Finite Group Databasebeta

← C3×D5×#388 #14320433

Subgroups — C3×D5×#388 #14320433

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
2C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
4C2×C3×D5×C22⋊C4C211yesmaximal, characteristic
5C2×C3×C42×D5C211yesmaximal, characteristic, complemented
6C3×C5×#388C211yesmaximal, characteristic, complemented
7C3×#65279C211yesmaximal, characteristic, complemented
8C3×#65240C211yesmaximal, characteristic, complemented
9C3×#65234C211yesmaximal, characteristic, complemented
10C3×#65233C211yesmaximal, characteristic, complemented
11C3×#65229C211yesmaximal, characteristic, complemented
12C3×#64959C211yesmaximal, characteristic, complemented
13C3×#64958C211yesmaximal, characteristic, complemented
14C3×D5×#95C211yesmaximal, characteristic, complemented
15C3×D5×#95C211yesmaximal, characteristic, complemented
16D5×#388C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic, complemented
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
39C2×C3×#683C2211yescharacteristic, complemented
40C2×C3×#683C2211yescharacteristic, complemented
41C2×C3×C4×Dic5C2211yescharacteristic, complemented
42C2×C3×C4×Dic5C2211yescharacteristic, complemented
43C2×C3×C4×Dic5C2211yescharacteristic, complemented
44C3×D5×C4⋊C4—24no—
45C3×D5×C22⋊C4—24no—
46C3×D5×C22⋊C4—24no—
47C3×D5×C22⋊C4C418yescomplemented
48C3×C42×D5—24no—
49C3×C5×#95C2211yescharacteristic, complemented
50C3×C5×#95C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55C3×#3963C2211yescharacteristic, complemented
56C3×#3963C2211yescharacteristic, complemented
57C2×C3×#388—51nomaximal, Hall
58C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
59C2×D5×C22⋊C4C2×C311yescharacteristic
60C2×D5×C22⋊C4C2×C311yescharacteristic
61C2×D5×C22⋊C4C2×C311yescharacteristic
62C2×C42×D5C2×C311yescharacteristic, complemented
63C5×#388C2×C311yescharacteristic, complemented
64#65279C2×C311yescharacteristic, complemented
65#65240C2×C311yescharacteristic, complemented
66#65234C2×C311yescharacteristic, complemented
67#65233C2×C311yescharacteristic, complemented
68#65229C2×C311yescharacteristic, complemented
69#64959C2×C311yescharacteristic, complemented
70#64958C2×C311yescharacteristic, complemented
71D5×#95C2×C311yescharacteristic, complemented
72D5×#95C2×C311yescharacteristic, complemented
73C24×C3×C5C2311yescharacteristic
74C23×C3×D5—22no—
75C23×C3×D5—22no—
76C23×C3×D5—22no—
77C23×C3×D5—22no—
78C23×C3×D5—22no—
79C23×C3×D5—22no—
80C23×C3×D5C2×C414yes—
81C23×C3×D5C2311yescharacteristic
82C23×C3×D5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×C3×C4×D5—22no—
96C2×C3×C4×D5—22no—
97C2×C3×C4×D5—22no—
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5—22no—
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—22no—
106C2×C3×C4×D5—22no—
107C2×C3×C4×D5—22no—
108C2×C3×C4×D5—22no—
109C2×C3×C4×D5C2×C414yes—
110C2×C3×C4×D5C2×C414yes—
111C2×C3×C4×D5D414yes—
112C2×C3×C4×D5D414yes—
113C3×C5×C4⋊C4—22no—
114C3×C5×C22⋊C4—22no—
115C3×C5×C22⋊C4—22no—
116C3×C5×C22⋊C4C2×C414yescomplemented
117C3×C42×C5—22no—
118C3×C22⋊Dic5—22no—
119C3×C22⋊Dic5—22no—
120C3×C22⋊Dic5C2×C414yescomplemented
121C3×#685—22no—
122C3×#685—22no—
123C3×#685—22no—
124C3×#685—22no—
125C3×#685C2×C414yescomplemented
126C3×#685C2×C414yescomplemented
127C3×C4⋊Dic5—22no—
128C3×#683—22no—
129C3×#683—22no—
130C3×C4×Dic5—22no—
131C3×C4×Dic5—22no—
132C3×C4×Dic5—22no—
133C22×C3×C4⋊C4—51no—
134C22×C3×C22⋊C4—51no—
135C22×C3×C22⋊C4—51no—
136C22×C3×C22⋊C4—51no—
137C22×C3×C42—51no—
138C3×#388—51no—
139C3×#388—51no—
140C3×#388—51no—
141C3×#388—51no—
142C3×#388—51no—
143C3×#388—51no—
144C3×#388—51no—
145C3×#388D511yescharacteristic, direct product factor
146C2×C3×#95—51no—
147C2×C3×#95—51no—
148C24×D5C22×C311yescharacteristic
149C22×C4×D5C22×C311yescharacteristic
150C22×C4×D5C22×C311yescharacteristic
151C22×C4×D5C22×C311yescharacteristic
152C22×C4×D5C22×C311yescharacteristic
153C22×C4×D5C22×C311yescharacteristic
154C22×C4×D5C22×C311yescharacteristic
155C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
156C2×C5×C22⋊C4C22×C311yescharacteristic
157C2×C5×C22⋊C4C22×C311yescharacteristic
158C2×C5×C22⋊C4C22×C311yescharacteristic
159C2×C42×C5C22×C311yescharacteristic, complemented
160C2×C22⋊Dic5C22×C311yescharacteristic
161C2×C22⋊Dic5C22×C311yescharacteristic
162C2×C22⋊Dic5C22×C311yescharacteristic
163C2×#685C22×C311yescharacteristic
164C2×#685C22×C311yescharacteristic
165C2×#685C22×C311yescharacteristic
166C2×#685C22×C311yescharacteristic
167C2×#685C22×C311yescharacteristic
168C2×#685C22×C311yescharacteristic
169C2×C4⋊Dic5C22×C311yescharacteristic, complemented
170C2×#683C22×C311yescharacteristic, complemented
171C2×#683C22×C311yescharacteristic, complemented
172C2×C4×Dic5C22×C311yescharacteristic, complemented
173C2×C4×Dic5C22×C311yescharacteristic, complemented
174C2×C4×Dic5C22×C311yescharacteristic, complemented
175D5×C4⋊C4—24no—
176D5×C22⋊C4—24no—
177D5×C22⋊C4—24no—
178D5×C22⋊C4C3×C418yescomplemented
179C42×D5—24no—
180C5×#95C22×C311yescharacteristic, complemented
181C5×#95C22×C311yescharacteristic, complemented
182#3963C22×C311yescharacteristic, complemented
183#3963C22×C311yescharacteristic, complemented
184#3963C22×C311yescharacteristic, complemented
185#3963C22×C311yescharacteristic, complemented
186#3963C22×C311yescharacteristic, complemented
187#3963C22×C311yescharacteristic, complemented
188C2×#388—51noSylow
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5C22×C412yes—
196C23×C3×C5C2411yescharacteristic
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—28no—
204C22×C3×D5—28no—
205C22×C3×D5—28no—
206C22×C3×D5—44no—
207C22×C3×D5—44no—
208C22×C3×D5—44no—
209C22×C3×D5—44no—
210C22×C3×D5C22×C412yes—
211C22×C3×D5C22×C412yes—
212C22×C3×D5C2×D412yes—
213C22×C3×D5C2×D412yes—
214C22×C3×D5#4112yes—
215C22×C3×D5#4112yes—
216C22×C3×D5#4112yes—
217C22×C3×D5#4112yes—
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—21no—
232C2×C3×C4×C5C22×C412yes—
233C2×C3×C4×C5C22×C412yes—
234C2×C3×C4×C5C2×D412yes—
235C2×C3×C4×C5C2×D412yes—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5C22×C412yes—
251C2×C3×Dic5C22×C412yes—
252C2×C3×Dic5C2×D412yes—
253C2×C3×Dic5C2×D412yes—
254C3×C4×D5—28no—
255C3×C4×D5—28no—
256C3×C4×D5—28no—
257C3×C4×D5—28no—
258C3×C4×D5—44no—
259C3×C4×D5—44no—
260C25×C3—51no—
261C23×C3×C4—51no—
262C23×C3×C4—51no—
263C23×C3×C4—51no—
264C23×C3×C4—51no—
265C23×C3×C4—51no—
266C23×C3×C4—51no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C4⋊C4—104no—
271C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
272C2×C3×C22⋊C4—51no—
273C2×C3×C22⋊C4—51no—
274C2×C3×C22⋊C4—51no—
275C2×C3×C22⋊C4—58no—
276C2×C3×C22⋊C4—51no—
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—104no—
283C2×C3×C22⋊C4—104no—
284C2×C3×C22⋊C4C2×D511yescharacteristic
285C2×C3×C22⋊C4C2×D511yescharacteristic
286C2×C3×C22⋊C4C2×D511yescharacteristic
287C2×C3×C42—51no—
288C2×C3×C42—51no—
289C2×C3×C42—51no—
290C2×C3×C42—104no—
291C2×C3×C42C2×D511yescharacteristic, complemented
292C3×#95—51no—
293C3×#95—51no—
294C3×#95—51no—
295C3×#95—51no—
296C3×#95—51no—
297C3×#95—51no—
298C3×#95C2×D511yescharacteristic, complemented
299C3×#95C2×D511yescharacteristic, complemented
300C24×C5C23×C311yescharacteristic
301C23×D5—22no—
302C23×D5—22no—
303C23×D5—22no—
304C23×D5—22no—
305C23×D5—22no—
306C23×D5—22no—
307C23×D5C2×C3×C414yes—
308C23×D5C23×C311yescharacteristic
309C23×D5C23×C311yescharacteristic
310C22×C4×C5C23×C311yescharacteristic
311C22×C4×C5C23×C311yescharacteristic
312C22×C4×C5C23×C311yescharacteristic
313C22×C4×C5C23×C311yescharacteristic
314C22×C4×C5C23×C311yescharacteristic
315C22×C4×C5C23×C311yescharacteristic
316C22×Dic5C23×C311yescharacteristic
317C22×Dic5C23×C311yescharacteristic
318C22×Dic5C23×C311yescharacteristic
319C22×Dic5C23×C311yescharacteristic
320C22×Dic5C23×C311yescharacteristic
321C22×Dic5C23×C311yescharacteristic
322C2×C4×D5—22no—
323C2×C4×D5—22no—
324C2×C4×D5—22no—
325C2×C4×D5—22no—
326C2×C4×D5—22no—
327C2×C4×D5—22no—
328C2×C4×D5—22no—
329C2×C4×D5—22no—
330C2×C4×D5—22no—
331C2×C4×D5—22no—
332C2×C4×D5—22no—
333C2×C4×D5—22no—
334C2×C4×D5—22no—
335C2×C4×D5—22no—
336C2×C4×D5C2×C3×C414yes—
337C2×C4×D5C2×C3×C414yes—
338C2×C4×D5C3×D414yes—
339C2×C4×D5C3×D414yes—
340C5×C4⋊C4—22no—
341C5×C22⋊C4—22no—
342C5×C22⋊C4—22no—
343C5×C22⋊C4C2×C3×C414yescomplemented
344C42×C5—22no—
345C22⋊Dic5—22no—
346C22⋊Dic5—22no—
347C22⋊Dic5C2×C3×C414yescomplemented
348#685—22no—
349#685—22no—
350#685—22no—
351#685—22no—
352#685C2×C3×C414yescomplemented
353#685C2×C3×C414yescomplemented
354C4⋊Dic5—22no—
355#683—22no—
356#683—22no—
357C4×Dic5—22no—
358C4×Dic5—22no—
359C4×Dic5—22no—
360C22×C4⋊C4—51no—
361C22×C22⋊C4—51no—
362C22×C22⋊C4—51no—
363C22×C22⋊C4—51no—
364C22×C42—51no—
365#388—51no—
366#388—51no—
367#388—51no—
368#388—51no—
369#388—51no—
370#388—51no—
371#388—51no—
372#388C3×D511yescharacteristic, direct product factor
373C2×#95—51no—
374C2×#95—51no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5C23×C411yescharacteristic
383C22×C3×C5C22×D411yescharacteristic
384C22×C3×C5C22×D411yescharacteristic
385C22×C3×C5C2×#4111yescharacteristic
386C22×C3×C5C2×#4111yescharacteristic
387C22×C3×C5C2×#4111yescharacteristic
388C22×C3×C5C2×#4111yescharacteristic
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—416no—
397C2×C3×D5#11714yes—
398C2×C3×D5C4×D414yes—
399C2×C3×D5C4×D414yes—
400C2×C3×D5#12114yes—
401C2×C3×D5#12314yes—
402C2×C3×D5#12414yes—
403C2×C3×D5#12614yes—
404C3×C4×C5—22no—
405C3×C4×C5—22no—
406C3×C4×C5—22no—
407C3×C4×C5—22no—
408C3×C4×C5—41no—
409C3×C4×C5—41no—
410C3×Dic5—22no—
411C3×Dic5—22no—
412C3×Dic5—22no—
413C3×Dic5—22no—
414C3×Dic5—41no—
415C3×Dic5—41no—
416C24×C3—51no—
417C24×C3—54no—
418C24×C3—51no—
419C24×C3—102no—
420C24×C3—102no—
421C24×C3—102no—
422C24×C3—102no—
423C24×C3—102no—
424C24×C3—102no—
425C24×C3C22×D511yescharacteristic
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4—54no—
431C22×C3×C4—54no—
432C22×C3×C4—54no—
433C22×C3×C4—54no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—102no—
437C22×C3×C4—102no—
438C22×C3×C4—102no—
439C22×C3×C4—102no—
440C22×C3×C4—102no—
441C22×C3×C4—102no—
442C22×C3×C4—102no—
443C22×C3×C4—102no—
444C22×C3×C4—102no—
445C22×C3×C4—102no—
446C22×C3×C4—102no—
447C22×C3×C4—102no—
448C22×C3×C4—102no—
449C22×C3×C4—102no—
450C22×C3×C4C22×D511yescharacteristic
451C22×C3×C4C22×D511yescharacteristic
452C22×C3×C4C22×D511yescharacteristic
453C22×C3×C4C22×D511yescharacteristic
454C22×C3×C4C22×D511yescharacteristic
455C22×C3×C4C22×D511yescharacteristic
456C3×C4⋊C4—22no—
457C3×C4⋊C4—102no—
458C3×C4⋊C4—102no—
459C3×C4⋊C4—102no—
460C3×C22⋊C4—22no—
461C3×C22⋊C4—22no—
462C3×C22⋊C4—54no—
463C3×C22⋊C4—54no—
464C3×C22⋊C4—54no—
465C3×C22⋊C4—102no—
466C3×C22⋊C4—102no—
467C3×C22⋊C4—102no—
468C3×C22⋊C4—102no—
469C3×C22⋊C4—102no—
470C3×C22⋊C4—102no—
471C3×C22⋊C4C4×D514yescomplemented
472C3×C42—22no—
473C3×C42—102no—
474C3×C42—102no—
475C3×C42—102no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5C22×C3×C412yes—
483C23×C5C24×C311yescharacteristic
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—21no—
490C22×D5—28no—
491C22×D5—28no—
492C22×D5—28no—
493C22×D5—44no—
494C22×D5—44no—
495C22×D5—44no—
496C22×D5—44no—
497C22×D5C22×C3×C412yes—
498C22×D5C22×C3×C412yes—
499C22×D5C2×C3×D412yes—
500C22×D5C2×C3×D412yes—
501C22×D5C3×#4112yes—
502C22×D5C3×#4112yes—
503C22×D5C3×#4112yes—
504C22×D5C3×#4112yes—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—21no—
512C2×C4×C5—21no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—21no—
516C2×C4×C5—21no—
517C2×C4×C5—21no—
518C2×C4×C5—21no—
519C2×C4×C5C22×C3×C412yes—
520C2×C4×C5C22×C3×C412yes—
521C2×C4×C5C2×C3×D412yes—
522C2×C4×C5C2×C3×D412yes—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—21no—
530C2×Dic5—21no—
531C2×Dic5—21no—
532C2×Dic5—21no—
533C2×Dic5—21no—
534C2×Dic5—21no—
535C2×Dic5—21no—
536C2×Dic5—21no—
537C2×Dic5C22×C3×C412yes—
538C2×Dic5C22×C3×C412yes—
539C2×Dic5C2×C3×D412yes—
540C2×Dic5C2×C3×D412yes—
541C4×D5—28no—
542C4×D5—28no—
543C4×D5—28no—
544C4×D5—28no—
545C4×D5—44no—
546C4×D5—44no—
547C25—51no—
548C23×C4—51no—
549C23×C4—51no—
550C23×C4—51no—
551C23×C4—51no—
552C23×C4—51no—
553C23×C4—51no—
554C2×C4⋊C4—51no—
555C2×C4⋊C4—51no—
556C2×C4⋊C4—51no—
557C2×C4⋊C4—104no—
558C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
559C2×C22⋊C4—51no—
560C2×C22⋊C4—51no—
561C2×C22⋊C4—51no—
562C2×C22⋊C4—58no—
563C2×C22⋊C4—51no—
564C2×C22⋊C4—51no—
565C2×C22⋊C4—51no—
566C2×C22⋊C4—51no—
567C2×C22⋊C4—51no—
568C2×C22⋊C4—51no—
569C2×C22⋊C4—104no—
570C2×C22⋊C4—104no—
571C2×C22⋊C4C2×C3×D511yescharacteristic
572C2×C22⋊C4C2×C3×D511yescharacteristic
573C2×C22⋊C4C2×C3×D511yescharacteristic
574C2×C42—51no—
575C2×C42—51no—
576C2×C42—51no—
577C2×C42—104no—
578C2×C42C2×C3×D511yescharacteristic, complemented
579#95—51no—
580#95—51no—
581#95—51no—
582#95—51no—
583#95—51no—
584#95—51no—
585#95C2×C3×D511yescharacteristic, complemented
586#95C2×C3×D511yescharacteristic, complemented
587C2×C3×C5—42no—
588C2×C3×C5C2×#11711yescharacteristic
589C2×C3×C5C2×C4×D411yescharacteristic
590C2×C3×C5C2×C4×D411yescharacteristic
591C2×C3×C5C2×#12111yescharacteristic
592C2×C3×C5C2×#12311yescharacteristic
593C2×C3×C5C2×#12411yescharacteristic
594C2×C3×C5C2×#12611yescharacteristic
595C3×D5—42no—
596C3×D5#38818yesdirect product factor
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—52no—
604C23×C3—52no—
605C23×C3—52no—
606C23×C3—52no—
607C23×C3—52no—
608C23×C3—52no—
609C23×C3—52no—
610C23×C3—52no—
611C23×C3—108no—
612C23×C3—108no—
613C23×C3—108no—
614C23×C3—101no—
615C23×C3—101no—
616C23×C3—101no—
617C23×C3—101no—
618C23×C3—101no—
619C23×C3—101no—
620C23×C3—204no—
621C23×C3—204no—
622C23×C3—204no—
623C23×C3—204no—
624C23×C3C2×C4×D512yes—
625C23×C3C23×D511yescharacteristic
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—52no—
641C2×C3×C4—52no—
642C2×C3×C4—52no—
643C2×C3×C4—52no—
644C2×C3×C4—108no—
645C2×C3×C4—108no—
646C2×C3×C4—108no—
647C2×C3×C4—108no—
648C2×C3×C4—101no—
649C2×C3×C4—101no—
650C2×C3×C4—101no—
651C2×C3×C4—101no—
652C2×C3×C4—101no—
653C2×C3×C4—101no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—101no—
660C2×C3×C4—101no—
661C2×C3×C4—101no—
662C2×C3×C4—204no—
663C2×C3×C4—204no—
664C2×C3×C4C2×C4×D512yes—
665C2×C3×C4C2×C4×D512yes—
666C2×C3×C4D4×D512yes—
667C2×C3×C4D4×D512yes—
668C22×C5—22no—
669C22×C5—22no—
670C22×C5—22no—
671C22×C5—41no—
672C22×C5—41no—
673C22×C5—41no—
674C22×C5—41no—
675C22×C5C23×C3×C411yescharacteristic
676C22×C5C22×C3×D411yescharacteristic
677C22×C5C22×C3×D411yescharacteristic
678C22×C5C2×C3×#4111yescharacteristic
679C22×C5C2×C3×#4111yescharacteristic
680C22×C5C2×C3×#4111yescharacteristic
681C22×C5C2×C3×#4111yescharacteristic
682C2×D5—22no—
683C2×D5—22no—
684C2×D5—22no—
685C2×D5—41no—
686C2×D5—41no—
687C2×D5—41no—
688C2×D5—41no—
689C2×D5—416no—
690C2×D5C3×#11714yes—
691C2×D5C3×C4×D414yes—
692C2×D5C3×C4×D414yes—
693C2×D5C3×#12114yes—
694C2×D5C3×#12314yes—
695C2×D5C3×#12414yes—
696C2×D5C3×#12614yes—
697C4×C5—22no—
698C4×C5—22no—
699C4×C5—22no—
700C4×C5—22no—
701C4×C5—41no—
702C4×C5—41no—
703Dic5—22no—
704Dic5—22no—
705Dic5—22no—
706Dic5—22no—
707Dic5—41no—
708Dic5—41no—
709C24—51no—
710C24—54no—
711C24—51no—
712C24—102no—
713C24—102no—
714C24—102no—
715C24—102no—
716C24—102no—
717C24—102no—
718C24C22×C3×D511yescharacteristic
719C22×C4—51no—
720C22×C4—51no—
721C22×C4—51no—
722C22×C4—51no—
723C22×C4—54no—
724C22×C4—54no—
725C22×C4—54no—
726C22×C4—54no—
727C22×C4—51no—
728C22×C4—51no—
729C22×C4—102no—
730C22×C4—102no—
731C22×C4—102no—
732C22×C4—102no—
733C22×C4—102no—
734C22×C4—102no—
735C22×C4—102no—
736C22×C4—102no—
737C22×C4—102no—
738C22×C4—102no—
739C22×C4—102no—
740C22×C4—102no—
741C22×C4—102no—
742C22×C4—102no—
743C22×C4C22×C3×D511yescharacteristic
744C22×C4C22×C3×D511yescharacteristic
745C22×C4C22×C3×D511yescharacteristic
746C22×C4C22×C3×D511yescharacteristic
747C22×C4C22×C3×D511yescharacteristic
748C22×C4C22×C3×D511yescharacteristic
749C4⋊C4—22no—
750C4⋊C4—102no—
751C4⋊C4—102no—
752C4⋊C4—102no—
753C22⋊C4—22no—
754C22⋊C4—22no—
755C22⋊C4—54no—
756C22⋊C4—54no—
757C22⋊C4—54no—
758C22⋊C4—102no—
759C22⋊C4—102no—
760C22⋊C4—102no—
761C22⋊C4—102no—
762C22⋊C4—102no—
763C22⋊C4—102no—
764C22⋊C4C3×C4×D514yescomplemented
765C42—22no—
766C42—102no—
767C42—102no—
768C42—102no—
769C3×C5C2×#38811yescharacteristic, complemented, Hall
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—41no—
774C22×C3—41no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—54no—
778C22×C3—54no—
779C22×C3—54no—
780C22×C3—54no—
781C22×C3—54no—
782C22×C3—54no—
783C22×C3—54no—
784C22×C3—102no—
785C22×C3—102no—
786C22×C3—102no—
787C22×C3—2016no—
788C22×C3—201no—
789C22×C3—201no—
790C22×C3—201no—
791C22×C3—201no—
792C22×C3C22×C4×D511yescharacteristic
793C22×C3C2×D4×D511yescharacteristic
794C22×C3C2×D4×D511yescharacteristic
795C22×C3D5×#4111yescharacteristic
796C22×C3D5×#4111yescharacteristic
797C22×C3D5×#4111yescharacteristic
798C22×C3D5×#4111yescharacteristic
799C3×C4—22no—
800C3×C4—22no—
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—102no—
806C3×C4—102no—
807C3×C4—102no—
808C3×C4—102no—
809C3×C4—201no—
810C3×C4—201no—
811C2×C5—42no—
812C2×C5C2×C3×#11711yescharacteristic
813C2×C5C2×C3×C4×D411yescharacteristic
814C2×C5C2×C3×C4×D411yescharacteristic
815C2×C5C2×C3×#12111yescharacteristic
816C2×C5C2×C3×#12311yescharacteristic
817C2×C5C2×C3×#12411yescharacteristic
818C2×C5C2×C3×#12611yescharacteristic
819D5—42no—
820D5C3×#38818yesdirect product factor
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—52no—
828C23—52no—
829C23—52no—
830C23—52no—
831C23—52no—
832C23—52no—
833C23—52no—
834C23—52no—
835C23—108no—
836C23—108no—
837C23—108no—
838C23—101no—
839C23—101no—
840C23—101no—
841C23—101no—
842C23—101no—
843C23—101no—
844C23—204no—
845C23—204no—
846C23—204no—
847C23—204no—
848C23C2×C3×C4×D512yes—
849C23C23×C3×D511yescharacteristic
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—52no—
865C2×C4—52no—
866C2×C4—52no—
867C2×C4—52no—
868C2×C4—108no—
869C2×C4—108no—
870C2×C4—108no—
871C2×C4—108no—
872C2×C4—101no—
873C2×C4—101no—
874C2×C4—101no—
875C2×C4—101no—
876C2×C4—101no—
877C2×C4—101no—
878C2×C4—101no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—101no—
886C2×C4—204no—
887C2×C4—204no—
888C2×C4C2×C3×C4×D512yes—
889C2×C4C2×C3×C4×D512yes—
890C2×C4C3×D4×D512yes—
891C2×C4C3×D4×D512yes—
892C2×C3—42no—
893C2×C3—58no—
894C2×C3—202no—
895C2×C3D5×#11711yescharacteristic
896C2×C3C4×D4×D511yescharacteristic
897C2×C3C4×D4×D511yescharacteristic
898C2×C3D5×#12111yescharacteristic
899C2×C3D5×#12311yescharacteristic
900C2×C3D5×#12411yescharacteristic
901C2×C3D5×#12611yescharacteristic
902C5C2×C3×#38811yescharacteristic, complemented, Sylow
903C22—22no—
904C22—22no—
905C22—22no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—54no—
911C22—54no—
912C22—54no—
913C22—54no—
914C22—54no—
915C22—54no—
916C22—54no—
917C22—102no—
918C22—102no—
919C22—102no—
920C22—2016no—
921C22—201no—
922C22—201no—
923C22—201no—
924C22—201no—
925C22C22×C3×C4×D511yescharacteristic
926C22C2×C3×D4×D511yescharacteristic
927C22C2×C3×D4×D511yescharacteristic
928C22C3×D5×#4111yescharacteristic
929C22C3×D5×#4111yescharacteristic
930C22C3×D5×#4111yescharacteristic
931C22C3×D5×#4111yescharacteristic
932C4—22no—
933C4—22no—
934C4—22no—
935C4—22no—
936C4—41no—
937C4—41no—
938C4—102no—
939C4—102no—
940C4—102no—
941C4—102no—
942C4—201no—
943C4—201no—
944C3D5×#38811yescharacteristic, direct product factor, Sylow
945C2—42no—
946C2—58no—
947C2—202no—
948C2C3×D5×#11711yescharacteristic
949C2C3×C4×D4×D511yescharacteristic
950C2C3×C4×D4×D511yescharacteristic
951C2C3×D5×#12111yescharacteristic
952C2C3×D5×#12311yescharacteristic
953C2C3×D5×#12411yescharacteristic
954C2C3×D5×#12611yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC24×C3×D5C22
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C2×C3×#388
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×D5×C4⋊C4C2semidirect
5. C2×C3×C42×D5C2semidirect
6. C3×C5×#388C2semidirect
7. C3×#65279C2semidirect
8. C3×#65240C2semidirect
9. C3×#65234C2semidirect
10. C3×#65233C2semidirect
11. C3×#65229C2semidirect
12. C3×#64959C2semidirect
13. C3×#64958C2semidirect
14. C3×D5×#95C2semidirect
15. C3×D5×#95C2semidirect
16. D5×#388C3direct (N × H)
24. C2×C3×C5×C4⋊C4C22semidirect
28. C2×C3×C42×C5C22semidirect
38. C2×C3×C4⋊Dic5C22semidirect
39. C2×C3×#683C22semidirect
40. C2×C3×#683C22semidirect
41. C2×C3×C4×Dic5C22semidirect
42. C2×C3×C4×Dic5C22semidirect
43. C2×C3×C4×Dic5C22semidirect
47. C3×D5×C22⋊C4C4semidirect
49. C3×C5×#95C22semidirect
50. C3×C5×#95C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. C3×#3963C22semidirect
56. C3×#3963C22semidirect
58. C2×D5×C4⋊C4C2×C3semidirect
62. C2×C42×D5C2×C3semidirect
63. C5×#388C2×C3semidirect
64. #65279C2×C3semidirect
65. #65240C2×C3semidirect
66. #65234C2×C3semidirect
67. #65233C2×C3semidirect
68. #65229C2×C3semidirect
69. #64959C2×C3semidirect
70. #64958C2×C3semidirect
71. D5×#95C2×C3semidirect
72. D5×#95C2×C3semidirect
116. C3×C5×C22⋊C4C2×C4semidirect
120. C3×C22⋊Dic5C2×C4semidirect
125. C3×#685C2×C4semidirect
126. C3×#685C2×C4semidirect
145. C3×#388D5direct (N × H)
155. C2×C5×C4⋊C4C22×C3semidirect
159. C2×C42×C5C22×C3semidirect
169. C2×C4⋊Dic5C22×C3semidirect
170. C2×#683C22×C3semidirect
171. C2×#683C22×C3semidirect
172. C2×C4×Dic5C22×C3semidirect
173. C2×C4×Dic5C22×C3semidirect
174. C2×C4×Dic5C22×C3semidirect
178. D5×C22⋊C4C3×C4semidirect
180. C5×#95C22×C3semidirect
181. C5×#95C22×C3semidirect
182. #3963C22×C3semidirect
183. #3963C22×C3semidirect
184. #3963C22×C3semidirect
185. #3963C22×C3semidirect
186. #3963C22×C3semidirect
187. #3963C22×C3semidirect
271. C2×C3×C4⋊C4C2×D5semidirect
291. C2×C3×C42C2×D5semidirect
298. C3×#95C2×D5semidirect
299. C3×#95C2×D5semidirect
343. C5×C22⋊C4C2×C3×C4semidirect
347. C22⋊Dic5C2×C3×C4semidirect
352. #685C2×C3×C4semidirect
353. #685C2×C3×C4semidirect
372. #388C3×D5direct (N × H)
471. C3×C22⋊C4C4×D5semidirect
558. C2×C4⋊C4C2×C3×D5semidirect
578. C2×C42C2×C3×D5semidirect
585. #95C2×C3×D5semidirect
586. #95C2×C3×D5semidirect
596. C3×D5#388direct (N × H)
764. C22⋊C4C3×C4×D5semidirect
769. C3×C5C2×#388semidirect
820. D5C3×#388direct (N × H)
902. C5C2×C3×#388semidirect
944. C3D5×#388direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3×D5×C4⋊C42
C2×C3×D5×C22⋊C42
C2×C3×C42×D52
C3×C5×#3882
C3×#652792
C3×#652402
C3×#652342
C3×#652332
C3×#652292
C3×#649592
C3×#649582
C3×D5×#952
D5×#3883
C2×C3×#3885