Finite Group Databasebeta

← C3×#10614129 #14328096

Subgroups — C3×#10614129 #14328096

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 1032 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×C4×C22⋊D5C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
6C3×#65509C211yesmaximal, characteristic, complemented
7C3×#65502C211yesmaximal, characteristic, complemented
8C3×#65499C211yesmaximal, characteristic, complemented
9C3×#65279C211yesmaximal, characteristic, complemented
10C3×#65278C211yesmaximal, characteristic, complemented
11C3×#65246C211yesmaximal, characteristic, complemented
12C3×#65245C211yesmaximal, characteristic, complemented
13C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14C3×#65229C211yesmaximal, characteristic, complemented
15C3×C4×#685C211yesmaximal, characteristic, complemented
16#10614129C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C23×C3×C4×C5C2211yescharacteristic, complemented
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×C3×C4×D5C2211yescharacteristic
26C3×C4×C5×D4—24no—
27C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
28C2×C3×C5×C22⋊C4C2211yescharacteristic
29C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
30C2×C3×C42×C5C2211yescharacteristic, complemented
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
34C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
35C3×#4083C418yescomplemented
36C3×C4×C22⋊D5—24no—
37C2×C3×#685—24no—
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic, complemented
47C2×C3×#683C2211yescharacteristic, complemented
48C2×C3×C4×Dic5C2211yescharacteristic, complemented
49C2×C3×C4×Dic5C2211yescharacteristic, complemented
50C3×D5×C22⋊C4—24no—
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55C3×#3963C2211yescharacteristic, complemented
56C3×#3963C2211yescharacteristic, complemented
57C3×#2358—51nomaximal, Hall
58C2×C4×C5×D4C2×C311yescharacteristic, complemented
59C2×#4083C2×C311yescharacteristic
60C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
61C22×#685C2×C311yescharacteristic, complemented
62C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
63#65509C2×C311yescharacteristic, complemented
64#65502C2×C311yescharacteristic, complemented
65#65499C2×C311yescharacteristic, complemented
66#65279C2×C311yescharacteristic, complemented
67#65278C2×C311yescharacteristic, complemented
68#65246C2×C311yescharacteristic, complemented
69#65245C2×C311yescharacteristic, complemented
70C22⋊C4×Dic5C2×C311yescharacteristic, complemented
71#65229C2×C311yescharacteristic, complemented
72C4×#685C2×C311yescharacteristic, complemented
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×C3×D5—22no—
76C23×C3×D5—22no—
77C23×C3×D5—22no—
78C23×C3×D5—22no—
79C23×C3×D5—41no—
80C23×C3×D5—41no—
81C23×C3×D5C2×C414yescomplemented
82C23×C3×D5C2311yescharacteristic
83C23×C3×D5C2311yescharacteristic
84C2×C3×C5×D4—22no—
85C2×C3×C5×D4—22no—
86C2×C3×C5×D4C2×C414yescomplemented
87C22×C3×C4×C5—22no—
88C22×C3×C4×C5—22no—
89C22×C3×C4×C5—22no—
90C22×C3×C4×C5—22no—
91C22×C3×C4×C5—41no—
92C22×C3×C4×C5—41no—
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C2×C3×C22⋊D5—22no—
99C2×C3×C22⋊D5—22no—
100C2×C3×C22⋊D5—41no—
101C2×C3×C22⋊D5—41no—
102C2×C3×C22⋊D5C2×C414yescomplemented
103C2×C3×C22⋊D5C2×C414yescomplemented
104C22×C3×Dic5—22no—
105C22×C3×Dic5—22no—
106C22×C3×Dic5—41no—
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C2×C3×C4×D5—22no—
114C2×C3×C4×D5—22no—
115C2×C3×C4×D5—22no—
116C2×C3×C4×D5—22no—
117C2×C3×C4×D5—41no—
118C2×C3×C4×D5—41no—
119C3×C5×C4⋊C4—22no—
120C3×C5×C22⋊C4—22no—
121C3×C5×C22⋊C4D414yescomplemented
122C3×C42×C5—22no—
123C3×C22⋊Dic5—22no—
124C3×C22⋊Dic5—22no—
125C3×C22⋊Dic5—41no—
126C3×C22⋊Dic5C2×C414yescomplemented
127C3×#685—22no—
128C3×#685—22no—
129C3×#685—22no—
130C3×#685—22no—
131C3×#685—22no—
132C3×#685C2×C414yescomplemented
133C3×#685C2×C414yescomplemented
134C3×#685D414yescomplemented
135C3×#683—22no—
136C3×#683—41no—
137C3×C4×Dic5—22no—
138C3×C4×Dic5—41no—
139C2×C3×#120—51no—
140C2×C3×C4×D4—51no—
141C2×C3×C4×D4D511yescharacteristic, complemented
142C22×C3×C22⋊C4—51no—
143C22×C3×C22⋊C4—51no—
144C3×#390—51no—
145C3×#388—51no—
146C3×#388—51no—
147C3×#386—51no—
148C3×#386—51no—
149C3×#386—51no—
150C3×#385—51no—
151C3×#385—51no—
152C3×C4×C22⋊C4—51no—
153C3×C4×C22⋊C4—51no—
154C24×D5C22×C311yescharacteristic
155C22×C5×D4C22×C311yescharacteristic
156C23×C4×C5C22×C311yescharacteristic
157C23×C4×C5C22×C311yescharacteristic, complemented
158C22×C22⋊D5C22×C311yescharacteristic
159C22×C22⋊D5C22×C311yescharacteristic
160C23×Dic5C22×C311yescharacteristic
161C22×C4×D5C22×C311yescharacteristic
162C22×C4×D5C22×C311yescharacteristic
163C4×C5×D4—24no—
164C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
165C2×C5×C22⋊C4C22×C311yescharacteristic
166C2×C5×C22⋊C4C22×C311yescharacteristic, complemented
167C2×C42×C5C22×C311yescharacteristic, complemented
168C2×C22⋊Dic5C22×C311yescharacteristic
169C2×C22⋊Dic5C22×C311yescharacteristic
170C2×C22⋊Dic5C22×C311yescharacteristic, complemented
171C2×C22⋊Dic5C22×C311yescharacteristic, complemented
172#4083C3×C418yescomplemented
173C4×C22⋊D5—24no—
174C2×#685—24no—
175C2×#685C22×C311yescharacteristic
176C2×#685C22×C311yescharacteristic
177C2×#685C22×C311yescharacteristic
178C2×#685C22×C311yescharacteristic
179C2×#685C22×C311yescharacteristic
180C2×#685C22×C311yescharacteristic
181C2×#685C22×C311yescharacteristic
182C2×#685C22×C311yescharacteristic
183C2×#683C22×C311yescharacteristic, complemented
184C2×#683C22×C311yescharacteristic, complemented
185C2×C4×Dic5C22×C311yescharacteristic, complemented
186C2×C4×Dic5C22×C311yescharacteristic, complemented
187D5×C22⋊C4—24no—
188#3963C22×C311yescharacteristic, complemented
189#3963C22×C311yescharacteristic, complemented
190#3963C22×C311yescharacteristic, complemented
191#3963C22×C311yescharacteristic, complemented
192#3963C22×C311yescharacteristic, complemented
193#3963C22×C311yescharacteristic, complemented
194#2358—51noSylow
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5—21no—
201C23×C3×C5—21no—
202C23×C3×C5—21no—
203C23×C3×C5—21no—
204C23×C3×C5—21no—
205C23×C3×C5C22×C412yes—
206C23×C3×C5C22×C412yes—
207C23×C3×C5C2×D412yes—
208C23×C3×C5#4112yes—
209C23×C3×C5C2411yescharacteristic
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—28no—
215C22×C3×D5—21no—
216C22×C3×D5—21no—
217C22×C3×D5—21no—
218C22×C3×D5—21no—
219C22×C3×D5—21no—
220C22×C3×D5—21no—
221C22×C3×D5—28no—
222C22×C3×D5—44no—
223C22×C3×D5—44no—
224C22×C3×D5—44no—
225C22×C3×D5—44no—
226C22×C3×D5—44no—
227C22×C3×D5C22×C412yes—
228C22×C3×D5C22×C412yes—
229C22×C3×D5C2×D412yes—
230C22×C3×D5#4112yes—
231C3×C5×D4—28no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5—21no—
239C2×C3×C4×C5—21no—
240C2×C3×C4×C5—21no—
241C2×C3×C4×C5—21no—
242C2×C3×C4×C5—21no—
243C2×C3×C4×C5—44no—
244C2×C3×C4×C5—44no—
245C2×C3×C4×C5C22×C412yes—
246C2×C3×C4×C5C2×D412yes—
247C2×C3×C4×C5C2×D412yes—
248C2×C3×C4×C5C2×D412yes—
249C3×C22⋊D5—28no—
250C3×C22⋊D5—44no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5—21no—
256C2×C3×Dic5—21no—
257C2×C3×Dic5—21no—
258C2×C3×Dic5—21no—
259C2×C3×Dic5—21no—
260C2×C3×Dic5—21no—
261C2×C3×Dic5—21no—
262C2×C3×Dic5—21no—
263C2×C3×Dic5—21no—
264C2×C3×Dic5—21no—
265C2×C3×Dic5—21no—
266C2×C3×Dic5—44no—
267C2×C3×Dic5C22×C412yes—
268C2×C3×Dic5C22×C412yes—
269C2×C3×Dic5C2×D412yes—
270C3×C4×D5—44no—
271C3×C4×D5—44no—
272C25×C3—51no—
273C22×C3×D4—51no—
274C22×C3×D4—51no—
275C22×C3×D4C2×D511yescharacteristic
276C23×C3×C4—51no—
277C23×C3×C4—51no—
278C23×C3×C4—51no—
279C23×C3×C4C2×D511yescharacteristic
280C23×C3×C4C2×D511yescharacteristic, complemented
281C3×#120—58no—
282C3×C4×D4—24no—
283C3×C4×D4—104no—
284C2×C3×C4⋊C4—51no—
285C2×C3×C4⋊C4—51no—
286C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
287C2×C3×C22⋊C4—51no—
288C2×C3×C22⋊C4—51no—
289C2×C3×C22⋊C4—51no—
290C2×C3×C22⋊C4—51no—
291C2×C3×C22⋊C4—51no—
292C2×C3×C22⋊C4—51no—
293C2×C3×C22⋊C4—51no—
294C2×C3×C22⋊C4—51no—
295C2×C3×C22⋊C4—51no—
296C2×C3×C22⋊C4—51no—
297C2×C3×C22⋊C4—51no—
298C2×C3×C22⋊C4—51no—
299C2×C3×C22⋊C4—104no—
300C2×C3×C22⋊C4—104no—
301C2×C3×C22⋊C4C2×D511yescharacteristic
302C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
303C2×C3×C42—51no—
304C2×C3×C42—51no—
305C2×C3×C42C2×D511yescharacteristic, complemented
306C3×#95—51no—
307C3×#95—51no—
308C3×#95—51no—
309C3×#95—51no—
310C3×#95—51no—
311C3×#95—51no—
312C24×C5C23×C311yescharacteristic
313C24×C5C23×C311yescharacteristic
314C23×D5—22no—
315C23×D5—22no—
316C23×D5—22no—
317C23×D5—22no—
318C23×D5—41no—
319C23×D5—41no—
320C23×D5C2×C3×C414yescomplemented
321C23×D5C23×C311yescharacteristic
322C23×D5C23×C311yescharacteristic
323C2×C5×D4—22no—
324C2×C5×D4—22no—
325C2×C5×D4C2×C3×C414yescomplemented
326C22×C4×C5—22no—
327C22×C4×C5—22no—
328C22×C4×C5—22no—
329C22×C4×C5—22no—
330C22×C4×C5—41no—
331C22×C4×C5—41no—
332C22×C4×C5C23×C311yescharacteristic
333C22×C4×C5C23×C311yescharacteristic
334C22×C4×C5C23×C311yescharacteristic
335C22×C4×C5C23×C311yescharacteristic
336C22×C4×C5C23×C311yescharacteristic
337C2×C22⋊D5—22no—
338C2×C22⋊D5—22no—
339C2×C22⋊D5—41no—
340C2×C22⋊D5—41no—
341C2×C22⋊D5C2×C3×C414yescomplemented
342C2×C22⋊D5C2×C3×C414yescomplemented
343C22×Dic5—22no—
344C22×Dic5—22no—
345C22×Dic5—41no—
346C22×Dic5C23×C311yescharacteristic
347C22×Dic5C23×C311yescharacteristic
348C22×Dic5C23×C311yescharacteristic
349C22×Dic5C23×C311yescharacteristic
350C22×Dic5C23×C311yescharacteristic
351C22×Dic5C23×C311yescharacteristic
352C2×C4×D5—22no—
353C2×C4×D5—22no—
354C2×C4×D5—22no—
355C2×C4×D5—22no—
356C2×C4×D5—41no—
357C2×C4×D5—41no—
358C5×C4⋊C4—22no—
359C5×C22⋊C4—22no—
360C5×C22⋊C4C3×D414yescomplemented
361C42×C5—22no—
362C22⋊Dic5—22no—
363C22⋊Dic5—22no—
364C22⋊Dic5—41no—
365C22⋊Dic5C2×C3×C414yescomplemented
366#685—22no—
367#685—22no—
368#685—22no—
369#685—22no—
370#685—22no—
371#685C2×C3×C414yescomplemented
372#685C2×C3×C414yescomplemented
373#685C3×D414yescomplemented
374#683—22no—
375#683—41no—
376C4×Dic5—22no—
377C4×Dic5—41no—
378C2×#120—51no—
379C2×C4×D4—51no—
380C2×C4×D4C3×D511yescharacteristic, complemented
381C22×C22⋊C4—51no—
382C22×C22⋊C4—51no—
383#390—51no—
384#388—51no—
385#388—51no—
386#386—51no—
387#386—51no—
388#386—51no—
389#385—51no—
390#385—51no—
391C4×C22⋊C4—51no—
392C4×C22⋊C4—51no—
393C22×C3×C5—22no—
394C22×C3×C5—22no—
395C22×C3×C5—22no—
396C22×C3×C5—22no—
397C22×C3×C5—22no—
398C22×C3×C5—22no—
399C22×C3×C5—22no—
400C22×C3×C5—22no—
401C22×C3×C5—22no—
402C22×C3×C5—41no—
403C22×C3×C5—41no—
404C22×C3×C5—41no—
405C22×C3×C5—41no—
406C22×C3×C5C4×D414yescomplemented
407C22×C3×C5C23×C411yescharacteristic
408C22×C3×C5C22×D411yescharacteristic
409C22×C3×C5C22×D411yescharacteristic
410C22×C3×C5C2×#4111yescharacteristic
411C22×C3×C5C2×#4111yescharacteristic
412C22×C3×C5H(5,𝔽2)11yescharacteristic
413C22×C3×C5H(5,𝔽2)11yescharacteristic
414C2×C3×D5—22no—
415C2×C3×D5—22no—
416C2×C3×D5—22no—
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—416no—
424C2×C3×D5—41no—
425C2×C3×D5—41no—
426C2×C3×D5—41no—
427C2×C3×D5—41no—
428C2×C3×D5C4×D414yescomplemented
429C3×C4×C5—22no—
430C3×C4×C5—22no—
431C3×C4×C5—22no—
432C3×C4×C5—22no—
433C3×C4×C5—41no—
434C3×Dic5—22no—
435C3×Dic5—22no—
436C3×Dic5—22no—
437C3×Dic5—41no—
438C3×Dic5—41no—
439C3×Dic5—41no—
440C24×C3—51no—
441C24×C3—51no—
442C24×C3—54no—
443C24×C3—102no—
444C24×C3—102no—
445C24×C3—102no—
446C24×C3—102no—
447C24×C3—201no—
448C24×C3—201no—
449C24×C3C22×D511yescharacteristic
450C24×C3C22×D511yescharacteristic
451C2×C3×D4—22no—
452C2×C3×D4—22no—
453C2×C3×D4—54no—
454C2×C3×D4—54no—
455C2×C3×D4—102no—
456C2×C3×D4—102no—
457C2×C3×D4—201no—
458C2×C3×D4—201no—
459C2×C3×D4C4×D514yescomplemented
460C22×C3×C4—22no—
461C22×C3×C4—22no—
462C22×C3×C4—22no—
463C22×C3×C4—22no—
464C22×C3×C4—41no—
465C22×C3×C4—41no—
466C22×C3×C4—51no—
467C22×C3×C4—51no—
468C22×C3×C4—51no—
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4—102no—
473C22×C3×C4—102no—
474C22×C3×C4—102no—
475C22×C3×C4—102no—
476C22×C3×C4—102no—
477C22×C3×C4—102no—
478C22×C3×C4—201no—
479C22×C3×C4—201no—
480C22×C3×C4—201no—
481C22×C3×C4C22×D511yescharacteristic
482C22×C3×C4C22×D511yescharacteristic
483C22×C3×C4C22×D511yescharacteristic
484C22×C3×C4C22×D511yescharacteristic
485C22×C3×C4C22×D511yescharacteristic
486C3×C4⋊C4—22no—
487C3×C4⋊C4—102no—
488C3×C4⋊C4—201no—
489C3×C22⋊C4—22no—
490C3×C22⋊C4—54no—
491C3×C22⋊C4—54no—
492C3×C22⋊C4—54no—
493C3×C22⋊C4—54no—
494C3×C22⋊C4—102no—
495C3×C22⋊C4—102no—
496C3×C22⋊C4—102no—
497C3×C22⋊C4—102no—
498C3×C22⋊C4—102no—
499C3×C22⋊C4—102no—
500C3×C22⋊C4—102no—
501C3×C22⋊C4—201no—
502C3×C22⋊C4C22⋊D514yescomplemented
503C3×C42—22no—
504C3×C42—102no—
505C3×C42—201no—
506C23×C5—21no—
507C23×C5—21no—
508C23×C5—21no—
509C23×C5—21no—
510C23×C5—21no—
511C23×C5—21no—
512C23×C5—21no—
513C23×C5—21no—
514C23×C5—21no—
515C23×C5—21no—
516C23×C5C22×C3×C412yes—
517C23×C5C22×C3×C412yes—
518C23×C5C2×C3×D412yes—
519C23×C5C3×#4112yes—
520C23×C5C24×C311yescharacteristic
521C22×D5—21no—
522C22×D5—21no—
523C22×D5—21no—
524C22×D5—21no—
525C22×D5—28no—
526C22×D5—21no—
527C22×D5—21no—
528C22×D5—21no—
529C22×D5—21no—
530C22×D5—21no—
531C22×D5—21no—
532C22×D5—28no—
533C22×D5—44no—
534C22×D5—44no—
535C22×D5—44no—
536C22×D5—44no—
537C22×D5—44no—
538C22×D5C22×C3×C412yes—
539C22×D5C22×C3×C412yes—
540C22×D5C2×C3×D412yes—
541C22×D5C3×#4112yes—
542C5×D4—28no—
543C2×C4×C5—21no—
544C2×C4×C5—21no—
545C2×C4×C5—21no—
546C2×C4×C5—21no—
547C2×C4×C5—21no—
548C2×C4×C5—21no—
549C2×C4×C5—21no—
550C2×C4×C5—21no—
551C2×C4×C5—21no—
552C2×C4×C5—21no—
553C2×C4×C5—21no—
554C2×C4×C5—44no—
555C2×C4×C5—44no—
556C2×C4×C5C22×C3×C412yes—
557C2×C4×C5C2×C3×D412yes—
558C2×C4×C5C2×C3×D412yes—
559C2×C4×C5C2×C3×D412yes—
560C22⋊D5—28no—
561C22⋊D5—44no—
562C2×Dic5—21no—
563C2×Dic5—21no—
564C2×Dic5—21no—
565C2×Dic5—21no—
566C2×Dic5—21no—
567C2×Dic5—21no—
568C2×Dic5—21no—
569C2×Dic5—21no—
570C2×Dic5—21no—
571C2×Dic5—21no—
572C2×Dic5—21no—
573C2×Dic5—21no—
574C2×Dic5—21no—
575C2×Dic5—21no—
576C2×Dic5—21no—
577C2×Dic5—44no—
578C2×Dic5C22×C3×C412yes—
579C2×Dic5C22×C3×C412yes—
580C2×Dic5C2×C3×D412yes—
581C4×D5—44no—
582C4×D5—44no—
583C25—51no—
584C22×D4—51no—
585C22×D4—51no—
586C22×D4C2×C3×D511yescharacteristic
587C23×C4—51no—
588C23×C4—51no—
589C23×C4—51no—
590C23×C4C2×C3×D511yescharacteristic
591C23×C4C2×C3×D511yescharacteristic, complemented
592#120—58no—
593C4×D4—24no—
594C4×D4—104no—
595C2×C4⋊C4—51no—
596C2×C4⋊C4—51no—
597C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
598C2×C22⋊C4—51no—
599C2×C22⋊C4—51no—
600C2×C22⋊C4—51no—
601C2×C22⋊C4—51no—
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⋊C4—51no—
609C2×C22⋊C4—51no—
610C2×C22⋊C4—104no—
611C2×C22⋊C4—104no—
612C2×C22⋊C4C2×C3×D511yescharacteristic
613C2×C22⋊C4C2×C3×D511yescharacteristic, complemented
614C2×C42—51no—
615C2×C42—51no—
616C2×C42C2×C3×D511yescharacteristic, complemented
617#95—51no—
618#95—51no—
619#95—51no—
620#95—51no—
621#95—51no—
622#95—51no—
623C2×C3×C5—24no—
624C2×C3×C5—42no—
625C2×C3×C5C2×C4×D411yescharacteristic
626C2×C3×C5C2×C4×D411yescharacteristic
627C2×C3×C5#51811yescharacteristic
628C2×C3×C5D4211yescharacteristic
629C2×C3×C5#54611yescharacteristic
630C2×C3×C5#54611yescharacteristic
631C2×C3×C5#55111yescharacteristic
632C3×D5—24no—
633C3×D5—42no—
634C23×C3—21no—
635C23×C3—21no—
636C23×C3—21no—
637C23×C3—21no—
638C23×C3—21no—
639C23×C3—21no—
640C23×C3—21no—
641C23×C3—21no—
642C23×C3—21no—
643C23×C3—21no—
644C23×C3—52no—
645C23×C3—52no—
646C23×C3—52no—
647C23×C3—52no—
648C23×C3—108no—
649C23×C3—101no—
650C23×C3—101no—
651C23×C3—101no—
652C23×C3—101no—
653C23×C3—101no—
654C23×C3—101no—
655C23×C3—101no—
656C23×C3—101no—
657C23×C3—101no—
658C23×C3—101no—
659C23×C3—108no—
660C23×C3—204no—
661C23×C3—204no—
662C23×C3—204no—
663C23×C3—204no—
664C23×C3—204no—
665C23×C3C2×C4×D512yes—
666C23×C3C2×C4×D512yes—
667C23×C3#70912yes—
668C23×C3C2×C22⋊D512yes—
669C23×C3C23×D511yescharacteristic
670C3×D4—28no—
671C3×D4—108no—
672C3×D4—204no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—44no—
685C2×C3×C4—44no—
686C2×C3×C4—52no—
687C2×C3×C4—52no—
688C2×C3×C4—52no—
689C2×C3×C4—101no—
690C2×C3×C4—101no—
691C2×C3×C4—101no—
692C2×C3×C4—101no—
693C2×C3×C4—101no—
694C2×C3×C4—101no—
695C2×C3×C4—101no—
696C2×C3×C4—101no—
697C2×C3×C4—101no—
698C2×C3×C4—101no—
699C2×C3×C4—101no—
700C2×C3×C4—101no—
701C2×C3×C4—101no—
702C2×C3×C4—101no—
703C2×C3×C4—101no—
704C2×C3×C4—204no—
705C2×C3×C4—204no—
706C2×C3×C4—204no—
707C2×C3×C4C2×C4×D512yes—
708C2×C3×C4D4×D512yes—
709C2×C3×C4C2×C22⋊D512yes—
710C2×C3×C4C2×C22⋊D512yes—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—22no—
716C22×C5—22no—
717C22×C5—22no—
718C22×C5—22no—
719C22×C5—22no—
720C22×C5—41no—
721C22×C5—41no—
722C22×C5—41no—
723C22×C5—41no—
724C22×C5C3×C4×D414yescomplemented
725C22×C5C23×C3×C411yescharacteristic
726C22×C5C22×C3×D411yescharacteristic
727C22×C5C22×C3×D411yescharacteristic
728C22×C5C2×C3×#4111yescharacteristic
729C22×C5C2×C3×#4111yescharacteristic
730C22×C5C3×H(5,𝔽2)11yescharacteristic
731C22×C5C3×H(5,𝔽2)11yescharacteristic
732C2×D5—22no—
733C2×D5—22no—
734C2×D5—22no—
735C2×D5—22no—
736C2×D5—22no—
737C2×D5—22no—
738C2×D5—22no—
739C2×D5—22no—
740C2×D5—22no—
741C2×D5—416no—
742C2×D5—41no—
743C2×D5—41no—
744C2×D5—41no—
745C2×D5—41no—
746C2×D5C3×C4×D414yescomplemented
747C4×C5—22no—
748C4×C5—22no—
749C4×C5—22no—
750C4×C5—22no—
751C4×C5—41no—
752Dic5—22no—
753Dic5—22no—
754Dic5—22no—
755Dic5—41no—
756Dic5—41no—
757Dic5—41no—
758C24—51no—
759C24—51no—
760C24—54no—
761C24—102no—
762C24—102no—
763C24—102no—
764C24—102no—
765C24—201no—
766C24—201no—
767C24C22×C3×D511yescharacteristic
768C24C22×C3×D511yescharacteristic
769C2×D4—22no—
770C2×D4—22no—
771C2×D4—54no—
772C2×D4—54no—
773C2×D4—102no—
774C2×D4—102no—
775C2×D4—201no—
776C2×D4—201no—
777C2×D4C3×C4×D514yescomplemented
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—22no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—51no—
787C22×C4—51no—
788C22×C4—51no—
789C22×C4—51no—
790C22×C4—102no—
791C22×C4—102no—
792C22×C4—102no—
793C22×C4—102no—
794C22×C4—102no—
795C22×C4—102no—
796C22×C4—201no—
797C22×C4—201no—
798C22×C4—201no—
799C22×C4C22×C3×D511yescharacteristic
800C22×C4C22×C3×D511yescharacteristic
801C22×C4C22×C3×D511yescharacteristic
802C22×C4C22×C3×D511yescharacteristic
803C22×C4C22×C3×D511yescharacteristic
804C4⋊C4—22no—
805C4⋊C4—102no—
806C4⋊C4—201no—
807C22⋊C4—22no—
808C22⋊C4—54no—
809C22⋊C4—54no—
810C22⋊C4—54no—
811C22⋊C4—54no—
812C22⋊C4—102no—
813C22⋊C4—102no—
814C22⋊C4—102no—
815C22⋊C4—102no—
816C22⋊C4—102no—
817C22⋊C4—102no—
818C22⋊C4—102no—
819C22⋊C4—201no—
820C22⋊C4C3×C22⋊D514yescomplemented
821C42—22no—
822C42—102no—
823C42—201no—
824C3×C5#235811yescharacteristic, complemented, Hall
825C22×C3—22no—
826C22×C3—22no—
827C22×C3—22no—
828C22×C3—22no—
829C22×C3—22no—
830C22×C3—22no—
831C22×C3—22no—
832C22×C3—22no—
833C22×C3—22no—
834C22×C3—41no—
835C22×C3—41no—
836C22×C3—41no—
837C22×C3—41no—
838C22×C3—54no—
839C22×C3—102no—
840C22×C3—102no—
841C22×C3—102no—
842C22×C3—102no—
843C22×C3—102no—
844C22×C3—102no—
845C22×C3—102no—
846C22×C3—102no—
847C22×C3—102no—
848C22×C3—2016no—
849C22×C3—201no—
850C22×C3—201no—
851C22×C3—201no—
852C22×C3—201no—
853C22×C3C4×C22⋊D514yescomplemented
854C22×C3C22×C4×D511yescharacteristic
855C22×C3C2×#70911yescharacteristic
856C22×C3C2×D4×D511yescharacteristic
857C22×C3#414411yescharacteristic
858C22×C3D5×#4111yescharacteristic
859C22×C3#414911yescharacteristic
860C22×C3C22×C22⋊D511yescharacteristic
861C3×C4—22no—
862C3×C4—22no—
863C3×C4—22no—
864C3×C4—22no—
865C3×C4—41no—
866C3×C4—102no—
867C3×C4—102no—
868C3×C4—102no—
869C3×C4—201no—
870C3×C4—201no—
871C3×C4—201no—
872C2×C5—24no—
873C2×C5—42no—
874C2×C5C2×C3×C4×D411yescharacteristic
875C2×C5C2×C3×C4×D411yescharacteristic
876C2×C5C3×#51811yescharacteristic
877C2×C5C3×D4211yescharacteristic
878C2×C5C3×#54611yescharacteristic
879C2×C5C3×#54611yescharacteristic
880C2×C5C3×#55111yescharacteristic
881D5—24no—
882D5—42no—
883C23—21no—
884C23—21no—
885C23—21no—
886C23—21no—
887C23—21no—
888C23—21no—
889C23—21no—
890C23—21no—
891C23—21no—
892C23—21no—
893C23—52no—
894C23—52no—
895C23—52no—
896C23—52no—
897C23—108no—
898C23—101no—
899C23—101no—
900C23—101no—
901C23—101no—
902C23—101no—
903C23—101no—
904C23—101no—
905C23—101no—
906C23—101no—
907C23—101no—
908C23—108no—
909C23—204no—
910C23—204no—
911C23—204no—
912C23—204no—
913C23—204no—
914C23C2×C3×C4×D512yes—
915C23C2×C3×C4×D512yes—
916C23C3×#70912yes—
917C23C2×C3×C22⋊D512yes—
918C23C23×C3×D511yescharacteristic
919D4—28no—
920D4—108no—
921D4—204no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—21no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—21no—
932C2×C4—21no—
933C2×C4—44no—
934C2×C4—44no—
935C2×C4—52no—
936C2×C4—52no—
937C2×C4—52no—
938C2×C4—101no—
939C2×C4—101no—
940C2×C4—101no—
941C2×C4—101no—
942C2×C4—101no—
943C2×C4—101no—
944C2×C4—101no—
945C2×C4—101no—
946C2×C4—101no—
947C2×C4—101no—
948C2×C4—101no—
949C2×C4—101no—
950C2×C4—101no—
951C2×C4—101no—
952C2×C4—101no—
953C2×C4—204no—
954C2×C4—204no—
955C2×C4—204no—
956C2×C4C2×C3×C4×D512yes—
957C2×C4C3×D4×D512yes—
958C2×C4C2×C3×C22⋊D512yes—
959C2×C4C2×C3×C22⋊D512yes—
960C2×C3—24no—
961C2×C3—42no—
962C2×C3—104no—
963C2×C3—202no—
964C2×C3C4×D4×D511yescharacteristic
965C2×C3#6587911yescharacteristic
966C2×C3#6588411yescharacteristic
967C2×C3#6589011yescharacteristic
968C2×C3C2×C4×C22⋊D511yescharacteristic
969C2×C3D4×C22⋊D511yescharacteristic
970C2×C3#6616311yescharacteristic
971C5C3×#235811yescharacteristic, complemented, Sylow
972C22—22no—
973C22—22no—
974C22—22no—
975C22—22no—
976C22—22no—
977C22—22no—
978C22—22no—
979C22—22no—
980C22—22no—
981C22—41no—
982C22—41no—
983C22—41no—
984C22—41no—
985C22—54no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—102no—
990C22—102no—
991C22—102no—
992C22—102no—
993C22—102no—
994C22—102no—
995C22—2016no—
996C22—201no—
997C22—201no—
998C22—201no—
999C22—201no—
1000C22C3×C4×C22⋊D514yescomplemented
1001C22C22×C3×C4×D511yescharacteristic
1002C22C2×C3×#70911yescharacteristic
1003C22C2×C3×D4×D511yescharacteristic
1004C22C3×#414411yescharacteristic
1005C22C3×D5×#4111yescharacteristic
1006C22C3×#414911yescharacteristic
1007C22C22×C3×C22⋊D511yescharacteristic
1008C4—22no—
1009C4—22no—
1010C4—22no—
1011C4—22no—
1012C4—41no—
1013C4—102no—
1014C4—102no—
1015C4—102no—
1016C4—201no—
1017C4—201no—
1018C4—201no—
1019C3#1061412911yescharacteristic, direct product factor, Sylow
1020C2—24no—
1021C2—42no—
1022C2—104no—
1023C2—202no—
1024C2C3×C4×D4×D511yescharacteristic
1025C2C3×#6587911yescharacteristic
1026C2C3×#6588411yescharacteristic
1027C2C3×#6589011yescharacteristic
1028C2C2×C3×C4×C22⋊D511yescharacteristic
1029C2C3×D4×C22⋊D511yescharacteristic
1030C2C3×#6616311yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×D4C2
socleC23×C3×C5C24
prime radicalC2×C3×#4083C2
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×D4D5
hypocenterC5C3×#2358
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×C4×C22⋊D5C2semidirect
4. C22×C3×#685C2semidirect
5. C2×C3×D5×C22⋊C4C2semidirect
6. C3×#65509C2semidirect
7. C3×#65502C2semidirect
8. C3×#65499C2semidirect
9. C3×#65279C2semidirect
10. C3×#65278C2semidirect
11. C3×#65246C2semidirect
12. C3×#65245C2semidirect
13. C3×C22⋊C4×Dic5C2semidirect
14. C3×#65229C2semidirect
15. C3×C4×#685C2semidirect
16. #10614129C3direct (N × H)
20. C23×C3×C4×C5C22semidirect
27. C2×C3×C5×C4⋊C4C22semidirect
29. C2×C3×C5×C22⋊C4C22semidirect
30. C2×C3×C42×C5C22semidirect
33. C2×C3×C22⋊Dic5C22semidirect
34. C2×C3×C22⋊Dic5C22semidirect
35. C3×#4083C4semidirect
46. C2×C3×#683C22semidirect
47. C2×C3×#683C22semidirect
48. C2×C3×C4×Dic5C22semidirect
49. C2×C3×C4×Dic5C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
55. C3×#3963C22semidirect
56. C3×#3963C22semidirect
58. C2×C4×C5×D4C2×C3semidirect
60. C2×C4×C22⋊D5C2×C3semidirect
61. C22×#685C2×C3semidirect
62. C2×D5×C22⋊C4C2×C3semidirect
63. #65509C2×C3semidirect
64. #65502C2×C3semidirect
65. #65499C2×C3semidirect
66. #65279C2×C3semidirect
67. #65278C2×C3semidirect
68. #65246C2×C3semidirect
69. #65245C2×C3semidirect
70. C22⋊C4×Dic5C2×C3semidirect
71. #65229C2×C3semidirect
72. C4×#685C2×C3semidirect
81. C23×C3×D5C2×C4semidirect
86. C2×C3×C5×D4C2×C4semidirect
102. C2×C3×C22⋊D5C2×C4semidirect
103. C2×C3×C22⋊D5C2×C4semidirect
121. C3×C5×C22⋊C4D4semidirect
126. C3×C22⋊Dic5C2×C4semidirect
132. C3×#685C2×C4semidirect
133. C3×#685C2×C4semidirect
134. C3×#685D4semidirect
141. C2×C3×C4×D4D5semidirect
157. C23×C4×C5C22×C3semidirect
164. C2×C5×C4⋊C4C22×C3semidirect
166. C2×C5×C22⋊C4C22×C3semidirect
167. C2×C42×C5C22×C3semidirect
170. C2×C22⋊Dic5C22×C3semidirect
171. C2×C22⋊Dic5C22×C3semidirect
172. #4083C3×C4semidirect
183. C2×#683C22×C3semidirect
184. C2×#683C22×C3semidirect
185. C2×C4×Dic5C22×C3semidirect
186. C2×C4×Dic5C22×C3semidirect
188. #3963C22×C3semidirect
189. #3963C22×C3semidirect
190. #3963C22×C3semidirect
191. #3963C22×C3semidirect
192. #3963C22×C3semidirect
193. #3963C22×C3semidirect
280. C23×C3×C4C2×D5semidirect
286. C2×C3×C4⋊C4C2×D5semidirect
302. C2×C3×C22⋊C4C2×D5semidirect
305. C2×C3×C42C2×D5semidirect
320. C23×D5C2×C3×C4semidirect
325. C2×C5×D4C2×C3×C4semidirect
341. C2×C22⋊D5C2×C3×C4semidirect
342. C2×C22⋊D5C2×C3×C4semidirect
360. C5×C22⋊C4C3×D4semidirect
365. C22⋊Dic5C2×C3×C4semidirect
371. #685C2×C3×C4semidirect
372. #685C2×C3×C4semidirect
373. #685C3×D4semidirect
380. C2×C4×D4C3×D5semidirect
406. C22×C3×C5C4×D4semidirect
428. C2×C3×D5C4×D4semidirect
459. C2×C3×D4C4×D5semidirect
502. C3×C22⋊C4C22⋊D5semidirect
591. C23×C4C2×C3×D5semidirect
597. C2×C4⋊C4C2×C3×D5semidirect
613. C2×C22⋊C4C2×C3×D5semidirect
616. C2×C42C2×C3×D5semidirect
724. C22×C5C3×C4×D4semidirect
746. C2×D5C3×C4×D4semidirect
777. C2×D4C3×C4×D5semidirect
820. C22⋊C4C3×C22⋊D5semidirect
824. C3×C5#2358semidirect
853. C22×C3C4×C22⋊D5semidirect
971. C5C3×#2358semidirect
1000. C22C3×C4×C22⋊D5semidirect
1019. C3#10614129direct (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×C4×C22⋊D52
C22×C3×#6852
C2×C3×D5×C22⋊C42
C3×#655092
C3×#655022
C3×#654992
C3×#652792
C3×#652782
C3×#652462
C3×#652452
C3×C22⋊C4×Dic52
C3×#652292
C3×C4×#6852
#106141293
C3×#23585