C4×C512yes—
443C2×C3×C4C2×C5×D414yes—
444C22×C5—22no—
445C22×C5—22no—
446C22×C5—22no—
447C22×C5—22no—
448C22×C5—24no—
449C22×C5—24no—
450C22×C5—24no—
451C22×C5—24no—
452C22×C5—22no—
453C22×C5—22no—
454C22×C5—22no—
455C22×C5—416no—
456C22×C5—42no—
457C22×C5—42no—
458C22×C5C3×#11714yescomplemented
459C22×C5C3×C4×D414yes—
460C22×C5C23×C3×C411yescharacteristic
461C22×C5C22×C3×D411yescharacteristic
462C22×C5C2×C3×#4112yes—
463C22×C5C2×C3×#4111yescharacteristic
464C22×C5C3×H(5,𝔽2)12yes—
465C4×C5—22no—
466C4×C5—22no—
467C4×C5—22no—
468C4×C5—22no—
469C4×C5—24no—
470C4×C5—42no—
471C4×C5—42no—
472C4×C5—42no—
473C24—22no—
474C24—24no—
475C24—22no—
476C24—42no—
477C24C2×C3×C4×C514yes—
478C24C23×C3×C511yescharacteristic
479C24C23×C3×C511yescharacteristic
480C24C23×C3×C511yescharacteristic
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4C2×C3×C4×C514yescomplemented
488C22×C4C2×C3×C4×C514yescomplemented
489C22×C4C23×C3×C512yes—
490C22×C4C23×C3×C512yes—
491C22×C4C23×C3×C512yes—
492C22×C4C23×C3×C511yescharacteristic
493C22×C4C23×C3×C511yescharacteristic
494C22×C4C23×C3×C511yescharacteristic
495C22×C4C23×C3×C511yescharacteristic
496C22×C4C23×C3×C512yes—
497C4⋊C4—24no—
498C4⋊C4—42no—
499C22⋊C4—22no—
500C22⋊C4—22no—
501C22⋊C4—24no—
502C22⋊C4—22no—
503C22⋊C4—24no—
504C22⋊C4—42no—
505C22⋊C4C2×C3×C4×C514yes—
506C22⋊C4C2×C3×C4×C514yes—
507C22⋊C4C2×C3×C4×C514yescomplemented
508C22⋊C4C2×C3×C4×C514yescomplemented
509C22⋊C4C3×C5×D414yes—
510C42—24no—
511C42—42no—
512C3×C5#234211yescharacteristic, direct product factor, Hall
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—24no—
518C22×C3—24no—
519C22×C3—24no—
520C22×C3—24no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—416no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3C5×#11714yescomplemented
528C22×C3C4×C5×D414yes—
529C22×C3C23×C4×C511yescharacteristic
530C22×C3C22×C5×D411yescharacteristic
531C22×C3C2×C5×#4112yes—
532C22×C3C2×C5×#4111yescharacteristic
533C22×C3C5×H(5,𝔽2)12yes—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—24no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—42no—
542C2×C5—24no—
543C2×C5—24no—
544C2×C5—42no—
545C2×C5C2×C3×#11711yescharacteristic
546C2×C5C2×C3×C4×D411yescharacteristic
547C2×C5C3×#51811yescharacteristic
548C2×C5C3×#54612yes—
549C2×C5C3×#55112yes—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—22no—
554C23—22no—
555C23—28no—
556C23—28no—
557C23—21no—
558C23—22no—
559C23—21no—
560C23—22no—
561C23—44no—
562C23—48no—
563C23—48no—
564C23C22×C3×C4×C512yes—
565C23C22×C3×C4×C512yes—
566C23C22×C3×C4×C512yes—
567C23C2×C3×C5×D412yes—
568C23C3×C5×#4114yes—
569C23C3×C5×#4112yes—
570C23C24×C3×C511yescharacteristic
571C2×C4—28no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—44no—
590C2×C4—48no—
591C2×C4C22×C3×C4×C512yes—
592C2×C4C22×C3×C4×C512yes—
593C2×C4C22×C3×C4×C512yes—
594C2×C4C22×C3×C4×C512yes—
595C2×C4C2×C3×C5×D414yes—
596C2×C3—24no—
597C2×C3—24no—
598C2×C3—42no—
599C2×C3C2×C5×#11711yescharacteristic
600C2×C3C2×C4×C5×D411yescharacteristic
601C2×C3C5×#51811yescharacteristic
602C2×C3C5×#54612yes—
603C2×C3C5×#55112yes—
604C5C3×#234211yescharacteristic, direct product factor, Sylow
605C22—22no—
606C22—22no—
607C22—22no—
608C22—22no—
609C22—24no—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—416no—
617C22—42no—
618C22—42no—
619C22C3×C5×#11714yescomplemented
620C22C3×C4×C5×D414yes—
621C22C23×C3×C4×C511yescharacteristic
622C22C22×C3×C5×D411yescharacteristic
623C22C2×C3×C5×#4112yes—
624C22C2×C3×C5×#4111yescharacteristic
625C22C3×C5×H(5,𝔽2)12yes—
626C4—22no—
627C4—22no—
628C4—22no—
629C4—22no—
630C4—24no—
631C4—42no—
632C4—42no—
633C4—42no—
634C3C5×#234211yescharacteristic, direct product factor, Sylow
635C2—24no—
636C2—24no—
637C2—42no—
638C2C2×C3×C5×#11711yescharacteristic
639C2C2×C3×C4×C5×D411yescharacteristic
640C2C3×C5×#51811yescharacteristic
641C2C3×C5×#54612yes—
642C2C3×C5×#55112yes—
subgroupG/H
center, socleC23×C3×C5C24
commutatorC22C23×C3×C4×C5
Frattini, cosocleC23C24×C3×C5
prime radicalC25×C3×C5C22
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#117C2semidirect
4. C3×C5×#388C2semidirect
5. C3×C5×#388C2semidirect
6. C3×C5×#385C2semidirect
7. C3×C5×#381C2semidirect
8. C3×C5×#380C2semidirect
10. C3×C4×C5×C22⋊C4C2semidirect
11. C3×C4×C5×C22⋊C4C2semidirect
12. C5×#2342C3direct (N × H)
18. C2×C3×C5×C4⋊C4C22semidirect
19. C2×C3×C5×C4⋊C4C22semidirect
21. C2×C3×C5×C22⋊C4C4semidirect
33. C2×C3×C42×C5C22semidirect
34. C2×C3×C42×C5C22semidirect
35. C3×C5×#95C22semidirect
36. C3×C5×#95C22semidirect
37. C3×C5×#95C22semidirect
38. C3×C5×#95C22semidirect
39. C3×#2342C5direct (N × H)
40. C2×C5×#117C2×C3semidirect
43. C5×#388C2×C3semidirect
44. C5×#388C2×C3semidirect
45. C5×#385C2×C3semidirect
46. C5×#381C2×C3semidirect
47. C5×#380C2×C3semidirect
49. C4×C5×C22⋊C4C2×C3semidirect
50. C4×C5×C22⋊C4C2×C3semidirect
65. C22×C3×C4×C5C2×C4semidirect
66. C22×C3×C4×C5C2×C4semidirect
85. C3×C5×C22⋊C4C2×C4semidirect
86. C3×C5×C22⋊C4C2×C4semidirect
90. C2×C3×#117C2×C5semidirect
93. C3×#388C2×C5semidirect
94. C3×#388C2×C5semidirect
95. C3×#385C2×C5semidirect
96. C3×#381C2×C5semidirect
97. C3×#380C2×C5semidirect
99. C3×C4×C22⋊C4C2×C5semidirect
100. C3×C4×C22⋊C4C2×C5semidirect
106. C2×C5×C4⋊C4C22×C3semidirect
107. C2×C5×C4⋊C4C22×C3semidirect
109. C2×C5×C22⋊C4C3×C4semidirect
121. C2×C42×C5C22×C3semidirect
122. C2×C42×C5C22×C3semidirect
123. C5×#95C22×C3semidirect
124. C5×#95C22×C3semidirect
125. C5×#95C22×C3semidirect
126. C5×#95C22×C3semidirect
127. #2342C3×C5direct (N × H)
179. C2×C3×C4⋊C4C22×C5semidirect
180. C2×C3×C4⋊C4C22×C5semidirect
182. C2×C3×C22⋊C4C4×C5semidirect
194. C2×C3×C42C22×C5semidirect
195. C2×C3×C42C22×C5semidirect
196. C3×#95C22×C5semidirect
197. C3×#95C22×C5semidirect
198. C3×#95C22×C5semidirect
199. C3×#95C22×C5semidirect
214. C22×C4×C5C2×C3×C4semidirect
215. C22×C4×C5C2×C3×C4semidirect
234. C5×C22⋊C4C2×C3×C4semidirect
235. C5×C22⋊C4C2×C3×C4semidirect
239. C2×#117C2×C3×C5semidirect
242. #388C2×C3×C5semidirect
243. #388C2×C3×C5semidirect
244. #385C2×C3×C5semidirect
245. #381C2×C3×C5semidirect
246. #380C2×C3×C5semidirect
248. C4×C22⋊C4C2×C3×C5semidirect
249. C4×C22⋊C4C2×C3×C5semidirect
264. C22×C3×C5#117semidirect
293. C22×C3×C4C2×C4×C5semidirect
294. C22×C3×C4C2×C4×C5semidirect
313. C3×C22⋊C4C2×C4×C5semidirect
314. C3×C22⋊C4C2×C4×C5semidirect
369. C2×C4⋊C4C22×C3×C5semidirect
370. C2×C4⋊C4C22×C3×C5semidirect
372. C2×C22⋊C4C3×C4×C5semidirect
384. C2×C42C22×C3×C5semidirect
385. C2×C42C22×C3×C5semidirect
386. #95C22×C3×C5semidirect
387. #95C22×C3×C5semidirect
388. #95C22×C3×C5semidirect
389. #95C22×C3×C5semidirect
458. C22×C5C3×#117semidirect
487. C22×C4C2×C3×C4×C5semidirect
488. C22×C4C2×C3×C4×C5semidirect
507. C22⋊C4C2×C3×C4×C5semidirect
508. C22⋊C4C2×C3×C4×C5semidirect
512. C3×C5#2342direct (N × H)
527. C22×C3C5×#117semidirect
604. C5C3×#2342direct (N × H)
619. C22C3×C5×#117semidirect
634. C3C5×#2342direct (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
C22×C3×C5×C22⋊C42
C3×C5×#3882
C3×C5×#3852
C3×C5×#3812
C3×C5×#3802
C3×C5×#3792
C3×C4×C5×C22⋊C42
C5×#23423
C3×#23425