Finite Group Databasebeta

← C3×#10611867 #14435587

Subgroups — C3×#10611867 #14435587

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66132C211yesmaximal, characteristic, complemented
2C3×#65977C211yesmaximal, characteristic, complemented
3C3×C5×#450C211yesmaximal, characteristic, complemented
4C3×#65506C211yesmaximal, characteristic
5C3×#65454C211yesmaximal, characteristic, complemented
6C3×#65454C211yesmaximal, characteristic, complemented
7C3×#65453C211yesmaximal, characteristic, complemented
8C3×SD16×Dic5C211yesmaximal, characteristic, complemented
9C3×#65334C211yesmaximal, characteristic, complemented
10C3×#65074C211yesmaximal, characteristic, complemented
11C3×#65050C211yesmaximal, characteristic, complemented
12C3×#65048C211yesmaximal, characteristic, complemented
13C3×#65045C211yesmaximal, characteristic, complemented
14C3×#65026C211yesmaximal, characteristic, complemented
15C3×#65009C211yesmaximal, characteristic, complemented
16#10611867C311yesmaximal, characteristic, direct product factor, Hall
17C22×C3×C5×D4C2211yescharacteristic
18C2×C3×C5×SD16C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C3×C5×C22⋊Q8C2211yescharacteristic
21C2×C3×C22⋊Dic5—21no—
22C2×C3×C22⋊Dic5—21no—
23C3×#4093C2211yescharacteristic, complemented
24C3×Q8×Dic5C2211yescharacteristic, complemented
25C3×D4×Dic5—21no—
26C3×D4×Dic5—21no—
27C3×D4×Dic5C2211yescharacteristic
28C3×D4×Dic5C2211yescharacteristic
29C3×D4×Dic5C2211yescharacteristic
30C3×D4×Dic5C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C2×C3×#686C2211yescharacteristic
33C3×#4076C2211yescharacteristic
34C3×#4072C2211yescharacteristic
35C3×#4072C2211yescharacteristic
36C3×#4044—21no—
37C3×#4043—21no—
38C3×#4039C2211yescharacteristic, complemented
39C3×#4034C2211yescharacteristic, complemented
40C3×#4031—21no—
41C3×#4029—21no—
42C3×C5×#102C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×#3967C2211yescharacteristic, complemented
46C3×#3967C2211yescharacteristic, complemented
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic
49C3×C22⋊#168C2211yescharacteristic
50C3×#3953C2211yescharacteristic, complemented
51C3×#3953C2211yescharacteristic, complemented
52C3×#3950C2211yescharacteristic, complemented
53C3×#3949C2211yescharacteristic, complemented
54C3×#3947C2211yescharacteristic, complemented
55C3×#3946C2211yescharacteristic, complemented
56C3×#3946C2211yescharacteristic, complemented
57C3×C8×Dic5C2211yescharacteristic, complemented
58C3×#3940C2211yescharacteristic, complemented
59C3×#3939C2211yescharacteristic, complemented
60C3×#3118—51nomaximal, Hall
61#66132C2×C311yescharacteristic, complemented
62#65977C2×C311yescharacteristic, complemented
63C5×#450C2×C311yescharacteristic, complemented
64#65506C2×C311yescharacteristic
65#65454C2×C311yescharacteristic, complemented
66#65454C2×C311yescharacteristic, complemented
67#65453C2×C311yescharacteristic, complemented
68SD16×Dic5C2×C311yescharacteristic, complemented
69#65334C2×C311yescharacteristic, complemented
70#65074C2×C311yescharacteristic, complemented
71#65050C2×C311yescharacteristic, complemented
72#65048C2×C311yescharacteristic, complemented
73#65045C2×C311yescharacteristic, complemented
74#65026C2×C311yescharacteristic, complemented
75#65009C2×C311yescharacteristic, complemented
76C24×C3×C5—21no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4—22no—
79C2×C3×C5×D4—22no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5C2311yescharacteristic
84C2×C3×C22⋊D5—21no—
85C22×C3×Dic5—21no—
86C22×C3×Dic5—21no—
87C22×C3×Dic5—21no—
88C22×C3×Dic5—21no—
89C2×C3×D20C2311yescharacteristic
90C2×C3×C4×D5—21no—
91C2×C3×Dic10—21no—
92C3×C5×SD16—22no—
93C3×C5×SD16—22no—
94C2×C3×C5×C8C2311yescharacteristic
95C2×C3×C5×C8C2311yescharacteristic
96C3×C5×C4⋊C4—21no—
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C22⋊C4—21no—
99C3×C22⋊Dic5—21no—
100C3×C22⋊Dic5—21no—
101C3×C22⋊Dic5—21no—
102C3×C22⋊Dic5—21no—
103C3×C22⋊Dic5—21no—
104C3×C22⋊Dic5D411yescharacteristic
105C3×C22⋊Dic5D411yescharacteristic
106C3×#686—22no—
107C3×#686—22no—
108C3×#685—21no—
109C3×#685—21no—
110C3×#685—21no—
111C3×#685—21no—
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5D411yescharacteristic
114C3×C4⋊Dic5D411yescharacteristic
115C3×C4⋊Dic5C2311yescharacteristic
116C3×C4⋊Dic5C2311yescharacteristic
117C3×C4⋊Dic5C2311yescharacteristic
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C3×C4×Dic5C2311yescharacteristic
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×#542—51no—
126C3×#518—51no—
127C3×#485—51no—
128C3×#482—51no—
129C3×#476—51no—
130C3×#474—51no—
131C3×#463—51no—
132C3×#463—51no—
133C3×#450D511yescharacteristic, complemented
134C3×#447—51no—
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C22×C5×D4C22×C311yescharacteristic
141C2×C5×SD16C22×C311yescharacteristic
142C2×C5×SD16C22×C311yescharacteristic
143C5×C22⋊Q8C22×C311yescharacteristic
144C2×C22⋊Dic5—21no—
145C2×C22⋊Dic5—21no—
146#4093C22×C311yescharacteristic, complemented
147Q8×Dic5C22×C311yescharacteristic, complemented
148D4×Dic5—21no—
149D4×Dic5—21no—
150D4×Dic5C22×C311yescharacteristic
151D4×Dic5C22×C311yescharacteristic
152D4×Dic5C22×C311yescharacteristic
153D4×Dic5C22×C311yescharacteristic
154C2×#686C22×C311yescharacteristic
155C2×#686C22×C311yescharacteristic
156#4076C22×C311yescharacteristic
157#4072C22×C311yescharacteristic
158#4072C22×C311yescharacteristic
159#4044—21no—
160#4043—21no—
161#4039C22×C311yescharacteristic, complemented
162#4034C22×C311yescharacteristic, complemented
163#4031—21no—
164#4029—21no—
165C5×#102C22×C311yescharacteristic
166C5×#102C22×C311yescharacteristic
167C5×C22⋊C8C22×C311yescharacteristic
168#3967C22×C311yescharacteristic, complemented
169#3967C22×C311yescharacteristic, complemented
170#3964C22×C311yescharacteristic
171#3964C22×C311yescharacteristic
172C22⋊#168C22×C311yescharacteristic
173#3953C22×C311yescharacteristic, complemented
174#3953C22×C311yescharacteristic, complemented
175#3950C22×C311yescharacteristic, complemented
176#3949C22×C311yescharacteristic, complemented
177#3947C22×C311yescharacteristic, complemented
178#3946C22×C311yescharacteristic, complemented
179#3946C22×C311yescharacteristic, complemented
180C8×Dic5C22×C311yescharacteristic, complemented
181#3940C22×C311yescharacteristic, complemented
182#3939C22×C311yescharacteristic, complemented
183#3118—51noSylow
184C23×C3×C5—24no—
185C23×C3×C5—21no—
186C23×C3×C5—21no—
187C23×C3×C5—81no—
188C23×C3×C5—81no—
189C23×C3×C5C2×D411yescharacteristic
190C22×C3×D5—21no—
191C3×C5×Q8—21no—
192C3×C5×Q8—21no—
193C3×C5×D4—24no—
194C3×C5×D4—21no—
195C3×C5×D4—21no—
196C3×C5×D4#4112yes—
197C3×C5×D4#4112yes—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5—21no—
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C3×C22⋊D5—81no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—81no—
209C2×C3×Dic5—81no—
210C2×C3×Dic5—81no—
211C2×C3×Dic5—81no—
212C2×C3×Dic5C2×D411yescharacteristic
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C3×D20—21no—
217C3×D20—21no—
218C3×C4×D5—81no—
219C3×Dic10—81no—
220C3×C5×C8—21no—
221C3×C5×C8—21no—
222C3×#168—21no—
223C3×#168—21no—
224C22×C3×D4C2×D511yescharacteristic
225C2×C3×SD16C2×D511yescharacteristic
226C2×C3×SD16C2×D511yescharacteristic
227C2×C3×D8—51no—
228C2×C3×D8—51no—
229C3×C4⋊Q8—51no—
230C3×#126—101no—
231C3×#124—51no—
232C3×#124—101no—
233C3×#123—101no—
234C3×C22⋊Q8—101no—
235C3×C22⋊Q8C2×D511yescharacteristic
236C3×#121—51no—
237C3×C4×Q8—51no—
238C3×C4×D4—51no—
239C3×C4×D4—51no—
240C3×C4×D4—51no—
241C3×C4×D4—51no—
242C3×C4×D4—51no—
243C3×C4×D4—101no—
244C3×C4×D4—101no—
245C3×#117—51no—
246C3×#117—51no—
247C2×C3×C22⋊C4—101no—
248C2×C3×C22⋊C4—101no—
249C3×#107—51no—
250C3×#107—51no—
251C3×#106—51no—
252C3×#106—51no—
253C3×C4⋊C8—51no—
254C3×C4⋊C8—51no—
255C3×#103—51no—
256C3×#103—51no—
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102C2×D511yescharacteristic
262C3×#102C2×D511yescharacteristic
263C3×C22⋊C8—51no—
264C3×C22⋊C8C2×D511yescharacteristic
265C3×#97—51no—
266C3×C4×C8—51no—
267C24×C5—21no—
268C2×C5×Q8C23×C311yescharacteristic
269C2×C5×D4—22no—
270C2×C5×D4—22no—
271C2×C5×D4—21no—
272C2×C5×D4C23×C311yescharacteristic
273C2×C5×D4C23×C311yescharacteristic
274C22×C4×C5C23×C311yescharacteristic
275C2×C22⋊D5—21no—
276C22×Dic5—21no—
277C22×Dic5—21no—
278C22×Dic5—21no—
279C22×Dic5—21no—
280C2×D20C23×C311yescharacteristic
281C2×C4×D5—21no—
282C2×Dic10—21no—
283C5×SD16—22no—
284C5×SD16—22no—
285C2×C5×C8C23×C311yescharacteristic
286C2×C5×C8C23×C311yescharacteristic
287C5×C4⋊C4—21no—
288C5×C4⋊C4C23×C311yescharacteristic
289C5×C22⋊C4—21no—
290C22⋊Dic5—21no—
291C22⋊Dic5—21no—
292C22⋊Dic5—21no—
293C22⋊Dic5—21no—
294C22⋊Dic5—21no—
295C22⋊Dic5C3×D411yescharacteristic
296C22⋊Dic5C3×D411yescharacteristic
297#686—22no—
298#686—22no—
299#685—21no—
300#685—21no—
301#685—21no—
302#685—21no—
303C4⋊Dic5—21no—
304C4⋊Dic5C3×D411yescharacteristic
305C4⋊Dic5C3×D411yescharacteristic
306C4⋊Dic5C23×C311yescharacteristic
307C4⋊Dic5C23×C311yescharacteristic
308C4⋊Dic5C23×C311yescharacteristic
309#683—21no—
310C4×Dic5—21no—
311C4×Dic5—21no—
312C4×Dic5C23×C311yescharacteristic
313C4×Dic5C23×C311yescharacteristic
314C2×#168C23×C311yescharacteristic
315C2×#168C23×C311yescharacteristic
316#542—51no—
317#518—51no—
318#485—51no—
319#482—51no—
320#476—51no—
321#474—51no—
322#463—51no—
323#463—51no—
324#450C3×D511yescharacteristic, complemented
325#447—51no—
326#442—51no—
327#440—51no—
328C4×SD16—51no—
329C4×D8—51no—
330#433—51no—
331C22×C3×C5—21no—
332C22×C3×C5—22no—
333C22×C3×C5—22no—
334C22×C3×C5—21no—
335C22×C3×C5—21no—
336C22×C3×C5—41no—
337C22×C3×C5—41no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5—84no—
341C22×C3×C5C22×D411yescharacteristic
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5—41no—
345C3×C4×C5—21no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×C4×C5C2×#4111yescharacteristic
349C3×C4×C5C2×#4111yescharacteristic
350C3×Dic5—21no—
351C3×Dic5—21no—
352C3×Dic5—21no—
353C3×Dic5—21no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×Dic5—41no—
357C24×C3—21no—
358C2×C3×Q8—101no—
359C2×C3×Q8C22×D511yescharacteristic
360C2×C3×D4—22no—
361C2×C3×D4—22no—
362C2×C3×D4—21no—
363C2×C3×D4—51no—
364C2×C3×D4—101no—
365C2×C3×D4C22×D511yescharacteristic
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—101no—
368C22×C3×C4—101no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4C22×D511yescharacteristic
373C3×SD16—22no—
374C3×SD16—22no—
375C3×D8—102no—
376C3×D8—102no—
377C2×C3×C8—51no—
378C2×C3×C8—51no—
379C2×C3×C8C22×D511yescharacteristic
380C2×C3×C8C22×D511yescharacteristic
381C3×C4⋊C4—21no—
382C3×C4⋊C4—51no—
383C3×C4⋊C4—51no—
384C3×C4⋊C4—51no—
385C3×C4⋊C4—51no—
386C3×C4⋊C4—51no—
387C3×C4⋊C4—101no—
388C3×C4⋊C4—101no—
389C3×C4⋊C4C22×D511yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—51no—
392C3×C22⋊C4—51no—
393C3×C22⋊C4—101no—
394C3×C22⋊C4—101no—
395C3×C22⋊C4—101no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C22⋊C4—101no—
402C3×C42—51no—
403C3×C42—51no—
404C3×C42—101no—
405C3×C42—101no—
406C23×C5—24no—
407C23×C5—21no—
408C23×C5—21no—
409C23×C5—81no—
410C23×C5—81no—
411C23×C5C2×C3×D411yescharacteristic
412C22×D5—21no—
413C5×Q8—21no—
414C5×Q8—21no—
415C5×D4—24no—
416C5×D4—21no—
417C5×D4—21no—
418C5×D4C3×#4112yes—
419C5×D4C3×#4112yes—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5C2×C3×D411yescharacteristic
425C2×C4×C5C24×C311yescharacteristic
426C22⋊D5—81no—
427C2×Dic5—21no—
428C2×Dic5—21no—
429C2×Dic5—21no—
430C2×Dic5—81no—
431C2×Dic5—81no—
432C2×Dic5—81no—
433C2×Dic5—81no—
434C2×Dic5C2×C3×D411yescharacteristic
435C2×Dic5C2×C3×D411yescharacteristic
436C2×Dic5C2×C3×D411yescharacteristic
437C2×Dic5C2×C3×D411yescharacteristic
438D20—21no—
439D20—21no—
440C4×D5—81no—
441Dic10—81no—
442C5×C8—21no—
443C5×C8—21no—
444#168—21no—
445#168—21no—
446C22×D4C2×C3×D511yescharacteristic
447C2×SD16C2×C3×D511yescharacteristic
448C2×SD16C2×C3×D511yescharacteristic
449C2×D8—51no—
450C2×D8—51no—
451C4⋊Q8—51no—
452#126—101no—
453#124—51no—
454#124—101no—
455#123—101no—
456C22⋊Q8—101no—
457C22⋊Q8C2×C3×D511yescharacteristic
458#121—51no—
459C4×Q8—51no—
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—51no—
463C4×D4—51no—
464C4×D4—51no—
465C4×D4—101no—
466C4×D4—101no—
467#117—51no—
468#117—51no—
469C2×C22⋊C4—101no—
470C2×C22⋊C4—101no—
471#107—51no—
472#107—51no—
473#106—51no—
474#106—51no—
475C4⋊C8—51no—
476C4⋊C8—51no—
477#103—51no—
478#103—51no—
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102C2×C3×D511yescharacteristic
484#102C2×C3×D511yescharacteristic
485C22⋊C8—51no—
486C22⋊C8C2×C3×D511yescharacteristic
487#97—51no—
488C4×C8—51no—
489C2×C3×C5—41no—
490C2×C3×C5—42no—
491C2×C3×C5—42no—
492C2×C3×C5#52511yescharacteristic
493C2×C3×C5#57611yescharacteristic
494C2×C3×C5#57711yescharacteristic
495C3×D5—81no—
496C23×C3—24no—
497C23×C3—21no—
498C23×C3—21no—
499C23×C3—81no—
500C23×C3—81no—
501C23×C3—101no—
502C23×C3D4×D511yescharacteristic
503C3×Q8—21no—
504C3×Q8—21no—
505C3×Q8—401no—
506C3×D4—24no—
507C3×D4—21no—
508C3×D4—21no—
509C3×D4—101no—
510C3×D4—101no—
511C3×D4—401no—
512C3×D4#71112yes—
513C3×D4#71112yes—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—51no—
519C2×C3×C4—51no—
520C2×C3×C4—51no—
521C2×C3×C4—51no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—401no—
526C2×C3×C4—401no—
527C2×C3×C4—401no—
528C2×C3×C4—401no—
529C2×C3×C4—401no—
530C2×C3×C4D4×D511yescharacteristic
531C2×C3×C4C23×D511yescharacteristic
532C3×C8—21no—
533C3×C8—21no—
534C3×C8—101no—
535C3×C8—101no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—21no—
539C22×C5—22no—
540C22×C5—22no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5—41no—
545C22×C5—84no—
546C22×C5C22×C3×D411yescharacteristic
547C2×D5—41no—
548C2×D5—41no—
549C2×D5—41no—
550C4×C5—21no—
551C4×C5—41no—
552C4×C5—41no—
553C4×C5C2×C3×#4111yescharacteristic
554C4×C5C2×C3×#4111yescharacteristic
555Dic5—21no—
556Dic5—21no—
557Dic5—21no—
558Dic5—21no—
559Dic5—41no—
560Dic5—41no—
561Dic5—41no—
562C24—21no—
563C2×Q8—101no—
564C2×Q8C22×C3×D511yescharacteristic
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—21no—
568C2×D4—51no—
569C2×D4—101no—
570C2×D4C22×C3×D511yescharacteristic
571C2×D4C22×C3×D511yescharacteristic
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4C22×C3×D511yescharacteristic
578SD16—22no—
579SD16—22no—
580D8—102no—
581D8—102no—
582C2×C8—51no—
583C2×C8—51no—
584C2×C8C22×C3×D511yescharacteristic
585C2×C8C22×C3×D511yescharacteristic
586C4⋊C4—21no—
587C4⋊C4—51no—
588C4⋊C4—51no—
589C4⋊C4—51no—
590C4⋊C4—51no—
591C4⋊C4—51no—
592C4⋊C4—101no—
593C4⋊C4—101no—
594C4⋊C4C22×C3×D511yescharacteristic
595C22⋊C4—21no—
596C22⋊C4—51no—
597C22⋊C4—51no—
598C22⋊C4—101no—
599C22⋊C4—101no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4—101no—
606C22⋊C4—101no—
607C42—51no—
608C42—51no—
609C42—101no—
610C42—101no—
611C3×C5#311811yescharacteristic, complemented, Hall
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—21no—
615C22×C3—22no—
616C22×C3—22no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—41no—
620C22×C3—41no—
621C22×C3—84no—
622C22×C3—201no—
623C22×C3—201no—
624C22×C3—201no—
625C22×C3C2×D4×D511yescharacteristic
626C3×C4—21no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—101no—
630C3×C4—101no—
631C3×C4—101no—
632C3×C4—101no—
633C3×C4—201no—
634C3×C4—201no—
635C3×C4—201no—
636C3×C4C2×#71111yescharacteristic
637C3×C4C2×#71111yescharacteristic
638C2×C5—41no—
639C2×C5—42no—
640C2×C5—42no—
641C2×C5C3×#52511yescharacteristic
642C2×C5C3×#57611yescharacteristic
643C2×C5C3×#57711yescharacteristic
644D5—81no—
645C23—24no—
646C23—21no—
647C23—21no—
648C23—81no—
649C23—81no—
650C23—101no—
651C23C3×D4×D511yescharacteristic
652Q8—21no—
653Q8—21no—
654Q8—401no—
655D4—24no—
656D4—21no—
657D4—21no—
658D4—101no—
659D4—101no—
660D4—401no—
661D4C3×#71112yes—
662D4C3×#71112yes—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—51no—
668C2×C4—51no—
669C2×C4—51no—
670C2×C4—51no—
671C2×C4—101no—
672C2×C4—101no—
673C2×C4—101no—
674C2×C4—401no—
675C2×C4—401no—
676C2×C4—401no—
677C2×C4—401no—
678C2×C4—401no—
679C2×C4C3×D4×D511yescharacteristic
680C2×C4C23×C3×D511yescharacteristic
681C8—21no—
682C8—21no—
683C8—101no—
684C8—101no—
685C2×C3—41no—
686C2×C3—42no—
687C2×C3—42no—
688C2×C3—401no—
689C2×C3#6592011yescharacteristic
690C2×C3#6609611yescharacteristic
691C2×C3#6610811yescharacteristic
692C5C3×#311811yescharacteristic, complemented, Sylow
693C22—21no—
694C22—21no—
695C22—22no—
696C22—22no—
697C22—21no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—84no—
703C22—201no—
704C22—201no—
705C22—201no—
706C22C2×C3×D4×D511yescharacteristic
707C4—21no—
708C4—41no—
709C4—41no—
710C4—101no—
711C4—101no—
712C4—101no—
713C4—101no—
714C4—201no—
715C4—201no—
716C4—201no—
717C4C2×C3×#71111yescharacteristic
718C4C2×C3×#71111yescharacteristic
719C3#1061186711yescharacteristic, direct product factor, Sylow
720C2—41no—
721C2—42no—
722C2—42no—
723C2—401no—
724C2C3×#6592011yescharacteristic
725C2C3×#6609611yescharacteristic
726C2C3×#6610811yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#450C2
socleC22×C3×C5C22×D4
prime radicalC3×#65506C2
hypercenterC3×#450D5
hypocenterC5C3×#3118
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#450

Complements

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

NH ≅ G/Ntype
1. C3×#66132C2semidirect
2. C3×#65977C2semidirect
3. C3×C5×#450C2semidirect
5. C3×#65454C2semidirect
6. C3×#65454C2semidirect
7. C3×#65453C2semidirect
8. C3×SD16×Dic5C2semidirect
9. C3×#65334C2semidirect
10. C3×#65074C2semidirect
11. C3×#65050C2semidirect
12. C3×#65048C2semidirect
13. C3×#65045C2semidirect
14. C3×#65026C2semidirect
15. C3×#65009C2semidirect
16. #10611867C3direct (N × H)
23. C3×#4093C22semidirect
24. C3×Q8×Dic5C22semidirect
38. C3×#4039C22semidirect
39. C3×#4034C22semidirect
45. C3×#3967C22semidirect
46. C3×#3967C22semidirect
50. C3×#3953C22semidirect
51. C3×#3953C22semidirect
52. C3×#3950C22semidirect
53. C3×#3949C22semidirect
54. C3×#3947C22semidirect
55. C3×#3946C22semidirect
56. C3×#3946C22semidirect
57. C3×C8×Dic5C22semidirect
58. C3×#3940C22semidirect
59. C3×#3939C22semidirect
61. #66132C2×C3semidirect
62. #65977C2×C3semidirect
63. C5×#450C2×C3semidirect
65. #65454C2×C3semidirect
66. #65454C2×C3semidirect
67. #65453C2×C3semidirect
68. SD16×Dic5C2×C3semidirect
69. #65334C2×C3semidirect
70. #65074C2×C3semidirect
71. #65050C2×C3semidirect
72. #65048C2×C3semidirect
73. #65045C2×C3semidirect
74. #65026C2×C3semidirect
75. #65009C2×C3semidirect
133. C3×#450D5semidirect
146. #4093C22×C3semidirect
147. Q8×Dic5C22×C3semidirect
161. #4039C22×C3semidirect
162. #4034C22×C3semidirect
168. #3967C22×C3semidirect
169. #3967C22×C3semidirect
173. #3953C22×C3semidirect
174. #3953C22×C3semidirect
175. #3950C22×C3semidirect
176. #3949C22×C3semidirect
177. #3947C22×C3semidirect
178. #3946C22×C3semidirect
179. #3946C22×C3semidirect
180. C8×Dic5C22×C3semidirect
181. #3940C22×C3semidirect
182. #3939C22×C3semidirect
324. #450C3×D5semidirect
611. C3×C5#3118semidirect
692. C5C3×#3118semidirect
719. C3#10611867direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661322
C3×#659772
C3×C5×#4502
C3×#655062
C3×#654542
C3×#654532
C3×SD16×Dic52
C3×#653342
C3×#650742
C3×#650502
C3×#650482
C3×#650452
C3×#650262
C3×#650092
#106118673
C3×#31185