Finite Group Databasebeta

← C3×C5×#2449 #14275483

Subgroups — C3×C5×#2449 #14275483

Order 1920.

1296 conjugacy classes of subgroups.

The subgroup lattice has 852 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×#399C211yesmaximal, characteristic, complemented
6C3×C5×#398C211yesmaximal, characteristic, complemented
7C3×C5×#396C211yesmaximal, characteristic, complemented
8C3×C5×#395C211yesmaximal, characteristic, complemented
9C3×C5×#389C211yesmaximal, characteristic, complemented
10C3×C5×#387C211yesmaximal, characteristic, complemented
11C3×C5×#386C211yesmaximal, characteristic
12C3×C5×#386C211yesmaximal, characteristic
13C3×C5×#385C211yesmaximal, characteristic, complemented
14C3×C5×#385C211yesmaximal, characteristic, complemented
15C3×C5×#385C211yesmaximal, characteristic, complemented
16C5×#2449C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C23×C3×C4×C5C2211yescharacteristic
21C23×C3×C4×C5C2211yescharacteristic
22C23×C3×C4×C5C2211yescharacteristic
23C3×C5×C22⋊Q8—24no—
24C3×C5×C22⋊Q8—24no—
25C3×C4×C5×D4—24no—
26C2×C3×C5×C4⋊C4—24no—
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C3×C5×C4⋊C4C2211yescharacteristic
29C2×C3×C5×C4⋊C4C2211yescharacteristic
30C2×C3×C5×C4⋊C4C2211yescharacteristic
31C2×C3×C5×C4⋊C4C2211yescharacteristic
32C2×C3×C5×C4⋊C4C2211yescharacteristic
33C2×C3×C5×C4⋊C4C2211yescharacteristic
34C2×C3×C5×C4⋊C4C2211yescharacteristic
35C2×C3×C5×C4⋊C4C2211yescharacteristic
36C2×C3×C5×C4⋊C4C2211yescharacteristic
37C2×C3×C5×C4⋊C4C2211yescharacteristic
38C2×C3×C5×C4⋊C4C2211yescharacteristic
39C2×C3×C5×C22⋊C4C2211yescharacteristic
40C2×C3×C5×C22⋊C4C2211yescharacteristic
41C2×C3×C5×C22⋊C4C2211yescharacteristic
42C2×C3×C5×C22⋊C4C2211yescharacteristic
43C2×C3×C5×C22⋊C4C2211yescharacteristic
44C2×C3×C5×C22⋊C4C2211yescharacteristic
45C2×C3×C5×C22⋊C4C2211yescharacteristic
46C2×C3×C5×C22⋊C4C2211yescharacteristic
47C2×C3×C42×C5C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49C3×C5×#95C2211yescharacteristic
50C3×C5×#95C2211yescharacteristic
51C3×C5×#95C2211yescharacteristic
52C3×C5×#95C2211yescharacteristic
53C3×C5×#95C2211yescharacteristic
54C3×C5×#95C2211yescharacteristic
55C3×C5×#95C2211yescharacteristic
56C3×#2449C511yesmaximal, characteristic, direct product factor, Hall
57C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
58C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
59C2×C4×C5×D4C2×C311yescharacteristic
60C22×C5×C4⋊C4C2×C311yescharacteristic, complemented
61C5×#399C2×C311yescharacteristic, complemented
62C5×#398C2×C311yescharacteristic, complemented
63C5×#396C2×C311yescharacteristic, complemented
64C5×#395C2×C311yescharacteristic, complemented
65C5×#389C2×C311yescharacteristic, complemented
66C5×#387C2×C311yescharacteristic, complemented
67C5×#386C2×C311yescharacteristic
68C5×#386C2×C311yescharacteristic
69C5×#385C2×C311yescharacteristic, complemented
70C5×#385C2×C311yescharacteristic, complemented
71C5×#385C2×C311yescharacteristic, complemented
72C24×C3×C5C2311yescharacteristic
73C24×C3×C5C2311yescharacteristic
74C2×C3×C5×Q8—22no—
75C2×C3×C5×Q8—22no—
76C2×C3×C5×Q8—41no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4Q814yescomplemented
80C22×C3×C4×C5—22no—
81C22×C3×C4×C5—22no—
82C22×C3×C4×C5—22no—
83C22×C3×C4×C5—22no—
84C22×C3×C4×C5—22no—
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—22no—
87C22×C3×C4×C5—22no—
88C22×C3×C4×C5—22no—
89C22×C3×C4×C5—41no—
90C22×C3×C4×C5—41no—
91C22×C3×C4×C5—41no—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2311yescharacteristic
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2311yescharacteristic
104C22×C3×C4×C5C2311yescharacteristic
105C3×C5×C4⋊C4—22no—
106C3×C5×C4⋊C4—22no—
107C3×C5×C4⋊C4—22no—
108C3×C5×C4⋊C4—22no—
109C3×C5×C4⋊C4—22no—
110C3×C5×C4⋊C4—22no—
111C3×C5×C4⋊C4—22no—
112C3×C5×C4⋊C4—22no—
113C3×C5×C4⋊C4—22no—
114C3×C5×C4⋊C4—22no—
115C3×C5×C4⋊C4—41no—
116C3×C5×C4⋊C4D414yescomplemented
117C3×C5×C22⋊C4—22no—
118C3×C5×C22⋊C4—22no—
119C3×C5×C22⋊C4—22no—
120C3×C5×C22⋊C4—22no—
121C3×C5×C22⋊C4—22no—
122C3×C5×C22⋊C4—22no—
123C3×C5×C22⋊C4—41no—
124C3×C5×C22⋊C4D414yes—
125C3×C42×C5—22no—
126C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
127C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
128C2×C3×C4×D4C2×C511yescharacteristic
129C22×C3×C4⋊C4C2×C511yescharacteristic, complemented
130C3×#399C2×C511yescharacteristic, complemented
131C3×#398C2×C511yescharacteristic, complemented
132C3×#396C2×C511yescharacteristic, complemented
133C3×#395C2×C511yescharacteristic, complemented
134C3×#389C2×C511yescharacteristic, complemented
135C3×#387C2×C511yescharacteristic, complemented
136C3×#386C2×C511yescharacteristic
137C3×#386C2×C511yescharacteristic
138C3×#385C2×C511yescharacteristic, complemented
139C3×#385C2×C511yescharacteristic, complemented
140C3×#385C2×C511yescharacteristic, complemented
141C22×C5×Q8C22×C311yescharacteristic
142C22×C5×D4C22×C311yescharacteristic
143C23×C4×C5C22×C311yescharacteristic
144C23×C4×C5C22×C311yescharacteristic
145C23×C4×C5C22×C311yescharacteristic
146C23×C4×C5C22×C311yescharacteristic
147C5×C22⋊Q8—24no—
148C5×C22⋊Q8—24no—
149C4×C5×D4—24no—
150C2×C5×C4⋊C4—24no—
151C2×C5×C4⋊C4C22×C311yescharacteristic
152C2×C5×C4⋊C4C22×C311yescharacteristic
153C2×C5×C4⋊C4C22×C311yescharacteristic
154C2×C5×C4⋊C4C22×C311yescharacteristic
155C2×C5×C4⋊C4C22×C311yescharacteristic
156C2×C5×C4⋊C4C22×C311yescharacteristic
157C2×C5×C4⋊C4C22×C311yescharacteristic
158C2×C5×C4⋊C4C22×C311yescharacteristic
159C2×C5×C4⋊C4C22×C311yescharacteristic
160C2×C5×C4⋊C4C22×C311yescharacteristic
161C2×C5×C4⋊C4C22×C311yescharacteristic
162C2×C5×C4⋊C4C22×C311yescharacteristic
163C2×C5×C22⋊C4C22×C311yescharacteristic
164C2×C5×C22⋊C4C22×C311yescharacteristic
165C2×C5×C22⋊C4C22×C311yescharacteristic
166C2×C5×C22⋊C4C22×C311yescharacteristic
167C2×C5×C22⋊C4C22×C311yescharacteristic
168C2×C5×C22⋊C4C22×C311yescharacteristic
169C2×C5×C22⋊C4C22×C311yescharacteristic
170C2×C5×C22⋊C4C22×C311yescharacteristic
171C2×C42×C5C22×C311yescharacteristic
172C5×#95C22×C311yescharacteristic
173C5×#95C22×C311yescharacteristic
174C5×#95C22×C311yescharacteristic
175C5×#95C22×C311yescharacteristic
176C5×#95C22×C311yescharacteristic
177C5×#95C22×C311yescharacteristic
178C5×#95C22×C311yescharacteristic
179C5×#95C22×C311yescharacteristic
180#2449C3×C511yescharacteristic, direct product factor, Sylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5C2×D412yes—
192C23×C3×C5C2×Q812yes—
193C23×C3×C5C2×Q812yes—
194C23×C3×C5#4112yes—
195C23×C3×C5C2411yescharacteristic
196C3×C5×Q8—44no—
197C3×C5×D4—28no—
198C2×C3×C4×C5—28no—
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—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—44no—
232C2×C3×C4×C5—44no—
233C2×C3×C4×C5—44no—
234C2×C3×C4×C5C2×D412yes—
235C2×C3×C4×C5C2×D412yes—
236C2×C3×C4×C5C2×D412yes—
237C2×C3×C4×C5C2×D412yes—
238C2×C3×C4×C5C2×D412yes—
239C2×C3×C4×C5C2×Q812yes—
240C2×C3×C4×C5#4112yes—
241C22×C3×Q8C22×C511yescharacteristic
242C22×C3×D4C22×C511yescharacteristic
243C23×C3×C4C22×C511yescharacteristic
244C23×C3×C4C22×C511yescharacteristic
245C23×C3×C4C22×C511yescharacteristic
246C23×C3×C4C22×C511yescharacteristic
247C3×C22⋊Q8—24no—
248C3×C22⋊Q8—24no—
249C3×C4×D4—24no—
250C2×C3×C4⋊C4—24no—
251C2×C3×C4⋊C4C22×C511yescharacteristic
252C2×C3×C4⋊C4C22×C511yescharacteristic
253C2×C3×C4⋊C4C22×C511yescharacteristic
254C2×C3×C4⋊C4C22×C511yescharacteristic
255C2×C3×C4⋊C4C22×C511yescharacteristic
256C2×C3×C4⋊C4C22×C511yescharacteristic
257C2×C3×C4⋊C4C22×C511yescharacteristic
258C2×C3×C4⋊C4C22×C511yescharacteristic
259C2×C3×C4⋊C4C22×C511yescharacteristic
260C2×C3×C4⋊C4C22×C511yescharacteristic
261C2×C3×C4⋊C4C22×C511yescharacteristic
262C2×C3×C4⋊C4C22×C511yescharacteristic
263C2×C3×C22⋊C4C22×C511yescharacteristic
264C2×C3×C22⋊C4C22×C511yescharacteristic
265C2×C3×C22⋊C4C22×C511yescharacteristic
266C2×C3×C22⋊C4C22×C511yescharacteristic
267C2×C3×C22⋊C4C22×C511yescharacteristic
268C2×C3×C22⋊C4C22×C511yescharacteristic
269C2×C3×C22⋊C4C22×C511yescharacteristic
270C2×C3×C22⋊C4C22×C511yescharacteristic
271C2×C3×C42C22×C511yescharacteristic
272C3×#95C22×C511yescharacteristic
273C3×#95C22×C511yescharacteristic
274C3×#95C22×C511yescharacteristic
275C3×#95C22×C511yescharacteristic
276C3×#95C22×C511yescharacteristic
277C3×#95C22×C511yescharacteristic
278C3×#95C22×C511yescharacteristic
279C3×#95C22×C511yescharacteristic
280C24×C5C23×C311yescharacteristic
281C24×C5C23×C311yescharacteristic
282C2×C5×Q8—22no—
283C2×C5×Q8—22no—
284C2×C5×Q8—41no—
285C2×C5×D4—22no—
286C2×C5×D4—22no—
287C2×C5×D4C3×Q814yescomplemented
288C22×C4×C5—22no—
289C22×C4×C5—22no—
290C22×C4×C5—22no—
291C22×C4×C5—22no—
292C22×C4×C5—22no—
293C22×C4×C5—22no—
294C22×C4×C5—22no—
295C22×C4×C5—22no—
296C22×C4×C5—22no—
297C22×C4×C5—41no—
298C22×C4×C5—41no—
299C22×C4×C5—41no—
300C22×C4×C5C23×C311yescharacteristic
301C22×C4×C5C23×C311yescharacteristic
302C22×C4×C5C23×C311yescharacteristic
303C22×C4×C5C23×C311yescharacteristic
304C22×C4×C5C23×C311yescharacteristic
305C22×C4×C5C23×C311yescharacteristic
306C22×C4×C5C23×C311yescharacteristic
307C22×C4×C5C23×C311yescharacteristic
308C22×C4×C5C23×C311yescharacteristic
309C22×C4×C5C23×C311yescharacteristic
310C22×C4×C5C23×C311yescharacteristic
311C22×C4×C5C23×C311yescharacteristic
312C22×C4×C5C23×C311yescharacteristic
313C5×C4⋊C4—22no—
314C5×C4⋊C4—22no—
315C5×C4⋊C4—22no—
316C5×C4⋊C4—22no—
317C5×C4⋊C4—22no—
318C5×C4⋊C4—22no—
319C5×C4⋊C4—22no—
320C5×C4⋊C4—22no—
321C5×C4⋊C4—22no—
322C5×C4⋊C4—22no—
323C5×C4⋊C4—41no—
324C5×C4⋊C4C3×D414yescomplemented
325C5×C22⋊C4—22no—
326C5×C22⋊C4—22no—
327C5×C22⋊C4—22no—
328C5×C22⋊C4—22no—
329C5×C22⋊C4—22no—
330C5×C22⋊C4—22no—
331C5×C22⋊C4—41no—
332C5×C22⋊C4C3×D414yes—
333C42×C5—22no—
334C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
335C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
336C2×C4×D4C2×C3×C511yescharacteristic
337C22×C4⋊C4C2×C3×C511yescharacteristic, complemented
338#399C2×C3×C511yescharacteristic, complemented
339#398C2×C3×C511yescharacteristic, complemented
340#396C2×C3×C511yescharacteristic, complemented
341#395C2×C3×C511yescharacteristic, complemented
342#389C2×C3×C511yescharacteristic, complemented
343#387C2×C3×C511yescharacteristic, complemented
344#386C2×C3×C511yescharacteristic
345#386C2×C3×C511yescharacteristic
346#385C2×C3×C511yescharacteristic, complemented
347#385C2×C3×C511yescharacteristic, complemented
348#385C2×C3×C511yescharacteristic, complemented
349C22×C3×C5—22no—
350C22×C3×C5—22no—
351C22×C3×C5—22no—
352C22×C3×C5—22no—
353C22×C3×C5—22no—
354C22×C3×C5—22no—
355C22×C3×C5—22no—
356C22×C3×C5—22no—
357C22×C3×C5—22no—
358C22×C3×C5—41no—
359C22×C3×C5—41no—
360C22×C3×C5—41no—
361C22×C3×C5—41no—
362C22×C3×C5C22⋊Q814yescomplemented
363C22×C3×C5C22×D411yescharacteristic
364C22×C3×C5C22×D411yescharacteristic
365C22×C3×C5C22×Q811yescharacteristic
366C22×C3×C5C2×#4111yescharacteristic
367C22×C3×C5C2×#4111yescharacteristic
368C22×C3×C5H(5,𝔽2)11yescharacteristic
369C22×C3×C52−1+411yescharacteristic
370C3×C4×C5—22no—
371C3×C4×C5—22no—
372C3×C4×C5—22no—
373C3×C4×C5—22no—
374C3×C4×C5—22no—
375C3×C4×C5—22no—
376C3×C4×C5—22no—
377C3×C4×C5—41no—
378C3×C4×C5—41no—
379C3×C4×C5—41no—
380C3×C4×C5—41no—
381C3×C4×C5—41no—
382C3×C4×C5—41no—
383C24×C3C23×C511yescharacteristic
384C24×C3C23×C511yescharacteristic
385C2×C3×Q8—22no—
386C2×C3×Q8—22no—
387C2×C3×Q8—41no—
388C2×C3×D4—22no—
389C2×C3×D4—22no—
390C2×C3×D4C5×Q814yescomplemented
391C22×C3×C4—22no—
392C22×C3×C4—22no—
393C22×C3×C4—22no—
394C22×C3×C4—22no—
395C22×C3×C4—22no—
396C22×C3×C4—22no—
397C22×C3×C4—22no—
398C22×C3×C4—22no—
399C22×C3×C4—22no—
400C22×C3×C4—41no—
401C22×C3×C4—41no—
402C22×C3×C4—41no—
403C22×C3×C4C23×C511yescharacteristic
404C22×C3×C4C23×C511yescharacteristic
405C22×C3×C4C23×C511yescharacteristic
406C22×C3×C4C23×C511yescharacteristic
407C22×C3×C4C23×C511yescharacteristic
408C22×C3×C4C23×C511yescharacteristic
409C22×C3×C4C23×C511yescharacteristic
410C22×C3×C4C23×C511yescharacteristic
411C22×C3×C4C23×C511yescharacteristic
412C22×C3×C4C23×C511yescharacteristic
413C22×C3×C4C23×C511yescharacteristic
414C22×C3×C4C23×C511yescharacteristic
415C22×C3×C4C23×C511yescharacteristic
416C3×C4⋊C4—22no—
417C3×C4⋊C4—22no—
418C3×C4⋊C4—22no—
419C3×C4⋊C4—22no—
420C3×C4⋊C4—22no—
421C3×C4⋊C4—22no—
422C3×C4⋊C4—22no—
423C3×C4⋊C4—22no—
424C3×C4⋊C4—22no—
425C3×C4⋊C4—22no—
426C3×C4⋊C4—41no—
427C3×C4⋊C4C5×D414yescomplemented
428C3×C22⋊C4—22no—
429C3×C22⋊C4—22no—
430C3×C22⋊C4—22no—
431C3×C22⋊C4—22no—
432C3×C22⋊C4—22no—
433C3×C22⋊C4—22no—
434C3×C22⋊C4—41no—
435C3×C22⋊C4C5×D414yes—
436C3×C42—22no—
437C23×C5—21no—
438C23×C5—21no—
439C23×C5—21no—
440C23×C5—21no—
441C23×C5—21no—
442C23×C5—21no—
443C23×C5—21no—
444C23×C5—21no—
445C23×C5—21no—
446C23×C5—21no—
447C23×C5C2×C3×D412yes—
448C23×C5C2×C3×Q812yes—
449C23×C5C2×C3×Q812yes—
450C23×C5C3×#4112yes—
451C23×C5C24×C311yescharacteristic
452C5×Q8—44no—
453C5×D4—28no—
454C2×C4×C5—28no—
455C2×C4×C5—21no—
456C2×C4×C5—21no—
457C2×C4×C5—21no—
458C2×C4×C5—21no—
459C2×C4×C5—21no—
460C2×C4×C5—21no—
461C2×C4×C5—21no—
462C2×C4×C5—21no—
463C2×C4×C5—21no—
464C2×C4×C5—21no—
465C2×C4×C5—21no—
466C2×C4×C5—21no—
467C2×C4×C5—21no—
468C2×C4×C5—21no—
469C2×C4×C5—21no—
470C2×C4×C5—21no—
471C2×C4×C5—21no—
472C2×C4×C5—21no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5—44no—
488C2×C4×C5—44no—
489C2×C4×C5—44no—
490C2×C4×C5C2×C3×D412yes—
491C2×C4×C5C2×C3×D412yes—
492C2×C4×C5C2×C3×D412yes—
493C2×C4×C5C2×C3×D412yes—
494C2×C4×C5C2×C3×D412yes—
495C2×C4×C5C2×C3×Q812yes—
496C2×C4×C5C3×#4112yes—
497C22×Q8C22×C3×C511yescharacteristic
498C22×D4C22×C3×C511yescharacteristic
499C23×C4C22×C3×C511yescharacteristic
500C23×C4C22×C3×C511yescharacteristic
501C23×C4C22×C3×C511yescharacteristic
502C23×C4C22×C3×C511yescharacteristic
503C22⋊Q8—24no—
504C22⋊Q8—24no—
505C4×D4—24no—
506C2×C4⋊C4—24no—
507C2×C4⋊C4C22×C3×C511yescharacteristic
508C2×C4⋊C4C22×C3×C511yescharacteristic
509C2×C4⋊C4C22×C3×C511yescharacteristic
510C2×C4⋊C4C22×C3×C511yescharacteristic
511C2×C4⋊C4C22×C3×C511yescharacteristic
512C2×C4⋊C4C22×C3×C511yescharacteristic
513C2×C4⋊C4C22×C3×C511yescharacteristic
514C2×C4⋊C4C22×C3×C511yescharacteristic
515C2×C4⋊C4C22×C3×C511yescharacteristic
516C2×C4⋊C4C22×C3×C511yescharacteristic
517C2×C4⋊C4C22×C3×C511yescharacteristic
518C2×C4⋊C4C22×C3×C511yescharacteristic
519C2×C22⋊C4C22×C3×C511yescharacteristic
520C2×C22⋊C4C22×C3×C511yescharacteristic
521C2×C22⋊C4C22×C3×C511yescharacteristic
522C2×C22⋊C4C22×C3×C511yescharacteristic
523C2×C22⋊C4C22×C3×C511yescharacteristic
524C2×C22⋊C4C22×C3×C511yescharacteristic
525C2×C22⋊C4C22×C3×C511yescharacteristic
526C2×C22⋊C4C22×C3×C511yescharacteristic
527C2×C42C22×C3×C511yescharacteristic
528#95C22×C3×C511yescharacteristic
529#95C22×C3×C511yescharacteristic
530#95C22×C3×C511yescharacteristic
531#95C22×C3×C511yescharacteristic
532#95C22×C3×C511yescharacteristic
533#95C22×C3×C511yescharacteristic
534#95C22×C3×C511yescharacteristic
535#95C22×C3×C511yescharacteristic
536C2×C3×C5—24no—
537C2×C3×C5—42no—
538C2×C3×C5C2×C22⋊Q811yescharacteristic
539C2×C3×C5#52511yescharacteristic
540C2×C3×C5#53911yescharacteristic
541C2×C3×C5D4211yescharacteristic
542C2×C3×C5#54711yescharacteristic
543C2×C3×C5D4×Q811yescharacteristic
544C2×C3×C5#55411yescharacteristic
545C23×C3—21no—
546C23×C3—21no—
547C23×C3—21no—
548C23×C3—21no—
549C23×C3—21no—
550C23×C3—21no—
551C23×C3—21no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3C2×C5×D412yes—
556C23×C3C2×C5×Q812yes—
557C23×C3C2×C5×Q812yes—
558C23×C3C5×#4112yes—
559C23×C3C24×C511yescharacteristic
560C3×Q8—44no—
561C3×D4—28no—
562C2×C3×C4—28no—
563C2×C3×C4—21no—
564C2×C3×C4—21no—
565C2×C3×C4—21no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—44no—
596C2×C3×C4—44no—
597C2×C3×C4—44no—
598C2×C3×C4C2×C5×D412yes—
599C2×C3×C4C2×C5×D412yes—
600C2×C3×C4C2×C5×D412yes—
601C2×C3×C4C2×C5×D412yes—
602C2×C3×C4C2×C5×D412yes—
603C2×C3×C4C2×C5×Q812yes—
604C2×C3×C4C5×#4112yes—
605C22×C5—22no—
606C22×C5—22no—
607C22×C5—22no—
608C22×C5—22no—
609C22×C5—22no—
610C22×C5—22no—
611C22×C5—22no—
612C22×C5—22no—
613C22×C5—22no—
614C22×C5—41no—
615C22×C5—41no—
616C22×C5—41no—
617C22×C5—41no—
618C22×C5C3×C22⋊Q814yescomplemented
619C22×C5C22×C3×D411yescharacteristic
620C22×C5C22×C3×D411yescharacteristic
621C22×C5C22×C3×Q811yescharacteristic
622C22×C5C2×C3×#4111yescharacteristic
623C22×C5C2×C3×#4111yescharacteristic
624C22×C5C3×H(5,𝔽2)11yescharacteristic
625C22×C5C3×2−1+411yescharacteristic
626C4×C5—22no—
627C4×C5—22no—
628C4×C5—22no—
629C4×C5—22no—
630C4×C5—22no—
631C4×C5—22no—
632C4×C5—22no—
633C4×C5—41no—
634C4×C5—41no—
635C4×C5—41no—
636C4×C5—41no—
637C4×C5—41no—
638C4×C5—41no—
639C24C23×C3×C511yescharacteristic
640C24C23×C3×C511yescharacteristic
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8—41no—
644C2×D4—22no—
645C2×D4—22no—
646C2×D4C3×C5×Q814yescomplemented
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—41no—
657C22×C4—41no—
658C22×C4—41no—
659C22×C4C23×C3×C511yescharacteristic
660C22×C4C23×C3×C511yescharacteristic
661C22×C4C23×C3×C511yescharacteristic
662C22×C4C23×C3×C511yescharacteristic
663C22×C4C23×C3×C511yescharacteristic
664C22×C4C23×C3×C511yescharacteristic
665C22×C4C23×C3×C511yescharacteristic
666C22×C4C23×C3×C511yescharacteristic
667C22×C4C23×C3×C511yescharacteristic
668C22×C4C23×C3×C511yescharacteristic
669C22×C4C23×C3×C511yescharacteristic
670C22×C4C23×C3×C511yescharacteristic
671C22×C4C23×C3×C511yescharacteristic
672C4⋊C4—22no—
673C4⋊C4—22no—
674C4⋊C4—22no—
675C4⋊C4—22no—
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—22no—
681C4⋊C4—22no—
682C4⋊C4—41no—
683C4⋊C4C3×C5×D414yescomplemented
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—22no—
690C22⋊C4—41no—
691C22⋊C4C3×C5×D414yes—
692C42—22no—
693C3×C5#244911yescharacteristic, direct product factor, Hall
694C22×C3—22no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—41no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3C5×C22⋊Q814yescomplemented
708C22×C3C22×C5×D411yescharacteristic
709C22×C3C22×C5×D411yescharacteristic
710C22×C3C22×C5×Q811yescharacteristic
711C22×C3C2×C5×#4111yescharacteristic
712C22×C3C2×C5×#4111yescharacteristic
713C22×C3C5×H(5,𝔽2)11yescharacteristic
714C22×C3C5×2−1+411yescharacteristic
715C3×C4—22no—
716C3×C4—22no—
717C3×C4—22no—
718C3×C4—22no—
719C3×C4—22no—
720C3×C4—22no—
721C3×C4—22no—
722C3×C4—41no—
723C3×C4—41no—
724C3×C4—41no—
725C3×C4—41no—
726C3×C4—41no—
727C3×C4—41no—
728C2×C5—24no—
729C2×C5—42no—
730C2×C5C2×C3×C22⋊Q811yescharacteristic
731C2×C5C3×#52511yescharacteristic
732C2×C5C3×#53911yescharacteristic
733C2×C5C3×D4211yescharacteristic
734C2×C5C3×#54711yescharacteristic
735C2×C5C3×D4×Q811yescharacteristic
736C2×C5C3×#55411yescharacteristic
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23C2×C3×C5×D412yes—
748C23C2×C3×C5×Q812yes—
749C23C2×C3×C5×Q812yes—
750C23C3×C5×#4112yes—
751C23C24×C3×C511yescharacteristic
752Q8—44no—
753D4—28no—
754C2×C4—28no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—44no—
788C2×C4—44no—
789C2×C4—44no—
790C2×C4C2×C3×C5×D412yes—
791C2×C4C2×C3×C5×D412yes—
792C2×C4C2×C3×C5×D412yes—
793C2×C4C2×C3×C5×D412yes—
794C2×C4C2×C3×C5×D412yes—
795C2×C4C2×C3×C5×Q812yes—
796C2×C4C3×C5×#4112yes—
797C2×C3—24no—
798C2×C3—42no—
799C2×C3C2×C5×C22⋊Q811yescharacteristic
800C2×C3C5×#52511yescharacteristic
801C2×C3C5×#53911yescharacteristic
802C2×C3C5×D4211yescharacteristic
803C2×C3C5×#54711yescharacteristic
804C2×C3C5×D4×Q811yescharacteristic
805C2×C3C5×#55411yescharacteristic
806C5C3×#244911yescharacteristic, direct product factor, Sylow
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22C3×C5×C22⋊Q814yescomplemented
821C22C22×C3×C5×D411yescharacteristic
822C22C22×C3×C5×D411yescharacteristic
823C22C22×C3×C5×Q811yescharacteristic
824C22C2×C3×C5×#4111yescharacteristic
825C22C2×C3×C5×#4111yescharacteristic
826C22C3×C5×H(5,𝔽2)11yescharacteristic
827C22C3×C5×2−1+411yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—22no—
833C4—22no—
834C4—22no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—41no—
840C4—41no—
841C3C5×#244911yescharacteristic, direct product factor, Sylow
842C2—24no—
843C2—42no—
844C2C2×C3×C5×C22⋊Q811yescharacteristic
845C2C3×C5×#52511yescharacteristic
846C2C3×C5×#53911yescharacteristic
847C2C3×C5×D4211yescharacteristic
848C2C3×C5×#54711yescharacteristic
849C2C3×C5×D4×Q811yescharacteristic
850C2C3×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×#399C2semidirect
6. C3×C5×#398C2semidirect
7. C3×C5×#396C2semidirect
8. C3×C5×#395C2semidirect
9. C3×C5×#389C2semidirect
10. C3×C5×#387C2semidirect
13. C3×C5×#385C2semidirect
14. C3×C5×#385C2semidirect
15. C3×C5×#385C2semidirect
16. C5×#2449C3direct (N × H)
56. C3×#2449C5direct (N × H)
57. C2×C5×C22⋊Q8C2×C3semidirect
58. C2×C5×C22⋊Q8C2×C3semidirect
60. C22×C5×C4⋊C4C2×C3semidirect
61. C5×#399C2×C3semidirect
62. C5×#398C2×C3semidirect
63. C5×#396C2×C3semidirect
64. C5×#395C2×C3semidirect
65. C5×#389C2×C3semidirect
66. C5×#387C2×C3semidirect
69. C5×#385C2×C3semidirect
70. C5×#385C2×C3semidirect
71. C5×#385C2×C3semidirect
79. C2×C3×C5×D4Q8semidirect
116. C3×C5×C4⋊C4D4semidirect
126. C2×C3×C22⋊Q8C2×C5semidirect
127. C2×C3×C22⋊Q8C2×C5semidirect
129. C22×C3×C4⋊C4C2×C5semidirect
130. C3×#399C2×C5semidirect
131. C3×#398C2×C5semidirect
132. C3×#396C2×C5semidirect
133. C3×#395C2×C5semidirect
134. C3×#389C2×C5semidirect
135. C3×#387C2×C5semidirect
138. C3×#385C2×C5semidirect
139. C3×#385C2×C5semidirect
140. C3×#385C2×C5semidirect
180. #2449C3×C5direct (N × H)
287. C2×C5×D4C3×Q8semidirect
324. C5×C4⋊C4C3×D4semidirect
334. C2×C22⋊Q8C2×C3×C5semidirect
335. C2×C22⋊Q8C2×C3×C5semidirect
337. C22×C4⋊C4C2×C3×C5semidirect
338. #399C2×C3×C5semidirect
339. #398C2×C3×C5semidirect
340. #396C2×C3×C5semidirect
341. #395C2×C3×C5semidirect
342. #389C2×C3×C5semidirect
343. #387C2×C3×C5semidirect
346. #385C2×C3×C5semidirect
347. #385C2×C3×C5semidirect
348. #385C2×C3×C5semidirect
362. C22×C3×C5C22⋊Q8semidirect
390. C2×C3×D4C5×Q8semidirect
427. C3×C4⋊C4C5×D4semidirect
618. C22×C5C3×C22⋊Q8semidirect
646. C2×D4C3×C5×Q8semidirect
683. C4⋊C4C3×C5×D4semidirect
693. C3×C5#2449direct (N × H)
707. C22×C3C5×C22⋊Q8semidirect
806. C5C3×#2449direct (N × H)
820. C22C3×C5×C22⋊Q8semidirect
841. C3C5×#2449direct (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×#3992
C3×C5×#3982
C3×C5×#3962
C3×C5×#3952
C3×C5×#3892
C3×C5×#3872
C3×C5×#3862
C3×C5×#3852
C5×#24493
C3×#24495