Finite Group Databasebeta

← C3×C5×#2432 #14275466

Subgroups — C3×C5×#2432 #14275466

Order 1920.

1672 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×#41C211yesmaximal, characteristic
2C2×C3×C5×C4⋊Q8C211yesmaximal, characteristic, complemented
3C2×C3×C5×#124C211yesmaximal, characteristic, complemented
4C2×C3×C5×C22⋊Q8C211yesmaximal, characteristic, complemented
5C3×C5×#394C214yesmaximal, complemented
6C3×C5×#391C211yesmaximal, characteristic, complemented
7C3×C5×#390C211yesmaximal, characteristic, complemented
8C3×C5×#385C214yesmaximal, complemented
9C3×C4×C5×C22⋊C4C211yesmaximal, characteristic, complemented
10C5×#2432C311yesmaximal, characteristic, direct product factor, Hall
11C2×C3×C5×#41—24no—
12C2×C3×C5×#41—24no—
13C2×C3×C5×#41—24no—
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C3×C5×Q8C2211yescharacteristic
16C22×C3×C5×D4C2212yes—
17C22×C3×C5×D4C2211yescharacteristic
18C23×C3×C4×C5C2212yes—
19C23×C3×C4×C5C2211yescharacteristic
20C3×C5×C4⋊Q8—24no—
21C3×C5×#124—24no—
22C3×C5×C22⋊Q8—24no—
23C2×C3×C5×C4⋊C4C2212yes—
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2214yes—
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C5×C22⋊C4C2214yes—
28C2×C3×C5×C22⋊C4C2212yes—
29C2×C3×C5×C22⋊C4C2214yes—
30C2×C3×C42×C5C2211yescharacteristic
31C2×C3×C42×C5C2211yescharacteristic
32C3×C5×#95C2212yes—
33C3×C5×#95C2214yes—
34C3×#2432C511yesmaximal, characteristic, direct product factor, Hall
35C22×C5×#41C2×C311yescharacteristic
36C2×C5×C4⋊Q8C2×C311yescharacteristic, complemented
37C2×C5×#124C2×C311yescharacteristic, complemented
38C2×C5×C22⋊Q8C2×C311yescharacteristic, complemented
39C5×#394C2×C314yescomplemented
40C5×#391C2×C311yescharacteristic, complemented
41C5×#390C2×C311yescharacteristic, complemented
42C5×#385C2×C314yescomplemented
43C4×C5×C22⋊C4C2×C311yescharacteristic, complemented
44C24×C3×C5C2312yes—
45C24×C3×C5C2311yescharacteristic
46C3×C5×#41—232no—
47C2×C3×C5×Q8—22no—
48C2×C3×C5×Q8—22no—
49C2×C3×C5×Q8—22no—
50C2×C3×C5×Q8—22no—
51C2×C3×C5×Q8—22no—
52C2×C3×C5×Q8D414yes—
53C2×C3×C5×D4—24no—
54C2×C3×C5×D4—24no—
55C2×C3×C5×D4—24no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4D414yes—
59C22×C3×C4×C5—24no—
60C22×C3×C4×C5—24no—
61C22×C3×C4×C5—24no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5D414yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C22×C3×C4×C5C2312yes—
68C22×C3×C4×C5C2311yescharacteristic
69C22×C3×C4×C5C2312yes—
70C22×C3×C4×C5C2312yes—
71C22×C3×C4×C5C2311yescharacteristic
72C3×C5×C4⋊C4—22no—
73C3×C5×C4⋊C4—24no—
74C3×C5×C4⋊C4—28no—
75C3×C5×C22⋊C4—24no—
76C3×C5×C22⋊C4—28no—
77C3×C5×C22⋊C4—24no—
78C3×C5×C22⋊C4—28no—
79C3×C42×C5—22no—
80C3×C42×C5—22no—
81C22×C3×#41C2×C511yescharacteristic
82C2×C3×C4⋊Q8C2×C511yescharacteristic, complemented
83C2×C3×#124C2×C511yescharacteristic, complemented
84C2×C3×C22⋊Q8C2×C511yescharacteristic, complemented
85C3×#394C2×C514yescomplemented
86C3×#391C2×C511yescharacteristic, complemented
87C3×#390C2×C511yescharacteristic, complemented
88C3×#385C2×C514yescomplemented
89C3×C4×C22⋊C4C2×C511yescharacteristic, complemented
90C2×C5×#41—24no—
91C2×C5×#41—24no—
92C2×C5×#41—24no—
93C22×C5×Q8C22×C311yescharacteristic
94C22×C5×Q8C22×C311yescharacteristic
95C22×C5×D4C22×C312yes—
96C22×C5×D4C22×C311yescharacteristic
97C23×C4×C5C22×C312yes—
98C23×C4×C5C22×C311yescharacteristic
99C5×C4⋊Q8—24no—
100C5×#124—24no—
101C5×C22⋊Q8—24no—
102C2×C5×C4⋊C4C22×C312yes—
103C2×C5×C4⋊C4C22×C314yes—
104C2×C5×C4⋊C4C22×C311yescharacteristic
105C2×C5×C22⋊C4C22×C312yes—
106C2×C5×C22⋊C4C22×C314yes—
107C2×C5×C22⋊C4C22×C314yes—
108C2×C5×C22⋊C4C22×C312yes—
109C2×C42×C5C22×C311yescharacteristic
110C2×C42×C5C22×C311yescharacteristic
111C5×#95C22×C312yes—
112C5×#95C22×C314yes—
113#2432C3×C511yescharacteristic, direct product factor, Sylow
114C23×C3×C5—22no—
115C23×C3×C5—21no—
116C23×C3×C5—22no—
117C23×C3×C5—21no—
118C23×C3×C5—22no—
119C23×C3×C5—24no—
120C23×C3×C5—22no—
121C23×C3×C5—24no—
122C23×C3×C5C2×D414yes—
123C23×C3×C5C2×D412yes—
124C23×C3×C5C2411yescharacteristic
125C3×C5×Q8—28no—
126C3×C5×Q8—44no—
127C3×C5×D4—216no—
128C3×C5×D4—28no—
129C2×C3×C4×C5—216no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—28no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—22no—
139C2×C3×C4×C5—22no—
140C2×C3×C4×C5—22no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—24no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2×D414yes—
147C2×C3×C4×C5C2×D412yes—
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5#4114yescomplemented
151C2×C3×#41—24no—
152C2×C3×#41—24no—
153C2×C3×#41—24no—
154C22×C3×Q8C22×C511yescharacteristic
155C22×C3×Q8C22×C511yescharacteristic
156C22×C3×D4C22×C512yes—
157C22×C3×D4C22×C511yescharacteristic
158C23×C3×C4C22×C512yes—
159C23×C3×C4C22×C511yescharacteristic
160C3×C4⋊Q8—24no—
161C3×#124—24no—
162C3×C22⋊Q8—24no—
163C2×C3×C4⋊C4C22×C512yes—
164C2×C3×C4⋊C4C22×C514yes—
165C2×C3×C4⋊C4C22×C511yescharacteristic
166C2×C3×C22⋊C4C22×C512yes—
167C2×C3×C22⋊C4C22×C514yes—
168C2×C3×C22⋊C4C22×C514yes—
169C2×C3×C22⋊C4C22×C512yes—
170C2×C3×C42C22×C511yescharacteristic
171C2×C3×C42C22×C511yescharacteristic
172C3×#95C22×C512yes—
173C3×#95C22×C514yes—
174C24×C5C23×C312yes—
175C24×C5C23×C311yescharacteristic
176C5×#41—232no—
177C2×C5×Q8—22no—
178C2×C5×Q8—22no—
179C2×C5×Q8—22no—
180C2×C5×Q8—22no—
181C2×C5×Q8—22no—
182C2×C5×Q8C3×D414yes—
183C2×C5×D4—24no—
184C2×C5×D4—24no—
185C2×C5×D4—24no—
186C2×C5×D4—22no—
187C2×C5×D4—22no—
188C2×C5×D4C3×D414yes—
189C22×C4×C5—24no—
190C22×C4×C5—24no—
191C22×C4×C5—24no—
192C22×C4×C5—22no—
193C22×C4×C5—22no—
194C22×C4×C5C3×D414yes—
195C22×C4×C5C23×C312yes—
196C22×C4×C5C23×C312yes—
197C22×C4×C5C23×C312yes—
198C22×C4×C5C23×C311yescharacteristic
199C22×C4×C5C23×C312yes—
200C22×C4×C5C23×C312yes—
201C22×C4×C5C23×C311yescharacteristic
202C5×C4⋊C4—22no—
203C5×C4⋊C4—24no—
204C5×C4⋊C4—28no—
205C5×C22⋊C4—24no—
206C5×C22⋊C4—28no—
207C5×C22⋊C4—24no—
208C5×C22⋊C4—28no—
209C42×C5—22no—
210C42×C5—22no—
211C22×#41C2×C3×C511yescharacteristic
212C2×C4⋊Q8C2×C3×C511yescharacteristic, complemented
213C2×#124C2×C3×C511yescharacteristic, complemented
214C2×C22⋊Q8C2×C3×C511yescharacteristic, complemented
215#394C2×C3×C514yescomplemented
216#391C2×C3×C511yescharacteristic, complemented
217#390C2×C3×C511yescharacteristic, complemented
218#385C2×C3×C514yescomplemented
219C4×C22⋊C4C2×C3×C511yescharacteristic, complemented
220C22×C3×C5—24no—
221C22×C3×C5—22no—
222C22×C3×C5—22no—
223C22×C3×C5—22no—
224C22×C3×C5—28no—
225C22×C3×C5—42no—
226C22×C3×C5—42no—
227C22×C3×C5—42no—
228C22×C3×C5—42no—
229C22×C3×C5—44no—
230C22×C3×C5C22×D411yescharacteristic
231C22×C3×C5C22×D411yescharacteristic
232C22×C3×C5C22×D411yescharacteristic
233C22×C3×C5C2×#4112yes—
234C22×C3×C52−1+412yes—
235C3×C4×C5—22no—
236C3×C4×C5—24no—
237C3×C4×C5—24no—
238C3×C4×C5—42no—
239C3×C4×C5—42no—
240C3×C4×C5—42no—
241C3×C4×C5#12014yes—
242C24×C3C23×C512yes—
243C24×C3C23×C511yescharacteristic
244C3×#41—232no—
245C2×C3×Q8—22no—
246C2×C3×Q8—22no—
247C2×C3×Q8—22no—
248C2×C3×Q8—22no—
249C2×C3×Q8—22no—
250C2×C3×Q8C5×D414yes—
251C2×C3×D4—24no—
252C2×C3×D4—24no—
253C2×C3×D4—24no—
254C2×C3×D4—22no—
255C2×C3×D4—22no—
256C2×C3×D4C5×D414yes—
257C22×C3×C4—24no—
258C22×C3×C4—24no—
259C22×C3×C4—24no—
260C22×C3×C4—22no—
261C22×C3×C4—22no—
262C22×C3×C4C5×D414yes—
263C22×C3×C4C23×C512yes—
264C22×C3×C4C23×C512yes—
265C22×C3×C4C23×C512yes—
266C22×C3×C4C23×C511yescharacteristic
267C22×C3×C4C23×C512yes—
268C22×C3×C4C23×C512yes—
269C22×C3×C4C23×C511yescharacteristic
270C3×C4⋊C4—22no—
271C3×C4⋊C4—24no—
272C3×C4⋊C4—28no—
273C3×C22⋊C4—24no—
274C3×C22⋊C4—28no—
275C3×C22⋊C4—24no—
276C3×C22⋊C4—28no—
277C3×C42—22no—
278C3×C42—22no—
279C23×C5—22no—
280C23×C5—21no—
281C23×C5—22no—
282C23×C5—21no—
283C23×C5—22no—
284C23×C5—24no—
285C23×C5—22no—
286C23×C5—24no—
287C23×C5C2×C3×D414yes—
288C23×C5C2×C3×D412yes—
289C23×C5C24×C311yescharacteristic
290C5×Q8—28no—
291C5×Q8—44no—
292C5×D4—216no—
293C5×D4—28no—
294C2×C4×C5—216no—
295C2×C4×C5—22no—
296C2×C4×C5—21no—
297C2×C4×C5—21no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—28no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—24no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5C2×C3×D412yes—
311C2×C4×C5C2×C3×D414yes—
312C2×C4×C5C2×C3×D412yes—
313C2×C4×C5C2×C3×D412yes—
314C2×C4×C5C2×C3×D412yes—
315C2×C4×C5C3×#4114yescomplemented
316C2×#41—24no—
317C2×#41—24no—
318C2×#41—24no—
319C22×Q8C22×C3×C511yescharacteristic
320C22×Q8C22×C3×C511yescharacteristic
321C22×D4C22×C3×C512yes—
322C22×D4C22×C3×C511yescharacteristic
323C23×C4C22×C3×C512yes—
324C23×C4C22×C3×C511yescharacteristic
325C4⋊Q8—24no—
326#124—24no—
327C22⋊Q8—24no—
328C2×C4⋊C4C22×C3×C512yes—
329C2×C4⋊C4C22×C3×C511yescharacteristic
330C2×C4⋊C4C22×C3×C514yes—
331C2×C22⋊C4C22×C3×C512yes—
332C2×C22⋊C4C22×C3×C514yes—
333C2×C22⋊C4C22×C3×C512yes—
334C2×C22⋊C4C22×C3×C514yes—
335C2×C42C22×C3×C511yescharacteristic
336C2×C42C22×C3×C511yescharacteristic
337#95C22×C3×C512yes—
338#95C22×C3×C514yes—
339C2×C3×C5—42no—
340C2×C3×C5—44no—
341C2×C3×C5C2×#12011yescharacteristic
342C2×C3×C5#53211yescharacteristic
343C2×C3×C5#53611yescharacteristic
344C2×C3×C5#54712yes—
345C2×C3×C5#54812yes—
346C23×C3—22no—
347C23×C3—21no—
348C23×C3—22no—
349C23×C3—21no—
350C23×C3—22no—
351C23×C3—24no—
352C23×C3—22no—
353C23×C3—24no—
354C23×C3C2×C5×D414yes—
355C23×C3C2×C5×D412yes—
356C23×C3C24×C511yescharacteristic
357C3×Q8—28no—
358C3×Q8—44no—
359C3×D4—216no—
360C3×D4—28no—
361C2×C3×C4—216no—
362C2×C3×C4—22no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—22no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—28no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—22no—
374C2×C3×C4—24no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4C2×C5×D412yes—
378C2×C3×C4C2×C5×D414yes—
379C2×C3×C4C2×C5×D412yes—
380C2×C3×C4C2×C5×D412yes—
381C2×C3×C4C2×C5×D412yes—
382C2×C3×C4C5×#4114yescomplemented
383C22×C5—24no—
384C22×C5—22no—
385C22×C5—22no—
386C22×C5—22no—
387C22×C5—28no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5—44no—
393C22×C5C22×C3×D411yescharacteristic
394C22×C5C22×C3×D411yescharacteristic
395C22×C5C22×C3×D411yescharacteristic
396C22×C5C2×C3×#4112yes—
397C22×C5C3×2−1+412yes—
398C4×C5—22no—
399C4×C5—24no—
400C4×C5—24no—
401C4×C5—42no—
402C4×C5—42no—
403C4×C5—42no—
404C4×C5C3×#12014yes—
405C24C23×C3×C512yes—
406C24C23×C3×C511yescharacteristic
407#41—232no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8C3×C5×D414yes—
414C2×D4—24no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4C3×C5×D414yes—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4C3×C5×D414yes—
426C22×C4C23×C3×C512yes—
427C22×C4C23×C3×C512yes—
428C22×C4C23×C3×C512yes—
429C22×C4C23×C3×C511yescharacteristic
430C22×C4C23×C3×C512yes—
431C22×C4C23×C3×C512yes—
432C22×C4C23×C3×C511yescharacteristic
433C4⋊C4—22no—
434C4⋊C4—24no—
435C4⋊C4—28no—
436C22⋊C4—24no—
437C22⋊C4—28no—
438C22⋊C4—24no—
439C22⋊C4—28no—
440C42—22no—
441C42—22no—
442C3×C5#243211yescharacteristic, direct product factor, Hall
443C22×C3—24no—
444C22×C3—22no—
445C22×C3—22no—
446C22×C3—22no—
447C22×C3—28no—
448C22×C3—42no—
449C22×C3—42no—
450C22×C3—42no—
451C22×C3—42no—
452C22×C3—44no—
453C22×C3C22×C5×D411yescharacteristic
454C22×C3C22×C5×D411yescharacteristic
455C22×C3C22×C5×D411yescharacteristic
456C22×C3C2×C5×#4112yes—
457C22×C3C5×2−1+412yes—
458C3×C4—22no—
459C3×C4—24no—
460C3×C4—24no—
461C3×C4—42no—
462C3×C4—42no—
463C3×C4—42no—
464C3×C4C5×#12014yes—
465C2×C5—42no—
466C2×C5—44no—
467C2×C5C2×C3×#12011yescharacteristic
468C2×C5C3×#53211yescharacteristic
469C2×C5C3×#53611yescharacteristic
470C2×C5C3×#54712yes—
471C2×C5C3×#54812yes—
472C23—22no—
473C23—21no—
474C23—22no—
475C23—21no—
476C23—22no—
477C23—24no—
478C23—22no—
479C23—24no—
480C23C2×C3×C5×D414yes—
481C23C2×C3×C5×D412yes—
482C23C24×C3×C511yescharacteristic
483Q8—28no—
484Q8—44no—
485D4—216no—
486D4—28no—
487C2×C4—216no—
488C2×C4—22no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—28no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4C2×C3×C5×D412yes—
504C2×C4C2×C3×C5×D414yes—
505C2×C4C2×C3×C5×D412yes—
506C2×C4C2×C3×C5×D412yes—
507C2×C4C2×C3×C5×D412yes—
508C2×C4C3×C5×#4114yescomplemented
509C2×C3—42no—
510C2×C3—44no—
511C2×C3C2×C5×#12011yescharacteristic
512C2×C3C5×#53211yescharacteristic
513C2×C3C5×#53611yescharacteristic
514C2×C3C5×#54712yes—
515C2×C3C5×#54812yes—
516C5C3×#243211yescharacteristic, direct product factor, Sylow
517C22—24no—
518C22—22no—
519C22—22no—
520C22—22no—
521C22—28no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—42no—
526C22—44no—
527C22C22×C3×C5×D411yescharacteristic
528C22C22×C3×C5×D411yescharacteristic
529C22C22×C3×C5×D411yescharacteristic
530C22C2×C3×C5×#4112yes—
531C22C3×C5×2−1+412yes—
532C4—22no—
533C4—24no—
534C4—24no—
535C4—42no—
536C4—42no—
537C4—42no—
538C4C3×C5×#12014yes—
539C3C5×#243211yescharacteristic, direct product factor, Sylow
540C2—42no—
541C2—44no—
542C2C2×C3×C5×#12011yescharacteristic
543C2C3×C5×#53211yescharacteristic
544C2C3×C5×#53611yescharacteristic
545C2C3×C5×#54712yes—
546C2C3×C5×#54812yes—
subgroupG/H
center, socleC23×C3×C5C24
commutator, Frattini, cosocleC23C24×C3×C5
prime radicalC22×C3×C5×#41C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C3×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×C4⋊Q8C2semidirect
3. C2×C3×C5×#124C2semidirect
4. C2×C3×C5×C22⋊Q8C2semidirect
5. C3×C5×#394C2semidirect
6. C3×C5×#391C2semidirect
7. C3×C5×#390C2semidirect
8. C3×C5×#385C2semidirect
9. C3×C4×C5×C22⋊C4C2semidirect
10. C5×#2432C3direct (N × H)
34. C3×#2432C5direct (N × H)
36. C2×C5×C4⋊Q8C2×C3semidirect
37. C2×C5×#124C2×C3semidirect
38. C2×C5×C22⋊Q8C2×C3semidirect
39. C5×#394C2×C3semidirect
40. C5×#391C2×C3semidirect
41. C5×#390C2×C3semidirect
42. C5×#385C2×C3semidirect
43. C4×C5×C22⋊C4C2×C3semidirect
82. C2×C3×C4⋊Q8C2×C5semidirect
83. C2×C3×#124C2×C5semidirect
84. C2×C3×C22⋊Q8C2×C5semidirect
85. C3×#394C2×C5semidirect
86. C3×#391C2×C5semidirect
87. C3×#390C2×C5semidirect
88. C3×#385C2×C5semidirect
89. C3×C4×C22⋊C4C2×C5semidirect
113. #2432C3×C5direct (N × H)
150. C2×C3×C4×C5#41semidirect
212. C2×C4⋊Q8C2×C3×C5semidirect
213. C2×#124C2×C3×C5semidirect
214. C2×C22⋊Q8C2×C3×C5semidirect
215. #394C2×C3×C5semidirect
216. #391C2×C3×C5semidirect
217. #390C2×C3×C5semidirect
218. #385C2×C3×C5semidirect
219. C4×C22⋊C4C2×C3×C5semidirect
315. C2×C4×C5C3×#41semidirect
382. C2×C3×C4C5×#41semidirect
442. C3×C5#2432direct (N × H)
508. C2×C4C3×C5×#41semidirect
516. C5C3×#2432direct (N × H)
539. C3C5×#2432direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×#412
C2×C3×C5×C4⋊Q82
C2×C3×C5×#1242
C2×C3×C5×C22⋊Q82
C3×C5×#3942
C3×C5×#3912
C3×C5×#3902
C3×C5×#3852
C3×C4×C5×C22⋊C42
C5×#24323
C3×#24325