Finite Group Databasebeta

← C3×#10606129 #14329512

Subgroups — C3×#10606129 #14329512

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C2×C3×#4033C211yesmaximal, characteristic, complemented
3C2×C3×#4031C211yesmaximal, characteristic
4C3×C5×#385C211yesmaximal, characteristic, complemented
5C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
6C3×#65279C211yesmaximal, characteristic, complemented
7C3×#65278C211yesmaximal, characteristic, complemented
8C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C3×#65246C211yesmaximal, characteristic
10C3×#65240C211yesmaximal, characteristic, complemented
11C3×#65233C211yesmaximal, characteristic, complemented
12C3×#64959C211yesmaximal, characteristic, complemented
13C3×#64955C211yesmaximal, characteristic, complemented
14C3×#64938C211yesmaximal, characteristic, complemented
15C3×#64935C211yesmaximal, characteristic, complemented
16#10606129C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C3×C4×C22⋊D5—24no—
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×C4×Dic5C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C2×C3×C4×Dic5C2211yescharacteristic
45C3×#4033—24no—
46C3×#4031C418yescomplemented
47C3×C5×#95C2211yescharacteristic
48C3×C5×#95C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2367—51nomaximal, Hall
56C2×C4×C22⋊D5C2×C311yescharacteristic
57C2×#4033C2×C311yescharacteristic, complemented
58C2×#4031C2×C311yescharacteristic
59C5×#385C2×C311yescharacteristic, complemented
60C4×C22⋊Dic5C2×C311yescharacteristic, complemented
61#65279C2×C311yescharacteristic, complemented
62#65278C2×C311yescharacteristic, complemented
63C4⋊C4×Dic5C2×C311yescharacteristic, complemented
64#65246C2×C311yescharacteristic
65#65240C2×C311yescharacteristic, complemented
66#65233C2×C311yescharacteristic, complemented
67#64959C2×C311yescharacteristic, complemented
68#64955C2×C311yescharacteristic, complemented
69#64938C2×C311yescharacteristic, complemented
70#64935C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×C3×C4×C5—22no—
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—41no—
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C2×C3×C22⋊D5—22no—
83C2×C3×C22⋊D5—22no—
84C2×C3×C22⋊D5C2×C414yes—
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C2×C3×C4×D5—22no—
93C2×C3×C4×D5—22no—
94C2×C3×C4×D5—41no—
95C2×C3×Dic10—22no—
96C2×C3×Dic10—22no—
97C2×C3×Dic10C2×C414yescomplemented
98C3×C5×C4⋊C4—22no—
99C3×C5×C4⋊C4—22no—
100C3×C5×C22⋊C4—41no—
101C3×C5×C22⋊C4C2×C414yescomplemented
102C3×C22⋊Dic5—22no—
103C3×C22⋊Dic5—22no—
104C3×C22⋊Dic5C2×C414yescomplemented
105C3×#685—22no—
106C3×#685—22no—
107C3×#685—41no—
108C3×#685C2×C414yescomplemented
109C3×#685C2×C414yescomplemented
110C3×C4⋊Dic5—22no—
111C3×#683—22no—
112C3×#683—22no—
113C3×#683D414yes—
114C3×C4×Dic5—22no—
115C3×C4×Dic5—22no—
116C3×C4×Dic5—22no—
117C3×C4×Dic5—22no—
118C3×C4×Dic5—41no—
119C3×C4×Dic5—41no—
120C3×C4×Dic5C2×C414yescomplemented
121C2×C3×#124—51no—
122C2×C3×C4×Q8—51no—
123C2×C3×C4×D4—51no—
124C3×#391—51no—
125C3×#390—51no—
126C3×#388—51no—
127C3×#388—51no—
128C3×#388—51no—
129C3×#388—51no—
130C3×#385—51no—
131C3×#385D511yescharacteristic, complemented
132C3×C4×C4⋊C4—51no—
133C3×C4×C4⋊C4—51no—
134C3×C4×C22⋊C4—51no—
135C3×C4×C22⋊C4—51no—
136C23×C4×C5C22×C311yescharacteristic
137C22×C22⋊D5C22×C311yescharacteristic
138C22×C4×D5C22×C311yescharacteristic
139C22×Dic10C22×C311yescharacteristic
140C2×C5×C4⋊C4C22×C311yescharacteristic
141C2×C5×C4⋊C4C22×C311yescharacteristic
142C2×C5×C22⋊C4C22×C311yescharacteristic
143C2×C5×C22⋊C4C22×C311yescharacteristic
144C2×C22⋊Dic5C22×C311yescharacteristic
145C2×C22⋊Dic5C22×C311yescharacteristic
146C2×C22⋊Dic5C22×C311yescharacteristic
147C4×C22⋊D5—24no—
148C2×#685C22×C311yescharacteristic
149C2×#685C22×C311yescharacteristic
150C2×#685C22×C311yescharacteristic
151C2×#685C22×C311yescharacteristic
152C2×#685C22×C311yescharacteristic
153C2×C4⋊Dic5C22×C311yescharacteristic
154C2×#683C22×C311yescharacteristic
155C2×#683C22×C311yescharacteristic
156C2×#683C22×C311yescharacteristic
157C2×C4×Dic5C22×C311yescharacteristic
158C2×C4×Dic5C22×C311yescharacteristic
159C2×C4×Dic5C22×C311yescharacteristic
160C2×C4×Dic5C22×C311yescharacteristic
161C2×C4×Dic5C22×C311yescharacteristic
162C2×C4×Dic5C22×C311yescharacteristic
163C2×C4×Dic5C22×C311yescharacteristic
164#4033—24no—
165#4031C3×C418yescomplemented
166C5×#95C22×C311yescharacteristic
167C5×#95C22×C311yescharacteristic
168#3963C22×C311yescharacteristic
169#3963C22×C311yescharacteristic
170#3963C22×C311yescharacteristic
171#3963C22×C311yescharacteristic
172#3963C22×C311yescharacteristic
173#3963C22×C311yescharacteristic
174#2367—51noSylow
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5—21no—
178C23×C3×C5—21no—
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5C22×C412yes—
182C23×C3×C5C2411yescharacteristic
183C22×C3×D5—21no—
184C22×C3×D5—21no—
185C22×C3×D5—21no—
186C22×C3×D5—21no—
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5C22×C412yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5—21no—
203C2×C3×C4×C5—21no—
204C2×C3×C4×C5—44no—
205C2×C3×C4×C5C22×C412yes—
206C2×C3×C4×C5C22×C412yes—
207C2×C3×C4×C5C2×D412yes—
208C2×C3×C4×C5#4112yes—
209C3×C22⋊D5—28no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5—21no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5C22×C412yes—
225C2×C3×Dic5C22×C412yes—
226C2×C3×Dic5C22×C412yes—
227C2×C3×Dic5C2×D412yes—
228C2×C3×Dic5C2×D412yes—
229C2×C3×Dic5#4112yes—
230C2×C3×Dic5#4112yes—
231C3×C4×D5—44no—
232C3×Dic10—28no—
233C22×C3×Q8—51no—
234C22×C3×D4—51no—
235C23×C3×C4—51no—
236C23×C3×C4C2×D511yescharacteristic
237C3×#124—58no—
238C3×C4×Q8—104no—
239C3×C4×D4—104no—
240C2×C3×C4⋊C4—51no—
241C2×C3×C4⋊C4—51no—
242C2×C3×C4⋊C4—51no—
243C2×C3×C4⋊C4—51no—
244C2×C3×C4⋊C4C2×D511yescharacteristic
245C2×C3×C4⋊C4C2×D511yescharacteristic
246C2×C3×C22⋊C4—51no—
247C2×C3×C22⋊C4—51no—
248C2×C3×C22⋊C4—51no—
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4—51no—
251C2×C3×C22⋊C4—51no—
252C2×C3×C22⋊C4—51no—
253C2×C3×C22⋊C4—51no—
254C2×C3×C22⋊C4C2×D511yescharacteristic
255C2×C3×C22⋊C4C2×D511yescharacteristic
256C2×C3×C42—51no—
257C2×C3×C42—51no—
258C2×C3×C42—51no—
259C2×C3×C42—51no—
260C2×C3×C42—51no—
261C2×C3×C42—51no—
262C2×C3×C42—51no—
263C3×#95—51no—
264C3×#95—51no—
265C3×#95—51no—
266C3×#95—51no—
267C3×#95—51no—
268C3×#95—51no—
269C3×#95C2×D511yescharacteristic
270C3×#95C2×D511yescharacteristic
271C24×C5C23×C311yescharacteristic
272C23×D5C23×C311yescharacteristic
273C22×C4×C5—22no—
274C22×C4×C5—22no—
275C22×C4×C5—41no—
276C22×C4×C5C23×C311yescharacteristic
277C22×C4×C5C23×C311yescharacteristic
278C22×C4×C5C23×C311yescharacteristic
279C22×C4×C5C23×C311yescharacteristic
280C22×C4×C5C23×C311yescharacteristic
281C22×C4×C5C23×C311yescharacteristic
282C2×C22⋊D5—22no—
283C2×C22⋊D5—22no—
284C2×C22⋊D5C2×C3×C414yes—
285C22×Dic5C23×C311yescharacteristic
286C22×Dic5C23×C311yescharacteristic
287C22×Dic5C23×C311yescharacteristic
288C22×Dic5C23×C311yescharacteristic
289C22×Dic5C23×C311yescharacteristic
290C22×Dic5C23×C311yescharacteristic
291C22×Dic5C23×C311yescharacteristic
292C2×C4×D5—22no—
293C2×C4×D5—22no—
294C2×C4×D5—41no—
295C2×Dic10—22no—
296C2×Dic10—22no—
297C2×Dic10C2×C3×C414yescomplemented
298C5×C4⋊C4—22no—
299C5×C4⋊C4—22no—
300C5×C22⋊C4—41no—
301C5×C22⋊C4C2×C3×C414yescomplemented
302C22⋊Dic5—22no—
303C22⋊Dic5—22no—
304C22⋊Dic5C2×C3×C414yescomplemented
305#685—22no—
306#685—22no—
307#685—41no—
308#685C2×C3×C414yescomplemented
309#685C2×C3×C414yescomplemented
310C4⋊Dic5—22no—
311#683—22no—
312#683—22no—
313#683C3×D414yes—
314C4×Dic5—22no—
315C4×Dic5—22no—
316C4×Dic5—22no—
317C4×Dic5—22no—
318C4×Dic5—41no—
319C4×Dic5—41no—
320C4×Dic5C2×C3×C414yescomplemented
321C2×#124—51no—
322C2×C4×Q8—51no—
323C2×C4×D4—51no—
324#391—51no—
325#390—51no—
326#388—51no—
327#388—51no—
328#388—51no—
329#388—51no—
330#385—51no—
331#385C3×D511yescharacteristic, complemented
332C4×C4⋊C4—51no—
333C4×C4⋊C4—51no—
334C4×C22⋊C4—51no—
335C4×C22⋊C4—51no—
336C22×C3×C5—22no—
337C22×C3×C5—22no—
338C22×C3×C5—22no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5—41no—
342C22×C3×C5—41no—
343C22×C3×C5C23×C411yescharacteristic
344C22×C3×C5C22×D411yescharacteristic
345C22×C3×C5C2×#4111yescharacteristic
346C22×C3×C5C2×#4111yescharacteristic
347C22×C3×C5C2×#4111yescharacteristic
348C22×C3×C5H(5,𝔽2)11yescharacteristic
349C22×C3×C52−1+411yescharacteristic
350C2×C3×D5—22no—
351C2×C3×D5—22no—
352C2×C3×D5—22no—
353C2×C3×D5—41no—
354C2×C3×D5—41no—
355C2×C3×D5—41no—
356C2×C3×D5—41no—
357C3×C4×C5—22no—
358C3×C4×C5—22no—
359C3×C4×C5—22no—
360C3×C4×C5—22no—
361C3×C4×C5—41no—
362C3×C4×C5—41no—
363C3×Dic5—22no—
364C3×Dic5—22no—
365C3×Dic5—22no—
366C3×Dic5—22no—
367C3×Dic5—41no—
368C3×Dic5—41no—
369C3×Dic5C4×D414yes—
370C24×C3—51no—
371C24×C3C22×D511yescharacteristic
372C2×C3×Q8—54no—
373C2×C3×Q8—102no—
374C2×C3×Q8—102no—
375C2×C3×D4—54no—
376C2×C3×D4—102no—
377C2×C3×D4—102no—
378C22×C3×C4—22no—
379C22×C3×C4—22no—
380C22×C3×C4—41no—
381C22×C3×C4—51no—
382C22×C3×C4—51no—
383C22×C3×C4—51no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—51no—
388C22×C3×C4—102no—
389C22×C3×C4—102no—
390C22×C3×C4—201no—
391C22×C3×C4C22×D511yescharacteristic
392C22×C3×C4C22×D511yescharacteristic
393C22×C3×C4C22×D511yescharacteristic
394C22×C3×C4C22×D511yescharacteristic
395C22×C3×C4C22×D511yescharacteristic
396C22×C3×C4C22×D511yescharacteristic
397C3×C4⋊C4—22no—
398C3×C4⋊C4—22no—
399C3×C4⋊C4—54no—
400C3×C4⋊C4—102no—
401C3×C4⋊C4—102no—
402C3×C4⋊C4—102no—
403C3×C22⋊C4—41no—
404C3×C22⋊C4—54no—
405C3×C22⋊C4—54no—
406C3×C22⋊C4—54no—
407C3×C22⋊C4—102no—
408C3×C22⋊C4—102no—
409C3×C22⋊C4—102no—
410C3×C22⋊C4—102no—
411C3×C22⋊C4—201no—
412C3×C22⋊C4C4×D514yescomplemented
413C3×C42—54no—
414C3×C42—102no—
415C3×C42—102no—
416C3×C42—102no—
417C3×C42—102no—
418C3×C42—201no—
419C3×C42—201no—
420C23×C5—21no—
421C23×C5—21no—
422C23×C5—21no—
423C23×C5—21no—
424C23×C5—21no—
425C23×C5—21no—
426C23×C5C22×C3×C412yes—
427C23×C5C24×C311yescharacteristic
428C22×D5—21no—
429C22×D5—21no—
430C22×D5—21no—
431C22×D5—21no—
432C22×D5—21no—
433C22×D5—21no—
434C22×D5C22×C3×C412yes—
435C2×C4×C5—21no—
436C2×C4×C5—21no—
437C2×C4×C5—21no—
438C2×C4×C5—21no—
439C2×C4×C5—21no—
440C2×C4×C5—21no—
441C2×C4×C5—21no—
442C2×C4×C5—21no—
443C2×C4×C5—21no—
444C2×C4×C5—21no—
445C2×C4×C5—21no—
446C2×C4×C5—21no—
447C2×C4×C5—21no—
448C2×C4×C5—21no—
449C2×C4×C5—44no—
450C2×C4×C5C22×C3×C412yes—
451C2×C4×C5C22×C3×C412yes—
452C2×C4×C5C2×C3×D412yes—
453C2×C4×C5C3×#4112yes—
454C22⋊D5—28no—
455C2×Dic5—21no—
456C2×Dic5—21no—
457C2×Dic5—21no—
458C2×Dic5—21no—
459C2×Dic5—21no—
460C2×Dic5—21no—
461C2×Dic5—21no—
462C2×Dic5—21no—
463C2×Dic5—21no—
464C2×Dic5—21no—
465C2×Dic5—21no—
466C2×Dic5—21no—
467C2×Dic5—21no—
468C2×Dic5—21no—
469C2×Dic5C22×C3×C412yes—
470C2×Dic5C22×C3×C412yes—
471C2×Dic5C22×C3×C412yes—
472C2×Dic5C2×C3×D412yes—
473C2×Dic5C2×C3×D412yes—
474C2×Dic5C3×#4112yes—
475C2×Dic5C3×#4112yes—
476C4×D5—44no—
477Dic10—28no—
478C22×Q8—51no—
479C22×D4—51no—
480C23×C4—51no—
481C23×C4C2×C3×D511yescharacteristic
482#124—58no—
483C4×Q8—104no—
484C4×D4—104no—
485C2×C4⋊C4—51no—
486C2×C4⋊C4—51no—
487C2×C4⋊C4—51no—
488C2×C4⋊C4—51no—
489C2×C4⋊C4C2×C3×D511yescharacteristic
490C2×C4⋊C4C2×C3×D511yescharacteristic
491C2×C22⋊C4—51no—
492C2×C22⋊C4—51no—
493C2×C22⋊C4—51no—
494C2×C22⋊C4—51no—
495C2×C22⋊C4—51no—
496C2×C22⋊C4—51no—
497C2×C22⋊C4—51no—
498C2×C22⋊C4—51no—
499C2×C22⋊C4C2×C3×D511yescharacteristic
500C2×C22⋊C4C2×C3×D511yescharacteristic
501C2×C42—51no—
502C2×C42—51no—
503C2×C42—51no—
504C2×C42—51no—
505C2×C42—51no—
506C2×C42—51no—
507C2×C42—51no—
508#95—51no—
509#95—51no—
510#95—51no—
511#95—51no—
512#95—51no—
513#95—51no—
514#95C2×C3×D511yescharacteristic
515#95C2×C3×D511yescharacteristic
516C2×C3×C5—42no—
517C2×C3×C5C2×C4×D411yescharacteristic
518C2×C3×C5C4×#4111yescharacteristic
519C2×C3×C5#52011yescharacteristic
520C2×C3×C5#54611yescharacteristic
521C2×C3×C5#54811yescharacteristic
522C2×C3×C5#55611yescharacteristic
523C2×C3×C5#55911yescharacteristic
524C3×D5—42no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—52no—
532C23×C3—101no—
533C23×C3—101no—
534C23×C3—101no—
535C23×C3—101no—
536C23×C3—101no—
537C23×C3—101no—
538C23×C3C2×C4×D512yes—
539C23×C3C23×D511yescharacteristic
540C3×Q8—108no—
541C3×D4—108no—
542C2×C3×C4—21no—
543C2×C3×C4—21no—
544C2×C3×C4—21no—
545C2×C3×C4—21no—
546C2×C3×C4—21no—
547C2×C3×C4—21no—
548C2×C3×C4—21no—
549C2×C3×C4—21no—
550C2×C3×C4—21no—
551C2×C3×C4—21no—
552C2×C3×C4—21no—
553C2×C3×C4—21no—
554C2×C3×C4—21no—
555C2×C3×C4—21no—
556C2×C3×C4—44no—
557C2×C3×C4—52no—
558C2×C3×C4—52no—
559C2×C3×C4—52no—
560C2×C3×C4—52no—
561C2×C3×C4—52no—
562C2×C3×C4—52no—
563C2×C3×C4—52no—
564C2×C3×C4—101no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—101no—
568C2×C3×C4—101no—
569C2×C3×C4—101no—
570C2×C3×C4—101no—
571C2×C3×C4—101no—
572C2×C3×C4—101no—
573C2×C3×C4—101no—
574C2×C3×C4—101no—
575C2×C3×C4—101no—
576C2×C3×C4—101no—
577C2×C3×C4—101no—
578C2×C3×C4—204no—
579C2×C3×C4C2×C4×D512yes—
580C2×C3×C4C2×C4×D512yes—
581C2×C3×C4D4×D512yes—
582C2×C3×C4#71112yes—
583C22×C5—22no—
584C22×C5—22no—
585C22×C5—22no—
586C22×C5—41no—
587C22×C5—41no—
588C22×C5—41no—
589C22×C5—41no—
590C22×C5C23×C3×C411yescharacteristic
591C22×C5C22×C3×D411yescharacteristic
592C22×C5C2×C3×#4111yescharacteristic
593C22×C5C2×C3×#4111yescharacteristic
594C22×C5C2×C3×#4111yescharacteristic
595C22×C5C3×H(5,𝔽2)11yescharacteristic
596C22×C5C3×2−1+411yescharacteristic
597C2×D5—22no—
598C2×D5—22no—
599C2×D5—22no—
600C2×D5—41no—
601C2×D5—41no—
602C2×D5—41no—
603C2×D5—41no—
604C4×C5—22no—
605C4×C5—22no—
606C4×C5—22no—
607C4×C5—22no—
608C4×C5—41no—
609C4×C5—41no—
610Dic5—22no—
611Dic5—22no—
612Dic5—22no—
613Dic5—22no—
614Dic5—41no—
615Dic5—41no—
616Dic5C3×C4×D414yes—
617C24—51no—
618C24C22×C3×D511yescharacteristic
619C2×Q8—54no—
620C2×Q8—102no—
621C2×Q8—102no—
622C2×D4—54no—
623C2×D4—102no—
624C2×D4—102no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—41no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—51no—
633C22×C4—51no—
634C22×C4—51no—
635C22×C4—102no—
636C22×C4—102no—
637C22×C4—201no—
638C22×C4C22×C3×D511yescharacteristic
639C22×C4C22×C3×D511yescharacteristic
640C22×C4C22×C3×D511yescharacteristic
641C22×C4C22×C3×D511yescharacteristic
642C22×C4C22×C3×D511yescharacteristic
643C22×C4C22×C3×D511yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—54no—
647C4⋊C4—102no—
648C4⋊C4—102no—
649C4⋊C4—102no—
650C22⋊C4—41no—
651C22⋊C4—54no—
652C22⋊C4—54no—
653C22⋊C4—54no—
654C22⋊C4—102no—
655C22⋊C4—102no—
656C22⋊C4—102no—
657C22⋊C4—102no—
658C22⋊C4—201no—
659C22⋊C4C3×C4×D514yescomplemented
660C42—54no—
661C42—102no—
662C42—102no—
663C42—102no—
664C42—102no—
665C42—201no—
666C42—201no—
667C3×C5#236711yescharacteristic, complemented, Hall
668C22×C3—22no—
669C22×C3—22no—
670C22×C3—22no—
671C22×C3—41no—
672C22×C3—41no—
673C22×C3—41no—
674C22×C3—41no—
675C22×C3—102no—
676C22×C3—102no—
677C22×C3—102no—
678C22×C3—201no—
679C22×C3—201no—
680C22×C3—201no—
681C22×C3—201no—
682C22×C3C22×C4×D511yescharacteristic
683C22×C3C2×D4×D511yescharacteristic
684C22×C3C2×#71111yescharacteristic
685C22×C3#414411yescharacteristic
686C22×C3#414711yescharacteristic
687C22×C3D5×#4111yescharacteristic
688C22×C3D5×#4111yescharacteristic
689C3×C4—22no—
690C3×C4—22no—
691C3×C4—22no—
692C3×C4—22no—
693C3×C4—41no—
694C3×C4—41no—
695C3×C4—54no—
696C3×C4—102no—
697C3×C4—102no—
698C3×C4—102no—
699C3×C4—102no—
700C3×C4—201no—
701C3×C4—201no—
702C2×C5—42no—
703C2×C5C2×C3×C4×D411yescharacteristic
704C2×C5C3×C4×#4111yescharacteristic
705C2×C5C3×#52011yescharacteristic
706C2×C5C3×#54611yescharacteristic
707C2×C5C3×#54811yescharacteristic
708C2×C5C3×#55611yescharacteristic
709C2×C5C3×#55911yescharacteristic
710D5—42no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—52no—
718C23—101no—
719C23—101no—
720C23—101no—
721C23—101no—
722C23—101no—
723C23—101no—
724C23C2×C3×C4×D512yes—
725C23C23×C3×D511yescharacteristic
726Q8—108no—
727D4—108no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—44no—
743C2×C4—52no—
744C2×C4—52no—
745C2×C4—52no—
746C2×C4—52no—
747C2×C4—52no—
748C2×C4—52no—
749C2×C4—52no—
750C2×C4—101no—
751C2×C4—101no—
752C2×C4—101no—
753C2×C4—101no—
754C2×C4—101no—
755C2×C4—101no—
756C2×C4—101no—
757C2×C4—101no—
758C2×C4—101no—
759C2×C4—101no—
760C2×C4—101no—
761C2×C4—101no—
762C2×C4—101no—
763C2×C4—101no—
764C2×C4—204no—
765C2×C4C2×C3×C4×D512yes—
766C2×C4C2×C3×C4×D512yes—
767C2×C4C3×D4×D512yes—
768C2×C4C3×#71112yes—
769C2×C3—42no—
770C2×C3—202no—
771C2×C3#6583811yescharacteristic
772C2×C3C4×#71111yescharacteristic
773C2×C3C4×D4×D511yescharacteristic
774C2×C3#6592511yescharacteristic
775C2×C3#6596711yescharacteristic
776C2×C3#6597511yescharacteristic
777C2×C3#6599811yescharacteristic
778C5C3×#236711yescharacteristic, complemented, Sylow
779C22—22no—
780C22—22no—
781C22—22no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—102no—
787C22—102no—
788C22—102no—
789C22—201no—
790C22—201no—
791C22—201no—
792C22—201no—
793C22C22×C3×C4×D511yescharacteristic
794C22C2×C3×D4×D511yescharacteristic
795C22C2×C3×#71111yescharacteristic
796C22C3×#414411yescharacteristic
797C22C3×#414711yescharacteristic
798C22C3×D5×#4111yescharacteristic
799C22C3×D5×#4111yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—22no—
804C4—41no—
805C4—41no—
806C4—54no—
807C4—102no—
808C4—102no—
809C4—102no—
810C4—102no—
811C4—201no—
812C4—201no—
813C3#1060612911yescharacteristic, direct product factor, Sylow
814C2—42no—
815C2—202no—
816C2C3×#6583811yescharacteristic
817C2C3×C4×#71111yescharacteristic
818C2C3×C4×D4×D511yescharacteristic
819C2C3×#6592511yescharacteristic
820C2C3×#6596711yescharacteristic
821C2C3×#6597511yescharacteristic
822C2C3×#6599811yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#385C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#385D5
hypocenterC5C3×#2367
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#385

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4033C2semidirect
4. C3×C5×#385C2semidirect
5. C3×C4×C22⋊Dic5C2semidirect
6. C3×#65279C2semidirect
7. C3×#65278C2semidirect
8. C3×C4⋊C4×Dic5C2semidirect
10. C3×#65240C2semidirect
11. C3×#65233C2semidirect
12. C3×#64959C2semidirect
13. C3×#64955C2semidirect
14. C3×#64938C2semidirect
15. C3×#64935C2semidirect
16. #10606129C3direct (N × H)
46. C3×#4031C4semidirect
57. C2×#4033C2×C3semidirect
59. C5×#385C2×C3semidirect
60. C4×C22⋊Dic5C2×C3semidirect
61. #65279C2×C3semidirect
62. #65278C2×C3semidirect
63. C4⋊C4×Dic5C2×C3semidirect
65. #65240C2×C3semidirect
66. #65233C2×C3semidirect
67. #64959C2×C3semidirect
68. #64955C2×C3semidirect
69. #64938C2×C3semidirect
70. #64935C2×C3semidirect
97. C2×C3×Dic10C2×C4semidirect
101. C3×C5×C22⋊C4C2×C4semidirect
104. C3×C22⋊Dic5C2×C4semidirect
108. C3×#685C2×C4semidirect
109. C3×#685C2×C4semidirect
120. C3×C4×Dic5C2×C4semidirect
131. C3×#385D5semidirect
165. #4031C3×C4semidirect
297. C2×Dic10C2×C3×C4semidirect
301. C5×C22⋊C4C2×C3×C4semidirect
304. C22⋊Dic5C2×C3×C4semidirect
308. #685C2×C3×C4semidirect
309. #685C2×C3×C4semidirect
320. C4×Dic5C2×C3×C4semidirect
331. #385C3×D5semidirect
412. C3×C22⋊C4C4×D5semidirect
659. C22⋊C4C3×C4×D5semidirect
667. C3×C5#2367semidirect
778. C5C3×#2367semidirect
813. C3#10606129direct (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×#40332
C2×C3×#40312
C3×C5×#3852
C3×C4×C22⋊Dic52
C3×#652792
C3×#652782
C3×C4⋊C4×Dic52
C3×#652462
C3×#652402
C3×#652332
C3×#649592
C3×#649552
C3×#649382
C3×#649352
#106061293
C3×#23675