Finite Group Databasebeta

← C3×#10606405 #14327505

Subgroups — C3×#10606405 #14327505

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D4×Dic5C211yesmaximal, characteristic
2C3×C5×#386C211yesmaximal, characteristic
3C3×#65509C211yesmaximal, characteristic
4C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
5C2×C3×#3963C211yesmaximal, characteristic, complemented
6C3×#65234C211yesmaximal, characteristic, complemented
7C3×#65233C211yesmaximal, characteristic, complemented
8C3×#65232C211yesmaximal, characteristic, complemented
9C3×#65231C211yesmaximal, characteristic, complemented
10C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
11C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12C3×#64943C211yesmaximal, characteristic, complemented
13C3×#64942C211yesmaximal, characteristic, complemented
14C3×#64940C211yesmaximal, characteristic, complemented
15C3×#64937C211yesmaximal, characteristic, complemented
16#10606405C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C3×D4×Dic5C418yescomplemented
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×C3×C4×Dic5C2211yescharacteristic
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41C3×#3963C2211yescharacteristic
42C3×#3963C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#2353—51nomaximal, Hall
54C2×D4×Dic5C2×C311yescharacteristic
55C5×#386C2×C311yescharacteristic
56#65509C2×C311yescharacteristic
57C4×C22⋊Dic5C2×C311yescharacteristic, complemented
58C2×#3963C2×C311yescharacteristic, complemented
59#65234C2×C311yescharacteristic, complemented
60#65233C2×C311yescharacteristic, complemented
61#65232C2×C311yescharacteristic, complemented
62#65231C2×C311yescharacteristic, complemented
63C22⋊C4×Dic5C2×C311yescharacteristic, complemented
64C22⋊C4×Dic5C2×C311yescharacteristic, complemented
65#64943C2×C311yescharacteristic, complemented
66#64942C2×C311yescharacteristic, complemented
67#64940C2×C311yescharacteristic, complemented
68#64937C2×C311yescharacteristic, complemented
69C24×C3×C5C2311yescharacteristic
70C24×C3×C5C2311yescharacteristic
71C2×C3×C5×D4—22no—
72C2×C3×C5×D4—22no—
73C2×C3×C5×D4C2×C414yes—
74C22×C3×C4×C5—22no—
75C22×C3×C4×C5—22no—
76C22×C3×C4×C5—41no—
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×Dic5—22no—
83C22×C3×Dic5—22no—
84C22×C3×Dic5—41no—
85C22×C3×Dic5—41no—
86C22×C3×Dic5—41no—
87C22×C3×Dic5—41no—
88C22×C3×Dic5—41no—
89C22×C3×Dic5C2×C414yes—
90C22×C3×Dic5C2×C414yescomplemented
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C3×C5×C22⋊C4—22no—
100C3×C5×C22⋊C4—22no—
101C3×C5×C22⋊C4—41no—
102C3×C22⋊Dic5—22no—
103C3×C22⋊Dic5—22no—
104C3×C22⋊Dic5—41no—
105C3×C22⋊Dic5C2×C414yes—
106C3×C22⋊Dic5C2×C414yescomplemented
107C3×C4⋊Dic5C2×C414yescomplemented
108C3×#683—41no—
109C3×#683—41no—
110C3×C4×Dic5—22no—
111C3×C4×Dic5—22no—
112C3×C4×Dic5—41no—
113C3×C4×Dic5—41no—
114C3×C4×Dic5C2×C414yescomplemented
115C2×C3×C4×D4—51no—
116C3×#388—51no—
117C3×#388—51no—
118C3×#387—51no—
119C3×#387—51no—
120C3×#386—51no—
121C3×#386D511yescharacteristic
122C3×#383—51no—
123C3×#381—51no—
124C3×#380—51no—
125C3×C4×C22⋊C4—51no—
126C3×C4×C22⋊C4—51no—
127C3×C4×C22⋊C4—51no—
128C3×#376—51no—
129C2×C3×#95—51no—
130C22×C5×D4C22×C311yescharacteristic
131C23×C4×C5C22×C311yescharacteristic
132C23×Dic5C22×C311yescharacteristic
133C23×Dic5C22×C311yescharacteristic
134C23×Dic5C22×C311yescharacteristic
135C2×C5×C22⋊C4C22×C311yescharacteristic
136C2×C5×C22⋊C4C22×C311yescharacteristic
137C2×C5×C22⋊C4C22×C311yescharacteristic
138C2×C22⋊Dic5C22×C311yescharacteristic
139C2×C22⋊Dic5C22×C311yescharacteristic
140C2×C22⋊Dic5C22×C311yescharacteristic
141C2×C22⋊Dic5C22×C311yescharacteristic
142C2×C22⋊Dic5C22×C311yescharacteristic
143D4×Dic5C3×C418yescomplemented
144C2×C4⋊Dic5C22×C311yescharacteristic
145C2×#683C22×C311yescharacteristic
146C2×#683C22×C311yescharacteristic
147C2×C4×Dic5C22×C311yescharacteristic
148C2×C4×Dic5C22×C311yescharacteristic
149C2×C4×Dic5C22×C311yescharacteristic
150C2×C4×Dic5C22×C311yescharacteristic
151C2×C4×Dic5C22×C311yescharacteristic
152C5×#95C22×C311yescharacteristic
153C5×#95C22×C311yescharacteristic
154#3963C22×C311yescharacteristic
155#3963C22×C311yescharacteristic
156#3963C22×C311yescharacteristic
157#3963C22×C311yescharacteristic
158#3963C22×C311yescharacteristic
159#3963C22×C311yescharacteristic
160#3963C22×C311yescharacteristic
161#3963C22×C311yescharacteristic
162#3963C22×C311yescharacteristic
163#3963C22×C311yescharacteristic
164#3963C22×C311yescharacteristic
165#3963C22×C311yescharacteristic
166#2353—51noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5—21no—
174C23×C3×C5—21no—
175C23×C3×C5—21no—
176C23×C3×C5—21no—
177C23×C3×C5C22×C412yes—
178C23×C3×C5C22×C412yes—
179C23×C3×C5#4112yes—
180C23×C3×C5#4112yes—
181C23×C3×C5C2411yescharacteristic
182C3×C5×D4—28no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
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—44no—
197C2×C3×C4×C5C22×C412yes—
198C2×C3×C4×C5#4112yes—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
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—44no—
219C2×C3×Dic5—44no—
220C2×C3×Dic5—44no—
221C2×C3×Dic5C22×C412yes—
222C2×C3×Dic5C22×C412yes—
223C2×C3×Dic5C22×C412yes—
224C2×C3×Dic5C22×C412yes—
225C2×C3×Dic5#4112yes—
226C22×C3×D4C2×D511yescharacteristic
227C23×C3×C4—51no—
228C23×C3×C4—51no—
229C23×C3×C4—51no—
230C23×C3×C4C2×D511yescharacteristic
231C3×C4×D4—58no—
232C2×C3×C4⋊C4—51no—
233C2×C3×C4⋊C4—51no—
234C2×C3×C4⋊C4—51no—
235C2×C3×C22⋊C4—51no—
236C2×C3×C22⋊C4—51no—
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C22⋊C4—51no—
240C2×C3×C22⋊C4C2×D511yescharacteristic
241C2×C3×C22⋊C4C2×D511yescharacteristic
242C2×C3×C22⋊C4C2×D511yescharacteristic
243C2×C3×C42—51no—
244C2×C3×C42—51no—
245C2×C3×C42—51no—
246C2×C3×C42—51no—
247C2×C3×C42—51no—
248C3×#95—51no—
249C3×#95—51no—
250C3×#95—51no—
251C3×#95—51no—
252C3×#95—51no—
253C3×#95—51no—
254C3×#95—51no—
255C3×#95—51no—
256C3×#95—51no—
257C3×#95—51no—
258C3×#95—51no—
259C3×#95—51no—
260C3×#95C2×D511yescharacteristic
261C3×#95C2×D511yescharacteristic
262C24×C5C23×C311yescharacteristic
263C24×C5C23×C311yescharacteristic
264C2×C5×D4—22no—
265C2×C5×D4—22no—
266C2×C5×D4C2×C3×C414yes—
267C22×C4×C5—22no—
268C22×C4×C5—22no—
269C22×C4×C5—41no—
270C22×C4×C5C23×C311yescharacteristic
271C22×C4×C5C23×C311yescharacteristic
272C22×C4×C5C23×C311yescharacteristic
273C22×C4×C5C23×C311yescharacteristic
274C22×C4×C5C23×C311yescharacteristic
275C22×Dic5—22no—
276C22×Dic5—22no—
277C22×Dic5—41no—
278C22×Dic5—41no—
279C22×Dic5—41no—
280C22×Dic5—41no—
281C22×Dic5—41no—
282C22×Dic5C2×C3×C414yes—
283C22×Dic5C2×C3×C414yescomplemented
284C22×Dic5C23×C311yescharacteristic
285C22×Dic5C23×C311yescharacteristic
286C22×Dic5C23×C311yescharacteristic
287C22×Dic5C23×C311yescharacteristic
288C22×Dic5C23×C311yescharacteristic
289C22×Dic5C23×C311yescharacteristic
290C22×Dic5C23×C311yescharacteristic
291C22×Dic5C23×C311yescharacteristic
292C5×C22⋊C4—22no—
293C5×C22⋊C4—22no—
294C5×C22⋊C4—41no—
295C22⋊Dic5—22no—
296C22⋊Dic5—22no—
297C22⋊Dic5—41no—
298C22⋊Dic5C2×C3×C414yes—
299C22⋊Dic5C2×C3×C414yescomplemented
300C4⋊Dic5C2×C3×C414yescomplemented
301#683—41no—
302#683—41no—
303C4×Dic5—22no—
304C4×Dic5—22no—
305C4×Dic5—41no—
306C4×Dic5—41no—
307C4×Dic5C2×C3×C414yescomplemented
308C2×C4×D4—51no—
309#388—51no—
310#388—51no—
311#387—51no—
312#387—51no—
313#386—51no—
314#386C3×D511yescharacteristic
315#383—51no—
316#381—51no—
317#380—51no—
318C4×C22⋊C4—51no—
319C4×C22⋊C4—51no—
320C4×C22⋊C4—51no—
321#376—51no—
322C2×#95—51no—
323C22×C3×C5—22no—
324C22×C3×C5—22no—
325C22×C3×C5—22no—
326C22×C3×C5—22no—
327C22×C3×C5—22no—
328C22×C3×C5—22no—
329C22×C3×C5—22no—
330C22×C3×C5—22no—
331C22×C3×C5—22no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5—41no—
335C22×C3×C5—41no—
336C22×C3×C5#11714yes—
337C22×C3×C5C23×C411yescharacteristic
338C22×C3×C5C2×#4111yescharacteristic
339C22×C3×C5C2×#4111yescharacteristic
340C22×C3×C5C2×#4111yescharacteristic
341C22×C3×C5C2×#4111yescharacteristic
342C22×C3×C5H(5,𝔽2)11yescharacteristic
343C22×C3×C5H(5,𝔽2)11yescharacteristic
344C3×C4×C5—22no—
345C3×C4×C5—22no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×C4×C5—41no—
349C3×Dic5—22no—
350C3×Dic5—22no—
351C3×Dic5—22no—
352C3×Dic5—22no—
353C3×Dic5—22no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×Dic5—41no—
357C24×C3C22×D511yescharacteristic
358C24×C3C22×D511yescharacteristic
359C2×C3×D4—22no—
360C2×C3×D4—22no—
361C2×C3×D4C4×D514yes—
362C22×C3×C4—22no—
363C22×C3×C4—22no—
364C22×C3×C4—41no—
365C22×C3×C4—51no—
366C22×C3×C4—51no—
367C22×C3×C4—51no—
368C22×C3×C4—51no—
369C22×C3×C4—51no—
370C22×C3×C4—54no—
371C22×C3×C4—54no—
372C22×C3×C4—51no—
373C22×C3×C4—51no—
374C22×C3×C4—51no—
375C22×C3×C4—102no—
376C22×C3×C4—102no—
377C22×C3×C4—201no—
378C22×C3×C4—201no—
379C22×C3×C4—201no—
380C22×C3×C4—201no—
381C22×C3×C4—201no—
382C22×C3×C4C22×D511yescharacteristic
383C22×C3×C4C22×D511yescharacteristic
384C22×C3×C4C22×D511yescharacteristic
385C22×C3×C4C22×D511yescharacteristic
386C22×C3×C4C22×D511yescharacteristic
387C3×C4⋊C4—54no—
388C3×C4⋊C4—201no—
389C3×C4⋊C4—201no—
390C3×C22⋊C4—22no—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—41no—
393C3×C22⋊C4—54no—
394C3×C22⋊C4—54no—
395C3×C22⋊C4—102no—
396C3×C22⋊C4—102no—
397C3×C22⋊C4—201no—
398C3×C42—54no—
399C3×C42—102no—
400C3×C42—102no—
401C3×C42—201no—
402C3×C42—201no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—21no—
410C23×C5—21no—
411C23×C5—21no—
412C23×C5—21no—
413C23×C5C22×C3×C412yes—
414C23×C5C22×C3×C412yes—
415C23×C5C3×#4112yes—
416C23×C5C3×#4112yes—
417C23×C5C24×C311yescharacteristic
418C5×D4—28no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—44no—
433C2×C4×C5C22×C3×C412yes—
434C2×C4×C5C3×#4112yes—
435C2×Dic5—21no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—21no—
451C2×Dic5—21no—
452C2×Dic5—21no—
453C2×Dic5—21no—
454C2×Dic5—44no—
455C2×Dic5—44no—
456C2×Dic5—44no—
457C2×Dic5C22×C3×C412yes—
458C2×Dic5C22×C3×C412yes—
459C2×Dic5C22×C3×C412yes—
460C2×Dic5C22×C3×C412yes—
461C2×Dic5C3×#4112yes—
462C22×D4C2×C3×D511yescharacteristic
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4C2×C3×D511yescharacteristic
467C4×D4—58no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—51no—
470C2×C4⋊C4—51no—
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—51no—
476C2×C22⋊C4C2×C3×D511yescharacteristic
477C2×C22⋊C4C2×C3×D511yescharacteristic
478C2×C22⋊C4C2×C3×D511yescharacteristic
479C2×C42—51no—
480C2×C42—51no—
481C2×C42—51no—
482C2×C42—51no—
483C2×C42—51no—
484#95—51no—
485#95—51no—
486#95—51no—
487#95—51no—
488#95—51no—
489#95—51no—
490#95—51no—
491#95—51no—
492#95—51no—
493#95—51no—
494#95—51no—
495#95—51no—
496#95C2×C3×D511yescharacteristic
497#95C2×C3×D511yescharacteristic
498C2×C3×C5—24no—
499C2×C3×C5—42no—
500C2×C3×C5C2×#11711yescharacteristic
501C2×C3×C5C4×#4111yescharacteristic
502C2×C3×C5#51811yescharacteristic
503C2×C3×C5#55111yescharacteristic
504C2×C3×C5#55111yescharacteristic
505C2×C3×C5#55311yescharacteristic
506C2×C3×C5#55311yescharacteristic
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—21no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
516C23×C3—21no—
517C23×C3C2×C4×D512yes—
518C23×C3C2×C4×D512yes—
519C23×C3#71112yes—
520C23×C3#71112yes—
521C23×C3C23×D511yescharacteristic
522C3×D4—28no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—44no—
537C2×C3×C4—52no—
538C2×C3×C4—52no—
539C2×C3×C4—52no—
540C2×C3×C4—52no—
541C2×C3×C4—52no—
542C2×C3×C4—101no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4—101no—
559C2×C3×C4—101no—
560C2×C3×C4—101no—
561C2×C3×C4—204no—
562C2×C3×C4—204no—
563C2×C3×C4—204no—
564C2×C3×C4C2×C4×D512yes—
565C2×C3×C4#71112yes—
566C22×C5—22no—
567C22×C5—22no—
568C22×C5—22no—
569C22×C5—22no—
570C22×C5—22no—
571C22×C5—22no—
572C22×C5—22no—
573C22×C5—22no—
574C22×C5—22no—
575C22×C5—41no—
576C22×C5—41no—
577C22×C5—41no—
578C22×C5—41no—
579C22×C5C3×#11714yes—
580C22×C5C23×C3×C411yescharacteristic
581C22×C5C2×C3×#4111yescharacteristic
582C22×C5C2×C3×#4111yescharacteristic
583C22×C5C2×C3×#4111yescharacteristic
584C22×C5C2×C3×#4111yescharacteristic
585C22×C5C3×H(5,𝔽2)11yescharacteristic
586C22×C5C3×H(5,𝔽2)11yescharacteristic
587C4×C5—22no—
588C4×C5—22no—
589C4×C5—41no—
590C4×C5—41no—
591C4×C5—41no—
592Dic5—22no—
593Dic5—22no—
594Dic5—22no—
595Dic5—22no—
596Dic5—22no—
597Dic5—41no—
598Dic5—41no—
599Dic5—41no—
600C24C22×C3×D511yescharacteristic
601C24C22×C3×D511yescharacteristic
602C2×D4—22no—
603C2×D4—22no—
604C2×D4C3×C4×D514yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—41no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—51no—
613C22×C4—54no—
614C22×C4—54no—
615C22×C4—51no—
616C22×C4—51no—
617C22×C4—51no—
618C22×C4—102no—
619C22×C4—102no—
620C22×C4—201no—
621C22×C4—201no—
622C22×C4—201no—
623C22×C4—201no—
624C22×C4—201no—
625C22×C4C22×C3×D511yescharacteristic
626C22×C4C22×C3×D511yescharacteristic
627C22×C4C22×C3×D511yescharacteristic
628C22×C4C22×C3×D511yescharacteristic
629C22×C4C22×C3×D511yescharacteristic
630C4⋊C4—54no—
631C4⋊C4—201no—
632C4⋊C4—201no—
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—41no—
636C22⋊C4—54no—
637C22⋊C4—54no—
638C22⋊C4—102no—
639C22⋊C4—102no—
640C22⋊C4—201no—
641C42—54no—
642C42—102no—
643C42—102no—
644C42—201no—
645C42—201no—
646C3×C5#235311yescharacteristic, complemented, Hall
647C22×C3—22no—
648C22×C3—22no—
649C22×C3—22no—
650C22×C3—22no—
651C22×C3—22no—
652C22×C3—22no—
653C22×C3—22no—
654C22×C3—22no—
655C22×C3—22no—
656C22×C3—41no—
657C22×C3—41no—
658C22×C3—41no—
659C22×C3—41no—
660C22×C3#402314yes—
661C22×C3C22×C4×D511yescharacteristic
662C22×C3C2×#71111yescharacteristic
663C22×C3C2×#71111yescharacteristic
664C22×C3C2×#71111yescharacteristic
665C22×C3#414411yescharacteristic
666C22×C3D5×#4111yescharacteristic
667C22×C3#414911yescharacteristic
668C3×C4—22no—
669C3×C4—22no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—41no—
673C3×C4—102no—
674C3×C4—102no—
675C3×C4—102no—
676C3×C4—102no—
677C3×C4—102no—
678C3×C4—201no—
679C3×C4—201no—
680C3×C4—201no—
681C2×C5—24no—
682C2×C5—42no—
683C2×C5C2×C3×#11711yescharacteristic
684C2×C5C3×C4×#4111yescharacteristic
685C2×C5C3×#51811yescharacteristic
686C2×C5C3×#55111yescharacteristic
687C2×C5C3×#55111yescharacteristic
688C2×C5C3×#55311yescharacteristic
689C2×C5C3×#55311yescharacteristic
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23C2×C3×C4×D512yes—
701C23C2×C3×C4×D512yes—
702C23C3×#71112yes—
703C23C3×#71112yes—
704C23C23×C3×D511yescharacteristic
705D4—28no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—44no—
720C2×C4—52no—
721C2×C4—52no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—52no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—101no—
736C2×C4—101no—
737C2×C4—101no—
738C2×C4—101no—
739C2×C4—101no—
740C2×C4—101no—
741C2×C4—101no—
742C2×C4—101no—
743C2×C4—101no—
744C2×C4—204no—
745C2×C4—204no—
746C2×C4—204no—
747C2×C4C2×C3×C4×D512yes—
748C2×C4C3×#71112yes—
749C2×C3—24no—
750C2×C3—42no—
751C2×C3C2×#402311yescharacteristic
752C2×C3C4×#71111yescharacteristic
753C2×C3#6587911yescharacteristic
754C2×C3#6592111yescharacteristic
755C2×C3#6593511yescharacteristic
756C2×C3#6595211yescharacteristic
757C2×C3#6599211yescharacteristic
758C5C3×#235311yescharacteristic, complemented, Sylow
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22C3×#402314yes—
773C22C22×C3×C4×D511yescharacteristic
774C22C2×C3×#71111yescharacteristic
775C22C2×C3×#71111yescharacteristic
776C22C2×C3×#71111yescharacteristic
777C22C3×#414411yescharacteristic
778C22C3×D5×#4111yescharacteristic
779C22C3×#414911yescharacteristic
780C4—22no—
781C4—22no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4—102no—
786C4—102no—
787C4—102no—
788C4—102no—
789C4—102no—
790C4—201no—
791C4—201no—
792C4—201no—
793C3#1060640511yescharacteristic, direct product factor, Sylow
794C2—24no—
795C2—42no—
796C2C2×C3×#402311yescharacteristic
797C2C3×C4×#71111yescharacteristic
798C2C3×#6587911yescharacteristic
799C2C3×#6592111yescharacteristic
800C2C3×#6593511yescharacteristic
801C2C3×#6595211yescharacteristic
802C2C3×#6599211yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2353
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
4. C3×C4×C22⋊Dic5C2semidirect
5. C2×C3×#3963C2semidirect
6. C3×#65234C2semidirect
7. C3×#65233C2semidirect
8. C3×#65232C2semidirect
9. C3×#65231C2semidirect
10. C3×C22⋊C4×Dic5C2semidirect
11. C3×C22⋊C4×Dic5C2semidirect
12. C3×#64943C2semidirect
13. C3×#64942C2semidirect
14. C3×#64940C2semidirect
15. C3×#64937C2semidirect
16. #10606405C3direct (N × H)
30. C3×D4×Dic5C4semidirect
57. C4×C22⋊Dic5C2×C3semidirect
58. C2×#3963C2×C3semidirect
59. #65234C2×C3semidirect
60. #65233C2×C3semidirect
61. #65232C2×C3semidirect
62. #65231C2×C3semidirect
63. C22⋊C4×Dic5C2×C3semidirect
64. C22⋊C4×Dic5C2×C3semidirect
65. #64943C2×C3semidirect
66. #64942C2×C3semidirect
67. #64940C2×C3semidirect
68. #64937C2×C3semidirect
90. C22×C3×Dic5C2×C4semidirect
106. C3×C22⋊Dic5C2×C4semidirect
107. C3×C4⋊Dic5C2×C4semidirect
114. C3×C4×Dic5C2×C4semidirect
143. D4×Dic5C3×C4semidirect
283. C22×Dic5C2×C3×C4semidirect
299. C22⋊Dic5C2×C3×C4semidirect
300. C4⋊Dic5C2×C3×C4semidirect
307. C4×Dic5C2×C3×C4semidirect
646. C3×C5#2353semidirect
758. C5C3×#2353semidirect
793. C3#10606405direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D4×Dic52
C3×C5×#3862
C3×#655092
C3×C4×C22⋊Dic52
C2×C3×#39632
C3×#652342
C3×#652332
C3×#652322
C3×#652312
C3×C22⋊C4×Dic52
C3×#649432
C3×#649422
C3×#649402
C3×#649372
#106064053
C3×#23535