Finite Group Databasebeta

← C3×#10605186 #14326393

Subgroups — C3×#10605186 #14326393

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4023C211yesmaximal, characteristic
2C3×C4×C5×C22⋊C4C211yesmaximal, characteristic
3C3×#65499C211yesmaximal, characteristic
4C2×C3×#3963C211yesmaximal, characteristic
5C3×#65235C211yesmaximal, characteristic
6C3×#65232C211yesmaximal, characteristic
7C3×C22⋊C4×Dic5C211yesmaximal, characteristic
8C3×#65222C211yesmaximal, characteristic, complemented
9C3×#65222C211yesmaximal, characteristic, complemented
10C3×#65221C211yesmaximal, characteristic, complemented
11C3×C4×#683C211yesmaximal, characteristic, complemented
12C3×#64941C211yesmaximal, characteristic, complemented
13C3×#64941C211yesmaximal, characteristic, complemented
14C3×#64940C211yesmaximal, characteristic, complemented
15C3×#64939C211yesmaximal, characteristic, complemented
16#10605186C311yesmaximal, characteristic, direct product factor, Hall
17C23×C3×C4×C5C2211yescharacteristic
18C23×C3×Dic5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C2×C3×C5×C22⋊C4C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×C3×C42×C5C2211yescharacteristic
23C2×C3×C42×C5C2211yescharacteristic
24C2×C3×C22⋊Dic5C2211yescharacteristic
25C2×C3×C22⋊Dic5C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×#683C2211yescharacteristic
31C2×C3×#683C2211yescharacteristic
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×C3×C4×Dic5C2211yescharacteristic
34C2×C3×C4×Dic5C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic
36C3×#4023C418yescomplemented
37C3×C5×#95C2211yescharacteristic
38C3×C5×#95C2211yescharacteristic
39C3×#3963C2211yescharacteristic
40C3×#3963C2211yescharacteristic
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×#2343—51nomaximal, Hall
54C2×#4023C2×C311yescharacteristic
55C4×C5×C22⋊C4C2×C311yescharacteristic
56#65499C2×C311yescharacteristic
57C2×#3963C2×C311yescharacteristic
58#65235C2×C311yescharacteristic
59#65232C2×C311yescharacteristic
60C22⋊C4×Dic5C2×C311yescharacteristic
61#65222C2×C311yescharacteristic, complemented
62#65222C2×C311yescharacteristic, complemented
63#65221C2×C311yescharacteristic, complemented
64C4×#683C2×C311yescharacteristic, complemented
65#64941C2×C311yescharacteristic, complemented
66#64941C2×C311yescharacteristic, complemented
67#64940C2×C311yescharacteristic, complemented
68#64939C2×C311yescharacteristic, complemented
69C24×C3×C5C2311yescharacteristic
70C22×C3×C4×C5—22no—
71C22×C3×C4×C5—22no—
72C22×C3×C4×C5—41no—
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C22×C3×Dic5—22no—
80C22×C3×Dic5—22no—
81C22×C3×Dic5—22no—
82C22×C3×Dic5—22no—
83C22×C3×Dic5—41no—
84C22×C3×Dic5C2×C414yes—
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C22×C3×Dic5C2311yescharacteristic
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C3×C5×C22⋊C4—22no—
94C3×C5×C22⋊C4C2×C414yes—
95C3×C42×C5—22no—
96C3×C42×C5—41no—
97C3×C22⋊Dic5—22no—
98C3×C22⋊Dic5C2×C414yes—
99C3×#683—22no—
100C3×#683—22no—
101C3×#683—41no—
102C3×#683—41no—
103C3×#683C2×C414yescomplemented
104C3×#683C2×C414yescomplemented
105C3×C4×Dic5—22no—
106C3×C4×Dic5—41no—
107C3×C4×Dic5C2×C414yescomplemented
108C3×C4×Dic5C2×C414yescomplemented
109C2×C3×#117—51no—
110C3×#387—51no—
111C3×#387—51no—
112C3×#387—51no—
113C3×#387—51no—
114C3×#385—51no—
115C3×#385—51no—
116C3×#383—51no—
117C3×#382—51no—
118C3×#381—51no—
119C3×C4×C4⋊C4—51no—
120C3×C4×C22⋊C4—51no—
121C3×C4×C22⋊C4D511yescharacteristic
122C3×#376—51no—
123C2×C3×#95—51no—
124C23×C4×C5C22×C311yescharacteristic
125C23×Dic5C22×C311yescharacteristic
126C23×Dic5C22×C311yescharacteristic
127C2×C5×C22⋊C4C22×C311yescharacteristic
128C2×C5×C22⋊C4C22×C311yescharacteristic
129C2×C42×C5C22×C311yescharacteristic
130C2×C42×C5C22×C311yescharacteristic
131C2×C22⋊Dic5C22×C311yescharacteristic
132C2×C22⋊Dic5C22×C311yescharacteristic
133C2×#683C22×C311yescharacteristic
134C2×#683C22×C311yescharacteristic
135C2×#683C22×C311yescharacteristic
136C2×#683C22×C311yescharacteristic
137C2×#683C22×C311yescharacteristic
138C2×#683C22×C311yescharacteristic
139C2×C4×Dic5C22×C311yescharacteristic
140C2×C4×Dic5C22×C311yescharacteristic
141C2×C4×Dic5C22×C311yescharacteristic
142C2×C4×Dic5C22×C311yescharacteristic
143#4023C3×C418yescomplemented
144C5×#95C22×C311yescharacteristic
145C5×#95C22×C311yescharacteristic
146#3963C22×C311yescharacteristic
147#3963C22×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#2343—51noSylow
161C23×C3×C5—21no—
162C23×C3×C5—21no—
163C23×C3×C5—21no—
164C23×C3×C5—21no—
165C23×C3×C5C22×C412yes—
166C23×C3×C5#4112yes—
167C23×C3×C5#4112yes—
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—44no—
185C2×C3×C4×C5C22×C412yes—
186C2×C3×C4×C5C22×C412yes—
187C2×C3×C4×C5#4112yes—
188C2×C3×Dic5—28no—
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—21no—
208C2×C3×Dic5—44no—
209C2×C3×Dic5C22×C412yes—
210C2×C3×Dic5C22×C412yes—
211C2×C3×Dic5C22×C412yes—
212C2×C3×Dic5C22×C412yes—
213C2×C3×Dic5#4112yes—
214C23×C3×C4—51no—
215C23×C3×C4—51no—
216C23×C3×C4C2×D511yescharacteristic
217C3×#117—58no—
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×C22⋊C4—51no—
225C2×C3×C22⋊C4—51no—
226C2×C3×C22⋊C4C2×D511yescharacteristic
227C2×C3×C22⋊C4C2×D511yescharacteristic
228C2×C3×C42—51no—
229C2×C3×C42—51no—
230C2×C3×C42—51no—
231C2×C3×C42—51no—
232C2×C3×C42C2×D511yescharacteristic
233C2×C3×C42C2×D511yescharacteristic
234C3×#95—51no—
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×#95—51no—
248C3×#95C2×D511yescharacteristic
249C3×#95C2×D511yescharacteristic
250C24×C5C23×C311yescharacteristic
251C22×C4×C5—22no—
252C22×C4×C5—22no—
253C22×C4×C5—41no—
254C22×C4×C5C23×C311yescharacteristic
255C22×C4×C5C23×C311yescharacteristic
256C22×C4×C5C23×C311yescharacteristic
257C22×C4×C5C23×C311yescharacteristic
258C22×C4×C5C23×C311yescharacteristic
259C22×C4×C5C23×C311yescharacteristic
260C22×Dic5—22no—
261C22×Dic5—22no—
262C22×Dic5—22no—
263C22×Dic5—22no—
264C22×Dic5—41no—
265C22×Dic5C2×C3×C414yes—
266C22×Dic5C23×C311yescharacteristic
267C22×Dic5C23×C311yescharacteristic
268C22×Dic5C23×C311yescharacteristic
269C22×Dic5C23×C311yescharacteristic
270C22×Dic5C23×C311yescharacteristic
271C22×Dic5C23×C311yescharacteristic
272C22×Dic5C23×C311yescharacteristic
273C22×Dic5C23×C311yescharacteristic
274C5×C22⋊C4—22no—
275C5×C22⋊C4C2×C3×C414yes—
276C42×C5—22no—
277C42×C5—41no—
278C22⋊Dic5—22no—
279C22⋊Dic5C2×C3×C414yes—
280#683—22no—
281#683—22no—
282#683—41no—
283#683—41no—
284#683C2×C3×C414yescomplemented
285#683C2×C3×C414yescomplemented
286C4×Dic5—22no—
287C4×Dic5—41no—
288C4×Dic5C2×C3×C414yescomplemented
289C4×Dic5C2×C3×C414yescomplemented
290C2×#117—51no—
291#387—51no—
292#387—51no—
293#387—51no—
294#387—51no—
295#385—51no—
296#385—51no—
297#383—51no—
298#382—51no—
299#381—51no—
300C4×C4⋊C4—51no—
301C4×C22⋊C4—51no—
302C4×C22⋊C4C3×D511yescharacteristic
303#376—51no—
304C2×#95—51no—
305C22×C3×C5—22no—
306C22×C3×C5—22no—
307C22×C3×C5—22no—
308C22×C3×C5—22no—
309C22×C3×C5—22no—
310C22×C3×C5—22no—
311C22×C3×C5#11714yes—
312C22×C3×C5C23×C411yescharacteristic
313C22×C3×C5C2×#4111yescharacteristic
314C22×C3×C5C2×#4111yescharacteristic
315C22×C3×C5C2×#4111yescharacteristic
316C22×C3×C5C2×#4111yescharacteristic
317C22×C3×C5H(5,𝔽2)11yescharacteristic
318C22×C3×C52−1+411yescharacteristic
319C3×C4×C5—22no—
320C3×C4×C5—22no—
321C3×C4×C5—22no—
322C3×C4×C5—41no—
323C3×C4×C5—41no—
324C3×C4×C5—41no—
325C3×Dic5—22no—
326C3×Dic5—22no—
327C3×Dic5—22no—
328C3×Dic5—22no—
329C3×Dic5—22no—
330C3×Dic5—41no—
331C3×Dic5—41no—
332C3×Dic5—41no—
333C24×C3C22×D511yescharacteristic
334C22×C3×C4—22no—
335C22×C3×C4—22no—
336C22×C3×C4—41no—
337C22×C3×C4—54no—
338C22×C3×C4—51no—
339C22×C3×C4—51no—
340C22×C3×C4—51no—
341C22×C3×C4—51no—
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C22×C3×C4—51no—
345C22×C3×C4—51no—
346C22×C3×C4—102no—
347C22×C3×C4—102no—
348C22×C3×C4—102no—
349C22×C3×C4—102no—
350C22×C3×C4—201no—
351C22×C3×C4C22×D511yescharacteristic
352C22×C3×C4C22×D511yescharacteristic
353C22×C3×C4C22×D511yescharacteristic
354C22×C3×C4C22×D511yescharacteristic
355C22×C3×C4C22×D511yescharacteristic
356C22×C3×C4C22×D511yescharacteristic
357C3×C4⋊C4—54no—
358C3×C4⋊C4—54no—
359C3×C4⋊C4—102no—
360C3×C4⋊C4—102no—
361C3×C4⋊C4—201no—
362C3×C4⋊C4—201no—
363C3×C22⋊C4—22no—
364C3×C22⋊C4—54no—
365C3×C22⋊C4—102no—
366C3×C22⋊C4C4×D514yes—
367C3×C42—22no—
368C3×C42—41no—
369C3×C42—54no—
370C3×C42—54no—
371C3×C42—102no—
372C3×C42—201no—
373C23×C5—21no—
374C23×C5—21no—
375C23×C5—21no—
376C23×C5—21no—
377C23×C5C22×C3×C412yes—
378C23×C5C3×#4112yes—
379C23×C5C3×#4112yes—
380C23×C5C24×C311yescharacteristic
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—44no—
397C2×C4×C5C22×C3×C412yes—
398C2×C4×C5C22×C3×C412yes—
399C2×C4×C5C3×#4112yes—
400C2×Dic5—28no—
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×Dic5—21no—
420C2×Dic5—44no—
421C2×Dic5C22×C3×C412yes—
422C2×Dic5C22×C3×C412yes—
423C2×Dic5C22×C3×C412yes—
424C2×Dic5C22×C3×C412yes—
425C2×Dic5C3×#4112yes—
426C23×C4—51no—
427C23×C4—51no—
428C23×C4C2×C3×D511yescharacteristic
429#117—58no—
430C2×C4⋊C4—51no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—51no—
433C2×C4⋊C4—51no—
434C2×C4⋊C4—51no—
435C2×C4⋊C4—51no—
436C2×C22⋊C4—51no—
437C2×C22⋊C4—51no—
438C2×C22⋊C4C2×C3×D511yescharacteristic
439C2×C22⋊C4C2×C3×D511yescharacteristic
440C2×C42—51no—
441C2×C42—51no—
442C2×C42—51no—
443C2×C42—51no—
444C2×C42C2×C3×D511yescharacteristic
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#95—51no—
459#95—51no—
460#95C2×C3×D511yescharacteristic
461#95C2×C3×D511yescharacteristic
462C2×C3×C5—24no—
463C2×C3×C5C2×#11711yescharacteristic
464C2×C3×C5C4×#4111yescharacteristic
465C2×C3×C5#52011yescharacteristic
466C2×C3×C5#55111yescharacteristic
467C2×C3×C5#55111yescharacteristic
468C2×C3×C5#55211yescharacteristic
469C2×C3×C5#55211yescharacteristic
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3C2×C4×D512yes—
475C23×C3#70912yes—
476C23×C3#70912yes—
477C23×C3C23×D511yescharacteristic
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—44no—
494C2×C3×C4—52no—
495C2×C3×C4—52no—
496C2×C3×C4—52no—
497C2×C3×C4—52no—
498C2×C3×C4—52no—
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—108no—
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—101no—
518C2×C3×C4—101no—
519C2×C3×C4—204no—
520C2×C3×C4C2×C4×D512yes—
521C2×C3×C4C2×C4×D512yes—
522C2×C3×C4#71112yes—
523C22×C5—22no—
524C22×C5—22no—
525C22×C5—22no—
526C22×C5—22no—
527C22×C5—22no—
528C22×C5—22no—
529C22×C5C3×#11714yes—
530C22×C5C23×C3×C411yescharacteristic
531C22×C5C2×C3×#4111yescharacteristic
532C22×C5C2×C3×#4111yescharacteristic
533C22×C5C2×C3×#4111yescharacteristic
534C22×C5C2×C3×#4111yescharacteristic
535C22×C5C3×H(5,𝔽2)11yescharacteristic
536C22×C5C3×2−1+411yescharacteristic
537C4×C5—22no—
538C4×C5—22no—
539C4×C5—22no—
540C4×C5—41no—
541C4×C5—41no—
542C4×C5—41no—
543Dic5—22no—
544Dic5—22no—
545Dic5—22no—
546Dic5—22no—
547Dic5—22no—
548Dic5—41no—
549Dic5—41no—
550Dic5—41no—
551C24C22×C3×D511yescharacteristic
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—41no—
555C22×C4—54no—
556C22×C4—51no—
557C22×C4—51no—
558C22×C4—51no—
559C22×C4—51no—
560C22×C4—51no—
561C22×C4—51no—
562C22×C4—51no—
563C22×C4—51no—
564C22×C4—102no—
565C22×C4—102no—
566C22×C4—102no—
567C22×C4—102no—
568C22×C4—201no—
569C22×C4C22×C3×D511yescharacteristic
570C22×C4C22×C3×D511yescharacteristic
571C22×C4C22×C3×D511yescharacteristic
572C22×C4C22×C3×D511yescharacteristic
573C22×C4C22×C3×D511yescharacteristic
574C22×C4C22×C3×D511yescharacteristic
575C4⋊C4—54no—
576C4⋊C4—54no—
577C4⋊C4—102no—
578C4⋊C4—102no—
579C4⋊C4—201no—
580C4⋊C4—201no—
581C22⋊C4—22no—
582C22⋊C4—54no—
583C22⋊C4—102no—
584C22⋊C4C3×C4×D514yes—
585C42—22no—
586C42—41no—
587C42—54no—
588C42—54no—
589C42—102no—
590C42—201no—
591C3×C5#234311yescharacteristic, complemented, Hall
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3#401814yes—
599C22×C3C22×C4×D511yescharacteristic
600C22×C3C2×#70911yescharacteristic
601C22×C3C2×#70911yescharacteristic
602C22×C3C2×#71111yescharacteristic
603C22×C3#414411yescharacteristic
604C22×C3D5×#4111yescharacteristic
605C22×C3#415011yescharacteristic
606C3×C4—22no—
607C3×C4—22no—
608C3×C4—22no—
609C3×C4—41no—
610C3×C4—41no—
611C3×C4—41no—
612C3×C4—102no—
613C3×C4—102no—
614C3×C4—102no—
615C3×C4—102no—
616C3×C4—102no—
617C3×C4—201no—
618C3×C4—201no—
619C3×C4—201no—
620C2×C5—24no—
621C2×C5C2×C3×#11711yescharacteristic
622C2×C5C3×C4×#4111yescharacteristic
623C2×C5C3×#52011yescharacteristic
624C2×C5C3×#55111yescharacteristic
625C2×C5C3×#55111yescharacteristic
626C2×C5C3×#55211yescharacteristic
627C2×C5C3×#55211yescharacteristic
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23C2×C3×C4×D512yes—
633C23C3×#70912yes—
634C23C3×#70912yes—
635C23C23×C3×D511yescharacteristic
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—44no—
652C2×C4—52no—
653C2×C4—52no—
654C2×C4—52no—
655C2×C4—52no—
656C2×C4—52no—
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—108no—
668C2×C4—101no—
669C2×C4—101no—
670C2×C4—101no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—101no—
674C2×C4—101no—
675C2×C4—101no—
676C2×C4—101no—
677C2×C4—204no—
678C2×C4C2×C3×C4×D512yes—
679C2×C4C2×C3×C4×D512yes—
680C2×C4C3×#71112yes—
681C2×C3—24no—
682C2×C3C2×#401811yescharacteristic
683C2×C3#6582911yescharacteristic
684C2×C3#6586511yescharacteristic
685C2×C3C4×#71111yescharacteristic
686C2×C3#6587511yescharacteristic
687C2×C3#6588011yescharacteristic
688C2×C3#6589011yescharacteristic
689C5C3×#234311yescharacteristic, complemented, Sylow
690C22—22no—
691C22—22no—
692C22—22no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22C3×#401814yes—
697C22C22×C3×C4×D511yescharacteristic
698C22C2×C3×#70911yescharacteristic
699C22C2×C3×#70911yescharacteristic
700C22C2×C3×#71111yescharacteristic
701C22C3×#414411yescharacteristic
702C22C3×D5×#4111yescharacteristic
703C22C3×#415011yescharacteristic
704C4—22no—
705C4—22no—
706C4—22no—
707C4—41no—
708C4—41no—
709C4—41no—
710C4—102no—
711C4—102no—
712C4—102no—
713C4—102no—
714C4—102no—
715C4—201no—
716C4—201no—
717C4—201no—
718C3#1060518611yescharacteristic, direct product factor, Sylow
719C2—24no—
720C2C2×C3×#401811yescharacteristic
721C2C3×#6582911yescharacteristic
722C2C3×#6586511yescharacteristic
723C2C3×C4×#71111yescharacteristic
724C2C3×#6587511yescharacteristic
725C2C3×#6588011yescharacteristic
726C2C3×#6589011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C4×C5×C22⋊C4C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
cosocleC23×C5C24×C3
hypercenterC3×C4×C22⋊C4D5
hypocenterC5C3×#2343
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. C3×#65222C2semidirect
9. C3×#65222C2semidirect
10. C3×#65221C2semidirect
11. C3×C4×#683C2semidirect
12. C3×#64941C2semidirect
13. C3×#64941C2semidirect
14. C3×#64940C2semidirect
15. C3×#64939C2semidirect
16. #10605186C3direct (N × H)
36. C3×#4023C4semidirect
61. #65222C2×C3semidirect
62. #65222C2×C3semidirect
63. #65221C2×C3semidirect
64. C4×#683C2×C3semidirect
65. #64941C2×C3semidirect
66. #64941C2×C3semidirect
67. #64940C2×C3semidirect
68. #64939C2×C3semidirect
103. C3×#683C2×C4semidirect
104. C3×#683C2×C4semidirect
107. C3×C4×Dic5C2×C4semidirect
108. C3×C4×Dic5C2×C4semidirect
143. #4023C3×C4semidirect
284. #683C2×C3×C4semidirect
285. #683C2×C3×C4semidirect
288. C4×Dic5C2×C3×C4semidirect
289. C4×Dic5C2×C3×C4semidirect
591. C3×C5#2343semidirect
689. C5C3×#2343semidirect
718. C3#10605186direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40232
C3×C4×C5×C22⋊C42
C3×#654992
C2×C3×#39632
C3×#652352
C3×#652322
C3×C22⋊C4×Dic52
C3×#652222
C3×#652212
C3×C4×#6832
C3×#649412
C3×#649402
C3×#649392
#106051863
C3×#23435