Finite Group Databasebeta

← C3×#10614197 #14329509

Subgroups — C3×#10614197 #14329509

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×Q8C211yesmaximal, characteristic, complemented
2C2×C3×#4093C211yesmaximal, characteristic
3C2×C3×#4039C211yesmaximal, characteristic
4C3×#65519C211yesmaximal, characteristic, complemented
5C3×#65279C212yesmaximal, complemented
6C3×#65278C212yesmaximal, complemented
7C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
8C3×#65229C212yesmaximal, complemented
9C3×#65228C211yesmaximal, characteristic
10C3×C4×#685C212yesmaximal, complemented
11C3×C4×#683C211yesmaximal, characteristic, complemented
12#10614197C311yesmaximal, characteristic, direct product factor, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5C2212yes—
16C3×C4×C5×Q8—24no—
17C2×C3×C5×C4⋊C4C2212yes—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C42×C5C2211yescharacteristic
20C2×C3×C42×C5C2212yes—
21C3×#4093C418yescomplemented
22C2×C3×#685C2212yes—
23C2×C3×#685C2212yes—
24C2×C3×#685C2212yes—
25C2×C3×#685C2212yes—
26C2×C3×#685C2212yes—
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2212yes—
32C2×C3×C4×Dic5C2211yescharacteristic
33C3×#4039—24no—
34C3×#3963C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36C3×#3963C2212yes—
37C3×#3963C2212yes—
38C3×#3963C2212yes—
39C3×#2367—51nomaximal, Hall
40C2×C4×C5×Q8C2×C311yescharacteristic, complemented
41C2×#4093C2×C311yescharacteristic
42C2×#4039C2×C311yescharacteristic
43#65519C2×C311yescharacteristic, complemented
44#65279C2×C312yescomplemented
45#65278C2×C312yescomplemented
46C4⋊C4×Dic5C2×C311yescharacteristic, complemented
47#65229C2×C312yescomplemented
48#65228C2×C311yescharacteristic
49C4×#685C2×C312yescomplemented
50C4×#683C2×C311yescharacteristic, complemented
51C23×C3×D5C2312yes—
52C2×C3×C5×Q8—22no—
53C2×C3×C5×Q8—22no—
54C2×C3×C5×Q8C2×C414yescomplemented
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×C3×C4×C5C2312yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2312yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2311yescharacteristic
64C22×C3×Dic5C2311yescharacteristic
65C2×C3×D20—22no—
66C2×C3×D20—22no—
67C2×C3×D20C2×C414yes—
68C2×C3×C4×D5—24no—
69C2×C3×C4×D5—24no—
70C2×C3×C4×D5—42no—
71C3×C5×C4⋊C4—24no—
72C3×C5×C4⋊C4D414yes—
73C3×C42×C5—24no—
74C3×C42×C5—22no—
75C3×#685—24no—
76C3×#685—24no—
77C3×#685—42no—
78C3×#685C2×C418yescomplemented
79C3×#685C2×C418yescomplemented
80C3×C4⋊Dic5—22no—
81C3×#683—22no—
82C3×#683—22no—
83C3×C4×Dic5—22no—
84C3×C4×Dic5—42no—
85C3×C4×Dic5C2×C414yescomplemented
86C2×C3×#124—51no—
87C2×C3×C4×Q8D511yescharacteristic, complemented
88C2×C3×C4×D4—51no—
89C3×#391—51no—
90C3×#390—51no—
91C3×#388—52no—
92C3×#388—52no—
93C3×#385—52no—
94C3×C4×C4⋊C4—51no—
95C3×C4×C4⋊C4—51no—
96C3×C4×C22⋊C4—52no—
97C22×C5×Q8C22×C311yescharacteristic
98C22×D20C22×C311yescharacteristic
99C22×C4×D5C22×C312yes—
100C4×C5×Q8—24no—
101C2×C5×C4⋊C4C22×C312yes—
102C2×C5×C4⋊C4C22×C311yescharacteristic
103C2×C42×C5C22×C311yescharacteristic
104C2×C42×C5C22×C312yes—
105#4093C3×C418yescomplemented
106C2×#685C22×C312yes—
107C2×#685C22×C312yes—
108C2×#685C22×C312yes—
109C2×#685C22×C312yes—
110C2×#685C22×C312yes—
111C2×C4⋊Dic5C22×C311yescharacteristic
112C2×#683C22×C311yescharacteristic
113C2×#683C22×C311yescharacteristic
114C2×C4×Dic5C22×C311yescharacteristic
115C2×C4×Dic5C22×C312yes—
116C2×C4×Dic5C22×C311yescharacteristic
117#4039—24no—
118#3963C22×C311yescharacteristic
119#3963C22×C311yescharacteristic
120#3963C22×C312yes—
121#3963C22×C312yes—
122#3963C22×C312yes—
123#2367—51noSylow
124C23×C3×C5C2411yescharacteristic
125C22×C3×D5—22no—
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5—22no—
129C22×C3×D5—22no—
130C22×C3×D5—22no—
131C22×C3×D5C22×C414yes—
132C3×C5×Q8—28no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5—22no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5C22×C414yes—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C2×D414yes—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5#4112yes—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—21no—
150C2×C3×Dic5—21no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—21no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—21no—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C22×C412yes—
162C2×C3×Dic5#4112yes—
163C3×D20—28no—
164C3×C4×D5—48no—
165C22×C3×Q8C2×D511yescharacteristic
166C22×C3×D4—51no—
167C23×C3×C4—52no—
168C3×#124—58no—
169C3×C4×Q8—24no—
170C3×C4×D4—104no—
171C2×C3×C4⋊C4—51no—
172C2×C3×C4⋊C4—51no—
173C2×C3×C4⋊C4—51no—
174C2×C3×C4⋊C4C2×D512yes—
175C2×C3×C4⋊C4C2×D511yescharacteristic
176C2×C3×C22⋊C4—52no—
177C2×C3×C22⋊C4—52no—
178C2×C3×C22⋊C4—52no—
179C2×C3×C22⋊C4—52no—
180C2×C3×C22⋊C4—52no—
181C2×C3×C42—51no—
182C2×C3×C42—51no—
183C2×C3×C42—52no—
184C2×C3×C42C2×D512yes—
185C2×C3×C42C2×D511yescharacteristic
186C3×#95—51no—
187C3×#95—52no—
188C3×#95—52no—
189C3×#95—51no—
190C3×#95—52no—
191C23×D5C23×C312yes—
192C2×C5×Q8—22no—
193C2×C5×Q8—22no—
194C2×C5×Q8C2×C3×C414yescomplemented
195C22×C4×C5C23×C311yescharacteristic
196C22×C4×C5C23×C312yes—
197C22×C4×C5C23×C312yes—
198C22×C4×C5C23×C311yescharacteristic
199C22×C4×C5C23×C311yescharacteristic
200C22×Dic5C23×C311yescharacteristic
201C22×Dic5C23×C312yes—
202C22×Dic5C23×C311yescharacteristic
203C22×Dic5C23×C311yescharacteristic
204C22×Dic5C23×C311yescharacteristic
205C2×D20—22no—
206C2×D20—22no—
207C2×D20C2×C3×C414yes—
208C2×C4×D5—24no—
209C2×C4×D5—24no—
210C2×C4×D5—42no—
211C5×C4⋊C4—24no—
212C5×C4⋊C4C3×D414yes—
213C42×C5—24no—
214C42×C5—22no—
215#685—24no—
216#685—24no—
217#685—42no—
218#685C2×C3×C418yescomplemented
219#685C2×C3×C418yescomplemented
220C4⋊Dic5—22no—
221#683—22no—
222#683—22no—
223C4×Dic5—22no—
224C4×Dic5—42no—
225C4×Dic5C2×C3×C414yescomplemented
226C2×#124—51no—
227C2×C4×Q8C3×D511yescharacteristic, complemented
228C2×C4×D4—51no—
229#391—51no—
230#390—51no—
231#388—52no—
232#388—52no—
233#385—52no—
234C4×C4⋊C4—51no—
235C4×C4⋊C4—51no—
236C4×C22⋊C4—52no—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5H(5,𝔽2)11yescharacteristic
243C22×C3×C52−1+411yescharacteristic
244C2×C3×D5—24no—
245C2×C3×D5—24no—
246C2×C3×D5—24no—
247C2×C3×D5—42no—
248C2×C3×D5—42no—
249C2×C3×D5—42no—
250C2×C3×D5—42no—
251C3×C4×C5—24no—
252C3×C4×C5—24no—
253C3×C4×C5—22no—
254C3×C4×C5—41no—
255C3×C4×C5C4×D414yes—
256C3×Dic5—22no—
257C3×Dic5—22no—
258C3×Dic5—22no—
259C3×Dic5—41no—
260C3×Dic5—42no—
261C24×C3—52no—
262C2×C3×Q8—22no—
263C2×C3×Q8—22no—
264C2×C3×Q8C4×D514yescomplemented
265C2×C3×D4—54no—
266C2×C3×D4—102no—
267C2×C3×D4—102no—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C22×C3×C4—51no—
271C22×C3×C4—52no—
272C22×C3×C4—51no—
273C22×C3×C4—104no—
274C22×C3×C4—104no—
275C22×C3×C4—202no—
276C22×C3×C4C22×D511yescharacteristic
277C22×C3×C4C22×D512yes—
278C22×C3×C4C22×D511yescharacteristic
279C22×C3×C4C22×D512yes—
280C22×C3×C4C22×D511yescharacteristic
281C3×C4⋊C4—24no—
282C3×C4⋊C4—102no—
283C3×C4⋊C4—102no—
284C3×C4⋊C4—102no—
285C3×C4⋊C4C22⋊D514yes—
286C3×C22⋊C4—58no—
287C3×C22⋊C4—58no—
288C3×C22⋊C4—104no—
289C3×C22⋊C4—104no—
290C3×C22⋊C4—202no—
291C3×C42—24no—
292C3×C42—22no—
293C3×C42—54no—
294C3×C42—102no—
295C3×C42—202no—
296C23×C5C24×C311yescharacteristic
297C22×D5—22no—
298C22×D5—22no—
299C22×D5—22no—
300C22×D5—22no—
301C22×D5—22no—
302C22×D5—22no—
303C22×D5C22×C3×C414yes—
304C5×Q8—28no—
305C2×C4×C5—21no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5C22×C3×C414yes—
315C2×C4×C5C22×C3×C412yes—
316C2×C4×C5C2×C3×D414yes—
317C2×C4×C5C2×C3×D412yes—
318C2×C4×C5C3×#4112yes—
319C2×C4×C5C3×#4112yes—
320C2×Dic5—21no—
321C2×Dic5—21no—
322C2×Dic5—21no—
323C2×Dic5—21no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—22no—
331C2×Dic5—21no—
332C2×Dic5C22×C3×C412yes—
333C2×Dic5C22×C3×C412yes—
334C2×Dic5C3×#4112yes—
335D20—28no—
336C4×D5—48no—
337C22×Q8C2×C3×D511yescharacteristic
338C22×D4—51no—
339C23×C4—52no—
340#124—58no—
341C4×Q8—24no—
342C4×D4—104no—
343C2×C4⋊C4—51no—
344C2×C4⋊C4—51no—
345C2×C4⋊C4—51no—
346C2×C4⋊C4C2×C3×D512yes—
347C2×C4⋊C4C2×C3×D511yescharacteristic
348C2×C22⋊C4—52no—
349C2×C22⋊C4—52no—
350C2×C22⋊C4—52no—
351C2×C22⋊C4—52no—
352C2×C22⋊C4—52no—
353C2×C42—51no—
354C2×C42—51no—
355C2×C42—52no—
356C2×C42C2×C3×D512yes—
357C2×C42C2×C3×D511yescharacteristic
358#95—51no—
359#95—52no—
360#95—52no—
361#95—51no—
362#95—52no—
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5C4×#4111yescharacteristic
365C2×C3×C5#52011yescharacteristic
366C2×C3×C5#54611yescharacteristic
367C2×C3×C5#54811yescharacteristic
368C2×C3×C5#55611yescharacteristic
369C2×C3×C5#55911yescharacteristic
370C3×D5—44no—
371C23×C3—54no—
372C23×C3—102no—
373C23×C3—102no—
374C23×C3—102no—
375C23×C3—102no—
376C23×C3—102no—
377C23×C3—102no—
378C23×C3C23×D511yescharacteristic
379C3×Q8—28no—
380C3×D4—108no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—52no—
391C2×C3×C4—52no—
392C2×C3×C4—52no—
393C2×C3×C4—101no—
394C2×C3×C4—101no—
395C2×C3×C4—101no—
396C2×C3×C4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—101no—
399C2×C3×C4—102no—
400C2×C3×C4—102no—
401C2×C3×C4—101no—
402C2×C3×C4—101no—
403C2×C3×C4—102no—
404C2×C3×C4—101no—
405C2×C3×C4—208no—
406C2×C3×C4C2×C4×D514yes—
407C2×C3×C4C2×C4×D512yes—
408C2×C3×C4#70912yes—
409C2×C3×C4#71312yes—
410C2×C3×C4C2×C22⋊D514yes—
411C2×C3×C4C2×C22⋊D512yes—
412C22×C5C23×C3×C411yescharacteristic
413C22×C5C22×C3×D411yescharacteristic
414C22×C5C2×C3×#4111yescharacteristic
415C22×C5C2×C3×#4111yescharacteristic
416C22×C5C2×C3×#4111yescharacteristic
417C22×C5C3×H(5,𝔽2)11yescharacteristic
418C22×C5C3×2−1+411yescharacteristic
419C2×D5—24no—
420C2×D5—24no—
421C2×D5—24no—
422C2×D5—42no—
423C2×D5—42no—
424C2×D5—42no—
425C2×D5—42no—
426C4×C5—24no—
427C4×C5—24no—
428C4×C5—22no—
429C4×C5—41no—
430C4×C5C3×C4×D414yes—
431Dic5—22no—
432Dic5—22no—
433Dic5—22no—
434Dic5—42no—
435Dic5—41no—
436C24—52no—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8C3×C4×D514yescomplemented
440C2×D4—54no—
441C2×D4—102no—
442C2×D4—102no—
443C22×C4—51no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—52no—
447C22×C4—51no—
448C22×C4—104no—
449C22×C4—104no—
450C22×C4—202no—
451C22×C4C22×C3×D511yescharacteristic
452C22×C4C22×C3×D512yes—
453C22×C4C22×C3×D511yescharacteristic
454C22×C4C22×C3×D512yes—
455C22×C4C22×C3×D511yescharacteristic
456C4⋊C4—24no—
457C4⋊C4—102no—
458C4⋊C4—102no—
459C4⋊C4—102no—
460C4⋊C4C3×C22⋊D514yes—
461C22⋊C4—58no—
462C22⋊C4—58no—
463C22⋊C4—104no—
464C22⋊C4—104no—
465C22⋊C4—202no—
466C42—24no—
467C42—22no—
468C42—54no—
469C42—102no—
470C42—202no—
471C3×C5#236711yescharacteristic, complemented, Hall
472C22×C3—104no—
473C22×C3—104no—
474C22×C3—104no—
475C22×C3—202no—
476C22×C3—202no—
477C22×C3—202no—
478C22×C3—202no—
479C22×C3C22×C4×D511yescharacteristic
480C22×C3C2×#70911yescharacteristic
481C22×C3C2×#71311yescharacteristic
482C22×C3#414711yescharacteristic
483C22×C3D5×#4111yescharacteristic
484C22×C3#414911yescharacteristic
485C22×C3C22×C22⋊D511yescharacteristic
486C3×C4—24no—
487C3×C4—22no—
488C3×C4—24no—
489C3×C4—41no—
490C3×C4—102no—
491C3×C4—102no—
492C3×C4—102no—
493C3×C4—201no—
494C3×C4—202no—
495C3×C4C4×C22⋊D514yes—
496C2×C5C2×C3×C4×D411yescharacteristic
497C2×C5C3×C4×#4111yescharacteristic
498C2×C5C3×#52011yescharacteristic
499C2×C5C3×#54611yescharacteristic
500C2×C5C3×#54811yescharacteristic
501C2×C5C3×#55611yescharacteristic
502C2×C5C3×#55911yescharacteristic
503D5—44no—
504C23—54no—
505C23—102no—
506C23—102no—
507C23—102no—
508C23—102no—
509C23—102no—
510C23—102no—
511C23C23×C3×D511yescharacteristic
512Q8—28no—
513D4—108no—
514C2×C4—22no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—21no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—52no—
524C2×C4—52no—
525C2×C4—52no—
526C2×C4—101no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—101no—
530C2×C4—101no—
531C2×C4—101no—
532C2×C4—102no—
533C2×C4—102no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—102no—
537C2×C4—101no—
538C2×C4—208no—
539C2×C4C2×C3×C4×D514yes—
540C2×C4C2×C3×C4×D512yes—
541C2×C4C3×#70912yes—
542C2×C4C3×#71312yes—
543C2×C4C2×C3×C22⋊D514yes—
544C2×C4C2×C3×C22⋊D512yes—
545C2×C3—204no—
546C2×C3#6590211yescharacteristic
547C2×C3C4×#71311yescharacteristic
548C2×C3#6590811yescharacteristic
549C2×C3#6591911yescharacteristic
550C2×C3C2×C4×C22⋊D511yescharacteristic
551C2×C3#6615111yescharacteristic
552C2×C3#6616311yescharacteristic
553C5C3×#236711yescharacteristic, complemented, Sylow
554C22—104no—
555C22—104no—
556C22—104no—
557C22—202no—
558C22—202no—
559C22—202no—
560C22—202no—
561C22C22×C3×C4×D511yescharacteristic
562C22C2×C3×#70911yescharacteristic
563C22C2×C3×#71311yescharacteristic
564C22C3×#414711yescharacteristic
565C22C3×D5×#4111yescharacteristic
566C22C3×#414911yescharacteristic
567C22C22×C3×C22⋊D511yescharacteristic
568C4—24no—
569C4—22no—
570C4—24no—
571C4—41no—
572C4—102no—
573C4—102no—
574C4—102no—
575C4—201no—
576C4—202no—
577C4C3×C4×C22⋊D514yes—
578C3#1061419711yescharacteristic, direct product factor, Sylow
579C2—204no—
580C2C3×#6590211yescharacteristic
581C2C3×C4×#71311yescharacteristic
582C2C3×#6590811yescharacteristic
583C2C3×#6591911yescharacteristic
584C2C2×C3×C4×C22⋊D511yescharacteristic
585C2C3×#6615111yescharacteristic
586C2C3×#6616311yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C4×C5×Q8C2
socleC23×C3×C5C24
prime radicalC22×C3×D20C22
cosocleC23×C5C24×C3
hypercenterC2×C3×C4×Q8D5
hypocenterC5C3×#2367
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×Q8C2semidirect
4. C3×#65519C2semidirect
5. C3×#65279C2semidirect
6. C3×#65278C2semidirect
7. C3×C4⋊C4×Dic5C2semidirect
8. C3×#65229C2semidirect
10. C3×C4×#685C2semidirect
11. C3×C4×#683C2semidirect
12. #10614197C3direct (N × H)
21. C3×#4093C4semidirect
40. C2×C4×C5×Q8C2×C3semidirect
43. #65519C2×C3semidirect
44. #65279C2×C3semidirect
45. #65278C2×C3semidirect
46. C4⋊C4×Dic5C2×C3semidirect
47. #65229C2×C3semidirect
49. C4×#685C2×C3semidirect
50. C4×#683C2×C3semidirect
54. C2×C3×C5×Q8C2×C4semidirect
78. C3×#685C2×C4semidirect
79. C3×#685C2×C4semidirect
85. C3×C4×Dic5C2×C4semidirect
87. C2×C3×C4×Q8D5semidirect
105. #4093C3×C4semidirect
194. C2×C5×Q8C2×C3×C4semidirect
218. #685C2×C3×C4semidirect
219. #685C2×C3×C4semidirect
225. C4×Dic5C2×C3×C4semidirect
227. C2×C4×Q8C3×D5semidirect
264. C2×C3×Q8C4×D5semidirect
439. C2×Q8C3×C4×D5semidirect
471. C3×C5#2367semidirect
553. C5C3×#2367semidirect
578. C3#10614197direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×Q82
C2×C3×#40932
C2×C3×#40392
C3×#655192
C3×#652792
C3×#652782
C3×C4⋊C4×Dic52
C3×#652292
C3×#652282
C3×C4×#6852
C3×C4×#6832
#106141973
C3×#23675