Finite Group Databasebeta

← C3×#10608036 #14329028

Subgroups — C3×#10608036 #14329028

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4085C211yesmaximal, characteristic
2C2×C3×#4027C211yesmaximal, characteristic, complemented
3C2×C3×#4023C211yesmaximal, characteristic, complemented
4C3×C5×#390C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6C3×#65279C211yesmaximal, characteristic, complemented
7C3×#65261C211yesmaximal, characteristic, complemented
8C3×#65246C211yesmaximal, characteristic, complemented
9C3×#65246C211yesmaximal, characteristic, complemented
10C3×#65245C211yesmaximal, characteristic, complemented
11C3×#65233C211yesmaximal, characteristic, complemented
12C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
13C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
14C3×C4×#685C211yesmaximal, characteristic, complemented
15C3×C4×#683C211yesmaximal, characteristic, complemented
16#10608036C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C3×#4085C418yescomplemented
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C2×C3×C4×Dic5C2211yescharacteristic
45C2×C3×C4×Dic5C2211yescharacteristic
46C2×C3×C4×Dic5C2211yescharacteristic
47C3×#4027—24no—
48C3×#4023—24no—
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2363—51nomaximal, Hall
56C2×#4085C2×C311yescharacteristic
57C2×#4027C2×C311yescharacteristic, complemented
58C2×#4023C2×C311yescharacteristic, complemented
59C5×#390C2×C311yescharacteristic, complemented
60#65509C2×C311yescharacteristic, complemented
61#65279C2×C311yescharacteristic, complemented
62#65261C2×C311yescharacteristic, complemented
63#65246C2×C311yescharacteristic, complemented
64#65246C2×C311yescharacteristic, complemented
65#65245C2×C311yescharacteristic, complemented
66#65233C2×C311yescharacteristic, complemented
67C22⋊C4×Dic5C2×C311yescharacteristic, complemented
68C22⋊C4×Dic5C2×C311yescharacteristic, complemented
69C4×#685C2×C311yescharacteristic, complemented
70C4×#683C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C2×C3×C5×D4—41no—
75C2×C3×C5×D4—41no—
76C2×C3×C5×D4C2×C414yescomplemented
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⋊D5—41no—
85C2×C3×C22⋊D5—41no—
86C2×C3×C22⋊D5C2×C414yes—
87C2×C3×C22⋊D5C2×C414yescomplemented
88C22×C3×Dic5—22no—
89C22×C3×Dic5—22no—
90C22×C3×Dic5—22no—
91C22×C3×Dic5—22no—
92C22×C3×Dic5—41no—
93C22×C3×Dic5C2×C414yescomplemented
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5—41no—
104C3×C5×C4⋊C4—41no—
105C3×C5×C22⋊C4—22no—
106C3×C5×C22⋊C4—22no—
107C3×C5×C22⋊C4—22no—
108C3×C5×C22⋊C4—22no—
109C3×C42×C5—41no—
110C3×C22⋊Dic5—22no—
111C3×C22⋊Dic5—22no—
112C3×C22⋊Dic5—41no—
113C3×C22⋊Dic5C2×C414yescomplemented
114C3×#685—22no—
115C3×#685—22no—
116C3×#685—41no—
117C3×#685C2×C414yescomplemented
118C3×#683—22no—
119C3×#683—41no—
120C3×#683C2×C414yescomplemented
121C3×#683D414yescomplemented
122C3×C4×Dic5—22no—
123C3×C4×Dic5—22no—
124C3×C4×Dic5—22no—
125C3×C4×Dic5—22no—
126C3×C4×Dic5—41no—
127C2×C3×#121—51no—
128C2×C3×C4×D4—51no—
129C2×C3×#117—51no—
130C3×#390—51no—
131C3×#390—51no—
132C3×#390D511yescharacteristic, complemented
133C3×#389—51no—
134C3×#388—51no—
135C3×#388—51no—
136C3×#386—51no—
137C3×#386—51no—
138C3×C4×C4⋊C4—51no—
139C3×C4×C22⋊C4—51no—
140C3×C4×C22⋊C4—51no—
141C3×C4×C22⋊C4—51no—
142C22×C5×D4C22×C311yescharacteristic
143C22×C22⋊D5C22×C311yescharacteristic
144C22×C22⋊D5C22×C311yescharacteristic
145C23×Dic5C22×C311yescharacteristic
146C23×Dic5C22×C311yescharacteristic
147C22×C4×D5C22×C311yescharacteristic
148C2×C5×C4⋊C4C22×C311yescharacteristic
149C2×C5×C22⋊C4C22×C311yescharacteristic
150C2×C5×C22⋊C4C22×C311yescharacteristic
151C2×C5×C22⋊C4C22×C311yescharacteristic
152C2×C5×C22⋊C4C22×C311yescharacteristic
153C2×C42×C5C22×C311yescharacteristic
154C2×C22⋊Dic5C22×C311yescharacteristic
155C2×C22⋊Dic5C22×C311yescharacteristic
156C2×C22⋊Dic5C22×C311yescharacteristic
157C2×C22⋊Dic5C22×C311yescharacteristic
158#4085C3×C418yescomplemented
159C2×#685C22×C311yescharacteristic
160C2×#685C22×C311yescharacteristic
161C2×#685C22×C311yescharacteristic
162C2×#685C22×C311yescharacteristic
163C2×#683C22×C311yescharacteristic
164C2×#683C22×C311yescharacteristic
165C2×#683C22×C311yescharacteristic
166C2×#683C22×C311yescharacteristic
167C2×C4×Dic5C22×C311yescharacteristic
168C2×C4×Dic5C22×C311yescharacteristic
169C2×C4×Dic5C22×C311yescharacteristic
170C2×C4×Dic5C22×C311yescharacteristic
171C2×C4×Dic5C22×C311yescharacteristic
172#4027—24no—
173#4023—24no—
174#3963C22×C311yescharacteristic
175#3963C22×C311yescharacteristic
176#3963C22×C311yescharacteristic
177#3963C22×C311yescharacteristic
178#3963C22×C311yescharacteristic
179#3963C22×C311yescharacteristic
180#2363—51noSylow
181C23×C3×C5—21no—
182C23×C3×C5—21no—
183C23×C3×C5—21no—
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C22×C412yes—
195C23×C3×C5C2411yescharacteristic
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×D5C22×C412yes—
203C3×C5×D4—44no—
204C2×C3×C4×C5—21no—
205C2×C3×C4×C5—21no—
206C2×C3×C4×C5—21no—
207C2×C3×C4×C5—21no—
208C2×C3×C4×C5—21no—
209C2×C3×C4×C5—21no—
210C2×C3×C4×C5—21no—
211C2×C3×C4×C5—21no—
212C2×C3×C4×C5—21no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5C22×C412yes—
217C2×C3×C4×C5C2×D412yes—
218C2×C3×C4×C5#4112yes—
219C3×C22⋊D5—28no—
220C3×C22⋊D5—44no—
221C2×C3×Dic5—21no—
222C2×C3×Dic5—21no—
223C2×C3×Dic5—21no—
224C2×C3×Dic5—21no—
225C2×C3×Dic5—21no—
226C2×C3×Dic5—21no—
227C2×C3×Dic5—21no—
228C2×C3×Dic5—21no—
229C2×C3×Dic5—28no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—44no—
237C2×C3×Dic5C22×C412yes—
238C2×C3×Dic5C22×C412yes—
239C2×C3×Dic5C22×C412yes—
240C2×C3×Dic5C2×D412yes—
241C2×C3×Dic5C2×D412yes—
242C2×C3×Dic5#4112yes—
243C2×C3×Dic5#4112yes—
244C3×C4×D5—44no—
245C22×C3×D4—51no—
246C22×C3×D4—51no—
247C22×C3×D4C2×D511yescharacteristic
248C23×C3×C4—51no—
249C23×C3×C4—51no—
250C23×C3×C4—51no—
251C3×#121—58no—
252C3×C4×D4—104no—
253C3×#117—104no—
254C2×C3×C4⋊C4—51no—
255C2×C3×C4⋊C4—51no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C4⋊C4C2×D511yescharacteristic
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
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⋊C4C2×D511yescharacteristic
268C2×C3×C22⋊C4C2×D511yescharacteristic
269C2×C3×C22⋊C4C2×D511yescharacteristic
270C2×C3×C22⋊C4C2×D511yescharacteristic
271C2×C3×C42—51no—
272C2×C3×C42—51no—
273C2×C3×C42—51no—
274C2×C3×C42—51no—
275C2×C3×C42—51no—
276C2×C3×C42C2×D511yescharacteristic
277C3×#95—51no—
278C3×#95—51no—
279C3×#95—51no—
280C3×#95—51no—
281C3×#95—51no—
282C3×#95—51no—
283C24×C5C23×C311yescharacteristic
284C24×C5C23×C311yescharacteristic
285C23×D5C23×C311yescharacteristic
286C2×C5×D4—41no—
287C2×C5×D4—41no—
288C2×C5×D4C2×C3×C414yescomplemented
289C22×C4×C5C23×C311yescharacteristic
290C22×C4×C5C23×C311yescharacteristic
291C22×C4×C5C23×C311yescharacteristic
292C22×C4×C5C23×C311yescharacteristic
293C22×C4×C5C23×C311yescharacteristic
294C2×C22⋊D5—22no—
295C2×C22⋊D5—22no—
296C2×C22⋊D5—41no—
297C2×C22⋊D5—41no—
298C2×C22⋊D5C2×C3×C414yes—
299C2×C22⋊D5C2×C3×C414yescomplemented
300C22×Dic5—22no—
301C22×Dic5—22no—
302C22×Dic5—22no—
303C22×Dic5—22no—
304C22×Dic5—41no—
305C22×Dic5C2×C3×C414yescomplemented
306C22×Dic5C23×C311yescharacteristic
307C22×Dic5C23×C311yescharacteristic
308C22×Dic5C23×C311yescharacteristic
309C22×Dic5C23×C311yescharacteristic
310C22×Dic5C23×C311yescharacteristic
311C22×Dic5C23×C311yescharacteristic
312C22×Dic5C23×C311yescharacteristic
313C2×C4×D5—22no—
314C2×C4×D5—22no—
315C2×C4×D5—41no—
316C5×C4⋊C4—41no—
317C5×C22⋊C4—22no—
318C5×C22⋊C4—22no—
319C5×C22⋊C4—22no—
320C5×C22⋊C4—22no—
321C42×C5—41no—
322C22⋊Dic5—22no—
323C22⋊Dic5—22no—
324C22⋊Dic5—41no—
325C22⋊Dic5C2×C3×C414yescomplemented
326#685—22no—
327#685—22no—
328#685—41no—
329#685C2×C3×C414yescomplemented
330#683—22no—
331#683—41no—
332#683C2×C3×C414yescomplemented
333#683C3×D414yescomplemented
334C4×Dic5—22no—
335C4×Dic5—22no—
336C4×Dic5—22no—
337C4×Dic5—22no—
338C4×Dic5—41no—
339C2×#121—51no—
340C2×C4×D4—51no—
341C2×#117—51no—
342#390—51no—
343#390—51no—
344#390C3×D511yescharacteristic, complemented
345#389—51no—
346#388—51no—
347#388—51no—
348#386—51no—
349#386—51no—
350C4×C4⋊C4—51no—
351C4×C22⋊C4—51no—
352C4×C22⋊C4—51no—
353C4×C22⋊C4—51no—
354C22×C3×C5—22no—
355C22×C3×C5—22no—
356C22×C3×C5—22no—
357C22×C3×C5—22no—
358C22×C3×C5—22no—
359C22×C3×C5—22no—
360C22×C3×C5—41no—
361C22×C3×C5—41no—
362C22×C3×C5—41no—
363C22×C3×C5—41no—
364C22×C3×C5—41no—
365C22×C3×C5—41no—
366C22×C3×C5—41no—
367C22×C3×C5—41no—
368C22×C3×C5C23×C411yescharacteristic
369C22×C3×C5C22×D411yescharacteristic
370C22×C3×C5C2×#4111yescharacteristic
371C22×C3×C5C2×#4111yescharacteristic
372C22×C3×C5C2×#4111yescharacteristic
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—41no—
379C2×C3×D5—41no—
380C2×C3×D5—41no—
381C2×C3×D5—41no—
382C3×C4×C5—22no—
383C3×C4×C5—22no—
384C3×C4×C5—22no—
385C3×C4×C5—41no—
386C3×C4×C5—41no—
387C3×Dic5—22no—
388C3×Dic5—22no—
389C3×Dic5—22no—
390C3×Dic5—22no—
391C3×Dic5—41no—
392C3×Dic5—41no—
393C3×Dic5C4×D414yes—
394C24×C3—51no—
395C24×C3C22×D511yescharacteristic
396C24×C3C22×D511yescharacteristic
397C2×C3×D4—41no—
398C2×C3×D4—41no—
399C2×C3×D4—54no—
400C2×C3×D4—54no—
401C2×C3×D4—102no—
402C2×C3×D4—102no—
403C2×C3×D4—201no—
404C2×C3×D4—201no—
405C2×C3×D4C4×D514yescomplemented
406C22×C3×C4—51no—
407C22×C3×C4—54no—
408C22×C3×C4—51no—
409C22×C3×C4—51no—
410C22×C3×C4—51no—
411C22×C3×C4—51no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4—102no—
415C22×C3×C4—102no—
416C22×C3×C4—102no—
417C22×C3×C4—102no—
418C22×C3×C4—102no—
419C22×C3×C4—102no—
420C22×C3×C4—201no—
421C22×C3×C4—201no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C22×C3×C4C22×D511yescharacteristic
425C22×C3×C4C22×D511yescharacteristic
426C22×C3×C4C22×D511yescharacteristic
427C3×C4⋊C4—41no—
428C3×C4⋊C4—54no—
429C3×C4⋊C4—54no—
430C3×C4⋊C4—102no—
431C3×C4⋊C4—201no—
432C3×C22⋊C4—22no—
433C3×C22⋊C4—22no—
434C3×C22⋊C4—22no—
435C3×C22⋊C4—22no—
436C3×C22⋊C4—54no—
437C3×C22⋊C4—54no—
438C3×C22⋊C4—102no—
439C3×C22⋊C4—102no—
440C3×C22⋊C4—102no—
441C3×C22⋊C4—102no—
442C3×C22⋊C4—201no—
443C3×C22⋊C4—201no—
444C3×C42—41no—
445C3×C42—102no—
446C3×C42—102no—
447C3×C42—102no—
448C3×C42—102no—
449C3×C42—201no—
450C23×C5—21no—
451C23×C5—21no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5—21no—
457C23×C5—21no—
458C23×C5—21no—
459C23×C5—21no—
460C23×C5—21no—
461C23×C5—21no—
462C23×C5C22×C3×C412yes—
463C23×C5C22×C3×C412yes—
464C23×C5C24×C311yescharacteristic
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5—21no—
471C22×D5C22×C3×C412yes—
472C5×D4—44no—
473C2×C4×C5—21no—
474C2×C4×C5—21no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—21no—
484C2×C4×C5—21no—
485C2×C4×C5C22×C3×C412yes—
486C2×C4×C5C2×C3×D412yes—
487C2×C4×C5C3×#4112yes—
488C22⋊D5—28no—
489C22⋊D5—44no—
490C2×Dic5—21no—
491C2×Dic5—21no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—28no—
499C2×Dic5—21no—
500C2×Dic5—21no—
501C2×Dic5—21no—
502C2×Dic5—21no—
503C2×Dic5—21no—
504C2×Dic5—21no—
505C2×Dic5—44no—
506C2×Dic5C22×C3×C412yes—
507C2×Dic5C22×C3×C412yes—
508C2×Dic5C22×C3×C412yes—
509C2×Dic5C2×C3×D412yes—
510C2×Dic5C2×C3×D412yes—
511C2×Dic5C3×#4112yes—
512C2×Dic5C3×#4112yes—
513C4×D5—44no—
514C22×D4—51no—
515C22×D4—51no—
516C22×D4C2×C3×D511yescharacteristic
517C23×C4—51no—
518C23×C4—51no—
519C23×C4—51no—
520#121—58no—
521C4×D4—104no—
522#117—104no—
523C2×C4⋊C4—51no—
524C2×C4⋊C4—51no—
525C2×C4⋊C4—51no—
526C2×C4⋊C4—51no—
527C2×C4⋊C4C2×C3×D511yescharacteristic
528C2×C22⋊C4—51no—
529C2×C22⋊C4—51no—
530C2×C22⋊C4—51no—
531C2×C22⋊C4—51no—
532C2×C22⋊C4—51no—
533C2×C22⋊C4—51no—
534C2×C22⋊C4—51no—
535C2×C22⋊C4—51no—
536C2×C22⋊C4C2×C3×D511yescharacteristic
537C2×C22⋊C4C2×C3×D511yescharacteristic
538C2×C22⋊C4C2×C3×D511yescharacteristic
539C2×C22⋊C4C2×C3×D511yescharacteristic
540C2×C42—51no—
541C2×C42—51no—
542C2×C42—51no—
543C2×C42—51no—
544C2×C42—51no—
545C2×C42C2×C3×D511yescharacteristic
546#95—51no—
547#95—51no—
548#95—51no—
549#95—51no—
550#95—51no—
551#95—51no—
552C2×C3×C5—42no—
553C2×C3×C5—42no—
554C2×C3×C5C2×C4×D411yescharacteristic
555C2×C3×C5C4×#4111yescharacteristic
556C2×C3×C5#51811yescharacteristic
557C2×C3×C5#54611yescharacteristic
558C2×C3×C5#55011yescharacteristic
559C2×C3×C5#55311yescharacteristic
560C2×C3×C5#55511yescharacteristic
561C3×D5—42no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—21no—
569C23×C3—21no—
570C23×C3—21no—
571C23×C3—21no—
572C23×C3—21no—
573C23×C3—21no—
574C23×C3—52no—
575C23×C3—101no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—101no—
580C23×C3—101no—
581C23×C3C2×C4×D512yes—
582C23×C3C2×C4×D512yes—
583C23×C3C23×D511yescharacteristic
584C3×D4—44no—
585C3×D4—108no—
586C3×D4—204no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—21no—
598C2×C3×C4—21no—
599C2×C3×C4—52no—
600C2×C3×C4—52no—
601C2×C3×C4—52no—
602C2×C3×C4—52no—
603C2×C3×C4—52no—
604C2×C3×C4—52no—
605C2×C3×C4—52no—
606C2×C3×C4—108no—
607C2×C3×C4—101no—
608C2×C3×C4—101no—
609C2×C3×C4—101no—
610C2×C3×C4—101no—
611C2×C3×C4—101no—
612C2×C3×C4—101no—
613C2×C3×C4—101no—
614C2×C3×C4—101no—
615C2×C3×C4—101no—
616C2×C3×C4—101no—
617C2×C3×C4—101no—
618C2×C3×C4—101no—
619C2×C3×C4—101no—
620C2×C3×C4—101no—
621C2×C3×C4—204no—
622C2×C3×C4—204no—
623C2×C3×C4C2×C4×D512yes—
624C2×C3×C4D4×D512yes—
625C2×C3×C4#71112yes—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—22no—
630C22×C5—22no—
631C22×C5—22no—
632C22×C5—41no—
633C22×C5—41no—
634C22×C5—41no—
635C22×C5—41no—
636C22×C5—41no—
637C22×C5—41no—
638C22×C5—41no—
639C22×C5—41no—
640C22×C5C23×C3×C411yescharacteristic
641C22×C5C22×C3×D411yescharacteristic
642C22×C5C2×C3×#4111yescharacteristic
643C22×C5C2×C3×#4111yescharacteristic
644C22×C5C2×C3×#4111yescharacteristic
645C22×C5C3×H(5,𝔽2)11yescharacteristic
646C22×C5C3×H(5,𝔽2)11yescharacteristic
647C2×D5—22no—
648C2×D5—22no—
649C2×D5—22no—
650C2×D5—41no—
651C2×D5—41no—
652C2×D5—41no—
653C2×D5—41no—
654C4×C5—22no—
655C4×C5—22no—
656C4×C5—22no—
657C4×C5—41no—
658C4×C5—41no—
659Dic5—22no—
660Dic5—22no—
661Dic5—22no—
662Dic5—22no—
663Dic5—41no—
664Dic5—41no—
665Dic5C3×C4×D414yes—
666C24—51no—
667C24C22×C3×D511yescharacteristic
668C24C22×C3×D511yescharacteristic
669C2×D4—41no—
670C2×D4—41no—
671C2×D4—54no—
672C2×D4—54no—
673C2×D4—102no—
674C2×D4—102no—
675C2×D4—201no—
676C2×D4—201no—
677C2×D4C3×C4×D514yescomplemented
678C22×C4—51no—
679C22×C4—54no—
680C22×C4—51no—
681C22×C4—51no—
682C22×C4—51no—
683C22×C4—51no—
684C22×C4—51no—
685C22×C4—51no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—102no—
692C22×C4—201no—
693C22×C4—201no—
694C22×C4C22×C3×D511yescharacteristic
695C22×C4C22×C3×D511yescharacteristic
696C22×C4C22×C3×D511yescharacteristic
697C22×C4C22×C3×D511yescharacteristic
698C22×C4C22×C3×D511yescharacteristic
699C4⋊C4—41no—
700C4⋊C4—54no—
701C4⋊C4—54no—
702C4⋊C4—102no—
703C4⋊C4—201no—
704C22⋊C4—22no—
705C22⋊C4—22no—
706C22⋊C4—22no—
707C22⋊C4—22no—
708C22⋊C4—54no—
709C22⋊C4—54no—
710C22⋊C4—102no—
711C22⋊C4—102no—
712C22⋊C4—102no—
713C22⋊C4—102no—
714C22⋊C4—201no—
715C22⋊C4—201no—
716C42—41no—
717C42—102no—
718C42—102no—
719C42—102no—
720C42—102no—
721C42—201no—
722C3×C5#236311yescharacteristic, complemented, Hall
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—41no—
730C22×C3—41no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—102no—
738C22×C3—102no—
739C22×C3—102no—
740C22×C3—201no—
741C22×C3—201no—
742C22×C3—201no—
743C22×C3—201no—
744C22×C3C22×C4×D511yescharacteristic
745C22×C3C2×D4×D511yescharacteristic
746C22×C3C2×#71111yescharacteristic
747C22×C3#414411yescharacteristic
748C22×C3#414411yescharacteristic
749C22×C3D5×#4111yescharacteristic
750C22×C3D5×#4111yescharacteristic
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—54no—
757C3×C4—102no—
758C3×C4—102no—
759C3×C4—102no—
760C3×C4—102no—
761C3×C4—201no—
762C3×C4—201no—
763C2×C5—42no—
764C2×C5—42no—
765C2×C5C2×C3×C4×D411yescharacteristic
766C2×C5C3×C4×#4111yescharacteristic
767C2×C5C3×#51811yescharacteristic
768C2×C5C3×#54611yescharacteristic
769C2×C5C3×#55011yescharacteristic
770C2×C5C3×#55311yescharacteristic
771C2×C5C3×#55511yescharacteristic
772D5—42no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—52no—
786C23—101no—
787C23—101no—
788C23—101no—
789C23—101no—
790C23—101no—
791C23—101no—
792C23C2×C3×C4×D512yes—
793C23C2×C3×C4×D512yes—
794C23C23×C3×D511yescharacteristic
795D4—44no—
796D4—108no—
797D4—204no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—52no—
811C2×C4—52no—
812C2×C4—52no—
813C2×C4—52no—
814C2×C4—52no—
815C2×C4—52no—
816C2×C4—52no—
817C2×C4—108no—
818C2×C4—101no—
819C2×C4—101no—
820C2×C4—101no—
821C2×C4—101no—
822C2×C4—101no—
823C2×C4—101no—
824C2×C4—101no—
825C2×C4—101no—
826C2×C4—101no—
827C2×C4—101no—
828C2×C4—101no—
829C2×C4—101no—
830C2×C4—101no—
831C2×C4—101no—
832C2×C4—204no—
833C2×C4—204no—
834C2×C4C2×C3×C4×D512yes—
835C2×C4C3×D4×D512yes—
836C2×C4C3×#71112yes—
837C2×C3—42no—
838C2×C3—42no—
839C2×C3—202no—
840C2×C3#6582011yescharacteristic
841C2×C3C4×#71111yescharacteristic
842C2×C3C4×D4×D511yescharacteristic
843C2×C3#6593511yescharacteristic
844C2×C3#6594411yescharacteristic
845C2×C3#6600411yescharacteristic
846C2×C3#6605211yescharacteristic
847C5C3×#236311yescharacteristic, complemented, Sylow
848C22—22no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—102no—
863C22—102no—
864C22—102no—
865C22—201no—
866C22—201no—
867C22—201no—
868C22—201no—
869C22C22×C3×C4×D511yescharacteristic
870C22C2×C3×D4×D511yescharacteristic
871C22C2×C3×#71111yescharacteristic
872C22C3×#414411yescharacteristic
873C22C3×#414411yescharacteristic
874C22C3×D5×#4111yescharacteristic
875C22C3×D5×#4111yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—41no—
880C4—41no—
881C4—54no—
882C4—102no—
883C4—102no—
884C4—102no—
885C4—102no—
886C4—201no—
887C4—201no—
888C3#1060803611yescharacteristic, direct product factor, Sylow
889C2—42no—
890C2—42no—
891C2—202no—
892C2C3×#6582011yescharacteristic
893C2C3×C4×#71111yescharacteristic
894C2C3×C4×D4×D511yescharacteristic
895C2C3×#6593511yescharacteristic
896C2C3×#6594411yescharacteristic
897C2C3×#6600411yescharacteristic
898C2C3×#6605211yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#390C2
socleC23×C3×C5C24
prime radicalC2×C3×#4085C2
cosocleC23×C5C24×C3
hypercenterC3×#390D5
hypocenterC5C3×#2363
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#390

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4027C2semidirect
3. C2×C3×#4023C2semidirect
4. C3×C5×#390C2semidirect
5. C3×#65509C2semidirect
6. C3×#65279C2semidirect
7. C3×#65261C2semidirect
8. C3×#65246C2semidirect
9. C3×#65246C2semidirect
10. C3×#65245C2semidirect
11. C3×#65233C2semidirect
12. C3×C22⋊C4×Dic5C2semidirect
13. C3×C22⋊C4×Dic5C2semidirect
14. C3×C4×#685C2semidirect
15. C3×C4×#683C2semidirect
16. #10608036C3direct (N × H)
33. C3×#4085C4semidirect
57. C2×#4027C2×C3semidirect
58. C2×#4023C2×C3semidirect
59. C5×#390C2×C3semidirect
60. #65509C2×C3semidirect
61. #65279C2×C3semidirect
62. #65261C2×C3semidirect
63. #65246C2×C3semidirect
64. #65246C2×C3semidirect
65. #65245C2×C3semidirect
66. #65233C2×C3semidirect
67. C22⋊C4×Dic5C2×C3semidirect
68. C22⋊C4×Dic5C2×C3semidirect
69. C4×#685C2×C3semidirect
70. C4×#683C2×C3semidirect
76. C2×C3×C5×D4C2×C4semidirect
87. C2×C3×C22⋊D5C2×C4semidirect
93. C22×C3×Dic5C2×C4semidirect
113. C3×C22⋊Dic5C2×C4semidirect
117. C3×#685C2×C4semidirect
120. C3×#683C2×C4semidirect
121. C3×#683D4semidirect
132. C3×#390D5semidirect
158. #4085C3×C4semidirect
288. C2×C5×D4C2×C3×C4semidirect
299. C2×C22⋊D5C2×C3×C4semidirect
305. C22×Dic5C2×C3×C4semidirect
325. C22⋊Dic5C2×C3×C4semidirect
329. #685C2×C3×C4semidirect
332. #683C2×C3×C4semidirect
333. #683C3×D4semidirect
344. #390C3×D5semidirect
405. C2×C3×D4C4×D5semidirect
677. C2×D4C3×C4×D5semidirect
722. C3×C5#2363semidirect
847. C5C3×#2363semidirect
888. C3#10608036direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40852
C2×C3×#40272
C2×C3×#40232
C3×C5×#3902
C3×#655092
C3×#652792
C3×#652612
C3×#652462
C3×#652452
C3×#652332
C3×C22⋊C4×Dic52
C3×C4×#6852
C3×C4×#6832
#106080363
C3×#23635