Finite Group Databasebeta

← C3×#10611803 #14435818

Subgroups — C3×#10611803 #14435818

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66161C211yesmaximal, characteristic, complemented
2C3×#65953C211yesmaximal, characteristic, complemented
3C3×C5×#449C211yesmaximal, characteristic, complemented
4C3×#65527C211yesmaximal, characteristic, complemented
5C3×#65453C211yesmaximal, characteristic, complemented
6C3×#65452C211yesmaximal, characteristic, complemented
7C3×#65439C211yesmaximal, characteristic, complemented
8C3×D8×Dic5C211yesmaximal, characteristic, complemented
9C3×#65323C211yesmaximal, characteristic, complemented
10C3×#65085C211yesmaximal, characteristic, complemented
11C3×#65077C211yesmaximal, characteristic, complemented
12C3×#65074C211yesmaximal, characteristic, complemented
13C3×#65055C211yesmaximal, characteristic, complemented
14C3×#65025C211yesmaximal, characteristic, complemented
15C3×#65009C211yesmaximal, characteristic, complemented
16#10611803C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×C3×C5×SD16C2211yescharacteristic
19C2×C3×C5×D8C2211yescharacteristic
20C3×C5×#121C2211yescharacteristic
21C3×Q8×Dic5C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C2×C3×#688C2211yescharacteristic
24C3×#4086C2211yescharacteristic
25C3×#4085—21no—
26C3×#4084—21no—
27C3×D4×Dic5—21no—
28C3×D4×Dic5—21no—
29C3×D4×Dic5C2211yescharacteristic
30C3×D4×Dic5C2211yescharacteristic
31C3×D4×Dic5C2211yescharacteristic
32C2×C3×#686C2211yescharacteristic
33C3×#4076C2211yescharacteristic
34C3×#4072—21no—
35C3×#4072C2211yescharacteristic
36C2×C3×C4⋊Dic5—21no—
37C2×C3×C4⋊Dic5C2211yescharacteristic
38C3×#4039C2211yescharacteristic
39C3×#4036C2211yescharacteristic
40C3×#4032—21no—
41C3×#4029—21no—
42C3×C5×#103C2211yescharacteristic
43C3×C5×#102C2211yescharacteristic
44C3×C5×C22⋊C8C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3964C2211yescharacteristic
48C3×#3964C2211yescharacteristic
49C3×C22⋊#168C2211yescharacteristic
50C3×#3953C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3950C2211yescharacteristic
53C3×#3950C2211yescharacteristic
54C3×#3947C2211yescharacteristic
55C3×#3946C2211yescharacteristic
56C3×#3946C2211yescharacteristic
57C3×C8×Dic5C2211yescharacteristic
58C3×#3940C2211yescharacteristic
59C3×#3940C2211yescharacteristic
60C3×#3119—51nomaximal, Hall
61#66161C2×C311yescharacteristic, complemented
62#65953C2×C311yescharacteristic, complemented
63C5×#449C2×C311yescharacteristic, complemented
64#65527C2×C311yescharacteristic, complemented
65#65453C2×C311yescharacteristic, complemented
66#65452C2×C311yescharacteristic, complemented
67#65439C2×C311yescharacteristic, complemented
68D8×Dic5C2×C311yescharacteristic, complemented
69#65323C2×C311yescharacteristic, complemented
70#65085C2×C311yescharacteristic, complemented
71#65077C2×C311yescharacteristic, complemented
72#65074C2×C311yescharacteristic, complemented
73#65055C2×C311yescharacteristic, complemented
74#65025C2×C311yescharacteristic, complemented
75#65009C2×C311yescharacteristic, complemented
76C3×C5×#41—22no—
77C3×C5×#41—22no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4—21no—
81C2×C3×C5×D4C2311yescharacteristic
82C2×C3×C5×D4C2311yescharacteristic
83C22×C3×C4×C5—21no—
84C22×C3×C4×C5C2311yescharacteristic
85C2×C3×C22⋊D5—21no—
86C2×C3×C22⋊D5—21no—
87C2×C3×C22⋊D5—21no—
88C22×C3×Dic5—21no—
89C22×C3×Dic5—21no—
90C22×C3×Dic5—21no—
91C22×C3×Dic5—21no—
92C2×C3×D20C2311yescharacteristic
93C2×C3×C4×D5—21no—
94C3×C5×SD16—22no—
95C3×C5×D8—22no—
96C2×C3×C5×C8C2311yescharacteristic
97C2×C3×C5×C8C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C22⋊Dic5—21no—
101C3×C22⋊Dic5—21no—
102C3×C22⋊Dic5—21no—
103C3×C22⋊Dic5D411yescharacteristic
104C3×C22⋊Dic5D411yescharacteristic
105C3×#688—22no—
106C3×#686—22no—
107C3×#685—21no—
108C3×#685—21no—
109C3×C4⋊Dic5—21no—
110C3×C4⋊Dic5—21no—
111C3×C4⋊Dic5—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×#540—51no—
126C3×#520—51no—
127C3×#481—51no—
128C3×#480—51no—
129C3×#479—51no—
130C3×#478—51no—
131C3×#460—51no—
132C3×#459—51no—
133C3×#449—51no—
134C3×#449D511yescharacteristic, complemented
135C3×#442—51no—
136C3×#440—51no—
137C3×C4×SD16—51no—
138C3×C4×D8—51no—
139C3×#433—51no—
140C2×C5×#41C22×C311yescharacteristic
141C2×C5×SD16C22×C311yescharacteristic
142C2×C5×D8C22×C311yescharacteristic
143C5×#121C22×C311yescharacteristic
144Q8×Dic5C22×C311yescharacteristic
145Q8×Dic5C22×C311yescharacteristic
146C2×#688C22×C311yescharacteristic
147#4086C22×C311yescharacteristic
148#4085—21no—
149#4084—21no—
150D4×Dic5—21no—
151D4×Dic5—21no—
152D4×Dic5C22×C311yescharacteristic
153D4×Dic5C22×C311yescharacteristic
154D4×Dic5C22×C311yescharacteristic
155C2×#686C22×C311yescharacteristic
156#4076C22×C311yescharacteristic
157#4072—21no—
158#4072C22×C311yescharacteristic
159C2×C4⋊Dic5—21no—
160C2×C4⋊Dic5C22×C311yescharacteristic
161#4039C22×C311yescharacteristic
162#4036C22×C311yescharacteristic
163#4032—21no—
164#4029—21no—
165C5×#103C22×C311yescharacteristic
166C5×#102C22×C311yescharacteristic
167C5×C22⋊C8C22×C311yescharacteristic
168#3967C22×C311yescharacteristic
169#3964C22×C311yescharacteristic
170#3964C22×C311yescharacteristic
171#3964C22×C311yescharacteristic
172C22⋊#168C22×C311yescharacteristic
173#3953C22×C311yescharacteristic
174#3953C22×C311yescharacteristic
175#3950C22×C311yescharacteristic
176#3950C22×C311yescharacteristic
177#3947C22×C311yescharacteristic
178#3946C22×C311yescharacteristic
179#3946C22×C311yescharacteristic
180C8×Dic5C22×C311yescharacteristic
181#3940C22×C311yescharacteristic
182#3940C22×C311yescharacteristic
183#3119—51noSylow
184C23×C3×C5—21no—
185C23×C3×C5—21no—
186C23×C3×C5C2×D411yescharacteristic
187C22×C3×D5—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8#4112yes—
190C3×C5×D4—24no—
191C3×C5×D4—21no—
192C3×C5×D4—21no—
193C3×C5×D4—21no—
194C3×C5×D4—81no—
195C3×C5×D4#4112yes—
196C2×C3×C4×C5—24no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—21no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2411yescharacteristic
203C3×C22⋊D5—81no—
204C3×C22⋊D5—81no—
205C3×C22⋊D5—81no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—81no—
210C2×C3×Dic5—81no—
211C2×C3×Dic5—81no—
212C2×C3×Dic5—81no—
213C2×C3×Dic5C2×D411yescharacteristic
214C2×C3×Dic5C2×D411yescharacteristic
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C3×D20—21no—
218C3×D20—21no—
219C3×C4×D5—81no—
220C3×C5×C8—21no—
221C3×C5×C8—21no—
222C3×#168—21no—
223C3×#168—21no—
224C2×C3×#41C2×D511yescharacteristic
225C2×C3×SD16—51no—
226C2×C3×SD16C2×D511yescharacteristic
227C2×C3×D8—51no—
228C2×C3×D8C2×D511yescharacteristic
229C3×#127—51no—
230C3×#125—51no—
231C3×#123—101no—
232C3×#123—101no—
233C3×#121—51no—
234C3×#121—101no—
235C3×#121—101no—
236C3×#121C2×D511yescharacteristic
237C3×C4×Q8—51no—
238C3×C4×Q8—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—101no—
247C2×C3×C4⋊C4—51no—
248C2×C3×C4⋊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×#103C2×D511yescharacteristic
257C3×#102—51no—
258C3×#102—51no—
259C3×#102—51no—
260C3×#102—51no—
261C3×#102—51no—
262C3×#102C2×D511yescharacteristic
263C3×C22⋊C8—51no—
264C3×C22⋊C8C2×D511yescharacteristic
265C3×#97—51no—
266C3×C4×C8—51no—
267C5×#41—22no—
268C5×#41—22no—
269C2×C5×Q8C23×C311yescharacteristic
270C2×C5×D4—21no—
271C2×C5×D4—21no—
272C2×C5×D4C23×C311yescharacteristic
273C2×C5×D4C23×C311yescharacteristic
274C22×C4×C5—21no—
275C22×C4×C5C23×C311yescharacteristic
276C2×C22⋊D5—21no—
277C2×C22⋊D5—21no—
278C2×C22⋊D5—21no—
279C22×Dic5—21no—
280C22×Dic5—21no—
281C22×Dic5—21no—
282C22×Dic5—21no—
283C2×D20C23×C311yescharacteristic
284C2×C4×D5—21no—
285C5×SD16—22no—
286C5×D8—22no—
287C2×C5×C8C23×C311yescharacteristic
288C2×C5×C8C23×C311yescharacteristic
289C5×C4⋊C4C23×C311yescharacteristic
290C5×C22⋊C4—21no—
291C22⋊Dic5—21no—
292C22⋊Dic5—21no—
293C22⋊Dic5—21no—
294C22⋊Dic5C3×D411yescharacteristic
295C22⋊Dic5C3×D411yescharacteristic
296#688—22no—
297#686—22no—
298#685—21no—
299#685—21no—
300C4⋊Dic5—21no—
301C4⋊Dic5—21no—
302C4⋊Dic5—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#540—51no—
317#520—51no—
318#481—51no—
319#480—51no—
320#479—51no—
321#478—51no—
322#460—51no—
323#459—51no—
324#449—51no—
325#449C3×D511yescharacteristic, complemented
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—21no—
334C22×C3×C5—21no—
335C22×C3×C5—41no—
336C22×C3×C5—41no—
337C22×C3×C5—41no—
338C22×C3×C5—41no—
339C22×C3×C5—41no—
340C22×C3×C5C22×D411yescharacteristic
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C3×C4×C5—21no—
345C3×C4×C5—22no—
346C3×C4×C5—41no—
347C3×C4×C5C2×#4111yescharacteristic
348C3×C4×C5C2×#4111yescharacteristic
349C3×Dic5—21no—
350C3×Dic5—21no—
351C3×Dic5—21no—
352C3×Dic5—21no—
353C3×Dic5—41no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×#41—22no—
357C3×#41—22no—
358C2×C3×Q8C22×D511yescharacteristic
359C2×C3×D4—21no—
360C2×C3×D4—21no—
361C2×C3×D4—51no—
362C2×C3×D4—101no—
363C2×C3×D4—101no—
364C2×C3×D4—101no—
365C2×C3×D4C22×D511yescharacteristic
366C2×C3×D4C22×D511yescharacteristic
367C22×C3×C4—21no—
368C22×C3×C4—101no—
369C22×C3×C4—101no—
370C22×C3×C4—101no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×C3×C4C22×D511yescharacteristic
374C3×SD16—22no—
375C3×SD16—102no—
376C3×D8—22no—
377C3×D8—102no—
378C2×C3×C8—51no—
379C2×C3×C8—51no—
380C2×C3×C8C22×D511yescharacteristic
381C2×C3×C8C22×D511yescharacteristic
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⋊C4—101no—
390C3×C4⋊C4—101no—
391C3×C4⋊C4—101no—
392C3×C4⋊C4C22×D511yescharacteristic
393C3×C22⋊C4—21no—
394C3×C22⋊C4—51no—
395C3×C22⋊C4—51no—
396C3×C22⋊C4—101no—
397C3×C22⋊C4—101no—
398C3×C22⋊C4—101no—
399C3×C22⋊C4—101no—
400C3×C22⋊C4—101no—
401C3×C42—51no—
402C3×C42—51no—
403C3×C42—101no—
404C3×C42—101no—
405C23×C5—21no—
406C23×C5—21no—
407C23×C5C2×C3×D411yescharacteristic
408C22×D5—21no—
409C5×Q8—21no—
410C5×Q8C3×#4112yes—
411C5×D4—24no—
412C5×D4—21no—
413C5×D4—21no—
414C5×D4—21no—
415C5×D4—81no—
416C5×D4C3×#4112yes—
417C2×C4×C5—24no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5C2×C3×D411yescharacteristic
423C2×C4×C5C24×C311yescharacteristic
424C22⋊D5—81no—
425C22⋊D5—81no—
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—
441C5×C8—21no—
442C5×C8—21no—
443#168—21no—
444#168—21no—
445C2×#41C2×C3×D511yescharacteristic
446C2×SD16—51no—
447C2×SD16C2×C3×D511yescharacteristic
448C2×D8—51no—
449C2×D8C2×C3×D511yescharacteristic
450#127—51no—
451#125—51no—
452#123—101no—
453#123—101no—
454#121—51no—
455#121—101no—
456#121—101no—
457#121C2×C3×D511yescharacteristic
458C4×Q8—51no—
459C4×Q8—51no—
460C4×D4—51no—
461C4×D4—51no—
462C4×D4—51no—
463C4×D4—51no—
464C4×D4—101no—
465C4×D4—101no—
466#117—51no—
467#117—101no—
468C2×C4⋊C4—51no—
469C2×C4⋊C4—101no—
470#107—51no—
471#107—51no—
472#106—51no—
473#106—51no—
474C4⋊C8—51no—
475C4⋊C8—51no—
476#103—51no—
477#103C2×C3×D511yescharacteristic
478#102—51no—
479#102—51no—
480#102—51no—
481#102—51no—
482#102—51no—
483#102C2×C3×D511yescharacteristic
484C22⋊C8—51no—
485C22⋊C8C2×C3×D511yescharacteristic
486#97—51no—
487C4×C8—51no—
488C2×C3×C5—41no—
489C2×C3×C5—42no—
490C2×C3×C5—81no—
491C2×C3×C5#52511yescharacteristic
492C2×C3×C5#57611yescharacteristic
493C2×C3×C5#57711yescharacteristic
494C3×D5—81no—
495C23×C3—21no—
496C23×C3—21no—
497C23×C3—101no—
498C23×C3D4×D511yescharacteristic
499C3×Q8—21no—
500C3×Q8#71112yes—
501C3×D4—24no—
502C3×D4—21no—
503C3×D4—21no—
504C3×D4—21no—
505C3×D4—81no—
506C3×D4—101no—
507C3×D4—101no—
508C3×D4—401no—
509C3×D4—401no—
510C3×D4—401no—
511C3×D4#71112yes—
512C2×C3×C4—24no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—51no—
518C2×C3×C4—51no—
519C2×C3×C4—51no—
520C2×C3×C4—51no—
521C2×C3×C4—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—401no—
525C2×C3×C4—401no—
526C2×C3×C4—401no—
527C2×C3×C4—401no—
528C2×C3×C4—401no—
529C2×C3×C4D4×D511yescharacteristic
530C2×C3×C4C23×D511yescharacteristic
531C3×C8—21no—
532C3×C8—21no—
533C3×C8—101no—
534C3×C8—101no—
535C22×C5—21no—
536C22×C5—21no—
537C22×C5—21no—
538C22×C5—22no—
539C22×C5—41no—
540C22×C5—41no—
541C22×C5—41no—
542C22×C5—41no—
543C22×C5—41no—
544C22×C5C22×C3×D411yescharacteristic
545C2×D5—41no—
546C2×D5—41no—
547C2×D5—41no—
548C4×C5—21no—
549C4×C5—22no—
550C4×C5—41no—
551C4×C5C2×C3×#4111yescharacteristic
552C4×C5C2×C3×#4111yescharacteristic
553Dic5—21no—
554Dic5—21no—
555Dic5—21no—
556Dic5—21no—
557Dic5—41no—
558Dic5—41no—
559Dic5—41no—
560#41—22no—
561#41—22no—
562C2×Q8C22×C3×D511yescharacteristic
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—51no—
566C2×D4—101no—
567C2×D4—101no—
568C2×D4—101no—
569C2×D4C22×C3×D511yescharacteristic
570C2×D4C22×C3×D511yescharacteristic
571C22×C4—21no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4C22×C3×D511yescharacteristic
578SD16—22no—
579SD16—102no—
580D8—22no—
581D8—102no—
582C2×C8—51no—
583C2×C8—51no—
584C2×C8C22×C3×D511yescharacteristic
585C2×C8C22×C3×D511yescharacteristic
586C4⋊C4—51no—
587C4⋊C4—51no—
588C4⋊C4—51no—
589C4⋊C4—51no—
590C4⋊C4—51no—
591C4⋊C4—101no—
592C4⋊C4—101no—
593C4⋊C4—101no—
594C4⋊C4—101no—
595C4⋊C4—101no—
596C4⋊C4C22×C3×D511yescharacteristic
597C22⋊C4—21no—
598C22⋊C4—51no—
599C22⋊C4—51no—
600C22⋊C4—101no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C42—51no—
606C42—51no—
607C42—101no—
608C42—101no—
609C3×C5#311911yescharacteristic, complemented, Hall
610C22×C3—21no—
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—22no—
614C22×C3—41no—
615C22×C3—41no—
616C22×C3—41no—
617C22×C3—41no—
618C22×C3—41no—
619C22×C3—201no—
620C22×C3—201no—
621C22×C3—201no—
622C22×C3C2×D4×D511yescharacteristic
623C3×C4—21no—
624C3×C4—22no—
625C3×C4—41no—
626C3×C4—101no—
627C3×C4—101no—
628C3×C4—101no—
629C3×C4—101no—
630C3×C4—201no—
631C3×C4—201no—
632C3×C4—201no—
633C3×C4C2×#71111yescharacteristic
634C3×C4C2×#71111yescharacteristic
635C2×C5—41no—
636C2×C5—42no—
637C2×C5—81no—
638C2×C5C3×#52511yescharacteristic
639C2×C5C3×#57611yescharacteristic
640C2×C5C3×#57711yescharacteristic
641D5—81no—
642C23—21no—
643C23—21no—
644C23—101no—
645C23C3×D4×D511yescharacteristic
646Q8—21no—
647Q8C3×#71112yes—
648D4—24no—
649D4—21no—
650D4—21no—
651D4—21no—
652D4—81no—
653D4—101no—
654D4—101no—
655D4—401no—
656D4—401no—
657D4—401no—
658D4C3×#71112yes—
659C2×C4—24no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—51no—
665C2×C4—51no—
666C2×C4—51no—
667C2×C4—51no—
668C2×C4—101no—
669C2×C4—101no—
670C2×C4—101no—
671C2×C4—401no—
672C2×C4—401no—
673C2×C4—401no—
674C2×C4—401no—
675C2×C4—401no—
676C2×C4C3×D4×D511yescharacteristic
677C2×C4C23×C3×D511yescharacteristic
678C8—21no—
679C8—21no—
680C8—101no—
681C8—101no—
682C2×C3—41no—
683C2×C3—42no—
684C2×C3—81no—
685C2×C3—401no—
686C2×C3#6592011yescharacteristic
687C2×C3#6610311yescharacteristic
688C2×C3#6610911yescharacteristic
689C5C3×#311911yescharacteristic, complemented, Sylow
690C22—21no—
691C22—21no—
692C22—21no—
693C22—22no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—201no—
700C22—201no—
701C22—201no—
702C22C2×C3×D4×D511yescharacteristic
703C4—21no—
704C4—22no—
705C4—41no—
706C4—101no—
707C4—101no—
708C4—101no—
709C4—101no—
710C4—201no—
711C4—201no—
712C4—201no—
713C4C2×C3×#71111yescharacteristic
714C4C2×C3×#71111yescharacteristic
715C3#1061180311yescharacteristic, direct product factor, Sylow
716C2—41no—
717C2—42no—
718C2—81no—
719C2—401no—
720C2C3×#6592011yescharacteristic
721C2C3×#6610311yescharacteristic
722C2C3×#6610911yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#449C2
socleC22×C3×C5C22×D4
hypercenterC3×#449D5
hypocenterC5C3×#3119
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#449

Complements

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

NH ≅ G/Ntype
1. C3×#66161C2semidirect
2. C3×#65953C2semidirect
3. C3×C5×#449C2semidirect
4. C3×#65527C2semidirect
5. C3×#65453C2semidirect
6. C3×#65452C2semidirect
7. C3×#65439C2semidirect
8. C3×D8×Dic5C2semidirect
9. C3×#65323C2semidirect
10. C3×#65085C2semidirect
11. C3×#65077C2semidirect
12. C3×#65074C2semidirect
13. C3×#65055C2semidirect
14. C3×#65025C2semidirect
15. C3×#65009C2semidirect
16. #10611803C3direct (N × H)
61. #66161C2×C3semidirect
62. #65953C2×C3semidirect
63. C5×#449C2×C3semidirect
64. #65527C2×C3semidirect
65. #65453C2×C3semidirect
66. #65452C2×C3semidirect
67. #65439C2×C3semidirect
68. D8×Dic5C2×C3semidirect
69. #65323C2×C3semidirect
70. #65085C2×C3semidirect
71. #65077C2×C3semidirect
72. #65074C2×C3semidirect
73. #65055C2×C3semidirect
74. #65025C2×C3semidirect
75. #65009C2×C3semidirect
134. C3×#449D5semidirect
325. #449C3×D5semidirect
609. C3×C5#3119semidirect
689. C5C3×#3119semidirect
715. C3#10611803direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#661612
C3×#659532
C3×C5×#4492
C3×#655272
C3×#654532
C3×#654522
C3×#654392
C3×D8×Dic52
C3×#653232
C3×#650852
C3×#650772
C3×#650742
C3×#650552
C3×#650252
C3×#650092
#106118033
C3×#31195