Finite Group Databasebeta

← C3×#10607224 #14331122

Subgroups — C3×#10607224 #14331122

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4031C211yesmaximal, characteristic
2C3×C5×#388C211yesmaximal, characteristic, complemented
3C3×#65279C211yesmaximal, characteristic, complemented
4C3×#65266C211yesmaximal, characteristic, complemented
5C3×#65247C211yesmaximal, characteristic
6C3×#65245C211yesmaximal, characteristic
7C3×#65239C211yesmaximal, characteristic, complemented
8C3×#65235C211yesmaximal, characteristic, complemented
9C3×#65233C211yesmaximal, characteristic, complemented
10C3×#65229C211yesmaximal, characteristic, complemented
11C3×#65218C211yesmaximal, characteristic, complemented
12C3×#64957C211yesmaximal, characteristic, complemented
13C3×#64957C211yesmaximal, characteristic, complemented
14C3×#64939C211yesmaximal, characteristic, complemented
15C3×#64935C211yesmaximal, characteristic, complemented
16#10607224C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C22⋊D5C2211yescharacteristic
18C23×C3×Dic5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C3×C5×C22⋊C4C2211yescharacteristic
23C2×C3×C5×C22⋊C4C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C42×C5C2211yescharacteristic
26C2×C3×C22⋊Dic5C2211yescharacteristic
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C2×C3×#683C2211yescharacteristic
36C2×C3×#683C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×C4×Dic5C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C3×#4031C418yescomplemented
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×#2379—51nomaximal, Hall
54C2×#4031C2×C311yescharacteristic
55C5×#388C2×C311yescharacteristic, complemented
56#65279C2×C311yescharacteristic, complemented
57#65266C2×C311yescharacteristic, complemented
58#65247C2×C311yescharacteristic
59#65245C2×C311yescharacteristic
60#65239C2×C311yescharacteristic, complemented
61#65235C2×C311yescharacteristic, complemented
62#65233C2×C311yescharacteristic, complemented
63#65229C2×C311yescharacteristic, complemented
64#65218C2×C311yescharacteristic, complemented
65#64957C2×C311yescharacteristic, complemented
66#64957C2×C311yescharacteristic, complemented
67#64939C2×C311yescharacteristic, complemented
68#64935C2×C311yescharacteristic, complemented
69C24×C3×C5C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×C3×C4×C5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C2×C3×C22⋊D5—41no—
78C2×C3×C22⋊D5—41no—
79C2×C3×C22⋊D5C2×C414yes—
80C22×C3×Dic5—41no—
81C22×C3×Dic5—41no—
82C22×C3×Dic5—41no—
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C22×C3×Dic5C2311yescharacteristic
88C22×C3×Dic5C2311yescharacteristic
89C22×C3×Dic5C2311yescharacteristic
90C2×C3×C4×D5—41no—
91C2×C3×C4×D5—41no—
92C2×C3×C4×D5—41no—
93C2×C3×Dic10—41no—
94C2×C3×Dic10—41no—
95C2×C3×Dic10C2×C414yescomplemented
96C3×C5×C4⋊C4—41no—
97C3×C5×C22⋊C4—41no—
98C3×C5×C22⋊C4—41no—
99C3×C5×C22⋊C4C2×C414yescomplemented
100C3×C42×C5—41no—
101C3×C22⋊Dic5—41no—
102C3×C22⋊Dic5C2×C414yescomplemented
103C3×#685—41no—
104C3×#685—41no—
105C3×#685—41no—
106C3×#685C2×C414yescomplemented
107C3×#685C2×C414yescomplemented
108C3×C4⋊Dic5—41no—
109C3×C4⋊Dic5—41no—
110C3×#683—41no—
111C3×#683—41no—
112C3×#683—41no—
113C3×C4×Dic5—41no—
114C3×C4×Dic5C2×C414yescomplemented
115C2×C3×#124—51no—
116C3×#391—51no—
117C3×#391—51no—
118C3×#388—51no—
119C3×#388—51no—
120C3×#388—51no—
121C3×#388D511yescharacteristic, complemented
122C3×#386—51no—
123C3×#386—51no—
124C3×#385—51no—
125C3×#385—51no—
126C3×#385—51no—
127C3×#385—51no—
128C3×#382—51no—
129C3×#382—51no—
130C22×C22⋊D5C22×C311yescharacteristic
131C23×Dic5C22×C311yescharacteristic
132C22×C4×D5C22×C311yescharacteristic
133C22×Dic10C22×C311yescharacteristic
134C2×C5×C4⋊C4C22×C311yescharacteristic
135C2×C5×C22⋊C4C22×C311yescharacteristic
136C2×C5×C22⋊C4C22×C311yescharacteristic
137C2×C5×C22⋊C4C22×C311yescharacteristic
138C2×C42×C5C22×C311yescharacteristic
139C2×C22⋊Dic5C22×C311yescharacteristic
140C2×C22⋊Dic5C22×C311yescharacteristic
141C2×#685C22×C311yescharacteristic
142C2×#685C22×C311yescharacteristic
143C2×#685C22×C311yescharacteristic
144C2×#685C22×C311yescharacteristic
145C2×#685C22×C311yescharacteristic
146C2×C4⋊Dic5C22×C311yescharacteristic
147C2×C4⋊Dic5C22×C311yescharacteristic
148C2×#683C22×C311yescharacteristic
149C2×#683C22×C311yescharacteristic
150C2×#683C22×C311yescharacteristic
151C2×C4×Dic5C22×C311yescharacteristic
152C2×C4×Dic5C22×C311yescharacteristic
153#4031C3×C418yescomplemented
154C5×#95C22×C311yescharacteristic
155C5×#95C22×C311yescharacteristic
156#3963C22×C311yescharacteristic
157#3963C22×C311yescharacteristic
158#3963C22×C311yescharacteristic
159#3963C22×C311yescharacteristic
160#3963C22×C311yescharacteristic
161#3963C22×C311yescharacteristic
162#3963C22×C311yescharacteristic
163#3963C22×C311yescharacteristic
164#3963C22×C311yescharacteristic
165#3963C22×C311yescharacteristic
166#2379—51noSylow
167C23×C3×C5—21no—
168C23×C3×C5—21no—
169C23×C3×C5—21no—
170C23×C3×C5—21no—
171C23×C3×C5—21no—
172C23×C3×C5—21no—
173C23×C3×C5C22×C412yes—
174C23×C3×C5C2411yescharacteristic
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5—21no—
181C22×C3×D5C22×C412yes—
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×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C22×C412yes—
199C2×C3×C4×C5C22×C412yes—
200C3×C22⋊D5—44no—
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—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—44no—
220C2×C3×Dic5C22×C412yes—
221C2×C3×Dic5C22×C412yes—
222C2×C3×Dic5C22×C412yes—
223C3×C4×D5—44no—
224C3×Dic10—44no—
225C22×C3×Q8—51no—
226C22×C3×D4—51no—
227C23×C3×C4—51no—
228C23×C3×C4—51no—
229C3×#124—58no—
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⋊C4C2×D511yescharacteristic
236C2×C3×C22⋊C4—51no—
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4—51no—
239C2×C3×C22⋊C4—51no—
240C2×C3×C22⋊C4—51no—
241C2×C3×C22⋊C4—51no—
242C2×C3×C22⋊C4—51no—
243C2×C3×C22⋊C4C2×D511yescharacteristic
244C2×C3×C22⋊C4C2×D511yescharacteristic
245C2×C3×C22⋊C4C2×D511yescharacteristic
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×#95—51no—
258C3×#95—51no—
259C3×#95C2×D511yescharacteristic
260C3×#95C2×D511yescharacteristic
261C24×C5C23×C311yescharacteristic
262C23×D5C23×C311yescharacteristic
263C22×C4×C5C23×C311yescharacteristic
264C22×C4×C5C23×C311yescharacteristic
265C22×C4×C5C23×C311yescharacteristic
266C22×C4×C5C23×C311yescharacteristic
267C22×C4×C5C23×C311yescharacteristic
268C22×C4×C5C23×C311yescharacteristic
269C2×C22⋊D5—41no—
270C2×C22⋊D5—41no—
271C2×C22⋊D5C2×C3×C414yes—
272C22×Dic5—41no—
273C22×Dic5—41no—
274C22×Dic5—41no—
275C22×Dic5C23×C311yescharacteristic
276C22×Dic5C23×C311yescharacteristic
277C22×Dic5C23×C311yescharacteristic
278C22×Dic5C23×C311yescharacteristic
279C22×Dic5C23×C311yescharacteristic
280C22×Dic5C23×C311yescharacteristic
281C22×Dic5C23×C311yescharacteristic
282C2×C4×D5—41no—
283C2×C4×D5—41no—
284C2×C4×D5—41no—
285C2×Dic10—41no—
286C2×Dic10—41no—
287C2×Dic10C2×C3×C414yescomplemented
288C5×C4⋊C4—41no—
289C5×C22⋊C4—41no—
290C5×C22⋊C4—41no—
291C5×C22⋊C4C2×C3×C414yescomplemented
292C42×C5—41no—
293C22⋊Dic5—41no—
294C22⋊Dic5C2×C3×C414yescomplemented
295#685—41no—
296#685—41no—
297#685—41no—
298#685C2×C3×C414yescomplemented
299#685C2×C3×C414yescomplemented
300C4⋊Dic5—41no—
301C4⋊Dic5—41no—
302#683—41no—
303#683—41no—
304#683—41no—
305C4×Dic5—41no—
306C4×Dic5C2×C3×C414yescomplemented
307C2×#124—51no—
308#391—51no—
309#391—51no—
310#388—51no—
311#388—51no—
312#388—51no—
313#388C3×D511yescharacteristic, complemented
314#386—51no—
315#386—51no—
316#385—51no—
317#385—51no—
318#385—51no—
319#385—51no—
320#382—51no—
321#382—51no—
322C22×C3×C5—22no—
323C22×C3×C5—22no—
324C22×C3×C5—22no—
325C22×C3×C5—41no—
326C22×C3×C5—41no—
327C22×C3×C5—41no—
328C22×C3×C5—41no—
329C22×C3×C5C23×C411yescharacteristic
330C22×C3×C5H(5,𝔽2)11yescharacteristic
331C22×C3×C5H(5,𝔽2)11yescharacteristic
332C22×C3×C5H(5,𝔽2)11yescharacteristic
333C22×C3×C5H(5,𝔽2)11yescharacteristic
334C22×C3×C52−1+411yescharacteristic
335C22×C3×C52−1+411yescharacteristic
336C2×C3×D5—22no—
337C2×C3×D5—22no—
338C2×C3×D5—22no—
339C2×C3×D5—41no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C3×C4×C5—22no—
344C3×C4×C5—22no—
345C3×C4×C5—41no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×C4×C5—41no—
349C3×Dic5—22no—
350C3×Dic5—22no—
351C3×Dic5—22no—
352C3×Dic5—41no—
353C3×Dic5—41no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C24×C3—51no—
357C24×C3C22×D511yescharacteristic
358C2×C3×Q8—54no—
359C2×C3×Q8—201no—
360C2×C3×Q8—201no—
361C2×C3×D4—54no—
362C2×C3×D4—201no—
363C2×C3×D4—201no—
364C22×C3×C4—51no—
365C22×C3×C4—51no—
366C22×C3×C4—51no—
367C22×C3×C4—51no—
368C22×C3×C4—51no—
369C22×C3×C4—51no—
370C22×C3×C4—51no—
371C22×C3×C4—201no—
372C22×C3×C4—201no—
373C22×C3×C4—201no—
374C22×C3×C4—201no—
375C22×C3×C4—201no—
376C22×C3×C4—201no—
377C22×C3×C4C22×D511yescharacteristic
378C22×C3×C4C22×D511yescharacteristic
379C22×C3×C4C22×D511yescharacteristic
380C22×C3×C4C22×D511yescharacteristic
381C22×C3×C4C22×D511yescharacteristic
382C22×C3×C4C22×D511yescharacteristic
383C3×C4⋊C4—41no—
384C3×C4⋊C4—201no—
385C3×C4⋊C4—201no—
386C3×C4⋊C4—201no—
387C3×C4⋊C4—201no—
388C3×C4⋊C4—201no—
389C3×C22⋊C4—41no—
390C3×C22⋊C4—41no—
391C3×C22⋊C4—54no—
392C3×C22⋊C4—54no—
393C3×C22⋊C4—54no—
394C3×C22⋊C4—201no—
395C3×C22⋊C4—201no—
396C3×C22⋊C4—201no—
397C3×C22⋊C4—201no—
398C3×C22⋊C4C4×D514yescomplemented
399C3×C42—41no—
400C3×C42—54no—
401C3×C42—201no—
402C23×C5—21no—
403C23×C5—21no—
404C23×C5—21no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5—21no—
408C23×C5C22×C3×C412yes—
409C23×C5C24×C311yescharacteristic
410C22×D5—21no—
411C22×D5—21no—
412C22×D5—21no—
413C22×D5—21no—
414C22×D5—21no—
415C22×D5—21no—
416C22×D5C22×C3×C412yes—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—21no—
428C2×C4×C5—21no—
429C2×C4×C5—21no—
430C2×C4×C5—21no—
431C2×C4×C5—21no—
432C2×C4×C5—21no—
433C2×C4×C5C22×C3×C412yes—
434C2×C4×C5C22×C3×C412yes—
435C22⋊D5—44no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—21no—
446C2×Dic5—21no—
447C2×Dic5—21no—
448C2×Dic5—21no—
449C2×Dic5—21no—
450C2×Dic5—21no—
451C2×Dic5—21no—
452C2×Dic5—21no—
453C2×Dic5—21no—
454C2×Dic5—44no—
455C2×Dic5C22×C3×C412yes—
456C2×Dic5C22×C3×C412yes—
457C2×Dic5C22×C3×C412yes—
458C4×D5—44no—
459Dic10—44no—
460C22×Q8—51no—
461C22×D4—51no—
462C23×C4—51no—
463C23×C4—51no—
464#124—58no—
465C2×C4⋊C4—51no—
466C2×C4⋊C4—51no—
467C2×C4⋊C4—51no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—51no—
470C2×C4⋊C4C2×C3×D511yescharacteristic
471C2×C22⋊C4—51no—
472C2×C22⋊C4—51no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—51no—
476C2×C22⋊C4—51no—
477C2×C22⋊C4—51no—
478C2×C22⋊C4C2×C3×D511yescharacteristic
479C2×C22⋊C4C2×C3×D511yescharacteristic
480C2×C22⋊C4C2×C3×D511yescharacteristic
481C2×C42—51no—
482C2×C42—51no—
483C2×C42C2×C3×D511yescharacteristic
484#95—51no—
485#95—51no—
486#95—51no—
487#95—51no—
488#95—51no—
489#95—51no—
490#95—51no—
491#95—51no—
492#95—51no—
493#95—51no—
494#95C2×C3×D511yescharacteristic
495#95C2×C3×D511yescharacteristic
496C2×C3×C5—42no—
497C2×C3×C5#51811yescharacteristic
498C2×C3×C5#52011yescharacteristic
499C2×C3×C5#52011yescharacteristic
500C2×C3×C5H(3,𝔽4)11yescharacteristic
501C2×C3×C5#56211yescharacteristic
502C2×C3×C5#56211yescharacteristic
503C2×C3×C5#56311yescharacteristic
504C3×D5—42no—
505C23×C3—21no—
506C23×C3—21no—
507C23×C3—21no—
508C23×C3—21no—
509C23×C3—21no—
510C23×C3—21no—
511C23×C3—52no—
512C23×C3—101no—
513C23×C3—101no—
514C23×C3—101no—
515C23×C3—101no—
516C23×C3—101no—
517C23×C3—101no—
518C23×C3C2×C4×D512yes—
519C23×C3C23×D511yescharacteristic
520C3×Q8—204no—
521C3×D4—204no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—21no—
537C2×C3×C4—21no—
538C2×C3×C4—52no—
539C2×C3×C4—52no—
540C2×C3×C4—52no—
541C2×C3×C4—101no—
542C2×C3×C4—101no—
543C2×C3×C4—101no—
544C2×C3×C4—101no—
545C2×C3×C4—101no—
546C2×C3×C4—101no—
547C2×C3×C4—101no—
548C2×C3×C4—101no—
549C2×C3×C4—101no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—101no—
553C2×C3×C4—101no—
554C2×C3×C4—101no—
555C2×C3×C4—101no—
556C2×C3×C4—101no—
557C2×C3×C4—101no—
558C2×C3×C4—101no—
559C2×C3×C4—204no—
560C2×C3×C4—204no—
561C2×C3×C4C2×C4×D512yes—
562C2×C3×C4C2×C4×D512yes—
563C22×C5—22no—
564C22×C5—22no—
565C22×C5—22no—
566C22×C5—41no—
567C22×C5—41no—
568C22×C5—41no—
569C22×C5—41no—
570C22×C5C23×C3×C411yescharacteristic
571C22×C5C3×H(5,𝔽2)11yescharacteristic
572C22×C5C3×H(5,𝔽2)11yescharacteristic
573C22×C5C3×H(5,𝔽2)11yescharacteristic
574C22×C5C3×H(5,𝔽2)11yescharacteristic
575C22×C5C3×2−1+411yescharacteristic
576C22×C5C3×2−1+411yescharacteristic
577C2×D5—22no—
578C2×D5—22no—
579C2×D5—22no—
580C2×D5—41no—
581C2×D5—41no—
582C2×D5—41no—
583C2×D5—41no—
584C4×C5—22no—
585C4×C5—22no—
586C4×C5—41no—
587C4×C5—41no—
588C4×C5—41no—
589C4×C5—41no—
590Dic5—22no—
591Dic5—22no—
592Dic5—22no—
593Dic5—41no—
594Dic5—41no—
595Dic5—41no—
596Dic5—41no—
597C24—51no—
598C24C22×C3×D511yescharacteristic
599C2×Q8—54no—
600C2×Q8—201no—
601C2×Q8—201no—
602C2×D4—54no—
603C2×D4—201no—
604C2×D4—201no—
605C22×C4—51no—
606C22×C4—51no—
607C22×C4—51no—
608C22×C4—51no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—201no—
613C22×C4—201no—
614C22×C4—201no—
615C22×C4—201no—
616C22×C4—201no—
617C22×C4—201no—
618C22×C4C22×C3×D511yescharacteristic
619C22×C4C22×C3×D511yescharacteristic
620C22×C4C22×C3×D511yescharacteristic
621C22×C4C22×C3×D511yescharacteristic
622C22×C4C22×C3×D511yescharacteristic
623C22×C4C22×C3×D511yescharacteristic
624C4⋊C4—41no—
625C4⋊C4—201no—
626C4⋊C4—201no—
627C4⋊C4—201no—
628C4⋊C4—201no—
629C4⋊C4—201no—
630C22⋊C4—41no—
631C22⋊C4—41no—
632C22⋊C4—54no—
633C22⋊C4—54no—
634C22⋊C4—54no—
635C22⋊C4—201no—
636C22⋊C4—201no—
637C22⋊C4—201no—
638C22⋊C4—201no—
639C22⋊C4C3×C4×D514yescomplemented
640C42—41no—
641C42—54no—
642C42—201no—
643C3×C5#237911yescharacteristic, complemented, Hall
644C22×C3—22no—
645C22×C3—22no—
646C22×C3—22no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—41no—
650C22×C3—41no—
651C22×C3—102no—
652C22×C3—102no—
653C22×C3—102no—
654C22×C3—201no—
655C22×C3—201no—
656C22×C3—201no—
657C22×C3—201no—
658C22×C3C22×C4×D511yescharacteristic
659C22×C3#414411yescharacteristic
660C22×C3#414411yescharacteristic
661C22×C3#414911yescharacteristic
662C22×C3#414911yescharacteristic
663C22×C3#415011yescharacteristic
664C22×C3#415011yescharacteristic
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—41no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—102no—
672C3×C4—102no—
673C3×C4—102no—
674C3×C4—201no—
675C3×C4—201no—
676C3×C4—201no—
677C3×C4—201no—
678C2×C5—42no—
679C2×C5C3×#51811yescharacteristic
680C2×C5C3×#52011yescharacteristic
681C2×C5C3×#52011yescharacteristic
682C2×C5C3×H(3,𝔽4)11yescharacteristic
683C2×C5C3×#56211yescharacteristic
684C2×C5C3×#56211yescharacteristic
685C2×C5C3×#56311yescharacteristic
686D5—42no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—52no—
694C23—101no—
695C23—101no—
696C23—101no—
697C23—101no—
698C23—101no—
699C23—101no—
700C23C2×C3×C4×D512yes—
701C23C23×C3×D511yescharacteristic
702Q8—204no—
703D4—204no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—52no—
721C2×C4—52no—
722C2×C4—52no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—101no—
733C2×C4—101no—
734C2×C4—101no—
735C2×C4—101no—
736C2×C4—101no—
737C2×C4—101no—
738C2×C4—101no—
739C2×C4—101no—
740C2×C4—101no—
741C2×C4—204no—
742C2×C4—204no—
743C2×C4C2×C3×C4×D512yes—
744C2×C4C2×C3×C4×D512yes—
745C2×C3—42no—
746C2×C3—202no—
747C2×C3#6585711yescharacteristic
748C2×C3#6587911yescharacteristic
749C2×C3#6588011yescharacteristic
750C2×C3#6595511yescharacteristic
751C2×C3#6600111yescharacteristic
752C2×C3#6601711yescharacteristic
753C2×C3#6604611yescharacteristic
754C5C3×#237911yescharacteristic, complemented, Sylow
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—102no—
763C22—102no—
764C22—102no—
765C22—201no—
766C22—201no—
767C22—201no—
768C22—201no—
769C22C22×C3×C4×D511yescharacteristic
770C22C3×#414411yescharacteristic
771C22C3×#414411yescharacteristic
772C22C3×#414911yescharacteristic
773C22C3×#414911yescharacteristic
774C22C3×#415011yescharacteristic
775C22C3×#415011yescharacteristic
776C4—22no—
777C4—22no—
778C4—41no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—102no—
783C4—102no—
784C4—102no—
785C4—201no—
786C4—201no—
787C4—201no—
788C4—201no—
789C3#1060722411yescharacteristic, direct product factor, Sylow
790C2—42no—
791C2—202no—
792C2C3×#6585711yescharacteristic
793C2C3×#6587911yescharacteristic
794C2C3×#6588011yescharacteristic
795C2C3×#6595511yescharacteristic
796C2C3×#6600111yescharacteristic
797C2C3×#6601711yescharacteristic
798C2C3×#6604611yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C3×#2379
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
2. C3×C5×#388C2semidirect
3. C3×#65279C2semidirect
4. C3×#65266C2semidirect
7. C3×#65239C2semidirect
8. C3×#65235C2semidirect
9. C3×#65233C2semidirect
10. C3×#65229C2semidirect
11. C3×#65218C2semidirect
12. C3×#64957C2semidirect
13. C3×#64957C2semidirect
14. C3×#64939C2semidirect
15. C3×#64935C2semidirect
16. #10607224C3direct (N × H)
40. C3×#4031C4semidirect
55. C5×#388C2×C3semidirect
56. #65279C2×C3semidirect
57. #65266C2×C3semidirect
60. #65239C2×C3semidirect
61. #65235C2×C3semidirect
62. #65233C2×C3semidirect
63. #65229C2×C3semidirect
64. #65218C2×C3semidirect
65. #64957C2×C3semidirect
66. #64957C2×C3semidirect
67. #64939C2×C3semidirect
68. #64935C2×C3semidirect
95. C2×C3×Dic10C2×C4semidirect
99. C3×C5×C22⋊C4C2×C4semidirect
102. C3×C22⋊Dic5C2×C4semidirect
106. C3×#685C2×C4semidirect
107. C3×#685C2×C4semidirect
114. C3×C4×Dic5C2×C4semidirect
121. C3×#388D5semidirect
153. #4031C3×C4semidirect
287. C2×Dic10C2×C3×C4semidirect
291. C5×C22⋊C4C2×C3×C4semidirect
294. C22⋊Dic5C2×C3×C4semidirect
298. #685C2×C3×C4semidirect
299. #685C2×C3×C4semidirect
306. C4×Dic5C2×C3×C4semidirect
313. #388C3×D5semidirect
398. C3×C22⋊C4C4×D5semidirect
639. C22⋊C4C3×C4×D5semidirect
643. C3×C5#2379semidirect
754. C5C3×#2379semidirect
789. C3#10607224direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40312
C3×C5×#3882
C3×#652792
C3×#652662
C3×#652472
C3×#652452
C3×#652392
C3×#652352
C3×#652332
C3×#652292
C3×#652182
C3×#649572
C3×#649392
C3×#649352
#106072243
C3×#23795