Finite Group Databasebeta

← C3×#10605734 #14322508

Subgroups — C3×#10605734 #14322508

Order 1920.

1760 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic
2C2×C3×#4038C211yesmaximal, characteristic, complemented
3C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
4C3×C5×#380C211yesmaximal, characteristic, complemented
5C3×#65501C211yesmaximal, characteristic, complemented
6C3×#65276C211yesmaximal, characteristic, complemented
7C3×#65276C211yesmaximal, characteristic, complemented
8C3×#65246C212yesmaximal, complemented
9C3×#65245C212yesmaximal, complemented
10C3×#64954C212yesmaximal, complemented
11C3×#64935C212yesmaximal, complemented
12#10605734C311yesmaximal, characteristic, direct product factor, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5C2211yescharacteristic
15C22×C3×C22⋊D5C2211yescharacteristic
16C2×C3×#709—24no—
17C2×C3×#709—24no—
18C2×C3×#709C418yescomplemented
19C22×C3×D20C2211yescharacteristic
20C22×C3×C4×D5C2211yescharacteristic
21C22×C3×C4×D5C2212yes—
22C22×C3×C4×D5C2211yescharacteristic
23C22×C3×Dic10C2211yescharacteristic
24C2×C3×C5×C4⋊C4C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C3×C5×C22⋊C4C2212yes—
27C2×C3×C22⋊Dic5C2212yes—
28C2×C3×#685C2212yes—
29C2×C3×#685C2212yes—
30C2×C3×#685C2212yes—
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4⋊Dic5C2211yescharacteristic
33C2×C3×#683C2212yes—
34C2×C3×C4×Dic5C2212yes—
35C3×#4038—24no—
36C3×D5×C4⋊C4—24no—
37C3×C5×#95C2212yes—
38C3×#3963C2212yes—
39C3×#3963C2212yes—
40C3×#3963C2212yes—
41C3×#2311—51nomaximal, Hall
42C22×#709C2×C311yescharacteristic
43C2×#4038C2×C311yescharacteristic, complemented
44C2×D5×C4⋊C4C2×C311yescharacteristic, complemented
45C5×#380C2×C311yescharacteristic, complemented
46#65501C2×C311yescharacteristic, complemented
47#65276C2×C311yescharacteristic, complemented
48#65276C2×C311yescharacteristic, complemented
49#65246C2×C312yescomplemented
50#65245C2×C312yescomplemented
51#64954C2×C312yescomplemented
52#64935C2×C312yescomplemented
53C24×C3×C5C2311yescharacteristic
54C23×C3×D5C2311yescharacteristic
55C23×C3×D5C2311yescharacteristic
56C22×C3×C4×C5—22no—
57C22×C3×C4×C5—22no—
58C22×C3×C4×C5C2×C414yescomplemented
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2312yes—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C2×C3×C22⋊D5—22no—
64C2×C3×C22⋊D5—22no—
65C2×C3×C22⋊D5—22no—
66C2×C3×C22⋊D5—22no—
67C2×C3×C22⋊D5C2×C414yes—
68C2×C3×C22⋊D5C2×C414yescomplemented
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2312yes—
71C22×C3×Dic5C2311yescharacteristic
72C22×C3×Dic5C2311yescharacteristic
73C3×#709—232no—
74C2×C3×D20—22no—
75C2×C3×D20—22no—
76C2×C3×D20C2×C414yes—
77C2×C3×C4×D5—22no—
78C2×C3×C4×D5—22no—
79C2×C3×C4×D5—24no—
80C2×C3×C4×D5—42no—
81C2×C3×C4×D5—42no—
82C2×C3×C4×D5C2×C414yes—
83C2×C3×C4×D5C2×C414yescomplemented
84C2×C3×C4×D5D414yes—
85C2×C3×C4×D5D414yes—
86C2×C3×Dic10—22no—
87C2×C3×Dic10—22no—
88C2×C3×Dic10C2×C414yescomplemented
89C3×C5×C4⋊C4—22no—
90C3×C5×C4⋊C4—22no—
91C3×C5×C22⋊C4—42no—
92C3×C22⋊Dic5—42no—
93C3×#685—24no—
94C3×#685—42no—
95C3×#685—42no—
96C3×C4⋊Dic5—22no—
97C3×C4⋊Dic5—22no—
98C3×#683—24no—
99C3×C4×Dic5—24no—
100C22×C3×#41—51no—
101C2×C3×#117—51no—
102C22×C3×C4⋊C4—51no—
103C3×#391—52no—
104C3×#390—52no—
105C3×#386—52no—
106C3×#386—52no—
107C3×#380—51no—
108C3×#380—51no—
109C3×#380—51no—
110C3×#380D511yescharacteristic, complemented
111C23×C4×C5C22×C311yescharacteristic
112C22×C22⋊D5C22×C311yescharacteristic
113C22×C22⋊D5C22×C311yescharacteristic
114C2×#709—24no—
115C2×#709—24no—
116C2×#709C3×C418yescomplemented
117C22×D20C22×C311yescharacteristic
118C22×C4×D5C22×C311yescharacteristic
119C22×C4×D5C22×C312yes—
120C22×C4×D5C22×C311yescharacteristic
121C22×Dic10C22×C311yescharacteristic
122C2×C5×C4⋊C4C22×C311yescharacteristic
123C2×C5×C4⋊C4C22×C311yescharacteristic
124C2×C5×C22⋊C4C22×C312yes—
125C2×C22⋊Dic5C22×C312yes—
126C2×#685C22×C312yes—
127C2×#685C22×C312yes—
128C2×#685C22×C312yes—
129C2×C4⋊Dic5C22×C311yescharacteristic
130C2×C4⋊Dic5C22×C311yescharacteristic
131C2×#683C22×C312yes—
132C2×C4×Dic5C22×C312yes—
133#4038—24no—
134D5×C4⋊C4—24no—
135C5×#95C22×C312yes—
136#3963C22×C312yes—
137#3963C22×C312yes—
138#3963C22×C312yes—
139#2311—51noSylow
140C23×C3×C5—21no—
141C23×C3×C5—21no—
142C23×C3×C5—21no—
143C23×C3×C5—21no—
144C23×C3×C5—21no—
145C23×C3×C5—21no—
146C23×C3×C5C22×C412yes—
147C23×C3×C5C2411yescharacteristic
148C22×C3×D5—21no—
149C22×C3×D5—21no—
150C22×C3×D5—21no—
151C22×C3×D5—21no—
152C22×C3×D5—21no—
153C22×C3×D5—21no—
154C22×C3×D5—21no—
155C22×C3×D5—21no—
156C22×C3×D5—21no—
157C22×C3×D5—21no—
158C22×C3×D5C22×C412yes—
159C22×C3×D5C22×C412yes—
160C22×C3×D5C2×D412yes—
161C22×C3×D5C2×D412yes—
162C2×C3×C4×C5—21no—
163C2×C3×C4×C5—21no—
164C2×C3×C4×C5—28no—
165C2×C3×C4×C5—22no—
166C2×C3×C4×C5—22no—
167C2×C3×C4×C5—22no—
168C2×C3×C4×C5—22no—
169C2×C3×C4×C5—22no—
170C2×C3×C4×C5—22no—
171C2×C3×C4×C5C22×C412yes—
172C2×C3×C4×C5C22×C412yes—
173C2×C3×C4×C5C2×D412yes—
174C2×C3×C4×C5C2×D412yes—
175C3×C22⋊D5—28no—
176C3×C22⋊D5—28no—
177C2×C3×Dic5—21no—
178C2×C3×Dic5—21no—
179C2×C3×Dic5—22no—
180C2×C3×Dic5—22no—
181C2×C3×Dic5—22no—
182C2×C3×Dic5—22no—
183C2×C3×Dic5—22no—
184C2×C3×Dic5—22no—
185C2×C3×Dic5C22×C412yes—
186C2×C3×Dic5C22×C412yes—
187C2×C3×Dic5C2×D412yes—
188C2×C3×Dic5C2×D412yes—
189C3×D20—28no—
190C3×C4×D5—28no—
191C3×C4×D5—48no—
192C3×C4×D5C22⋊C4116yescomplemented
193C3×Dic10—28no—
194C2×C3×#41—58no—
195C2×C3×#41—104no—
196C2×C3×#41—104no—
197C22×C3×Q8—51no—
198C22×C3×D4—51no—
199C22×C3×D4—51no—
200C22×C3×D4—51no—
201C23×C3×C4—51no—
202C23×C3×C4—51no—
203C23×C3×C4—52no—
204C23×C3×C4C2×D511yescharacteristic
205C3×#117—104no—
206C2×C3×C4⋊C4—51no—
207C2×C3×C4⋊C4—51no—
208C2×C3×C4⋊C4—52no—
209C2×C3×C4⋊C4—104no—
210C2×C3×C4⋊C4C2×D511yescharacteristic
211C2×C3×C4⋊C4C2×D511yescharacteristic
212C2×C3×C22⋊C4—52no—
213C2×C3×C22⋊C4—52no—
214C2×C3×C22⋊C4—52no—
215C2×C3×C22⋊C4—52no—
216C2×C3×C22⋊C4C2×D512yes—
217C2×C3×C42—52no—
218C3×#95—52no—
219C3×#95—52no—
220C3×#95—52no—
221C3×#95C2×D512yes—
222C24×C5C23×C311yescharacteristic
223C23×D5C23×C311yescharacteristic
224C23×D5C23×C311yescharacteristic
225C22×C4×C5—22no—
226C22×C4×C5—22no—
227C22×C4×C5C2×C3×C414yescomplemented
228C22×C4×C5C23×C312yes—
229C22×C4×C5C23×C312yes—
230C22×C4×C5C23×C311yescharacteristic
231C22×C4×C5C23×C311yescharacteristic
232C2×C22⋊D5—22no—
233C2×C22⋊D5—22no—
234C2×C22⋊D5—22no—
235C2×C22⋊D5—22no—
236C2×C22⋊D5C2×C3×C414yes—
237C2×C22⋊D5C2×C3×C414yescomplemented
238C22×Dic5C23×C312yes—
239C22×Dic5C23×C312yes—
240C22×Dic5C23×C311yescharacteristic
241C22×Dic5C23×C311yescharacteristic
242#709—232no—
243C2×D20—22no—
244C2×D20—22no—
245C2×D20C2×C3×C414yes—
246C2×C4×D5—22no—
247C2×C4×D5—22no—
248C2×C4×D5—24no—
249C2×C4×D5—42no—
250C2×C4×D5—42no—
251C2×C4×D5C2×C3×C414yes—
252C2×C4×D5C2×C3×C414yescomplemented
253C2×C4×D5C3×D414yes—
254C2×C4×D5C3×D414yes—
255C2×Dic10—22no—
256C2×Dic10—22no—
257C2×Dic10C2×C3×C414yescomplemented
258C5×C4⋊C4—22no—
259C5×C4⋊C4—22no—
260C5×C22⋊C4—42no—
261C22⋊Dic5—42no—
262#685—24no—
263#685—42no—
264#685—42no—
265C4⋊Dic5—22no—
266C4⋊Dic5—22no—
267#683—24no—
268C4×Dic5—24no—
269C22×#41—51no—
270C2×#117—51no—
271C22×C4⋊C4—51no—
272#391—52no—
273#390—52no—
274#386—52no—
275#386—52no—
276#380—51no—
277#380—51no—
278#380—51no—
279#380C3×D511yescharacteristic, complemented
280C22×C3×C5—22no—
281C22×C3×C5—22no—
282C22×C3×C5—22no—
283C22×C3×C5—41no—
284C22×C3×C5—41no—
285C22×C3×C5—41no—
286C22×C3×C5—41no—
287C22×C3×C5C23×C411yescharacteristic
288C22×C3×C5C22×D411yescharacteristic
289C22×C3×C5C22×D411yescharacteristic
290C22×C3×C5H(5,𝔽2)11yescharacteristic
291C22×C3×C5H(5,𝔽2)11yescharacteristic
292C22×C3×C52−1+411yescharacteristic
293C22×C3×C52−1+411yescharacteristic
294C2×C3×D5—22no—
295C2×C3×D5—22no—
296C2×C3×D5—22no—
297C2×C3×D5—22no—
298C2×C3×D5—22no—
299C2×C3×D5—22no—
300C2×C3×D5—22no—
301C2×C3×D5—22no—
302C2×C3×D5—22no—
303C2×C3×D5—41no—
304C2×C3×D5—41no—
305C2×C3×D5—41no—
306C2×C3×D5—41no—
307C2×C3×D5C2×C22⋊C414yes—
308C3×C4×C5—22no—
309C3×C4×C5—42no—
310C3×C4×C5—42no—
311C3×C4×C5C2×C22⋊C414yes—
312C3×Dic5—22no—
313C3×Dic5—42no—
314C3×Dic5—42no—
315C3×Dic5C2×C22⋊C414yes—
316C24×C3—51no—
317C24×C3—51no—
318C24×C3C22×D511yescharacteristic
319C3×#41—1032no—
320C2×C3×Q8—54no—
321C2×C3×Q8—102no—
322C2×C3×Q8—102no—
323C2×C3×D4—54no—
324C2×C3×D4—54no—
325C2×C3×D4—54no—
326C2×C3×D4—102no—
327C2×C3×D4—102no—
328C2×C3×D4—102no—
329C2×C3×D4—102no—
330C2×C3×D4—102no—
331C2×C3×D4—102no—
332C22×C3×C4—22no—
333C22×C3×C4—22no—
334C22×C3×C4—51no—
335C22×C3×C4—54no—
336C22×C3×C4—54no—
337C22×C3×C4—54no—
338C22×C3×C4—51no—
339C22×C3×C4—54no—
340C22×C3×C4—52no—
341C22×C3×C4—52no—
342C22×C3×C4—104no—
343C22×C3×C4—102no—
344C22×C3×C4—102no—
345C22×C3×C4—202no—
346C22×C3×C4—202no—
347C22×C3×C4C4×D514yescomplemented
348C22×C3×C4C22×D512yes—
349C22×C3×C4C22×D512yes—
350C22×C3×C4C22×D511yescharacteristic
351C22×C3×C4C22×D511yescharacteristic
352C3×C4⋊C4—22no—
353C3×C4⋊C4—22no—
354C3×C4⋊C4—104no—
355C3×C4⋊C4—102no—
356C3×C4⋊C4—102no—
357C3×C22⋊C4—42no—
358C3×C22⋊C4—104no—
359C3×C22⋊C4—202no—
360C3×C22⋊C4—202no—
361C3×C22⋊C4—202no—
362C3×C42—104no—
363C23×C5—21no—
364C23×C5—21no—
365C23×C5—21no—
366C23×C5—21no—
367C23×C5—21no—
368C23×C5—21no—
369C23×C5C22×C3×C412yes—
370C23×C5C24×C311yescharacteristic
371C22×D5—21no—
372C22×D5—21no—
373C22×D5—21no—
374C22×D5—21no—
375C22×D5—21no—
376C22×D5—21no—
377C22×D5—21no—
378C22×D5—21no—
379C22×D5—21no—
380C22×D5—21no—
381C22×D5C22×C3×C412yes—
382C22×D5C22×C3×C412yes—
383C22×D5C2×C3×D412yes—
384C22×D5C2×C3×D412yes—
385C2×C4×C5—21no—
386C2×C4×C5—21no—
387C2×C4×C5—28no—
388C2×C4×C5—22no—
389C2×C4×C5—22no—
390C2×C4×C5—22no—
391C2×C4×C5—22no—
392C2×C4×C5—22no—
393C2×C4×C5—22no—
394C2×C4×C5C22×C3×C412yes—
395C2×C4×C5C22×C3×C412yes—
396C2×C4×C5C2×C3×D412yes—
397C2×C4×C5C2×C3×D412yes—
398C22⋊D5—28no—
399C22⋊D5—28no—
400C2×Dic5—21no—
401C2×Dic5—21no—
402C2×Dic5—22no—
403C2×Dic5—22no—
404C2×Dic5—22no—
405C2×Dic5—22no—
406C2×Dic5—22no—
407C2×Dic5—22no—
408C2×Dic5C22×C3×C412yes—
409C2×Dic5C22×C3×C412yes—
410C2×Dic5C2×C3×D412yes—
411C2×Dic5C2×C3×D412yes—
412D20—28no—
413C4×D5—28no—
414C4×D5—48no—
415C4×D5C3×C22⋊C4116yescomplemented
416Dic10—28no—
417C2×#41—58no—
418C2×#41—104no—
419C2×#41—104no—
420C22×Q8—51no—
421C22×D4—51no—
422C22×D4—51no—
423C22×D4—51no—
424C23×C4—51no—
425C23×C4—51no—
426C23×C4—52no—
427C23×C4C2×C3×D511yescharacteristic
428#117—104no—
429C2×C4⋊C4—51no—
430C2×C4⋊C4—52no—
431C2×C4⋊C4—51no—
432C2×C4⋊C4—104no—
433C2×C4⋊C4C2×C3×D511yescharacteristic
434C2×C4⋊C4C2×C3×D511yescharacteristic
435C2×C22⋊C4—52no—
436C2×C22⋊C4—52no—
437C2×C22⋊C4—52no—
438C2×C22⋊C4—52no—
439C2×C22⋊C4C2×C3×D512yes—
440C2×C42—52no—
441#95—52no—
442#95—52no—
443#95—52no—
444#95C2×C3×D512yes—
445C2×C3×C5—42no—
446C2×C3×C5C22×C22⋊C411yescharacteristic
447C2×C3×C5#52011yescharacteristic
448C2×C3×C5#52011yescharacteristic
449C2×C3×C5#53511yescharacteristic
450C2×C3×C5#53611yescharacteristic
451C2×C3×C5#53711yescharacteristic
452C2×C3×C5#53711yescharacteristic
453C3×D5—24no—
454C3×D5—42no—
455C23×C3—21no—
456C23×C3—21no—
457C23×C3—21no—
458C23×C3—21no—
459C23×C3—21no—
460C23×C3—21no—
461C23×C3—52no—
462C23×C3—52no—
463C23×C3—52no—
464C23×C3—52no—
465C23×C3—101no—
466C23×C3—101no—
467C23×C3—101no—
468C23×C3—101no—
469C23×C3—101no—
470C23×C3—101no—
471C23×C3—101no—
472C23×C3—101no—
473C23×C3—101no—
474C23×C3—101no—
475C23×C3C2×C4×D512yes—
476C23×C3C23×D511yescharacteristic
477C3×Q8—108no—
478C3×D4—108no—
479C3×D4—108no—
480C3×D4—108no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—28no—
484C2×C3×C4—22no—
485C2×C3×C4—22no—
486C2×C3×C4—22no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—22no—
490C2×C3×C4—52no—
491C2×C3×C4—52no—
492C2×C3×C4—52no—
493C2×C3×C4—516no—
494C2×C3×C4—52no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4—108no—
498C2×C3×C4—102no—
499C2×C3×C4—102no—
500C2×C3×C4—102no—
501C2×C3×C4—102no—
502C2×C3×C4—102no—
503C2×C3×C4—102no—
504C2×C3×C4—208no—
505C2×C3×C4C2×C4×D512yes—
506C2×C3×C4C2×C4×D512yes—
507C2×C3×C4D4×D512yes—
508C2×C3×C4D4×D512yes—
509C22×C5—22no—
510C22×C5—22no—
511C22×C5—22no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—41no—
515C22×C5—41no—
516C22×C5C23×C3×C411yescharacteristic
517C22×C5C22×C3×D411yescharacteristic
518C22×C5C22×C3×D411yescharacteristic
519C22×C5C3×H(5,𝔽2)11yescharacteristic
520C22×C5C3×H(5,𝔽2)11yescharacteristic
521C22×C5C3×2−1+411yescharacteristic
522C22×C5C3×2−1+411yescharacteristic
523C2×D5—22no—
524C2×D5—22no—
525C2×D5—22no—
526C2×D5—22no—
527C2×D5—22no—
528C2×D5—22no—
529C2×D5—22no—
530C2×D5—22no—
531C2×D5—22no—
532C2×D5—41no—
533C2×D5—41no—
534C2×D5—41no—
535C2×D5—41no—
536C2×D5C2×C3×C22⋊C414yes—
537C4×C5—22no—
538C4×C5—42no—
539C4×C5—42no—
540C4×C5C2×C3×C22⋊C414yes—
541Dic5—22no—
542Dic5—42no—
543Dic5—42no—
544Dic5C2×C3×C22⋊C414yes—
545C24—51no—
546C24—51no—
547C24C22×C3×D511yescharacteristic
548#41—1032no—
549C2×Q8—54no—
550C2×Q8—102no—
551C2×Q8—102no—
552C2×D4—54no—
553C2×D4—54no—
554C2×D4—54no—
555C2×D4—102no—
556C2×D4—102no—
557C2×D4—102no—
558C2×D4—102no—
559C2×D4—102no—
560C2×D4—102no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—51no—
564C22×C4—54no—
565C22×C4—54no—
566C22×C4—54no—
567C22×C4—51no—
568C22×C4—54no—
569C22×C4—52no—
570C22×C4—52no—
571C22×C4—104no—
572C22×C4—102no—
573C22×C4—102no—
574C22×C4—202no—
575C22×C4—202no—
576C22×C4C3×C4×D514yescomplemented
577C22×C4C22×C3×D512yes—
578C22×C4C22×C3×D512yes—
579C22×C4C22×C3×D511yescharacteristic
580C22×C4C22×C3×D511yescharacteristic
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—104no—
584C4⋊C4—102no—
585C4⋊C4—102no—
586C22⋊C4—42no—
587C22⋊C4—104no—
588C22⋊C4—202no—
589C22⋊C4—202no—
590C22⋊C4—202no—
591C42—104no—
592C3×C5#231111yescharacteristic, complemented, Hall
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—41no—
597C22×C3—41no—
598C22×C3—41no—
599C22×C3—41no—
600C22×C3—54no—
601C22×C3—102no—
602C22×C3—102no—
603C22×C3—102no—
604C22×C3—102no—
605C22×C3—102no—
606C22×C3—102no—
607C22×C3—102no—
608C22×C3—102no—
609C22×C3—102no—
610C22×C3—201no—
611C22×C3—201no—
612C22×C3—201no—
613C22×C3—201no—
614C22×C3C22×C4×D511yescharacteristic
615C22×C3C2×D4×D511yescharacteristic
616C22×C3C2×D4×D511yescharacteristic
617C22×C3#414411yescharacteristic
618C22×C3#414711yescharacteristic
619C22×C3#414911yescharacteristic
620C22×C3#415011yescharacteristic
621C3×C4—22no—
622C3×C4—42no—
623C3×C4—42no—
624C3×C4—54no—
625C3×C4—102no—
626C3×C4—202no—
627C3×C4—202no—
628C3×C4D5×C22⋊C414yes—
629C2×C5—42no—
630C2×C5C22×C3×C22⋊C411yescharacteristic
631C2×C5C3×#52011yescharacteristic
632C2×C5C3×#52011yescharacteristic
633C2×C5C3×#53511yescharacteristic
634C2×C5C3×#53611yescharacteristic
635C2×C5C3×#53711yescharacteristic
636C2×C5C3×#53711yescharacteristic
637D5—24no—
638D5—42no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—52no—
646C23—52no—
647C23—52no—
648C23—52no—
649C23—101no—
650C23—101no—
651C23—101no—
652C23—101no—
653C23—101no—
654C23—101no—
655C23—101no—
656C23—101no—
657C23—101no—
658C23—101no—
659C23C2×C3×C4×D512yes—
660C23C23×C3×D511yescharacteristic
661Q8—108no—
662D4—108no—
663D4—108no—
664D4—108no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—28no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—52no—
675C2×C4—52no—
676C2×C4—52no—
677C2×C4—516no—
678C2×C4—52no—
679C2×C4—101no—
680C2×C4—101no—
681C2×C4—108no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—208no—
689C2×C4C2×C3×C4×D512yes—
690C2×C4C2×C3×C4×D512yes—
691C2×C4C3×D4×D512yes—
692C2×C4C3×D4×D512yes—
693C2×C3—42no—
694C2×C3—104no—
695C2×C3—202no—
696C2×C3C2×D5×C22⋊C411yescharacteristic
697C2×C3#6583811yescharacteristic
698C2×C3#6585711yescharacteristic
699C2×C3#6594111yescharacteristic
700C2×C3#6594211yescharacteristic
701C2×C3#6596211yescharacteristic
702C2×C3#6596311yescharacteristic
703C5C3×#231111yescharacteristic, complemented, Sylow
704C22—22no—
705C22—22no—
706C22—22no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—54no—
712C22—102no—
713C22—102no—
714C22—102no—
715C22—102no—
716C22—102no—
717C22—102no—
718C22—102no—
719C22—102no—
720C22—102no—
721C22—201no—
722C22—201no—
723C22—201no—
724C22—201no—
725C22C22×C3×C4×D511yescharacteristic
726C22C2×C3×D4×D511yescharacteristic
727C22C2×C3×D4×D511yescharacteristic
728C22C3×#414411yescharacteristic
729C22C3×#414711yescharacteristic
730C22C3×#414911yescharacteristic
731C22C3×#415011yescharacteristic
732C4—22no—
733C4—42no—
734C4—42no—
735C4—54no—
736C4—102no—
737C4—202no—
738C4—202no—
739C4C3×D5×C22⋊C414yes—
740C3#1060573411yescharacteristic, direct product factor, Sylow
741C2—42no—
742C2—104no—
743C2—202no—
744C2C2×C3×D5×C22⋊C411yescharacteristic
745C2C3×#6583811yescharacteristic
746C2C3×#6585711yescharacteristic
747C2C3×#6594111yescharacteristic
748C2C3×#6594211yescharacteristic
749C2C3×#6596211yescharacteristic
750C2C3×#6596311yescharacteristic
subgroupG/H
centerC23×C3C23×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC3×C5×#380C2
socleC23×C3×C5C24
prime radicalC22×C3×#709C2
cosocleC23×C5C24×C3
hypercenterC3×#380D5
hypocenterC5C3×#2311
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C3×#380

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4038C2semidirect
3. C2×C3×D5×C4⋊C4C2semidirect
4. C3×C5×#380C2semidirect
5. C3×#65501C2semidirect
6. C3×#65276C2semidirect
7. C3×#65276C2semidirect
8. C3×#65246C2semidirect
9. C3×#65245C2semidirect
10. C3×#64954C2semidirect
11. C3×#64935C2semidirect
12. #10605734C3direct (N × H)
18. C2×C3×#709C4semidirect
43. C2×#4038C2×C3semidirect
44. C2×D5×C4⋊C4C2×C3semidirect
45. C5×#380C2×C3semidirect
46. #65501C2×C3semidirect
47. #65276C2×C3semidirect
48. #65276C2×C3semidirect
49. #65246C2×C3semidirect
50. #65245C2×C3semidirect
51. #64954C2×C3semidirect
52. #64935C2×C3semidirect
58. C22×C3×C4×C5C2×C4semidirect
68. C2×C3×C22⋊D5C2×C4semidirect
83. C2×C3×C4×D5C2×C4semidirect
88. C2×C3×Dic10C2×C4semidirect
110. C3×#380D5semidirect
116. C2×#709C3×C4semidirect
192. C3×C4×D5C22⋊C4semidirect
227. C22×C4×C5C2×C3×C4semidirect
237. C2×C22⋊D5C2×C3×C4semidirect
252. C2×C4×D5C2×C3×C4semidirect
257. C2×Dic10C2×C3×C4semidirect
279. #380C3×D5semidirect
347. C22×C3×C4C4×D5semidirect
415. C4×D5C3×C22⋊C4semidirect
576. C22×C4C3×C4×D5semidirect
592. C3×C5#2311semidirect
703. C5C3×#2311semidirect
740. C3#10605734direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×C3×#40382
C2×C3×D5×C4⋊C42
C3×C5×#3802
C3×#655012
C3×#652762
C3×#652462
C3×#652452
C3×#649542
C3×#649352
#106057343
C3×#23115