Finite Group Databasebeta

← C2×C3×#65989 #14482671

Subgroups — C2×C3×#65989 #14482671

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#711C211yesmaximal, characteristic, complemented
2C22×C3×#709C211yesmaximal, characteristic, complemented
3C2×C3×C5×#123C211yesmaximal, characteristic, complemented
4C2×C3×#4085C211yesmaximal, characteristic, complemented
5C22×C3×#683C211yesmaximal, characteristic, complemented
6C3×#65989C2116yesmaximal, direct product factor
7C2×C3×#4042C211yesmaximal, characteristic, complemented
8C2×C3×#4040C211yesmaximal, characteristic, complemented
9C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
10C2×C3×#4034C211yesmaximal, characteristic, complemented
11C2×C3×#4032C211yesmaximal, characteristic, complemented
12C2×C3×#4030C211yesmaximal, characteristic, complemented
13C2×C3×#4029C211yesmaximal, characteristic, complemented
14C2×C3×#4027C211yesmaximal, characteristic, complemented
15C2×C3×#4027C211yesmaximal, characteristic, complemented
16C2×C3×#4024C211yesmaximal, characteristic, complemented
17C2×#65989C311yesmaximal, characteristic, direct product factor, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C23×C3×Dic5C2211yescharacteristic
25C23×C3×Dic5C2211yescharacteristic
26C23×C3×Dic5C2211yescharacteristic
27C2×C3×#711—28no—
28C2×C3×#711C2218yescomplemented
29C2×C3×#709—28no—
30C2×C3×#709C2218yescomplemented
31C22×C3×D20C2211yescharacteristic
32C22×C3×C4×D5C2211yescharacteristic
33C22×C3×C4×D5C2211yescharacteristic
34C22×C3×C4×D5C2211yescharacteristic
35C22×C3×C4×D5C2211yescharacteristic
36C22×C3×Dic10C2211yescharacteristic
37C22×C3×Dic10C2211yescharacteristic
38C3×C5×#123C2218yescomplemented
39C2×C3×C5×C4⋊C4C2211yescharacteristic
40C2×C3×C5×C4⋊C4C2211yescharacteristic
41C2×C3×C5×C22⋊C4C2211yescharacteristic
42C2×C3×C5×C22⋊C4C2211yescharacteristic
43C2×C3×C5×C22⋊C4C2211yescharacteristic
44C2×C3×C22⋊Dic5C2211yescharacteristic
45C3×#4085C2218yescomplemented
46C2×C3×#685C2211yescharacteristic
47C2×C3×#685C2211yescharacteristic
48C2×C3×#685C2211yescharacteristic
49C2×C3×#685C2211yescharacteristic
50C2×C3×C4⋊Dic5C2211yescharacteristic
51C2×C3×C4⋊Dic5C2211yescharacteristic
52C2×C3×#683C2211yescharacteristic
53C2×C3×#683C2211yescharacteristic
54C2×C3×#683C2211yescharacteristic
55C2×C3×#683C2211yescharacteristic
56C2×C3×#683C2211yescharacteristic
57C2×C3×#683C2211yescharacteristic
58C2×C3×#683C2218yescomplemented
59C2×C3×C4×Dic5C2211yescharacteristic
60C3×#4042C2218yescomplemented
61C3×#4040C2218yescomplemented
62C3×D5×C4⋊C4C2218yescomplemented
63C3×#4034C2218yescomplemented
64C3×#4032C2218yescomplemented
65C3×#4030C2218yescomplemented
66C3×#4029C2218yescomplemented
67C3×#4027C2218yescomplemented
68C3×#4027C2218yescomplemented
69C3×#4024C2218yescomplemented
70C2×C3×#547—51nomaximal, Hall
71C22×#711C2×C311yescharacteristic, complemented
72C22×#709C2×C311yescharacteristic, complemented
73C2×C5×#123C2×C311yescharacteristic, complemented
74C2×#4085C2×C311yescharacteristic, complemented
75C22×#683C2×C311yescharacteristic, complemented
76#65989C2×C3116yesdirect product factor
77C2×#4042C2×C311yescharacteristic, complemented
78C2×#4040C2×C311yescharacteristic, complemented
79C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
80C2×#4034C2×C311yescharacteristic, complemented
81C2×#4032C2×C311yescharacteristic, complemented
82C2×#4030C2×C311yescharacteristic, complemented
83C2×#4029C2×C311yescharacteristic, complemented
84C2×#4027C2×C311yescharacteristic, complemented
85C2×#4027C2×C311yescharacteristic, complemented
86C2×#4024C2×C311yescharacteristic, complemented
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C2×C3×C5×D4—24no—
92C2×C3×C5×D4C2314yes—
93C22×C3×C4×C5—24no—
94C22×C3×C4×C5C2311yescharacteristic
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2314yes—
99C22×C3×C4×C5C2311yescharacteristic
100C2×C3×C22⋊D5—24no—
101C2×C3×C22⋊D5—24no—
102C2×C3×C22⋊D5—24no—
103C2×C3×C22⋊D5D418yescomplemented
104C2×C3×C22⋊D5C2314yes—
105C2×C3×C22⋊D5C2314yes—
106C2×C3×C22⋊D5C2314yes—
107C2×C3×C22⋊D5C2314yes—
108C22×C3×Dic5—24no—
109C22×C3×Dic5—24no—
110C22×C3×Dic5—24no—
111C22×C3×Dic5C2314yes—
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C22×C3×Dic5C2314yes—
117C22×C3×Dic5C2314yes—
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C3×#711—232no—
121C3×#709—232no—
122C2×C3×D20—24no—
123C2×C3×D20C2314yes—
124C2×C3×C4×D5—24no—
125C2×C3×C4×D5—24no—
126C2×C3×C4×D5—24no—
127C2×C3×C4×D5—24no—
128C2×C3×C4×D5C2314yes—
129C2×C3×C4×D5C2314yes—
130C2×C3×C4×D5C2314yes—
131C2×C3×C4×D5C2314yes—
132C2×C3×Dic10—24no—
133C2×C3×Dic10—24no—
134C2×C3×Dic10C2314yes—
135C2×C3×Dic10C2314yes—
136C3×C5×C4⋊C4C2314yes—
137C3×C5×C4⋊C4C2314yes—
138C3×C5×C22⋊C4C2314yes—
139C3×C5×C22⋊C4C2314yes—
140C3×C5×C22⋊C4C2314yes—
141C3×C22⋊Dic5C2314yes—
142C3×#685C2314yes—
143C3×#685C2314yes—
144C3×#685C2314yes—
145C3×#685C2314yes—
146C3×C4⋊Dic5C2314yes—
147C3×C4⋊Dic5C2314yes—
148C3×#683C2314yes—
149C3×#683C2314yes—
150C3×#683C2314yes—
151C3×#683C2314yes—
152C3×#683C2314yes—
153C3×#683C2314yes—
154C3×C4×Dic5C2314yes—
155C22×C3×#41—51no—
156C22×C3×#41—51no—
157C3×#547—516no—
158C2×C3×C4⋊Q8—51no—
159C2×C3×#123—51no—
160C2×C3×#123—51no—
161C2×C3×#123—51no—
162C2×C3×#123D511yescharacteristic, complemented
163C2×C3×C22⋊Q8—51no—
164C2×C3×C22⋊Q8—51no—
165C2×C3×#121—51no—
166C2×C3×#121—51no—
167C2×C3×C4×D4—51no—
168C2×C3×C4×D4—51no—
169C22×C3×C4⋊C4—51no—
170C22×C3×C4⋊C4—51no—
171C22×C5×D4C22×C311yescharacteristic
172C23×C4×C5C22×C311yescharacteristic
173C22×C22⋊D5C22×C311yescharacteristic
174C22×C22⋊D5C22×C311yescharacteristic
175C22×C22⋊D5C22×C311yescharacteristic
176C22×C22⋊D5C22×C311yescharacteristic
177C23×Dic5C22×C311yescharacteristic
178C23×Dic5C22×C311yescharacteristic
179C23×Dic5C22×C311yescharacteristic
180C2×#711—28no—
181C2×#711C22×C318yescomplemented
182C2×#709—28no—
183C2×#709C22×C318yescomplemented
184C22×D20C22×C311yescharacteristic
185C22×C4×D5C22×C311yescharacteristic
186C22×C4×D5C22×C311yescharacteristic
187C22×C4×D5C22×C311yescharacteristic
188C22×C4×D5C22×C311yescharacteristic
189C22×Dic10C22×C311yescharacteristic
190C22×Dic10C22×C311yescharacteristic
191C5×#123C22×C318yescomplemented
192C2×C5×C4⋊C4C22×C311yescharacteristic
193C2×C5×C4⋊C4C22×C311yescharacteristic
194C2×C5×C22⋊C4C22×C311yescharacteristic
195C2×C5×C22⋊C4C22×C311yescharacteristic
196C2×C5×C22⋊C4C22×C311yescharacteristic
197C2×C22⋊Dic5C22×C311yescharacteristic
198#4085C22×C318yescomplemented
199C2×#685C22×C311yescharacteristic
200C2×#685C22×C311yescharacteristic
201C2×#685C22×C311yescharacteristic
202C2×#685C22×C311yescharacteristic
203C2×C4⋊Dic5C22×C311yescharacteristic
204C2×C4⋊Dic5C22×C311yescharacteristic
205C2×#683C22×C311yescharacteristic
206C2×#683C22×C311yescharacteristic
207C2×#683C22×C311yescharacteristic
208C2×#683C22×C311yescharacteristic
209C2×#683C22×C311yescharacteristic
210C2×#683C22×C311yescharacteristic
211C2×#683C22×C318yescomplemented
212C2×C4×Dic5C22×C311yescharacteristic
213#4042C22×C318yescomplemented
214#4040C22×C318yescomplemented
215D5×C4⋊C4C22×C318yescomplemented
216#4034C22×C318yescomplemented
217#4032C22×C318yescomplemented
218#4030C22×C318yescomplemented
219#4029C22×C318yescomplemented
220#4027C22×C318yescomplemented
221#4027C22×C318yescomplemented
222#4024C22×C318yescomplemented
223C2×#547—51noSylow
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5C2×D414yes—
230C23×C3×C5C2412yes—
231C23×C3×C5C2412yes—
232C23×C3×C5C2411yescharacteristic
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5—22no—
238C22×C3×D5C2×D414yes—
239C22×C3×D5C2412yes—
240C22×C3×D5C2412yes—
241C3×C5×D4—28no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—22no—
244C2×C3×C4×C5—22no—
245C2×C3×C4×C5—28no—
246C2×C3×C4×C5—22no—
247C2×C3×C4×C5—22no—
248C2×C3×C4×C5C2412yes—
249C2×C3×C4×C5C2412yes—
250C2×C3×C4×C5C2412yes—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253C3×C22⋊D5—28no—
254C3×C22⋊D5—28no—
255C3×C22⋊D5—28no—
256C3×C22⋊D5C2×D4116yescomplemented
257C2×C3×Dic5—22no—
258C2×C3×Dic5—22no—
259C2×C3×Dic5—22no—
260C2×C3×Dic5—28no—
261C2×C3×Dic5—22no—
262C2×C3×Dic5—28no—
263C2×C3×Dic5—28no—
264C2×C3×Dic5C2×D414yes—
265C2×C3×Dic5#4114yescomplemented
266C2×C3×Dic5C2412yes—
267C2×C3×Dic5C2412yes—
268C2×C3×Dic5C2412yes—
269C2×C3×Dic5C2412yes—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C3×D20—28no—
273C3×C4×D5—28no—
274C3×C4×D5—28no—
275C3×C4×D5—28no—
276C3×C4×D5—28no—
277C3×Dic10—28no—
278C3×Dic10—28no—
279C2×C3×#41—58no—
280C2×C3×#41—58no—
281C2×C3×#41—108no—
282C2×C3×#41—108no—
283C22×C3×Q8—51no—
284C22×C3×Q8—51no—
285C22×C3×D4—51no—
286C22×C3×D4—51no—
287C22×C3×D4—51no—
288C22×C3×D4—51no—
289C22×C3×D4—51no—
290C22×C3×D4C2×D511yescharacteristic
291C23×C3×C4—51no—
292C23×C3×C4—51no—
293C23×C3×C4—51no—
294C23×C3×C4—51no—
295C23×C3×C4—51no—
296C23×C3×C4—51no—
297C23×C3×C4—51no—
298C23×C3×C4C2×D511yescharacteristic
299C3×C4⋊Q8—58no—
300C3×#123—58no—
301C3×#123—58no—
302C3×#123—58no—
303C3×#123C2×D518yescomplemented
304C3×C22⋊Q8—58no—
305C3×C22⋊Q8—58no—
306C3×#121—58no—
307C3×#121—58no—
308C3×C4×D4—58no—
309C3×C4×D4—58no—
310C2×C3×C4⋊C4—51no—
311C2×C3×C4⋊C4—51no—
312C2×C3×C4⋊C4—51no—
313C2×C3×C4⋊C4—51no—
314C2×C3×C4⋊C4—51no—
315C2×C3×C4⋊C4—51no—
316C2×C3×C4⋊C4—58no—
317C2×C3×C4⋊C4—51no—
318C2×C3×C4⋊C4—51no—
319C2×C3×C4⋊C4—58no—
320C2×C3×C4⋊C4C2×D511yescharacteristic
321C2×C3×C4⋊C4C2×D511yescharacteristic
322C2×C3×C22⋊C4—51no—
323C2×C3×C22⋊C4—51no—
324C2×C3×C22⋊C4—51no—
325C2×C3×C22⋊C4—51no—
326C2×C3×C22⋊C4—51no—
327C2×C3×C22⋊C4C2×D511yescharacteristic
328C2×C3×C22⋊C4C2×D511yescharacteristic
329C2×C3×C22⋊C4C2×D511yescharacteristic
330C2×C3×C42—51no—
331C24×C5C23×C311yescharacteristic
332C24×C5C23×C311yescharacteristic
333C23×D5C23×C311yescharacteristic
334C23×D5C23×C311yescharacteristic
335C2×C5×D4—24no—
336C2×C5×D4C23×C314yes—
337C22×C4×C5—24no—
338C22×C4×C5C23×C311yescharacteristic
339C22×C4×C5C23×C311yescharacteristic
340C22×C4×C5C23×C311yescharacteristic
341C22×C4×C5C23×C311yescharacteristic
342C22×C4×C5C23×C311yescharacteristic
343C22×C4×C5C23×C314yes—
344C2×C22⋊D5—24no—
345C2×C22⋊D5—24no—
346C2×C22⋊D5—24no—
347C2×C22⋊D5C3×D418yescomplemented
348C2×C22⋊D5C23×C314yes—
349C2×C22⋊D5C23×C314yes—
350C2×C22⋊D5C23×C314yes—
351C2×C22⋊D5C23×C314yes—
352C22×Dic5—24no—
353C22×Dic5—24no—
354C22×Dic5—24no—
355C22×Dic5C23×C311yescharacteristic
356C22×Dic5C23×C311yescharacteristic
357C22×Dic5C23×C311yescharacteristic
358C22×Dic5C23×C311yescharacteristic
359C22×Dic5C23×C314yes—
360C22×Dic5C23×C314yes—
361C22×Dic5C23×C314yes—
362C22×Dic5C23×C311yescharacteristic
363C22×Dic5C23×C311yescharacteristic
364#711—232no—
365#709—232no—
366C2×D20—24no—
367C2×D20C23×C314yes—
368C2×C4×D5—24no—
369C2×C4×D5—24no—
370C2×C4×D5—24no—
371C2×C4×D5—24no—
372C2×C4×D5C23×C314yes—
373C2×C4×D5C23×C314yes—
374C2×C4×D5C23×C314yes—
375C2×C4×D5C23×C314yes—
376C2×Dic10—24no—
377C2×Dic10—24no—
378C2×Dic10C23×C314yes—
379C2×Dic10C23×C314yes—
380C5×C4⋊C4C23×C314yes—
381C5×C4⋊C4C23×C314yes—
382C5×C22⋊C4C23×C314yes—
383C5×C22⋊C4C23×C314yes—
384C5×C22⋊C4C23×C314yes—
385C22⋊Dic5C23×C314yes—
386#685C23×C314yes—
387#685C23×C314yes—
388#685C23×C314yes—
389#685C23×C314yes—
390C4⋊Dic5C23×C314yes—
391C4⋊Dic5C23×C314yes—
392#683C23×C314yes—
393#683C23×C314yes—
394#683C23×C314yes—
395#683C23×C314yes—
396#683C23×C314yes—
397#683C23×C314yes—
398C4×Dic5C23×C314yes—
399C22×#41—51no—
400C22×#41—51no—
401#547—516no—
402C2×C4⋊Q8—51no—
403C2×#123—51no—
404C2×#123—51no—
405C2×#123—51no—
406C2×#123C3×D511yescharacteristic, complemented
407C2×C22⋊Q8—51no—
408C2×C22⋊Q8—51no—
409C2×#121—51no—
410C2×#121—51no—
411C2×C4×D4—51no—
412C2×C4×D4—51no—
413C22×C4⋊C4—51no—
414C22×C4⋊C4—51no—
415C22×C3×C5—28no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—44no—
422C22×C3×C5C22×D414yes—
423C22×C3×C5C22×D412yes—
424C22×C3×C5C2×#4112yes—
425C22×C3×C52−1+412yes—
426C22×C3×C5C2511yescharacteristic
427C2×C3×D5—28no—
428C2×C3×D5—22no—
429C2×C3×D5—22no—
430C2×C3×D5—22no—
431C2×C3×D5—22no—
432C2×C3×D5—22no—
433C2×C3×D5—44no—
434C2×C3×D5C22×D414yes—
435C3×C4×C5—22no—
436C3×C4×C5—22no—
437C3×C4×C5—22no—
438C3×C4×C5—22no—
439C3×C4×C5—22no—
440C3×Dic5—22no—
441C3×Dic5—22no—
442C3×Dic5—22no—
443C3×Dic5—22no—
444C3×Dic5C22×D414yes—
445C3×Dic5C2×#4114yescomplemented
446C24×C3—51no—
447C24×C3—51no—
448C24×C3C22×D511yescharacteristic
449C24×C3C22×D511yescharacteristic
450C3×#41—1032no—
451C3×#41—1032no—
452C2×C3×Q8—54no—
453C2×C3×Q8—54no—
454C2×C3×Q8—104no—
455C2×C3×Q8—104no—
456C2×C3×D4—24no—
457C2×C3×D4—58no—
458C2×C3×D4—54no—
459C2×C3×D4—54no—
460C2×C3×D4—54no—
461C2×C3×D4—54no—
462C2×C3×D4—54no—
463C2×C3×D4—104no—
464C2×C3×D4—104no—
465C2×C3×D4—104no—
466C2×C3×D4—104no—
467C2×C3×D4C22×D514yes—
468C22×C3×C4—24no—
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—54no—
472C22×C3×C4—54no—
473C22×C3×C4—54no—
474C22×C3×C4—51no—
475C22×C3×C4—51no—
476C22×C3×C4—51no—
477C22×C3×C4—51no—
478C22×C3×C4—54no—
479C22×C3×C4—54no—
480C22×C3×C4—54no—
481C22×C3×C4—54no—
482C22×C3×C4—104no—
483C22×C3×C4—104no—
484C22×C3×C4—104no—
485C22×C3×C4—104no—
486C22×C3×C4—104no—
487C22×C3×C4—104no—
488C22×C3×C4—104no—
489C22×C3×C4C22×D514yes—
490C22×C3×C4C22×D511yescharacteristic
491C22×C3×C4C22×D511yescharacteristic
492C22×C3×C4C22×D511yescharacteristic
493C22×C3×C4C22×D511yescharacteristic
494C22×C3×C4C22×D511yescharacteristic
495C3×C4⋊C4—54no—
496C3×C4⋊C4—54no—
497C3×C4⋊C4—54no—
498C3×C4⋊C4—54no—
499C3×C4⋊C4—54no—
500C3×C4⋊C4—54no—
501C3×C4⋊C4—54no—
502C3×C4⋊C4—54no—
503C3×C4⋊C4C22×D514yes—
504C3×C4⋊C4C22×D514yes—
505C3×C22⋊C4—54no—
506C3×C22⋊C4—54no—
507C3×C22⋊C4—54no—
508C3×C22⋊C4—54no—
509C3×C22⋊C4—54no—
510C3×C22⋊C4C22×D514yes—
511C3×C22⋊C4C22×D514yes—
512C3×C22⋊C4C22×D514yes—
513C3×C42—54no—
514C23×C5—22no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—22no—
518C23×C5—22no—
519C23×C5C2×C3×D414yes—
520C23×C5C24×C312yes—
521C23×C5C24×C312yes—
522C23×C5C24×C311yescharacteristic
523C22×D5—22no—
524C22×D5—22no—
525C22×D5—22no—
526C22×D5—22no—
527C22×D5—22no—
528C22×D5C2×C3×D414yes—
529C22×D5C24×C312yes—
530C22×D5C24×C312yes—
531C5×D4—28no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—22no—
535C2×C4×C5—28no—
536C2×C4×C5—22no—
537C2×C4×C5—22no—
538C2×C4×C5C24×C312yes—
539C2×C4×C5C24×C312yes—
540C2×C4×C5C24×C312yes—
541C2×C4×C5C24×C312yes—
542C2×C4×C5C24×C312yes—
543C22⋊D5—28no—
544C22⋊D5—28no—
545C22⋊D5—28no—
546C22⋊D5C2×C3×D4116yescomplemented
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—22no—
550C2×Dic5—28no—
551C2×Dic5—22no—
552C2×Dic5—28no—
553C2×Dic5—28no—
554C2×Dic5C2×C3×D414yes—
555C2×Dic5C3×#4114yescomplemented
556C2×Dic5C24×C312yes—
557C2×Dic5C24×C312yes—
558C2×Dic5C24×C312yes—
559C2×Dic5C24×C312yes—
560C2×Dic5C24×C312yes—
561C2×Dic5C24×C312yes—
562D20—28no—
563C4×D5—28no—
564C4×D5—28no—
565C4×D5—28no—
566C4×D5—28no—
567Dic10—28no—
568Dic10—28no—
569C2×#41—58no—
570C2×#41—58no—
571C2×#41—108no—
572C2×#41—108no—
573C22×Q8—51no—
574C22×Q8—51no—
575C22×D4—51no—
576C22×D4—51no—
577C22×D4—51no—
578C22×D4—51no—
579C22×D4—51no—
580C22×D4C2×C3×D511yescharacteristic
581C23×C4—51no—
582C23×C4—51no—
583C23×C4—51no—
584C23×C4—51no—
585C23×C4—51no—
586C23×C4—51no—
587C23×C4—51no—
588C23×C4C2×C3×D511yescharacteristic
589C4⋊Q8—58no—
590#123—58no—
591#123—58no—
592#123—58no—
593#123C2×C3×D518yescomplemented
594C22⋊Q8—58no—
595C22⋊Q8—58no—
596#121—58no—
597#121—58no—
598C4×D4—58no—
599C4×D4—58no—
600C2×C4⋊C4—51no—
601C2×C4⋊C4—51no—
602C2×C4⋊C4—51no—
603C2×C4⋊C4—51no—
604C2×C4⋊C4—51no—
605C2×C4⋊C4—51no—
606C2×C4⋊C4—58no—
607C2×C4⋊C4—51no—
608C2×C4⋊C4—51no—
609C2×C4⋊C4—58no—
610C2×C4⋊C4C2×C3×D511yescharacteristic
611C2×C4⋊C4C2×C3×D511yescharacteristic
612C2×C22⋊C4—51no—
613C2×C22⋊C4—51no—
614C2×C22⋊C4—51no—
615C2×C22⋊C4—51no—
616C2×C22⋊C4—51no—
617C2×C22⋊C4C2×C3×D511yescharacteristic
618C2×C22⋊C4C2×C3×D511yescharacteristic
619C2×C22⋊C4C2×C3×D511yescharacteristic
620C2×C42—51no—
621C2×C3×C5—24no—
622C2×C3×C5—42no—
623C2×C3×C5#54714yescomplemented
624C2×C3×C5C23×D411yescharacteristic
625C2×C3×C5C22×#4111yescharacteristic
626C2×C3×C5C2×2−1+411yescharacteristic
627C3×D5—24no—
628C3×D5—42no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—54no—
635C23×C3—52no—
636C23×C3—52no—
637C23×C3—102no—
638C23×C3—102no—
639C23×C3—102no—
640C23×C3—102no—
641C23×C3—102no—
642C23×C3D4×D514yes—
643C23×C3C23×D512yes—
644C23×C3C23×D512yes—
645C23×C3C23×D511yescharacteristic
646C3×Q8—108no—
647C3×Q8—108no—
648C3×D4—28no—
649C3×D4—516no—
650C3×D4—108no—
651C3×D4—108no—
652C3×D4—108no—
653C3×D4—108no—
654C2×C3×C4—22no—
655C2×C3×C4—22no—
656C2×C3×C4—28no—
657C2×C3×C4—22no—
658C2×C3×C4—22no—
659C2×C3×C4—22no—
660C2×C3×C4—54no—
661C2×C3×C4—54no—
662C2×C3×C4—52no—
663C2×C3×C4—52no—
664C2×C3×C4—52no—
665C2×C3×C4—52no—
666C2×C3×C4—52no—
667C2×C3×C4—52no—
668C2×C3×C4—108no—
669C2×C3×C4—108no—
670C2×C3×C4—108no—
671C2×C3×C4—108no—
672C2×C3×C4—108no—
673C2×C3×C4—108no—
674C2×C3×C4—102no—
675C2×C3×C4—102no—
676C2×C3×C4—102no—
677C2×C3×C4—108no—
678C2×C3×C4—102no—
679C2×C3×C4C23×D512yes—
680C2×C3×C4C23×D512yes—
681C2×C3×C4C23×D512yes—
682C2×C3×C4C23×D512yes—
683C2×C3×C4C23×D512yes—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—28no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—44no—
691C22×C5C22×C3×D414yes—
692C22×C5C22×C3×D412yes—
693C22×C5C2×C3×#4112yes—
694C22×C5C3×2−1+412yes—
695C22×C5C25×C311yescharacteristic
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—28no—
699C2×D5—22no—
700C2×D5—22no—
701C2×D5—22no—
702C2×D5—44no—
703C2×D5C22×C3×D414yes—
704C4×C5—22no—
705C4×C5—22no—
706C4×C5—22no—
707C4×C5—22no—
708C4×C5—22no—
709Dic5—22no—
710Dic5—22no—
711Dic5—22no—
712Dic5—22no—
713Dic5C22×C3×D414yes—
714Dic5C2×C3×#4114yescomplemented
715C24—51no—
716C24—51no—
717C24C22×C3×D511yescharacteristic
718C24C22×C3×D511yescharacteristic
719#41—1032no—
720#41—1032no—
721C2×Q8—54no—
722C2×Q8—54no—
723C2×Q8—104no—
724C2×Q8—104no—
725C2×D4—24no—
726C2×D4—58no—
727C2×D4—54no—
728C2×D4—54no—
729C2×D4—54no—
730C2×D4—54no—
731C2×D4—54no—
732C2×D4—104no—
733C2×D4—104no—
734C2×D4—104no—
735C2×D4—104no—
736C2×D4C22×C3×D514yes—
737C22×C4—24no—
738C22×C4—51no—
739C22×C4—51no—
740C22×C4—51no—
741C22×C4—51no—
742C22×C4—51no—
743C22×C4—51no—
744C22×C4—54no—
745C22×C4—54no—
746C22×C4—54no—
747C22×C4—54no—
748C22×C4—54no—
749C22×C4—54no—
750C22×C4—54no—
751C22×C4—104no—
752C22×C4—104no—
753C22×C4—104no—
754C22×C4—104no—
755C22×C4—104no—
756C22×C4—104no—
757C22×C4—104no—
758C22×C4C22×C3×D511yescharacteristic
759C22×C4C22×C3×D511yescharacteristic
760C22×C4C22×C3×D511yescharacteristic
761C22×C4C22×C3×D511yescharacteristic
762C22×C4C22×C3×D511yescharacteristic
763C22×C4C22×C3×D514yes—
764C4⋊C4—54no—
765C4⋊C4—54no—
766C4⋊C4—54no—
767C4⋊C4—54no—
768C4⋊C4—54no—
769C4⋊C4—54no—
770C4⋊C4—54no—
771C4⋊C4—54no—
772C4⋊C4C22×C3×D514yes—
773C4⋊C4C22×C3×D514yes—
774C22⋊C4—54no—
775C22⋊C4—54no—
776C22⋊C4—54no—
777C22⋊C4—54no—
778C22⋊C4—54no—
779C22⋊C4C22×C3×D514yes—
780C22⋊C4C22×C3×D514yes—
781C22⋊C4C22×C3×D514yes—
782C42—54no—
783C3×C5C2×#54711yescharacteristic, complemented, Hall
784C22×C3—28no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—44no—
791C22×C3—54no—
792C22×C3—108no—
793C22×C3—102no—
794C22×C3—102no—
795C22×C3—102no—
796C22×C3—102no—
797C22×C3—102no—
798C22×C3—204no—
799C22×C3C2×D4×D514yes—
800C22×C3C2×D4×D512yes—
801C22×C3D5×#4112yes—
802C22×C3#415012yes—
803C22×C3C24×D511yescharacteristic
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—22no—
807C3×C4—22no—
808C3×C4—22no—
809C3×C4—54no—
810C3×C4—54no—
811C3×C4—102no—
812C3×C4—102no—
813C3×C4—102no—
814C3×C4—102no—
815C2×C5—24no—
816C2×C5—42no—
817C2×C5C3×#54714yescomplemented
818C2×C5C23×C3×D411yescharacteristic
819C2×C5C22×C3×#4111yescharacteristic
820C2×C5C2×C3×2−1+411yescharacteristic
821D5—24no—
822D5—42no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—54no—
829C23—52no—
830C23—52no—
831C23—102no—
832C23—102no—
833C23—102no—
834C23—102no—
835C23—102no—
836C23C3×D4×D514yes—
837C23C23×C3×D512yes—
838C23C23×C3×D512yes—
839C23C23×C3×D511yescharacteristic
840Q8—108no—
841Q8—108no—
842D4—28no—
843D4—516no—
844D4—108no—
845D4—108no—
846D4—108no—
847D4—108no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—28no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—54no—
855C2×C4—54no—
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—108no—
865C2×C4—108no—
866C2×C4—108no—
867C2×C4—108no—
868C2×C4—102no—
869C2×C4—102no—
870C2×C4—102no—
871C2×C4—108no—
872C2×C4—102no—
873C2×C4C23×C3×D512yes—
874C2×C4C23×C3×D512yes—
875C2×C4C23×C3×D512yes—
876C2×C4C23×C3×D512yes—
877C2×C4C23×C3×D512yes—
878C2×C3—24no—
879C2×C3—42no—
880C2×C3—104no—
881C2×C3—202no—
882C2×C3#6598914yesdirect product factor
883C2×C3C22×D4×D511yescharacteristic
884C2×C3C2×D5×#4111yescharacteristic
885C2×C3C2×#415011yescharacteristic
886C5C2×C3×#54711yescharacteristic, complemented, Sylow
887C22—22no—
888C22—22no—
889C22—28no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—54no—
895C22—102no—
896C22—102no—
897C22—108no—
898C22—102no—
899C22—102no—
900C22—102no—
901C22—204no—
902C22C2×C3×D4×D514yes—
903C22C2×C3×D4×D512yes—
904C22C3×D5×#4112yes—
905C22C3×#415012yes—
906C22C24×C3×D511yescharacteristic
907C4—22no—
908C4—22no—
909C4—22no—
910C4—22no—
911C4—22no—
912C4—54no—
913C4—54no—
914C4—102no—
915C4—102no—
916C4—102no—
917C4—102no—
918C3C2×#6598911yescharacteristic, direct product factor, Sylow
919C2—24no—
920C2—42no—
921C2—104no—
922C2—202no—
923C2C3×#6598914yesdirect product factor
924C2C22×C3×D4×D511yescharacteristic
925C2C2×C3×D5×#4111yescharacteristic
926C2C2×C3×#415011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#123C2
socleC23×C3×C5C24
hypercenterC2×C3×#123D5
hypocenterC5C2×C3×#547
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#711C2semidirect
2. C22×C3×#709C2semidirect
3. C2×C3×C5×#123C2semidirect
4. C2×C3×#4085C2semidirect
5. C22×C3×#683C2semidirect
6. C3×#65989C2direct (N × H)
7. C2×C3×#4042C2semidirect
8. C2×C3×#4040C2semidirect
9. C2×C3×D5×C4⋊C4C2semidirect
10. C2×C3×#4034C2semidirect
11. C2×C3×#4032C2semidirect
12. C2×C3×#4030C2semidirect
13. C2×C3×#4029C2semidirect
14. C2×C3×#4027C2semidirect
15. C2×C3×#4027C2semidirect
16. C2×C3×#4024C2semidirect
17. C2×#65989C3direct (N × H)
28. C2×C3×#711C22semidirect
30. C2×C3×#709C22semidirect
38. C3×C5×#123C22semidirect
45. C3×#4085C22semidirect
58. C2×C3×#683C22semidirect
60. C3×#4042C22semidirect
61. C3×#4040C22semidirect
62. C3×D5×C4⋊C4C22semidirect
63. C3×#4034C22semidirect
64. C3×#4032C22semidirect
65. C3×#4030C22semidirect
66. C3×#4029C22semidirect
67. C3×#4027C22semidirect
68. C3×#4027C22semidirect
69. C3×#4024C22semidirect
71. C22×#711C2×C3semidirect
72. C22×#709C2×C3semidirect
73. C2×C5×#123C2×C3semidirect
74. C2×#4085C2×C3semidirect
75. C22×#683C2×C3semidirect
76. #65989C2×C3direct (N × H)
77. C2×#4042C2×C3semidirect
78. C2×#4040C2×C3semidirect
79. C2×D5×C4⋊C4C2×C3semidirect
80. C2×#4034C2×C3semidirect
81. C2×#4032C2×C3semidirect
82. C2×#4030C2×C3semidirect
83. C2×#4029C2×C3semidirect
84. C2×#4027C2×C3semidirect
85. C2×#4027C2×C3semidirect
86. C2×#4024C2×C3semidirect
103. C2×C3×C22⋊D5D4semidirect
162. C2×C3×#123D5semidirect
181. C2×#711C22×C3semidirect
183. C2×#709C22×C3semidirect
191. C5×#123C22×C3semidirect
198. #4085C22×C3semidirect
211. C2×#683C22×C3semidirect
213. #4042C22×C3semidirect
214. #4040C22×C3semidirect
215. D5×C4⋊C4C22×C3semidirect
216. #4034C22×C3semidirect
217. #4032C22×C3semidirect
218. #4030C22×C3semidirect
219. #4029C22×C3semidirect
220. #4027C22×C3semidirect
221. #4027C22×C3semidirect
222. #4024C22×C3semidirect
256. C3×C22⋊D5C2×D4semidirect
265. C2×C3×Dic5#41semidirect
303. C3×#123C2×D5semidirect
347. C2×C22⋊D5C3×D4semidirect
406. C2×#123C3×D5semidirect
445. C3×Dic5C2×#41semidirect
546. C22⋊D5C2×C3×D4semidirect
555. C2×Dic5C3×#41semidirect
593. #123C2×C3×D5semidirect
623. C2×C3×C5#547semidirect
714. Dic5C2×C3×#41semidirect
783. C3×C5C2×#547semidirect
817. C2×C5C3×#547semidirect
882. C2×C3#65989direct (N × H)
886. C5C2×C3×#547semidirect
918. C3C2×#65989direct (N × H)
923. C2C3×#65989direct (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
C22×C3×#7092
C2×C3×C5×#1232
C2×C3×#40852
C22×C3×#6832
C3×#659892
C2×C3×#40422
C2×C3×#40402
C2×C3×D5×C4⋊C42
C2×C3×#40342
C2×C3×#40322
C2×C3×#40302
C2×C3×#40292
C2×C3×#40272
C2×C3×#40242
C2×#659893
C2×C3×#5475