Finite Group Databasebeta

← C3×C5×#2481 #14275515

Subgroups — C3×C5×#2481 #14275515

Order 1920.

1092 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#126C211yesmaximal, characteristic, complemented
2C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
3C3×C5×#400C211yesmaximal, characteristic, complemented
4C3×C5×#400C211yesmaximal, characteristic, complemented
5C3×C5×#397C211yesmaximal, characteristic, complemented
6C3×C5×#396C211yesmaximal, characteristic, complemented
7C3×C5×#388C211yesmaximal, characteristic, complemented
8C3×C5×#387C211yesmaximal, characteristic, complemented
9C3×C5×#387C211yesmaximal, characteristic, complemented
10C3×C5×#386C211yesmaximal, characteristic
11C3×C5×#386C211yesmaximal, characteristic
12C3×C5×#386C211yesmaximal, characteristic
13C3×C5×#385C211yesmaximal, characteristic, complemented
14C3×C5×#380C211yesmaximal, characteristic, complemented
15C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
16C5×#2481C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C23×C3×C4×C5C2211yescharacteristic
21C3×C5×#126—24no—
22C2×C3×C5×C4⋊C4—24no—
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2211yescharacteristic
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×C5×C4⋊C4C2211yescharacteristic
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×C3×C5×C22⋊C4C2211yescharacteristic
36C2×C3×C5×C22⋊C4C2211yescharacteristic
37C2×C3×C5×C22⋊C4C2211yescharacteristic
38C2×C3×C5×C22⋊C4C2211yescharacteristic
39C2×C3×C5×C22⋊C4C2211yescharacteristic
40C2×C3×C42×C5C2211yescharacteristic
41C2×C3×C42×C5C2211yescharacteristic
42C3×C5×#95C2211yescharacteristic
43C3×C5×#95C2211yescharacteristic
44C3×C5×#95C2211yescharacteristic
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×C5×#95C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49C3×C5×#95C2211yescharacteristic
50C3×C5×#95C2211yescharacteristic
51C3×C5×#95C2211yescharacteristic
52C3×C5×#95C2211yescharacteristic
53C3×C5×#95C2211yescharacteristic
54C3×#2481C511yesmaximal, characteristic, direct product factor, Hall
55C2×C5×#126C2×C311yescharacteristic, complemented
56C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
57C5×#400C2×C311yescharacteristic, complemented
58C5×#400C2×C311yescharacteristic, complemented
59C5×#397C2×C311yescharacteristic, complemented
60C5×#396C2×C311yescharacteristic, complemented
61C5×#388C2×C311yescharacteristic, complemented
62C5×#387C2×C311yescharacteristic, complemented
63C5×#387C2×C311yescharacteristic, complemented
64C5×#386C2×C311yescharacteristic
65C5×#386C2×C311yescharacteristic
66C5×#386C2×C311yescharacteristic
67C5×#385C2×C311yescharacteristic, complemented
68C5×#380C2×C311yescharacteristic, complemented
69C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
70C24×C3×C5C2311yescharacteristic
71C24×C3×C5C2311yescharacteristic
72C2×C3×C5×D4—22no—
73C2×C3×C5×D4—22no—
74C2×C3×C5×D4—22no—
75C22×C3×C4×C5—22no—
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×C5—22no—
82C22×C3×C4×C5—41no—
83C22×C3×C4×C5—41no—
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C3×C5×C4⋊C4—22no—
98C3×C5×C4⋊C4—22no—
99C3×C5×C4⋊C4—22no—
100C3×C5×C4⋊C4—22no—
101C3×C5×C4⋊C4—22no—
102C3×C5×C4⋊C4—22no—
103C3×C5×C4⋊C4—41no—
104C3×C5×C4⋊C4D414yescomplemented
105C3×C5×C22⋊C4—22no—
106C3×C5×C22⋊C4—22no—
107C3×C5×C22⋊C4—22no—
108C3×C5×C22⋊C4—22no—
109C3×C5×C22⋊C4—22no—
110C3×C5×C22⋊C4—22no—
111C3×C5×C22⋊C4—22no—
112C3×C5×C22⋊C4—41no—
113C3×C5×C22⋊C4—41no—
114C3×C42×C5—22no—
115C3×C42×C5—41no—
116C2×C3×#126C2×C511yescharacteristic, complemented
117C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
118C3×#400C2×C511yescharacteristic, complemented
119C3×#400C2×C511yescharacteristic, complemented
120C3×#397C2×C511yescharacteristic, complemented
121C3×#396C2×C511yescharacteristic, complemented
122C3×#388C2×C511yescharacteristic, complemented
123C3×#387C2×C511yescharacteristic, complemented
124C3×#387C2×C511yescharacteristic, complemented
125C3×#386C2×C511yescharacteristic
126C3×#386C2×C511yescharacteristic
127C3×#386C2×C511yescharacteristic
128C3×#385C2×C511yescharacteristic, complemented
129C3×#380C2×C511yescharacteristic, complemented
130C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
131C22×C5×D4C22×C311yescharacteristic
132C23×C4×C5C22×C311yescharacteristic
133C23×C4×C5C22×C311yescharacteristic
134C23×C4×C5C22×C311yescharacteristic
135C5×#126—24no—
136C2×C5×C4⋊C4—24no—
137C2×C5×C4⋊C4C22×C311yescharacteristic
138C2×C5×C4⋊C4C22×C311yescharacteristic
139C2×C5×C4⋊C4C22×C311yescharacteristic
140C2×C5×C4⋊C4C22×C311yescharacteristic
141C2×C5×C4⋊C4C22×C311yescharacteristic
142C2×C5×C4⋊C4C22×C311yescharacteristic
143C2×C5×C4⋊C4C22×C311yescharacteristic
144C2×C5×C4⋊C4C22×C311yescharacteristic
145C2×C5×C22⋊C4C22×C311yescharacteristic
146C2×C5×C22⋊C4C22×C311yescharacteristic
147C2×C5×C22⋊C4C22×C311yescharacteristic
148C2×C5×C22⋊C4C22×C311yescharacteristic
149C2×C5×C22⋊C4C22×C311yescharacteristic
150C2×C5×C22⋊C4C22×C311yescharacteristic
151C2×C5×C22⋊C4C22×C311yescharacteristic
152C2×C5×C22⋊C4C22×C311yescharacteristic
153C2×C5×C22⋊C4C22×C311yescharacteristic
154C2×C42×C5C22×C311yescharacteristic
155C2×C42×C5C22×C311yescharacteristic
156C5×#95C22×C311yescharacteristic
157C5×#95C22×C311yescharacteristic
158C5×#95C22×C311yescharacteristic
159C5×#95C22×C311yescharacteristic
160C5×#95C22×C311yescharacteristic
161C5×#95C22×C311yescharacteristic
162C5×#95C22×C311yescharacteristic
163C5×#95C22×C311yescharacteristic
164C5×#95C22×C311yescharacteristic
165C5×#95C22×C311yescharacteristic
166C5×#95C22×C311yescharacteristic
167C5×#95C22×C311yescharacteristic
168#2481C3×C511yescharacteristic, direct product factor, Sylow
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5#4112yes—
181C23×C3×C5#4112yes—
182C23×C3×C5#4112yes—
183C23×C3×C5C2411yescharacteristic
184C3×C5×D4—44no—
185C2×C3×C4×C5—28no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—44no—
222C2×C3×C4×C5—44no—
223C2×C3×C4×C5C2×D412yes—
224C2×C3×C4×C5C2×D412yes—
225C2×C3×C4×C5C2×D412yes—
226C2×C3×C4×C5#4112yes—
227C22×C3×D4C22×C511yescharacteristic
228C23×C3×C4C22×C511yescharacteristic
229C23×C3×C4C22×C511yescharacteristic
230C23×C3×C4C22×C511yescharacteristic
231C3×#126—24no—
232C2×C3×C4⋊C4—24no—
233C2×C3×C4⋊C4C22×C511yescharacteristic
234C2×C3×C4⋊C4C22×C511yescharacteristic
235C2×C3×C4⋊C4C22×C511yescharacteristic
236C2×C3×C4⋊C4C22×C511yescharacteristic
237C2×C3×C4⋊C4C22×C511yescharacteristic
238C2×C3×C4⋊C4C22×C511yescharacteristic
239C2×C3×C4⋊C4C22×C511yescharacteristic
240C2×C3×C4⋊C4C22×C511yescharacteristic
241C2×C3×C22⋊C4C22×C511yescharacteristic
242C2×C3×C22⋊C4C22×C511yescharacteristic
243C2×C3×C22⋊C4C22×C511yescharacteristic
244C2×C3×C22⋊C4C22×C511yescharacteristic
245C2×C3×C22⋊C4C22×C511yescharacteristic
246C2×C3×C22⋊C4C22×C511yescharacteristic
247C2×C3×C22⋊C4C22×C511yescharacteristic
248C2×C3×C22⋊C4C22×C511yescharacteristic
249C2×C3×C22⋊C4C22×C511yescharacteristic
250C2×C3×C42C22×C511yescharacteristic
251C2×C3×C42C22×C511yescharacteristic
252C3×#95C22×C511yescharacteristic
253C3×#95C22×C511yescharacteristic
254C3×#95C22×C511yescharacteristic
255C3×#95C22×C511yescharacteristic
256C3×#95C22×C511yescharacteristic
257C3×#95C22×C511yescharacteristic
258C3×#95C22×C511yescharacteristic
259C3×#95C22×C511yescharacteristic
260C3×#95C22×C511yescharacteristic
261C3×#95C22×C511yescharacteristic
262C3×#95C22×C511yescharacteristic
263C3×#95C22×C511yescharacteristic
264C24×C5C23×C311yescharacteristic
265C24×C5C23×C311yescharacteristic
266C2×C5×D4—22no—
267C2×C5×D4—22no—
268C2×C5×D4—22no—
269C22×C4×C5—22no—
270C22×C4×C5—22no—
271C22×C4×C5—22no—
272C22×C4×C5—22no—
273C22×C4×C5—22no—
274C22×C4×C5—22no—
275C22×C4×C5—22no—
276C22×C4×C5—41no—
277C22×C4×C5—41no—
278C22×C4×C5C23×C311yescharacteristic
279C22×C4×C5C23×C311yescharacteristic
280C22×C4×C5C23×C311yescharacteristic
281C22×C4×C5C23×C311yescharacteristic
282C22×C4×C5C23×C311yescharacteristic
283C22×C4×C5C23×C311yescharacteristic
284C22×C4×C5C23×C311yescharacteristic
285C22×C4×C5C23×C311yescharacteristic
286C22×C4×C5C23×C311yescharacteristic
287C22×C4×C5C23×C311yescharacteristic
288C22×C4×C5C23×C311yescharacteristic
289C22×C4×C5C23×C311yescharacteristic
290C22×C4×C5C23×C311yescharacteristic
291C5×C4⋊C4—22no—
292C5×C4⋊C4—22no—
293C5×C4⋊C4—22no—
294C5×C4⋊C4—22no—
295C5×C4⋊C4—22no—
296C5×C4⋊C4—22no—
297C5×C4⋊C4—41no—
298C5×C4⋊C4C3×D414yescomplemented
299C5×C22⋊C4—22no—
300C5×C22⋊C4—22no—
301C5×C22⋊C4—22no—
302C5×C22⋊C4—22no—
303C5×C22⋊C4—22no—
304C5×C22⋊C4—22no—
305C5×C22⋊C4—22no—
306C5×C22⋊C4—41no—
307C5×C22⋊C4—41no—
308C42×C5—22no—
309C42×C5—41no—
310C2×#126C2×C3×C511yescharacteristic, complemented
311C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
312#400C2×C3×C511yescharacteristic, complemented
313#400C2×C3×C511yescharacteristic, complemented
314#397C2×C3×C511yescharacteristic, complemented
315#396C2×C3×C511yescharacteristic, complemented
316#388C2×C3×C511yescharacteristic, complemented
317#387C2×C3×C511yescharacteristic, complemented
318#387C2×C3×C511yescharacteristic, complemented
319#386C2×C3×C511yescharacteristic
320#386C2×C3×C511yescharacteristic
321#386C2×C3×C511yescharacteristic
322#385C2×C3×C511yescharacteristic, complemented
323#380C2×C3×C511yescharacteristic, complemented
324C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
325C22×C3×C5—22no—
326C22×C3×C5—22no—
327C22×C3×C5—22no—
328C22×C3×C5—22no—
329C22×C3×C5—22no—
330C22×C3×C5—22no—
331C22×C3×C5—41no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5—41no—
335C22×C3×C5—41no—
336C22×C3×C5—41no—
337C22×C3×C5—41no—
338C22×C3×C5#12614yescomplemented
339C22×C3×C5C22×D411yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5C2×#4111yescharacteristic
343C22×C3×C5C2×#4111yescharacteristic
344C22×C3×C5H(5,𝔽2)11yescharacteristic
345C22×C3×C52−1+411yescharacteristic
346C3×C4×C5—22no—
347C3×C4×C5—22no—
348C3×C4×C5—22no—
349C3×C4×C5—22no—
350C3×C4×C5—41no—
351C3×C4×C5—41no—
352C3×C4×C5—41no—
353C3×C4×C5—41no—
354C3×C4×C5—41no—
355C3×C4×C5—41no—
356C3×C4×C5—41no—
357C3×C4×C5—41no—
358C3×C4×C5—41no—
359C24×C3C23×C511yescharacteristic
360C24×C3C23×C511yescharacteristic
361C2×C3×D4—22no—
362C2×C3×D4—22no—
363C2×C3×D4—22no—
364C22×C3×C4—22no—
365C22×C3×C4—22no—
366C22×C3×C4—22no—
367C22×C3×C4—22no—
368C22×C3×C4—22no—
369C22×C3×C4—22no—
370C22×C3×C4—22no—
371C22×C3×C4—41no—
372C22×C3×C4—41no—
373C22×C3×C4C23×C511yescharacteristic
374C22×C3×C4C23×C511yescharacteristic
375C22×C3×C4C23×C511yescharacteristic
376C22×C3×C4C23×C511yescharacteristic
377C22×C3×C4C23×C511yescharacteristic
378C22×C3×C4C23×C511yescharacteristic
379C22×C3×C4C23×C511yescharacteristic
380C22×C3×C4C23×C511yescharacteristic
381C22×C3×C4C23×C511yescharacteristic
382C22×C3×C4C23×C511yescharacteristic
383C22×C3×C4C23×C511yescharacteristic
384C22×C3×C4C23×C511yescharacteristic
385C22×C3×C4C23×C511yescharacteristic
386C3×C4⋊C4—22no—
387C3×C4⋊C4—22no—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—22no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—22no—
392C3×C4⋊C4—41no—
393C3×C4⋊C4C5×D414yescomplemented
394C3×C22⋊C4—22no—
395C3×C22⋊C4—22no—
396C3×C22⋊C4—22no—
397C3×C22⋊C4—22no—
398C3×C22⋊C4—22no—
399C3×C22⋊C4—22no—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—41no—
402C3×C22⋊C4—41no—
403C3×C42—22no—
404C3×C42—41no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—21no—
410C23×C5—21no—
411C23×C5—21no—
412C23×C5—21no—
413C23×C5—21no—
414C23×C5—21no—
415C23×C5—21no—
416C23×C5C3×#4112yes—
417C23×C5C3×#4112yes—
418C23×C5C3×#4112yes—
419C23×C5C24×C311yescharacteristic
420C5×D4—44no—
421C2×C4×C5—28no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5—21no—
434C2×C4×C5—21no—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—21no—
450C2×C4×C5—21no—
451C2×C4×C5—21no—
452C2×C4×C5—21no—
453C2×C4×C5—21no—
454C2×C4×C5—21no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—44no—
458C2×C4×C5—44no—
459C2×C4×C5C2×C3×D412yes—
460C2×C4×C5C2×C3×D412yes—
461C2×C4×C5C2×C3×D412yes—
462C2×C4×C5C3×#4112yes—
463C22×D4C22×C3×C511yescharacteristic
464C23×C4C22×C3×C511yescharacteristic
465C23×C4C22×C3×C511yescharacteristic
466C23×C4C22×C3×C511yescharacteristic
467#126—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4C22×C3×C511yescharacteristic
470C2×C4⋊C4C22×C3×C511yescharacteristic
471C2×C4⋊C4C22×C3×C511yescharacteristic
472C2×C4⋊C4C22×C3×C511yescharacteristic
473C2×C4⋊C4C22×C3×C511yescharacteristic
474C2×C4⋊C4C22×C3×C511yescharacteristic
475C2×C4⋊C4C22×C3×C511yescharacteristic
476C2×C4⋊C4C22×C3×C511yescharacteristic
477C2×C22⋊C4C22×C3×C511yescharacteristic
478C2×C22⋊C4C22×C3×C511yescharacteristic
479C2×C22⋊C4C22×C3×C511yescharacteristic
480C2×C22⋊C4C22×C3×C511yescharacteristic
481C2×C22⋊C4C22×C3×C511yescharacteristic
482C2×C22⋊C4C22×C3×C511yescharacteristic
483C2×C22⋊C4C22×C3×C511yescharacteristic
484C2×C22⋊C4C22×C3×C511yescharacteristic
485C2×C22⋊C4C22×C3×C511yescharacteristic
486C2×C42C22×C3×C511yescharacteristic
487C2×C42C22×C3×C511yescharacteristic
488#95C22×C3×C511yescharacteristic
489#95C22×C3×C511yescharacteristic
490#95C22×C3×C511yescharacteristic
491#95C22×C3×C511yescharacteristic
492#95C22×C3×C511yescharacteristic
493#95C22×C3×C511yescharacteristic
494#95C22×C3×C511yescharacteristic
495#95C22×C3×C511yescharacteristic
496#95C22×C3×C511yescharacteristic
497#95C22×C3×C511yescharacteristic
498#95C22×C3×C511yescharacteristic
499#95C22×C3×C511yescharacteristic
500C2×C3×C5—24no—
501C2×C3×C5—81no—
502C2×C3×C5#52511yescharacteristic
503C2×C3×C5C2×#12611yescharacteristic
504C2×C3×C5#53911yescharacteristic
505C2×C3×C5#54611yescharacteristic
506C2×C3×C5#54811yescharacteristic
507C2×C3×C5#55211yescharacteristic
508C2×C3×C5#55311yescharacteristic
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
519C23×C3—21no—
520C23×C3C5×#4112yes—
521C23×C3C5×#4112yes—
522C23×C3C5×#4112yes—
523C23×C3C24×C511yescharacteristic
524C3×D4—44no—
525C2×C3×C4—28no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—21no—
539C2×C3×C4—21no—
540C2×C3×C4—21no—
541C2×C3×C4—21no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—21no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—21no—
561C2×C3×C4—44no—
562C2×C3×C4—44no—
563C2×C3×C4C2×C5×D412yes—
564C2×C3×C4C2×C5×D412yes—
565C2×C3×C4C2×C5×D412yes—
566C2×C3×C4C5×#4112yes—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—22no—
572C22×C5—22no—
573C22×C5—41no—
574C22×C5—41no—
575C22×C5—41no—
576C22×C5—41no—
577C22×C5—41no—
578C22×C5—41no—
579C22×C5—41no—
580C22×C5C3×#12614yescomplemented
581C22×C5C22×C3×D411yescharacteristic
582C22×C5C2×C3×#4111yescharacteristic
583C22×C5C2×C3×#4111yescharacteristic
584C22×C5C2×C3×#4111yescharacteristic
585C22×C5C2×C3×#4111yescharacteristic
586C22×C5C3×H(5,𝔽2)11yescharacteristic
587C22×C5C3×2−1+411yescharacteristic
588C4×C5—22no—
589C4×C5—22no—
590C4×C5—22no—
591C4×C5—22no—
592C4×C5—41no—
593C4×C5—41no—
594C4×C5—41no—
595C4×C5—41no—
596C4×C5—41no—
597C4×C5—41no—
598C4×C5—41no—
599C4×C5—41no—
600C4×C5—41no—
601C24C23×C3×C511yescharacteristic
602C24C23×C3×C511yescharacteristic
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—41no—
614C22×C4—41no—
615C22×C4C23×C3×C511yescharacteristic
616C22×C4C23×C3×C511yescharacteristic
617C22×C4C23×C3×C511yescharacteristic
618C22×C4C23×C3×C511yescharacteristic
619C22×C4C23×C3×C511yescharacteristic
620C22×C4C23×C3×C511yescharacteristic
621C22×C4C23×C3×C511yescharacteristic
622C22×C4C23×C3×C511yescharacteristic
623C22×C4C23×C3×C511yescharacteristic
624C22×C4C23×C3×C511yescharacteristic
625C22×C4C23×C3×C511yescharacteristic
626C22×C4C23×C3×C511yescharacteristic
627C22×C4C23×C3×C511yescharacteristic
628C4⋊C4—22no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—41no—
635C4⋊C4C3×C5×D414yescomplemented
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—22no—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—41no—
644C22⋊C4—41no—
645C42—22no—
646C42—41no—
647C3×C5#248111yescharacteristic, direct product factor, Hall
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—41no—
655C22×C3—41no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3—41no—
661C22×C3C5×#12614yescomplemented
662C22×C3C22×C5×D411yescharacteristic
663C22×C3C2×C5×#4111yescharacteristic
664C22×C3C2×C5×#4111yescharacteristic
665C22×C3C2×C5×#4111yescharacteristic
666C22×C3C2×C5×#4111yescharacteristic
667C22×C3C5×H(5,𝔽2)11yescharacteristic
668C22×C3C5×2−1+411yescharacteristic
669C3×C4—22no—
670C3×C4—22no—
671C3×C4—22no—
672C3×C4—22no—
673C3×C4—41no—
674C3×C4—41no—
675C3×C4—41no—
676C3×C4—41no—
677C3×C4—41no—
678C3×C4—41no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C2×C5—24no—
683C2×C5—81no—
684C2×C5C3×#52511yescharacteristic
685C2×C5C2×C3×#12611yescharacteristic
686C2×C5C3×#53911yescharacteristic
687C2×C5C3×#54611yescharacteristic
688C2×C5C3×#54811yescharacteristic
689C2×C5C3×#55211yescharacteristic
690C2×C5C3×#55311yescharacteristic
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23C3×C5×#4112yes—
703C23C3×C5×#4112yes—
704C23C3×C5×#4112yes—
705C23C24×C3×C511yescharacteristic
706D4—44no—
707C2×C4—28no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4C2×C3×C5×D412yes—
746C2×C4C2×C3×C5×D412yes—
747C2×C4C2×C3×C5×D412yes—
748C2×C4C3×C5×#4112yes—
749C2×C3—24no—
750C2×C3—81no—
751C2×C3C5×#52511yescharacteristic
752C2×C3C2×C5×#12611yescharacteristic
753C2×C3C5×#53911yescharacteristic
754C2×C3C5×#54611yescharacteristic
755C2×C3C5×#54811yescharacteristic
756C2×C3C5×#55211yescharacteristic
757C2×C3C5×#55311yescharacteristic
758C5C3×#248111yescharacteristic, direct product factor, Sylow
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22C3×C5×#12614yescomplemented
773C22C22×C3×C5×D411yescharacteristic
774C22C2×C3×C5×#4111yescharacteristic
775C22C2×C3×C5×#4111yescharacteristic
776C22C2×C3×C5×#4111yescharacteristic
777C22C2×C3×C5×#4111yescharacteristic
778C22C3×C5×H(5,𝔽2)11yescharacteristic
779C22C3×C5×2−1+411yescharacteristic
780C4—22no—
781C4—22no—
782C4—22no—
783C4—22no—
784C4—41no—
785C4—41no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—41no—
790C4—41no—
791C4—41no—
792C4—41no—
793C3C5×#248111yescharacteristic, direct product factor, Sylow
794C2—24no—
795C2—81no—
796C2C3×C5×#52511yescharacteristic
797C2C2×C3×C5×#12611yescharacteristic
798C2C3×C5×#53911yescharacteristic
799C2C3×C5×#54611yescharacteristic
800C2C3×C5×#54811yescharacteristic
801C2C3×C5×#55211yescharacteristic
802C2C3×C5×#55311yescharacteristic
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
1. C2×C3×C5×#126C2semidirect
2. C22×C3×C5×C4⋊C4C2semidirect
3. C3×C5×#400C2semidirect
4. C3×C5×#400C2semidirect
5. C3×C5×#397C2semidirect
6. C3×C5×#396C2semidirect
7. C3×C5×#388C2semidirect
8. C3×C5×#387C2semidirect
9. C3×C5×#387C2semidirect
13. C3×C5×#385C2semidirect
14. C3×C5×#380C2semidirect
15. C3×C4×C5×C22⋊C4C2semidirect
16. C5×#2481C3direct (N × H)
54. C3×#2481C5direct (N × H)
55. C2×C5×#126C2×C3semidirect
56. C22×C5×C4⋊C4C2×C3semidirect
57. C5×#400C2×C3semidirect
58. C5×#400C2×C3semidirect
59. C5×#397C2×C3semidirect
60. C5×#396C2×C3semidirect
61. C5×#388C2×C3semidirect
62. C5×#387C2×C3semidirect
63. C5×#387C2×C3semidirect
67. C5×#385C2×C3semidirect
68. C5×#380C2×C3semidirect
69. C4×C5×C22⋊C4C2×C3semidirect
104. C3×C5×C4⋊C4D4semidirect
116. C2×C3×#126C2×C5semidirect
117. C22×C3×C4⋊C4C2×C5semidirect
118. C3×#400C2×C5semidirect
119. C3×#400C2×C5semidirect
120. C3×#397C2×C5semidirect
121. C3×#396C2×C5semidirect
122. C3×#388C2×C5semidirect
123. C3×#387C2×C5semidirect
124. C3×#387C2×C5semidirect
128. C3×#385C2×C5semidirect
129. C3×#380C2×C5semidirect
130. C3×C4×C22⋊C4C2×C5semidirect
168. #2481C3×C5direct (N × H)
298. C5×C4⋊C4C3×D4semidirect
310. C2×#126C2×C3×C5semidirect
311. C22×C4⋊C4C2×C3×C5semidirect
312. #400C2×C3×C5semidirect
313. #400C2×C3×C5semidirect
314. #397C2×C3×C5semidirect
315. #396C2×C3×C5semidirect
316. #388C2×C3×C5semidirect
317. #387C2×C3×C5semidirect
318. #387C2×C3×C5semidirect
322. #385C2×C3×C5semidirect
323. #380C2×C3×C5semidirect
324. C4×C22⋊C4C2×C3×C5semidirect
338. C22×C3×C5#126semidirect
393. C3×C4⋊C4C5×D4semidirect
580. C22×C5C3×#126semidirect
635. C4⋊C4C3×C5×D4semidirect
647. C3×C5#2481direct (N × H)
661. C22×C3C5×#126semidirect
758. C5C3×#2481direct (N × H)
772. C22C3×C5×#126semidirect
793. C3C5×#2481direct (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×#1262
C22×C3×C5×C4⋊C42
C3×C5×#4002
C3×C5×#3972
C3×C5×#3962
C3×C5×#3882
C3×C5×#3872
C3×C5×#3862
C3×C5×#3852
C3×C5×#3802
C3×C4×C5×C22⋊C42
C5×#24813
C3×#24815