Finite Group Databasebeta

← C3×C4×#4030 #14321426

Subgroups — C3×C4×#4030 #14321426

Order 1920.

1648 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic
4C2×C3×C4×D20C211yesmaximal, characteristic, complemented
5C2×C3×C42×D5C211yesmaximal, characteristic, complemented
6C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
7C3×#65246C211yesmaximal, characteristic, complemented
8C3×#65245C211yesmaximal, characteristic, complemented
9C3×#65240C211yesmaximal, characteristic, complemented
10C3×C4×#685C211yesmaximal, characteristic, complemented
11C3×C4×#683C211yesmaximal, characteristic, complemented
12C3×#64958C211yesmaximal, characteristic, complemented
13C3×#64956C211yesmaximal, characteristic, complemented
14C3×#64954C211yesmaximal, characteristic, complemented
15C3×#64936C211yesmaximal, characteristic, complemented
16C4×#4030C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C42×C5C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C3×C4×C22⋊D5—24no—
32C3×C4×C22⋊D5—24no—
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×C4⋊Dic5C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×C4×Dic5C2211yescharacteristic
45C2×C3×C4×Dic5C2211yescharacteristic
46C2×C3×C4×Dic5C2211yescharacteristic
47C2×C3×C4×Dic5C2211yescharacteristic
48C3×#4030C418yesdirect product factor
49C3×C4×D20—24no—
50C3×C42×D5—24no—
51C3×C5×#95C2211yescharacteristic
52C3×C5×#95C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#3963C2211yescharacteristic
56C3×#3963C2211yescharacteristic
57C3×C4×#121—51nomaximal, Hall
58C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
59C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
60C2×#4030C2×C311yescharacteristic
61C2×C4×D20C2×C311yescharacteristic, complemented
62C2×C42×D5C2×C311yescharacteristic, complemented
63C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
64#65246C2×C311yescharacteristic, complemented
65#65245C2×C311yescharacteristic, complemented
66#65240C2×C311yescharacteristic, complemented
67C4×#685C2×C311yescharacteristic, complemented
68C4×#683C2×C311yescharacteristic, complemented
69#64958C2×C311yescharacteristic, complemented
70#64956C2×C311yescharacteristic, complemented
71#64954C2×C311yescharacteristic, complemented
72#64936C2×C311yescharacteristic, complemented
73C24×C3×C5C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C22×C3×C4×C5—22no—
77C22×C3×C4×C5—22no—
78C22×C3×C4×C5—22no—
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C2×C3×C22⋊D5—22no—
86C2×C3×C22⋊D5—22no—
87C2×C3×C22⋊D5—22no—
88C2×C3×C22⋊D5—22no—
89C2×C3×C22⋊D5C2×C414yescomplemented
90C2×C3×C22⋊D5C2×C414yescomplemented
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C2×C3×D20—22no—
98C2×C3×D20—22no—
99C2×C3×D20C2×C414yescomplemented
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×D5—22no—
110C2×C3×C4×D5C2×C414yescomplemented
111C2×C3×C4×D5D414yescomplemented
112C3×C5×C22⋊C4—22no—
113C3×C5×C22⋊C4C2×C414yescomplemented
114C3×C42×C5—22no—
115C3×C42×C5—22no—
116C3×C22⋊Dic5—22no—
117C3×C22⋊Dic5—22no—
118C3×#685—22no—
119C3×#685—22no—
120C3×#685—22no—
121C3×#685—22no—
122C3×#685—22no—
123C3×#685C2×C414yescomplemented
124C3×C4⋊Dic5—22no—
125C3×#683—22no—
126C3×#683—22no—
127C3×#683—22no—
128C3×#683C2×C414yescomplemented
129C3×C4×Dic5—22no—
130C3×C4×Dic5—22no—
131C3×C4×Dic5—22no—
132C3×C4×Dic5D414yescomplemented
133C2×C3×#121—51no—
134C2×C3×C4×D4—51no—
135C2×C3×C4×D4—51no—
136C2×C3×C4×D4—51no—
137C22×C3×C42—51no—
138C3×#390—51no—
139C3×#389—51no—
140C3×#388—51no—
141C3×#388—51no—
142C3×#386—51no—
143C3×#386—51no—
144C3×#380—51no—
145C3×C4×C4⋊C4—51no—
146C3×C4×C22⋊C4—51no—
147C3×C4×C22⋊C4D511yescharacteristic, complemented
148C23×C4×C5C22×C311yescharacteristic
149C22×C22⋊D5C22×C311yescharacteristic
150C22×C22⋊D5C22×C311yescharacteristic
151C22×D20C22×C311yescharacteristic
152C22×C4×D5C22×C311yescharacteristic
153C22×C4×D5C22×C311yescharacteristic
154C22×C4×D5C22×C311yescharacteristic
155C22×C4×D5C22×C311yescharacteristic
156C2×C5×C22⋊C4C22×C311yescharacteristic
157C2×C5×C22⋊C4C22×C311yescharacteristic
158C2×C42×C5C22×C311yescharacteristic
159C2×C42×C5C22×C311yescharacteristic
160C2×C22⋊Dic5C22×C311yescharacteristic
161C2×C22⋊Dic5C22×C311yescharacteristic
162C4×C22⋊D5—24no—
163C4×C22⋊D5—24no—
164C2×#685C22×C311yescharacteristic
165C2×#685C22×C311yescharacteristic
166C2×#685C22×C311yescharacteristic
167C2×#685C22×C311yescharacteristic
168C2×#685C22×C311yescharacteristic
169C2×#685C22×C311yescharacteristic
170C2×C4⋊Dic5C22×C311yescharacteristic
171C2×#683C22×C311yescharacteristic
172C2×#683C22×C311yescharacteristic
173C2×#683C22×C311yescharacteristic
174C2×#683C22×C311yescharacteristic
175C2×C4×Dic5C22×C311yescharacteristic
176C2×C4×Dic5C22×C311yescharacteristic
177C2×C4×Dic5C22×C311yescharacteristic
178C2×C4×Dic5C22×C311yescharacteristic
179#4030C3×C418yesdirect product factor
180C4×D20—24no—
181C42×D5—24no—
182C5×#95C22×C311yescharacteristic
183C5×#95C22×C311yescharacteristic
184#3963C22×C311yescharacteristic
185#3963C22×C311yescharacteristic
186#3963C22×C311yescharacteristic
187#3963C22×C311yescharacteristic
188C4×#121—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—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5C22×C412yes—
208C22×C3×D5C22×C412yes—
209C22×C3×D5C2×D412yes—
210C22×C3×D5#4112yes—
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—44no—
224C2×C3×C4×C5C22×C412yes—
225C2×C3×C4×C5C22×C412yes—
226C2×C3×C4×C5C2×D412yes—
227C2×C3×C4×C5C2×D412yes—
228C2×C3×C4×C5#4112yes—
229C2×C3×C4×C5#4112yes—
230C3×C22⋊D5—28no—
231C3×C22⋊D5—28no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
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×Dic5C22×C412yes—
245C2×C3×Dic5C22×C412yes—
246C2×C3×Dic5C2×D412yes—
247C2×C3×Dic5C2×D412yes—
248C2×C3×Dic5C2×D412yes—
249C2×C3×Dic5#4112yes—
250C3×D20—28no—
251C3×C4×D5—28no—
252C3×C4×D5—28no—
253C3×C4×D5—28no—
254C3×C4×D5—44no—
255C22×C3×D4—51no—
256C22×C3×D4—51no—
257C22×C3×D4—51no—
258C23×C3×C4—51no—
259C23×C3×C4—51no—
260C23×C3×C4—51no—
261C23×C3×C4—51no—
262C23×C3×C4C2×D511yescharacteristic
263C3×#121—58no—
264C3×C4×D4—104no—
265C3×C4×D4—104no—
266C3×C4×D4—104no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C4⋊C4—51no—
271C2×C3×C4⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C22⋊C4—51no—
274C2×C3×C22⋊C4—51no—
275C2×C3×C22⋊C4—51no—
276C2×C3×C22⋊C4—51no—
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4C2×D511yescharacteristic
281C2×C3×C22⋊C4C2×D511yescharacteristic
282C2×C3×C42—51no—
283C2×C3×C42—51no—
284C2×C3×C42—51no—
285C2×C3×C42—51no—
286C2×C3×C42—104no—
287C2×C3×C42C2×D511yescharacteristic
288C2×C3×C42C2×D511yescharacteristic
289C3×#95—51no—
290C3×#95—51no—
291C3×#95—51no—
292C3×#95—51no—
293C3×#95C2×D511yescharacteristic
294C3×#95C2×D511yescharacteristic
295C24×C5C23×C311yescharacteristic
296C23×D5C23×C311yescharacteristic
297C23×D5C23×C311yescharacteristic
298C22×C4×C5—22no—
299C22×C4×C5—22no—
300C22×C4×C5—22no—
301C22×C4×C5C23×C311yescharacteristic
302C22×C4×C5C23×C311yescharacteristic
303C22×C4×C5C23×C311yescharacteristic
304C22×C4×C5C23×C311yescharacteristic
305C22×C4×C5C23×C311yescharacteristic
306C22×C4×C5C23×C311yescharacteristic
307C2×C22⋊D5—22no—
308C2×C22⋊D5—22no—
309C2×C22⋊D5—22no—
310C2×C22⋊D5—22no—
311C2×C22⋊D5C2×C3×C414yescomplemented
312C2×C22⋊D5C2×C3×C414yescomplemented
313C22×Dic5C23×C311yescharacteristic
314C22×Dic5C23×C311yescharacteristic
315C22×Dic5C23×C311yescharacteristic
316C22×Dic5C23×C311yescharacteristic
317C22×Dic5C23×C311yescharacteristic
318C22×Dic5C23×C311yescharacteristic
319C2×D20—22no—
320C2×D20—22no—
321C2×D20C2×C3×C414yescomplemented
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×D5C2×C3×C414yescomplemented
333C2×C4×D5C3×D414yescomplemented
334C5×C22⋊C4—22no—
335C5×C22⋊C4C2×C3×C414yescomplemented
336C42×C5—22no—
337C42×C5—22no—
338C22⋊Dic5—22no—
339C22⋊Dic5—22no—
340#685—22no—
341#685—22no—
342#685—22no—
343#685—22no—
344#685—22no—
345#685C2×C3×C414yescomplemented
346C4⋊Dic5—22no—
347#683—22no—
348#683—22no—
349#683—22no—
350#683C2×C3×C414yescomplemented
351C4×Dic5—22no—
352C4×Dic5—22no—
353C4×Dic5—22no—
354C4×Dic5C3×D414yescomplemented
355C2×#121—51no—
356C2×C4×D4—51no—
357C2×C4×D4—51no—
358C2×C4×D4—51no—
359C22×C42—51no—
360#390—51no—
361#389—51no—
362#388—51no—
363#388—51no—
364#386—51no—
365#386—51no—
366#380—51no—
367C4×C4⋊C4—51no—
368C4×C22⋊C4—51no—
369C4×C22⋊C4C3×D511yescharacteristic, complemented
370C22×C3×C5—22no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—41no—
374C22×C3×C5—41no—
375C22×C3×C5—41no—
376C22×C3×C5—41no—
377C22×C3×C5C23×C411yescharacteristic
378C22×C3×C5C22×D411yescharacteristic
379C22×C3×C5C22×D411yescharacteristic
380C22×C3×C5C2×#4111yescharacteristic
381C22×C3×C5C2×#4111yescharacteristic
382C22×C3×C5C2×#4111yescharacteristic
383C22×C3×C5C2×#4111yescharacteristic
384C2×C3×D5—22no—
385C2×C3×D5—22no—
386C2×C3×D5—22no—
387C2×C3×D5—22no—
388C2×C3×D5—22no—
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C2×C3×D5C4×D414yescomplemented
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401C3×C4×C5—41no—
402C3×C4×C5—41no—
403C3×C4×C5#12114yescomplemented
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C3×Dic5—41no—
408C3×Dic5—41no—
409C3×Dic5C4×D414yescomplemented
410C24×C3—51no—
411C24×C3—51no—
412C24×C3C22×D511yescharacteristic
413C2×C3×D4—54no—
414C2×C3×D4—54no—
415C2×C3×D4—54no—
416C2×C3×D4—102no—
417C2×C3×D4—102no—
418C2×C3×D4—102no—
419C2×C3×D4—102no—
420C2×C3×D4—102no—
421C2×C3×D4—102no—
422C22×C3×C4—22no—
423C22×C3×C4—22no—
424C22×C3×C4—22no—
425C22×C3×C4—51no—
426C22×C3×C4—51no—
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—54no—
430C22×C3×C4—54no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—102no—
434C22×C3×C4—102no—
435C22×C3×C4—102no—
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×C4C22×D511yescharacteristic
444C22×C3×C4C22×D511yescharacteristic
445C22×C3×C4C22×D511yescharacteristic
446C22×C3×C4C22×D511yescharacteristic
447C22×C3×C4C22×D511yescharacteristic
448C22×C3×C4C22×D511yescharacteristic
449C3×C4⋊C4—54no—
450C3×C4⋊C4—102no—
451C3×C4⋊C4—102no—
452C3×C4⋊C4—102no—
453C3×C4⋊C4—102no—
454C3×C22⋊C4—22no—
455C3×C22⋊C4—54no—
456C3×C22⋊C4—102no—
457C3×C22⋊C4—102no—
458C3×C22⋊C4—102no—
459C3×C22⋊C4—102no—
460C3×C22⋊C4—102no—
461C3×C22⋊C4—102no—
462C3×C22⋊C4—102no—
463C3×C22⋊C4C4×D514yescomplemented
464C3×C42—22no—
465C3×C42—22no—
466C3×C42—54no—
467C3×C42—102no—
468C3×C42—102no—
469C3×C42—102no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5—21no—
473C23×C5—21no—
474C23×C5—21no—
475C23×C5—21no—
476C23×C5C22×C3×C412yes—
477C23×C5C24×C311yescharacteristic
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5C22×C3×C412yes—
489C22×D5C22×C3×C412yes—
490C22×D5C2×C3×D412yes—
491C22×D5C3×#4112yes—
492C2×C4×C5—21no—
493C2×C4×C5—21no—
494C2×C4×C5—21no—
495C2×C4×C5—21no—
496C2×C4×C5—21no—
497C2×C4×C5—21no—
498C2×C4×C5—21no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—44no—
505C2×C4×C5C22×C3×C412yes—
506C2×C4×C5C22×C3×C412yes—
507C2×C4×C5C2×C3×D412yes—
508C2×C4×C5C2×C3×D412yes—
509C2×C4×C5C3×#4112yes—
510C2×C4×C5C3×#4112yes—
511C22⋊D5—28no—
512C22⋊D5—28no—
513C2×Dic5—21no—
514C2×Dic5—21no—
515C2×Dic5—21no—
516C2×Dic5—21no—
517C2×Dic5—21no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5C22×C3×C412yes—
526C2×Dic5C22×C3×C412yes—
527C2×Dic5C2×C3×D412yes—
528C2×Dic5C2×C3×D412yes—
529C2×Dic5C2×C3×D412yes—
530C2×Dic5C3×#4112yes—
531D20—28no—
532C4×D5—28no—
533C4×D5—28no—
534C4×D5—28no—
535C4×D5—44no—
536C22×D4—51no—
537C22×D4—51no—
538C22×D4—51no—
539C23×C4—51no—
540C23×C4—51no—
541C23×C4—51no—
542C23×C4—51no—
543C23×C4C2×C3×D511yescharacteristic
544#121—58no—
545C4×D4—104no—
546C4×D4—104no—
547C4×D4—104no—
548C2×C4⋊C4—51no—
549C2×C4⋊C4—51no—
550C2×C4⋊C4—51no—
551C2×C4⋊C4—51no—
552C2×C4⋊C4—51no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—51no—
560C2×C22⋊C4—51no—
561C2×C22⋊C4C2×C3×D511yescharacteristic
562C2×C22⋊C4C2×C3×D511yescharacteristic
563C2×C42—51no—
564C2×C42—51no—
565C2×C42—51no—
566C2×C42—51no—
567C2×C42—104no—
568C2×C42C2×C3×D511yescharacteristic
569C2×C42C2×C3×D511yescharacteristic
570#95—51no—
571#95—51no—
572#95—51no—
573#95—51no—
574#95C2×C3×D511yescharacteristic
575#95C2×C3×D511yescharacteristic
576C2×C3×C5—42no—
577C2×C3×C5C2×C4×D411yescharacteristic
578C2×C3×C5C2×C4×D411yescharacteristic
579C2×C3×C5C4×#4111yescharacteristic
580C2×C3×C5C2×#12111yescharacteristic
581C2×C3×C5#52511yescharacteristic
582C2×C3×C5#52911yescharacteristic
583C2×C3×C5#53211yescharacteristic
584C3×D5—24no—
585C3×D5—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—52no—
593C23×C3—52no—
594C23×C3—52no—
595C23×C3—52no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3—101no—
603C23×C3—101no—
604C23×C3—101no—
605C23×C3—101no—
606C23×C3C2×C4×D512yes—
607C23×C3C23×D511yescharacteristic
608C3×D4—108no—
609C3×D4—108no—
610C3×D4—108no—
611C2×C3×C4—21no—
612C2×C3×C4—21no—
613C2×C3×C4—21no—
614C2×C3×C4—21no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—21no—
618C2×C3×C4—21no—
619C2×C3×C4—21no—
620C2×C3×C4—21no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—44no—
624C2×C3×C4—52no—
625C2×C3×C4—52no—
626C2×C3×C4—52no—
627C2×C3×C4—52no—
628C2×C3×C4—52no—
629C2×C3×C4—52no—
630C2×C3×C4—108no—
631C2×C3×C4—108no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—108no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—204no—
646C2×C3×C4C2×C4×D512yes—
647C2×C3×C4C2×C4×D512yes—
648C2×C3×C4#70912yes—
649C2×C3×C4#70912yes—
650C2×C3×C4D4×D512yes—
651C2×C3×C4D4×D512yes—
652C22×C5—22no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—41no—
656C22×C5—41no—
657C22×C5—41no—
658C22×C5—41no—
659C22×C5C23×C3×C411yescharacteristic
660C22×C5C22×C3×D411yescharacteristic
661C22×C5C22×C3×D411yescharacteristic
662C22×C5C2×C3×#4111yescharacteristic
663C22×C5C2×C3×#4111yescharacteristic
664C22×C5C2×C3×#4111yescharacteristic
665C22×C5C2×C3×#4111yescharacteristic
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—22no—
669C2×D5—22no—
670C2×D5—22no—
671C2×D5—22no—
672C2×D5—22no—
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—41no—
676C2×D5—41no—
677C2×D5—41no—
678C2×D5—41no—
679C2×D5C3×C4×D414yescomplemented
680C4×C5—22no—
681C4×C5—22no—
682C4×C5—22no—
683C4×C5—41no—
684C4×C5—41no—
685C4×C5C3×#12114yescomplemented
686Dic5—22no—
687Dic5—22no—
688Dic5—22no—
689Dic5—41no—
690Dic5—41no—
691Dic5C3×C4×D414yescomplemented
692C24—51no—
693C24—51no—
694C24C22×C3×D511yescharacteristic
695C2×D4—54no—
696C2×D4—54no—
697C2×D4—54no—
698C2×D4—102no—
699C2×D4—102no—
700C2×D4—102no—
701C2×D4—102no—
702C2×D4—102no—
703C2×D4—102no—
704C22×C4—22no—
705C22×C4—22no—
706C22×C4—22no—
707C22×C4—51no—
708C22×C4—51no—
709C22×C4—51no—
710C22×C4—51no—
711C22×C4—54no—
712C22×C4—54no—
713C22×C4—51no—
714C22×C4—51no—
715C22×C4—102no—
716C22×C4—102no—
717C22×C4—102no—
718C22×C4—102no—
719C22×C4—102no—
720C22×C4—102no—
721C22×C4—102no—
722C22×C4—102no—
723C22×C4—102no—
724C22×C4—102no—
725C22×C4C22×C3×D511yescharacteristic
726C22×C4C22×C3×D511yescharacteristic
727C22×C4C22×C3×D511yescharacteristic
728C22×C4C22×C3×D511yescharacteristic
729C22×C4C22×C3×D511yescharacteristic
730C22×C4C22×C3×D511yescharacteristic
731C4⋊C4—54no—
732C4⋊C4—102no—
733C4⋊C4—102no—
734C4⋊C4—102no—
735C4⋊C4—102no—
736C22⋊C4—22no—
737C22⋊C4—54no—
738C22⋊C4—102no—
739C22⋊C4—102no—
740C22⋊C4—102no—
741C22⋊C4—102no—
742C22⋊C4—102no—
743C22⋊C4—102no—
744C22⋊C4—102no—
745C22⋊C4C3×C4×D514yescomplemented
746C42—22no—
747C42—22no—
748C42—54no—
749C42—102no—
750C42—102no—
751C42—102no—
752C3×C5C4×#12111yescharacteristic, complemented, Hall
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—54no—
761C22×C3—102no—
762C22×C3—102no—
763C22×C3—102no—
764C22×C3—102no—
765C22×C3—102no—
766C22×C3—102no—
767C22×C3—102no—
768C22×C3—102no—
769C22×C3—102no—
770C22×C3—201no—
771C22×C3—201no—
772C22×C3—201no—
773C22×C3—201no—
774C22×C3C22×C4×D511yescharacteristic
775C22×C3C2×#70911yescharacteristic
776C22×C3C2×#70911yescharacteristic
777C22×C3C2×D4×D511yescharacteristic
778C22×C3C2×D4×D511yescharacteristic
779C22×C3D5×#4111yescharacteristic
780C22×C3D5×#4111yescharacteristic
781C3×C4—22no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—41no—
785C3×C4—41no—
786C3×C4—54no—
787C3×C4—102no—
788C3×C4—102no—
789C3×C4—102no—
790C3×C4—201no—
791C3×C4—201no—
792C3×C4#403014yesdirect product factor
793C2×C5—42no—
794C2×C5C2×C3×C4×D411yescharacteristic
795C2×C5C2×C3×C4×D411yescharacteristic
796C2×C5C3×C4×#4111yescharacteristic
797C2×C5C2×C3×#12111yescharacteristic
798C2×C5C3×#52511yescharacteristic
799C2×C5C3×#52911yescharacteristic
800C2×C5C3×#53211yescharacteristic
801D5—24no—
802D5—42no—
803C23—21no—
804C23—21no—
805C23—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—52no—
810C23—52no—
811C23—52no—
812C23—52no—
813C23—101no—
814C23—101no—
815C23—101no—
816C23—101no—
817C23—101no—
818C23—101no—
819C23—101no—
820C23—101no—
821C23—101no—
822C23—101no—
823C23C2×C3×C4×D512yes—
824C23C23×C3×D511yescharacteristic
825D4—108no—
826D4—108no—
827D4—108no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—44no—
841C2×C4—52no—
842C2×C4—52no—
843C2×C4—52no—
844C2×C4—52no—
845C2×C4—52no—
846C2×C4—52no—
847C2×C4—108no—
848C2×C4—108no—
849C2×C4—101no—
850C2×C4—101no—
851C2×C4—101no—
852C2×C4—101no—
853C2×C4—101no—
854C2×C4—101no—
855C2×C4—108no—
856C2×C4—101no—
857C2×C4—101no—
858C2×C4—101no—
859C2×C4—101no—
860C2×C4—101no—
861C2×C4—101no—
862C2×C4—204no—
863C2×C4C2×C3×C4×D512yes—
864C2×C4C2×C3×C4×D512yes—
865C2×C4C3×#70912yes—
866C2×C4C3×#70912yes—
867C2×C4C3×D4×D512yes—
868C2×C4C3×D4×D512yes—
869C2×C3—42no—
870C2×C3—104no—
871C2×C3—202no—
872C2×C3C4×#70911yescharacteristic
873C2×C3C2×#403011yescharacteristic
874C2×C3#6586211yescharacteristic
875C2×C3C4×D4×D511yescharacteristic
876C2×C3C4×D4×D511yescharacteristic
877C2×C3#6588111yescharacteristic
878C2×C3#6588211yescharacteristic
879C5C3×C4×#12111yescharacteristic, complemented, Sylow
880C22—22no—
881C22—22no—
882C22—22no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—54no—
888C22—102no—
889C22—102no—
890C22—102no—
891C22—102no—
892C22—102no—
893C22—102no—
894C22—102no—
895C22—102no—
896C22—102no—
897C22—201no—
898C22—201no—
899C22—201no—
900C22—201no—
901C22C22×C3×C4×D511yescharacteristic
902C22C2×C3×#70911yescharacteristic
903C22C2×C3×#70911yescharacteristic
904C22C2×C3×D4×D511yescharacteristic
905C22C2×C3×D4×D511yescharacteristic
906C22C3×D5×#4111yescharacteristic
907C22C3×D5×#4111yescharacteristic
908C4—22no—
909C4—22no—
910C4—22no—
911C4—41no—
912C4—41no—
913C4—54no—
914C4—102no—
915C4—102no—
916C4—102no—
917C4—201no—
918C4—201no—
919C4C3×#403014yesdirect product factor
920C3C4×#403011yescharacteristic, direct product factor, Sylow
921C2—42no—
922C2—104no—
923C2—202no—
924C2C3×C4×#70911yescharacteristic
925C2C2×C3×#403011yescharacteristic
926C2C3×#6586211yescharacteristic
927C2C3×C4×D4×D511yescharacteristic
928C2C3×C4×D4×D511yescharacteristic
929C2C3×#6588111yescharacteristic
930C2C3×#6588211yescharacteristic
subgroupG/H
centerC22×C3×C4C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4030C2
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×C4×#121
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C3×C4 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C22⋊D5C2semidirect
2. C2×C3×C4×C22⋊D5C2semidirect
4. C2×C3×C4×D20C2semidirect
5. C2×C3×C42×D5C2semidirect
6. C3×C4×C5×C22⋊C4C2semidirect
7. C3×#65246C2semidirect
8. C3×#65245C2semidirect
9. C3×#65240C2semidirect
10. C3×C4×#685C2semidirect
11. C3×C4×#683C2semidirect
12. C3×#64958C2semidirect
13. C3×#64956C2semidirect
14. C3×#64954C2semidirect
15. C3×#64936C2semidirect
16. C4×#4030C3direct (N × H)
48. C3×#4030C4direct (N × H)
58. C2×C4×C22⋊D5C2×C3semidirect
59. C2×C4×C22⋊D5C2×C3semidirect
61. C2×C4×D20C2×C3semidirect
62. C2×C42×D5C2×C3semidirect
63. C4×C5×C22⋊C4C2×C3semidirect
64. #65246C2×C3semidirect
65. #65245C2×C3semidirect
66. #65240C2×C3semidirect
67. C4×#685C2×C3semidirect
68. C4×#683C2×C3semidirect
69. #64958C2×C3semidirect
70. #64956C2×C3semidirect
71. #64954C2×C3semidirect
72. #64936C2×C3semidirect
89. C2×C3×C22⋊D5C2×C4semidirect
90. C2×C3×C22⋊D5C2×C4semidirect
99. C2×C3×D20C2×C4semidirect
110. C2×C3×C4×D5C2×C4semidirect
111. C2×C3×C4×D5D4semidirect
113. C3×C5×C22⋊C4C2×C4semidirect
123. C3×#685C2×C4semidirect
128. C3×#683C2×C4semidirect
132. C3×C4×Dic5D4semidirect
147. C3×C4×C22⋊C4D5semidirect
179. #4030C3×C4direct (N × H)
311. C2×C22⋊D5C2×C3×C4semidirect
312. C2×C22⋊D5C2×C3×C4semidirect
321. C2×D20C2×C3×C4semidirect
332. C2×C4×D5C2×C3×C4semidirect
333. C2×C4×D5C3×D4semidirect
335. C5×C22⋊C4C2×C3×C4semidirect
345. #685C2×C3×C4semidirect
350. #683C2×C3×C4semidirect
354. C4×Dic5C3×D4semidirect
369. C4×C22⋊C4C3×D5semidirect
397. C2×C3×D5C4×D4semidirect
403. C3×C4×C5#121semidirect
409. C3×Dic5C4×D4semidirect
463. C3×C22⋊C4C4×D5semidirect
679. C2×D5C3×C4×D4semidirect
685. C4×C5C3×#121semidirect
691. Dic5C3×C4×D4semidirect
745. C22⋊C4C3×C4×D5semidirect
752. C3×C5C4×#121semidirect
792. C3×C4#4030direct (N × H)
879. C5C3×C4×#121semidirect
919. C4C3×#4030direct (N × H)
920. C3C4×#4030direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C2×C3×#40302
C2×C3×C4×D202
C2×C3×C42×D52
C3×C4×C5×C22⋊C42
C3×#652462
C3×#652452
C3×#652402
C3×C4×#6852
C3×C4×#6832
C3×#649582
C3×#649562
C3×#649542
C3×#649362
C4×#40303
C3×C4×#1215