Finite Group Databasebeta

← C3×#10607191 #14323700

Subgroups — C3×#10607191 #14323700

Order 1920.

1112 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4024C211yesmaximal, characteristic
2C2×C3×#4023C211yesmaximal, characteristic
3C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
4C3×C5×#388C211yesmaximal, characteristic
5C3×#65262C211yesmaximal, characteristic, complemented
6C3×#65261C211yesmaximal, characteristic, complemented
7C3×#65240C211yesmaximal, characteristic
8C3×#65233C211yesmaximal, characteristic
9C3×#65233C211yesmaximal, characteristic
10C3×#65231C211yesmaximal, characteristic
11C3×#65222C211yesmaximal, characteristic, complemented
12C3×#64942C211yesmaximal, characteristic, complemented
13C3×#64938C211yesmaximal, characteristic, complemented
14C3×#64936C211yesmaximal, characteristic, complemented
15C3×#64935C211yesmaximal, characteristic, complemented
16#10607191C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×Dic5C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×C3×C4×Dic5C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C3×#4024C418yescomplemented
43C3×#4023—24no—
44C3×C4×Dic10—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#2323—51nomaximal, Hall
56C2×#4024C2×C311yescharacteristic
57C2×#4023C2×C311yescharacteristic
58C2×C4×Dic10C2×C311yescharacteristic, complemented
59C5×#388C2×C311yescharacteristic
60#65262C2×C311yescharacteristic, complemented
61#65261C2×C311yescharacteristic, complemented
62#65240C2×C311yescharacteristic
63#65233C2×C311yescharacteristic
64#65233C2×C311yescharacteristic
65#65231C2×C311yescharacteristic
66#65222C2×C311yescharacteristic, complemented
67#64942C2×C311yescharacteristic, complemented
68#64938C2×C311yescharacteristic, complemented
69#64936C2×C311yescharacteristic, complemented
70#64935C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×Dic5—22no—
79C22×C3×Dic5—22no—
80C22×C3×Dic5C2×C414yes—
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C2×C3×Dic10—22no—
90C2×C3×Dic10—22no—
91C2×C3×Dic10C2×C414yes—
92C3×C5×C4⋊C4—41no—
93C3×C5×C22⋊C4—22no—
94C3×C5×C22⋊C4—41no—
95C3×C5×C22⋊C4C2×C414yes—
96C3×C42×C5—22no—
97C3×C22⋊Dic5—22no—
98C3×C22⋊Dic5—41no—
99C3×C22⋊Dic5C2×C414yes—
100C3×C4⋊Dic5—22no—
101C3×C4⋊Dic5C2×C414yes—
102C3×#683—22no—
103C3×#683—22no—
104C3×#683—22no—
105C3×#683—22no—
106C3×#683—22no—
107C3×#683—41no—
108C3×#683C2×C414yes—
109C3×#683C2×C414yes—
110C3×C4×Dic5—22no—
111C3×C4×Dic5—22no—
112C3×C4×Dic5—41no—
113C3×C4×Dic5—41no—
114C3×C4×Dic5D414yes—
115C2×C3×C22⋊Q8—51no—
116C2×C3×C4×Q8—51no—
117C2×C3×#117—51no—
118C3×#391—51no—
119C3×#389—51no—
120C3×#389—51no—
121C3×#389—51no—
122C3×#388—51no—
123C3×#388—51no—
124C3×#388—51no—
125C3×#388D511yescharacteristic
126C3×#387—51no—
127C3×#387—51no—
128C3×#380—51no—
129C3×C4×C4⋊C4—51no—
130C23×Dic5C22×C311yescharacteristic
131C22×Dic10C22×C311yescharacteristic
132C2×C5×C4⋊C4C22×C311yescharacteristic
133C2×C5×C22⋊C4C22×C311yescharacteristic
134C2×C5×C22⋊C4C22×C311yescharacteristic
135C2×C5×C22⋊C4C22×C311yescharacteristic
136C2×C42×C5C22×C311yescharacteristic
137C2×C22⋊Dic5C22×C311yescharacteristic
138C2×C22⋊Dic5C22×C311yescharacteristic
139C2×C22⋊Dic5C22×C311yescharacteristic
140C2×C4⋊Dic5C22×C311yescharacteristic
141C2×C4⋊Dic5C22×C311yescharacteristic
142C2×#683C22×C311yescharacteristic
143C2×#683C22×C311yescharacteristic
144C2×#683C22×C311yescharacteristic
145C2×#683C22×C311yescharacteristic
146C2×#683C22×C311yescharacteristic
147C2×#683C22×C311yescharacteristic
148C2×#683C22×C311yescharacteristic
149C2×#683C22×C311yescharacteristic
150C2×C4×Dic5C22×C311yescharacteristic
151C2×C4×Dic5C22×C311yescharacteristic
152C2×C4×Dic5C22×C311yescharacteristic
153C2×C4×Dic5C22×C311yescharacteristic
154C2×C4×Dic5C22×C311yescharacteristic
155#4024C3×C418yescomplemented
156#4023—24no—
157C4×Dic10—24no—
158C5×#95C22×C311yescharacteristic
159C5×#95C22×C311yescharacteristic
160#3963C22×C311yescharacteristic
161#3963C22×C311yescharacteristic
162#3963C22×C311yescharacteristic
163#3963C22×C311yescharacteristic
164#3963C22×C311yescharacteristic
165#3963C22×C311yescharacteristic
166#3963C22×C311yescharacteristic
167#3963C22×C311yescharacteristic
168#2323—51noSylow
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×C5C22×C412yes—
176C23×C3×C5C2411yescharacteristic
177C2×C3×C4×C5—21no—
178C2×C3×C4×C5—21no—
179C2×C3×C4×C5—21no—
180C2×C3×C4×C5—21no—
181C2×C3×C4×C5—21no—
182C2×C3×C4×C5—21no—
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×C5C22×C412yes—
193C2×C3×C4×C5C22×C412yes—
194C2×C3×C4×C5C2×D412yes—
195C2×C3×Dic5—21no—
196C2×C3×Dic5—21no—
197C2×C3×Dic5—21no—
198C2×C3×Dic5—21no—
199C2×C3×Dic5—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—28no—
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×Dic5C22×C412yes—
214C2×C3×Dic5C22×C412yes—
215C2×C3×Dic5C22×C412yes—
216C2×C3×Dic5C22×C412yes—
217C2×C3×Dic5C2×D412yes—
218C2×C3×Dic5C2×D412yes—
219C2×C3×Dic5#4112yes—
220C3×Dic10—28no—
221C22×C3×Q8—51no—
222C23×C3×C4—51no—
223C3×C22⋊Q8—58no—
224C3×C4×Q8—104no—
225C3×#117—104no—
226C2×C3×C4⋊C4—51no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—51no—
229C2×C3×C4⋊C4—51no—
230C2×C3×C4⋊C4—51no—
231C2×C3×C4⋊C4—51no—
232C2×C3×C4⋊C4—51no—
233C2×C3×C4⋊C4—51no—
234C2×C3×C4⋊C4—51no—
235C2×C3×C4⋊C4—51no—
236C2×C3×C4⋊C4C2×D511yescharacteristic
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—
248C2×C3×C42C2×D511yescharacteristic
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×#95C2×D511yescharacteristic
258C3×#95C2×D511yescharacteristic
259C24×C5C23×C311yescharacteristic
260C22×C4×C5C23×C311yescharacteristic
261C22×C4×C5C23×C311yescharacteristic
262C22×C4×C5C23×C311yescharacteristic
263C22×C4×C5C23×C311yescharacteristic
264C22×C4×C5C23×C311yescharacteristic
265C22×C4×C5C23×C311yescharacteristic
266C22×Dic5—22no—
267C22×Dic5—22no—
268C22×Dic5C2×C3×C414yes—
269C22×Dic5C23×C311yescharacteristic
270C22×Dic5C23×C311yescharacteristic
271C22×Dic5C23×C311yescharacteristic
272C22×Dic5C23×C311yescharacteristic
273C22×Dic5C23×C311yescharacteristic
274C22×Dic5C23×C311yescharacteristic
275C22×Dic5C23×C311yescharacteristic
276C22×Dic5C23×C311yescharacteristic
277C2×Dic10—22no—
278C2×Dic10—22no—
279C2×Dic10C2×C3×C414yes—
280C5×C4⋊C4—41no—
281C5×C22⋊C4—22no—
282C5×C22⋊C4—41no—
283C5×C22⋊C4C2×C3×C414yes—
284C42×C5—22no—
285C22⋊Dic5—22no—
286C22⋊Dic5—41no—
287C22⋊Dic5C2×C3×C414yes—
288C4⋊Dic5—22no—
289C4⋊Dic5C2×C3×C414yes—
290#683—22no—
291#683—22no—
292#683—22no—
293#683—22no—
294#683—22no—
295#683—41no—
296#683C2×C3×C414yes—
297#683C2×C3×C414yes—
298C4×Dic5—22no—
299C4×Dic5—22no—
300C4×Dic5—41no—
301C4×Dic5—41no—
302C4×Dic5C3×D414yes—
303C2×C22⋊Q8—51no—
304C2×C4×Q8—51no—
305C2×#117—51no—
306#391—51no—
307#389—51no—
308#389—51no—
309#389—51no—
310#388—51no—
311#388—51no—
312#388—51no—
313#388C3×D511yescharacteristic
314#387—51no—
315#387—51no—
316#380—51no—
317C4×C4⋊C4—51no—
318C22×C3×C5—22no—
319C22×C3×C5—22no—
320C22×C3×C5—22no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5—41no—
325C22×C3×C5C23×C411yescharacteristic
326C22×C3×C5C22×D411yescharacteristic
327C22×C3×C5C2×#4111yescharacteristic
328C22×C3×C5H(5,𝔽2)11yescharacteristic
329C22×C3×C52−1+411yescharacteristic
330C22×C3×C52−1+411yescharacteristic
331C22×C3×C52−1+411yescharacteristic
332C3×C4×C5—22no—
333C3×C4×C5—22no—
334C3×C4×C5—22no—
335C3×C4×C5—41no—
336C3×C4×C5—41no—
337C3×C4×C5—41no—
338C3×Dic5—22no—
339C3×Dic5—22no—
340C3×Dic5—22no—
341C3×Dic5—22no—
342C3×Dic5—41no—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C3×Dic5C4×D414yes—
346C24×C3C22×D511yescharacteristic
347C2×C3×Q8—54no—
348C2×C3×Q8—102no—
349C2×C3×Q8—102no—
350C22×C3×C4—51no—
351C22×C3×C4—54no—
352C22×C3×C4—51no—
353C22×C3×C4—51no—
354C22×C3×C4—51no—
355C22×C3×C4—51no—
356C22×C3×C4—51no—
357C22×C3×C4—51no—
358C22×C3×C4—51no—
359C22×C3×C4—102no—
360C22×C3×C4—102no—
361C22×C3×C4C22×D511yescharacteristic
362C22×C3×C4C22×D511yescharacteristic
363C22×C3×C4C22×D511yescharacteristic
364C22×C3×C4C22×D511yescharacteristic
365C22×C3×C4C22×D511yescharacteristic
366C22×C3×C4C22×D511yescharacteristic
367C3×C4⋊C4—41no—
368C3×C4⋊C4—54no—
369C3×C4⋊C4—54no—
370C3×C4⋊C4—54no—
371C3×C4⋊C4—102no—
372C3×C4⋊C4—102no—
373C3×C4⋊C4—102no—
374C3×C4⋊C4—102no—
375C3×C4⋊C4—102no—
376C3×C4⋊C4—102no—
377C3×C4⋊C4—201no—
378C3×C22⋊C4—22no—
379C3×C22⋊C4—41no—
380C3×C22⋊C4—54no—
381C3×C22⋊C4—102no—
382C3×C22⋊C4—201no—
383C3×C22⋊C4C4×D514yes—
384C3×C42—22no—
385C3×C42—54no—
386C3×C42—102no—
387C3×C42—102no—
388C3×C42—201no—
389C3×C42—201no—
390C23×C5—21no—
391C23×C5—21no—
392C23×C5—21no—
393C23×C5—21no—
394C23×C5—21no—
395C23×C5—21no—
396C23×C5C22×C3×C412yes—
397C23×C5C24×C311yescharacteristic
398C2×C4×C5—21no—
399C2×C4×C5—21no—
400C2×C4×C5—21no—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—21no—
412C2×C4×C5—21no—
413C2×C4×C5C22×C3×C412yes—
414C2×C4×C5C22×C3×C412yes—
415C2×C4×C5C2×C3×D412yes—
416C2×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—21no—
421C2×Dic5—21no—
422C2×Dic5—21no—
423C2×Dic5—21no—
424C2×Dic5—28no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5—21no—
431C2×Dic5—21no—
432C2×Dic5—21no—
433C2×Dic5—21no—
434C2×Dic5C22×C3×C412yes—
435C2×Dic5C22×C3×C412yes—
436C2×Dic5C22×C3×C412yes—
437C2×Dic5C22×C3×C412yes—
438C2×Dic5C2×C3×D412yes—
439C2×Dic5C2×C3×D412yes—
440C2×Dic5C3×#4112yes—
441Dic10—28no—
442C22×Q8—51no—
443C23×C4—51no—
444C22⋊Q8—58no—
445C4×Q8—104no—
446#117—104no—
447C2×C4⋊C4—51no—
448C2×C4⋊C4—51no—
449C2×C4⋊C4—51no—
450C2×C4⋊C4—51no—
451C2×C4⋊C4—51no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—51no—
454C2×C4⋊C4—51no—
455C2×C4⋊C4—51no—
456C2×C4⋊C4—51no—
457C2×C4⋊C4C2×C3×D511yescharacteristic
458C2×C22⋊C4—51no—
459C2×C22⋊C4—51no—
460C2×C22⋊C4—51no—
461C2×C22⋊C4C2×C3×D511yescharacteristic
462C2×C22⋊C4C2×C3×D511yescharacteristic
463C2×C22⋊C4C2×C3×D511yescharacteristic
464C2×C42—51no—
465C2×C42—51no—
466C2×C42—51no—
467C2×C42—51no—
468C2×C42—51no—
469C2×C42C2×C3×D511yescharacteristic
470#95—51no—
471#95—51no—
472#95—51no—
473#95—51no—
474#95—51no—
475#95—51no—
476#95—51no—
477#95—51no—
478#95C2×C3×D511yescharacteristic
479#95C2×C3×D511yescharacteristic
480C2×C3×C5—42no—
481C2×C3×C5C2×C4×D411yescharacteristic
482C2×C3×C5#51911yescharacteristic
483C2×C3×C5#52011yescharacteristic
484C2×C3×C5#53611yescharacteristic
485C2×C3×C5#53711yescharacteristic
486C2×C3×C5#54111yescharacteristic
487C2×C3×C5#54211yescharacteristic
488C23×C3—21no—
489C23×C3—21no—
490C23×C3—21no—
491C23×C3—21no—
492C23×C3—21no—
493C23×C3—21no—
494C23×C3C2×C4×D512yes—
495C23×C3C23×D511yescharacteristic
496C3×Q8—108no—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—52no—
513C2×C3×C4—52no—
514C2×C3×C4—52no—
515C2×C3×C4—52no—
516C2×C3×C4—52no—
517C2×C3×C4—52no—
518C2×C3×C4—52no—
519C2×C3×C4—108no—
520C2×C3×C4—101no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—101no—
527C2×C3×C4—101no—
528C2×C3×C4—101no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4C2×C4×D512yes—
538C2×C3×C4C2×C4×D512yes—
539C2×C3×C4D4×D512yes—
540C22×C5—22no—
541C22×C5—22no—
542C22×C5—22no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—41no—
546C22×C5—41no—
547C22×C5C23×C3×C411yescharacteristic
548C22×C5C22×C3×D411yescharacteristic
549C22×C5C2×C3×#4111yescharacteristic
550C22×C5C3×H(5,𝔽2)11yescharacteristic
551C22×C5C3×2−1+411yescharacteristic
552C22×C5C3×2−1+411yescharacteristic
553C22×C5C3×2−1+411yescharacteristic
554C4×C5—22no—
555C4×C5—22no—
556C4×C5—22no—
557C4×C5—41no—
558C4×C5—41no—
559C4×C5—41no—
560Dic5—22no—
561Dic5—22no—
562Dic5—22no—
563Dic5—22no—
564Dic5—41no—
565Dic5—41no—
566Dic5—41no—
567Dic5C3×C4×D414yes—
568C24C22×C3×D511yescharacteristic
569C2×Q8—54no—
570C2×Q8—102no—
571C2×Q8—102no—
572C22×C4—51no—
573C22×C4—54no—
574C22×C4—51no—
575C22×C4—51no—
576C22×C4—51no—
577C22×C4—51no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—51no—
581C22×C4—102no—
582C22×C4—102no—
583C22×C4C22×C3×D511yescharacteristic
584C22×C4C22×C3×D511yescharacteristic
585C22×C4C22×C3×D511yescharacteristic
586C22×C4C22×C3×D511yescharacteristic
587C22×C4C22×C3×D511yescharacteristic
588C22×C4C22×C3×D511yescharacteristic
589C4⋊C4—41no—
590C4⋊C4—54no—
591C4⋊C4—54no—
592C4⋊C4—54no—
593C4⋊C4—102no—
594C4⋊C4—102no—
595C4⋊C4—102no—
596C4⋊C4—102no—
597C4⋊C4—102no—
598C4⋊C4—102no—
599C4⋊C4—201no—
600C22⋊C4—22no—
601C22⋊C4—41no—
602C22⋊C4—54no—
603C22⋊C4—102no—
604C22⋊C4—201no—
605C22⋊C4C3×C4×D514yes—
606C42—22no—
607C42—54no—
608C42—102no—
609C42—102no—
610C42—201no—
611C42—201no—
612C3×C5#232311yescharacteristic, complemented, Hall
613C22×C3—22no—
614C22×C3—22no—
615C22×C3—22no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3C22×C4×D511yescharacteristic
621C22×C3C2×D4×D511yescharacteristic
622C22×C3#414411yescharacteristic
623C22×C3D5×#4111yescharacteristic
624C22×C3#415011yescharacteristic
625C22×C3#415011yescharacteristic
626C22×C3#415011yescharacteristic
627C3×C4—22no—
628C3×C4—22no—
629C3×C4—22no—
630C3×C4—41no—
631C3×C4—41no—
632C3×C4—41no—
633C3×C4—54no—
634C3×C4—102no—
635C3×C4—102no—
636C3×C4—102no—
637C3×C4—102no—
638C3×C4—201no—
639C3×C4—201no—
640C3×C4—201no—
641C2×C5—42no—
642C2×C5C2×C3×C4×D411yescharacteristic
643C2×C5C3×#51911yescharacteristic
644C2×C5C3×#52011yescharacteristic
645C2×C5C3×#53611yescharacteristic
646C2×C5C3×#53711yescharacteristic
647C2×C5C3×#54111yescharacteristic
648C2×C5C3×#54211yescharacteristic
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23C2×C3×C4×D512yes—
656C23C23×C3×D511yescharacteristic
657Q8—108no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—52no—
674C2×C4—52no—
675C2×C4—52no—
676C2×C4—52no—
677C2×C4—52no—
678C2×C4—52no—
679C2×C4—52no—
680C2×C4—108no—
681C2×C4—101no—
682C2×C4—101no—
683C2×C4—101no—
684C2×C4—101no—
685C2×C4—101no—
686C2×C4—101no—
687C2×C4—101no—
688C2×C4—101no—
689C2×C4—101no—
690C2×C4—101no—
691C2×C4—101no—
692C2×C4—101no—
693C2×C4—101no—
694C2×C4—101no—
695C2×C4—101no—
696C2×C4—101no—
697C2×C4—101no—
698C2×C4C2×C3×C4×D512yes—
699C2×C4C2×C3×C4×D512yes—
700C2×C4C3×D4×D512yes—
701C2×C3—42no—
702C2×C3#6585011yescharacteristic
703C2×C3C4×D4×D511yescharacteristic
704C2×C3#6588011yescharacteristic
705C2×C3#6594211yescharacteristic
706C2×C3#6598211yescharacteristic
707C2×C3#6600311yescharacteristic
708C2×C3#6603511yescharacteristic
709C5C3×#232311yescharacteristic, complemented, Sylow
710C22—22no—
711C22—22no—
712C22—22no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22C22×C3×C4×D511yescharacteristic
718C22C2×C3×D4×D511yescharacteristic
719C22C3×#414411yescharacteristic
720C22C3×D5×#4111yescharacteristic
721C22C3×#415011yescharacteristic
722C22C3×#415011yescharacteristic
723C22C3×#415011yescharacteristic
724C4—22no—
725C4—22no—
726C4—22no—
727C4—41no—
728C4—41no—
729C4—41no—
730C4—54no—
731C4—102no—
732C4—102no—
733C4—102no—
734C4—102no—
735C4—201no—
736C4—201no—
737C4—201no—
738C3#1060719111yescharacteristic, direct product factor, Sylow
739C2—42no—
740C2C3×#6585011yescharacteristic
741C2C3×C4×D4×D511yescharacteristic
742C2C3×#6588011yescharacteristic
743C2C3×#6594211yescharacteristic
744C2C3×#6598211yescharacteristic
745C2C3×#6600311yescharacteristic
746C2C3×#6603511yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C3×#2323
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
3. C2×C3×C4×Dic10C2semidirect
5. C3×#65262C2semidirect
6. C3×#65261C2semidirect
11. C3×#65222C2semidirect
12. C3×#64942C2semidirect
13. C3×#64938C2semidirect
14. C3×#64936C2semidirect
15. C3×#64935C2semidirect
16. #10607191C3direct (N × H)
42. C3×#4024C4semidirect
58. C2×C4×Dic10C2×C3semidirect
60. #65262C2×C3semidirect
61. #65261C2×C3semidirect
66. #65222C2×C3semidirect
67. #64942C2×C3semidirect
68. #64938C2×C3semidirect
69. #64936C2×C3semidirect
70. #64935C2×C3semidirect
155. #4024C3×C4semidirect
612. C3×C5#2323semidirect
709. C5C3×#2323semidirect
738. C3#10607191direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40242
C2×C3×#40232
C2×C3×C4×Dic102
C3×C5×#3882
C3×#652622
C3×#652612
C3×#652402
C3×#652332
C3×#652312
C3×#652222
C3×#649422
C3×#649382
C3×#649362
C3×#649352
#106071913
C3×#23235