Finite Group Databasebeta

← C2×C3×#66035 #14481191

Subgroups — C2×C3×#66035 #14481191

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#126C211yesmaximal, characteristic
2C3×#66035C2116yesmaximal, direct product factor
3C2×C3×#4036C211yesmaximal, characteristic, complemented
4C2×C3×#4035C211yesmaximal, characteristic, complemented
5C2×C3×#4035C211yesmaximal, characteristic, complemented
6C2×C3×#4035C211yesmaximal, characteristic, complemented
7C2×C3×#4034C211yesmaximal, characteristic, complemented
8C2×C3×#4033C211yesmaximal, characteristic, complemented
9C2×C3×#4025C211yesmaximal, characteristic
10C2×C3×#4025C211yesmaximal, characteristic
11C2×C3×#4025C211yesmaximal, characteristic
12C2×C3×#4024C211yesmaximal, characteristic
13C2×C3×#4024C211yesmaximal, characteristic
14C2×C3×#4023C211yesmaximal, characteristic
15C2×C3×#4016C211yesmaximal, characteristic, complemented
16C2×C3×C4×Dic10C211yesmaximal, characteristic, complemented
17C2×#66035C311yesmaximal, characteristic, direct product factor, Hall
18C23×C3×Dic5C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C3×C5×#126C2218yes—
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×C3×C5×C4⋊C4C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×C3×C42×C5C2211yescharacteristic
29C2×C3×C22⋊Dic5C2211yescharacteristic
30C2×C3×C22⋊Dic5C2211yescharacteristic
31C2×C3×C22⋊Dic5C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×C4⋊Dic5C2211yescharacteristic
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C2×C3×C4⋊Dic5C2211yescharacteristic
36C2×C3×C4⋊Dic5C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×#683C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic
47C2×C3×#683C2211yescharacteristic
48C2×C3×#683C2211yescharacteristic
49C2×C3×C4×Dic5C2211yescharacteristic
50C2×C3×C4×Dic5C2211yescharacteristic
51C2×C3×C4×Dic5C2211yescharacteristic
52C2×C3×C4×Dic5C2211yescharacteristic
53C2×C3×C4×Dic5C2211yescharacteristic
54C3×#4036C2218yescomplemented
55C3×#4035C2218yescomplemented
56C3×#4035C2218yescomplemented
57C3×#4035C2218yescomplemented
58C3×#4034C2218yescomplemented
59C3×#4033C2218yescomplemented
60C3×#4025C2218yes—
61C3×#4025C2218yes—
62C3×#4025C2218yes—
63C3×#4024C2218yes—
64C3×#4024C2218yes—
65C3×#4023C2218yes—
66C3×#4016C2218yescomplemented
67C3×C4×Dic10C2218yescomplemented
68C2×C3×#541—51nomaximal, Hall
69C2×C5×#126C2×C311yescharacteristic
70#66035C2×C3116yesdirect product factor
71C2×#4036C2×C311yescharacteristic, complemented
72C2×#4035C2×C311yescharacteristic, complemented
73C2×#4035C2×C311yescharacteristic, complemented
74C2×#4035C2×C311yescharacteristic, complemented
75C2×#4034C2×C311yescharacteristic, complemented
76C2×#4033C2×C311yescharacteristic, complemented
77C2×#4025C2×C311yescharacteristic
78C2×#4025C2×C311yescharacteristic
79C2×#4025C2×C311yescharacteristic
80C2×#4024C2×C311yescharacteristic
81C2×#4024C2×C311yescharacteristic
82C2×#4023C2×C311yescharacteristic
83C2×#4016C2×C311yescharacteristic, complemented
84C2×C4×Dic10C2×C311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×Dic5—24no—
93C22×C3×Dic5C2311yescharacteristic
94C22×C3×Dic5C2311yescharacteristic
95C22×C3×Dic5C2311yescharacteristic
96C22×C3×Dic5C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2314yes—
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C2×C3×Dic10—24no—
103C2×C3×Dic10—24no—
104C2×C3×Dic10C2314yes—
105C2×C3×Dic10C2314yes—
106C3×C5×C4⋊C4C2314yes—
107C3×C5×C4⋊C4C2314yes—
108C3×C5×C4⋊C4C2314yes—
109C3×C5×C22⋊C4C2314yes—
110C3×C5×C22⋊C4C2314yes—
111C3×C5×C22⋊C4C2314yes—
112C3×C42×C5C2314yes—
113C3×C22⋊Dic5C2314yes—
114C3×C22⋊Dic5C2314yes—
115C3×C22⋊Dic5C2314yes—
116C3×C4⋊Dic5C2314yes—
117C3×C4⋊Dic5C2314yes—
118C3×C4⋊Dic5C2314yes—
119C3×C4⋊Dic5C2314yes—
120C3×C4⋊Dic5C2314yes—
121C3×#683C2314yes—
122C3×#683C2314yes—
123C3×#683C2314yes—
124C3×#683C2314yes—
125C3×#683C2314yes—
126C3×#683C2314yes—
127C3×#683C2314yes—
128C3×#683C2314yes—
129C3×#683C2314yes—
130C3×#683C2314yes—
131C3×#683C2314yes—
132C3×#683C2314yes—
133C3×C4×Dic5C2314yes—
134C3×C4×Dic5C2314yes—
135C3×C4×Dic5C2314yes—
136C3×C4×Dic5C2314yes—
137C3×C4×Dic5C2314yes—
138C3×#541—516no—
139C2×C3×C4⋊Q8—51no—
140C2×C3×#126—51no—
141C2×C3×#126—51no—
142C2×C3×#126—51no—
143C2×C3×#126D511yescharacteristic
144C2×C3×#125—51no—
145C2×C3×#125—51no—
146C2×C3×#125—51no—
147C2×C3×#125—51no—
148C2×C3×#125—51no—
149C2×C3×C22⋊Q8—51no—
150C2×C3×C22⋊Q8—51no—
151C2×C3×C4×Q8—51no—
152C2×C3×C4×Q8—51no—
153C2×C3×#117—51no—
154C23×Dic5C22×C311yescharacteristic
155C22×Dic10C22×C311yescharacteristic
156C22×Dic10C22×C311yescharacteristic
157C5×#126C22×C318yes—
158C2×C5×C4⋊C4C22×C311yescharacteristic
159C2×C5×C4⋊C4C22×C311yescharacteristic
160C2×C5×C4⋊C4C22×C311yescharacteristic
161C2×C5×C22⋊C4C22×C311yescharacteristic
162C2×C5×C22⋊C4C22×C311yescharacteristic
163C2×C5×C22⋊C4C22×C311yescharacteristic
164C2×C42×C5C22×C311yescharacteristic
165C2×C22⋊Dic5C22×C311yescharacteristic
166C2×C22⋊Dic5C22×C311yescharacteristic
167C2×C22⋊Dic5C22×C311yescharacteristic
168C2×C4⋊Dic5C22×C311yescharacteristic
169C2×C4⋊Dic5C22×C311yescharacteristic
170C2×C4⋊Dic5C22×C311yescharacteristic
171C2×C4⋊Dic5C22×C311yescharacteristic
172C2×C4⋊Dic5C22×C311yescharacteristic
173C2×#683C22×C311yescharacteristic
174C2×#683C22×C311yescharacteristic
175C2×#683C22×C311yescharacteristic
176C2×#683C22×C311yescharacteristic
177C2×#683C22×C311yescharacteristic
178C2×#683C22×C311yescharacteristic
179C2×#683C22×C311yescharacteristic
180C2×#683C22×C311yescharacteristic
181C2×#683C22×C311yescharacteristic
182C2×#683C22×C311yescharacteristic
183C2×#683C22×C311yescharacteristic
184C2×#683C22×C311yescharacteristic
185C2×C4×Dic5C22×C311yescharacteristic
186C2×C4×Dic5C22×C311yescharacteristic
187C2×C4×Dic5C22×C311yescharacteristic
188C2×C4×Dic5C22×C311yescharacteristic
189C2×C4×Dic5C22×C311yescharacteristic
190#4036C22×C318yescomplemented
191#4035C22×C318yescomplemented
192#4035C22×C318yescomplemented
193#4035C22×C318yescomplemented
194#4034C22×C318yescomplemented
195#4033C22×C318yescomplemented
196#4025C22×C318yes—
197#4025C22×C318yes—
198#4025C22×C318yes—
199#4024C22×C318yes—
200#4024C22×C318yes—
201#4023C22×C318yes—
202#4016C22×C318yescomplemented
203C4×Dic10C22×C318yescomplemented
204C2×#541—51noSylow
205C23×C3×C5—22no—
206C23×C3×C5—22no—
207C23×C3×C5—22no—
208C23×C3×C5C2412yes—
209C23×C3×C5C2411yescharacteristic
210C2×C3×C4×C5—22no—
211C2×C3×C4×C5—22no—
212C2×C3×C4×C5—22no—
213C2×C3×C4×C5—22no—
214C2×C3×C4×C5—22no—
215C2×C3×C4×C5—22no—
216C2×C3×C4×C5C2412yes—
217C2×C3×C4×C5C2412yes—
218C2×C3×C4×C5C2412yes—
219C2×C3×C4×C5C2412yes—
220C2×C3×C4×C5C2412yes—
221C2×C3×C4×C5C2412yes—
222C2×C3×Dic5—22no—
223C2×C3×Dic5—22no—
224C2×C3×Dic5—22no—
225C2×C3×Dic5—22no—
226C2×C3×Dic5—22no—
227C2×C3×Dic5—22no—
228C2×C3×Dic5—22no—
229C2×C3×Dic5—28no—
230C2×C3×Dic5#4114yes—
231C2×C3×Dic5C2412yes—
232C2×C3×Dic5C2412yes—
233C2×C3×Dic5C2412yes—
234C2×C3×Dic5C2412yes—
235C2×C3×Dic5C2412yes—
236C2×C3×Dic5C2412yes—
237C2×C3×Dic5C2412yes—
238C2×C3×Dic5C2412yes—
239C3×Dic10—28no—
240C3×Dic10—28no—
241C22×C3×Q8—51no—
242C22×C3×Q8—51no—
243C23×C3×C4—51no—
244C3×C4⋊Q8—58no—
245C3×#126—58no—
246C3×#126—58no—
247C3×#126—58no—
248C3×#126C2×D518yes—
249C3×#125—58no—
250C3×#125—58no—
251C3×#125—58no—
252C3×#125—58no—
253C3×#125—58no—
254C3×C22⋊Q8—58no—
255C3×C22⋊Q8—58no—
256C3×C4×Q8—58no—
257C3×C4×Q8—58no—
258C3×#117—58no—
259C2×C3×C4⋊C4—51no—
260C2×C3×C4⋊C4—51no—
261C2×C3×C4⋊C4—51no—
262C2×C3×C4⋊C4—51no—
263C2×C3×C4⋊C4—51no—
264C2×C3×C4⋊C4—51no—
265C2×C3×C4⋊C4—51no—
266C2×C3×C4⋊C4—51no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C4⋊C4—51no—
271C2×C3×C4⋊C4—51no—
272C2×C3×C4⋊C4—51no—
273C2×C3×C4⋊C4—51no—
274C2×C3×C4⋊C4—51no—
275C2×C3×C4⋊C4—51no—
276C2×C3×C4⋊C4C2×D511yescharacteristic
277C2×C3×C4⋊C4C2×D511yescharacteristic
278C2×C3×C4⋊C4C2×D511yescharacteristic
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—
287C2×C3×C42—51no—
288C2×C3×C42—51no—
289C2×C3×C42—51no—
290C2×C3×C42C2×D511yescharacteristic
291C24×C5C23×C311yescharacteristic
292C22×C4×C5C23×C311yescharacteristic
293C22×C4×C5C23×C311yescharacteristic
294C22×C4×C5C23×C311yescharacteristic
295C22×C4×C5C23×C311yescharacteristic
296C22×C4×C5C23×C311yescharacteristic
297C22×C4×C5C23×C311yescharacteristic
298C22×Dic5—24no—
299C22×Dic5C23×C311yescharacteristic
300C22×Dic5C23×C311yescharacteristic
301C22×Dic5C23×C311yescharacteristic
302C22×Dic5C23×C311yescharacteristic
303C22×Dic5C23×C311yescharacteristic
304C22×Dic5C23×C311yescharacteristic
305C22×Dic5C23×C314yes—
306C22×Dic5C23×C311yescharacteristic
307C22×Dic5C23×C311yescharacteristic
308C2×Dic10—24no—
309C2×Dic10—24no—
310C2×Dic10C23×C314yes—
311C2×Dic10C23×C314yes—
312C5×C4⋊C4C23×C314yes—
313C5×C4⋊C4C23×C314yes—
314C5×C4⋊C4C23×C314yes—
315C5×C22⋊C4C23×C314yes—
316C5×C22⋊C4C23×C314yes—
317C5×C22⋊C4C23×C314yes—
318C42×C5C23×C314yes—
319C22⋊Dic5C23×C314yes—
320C22⋊Dic5C23×C314yes—
321C22⋊Dic5C23×C314yes—
322C4⋊Dic5C23×C314yes—
323C4⋊Dic5C23×C314yes—
324C4⋊Dic5C23×C314yes—
325C4⋊Dic5C23×C314yes—
326C4⋊Dic5C23×C314yes—
327#683C23×C314yes—
328#683C23×C314yes—
329#683C23×C314yes—
330#683C23×C314yes—
331#683C23×C314yes—
332#683C23×C314yes—
333#683C23×C314yes—
334#683C23×C314yes—
335#683C23×C314yes—
336#683C23×C314yes—
337#683C23×C314yes—
338#683C23×C314yes—
339C4×Dic5C23×C314yes—
340C4×Dic5C23×C314yes—
341C4×Dic5C23×C314yes—
342C4×Dic5C23×C314yes—
343C4×Dic5C23×C314yes—
344#541—516no—
345C2×C4⋊Q8—51no—
346C2×#126—51no—
347C2×#126—51no—
348C2×#126—51no—
349C2×#126C3×D511yescharacteristic
350C2×#125—51no—
351C2×#125—51no—
352C2×#125—51no—
353C2×#125—51no—
354C2×#125—51no—
355C2×C22⋊Q8—51no—
356C2×C22⋊Q8—51no—
357C2×C4×Q8—51no—
358C2×C4×Q8—51no—
359C2×#117—51no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—44no—
364C22×C3×C5C2×#4112yes—
365C22×C3×C52−1+412yes—
366C22×C3×C52−1+412yes—
367C22×C3×C5C2511yescharacteristic
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370C3×C4×C5—22no—
371C3×C4×C5—22no—
372C3×C4×C5—22no—
373C3×C4×C5—22no—
374C3×Dic5—22no—
375C3×Dic5—22no—
376C3×Dic5—22no—
377C3×Dic5—22no—
378C3×Dic5—22no—
379C3×Dic5—22no—
380C3×Dic5—22no—
381C3×Dic5C2×#4114yes—
382C24×C3C22×D511yescharacteristic
383C2×C3×Q8—54no—
384C2×C3×Q8—54no—
385C2×C3×Q8—104no—
386C2×C3×Q8—104no—
387C22×C3×C4—51no—
388C22×C3×C4—54no—
389C22×C3×C4—51no—
390C22×C3×C4—51no—
391C22×C3×C4—51no—
392C22×C3×C4—51no—
393C22×C3×C4—51no—
394C22×C3×C4—51no—
395C22×C3×C4—51no—
396C22×C3×C4—104no—
397C22×C3×C4C22×D511yescharacteristic
398C22×C3×C4C22×D511yescharacteristic
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C22×C3×C4C22×D511yescharacteristic
402C22×C3×C4C22×D511yescharacteristic
403C3×C4⋊C4—54no—
404C3×C4⋊C4—54no—
405C3×C4⋊C4—54no—
406C3×C4⋊C4—54no—
407C3×C4⋊C4—54no—
408C3×C4⋊C4—54no—
409C3×C4⋊C4—54no—
410C3×C4⋊C4—54no—
411C3×C4⋊C4—54no—
412C3×C4⋊C4—54no—
413C3×C4⋊C4—54no—
414C3×C4⋊C4—54no—
415C3×C4⋊C4—54no—
416C3×C4⋊C4—54no—
417C3×C4⋊C4—54no—
418C3×C4⋊C4—54no—
419C3×C4⋊C4—54no—
420C3×C4⋊C4C22×D514yes—
421C3×C4⋊C4C22×D514yes—
422C3×C4⋊C4C22×D514yes—
423C3×C22⋊C4—54no—
424C3×C22⋊C4—54no—
425C3×C22⋊C4—54no—
426C3×C22⋊C4C22×D514yes—
427C3×C22⋊C4C22×D514yes—
428C3×C22⋊C4C22×D514yes—
429C3×C42—54no—
430C3×C42—54no—
431C3×C42—54no—
432C3×C42—54no—
433C3×C42—54no—
434C3×C42C22×D514yes—
435C23×C5—22no—
436C23×C5—22no—
437C23×C5—22no—
438C23×C5C24×C312yes—
439C23×C5C24×C311yescharacteristic
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—22no—
444C2×C4×C5—22no—
445C2×C4×C5—22no—
446C2×C4×C5C24×C312yes—
447C2×C4×C5C24×C312yes—
448C2×C4×C5C24×C312yes—
449C2×C4×C5C24×C312yes—
450C2×C4×C5C24×C312yes—
451C2×C4×C5C24×C312yes—
452C2×Dic5—22no—
453C2×Dic5—22no—
454C2×Dic5—22no—
455C2×Dic5—22no—
456C2×Dic5—22no—
457C2×Dic5—22no—
458C2×Dic5—22no—
459C2×Dic5—28no—
460C2×Dic5C3×#4114yes—
461C2×Dic5C24×C312yes—
462C2×Dic5C24×C312yes—
463C2×Dic5C24×C312yes—
464C2×Dic5C24×C312yes—
465C2×Dic5C24×C312yes—
466C2×Dic5C24×C312yes—
467C2×Dic5C24×C312yes—
468C2×Dic5C24×C312yes—
469Dic10—28no—
470Dic10—28no—
471C22×Q8—51no—
472C22×Q8—51no—
473C23×C4—51no—
474C4⋊Q8—58no—
475#126—58no—
476#126—58no—
477#126—58no—
478#126C2×C3×D518yes—
479#125—58no—
480#125—58no—
481#125—58no—
482#125—58no—
483#125—58no—
484C22⋊Q8—58no—
485C22⋊Q8—58no—
486C4×Q8—58no—
487C4×Q8—58no—
488#117—58no—
489C2×C4⋊C4—51no—
490C2×C4⋊C4—51no—
491C2×C4⋊C4—51no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
496C2×C4⋊C4—51no—
497C2×C4⋊C4—51no—
498C2×C4⋊C4—51no—
499C2×C4⋊C4—51no—
500C2×C4⋊C4—51no—
501C2×C4⋊C4—51no—
502C2×C4⋊C4—51no—
503C2×C4⋊C4—51no—
504C2×C4⋊C4—51no—
505C2×C4⋊C4—51no—
506C2×C4⋊C4C2×C3×D511yescharacteristic
507C2×C4⋊C4C2×C3×D511yescharacteristic
508C2×C4⋊C4C2×C3×D511yescharacteristic
509C2×C22⋊C4—51no—
510C2×C22⋊C4—51no—
511C2×C22⋊C4—51no—
512C2×C22⋊C4C2×C3×D511yescharacteristic
513C2×C22⋊C4C2×C3×D511yescharacteristic
514C2×C22⋊C4C2×C3×D511yescharacteristic
515C2×C42—51no—
516C2×C42—51no—
517C2×C42—51no—
518C2×C42—51no—
519C2×C42—51no—
520C2×C42C2×C3×D511yescharacteristic
521C2×C3×C5—42no—
522C2×C3×C5#54114yescomplemented
523C2×C3×C5C22×#4111yescharacteristic
524C2×C3×C5C2×2−1+411yescharacteristic
525C2×C3×C5C2×2−1+411yescharacteristic
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3C23×D512yes—
530C23×C3C23×D511yescharacteristic
531C3×Q8—108no—
532C3×Q8—108no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—54no—
540C2×C3×C4—52no—
541C2×C3×C4—52no—
542C2×C3×C4—52no—
543C2×C3×C4—52no—
544C2×C3×C4—52no—
545C2×C3×C4—52no—
546C2×C3×C4—52no—
547C2×C3×C4—52no—
548C2×C3×C4—108no—
549C2×C3×C4—102no—
550C2×C3×C4—102no—
551C2×C3×C4—102no—
552C2×C3×C4—102no—
553C2×C3×C4—102no—
554C2×C3×C4—102no—
555C2×C3×C4—102no—
556C2×C3×C4C23×D512yes—
557C2×C3×C4C23×D512yes—
558C2×C3×C4C23×D512yes—
559C2×C3×C4C23×D512yes—
560C2×C3×C4C23×D512yes—
561C2×C3×C4C23×D512yes—
562C22×C5—22no—
563C22×C5—22no—
564C22×C5—22no—
565C22×C5—44no—
566C22×C5C2×C3×#4112yes—
567C22×C5C3×2−1+412yes—
568C22×C5C3×2−1+412yes—
569C22×C5C25×C311yescharacteristic
570C4×C5—22no—
571C4×C5—22no—
572C4×C5—22no—
573C4×C5—22no—
574C4×C5—22no—
575C4×C5—22no—
576Dic5—22no—
577Dic5—22no—
578Dic5—22no—
579Dic5—22no—
580Dic5—22no—
581Dic5—22no—
582Dic5—22no—
583Dic5C2×C3×#4114yes—
584C24C22×C3×D511yescharacteristic
585C2×Q8—54no—
586C2×Q8—54no—
587C2×Q8—104no—
588C2×Q8—104no—
589C22×C4—51no—
590C22×C4—51no—
591C22×C4—51no—
592C22×C4—51no—
593C22×C4—51no—
594C22×C4—51no—
595C22×C4—51no—
596C22×C4—51no—
597C22×C4—54no—
598C22×C4—104no—
599C22×C4C22×C3×D511yescharacteristic
600C22×C4C22×C3×D511yescharacteristic
601C22×C4C22×C3×D511yescharacteristic
602C22×C4C22×C3×D511yescharacteristic
603C22×C4C22×C3×D511yescharacteristic
604C22×C4C22×C3×D511yescharacteristic
605C4⋊C4—54no—
606C4⋊C4—54no—
607C4⋊C4—54no—
608C4⋊C4—54no—
609C4⋊C4—54no—
610C4⋊C4—54no—
611C4⋊C4—54no—
612C4⋊C4—54no—
613C4⋊C4—54no—
614C4⋊C4—54no—
615C4⋊C4—54no—
616C4⋊C4—54no—
617C4⋊C4—54no—
618C4⋊C4—54no—
619C4⋊C4—54no—
620C4⋊C4—54no—
621C4⋊C4—54no—
622C4⋊C4C22×C3×D514yes—
623C4⋊C4C22×C3×D514yes—
624C4⋊C4C22×C3×D514yes—
625C22⋊C4—54no—
626C22⋊C4—54no—
627C22⋊C4—54no—
628C22⋊C4C22×C3×D514yes—
629C22⋊C4C22×C3×D514yes—
630C22⋊C4C22×C3×D514yes—
631C42—54no—
632C42—54no—
633C42—54no—
634C42—54no—
635C42—54no—
636C42C22×C3×D514yes—
637C3×C5C2×#54111yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—44no—
642C22×C3D5×#4112yes—
643C22×C3#415012yes—
644C22×C3#415012yes—
645C22×C3C24×D511yescharacteristic
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—22no—
650C3×C4—22no—
651C3×C4—22no—
652C3×C4—54no—
653C3×C4—102no—
654C3×C4—102no—
655C3×C4—102no—
656C3×C4—102no—
657C3×C4—102no—
658C3×C4—102no—
659C3×C4—102no—
660C2×C5—42no—
661C2×C5C3×#54114yescomplemented
662C2×C5C22×C3×#4111yescharacteristic
663C2×C5C2×C3×2−1+411yescharacteristic
664C2×C5C2×C3×2−1+411yescharacteristic
665C23—22no—
666C23—22no—
667C23—22no—
668C23C23×C3×D512yes—
669C23C23×C3×D511yescharacteristic
670Q8—108no—
671Q8—108no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—54no—
679C2×C4—52no—
680C2×C4—52no—
681C2×C4—52no—
682C2×C4—52no—
683C2×C4—52no—
684C2×C4—52no—
685C2×C4—52no—
686C2×C4—52no—
687C2×C4—108no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4C23×C3×D512yes—
696C2×C4C23×C3×D512yes—
697C2×C4C23×C3×D512yes—
698C2×C4C23×C3×D512yes—
699C2×C4C23×C3×D512yes—
700C2×C4C23×C3×D512yes—
701C2×C3—42no—
702C2×C3#6603514yesdirect product factor
703C2×C3C2×D5×#4111yescharacteristic
704C2×C3C2×#415011yescharacteristic
705C2×C3C2×#415011yescharacteristic
706C5C2×C3×#54111yescharacteristic, complemented, Sylow
707C22—22no—
708C22—22no—
709C22—22no—
710C22—44no—
711C22C3×D5×#4112yes—
712C22C3×#415012yes—
713C22C3×#415012yes—
714C22C24×C3×D511yescharacteristic
715C4—22no—
716C4—22no—
717C4—22no—
718C4—22no—
719C4—22no—
720C4—22no—
721C4—54no—
722C4—102no—
723C4—102no—
724C4—102no—
725C4—102no—
726C4—102no—
727C4—102no—
728C4—102no—
729C3C2×#6603511yescharacteristic, direct product factor, Sylow
730C2—42no—
731C2C3×#6603514yesdirect product factor
732C2C2×C3×D5×#4111yescharacteristic
733C2C2×C3×#415011yescharacteristic
734C2C2×C3×#415011yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#126C2
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C3×#126D5
hypocenterC5C2×C3×#541
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#126

Complements

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

NH ≅ G/Ntype
2. C3×#66035C2direct (N × H)
3. C2×C3×#4036C2semidirect
4. C2×C3×#4035C2semidirect
5. C2×C3×#4035C2semidirect
6. C2×C3×#4035C2semidirect
7. C2×C3×#4034C2semidirect
8. C2×C3×#4033C2semidirect
15. C2×C3×#4016C2semidirect
16. C2×C3×C4×Dic10C2semidirect
17. C2×#66035C3direct (N × H)
54. C3×#4036C22semidirect
55. C3×#4035C22semidirect
56. C3×#4035C22semidirect
57. C3×#4035C22semidirect
58. C3×#4034C22semidirect
59. C3×#4033C22semidirect
66. C3×#4016C22semidirect
67. C3×C4×Dic10C22semidirect
70. #66035C2×C3direct (N × H)
71. C2×#4036C2×C3semidirect
72. C2×#4035C2×C3semidirect
73. C2×#4035C2×C3semidirect
74. C2×#4035C2×C3semidirect
75. C2×#4034C2×C3semidirect
76. C2×#4033C2×C3semidirect
83. C2×#4016C2×C3semidirect
84. C2×C4×Dic10C2×C3semidirect
190. #4036C22×C3semidirect
191. #4035C22×C3semidirect
192. #4035C22×C3semidirect
193. #4035C22×C3semidirect
194. #4034C22×C3semidirect
195. #4033C22×C3semidirect
202. #4016C22×C3semidirect
203. C4×Dic10C22×C3semidirect
522. C2×C3×C5#541semidirect
637. C3×C5C2×#541semidirect
661. C2×C5C3×#541semidirect
702. C2×C3#66035direct (N × H)
706. C5C2×C3×#541semidirect
729. C3C2×#66035direct (N × H)
731. C2C3×#66035direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1262
C3×#660352
C2×C3×#40362
C2×C3×#40352
C2×C3×#40342
C2×C3×#40332
C2×C3×#40252
C2×C3×#40242
C2×C3×#40232
C2×C3×#40162
C2×C3×C4×Dic102
C2×#660353
C2×C3×#5415