Finite Group Databasebeta

← C3×#10613275 #14459944

Subgroups — C3×#10613275 #14459944

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65965C211yesmaximal, characteristic
2C3×#65867C211yesmaximal, characteristic, complemented
3C3×C5×#485C211yesmaximal, characteristic, complemented
4C3×#65340C211yesmaximal, characteristic, complemented
5C3×#65291C211yesmaximal, characteristic, complemented
6C3×#65179C211yesmaximal, characteristic, complemented
7C3×#65176C211yesmaximal, characteristic, complemented
8C3×#65156C211yesmaximal, characteristic, complemented
9C3×#65141C211yesmaximal, characteristic, complemented
10C3×#65099C211yesmaximal, characteristic, complemented
11C3×#65093C211yesmaximal, characteristic, complemented
12C3×#65082C211yesmaximal, characteristic, complemented
13C3×#65081C211yesmaximal, characteristic, complemented
14C3×#65022C211yesmaximal, characteristic, complemented
15C3×#65014C211yesmaximal, characteristic, complemented
16#10613275C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#709C2211yescharacteristic
19C3×C5×C22⋊Q8C2211yescharacteristic
20C3×C5×#117C2211yescharacteristic
21C3×#4090C2211yescharacteristic
22C2×C3×#689C2211yescharacteristic
23C3×C4×C22⋊D5C2211yescharacteristic
24C3×#4070C2211yescharacteristic
25C22×C3×#168C2211yescharacteristic
26C2×C3×Dic20C2211yescharacteristic
27C2×C3×#677C2211yescharacteristic
28C2×C3×C8×D5C2211yescharacteristic
29C3×#4043C2211yescharacteristic
30C3×#4043C2211yescharacteristic
31C3×#4040—21no—
32C3×#4039C2211yescharacteristic
33C3×#4038C2211yescharacteristic
34C3×D5×C4⋊C4—21no—
35C3×#4034C2211yescharacteristic
36C3×#4033C2211yescharacteristic
37C3×#4031—21no—
38C3×#4030—21no—
39C3×#4029—21no—
40C3×#4025—21no—
41C3×#4022—21no—
42C3×C4×Dic10—21no—
43C3×C5×#107C2211yescharacteristic
44C3×C5×#106C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46C3×C5×#103C2211yescharacteristic
47C3×C5×C22⋊C8C2211yescharacteristic
48C3×#3967C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3952C2211yescharacteristic
51C3×#3948C2211yescharacteristic
52C3×#3946C2211yescharacteristic
53C3×C8×Dic5C2211yescharacteristic
54C3×#3942C2211yescharacteristic
55C3×#3942C2211yescharacteristic
56C3×#3942C2211yescharacteristic
57C3×#3941C2211yescharacteristic
58C3×#3941C2211yescharacteristic
59C3×#3939C2211yescharacteristic
60C3×#3302—51nomaximal, Hall
61#65965C2×C311yescharacteristic
62#65867C2×C311yescharacteristic, complemented
63C5×#485C2×C311yescharacteristic, complemented
64#65340C2×C311yescharacteristic, complemented
65#65291C2×C311yescharacteristic, complemented
66#65179C2×C311yescharacteristic, complemented
67#65176C2×C311yescharacteristic, complemented
68#65156C2×C311yescharacteristic, complemented
69#65141C2×C311yescharacteristic, complemented
70#65099C2×C311yescharacteristic, complemented
71#65093C2×C311yescharacteristic, complemented
72#65082C2×C311yescharacteristic, complemented
73#65081C2×C311yescharacteristic, complemented
74#65022C2×C311yescharacteristic, complemented
75#65014C2×C311yescharacteristic, complemented
76C2×C3×C5×Q8C2311yescharacteristic
77C22×C3×C4×C5C2311yescharacteristic
78C2×C3×C22⋊D5—21no—
79C2×C3×C22⋊D5D411yescharacteristic
80C3×#713—22no—
81C3×#713—41no—
82C3×#709—22no—
83C3×#709—41no—
84C2×C3×D20—21no—
85C2×C3×D20C2311yescharacteristic
86C2×C3×C4×D5—21no—
87C2×C3×C4×D5—21no—
88C2×C3×C4×D5—21no—
89C2×C3×C4×D5C2311yescharacteristic
90C2×C3×Dic10—21no—
91C2×C3×Dic10C2311yescharacteristic
92C2×C3×Dic10C2311yescharacteristic
93C2×C3×C5×C8C2311yescharacteristic
94C2×C3×C5×C8C2311yescharacteristic
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4C2311yescharacteristic
97C3×C5×C4⋊C4C2311yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C22⋊C4—21no—
100C3×C5×C22⋊C4—21no—
101C3×C42×C5—21no—
102C3×C22⋊Dic5—21no—
103C3×C22⋊Dic5D411yescharacteristic
104C3×#689—41no—
105C3×#685—21no—
106C3×#685—21no—
107C3×#685—21no—
108C3×#685—21no—
109C3×#685D411yescharacteristic
110C3×C4⋊Dic5—21no—
111C3×C4⋊Dic5—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×#683—21no—
115C3×#683—21no—
116C3×#683—21no—
117C3×#683—21no—
118C3×#683D411yescharacteristic
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121C3×C4×Dic5C2311yescharacteristic
122C2×C3×#168—41no—
123C2×C3×#168C2311yescharacteristic
124C2×C3×#168C2311yescharacteristic
125C3×Dic20—41no—
126C3×#677—22no—
127C3×C8×D5—41no—
128C3×#556—51no—
129C3×#547—51no—
130C3×#487—51no—
131C3×#485—51no—
132C3×#485D511yescharacteristic, complemented
133C3×#474—51no—
134C3×#467—51no—
135C3×#467—51no—
136C3×#462—51no—
137C3×#452—51no—
138C3×#452—51no—
139C3×C4×SD16—51no—
140C3×C8×D4—51no—
141C3×#416—51no—
142C3×#416—51no—
143C2×#713C22×C311yescharacteristic
144C2×#709C22×C311yescharacteristic
145C5×C22⋊Q8C22×C311yescharacteristic
146C5×#117C22×C311yescharacteristic
147#4090C22×C311yescharacteristic
148C2×#689C22×C311yescharacteristic
149C4×C22⋊D5C22×C311yescharacteristic
150#4070C22×C311yescharacteristic
151C22×#168C22×C311yescharacteristic
152C2×Dic20C22×C311yescharacteristic
153C2×#677C22×C311yescharacteristic
154C2×C8×D5C22×C311yescharacteristic
155#4043C22×C311yescharacteristic
156#4043C22×C311yescharacteristic
157#4040—21no—
158#4039C22×C311yescharacteristic
159#4038C22×C311yescharacteristic
160D5×C4⋊C4—21no—
161#4034C22×C311yescharacteristic
162#4033C22×C311yescharacteristic
163#4031—21no—
164#4030—21no—
165#4029—21no—
166#4025—21no—
167#4022—21no—
168C4×Dic10—21no—
169C5×#107C22×C311yescharacteristic
170C5×#106C22×C311yescharacteristic
171C5×#103C22×C311yescharacteristic
172C5×#103C22×C311yescharacteristic
173C5×C22⋊C8C22×C311yescharacteristic
174#3967C22×C311yescharacteristic
175#3953C22×C311yescharacteristic
176#3952C22×C311yescharacteristic
177#3948C22×C311yescharacteristic
178#3946C22×C311yescharacteristic
179C8×Dic5C22×C311yescharacteristic
180#3942C22×C311yescharacteristic
181#3942C22×C311yescharacteristic
182#3942C22×C311yescharacteristic
183#3941C22×C311yescharacteristic
184#3941C22×C311yescharacteristic
185#3939C22×C311yescharacteristic
186#3302—51noSylow
187C23×C3×C5C2×D411yescharacteristic
188C22×C3×D5—21no—
189C22×C3×D5C2×D411yescharacteristic
190C3×C5×Q8—21no—
191C3×C5×Q8—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5—21no—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2411yescharacteristic
200C3×C22⋊D5—22no—
201C3×C22⋊D5—42no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5—21no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5C2×D411yescharacteristic
206C2×C3×Dic5C2×D411yescharacteristic
207C2×C3×Dic5C2×D411yescharacteristic
208C3×D20—21no—
209C3×D20—42no—
210C3×D20#4112yes—
211C3×C4×D5—21no—
212C3×C4×D5—21no—
213C3×C4×D5—42no—
214C3×C4×D5—42no—
215C3×C4×D5—42no—
216C3×Dic10—21no—
217C3×Dic10—21no—
218C3×Dic10—21no—
219C3×Dic10—21no—
220C3×Dic10—42no—
221C3×C5×C8—21no—
222C3×C5×C8—21no—
223C3×#168—21no—
224C3×#168—21no—
225C2×C3×#41—51no—
226C2×C3×#41—51no—
227C2×C3×Q16—51no—
228C2×C3×Q16—51no—
229C2×C3×SD16—51no—
230C22×C3×C8—51no—
231C22×C3×C8—51no—
232C3×C4⋊Q8—51no—
233C3×C4⋊Q8—51no—
234C3×#126—101no—
235C3×#126—101no—
236C3×#124—101no—
237C3×#123—101no—
238C3×#123—101no—
239C3×C22⋊Q8—51no—
240C3×C22⋊Q8—51no—
241C3×C22⋊Q8—51no—
242C3×C22⋊Q8C2×D511yescharacteristic
243C3×#121—101no—
244C3×C4×Q8—51no—
245C3×C4×Q8—101no—
246C3×C4×D4—51no—
247C3×C4×D4—51no—
248C3×#117—51no—
249C3×#117C2×D511yescharacteristic
250C2×C3×C4⋊C4—101no—
251C3×#107—51no—
252C3×#107C2×D511yescharacteristic
253C3×#106C2×D511yescharacteristic
254C3×C4⋊C8—51no—
255C3×#103—51no—
256C3×#103—51no—
257C3×#103—51no—
258C3×#103—51no—
259C3×#103—51no—
260C3×#103C2×D511yescharacteristic
261C3×#103C2×D511yescharacteristic
262C3×#102—51no—
263C3×#102—51no—
264C3×#102—51no—
265C3×C22⋊C8—51no—
266C3×C22⋊C8C2×D511yescharacteristic
267C3×C4×C8—51no—
268C2×C5×Q8C23×C311yescharacteristic
269C22×C4×C5C23×C311yescharacteristic
270C2×C22⋊D5—21no—
271C2×C22⋊D5C3×D411yescharacteristic
272#713—22no—
273#713—41no—
274#709—22no—
275#709—41no—
276C2×D20—21no—
277C2×D20C23×C311yescharacteristic
278C2×C4×D5—21no—
279C2×C4×D5—21no—
280C2×C4×D5—21no—
281C2×C4×D5C23×C311yescharacteristic
282C2×Dic10—21no—
283C2×Dic10C23×C311yescharacteristic
284C2×Dic10C23×C311yescharacteristic
285C2×C5×C8C23×C311yescharacteristic
286C2×C5×C8C23×C311yescharacteristic
287C5×C4⋊C4—21no—
288C5×C4⋊C4C23×C311yescharacteristic
289C5×C4⋊C4C23×C311yescharacteristic
290C5×C4⋊C4C23×C311yescharacteristic
291C5×C22⋊C4—21no—
292C5×C22⋊C4—21no—
293C42×C5—21no—
294C22⋊Dic5—21no—
295C22⋊Dic5C3×D411yescharacteristic
296#689—41no—
297#685—21no—
298#685—21no—
299#685—21no—
300#685—21no—
301#685C3×D411yescharacteristic
302C4⋊Dic5—21no—
303C4⋊Dic5—21no—
304C4⋊Dic5C23×C311yescharacteristic
305#683—21no—
306#683—21no—
307#683—21no—
308#683—21no—
309#683—21no—
310#683C3×D411yescharacteristic
311C4×Dic5—21no—
312C4×Dic5—21no—
313C4×Dic5C23×C311yescharacteristic
314C2×#168—41no—
315C2×#168C23×C311yescharacteristic
316C2×#168C23×C311yescharacteristic
317Dic20—41no—
318#677—22no—
319C8×D5—41no—
320#556—51no—
321#547—51no—
322#487—51no—
323#485—51no—
324#485C3×D511yescharacteristic, complemented
325#474—51no—
326#467—51no—
327#467—51no—
328#462—51no—
329#452—51no—
330#452—51no—
331C4×SD16—51no—
332C8×D4—51no—
333#416—51no—
334#416—51no—
335C22×C3×C5—21no—
336C22×C3×C5—21no—
337C22×C3×C5—21no—
338C22×C3×C5C22×D411yescharacteristic
339C2×C3×D5—21no—
340C2×C3×D5—22no—
341C2×C3×D5—21no—
342C2×C3×D5—21no—
343C2×C3×D5—41no—
344C2×C3×D5—41no—
345C3×C4×C5—21no—
346C3×C4×C5—41no—
347C3×C4×C5—41no—
348C3×C4×C5—41no—
349C3×C4×C5—41no—
350C3×C4×C5C2×#4111yescharacteristic
351C3×C4×C5H(5,𝔽2)11yescharacteristic
352C3×Dic5—21no—
353C3×Dic5—21no—
354C3×Dic5—41no—
355C3×Dic5—41no—
356C3×Dic5—41no—
357C3×Dic5#13512yes—
358C3×#41—102no—
359C3×#41—102no—
360C3×#41—201no—
361C3×#41—201no—
362C2×C3×Q8—51no—
363C2×C3×Q8—51no—
364C2×C3×Q8—101no—
365C2×C3×Q8C22×D511yescharacteristic
366C2×C3×D4—51no—
367C2×C3×D4—51no—
368C2×C3×D4—101no—
369C2×C3×D4—101no—
370C22×C3×C4—51no—
371C22×C3×C4—101no—
372C22×C3×C4—101no—
373C22×C3×C4—101no—
374C22×C3×C4C22×D511yescharacteristic
375C3×Q16—201no—
376C3×Q16—201no—
377C3×SD16—102no—
378C2×C3×C8—51no—
379C2×C3×C8—51no—
380C2×C3×C8—201no—
381C2×C3×C8—201no—
382C2×C3×C8C22×D511yescharacteristic
383C2×C3×C8C22×D511yescharacteristic
384C3×C4⋊C4—21no—
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⋊C4—101no—
393C3×C4⋊C4—101no—
394C3×C4⋊C4C22×D511yescharacteristic
395C3×C4⋊C4C22×D511yescharacteristic
396C3×C4⋊C4C22×D511yescharacteristic
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C22⋊C4—51no—
400C3×C22⋊C4—51no—
401C3×C22⋊C4—101no—
402C3×C22⋊C4—101no—
403C3×C22⋊C4—101no—
404C3×C22⋊C4—101no—
405C3×C22⋊C4—101no—
406C3×C42—21no—
407C3×C42—51no—
408C3×C42—101no—
409C3×C42—101no—
410C23×C5C2×C3×D411yescharacteristic
411C22×D5—21no—
412C22×D5C2×C3×D411yescharacteristic
413C5×Q8—21no—
414C5×Q8—21no—
415C2×C4×C5—21no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5C2×C3×D411yescharacteristic
422C2×C4×C5C24×C311yescharacteristic
423C22⋊D5—22no—
424C22⋊D5—42no—
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5C2×C3×D411yescharacteristic
429C2×Dic5C2×C3×D411yescharacteristic
430C2×Dic5C2×C3×D411yescharacteristic
431D20—21no—
432D20—42no—
433D20C3×#4112yes—
434C4×D5—21no—
435C4×D5—21no—
436C4×D5—42no—
437C4×D5—42no—
438C4×D5—42no—
439Dic10—21no—
440Dic10—21no—
441Dic10—21no—
442Dic10—21no—
443Dic10—42no—
444C5×C8—21no—
445C5×C8—21no—
446#168—21no—
447#168—21no—
448C2×#41—51no—
449C2×#41—51no—
450C2×Q16—51no—
451C2×Q16—51no—
452C2×SD16—51no—
453C22×C8—51no—
454C22×C8—51no—
455C4⋊Q8—51no—
456C4⋊Q8—51no—
457#126—101no—
458#126—101no—
459#124—101no—
460#123—101no—
461#123—101no—
462C22⋊Q8—51no—
463C22⋊Q8—51no—
464C22⋊Q8—51no—
465C22⋊Q8C2×C3×D511yescharacteristic
466#121—101no—
467C4×Q8—51no—
468C4×Q8—101no—
469C4×D4—51no—
470C4×D4—51no—
471#117—51no—
472#117C2×C3×D511yescharacteristic
473C2×C4⋊C4—101no—
474#107—51no—
475#107C2×C3×D511yescharacteristic
476#106C2×C3×D511yescharacteristic
477C4⋊C8—51no—
478#103—51no—
479#103—51no—
480#103—51no—
481#103—51no—
482#103—51no—
483#103C2×C3×D511yescharacteristic
484#103C2×C3×D511yescharacteristic
485#102—51no—
486#102—51no—
487#102—51no—
488C22⋊C8—51no—
489C22⋊C8C2×C3×D511yescharacteristic
490C4×C8—51no—
491C2×C3×C5—41no—
492C2×C3×C5#54611yescharacteristic
493C2×C3×C5C2×#13511yescharacteristic
494C2×C3×C5#57811yescharacteristic
495C3×D5—41no—
496C3×D5—42no—
497C23×C3—51no—
498C23×C3—101no—
499C23×C3D4×D511yescharacteristic
500C3×Q8—21no—
501C3×Q8—21no—
502C3×Q8—101no—
503C3×Q8—101no—
504C3×Q8—101no—
505C3×Q8—101no—
506C3×Q8—202no—
507C3×D4—52no—
508C3×D4—102no—
509C3×D4—101no—
510C3×D4—202no—
511C3×D4—202no—
512C2×C3×C4—21no—
513C2×C3×C4—21no—
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—101no—
522C2×C3×C4—101no—
523C2×C3×C4—101no—
524C2×C3×C4—101no—
525C2×C3×C4—101no—
526C2×C3×C4—202no—
527C2×C3×C4—202no—
528C2×C3×C4—202no—
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×C5C22×C3×D411yescharacteristic
539C2×D5—21no—
540C2×D5—21no—
541C2×D5—21no—
542C2×D5—22no—
543C2×D5—41no—
544C2×D5—41no—
545C4×C5—21no—
546C4×C5—41no—
547C4×C5—41no—
548C4×C5—41no—
549C4×C5—41no—
550C4×C5C2×C3×#4111yescharacteristic
551C4×C5C3×H(5,𝔽2)11yescharacteristic
552Dic5—21no—
553Dic5—21no—
554Dic5—41no—
555Dic5—41no—
556Dic5—41no—
557Dic5C3×#13512yes—
558#41—102no—
559#41—102no—
560#41—201no—
561#41—201no—
562C2×Q8—51no—
563C2×Q8—51no—
564C2×Q8—101no—
565C2×Q8C22×C3×D511yescharacteristic
566C2×D4—51no—
567C2×D4—51no—
568C2×D4—101no—
569C2×D4—101no—
570C22×C4—51no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4C22×C3×D511yescharacteristic
575Q16—201no—
576Q16—201no—
577SD16—102no—
578C2×C8—51no—
579C2×C8—51no—
580C2×C8—201no—
581C2×C8—201no—
582C2×C8C22×C3×D511yescharacteristic
583C2×C8C22×C3×D511yescharacteristic
584C4⋊C4—21no—
585C4⋊C4—51no—
586C4⋊C4—51no—
587C4⋊C4—101no—
588C4⋊C4—101no—
589C4⋊C4—101no—
590C4⋊C4—101no—
591C4⋊C4—101no—
592C4⋊C4—101no—
593C4⋊C4—101no—
594C4⋊C4C22×C3×D511yescharacteristic
595C4⋊C4C22×C3×D511yescharacteristic
596C4⋊C4C22×C3×D511yescharacteristic
597C22⋊C4—21no—
598C22⋊C4—21no—
599C22⋊C4—51no—
600C22⋊C4—51no—
601C22⋊C4—101no—
602C22⋊C4—101no—
603C22⋊C4—101no—
604C22⋊C4—101no—
605C22⋊C4—101no—
606C42—21no—
607C42—51no—
608C42—101no—
609C42—101no—
610C3×C5#330211yescharacteristic, complemented, Hall
611C22×C3—21no—
612C22×C3—21no—
613C22×C3—21no—
614C22×C3—101no—
615C22×C3—101no—
616C22×C3—101no—
617C22×C3—102no—
618C22×C3—201no—
619C22×C3—201no—
620C22×C3C2×D4×D511yescharacteristic
621C3×C4—21no—
622C3×C4—41no—
623C3×C4—41no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—52no—
627C3×C4—101no—
628C3×C4—101no—
629C3×C4—201no—
630C3×C4—201no—
631C3×C4—201no—
632C3×C4D5×#4111yescharacteristic
633C3×C4#414911yescharacteristic
634C2×C5—41no—
635C2×C5C3×#54611yescharacteristic
636C2×C5C2×C3×#13511yescharacteristic
637C2×C5C3×#57811yescharacteristic
638D5—41no—
639D5—42no—
640C23—51no—
641C23—101no—
642C23C3×D4×D511yescharacteristic
643Q8—21no—
644Q8—21no—
645Q8—101no—
646Q8—101no—
647Q8—101no—
648Q8—101no—
649Q8—202no—
650D4—52no—
651D4—102no—
652D4—101no—
653D4—202no—
654D4—202no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—51no—
662C2×C4—51no—
663C2×C4—51no—
664C2×C4—101no—
665C2×C4—101no—
666C2×C4—101no—
667C2×C4—101no—
668C2×C4—101no—
669C2×C4—202no—
670C2×C4—202no—
671C2×C4—202no—
672C2×C4C3×D4×D511yescharacteristic
673C2×C4C23×C3×D511yescharacteristic
674C8—21no—
675C8—21no—
676C8—101no—
677C8—101no—
678C2×C3—41no—
679C2×C3—201no—
680C2×C3—202no—
681C2×C3#6598811yescharacteristic
682C2×C3D5×#13511yescharacteristic
683C2×C3#6611311yescharacteristic
684C5C3×#330211yescharacteristic, complemented, Sylow
685C22—21no—
686C22—21no—
687C22—21no—
688C22—101no—
689C22—101no—
690C22—101no—
691C22—102no—
692C22—201no—
693C22—201no—
694C22C2×C3×D4×D511yescharacteristic
695C4—21no—
696C4—41no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—52no—
701C4—101no—
702C4—101no—
703C4—201no—
704C4—201no—
705C4—201no—
706C4C3×D5×#4111yescharacteristic
707C4C3×#414911yescharacteristic
708C3#1061327511yescharacteristic, direct product factor, Sylow
709C2—41no—
710C2—201no—
711C2—202no—
712C2C3×#6598811yescharacteristic
713C2C3×D5×#13511yescharacteristic
714C2C3×#6611311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutator, cosocleC2×C4×C5C24×C3
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#485C2
socleC22×C3×C5C22×D4
prime radicalC3×#65965C2
hypercenterC3×#485D5
hypocenterC5C3×#3302
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C3×#485

Complements

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

NH ≅ G/Ntype
2. C3×#65867C2semidirect
3. C3×C5×#485C2semidirect
4. C3×#65340C2semidirect
5. C3×#65291C2semidirect
6. C3×#65179C2semidirect
7. C3×#65176C2semidirect
8. C3×#65156C2semidirect
9. C3×#65141C2semidirect
10. C3×#65099C2semidirect
11. C3×#65093C2semidirect
12. C3×#65082C2semidirect
13. C3×#65081C2semidirect
14. C3×#65022C2semidirect
15. C3×#65014C2semidirect
16. #10613275C3direct (N × H)
62. #65867C2×C3semidirect
63. C5×#485C2×C3semidirect
64. #65340C2×C3semidirect
65. #65291C2×C3semidirect
66. #65179C2×C3semidirect
67. #65176C2×C3semidirect
68. #65156C2×C3semidirect
69. #65141C2×C3semidirect
70. #65099C2×C3semidirect
71. #65093C2×C3semidirect
72. #65082C2×C3semidirect
73. #65081C2×C3semidirect
74. #65022C2×C3semidirect
75. #65014C2×C3semidirect
132. C3×#485D5semidirect
324. #485C3×D5semidirect
610. C3×C5#3302semidirect
684. C5C3×#3302semidirect
708. C3#10613275direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#659652
C3×#658672
C3×C5×#4852
C3×#653402
C3×#652912
C3×#651792
C3×#651762
C3×#651562
C3×#651412
C3×#650992
C3×#650932
C3×#650822
C3×#650812
C3×#650222
C3×#650142
#106132753
C3×#33025