Finite Group Databasebeta

← C3×#10606403 #14326007

Subgroups — C3×#10606403 #14326007

Order 1920.

1856 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#711C211yesmaximal, characteristic
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C3×#4027C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic, complemented
5C3×#65509C211yesmaximal, characteristic, complemented
6C2×C3×#3963C211yesmaximal, characteristic, complemented
7C3×#65245C211yesmaximal, characteristic, complemented
8C3×#65245C211yesmaximal, characteristic, complemented
9C3×#65232C211yesmaximal, characteristic, complemented
10C3×#65231C211yesmaximal, characteristic, complemented
11C3×C22⋊C4×Dic5C211yesmaximal, characteristic, complemented
12C3×#64953C211yesmaximal, characteristic, complemented
13C3×D5×#95C211yesmaximal, characteristic, complemented
14C3×#64935C211yesmaximal, characteristic, complemented
15C3×#64935C211yesmaximal, characteristic, complemented
16#10606403C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2211yescharacteristic
19C22×C3×C22⋊D5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C23×C3×Dic5C2211yescharacteristic
22C23×C3×Dic5C2211yescharacteristic
23C23×C3×Dic5C2211yescharacteristic
24C2×C3×#711—24no—
25C2×C3×#711—24no—
26C2×C3×#711C418yescomplemented
27C22×C3×C4×D5C2211yescharacteristic
28C22×C3×C4×D5C2211yescharacteristic
29C22×C3×C4×D5C2211yescharacteristic
30C22×C3×Dic10C2211yescharacteristic
31C2×C3×C5×C22⋊C4C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic
33C2×C3×C5×C22⋊C4C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C22⋊Dic5C2211yescharacteristic
37C3×C4×C22⋊D5—24no—
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C3×#4027—24no—
45C3×C5×#95C2211yescharacteristic
46C3×C5×#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51C3×#3963C2211yescharacteristic
52C3×#3963C2211yescharacteristic
53C3×#3963C2211yescharacteristic
54C3×#3963C2211yescharacteristic
55C3×#3963C2211yescharacteristic
56C3×#3963C2211yescharacteristic
57C3×#2339—51nomaximal, Hall
58C22×#711C2×C311yescharacteristic
59C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
60C2×#4027C2×C311yescharacteristic, complemented
61C5×#386C2×C311yescharacteristic, complemented
62#65509C2×C311yescharacteristic, complemented
63C2×#3963C2×C311yescharacteristic, complemented
64#65245C2×C311yescharacteristic, complemented
65#65245C2×C311yescharacteristic, complemented
66#65232C2×C311yescharacteristic, complemented
67#65231C2×C311yescharacteristic, complemented
68C22⋊C4×Dic5C2×C311yescharacteristic, complemented
69#64953C2×C311yescharacteristic, complemented
70D5×#95C2×C311yescharacteristic, complemented
71#64935C2×C311yescharacteristic, complemented
72#64935C2×C311yescharacteristic, complemented
73C24×C3×C5C2311yescharacteristic
74C24×C3×C5C2311yescharacteristic
75C23×C3×D5C2311yescharacteristic
76C2×C3×C5×D4—22no—
77C2×C3×C5×D4—22no—
78C2×C3×C5×D4C2×C414yescomplemented
79C22×C3×C4×C5—22no—
80C22×C3×C4×C5—22no—
81C22×C3×C4×C5—41no—
82C22×C3×C4×C5C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C22×C3×C4×C5C2311yescharacteristic
85C22×C3×C4×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C2×C3×C22⋊D5—22no—
88C2×C3×C22⋊D5—22no—
89C2×C3×C22⋊D5C2×C414yes—
90C2×C3×C22⋊D5C2×C414yescomplemented
91C2×C3×C22⋊D5D414yes—
92C2×C3×C22⋊D5D414yes—
93C22×C3×Dic5—22no—
94C22×C3×Dic5—22no—
95C22×C3×Dic5—22no—
96C22×C3×Dic5—22no—
97C22×C3×Dic5—22no—
98C22×C3×Dic5—22no—
99C22×C3×Dic5—41no—
100C22×C3×Dic5C2×C414yescomplemented
101C22×C3×Dic5C2×C414yescomplemented
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C3×#711—232no—
110C2×C3×C4×D5—22no—
111C2×C3×C4×D5—22no—
112C2×C3×C4×D5—22no—
113C2×C3×C4×D5—22no—
114C2×C3×C4×D5—22no—
115C2×C3×C4×D5—22no—
116C2×C3×C4×D5—41no—
117C2×C3×C4×D5—41no—
118C2×C3×C4×D5C2×C414yescomplemented
119C2×C3×Dic10—22no—
120C2×C3×Dic10—22no—
121C2×C3×Dic10C2×C414yescomplemented
122C3×C5×C22⋊C4—22no—
123C3×C5×C22⋊C4—22no—
124C3×C5×C22⋊C4—41no—
125C3×C22⋊Dic5—22no—
126C3×C22⋊Dic5—22no—
127C3×C22⋊Dic5—41no—
128C3×#685—22no—
129C3×#685—22no—
130C3×#683—22no—
131C3×#683—22no—
132C3×C4×Dic5—22no—
133C3×C4×Dic5—22no—
134C22×C3×#41—51no—
135C2×C3×C4×D4—51no—
136C2×C3×C4×D4—51no—
137C3×#391—51no—
138C3×#391—51no—
139C3×#386—51no—
140C3×#386—51no—
141C3×#386—51no—
142C3×#386D511yescharacteristic, complemented
143C3×#381—51no—
144C3×#381—51no—
145C3×#380—51no—
146C3×C4×C22⋊C4—51no—
147C2×C3×#95—51no—
148C2×C3×#95—51no—
149C22×C5×D4C22×C311yescharacteristic
150C23×C4×C5C22×C311yescharacteristic
151C22×C22⋊D5C22×C311yescharacteristic
152C22×C22⋊D5C22×C311yescharacteristic
153C23×Dic5C22×C311yescharacteristic
154C23×Dic5C22×C311yescharacteristic
155C23×Dic5C22×C311yescharacteristic
156C2×#711—24no—
157C2×#711—24no—
158C2×#711C3×C418yescomplemented
159C22×C4×D5C22×C311yescharacteristic
160C22×C4×D5C22×C311yescharacteristic
161C22×C4×D5C22×C311yescharacteristic
162C22×Dic10C22×C311yescharacteristic
163C2×C5×C22⋊C4C22×C311yescharacteristic
164C2×C5×C22⋊C4C22×C311yescharacteristic
165C2×C5×C22⋊C4C22×C311yescharacteristic
166C2×C22⋊Dic5C22×C311yescharacteristic
167C2×C22⋊Dic5C22×C311yescharacteristic
168C2×C22⋊Dic5C22×C311yescharacteristic
169C4×C22⋊D5—24no—
170C2×#685C22×C311yescharacteristic
171C2×#685C22×C311yescharacteristic
172C2×#683C22×C311yescharacteristic
173C2×#683C22×C311yescharacteristic
174C2×C4×Dic5C22×C311yescharacteristic
175C2×C4×Dic5C22×C311yescharacteristic
176#4027—24no—
177C5×#95C22×C311yescharacteristic
178C5×#95C22×C311yescharacteristic
179#3963C22×C311yescharacteristic
180#3963C22×C311yescharacteristic
181#3963C22×C311yescharacteristic
182#3963C22×C311yescharacteristic
183#3963C22×C311yescharacteristic
184#3963C22×C311yescharacteristic
185#3963C22×C311yescharacteristic
186#3963C22×C311yescharacteristic
187#3963C22×C311yescharacteristic
188#3963C22×C311yescharacteristic
189#2339—51noSylow
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5—21no—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C22×C412yes—
202C23×C3×C5C2×D412yes—
203C23×C3×C5C2×D412yes—
204C23×C3×C5C2411yescharacteristic
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5—21no—
208C22×C3×D5—21no—
209C22×C3×D5C22×C412yes—
210C22×C3×D5C2×D412yes—
211C22×C3×D5C2×D412yes—
212C3×C5×D4—28no—
213C2×C3×C4×C5—21no—
214C2×C3×C4×C5—21no—
215C2×C3×C4×C5—21no—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—21no—
226C2×C3×C4×C5—44no—
227C2×C3×C4×C5C22×C412yes—
228C2×C3×C4×C5#4112yescomplemented
229C3×C22⋊D5—28no—
230C3×C22⋊D5C22⋊C4116yescomplemented
231C2×C3×Dic5—28no—
232C2×C3×Dic5—21no—
233C2×C3×Dic5—21no—
234C2×C3×Dic5—21no—
235C2×C3×Dic5—21no—
236C2×C3×Dic5—21no—
237C2×C3×Dic5—21no—
238C2×C3×Dic5—28no—
239C2×C3×Dic5—21no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
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—44no—
249C2×C3×Dic5C22×C412yes—
250C2×C3×Dic5C22×C412yes—
251C2×C3×Dic5C22×C412yes—
252C2×C3×Dic5C2×D412yes—
253C2×C3×Dic5C2×D412yes—
254C2×C3×Dic5#4112yescomplemented
255C3×C4×D5—28no—
256C3×C4×D5—44no—
257C3×C4×D5—44no—
258C3×Dic10—28no—
259C2×C3×#41—58no—
260C2×C3×#41—104no—
261C2×C3×#41—104no—
262C22×C3×Q8—51no—
263C22×C3×D4—51no—
264C22×C3×D4—51no—
265C22×C3×D4C2×D511yescharacteristic
266C23×C3×C4—51no—
267C23×C3×C4—51no—
268C23×C3×C4—51no—
269C23×C3×C4—51no—
270C23×C3×C4—51no—
271C23×C3×C4—51no—
272C23×C3×C4C2×D511yescharacteristic
273C3×C4×D4—104no—
274C3×C4×D4—104no—
275C2×C3×C4⋊C4—51no—
276C2×C3×C4⋊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⋊C4C2×D511yescharacteristic
283C2×C3×C22⋊C4C2×D511yescharacteristic
284C2×C3×C22⋊C4C2×D511yescharacteristic
285C2×C3×C42—51no—
286C2×C3×C42—51no—
287C3×#95—51no—
288C3×#95—51no—
289C3×#95—51no—
290C3×#95—51no—
291C3×#95—51no—
292C3×#95—51no—
293C3×#95—51no—
294C3×#95—51no—
295C3×#95—51no—
296C3×#95—51no—
297C3×#95C2×D511yescharacteristic
298C3×#95C2×D511yescharacteristic
299C24×C5C23×C311yescharacteristic
300C24×C5C23×C311yescharacteristic
301C23×D5C23×C311yescharacteristic
302C2×C5×D4—22no—
303C2×C5×D4—22no—
304C2×C5×D4C2×C3×C414yescomplemented
305C22×C4×C5—22no—
306C22×C4×C5—22no—
307C22×C4×C5—41no—
308C22×C4×C5C23×C311yescharacteristic
309C22×C4×C5C23×C311yescharacteristic
310C22×C4×C5C23×C311yescharacteristic
311C22×C4×C5C23×C311yescharacteristic
312C22×C4×C5C23×C311yescharacteristic
313C2×C22⋊D5—22no—
314C2×C22⋊D5—22no—
315C2×C22⋊D5C2×C3×C414yes—
316C2×C22⋊D5C2×C3×C414yescomplemented
317C2×C22⋊D5C3×D414yes—
318C2×C22⋊D5C3×D414yes—
319C22×Dic5—22no—
320C22×Dic5—22no—
321C22×Dic5—22no—
322C22×Dic5—22no—
323C22×Dic5—22no—
324C22×Dic5—22no—
325C22×Dic5—41no—
326C22×Dic5C2×C3×C414yescomplemented
327C22×Dic5C2×C3×C414yescomplemented
328C22×Dic5C23×C311yescharacteristic
329C22×Dic5C23×C311yescharacteristic
330C22×Dic5C23×C311yescharacteristic
331C22×Dic5C23×C311yescharacteristic
332C22×Dic5C23×C311yescharacteristic
333C22×Dic5C23×C311yescharacteristic
334C22×Dic5C23×C311yescharacteristic
335#711—232no—
336C2×C4×D5—22no—
337C2×C4×D5—22no—
338C2×C4×D5—22no—
339C2×C4×D5—22no—
340C2×C4×D5—22no—
341C2×C4×D5—22no—
342C2×C4×D5—41no—
343C2×C4×D5—41no—
344C2×C4×D5C2×C3×C414yescomplemented
345C2×Dic10—22no—
346C2×Dic10—22no—
347C2×Dic10C2×C3×C414yescomplemented
348C5×C22⋊C4—22no—
349C5×C22⋊C4—22no—
350C5×C22⋊C4—41no—
351C22⋊Dic5—22no—
352C22⋊Dic5—22no—
353C22⋊Dic5—41no—
354#685—22no—
355#685—22no—
356#683—22no—
357#683—22no—
358C4×Dic5—22no—
359C4×Dic5—22no—
360C22×#41—51no—
361C2×C4×D4—51no—
362C2×C4×D4—51no—
363#391—51no—
364#391—51no—
365#386—51no—
366#386—51no—
367#386—51no—
368#386C3×D511yescharacteristic, complemented
369#381—51no—
370#381—51no—
371#380—51no—
372C4×C22⋊C4—51no—
373C2×#95—51no—
374C2×#95—51no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—22no—
378C22×C3×C5—22no—
379C22×C3×C5—22no—
380C22×C3×C5—22no—
381C22×C3×C5—22no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5C2×C22⋊C414yes—
389C22×C3×C5C23×C411yescharacteristic
390C22×C3×C5C22×D411yescharacteristic
391C22×C3×C5C22×D411yescharacteristic
392C22×C3×C5C2×#4111yescharacteristic
393C22×C3×C5C2×#4111yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C22×C3×C52−1+411yescharacteristic
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×D5C2×C22⋊C414yes—
403C3×C4×C5—22no—
404C3×C4×C5—22no—
405C3×C4×C5—41no—
406C3×C4×C5—41no—
407C3×C4×C5—41no—
408C3×Dic5—22no—
409C3×Dic5—22no—
410C3×Dic5—22no—
411C3×Dic5—41no—
412C3×Dic5—41no—
413C3×Dic5—41no—
414C3×Dic5C2×C22⋊C414yes—
415C24×C3—51no—
416C24×C3C22×D511yescharacteristic
417C24×C3C22×D511yescharacteristic
418C3×#41—1032no—
419C2×C3×Q8—54no—
420C2×C3×Q8—102no—
421C2×C3×Q8—102no—
422C2×C3×D4—22no—
423C2×C3×D4—22no—
424C2×C3×D4—54no—
425C2×C3×D4—54no—
426C2×C3×D4—54no—
427C2×C3×D4—54no—
428C2×C3×D4—102no—
429C2×C3×D4—102no—
430C2×C3×D4C4×D514yescomplemented
431C22×C3×C4—22no—
432C22×C3×C4—22no—
433C22×C3×C4—41no—
434C22×C3×C4—51no—
435C22×C3×C4—54no—
436C22×C3×C4—54no—
437C22×C3×C4—51no—
438C22×C3×C4—51no—
439C22×C3×C4—51no—
440C22×C3×C4—54no—
441C22×C3×C4—51no—
442C22×C3×C4—51no—
443C22×C3×C4—51no—
444C22×C3×C4—102no—
445C22×C3×C4—102no—
446C22×C3×C4—102no—
447C22×C3×C4—102no—
448C22×C3×C4—102no—
449C22×C3×C4—102no—
450C22×C3×C4—102no—
451C22×C3×C4—102no—
452C22×C3×C4—102no—
453C22×C3×C4—102no—
454C22×C3×C4—102no—
455C22×C3×C4—102no—
456C22×C3×C4—201no—
457C22×C3×C4—201no—
458C22×C3×C4—201no—
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D511yescharacteristic
462C22×C3×C4C22×D511yescharacteristic
463C22×C3×C4C22×D511yescharacteristic
464C3×C4⋊C4—102no—
465C3×C4⋊C4—102no—
466C3×C22⋊C4—22no—
467C3×C22⋊C4—22no—
468C3×C22⋊C4—41no—
469C3×C22⋊C4—102no—
470C3×C22⋊C4—102no—
471C3×C22⋊C4—102no—
472C3×C22⋊C4—102no—
473C3×C22⋊C4—201no—
474C3×C42—102no—
475C3×C42—102no—
476C23×C5—21no—
477C23×C5—21no—
478C23×C5—21no—
479C23×C5—21no—
480C23×C5—21no—
481C23×C5—21no—
482C23×C5—21no—
483C23×C5—21no—
484C23×C5—21no—
485C23×C5—21no—
486C23×C5C22×C3×C412yes—
487C23×C5C22×C3×C412yes—
488C23×C5C2×C3×D412yes—
489C23×C5C2×C3×D412yes—
490C23×C5C24×C311yescharacteristic
491C22×D5—21no—
492C22×D5—21no—
493C22×D5—21no—
494C22×D5—21no—
495C22×D5C22×C3×C412yes—
496C22×D5C2×C3×D412yes—
497C22×D5C2×C3×D412yes—
498C5×D4—28no—
499C2×C4×C5—21no—
500C2×C4×C5—21no—
501C2×C4×C5—21no—
502C2×C4×C5—21no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—21no—
512C2×C4×C5—44no—
513C2×C4×C5C22×C3×C412yes—
514C2×C4×C5C3×#4112yescomplemented
515C22⋊D5—28no—
516C22⋊D5C3×C22⋊C4116yescomplemented
517C2×Dic5—28no—
518C2×Dic5—21no—
519C2×Dic5—21no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—28no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—21no—
529C2×Dic5—21no—
530C2×Dic5—21no—
531C2×Dic5—21no—
532C2×Dic5—21no—
533C2×Dic5—21no—
534C2×Dic5—44no—
535C2×Dic5C22×C3×C412yes—
536C2×Dic5C22×C3×C412yes—
537C2×Dic5C22×C3×C412yes—
538C2×Dic5C2×C3×D412yes—
539C2×Dic5C2×C3×D412yes—
540C2×Dic5C3×#4112yescomplemented
541C4×D5—28no—
542C4×D5—44no—
543C4×D5—44no—
544Dic10—28no—
545C2×#41—58no—
546C2×#41—104no—
547C2×#41—104no—
548C22×Q8—51no—
549C22×D4—51no—
550C22×D4—51no—
551C22×D4C2×C3×D511yescharacteristic
552C23×C4—51no—
553C23×C4—51no—
554C23×C4—51no—
555C23×C4—51no—
556C23×C4—51no—
557C23×C4—51no—
558C23×C4C2×C3×D511yescharacteristic
559C4×D4—104no—
560C4×D4—104no—
561C2×C4⋊C4—51no—
562C2×C4⋊C4—51no—
563C2×C22⋊C4—51no—
564C2×C22⋊C4—51no—
565C2×C22⋊C4—51no—
566C2×C22⋊C4—51no—
567C2×C22⋊C4—51no—
568C2×C22⋊C4C2×C3×D511yescharacteristic
569C2×C22⋊C4C2×C3×D511yescharacteristic
570C2×C22⋊C4C2×C3×D511yescharacteristic
571C2×C42—51no—
572C2×C42—51no—
573#95—51no—
574#95—51no—
575#95—51no—
576#95—51no—
577#95—51no—
578#95—51no—
579#95—51no—
580#95—51no—
581#95—51no—
582#95—51no—
583#95C2×C3×D511yescharacteristic
584#95C2×C3×D511yescharacteristic
585C2×C3×C5—24no—
586C2×C3×C5—42no—
587C2×C3×C5C22×C22⋊C411yescharacteristic
588C2×C3×C5C4×#4111yescharacteristic
589C2×C3×C5#52011yescharacteristic
590C2×C3×C5#54611yescharacteristic
591C2×C3×C5#54611yescharacteristic
592C2×C3×C5#54711yescharacteristic
593C2×C3×C5#54711yescharacteristic
594C3×D5—24no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—52no—
606C23×C3—52no—
607C23×C3—52no—
608C23×C3—101no—
609C23×C3—101no—
610C23×C3—101no—
611C23×C3—101no—
612C23×C3C2×C4×D512yes—
613C23×C3C2×C4×D512yes—
614C23×C3D4×D512yes—
615C23×C3D4×D512yes—
616C23×C3C23×D511yescharacteristic
617C3×Q8—108no—
618C3×D4—28no—
619C3×D4—516no—
620C3×D4—108no—
621C2×C3×C4—21no—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—21no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—21no—
634C2×C3×C4—44no—
635C2×C3×C4—52no—
636C2×C3×C4—52no—
637C2×C3×C4—52no—
638C2×C3×C4—52no—
639C2×C3×C4—52no—
640C2×C3×C4—52no—
641C2×C3×C4—108no—
642C2×C3×C4—108no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—101no—
648C2×C3×C4—101no—
649C2×C3×C4—108no—
650C2×C3×C4—101no—
651C2×C3×C4—101no—
652C2×C3×C4—101no—
653C2×C3×C4—101no—
654C2×C3×C4—101no—
655C2×C3×C4—101no—
656C2×C3×C4—101no—
657C2×C3×C4—101no—
658C2×C3×C4—101no—
659C2×C3×C4—204no—
660C2×C3×C4—204no—
661C2×C3×C4—204no—
662C2×C3×C4C2×C4×D512yes—
663C2×C3×C4#71112yescomplemented
664C22×C5—22no—
665C22×C5—22no—
666C22×C5—22no—
667C22×C5—22no—
668C22×C5—22no—
669C22×C5—22no—
670C22×C5—22no—
671C22×C5—22no—
672C22×C5—22no—
673C22×C5—41no—
674C22×C5—41no—
675C22×C5—41no—
676C22×C5—41no—
677C22×C5C2×C3×C22⋊C414yes—
678C22×C5C23×C3×C411yescharacteristic
679C22×C5C22×C3×D411yescharacteristic
680C22×C5C22×C3×D411yescharacteristic
681C22×C5C2×C3×#4111yescharacteristic
682C22×C5C2×C3×#4111yescharacteristic
683C22×C5C3×H(5,𝔽2)11yescharacteristic
684C22×C5C3×2−1+411yescharacteristic
685C2×D5—22no—
686C2×D5—22no—
687C2×D5—22no—
688C2×D5—22no—
689C2×D5—22no—
690C2×D5—22no—
691C2×D5C2×C3×C22⋊C414yes—
692C4×C5—22no—
693C4×C5—22no—
694C4×C5—41no—
695C4×C5—41no—
696C4×C5—41no—
697Dic5—22no—
698Dic5—22no—
699Dic5—22no—
700Dic5—41no—
701Dic5—41no—
702Dic5—41no—
703Dic5C2×C3×C22⋊C414yes—
704C24—51no—
705C24C22×C3×D511yescharacteristic
706C24C22×C3×D511yescharacteristic
707#41—1032no—
708C2×Q8—54no—
709C2×Q8—102no—
710C2×Q8—102no—
711C2×D4—22no—
712C2×D4—22no—
713C2×D4—54no—
714C2×D4—54no—
715C2×D4—54no—
716C2×D4—54no—
717C2×D4—102no—
718C2×D4—102no—
719C2×D4C3×C4×D514yescomplemented
720C22×C4—22no—
721C22×C4—22no—
722C22×C4—41no—
723C22×C4—51no—
724C22×C4—54no—
725C22×C4—54no—
726C22×C4—51no—
727C22×C4—51no—
728C22×C4—51no—
729C22×C4—54no—
730C22×C4—51no—
731C22×C4—51no—
732C22×C4—51no—
733C22×C4—102no—
734C22×C4—102no—
735C22×C4—102no—
736C22×C4—102no—
737C22×C4—102no—
738C22×C4—102no—
739C22×C4—102no—
740C22×C4—102no—
741C22×C4—102no—
742C22×C4—102no—
743C22×C4—102no—
744C22×C4—102no—
745C22×C4—201no—
746C22×C4—201no—
747C22×C4—201no—
748C22×C4C22×C3×D511yescharacteristic
749C22×C4C22×C3×D511yescharacteristic
750C22×C4C22×C3×D511yescharacteristic
751C22×C4C22×C3×D511yescharacteristic
752C22×C4C22×C3×D511yescharacteristic
753C4⋊C4—102no—
754C4⋊C4—102no—
755C22⋊C4—22no—
756C22⋊C4—22no—
757C22⋊C4—41no—
758C22⋊C4—102no—
759C22⋊C4—102no—
760C22⋊C4—102no—
761C22⋊C4—102no—
762C22⋊C4—201no—
763C42—102no—
764C42—102no—
765C3×C5#233911yescharacteristic, complemented, Hall
766C22×C3—22no—
767C22×C3—22no—
768C22×C3—22no—
769C22×C3—22no—
770C22×C3—22no—
771C22×C3—22no—
772C22×C3—22no—
773C22×C3—22no—
774C22×C3—22no—
775C22×C3—41no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—54no—
780C22×C3—102no—
781C22×C3—102no—
782C22×C3—102no—
783C22×C3—102no—
784C22×C3—102no—
785C22×C3—102no—
786C22×C3D5×C22⋊C414yes—
787C22×C3C22×C4×D511yescharacteristic
788C22×C3C2×D4×D511yescharacteristic
789C22×C3C2×D4×D511yescharacteristic
790C22×C3C2×#71111yescharacteristic
791C22×C3#414411yescharacteristic
792C22×C3D5×#4111yescharacteristic
793C22×C3#415011yescharacteristic
794C3×C4—22no—
795C3×C4—22no—
796C3×C4—41no—
797C3×C4—41no—
798C3×C4—41no—
799C3×C4—54no—
800C3×C4—102no—
801C3×C4—102no—
802C3×C4—102no—
803C3×C4—201no—
804C3×C4—201no—
805C3×C4—201no—
806C2×C5—24no—
807C2×C5—42no—
808C2×C5C22×C3×C22⋊C411yescharacteristic
809C2×C5C3×C4×#4111yescharacteristic
810C2×C5C3×#52011yescharacteristic
811C2×C5C3×#54611yescharacteristic
812C2×C5C3×#54611yescharacteristic
813C2×C5C3×#54711yescharacteristic
814C2×C5C3×#54711yescharacteristic
815D5—24no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—52no—
827C23—52no—
828C23—52no—
829C23—101no—
830C23—101no—
831C23—101no—
832C23—101no—
833C23C2×C3×C4×D512yes—
834C23C2×C3×C4×D512yes—
835C23C3×D4×D512yes—
836C23C3×D4×D512yes—
837C23C23×C3×D511yescharacteristic
838Q8—108no—
839D4—28no—
840D4—516no—
841D4—108no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—44no—
856C2×C4—52no—
857C2×C4—52no—
858C2×C4—52no—
859C2×C4—52no—
860C2×C4—52no—
861C2×C4—52no—
862C2×C4—108no—
863C2×C4—108no—
864C2×C4—101no—
865C2×C4—101no—
866C2×C4—101no—
867C2×C4—101no—
868C2×C4—101no—
869C2×C4—101no—
870C2×C4—108no—
871C2×C4—101no—
872C2×C4—101no—
873C2×C4—101no—
874C2×C4—101no—
875C2×C4—101no—
876C2×C4—101no—
877C2×C4—101no—
878C2×C4—101no—
879C2×C4—101no—
880C2×C4—204no—
881C2×C4—204no—
882C2×C4—204no—
883C2×C4C2×C3×C4×D512yes—
884C2×C4C3×#71112yescomplemented
885C2×C3—24no—
886C2×C3—42no—
887C2×C3—104no—
888C2×C3C2×D5×C22⋊C411yescharacteristic
889C2×C3C4×#71111yescharacteristic
890C2×C3#6588011yescharacteristic
891C2×C3#6592511yescharacteristic
892C2×C3#6594411yescharacteristic
893C2×C3#6594511yescharacteristic
894C2×C3#6598911yescharacteristic
895C5C3×#233911yescharacteristic, complemented, Sylow
896C22—22no—
897C22—22no—
898C22—22no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—54no—
910C22—102no—
911C22—102no—
912C22—102no—
913C22—102no—
914C22—102no—
915C22—102no—
916C22C3×D5×C22⋊C414yes—
917C22C22×C3×C4×D511yescharacteristic
918C22C2×C3×D4×D511yescharacteristic
919C22C2×C3×D4×D511yescharacteristic
920C22C2×C3×#71111yescharacteristic
921C22C3×#414411yescharacteristic
922C22C3×D5×#4111yescharacteristic
923C22C3×#415011yescharacteristic
924C4—22no—
925C4—22no—
926C4—41no—
927C4—41no—
928C4—41no—
929C4—54no—
930C4—102no—
931C4—102no—
932C4—102no—
933C4—201no—
934C4—201no—
935C4—201no—
936C3#1060640311yescharacteristic, direct product factor, Sylow
937C2—24no—
938C2—42no—
939C2—104no—
940C2C2×C3×D5×C22⋊C411yescharacteristic
941C2C3×C4×#71111yescharacteristic
942C2C3×#6588011yescharacteristic
943C2C3×#6592511yescharacteristic
944C2C3×#6594411yescharacteristic
945C2C3×#6594511yescharacteristic
946C2C3×#6598911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC22×C3×#711C2
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2339
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#386

Complements

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

NH ≅ G/Ntype
2. C2×C3×C4×C22⋊D5C2semidirect
3. C2×C3×#4027C2semidirect
4. C3×C5×#386C2semidirect
5. C3×#65509C2semidirect
6. C2×C3×#3963C2semidirect
7. C3×#65245C2semidirect
8. C3×#65245C2semidirect
9. C3×#65232C2semidirect
10. C3×#65231C2semidirect
11. C3×C22⋊C4×Dic5C2semidirect
12. C3×#64953C2semidirect
13. C3×D5×#95C2semidirect
14. C3×#64935C2semidirect
15. C3×#64935C2semidirect
16. #10606403C3direct (N × H)
26. C2×C3×#711C4semidirect
59. C2×C4×C22⋊D5C2×C3semidirect
60. C2×#4027C2×C3semidirect
61. C5×#386C2×C3semidirect
62. #65509C2×C3semidirect
63. C2×#3963C2×C3semidirect
64. #65245C2×C3semidirect
65. #65245C2×C3semidirect
66. #65232C2×C3semidirect
67. #65231C2×C3semidirect
68. C22⋊C4×Dic5C2×C3semidirect
69. #64953C2×C3semidirect
70. D5×#95C2×C3semidirect
71. #64935C2×C3semidirect
72. #64935C2×C3semidirect
78. C2×C3×C5×D4C2×C4semidirect
90. C2×C3×C22⋊D5C2×C4semidirect
100. C22×C3×Dic5C2×C4semidirect
101. C22×C3×Dic5C2×C4semidirect
118. C2×C3×C4×D5C2×C4semidirect
121. C2×C3×Dic10C2×C4semidirect
142. C3×#386D5semidirect
158. C2×#711C3×C4semidirect
228. C2×C3×C4×C5#41semidirect
230. C3×C22⋊D5C22⋊C4semidirect
254. C2×C3×Dic5#41semidirect
304. C2×C5×D4C2×C3×C4semidirect
316. C2×C22⋊D5C2×C3×C4semidirect
326. C22×Dic5C2×C3×C4semidirect
327. C22×Dic5C2×C3×C4semidirect
344. C2×C4×D5C2×C3×C4semidirect
347. C2×Dic10C2×C3×C4semidirect
368. #386C3×D5semidirect
430. C2×C3×D4C4×D5semidirect
514. C2×C4×C5C3×#41semidirect
516. C22⋊D5C3×C22⋊C4semidirect
540. C2×Dic5C3×#41semidirect
663. C2×C3×C4#711semidirect
719. C2×D4C3×C4×D5semidirect
765. C3×C5#2339semidirect
884. C2×C4C3×#711semidirect
895. C5C3×#2339semidirect
936. C3#10606403direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7112
C2×C3×C4×C22⋊D52
C2×C3×#40272
C3×C5×#3862
C3×#655092
C2×C3×#39632
C3×#652452
C3×#652322
C3×#652312
C3×C22⋊C4×Dic52
C3×#649532
C3×D5×#952
C3×#649352
#106064033
C3×#23395