Finite Group Databasebeta

← C3×#10606707 #14330992

Subgroups — C3×#10606707 #14330992

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4042C211yesmaximal, characteristic
2C3×C5×#387C211yesmaximal, characteristic, complemented
3C3×#65276C211yesmaximal, characteristic
4C3×#65274C211yesmaximal, characteristic, complemented
5C3×#65261C211yesmaximal, characteristic, complemented
6C3×#65229C211yesmaximal, characteristic
7C3×#65218C211yesmaximal, characteristic, complemented
8C3×#64959C211yesmaximal, characteristic
9C3×#64959C211yesmaximal, characteristic
10C3×#64958C211yesmaximal, characteristic
11C3×#64953C211yesmaximal, characteristic
12C3×#64944C211yesmaximal, characteristic, complemented
13C3×#64944C211yesmaximal, characteristic, complemented
14C3×#64941C211yesmaximal, characteristic, complemented
15C3×#64935C211yesmaximal, characteristic, complemented
16#10606707C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C4×D5C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C2×C3×C5×C4⋊C4C2211yescharacteristic
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C2×C3×C42×C5C2211yescharacteristic
22C2×C3×#685C2211yescharacteristic
23C2×C3×#685C2211yescharacteristic
24C2×C3×#685C2211yescharacteristic
25C2×C3×#685C2211yescharacteristic
26C2×C3×#685C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×C4⋊Dic5C2211yescharacteristic
29C2×C3×C4⋊Dic5C2211yescharacteristic
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×#683C2211yescharacteristic
33C2×C3×#683C2211yescharacteristic
34C2×C3×#683C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C3×#4042C418yescomplemented
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41C3×C5×#95C2211yescharacteristic
42C3×C5×#95C2211yescharacteristic
43C3×#3963C2211yescharacteristic
44C3×#3963C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#2378—51nomaximal, Hall
54C2×#4042C2×C311yescharacteristic
55C5×#387C2×C311yescharacteristic, complemented
56#65276C2×C311yescharacteristic
57#65274C2×C311yescharacteristic, complemented
58#65261C2×C311yescharacteristic, complemented
59#65229C2×C311yescharacteristic
60#65218C2×C311yescharacteristic, complemented
61#64959C2×C311yescharacteristic
62#64959C2×C311yescharacteristic
63#64958C2×C311yescharacteristic
64#64953C2×C311yescharacteristic
65#64944C2×C311yescharacteristic, complemented
66#64944C2×C311yescharacteristic, complemented
67#64941C2×C311yescharacteristic, complemented
68#64935C2×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—41no—
85C2×C3×C4×D5—41no—
86C2×C3×C4×D5C2×C414yes—
87C2×C3×Dic10—41no—
88C2×C3×Dic10—41no—
89C2×C3×Dic10C2×C414yes—
90C3×C5×C4⋊C4—41no—
91C3×C5×C4⋊C4C2×C414yes—
92C3×C42×C5—41no—
93C3×#685—41no—
94C3×#685—41no—
95C3×#685—41no—
96C3×#685—41no—
97C3×#685C2×C414yes—
98C3×#685C2×C414yes—
99C3×C4⋊Dic5—41no—
100C3×C4⋊Dic5—41no—
101C3×C4⋊Dic5—41no—
102C3×#683—41no—
103C3×#683—41no—
104C3×#683C2×C414yes—
105C3×#683C2×C414yes—
106C3×C4×Dic5—41no—
107C3×C4×Dic5—41no—
108C3×C4×Dic5—41no—
109C2×C3×C22⋊Q8—51no—
110C3×#391—51no—
111C3×#391—51no—
112C3×#389—51no—
113C3×#389—51no—
114C3×#388—51no—
115C3×#388—51no—
116C3×#388—51no—
117C3×#388—51no—
118C3×#387—51no—
119C3×#387—51no—
120C3×#387—51no—
121C3×#387D511yescharacteristic, complemented
122C3×#381—51no—
123C3×#380—51no—
124C22×C4×D5C22×C311yescharacteristic
125C22×Dic10C22×C311yescharacteristic
126C2×C5×C4⋊C4C22×C311yescharacteristic
127C2×C5×C4⋊C4C22×C311yescharacteristic
128C2×C42×C5C22×C311yescharacteristic
129C2×#685C22×C311yescharacteristic
130C2×#685C22×C311yescharacteristic
131C2×#685C22×C311yescharacteristic
132C2×#685C22×C311yescharacteristic
133C2×#685C22×C311yescharacteristic
134C2×#685C22×C311yescharacteristic
135C2×C4⋊Dic5C22×C311yescharacteristic
136C2×C4⋊Dic5C22×C311yescharacteristic
137C2×C4⋊Dic5C22×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
145#4042C3×C418yescomplemented
146C5×#95C22×C311yescharacteristic
147C5×#95C22×C311yescharacteristic
148C5×#95C22×C311yescharacteristic
149C5×#95C22×C311yescharacteristic
150#3963C22×C311yescharacteristic
151#3963C22×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#2378—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×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5C22×C412yes—
209C2×C3×Dic5C22×C412yes—
210C2×C3×Dic5C22×C412yes—
211C3×C4×D5—44no—
212C3×Dic10—44no—
213C22×C3×Q8—51no—
214C23×C3×C4—51no—
215C3×C22⋊Q8—58no—
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⋊C4—51no—
223C2×C3×C4⋊C4C2×D511yescharacteristic
224C2×C3×C4⋊C4C2×D511yescharacteristic
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×C22⋊C4—51no—
231C2×C3×C42—51no—
232C2×C3×C42—51no—
233C2×C3×C42—51no—
234C2×C3×C42C2×D511yescharacteristic
235C3×#95—51no—
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×#95—51no—
245C3×#95C2×D511yescharacteristic
246C3×#95C2×D511yescharacteristic
247C3×#95C2×D511yescharacteristic
248C3×#95C2×D511yescharacteristic
249C23×D5C23×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×C4×C5C23×C311yescharacteristic
257C22×Dic5C23×C311yescharacteristic
258C22×Dic5C23×C311yescharacteristic
259C22×Dic5C23×C311yescharacteristic
260C22×Dic5C23×C311yescharacteristic
261C22×Dic5C23×C311yescharacteristic
262C22×Dic5C23×C311yescharacteristic
263C22×Dic5C23×C311yescharacteristic
264C2×C4×D5—41no—
265C2×C4×D5—41no—
266C2×C4×D5C2×C3×C414yes—
267C2×Dic10—41no—
268C2×Dic10—41no—
269C2×Dic10C2×C3×C414yes—
270C5×C4⋊C4—41no—
271C5×C4⋊C4C2×C3×C414yes—
272C42×C5—41no—
273#685—41no—
274#685—41no—
275#685—41no—
276#685—41no—
277#685C2×C3×C414yes—
278#685C2×C3×C414yes—
279C4⋊Dic5—41no—
280C4⋊Dic5—41no—
281C4⋊Dic5—41no—
282#683—41no—
283#683—41no—
284#683C2×C3×C414yes—
285#683C2×C3×C414yes—
286C4×Dic5—41no—
287C4×Dic5—41no—
288C4×Dic5—41no—
289C2×C22⋊Q8—51no—
290#391—51no—
291#391—51no—
292#389—51no—
293#389—51no—
294#388—51no—
295#388—51no—
296#388—51no—
297#388—51no—
298#387—51no—
299#387—51no—
300#387—51no—
301#387C3×D511yescharacteristic, complemented
302#381—51no—
303#380—51no—
304C22×C3×C5C23×C411yescharacteristic
305C22×C3×C5H(5,𝔽2)11yescharacteristic
306C22×C3×C5H(5,𝔽2)11yescharacteristic
307C22×C3×C5H(5,𝔽2)11yescharacteristic
308C22×C3×C52−1+411yescharacteristic
309C22×C3×C52−1+411yescharacteristic
310C22×C3×C52−1+411yescharacteristic
311C2×C3×D5—22no—
312C2×C3×D5—22no—
313C2×C3×D5—22no—
314C2×C3×D5—41no—
315C2×C3×D5—41no—
316C2×C3×D5—41no—
317C2×C3×D5—41no—
318C3×C4×C5—22no—
319C3×C4×C5—22no—
320C3×C4×C5—22no—
321C3×C4×C5—41no—
322C3×C4×C5—41no—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×Dic5—22no—
326C3×Dic5—22no—
327C3×Dic5—22no—
328C3×Dic5—41no—
329C3×Dic5—41no—
330C3×Dic5—41no—
331C3×Dic5—41no—
332C24×C3—51no—
333C2×C3×Q8—54no—
334C2×C3×Q8—201no—
335C2×C3×Q8—201no—
336C22×C3×C4—51no—
337C22×C3×C4—51no—
338C22×C3×C4—51no—
339C22×C3×C4—54no—
340C22×C3×C4—51no—
341C22×C3×C4—51no—
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C22×C3×C4—201no—
345C22×C3×C4—201no—
346C22×C3×C4C22×D511yescharacteristic
347C22×C3×C4C22×D511yescharacteristic
348C22×C3×C4C22×D511yescharacteristic
349C22×C3×C4C22×D511yescharacteristic
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D511yescharacteristic
352C22×C3×C4C22×D511yescharacteristic
353C3×C4⋊C4—41no—
354C3×C4⋊C4—54no—
355C3×C4⋊C4—54no—
356C3×C4⋊C4—201no—
357C3×C4⋊C4—201no—
358C3×C4⋊C4—201no—
359C3×C4⋊C4—201no—
360C3×C4⋊C4—201no—
361C3×C4⋊C4C4×D514yes—
362C3×C22⋊C4—54no—
363C3×C22⋊C4—54no—
364C3×C22⋊C4—201no—
365C3×C22⋊C4—201no—
366C3×C22⋊C4—201no—
367C3×C22⋊C4—201no—
368C3×C42—41no—
369C3×C42—201no—
370C3×C42—201no—
371C3×C42—201no—
372C23×C5C24×C311yescharacteristic
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—21no—
376C22×D5—21no—
377C22×D5—21no—
378C22×D5—21no—
379C22×D5C22×C3×C412yes—
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×C5—21no—
398C2×C4×C5C22×C3×C412yes—
399C2×C4×C5C22×C3×C412yes—
400C2×C4×C5C22×C3×C412yes—
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×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5C22×C3×C412yes—
420C2×Dic5C22×C3×C412yes—
421C2×Dic5C22×C3×C412yes—
422C4×D5—44no—
423Dic10—44no—
424C22×Q8—51no—
425C23×C4—51no—
426C22⋊Q8—58no—
427C2×C4⋊C4—51no—
428C2×C4⋊C4—51no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—51no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4C2×C3×D511yescharacteristic
435C2×C4⋊C4C2×C3×D511yescharacteristic
436C2×C22⋊C4—51no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—51no—
439C2×C22⋊C4—51no—
440C2×C22⋊C4—51no—
441C2×C22⋊C4—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#95—51no—
455#95—51no—
456#95C2×C3×D511yescharacteristic
457#95C2×C3×D511yescharacteristic
458#95C2×C3×D511yescharacteristic
459#95C2×C3×D511yescharacteristic
460C2×C3×C5#51811yescharacteristic
461C2×C3×C5#51911yescharacteristic
462C2×C3×C5#52011yescharacteristic
463C2×C3×C5#56211yescharacteristic
464C2×C3×C5#56211yescharacteristic
465C2×C3×C5#56311yescharacteristic
466C2×C3×C5#56311yescharacteristic
467C3×D5—42no—
468C23×C3—52no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3—101no—
474C23×C3—101no—
475C23×C3C23×D511yescharacteristic
476C3×Q8—204no—
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—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—52no—
496C2×C3×C4—52no—
497C2×C3×C4—52no—
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×C4—101no—
515C2×C3×C4—101no—
516C2×C3×C4—204no—
517C2×C3×C4C2×C4×D512yes—
518C2×C3×C4C2×C4×D512yes—
519C2×C3×C4C2×C4×D512yes—
520C22×C5C23×C3×C411yescharacteristic
521C22×C5C3×H(5,𝔽2)11yescharacteristic
522C22×C5C3×H(5,𝔽2)11yescharacteristic
523C22×C5C3×H(5,𝔽2)11yescharacteristic
524C22×C5C3×2−1+411yescharacteristic
525C22×C5C3×2−1+411yescharacteristic
526C22×C5C3×2−1+411yescharacteristic
527C2×D5—22no—
528C2×D5—22no—
529C2×D5—22no—
530C2×D5—41no—
531C2×D5—41no—
532C2×D5—41no—
533C2×D5—41no—
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—22no—
537C4×C5—41no—
538C4×C5—41no—
539C4×C5—41no—
540C4×C5—41no—
541Dic5—22no—
542Dic5—22no—
543Dic5—22no—
544Dic5—41no—
545Dic5—41no—
546Dic5—41no—
547Dic5—41no—
548C24—51no—
549C2×Q8—54no—
550C2×Q8—201no—
551C2×Q8—201no—
552C22×C4—51no—
553C22×C4—51no—
554C22×C4—51no—
555C22×C4—54no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—201no—
561C22×C4—201no—
562C22×C4C22×C3×D511yescharacteristic
563C22×C4C22×C3×D511yescharacteristic
564C22×C4C22×C3×D511yescharacteristic
565C22×C4C22×C3×D511yescharacteristic
566C22×C4C22×C3×D511yescharacteristic
567C22×C4C22×C3×D511yescharacteristic
568C22×C4C22×C3×D511yescharacteristic
569C4⋊C4—41no—
570C4⋊C4—54no—
571C4⋊C4—54no—
572C4⋊C4—201no—
573C4⋊C4—201no—
574C4⋊C4—201no—
575C4⋊C4—201no—
576C4⋊C4—201no—
577C4⋊C4C3×C4×D514yes—
578C22⋊C4—54no—
579C22⋊C4—54no—
580C22⋊C4—201no—
581C22⋊C4—201no—
582C22⋊C4—201no—
583C22⋊C4—201no—
584C42—41no—
585C42—201no—
586C42—201no—
587C42—201no—
588C3×C5#237811yescharacteristic, complemented, Hall
589C22×C3—102no—
590C22×C3—102no—
591C22×C3—102no—
592C22×C3—201no—
593C22×C3—201no—
594C22×C3—201no—
595C22×C3—201no—
596C22×C3C22×C4×D511yescharacteristic
597C22×C3#414411yescharacteristic
598C22×C3#414711yescharacteristic
599C22×C3#414911yescharacteristic
600C22×C3#414911yescharacteristic
601C22×C3#415011yescharacteristic
602C22×C3#415011yescharacteristic
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—22no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—41no—
610C3×C4—102no—
611C3×C4—102no—
612C3×C4—102no—
613C3×C4—201no—
614C3×C4—201no—
615C3×C4—201no—
616C3×C4—201no—
617C2×C5C3×#51811yescharacteristic
618C2×C5C3×#51911yescharacteristic
619C2×C5C3×#52011yescharacteristic
620C2×C5C3×#56211yescharacteristic
621C2×C5C3×#56211yescharacteristic
622C2×C5C3×#56311yescharacteristic
623C2×C5C3×#56311yescharacteristic
624D5—42no—
625C23—52no—
626C23—101no—
627C23—101no—
628C23—101no—
629C23—101no—
630C23—101no—
631C23—101no—
632C23C23×C3×D511yescharacteristic
633Q8—204no—
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—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—52no—
653C2×C4—52no—
654C2×C4—52no—
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×C4—101no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—204no—
674C2×C4C2×C3×C4×D512yes—
675C2×C4C2×C3×C4×D512yes—
676C2×C4C2×C3×C4×D512yes—
677C2×C3—202no—
678C2×C3#6585711yescharacteristic
679C2×C3#6587911yescharacteristic
680C2×C3#6590611yescharacteristic
681C2×C3#6598011yescharacteristic
682C2×C3#6600111yescharacteristic
683C2×C3#6603411yescharacteristic
684C2×C3#6604611yescharacteristic
685C5C3×#237811yescharacteristic, complemented, Sylow
686C22—102no—
687C22—102no—
688C22—102no—
689C22—201no—
690C22—201no—
691C22—201no—
692C22—201no—
693C22C22×C3×C4×D511yescharacteristic
694C22C3×#414411yescharacteristic
695C22C3×#414711yescharacteristic
696C22C3×#414911yescharacteristic
697C22C3×#414911yescharacteristic
698C22C3×#415011yescharacteristic
699C22C3×#415011yescharacteristic
700C4—22no—
701C4—22no—
702C4—22no—
703C4—41no—
704C4—41no—
705C4—41no—
706C4—41no—
707C4—102no—
708C4—102no—
709C4—102no—
710C4—201no—
711C4—201no—
712C4—201no—
713C4—201no—
714C3#1060670711yescharacteristic, direct product factor, Sylow
715C2—202no—
716C2C3×#6585711yescharacteristic
717C2C3×#6587911yescharacteristic
718C2C3×#6590611yescharacteristic
719C2C3×#6598011yescharacteristic
720C2C3×#6600111yescharacteristic
721C2C3×#6603411yescharacteristic
722C2C3×#6604611yescharacteristic
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×#2378
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×#65274C2semidirect
5. C3×#65261C2semidirect
7. C3×#65218C2semidirect
12. C3×#64944C2semidirect
13. C3×#64944C2semidirect
14. C3×#64941C2semidirect
15. C3×#64935C2semidirect
16. #10606707C3direct (N × H)
38. C3×#4042C4semidirect
55. C5×#387C2×C3semidirect
57. #65274C2×C3semidirect
58. #65261C2×C3semidirect
60. #65218C2×C3semidirect
65. #64944C2×C3semidirect
66. #64944C2×C3semidirect
67. #64941C2×C3semidirect
68. #64935C2×C3semidirect
121. C3×#387D5semidirect
145. #4042C3×C4semidirect
301. #387C3×D5semidirect
588. C3×C5#2378semidirect
685. C5C3×#2378semidirect
714. C3#10606707direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40422
C3×C5×#3872
C3×#652762
C3×#652742
C3×#652612
C3×#652292
C3×#652182
C3×#649592
C3×#649582
C3×#649532
C3×#649442
C3×#649412
C3×#649352
#106067073
C3×#23785