Finite Group Databasebeta

← C3×#10607223 #14330998

Subgroups — C3×#10607223 #14330998

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×#4024C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic
3C3×#65267C211yesmaximal, characteristic, complemented
4C3×#65262C211yesmaximal, characteristic, complemented
5C3×#65240C211yesmaximal, characteristic
6C3×#65234C211yesmaximal, characteristic
7C3×#65234C211yesmaximal, characteristic
8C3×#65232C211yesmaximal, characteristic
9C3×#65231C211yesmaximal, characteristic
10C3×#65222C211yesmaximal, characteristic, complemented
11C3×#65218C211yesmaximal, characteristic, complemented
12C3×#64942C211yesmaximal, characteristic, complemented
13C3×#64941C211yesmaximal, characteristic, complemented
14C3×#64936C211yesmaximal, characteristic, complemented
15C3×#64935C211yesmaximal, characteristic, complemented
16#10607223C311yesmaximal, 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×C4×Dic5C2211yescharacteristic
36C2×C3×C4×Dic5C2211yescharacteristic
37C2×C3×C4×Dic5C2211yescharacteristic
38C3×#4024C418yescomplemented
39C3×C5×#95C2211yescharacteristic
40C3×C5×#95C2211yescharacteristic
41C3×#3963C2211yescharacteristic
42C3×#3963C2211yescharacteristic
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×#4024C2×C311yescharacteristic
55C5×#388C2×C311yescharacteristic
56#65267C2×C311yescharacteristic, complemented
57#65262C2×C311yescharacteristic, complemented
58#65240C2×C311yescharacteristic
59#65234C2×C311yescharacteristic
60#65234C2×C311yescharacteristic
61#65232C2×C311yescharacteristic
62#65231C2×C311yescharacteristic
63#65222C2×C311yescharacteristic, complemented
64#65218C2×C311yescharacteristic, complemented
65#64942C2×C311yescharacteristic, complemented
66#64941C2×C311yescharacteristic, complemented
67#64936C2×C311yescharacteristic, complemented
68#64935C2×C311yescharacteristic, complemented
69C24×C3×C5C2311yescharacteristic
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×Dic5—41no—
77C22×C3×Dic5—41no—
78C22×C3×Dic5C2×C414yes—
79C22×C3×Dic5C2311yescharacteristic
80C22×C3×Dic5C2311yescharacteristic
81C22×C3×Dic5C2311yescharacteristic
82C22×C3×Dic5C2311yescharacteristic
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×C3×Dic10—41no—
88C2×C3×Dic10—41no—
89C2×C3×Dic10C2×C414yes—
90C3×C5×C4⋊C4—41no—
91C3×C5×C22⋊C4—41no—
92C3×C5×C22⋊C4—41no—
93C3×C5×C22⋊C4C2×C414yes—
94C3×C42×C5—41no—
95C3×C22⋊Dic5—41no—
96C3×C22⋊Dic5—41no—
97C3×C22⋊Dic5C2×C414yes—
98C3×C4⋊Dic5—41no—
99C3×C4⋊Dic5C2×C414yes—
100C3×#683—41no—
101C3×#683—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×#388D511yescharacteristic
118C3×#387—51no—
119C3×#387—51no—
120C3×#387—51no—
121C3×#387—51no—
122C3×#381—51no—
123C3×#380—51no—
124C23×Dic5C22×C311yescharacteristic
125C22×Dic10C22×C311yescharacteristic
126C2×C5×C4⋊C4C22×C311yescharacteristic
127C2×C5×C22⋊C4C22×C311yescharacteristic
128C2×C5×C22⋊C4C22×C311yescharacteristic
129C2×C5×C22⋊C4C22×C311yescharacteristic
130C2×C42×C5C22×C311yescharacteristic
131C2×C22⋊Dic5C22×C311yescharacteristic
132C2×C22⋊Dic5C22×C311yescharacteristic
133C2×C22⋊Dic5C22×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
145#4024C3×C418yescomplemented
146C5×#95C22×C311yescharacteristic
147C5×#95C22×C311yescharacteristic
148#3963C22×C311yescharacteristic
149#3963C22×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×C5—21no—
162C23×C3×C5—21no—
163C23×C3×C5—21no—
164C23×C3×C5—21no—
165C23×C3×C5—21no—
166C23×C3×C5—21no—
167C23×C3×C5C22×C412yes—
168C23×C3×C5C2411yescharacteristic
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×C5C22×C412yes—
186C2×C3×C4×C5C22×C412yes—
187C2×C3×Dic5—21no—
188C2×C3×Dic5—21no—
189C2×C3×Dic5—21no—
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—44no—
208C2×C3×Dic5C22×C412yes—
209C2×C3×Dic5C22×C412yes—
210C2×C3×Dic5C22×C412yes—
211C2×C3×Dic5C22×C412yes—
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⋊C4—51no—
224C2×C3×C4⋊C4C2×D511yescharacteristic
225C2×C3×C22⋊C4—51no—
226C2×C3×C22⋊C4—51no—
227C2×C3×C22⋊C4—51no—
228C2×C3×C22⋊C4C2×D511yescharacteristic
229C2×C3×C22⋊C4C2×D511yescharacteristic
230C2×C3×C22⋊C4C2×D511yescharacteristic
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×#95—51no—
246C3×#95—51no—
247C3×#95C2×D511yescharacteristic
248C3×#95C2×D511yescharacteristic
249C24×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×Dic5—41no—
257C22×Dic5—41no—
258C22×Dic5C2×C3×C414yes—
259C22×Dic5C23×C311yescharacteristic
260C22×Dic5C23×C311yescharacteristic
261C22×Dic5C23×C311yescharacteristic
262C22×Dic5C23×C311yescharacteristic
263C22×Dic5C23×C311yescharacteristic
264C22×Dic5C23×C311yescharacteristic
265C22×Dic5C23×C311yescharacteristic
266C22×Dic5C23×C311yescharacteristic
267C2×Dic10—41no—
268C2×Dic10—41no—
269C2×Dic10C2×C3×C414yes—
270C5×C4⋊C4—41no—
271C5×C22⋊C4—41no—
272C5×C22⋊C4—41no—
273C5×C22⋊C4C2×C3×C414yes—
274C42×C5—41no—
275C22⋊Dic5—41no—
276C22⋊Dic5—41no—
277C22⋊Dic5C2×C3×C414yes—
278C4⋊Dic5—41no—
279C4⋊Dic5C2×C3×C414yes—
280#683—41no—
281#683—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#388C3×D511yescharacteristic
298#387—51no—
299#387—51no—
300#387—51no—
301#387—51no—
302#381—51no—
303#380—51no—
304C22×C3×C5—22no—
305C22×C3×C5—22no—
306C22×C3×C5—22no—
307C22×C3×C5—41no—
308C22×C3×C5—41no—
309C22×C3×C5—41no—
310C22×C3×C5—41no—
311C22×C3×C5C23×C411yescharacteristic
312C22×C3×C5H(5,𝔽2)11yescharacteristic
313C22×C3×C5H(5,𝔽2)11yescharacteristic
314C22×C3×C5H(5,𝔽2)11yescharacteristic
315C22×C3×C52−1+411yescharacteristic
316C22×C3×C52−1+411yescharacteristic
317C22×C3×C52−1+411yescharacteristic
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—22no—
327C3×Dic5—22no—
328C3×Dic5—41no—
329C3×Dic5—41no—
330C3×Dic5—41no—
331C3×Dic5—41no—
332C24×C3C22×D511yescharacteristic
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—51no—
340C22×C3×C4—54no—
341C22×C3×C4—51no—
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C22×C3×C4—51no—
345C22×C3×C4—201no—
346C22×C3×C4—201no—
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—54no—
357C3×C4⋊C4—201no—
358C3×C4⋊C4—201no—
359C3×C4⋊C4—201no—
360C3×C4⋊C4—201no—
361C3×C4⋊C4—201no—
362C3×C22⋊C4—41no—
363C3×C22⋊C4—41no—
364C3×C22⋊C4—54no—
365C3×C22⋊C4—201no—
366C3×C22⋊C4—201no—
367C3×C22⋊C4C4×D514yes—
368C3×C42—41no—
369C3×C42—201no—
370C3×C42—201no—
371C3×C42—201no—
372C23×C5—21no—
373C23×C5—21no—
374C23×C5—21no—
375C23×C5—21no—
376C23×C5—21no—
377C23×C5—21no—
378C23×C5C22×C3×C412yes—
379C23×C5C24×C311yescharacteristic
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×C5C22×C3×C412yes—
397C2×C4×C5C22×C3×C412yes—
398C2×Dic5—21no—
399C2×Dic5—21no—
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×Dic5—21no—
417C2×Dic5—21no—
418C2×Dic5—44no—
419C2×Dic5C22×C3×C412yes—
420C2×Dic5C22×C3×C412yes—
421C2×Dic5C22×C3×C412yes—
422C2×Dic5C22×C3×C412yes—
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⋊C4—51no—
435C2×C4⋊C4C2×C3×D511yescharacteristic
436C2×C22⋊C4—51no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4—51no—
439C2×C22⋊C4C2×C3×D511yescharacteristic
440C2×C22⋊C4C2×C3×D511yescharacteristic
441C2×C22⋊C4C2×C3×D511yescharacteristic
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#95—51no—
457#95—51no—
458#95C2×C3×D511yescharacteristic
459#95C2×C3×D511yescharacteristic
460C2×C3×C5—42no—
461C2×C3×C5#51811yescharacteristic
462C2×C3×C5#51911yescharacteristic
463C2×C3×C5#52011yescharacteristic
464C2×C3×C5#56211yescharacteristic
465C2×C3×C5#56211yescharacteristic
466C2×C3×C5#56311yescharacteristic
467C2×C3×C5#56311yescharacteristic
468C23×C3—21no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3C2×C4×D512yes—
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—52no—
494C2×C3×C4—52no—
495C2×C3×C4—52no—
496C2×C3×C4—52no—
497C2×C3×C4—101no—
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—101no—
517C2×C3×C4—204no—
518C2×C3×C4C2×C4×D512yes—
519C2×C3×C4C2×C4×D512yes—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—22no—
523C22×C5—41no—
524C22×C5—41no—
525C22×C5—41no—
526C22×C5—41no—
527C22×C5C23×C3×C411yescharacteristic
528C22×C5C3×H(5,𝔽2)11yescharacteristic
529C22×C5C3×H(5,𝔽2)11yescharacteristic
530C22×C5C3×H(5,𝔽2)11yescharacteristic
531C22×C5C3×2−1+411yescharacteristic
532C22×C5C3×2−1+411yescharacteristic
533C22×C5C3×2−1+411yescharacteristic
534C4×C5—22no—
535C4×C5—22no—
536C4×C5—41no—
537C4×C5—41no—
538C4×C5—41no—
539C4×C5—41no—
540Dic5—22no—
541Dic5—22no—
542Dic5—22no—
543Dic5—22no—
544Dic5—41no—
545Dic5—41no—
546Dic5—41no—
547Dic5—41no—
548C24C22×C3×D511yescharacteristic
549C2×Q8—54no—
550C2×Q8—201no—
551C2×Q8—201no—
552C22×C4—51no—
553C22×C4—51no—
554C22×C4—51no—
555C22×C4—51no—
556C22×C4—54no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—51no—
561C22×C4—201no—
562C22×C4—201no—
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—54no—
573C4⋊C4—201no—
574C4⋊C4—201no—
575C4⋊C4—201no—
576C4⋊C4—201no—
577C4⋊C4—201no—
578C22⋊C4—41no—
579C22⋊C4—41no—
580C22⋊C4—54no—
581C22⋊C4—201no—
582C22⋊C4—201no—
583C22⋊C4C3×C4×D514yes—
584C42—41no—
585C42—201no—
586C42—201no—
587C42—201no—
588C3×C5#237811yescharacteristic, complemented, Hall
589C22×C3—22no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—41no—
593C22×C3—41no—
594C22×C3—41no—
595C22×C3—41no—
596C22×C3C22×C4×D511yescharacteristic
597C22×C3#414411yescharacteristic
598C22×C3#414411yescharacteristic
599C22×C3#414911yescharacteristic
600C22×C3#415011yescharacteristic
601C22×C3#415011yescharacteristic
602C22×C3#415011yescharacteristic
603C3×C4—22no—
604C3×C4—22no—
605C3×C4—41no—
606C3×C4—41no—
607C3×C4—41no—
608C3×C4—41no—
609C3×C4—102no—
610C3×C4—102no—
611C3×C4—102no—
612C3×C4—102no—
613C3×C4—201no—
614C3×C4—201no—
615C3×C4—201no—
616C3×C4—201no—
617C2×C5—42no—
618C2×C5C3×#51811yescharacteristic
619C2×C5C3×#51911yescharacteristic
620C2×C5C3×#52011yescharacteristic
621C2×C5C3×#56211yescharacteristic
622C2×C5C3×#56211yescharacteristic
623C2×C5C3×#56311yescharacteristic
624C2×C5C3×#56311yescharacteristic
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23C2×C3×C4×D512yes—
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—52no—
651C2×C4—52no—
652C2×C4—52no—
653C2×C4—52no—
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×C4—101no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—101no—
674C2×C4—204no—
675C2×C4C2×C3×C4×D512yes—
676C2×C4C2×C3×C4×D512yes—
677C2×C3—42no—
678C2×C3#6585011yescharacteristic
679C2×C3#6587911yescharacteristic
680C2×C3#6588011yescharacteristic
681C2×C3#6595511yescharacteristic
682C2×C3#6598511yescharacteristic
683C2×C3#6601811yescharacteristic
684C2×C3#6604611yescharacteristic
685C5C3×#237811yescharacteristic, complemented, Sylow
686C22—22no—
687C22—22no—
688C22—22no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22C22×C3×C4×D511yescharacteristic
694C22C3×#414411yescharacteristic
695C22C3×#414411yescharacteristic
696C22C3×#414911yescharacteristic
697C22C3×#415011yescharacteristic
698C22C3×#415011yescharacteristic
699C22C3×#415011yescharacteristic
700C4—22no—
701C4—22no—
702C4—41no—
703C4—41no—
704C4—41no—
705C4—41no—
706C4—102no—
707C4—102no—
708C4—102no—
709C4—102no—
710C4—201no—
711C4—201no—
712C4—201no—
713C4—201no—
714C3#1060722311yescharacteristic, direct product factor, Sylow
715C2—42no—
716C2C3×#6585011yescharacteristic
717C2C3×#6587911yescharacteristic
718C2C3×#6588011yescharacteristic
719C2C3×#6595511yescharacteristic
720C2C3×#6598511yescharacteristic
721C2C3×#6601811yescharacteristic
722C2C3×#6604611yescharacteristic
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×#2378
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
3. C3×#65267C2semidirect
4. C3×#65262C2semidirect
10. C3×#65222C2semidirect
11. C3×#65218C2semidirect
12. C3×#64942C2semidirect
13. C3×#64941C2semidirect
14. C3×#64936C2semidirect
15. C3×#64935C2semidirect
16. #10607223C3direct (N × H)
38. C3×#4024C4semidirect
56. #65267C2×C3semidirect
57. #65262C2×C3semidirect
63. #65222C2×C3semidirect
64. #65218C2×C3semidirect
65. #64942C2×C3semidirect
66. #64941C2×C3semidirect
67. #64936C2×C3semidirect
68. #64935C2×C3semidirect
145. #4024C3×C4semidirect
588. C3×C5#2378semidirect
685. C5C3×#2378semidirect
714. C3#10607223direct (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
C3×C5×#3882
C3×#652672
C3×#652622
C3×#652402
C3×#652342
C3×#652322
C3×#652312
C3×#652222
C3×#652182
C3×#649422
C3×#649412
C3×#649362
C3×#649352
#106072233
C3×#23785