Finite Group Databasebeta

← C3×C5×#2417 #14275451

Subgroups — C3×C5×#2417 #14275451

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×C4×C5×D4C211yesmaximal, characteristic
4C22×C3×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×C5×#398C212yesmaximal, complemented
6C3×C5×#396C212yesmaximal, complemented
7C3×C5×#391C211yesmaximal, characteristic, complemented
8C3×C5×#389C211yesmaximal, characteristic, complemented
9C3×C5×#386C212yesmaximal
10C3×C5×#380C212yesmaximal, complemented
11C3×C5×#380C211yesmaximal, characteristic, complemented
12C5×#2417C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C23×C3×C4×C5C2211yescharacteristic
16C23×C3×C4×C5C2212yes—
17C23×C3×C4×C5C2211yescharacteristic
18C3×C5×C22⋊Q8—24no—
19C3×C5×C22⋊Q8—24no—
20C3×C4×C5×D4—24no—
21C2×C3×C5×C4⋊C4—24no—
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2212yes—
27C2×C3×C5×C4⋊C4C2212yes—
28C2×C3×C5×C4⋊C4C2212yes—
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2212yes—
33C2×C3×C5×C22⋊C4C2212yes—
34C2×C3×C5×C22⋊C4C2212yes—
35C2×C3×C42×C5C2211yescharacteristic
36C3×C5×#95C2212yes—
37C3×C5×#95C2212yes—
38C3×C5×#95C2212yes—
39C3×C5×#95C2212yes—
40C3×#2417C511yesmaximal, characteristic, direct product factor, Hall
41C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
42C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
43C2×C4×C5×D4C2×C311yescharacteristic
44C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
45C5×#398C2×C312yescomplemented
46C5×#396C2×C312yescomplemented
47C5×#391C2×C311yescharacteristic, complemented
48C5×#389C2×C311yescharacteristic, complemented
49C5×#386C2×C312yes—
50C5×#380C2×C312yescomplemented
51C5×#380C2×C311yescharacteristic, complemented
52C24×C3×C5C2311yescharacteristic
53C24×C3×C5C2311yescharacteristic
54C2×C3×C5×Q8—22no—
55C2×C3×C5×Q8—22no—
56C2×C3×C5×Q8—22no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4—22no—
59C2×C3×C5×D4Q814yescomplemented
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—24no—
63C22×C3×C4×C5—24no—
64C22×C3×C4×C5—22no—
65C22×C3×C4×C5—22no—
66C22×C3×C4×C5—22no—
67C22×C3×C4×C5—42no—
68C22×C3×C4×C5D414yes—
69C22×C3×C4×C5C2311yescharacteristic
70C22×C3×C4×C5C2312yes—
71C22×C3×C4×C5C2312yes—
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2312yes—
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2312yes—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C3×C5×C4⋊C4—24no—
79C3×C5×C4⋊C4—22no—
80C3×C5×C4⋊C4—22no—
81C3×C5×C4⋊C4—22no—
82C3×C5×C4⋊C4—24no—
83C3×C5×C4⋊C4—24no—
84C3×C5×C4⋊C4—42no—
85C3×C5×C4⋊C4D414yescomplemented
86C3×C5×C22⋊C4—22no—
87C3×C5×C22⋊C4—24no—
88C3×C5×C22⋊C4—22no—
89C3×C5×C22⋊C4—24no—
90C3×C5×C22⋊C4—42no—
91C3×C42×C5—22no—
92C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
93C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
94C2×C3×C4×D4C2×C511yescharacteristic
95C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
96C3×#398C2×C512yescomplemented
97C3×#396C2×C512yescomplemented
98C3×#391C2×C511yescharacteristic, complemented
99C3×#389C2×C511yescharacteristic, complemented
100C3×#386C2×C512yes—
101C3×#380C2×C511yescharacteristic, complemented
102C3×#380C2×C512yescomplemented
103C22×C5×Q8C22×C311yescharacteristic
104C22×C5×D4C22×C311yescharacteristic
105C23×C4×C5C22×C311yescharacteristic
106C23×C4×C5C22×C312yes—
107C23×C4×C5C22×C311yescharacteristic
108C5×C22⋊Q8—24no—
109C5×C22⋊Q8—24no—
110C4×C5×D4—24no—
111C2×C5×C4⋊C4—24no—
112C2×C5×C4⋊C4C22×C311yescharacteristic
113C2×C5×C4⋊C4C22×C311yescharacteristic
114C2×C5×C4⋊C4C22×C312yes—
115C2×C5×C4⋊C4C22×C312yes—
116C2×C5×C4⋊C4C22×C312yes—
117C2×C5×C4⋊C4C22×C311yescharacteristic
118C2×C5×C4⋊C4C22×C312yes—
119C2×C5×C4⋊C4C22×C311yescharacteristic
120C2×C5×C22⋊C4C22×C311yescharacteristic
121C2×C5×C22⋊C4C22×C312yes—
122C2×C5×C22⋊C4C22×C312yes—
123C2×C5×C22⋊C4C22×C311yescharacteristic
124C2×C5×C22⋊C4C22×C312yes—
125C2×C42×C5C22×C311yescharacteristic
126C5×#95C22×C312yes—
127C5×#95C22×C312yes—
128C5×#95C22×C312yes—
129C5×#95C22×C312yes—
130#2417C3×C511yescharacteristic, direct product factor, Sylow
131C23×C3×C5—21no—
132C23×C3×C5—21no—
133C23×C3×C5—21no—
134C23×C3×C5—21no—
135C23×C3×C5—21no—
136C23×C3×C5—21no—
137C23×C3×C5—21no—
138C23×C3×C5—21no—
139C23×C3×C5—21no—
140C23×C3×C5—21no—
141C23×C3×C5C2×D412yes—
142C23×C3×C5C2×Q812yes—
143C23×C3×C5C2×Q812yes—
144C23×C3×C5#4112yes—
145C23×C3×C5C2411yescharacteristic
146C3×C5×Q8—44no—
147C3×C5×D4—28no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—21no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—28no—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—22no—
157C2×C3×C4×C5—21no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—21no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—21no—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—22no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5—21no—
168C2×C3×C4×C5—21no—
169C2×C3×C4×C5—22no—
170C2×C3×C4×C5—48no—
171C2×C3×C4×C5—44no—
172C2×C3×C4×C5C2×D412yes—
173C2×C3×C4×C5C2×D414yes—
174C2×C3×C4×C5C2×D412yes—
175C2×C3×C4×C5C2×D412yes—
176C2×C3×C4×C5C2×Q812yes—
177C2×C3×C4×C5#4112yes—
178C22×C3×Q8C22×C511yescharacteristic
179C22×C3×D4C22×C511yescharacteristic
180C23×C3×C4C22×C511yescharacteristic
181C23×C3×C4C22×C512yes—
182C23×C3×C4C22×C511yescharacteristic
183C3×C22⋊Q8—24no—
184C3×C22⋊Q8—24no—
185C3×C4×D4—24no—
186C2×C3×C4⋊C4—24no—
187C2×C3×C4⋊C4C22×C511yescharacteristic
188C2×C3×C4⋊C4C22×C511yescharacteristic
189C2×C3×C4⋊C4C22×C512yes—
190C2×C3×C4⋊C4C22×C512yes—
191C2×C3×C4⋊C4C22×C512yes—
192C2×C3×C4⋊C4C22×C511yescharacteristic
193C2×C3×C4⋊C4C22×C512yes—
194C2×C3×C4⋊C4C22×C511yescharacteristic
195C2×C3×C22⋊C4C22×C511yescharacteristic
196C2×C3×C22⋊C4C22×C512yes—
197C2×C3×C22⋊C4C22×C512yes—
198C2×C3×C22⋊C4C22×C511yescharacteristic
199C2×C3×C22⋊C4C22×C512yes—
200C2×C3×C42C22×C511yescharacteristic
201C3×#95C22×C512yes—
202C3×#95C22×C512yes—
203C3×#95C22×C512yes—
204C3×#95C22×C512yes—
205C24×C5C23×C311yescharacteristic
206C24×C5C23×C311yescharacteristic
207C2×C5×Q8—22no—
208C2×C5×Q8—22no—
209C2×C5×Q8—22no—
210C2×C5×D4—22no—
211C2×C5×D4—22no—
212C2×C5×D4C3×Q814yescomplemented
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—24no—
216C22×C4×C5—24no—
217C22×C4×C5—22no—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—42no—
221C22×C4×C5C3×D414yes—
222C22×C4×C5C23×C311yescharacteristic
223C22×C4×C5C23×C312yes—
224C22×C4×C5C23×C312yes—
225C22×C4×C5C23×C311yescharacteristic
226C22×C4×C5C23×C312yes—
227C22×C4×C5C23×C311yescharacteristic
228C22×C4×C5C23×C312yes—
229C22×C4×C5C23×C311yescharacteristic
230C22×C4×C5C23×C311yescharacteristic
231C5×C4⋊C4—24no—
232C5×C4⋊C4—22no—
233C5×C4⋊C4—22no—
234C5×C4⋊C4—22no—
235C5×C4⋊C4—24no—
236C5×C4⋊C4—24no—
237C5×C4⋊C4—42no—
238C5×C4⋊C4C3×D414yescomplemented
239C5×C22⋊C4—22no—
240C5×C22⋊C4—24no—
241C5×C22⋊C4—22no—
242C5×C22⋊C4—24no—
243C5×C22⋊C4—42no—
244C42×C5—22no—
245C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
246C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
247C2×C4×D4C2×C3×C511yescharacteristic
248C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
249#398C2×C3×C512yescomplemented
250#396C2×C3×C512yescomplemented
251#391C2×C3×C511yescharacteristic, complemented
252#389C2×C3×C511yescharacteristic, complemented
253#386C2×C3×C512yes—
254#380C2×C3×C511yescharacteristic, complemented
255#380C2×C3×C512yescomplemented
256C22×C3×C5—22no—
257C22×C3×C5—22no—
258C22×C3×C5—22no—
259C22×C3×C5—22no—
260C22×C3×C5—22no—
261C22×C3×C5—22no—
262C22×C3×C5—22no—
263C22×C3×C5—22no—
264C22×C3×C5—22no—
265C22×C3×C5—41no—
266C22×C3×C5—41no—
267C22×C3×C5—41no—
268C22×C3×C5—41no—
269C22×C3×C5C22⋊Q814yescomplemented
270C22×C3×C5C22×D411yescharacteristic
271C22×C3×C5C22×D411yescharacteristic
272C22×C3×C5C22×Q811yescharacteristic
273C22×C3×C5C2×#4111yescharacteristic
274C22×C3×C5C2×#4111yescharacteristic
275C22×C3×C5H(5,𝔽2)11yescharacteristic
276C22×C3×C52−1+411yescharacteristic
277C3×C4×C5—22no—
278C3×C4×C5—22no—
279C3×C4×C5—24no—
280C3×C4×C5—41no—
281C3×C4×C5—42no—
282C3×C4×C5—41no—
283C3×C4×C5—42no—
284C3×C4×C5—42no—
285C3×C4×C5#12114yes—
286C24×C3C23×C511yescharacteristic
287C24×C3C23×C511yescharacteristic
288C2×C3×Q8—22no—
289C2×C3×Q8—22no—
290C2×C3×Q8—22no—
291C2×C3×D4—22no—
292C2×C3×D4—22no—
293C2×C3×D4C5×Q814yescomplemented
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4—24no—
297C22×C3×C4—24no—
298C22×C3×C4—22no—
299C22×C3×C4—22no—
300C22×C3×C4—22no—
301C22×C3×C4—42no—
302C22×C3×C4C5×D414yes—
303C22×C3×C4C23×C512yes—
304C22×C3×C4C23×C511yescharacteristic
305C22×C3×C4C23×C512yes—
306C22×C3×C4C23×C512yes—
307C22×C3×C4C23×C511yescharacteristic
308C22×C3×C4C23×C512yes—
309C22×C3×C4C23×C511yescharacteristic
310C22×C3×C4C23×C511yescharacteristic
311C22×C3×C4C23×C511yescharacteristic
312C3×C4⋊C4—24no—
313C3×C4⋊C4—22no—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—24no—
317C3×C4⋊C4—24no—
318C3×C4⋊C4—42no—
319C3×C4⋊C4C5×D414yescomplemented
320C3×C22⋊C4—22no—
321C3×C22⋊C4—24no—
322C3×C22⋊C4—22no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—42no—
325C3×C42—22no—
326C23×C5—21no—
327C23×C5—21no—
328C23×C5—21no—
329C23×C5—21no—
330C23×C5—21no—
331C23×C5—21no—
332C23×C5—21no—
333C23×C5—21no—
334C23×C5—21no—
335C23×C5—21no—
336C23×C5C2×C3×D412yes—
337C23×C5C2×C3×Q812yes—
338C23×C5C2×C3×Q812yes—
339C23×C5C3×#4112yes—
340C23×C5C24×C311yescharacteristic
341C5×Q8—44no—
342C5×D4—28no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5—21no—
346C2×C4×C5—22no—
347C2×C4×C5—21no—
348C2×C4×C5—22no—
349C2×C4×C5—28no—
350C2×C4×C5—21no—
351C2×C4×C5—22no—
352C2×C4×C5—21no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—21no—
356C2×C4×C5—22no—
357C2×C4×C5—21no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—21no—
363C2×C4×C5—21no—
364C2×C4×C5—22no—
365C2×C4×C5—48no—
366C2×C4×C5—44no—
367C2×C4×C5C2×C3×D412yes—
368C2×C4×C5C2×C3×D414yes—
369C2×C4×C5C2×C3×D412yes—
370C2×C4×C5C2×C3×D412yes—
371C2×C4×C5C2×C3×Q812yes—
372C2×C4×C5C3×#4112yes—
373C22×Q8C22×C3×C511yescharacteristic
374C22×D4C22×C3×C511yescharacteristic
375C23×C4C22×C3×C511yescharacteristic
376C23×C4C22×C3×C512yes—
377C23×C4C22×C3×C511yescharacteristic
378C22⋊Q8—24no—
379C22⋊Q8—24no—
380C4×D4—24no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4C22×C3×C511yescharacteristic
383C2×C4⋊C4C22×C3×C512yes—
384C2×C4⋊C4C22×C3×C511yescharacteristic
385C2×C4⋊C4C22×C3×C511yescharacteristic
386C2×C4⋊C4C22×C3×C512yes—
387C2×C4⋊C4C22×C3×C512yes—
388C2×C4⋊C4C22×C3×C512yes—
389C2×C4⋊C4C22×C3×C511yescharacteristic
390C2×C22⋊C4C22×C3×C511yescharacteristic
391C2×C22⋊C4C22×C3×C511yescharacteristic
392C2×C22⋊C4C22×C3×C512yes—
393C2×C22⋊C4C22×C3×C512yes—
394C2×C22⋊C4C22×C3×C512yes—
395C2×C42C22×C3×C511yescharacteristic
396#95C22×C3×C512yes—
397#95C22×C3×C512yes—
398#95C22×C3×C512yes—
399#95C22×C3×C512yes—
400C2×C3×C5—24no—
401C2×C3×C5—42no—
402C2×C3×C5C2×#12111yescharacteristic
403C2×C3×C5C2×C22⋊Q811yescharacteristic
404C2×C3×C5#53711yescharacteristic
405C2×C3×C5#54611yescharacteristic
406C2×C3×C5D4×Q811yescharacteristic
407C2×C3×C5#55211yescharacteristic
408C2×C3×C5#55411yescharacteristic
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—21no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3C2×C5×D412yes—
420C23×C3C2×C5×Q812yes—
421C23×C3C2×C5×Q812yes—
422C23×C3C5×#4112yes—
423C23×C3C24×C511yescharacteristic
424C3×Q8—44no—
425C3×D4—28no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—22no—
430C2×C3×C4—21no—
431C2×C3×C4—22no—
432C2×C3×C4—28no—
433C2×C3×C4—21no—
434C2×C3×C4—22no—
435C2×C3×C4—21no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—48no—
449C2×C3×C4—44no—
450C2×C3×C4C2×C5×D412yes—
451C2×C3×C4C2×C5×D414yes—
452C2×C3×C4C2×C5×D412yes—
453C2×C3×C4C2×C5×D412yes—
454C2×C3×C4C2×C5×Q812yes—
455C2×C3×C4C5×#4112yes—
456C22×C5—22no—
457C22×C5—22no—
458C22×C5—22no—
459C22×C5—22no—
460C22×C5—22no—
461C22×C5—22no—
462C22×C5—22no—
463C22×C5—22no—
464C22×C5—22no—
465C22×C5—41no—
466C22×C5—41no—
467C22×C5—41no—
468C22×C5—41no—
469C22×C5C3×C22⋊Q814yescomplemented
470C22×C5C22×C3×D411yescharacteristic
471C22×C5C22×C3×D411yescharacteristic
472C22×C5C22×C3×Q811yescharacteristic
473C22×C5C2×C3×#4111yescharacteristic
474C22×C5C2×C3×#4111yescharacteristic
475C22×C5C3×H(5,𝔽2)11yescharacteristic
476C22×C5C3×2−1+411yescharacteristic
477C4×C5—22no—
478C4×C5—22no—
479C4×C5—24no—
480C4×C5—41no—
481C4×C5—42no—
482C4×C5—41no—
483C4×C5—42no—
484C4×C5—42no—
485C4×C5C3×#12114yes—
486C24C23×C3×C511yescharacteristic
487C24C23×C3×C511yescharacteristic
488C2×Q8—22no—
489C2×Q8—22no—
490C2×Q8—22no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4C3×C5×Q814yescomplemented
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—42no—
502C22×C4C3×C5×D414yes—
503C22×C4C23×C3×C512yes—
504C22×C4C23×C3×C511yescharacteristic
505C22×C4C23×C3×C512yes—
506C22×C4C23×C3×C512yes—
507C22×C4C23×C3×C511yescharacteristic
508C22×C4C23×C3×C512yes—
509C22×C4C23×C3×C511yescharacteristic
510C22×C4C23×C3×C511yescharacteristic
511C22×C4C23×C3×C511yescharacteristic
512C4⋊C4—24no—
513C4⋊C4—22no—
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—24no—
517C4⋊C4—24no—
518C4⋊C4—42no—
519C4⋊C4C3×C5×D414yescomplemented
520C22⋊C4—22no—
521C22⋊C4—24no—
522C22⋊C4—22no—
523C22⋊C4—24no—
524C22⋊C4—42no—
525C42—22no—
526C3×C5#241711yescharacteristic, direct product factor, Hall
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3C5×C22⋊Q814yescomplemented
541C22×C3C22×C5×D411yescharacteristic
542C22×C3C22×C5×D411yescharacteristic
543C22×C3C22×C5×Q811yescharacteristic
544C22×C3C2×C5×#4111yescharacteristic
545C22×C3C2×C5×#4111yescharacteristic
546C22×C3C5×H(5,𝔽2)11yescharacteristic
547C22×C3C5×2−1+411yescharacteristic
548C3×C4—22no—
549C3×C4—22no—
550C3×C4—24no—
551C3×C4—41no—
552C3×C4—42no—
553C3×C4—41no—
554C3×C4—42no—
555C3×C4—42no—
556C3×C4C5×#12114yes—
557C2×C5—24no—
558C2×C5—42no—
559C2×C5C2×C3×#12111yescharacteristic
560C2×C5C2×C3×C22⋊Q811yescharacteristic
561C2×C5C3×#53711yescharacteristic
562C2×C5C3×#54611yescharacteristic
563C2×C5C3×D4×Q811yescharacteristic
564C2×C5C3×#55211yescharacteristic
565C2×C5C3×#55411yescharacteristic
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23C2×C3×C5×D412yes—
577C23C2×C3×C5×Q812yes—
578C23C2×C3×C5×Q812yes—
579C23C3×C5×#4112yes—
580C23C24×C3×C511yescharacteristic
581Q8—44no—
582D4—28no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—28no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—22no—
605C2×C4—48no—
606C2×C4—44no—
607C2×C4C2×C3×C5×D412yes—
608C2×C4C2×C3×C5×D414yes—
609C2×C4C2×C3×C5×D412yes—
610C2×C4C2×C3×C5×D412yes—
611C2×C4C2×C3×C5×Q812yes—
612C2×C4C3×C5×#4112yes—
613C2×C3—24no—
614C2×C3—42no—
615C2×C3C2×C5×#12111yescharacteristic
616C2×C3C2×C5×C22⋊Q811yescharacteristic
617C2×C3C5×#53711yescharacteristic
618C2×C3C5×#54611yescharacteristic
619C2×C3C5×D4×Q811yescharacteristic
620C2×C3C5×#55211yescharacteristic
621C2×C3C5×#55411yescharacteristic
622C5C3×#241711yescharacteristic, direct product factor, Sylow
623C22—22no—
624C22—22no—
625C22—22no—
626C22—22no—
627C22—22no—
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22C3×C5×C22⋊Q814yescomplemented
637C22C22×C3×C5×D411yescharacteristic
638C22C22×C3×C5×D411yescharacteristic
639C22C22×C3×C5×Q811yescharacteristic
640C22C2×C3×C5×#4111yescharacteristic
641C22C2×C3×C5×#4111yescharacteristic
642C22C3×C5×H(5,𝔽2)11yescharacteristic
643C22C3×C5×2−1+411yescharacteristic
644C4—22no—
645C4—22no—
646C4—24no—
647C4—41no—
648C4—42no—
649C4—41no—
650C4—42no—
651C4—42no—
652C4C3×C5×#12114yes—
653C3C5×#241711yescharacteristic, direct product factor, Sylow
654C2—24no—
655C2—42no—
656C2C2×C3×C5×#12111yescharacteristic
657C2C2×C3×C5×C22⋊Q811yescharacteristic
658C2C3×C5×#53711yescharacteristic
659C2C3×C5×#54611yescharacteristic
660C2C3×C5×D4×Q811yescharacteristic
661C2C3×C5×#55211yescharacteristic
662C2C3×C5×#55411yescharacteristic
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×C22⋊Q8C2semidirect
2. C2×C3×C5×C22⋊Q8C2semidirect
4. C22×C3×C5×C4⋊C4C2semidirect
5. C3×C5×#398C2semidirect
6. C3×C5×#396C2semidirect
7. C3×C5×#391C2semidirect
8. C3×C5×#389C2semidirect
10. C3×C5×#380C2semidirect
11. C3×C5×#380C2semidirect
12. C5×#2417C3direct (N × H)
40. C3×#2417C5direct (N × H)
41. C2×C5×C22⋊Q8C2×C3semidirect
42. C2×C5×C22⋊Q8C2×C3semidirect
44. C22×C5×C4⋊C4C2×C3semidirect
45. C5×#398C2×C3semidirect
46. C5×#396C2×C3semidirect
47. C5×#391C2×C3semidirect
48. C5×#389C2×C3semidirect
50. C5×#380C2×C3semidirect
51. C5×#380C2×C3semidirect
59. C2×C3×C5×D4Q8semidirect
85. C3×C5×C4⋊C4D4semidirect
92. C2×C3×C22⋊Q8C2×C5semidirect
93. C2×C3×C22⋊Q8C2×C5semidirect
95. C22×C3×C4⋊C4C2×C5semidirect
96. C3×#398C2×C5semidirect
97. C3×#396C2×C5semidirect
98. C3×#391C2×C5semidirect
99. C3×#389C2×C5semidirect
101. C3×#380C2×C5semidirect
102. C3×#380C2×C5semidirect
130. #2417C3×C5direct (N × H)
212. C2×C5×D4C3×Q8semidirect
238. C5×C4⋊C4C3×D4semidirect
245. C2×C22⋊Q8C2×C3×C5semidirect
246. C2×C22⋊Q8C2×C3×C5semidirect
248. C22×C4⋊C4C2×C3×C5semidirect
249. #398C2×C3×C5semidirect
250. #396C2×C3×C5semidirect
251. #391C2×C3×C5semidirect
252. #389C2×C3×C5semidirect
254. #380C2×C3×C5semidirect
255. #380C2×C3×C5semidirect
269. C22×C3×C5C22⋊Q8semidirect
293. C2×C3×D4C5×Q8semidirect
319. C3×C4⋊C4C5×D4semidirect
469. C22×C5C3×C22⋊Q8semidirect
493. C2×D4C3×C5×Q8semidirect
519. C4⋊C4C3×C5×D4semidirect
526. C3×C5#2417direct (N × H)
540. C22×C3C5×C22⋊Q8semidirect
622. C5C3×#2417direct (N × H)
636. C22C3×C5×C22⋊Q8semidirect
653. C3C5×#2417direct (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×C22⋊Q82
C2×C3×C4×C5×D42
C22×C3×C5×C4⋊C42
C3×C5×#3982
C3×C5×#3962
C3×C5×#3912
C3×C5×#3892
C3×C5×#3862
C3×C5×#3802
C5×#24173
C3×#24175