Finite Group Databasebeta

← C3×#10607557 #14323346

Subgroups — C3×#10607557 #14323346

Order 1920.

1616 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic, complemented
2C2×C3×#4028C211yesmaximal, characteristic
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×C5×#388C211yesmaximal, characteristic, complemented
5C3×#65279C211yesmaximal, characteristic, complemented
6C3×#65246C211yesmaximal, characteristic, complemented
7C3×#65245C211yesmaximal, characteristic, complemented
8C3×#65244C211yesmaximal, characteristic, complemented
9C3×#65240C211yesmaximal, characteristic, complemented
10C3×#65228C211yesmaximal, characteristic, complemented
11C3×C4×#685C211yesmaximal, characteristic, complemented
12C3×#64958C211yesmaximal, characteristic, complemented
13C3×#64957C211yesmaximal, characteristic, complemented
14C3×#64954C211yesmaximal, characteristic, complemented
15C3×#64954C211yesmaximal, characteristic, complemented
16#10607557C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C22⋊D5C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×D20C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic, complemented
24C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic, complemented
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic, complemented
40C2×C3×#685C2211yescharacteristic, complemented
41C2×C3×#685C2211yescharacteristic, complemented
42C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
43C2×C3×#683C2211yescharacteristic, complemented
44C2×C3×C4×Dic5C2211yescharacteristic, complemented
45C2×C3×C4×Dic5C2211yescharacteristic, complemented
46C3×#4039—24no—
47C3×#4028C418yescomplemented
48C3×D5×C22⋊C4—24no—
49C3×C5×#95C2211yescharacteristic, complemented
50C3×C5×#95C2211yescharacteristic, complemented
51C3×#3963C2211yescharacteristic, complemented
52C3×#3963C2211yescharacteristic, complemented
53C3×#3963C2211yescharacteristic, complemented
54C3×#3963C2211yescharacteristic, complemented
55C3×#2321—51nomaximal, Hall
56C2×#4039C2×C311yescharacteristic, complemented
57C2×#4028C2×C311yescharacteristic
58C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
59C5×#388C2×C311yescharacteristic, complemented
60#65279C2×C311yescharacteristic, complemented
61#65246C2×C311yescharacteristic, complemented
62#65245C2×C311yescharacteristic, complemented
63#65244C2×C311yescharacteristic, complemented
64#65240C2×C311yescharacteristic, complemented
65#65228C2×C311yescharacteristic, complemented
66C4×#685C2×C311yescharacteristic, complemented
67#64958C2×C311yescharacteristic, complemented
68#64957C2×C311yescharacteristic, complemented
69#64954C2×C311yescharacteristic, complemented
70#64954C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C23×C3×D5—22no—
73C23×C3×D5—22no—
74C23×C3×D5—41no—
75C23×C3×D5—41no—
76C23×C3×D5—41no—
77C23×C3×D5—41no—
78C23×C3×D5C2×C414yescomplemented
79C23×C3×D5C2311yescharacteristic
80C23×C3×D5C2311yescharacteristic
81C23×C3×D5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C2×C3×C22⋊D5—41no—
89C2×C3×C22⋊D5—41no—
90C2×C3×C22⋊D5C2×C414yescomplemented
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C2×C3×D20—22no—
97C2×C3×D20—22no—
98C2×C3×D20—41no—
99C2×C3×D20—41no—
100C2×C3×D20C2×C414yes—
101C2×C3×D20C2×C414yescomplemented
102C2×C3×C4×D5—22no—
103C2×C3×C4×D5—22no—
104C2×C3×C4×D5—41no—
105C2×C3×C4×D5—41no—
106C2×C3×C4×D5—41no—
107C2×C3×C4×D5—41no—
108C2×C3×C4×D5—41no—
109C2×C3×C4×D5—41no—
110C2×C3×C4×D5D414yescomplemented
111C3×C5×C4⋊C4—22no—
112C3×C5×C22⋊C4—22no—
113C3×C5×C22⋊C4—41no—
114C3×C5×C22⋊C4C2×C414yescomplemented
115C3×C42×C5—41no—
116C3×C22⋊Dic5—22no—
117C3×C22⋊Dic5—41no—
118C3×#685—22no—
119C3×#685—22no—
120C3×#685—22no—
121C3×#685—22no—
122C3×#685—22no—
123C3×#685—41no—
124C3×#685—41no—
125C3×#685—41no—
126C3×#685—41no—
127C3×#685C2×C414yescomplemented
128C3×#685C2×C414yescomplemented
129C3×C4⋊Dic5—41no—
130C3×#683—41no—
131C3×C4×Dic5—22no—
132C3×C4×Dic5—41no—
133C2×C3×#120—51no—
134C2×C3×C4×D4—51no—
135C22×C3×C22⋊C4—51no—
136C3×#390—51no—
137C3×#390—51no—
138C3×#388—51no—
139C3×#388—51no—
140C3×#388—51no—
141C3×#388D511yescharacteristic, complemented
142C3×#386—51no—
143C3×#386—51no—
144C3×#386—51no—
145C3×#385—51no—
146C3×#379—51no—
147C3×C4×C22⋊C4—51no—
148C24×D5C22×C311yescharacteristic
149C22×C22⋊D5C22×C311yescharacteristic
150C22×D20C22×C311yescharacteristic
151C22×D20C22×C311yescharacteristic
152C22×C4×D5C22×C311yescharacteristic
153C22×C4×D5C22×C311yescharacteristic
154C22×C4×D5C22×C311yescharacteristic, complemented
155C2×C5×C4⋊C4C22×C311yescharacteristic, complemented
156C2×C5×C22⋊C4C22×C311yescharacteristic
157C2×C5×C22⋊C4C22×C311yescharacteristic
158C2×C5×C22⋊C4C22×C311yescharacteristic
159C2×C42×C5C22×C311yescharacteristic, complemented
160C2×C22⋊Dic5C22×C311yescharacteristic
161C2×C22⋊Dic5C22×C311yescharacteristic
162C2×#685C22×C311yescharacteristic
163C2×#685C22×C311yescharacteristic
164C2×#685C22×C311yescharacteristic
165C2×#685C22×C311yescharacteristic
166C2×#685C22×C311yescharacteristic
167C2×#685C22×C311yescharacteristic
168C2×#685C22×C311yescharacteristic
169C2×#685C22×C311yescharacteristic
170C2×#685C22×C311yescharacteristic, complemented
171C2×#685C22×C311yescharacteristic, complemented
172C2×#685C22×C311yescharacteristic, complemented
173C2×C4⋊Dic5C22×C311yescharacteristic, complemented
174C2×#683C22×C311yescharacteristic, complemented
175C2×C4×Dic5C22×C311yescharacteristic, complemented
176C2×C4×Dic5C22×C311yescharacteristic, complemented
177#4039—24no—
178#4028C3×C418yescomplemented
179D5×C22⋊C4—24no—
180C5×#95C22×C311yescharacteristic, complemented
181C5×#95C22×C311yescharacteristic, complemented
182#3963C22×C311yescharacteristic, complemented
183#3963C22×C311yescharacteristic, complemented
184#3963C22×C311yescharacteristic, complemented
185#3963C22×C311yescharacteristic, complemented
186#2321—51noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C2411yescharacteristic
195C22×C3×D5—21no—
196C22×C3×D5—21no—
197C22×C3×D5—21no—
198C22×C3×D5—21no—
199C22×C3×D5—21no—
200C22×C3×D5—21no—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—28no—
212C22×C3×D5—44no—
213C22×C3×D5—44no—
214C22×C3×D5—44no—
215C22×C3×D5—44no—
216C22×C3×D5—44no—
217C22×C3×D5—44no—
218C22×C3×D5C22×C412yes—
219C22×C3×D5C22×C412yes—
220C22×C3×D5C22×C412yes—
221C22×C3×D5C2×D412yes—
222C22×C3×D5#4112yes—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—21no—
227C2×C3×C4×C5—21no—
228C2×C3×C4×C5—21no—
229C2×C3×C4×C5—21no—
230C2×C3×C4×C5—21no—
231C2×C3×C4×C5—21no—
232C2×C3×C4×C5—21no—
233C2×C3×C4×C5—21no—
234C2×C3×C4×C5—21no—
235C2×C3×C4×C5—21no—
236C2×C3×C4×C5—21no—
237C2×C3×C4×C5—21no—
238C2×C3×C4×C5C22×C412yes—
239C2×C3×C4×C5C22×C412yes—
240C2×C3×C4×C5C2×D412yes—
241C3×C22⋊D5—44no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5—21no—
255C2×C3×Dic5C22×C412yes—
256C2×C3×Dic5C2×D412yes—
257C3×D20—28no—
258C3×D20—44no—
259C3×C4×D5—44no—
260C3×C4×D5—44no—
261C3×C4×D5—44no—
262C25×C3—51no—
263C22×C3×D4—51no—
264C22×C3×D4—51no—
265C22×C3×D4—51no—
266C23×C3×C4—51no—
267C23×C3×C4—51no—
268C23×C3×C4—51no—
269C3×#120—58no—
270C3×C4×D4—104no—
271C2×C3×C4⋊C4—51no—
272C2×C3×C4⋊C4—51no—
273C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
274C2×C3×C22⋊C4—51no—
275C2×C3×C22⋊C4—51no—
276C2×C3×C22⋊C4—51no—
277C2×C3×C22⋊C4—51no—
278C2×C3×C22⋊C4—51no—
279C2×C3×C22⋊C4—51no—
280C2×C3×C22⋊C4—51no—
281C2×C3×C22⋊C4—51no—
282C2×C3×C22⋊C4—51no—
283C2×C3×C22⋊C4—51no—
284C2×C3×C22⋊C4—51no—
285C2×C3×C22⋊C4—51no—
286C2×C3×C22⋊C4—51no—
287C2×C3×C22⋊C4—104no—
288C2×C3×C22⋊C4C2×D511yescharacteristic
289C2×C3×C22⋊C4C2×D511yescharacteristic
290C2×C3×C22⋊C4C2×D511yescharacteristic
291C2×C3×C42—51no—
292C2×C3×C42—51no—
293C2×C3×C42C2×D511yescharacteristic, complemented
294C3×#95—51no—
295C3×#95—51no—
296C3×#95—51no—
297C3×#95—51no—
298C3×#95C2×D511yescharacteristic, complemented
299C3×#95C2×D511yescharacteristic, complemented
300C24×C5C23×C311yescharacteristic
301C23×D5—22no—
302C23×D5—22no—
303C23×D5—41no—
304C23×D5—41no—
305C23×D5—41no—
306C23×D5—41no—
307C23×D5C2×C3×C414yescomplemented
308C23×D5C23×C311yescharacteristic
309C23×D5C23×C311yescharacteristic
310C23×D5C23×C311yescharacteristic
311C22×C4×C5C23×C311yescharacteristic
312C22×C4×C5C23×C311yescharacteristic
313C22×C4×C5C23×C311yescharacteristic
314C22×C4×C5C23×C311yescharacteristic
315C22×C4×C5C23×C311yescharacteristic
316C22×C4×C5C23×C311yescharacteristic
317C2×C22⋊D5—41no—
318C2×C22⋊D5—41no—
319C2×C22⋊D5C2×C3×C414yescomplemented
320C22×Dic5C23×C311yescharacteristic
321C22×Dic5C23×C311yescharacteristic
322C22×Dic5C23×C311yescharacteristic
323C22×Dic5C23×C311yescharacteristic
324C22×Dic5C23×C311yescharacteristic
325C2×D20—22no—
326C2×D20—22no—
327C2×D20—41no—
328C2×D20—41no—
329C2×D20C2×C3×C414yes—
330C2×D20C2×C3×C414yescomplemented
331C2×C4×D5—22no—
332C2×C4×D5—22no—
333C2×C4×D5—41no—
334C2×C4×D5—41no—
335C2×C4×D5—41no—
336C2×C4×D5—41no—
337C2×C4×D5—41no—
338C2×C4×D5—41no—
339C2×C4×D5C3×D414yescomplemented
340C5×C4⋊C4—22no—
341C5×C22⋊C4—22no—
342C5×C22⋊C4—41no—
343C5×C22⋊C4C2×C3×C414yescomplemented
344C42×C5—41no—
345C22⋊Dic5—22no—
346C22⋊Dic5—41no—
347#685—22no—
348#685—22no—
349#685—22no—
350#685—22no—
351#685—22no—
352#685—41no—
353#685—41no—
354#685—41no—
355#685—41no—
356#685C2×C3×C414yescomplemented
357#685C2×C3×C414yescomplemented
358C4⋊Dic5—41no—
359#683—41no—
360C4×Dic5—22no—
361C4×Dic5—41no—
362C2×#120—51no—
363C2×C4×D4—51no—
364C22×C22⋊C4—51no—
365#390—51no—
366#390—51no—
367#388—51no—
368#388—51no—
369#388—51no—
370#388C3×D511yescharacteristic, complemented
371#386—51no—
372#386—51no—
373#386—51no—
374#385—51no—
375#379—51no—
376C4×C22⋊C4—51no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—41no—
381C22×C3×C5—41no—
382C22×C3×C5—41no—
383C22×C3×C5—41no—
384C22×C3×C5C23×C411yescharacteristic
385C22×C3×C5C22×D411yescharacteristic
386C22×C3×C5C2×#4111yescharacteristic
387C22×C3×C5H(5,𝔽2)11yescharacteristic
388C22×C3×C5H(5,𝔽2)11yescharacteristic
389C22×C3×C5H(5,𝔽2)11yescharacteristic
390C22×C3×C5H(5,𝔽2)11yescharacteristic
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5—22no—
397C2×C3×D5—22no—
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—22no—
402C2×C3×D5—22no—
403C2×C3×D5—416no—
404C2×C3×D5—41no—
405C2×C3×D5—41no—
406C2×C3×D5—41no—
407C2×C3×D5—41no—
408C2×C3×D5—41no—
409C2×C3×D5—41no—
410C2×C3×D5—41no—
411C2×C3×D5—41no—
412C2×C3×D5C4×D414yes—
413C3×C4×C5—22no—
414C3×C4×C5—22no—
415C3×C4×C5—22no—
416C3×C4×C5—41no—
417C3×C4×C5—41no—
418C3×C4×C5—41no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—41no—
422C3×Dic5—41no—
423C3×Dic5—41no—
424C24×C3—51no—
425C24×C3—51no—
426C24×C3—51no—
427C24×C3—54no—
428C24×C3—102no—
429C24×C3—102no—
430C24×C3—201no—
431C24×C3—201no—
432C24×C3—201no—
433C24×C3—201no—
434C24×C3C22×D511yescharacteristic
435C2×C3×D4—54no—
436C2×C3×D4—54no—
437C2×C3×D4—54no—
438C2×C3×D4—102no—
439C2×C3×D4—102no—
440C2×C3×D4—201no—
441C2×C3×D4—201no—
442C2×C3×D4—201no—
443C2×C3×D4—201no—
444C22×C3×C4—51no—
445C22×C3×C4—51no—
446C22×C3×C4—54no—
447C22×C3×C4—51no—
448C22×C3×C4—51no—
449C22×C3×C4—51no—
450C22×C3×C4—102no—
451C22×C3×C4—102no—
452C22×C3×C4—201no—
453C22×C3×C4—201no—
454C22×C3×C4—201no—
455C22×C3×C4—201no—
456C22×C3×C4—201no—
457C22×C3×C4—201no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D511yescharacteristic
463C22×C3×C4C22×D511yescharacteristic
464C3×C4⋊C4—22no—
465C3×C4⋊C4—201no—
466C3×C4⋊C4—201no—
467C3×C22⋊C4—22no—
468C3×C22⋊C4—41no—
469C3×C22⋊C4—54no—
470C3×C22⋊C4—54no—
471C3×C22⋊C4—102no—
472C3×C22⋊C4—102no—
473C3×C22⋊C4—102no—
474C3×C22⋊C4—102no—
475C3×C22⋊C4—102no—
476C3×C22⋊C4—102no—
477C3×C22⋊C4—201no—
478C3×C22⋊C4—201no—
479C3×C22⋊C4—201no—
480C3×C22⋊C4—201no—
481C3×C22⋊C4—201no—
482C3×C22⋊C4C4×D514yescomplemented
483C3×C42—41no—
484C3×C42—102no—
485C3×C42—201no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5C22×C3×C412yes—
493C23×C5C24×C311yescharacteristic
494C22×D5—21no—
495C22×D5—21no—
496C22×D5—21no—
497C22×D5—21no—
498C22×D5—21no—
499C22×D5—21no—
500C22×D5—21no—
501C22×D5—21no—
502C22×D5—21no—
503C22×D5—21no—
504C22×D5—21no—
505C22×D5—21no—
506C22×D5—21no—
507C22×D5—21no—
508C22×D5—21no—
509C22×D5—21no—
510C22×D5—28no—
511C22×D5—44no—
512C22×D5—44no—
513C22×D5—44no—
514C22×D5—44no—
515C22×D5—44no—
516C22×D5—44no—
517C22×D5C22×C3×C412yes—
518C22×D5C22×C3×C412yes—
519C22×D5C22×C3×C412yes—
520C22×D5C2×C3×D412yes—
521C22×D5C3×#4112yes—
522C2×C4×C5—21no—
523C2×C4×C5—21no—
524C2×C4×C5—21no—
525C2×C4×C5—21no—
526C2×C4×C5—21no—
527C2×C4×C5—21no—
528C2×C4×C5—21no—
529C2×C4×C5—21no—
530C2×C4×C5—21no—
531C2×C4×C5—21no—
532C2×C4×C5—21no—
533C2×C4×C5—21no—
534C2×C4×C5—21no—
535C2×C4×C5—21no—
536C2×C4×C5—21no—
537C2×C4×C5C22×C3×C412yes—
538C2×C4×C5C22×C3×C412yes—
539C2×C4×C5C2×C3×D412yes—
540C22⋊D5—44no—
541C2×Dic5—21no—
542C2×Dic5—21no—
543C2×Dic5—21no—
544C2×Dic5—21no—
545C2×Dic5—21no—
546C2×Dic5—21no—
547C2×Dic5—21no—
548C2×Dic5—21no—
549C2×Dic5—21no—
550C2×Dic5—21no—
551C2×Dic5—21no—
552C2×Dic5—21no—
553C2×Dic5—21no—
554C2×Dic5C22×C3×C412yes—
555C2×Dic5C2×C3×D412yes—
556D20—28no—
557D20—44no—
558C4×D5—44no—
559C4×D5—44no—
560C4×D5—44no—
561C25—51no—
562C22×D4—51no—
563C22×D4—51no—
564C22×D4—51no—
565C23×C4—51no—
566C23×C4—51no—
567C23×C4—51no—
568#120—58no—
569C4×D4—104no—
570C2×C4⋊C4—51no—
571C2×C4⋊C4—51no—
572C2×C4⋊C4C2×C3×D511yescharacteristic, complemented
573C2×C22⋊C4—51no—
574C2×C22⋊C4—51no—
575C2×C22⋊C4—51no—
576C2×C22⋊C4—51no—
577C2×C22⋊C4—51no—
578C2×C22⋊C4—51no—
579C2×C22⋊C4—51no—
580C2×C22⋊C4—51no—
581C2×C22⋊C4—51no—
582C2×C22⋊C4—51no—
583C2×C22⋊C4—51no—
584C2×C22⋊C4—51no—
585C2×C22⋊C4—51no—
586C2×C22⋊C4—104no—
587C2×C22⋊C4C2×C3×D511yescharacteristic
588C2×C22⋊C4C2×C3×D511yescharacteristic
589C2×C22⋊C4C2×C3×D511yescharacteristic
590C2×C42—51no—
591C2×C42—51no—
592C2×C42C2×C3×D511yescharacteristic, complemented
593#95—51no—
594#95—51no—
595#95—51no—
596#95—51no—
597#95C2×C3×D511yescharacteristic, complemented
598#95C2×C3×D511yescharacteristic, complemented
599C2×C3×C5—42no—
600C2×C3×C5C2×C4×D411yescharacteristic
601C2×C3×C5#51811yescharacteristic
602C2×C3×C5#51811yescharacteristic
603C2×C3×C5#53411yescharacteristic
604C2×C3×C5#53511yescharacteristic
605C2×C3×C5#53811yescharacteristic
606C2×C3×C5#53811yescharacteristic
607C3×D5—24no—
608C3×D5—42no—
609C3×D5—42no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—21no—
616C23×C3—52no—
617C23×C3—52no—
618C23×C3—52no—
619C23×C3—52no—
620C23×C3—52no—
621C23×C3—108no—
622C23×C3—101no—
623C23×C3—101no—
624C23×C3—101no—
625C23×C3—101no—
626C23×C3—101no—
627C23×C3—101no—
628C23×C3—101no—
629C23×C3—101no—
630C23×C3—101no—
631C23×C3—101no—
632C23×C3—101no—
633C23×C3—101no—
634C23×C3—101no—
635C23×C3—101no—
636C23×C3—101no—
637C23×C3—101no—
638C23×C3—204no—
639C23×C3—204no—
640C23×C3—204no—
641C23×C3—204no—
642C23×C3—204no—
643C23×C3—204no—
644C23×C3C2×C4×D512yes—
645C23×C3C23×D511yescharacteristic
646C3×D4—108no—
647C3×D4—204no—
648C3×D4—204no—
649C2×C3×C4—21no—
650C2×C3×C4—21no—
651C2×C3×C4—21no—
652C2×C3×C4—21no—
653C2×C3×C4—21no—
654C2×C3×C4—21no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—52no—
665C2×C3×C4—52no—
666C2×C3×C4—101no—
667C2×C3×C4—101no—
668C2×C3×C4—101no—
669C2×C3×C4—101no—
670C2×C3×C4—101no—
671C2×C3×C4—101no—
672C2×C3×C4—101no—
673C2×C3×C4—101no—
674C2×C3×C4—101no—
675C2×C3×C4—101no—
676C2×C3×C4—101no—
677C2×C3×C4—101no—
678C2×C3×C4—101no—
679C2×C3×C4—204no—
680C2×C3×C4—204no—
681C2×C3×C4—204no—
682C2×C3×C4C2×C4×D512yes—
683C2×C3×C4C2×C4×D512yes—
684C2×C3×C4D4×D512yes—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—41no—
689C22×C5—41no—
690C22×C5—41no—
691C22×C5—41no—
692C22×C5C23×C3×C411yescharacteristic
693C22×C5C22×C3×D411yescharacteristic
694C22×C5C2×C3×#4111yescharacteristic
695C22×C5C3×H(5,𝔽2)11yescharacteristic
696C22×C5C3×H(5,𝔽2)11yescharacteristic
697C22×C5C3×H(5,𝔽2)11yescharacteristic
698C22×C5C3×H(5,𝔽2)11yescharacteristic
699C2×D5—22no—
700C2×D5—22no—
701C2×D5—22no—
702C2×D5—22no—
703C2×D5—22no—
704C2×D5—22no—
705C2×D5—22no—
706C2×D5—22no—
707C2×D5—22no—
708C2×D5—22no—
709C2×D5—22no—
710C2×D5—22no—
711C2×D5—416no—
712C2×D5—41no—
713C2×D5—41no—
714C2×D5—41no—
715C2×D5—41no—
716C2×D5—41no—
717C2×D5—41no—
718C2×D5—41no—
719C2×D5—41no—
720C2×D5C3×C4×D414yes—
721C4×C5—22no—
722C4×C5—22no—
723C4×C5—22no—
724C4×C5—41no—
725C4×C5—41no—
726C4×C5—41no—
727Dic5—22no—
728Dic5—22no—
729Dic5—41no—
730Dic5—41no—
731Dic5—41no—
732C24—51no—
733C24—51no—
734C24—51no—
735C24—54no—
736C24—102no—
737C24—102no—
738C24—201no—
739C24—201no—
740C24—201no—
741C24—201no—
742C24C22×C3×D511yescharacteristic
743C2×D4—54no—
744C2×D4—54no—
745C2×D4—54no—
746C2×D4—102no—
747C2×D4—102no—
748C2×D4—201no—
749C2×D4—201no—
750C2×D4—201no—
751C2×D4—201no—
752C22×C4—51no—
753C22×C4—51no—
754C22×C4—54no—
755C22×C4—51no—
756C22×C4—51no—
757C22×C4—51no—
758C22×C4—102no—
759C22×C4—102no—
760C22×C4—201no—
761C22×C4—201no—
762C22×C4—201no—
763C22×C4—201no—
764C22×C4—201no—
765C22×C4—201no—
766C22×C4C22×C3×D511yescharacteristic
767C22×C4C22×C3×D511yescharacteristic
768C22×C4C22×C3×D511yescharacteristic
769C22×C4C22×C3×D511yescharacteristic
770C22×C4C22×C3×D511yescharacteristic
771C22×C4C22×C3×D511yescharacteristic
772C4⋊C4—22no—
773C4⋊C4—201no—
774C4⋊C4—201no—
775C22⋊C4—22no—
776C22⋊C4—41no—
777C22⋊C4—54no—
778C22⋊C4—54no—
779C22⋊C4—102no—
780C22⋊C4—102no—
781C22⋊C4—102no—
782C22⋊C4—102no—
783C22⋊C4—102no—
784C22⋊C4—102no—
785C22⋊C4—201no—
786C22⋊C4—201no—
787C22⋊C4—201no—
788C22⋊C4—201no—
789C22⋊C4—201no—
790C22⋊C4C3×C4×D514yescomplemented
791C42—41no—
792C42—102no—
793C42—201no—
794C3×C5#232111yescharacteristic, complemented, Hall
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—41no—
799C22×C3—41no—
800C22×C3—41no—
801C22×C3—41no—
802C22×C3—54no—
803C22×C3—102no—
804C22×C3—102no—
805C22×C3—102no—
806C22×C3—102no—
807C22×C3—102no—
808C22×C3—102no—
809C22×C3—102no—
810C22×C3—102no—
811C22×C3—102no—
812C22×C3—102no—
813C22×C3—102no—
814C22×C3—102no—
815C22×C3—2016no—
816C22×C3—201no—
817C22×C3—201no—
818C22×C3—201no—
819C22×C3—201no—
820C22×C3—201no—
821C22×C3—201no—
822C22×C3—201no—
823C22×C3—201no—
824C22×C3C22×C4×D511yescharacteristic
825C22×C3C2×D4×D511yescharacteristic
826C22×C3#414411yescharacteristic
827C22×C3D5×#4111yescharacteristic
828C22×C3#414911yescharacteristic
829C22×C3#414911yescharacteristic
830C22×C3#414911yescharacteristic
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—22no—
834C3×C4—41no—
835C3×C4—41no—
836C3×C4—41no—
837C3×C4—102no—
838C3×C4—102no—
839C3×C4—201no—
840C3×C4—201no—
841C3×C4—201no—
842C2×C5—42no—
843C2×C5C2×C3×C4×D411yescharacteristic
844C2×C5C3×#51811yescharacteristic
845C2×C5C3×#51811yescharacteristic
846C2×C5C3×#53411yescharacteristic
847C2×C5C3×#53511yescharacteristic
848C2×C5C3×#53811yescharacteristic
849C2×C5C3×#53811yescharacteristic
850D5—24no—
851D5—42no—
852D5—42no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—52no—
860C23—52no—
861C23—52no—
862C23—52no—
863C23—52no—
864C23—108no—
865C23—101no—
866C23—101no—
867C23—101no—
868C23—101no—
869C23—101no—
870C23—101no—
871C23—101no—
872C23—101no—
873C23—101no—
874C23—101no—
875C23—101no—
876C23—101no—
877C23—101no—
878C23—101no—
879C23—101no—
880C23—101no—
881C23—204no—
882C23—204no—
883C23—204no—
884C23—204no—
885C23—204no—
886C23—204no—
887C23C2×C3×C4×D512yes—
888C23C23×C3×D511yescharacteristic
889D4—108no—
890D4—204no—
891D4—204no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—21no—
896C2×C4—21no—
897C2×C4—21no—
898C2×C4—21no—
899C2×C4—21no—
900C2×C4—21no—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—52no—
908C2×C4—52no—
909C2×C4—101no—
910C2×C4—101no—
911C2×C4—101no—
912C2×C4—101no—
913C2×C4—101no—
914C2×C4—101no—
915C2×C4—101no—
916C2×C4—101no—
917C2×C4—101no—
918C2×C4—101no—
919C2×C4—101no—
920C2×C4—101no—
921C2×C4—101no—
922C2×C4—204no—
923C2×C4—204no—
924C2×C4—204no—
925C2×C4C2×C3×C4×D512yes—
926C2×C4C2×C3×C4×D512yes—
927C2×C4C3×D4×D512yes—
928C2×C3—42no—
929C2×C3—104no—
930C2×C3—202no—
931C2×C3—202no—
932C2×C3#6585511yescharacteristic
933C2×C3C4×D4×D511yescharacteristic
934C2×C3#6587911yescharacteristic
935C2×C3#6593911yescharacteristic
936C2×C3#6599111yescharacteristic
937C2×C3#6600811yescharacteristic
938C2×C3#6603811yescharacteristic
939C5C3×#232111yescharacteristic, complemented, Sylow
940C22—22no—
941C22—22no—
942C22—22no—
943C22—41no—
944C22—41no—
945C22—41no—
946C22—41no—
947C22—54no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—102no—
952C22—102no—
953C22—102no—
954C22—102no—
955C22—102no—
956C22—102no—
957C22—102no—
958C22—102no—
959C22—102no—
960C22—2016no—
961C22—201no—
962C22—201no—
963C22—201no—
964C22—201no—
965C22—201no—
966C22—201no—
967C22—201no—
968C22—201no—
969C22C22×C3×C4×D511yescharacteristic
970C22C2×C3×D4×D511yescharacteristic
971C22C3×#414411yescharacteristic
972C22C3×D5×#4111yescharacteristic
973C22C3×#414911yescharacteristic
974C22C3×#414911yescharacteristic
975C22C3×#414911yescharacteristic
976C4—22no—
977C4—22no—
978C4—22no—
979C4—41no—
980C4—41no—
981C4—41no—
982C4—102no—
983C4—102no—
984C4—201no—
985C4—201no—
986C4—201no—
987C3#1060755711yescharacteristic, direct product factor, Sylow
988C2—42no—
989C2—104no—
990C2—202no—
991C2—202no—
992C2C3×#6585511yescharacteristic
993C2C3×C4×D4×D511yescharacteristic
994C2C3×#6587911yescharacteristic
995C2C3×#6593911yescharacteristic
996C2C3×#6599111yescharacteristic
997C2C3×#6600811yescharacteristic
998C2C3×#6603811yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#388C2
socleC23×C3×C5C24
prime radicalC2×C3×#4028C2
cosocleC23×C5C24×C3
hypercenterC3×#388D5
hypocenterC5C3×#2321
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#388

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4039C2semidirect
3. C2×C3×D5×C22⋊C4C2semidirect
4. C3×C5×#388C2semidirect
5. C3×#65279C2semidirect
6. C3×#65246C2semidirect
7. C3×#65245C2semidirect
8. C3×#65244C2semidirect
9. C3×#65240C2semidirect
10. C3×#65228C2semidirect
11. C3×C4×#685C2semidirect
12. C3×#64958C2semidirect
13. C3×#64957C2semidirect
14. C3×#64954C2semidirect
15. C3×#64954C2semidirect
16. #10607557C3direct (N × H)
23. C22×C3×C4×D5C22semidirect
24. C2×C3×C5×C4⋊C4C22semidirect
28. C2×C3×C42×C5C22semidirect
39. C2×C3×#685C22semidirect
40. C2×C3×#685C22semidirect
41. C2×C3×#685C22semidirect
42. C2×C3×C4⋊Dic5C22semidirect
43. C2×C3×#683C22semidirect
44. C2×C3×C4×Dic5C22semidirect
45. C2×C3×C4×Dic5C22semidirect
47. C3×#4028C4semidirect
49. C3×C5×#95C22semidirect
50. C3×C5×#95C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
56. C2×#4039C2×C3semidirect
58. C2×D5×C22⋊C4C2×C3semidirect
59. C5×#388C2×C3semidirect
60. #65279C2×C3semidirect
61. #65246C2×C3semidirect
62. #65245C2×C3semidirect
63. #65244C2×C3semidirect
64. #65240C2×C3semidirect
65. #65228C2×C3semidirect
66. C4×#685C2×C3semidirect
67. #64958C2×C3semidirect
68. #64957C2×C3semidirect
69. #64954C2×C3semidirect
70. #64954C2×C3semidirect
78. C23×C3×D5C2×C4semidirect
90. C2×C3×C22⋊D5C2×C4semidirect
101. C2×C3×D20C2×C4semidirect
110. C2×C3×C4×D5D4semidirect
114. C3×C5×C22⋊C4C2×C4semidirect
127. C3×#685C2×C4semidirect
128. C3×#685C2×C4semidirect
141. C3×#388D5semidirect
154. C22×C4×D5C22×C3semidirect
155. C2×C5×C4⋊C4C22×C3semidirect
159. C2×C42×C5C22×C3semidirect
170. C2×#685C22×C3semidirect
171. C2×#685C22×C3semidirect
172. C2×#685C22×C3semidirect
173. C2×C4⋊Dic5C22×C3semidirect
174. C2×#683C22×C3semidirect
175. C2×C4×Dic5C22×C3semidirect
176. C2×C4×Dic5C22×C3semidirect
178. #4028C3×C4semidirect
180. C5×#95C22×C3semidirect
181. C5×#95C22×C3semidirect
182. #3963C22×C3semidirect
183. #3963C22×C3semidirect
184. #3963C22×C3semidirect
185. #3963C22×C3semidirect
273. C2×C3×C4⋊C4C2×D5semidirect
293. C2×C3×C42C2×D5semidirect
298. C3×#95C2×D5semidirect
299. C3×#95C2×D5semidirect
307. C23×D5C2×C3×C4semidirect
319. C2×C22⋊D5C2×C3×C4semidirect
330. C2×D20C2×C3×C4semidirect
339. C2×C4×D5C3×D4semidirect
343. C5×C22⋊C4C2×C3×C4semidirect
356. #685C2×C3×C4semidirect
357. #685C2×C3×C4semidirect
370. #388C3×D5semidirect
482. C3×C22⋊C4C4×D5semidirect
572. C2×C4⋊C4C2×C3×D5semidirect
592. C2×C42C2×C3×D5semidirect
597. #95C2×C3×D5semidirect
598. #95C2×C3×D5semidirect
790. C22⋊C4C3×C4×D5semidirect
794. C3×C5#2321semidirect
939. C5C3×#2321semidirect
987. C3#10607557direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40392
C2×C3×#40282
C2×C3×D5×C22⋊C42
C3×C5×#3882
C3×#652792
C3×#652462
C3×#652452
C3×#652442
C3×#652402
C3×#652282
C3×C4×#6852
C3×#649582
C3×#649572
C3×#649542
#106075573
C3×#23215