Finite Group Databasebeta

← C2×C3×#65890 #14483251

Subgroups — C2×C3×#65890 #14483251

Order 1920.

2656 conjugacy classes of subgroups.

The subgroup lattice has 888 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×#4083C211yesmaximal, characteristic
3C2×C3×#4081C211yesmaximal, characteristic, complemented
4C2×C3×#4075C211yesmaximal, characteristic, complemented
5C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
6C22×C3×#685C211yesmaximal, characteristic, complemented
7C2×C3×#4070C211yesmaximal, characteristic, complemented
8C3×#65890C2116yesmaximal, direct product factor
9C2×C3×#4044C211yesmaximal, characteristic, complemented
10C2×C3×#4042C211yesmaximal, characteristic, complemented
11C2×C3×#4031C211yesmaximal, characteristic, complemented
12C2×C3×#4029C211yesmaximal, characteristic, complemented
13C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
14C2×C3×#4023C211yesmaximal, characteristic, complemented
15C2×C3×#4022C211yesmaximal, characteristic, complemented
16C2×C3×#4018C211yesmaximal, characteristic, complemented
17C2×#65890C311yesmaximal, 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
24C23×C3×Dic5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C22×C3×C4×D5C2211yescharacteristic
27C22×C3×Dic10C2211yescharacteristic, complemented
28C3×C4×C5×D4C2218yescomplemented
29C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
30C2×C3×C5×C22⋊C4C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
32C2×C3×C42×C5C2211yescharacteristic, complemented
33C2×C3×C22⋊Dic5C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
36C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
37C3×#4083C2218yes—
38C3×#4081C2218yescomplemented
39C3×#4075C2218yescomplemented
40C3×C4×C22⋊D5C2218yescomplemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic
47C2×C3×#685C2211yescharacteristic
48C2×C3×#685C2211yescharacteristic
49C2×C3×#685C2218yescomplemented
50C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
51C3×#4070C2218yescomplemented
52C2×C3×#683C2211yescharacteristic, complemented
53C2×C3×#683C2211yescharacteristic, complemented
54C2×C3×#683C2211yescharacteristic, complemented
55C2×C3×#683C2211yescharacteristic, complemented
56C2×C3×#683C2211yescharacteristic, complemented
57C2×C3×#683C2211yescharacteristic, complemented
58C2×C3×C4×Dic5C2211yescharacteristic, complemented
59C2×C3×C4×Dic5C2211yescharacteristic, complemented
60C3×#4044C2218yescomplemented
61C3×#4042C2218yescomplemented
62C3×#4031C2218yescomplemented
63C3×#4029C2218yescomplemented
64C3×D5×C22⋊C4C2218yescomplemented
65C3×#4023C2218yescomplemented
66C3×#4022C2218yescomplemented
67C3×#4018C2218yescomplemented
68C2×C3×#551—51nomaximal, Hall
69C2×C4×C5×D4C2×C311yescharacteristic, complemented
70C2×#4083C2×C311yescharacteristic
71C2×#4081C2×C311yescharacteristic, complemented
72C2×#4075C2×C311yescharacteristic, complemented
73C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
74C22×#685C2×C311yescharacteristic, complemented
75C2×#4070C2×C311yescharacteristic, complemented
76#65890C2×C3116yesdirect product factor
77C2×#4044C2×C311yescharacteristic, complemented
78C2×#4042C2×C311yescharacteristic, complemented
79C2×#4031C2×C311yescharacteristic, complemented
80C2×#4029C2×C311yescharacteristic, complemented
81C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
82C2×#4023C2×C311yescharacteristic, complemented
83C2×#4022C2×C311yescharacteristic, complemented
84C2×#4018C2×C311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×C3×D5—24no—
88C23×C3×D5—24no—
89C23×C3×D5—42no—
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2314yes—
92C23×C3×D5C2311yescharacteristic
93C2×C3×C5×D4—24no—
94C2×C3×C5×D4C2314yes—
95C22×C3×C4×C5—42no—
96C22×C3×C4×C5—42no—
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2311yescharacteristic
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2311yescharacteristic
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2314yes—
103C22×C3×C4×C5C2314yescomplemented
104C2×C3×C22⋊D5—24no—
105C2×C3×C22⋊D5—42no—
106C2×C3×C22⋊D5C2314yes—
107C2×C3×C22⋊D5C2314yes—
108C22×C3×Dic5—24no—
109C22×C3×Dic5C2314yes—
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C2×C3×C4×D5—24no—
117C2×C3×C4×D5—42no—
118C2×C3×C4×D5C2314yes—
119C2×C3×C4×D5C2314yes—
120C2×C3×Dic10—42no—
121C2×C3×Dic10C2314yescomplemented
122C3×C5×C4⋊C4C2314yescomplemented
123C3×C5×C22⋊C4C2314yes—
124C3×C5×C22⋊C4C2314yescomplemented
125C3×C42×C5C2314yescomplemented
126C3×C22⋊Dic5C2314yes—
127C3×C22⋊Dic5C2314yes—
128C3×C22⋊Dic5C2314yescomplemented
129C3×C22⋊Dic5C2314yescomplemented
130C3×#685C2314yes—
131C3×#685C2314yes—
132C3×#685C2314yes—
133C3×#685C2314yes—
134C3×#685C2314yes—
135C3×#685C2314yes—
136C3×#685C2314yes—
137C3×#685C2314yes—
138C3×C4⋊Dic5C2314yescomplemented
139C3×#683C2314yescomplemented
140C3×#683C2314yescomplemented
141C3×#683C2314yescomplemented
142C3×#683C2314yescomplemented
143C3×#683C2314yescomplemented
144C3×#683C2314yescomplemented
145C3×C4×Dic5C2314yescomplemented
146C3×C4×Dic5C2314yescomplemented
147C3×#551—516no—
148C2×C3×#126—51no—
149C2×C3×#126—51no—
150C2×C3×#124—51no—
151C2×C3×#123—51no—
152C2×C3×#123—51no—
153C2×C3×#123—51no—
154C2×C3×C22⋊Q8—51no—
155C2×C3×C22⋊Q8—51no—
156C2×C3×#120—51no—
157C2×C3×C4×D4—51no—
158C2×C3×C4×D4D511yescharacteristic, complemented
159C2×C3×#117—51no—
160C2×C3×#117—51no—
161C22×C3×C22⋊C4—51no—
162C22×C3×C22⋊C4—51no—
163C24×D5C22×C311yescharacteristic
164C22×C5×D4C22×C311yescharacteristic
165C23×C4×C5C22×C311yescharacteristic
166C23×C4×C5C22×C311yescharacteristic, complemented
167C22×C22⋊D5C22×C311yescharacteristic
168C22×C22⋊D5C22×C311yescharacteristic
169C23×Dic5C22×C311yescharacteristic
170C22×C4×D5C22×C311yescharacteristic
171C22×C4×D5C22×C311yescharacteristic
172C22×Dic10C22×C311yescharacteristic, complemented
173C4×C5×D4C22×C318yescomplemented
174C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
175C2×C5×C22⋊C4C22×C311yescharacteristic
176C2×C5×C22⋊C4C22×C311yescharacteristic, complemented
177C2×C42×C5C22×C311yescharacteristic, complemented
178C2×C22⋊Dic5C22×C311yescharacteristic
179C2×C22⋊Dic5C22×C311yescharacteristic
180C2×C22⋊Dic5C22×C311yescharacteristic, complemented
181C2×C22⋊Dic5C22×C311yescharacteristic, complemented
182#4083C22×C318yes—
183#4081C22×C318yescomplemented
184#4075C22×C318yescomplemented
185C4×C22⋊D5C22×C318yescomplemented
186C2×#685C22×C311yescharacteristic
187C2×#685C22×C311yescharacteristic
188C2×#685C22×C311yescharacteristic
189C2×#685C22×C311yescharacteristic
190C2×#685C22×C311yescharacteristic
191C2×#685C22×C311yescharacteristic
192C2×#685C22×C311yescharacteristic
193C2×#685C22×C311yescharacteristic
194C2×#685C22×C318yescomplemented
195C2×C4⋊Dic5C22×C311yescharacteristic, complemented
196#4070C22×C318yescomplemented
197C2×#683C22×C311yescharacteristic, complemented
198C2×#683C22×C311yescharacteristic, complemented
199C2×#683C22×C311yescharacteristic, complemented
200C2×#683C22×C311yescharacteristic, complemented
201C2×#683C22×C311yescharacteristic, complemented
202C2×#683C22×C311yescharacteristic, complemented
203C2×C4×Dic5C22×C311yescharacteristic, complemented
204C2×C4×Dic5C22×C311yescharacteristic, complemented
205#4044C22×C318yescomplemented
206#4042C22×C318yescomplemented
207#4031C22×C318yescomplemented
208#4029C22×C318yescomplemented
209D5×C22⋊C4C22×C318yescomplemented
210#4023C22×C318yescomplemented
211#4022C22×C318yescomplemented
212#4018C22×C318yescomplemented
213C2×#551—51noSylow
214C23×C3×C5—22no—
215C23×C3×C5—22no—
216C23×C3×C5—22no—
217C23×C3×C5—22no—
218C23×C3×C5—22no—
219C23×C3×C5#4114yes—
220C23×C3×C5C2412yes—
221C23×C3×C5C2412yes—
222C23×C3×C5C2411yescharacteristic
223C22×C3×D5—22no—
224C22×C3×D5—22no—
225C22×C3×D5—28no—
226C22×C3×D5—22no—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5—28no—
230C22×C3×D5—44no—
231C22×C3×D5—416no—
232C22×C3×D5#4114yes—
233C22×C3×D5C2412yes—
234C22×C3×D5C2412yes—
235C3×C5×D4—28no—
236C2×C3×C4×C5—22no—
237C2×C3×C4×C5—22no—
238C2×C3×C4×C5—22no—
239C2×C3×C4×C5—22no—
240C2×C3×C4×C5—22no—
241C2×C3×C4×C5—44no—
242C2×C3×C4×C5—44no—
243C2×C3×C4×C5C2412yes—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246C2×C3×C4×C5C2412yes—
247C2×C3×C4×C5C2412yes—
248C3×C22⋊D5—28no—
249C3×C22⋊D5—44no—
250C2×C3×Dic5—22no—
251C2×C3×Dic5—28no—
252C2×C3×Dic5—22no—
253C2×C3×Dic5—22no—
254C2×C3×Dic5—22no—
255C2×C3×Dic5—22no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5C2412yes—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261C2×C3×Dic5C2412yes—
262C2×C3×Dic5C2412yes—
263C3×C4×D5—28no—
264C3×C4×D5—44no—
265C3×Dic10—44no—
266C25×C3—51no—
267C22×C3×Q8—51no—
268C22×C3×D4—51no—
269C22×C3×D4—51no—
270C22×C3×D4C2×D511yescharacteristic
271C23×C3×C4—51no—
272C23×C3×C4—51no—
273C23×C3×C4—51no—
274C23×C3×C4C2×D511yescharacteristic
275C23×C3×C4C2×D511yescharacteristic, complemented
276C3×#126—58no—
277C3×#126—58no—
278C3×#124—58no—
279C3×#123—58no—
280C3×#123—58no—
281C3×#123—58no—
282C3×C22⋊Q8—58no—
283C3×C22⋊Q8—58no—
284C3×#120—58no—
285C3×C4×D4—58no—
286C3×C4×D4C2×D518yescomplemented
287C3×#117—58no—
288C3×#117—58no—
289C2×C3×C4⋊C4—51no—
290C2×C3×C4⋊C4—51no—
291C2×C3×C4⋊C4—51no—
292C2×C3×C4⋊C4—51no—
293C2×C3×C4⋊C4—51no—
294C2×C3×C4⋊C4—51no—
295C2×C3×C4⋊C4—51no—
296C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
297C2×C3×C22⋊C4—51no—
298C2×C3×C22⋊C4—51no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4—51no—
305C2×C3×C22⋊C4—51no—
306C2×C3×C22⋊C4—51no—
307C2×C3×C22⋊C4—58no—
308C2×C3×C22⋊C4—51no—
309C2×C3×C22⋊C4—51no—
310C2×C3×C22⋊C4—58no—
311C2×C3×C22⋊C4C2×D511yescharacteristic
312C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
313C2×C3×C42—51no—
314C2×C3×C42—51no—
315C2×C3×C42C2×D511yescharacteristic, complemented
316C24×C5C23×C311yescharacteristic
317C24×C5C23×C311yescharacteristic
318C23×D5—24no—
319C23×D5—24no—
320C23×D5—42no—
321C23×D5C23×C311yescharacteristic
322C23×D5C23×C314yes—
323C23×D5C23×C311yescharacteristic
324C2×C5×D4—24no—
325C2×C5×D4C23×C314yes—
326C22×C4×C5—42no—
327C22×C4×C5—42no—
328C22×C4×C5C23×C311yescharacteristic
329C22×C4×C5C23×C311yescharacteristic
330C22×C4×C5C23×C311yescharacteristic
331C22×C4×C5C23×C311yescharacteristic
332C22×C4×C5C23×C311yescharacteristic
333C22×C4×C5C23×C314yes—
334C22×C4×C5C23×C314yescomplemented
335C2×C22⋊D5—24no—
336C2×C22⋊D5—42no—
337C2×C22⋊D5C23×C314yes—
338C2×C22⋊D5C23×C314yes—
339C22×Dic5—24no—
340C22×Dic5C23×C311yescharacteristic
341C22×Dic5C23×C311yescharacteristic
342C22×Dic5C23×C311yescharacteristic
343C22×Dic5C23×C311yescharacteristic
344C22×Dic5C23×C311yescharacteristic
345C22×Dic5C23×C311yescharacteristic
346C22×Dic5C23×C314yes—
347C2×C4×D5—24no—
348C2×C4×D5—42no—
349C2×C4×D5C23×C314yes—
350C2×C4×D5C23×C314yes—
351C2×Dic10—42no—
352C2×Dic10C23×C314yescomplemented
353C5×C4⋊C4C23×C314yescomplemented
354C5×C22⋊C4C23×C314yes—
355C5×C22⋊C4C23×C314yescomplemented
356C42×C5C23×C314yescomplemented
357C22⋊Dic5C23×C314yes—
358C22⋊Dic5C23×C314yes—
359C22⋊Dic5C23×C314yescomplemented
360C22⋊Dic5C23×C314yescomplemented
361#685C23×C314yes—
362#685C23×C314yes—
363#685C23×C314yes—
364#685C23×C314yes—
365#685C23×C314yes—
366#685C23×C314yes—
367#685C23×C314yes—
368#685C23×C314yes—
369C4⋊Dic5C23×C314yescomplemented
370#683C23×C314yescomplemented
371#683C23×C314yescomplemented
372#683C23×C314yescomplemented
373#683C23×C314yescomplemented
374#683C23×C314yescomplemented
375#683C23×C314yescomplemented
376C4×Dic5C23×C314yescomplemented
377C4×Dic5C23×C314yescomplemented
378#551—516no—
379C2×#126—51no—
380C2×#126—51no—
381C2×#124—51no—
382C2×#123—51no—
383C2×#123—51no—
384C2×#123—51no—
385C2×C22⋊Q8—51no—
386C2×C22⋊Q8—51no—
387C2×#120—51no—
388C2×C4×D4—51no—
389C2×C4×D4C3×D511yescharacteristic, complemented
390C2×#117—51no—
391C2×#117—51no—
392C22×C22⋊C4—51no—
393C22×C22⋊C4—51no—
394C22×C3×C5—28no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—44no—
401C22×C3×C5C2×#4114yes—
402C22×C3×C5C2×#4112yes—
403C22×C3×C5C2×#4112yes—
404C22×C3×C5H(5,𝔽2)12yes—
405C22×C3×C5C2511yescharacteristic
406C2×C3×D5—28no—
407C2×C3×D5—22no—
408C2×C3×D5—22no—
409C2×C3×D5—22no—
410C2×C3×D5—22no—
411C2×C3×D5—22no—
412C2×C3×D5—416no—
413C2×C3×D5—44no—
414C2×C3×D5C2×#4114yes—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417C3×C4×C5—22no—
418C3×C4×C5—22no—
419C3×C4×C5—22no—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C3×Dic5—22no—
423C3×Dic5—22no—
424C3×Dic5—22no—
425C3×Dic5—22no—
426C24×C3—51no—
427C24×C3—51no—
428C24×C3—54no—
429C24×C3—104no—
430C24×C3—104no—
431C24×C3—202no—
432C24×C3C22×D511yescharacteristic
433C24×C3C22×D511yescharacteristic
434C2×C3×Q8—54no—
435C2×C3×Q8—202no—
436C2×C3×D4—24no—
437C2×C3×D4—54no—
438C2×C3×D4—54no—
439C2×C3×D4—104no—
440C2×C3×D4—202no—
441C2×C3×D4C22×D514yes—
442C22×C3×C4—42no—
443C22×C3×C4—42no—
444C22×C3×C4—54no—
445C22×C3×C4—51no—
446C22×C3×C4—51no—
447C22×C3×C4—51no—
448C22×C3×C4—51no—
449C22×C3×C4—51no—
450C22×C3×C4—51no—
451C22×C3×C4—54no—
452C22×C3×C4—54no—
453C22×C3×C4—104no—
454C22×C3×C4—104no—
455C22×C3×C4—202no—
456C22×C3×C4C22×D511yescharacteristic
457C22×C3×C4C22×D511yescharacteristic
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D514yes—
462C22×C3×C4C22×D514yescomplemented
463C3×C4⋊C4—54no—
464C3×C4⋊C4—54no—
465C3×C4⋊C4—54no—
466C3×C4⋊C4—54no—
467C3×C4⋊C4—54no—
468C3×C4⋊C4—54no—
469C3×C4⋊C4—54no—
470C3×C4⋊C4C22×D514yescomplemented
471C3×C22⋊C4—54no—
472C3×C22⋊C4—54no—
473C3×C22⋊C4—54no—
474C3×C22⋊C4—54no—
475C3×C22⋊C4—54no—
476C3×C22⋊C4—54no—
477C3×C22⋊C4—54no—
478C3×C22⋊C4—54no—
479C3×C22⋊C4—54no—
480C3×C22⋊C4—54no—
481C3×C22⋊C4—54no—
482C3×C22⋊C4—54no—
483C3×C22⋊C4C22×D514yes—
484C3×C22⋊C4C22×D514yescomplemented
485C3×C42—54no—
486C3×C42—54no—
487C3×C42C22×D514yescomplemented
488C23×C5—22no—
489C23×C5—22no—
490C23×C5—22no—
491C23×C5—22no—
492C23×C5—22no—
493C23×C5C3×#4114yes—
494C23×C5C24×C312yes—
495C23×C5C24×C312yes—
496C23×C5C24×C311yescharacteristic
497C22×D5—22no—
498C22×D5—22no—
499C22×D5—28no—
500C22×D5—22no—
501C22×D5—22no—
502C22×D5—22no—
503C22×D5—28no—
504C22×D5—44no—
505C22×D5—416no—
506C22×D5C3×#4114yes—
507C22×D5C24×C312yes—
508C22×D5C24×C312yes—
509C5×D4—28no—
510C2×C4×C5—22no—
511C2×C4×C5—22no—
512C2×C4×C5—22no—
513C2×C4×C5—22no—
514C2×C4×C5—22no—
515C2×C4×C5—44no—
516C2×C4×C5—44no—
517C2×C4×C5C24×C312yes—
518C2×C4×C5C24×C312yes—
519C2×C4×C5C24×C312yes—
520C2×C4×C5C24×C312yes—
521C2×C4×C5C24×C312yes—
522C22⋊D5—28no—
523C22⋊D5—44no—
524C2×Dic5—22no—
525C2×Dic5—28no—
526C2×Dic5—22no—
527C2×Dic5—22no—
528C2×Dic5—22no—
529C2×Dic5—22no—
530C2×Dic5—22no—
531C2×Dic5C24×C312yes—
532C2×Dic5C24×C312yes—
533C2×Dic5C24×C312yes—
534C2×Dic5C24×C312yes—
535C2×Dic5C24×C312yes—
536C2×Dic5C24×C312yes—
537C4×D5—28no—
538C4×D5—44no—
539Dic10—44no—
540C25—51no—
541C22×Q8—51no—
542C22×D4—51no—
543C22×D4—51no—
544C22×D4C2×C3×D511yescharacteristic
545C23×C4—51no—
546C23×C4—51no—
547C23×C4—51no—
548C23×C4C2×C3×D511yescharacteristic
549C23×C4C2×C3×D511yescharacteristic, complemented
550#126—58no—
551#126—58no—
552#124—58no—
553#123—58no—
554#123—58no—
555#123—58no—
556C22⋊Q8—58no—
557C22⋊Q8—58no—
558#120—58no—
559C4×D4—58no—
560C4×D4C2×C3×D518yescomplemented
561#117—58no—
562#117—58no—
563C2×C4⋊C4—51no—
564C2×C4⋊C4—51no—
565C2×C4⋊C4—51no—
566C2×C4⋊C4—51no—
567C2×C4⋊C4—51no—
568C2×C4⋊C4—51no—
569C2×C4⋊C4—51no—
570C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
571C2×C22⋊C4—51no—
572C2×C22⋊C4—51no—
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—51no—
580C2×C22⋊C4—51no—
581C2×C22⋊C4—58no—
582C2×C22⋊C4—51no—
583C2×C22⋊C4—51no—
584C2×C22⋊C4—58no—
585C2×C22⋊C4C2×C3×D511yescharacteristic
586C2×C22⋊C4C2×C3×D511yescharacteristic, complemented
587C2×C42—51no—
588C2×C42—51no—
589C2×C42C2×C3×D511yescharacteristic, complemented
590C2×C3×C5—24no—
591C2×C3×C5—42no—
592C2×C3×C5#55114yescomplemented
593C2×C3×C5C22×#4111yescharacteristic
594C2×C3×C5C22×#4111yescharacteristic
595C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
596C3×D5—24no—
597C3×D5—42no—
598C23×C3—22no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—22no—
602C23×C3—22no—
603C23×C3—54no—
604C23×C3—52no—
605C23×C3—52no—
606C23×C3—108no—
607C23×C3—102no—
608C23×C3—102no—
609C23×C3—108no—
610C23×C3—102no—
611C23×C3—102no—
612C23×C3—102no—
613C23×C3—204no—
614C23×C3—2016no—
615C23×C3#70914yes—
616C23×C3C23×D512yes—
617C23×C3C23×D512yes—
618C23×C3C23×D511yescharacteristic
619C3×Q8—204no—
620C3×D4—28no—
621C3×D4—108no—
622C3×D4—204no—
623C2×C3×C4—22no—
624C2×C3×C4—22no—
625C2×C3×C4—22no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—44no—
629C2×C3×C4—44no—
630C2×C3×C4—52no—
631C2×C3×C4—52no—
632C2×C3×C4—52no—
633C2×C3×C4—52no—
634C2×C3×C4—52no—
635C2×C3×C4—52no—
636C2×C3×C4—108no—
637C2×C3×C4—108no—
638C2×C3×C4—102no—
639C2×C3×C4—102no—
640C2×C3×C4—102no—
641C2×C3×C4—102no—
642C2×C3×C4—102no—
643C2×C3×C4—102no—
644C2×C3×C4—204no—
645C2×C3×C4C23×D512yes—
646C2×C3×C4C23×D512yes—
647C2×C3×C4C23×D512yes—
648C2×C3×C4C23×D512yes—
649C2×C3×C4C23×D512yes—
650C22×C5—22no—
651C22×C5—22no—
652C22×C5—28no—
653C22×C5—22no—
654C22×C5—22no—
655C22×C5—22no—
656C22×C5—44no—
657C22×C5C2×C3×#4114yes—
658C22×C5C2×C3×#4112yes—
659C22×C5C2×C3×#4112yes—
660C22×C5C3×H(5,𝔽2)12yes—
661C22×C5C25×C311yescharacteristic
662C2×D5—22no—
663C2×D5—22no—
664C2×D5—28no—
665C2×D5—22no—
666C2×D5—22no—
667C2×D5—22no—
668C2×D5—416no—
669C2×D5—44no—
670C2×D5C2×C3×#4114yes—
671C4×C5—22no—
672C4×C5—22no—
673C4×C5—22no—
674C4×C5—22no—
675C4×C5—22no—
676Dic5—22no—
677Dic5—22no—
678Dic5—22no—
679Dic5—22no—
680Dic5—22no—
681Dic5—22no—
682C24—51no—
683C24—51no—
684C24—54no—
685C24—104no—
686C24—104no—
687C24—202no—
688C24C22×C3×D511yescharacteristic
689C24C22×C3×D511yescharacteristic
690C2×Q8—54no—
691C2×Q8—202no—
692C2×D4—24no—
693C2×D4—54no—
694C2×D4—54no—
695C2×D4—104no—
696C2×D4—202no—
697C2×D4C22×C3×D514yes—
698C22×C4—42no—
699C22×C4—42no—
700C22×C4—51no—
701C22×C4—51no—
702C22×C4—51no—
703C22×C4—51no—
704C22×C4—51no—
705C22×C4—51no—
706C22×C4—54no—
707C22×C4—54no—
708C22×C4—54no—
709C22×C4—104no—
710C22×C4—104no—
711C22×C4—202no—
712C22×C4C22×C3×D511yescharacteristic
713C22×C4C22×C3×D511yescharacteristic
714C22×C4C22×C3×D511yescharacteristic
715C22×C4C22×C3×D511yescharacteristic
716C22×C4C22×C3×D511yescharacteristic
717C22×C4C22×C3×D514yes—
718C22×C4C22×C3×D514yescomplemented
719C4⋊C4—54no—
720C4⋊C4—54no—
721C4⋊C4—54no—
722C4⋊C4—54no—
723C4⋊C4—54no—
724C4⋊C4—54no—
725C4⋊C4—54no—
726C4⋊C4C22×C3×D514yescomplemented
727C22⋊C4—54no—
728C22⋊C4—54no—
729C22⋊C4—54no—
730C22⋊C4—54no—
731C22⋊C4—54no—
732C22⋊C4—54no—
733C22⋊C4—54no—
734C22⋊C4—54no—
735C22⋊C4—54no—
736C22⋊C4—54no—
737C22⋊C4—54no—
738C22⋊C4—54no—
739C22⋊C4C22×C3×D514yes—
740C22⋊C4C22×C3×D514yescomplemented
741C42—54no—
742C42—54no—
743C42C22×C3×D514yescomplemented
744C3×C5C2×#55111yescharacteristic, complemented, Hall
745C22×C3—28no—
746C22×C3—22no—
747C22×C3—22no—
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—44no—
752C22×C3—54no—
753C22×C3—108no—
754C22×C3—102no—
755C22×C3—102no—
756C22×C3—102no—
757C22×C3—102no—
758C22×C3—102no—
759C22×C3—2016no—
760C22×C3—204no—
761C22×C3C2×#70914yes—
762C22×C3C2×#70912yes—
763C22×C3#414412yes—
764C22×C3D5×#4112yes—
765C22×C3C24×D511yescharacteristic
766C3×C4—22no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—22no—
770C3×C4—22no—
771C3×C4—102no—
772C3×C4—102no—
773C3×C4—102no—
774C3×C4—102no—
775C3×C4—102no—
776C3×C4—102no—
777C2×C5—24no—
778C2×C5—42no—
779C2×C5C3×#55114yescomplemented
780C2×C5C22×C3×#4111yescharacteristic
781C2×C5C22×C3×#4111yescharacteristic
782C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
783D5—24no—
784D5—42no—
785C23—22no—
786C23—22no—
787C23—22no—
788C23—22no—
789C23—22no—
790C23—54no—
791C23—52no—
792C23—52no—
793C23—108no—
794C23—102no—
795C23—102no—
796C23—108no—
797C23—102no—
798C23—102no—
799C23—102no—
800C23—204no—
801C23—2016no—
802C23C3×#70914yes—
803C23C23×C3×D512yes—
804C23C23×C3×D512yes—
805C23C23×C3×D511yescharacteristic
806Q8—204no—
807D4—28no—
808D4—108no—
809D4—204no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—44no—
816C2×C4—44no—
817C2×C4—52no—
818C2×C4—52no—
819C2×C4—52no—
820C2×C4—52no—
821C2×C4—52no—
822C2×C4—52no—
823C2×C4—108no—
824C2×C4—108no—
825C2×C4—102no—
826C2×C4—102no—
827C2×C4—102no—
828C2×C4—102no—
829C2×C4—102no—
830C2×C4—102no—
831C2×C4—204no—
832C2×C4C23×C3×D512yes—
833C2×C4C23×C3×D512yes—
834C2×C4C23×C3×D512yes—
835C2×C4C23×C3×D512yes—
836C2×C4C23×C3×D512yes—
837C2×C3—24no—
838C2×C3—42no—
839C2×C3—104no—
840C2×C3—202no—
841C2×C3#6589014yesdirect product factor
842C2×C3C22×#70911yescharacteristic
843C2×C3C2×#414411yescharacteristic
844C2×C3C2×D5×#4111yescharacteristic
845C5C2×C3×#55111yescharacteristic, complemented, Sylow
846C22—22no—
847C22—28no—
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—54no—
854C22—102no—
855C22—102no—
856C22—108no—
857C22—102no—
858C22—102no—
859C22—102no—
860C22—2016no—
861C22—204no—
862C22C2×C3×#70914yes—
863C22C2×C3×#70912yes—
864C22C3×#414412yes—
865C22C3×D5×#4112yes—
866C22C24×C3×D511yescharacteristic
867C4—22no—
868C4—22no—
869C4—22no—
870C4—22no—
871C4—22no—
872C4—102no—
873C4—102no—
874C4—102no—
875C4—102no—
876C4—102no—
877C4—102no—
878C3C2×#6589011yescharacteristic, direct product factor, Sylow
879C2—24no—
880C2—42no—
881C2—104no—
882C2—202no—
883C2C3×#6589014yesdirect product factor
884C2C22×C3×#70911yescharacteristic
885C2C2×C3×#414411yescharacteristic
886C2C2×C3×D5×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4083C2
hypercenterC2×C3×C4×D4D5
hypocenterC5C2×C3×#551
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
3. C2×C3×#4081C2semidirect
4. C2×C3×#4075C2semidirect
5. C2×C3×C4×C22⋊D5C2semidirect
6. C22×C3×#685C2semidirect
7. C2×C3×#4070C2semidirect
8. C3×#65890C2direct (N × H)
9. C2×C3×#4044C2semidirect
10. C2×C3×#4042C2semidirect
11. C2×C3×#4031C2semidirect
12. C2×C3×#4029C2semidirect
13. C2×C3×D5×C22⋊C4C2semidirect
14. C2×C3×#4023C2semidirect
15. C2×C3×#4022C2semidirect
16. C2×C3×#4018C2semidirect
17. C2×#65890C3direct (N × H)
21. C23×C3×C4×C5C22semidirect
27. C22×C3×Dic10C22semidirect
28. C3×C4×C5×D4C22semidirect
29. C2×C3×C5×C4⋊C4C22semidirect
31. C2×C3×C5×C22⋊C4C22semidirect
32. C2×C3×C42×C5C22semidirect
35. C2×C3×C22⋊Dic5C22semidirect
36. C2×C3×C22⋊Dic5C22semidirect
38. C3×#4081C22semidirect
39. C3×#4075C22semidirect
40. C3×C4×C22⋊D5C22semidirect
49. C2×C3×#685C22semidirect
50. C2×C3×C4⋊Dic5C22semidirect
51. C3×#4070C22semidirect
52. C2×C3×#683C22semidirect
53. C2×C3×#683C22semidirect
54. C2×C3×#683C22semidirect
55. C2×C3×#683C22semidirect
56. C2×C3×#683C22semidirect
57. C2×C3×#683C22semidirect
58. C2×C3×C4×Dic5C22semidirect
59. C2×C3×C4×Dic5C22semidirect
60. C3×#4044C22semidirect
61. C3×#4042C22semidirect
62. C3×#4031C22semidirect
63. C3×#4029C22semidirect
64. C3×D5×C22⋊C4C22semidirect
65. C3×#4023C22semidirect
66. C3×#4022C22semidirect
67. C3×#4018C22semidirect
69. C2×C4×C5×D4C2×C3semidirect
71. C2×#4081C2×C3semidirect
72. C2×#4075C2×C3semidirect
73. C2×C4×C22⋊D5C2×C3semidirect
74. C22×#685C2×C3semidirect
75. C2×#4070C2×C3semidirect
76. #65890C2×C3direct (N × H)
77. C2×#4044C2×C3semidirect
78. C2×#4042C2×C3semidirect
79. C2×#4031C2×C3semidirect
80. C2×#4029C2×C3semidirect
81. C2×D5×C22⋊C4C2×C3semidirect
82. C2×#4023C2×C3semidirect
83. C2×#4022C2×C3semidirect
84. C2×#4018C2×C3semidirect
103. C22×C3×C4×C5C23semidirect
121. C2×C3×Dic10C23semidirect
122. C3×C5×C4⋊C4C23semidirect
124. C3×C5×C22⋊C4C23semidirect
125. C3×C42×C5C23semidirect
128. C3×C22⋊Dic5C23semidirect
129. C3×C22⋊Dic5C23semidirect
138. C3×C4⋊Dic5C23semidirect
139. C3×#683C23semidirect
140. C3×#683C23semidirect
141. C3×#683C23semidirect
142. C3×#683C23semidirect
143. C3×#683C23semidirect
144. C3×#683C23semidirect
145. C3×C4×Dic5C23semidirect
146. C3×C4×Dic5C23semidirect
158. C2×C3×C4×D4D5semidirect
166. C23×C4×C5C22×C3semidirect
172. C22×Dic10C22×C3semidirect
173. C4×C5×D4C22×C3semidirect
174. C2×C5×C4⋊C4C22×C3semidirect
176. C2×C5×C22⋊C4C22×C3semidirect
177. C2×C42×C5C22×C3semidirect
180. C2×C22⋊Dic5C22×C3semidirect
181. C2×C22⋊Dic5C22×C3semidirect
183. #4081C22×C3semidirect
184. #4075C22×C3semidirect
185. C4×C22⋊D5C22×C3semidirect
194. C2×#685C22×C3semidirect
195. C2×C4⋊Dic5C22×C3semidirect
196. #4070C22×C3semidirect
197. C2×#683C22×C3semidirect
198. C2×#683C22×C3semidirect
199. C2×#683C22×C3semidirect
200. C2×#683C22×C3semidirect
201. C2×#683C22×C3semidirect
202. C2×#683C22×C3semidirect
203. C2×C4×Dic5C22×C3semidirect
204. C2×C4×Dic5C22×C3semidirect
205. #4044C22×C3semidirect
206. #4042C22×C3semidirect
207. #4031C22×C3semidirect
208. #4029C22×C3semidirect
209. D5×C22⋊C4C22×C3semidirect
210. #4023C22×C3semidirect
211. #4022C22×C3semidirect
212. #4018C22×C3semidirect
275. C23×C3×C4C2×D5semidirect
286. C3×C4×D4C2×D5semidirect
296. C2×C3×C4⋊C4C2×D5semidirect
312. C2×C3×C22⋊C4C2×D5semidirect
315. C2×C3×C42C2×D5semidirect
334. C22×C4×C5C23×C3semidirect
352. C2×Dic10C23×C3semidirect
353. C5×C4⋊C4C23×C3semidirect
355. C5×C22⋊C4C23×C3semidirect
356. C42×C5C23×C3semidirect
359. C22⋊Dic5C23×C3semidirect
360. C22⋊Dic5C23×C3semidirect
369. C4⋊Dic5C23×C3semidirect
370. #683C23×C3semidirect
371. #683C23×C3semidirect
372. #683C23×C3semidirect
373. #683C23×C3semidirect
374. #683C23×C3semidirect
375. #683C23×C3semidirect
376. C4×Dic5C23×C3semidirect
377. C4×Dic5C23×C3semidirect
389. C2×C4×D4C3×D5semidirect
462. C22×C3×C4C22×D5semidirect
470. C3×C4⋊C4C22×D5semidirect
484. C3×C22⋊C4C22×D5semidirect
487. C3×C42C22×D5semidirect
549. C23×C4C2×C3×D5semidirect
560. C4×D4C2×C3×D5semidirect
570. C2×C4⋊C4C2×C3×D5semidirect
586. C2×C22⋊C4C2×C3×D5semidirect
589. C2×C42C2×C3×D5semidirect
592. C2×C3×C5#551semidirect
718. C22×C4C22×C3×D5semidirect
726. C4⋊C4C22×C3×D5semidirect
740. C22⋊C4C22×C3×D5semidirect
743. C42C22×C3×D5semidirect
744. C3×C5C2×#551semidirect
779. C2×C5C3×#551semidirect
841. C2×C3#65890direct (N × H)
845. C5C2×C3×#551semidirect
878. C3C2×#65890direct (N × H)
883. C2C3×#65890direct (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×#40832
C2×C3×#40812
C2×C3×#40752
C2×C3×C4×C22⋊D52
C22×C3×#6852
C2×C3×#40702
C3×#658902
C2×C3×#40442
C2×C3×#40422
C2×C3×#40312
C2×C3×#40292
C2×C3×D5×C22⋊C42
C2×C3×#40232
C2×C3×#40222
C2×C3×#40182
C2×#658903
C2×C3×#5515