Finite Group Databasebeta

← C3×#10607211 #14329022

Subgroups — C3×#10607211 #14329022

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×#4030C211yesmaximal, characteristic
2C2×C3×#4027C211yesmaximal, characteristic, complemented
3C2×C3×#4018C211yesmaximal, characteristic, complemented
4C3×C5×#388C211yesmaximal, characteristic, complemented
5C3×#65277C211yesmaximal, characteristic, complemented
6C3×#65261C211yesmaximal, characteristic, complemented
7C3×#65247C211yesmaximal, characteristic, complemented
8C3×#65246C211yesmaximal, characteristic, complemented
9C3×#65246C211yesmaximal, characteristic, complemented
10C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
11C3×C4×#685C211yesmaximal, characteristic, complemented
12C3×#64958C211yesmaximal, characteristic, complemented
13C3×#64955C211yesmaximal, characteristic, complemented
14C3×#64954C211yesmaximal, characteristic, complemented
15C3×#64938C211yesmaximal, characteristic, complemented
16#10607211C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C22⋊D5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
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×C42×C5C2211yescharacteristic
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×#683C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C2×C3×C4×Dic5C2211yescharacteristic
45C2×C3×C4×Dic5C2211yescharacteristic
46C3×#4030C418yescomplemented
47C3×#4027—24no—
48C3×#4018—24no—
49C3×C5×#95C2211yescharacteristic
50C3×C5×#95C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2363—51nomaximal, Hall
56C2×#4030C2×C311yescharacteristic
57C2×#4027C2×C311yescharacteristic, complemented
58C2×#4018C2×C311yescharacteristic, complemented
59C5×#388C2×C311yescharacteristic, complemented
60#65277C2×C311yescharacteristic, complemented
61#65261C2×C311yescharacteristic, complemented
62#65247C2×C311yescharacteristic, complemented
63#65246C2×C311yescharacteristic, complemented
64#65246C2×C311yescharacteristic, complemented
65C22⋊C4×Dic5C2×C311yescharacteristic, complemented
66C4×#685C2×C311yescharacteristic, complemented
67#64958C2×C311yescharacteristic, complemented
68#64955C2×C311yescharacteristic, complemented
69#64954C2×C311yescharacteristic, complemented
70#64938C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C23×C3×D5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×C4×C5C2311yescharacteristic
80C2×C3×C22⋊D5—22no—
81C2×C3×C22⋊D5—22no—
82C2×C3×C22⋊D5—41no—
83C2×C3×C22⋊D5—41no—
84C2×C3×C22⋊D5C2×C414yes—
85C2×C3×C22⋊D5C2×C414yescomplemented
86C22×C3×Dic5—22no—
87C22×C3×Dic5—22no—
88C22×C3×Dic5—41no—
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C2×C3×D20—41no—
96C2×C3×D20—41no—
97C2×C3×D20C2×C414yescomplemented
98C2×C3×C4×D5—22no—
99C2×C3×C4×D5—22no—
100C2×C3×C4×D5—22no—
101C2×C3×C4×D5—22no—
102C2×C3×C4×D5—41no—
103C2×C3×C4×D5C2×C414yescomplemented
104C3×C5×C4⋊C4—41no—
105C3×C5×C22⋊C4—22no—
106C3×C5×C22⋊C4—41no—
107C3×C5×C22⋊C4C2×C414yescomplemented
108C3×C42×C5—22no—
109C3×C22⋊Dic5—22no—
110C3×#685—22no—
111C3×#685—22no—
112C3×#685—22no—
113C3×#685—22no—
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—41no—
126C3×C4×Dic5—41no—
127C2×C3×#121—51no—
128C2×C3×C4×D4—51no—
129C2×C3×#117—51no—
130C3×#390—51no—
131C3×#390—51no—
132C3×#390—51no—
133C3×#389—51no—
134C3×#388—51no—
135C3×#388D511yescharacteristic, complemented
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×C22⋊D5C22×C311yescharacteristic
143C22×C22⋊D5C22×C311yescharacteristic
144C23×Dic5C22×C311yescharacteristic
145C22×D20C22×C311yescharacteristic
146C22×C4×D5C22×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×C42×C5C22×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×#683C22×C311yescharacteristic
163C2×#683C22×C311yescharacteristic
164C2×#683C22×C311yescharacteristic
165C2×#683C22×C311yescharacteristic
166C2×C4×Dic5C22×C311yescharacteristic
167C2×C4×Dic5C22×C311yescharacteristic
168C2×C4×Dic5C22×C311yescharacteristic
169C2×C4×Dic5C22×C311yescharacteristic
170C2×C4×Dic5C22×C311yescharacteristic
171#4030C3×C418yescomplemented
172#4027—24no—
173#4018—24no—
174C5×#95C22×C311yescharacteristic
175C5×#95C22×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×C5C22×C412yes—
188C23×C3×C5C2411yescharacteristic
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×D5C22×C412yes—
202C22×C3×D5C22×C412yes—
203C2×C3×C4×C5—21no—
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×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5C22×C412yes—
219C2×C3×C4×C5C22×C412yes—
220C2×C3×C4×C5C2×D412yes—
221C3×C22⋊D5—28no—
222C3×C22⋊D5—44no—
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—21no—
230C2×C3×Dic5—21no—
231C2×C3×Dic5—21no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—44no—
235C2×C3×Dic5C22×C412yes—
236C2×C3×Dic5C22×C412yes—
237C2×C3×Dic5C2×D412yes—
238C2×C3×Dic5C2×D412yes—
239C2×C3×Dic5#4112yes—
240C2×C3×Dic5#4112yes—
241C2×C3×Dic5#4112yes—
242C3×D20—44no—
243C3×C4×D5—28no—
244C3×C4×D5—44no—
245C22×C3×D4—51no—
246C22×C3×D4—51no—
247C22×C3×D4—51no—
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⋊C4—51no—
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×#95C2×D511yescharacteristic
282C3×#95C2×D511yescharacteristic
283C24×C5C23×C311yescharacteristic
284C23×D5C23×C311yescharacteristic
285C23×D5C23×C311yescharacteristic
286C22×C4×C5C23×C311yescharacteristic
287C22×C4×C5C23×C311yescharacteristic
288C22×C4×C5C23×C311yescharacteristic
289C22×C4×C5C23×C311yescharacteristic
290C22×C4×C5C23×C311yescharacteristic
291C22×C4×C5C23×C311yescharacteristic
292C2×C22⋊D5—22no—
293C2×C22⋊D5—22no—
294C2×C22⋊D5—41no—
295C2×C22⋊D5—41no—
296C2×C22⋊D5C2×C3×C414yes—
297C2×C22⋊D5C2×C3×C414yescomplemented
298C22×Dic5—22no—
299C22×Dic5—22no—
300C22×Dic5—41no—
301C22×Dic5C23×C311yescharacteristic
302C22×Dic5C23×C311yescharacteristic
303C22×Dic5C23×C311yescharacteristic
304C22×Dic5C23×C311yescharacteristic
305C22×Dic5C23×C311yescharacteristic
306C22×Dic5C23×C311yescharacteristic
307C2×D20—41no—
308C2×D20—41no—
309C2×D20C2×C3×C414yescomplemented
310C2×C4×D5—22no—
311C2×C4×D5—22no—
312C2×C4×D5—22no—
313C2×C4×D5—22no—
314C2×C4×D5—41no—
315C2×C4×D5C2×C3×C414yescomplemented
316C5×C4⋊C4—41no—
317C5×C22⋊C4—22no—
318C5×C22⋊C4—41no—
319C5×C22⋊C4C2×C3×C414yescomplemented
320C42×C5—22no—
321C22⋊Dic5—22no—
322#685—22no—
323#685—22no—
324#685—22no—
325#685—22no—
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—41no—
338C4×Dic5—41no—
339C2×#121—51no—
340C2×C4×D4—51no—
341C2×#117—51no—
342#390—51no—
343#390—51no—
344#390—51no—
345#389—51no—
346#388—51no—
347#388C3×D511yescharacteristic, complemented
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—41no—
358C22×C3×C5—41no—
359C22×C3×C5—41no—
360C22×C3×C5—41no—
361C22×C3×C5C23×C411yescharacteristic
362C22×C3×C5C22×D411yescharacteristic
363C22×C3×C5C2×#4111yescharacteristic
364C22×C3×C5C2×#4111yescharacteristic
365C22×C3×C5C2×#4111yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C5H(5,𝔽2)11yescharacteristic
368C2×C3×D5—22no—
369C2×C3×D5—22no—
370C2×C3×D5—22no—
371C2×C3×D5—22no—
372C2×C3×D5—22no—
373C2×C3×D5—22no—
374C2×C3×D5—41no—
375C2×C3×D5—41no—
376C2×C3×D5—41no—
377C2×C3×D5—41no—
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×C4×C5—41no—
388C3×Dic5—22no—
389C3×Dic5—22no—
390C3×Dic5—22no—
391C3×Dic5—22no—
392C3×Dic5—41no—
393C3×Dic5C4×D414yes—
394C24×C3—51no—
395C24×C3—51no—
396C24×C3C22×D511yescharacteristic
397C2×C3×D4—54no—
398C2×C3×D4—54no—
399C2×C3×D4—54no—
400C2×C3×D4—102no—
401C2×C3×D4—102no—
402C2×C3×D4—201no—
403C2×C3×D4—201no—
404C2×C3×D4—201no—
405C2×C3×D4—201no—
406C22×C3×C4—51no—
407C22×C3×C4—51no—
408C22×C3×C4—51no—
409C22×C3×C4—51no—
410C22×C3×C4—51no—
411C22×C3×C4—54no—
412C22×C3×C4—51no—
413C22×C3×C4—102no—
414C22×C3×C4—102no—
415C22×C3×C4—102no—
416C22×C3×C4—102no—
417C22×C3×C4—102no—
418C22×C3×C4—102no—
419C22×C3×C4—201no—
420C22×C3×C4—201no—
421C22×C3×C4C22×D511yescharacteristic
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—41no—
434C3×C22⋊C4—54no—
435C3×C22⋊C4—102no—
436C3×C22⋊C4—102no—
437C3×C22⋊C4—102no—
438C3×C22⋊C4—102no—
439C3×C22⋊C4—102no—
440C3×C22⋊C4—102no—
441C3×C22⋊C4—102no—
442C3×C22⋊C4—201no—
443C3×C22⋊C4C4×D514yescomplemented
444C3×C42—22no—
445C3×C42—102no—
446C3×C42—102no—
447C3×C42—102no—
448C3×C42—201no—
449C3×C42—201no—
450C23×C5—21no—
451C23×C5—21no—
452C23×C5—21no—
453C23×C5—21no—
454C23×C5—21no—
455C23×C5—21no—
456C23×C5C22×C3×C412yes—
457C23×C5C24×C311yescharacteristic
458C22×D5—21no—
459C22×D5—21no—
460C22×D5—21no—
461C22×D5—21no—
462C22×D5—21no—
463C22×D5—21no—
464C22×D5—21no—
465C22×D5—21no—
466C22×D5—21no—
467C22×D5—21no—
468C22×D5—21no—
469C22×D5—21no—
470C22×D5C22×C3×C412yes—
471C22×D5C22×C3×C412yes—
472C2×C4×C5—21no—
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×C5—21no—
486C2×C4×C5—21no—
487C2×C4×C5C22×C3×C412yes—
488C2×C4×C5C22×C3×C412yes—
489C2×C4×C5C2×C3×D412yes—
490C22⋊D5—28no—
491C22⋊D5—44no—
492C2×Dic5—21no—
493C2×Dic5—21no—
494C2×Dic5—21no—
495C2×Dic5—21no—
496C2×Dic5—21no—
497C2×Dic5—21no—
498C2×Dic5—21no—
499C2×Dic5—21no—
500C2×Dic5—21no—
501C2×Dic5—21no—
502C2×Dic5—21no—
503C2×Dic5—44no—
504C2×Dic5C22×C3×C412yes—
505C2×Dic5C22×C3×C412yes—
506C2×Dic5C2×C3×D412yes—
507C2×Dic5C2×C3×D412yes—
508C2×Dic5C3×#4112yes—
509C2×Dic5C3×#4112yes—
510C2×Dic5C3×#4112yes—
511D20—44no—
512C4×D5—28no—
513C4×D5—44no—
514C22×D4—51no—
515C22×D4—51no—
516C22×D4—51no—
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⋊C4—51no—
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#95C2×C3×D511yescharacteristic
551#95C2×C3×D511yescharacteristic
552C2×C3×C5—42no—
553C2×C3×C5C2×C4×D411yescharacteristic
554C2×C3×C5C4×#4111yescharacteristic
555C2×C3×C5#51811yescharacteristic
556C2×C3×C5#54611yescharacteristic
557C2×C3×C5#55011yescharacteristic
558C2×C3×C5#55311yescharacteristic
559C2×C3×C5#55511yescharacteristic
560C3×D5—42no—
561C3×D5—42no—
562C23×C3—21no—
563C23×C3—21no—
564C23×C3—21no—
565C23×C3—21no—
566C23×C3—21no—
567C23×C3—21no—
568C23×C3—52no—
569C23×C3—52no—
570C23×C3—101no—
571C23×C3—101no—
572C23×C3—101no—
573C23×C3—101no—
574C23×C3—101no—
575C23×C3—101no—
576C23×C3—101no—
577C23×C3—101no—
578C23×C3—101no—
579C23×C3—101no—
580C23×C3—101no—
581C23×C3—101no—
582C23×C3C2×C4×D512yes—
583C23×C3C23×D511yescharacteristic
584C3×D4—108no—
585C3×D4—204no—
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—21no—
600C2×C3×C4—21no—
601C2×C3×C4—21no—
602C2×C3×C4—52no—
603C2×C3×C4—52no—
604C2×C3×C4—52no—
605C2×C3×C4—52no—
606C2×C3×C4—52no—
607C2×C3×C4—52no—
608C2×C3×C4—52no—
609C2×C3×C4—108no—
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×C4C2×C4×D512yes—
625C2×C3×C4D4×D512yes—
626C22×C5—22no—
627C22×C5—22no—
628C22×C5—22no—
629C22×C5—41no—
630C22×C5—41no—
631C22×C5—41no—
632C22×C5—41no—
633C22×C5C23×C3×C411yescharacteristic
634C22×C5C22×C3×D411yescharacteristic
635C22×C5C2×C3×#4111yescharacteristic
636C22×C5C2×C3×#4111yescharacteristic
637C22×C5C2×C3×#4111yescharacteristic
638C22×C5C3×H(5,𝔽2)11yescharacteristic
639C22×C5C3×H(5,𝔽2)11yescharacteristic
640C2×D5—22no—
641C2×D5—22no—
642C2×D5—22no—
643C2×D5—22no—
644C2×D5—22no—
645C2×D5—22no—
646C2×D5—41no—
647C2×D5—41no—
648C2×D5—41no—
649C2×D5—41no—
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—
659C4×C5—41no—
660Dic5—22no—
661Dic5—22no—
662Dic5—22no—
663Dic5—22no—
664Dic5—41no—
665Dic5C3×C4×D414yes—
666C24—51no—
667C24—51no—
668C24C22×C3×D511yescharacteristic
669C2×D4—54no—
670C2×D4—54no—
671C2×D4—54no—
672C2×D4—102no—
673C2×D4—102no—
674C2×D4—201no—
675C2×D4—201no—
676C2×D4—201no—
677C2×D4—201no—
678C22×C4—51no—
679C22×C4—51no—
680C22×C4—51no—
681C22×C4—51no—
682C22×C4—51no—
683C22×C4—54no—
684C22×C4—51no—
685C22×C4—102no—
686C22×C4—102no—
687C22×C4—102no—
688C22×C4—102no—
689C22×C4—102no—
690C22×C4—102no—
691C22×C4—201no—
692C22×C4—201no—
693C22×C4C22×C3×D511yescharacteristic
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—41no—
706C22⋊C4—54no—
707C22⋊C4—102no—
708C22⋊C4—102no—
709C22⋊C4—102no—
710C22⋊C4—102no—
711C22⋊C4—102no—
712C22⋊C4—102no—
713C22⋊C4—102no—
714C22⋊C4—201no—
715C22⋊C4C3×C4×D514yescomplemented
716C42—22no—
717C42—102no—
718C42—102no—
719C42—102no—
720C42—201no—
721C42—201no—
722C3×C5#236311yescharacteristic, complemented, Hall
723C22×C3—22no—
724C22×C3—22no—
725C22×C3—22no—
726C22×C3—41no—
727C22×C3—41no—
728C22×C3—41no—
729C22×C3—41no—
730C22×C3—102no—
731C22×C3—102no—
732C22×C3—102no—
733C22×C3—102no—
734C22×C3—102no—
735C22×C3—102no—
736C22×C3—201no—
737C22×C3—201no—
738C22×C3—201no—
739C22×C3—201no—
740C22×C3—201no—
741C22×C3—201no—
742C22×C3—201no—
743C22×C3—201no—
744C22×C3C22×C4×D511yescharacteristic
745C22×C3C2×D4×D511yescharacteristic
746C22×C3#414411yescharacteristic
747C22×C3D5×#4111yescharacteristic
748C22×C3D5×#4111yescharacteristic
749C22×C3D5×#4111yescharacteristic
750C22×C3#414911yescharacteristic
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—22no—
754C3×C4—41no—
755C3×C4—41no—
756C3×C4—41no—
757C3×C4—54no—
758C3×C4—102no—
759C3×C4—102no—
760C3×C4—102no—
761C3×C4—102no—
762C3×C4—201no—
763C2×C5—42no—
764C2×C5C2×C3×C4×D411yescharacteristic
765C2×C5C3×C4×#4111yescharacteristic
766C2×C5C3×#51811yescharacteristic
767C2×C5C3×#54611yescharacteristic
768C2×C5C3×#55011yescharacteristic
769C2×C5C3×#55311yescharacteristic
770C2×C5C3×#55511yescharacteristic
771D5—42no—
772D5—42no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—52no—
780C23—52no—
781C23—101no—
782C23—101no—
783C23—101no—
784C23—101no—
785C23—101no—
786C23—101no—
787C23—101no—
788C23—101no—
789C23—101no—
790C23—101no—
791C23—101no—
792C23—101no—
793C23C2×C3×C4×D512yes—
794C23C23×C3×D511yescharacteristic
795D4—108no—
796D4—204no—
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—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—52no—
814C2×C4—52no—
815C2×C4—52no—
816C2×C4—52no—
817C2×C4—52no—
818C2×C4—52no—
819C2×C4—52no—
820C2×C4—108no—
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×C4C2×C3×C4×D512yes—
836C2×C4C3×D4×D512yes—
837C2×C3—42no—
838C2×C3—202no—
839C2×C3—202no—
840C2×C3#6585611yescharacteristic
841C2×C3C4×D4×D511yescharacteristic
842C2×C3#6587911yescharacteristic
843C2×C3#6593311yescharacteristic
844C2×C3#6598811yescharacteristic
845C2×C3#6600411yescharacteristic
846C2×C3#6604311yescharacteristic
847C5C3×#236311yescharacteristic, complemented, Sylow
848C22—22no—
849C22—22no—
850C22—22no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—102no—
856C22—102no—
857C22—102no—
858C22—102no—
859C22—102no—
860C22—102no—
861C22—201no—
862C22—201no—
863C22—201no—
864C22—201no—
865C22—201no—
866C22—201no—
867C22—201no—
868C22—201no—
869C22C22×C3×C4×D511yescharacteristic
870C22C2×C3×D4×D511yescharacteristic
871C22C3×#414411yescharacteristic
872C22C3×D5×#4111yescharacteristic
873C22C3×D5×#4111yescharacteristic
874C22C3×D5×#4111yescharacteristic
875C22C3×#414911yescharacteristic
876C4—22no—
877C4—22no—
878C4—22no—
879C4—41no—
880C4—41no—
881C4—41no—
882C4—54no—
883C4—102no—
884C4—102no—
885C4—102no—
886C4—102no—
887C4—201no—
888C3#1060721111yescharacteristic, direct product factor, Sylow
889C2—42no—
890C2—202no—
891C2—202no—
892C2C3×#6585611yescharacteristic
893C2C3×C4×D4×D511yescharacteristic
894C2C3×#6587911yescharacteristic
895C2C3×#6593311yescharacteristic
896C2C3×#6598811yescharacteristic
897C2C3×#6600411yescharacteristic
898C2C3×#6604311yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC2×C3×#4030C2
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C3×#2363
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4027C2semidirect
3. C2×C3×#4018C2semidirect
4. C3×C5×#388C2semidirect
5. C3×#65277C2semidirect
6. C3×#65261C2semidirect
7. C3×#65247C2semidirect
8. C3×#65246C2semidirect
9. C3×#65246C2semidirect
10. C3×C22⋊C4×Dic5C2semidirect
11. C3×C4×#685C2semidirect
12. C3×#64958C2semidirect
13. C3×#64955C2semidirect
14. C3×#64954C2semidirect
15. C3×#64938C2semidirect
16. #10607211C3direct (N × H)
46. C3×#4030C4semidirect
57. C2×#4027C2×C3semidirect
58. C2×#4018C2×C3semidirect
59. C5×#388C2×C3semidirect
60. #65277C2×C3semidirect
61. #65261C2×C3semidirect
62. #65247C2×C3semidirect
63. #65246C2×C3semidirect
64. #65246C2×C3semidirect
65. C22⋊C4×Dic5C2×C3semidirect
66. C4×#685C2×C3semidirect
67. #64958C2×C3semidirect
68. #64955C2×C3semidirect
69. #64954C2×C3semidirect
70. #64938C2×C3semidirect
85. C2×C3×C22⋊D5C2×C4semidirect
97. C2×C3×D20C2×C4semidirect
103. C2×C3×C4×D5C2×C4semidirect
107. C3×C5×C22⋊C4C2×C4semidirect
117. C3×#685C2×C4semidirect
120. C3×#683C2×C4semidirect
121. C3×#683D4semidirect
135. C3×#388D5semidirect
171. #4030C3×C4semidirect
297. C2×C22⋊D5C2×C3×C4semidirect
309. C2×D20C2×C3×C4semidirect
315. C2×C4×D5C2×C3×C4semidirect
319. C5×C22⋊C4C2×C3×C4semidirect
329. #685C2×C3×C4semidirect
332. #683C2×C3×C4semidirect
333. #683C3×D4semidirect
347. #388C3×D5semidirect
443. C3×C22⋊C4C4×D5semidirect
715. C22⋊C4C3×C4×D5semidirect
722. C3×C5#2363semidirect
847. C5C3×#2363semidirect
888. C3#10607211direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40302
C2×C3×#40272
C2×C3×#40182
C3×C5×#3882
C3×#652772
C3×#652612
C3×#652472
C3×#652462
C3×C22⋊C4×Dic52
C3×C4×#6852
C3×#649582
C3×#649552
C3×#649542
C3×#649382
#106072113
C3×#23635