Finite Group Databasebeta

← C3×#10611509 #14417618

Subgroups — C3×#10611509 #14417618

Order 1920.

968 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
1C2×C3×#4062C211yesmaximal, characteristic
2C3×#65908C211yesmaximal, characteristic, complemented
3C3×#65880C211yesmaximal, characteristic, complemented
4C3×C5×#440C211yesmaximal, characteristic, complemented
5C3×#65453C211yesmaximal, characteristic, complemented
6C3×C4×#689C211yesmaximal, characteristic, complemented
7C3×C4×#686C211yesmaximal, characteristic, complemented
8C3×#65178C211yesmaximal, characteristic, complemented
9C3×D5×#107C211yesmaximal, characteristic, complemented
10C3×#65092C211yesmaximal, characteristic, complemented
11C3×#65079C211yesmaximal, characteristic, complemented
12C3×#65060C211yesmaximal, characteristic, complemented
13C3×#65045C211yesmaximal, characteristic, complemented
14C3×#64999C211yesmaximal, characteristic, complemented
15C3×#64997C211yesmaximal, characteristic, complemented
16#10611509C311yesmaximal, characteristic, direct product factor, Hall
17C2×C3×#713C2211yescharacteristic
18C2×C3×#711C2211yescharacteristic
19C2×C3×C5×SD16C2211yescharacteristic
20C3×C4×C5×Q8C2211yescharacteristic
21C3×C4×C5×D4C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C2×C3×#689C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C2×C3×#686C2211yescharacteristic
26C3×C4×C22⋊D5—21no—
27C2×C3×#683—21no—
28C3×#4062C418yescomplemented
29C2×C3×#677C2211yescharacteristic
30C2×C3×#676C2211yescharacteristic
31C2×C3×C8×D5C2211yescharacteristic
32C3×#4039—21no—
33C3×#4039C2211yescharacteristic
34C3×D5×C4⋊C4—21no—
35C3×D5×C4⋊C4C2211yescharacteristic
36C3×D5×C4⋊C4C2211yescharacteristic
37C3×#4033C2211yescharacteristic
38C3×#4027—21no—
39C3×#4023—21no—
40C3×C4×D20—21no—
41C3×C4×D20C2211yescharacteristic
42C3×#4018—21no—
43C3×#4018C2211yescharacteristic
44C3×C4×Dic10C2211yescharacteristic
45C3×C5×#107C2211yescharacteristic
46C3×C5×#103C2211yescharacteristic
47C3×C5×#102C2211yescharacteristic
48C3×C5×#97C2211yescharacteristic
49C3×#3967C2211yescharacteristic
50C3×#3964C2211yescharacteristic
51C3×#3953C2211yescharacteristic
52C3×#3950C2211yescharacteristic
53C3×#3948C2211yescharacteristic
54C3×#3947C2211yescharacteristic
55C3×C8×Dic5C2211yescharacteristic
56C3×#3942C2211yescharacteristic
57C3×#3941C2211yescharacteristic
58C3×#3939C2211yescharacteristic
59C3×#3939C2211yescharacteristic
60C3×C4×#168C2211yescharacteristic
61C3×#2951—51nomaximal, Hall
62C2×#4062C2×C311yescharacteristic
63#65908C2×C311yescharacteristic, complemented
64#65880C2×C311yescharacteristic, complemented
65C5×#440C2×C311yescharacteristic, complemented
66#65453C2×C311yescharacteristic, complemented
67C4×#689C2×C311yescharacteristic, complemented
68C4×#686C2×C311yescharacteristic, complemented
69#65178C2×C311yescharacteristic, complemented
70D5×#107C2×C311yescharacteristic, complemented
71#65092C2×C311yescharacteristic, complemented
72#65079C2×C311yescharacteristic, complemented
73#65060C2×C311yescharacteristic, complemented
74#65045C2×C311yescharacteristic, complemented
75#64999C2×C311yescharacteristic, complemented
76#64997C2×C311yescharacteristic, complemented
77C2×C3×C5×Q8C2311yescharacteristic
78C2×C3×C5×D4C2311yescharacteristic
79C22×C3×C4×C5—21no—
80C2×C3×C22⋊D5—21no—
81C22×C3×Dic5—21no—
82C22×C3×Dic5—21no—
83C3×#713—22no—
84C3×#713C2×C414yescomplemented
85C3×#711—22no—
86C3×#711C2×C414yescomplemented
87C2×C3×D20—21no—
88C2×C3×D20C2311yescharacteristic
89C2×C3×C4×D5—21no—
90C2×C3×C4×D5—21no—
91C2×C3×C4×D5—21no—
92C2×C3×C4×D5—21no—
93C2×C3×C4×D5—21no—
94C2×C3×C4×D5C2311yescharacteristic
95C2×C3×Dic10C2311yescharacteristic
96C3×C5×SD16C2×C414yescomplemented
97C2×C3×C5×C8C2311yescharacteristic
98C2×C3×C5×C8C2311yescharacteristic
99C3×C5×C4⋊C4—21no—
100C3×C5×C4⋊C4C2311yescharacteristic
101C3×C5×C4⋊C4C2311yescharacteristic
102C3×C5×C22⋊C4—21no—
103C3×C42×C5—21no—
104C3×C42×C5C2311yescharacteristic
105C3×C22⋊Dic5—21no—
106C3×#689C2×C414yescomplemented
107C3×#686C2×C414yescomplemented
108C3×#685—21no—
109C3×#685—21no—
110C3×#685D411yescharacteristic
111C3×#685D411yescharacteristic
112C3×C4⋊Dic5—21no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×C4⋊Dic5C2311yescharacteristic
115C3×#683—21no—
116C3×#683—21no—
117C3×#683—21no—
118C3×#683—21no—
119C3×#683D411yescharacteristic
120C3×#683D411yescharacteristic
121C3×C4×Dic5—21no—
122C3×C4×Dic5—21no—
123C3×C4×Dic5—21no—
124C3×C4×Dic5C2311yescharacteristic
125C2×C3×#168C2311yescharacteristic
126C2×C3×#168C2311yescharacteristic
127C3×#677C2×C414yescomplemented
128C3×#676—22no—
129C3×C8×D5C2×C414yescomplemented
130C2×C3×#135—51no—
131C3×#520—51no—
132C3×#520—51no—
133C3×#440—51no—
134C3×#440—51no—
135C3×#440—51no—
136C3×#440D511yescharacteristic, complemented
137C3×C4×Q16—51no—
138C3×C4×Q16—51no—
139C3×C4×D8—51no—
140C3×C4×D8—51no—
141C2×C3×#107—51no—
142C3×#417—51no—
143C3×#417—51no—
144C3×#405—51no—
145C2×#713C22×C311yescharacteristic
146C2×#711C22×C311yescharacteristic
147C2×C5×SD16C22×C311yescharacteristic
148C4×C5×Q8C22×C311yescharacteristic
149C4×C5×D4C22×C311yescharacteristic
150Q8×Dic5C22×C311yescharacteristic
151C2×#689C22×C311yescharacteristic
152D4×Dic5C22×C311yescharacteristic
153C2×#686C22×C311yescharacteristic
154C4×C22⋊D5—21no—
155C2×#683—21no—
156#4062C3×C418yescomplemented
157C2×#677C22×C311yescharacteristic
158C2×#676C22×C311yescharacteristic
159C2×C8×D5C22×C311yescharacteristic
160#4039—21no—
161#4039C22×C311yescharacteristic
162D5×C4⋊C4—21no—
163D5×C4⋊C4C22×C311yescharacteristic
164D5×C4⋊C4C22×C311yescharacteristic
165#4033C22×C311yescharacteristic
166#4027—21no—
167#4023—21no—
168C4×D20—21no—
169C4×D20C22×C311yescharacteristic
170#4018—21no—
171#4018C22×C311yescharacteristic
172C4×Dic10C22×C311yescharacteristic
173C5×#107C22×C311yescharacteristic
174C5×#103C22×C311yescharacteristic
175C5×#102C22×C311yescharacteristic
176C5×#97C22×C311yescharacteristic
177#3967C22×C311yescharacteristic
178#3964C22×C311yescharacteristic
179#3953C22×C311yescharacteristic
180#3950C22×C311yescharacteristic
181#3948C22×C311yescharacteristic
182#3947C22×C311yescharacteristic
183C8×Dic5C22×C311yescharacteristic
184#3942C22×C311yescharacteristic
185#3941C22×C311yescharacteristic
186#3939C22×C311yescharacteristic
187#3939C22×C311yescharacteristic
188C4×#168C22×C311yescharacteristic
189#2951—51noSylow
190C23×C3×C5—21no—
191C22×C3×D5—21no—
192C22×C3×D5C2×D411yescharacteristic
193C3×C5×Q8—21no—
194C3×C5×Q8C22×C412yes—
195C3×C5×D4—21no—
196C3×C5×D4C22×C412yes—
197C2×C3×C4×C5—21no—
198C2×C3×C4×C5—21no—
199C2×C3×C4×C5—21no—
200C2×C3×C4×C5—81no—
201C2×C3×C4×C5C2×D411yescharacteristic
202C2×C3×C4×C5C2×D411yescharacteristic
203C2×C3×C4×C5C2411yescharacteristic
204C3×C22⋊D5—24no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—24no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—81no—
210C2×C3×Dic5C2×D411yescharacteristic
211C2×C3×Dic5C2×D411yescharacteristic
212C2×C3×Dic5C2×D411yescharacteristic
213C3×D20—24no—
214C3×D20—21no—
215C3×D20C22×C412yes—
216C3×C4×D5—24no—
217C3×C4×D5—81no—
218C3×C4×D5—81no—
219C3×C4×D5—81no—
220C3×C4×D5—81no—
221C3×C4×D5C22×C412yes—
222C3×C4×D5#4112yes—
223C3×Dic10—21no—
224C3×Dic10C22×C412yes—
225C3×C5×C8—21no—
226C3×C5×C8C22×C412yes—
227C3×#168—21no—
228C3×#168C22×C412yes—
229C2×C3×#41—51no—
230C2×C3×#41—51no—
231C3×#135—58no—
232C2×C3×Q16—51no—
233C2×C3×SD16—51no—
234C2×C3×SD16C2×D511yescharacteristic
235C2×C3×D8—51no—
236C2×C3×M16—51no—
237C22×C3×C8—51no—
238C3×C4×Q8—51no—
239C3×C4×Q8—51no—
240C3×C4×Q8—51no—
241C3×C4×Q8C2×D511yescharacteristic
242C3×C4×D4—51no—
243C3×C4×D4—51no—
244C3×C4×D4—51no—
245C3×C4×D4—101no—
246C3×C4×D4—101no—
247C3×C4×D4—101no—
248C3×C4×D4—101no—
249C3×C4×D4C2×D511yescharacteristic
250C3×#117—51no—
251C3×#117—101no—
252C3×#117—101no—
253C2×C3×C4⋊C4—51no—
254C2×C3×C4⋊C4—51no—
255C2×C3×C4⋊C4—101no—
256C2×C3×C4⋊C4—101no—
257C3×#107—51no—
258C3×#107—51no—
259C3×#107—51no—
260C3×#107C2×D511yescharacteristic
261C3×#103—51no—
262C3×#103—51no—
263C3×#103—51no—
264C3×#103C2×D511yescharacteristic
265C3×#102—51no—
266C3×#102—51no—
267C3×#102—51no—
268C3×#102C2×D511yescharacteristic
269C3×#97—51no—
270C3×#97C2×D511yescharacteristic
271C3×C4×C8—51no—
272C3×C4×C8—51no—
273C2×C5×Q8C23×C311yescharacteristic
274C2×C5×D4C23×C311yescharacteristic
275C22×C4×C5—21no—
276C2×C22⋊D5—21no—
277C22×Dic5—21no—
278C22×Dic5—21no—
279#713—22no—
280#713C2×C3×C414yescomplemented
281#711—22no—
282#711C2×C3×C414yescomplemented
283C2×D20—21no—
284C2×D20C23×C311yescharacteristic
285C2×C4×D5—21no—
286C2×C4×D5—21no—
287C2×C4×D5—21no—
288C2×C4×D5—21no—
289C2×C4×D5—21no—
290C2×C4×D5C23×C311yescharacteristic
291C2×Dic10C23×C311yescharacteristic
292C5×SD16C2×C3×C414yescomplemented
293C2×C5×C8C23×C311yescharacteristic
294C2×C5×C8C23×C311yescharacteristic
295C5×C4⋊C4—21no—
296C5×C4⋊C4C23×C311yescharacteristic
297C5×C4⋊C4C23×C311yescharacteristic
298C5×C22⋊C4—21no—
299C42×C5—21no—
300C42×C5C23×C311yescharacteristic
301C22⋊Dic5—21no—
302#689C2×C3×C414yescomplemented
303#686C2×C3×C414yescomplemented
304#685—21no—
305#685—21no—
306#685C3×D411yescharacteristic
307#685C3×D411yescharacteristic
308C4⋊Dic5—21no—
309C4⋊Dic5C23×C311yescharacteristic
310C4⋊Dic5C23×C311yescharacteristic
311#683—21no—
312#683—21no—
313#683—21no—
314#683—21no—
315#683C3×D411yescharacteristic
316#683C3×D411yescharacteristic
317C4×Dic5—21no—
318C4×Dic5—21no—
319C4×Dic5—21no—
320C4×Dic5C23×C311yescharacteristic
321C2×#168C23×C311yescharacteristic
322C2×#168C23×C311yescharacteristic
323#677C2×C3×C414yescomplemented
324#676—22no—
325C8×D5C2×C3×C414yescomplemented
326C2×#135—51no—
327#520—51no—
328#520—51no—
329#440—51no—
330#440—51no—
331#440—51no—
332#440C3×D511yescharacteristic, complemented
333C4×Q16—51no—
334C4×Q16—51no—
335C4×D8—51no—
336C4×D8—51no—
337C2×#107—51no—
338#417—51no—
339#417—51no—
340#405—51no—
341C22×C3×C5—22no—
342C22×C3×C5—41no—
343C22×C3×C5—41no—
344C22×C3×C5C22×D411yescharacteristic
345C2×C3×D5—21no—
346C2×C3×D5—21no—
347C2×C3×D5—22no—
348C2×C3×D5—41no—
349C2×C3×D5—41no—
350C2×C3×D5C4×D412yes—
351C3×C4×C5—22no—
352C3×C4×C5—21no—
353C3×C4×C5—21no—
354C3×C4×C5—41no—
355C3×C4×C5—41no—
356C3×C4×C5C23×C411yescharacteristic
357C3×C4×C5C2×#4111yescharacteristic
358C3×Dic5—22no—
359C3×Dic5—21no—
360C3×Dic5—21no—
361C3×Dic5—41no—
362C3×Dic5—41no—
363C3×Dic5C4×D412yes—
364C3×#41—54no—
365C3×#41—54no—
366C3×#41—102no—
367C3×#41—102no—
368C2×C3×Q8—51no—
369C2×C3×Q8C22×D511yescharacteristic
370C2×C3×D4—51no—
371C2×C3×D4—101no—
372C2×C3×D4—101no—
373C2×C3×D4C22×D511yescharacteristic
374C22×C3×C4—21no—
375C22×C3×C4—51no—
376C22×C3×C4—101no—
377C22×C3×C4—101no—
378C22×C3×C4—101no—
379C22×C3×C4—101no—
380C22×C3×C4—101no—
381C22×C3×C4—101no—
382C22×C3×C4—101no—
383C3×Q16—54no—
384C3×SD16—54no—
385C3×SD16C4×D514yescomplemented
386C3×D8—54no—
387C3×M16—102no—
388C2×C3×C8—51no—
389C2×C3×C8—54no—
390C2×C3×C8—51no—
391C2×C3×C8C22×D511yescharacteristic
392C2×C3×C8C22×D511yescharacteristic
393C3×C4⋊C4—21no—
394C3×C4⋊C4—51no—
395C3×C4⋊C4—51no—
396C3×C4⋊C4—51no—
397C3×C4⋊C4—51no—
398C3×C4⋊C4—101no—
399C3×C4⋊C4—101no—
400C3×C4⋊C4—101no—
401C3×C4⋊C4—101no—
402C3×C4⋊C4—101no—
403C3×C4⋊C4C22×D511yescharacteristic
404C3×C4⋊C4C22×D511yescharacteristic
405C3×C22⋊C4—21no—
406C3×C22⋊C4—51no—
407C3×C22⋊C4—51no—
408C3×C22⋊C4—101no—
409C3×C22⋊C4—101no—
410C3×C22⋊C4—101no—
411C3×C42—21no—
412C3×C42—51no—
413C3×C42—101no—
414C3×C42—101no—
415C3×C42—101no—
416C3×C42C22×D511yescharacteristic
417C23×C5—21no—
418C22×D5—21no—
419C22×D5C2×C3×D411yescharacteristic
420C5×Q8—21no—
421C5×Q8C22×C3×C412yes—
422C5×D4—21no—
423C5×D4C22×C3×C412yes—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—21no—
427C2×C4×C5—81no—
428C2×C4×C5C2×C3×D411yescharacteristic
429C2×C4×C5C2×C3×D411yescharacteristic
430C2×C4×C5C24×C311yescharacteristic
431C22⋊D5—24no—
432C2×Dic5—21no—
433C2×Dic5—24no—
434C2×Dic5—21no—
435C2×Dic5—21no—
436C2×Dic5—81no—
437C2×Dic5C2×C3×D411yescharacteristic
438C2×Dic5C2×C3×D411yescharacteristic
439C2×Dic5C2×C3×D411yescharacteristic
440D20—24no—
441D20—21no—
442D20C22×C3×C412yes—
443C4×D5—24no—
444C4×D5—81no—
445C4×D5—81no—
446C4×D5—81no—
447C4×D5—81no—
448C4×D5C22×C3×C412yes—
449C4×D5C3×#4112yes—
450Dic10—21no—
451Dic10C22×C3×C412yes—
452C5×C8—21no—
453C5×C8C22×C3×C412yes—
454#168—21no—
455#168C22×C3×C412yes—
456C2×#41—51no—
457C2×#41—51no—
458#135—58no—
459C2×Q16—51no—
460C2×SD16—51no—
461C2×SD16C2×C3×D511yescharacteristic
462C2×D8—51no—
463C2×M16—51no—
464C22×C8—51no—
465C4×Q8—51no—
466C4×Q8—51no—
467C4×Q8—51no—
468C4×Q8C2×C3×D511yescharacteristic
469C4×D4—51no—
470C4×D4—51no—
471C4×D4—51no—
472C4×D4—101no—
473C4×D4—101no—
474C4×D4—101no—
475C4×D4—101no—
476C4×D4C2×C3×D511yescharacteristic
477#117—51no—
478#117—101no—
479#117—101no—
480C2×C4⋊C4—51no—
481C2×C4⋊C4—51no—
482C2×C4⋊C4—101no—
483C2×C4⋊C4—101no—
484#107—51no—
485#107—51no—
486#107—51no—
487#107C2×C3×D511yescharacteristic
488#103—51no—
489#103—51no—
490#103—51no—
491#103C2×C3×D511yescharacteristic
492#102—51no—
493#102—51no—
494#102—51no—
495#102C2×C3×D511yescharacteristic
496#97—51no—
497#97C2×C3×D511yescharacteristic
498C4×C8—51no—
499C4×C8—51no—
500C2×C3×C5—42no—
501C2×C3×C5C2×C4×D411yescharacteristic
502C2×C3×C5#57611yescharacteristic
503C2×C3×C5#57811yescharacteristic
504C3×D5—22no—
505C3×D5—42no—
506C23×C3—21no—
507C23×C3—51no—
508C23×C3—101no—
509C3×Q8—21no—
510C3×Q8—52no—
511C3×Q8—101no—
512C3×Q8C2×C4×D512yes—
513C3×D4—21no—
514C3×D4—52no—
515C3×D4—104no—
516C3×D4—104no—
517C3×D4—101no—
518C3×D4C2×C4×D512yes—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—51no—
523C2×C3×C4—52no—
524C2×C3×C4—52no—
525C2×C3×C4—51no—
526C2×C3×C4—51no—
527C2×C3×C4—81no—
528C2×C3×C4—104no—
529C2×C3×C4—104no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—401no—
534C2×C3×C4—401no—
535C2×C3×C4—401no—
536C2×C3×C4—401no—
537C2×C3×C4—401no—
538C2×C3×C4D4×D511yescharacteristic
539C2×C3×C4D4×D511yescharacteristic
540C2×C3×C4C23×D511yescharacteristic
541C3×C8—21no—
542C3×C8—52no—
543C3×C8—101no—
544C3×C8C2×C4×D512yes—
545C22×C5—22no—
546C22×C5—41no—
547C22×C5—41no—
548C22×C5C22×C3×D411yescharacteristic
549C2×D5—21no—
550C2×D5—21no—
551C2×D5—22no—
552C2×D5—41no—
553C2×D5—41no—
554C2×D5C3×C4×D412yes—
555C4×C5—21no—
556C4×C5—21no—
557C4×C5—22no—
558C4×C5—41no—
559C4×C5—41no—
560C4×C5C23×C3×C411yescharacteristic
561C4×C5C2×C3×#4111yescharacteristic
562Dic5—21no—
563Dic5—21no—
564Dic5—22no—
565Dic5—41no—
566Dic5—41no—
567Dic5C3×C4×D412yes—
568#41—54no—
569#41—54no—
570#41—102no—
571#41—102no—
572C2×Q8—51no—
573C2×Q8C22×C3×D511yescharacteristic
574C2×D4—51no—
575C2×D4—101no—
576C2×D4—101no—
577C2×D4C22×C3×D511yescharacteristic
578C22×C4—21no—
579C22×C4—51no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587Q16—54no—
588SD16—54no—
589SD16C3×C4×D514yescomplemented
590D8—54no—
591M16—102no—
592C2×C8—51no—
593C2×C8—54no—
594C2×C8—51no—
595C2×C8C22×C3×D511yescharacteristic
596C2×C8C22×C3×D511yescharacteristic
597C4⋊C4—21no—
598C4⋊C4—51no—
599C4⋊C4—51no—
600C4⋊C4—51no—
601C4⋊C4—51no—
602C4⋊C4—101no—
603C4⋊C4—101no—
604C4⋊C4—101no—
605C4⋊C4—101no—
606C4⋊C4—101no—
607C4⋊C4C22×C3×D511yescharacteristic
608C4⋊C4C22×C3×D511yescharacteristic
609C22⋊C4—21no—
610C22⋊C4—51no—
611C22⋊C4—51no—
612C22⋊C4—101no—
613C22⋊C4—101no—
614C22⋊C4—101no—
615C42—21no—
616C42—51no—
617C42—101no—
618C42—101no—
619C42—101no—
620C42C22×C3×D511yescharacteristic
621C3×C5#295111yescharacteristic, complemented, Hall
622C22×C3—22no—
623C22×C3—41no—
624C22×C3—41no—
625C22×C3—52no—
626C22×C3—101no—
627C22×C3—101no—
628C22×C3—102no—
629C22×C3—201no—
630C22×C3—201no—
631C22×C3C2×D4×D511yescharacteristic
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—22no—
635C3×C4—41no—
636C3×C4—41no—
637C3×C4—52no—
638C3×C4—101no—
639C3×C4—101no—
640C3×C4—102no—
641C3×C4—201no—
642C3×C4—201no—
643C3×C4C22×C4×D511yescharacteristic
644C3×C4D5×#4111yescharacteristic
645C2×C5—42no—
646C2×C5C2×C3×C4×D411yescharacteristic
647C2×C5C3×#57611yescharacteristic
648C2×C5C3×#57811yescharacteristic
649D5—22no—
650D5—42no—
651C23—21no—
652C23—51no—
653C23—101no—
654Q8—21no—
655Q8—52no—
656Q8—101no—
657Q8C2×C3×C4×D512yes—
658D4—21no—
659D4—52no—
660D4—104no—
661D4—104no—
662D4—101no—
663D4C2×C3×C4×D512yes—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—51no—
668C2×C4—52no—
669C2×C4—52no—
670C2×C4—51no—
671C2×C4—51no—
672C2×C4—81no—
673C2×C4—104no—
674C2×C4—104no—
675C2×C4—101no—
676C2×C4—101no—
677C2×C4—101no—
678C2×C4—401no—
679C2×C4—401no—
680C2×C4—401no—
681C2×C4—401no—
682C2×C4—401no—
683C2×C4C3×D4×D511yescharacteristic
684C2×C4C3×D4×D511yescharacteristic
685C2×C4C23×C3×D511yescharacteristic
686C8—21no—
687C8—52no—
688C8—101no—
689C8C2×C3×C4×D512yes—
690C2×C3—42no—
691C2×C3—102no—
692C2×C3—202no—
693C2×C3C4×D4×D511yescharacteristic
694C2×C3#6610811yescharacteristic
695C2×C3#6611311yescharacteristic
696C5C3×#295111yescharacteristic, complemented, Sylow
697C22—22no—
698C22—41no—
699C22—41no—
700C22—52no—
701C22—101no—
702C22—101no—
703C22—102no—
704C22—201no—
705C22—201no—
706C22C2×C3×D4×D511yescharacteristic
707C4—21no—
708C4—21no—
709C4—22no—
710C4—41no—
711C4—41no—
712C4—52no—
713C4—101no—
714C4—101no—
715C4—102no—
716C4—201no—
717C4—201no—
718C4C22×C3×C4×D511yescharacteristic
719C4C3×D5×#4111yescharacteristic
720C3#1061150911yescharacteristic, direct product factor, Sylow
721C2—42no—
722C2—102no—
723C2—202no—
724C2C3×C4×D4×D511yescharacteristic
725C2C3×#6610811yescharacteristic
726C2C3×#6611311yescharacteristic
subgroupG/H
centerC22×C3C2×D4×D5
commutatorC4×C5C23×C3×C4
FrattiniC2×C4C23×C3×D5
FittingC3×C5×#440C2
socleC22×C3×C5C22×D4
prime radicalC2×C3×#4062C2
cosocleC2×C4×C5C24×C3
hypercenterC3×#440D5
hypocenterC5C3×#2951
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C3 ◁ C3×C42 ◁ C3×#440

Complements

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

NH ≅ G/Ntype
2. C3×#65908C2semidirect
3. C3×#65880C2semidirect
4. C3×C5×#440C2semidirect
5. C3×#65453C2semidirect
6. C3×C4×#689C2semidirect
7. C3×C4×#686C2semidirect
8. C3×#65178C2semidirect
9. C3×D5×#107C2semidirect
10. C3×#65092C2semidirect
11. C3×#65079C2semidirect
12. C3×#65060C2semidirect
13. C3×#65045C2semidirect
14. C3×#64999C2semidirect
15. C3×#64997C2semidirect
16. #10611509C3direct (N × H)
28. C3×#4062C4semidirect
63. #65908C2×C3semidirect
64. #65880C2×C3semidirect
65. C5×#440C2×C3semidirect
66. #65453C2×C3semidirect
67. C4×#689C2×C3semidirect
68. C4×#686C2×C3semidirect
69. #65178C2×C3semidirect
70. D5×#107C2×C3semidirect
71. #65092C2×C3semidirect
72. #65079C2×C3semidirect
73. #65060C2×C3semidirect
74. #65045C2×C3semidirect
75. #64999C2×C3semidirect
76. #64997C2×C3semidirect
84. C3×#713C2×C4semidirect
86. C3×#711C2×C4semidirect
96. C3×C5×SD16C2×C4semidirect
106. C3×#689C2×C4semidirect
107. C3×#686C2×C4semidirect
127. C3×#677C2×C4semidirect
129. C3×C8×D5C2×C4semidirect
136. C3×#440D5semidirect
156. #4062C3×C4semidirect
280. #713C2×C3×C4semidirect
282. #711C2×C3×C4semidirect
292. C5×SD16C2×C3×C4semidirect
302. #689C2×C3×C4semidirect
303. #686C2×C3×C4semidirect
323. #677C2×C3×C4semidirect
325. C8×D5C2×C3×C4semidirect
332. #440C3×D5semidirect
385. C3×SD16C4×D5semidirect
589. SD16C3×C4×D5semidirect
621. C3×C5#2951semidirect
696. C5C3×#2951semidirect
720. C3#10611509direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#40622
C3×#659082
C3×#658802
C3×C5×#4402
C3×#654532
C3×C4×#6892
C3×C4×#6862
C3×#651782
C3×D5×#1072
C3×#650922
C3×#650792
C3×#650602
C3×#650452
C3×#649992
C3×#649972
#106115093
C3×#29515