Finite Group Databasebeta

← C2×C3×#66029 #14483623

Subgroups — C2×C3×#66029 #14483623

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#125C211yesmaximal, characteristic, complemented
2C3×#66029C2116yesmaximal, direct product factor
3C2×C3×#4044C212yesmaximal, complemented
4C2×C3×#4041C211yesmaximal, characteristic, complemented
5C2×C3×#4041C211yesmaximal, characteristic, complemented
6C2×C3×#4041C212yesmaximal, complemented
7C2×C3×#4040C212yesmaximal, complemented
8C2×C3×#4039C212yesmaximal, complemented
9C2×C3×#4038C211yesmaximal, characteristic, complemented
10C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
11C2×C3×C4×D20C211yesmaximal, characteristic, complemented
12C2×C3×C4×D20C211yesmaximal, characteristic, complemented
13C2×#66029C311yesmaximal, characteristic, direct product factor, Hall
14C22×C3×D20C2211yescharacteristic
15C22×C3×D20C2211yescharacteristic
16C22×C3×D20C2212yes—
17C22×C3×D20C2212yes—
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×C4×D5C2211yescharacteristic
20C22×C3×C4×D5C2212yes—
21C22×C3×C4×D5C2212yes—
22C3×C5×#125C2218yescomplemented
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C4⋊C4C2212yes—
27C2×C3×C42×C5C2211yescharacteristic
28C2×C3×#685C2212yes—
29C2×C3×#685C2212yes—
30C2×C3×#685C2212yes—
31C2×C3×#685C2211yescharacteristic
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2212yes—
34C2×C3×C4⋊Dic5C2211yescharacteristic
35C2×C3×C4⋊Dic5C2211yescharacteristic
36C2×C3×#683C2212yes—
37C2×C3×C4×Dic5C2212yes—
38C3×#4044C22116yescomplemented
39C3×#4041C22116yescomplemented
40C3×#4041C2218yescomplemented
41C3×#4041C2218yescomplemented
42C3×#4040C22116yescomplemented
43C3×#4039C22116yescomplemented
44C3×#4038C2218yescomplemented
45C3×D5×C4⋊C4C2218yescomplemented
46C3×C4×D20C2218yescomplemented
47C3×C4×D20C2218yescomplemented
48C2×C3×#553—51nomaximal, Hall
49C2×C5×#125C2×C311yescharacteristic, complemented
50#66029C2×C3116yesdirect product factor
51C2×#4044C2×C312yescomplemented
52C2×#4041C2×C311yescharacteristic, complemented
53C2×#4041C2×C311yescharacteristic, complemented
54C2×#4041C2×C312yescomplemented
55C2×#4040C2×C312yescomplemented
56C2×#4039C2×C312yescomplemented
57C2×#4038C2×C311yescharacteristic, complemented
58C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
59C2×C4×D20C2×C311yescharacteristic, complemented
60C2×C4×D20C2×C311yescharacteristic, complemented
61C23×C3×D5C2311yescharacteristic
62C23×C3×D5C2312yes—
63C23×C3×D5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2311yescharacteristic
71C22×C3×Dic5C2311yescharacteristic
72C2×C3×D20—24no—
73C2×C3×D20—28no—
74C2×C3×D20—24no—
75C2×C3×D20—44no—
76C2×C3×D20C2314yes—
77C2×C3×D20C2314yes—
78C2×C3×D20C2318yes—
79C2×C3×D20C2318yes—
80C2×C3×C4×D5—24no—
81C2×C3×C4×D5—24no—
82C2×C3×C4×D5—44no—
83C2×C3×C4×D5—44no—
84C2×C3×C4×D5C2314yes—
85C2×C3×C4×D5C2314yes—
86C2×C3×C4×D5C2318yes—
87C2×C3×C4×D5C2318yes—
88C3×C5×C4⋊C4C2314yes—
89C3×C5×C4⋊C4C2314yes—
90C3×C5×C4⋊C4C2318yes—
91C3×C5×C4⋊C4C2318yes—
92C3×C42×C5C2314yes—
93C3×#685C2314yes—
94C3×#685C2314yes—
95C3×#685C2318yes—
96C3×#685C2318yes—
97C3×#685C2318yes—
98C3×#685C2318yes—
99C3×C4⋊Dic5C2314yes—
100C3×C4⋊Dic5C2314yes—
101C3×#683C2318yes—
102C3×C4×Dic5C2318yes—
103C3×#553—516no—
104C2×C3×#126—52no—
105C2×C3×#125D511yescharacteristic, complemented
106C2×C3×#123—52no—
107C2×C3×#121—52no—
108C2×C3×#121—51no—
109C2×C3×#121—51no—
110C2×C3×C4×D4—52no—
111C2×C3×C4×D4—51no—
112C2×C3×C4×D4—51no—
113C2×C3×#117—51no—
114C22×C3×C4⋊C4—51no—
115C22×D20C22×C311yescharacteristic
116C22×D20C22×C311yescharacteristic
117C22×D20C22×C312yes—
118C22×D20C22×C312yes—
119C22×C4×D5C22×C311yescharacteristic
120C22×C4×D5C22×C311yescharacteristic
121C22×C4×D5C22×C312yes—
122C22×C4×D5C22×C312yes—
123C5×#125C22×C318yescomplemented
124C2×C5×C4⋊C4C22×C311yescharacteristic
125C2×C5×C4⋊C4C22×C311yescharacteristic
126C2×C5×C4⋊C4C22×C312yes—
127C2×C5×C4⋊C4C22×C312yes—
128C2×C42×C5C22×C311yescharacteristic
129C2×#685C22×C311yescharacteristic
130C2×#685C22×C311yescharacteristic
131C2×#685C22×C312yes—
132C2×#685C22×C312yes—
133C2×#685C22×C312yes—
134C2×#685C22×C312yes—
135C2×C4⋊Dic5C22×C311yescharacteristic
136C2×C4⋊Dic5C22×C311yescharacteristic
137C2×#683C22×C312yes—
138C2×C4×Dic5C22×C312yes—
139#4044C22×C3116yescomplemented
140#4041C22×C3116yescomplemented
141#4041C22×C318yescomplemented
142#4041C22×C318yescomplemented
143#4040C22×C3116yescomplemented
144#4039C22×C3116yescomplemented
145#4038C22×C318yescomplemented
146D5×C4⋊C4C22×C318yescomplemented
147C4×D20C22×C318yescomplemented
148C4×D20C22×C318yescomplemented
149C2×#553—51noSylow
150C23×C3×C5C2411yescharacteristic
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5—22no—
154C22×C3×D5—24no—
155C22×C3×D5—22no—
156C22×C3×D5—24no—
157C22×C3×D5—24no—
158C22×C3×D5—22no—
159C22×C3×D5#4114yes—
160C22×C3×D5C2412yes—
161C22×C3×D5C2414yes—
162C22×C3×D5C2412yes—
163C2×C3×C4×C5—22no—
164C2×C3×C4×C5—24no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—24no—
167C2×C3×C4×C5#4114yes—
168C2×C3×C4×C5C2414yes—
169C2×C3×C4×C5C2414yes—
170C2×C3×C4×C5C2412yes—
171C2×C3×C4×C5C2412yes—
172C2×C3×C4×C5C2412yes—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5—24no—
176C2×C3×Dic5C2412yes—
177C2×C3×Dic5C2414yes—
178C2×C3×Dic5C2412yes—
179C3×D20—28no—
180C3×D20—216no—
181C3×D20—28no—
182C3×D20—48no—
183C3×C4×D5—28no—
184C3×C4×D5—28no—
185C3×C4×D5—48no—
186C3×C4×D5—48no—
187C22×C3×D4—52no—
188C22×C3×D4—51no—
189C22×C3×D4—51no—
190C22×C3×D4—52no—
191C23×C3×C4—51no—
192C23×C3×C4—51no—
193C23×C3×C4—52no—
194C23×C3×C4—52no—
195C3×#126—516no—
196C3×#125C2×D518yescomplemented
197C3×#123—516no—
198C3×#121—516no—
199C3×#121—58no—
200C3×#121—58no—
201C3×C4×D4—516no—
202C3×C4×D4—58no—
203C3×C4×D4—58no—
204C3×#117—58no—
205C2×C3×C4⋊C4—51no—
206C2×C3×C4⋊C4—52no—
207C2×C3×C4⋊C4—51no—
208C2×C3×C4⋊C4—58no—
209C2×C3×C4⋊C4C2×D511yescharacteristic
210C2×C3×C4⋊C4C2×D511yescharacteristic
211C2×C3×C4⋊C4C2×D512yes—
212C2×C3×C4⋊C4C2×D512yes—
213C2×C3×C22⋊C4—52no—
214C2×C3×C22⋊C4—51no—
215C2×C3×C22⋊C4—52no—
216C2×C3×C22⋊C4—52no—
217C2×C3×C22⋊C4—51no—
218C2×C3×C22⋊C4—52no—
219C2×C3×C42—52no—
220C2×C3×C42C2×D511yescharacteristic
221C23×D5C23×C311yescharacteristic
222C23×D5C23×C312yes—
223C23×D5C23×C311yescharacteristic
224C22×C4×C5C23×C311yescharacteristic
225C22×C4×C5C23×C311yescharacteristic
226C22×C4×C5C23×C312yes—
227C22×C4×C5C23×C312yes—
228C22×C4×C5C23×C311yescharacteristic
229C22×Dic5C23×C312yes—
230C22×Dic5C23×C311yescharacteristic
231C22×Dic5C23×C311yescharacteristic
232C2×D20—24no—
233C2×D20—28no—
234C2×D20—24no—
235C2×D20—44no—
236C2×D20C23×C314yes—
237C2×D20C23×C314yes—
238C2×D20C23×C318yes—
239C2×D20C23×C318yes—
240C2×C4×D5—24no—
241C2×C4×D5—24no—
242C2×C4×D5—44no—
243C2×C4×D5—44no—
244C2×C4×D5C23×C314yes—
245C2×C4×D5C23×C314yes—
246C2×C4×D5C23×C318yes—
247C2×C4×D5C23×C318yes—
248C5×C4⋊C4C23×C314yes—
249C5×C4⋊C4C23×C314yes—
250C5×C4⋊C4C23×C318yes—
251C5×C4⋊C4C23×C318yes—
252C42×C5C23×C314yes—
253#685C23×C314yes—
254#685C23×C314yes—
255#685C23×C318yes—
256#685C23×C318yes—
257#685C23×C318yes—
258#685C23×C318yes—
259C4⋊Dic5C23×C314yes—
260C4⋊Dic5C23×C314yes—
261#683C23×C318yes—
262C4×Dic5C23×C318yes—
263#553—516no—
264C2×#126—52no—
265C2×#125C3×D511yescharacteristic, complemented
266C2×#123—52no—
267C2×#121—52no—
268C2×#121—51no—
269C2×#121—51no—
270C2×C4×D4—52no—
271C2×C4×D4—51no—
272C2×C4×D4—51no—
273C2×#117—51no—
274C22×C4⋊C4—51no—
275C22×C3×C5C2×#4112yes—
276C22×C3×C5C2×#4112yes—
277C22×C3×C5H(5,𝔽2)12yes—
278C22×C3×C5C2511yescharacteristic
279C2×C3×D5—28no—
280C2×C3×D5—22no—
281C2×C3×D5—22no—
282C2×C3×D5—22no—
283C2×C3×D5—24no—
284C2×C3×D5—22no—
285C2×C3×D5—24no—
286C2×C3×D5—24no—
287C2×C3×D5—22no—
288C2×C3×D5—44no—
289C2×C3×D5—48no—
290C2×C3×D5C2×#4114yes—
291C3×C4×C5—24no—
292C3×C4×C5—22no—
293C3×C4×C5—22no—
294C3×C4×C5—24no—
295C3×C4×C5C2×#4114yes—
296C3×Dic5—22no—
297C3×Dic5—22no—
298C3×Dic5—24no—
299C24×C3—51no—
300C24×C3—51no—
301C24×C3—52no—
302C2×C3×D4—58no—
303C2×C3×D4—54no—
304C2×C3×D4—54no—
305C2×C3×D4—58no—
306C2×C3×D4—108no—
307C2×C3×D4—104no—
308C2×C3×D4—104no—
309C2×C3×D4—204no—
310C22×C3×C4—51no—
311C22×C3×C4—52no—
312C22×C3×C4—51no—
313C22×C3×C4—54no—
314C22×C3×C4—54no—
315C22×C3×C4—58no—
316C22×C3×C4—58no—
317C22×C3×C4—104no—
318C22×C3×C4—104no—
319C22×C3×C4—204no—
320C22×C3×C4—204no—
321C22×C3×C4C22×D512yes—
322C22×C3×C4C22×D511yescharacteristic
323C22×C3×C4C22×D511yescharacteristic
324C22×C3×C4C22×D512yes—
325C22×C3×C4C22×D511yescharacteristic
326C3×C4⋊C4—58no—
327C3×C4⋊C4—54no—
328C3×C4⋊C4—54no—
329C3×C4⋊C4C22×D514yes—
330C3×C4⋊C4C22×D514yes—
331C3×C4⋊C4C22×D518yes—
332C3×C4⋊C4C22×D518yes—
333C3×C22⋊C4—58no—
334C3×C22⋊C4—54no—
335C3×C22⋊C4—58no—
336C3×C22⋊C4—58no—
337C3×C22⋊C4—54no—
338C3×C22⋊C4—58no—
339C3×C42—58no—
340C3×C42C22×D514yes—
341C23×C5C24×C311yescharacteristic
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—24no—
346C22×D5—22no—
347C22×D5—24no—
348C22×D5—24no—
349C22×D5—22no—
350C22×D5C3×#4114yes—
351C22×D5C24×C312yes—
352C22×D5C24×C314yes—
353C22×D5C24×C312yes—
354C2×C4×C5—22no—
355C2×C4×C5—24no—
356C2×C4×C5—22no—
357C2×C4×C5—24no—
358C2×C4×C5C3×#4114yes—
359C2×C4×C5C24×C314yes—
360C2×C4×C5C24×C314yes—
361C2×C4×C5C24×C312yes—
362C2×C4×C5C24×C312yes—
363C2×C4×C5C24×C312yes—
364C2×Dic5—22no—
365C2×Dic5—22no—
366C2×Dic5—24no—
367C2×Dic5C24×C312yes—
368C2×Dic5C24×C314yes—
369C2×Dic5C24×C312yes—
370D20—28no—
371D20—216no—
372D20—28no—
373D20—48no—
374C4×D5—28no—
375C4×D5—28no—
376C4×D5—48no—
377C4×D5—48no—
378C22×D4—52no—
379C22×D4—51no—
380C22×D4—51no—
381C22×D4—52no—
382C23×C4—51no—
383C23×C4—51no—
384C23×C4—52no—
385C23×C4—52no—
386#126—516no—
387#125C2×C3×D518yescomplemented
388#123—516no—
389#121—516no—
390#121—58no—
391#121—58no—
392C4×D4—516no—
393C4×D4—58no—
394C4×D4—58no—
395#117—58no—
396C2×C4⋊C4—51no—
397C2×C4⋊C4—52no—
398C2×C4⋊C4—51no—
399C2×C4⋊C4—58no—
400C2×C4⋊C4C2×C3×D511yescharacteristic
401C2×C4⋊C4C2×C3×D511yescharacteristic
402C2×C4⋊C4C2×C3×D512yes—
403C2×C4⋊C4C2×C3×D512yes—
404C2×C22⋊C4—52no—
405C2×C22⋊C4—51no—
406C2×C22⋊C4—52no—
407C2×C22⋊C4—52no—
408C2×C22⋊C4—51no—
409C2×C22⋊C4—52no—
410C2×C42—52no—
411C2×C42C2×C3×D511yescharacteristic
412C2×C3×C5#55314yescomplemented
413C2×C3×C5C22×#4111yescharacteristic
414C2×C3×C5C22×#4111yescharacteristic
415C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
416C3×D5—24no—
417C3×D5—42no—
418C3×D5—44no—
419C23×C3—54no—
420C23×C3—52no—
421C23×C3—52no—
422C23×C3—54no—
423C23×C3—102no—
424C23×C3—102no—
425C23×C3—102no—
426C23×C3—104no—
427C23×C3—102no—
428C23×C3—104no—
429C23×C3—104no—
430C23×C3—102no—
431C23×C3C23×D511yescharacteristic
432C3×D4—1016no—
433C3×D4—108no—
434C3×D4—108no—
435C3×D4—208no—
436C2×C3×C4—24no—
437C2×C3×C4—22no—
438C2×C3×C4—22no—
439C2×C3×C4—24no—
440C2×C3×C4—52no—
441C2×C3×C4—54no—
442C2×C3×C4—52no—
443C2×C3×C4—102no—
444C2×C3×C4—102no—
445C2×C3×C4—104no—
446C2×C3×C4—108no—
447C2×C3×C4—108no—
448C2×C3×C4—208no—
449C2×C3×C4—208no—
450C2×C3×C4#71314yes—
451C2×C3×C4C23×D514yes—
452C2×C3×C4C23×D512yes—
453C2×C3×C4C23×D512yes—
454C2×C3×C4C23×D514yes—
455C2×C3×C4C23×D512yes—
456C22×C5C2×C3×#4112yes—
457C22×C5C2×C3×#4112yes—
458C22×C5C3×H(5,𝔽2)12yes—
459C22×C5C25×C311yescharacteristic
460C2×D5—22no—
461C2×D5—22no—
462C2×D5—28no—
463C2×D5—22no—
464C2×D5—24no—
465C2×D5—22no—
466C2×D5—24no—
467C2×D5—24no—
468C2×D5—22no—
469C2×D5—44no—
470C2×D5—48no—
471C2×D5C2×C3×#4114yes—
472C4×C5—24no—
473C4×C5—22no—
474C4×C5—22no—
475C4×C5—24no—
476C4×C5C2×C3×#4114yes—
477Dic5—22no—
478Dic5—22no—
479Dic5—24no—
480C24—51no—
481C24—51no—
482C24—52no—
483C2×D4—58no—
484C2×D4—54no—
485C2×D4—54no—
486C2×D4—58no—
487C2×D4—108no—
488C2×D4—104no—
489C2×D4—104no—
490C2×D4—204no—
491C22×C4—51no—
492C22×C4—52no—
493C22×C4—51no—
494C22×C4—54no—
495C22×C4—54no—
496C22×C4—58no—
497C22×C4—58no—
498C22×C4—104no—
499C22×C4—104no—
500C22×C4—204no—
501C22×C4—204no—
502C22×C4C22×C3×D512yes—
503C22×C4C22×C3×D511yescharacteristic
504C22×C4C22×C3×D511yescharacteristic
505C22×C4C22×C3×D512yes—
506C22×C4C22×C3×D511yescharacteristic
507C4⋊C4—54no—
508C4⋊C4—58no—
509C4⋊C4—54no—
510C4⋊C4C22×C3×D514yes—
511C4⋊C4C22×C3×D514yes—
512C4⋊C4C22×C3×D518yes—
513C4⋊C4C22×C3×D518yes—
514C22⋊C4—58no—
515C22⋊C4—54no—
516C22⋊C4—58no—
517C22⋊C4—58no—
518C22⋊C4—54no—
519C22⋊C4—58no—
520C42—58no—
521C42C22×C3×D514yes—
522C3×C5C2×#55311yescharacteristic, complemented, Hall
523C22×C3—54no—
524C22×C3—102no—
525C22×C3—102no—
526C22×C3—108no—
527C22×C3—102no—
528C22×C3—104no—
529C22×C3—102no—
530C22×C3—104no—
531C22×C3—104no—
532C22×C3—102no—
533C22×C3—204no—
534C22×C3—208no—
535C22×C3C2×#71312yes—
536C22×C3D5×#4112yes—
537C22×C3#414912yes—
538C22×C3C24×D511yescharacteristic
539C3×C4—24no—
540C3×C4—22no—
541C3×C4—22no—
542C3×C4—24no—
543C3×C4—102no—
544C3×C4—102no—
545C3×C4—104no—
546C3×C4C2×#71314yes—
547C2×C5C3×#55314yescomplemented
548C2×C5C22×C3×#4111yescharacteristic
549C2×C5C22×C3×#4111yescharacteristic
550C2×C5C2×C3×H(5,𝔽2)11yescharacteristic
551D5—24no—
552D5—42no—
553D5—44no—
554C23—54no—
555C23—52no—
556C23—52no—
557C23—54no—
558C23—102no—
559C23—102no—
560C23—102no—
561C23—104no—
562C23—102no—
563C23—104no—
564C23—104no—
565C23—102no—
566C23C23×C3×D511yescharacteristic
567D4—1016no—
568D4—108no—
569D4—108no—
570D4—208no—
571C2×C4—24no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—24no—
575C2×C4—52no—
576C2×C4—54no—
577C2×C4—52no—
578C2×C4—102no—
579C2×C4—102no—
580C2×C4—104no—
581C2×C4—108no—
582C2×C4—108no—
583C2×C4—208no—
584C2×C4—208no—
585C2×C4C3×#71314yes—
586C2×C4C23×C3×D514yes—
587C2×C4C23×C3×D512yes—
588C2×C4C23×C3×D512yes—
589C2×C4C23×C3×D514yes—
590C2×C4C23×C3×D512yes—
591C2×C3—104no—
592C2×C3—202no—
593C2×C3—204no—
594C2×C3#6602914yesdirect product factor
595C2×C3C22×#71311yescharacteristic
596C2×C3C2×D5×#4111yescharacteristic
597C2×C3C2×#414911yescharacteristic
598C5C2×C3×#55311yescharacteristic, complemented, Sylow
599C22—54no—
600C22—102no—
601C22—102no—
602C22—108no—
603C22—102no—
604C22—104no—
605C22—102no—
606C22—104no—
607C22—104no—
608C22—102no—
609C22—204no—
610C22—208no—
611C22C2×C3×#71312yes—
612C22C3×D5×#4112yes—
613C22C3×#414912yes—
614C22C24×C3×D511yescharacteristic
615C4—24no—
616C4—22no—
617C4—22no—
618C4—24no—
619C4—102no—
620C4—102no—
621C4—104no—
622C4C2×C3×#71314yes—
623C3C2×#6602911yescharacteristic, direct product factor, Sylow
624C2—104no—
625C2—202no—
626C2—204no—
627C2C3×#6602914yesdirect product factor
628C2C22×C3×#71311yescharacteristic
629C2C2×C3×D5×#4111yescharacteristic
630C2C2×C3×#414911yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutator, cosocleC22×C5C25×C3
FrattiniC22C24×C3×D5
FittingC2×C3×C5×#125C2
socleC23×C3×C5C24
hypercenterC2×C3×#125D5
hypocenterC5C2×C3×#553
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×#125

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×#125C2semidirect
2. C3×#66029C2direct (N × H)
3. C2×C3×#4044C2semidirect
4. C2×C3×#4041C2semidirect
5. C2×C3×#4041C2semidirect
6. C2×C3×#4041C2semidirect
7. C2×C3×#4040C2semidirect
8. C2×C3×#4039C2semidirect
9. C2×C3×#4038C2semidirect
10. C2×C3×D5×C4⋊C4C2semidirect
11. C2×C3×C4×D20C2semidirect
12. C2×C3×C4×D20C2semidirect
13. C2×#66029C3direct (N × H)
22. C3×C5×#125C22semidirect
38. C3×#4044C22semidirect
39. C3×#4041C22semidirect
40. C3×#4041C22semidirect
41. C3×#4041C22semidirect
42. C3×#4040C22semidirect
43. C3×#4039C22semidirect
44. C3×#4038C22semidirect
45. C3×D5×C4⋊C4C22semidirect
46. C3×C4×D20C22semidirect
47. C3×C4×D20C22semidirect
49. C2×C5×#125C2×C3semidirect
50. #66029C2×C3direct (N × H)
51. C2×#4044C2×C3semidirect
52. C2×#4041C2×C3semidirect
53. C2×#4041C2×C3semidirect
54. C2×#4041C2×C3semidirect
55. C2×#4040C2×C3semidirect
56. C2×#4039C2×C3semidirect
57. C2×#4038C2×C3semidirect
58. C2×D5×C4⋊C4C2×C3semidirect
59. C2×C4×D20C2×C3semidirect
60. C2×C4×D20C2×C3semidirect
105. C2×C3×#125D5semidirect
123. C5×#125C22×C3semidirect
139. #4044C22×C3semidirect
140. #4041C22×C3semidirect
141. #4041C22×C3semidirect
142. #4041C22×C3semidirect
143. #4040C22×C3semidirect
144. #4039C22×C3semidirect
145. #4038C22×C3semidirect
146. D5×C4⋊C4C22×C3semidirect
147. C4×D20C22×C3semidirect
148. C4×D20C22×C3semidirect
196. C3×#125C2×D5semidirect
265. C2×#125C3×D5semidirect
387. #125C2×C3×D5semidirect
412. C2×C3×C5#553semidirect
522. C3×C5C2×#553semidirect
547. C2×C5C3×#553semidirect
594. C2×C3#66029direct (N × H)
598. C5C2×C3×#553semidirect
623. C3C2×#66029direct (N × H)
627. C2C3×#66029direct (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×#1252
C3×#660292
C2×C3×#40442
C2×C3×#40412
C2×C3×#40402
C2×C3×#40392
C2×C3×#40382
C2×C3×D5×C4⋊C42
C2×C3×C4×D202
C2×#660293
C2×C3×#5535