Finite Group Databasebeta

← C3×#10607571 #14330635

Subgroups — C3×#10607571 #14330635

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4028C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic, complemented
3C3×#65279C211yesmaximal, characteristic, complemented
4C3×#65277C211yesmaximal, characteristic, complemented
5C3×#65246C211yesmaximal, characteristic, complemented
6C3×#65245C211yesmaximal, characteristic, complemented
7C3×#65244C211yesmaximal, characteristic, complemented
8C3×#65244C211yesmaximal, characteristic, complemented
9C3×#65240C211yesmaximal, characteristic, complemented
10C3×#65229C211yesmaximal, characteristic, complemented
11C3×#65228C211yesmaximal, characteristic, complemented
12C3×#64959C211yesmaximal, characteristic, complemented
13C3×#64958C211yesmaximal, characteristic, complemented
14C3×#64954C211yesmaximal, characteristic, complemented
15C3×#64954C211yesmaximal, characteristic, complemented
16#10607571C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic, complemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C42×C5C2211yescharacteristic, complemented
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic, complemented
40C2×C3×#685C2211yescharacteristic, complemented
41C2×C3×#685C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
43C2×C3×#683C2211yescharacteristic, complemented
44C2×C3×C4×Dic5C2211yescharacteristic, complemented
45C2×C3×C4×Dic5C2211yescharacteristic, complemented
46C3×#4028C418yescomplemented
47C3×C5×#95C2211yescharacteristic, complemented
48C3×C5×#95C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53C3×#2375—51nomaximal, Hall
54C2×#4028C2×C311yescharacteristic
55C5×#388C2×C311yescharacteristic, complemented
56#65279C2×C311yescharacteristic, complemented
57#65277C2×C311yescharacteristic, complemented
58#65246C2×C311yescharacteristic, complemented
59#65245C2×C311yescharacteristic, complemented
60#65244C2×C311yescharacteristic, complemented
61#65244C2×C311yescharacteristic, complemented
62#65240C2×C311yescharacteristic, complemented
63#65229C2×C311yescharacteristic, complemented
64#65228C2×C311yescharacteristic, complemented
65#64959C2×C311yescharacteristic, complemented
66#64958C2×C311yescharacteristic, complemented
67#64954C2×C311yescharacteristic, complemented
68#64954C2×C311yescharacteristic, complemented
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5—41no—
71C23×C3×D5—41no—
72C23×C3×D5—41no—
73C23×C3×D5—41no—
74C23×C3×D5—41no—
75C23×C3×D5—41no—
76C23×C3×D5C2×C414yescomplemented
77C23×C3×D5C2311yescharacteristic
78C23×C3×D5C2311yescharacteristic
79C23×C3×D5C2311yescharacteristic
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C2×C3×C22⋊D5—41no—
87C2×C3×C22⋊D5—41no—
88C2×C3×C22⋊D5C2×C414yes—
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×C3×D20—41no—
95C2×C3×D20—41no—
96C2×C3×D20—41no—
97C2×C3×D20—41no—
98C2×C3×D20C2×C414yes—
99C2×C3×D20C2×C414yes—
100C2×C3×C4×D5—41no—
101C2×C3×C4×D5—41no—
102C2×C3×C4×D5—41no—
103C3×C5×C4⋊C4—41no—
104C3×C5×C22⋊C4—41no—
105C3×C5×C22⋊C4—41no—
106C3×C5×C22⋊C4C2×C414yescomplemented
107C3×C42×C5—41no—
108C3×C22⋊Dic5—41no—
109C3×C22⋊Dic5—41no—
110C3×#685—41no—
111C3×#685—41no—
112C3×#685—41no—
113C3×#685—41no—
114C3×#685—41no—
115C3×#685—41no—
116C3×#685—41no—
117C3×#685—41no—
118C3×#685—41no—
119C3×#685—41no—
120C3×#685—41no—
121C3×#685C2×C414yescomplemented
122C3×#685C2×C414yescomplemented
123C3×C4⋊Dic5—41no—
124C3×#683—41no—
125C3×C4×Dic5—41no—
126C3×C4×Dic5—41no—
127C2×C3×#120—51no—
128C3×#390—51no—
129C3×#390—51no—
130C3×#390—51no—
131C3×#388—51no—
132C3×#388—51no—
133C3×#388—51no—
134C3×#388—51no—
135C3×#388—51no—
136C3×#388D511yescharacteristic, complemented
137C3×#386—51no—
138C3×#386—51no—
139C3×#386—51no—
140C3×#379—51no—
141C3×#379—51no—
142C24×D5C22×C311yescharacteristic
143C22×C22⋊D5C22×C311yescharacteristic
144C22×D20C22×C311yescharacteristic
145C22×D20C22×C311yescharacteristic
146C22×C4×D5C22×C311yescharacteristic, complemented
147C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
148C2×C5×C22⋊C4C22×C311yescharacteristic
149C2×C5×C22⋊C4C22×C311yescharacteristic
150C2×C5×C22⋊C4C22×C311yescharacteristic
151C2×C42×C5C22×C311yescharacteristic, complemented
152C2×C22⋊Dic5C22×C311yescharacteristic
153C2×C22⋊Dic5C22×C311yescharacteristic
154C2×#685C22×C311yescharacteristic
155C2×#685C22×C311yescharacteristic
156C2×#685C22×C311yescharacteristic
157C2×#685C22×C311yescharacteristic
158C2×#685C22×C311yescharacteristic
159C2×#685C22×C311yescharacteristic
160C2×#685C22×C311yescharacteristic
161C2×#685C22×C311yescharacteristic
162C2×#685C22×C311yescharacteristic
163C2×#685C22×C311yescharacteristic
164C2×#685C22×C311yescharacteristic, complemented
165C2×#685C22×C311yescharacteristic, complemented
166C2×#685C22×C311yescharacteristic, complemented
167C2×C4⋊Dic5C22×C311yescharacteristic, complemented
168C2×#683C22×C311yescharacteristic, complemented
169C2×C4×Dic5C22×C311yescharacteristic, complemented
170C2×C4×Dic5C22×C311yescharacteristic, complemented
171#4028C3×C418yescomplemented
172C5×#95C22×C311yescharacteristic, complemented
173C5×#95C22×C311yescharacteristic, complemented
174#3963C22×C311yescharacteristic, complemented
175#3963C22×C311yescharacteristic, complemented
176#3963C22×C311yescharacteristic, complemented
177#3963C22×C311yescharacteristic, complemented
178#2375—51noSylow
179C23×C3×C5—21no—
180C23×C3×C5—21no—
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5C22×C412yes—
186C23×C3×C5C2411yescharacteristic
187C22×C3×D5—21no—
188C22×C3×D5—21no—
189C22×C3×D5—21no—
190C22×C3×D5—21no—
191C22×C3×D5—21no—
192C22×C3×D5—21no—
193C22×C3×D5—21no—
194C22×C3×D5—21no—
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—44no—
206C22×C3×D5—44no—
207C22×C3×D5—44no—
208C22×C3×D5—44no—
209C22×C3×D5—44no—
210C22×C3×D5—44no—
211C22×C3×D5—44no—
212C22×C3×D5C22×C412yes—
213C22×C3×D5C22×C412yes—
214C22×C3×D5C22×C412yes—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5C22×C412yes—
232C2×C3×C4×C5C22×C412yes—
233C3×C22⋊D5—44no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—21no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5C22×C412yes—
249C3×D20—44no—
250C3×D20—44no—
251C3×C4×D5—44no—
252C25×C3—51no—
253C22×C3×D4—51no—
254C22×C3×D4—51no—
255C22×C3×D4—51no—
256C23×C3×C4—51no—
257C3×#120—58no—
258C2×C3×C4⋊C4—51no—
259C2×C3×C4⋊C4—51no—
260C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
261C2×C3×C22⋊C4—51no—
262C2×C3×C22⋊C4—51no—
263C2×C3×C22⋊C4—51no—
264C2×C3×C22⋊C4—51no—
265C2×C3×C22⋊C4—51no—
266C2×C3×C22⋊C4—51no—
267C2×C3×C22⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×C3×C22⋊C4—51no—
274C2×C3×C22⋊C4—51no—
275C2×C3×C22⋊C4—51no—
276C2×C3×C22⋊C4C2×D511yescharacteristic
277C2×C3×C22⋊C4C2×D511yescharacteristic
278C2×C3×C22⋊C4C2×D511yescharacteristic
279C2×C3×C42—51no—
280C2×C3×C42—51no—
281C2×C3×C42C2×D511yescharacteristic, complemented
282C3×#95—51no—
283C3×#95—51no—
284C3×#95—51no—
285C3×#95—51no—
286C3×#95C2×D511yescharacteristic, complemented
287C3×#95C2×D511yescharacteristic, complemented
288C24×C5C23×C311yescharacteristic
289C23×D5—41no—
290C23×D5—41no—
291C23×D5—41no—
292C23×D5—41no—
293C23×D5—41no—
294C23×D5—41no—
295C23×D5C2×C3×C414yescomplemented
296C23×D5C23×C311yescharacteristic
297C23×D5C23×C311yescharacteristic
298C23×D5C23×C311yescharacteristic
299C22×C4×C5C23×C311yescharacteristic
300C22×C4×C5C23×C311yescharacteristic
301C22×C4×C5C23×C311yescharacteristic
302C22×C4×C5C23×C311yescharacteristic
303C22×C4×C5C23×C311yescharacteristic
304C22×C4×C5C23×C311yescharacteristic
305C2×C22⋊D5—41no—
306C2×C22⋊D5—41no—
307C2×C22⋊D5C2×C3×C414yes—
308C22×Dic5C23×C311yescharacteristic
309C22×Dic5C23×C311yescharacteristic
310C22×Dic5C23×C311yescharacteristic
311C22×Dic5C23×C311yescharacteristic
312C22×Dic5C23×C311yescharacteristic
313C2×D20—41no—
314C2×D20—41no—
315C2×D20—41no—
316C2×D20—41no—
317C2×D20C2×C3×C414yes—
318C2×D20C2×C3×C414yes—
319C2×C4×D5—41no—
320C2×C4×D5—41no—
321C2×C4×D5—41no—
322C5×C4⋊C4—41no—
323C5×C22⋊C4—41no—
324C5×C22⋊C4—41no—
325C5×C22⋊C4C2×C3×C414yescomplemented
326C42×C5—41no—
327C22⋊Dic5—41no—
328C22⋊Dic5—41no—
329#685—41no—
330#685—41no—
331#685—41no—
332#685—41no—
333#685—41no—
334#685—41no—
335#685—41no—
336#685—41no—
337#685—41no—
338#685—41no—
339#685—41no—
340#685C2×C3×C414yescomplemented
341#685C2×C3×C414yescomplemented
342C4⋊Dic5—41no—
343#683—41no—
344C4×Dic5—41no—
345C4×Dic5—41no—
346C2×#120—51no—
347#390—51no—
348#390—51no—
349#390—51no—
350#388—51no—
351#388—51no—
352#388—51no—
353#388—51no—
354#388—51no—
355#388C3×D511yescharacteristic, complemented
356#386—51no—
357#386—51no—
358#386—51no—
359#379—51no—
360#379—51no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—22no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5H(5,𝔽2)11yescharacteristic
370C22×C3×C5H(5,𝔽2)11yescharacteristic
371C22×C3×C5H(5,𝔽2)11yescharacteristic
372C22×C3×C5H(5,𝔽2)11yescharacteristic
373C22×C3×C5H(5,𝔽2)11yescharacteristic
374C22×C3×C5H(5,𝔽2)11yescharacteristic
375C2×C3×D5—22no—
376C2×C3×D5—22no—
377C2×C3×D5—22no—
378C2×C3×D5—22no—
379C2×C3×D5—22no—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5—22no—
383C2×C3×D5—22no—
384C2×C3×D5—416no—
385C2×C3×D5—41no—
386C2×C3×D5—41no—
387C2×C3×D5—41no—
388C2×C3×D5—41no—
389C2×C3×D5—41no—
390C2×C3×D5—41no—
391C2×C3×D5—41no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396C2×C3×D5—41no—
397C3×C4×C5—22no—
398C3×C4×C5—22no—
399C3×C4×C5—41no—
400C3×C4×C5—41no—
401C3×C4×C5—41no—
402C3×C4×C5—41no—
403C3×Dic5—22no—
404C3×Dic5—41no—
405C3×Dic5—41no—
406C3×Dic5—41no—
407C3×Dic5—41no—
408C24×C3—51no—
409C24×C3—51no—
410C24×C3—51no—
411C24×C3—54no—
412C24×C3—201no—
413C24×C3—201no—
414C24×C3—201no—
415C24×C3—201no—
416C24×C3—201no—
417C24×C3—201no—
418C24×C3C22×D511yescharacteristic
419C2×C3×D4—54no—
420C2×C3×D4—54no—
421C2×C3×D4—54no—
422C2×C3×D4—201no—
423C2×C3×D4—201no—
424C2×C3×D4—201no—
425C2×C3×D4—201no—
426C2×C3×D4—201no—
427C2×C3×D4—201no—
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4—51no—
431C22×C3×C4—51no—
432C22×C3×C4—51no—
433C22×C3×C4—201no—
434C22×C3×C4—201no—
435C22×C3×C4—201no—
436C22×C3×C4C22×D511yescharacteristic
437C22×C3×C4C22×D511yescharacteristic
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D511yescharacteristic
441C22×C3×C4C22×D511yescharacteristic
442C3×C4⋊C4—41no—
443C3×C4⋊C4—201no—
444C3×C4⋊C4—201no—
445C3×C22⋊C4—41no—
446C3×C22⋊C4—41no—
447C3×C22⋊C4—54no—
448C3×C22⋊C4—54no—
449C3×C22⋊C4—201no—
450C3×C22⋊C4—201no—
451C3×C22⋊C4—201no—
452C3×C22⋊C4—201no—
453C3×C22⋊C4—201no—
454C3×C22⋊C4—201no—
455C3×C22⋊C4—201no—
456C3×C22⋊C4—201no—
457C3×C22⋊C4—201no—
458C3×C22⋊C4—201no—
459C3×C22⋊C4—201no—
460C3×C22⋊C4—201no—
461C3×C22⋊C4—201no—
462C3×C22⋊C4C4×D514yescomplemented
463C3×C42—41no—
464C3×C42—201no—
465C3×C42—201no—
466C23×C5—21no—
467C23×C5—21no—
468C23×C5—21no—
469C23×C5—21no—
470C23×C5—21no—
471C23×C5—21no—
472C23×C5C22×C3×C412yes—
473C23×C5C24×C311yescharacteristic
474C22×D5—21no—
475C22×D5—21no—
476C22×D5—21no—
477C22×D5—21no—
478C22×D5—21no—
479C22×D5—21no—
480C22×D5—21no—
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—21no—
488C22×D5—21no—
489C22×D5—21no—
490C22×D5—21no—
491C22×D5—21no—
492C22×D5—44no—
493C22×D5—44no—
494C22×D5—44no—
495C22×D5—44no—
496C22×D5—44no—
497C22×D5—44no—
498C22×D5—44no—
499C22×D5C22×C3×C412yes—
500C22×D5C22×C3×C412yes—
501C22×D5C22×C3×C412yes—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—21no—
512C2×C4×C5—21no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—21no—
516C2×C4×C5—21no—
517C2×C4×C5—21no—
518C2×C4×C5C22×C3×C412yes—
519C2×C4×C5C22×C3×C412yes—
520C22⋊D5—44no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—21no—
530C2×Dic5—21no—
531C2×Dic5—21no—
532C2×Dic5—21no—
533C2×Dic5—21no—
534C2×Dic5—21no—
535C2×Dic5C22×C3×C412yes—
536D20—44no—
537D20—44no—
538C4×D5—44no—
539C25—51no—
540C22×D4—51no—
541C22×D4—51no—
542C22×D4—51no—
543C23×C4—51no—
544#120—58no—
545C2×C4⋊C4—51no—
546C2×C4⋊C4—51no—
547C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
548C2×C22⋊C4—51no—
549C2×C22⋊C4—51no—
550C2×C22⋊C4—51no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—51no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—51no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—51no—
559C2×C22⋊C4—51no—
560C2×C22⋊C4—51no—
561C2×C22⋊C4—51no—
562C2×C22⋊C4—51no—
563C2×C22⋊C4C2×C3×D511yescharacteristic
564C2×C22⋊C4C2×C3×D511yescharacteristic
565C2×C22⋊C4C2×C3×D511yescharacteristic
566C2×C42—51no—
567C2×C42—51no—
568C2×C42C2×C3×D511yescharacteristic, complemented
569#95—51no—
570#95—51no—
571#95—51no—
572#95—51no—
573#95C2×C3×D511yescharacteristic, complemented
574#95C2×C3×D511yescharacteristic, complemented
575C2×C3×C5—42no—
576C2×C3×C5#51811yescharacteristic
577C2×C3×C5#51811yescharacteristic
578C2×C3×C5#51811yescharacteristic
579C2×C3×C5#56011yescharacteristic
580C2×C3×C5#56011yescharacteristic
581C2×C3×C5#56011yescharacteristic
582C2×C3×C5H(3,𝔽4)11yescharacteristic
583C3×D5—42no—
584C3×D5—42no—
585C3×D5—42no—
586C23×C3—21no—
587C23×C3—21no—
588C23×C3—21no—
589C23×C3—21no—
590C23×C3—21no—
591C23×C3—21no—
592C23×C3—52no—
593C23×C3—52no—
594C23×C3—52no—
595C23×C3—101no—
596C23×C3—101no—
597C23×C3—101no—
598C23×C3—101no—
599C23×C3—101no—
600C23×C3—101no—
601C23×C3—101no—
602C23×C3—101no—
603C23×C3—101no—
604C23×C3—101no—
605C23×C3—101no—
606C23×C3—101no—
607C23×C3—101no—
608C23×C3—101no—
609C23×C3—101no—
610C23×C3—101no—
611C23×C3—101no—
612C23×C3—101no—
613C23×C3—204no—
614C23×C3—204no—
615C23×C3—204no—
616C23×C3—204no—
617C23×C3—204no—
618C23×C3—204no—
619C23×C3—204no—
620C23×C3C2×C4×D512yes—
621C23×C3C23×D511yescharacteristic
622C3×D4—204no—
623C3×D4—204no—
624C3×D4—204no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—21no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—52no—
642C2×C3×C4—101no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—101no—
648C2×C3×C4—101no—
649C2×C3×C4—101no—
650C2×C3×C4—101no—
651C2×C3×C4—101no—
652C2×C3×C4—101no—
653C2×C3×C4—101no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4—204no—
657C2×C3×C4C2×C4×D512yes—
658C2×C3×C4C2×C4×D512yes—
659C22×C5—22no—
660C22×C5—22no—
661C22×C5—22no—
662C22×C5—41no—
663C22×C5—41no—
664C22×C5—41no—
665C22×C5—41no—
666C22×C5C23×C3×C411yescharacteristic
667C22×C5C3×H(5,𝔽2)11yescharacteristic
668C22×C5C3×H(5,𝔽2)11yescharacteristic
669C22×C5C3×H(5,𝔽2)11yescharacteristic
670C22×C5C3×H(5,𝔽2)11yescharacteristic
671C22×C5C3×H(5,𝔽2)11yescharacteristic
672C22×C5C3×H(5,𝔽2)11yescharacteristic
673C2×D5—22no—
674C2×D5—22no—
675C2×D5—22no—
676C2×D5—22no—
677C2×D5—22no—
678C2×D5—22no—
679C2×D5—22no—
680C2×D5—22no—
681C2×D5—22no—
682C2×D5—416no—
683C2×D5—41no—
684C2×D5—41no—
685C2×D5—41no—
686C2×D5—41no—
687C2×D5—41no—
688C2×D5—41no—
689C2×D5—41no—
690C2×D5—41no—
691C2×D5—41no—
692C2×D5—41no—
693C2×D5—41no—
694C2×D5—41no—
695C4×C5—22no—
696C4×C5—22no—
697C4×C5—41no—
698C4×C5—41no—
699C4×C5—41no—
700C4×C5—41no—
701Dic5—22no—
702Dic5—41no—
703Dic5—41no—
704Dic5—41no—
705Dic5—41no—
706C24—51no—
707C24—51no—
708C24—51no—
709C24—54no—
710C24—201no—
711C24—201no—
712C24—201no—
713C24—201no—
714C24—201no—
715C24—201no—
716C24C22×C3×D511yescharacteristic
717C2×D4—54no—
718C2×D4—54no—
719C2×D4—54no—
720C2×D4—201no—
721C2×D4—201no—
722C2×D4—201no—
723C2×D4—201no—
724C2×D4—201no—
725C2×D4—201no—
726C22×C4—51no—
727C22×C4—51no—
728C22×C4—51no—
729C22×C4—51no—
730C22×C4—51no—
731C22×C4—201no—
732C22×C4—201no—
733C22×C4—201no—
734C22×C4C22×C3×D511yescharacteristic
735C22×C4C22×C3×D511yescharacteristic
736C22×C4C22×C3×D511yescharacteristic
737C22×C4C22×C3×D511yescharacteristic
738C22×C4C22×C3×D511yescharacteristic
739C22×C4C22×C3×D511yescharacteristic
740C4⋊C4—41no—
741C4⋊C4—201no—
742C4⋊C4—201no—
743C22⋊C4—41no—
744C22⋊C4—41no—
745C22⋊C4—54no—
746C22⋊C4—54no—
747C22⋊C4—201no—
748C22⋊C4—201no—
749C22⋊C4—201no—
750C22⋊C4—201no—
751C22⋊C4—201no—
752C22⋊C4—201no—
753C22⋊C4—201no—
754C22⋊C4—201no—
755C22⋊C4—201no—
756C22⋊C4—201no—
757C22⋊C4—201no—
758C22⋊C4—201no—
759C22⋊C4—201no—
760C22⋊C4C3×C4×D514yescomplemented
761C42—41no—
762C42—201no—
763C42—201no—
764C3×C5#237511yescharacteristic, complemented, Hall
765C22×C3—22no—
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—41no—
769C22×C3—41no—
770C22×C3—41no—
771C22×C3—41no—
772C22×C3—102no—
773C22×C3—102no—
774C22×C3—102no—
775C22×C3—102no—
776C22×C3—102no—
777C22×C3—102no—
778C22×C3—102no—
779C22×C3—102no—
780C22×C3—102no—
781C22×C3—2016no—
782C22×C3—201no—
783C22×C3—201no—
784C22×C3—201no—
785C22×C3—201no—
786C22×C3—201no—
787C22×C3—201no—
788C22×C3—201no—
789C22×C3—201no—
790C22×C3—201no—
791C22×C3—201no—
792C22×C3—201no—
793C22×C3—201no—
794C22×C3C22×C4×D511yescharacteristic
795C22×C3#414411yescharacteristic
796C22×C3#414411yescharacteristic
797C22×C3#414911yescharacteristic
798C22×C3#414911yescharacteristic
799C22×C3#414911yescharacteristic
800C22×C3#414911yescharacteristic
801C3×C4—22no—
802C3×C4—22no—
803C3×C4—41no—
804C3×C4—41no—
805C3×C4—41no—
806C3×C4—41no—
807C3×C4—102no—
808C3×C4—201no—
809C3×C4—201no—
810C3×C4—201no—
811C3×C4—201no—
812C2×C5—42no—
813C2×C5C3×#51811yescharacteristic
814C2×C5C3×#51811yescharacteristic
815C2×C5C3×#51811yescharacteristic
816C2×C5C3×#56011yescharacteristic
817C2×C5C3×#56011yescharacteristic
818C2×C5C3×#56011yescharacteristic
819C2×C5C3×H(3,𝔽4)11yescharacteristic
820D5—42no—
821D5—42no—
822D5—42no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—52no—
830C23—52no—
831C23—52no—
832C23—101no—
833C23—101no—
834C23—101no—
835C23—101no—
836C23—101no—
837C23—101no—
838C23—101no—
839C23—101no—
840C23—101no—
841C23—101no—
842C23—101no—
843C23—101no—
844C23—101no—
845C23—101no—
846C23—101no—
847C23—101no—
848C23—101no—
849C23—101no—
850C23—204no—
851C23—204no—
852C23—204no—
853C23—204no—
854C23—204no—
855C23—204no—
856C23—204no—
857C23C2×C3×C4×D512yes—
858C23C23×C3×D511yescharacteristic
859D4—204no—
860D4—204no—
861D4—204no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—52no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—101no—
886C2×C4—101no—
887C2×C4—101no—
888C2×C4—101no—
889C2×C4—101no—
890C2×C4—101no—
891C2×C4—101no—
892C2×C4—101no—
893C2×C4—204no—
894C2×C4C2×C3×C4×D512yes—
895C2×C4C2×C3×C4×D512yes—
896C2×C3—42no—
897C2×C3—202no—
898C2×C3—202no—
899C2×C3—202no—
900C2×C3#6585511yescharacteristic
901C2×C3#6587911yescharacteristic
902C2×C3#6587911yescharacteristic
903C2×C3#6595411yescharacteristic
904C2×C3#6600011yescharacteristic
905C2×C3#6601711yescharacteristic
906C2×C3#6604511yescharacteristic
907C5C3×#237511yescharacteristic, complemented, Sylow
908C22—22no—
909C22—22no—
910C22—22no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—102no—
916C22—102no—
917C22—102no—
918C22—102no—
919C22—102no—
920C22—102no—
921C22—102no—
922C22—102no—
923C22—102no—
924C22—2016no—
925C22—201no—
926C22—201no—
927C22—201no—
928C22—201no—
929C22—201no—
930C22—201no—
931C22—201no—
932C22—201no—
933C22—201no—
934C22—201no—
935C22—201no—
936C22—201no—
937C22C22×C3×C4×D511yescharacteristic
938C22C3×#414411yescharacteristic
939C22C3×#414411yescharacteristic
940C22C3×#414911yescharacteristic
941C22C3×#414911yescharacteristic
942C22C3×#414911yescharacteristic
943C22C3×#414911yescharacteristic
944C4—22no—
945C4—22no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—102no—
951C4—201no—
952C4—201no—
953C4—201no—
954C4—201no—
955C3#1060757111yescharacteristic, direct product factor, Sylow
956C2—42no—
957C2—202no—
958C2—202no—
959C2—202no—
960C2C3×#6585511yescharacteristic
961C2C3×#6587911yescharacteristic
962C2C3×#6587911yescharacteristic
963C2C3×#6595411yescharacteristic
964C2C3×#6600011yescharacteristic
965C2C3×#6601711yescharacteristic
966C2C3×#6604511yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC2×C3×#4028C2
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C3×#2375
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
2. C3×C5×#388C2semidirect
3. C3×#65279C2semidirect
4. C3×#65277C2semidirect
5. C3×#65246C2semidirect
6. C3×#65245C2semidirect
7. C3×#65244C2semidirect
8. C3×#65244C2semidirect
9. C3×#65240C2semidirect
10. C3×#65229C2semidirect
11. C3×#65228C2semidirect
12. C3×#64959C2semidirect
13. C3×#64958C2semidirect
14. C3×#64954C2semidirect
15. C3×#64954C2semidirect
16. #10607571C3direct (N × H)
21. C22×C3×C4×D5C22semidirect
22. C2×C3×C5×C4⋊C4C22semidirect
26. C2×C3×C42×C5C22semidirect
39. C2×C3×#685C22semidirect
40. C2×C3×#685C22semidirect
41. C2×C3×#685C22semidirect
42. C2×C3×C4⋊Dic5C22semidirect
43. C2×C3×#683C22semidirect
44. C2×C3×C4×Dic5C22semidirect
45. C2×C3×C4×Dic5C22semidirect
46. C3×#4028C4semidirect
47. C3×C5×#95C22semidirect
48. C3×C5×#95C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
55. C5×#388C2×C3semidirect
56. #65279C2×C3semidirect
57. #65277C2×C3semidirect
58. #65246C2×C3semidirect
59. #65245C2×C3semidirect
60. #65244C2×C3semidirect
61. #65244C2×C3semidirect
62. #65240C2×C3semidirect
63. #65229C2×C3semidirect
64. #65228C2×C3semidirect
65. #64959C2×C3semidirect
66. #64958C2×C3semidirect
67. #64954C2×C3semidirect
68. #64954C2×C3semidirect
76. C23×C3×D5C2×C4semidirect
106. C3×C5×C22⋊C4C2×C4semidirect
121. C3×#685C2×C4semidirect
122. C3×#685C2×C4semidirect
136. C3×#388D5semidirect
146. C22×C4×D5C22×C3semidirect
147. C2×C5×C4⋊C4C22×C3semidirect
151. C2×C42×C5C22×C3semidirect
164. C2×#685C22×C3semidirect
165. C2×#685C22×C3semidirect
166. C2×#685C22×C3semidirect
167. C2×C4⋊Dic5C22×C3semidirect
168. C2×#683C22×C3semidirect
169. C2×C4×Dic5C22×C3semidirect
170. C2×C4×Dic5C22×C3semidirect
171. #4028C3×C4semidirect
172. C5×#95C22×C3semidirect
173. C5×#95C22×C3semidirect
174. #3963C22×C3semidirect
175. #3963C22×C3semidirect
176. #3963C22×C3semidirect
177. #3963C22×C3semidirect
260. C2×C3×C4⋊C4C2×D5semidirect
281. C2×C3×C42C2×D5semidirect
286. C3×#95C2×D5semidirect
287. C3×#95C2×D5semidirect
295. C23×D5C2×C3×C4semidirect
325. C5×C22⋊C4C2×C3×C4semidirect
340. #685C2×C3×C4semidirect
341. #685C2×C3×C4semidirect
355. #388C3×D5semidirect
462. C3×C22⋊C4C4×D5semidirect
547. C2×C4⋊C4C2×C3×D5semidirect
568. C2×C42C2×C3×D5semidirect
573. #95C2×C3×D5semidirect
574. #95C2×C3×D5semidirect
760. C22⋊C4C3×C4×D5semidirect
764. C3×C5#2375semidirect
907. C5C3×#2375semidirect
955. C3#10607571direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40282
C3×C5×#3882
C3×#652792
C3×#652772
C3×#652462
C3×#652452
C3×#652442
C3×#652402
C3×#652292
C3×#652282
C3×#649592
C3×#649582
C3×#649542
#106075713
C3×#23755