Finite Group Databasebeta

← C3×#10606607 #14323355

Subgroups — C3×#10606607 #14323355

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×#4083C211yesmaximal, characteristic
2C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
3C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
4C3×C5×#386C211yesmaximal, characteristic, complemented
5C3×#65510C211yesmaximal, characteristic, complemented
6C3×#65502C211yesmaximal, characteristic, complemented
7C3×#65246C211yesmaximal, characteristic, complemented
8C3×#65245C211yesmaximal, characteristic, complemented
9C3×#65244C211yesmaximal, characteristic, complemented
10C3×#65233C211yesmaximal, characteristic, complemented
11C3×#65233C211yesmaximal, characteristic, complemented
12C3×#64959C211yesmaximal, characteristic, complemented
13C3×#64958C211yesmaximal, characteristic, complemented
14C3×#64957C211yesmaximal, characteristic, complemented
15C3×#64955C211yesmaximal, characteristic, complemented
16#10606607C311yesmaximal, characteristic, direct product factor, Hall
17C24×C3×D5C2211yescharacteristic
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic, complemented
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
27C2×C3×C22⋊Dic5C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
31C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
32C3×#4083C418yescomplemented
33C3×C4×C22⋊D5—24no—
34C2×C3×#685C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×#685C2211yescharacteristic
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
43C2×C3×#683C2211yescharacteristic, complemented
44C2×C3×#683C2211yescharacteristic, complemented
45C2×C3×C4×Dic5C2211yescharacteristic, complemented
46C2×C3×C4×Dic5C2211yescharacteristic, complemented
47C2×C3×C4×Dic5C2211yescharacteristic, complemented
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×#4083C2×C311yescharacteristic
57C2×C4×C22⋊D5C2×C311yescharacteristic, complemented
58C2×D5×C22⋊C4C2×C311yescharacteristic, complemented
59C5×#386C2×C311yescharacteristic, complemented
60#65510C2×C311yescharacteristic, complemented
61#65502C2×C311yescharacteristic, complemented
62#65246C2×C311yescharacteristic, complemented
63#65245C2×C311yescharacteristic, complemented
64#65244C2×C311yescharacteristic, complemented
65#65233C2×C311yescharacteristic, complemented
66#65233C2×C311yescharacteristic, complemented
67#64959C2×C311yescharacteristic, complemented
68#64958C2×C311yescharacteristic, complemented
69#64957C2×C311yescharacteristic, complemented
70#64955C2×C311yescharacteristic, complemented
71C24×C3×C5C2311yescharacteristic
72C24×C3×C5C2311yescharacteristic
73C23×C3×D5—22no—
74C23×C3×D5—22no—
75C23×C3×D5—41no—
76C23×C3×D5—41no—
77C23×C3×D5—41no—
78C23×C3×D5—41no—
79C23×C3×D5C2×C414yescomplemented
80C23×C3×D5C2311yescharacteristic
81C23×C3×D5C2311yescharacteristic
82C2×C3×C5×D4—41no—
83C2×C3×C5×D4—41no—
84C2×C3×C5×D4C2×C414yescomplemented
85C22×C3×C4×C5—22no—
86C22×C3×C4×C5—41no—
87C22×C3×C4×C5—41no—
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C2×C3×C22⋊D5—22no—
94C2×C3×C22⋊D5—22no—
95C2×C3×C22⋊D5—41no—
96C2×C3×C22⋊D5—41no—
97C2×C3×C22⋊D5C2×C414yes—
98C2×C3×C22⋊D5C2×C414yescomplemented
99C22×C3×Dic5C2311yescharacteristic
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C2×C3×C4×D5—22no—
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×C22⋊C4—22no—
112C3×C5×C22⋊C4—41no—
113C3×C5×C22⋊C4—41no—
114C3×C22⋊Dic5—22no—
115C3×C22⋊Dic5—22no—
116C3×C22⋊Dic5—41no—
117C3×C22⋊Dic5—41no—
118C3×C22⋊Dic5C2×C414yescomplemented
119C3×#685—22no—
120C3×#685—22no—
121C3×#685—22no—
122C3×#685—22no—
123C3×#685—41no—
124C3×#685—41no—
125C3×#685C2×C414yescomplemented
126C3×#685C2×C414yescomplemented
127C3×C4⋊Dic5—41no—
128C3×#683—22no—
129C3×#683—41no—
130C3×C4×Dic5—22no—
131C3×C4×Dic5—41no—
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×#388—51no—
142C3×#386—51no—
143C3×#386—51no—
144C3×#386D511yescharacteristic, complemented
145C3×#385—51no—
146C3×#379—51no—
147C3×C4×C22⋊C4—51no—
148C24×D5C22×C311yescharacteristic
149C22×C5×D4C22×C311yescharacteristic
150C23×C4×C5C22×C311yescharacteristic, complemented
151C22×C22⋊D5C22×C311yescharacteristic
152C22×C22⋊D5C22×C311yescharacteristic
153C22×C4×D5C22×C311yescharacteristic
154C22×C4×D5C22×C311yescharacteristic
155C2×C5×C22⋊C4C22×C311yescharacteristic
156C2×C5×C22⋊C4C22×C311yescharacteristic
157C2×C5×C22⋊C4C22×C311yescharacteristic, complemented
158C2×C22⋊Dic5C22×C311yescharacteristic
159C2×C22⋊Dic5C22×C311yescharacteristic
160C2×C22⋊Dic5C22×C311yescharacteristic
161C2×C22⋊Dic5C22×C311yescharacteristic, complemented
162C2×C22⋊Dic5C22×C311yescharacteristic, complemented
163#4083C3×C418yescomplemented
164C4×C22⋊D5—24no—
165C2×#685C22×C311yescharacteristic
166C2×#685C22×C311yescharacteristic
167C2×#685C22×C311yescharacteristic
168C2×#685C22×C311yescharacteristic
169C2×#685C22×C311yescharacteristic
170C2×#685C22×C311yescharacteristic
171C2×#685C22×C311yescharacteristic
172C2×#685C22×C311yescharacteristic
173C2×C4⋊Dic5C22×C311yescharacteristic, complemented
174C2×#683C22×C311yescharacteristic, complemented
175C2×#683C22×C311yescharacteristic, complemented
176C2×C4×Dic5C22×C311yescharacteristic, complemented
177C2×C4×Dic5C22×C311yescharacteristic, complemented
178C2×C4×Dic5C22×C311yescharacteristic, complemented
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×C5—21no—
194C23×C3×C5—21no—
195C23×C3×C5—21no—
196C23×C3×C5—21no—
197C23×C3×C5—21no—
198C23×C3×C5—21no—
199C23×C3×C5C22×C412yes—
200C23×C3×C5C22×C412yes—
201C23×C3×C5C2411yescharacteristic
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—21no—
212C22×C3×D5—28no—
213C22×C3×D5—44no—
214C22×C3×D5—44no—
215C22×C3×D5—44no—
216C22×C3×D5—44no—
217C22×C3×D5—44no—
218C22×C3×D5—44no—
219C22×C3×D5C22×C412yes—
220C22×C3×D5C22×C412yes—
221C22×C3×D5C2×D412yes—
222C22×C3×D5#4112yes—
223C3×C5×D4—44no—
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—44no—
238C2×C3×C4×C5C22×C412yes—
239C2×C3×C4×C5C2×D412yes—
240C3×C22⋊D5—28no—
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×Dic5—21no—
256C2×C3×Dic5—21no—
257C2×C3×Dic5C22×C412yes—
258C2×C3×Dic5C22×C412yes—
259C2×C3×Dic5C2×D412yes—
260C3×C4×D5—44no—
261C3×C4×D5—44no—
262C25×C3—51no—
263C22×C3×D4—51no—
264C22×C3×D4—51no—
265C22×C3×D4C2×D511yescharacteristic
266C23×C3×C4—51no—
267C23×C3×C4—51no—
268C23×C3×C4C2×D511yescharacteristic, complemented
269C3×#120—58no—
270C3×C4×D4—104no—
271C2×C3×C4⋊C4—51no—
272C2×C3×C4⋊C4—51no—
273C2×C3×C4⋊C4—51no—
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, complemented
291C2×C3×C42—51no—
292C2×C3×C42—51no—
293C2×C3×C42—51no—
294C3×#95—51no—
295C3×#95—51no—
296C3×#95—51no—
297C3×#95—51no—
298C3×#95C2×D511yescharacteristic, complemented
299C3×#95C2×D511yescharacteristic, complemented
300C24×C5C23×C311yescharacteristic
301C24×C5C23×C311yescharacteristic
302C23×D5—22no—
303C23×D5—22no—
304C23×D5—41no—
305C23×D5—41no—
306C23×D5—41no—
307C23×D5—41no—
308C23×D5C2×C3×C414yescomplemented
309C23×D5C23×C311yescharacteristic
310C23×D5C23×C311yescharacteristic
311C2×C5×D4—41no—
312C2×C5×D4—41no—
313C2×C5×D4C2×C3×C414yescomplemented
314C22×C4×C5—22no—
315C22×C4×C5—41no—
316C22×C4×C5—41no—
317C22×C4×C5C23×C311yescharacteristic
318C22×C4×C5C23×C311yescharacteristic
319C22×C4×C5C23×C311yescharacteristic
320C22×C4×C5C23×C311yescharacteristic
321C22×C4×C5C23×C311yescharacteristic
322C2×C22⋊D5—22no—
323C2×C22⋊D5—22no—
324C2×C22⋊D5—41no—
325C2×C22⋊D5—41no—
326C2×C22⋊D5C2×C3×C414yes—
327C2×C22⋊D5C2×C3×C414yescomplemented
328C22×Dic5C23×C311yescharacteristic
329C22×Dic5C23×C311yescharacteristic
330C22×Dic5C23×C311yescharacteristic
331C22×Dic5C23×C311yescharacteristic
332C22×Dic5C23×C311yescharacteristic
333C22×Dic5C23×C311yescharacteristic
334C2×C4×D5—22no—
335C2×C4×D5—41no—
336C2×C4×D5—41no—
337C2×C4×D5—41no—
338C2×C4×D5—41no—
339C2×C4×D5C3×D414yescomplemented
340C5×C22⋊C4—22no—
341C5×C22⋊C4—41no—
342C5×C22⋊C4—41no—
343C22⋊Dic5—22no—
344C22⋊Dic5—22no—
345C22⋊Dic5—41no—
346C22⋊Dic5—41no—
347C22⋊Dic5C2×C3×C414yescomplemented
348#685—22no—
349#685—22no—
350#685—22no—
351#685—22no—
352#685—41no—
353#685—41no—
354#685C2×C3×C414yescomplemented
355#685C2×C3×C414yescomplemented
356C4⋊Dic5—41no—
357#683—22no—
358#683—41no—
359C4×Dic5—22no—
360C4×Dic5—41no—
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#388—51no—
371#386—51no—
372#386—51no—
373#386C3×D511yescharacteristic, complemented
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—22no—
381C22×C3×C5—22no—
382C22×C3×C5—22no—
383C22×C3×C5—41no—
384C22×C3×C5—41no—
385C22×C3×C5—41no—
386C22×C3×C5—41no—
387C22×C3×C5—41no—
388C22×C3×C5—41no—
389C22×C3×C5—41no—
390C22×C3×C5—41no—
391C22×C3×C5C23×C411yescharacteristic
392C22×C3×C5C22×D411yescharacteristic
393C22×C3×C5C2×#4111yescharacteristic
394C22×C3×C5H(5,𝔽2)11yescharacteristic
395C22×C3×C5H(5,𝔽2)11yescharacteristic
396C22×C3×C5H(5,𝔽2)11yescharacteristic
397C22×C3×C5H(5,𝔽2)11yescharacteristic
398C2×C3×D5—22no—
399C2×C3×D5—22no—
400C2×C3×D5—22no—
401C2×C3×D5—22no—
402C2×C3×D5—22no—
403C2×C3×D5—22no—
404C2×C3×D5—22no—
405C2×C3×D5—22no—
406C2×C3×D5—22no—
407C2×C3×D5—416no—
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—41no—
416C3×C4×C5—41no—
417C3×C4×C5—41no—
418C3×Dic5—22no—
419C3×Dic5—22no—
420C3×Dic5—22no—
421C3×Dic5—41no—
422C3×Dic5—41no—
423C3×Dic5—41no—
424C24×C3—51no—
425C24×C3—51no—
426C24×C3—54no—
427C24×C3—102no—
428C24×C3—102no—
429C24×C3—201no—
430C24×C3—201no—
431C24×C3—201no—
432C24×C3—201no—
433C24×C3C22×D511yescharacteristic
434C24×C3C22×D511yescharacteristic
435C2×C3×D4—41no—
436C2×C3×D4—41no—
437C2×C3×D4—54no—
438C2×C3×D4—54no—
439C2×C3×D4—102no—
440C2×C3×D4—102no—
441C2×C3×D4—201no—
442C2×C3×D4—201no—
443C2×C3×D4C4×D514yescomplemented
444C22×C3×C4—22no—
445C22×C3×C4—41no—
446C22×C3×C4—41no—
447C22×C3×C4—51no—
448C22×C3×C4—51no—
449C22×C3×C4—51no—
450C22×C3×C4—54no—
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—102no—
455C22×C3×C4—201no—
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—201no—
466C3×C4⋊C4—201no—
467C3×C22⋊C4—22no—
468C3×C22⋊C4—41no—
469C3×C22⋊C4—41no—
470C3×C22⋊C4—54no—
471C3×C22⋊C4—54no—
472C3×C22⋊C4—54no—
473C3×C22⋊C4—102no—
474C3×C22⋊C4—102no—
475C3×C22⋊C4—102no—
476C3×C22⋊C4—102no—
477C3×C22⋊C4—102no—
478C3×C22⋊C4—102no—
479C3×C22⋊C4—201no—
480C3×C22⋊C4—201no—
481C3×C22⋊C4—201no—
482C3×C22⋊C4—201no—
483C3×C42—102no—
484C3×C42—201no—
485C3×C42—201no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—21no—
489C23×C5—21no—
490C23×C5—21no—
491C23×C5—21no—
492C23×C5—21no—
493C23×C5—21no—
494C23×C5—21no—
495C23×C5—21no—
496C23×C5—21no—
497C23×C5—21no—
498C23×C5C22×C3×C412yes—
499C23×C5C22×C3×C412yes—
500C23×C5C24×C311yescharacteristic
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—21no—
511C22×D5—28no—
512C22×D5—44no—
513C22×D5—44no—
514C22×D5—44no—
515C22×D5—44no—
516C22×D5—44no—
517C22×D5—44no—
518C22×D5C22×C3×C412yes—
519C22×D5C22×C3×C412yes—
520C22×D5C2×C3×D412yes—
521C22×D5C3×#4112yes—
522C5×D4—44no—
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—44no—
537C2×C4×C5C22×C3×C412yes—
538C2×C4×C5C2×C3×D412yes—
539C22⋊D5—28no—
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×Dic5—21no—
555C2×Dic5—21no—
556C2×Dic5C22×C3×C412yes—
557C2×Dic5C22×C3×C412yes—
558C2×Dic5C2×C3×D412yes—
559C4×D5—44no—
560C4×D5—44no—
561C25—51no—
562C22×D4—51no—
563C22×D4—51no—
564C22×D4C2×C3×D511yescharacteristic
565C23×C4—51no—
566C23×C4—51no—
567C23×C4C2×C3×D511yescharacteristic, complemented
568#120—58no—
569C4×D4—104no—
570C2×C4⋊C4—51no—
571C2×C4⋊C4—51no—
572C2×C4⋊C4—51no—
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, complemented
590C2×C42—51no—
591C2×C42—51no—
592C2×C42—51no—
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×C5—42no—
601C2×C3×C5C2×C4×D411yescharacteristic
602C2×C3×C5#51811yescharacteristic
603C2×C3×C5#51811yescharacteristic
604C2×C3×C5#53411yescharacteristic
605C2×C3×C5#53511yescharacteristic
606C2×C3×C5#53811yescharacteristic
607C2×C3×C5#53811yescharacteristic
608C3×D5—24no—
609C3×D5—42no—
610C23×C3—21no—
611C23×C3—21no—
612C23×C3—21no—
613C23×C3—21no—
614C23×C3—21no—
615C23×C3—21no—
616C23×C3—21no—
617C23×C3—21no—
618C23×C3—21no—
619C23×C3—21no—
620C23×C3—21no—
621C23×C3—21no—
622C23×C3—52no—
623C23×C3—52no—
624C23×C3—52no—
625C23×C3—52no—
626C23×C3—108no—
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—204no—
638C23×C3—204no—
639C23×C3—204no—
640C23×C3—204no—
641C23×C3—204no—
642C23×C3—204no—
643C23×C3C2×C4×D512yes—
644C23×C3C2×C4×D512yes—
645C23×C3C23×D511yescharacteristic
646C3×D4—44no—
647C3×D4—108no—
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—44no—
663C2×C3×C4—52no—
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—101no—
680C2×C3×C4—101no—
681C2×C3×C4—204no—
682C2×C3×C4—204no—
683C2×C3×C4C2×C4×D512yes—
684C2×C3×C4D4×D512yes—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—22no—
691C22×C5—41no—
692C22×C5—41no—
693C22×C5—41no—
694C22×C5—41no—
695C22×C5—41no—
696C22×C5—41no—
697C22×C5—41no—
698C22×C5—41no—
699C22×C5C23×C3×C411yescharacteristic
700C22×C5C22×C3×D411yescharacteristic
701C22×C5C2×C3×#4111yescharacteristic
702C22×C5C3×H(5,𝔽2)11yescharacteristic
703C22×C5C3×H(5,𝔽2)11yescharacteristic
704C22×C5C3×H(5,𝔽2)11yescharacteristic
705C22×C5C3×H(5,𝔽2)11yescharacteristic
706C2×D5—22no—
707C2×D5—22no—
708C2×D5—22no—
709C2×D5—22no—
710C2×D5—22no—
711C2×D5—22no—
712C2×D5—22no—
713C2×D5—22no—
714C2×D5—22no—
715C2×D5—416no—
716C2×D5—41no—
717C2×D5—41no—
718C2×D5—41no—
719C2×D5—41no—
720C2×D5C3×C4×D414yes—
721C4×C5—22no—
722C4×C5—22no—
723C4×C5—41no—
724C4×C5—41no—
725C4×C5—41no—
726Dic5—22no—
727Dic5—22no—
728Dic5—22no—
729Dic5—41no—
730Dic5—41no—
731Dic5—41no—
732C24—51no—
733C24—51no—
734C24—54no—
735C24—102no—
736C24—102no—
737C24—201no—
738C24—201no—
739C24—201no—
740C24—201no—
741C24C22×C3×D511yescharacteristic
742C24C22×C3×D511yescharacteristic
743C2×D4—41no—
744C2×D4—41no—
745C2×D4—54no—
746C2×D4—54no—
747C2×D4—102no—
748C2×D4—102no—
749C2×D4—201no—
750C2×D4—201no—
751C2×D4C3×C4×D514yescomplemented
752C22×C4—22no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—51no—
756C22×C4—51no—
757C22×C4—51no—
758C22×C4—54no—
759C22×C4—51no—
760C22×C4—51no—
761C22×C4—51no—
762C22×C4—102no—
763C22×C4—201no—
764C22×C4—201no—
765C22×C4—201no—
766C22×C4—201no—
767C22×C4C22×C3×D511yescharacteristic
768C22×C4C22×C3×D511yescharacteristic
769C22×C4C22×C3×D511yescharacteristic
770C22×C4C22×C3×D511yescharacteristic
771C22×C4C22×C3×D511yescharacteristic
772C4⋊C4—102no—
773C4⋊C4—201no—
774C4⋊C4—201no—
775C22⋊C4—22no—
776C22⋊C4—41no—
777C22⋊C4—41no—
778C22⋊C4—54no—
779C22⋊C4—54no—
780C22⋊C4—54no—
781C22⋊C4—102no—
782C22⋊C4—102no—
783C22⋊C4—102no—
784C22⋊C4—102no—
785C22⋊C4—102no—
786C22⋊C4—102no—
787C22⋊C4—201no—
788C22⋊C4—201no—
789C22⋊C4—201no—
790C22⋊C4—201no—
791C42—102no—
792C42—201no—
793C42—201no—
794C3×C5#232111yescharacteristic, complemented, Hall
795C22×C3—22no—
796C22×C3—22no—
797C22×C3—22no—
798C22×C3—22no—
799C22×C3—22no—
800C22×C3—22no—
801C22×C3—41no—
802C22×C3—41no—
803C22×C3—41no—
804C22×C3—41no—
805C22×C3—41no—
806C22×C3—41no—
807C22×C3—41no—
808C22×C3—41no—
809C22×C3—54no—
810C22×C3—102no—
811C22×C3—102no—
812C22×C3—102no—
813C22×C3—102no—
814C22×C3—102no—
815C22×C3—102no—
816C22×C3—102no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—2016no—
820C22×C3—201no—
821C22×C3—201no—
822C22×C3—201no—
823C22×C3—201no—
824C22×C3C22×C4×D511yescharacteristic
825C22×C3C2×D4×D511yescharacteristic
826C22×C3#414411yescharacteristic
827C22×C3#414411yescharacteristic
828C22×C3#414411yescharacteristic
829C22×C3D5×#4111yescharacteristic
830C22×C3#414911yescharacteristic
831C3×C4—22no—
832C3×C4—22no—
833C3×C4—41no—
834C3×C4—41no—
835C3×C4—41no—
836C3×C4—102no—
837C3×C4—102no—
838C3×C4—102no—
839C3×C4—201no—
840C3×C4—201no—
841C3×C4—201no—
842C2×C5—42no—
843C2×C5—42no—
844C2×C5C2×C3×C4×D411yescharacteristic
845C2×C5C3×#51811yescharacteristic
846C2×C5C3×#51811yescharacteristic
847C2×C5C3×#53411yescharacteristic
848C2×C5C3×#53511yescharacteristic
849C2×C5C3×#53811yescharacteristic
850C2×C5C3×#53811yescharacteristic
851D5—24no—
852D5—42no—
853C23—21no—
854C23—21no—
855C23—21no—
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—21no—
863C23—21no—
864C23—21no—
865C23—52no—
866C23—52no—
867C23—52no—
868C23—52no—
869C23—108no—
870C23—101no—
871C23—101no—
872C23—101no—
873C23—101no—
874C23—101no—
875C23—101no—
876C23—101no—
877C23—101no—
878C23—101no—
879C23—101no—
880C23—204no—
881C23—204no—
882C23—204no—
883C23—204no—
884C23—204no—
885C23—204no—
886C23C2×C3×C4×D512yes—
887C23C2×C3×C4×D512yes—
888C23C23×C3×D511yescharacteristic
889D4—44no—
890D4—108no—
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—44no—
906C2×C4—52no—
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—101no—
923C2×C4—101no—
924C2×C4—204no—
925C2×C4—204no—
926C2×C4C2×C3×C4×D512yes—
927C2×C4C3×D4×D512yes—
928C2×C3—42no—
929C2×C3—42no—
930C2×C3—104no—
931C2×C3—202no—
932C2×C3#6582011yescharacteristic
933C2×C3C4×D4×D511yescharacteristic
934C2×C3#6587911yescharacteristic
935C2×C3#6592311yescharacteristic
936C2×C3#6594111yescharacteristic
937C2×C3#6594711yescharacteristic
938C2×C3#6599111yescharacteristic
939C5C3×#232111yescharacteristic, complemented, Sylow
940C22—22no—
941C22—22no—
942C22—22no—
943C22—22no—
944C22—22no—
945C22—22no—
946C22—41no—
947C22—41no—
948C22—41no—
949C22—41no—
950C22—41no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—54no—
955C22—102no—
956C22—102no—
957C22—102no—
958C22—102no—
959C22—102no—
960C22—102no—
961C22—102no—
962C22—102no—
963C22—102no—
964C22—2016no—
965C22—201no—
966C22—201no—
967C22—201no—
968C22—201no—
969C22C22×C3×C4×D511yescharacteristic
970C22C2×C3×D4×D511yescharacteristic
971C22C3×#414411yescharacteristic
972C22C3×#414411yescharacteristic
973C22C3×#414411yescharacteristic
974C22C3×D5×#4111yescharacteristic
975C22C3×#414911yescharacteristic
976C4—22no—
977C4—22no—
978C4—41no—
979C4—41no—
980C4—41no—
981C4—102no—
982C4—102no—
983C4—102no—
984C4—201no—
985C4—201no—
986C4—201no—
987C3#1060660711yescharacteristic, direct product factor, Sylow
988C2—42no—
989C2—42no—
990C2—104no—
991C2—202no—
992C2C3×#6582011yescharacteristic
993C2C3×C4×D4×D511yescharacteristic
994C2C3×#6587911yescharacteristic
995C2C3×#6592311yescharacteristic
996C2C3×#6594111yescharacteristic
997C2C3×#6594711yescharacteristic
998C2C3×#6599111yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#386C2
socleC23×C3×C5C24
prime radicalC2×C3×#4083C2
cosocleC23×C5C24×C3
hypercenterC3×#386D5
hypocenterC5C3×#2321
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×D5×C22⋊C4C2semidirect
4. C3×C5×#386C2semidirect
5. C3×#65510C2semidirect
6. C3×#65502C2semidirect
7. C3×#65246C2semidirect
8. C3×#65245C2semidirect
9. C3×#65244C2semidirect
10. C3×#65233C2semidirect
11. C3×#65233C2semidirect
12. C3×#64959C2semidirect
13. C3×#64958C2semidirect
14. C3×#64957C2semidirect
15. C3×#64955C2semidirect
16. #10606607C3direct (N × H)
19. C23×C3×C4×C5C22semidirect
26. C2×C3×C5×C22⋊C4C22semidirect
30. C2×C3×C22⋊Dic5C22semidirect
31. C2×C3×C22⋊Dic5C22semidirect
32. C3×#4083C4semidirect
42. C2×C3×C4⋊Dic5C22semidirect
43. C2×C3×#683C22semidirect
44. C2×C3×#683C22semidirect
45. C2×C3×C4×Dic5C22semidirect
46. C2×C3×C4×Dic5C22semidirect
47. C2×C3×C4×Dic5C22semidirect
49. C3×C5×#95C22semidirect
50. C3×C5×#95C22semidirect
51. C3×#3963C22semidirect
52. C3×#3963C22semidirect
53. C3×#3963C22semidirect
54. C3×#3963C22semidirect
57. C2×C4×C22⋊D5C2×C3semidirect
58. C2×D5×C22⋊C4C2×C3semidirect
59. C5×#386C2×C3semidirect
60. #65510C2×C3semidirect
61. #65502C2×C3semidirect
62. #65246C2×C3semidirect
63. #65245C2×C3semidirect
64. #65244C2×C3semidirect
65. #65233C2×C3semidirect
66. #65233C2×C3semidirect
67. #64959C2×C3semidirect
68. #64958C2×C3semidirect
69. #64957C2×C3semidirect
70. #64955C2×C3semidirect
79. C23×C3×D5C2×C4semidirect
84. C2×C3×C5×D4C2×C4semidirect
98. C2×C3×C22⋊D5C2×C4semidirect
110. C2×C3×C4×D5D4semidirect
118. C3×C22⋊Dic5C2×C4semidirect
125. C3×#685C2×C4semidirect
126. C3×#685C2×C4semidirect
144. C3×#386D5semidirect
150. C23×C4×C5C22×C3semidirect
157. C2×C5×C22⋊C4C22×C3semidirect
161. C2×C22⋊Dic5C22×C3semidirect
162. C2×C22⋊Dic5C22×C3semidirect
163. #4083C3×C4semidirect
173. C2×C4⋊Dic5C22×C3semidirect
174. C2×#683C22×C3semidirect
175. C2×#683C22×C3semidirect
176. C2×C4×Dic5C22×C3semidirect
177. C2×C4×Dic5C22×C3semidirect
178. C2×C4×Dic5C22×C3semidirect
180. C5×#95C22×C3semidirect
181. C5×#95C22×C3semidirect
182. #3963C22×C3semidirect
183. #3963C22×C3semidirect
184. #3963C22×C3semidirect
185. #3963C22×C3semidirect
268. C23×C3×C4C2×D5semidirect
290. C2×C3×C22⋊C4C2×D5semidirect
298. C3×#95C2×D5semidirect
299. C3×#95C2×D5semidirect
308. C23×D5C2×C3×C4semidirect
313. C2×C5×D4C2×C3×C4semidirect
327. C2×C22⋊D5C2×C3×C4semidirect
339. C2×C4×D5C3×D4semidirect
347. C22⋊Dic5C2×C3×C4semidirect
354. #685C2×C3×C4semidirect
355. #685C2×C3×C4semidirect
373. #386C3×D5semidirect
443. C2×C3×D4C4×D5semidirect
567. C23×C4C2×C3×D5semidirect
589. C2×C22⋊C4C2×C3×D5semidirect
597. #95C2×C3×D5semidirect
598. #95C2×C3×D5semidirect
751. C2×D4C3×C4×D5semidirect
794. C3×C5#2321semidirect
939. C5C3×#2321semidirect
987. C3#10606607direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40832
C2×C3×C4×C22⋊D52
C2×C3×D5×C22⋊C42
C3×C5×#3862
C3×#655102
C3×#655022
C3×#652462
C3×#652452
C3×#652442
C3×#652332
C3×#649592
C3×#649582
C3×#649572
C3×#649552
#106066073
C3×#23215