Finite Group Databasebeta

← C2×C3×#65894 #14480753

Subgroups — C2×C3×#65894 #14480753

Order 1920.

2672 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×C3×#4085C211yesmaximal, characteristic, complemented
3C2×C3×#4083C211yesmaximal, characteristic, complemented
4C2×C3×#4076C211yesmaximal, characteristic, complemented
5C2×C3×#4075C211yesmaximal, characteristic, complemented
6C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
7C22×C3×#685C211yesmaximal, characteristic, complemented
8C3×#65894C2116yesmaximal, direct product factor
9C2×C3×#4044C211yesmaximal, characteristic, complemented
10C2×C3×#4040C211yesmaximal, characteristic, complemented
11C2×C3×#4031C211yesmaximal, characteristic, complemented
12C2×C3×#4030C211yesmaximal, characteristic, complemented
13C2×C3×#4028C211yesmaximal, characteristic, complemented
14C2×C3×#4024C211yesmaximal, characteristic, complemented
15C2×C3×#4022C211yesmaximal, characteristic, complemented
16C2×C3×#4021C211yesmaximal, characteristic, complemented
17C2×#65894C311yesmaximal, characteristic, direct product factor, Hall
18C24×C3×D5C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C23×C3×C4×C5C2211yescharacteristic
21C23×C3×C4×C5C2211yescharacteristic, complemented
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic, complemented
26C23×C3×Dic5C2211yescharacteristic
27C22×C3×D20C2211yescharacteristic
28C22×C3×D20C2211yescharacteristic
29C22×C3×C4×D5C2211yescharacteristic, complemented
30C22×C3×Dic10C2211yescharacteristic, complemented
31C3×C4×C5×D4C2218yescomplemented
32C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
35C2×C3×C42×C5C2211yescharacteristic, complemented
36C2×C3×C22⋊Dic5C2211yescharacteristic
37C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
38C3×#4085C2218yescomplemented
39C3×#4083C2218yescomplemented
40C3×#4076C2218yescomplemented
41C3×#4075C2218yescomplemented
42C3×C4×C22⋊D5C2218yescomplemented
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic
47C2×C3×#685C2211yescharacteristic
48C2×C3×#685C2211yescharacteristic
49C2×C3×#685C2211yescharacteristic
50C2×C3×#685C2211yescharacteristic
51C2×C3×#685C2218yescomplemented
52C2×C3×#685C2211yescharacteristic, complemented
53C2×C3×#685C2211yescharacteristic, complemented
54C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
55C2×C3×#683C2211yescharacteristic, complemented
56C2×C3×#683C2211yescharacteristic, complemented
57C2×C3×#683C2211yescharacteristic, complemented
58C2×C3×#683C2211yescharacteristic, complemented
59C2×C3×C4×Dic5C2211yescharacteristic, complemented
60C3×#4044C2218yescomplemented
61C3×#4040C2218yescomplemented
62C3×#4031C2218yescomplemented
63C3×#4030C2218yescomplemented
64C3×#4028C2218yescomplemented
65C3×#4024C2218yescomplemented
66C3×#4022C2218yescomplemented
67C3×#4021C2218yescomplemented
68C2×C3×#538—51nomaximal, Hall
69C2×C4×C5×D4C2×C311yescharacteristic, complemented
70C2×#4085C2×C311yescharacteristic, complemented
71C2×#4083C2×C311yescharacteristic, complemented
72C2×#4076C2×C311yescharacteristic, complemented
73C2×#4075C2×C311yescharacteristic, complemented
74C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
75C22×#685C2×C311yescharacteristic, complemented
76#65894C2×C3116yesdirect product factor
77C2×#4044C2×C311yescharacteristic, complemented
78C2×#4040C2×C311yescharacteristic, complemented
79C2×#4031C2×C311yescharacteristic, complemented
80C2×#4030C2×C311yescharacteristic, complemented
81C2×#4028C2×C311yescharacteristic, complemented
82C2×#4024C2×C311yescharacteristic, complemented
83C2×#4022C2×C311yescharacteristic, complemented
84C2×#4021C2×C311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×C3×D5—24no—
88C23×C3×D5—42no—
89C23×C3×D5—42no—
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2314yes—
94C2×C3×C5×D4—24no—
95C2×C3×C5×D4C2314yes—
96C22×C3×C4×C5—42no—
97C22×C3×C4×C5—42no—
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2311yescharacteristic
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2314yes—
104C22×C3×C4×C5C2314yescomplemented
105C2×C3×C22⋊D5—24no—
106C2×C3×C22⋊D5—42no—
107C2×C3×C22⋊D5—42no—
108C2×C3×C22⋊D5—42no—
109C2×C3×C22⋊D5C2314yes—
110C2×C3×C22⋊D5C2314yes—
111C2×C3×C22⋊D5C2314yes—
112C2×C3×C22⋊D5C2314yescomplemented
113C22×C3×Dic5—42no—
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2314yes—
120C2×C3×D20—42no—
121C2×C3×D20—42no—
122C2×C3×D20C2314yes—
123C2×C3×D20C2314yes—
124C2×C3×C4×D5—42no—
125C2×C3×C4×D5C2314yescomplemented
126C2×C3×Dic10—42no—
127C2×C3×Dic10C2314yescomplemented
128C3×C5×C4⋊C4C2314yescomplemented
129C3×C5×C22⋊C4C2314yes—
130C3×C5×C22⋊C4C2314yescomplemented
131C3×C42×C5C2314yescomplemented
132C3×C22⋊Dic5C2314yes—
133C3×C22⋊Dic5C2314yescomplemented
134C3×#685C2314yes—
135C3×#685C2314yes—
136C3×#685C2314yes—
137C3×#685C2314yes—
138C3×#685C2314yes—
139C3×#685C2314yes—
140C3×#685C2314yes—
141C3×#685C2314yes—
142C3×#685C2314yescomplemented
143C3×#685C2314yescomplemented
144C3×C4⋊Dic5C2314yescomplemented
145C3×#683C2314yescomplemented
146C3×#683C2314yescomplemented
147C3×#683C2314yescomplemented
148C3×#683C2314yescomplemented
149C3×C4×Dic5C2314yescomplemented
150C3×#538—516no—
151C2×C3×#126—51no—
152C2×C3×#126—51no—
153C2×C3×#124—51no—
154C2×C3×#124—51no—
155C2×C3×#123—51no—
156C2×C3×#123—51no—
157C2×C3×C22⋊Q8—51no—
158C2×C3×#121—51no—
159C2×C3×#121—51no—
160C2×C3×#121—51no—
161C2×C3×#120—51no—
162C2×C3×#120—51no—
163C2×C3×C4×D4—51no—
164C2×C3×C4×D4D511yescharacteristic, complemented
165C22×C3×C22⋊C4—51no—
166C24×D5C22×C311yescharacteristic
167C22×C5×D4C22×C311yescharacteristic
168C23×C4×C5C22×C311yescharacteristic
169C23×C4×C5C22×C311yescharacteristic, complemented
170C22×C22⋊D5C22×C311yescharacteristic
171C22×C22⋊D5C22×C311yescharacteristic
172C22×C22⋊D5C22×C311yescharacteristic
173C22×C22⋊D5C22×C311yescharacteristic, complemented
174C23×Dic5C22×C311yescharacteristic
175C22×D20C22×C311yescharacteristic
176C22×D20C22×C311yescharacteristic
177C22×C4×D5C22×C311yescharacteristic, complemented
178C22×Dic10C22×C311yescharacteristic, complemented
179C4×C5×D4C22×C318yescomplemented
180C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
181C2×C5×C22⋊C4C22×C311yescharacteristic
182C2×C5×C22⋊C4C22×C311yescharacteristic, complemented
183C2×C42×C5C22×C311yescharacteristic, complemented
184C2×C22⋊Dic5C22×C311yescharacteristic
185C2×C22⋊Dic5C22×C311yescharacteristic, complemented
186#4085C22×C318yescomplemented
187#4083C22×C318yescomplemented
188#4076C22×C318yescomplemented
189#4075C22×C318yescomplemented
190C4×C22⋊D5C22×C318yescomplemented
191C2×#685C22×C311yescharacteristic
192C2×#685C22×C311yescharacteristic
193C2×#685C22×C311yescharacteristic
194C2×#685C22×C311yescharacteristic
195C2×#685C22×C311yescharacteristic
196C2×#685C22×C311yescharacteristic
197C2×#685C22×C311yescharacteristic
198C2×#685C22×C311yescharacteristic
199C2×#685C22×C318yescomplemented
200C2×#685C22×C311yescharacteristic, complemented
201C2×#685C22×C311yescharacteristic, complemented
202C2×C4⋊Dic5C22×C311yescharacteristic, complemented
203C2×#683C22×C311yescharacteristic, complemented
204C2×#683C22×C311yescharacteristic, complemented
205C2×#683C22×C311yescharacteristic, complemented
206C2×#683C22×C311yescharacteristic, complemented
207C2×C4×Dic5C22×C311yescharacteristic, complemented
208#4044C22×C318yescomplemented
209#4040C22×C318yescomplemented
210#4031C22×C318yescomplemented
211#4030C22×C318yescomplemented
212#4028C22×C318yescomplemented
213#4024C22×C318yescomplemented
214#4022C22×C318yescomplemented
215#4021C22×C318yescomplemented
216C2×#538—51noSylow
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5#4114yes—
223C23×C3×C5C2412yes—
224C23×C3×C5C2412yes—
225C23×C3×C5C2411yescharacteristic
226C22×C3×D5—22no—
227C22×C3×D5—28no—
228C22×C3×D5—22no—
229C22×C3×D5—22no—
230C22×C3×D5—22no—
231C22×C3×D5—22no—
232C22×C3×D5—22no—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—44no—
237C22×C3×D5—44no—
238C22×C3×D5—416no—
239C22×C3×D5C2412yes—
240C22×C3×D5C2412yes—
241C22×C3×D5C2412yes—
242C3×C5×D4—28no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5—22no—
245C2×C3×C4×C5—22no—
246C2×C3×C4×C5—22no—
247C2×C3×C4×C5—22no—
248C2×C3×C4×C5—44no—
249C2×C3×C4×C5—44no—
250C2×C3×C4×C5C2412yes—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253C2×C3×C4×C5C2412yes—
254C2×C3×C4×C5C2412yes—
255C3×C22⋊D5—28no—
256C3×C22⋊D5—44no—
257C3×C22⋊D5—44no—
258C3×C22⋊D5—44no—
259C2×C3×Dic5—22no—
260C2×C3×Dic5—22no—
261C2×C3×Dic5—22no—
262C2×C3×Dic5—22no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—44no—
265C2×C3×Dic5C2412yes—
266C2×C3×Dic5C2412yes—
267C2×C3×Dic5C2412yes—
268C2×C3×Dic5C2412yes—
269C2×C3×Dic5C2412yes—
270C3×D20—44no—
271C3×D20—44no—
272C3×C4×D5—44no—
273C3×Dic10—44no—
274C25×C3—51no—
275C22×C3×Q8—51no—
276C22×C3×D4—51no—
277C22×C3×D4—51no—
278C22×C3×D4—51no—
279C22×C3×D4—51no—
280C22×C3×D4—51no—
281C22×C3×D4—51no—
282C22×C3×D4C2×D511yescharacteristic
283C23×C3×C4—51no—
284C23×C3×C4—51no—
285C23×C3×C4C2×D511yescharacteristic
286C23×C3×C4C2×D511yescharacteristic, complemented
287C3×#126—58no—
288C3×#126—58no—
289C3×#124—58no—
290C3×#124—58no—
291C3×#123—58no—
292C3×#123—58no—
293C3×C22⋊Q8—58no—
294C3×#121—58no—
295C3×#121—58no—
296C3×#121—58no—
297C3×#120—58no—
298C3×#120—58no—
299C3×C4×D4—58no—
300C3×C4×D4C2×D518yescomplemented
301C2×C3×C4⋊C4—51no—
302C2×C3×C4⋊C4—51no—
303C2×C3×C4⋊C4—51no—
304C2×C3×C4⋊C4—51no—
305C2×C3×C4⋊C4—51no—
306C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
307C2×C3×C22⋊C4—51no—
308C2×C3×C22⋊C4—51no—
309C2×C3×C22⋊C4—51no—
310C2×C3×C22⋊C4—51no—
311C2×C3×C22⋊C4—51no—
312C2×C3×C22⋊C4—51no—
313C2×C3×C22⋊C4—58no—
314C2×C3×C22⋊C4—51no—
315C2×C3×C22⋊C4—51no—
316C2×C3×C22⋊C4—51no—
317C2×C3×C22⋊C4—51no—
318C2×C3×C22⋊C4—51no—
319C2×C3×C22⋊C4—51no—
320C2×C3×C22⋊C4C2×D511yescharacteristic
321C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
322C2×C3×C42—51no—
323C2×C3×C42C2×D511yescharacteristic, complemented
324C24×C5C23×C311yescharacteristic
325C24×C5C23×C311yescharacteristic
326C23×D5—24no—
327C23×D5—42no—
328C23×D5—42no—
329C23×D5C23×C311yescharacteristic
330C23×D5C23×C311yescharacteristic
331C23×D5C23×C311yescharacteristic
332C23×D5C23×C314yes—
333C2×C5×D4—24no—
334C2×C5×D4C23×C314yes—
335C22×C4×C5—42no—
336C22×C4×C5—42no—
337C22×C4×C5C23×C311yescharacteristic
338C22×C4×C5C23×C311yescharacteristic
339C22×C4×C5C23×C311yescharacteristic
340C22×C4×C5C23×C311yescharacteristic
341C22×C4×C5C23×C311yescharacteristic
342C22×C4×C5C23×C314yes—
343C22×C4×C5C23×C314yescomplemented
344C2×C22⋊D5—24no—
345C2×C22⋊D5—42no—
346C2×C22⋊D5—42no—
347C2×C22⋊D5—42no—
348C2×C22⋊D5C23×C314yes—
349C2×C22⋊D5C23×C314yes—
350C2×C22⋊D5C23×C314yes—
351C2×C22⋊D5C23×C314yescomplemented
352C22×Dic5—42no—
353C22×Dic5C23×C311yescharacteristic
354C22×Dic5C23×C311yescharacteristic
355C22×Dic5C23×C311yescharacteristic
356C22×Dic5C23×C311yescharacteristic
357C22×Dic5C23×C311yescharacteristic
358C22×Dic5C23×C314yes—
359C2×D20—42no—
360C2×D20—42no—
361C2×D20C23×C314yes—
362C2×D20C23×C314yes—
363C2×C4×D5—42no—
364C2×C4×D5C23×C314yescomplemented
365C2×Dic10—42no—
366C2×Dic10C23×C314yescomplemented
367C5×C4⋊C4C23×C314yescomplemented
368C5×C22⋊C4C23×C314yes—
369C5×C22⋊C4C23×C314yescomplemented
370C42×C5C23×C314yescomplemented
371C22⋊Dic5C23×C314yes—
372C22⋊Dic5C23×C314yescomplemented
373#685C23×C314yes—
374#685C23×C314yes—
375#685C23×C314yes—
376#685C23×C314yes—
377#685C23×C314yes—
378#685C23×C314yes—
379#685C23×C314yes—
380#685C23×C314yes—
381#685C23×C314yescomplemented
382#685C23×C314yescomplemented
383C4⋊Dic5C23×C314yescomplemented
384#683C23×C314yescomplemented
385#683C23×C314yescomplemented
386#683C23×C314yescomplemented
387#683C23×C314yescomplemented
388C4×Dic5C23×C314yescomplemented
389#538—516no—
390C2×#126—51no—
391C2×#126—51no—
392C2×#124—51no—
393C2×#124—51no—
394C2×#123—51no—
395C2×#123—51no—
396C2×C22⋊Q8—51no—
397C2×#121—51no—
398C2×#121—51no—
399C2×#121—51no—
400C2×#120—51no—
401C2×#120—51no—
402C2×C4×D4—51no—
403C2×C4×D4C3×D511yescharacteristic, complemented
404C22×C22⋊C4—51no—
405C22×C3×C5—28no—
406C22×C3×C5—22no—
407C22×C3×C5—22no—
408C22×C3×C5—22no—
409C22×C3×C5—22no—
410C22×C3×C5—22no—
411C22×C3×C5—44no—
412C22×C3×C5C2×#4114yes—
413C22×C3×C5C2×#4112yes—
414C22×C3×C5H(5,𝔽2)12yes—
415C22×C3×C5H(5,𝔽2)12yes—
416C22×C3×C5C2511yescharacteristic
417C2×C3×D5—22no—
418C2×C3×D5—22no—
419C2×C3×D5—22no—
420C2×C3×D5—22no—
421C2×C3×D5—22no—
422C2×C3×D5—22no—
423C2×C3×D5—22no—
424C2×C3×D5—22no—
425C2×C3×D5—22no—
426C2×C3×D5—416no—
427C2×C3×D5—44no—
428C2×C3×D5—44no—
429C2×C3×D5—44no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433C3×C4×C5—22no—
434C3×C4×C5—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—22no—
438C3×Dic5—22no—
439C3×Dic5—22no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—51no—
443C24×C3—54no—
444C24×C3—104no—
445C24×C3—202no—
446C24×C3—202no—
447C24×C3C22×D511yescharacteristic
448C24×C3C22×D511yescharacteristic
449C2×C3×Q8—54no—
450C2×C3×Q8—202no—
451C2×C3×D4—24no—
452C2×C3×D4—54no—
453C2×C3×D4—54no—
454C2×C3×D4—54no—
455C2×C3×D4—54no—
456C2×C3×D4—54no—
457C2×C3×D4—54no—
458C2×C3×D4—104no—
459C2×C3×D4—202no—
460C2×C3×D4—202no—
461C2×C3×D4—202no—
462C2×C3×D4—202no—
463C2×C3×D4—202no—
464C2×C3×D4C22×D514yes—
465C22×C3×C4—42no—
466C22×C3×C4—42no—
467C22×C3×C4—51no—
468C22×C3×C4—51no—
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—54no—
473C22×C3×C4—54no—
474C22×C3×C4—202no—
475C22×C3×C4—202no—
476C22×C3×C4C22×D511yescharacteristic
477C22×C3×C4C22×D511yescharacteristic
478C22×C3×C4C22×D511yescharacteristic
479C22×C3×C4C22×D511yescharacteristic
480C22×C3×C4C22×D511yescharacteristic
481C22×C3×C4C22×D514yes—
482C22×C3×C4C22×D514yescomplemented
483C3×C4⋊C4—54no—
484C3×C4⋊C4—54no—
485C3×C4⋊C4—54no—
486C3×C4⋊C4—54no—
487C3×C4⋊C4—54no—
488C3×C4⋊C4C22×D514yescomplemented
489C3×C22⋊C4—54no—
490C3×C22⋊C4—54no—
491C3×C22⋊C4—54no—
492C3×C22⋊C4—54no—
493C3×C22⋊C4—54no—
494C3×C22⋊C4—54no—
495C3×C22⋊C4—54no—
496C3×C22⋊C4—54no—
497C3×C22⋊C4—54no—
498C3×C22⋊C4—54no—
499C3×C22⋊C4—54no—
500C3×C22⋊C4—54no—
501C3×C22⋊C4C22×D514yes—
502C3×C22⋊C4C22×D514yescomplemented
503C3×C42—54no—
504C3×C42C22×D514yescomplemented
505C23×C5—22no—
506C23×C5—22no—
507C23×C5—22no—
508C23×C5—22no—
509C23×C5—22no—
510C23×C5C3×#4114yes—
511C23×C5C24×C312yes—
512C23×C5C24×C312yes—
513C23×C5C24×C311yescharacteristic
514C22×D5—22no—
515C22×D5—28no—
516C22×D5—22no—
517C22×D5—22no—
518C22×D5—22no—
519C22×D5—22no—
520C22×D5—22no—
521C22×D5—22no—
522C22×D5—22no—
523C22×D5—22no—
524C22×D5—44no—
525C22×D5—44no—
526C22×D5—416no—
527C22×D5C24×C312yes—
528C22×D5C24×C312yes—
529C22×D5C24×C312yes—
530C5×D4—28no—
531C2×C4×C5—22no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—22no—
536C2×C4×C5—44no—
537C2×C4×C5—44no—
538C2×C4×C5C24×C312yes—
539C2×C4×C5C24×C312yes—
540C2×C4×C5C24×C312yes—
541C2×C4×C5C24×C312yes—
542C2×C4×C5C24×C312yes—
543C22⋊D5—28no—
544C22⋊D5—44no—
545C22⋊D5—44no—
546C22⋊D5—44no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—22no—
550C2×Dic5—22no—
551C2×Dic5—22no—
552C2×Dic5—44no—
553C2×Dic5C24×C312yes—
554C2×Dic5C24×C312yes—
555C2×Dic5C24×C312yes—
556C2×Dic5C24×C312yes—
557C2×Dic5C24×C312yes—
558D20—44no—
559D20—44no—
560C4×D5—44no—
561Dic10—44no—
562C25—51no—
563C22×Q8—51no—
564C22×D4—51no—
565C22×D4—51no—
566C22×D4—51no—
567C22×D4—51no—
568C22×D4—51no—
569C22×D4—51no—
570C22×D4C2×C3×D511yescharacteristic
571C23×C4—51no—
572C23×C4—51no—
573C23×C4C2×C3×D511yescharacteristic
574C23×C4C2×C3×D511yescharacteristic, complemented
575#126—58no—
576#126—58no—
577#124—58no—
578#124—58no—
579#123—58no—
580#123—58no—
581C22⋊Q8—58no—
582#121—58no—
583#121—58no—
584#121—58no—
585#120—58no—
586#120—58no—
587C4×D4—58no—
588C4×D4C2×C3×D518yescomplemented
589C2×C4⋊C4—51no—
590C2×C4⋊C4—51no—
591C2×C4⋊C4—51no—
592C2×C4⋊C4—51no—
593C2×C4⋊C4—51no—
594C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
595C2×C22⋊C4—51no—
596C2×C22⋊C4—51no—
597C2×C22⋊C4—51no—
598C2×C22⋊C4—51no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—58no—
602C2×C22⋊C4—51no—
603C2×C22⋊C4—51no—
604C2×C22⋊C4—51no—
605C2×C22⋊C4—51no—
606C2×C22⋊C4—51no—
607C2×C22⋊C4—51no—
608C2×C22⋊C4C2×C3×D511yescharacteristic
609C2×C22⋊C4C2×C3×D511yescharacteristic, complemented
610C2×C42—51no—
611C2×C42C2×C3×D511yescharacteristic, complemented
612C2×C3×C5—24no—
613C2×C3×C5—42no—
614C2×C3×C5#53814yescomplemented
615C2×C3×C5C22×#4111yescharacteristic
616C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
617C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
618C3×D5—42no—
619C3×D5—42no—
620C3×D5—42no—
621C23×C3—22no—
622C23×C3—22no—
623C23×C3—22no—
624C23×C3—22no—
625C23×C3—22no—
626C23×C3—52no—
627C23×C3—52no—
628C23×C3—52no—
629C23×C3—102no—
630C23×C3—108no—
631C23×C3—102no—
632C23×C3—102no—
633C23×C3—102no—
634C23×C3—102no—
635C23×C3—102no—
636C23×C3—102no—
637C23×C3—102no—
638C23×C3—102no—
639C23×C3—204no—
640C23×C3—204no—
641C23×C3—2016no—
642C23×C3#70914yes—
643C23×C3C23×D512yes—
644C23×C3C23×D512yes—
645C23×C3C23×D511yescharacteristic
646C3×Q8—204no—
647C3×D4—28no—
648C3×D4—108no—
649C3×D4—204no—
650C3×D4—204no—
651C3×D4—204no—
652C3×D4—204no—
653C3×D4—204no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—22no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—44no—
660C2×C3×C4—44no—
661C2×C3×C4—52no—
662C2×C3×C4—52no—
663C2×C3×C4—52no—
664C2×C3×C4—52no—
665C2×C3×C4—52no—
666C2×C3×C4—102no—
667C2×C3×C4—102no—
668C2×C3×C4—102no—
669C2×C3×C4—102no—
670C2×C3×C4—102no—
671C2×C3×C4—204no—
672C2×C3×C4—204no—
673C2×C3×C4C23×D512yes—
674C2×C3×C4C23×D512yes—
675C2×C3×C4C23×D512yes—
676C2×C3×C4C23×D512yes—
677C2×C3×C4C23×D512yes—
678C22×C5—22no—
679C22×C5—22no—
680C22×C5—28no—
681C22×C5—22no—
682C22×C5—22no—
683C22×C5—22no—
684C22×C5—44no—
685C22×C5C2×C3×#4114yes—
686C22×C5C2×C3×#4112yes—
687C22×C5C3×H(5,𝔽2)12yes—
688C22×C5C3×H(5,𝔽2)12yes—
689C22×C5C25×C311yescharacteristic
690C2×D5—22no—
691C2×D5—22no—
692C2×D5—22no—
693C2×D5—22no—
694C2×D5—22no—
695C2×D5—22no—
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—22no—
699C2×D5—416no—
700C2×D5—44no—
701C2×D5—44no—
702C2×D5—44no—
703C4×C5—22no—
704C4×C5—22no—
705C4×C5—22no—
706C4×C5—22no—
707C4×C5—22no—
708Dic5—22no—
709Dic5—22no—
710Dic5—22no—
711Dic5—22no—
712Dic5—22no—
713C24—51no—
714C24—51no—
715C24—51no—
716C24—54no—
717C24—104no—
718C24—202no—
719C24—202no—
720C24C22×C3×D511yescharacteristic
721C24C22×C3×D511yescharacteristic
722C2×Q8—54no—
723C2×Q8—202no—
724C2×D4—24no—
725C2×D4—54no—
726C2×D4—54no—
727C2×D4—54no—
728C2×D4—54no—
729C2×D4—54no—
730C2×D4—54no—
731C2×D4—104no—
732C2×D4—202no—
733C2×D4—202no—
734C2×D4—202no—
735C2×D4—202no—
736C2×D4—202no—
737C2×D4C22×C3×D514yes—
738C22×C4—42no—
739C22×C4—42no—
740C22×C4—51no—
741C22×C4—51no—
742C22×C4—51no—
743C22×C4—51no—
744C22×C4—51no—
745C22×C4—54no—
746C22×C4—54no—
747C22×C4—202no—
748C22×C4—202no—
749C22×C4C22×C3×D511yescharacteristic
750C22×C4C22×C3×D511yescharacteristic
751C22×C4C22×C3×D511yescharacteristic
752C22×C4C22×C3×D511yescharacteristic
753C22×C4C22×C3×D511yescharacteristic
754C22×C4C22×C3×D514yes—
755C22×C4C22×C3×D514yescomplemented
756C4⋊C4—54no—
757C4⋊C4—54no—
758C4⋊C4—54no—
759C4⋊C4—54no—
760C4⋊C4—54no—
761C4⋊C4C22×C3×D514yescomplemented
762C22⋊C4—54no—
763C22⋊C4—54no—
764C22⋊C4—54no—
765C22⋊C4—54no—
766C22⋊C4—54no—
767C22⋊C4—54no—
768C22⋊C4—54no—
769C22⋊C4—54no—
770C22⋊C4—54no—
771C22⋊C4—54no—
772C22⋊C4—54no—
773C22⋊C4—54no—
774C22⋊C4C22×C3×D514yes—
775C22⋊C4C22×C3×D514yescomplemented
776C42—54no—
777C42C22×C3×D514yescomplemented
778C3×C5C2×#53811yescharacteristic, complemented, Hall
779C22×C3—28no—
780C22×C3—22no—
781C22×C3—22no—
782C22×C3—22no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—44no—
786C22×C3—102no—
787C22×C3—102no—
788C22×C3—102no—
789C22×C3—102no—
790C22×C3—102no—
791C22×C3—102no—
792C22×C3—102no—
793C22×C3—102no—
794C22×C3—102no—
795C22×C3—2016no—
796C22×C3—204no—
797C22×C3—204no—
798C22×C3—204no—
799C22×C3C2×#70914yes—
800C22×C3C2×#70912yes—
801C22×C3#414412yes—
802C22×C3#414912yes—
803C22×C3C24×D511yescharacteristic
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—102no—
810C3×C4—102no—
811C3×C4—102no—
812C3×C4—102no—
813C3×C4—102no—
814C2×C5—24no—
815C2×C5—42no—
816C2×C5C3×#53814yescomplemented
817C2×C5C22×C3×#4111yescharacteristic
818C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
819C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
820D5—42no—
821D5—42no—
822D5—42no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—52no—
829C23—52no—
830C23—52no—
831C23—102no—
832C23—108no—
833C23—102no—
834C23—102no—
835C23—102no—
836C23—102no—
837C23—102no—
838C23—102no—
839C23—102no—
840C23—102no—
841C23—204no—
842C23—204no—
843C23—2016no—
844C23C3×#70914yes—
845C23C23×C3×D512yes—
846C23C23×C3×D512yes—
847C23C23×C3×D511yescharacteristic
848Q8—204no—
849D4—28no—
850D4—108no—
851D4—204no—
852D4—204no—
853D4—204no—
854D4—204no—
855D4—204no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—52no—
864C2×C4—52no—
865C2×C4—52no—
866C2×C4—52no—
867C2×C4—52no—
868C2×C4—102no—
869C2×C4—102no—
870C2×C4—102no—
871C2×C4—102no—
872C2×C4—102no—
873C2×C4—204no—
874C2×C4—204no—
875C2×C4C23×C3×D512yes—
876C2×C4C23×C3×D512yes—
877C2×C4C23×C3×D512yes—
878C2×C4C23×C3×D512yes—
879C2×C4C23×C3×D512yes—
880C2×C3—24no—
881C2×C3—42no—
882C2×C3—202no—
883C2×C3—202no—
884C2×C3—202no—
885C2×C3#6589414yesdirect product factor
886C2×C3C22×#70911yescharacteristic
887C2×C3C2×#414411yescharacteristic
888C2×C3C2×#414911yescharacteristic
889C5C2×C3×#53811yescharacteristic, complemented, Sylow
890C22—22no—
891C22—22no—
892C22—28no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—44no—
897C22—102no—
898C22—102no—
899C22—102no—
900C22—102no—
901C22—102no—
902C22—102no—
903C22—102no—
904C22—102no—
905C22—102no—
906C22—2016no—
907C22—204no—
908C22—204no—
909C22—204no—
910C22C2×C3×#70914yes—
911C22C2×C3×#70912yes—
912C22C3×#414412yes—
913C22C3×#414912yes—
914C22C24×C3×D511yescharacteristic
915C4—22no—
916C4—22no—
917C4—22no—
918C4—22no—
919C4—22no—
920C4—102no—
921C4—102no—
922C4—102no—
923C4—102no—
924C4—102no—
925C3C2×#6589411yescharacteristic, direct product factor, Sylow
926C2—24no—
927C2—42no—
928C2—202no—
929C2—202no—
930C2—202no—
931C2C3×#6589414yesdirect product factor
932C2C22×C3×#70911yescharacteristic
933C2C2×C3×#414411yescharacteristic
934C2C2×C3×#414911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
hypercenterC2×C3×C4×D4D5
hypocenterC5C2×C3×#538
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
2. C2×C3×#4085C2semidirect
3. C2×C3×#4083C2semidirect
4. C2×C3×#4076C2semidirect
5. C2×C3×#4075C2semidirect
6. C2×C3×C4×C22⋊D5C2semidirect
7. C22×C3×#685C2semidirect
8. C3×#65894C2direct (N × H)
9. C2×C3×#4044C2semidirect
10. C2×C3×#4040C2semidirect
11. C2×C3×#4031C2semidirect
12. C2×C3×#4030C2semidirect
13. C2×C3×#4028C2semidirect
14. C2×C3×#4024C2semidirect
15. C2×C3×#4022C2semidirect
16. C2×C3×#4021C2semidirect
17. C2×#65894C3direct (N × H)
21. C23×C3×C4×C5C22semidirect
25. C22×C3×C22⋊D5C22semidirect
29. C22×C3×C4×D5C22semidirect
30. C22×C3×Dic10C22semidirect
31. C3×C4×C5×D4C22semidirect
32. C2×C3×C5×C4⋊C4C22semidirect
34. C2×C3×C5×C22⋊C4C22semidirect
35. C2×C3×C42×C5C22semidirect
37. C2×C3×C22⋊Dic5C22semidirect
38. C3×#4085C22semidirect
39. C3×#4083C22semidirect
40. C3×#4076C22semidirect
41. C3×#4075C22semidirect
42. C3×C4×C22⋊D5C22semidirect
51. C2×C3×#685C22semidirect
52. C2×C3×#685C22semidirect
53. C2×C3×#685C22semidirect
54. C2×C3×C4⋊Dic5C22semidirect
55. C2×C3×#683C22semidirect
56. C2×C3×#683C22semidirect
57. C2×C3×#683C22semidirect
58. C2×C3×#683C22semidirect
59. C2×C3×C4×Dic5C22semidirect
60. C3×#4044C22semidirect
61. C3×#4040C22semidirect
62. C3×#4031C22semidirect
63. C3×#4030C22semidirect
64. C3×#4028C22semidirect
65. C3×#4024C22semidirect
66. C3×#4022C22semidirect
67. C3×#4021C22semidirect
69. C2×C4×C5×D4C2×C3semidirect
70. C2×#4085C2×C3semidirect
71. C2×#4083C2×C3semidirect
72. C2×#4076C2×C3semidirect
73. C2×#4075C2×C3semidirect
74. C2×C4×C22⋊D5C2×C3semidirect
75. C22×#685C2×C3semidirect
76. #65894C2×C3direct (N × H)
77. C2×#4044C2×C3semidirect
78. C2×#4040C2×C3semidirect
79. C2×#4031C2×C3semidirect
80. C2×#4030C2×C3semidirect
81. C2×#4028C2×C3semidirect
82. C2×#4024C2×C3semidirect
83. C2×#4022C2×C3semidirect
84. C2×#4021C2×C3semidirect
104. C22×C3×C4×C5C23semidirect
112. C2×C3×C22⋊D5C23semidirect
125. C2×C3×C4×D5C23semidirect
127. C2×C3×Dic10C23semidirect
128. C3×C5×C4⋊C4C23semidirect
130. C3×C5×C22⋊C4C23semidirect
131. C3×C42×C5C23semidirect
133. C3×C22⋊Dic5C23semidirect
142. C3×#685C23semidirect
143. C3×#685C23semidirect
144. C3×C4⋊Dic5C23semidirect
145. C3×#683C23semidirect
146. C3×#683C23semidirect
147. C3×#683C23semidirect
148. C3×#683C23semidirect
149. C3×C4×Dic5C23semidirect
164. C2×C3×C4×D4D5semidirect
169. C23×C4×C5C22×C3semidirect
173. C22×C22⋊D5C22×C3semidirect
177. C22×C4×D5C22×C3semidirect
178. C22×Dic10C22×C3semidirect
179. C4×C5×D4C22×C3semidirect
180. C2×C5×C4⋊C4C22×C3semidirect
182. C2×C5×C22⋊C4C22×C3semidirect
183. C2×C42×C5C22×C3semidirect
185. C2×C22⋊Dic5C22×C3semidirect
186. #4085C22×C3semidirect
187. #4083C22×C3semidirect
188. #4076C22×C3semidirect
189. #4075C22×C3semidirect
190. C4×C22⋊D5C22×C3semidirect
199. C2×#685C22×C3semidirect
200. C2×#685C22×C3semidirect
201. C2×#685C22×C3semidirect
202. C2×C4⋊Dic5C22×C3semidirect
203. C2×#683C22×C3semidirect
204. C2×#683C22×C3semidirect
205. C2×#683C22×C3semidirect
206. C2×#683C22×C3semidirect
207. C2×C4×Dic5C22×C3semidirect
208. #4044C22×C3semidirect
209. #4040C22×C3semidirect
210. #4031C22×C3semidirect
211. #4030C22×C3semidirect
212. #4028C22×C3semidirect
213. #4024C22×C3semidirect
214. #4022C22×C3semidirect
215. #4021C22×C3semidirect
286. C23×C3×C4C2×D5semidirect
300. C3×C4×D4C2×D5semidirect
306. C2×C3×C4⋊C4C2×D5semidirect
321. C2×C3×C22⋊C4C2×D5semidirect
323. C2×C3×C42C2×D5semidirect
343. C22×C4×C5C23×C3semidirect
351. C2×C22⋊D5C23×C3semidirect
364. C2×C4×D5C23×C3semidirect
366. C2×Dic10C23×C3semidirect
367. C5×C4⋊C4C23×C3semidirect
369. C5×C22⋊C4C23×C3semidirect
370. C42×C5C23×C3semidirect
372. C22⋊Dic5C23×C3semidirect
381. #685C23×C3semidirect
382. #685C23×C3semidirect
383. C4⋊Dic5C23×C3semidirect
384. #683C23×C3semidirect
385. #683C23×C3semidirect
386. #683C23×C3semidirect
387. #683C23×C3semidirect
388. C4×Dic5C23×C3semidirect
403. C2×C4×D4C3×D5semidirect
482. C22×C3×C4C22×D5semidirect
488. C3×C4⋊C4C22×D5semidirect
502. C3×C22⋊C4C22×D5semidirect
504. C3×C42C22×D5semidirect
574. C23×C4C2×C3×D5semidirect
588. C4×D4C2×C3×D5semidirect
594. C2×C4⋊C4C2×C3×D5semidirect
609. C2×C22⋊C4C2×C3×D5semidirect
611. C2×C42C2×C3×D5semidirect
614. C2×C3×C5#538semidirect
755. C22×C4C22×C3×D5semidirect
761. C4⋊C4C22×C3×D5semidirect
775. C22⋊C4C22×C3×D5semidirect
777. C42C22×C3×D5semidirect
778. C3×C5C2×#538semidirect
816. C2×C5C3×#538semidirect
885. C2×C3#65894direct (N × H)
889. C5C2×C3×#538semidirect
925. C3C2×#65894direct (N × H)
931. C2C3×#65894direct (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×C5×D42
C2×C3×#40852
C2×C3×#40832
C2×C3×#40762
C2×C3×#40752
C2×C3×C4×C22⋊D52
C22×C3×#6852
C3×#658942
C2×C3×#40442
C2×C3×#40402
C2×C3×#40312
C2×C3×#40302
C2×C3×#40282
C2×C3×#40242
C2×C3×#40222
C2×C3×#40212
C2×#658943
C2×C3×#5385