Finite Group Databasebeta

← C3×#10606675 #14322705

Subgroups — C3×#10606675 #14322705

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4038C211yesmaximal, characteristic
2C3×C5×#387C211yesmaximal, characteristic, complemented
3C3×#65279C211yesmaximal, characteristic
4C3×#65270C211yesmaximal, characteristic, complemented
5C3×#65265C211yesmaximal, characteristic, complemented
6C3×#65229C211yesmaximal, characteristic
7C3×C4×#683C211yesmaximal, characteristic, complemented
8C3×#64959C211yesmaximal, characteristic
9C3×#64958C211yesmaximal, characteristic
10C3×#64956C211yesmaximal, characteristic
11C3×#64956C211yesmaximal, characteristic
12C3×#64943C211yesmaximal, characteristic, complemented
13C3×#64942C211yesmaximal, characteristic, complemented
14C3×#64939C211yesmaximal, characteristic, complemented
15C3×#64938C211yesmaximal, characteristic, complemented
16#10606675C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×C3×#685C2211yescharacteristic
22C2×C3×#685C2211yescharacteristic
23C2×C3×#685C2211yescharacteristic
24C2×C3×#685C2211yescharacteristic
25C2×C3×#685C2211yescharacteristic
26C2×C3×#685C2211yescharacteristic
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×C4×Dic5C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C2×C3×C4×Dic5C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C3×#4038C418yescomplemented
41C3×C5×#95C2211yescharacteristic
42C3×C5×#95C2211yescharacteristic
43C3×C5×#95C2211yescharacteristic
44C3×C5×#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#2314—51nomaximal, Hall
54C2×#4038C2×C311yescharacteristic
55C5×#387C2×C311yescharacteristic, complemented
56#65279C2×C311yescharacteristic
57#65270C2×C311yescharacteristic, complemented
58#65265C2×C311yescharacteristic, complemented
59#65229C2×C311yescharacteristic
60C4×#683C2×C311yescharacteristic, complemented
61#64959C2×C311yescharacteristic
62#64958C2×C311yescharacteristic
63#64956C2×C311yescharacteristic
64#64956C2×C311yescharacteristic
65#64943C2×C311yescharacteristic, complemented
66#64942C2×C311yescharacteristic, complemented
67#64939C2×C311yescharacteristic, complemented
68#64938C2×C311yescharacteristic, complemented
69C23×C3×D5C2311yescharacteristic
70C22×C3×C4×C5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×Dic5C2311yescharacteristic
78C22×C3×Dic5C2311yescharacteristic
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C2×C3×C4×D5—22no—
85C2×C3×C4×D5—22no—
86C2×C3×C4×D5C2×C414yes—
87C3×C5×C4⋊C4—41no—
88C3×C5×C4⋊C4C2×C414yes—
89C3×C42×C5—41no—
90C3×#685—41no—
91C3×#685—41no—
92C3×#685—41no—
93C3×#685—41no—
94C3×#685C2×C414yes—
95C3×#685C2×C414yes—
96C3×C4⋊Dic5—41no—
97C3×C4⋊Dic5C2×C414yes—
98C3×#683—22no—
99C3×#683—22no—
100C3×#683—22no—
101C3×#683—22no—
102C3×#683—41no—
103C3×#683—41no—
104C3×C4×Dic5—41no—
105C3×C4×Dic5—41no—
106C3×C4×Dic5—41no—
107C3×C4×Dic5C2×C414yes—
108C3×C4×Dic5C2×C414yes—
109C2×C3×#117—51no—
110C3×#388—51no—
111C3×#388—51no—
112C3×#388—51no—
113C3×#388—51no—
114C3×#387—51no—
115C3×#387—51no—
116C3×#387—51no—
117C3×#387D511yescharacteristic, complemented
118C3×#384—51no—
119C3×#382—51no—
120C3×#380—51no—
121C3×#380—51no—
122C3×C4×C4⋊C4—51no—
123C3×C4×C4⋊C4—51no—
124C22×C4×D5C22×C311yescharacteristic
125C2×C5×C4⋊C4C22×C311yescharacteristic
126C2×C5×C4⋊C4C22×C311yescharacteristic
127C2×C42×C5C22×C311yescharacteristic
128C2×#685C22×C311yescharacteristic
129C2×#685C22×C311yescharacteristic
130C2×#685C22×C311yescharacteristic
131C2×#685C22×C311yescharacteristic
132C2×#685C22×C311yescharacteristic
133C2×#685C22×C311yescharacteristic
134C2×C4⋊Dic5C22×C311yescharacteristic
135C2×C4⋊Dic5C22×C311yescharacteristic
136C2×#683C22×C311yescharacteristic
137C2×#683C22×C311yescharacteristic
138C2×#683C22×C311yescharacteristic
139C2×#683C22×C311yescharacteristic
140C2×#683C22×C311yescharacteristic
141C2×#683C22×C311yescharacteristic
142C2×C4×Dic5C22×C311yescharacteristic
143C2×C4×Dic5C22×C311yescharacteristic
144C2×C4×Dic5C22×C311yescharacteristic
145C2×C4×Dic5C22×C311yescharacteristic
146C2×C4×Dic5C22×C311yescharacteristic
147#4038C3×C418yescomplemented
148C5×#95C22×C311yescharacteristic
149C5×#95C22×C311yescharacteristic
150C5×#95C22×C311yescharacteristic
151C5×#95C22×C311yescharacteristic
152#3963C22×C311yescharacteristic
153#3963C22×C311yescharacteristic
154#3963C22×C311yescharacteristic
155#3963C22×C311yescharacteristic
156#3963C22×C311yescharacteristic
157#3963C22×C311yescharacteristic
158#3963C22×C311yescharacteristic
159#3963C22×C311yescharacteristic
160#2314—51noSylow
161C23×C3×C5C2411yescharacteristic
162C22×C3×D5—21no—
163C22×C3×D5—21no—
164C22×C3×D5—21no—
165C22×C3×D5—21no—
166C22×C3×D5—21no—
167C22×C3×D5—21no—
168C22×C3×D5C22×C412yes—
169C2×C3×C4×C5—21no—
170C2×C3×C4×C5—21no—
171C2×C3×C4×C5—21no—
172C2×C3×C4×C5—21no—
173C2×C3×C4×C5—21no—
174C2×C3×C4×C5—21no—
175C2×C3×C4×C5—21no—
176C2×C3×C4×C5—21no—
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×C5C22×C412yes—
188C2×C3×C4×C5C22×C412yes—
189C2×C3×C4×C5C22×C412yes—
190C2×C3×Dic5—21no—
191C2×C3×Dic5—21no—
192C2×C3×Dic5—21no—
193C2×C3×Dic5—21no—
194C2×C3×Dic5—21no—
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—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5C22×C412yes—
207C2×C3×Dic5C22×C412yes—
208C2×C3×Dic5C22×C412yes—
209C2×C3×Dic5#4112yes—
210C2×C3×Dic5#4112yes—
211C3×C4×D5—28no—
212C23×C3×C4—51no—
213C3×#117—58no—
214C2×C3×C4⋊C4—51no—
215C2×C3×C4⋊C4—51no—
216C2×C3×C4⋊C4—51no—
217C2×C3×C4⋊C4—51no—
218C2×C3×C4⋊C4—51no—
219C2×C3×C4⋊C4—51no—
220C2×C3×C4⋊C4—51no—
221C2×C3×C4⋊C4—51no—
222C2×C3×C4⋊C4C2×D511yescharacteristic
223C2×C3×C4⋊C4C2×D511yescharacteristic
224C2×C3×C22⋊C4—51no—
225C2×C3×C22⋊C4—51no—
226C2×C3×C22⋊C4—51no—
227C2×C3×C22⋊C4—51no—
228C2×C3×C22⋊C4—51no—
229C2×C3×C22⋊C4—51no—
230C2×C3×C42—51no—
231C2×C3×C42—51no—
232C2×C3×C42—51no—
233C2×C3×C42—51no—
234C2×C3×C42—51no—
235C2×C3×C42C2×D511yescharacteristic
236C3×#95—51no—
237C3×#95—51no—
238C3×#95—51no—
239C3×#95—51no—
240C3×#95—51no—
241C3×#95—51no—
242C3×#95—51no—
243C3×#95—51no—
244C3×#95C2×D511yescharacteristic
245C3×#95C2×D511yescharacteristic
246C3×#95C2×D511yescharacteristic
247C3×#95C2×D511yescharacteristic
248C23×D5C23×C311yescharacteristic
249C22×C4×C5C23×C311yescharacteristic
250C22×C4×C5C23×C311yescharacteristic
251C22×C4×C5C23×C311yescharacteristic
252C22×C4×C5C23×C311yescharacteristic
253C22×C4×C5C23×C311yescharacteristic
254C22×C4×C5C23×C311yescharacteristic
255C22×C4×C5C23×C311yescharacteristic
256C22×Dic5C23×C311yescharacteristic
257C22×Dic5C23×C311yescharacteristic
258C22×Dic5C23×C311yescharacteristic
259C22×Dic5C23×C311yescharacteristic
260C22×Dic5C23×C311yescharacteristic
261C22×Dic5C23×C311yescharacteristic
262C22×Dic5C23×C311yescharacteristic
263C2×C4×D5—22no—
264C2×C4×D5—22no—
265C2×C4×D5C2×C3×C414yes—
266C5×C4⋊C4—41no—
267C5×C4⋊C4C2×C3×C414yes—
268C42×C5—41no—
269#685—41no—
270#685—41no—
271#685—41no—
272#685—41no—
273#685C2×C3×C414yes—
274#685C2×C3×C414yes—
275C4⋊Dic5—41no—
276C4⋊Dic5C2×C3×C414yes—
277#683—22no—
278#683—22no—
279#683—22no—
280#683—22no—
281#683—41no—
282#683—41no—
283C4×Dic5—41no—
284C4×Dic5—41no—
285C4×Dic5—41no—
286C4×Dic5C2×C3×C414yes—
287C4×Dic5C2×C3×C414yes—
288C2×#117—51no—
289#388—51no—
290#388—51no—
291#388—51no—
292#388—51no—
293#387—51no—
294#387—51no—
295#387—51no—
296#387C3×D511yescharacteristic, complemented
297#384—51no—
298#382—51no—
299#380—51no—
300#380—51no—
301C4×C4⋊C4—51no—
302C4×C4⋊C4—51no—
303C22×C3×C5C23×C411yescharacteristic
304C22×C3×C5C2×#4111yescharacteristic
305C22×C3×C5C2×#4111yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C22×C3×C52−1+411yescharacteristic
309C22×C3×C52−1+411yescharacteristic
310C2×C3×D5—22no—
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—41no—
314C2×C3×D5—41no—
315C2×C3×D5—41no—
316C2×C3×D5—41no—
317C3×C4×C5—22no—
318C3×C4×C5—22no—
319C3×C4×C5—22no—
320C3×C4×C5—41no—
321C3×C4×C5—41no—
322C3×C4×C5—41no—
323C3×C4×C5—41no—
324C3×Dic5—22no—
325C3×Dic5—22no—
326C3×Dic5—41no—
327C3×Dic5—41no—
328C3×Dic5—41no—
329C3×Dic5—41no—
330C3×Dic5#11714yes—
331C24×C3—51no—
332C22×C3×C4—51no—
333C22×C3×C4—51no—
334C22×C3×C4—51no—
335C22×C3×C4—54no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4—51no—
339C22×C3×C4—51no—
340C22×C3×C4—102no—
341C22×C3×C4—102no—
342C22×C3×C4C22×D511yescharacteristic
343C22×C3×C4C22×D511yescharacteristic
344C22×C3×C4C22×D511yescharacteristic
345C22×C3×C4C22×D511yescharacteristic
346C22×C3×C4C22×D511yescharacteristic
347C22×C3×C4C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C3×C4⋊C4—41no—
350C3×C4⋊C4—54no—
351C3×C4⋊C4—102no—
352C3×C4⋊C4—102no—
353C3×C4⋊C4—102no—
354C3×C4⋊C4—102no—
355C3×C4⋊C4—201no—
356C3×C4⋊C4—201no—
357C3×C4⋊C4—201no—
358C3×C4⋊C4C4×D514yes—
359C3×C22⋊C4—54no—
360C3×C22⋊C4—54no—
361C3×C22⋊C4—201no—
362C3×C22⋊C4—201no—
363C3×C22⋊C4—201no—
364C3×C22⋊C4—201no—
365C3×C42—41no—
366C3×C42—54no—
367C3×C42—54no—
368C3×C42—201no—
369C3×C42—201no—
370C3×C42—201no—
371C23×C5C24×C311yescharacteristic
372C22×D5—21no—
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—21no—
376C22×D5—21no—
377C22×D5—21no—
378C22×D5C22×C3×C412yes—
379C2×C4×C5—21no—
380C2×C4×C5—21no—
381C2×C4×C5—21no—
382C2×C4×C5—21no—
383C2×C4×C5—21no—
384C2×C4×C5—21no—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—21no—
388C2×C4×C5—21no—
389C2×C4×C5—21no—
390C2×C4×C5—21no—
391C2×C4×C5—21no—
392C2×C4×C5—21no—
393C2×C4×C5—21no—
394C2×C4×C5—21no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5C22×C3×C412yes—
398C2×C4×C5C22×C3×C412yes—
399C2×C4×C5C22×C3×C412yes—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—21no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—21no—
410C2×Dic5—21no—
411C2×Dic5—21no—
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—21no—
415C2×Dic5—21no—
416C2×Dic5C22×C3×C412yes—
417C2×Dic5C22×C3×C412yes—
418C2×Dic5C22×C3×C412yes—
419C2×Dic5C3×#4112yes—
420C2×Dic5C3×#4112yes—
421C4×D5—28no—
422C23×C4—51no—
423#117—58no—
424C2×C4⋊C4—51no—
425C2×C4⋊C4—51no—
426C2×C4⋊C4—51no—
427C2×C4⋊C4—51no—
428C2×C4⋊C4—51no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—51no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4C2×C3×D511yescharacteristic
433C2×C4⋊C4C2×C3×D511yescharacteristic
434C2×C22⋊C4—51no—
435C2×C22⋊C4—51no—
436C2×C22⋊C4—51no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—51no—
439C2×C22⋊C4—51no—
440C2×C42—51no—
441C2×C42—51no—
442C2×C42—51no—
443C2×C42—51no—
444C2×C42—51no—
445C2×C42C2×C3×D511yescharacteristic
446#95—51no—
447#95—51no—
448#95—51no—
449#95—51no—
450#95—51no—
451#95—51no—
452#95—51no—
453#95—51no—
454#95C2×C3×D511yescharacteristic
455#95C2×C3×D511yescharacteristic
456#95C2×C3×D511yescharacteristic
457#95C2×C3×D511yescharacteristic
458C2×C3×C5C2×#11711yescharacteristic
459C2×C3×C5#52011yescharacteristic
460C2×C3×C5#52011yescharacteristic
461C2×C3×C5#54011yescharacteristic
462C2×C3×C5#54111yescharacteristic
463C2×C3×C5#54211yescharacteristic
464C2×C3×C5#54211yescharacteristic
465C3×D5—42no—
466C23×C3—52no—
467C23×C3—101no—
468C23×C3—101no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3C23×D511yescharacteristic
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—52no—
493C2×C3×C4—52no—
494C2×C3×C4—52no—
495C2×C3×C4—52no—
496C2×C3×C4—52no—
497C2×C3×C4—108no—
498C2×C3×C4—101no—
499C2×C3×C4—101no—
500C2×C3×C4—101no—
501C2×C3×C4—101no—
502C2×C3×C4—101no—
503C2×C3×C4—101no—
504C2×C3×C4—101no—
505C2×C3×C4—101no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4—101no—
509C2×C3×C4—101no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—101no—
513C2×C3×C4—101no—
514C2×C3×C4C2×C4×D512yes—
515C2×C3×C4C2×C4×D512yes—
516C2×C3×C4C2×C4×D512yes—
517C22×C5C23×C3×C411yescharacteristic
518C22×C5C2×C3×#4111yescharacteristic
519C22×C5C2×C3×#4111yescharacteristic
520C22×C5C3×H(5,𝔽2)11yescharacteristic
521C22×C5C3×H(5,𝔽2)11yescharacteristic
522C22×C5C3×2−1+411yescharacteristic
523C22×C5C3×2−1+411yescharacteristic
524C2×D5—22no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—41no—
528C2×D5—41no—
529C2×D5—41no—
530C2×D5—41no—
531C4×C5—22no—
532C4×C5—22no—
533C4×C5—22no—
534C4×C5—41no—
535C4×C5—41no—
536C4×C5—41no—
537C4×C5—41no—
538Dic5—22no—
539Dic5—22no—
540Dic5—41no—
541Dic5—41no—
542Dic5—41no—
543Dic5—41no—
544Dic5C3×#11714yes—
545C24—51no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4—51no—
549C22×C4—54no—
550C22×C4—51no—
551C22×C4—51no—
552C22×C4—51no—
553C22×C4—51no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4C22×C3×D511yescharacteristic
557C22×C4C22×C3×D511yescharacteristic
558C22×C4C22×C3×D511yescharacteristic
559C22×C4C22×C3×D511yescharacteristic
560C22×C4C22×C3×D511yescharacteristic
561C22×C4C22×C3×D511yescharacteristic
562C22×C4C22×C3×D511yescharacteristic
563C4⋊C4—41no—
564C4⋊C4—54no—
565C4⋊C4—102no—
566C4⋊C4—102no—
567C4⋊C4—102no—
568C4⋊C4—102no—
569C4⋊C4—201no—
570C4⋊C4—201no—
571C4⋊C4—201no—
572C4⋊C4C3×C4×D514yes—
573C22⋊C4—54no—
574C22⋊C4—54no—
575C22⋊C4—201no—
576C22⋊C4—201no—
577C22⋊C4—201no—
578C22⋊C4—201no—
579C42—41no—
580C42—54no—
581C42—54no—
582C42—201no—
583C42—201no—
584C42—201no—
585C3×C5#231411yescharacteristic, complemented, Hall
586C22×C3—102no—
587C22×C3—102no—
588C22×C3—102no—
589C22×C3—201no—
590C22×C3—201no—
591C22×C3—201no—
592C22×C3—201no—
593C22×C3C22×C4×D511yescharacteristic
594C22×C3#414411yescharacteristic
595C22×C3#414711yescharacteristic
596C22×C3D5×#4111yescharacteristic
597C22×C3D5×#4111yescharacteristic
598C22×C3#414911yescharacteristic
599C22×C3#415011yescharacteristic
600C3×C4—22no—
601C3×C4—22no—
602C3×C4—22no—
603C3×C4—41no—
604C3×C4—41no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—54no—
608C3×C4—102no—
609C3×C4—102no—
610C3×C4—201no—
611C3×C4—201no—
612C3×C4—201no—
613C3×C4—201no—
614C2×C5C2×C3×#11711yescharacteristic
615C2×C5C3×#52011yescharacteristic
616C2×C5C3×#52011yescharacteristic
617C2×C5C3×#54011yescharacteristic
618C2×C5C3×#54111yescharacteristic
619C2×C5C3×#54211yescharacteristic
620C2×C5C3×#54211yescharacteristic
621D5—42no—
622C23—52no—
623C23—101no—
624C23—101no—
625C23—101no—
626C23—101no—
627C23—101no—
628C23—101no—
629C23C23×C3×D511yescharacteristic
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—52no—
649C2×C4—52no—
650C2×C4—52no—
651C2×C4—52no—
652C2×C4—52no—
653C2×C4—108no—
654C2×C4—101no—
655C2×C4—101no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—101no—
659C2×C4—101no—
660C2×C4—101no—
661C2×C4—101no—
662C2×C4—101no—
663C2×C4—101no—
664C2×C4—101no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—101no—
668C2×C4—101no—
669C2×C4—101no—
670C2×C4C2×C3×C4×D512yes—
671C2×C4C2×C3×C4×D512yes—
672C2×C4C2×C3×C4×D512yes—
673C2×C3—202no—
674C2×C3D5×#11711yescharacteristic
675C2×C3#6588011yescharacteristic
676C2×C3#6590811yescharacteristic
677C2×C3#6597411yescharacteristic
678C2×C3#6599711yescharacteristic
679C2×C3#6603011yescharacteristic
680C2×C3#6604411yescharacteristic
681C5C3×#231411yescharacteristic, complemented, Sylow
682C22—102no—
683C22—102no—
684C22—102no—
685C22—201no—
686C22—201no—
687C22—201no—
688C22—201no—
689C22C22×C3×C4×D511yescharacteristic
690C22C3×#414411yescharacteristic
691C22C3×#414711yescharacteristic
692C22C3×D5×#4111yescharacteristic
693C22C3×D5×#4111yescharacteristic
694C22C3×#414911yescharacteristic
695C22C3×#415011yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—41no—
701C4—41no—
702C4—41no—
703C4—54no—
704C4—102no—
705C4—102no—
706C4—201no—
707C4—201no—
708C4—201no—
709C4—201no—
710C3#1060667511yescharacteristic, direct product factor, Sylow
711C2—202no—
712C2C3×D5×#11711yescharacteristic
713C2C3×#6588011yescharacteristic
714C2C3×#6590811yescharacteristic
715C2C3×#6597411yescharacteristic
716C2C3×#6599711yescharacteristic
717C2C3×#6603011yescharacteristic
718C2C3×#6604411yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#387C2
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
cosocleC23×C5C24×C3
hypercenterC3×#387D5
hypocenterC5C3×#2314
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#387

Complements

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

NH ≅ G/Ntype
2. C3×C5×#387C2semidirect
4. C3×#65270C2semidirect
5. C3×#65265C2semidirect
7. C3×C4×#683C2semidirect
12. C3×#64943C2semidirect
13. C3×#64942C2semidirect
14. C3×#64939C2semidirect
15. C3×#64938C2semidirect
16. #10606675C3direct (N × H)
40. C3×#4038C4semidirect
55. C5×#387C2×C3semidirect
57. #65270C2×C3semidirect
58. #65265C2×C3semidirect
60. C4×#683C2×C3semidirect
65. #64943C2×C3semidirect
66. #64942C2×C3semidirect
67. #64939C2×C3semidirect
68. #64938C2×C3semidirect
117. C3×#387D5semidirect
147. #4038C3×C4semidirect
296. #387C3×D5semidirect
585. C3×C5#2314semidirect
681. C5C3×#2314semidirect
710. C3#10606675direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40382
C3×C5×#3872
C3×#652792
C3×#652702
C3×#652652
C3×#652292
C3×C4×#6832
C3×#649592
C3×#649582
C3×#649562
C3×#649432
C3×#649422
C3×#649392
C3×#649382
#106066753
C3×#23145