Finite Group Databasebeta

← C3×#10600214 #14280259

Subgroups — C3×#10600214 #14280259

Order 1920.

1040 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#683C211yesmaximal, characteristic
2C2×C3×C5×#95C211yesmaximal, characteristic
3C2×C3×#3963C211yesmaximal, characteristic
4C2×C3×#3963C211yesmaximal, characteristic
5C2×C3×#3963C211yesmaximal, characteristic
6C2×C3×#3963C211yesmaximal, characteristic
7C2×C3×#3963C211yesmaximal, characteristic
8#10600214C311yesmaximal, characteristic, direct product factor, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×Dic5C2211yescharacteristic
13C23×C3×Dic5C2211yescharacteristic
14C23×C3×Dic5C2211yescharacteristic
15C23×C3×Dic5C2211yescharacteristic
16C2×C3×#683—22no—
17C2×C3×#683—22no—
18C2×C3×#683C414yescomplemented
19C3×C5×#95—22no—
20C3×#3963—22no—
21C3×#3963—22no—
22C3×#3963—22no—
23C3×#3963—22no—
24C3×#3963—22no—
25C3×#1445—51nomaximal, Hall
26C22×#683C2×C311yescharacteristic
27C2×C5×#95C2×C311yescharacteristic
28C2×#3963C2×C311yescharacteristic
29C2×#3963C2×C311yescharacteristic
30C2×#3963C2×C311yescharacteristic
31C2×#3963C2×C311yescharacteristic
32C2×#3963C2×C311yescharacteristic
33C24×C3×C5C2311yescharacteristic
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5—21no—
52C22×C3×C4×C5C2×C412yes—
53C22×C3×C4×C5D412yes—
54C22×C3×C4×C5Q812yes—
55C22×C3×Dic5—21no—
56C22×C3×Dic5—21no—
57C22×C3×Dic5—21no—
58C22×C3×Dic5—21no—
59C22×C3×Dic5—21no—
60C22×C3×Dic5—21no—
61C22×C3×Dic5—21no—
62C22×C3×Dic5—21no—
63C22×C3×Dic5—21no—
64C22×C3×Dic5—21no—
65C22×C3×Dic5—21no—
66C22×C3×Dic5—21no—
67C22×C3×Dic5—21no—
68C22×C3×Dic5—21no—
69C22×C3×Dic5—21no—
70C22×C3×Dic5—21no—
71C22×C3×Dic5—21no—
72C22×C3×Dic5—21no—
73C22×C3×Dic5—21no—
74C22×C3×Dic5—21no—
75C22×C3×Dic5—21no—
76C22×C3×Dic5—21no—
77C22×C3×Dic5C2×C412yes—
78C22×C3×Dic5C2×C412yes—
79C22×C3×Dic5D412yes—
80C22×C3×Dic5D412yes—
81C22×C3×Dic5D412yes—
82C22×C3×Dic5Q812yes—
83C3×#683—28no—
84C22×C3×C4⋊C4—51no—
85C2×C3×#95—51no—
86C2×C3×#95—51no—
87C2×C3×#95—51no—
88C2×C3×#95—51no—
89C2×C3×#95—51no—
90C2×C3×#95D511yescharacteristic
91C23×C4×C5C22×C311yescharacteristic
92C23×C4×C5C22×C311yescharacteristic
93C23×C4×C5C22×C311yescharacteristic
94C23×Dic5C22×C311yescharacteristic
95C23×Dic5C22×C311yescharacteristic
96C23×Dic5C22×C311yescharacteristic
97C23×Dic5C22×C311yescharacteristic
98C2×#683—22no—
99C2×#683—22no—
100C2×#683C3×C414yescomplemented
101C5×#95—22no—
102#3963—22no—
103#3963—22no—
104#3963—22no—
105#3963—22no—
106#3963—22no—
107#1445—51noSylow
108C23×C3×C5C22×C411yescharacteristic
109C23×C3×C5C2×D411yescharacteristic
110C23×C3×C5C2×D411yescharacteristic
111C23×C3×C5C2×D411yescharacteristic
112C23×C3×C5C2×D411yescharacteristic
113C23×C3×C5C2×Q811yescharacteristic
114C23×C3×C5C2×Q811yescharacteristic
115C23×C3×C5#4111yescharacteristic
116C23×C3×C5#4111yescharacteristic
117C23×C3×C5#4111yescharacteristic
118C23×C3×C5#4111yescharacteristic
119C23×C3×C5#4111yescharacteristic
120C23×C3×C5#4111yescharacteristic
121C23×C3×C5#4111yescharacteristic
122C23×C3×C5#4111yescharacteristic
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—22no—
130C2×C3×C4×C5—22no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5—41no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5—41no—
138C2×C3×C4×C5—41no—
139C2×C3×C4×C5—41no—
140C2×C3×C4×C5—41no—
141C2×C3×C4×C5—41no—
142C2×C3×C4×C5—41no—
143C2×C3×C4×C5—41no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—22no—
159C2×C3×Dic5—41no—
160C2×C3×Dic5—41no—
161C2×C3×Dic5—41no—
162C2×C3×Dic5—41no—
163C2×C3×Dic5—41no—
164C2×C3×Dic5—41no—
165C2×C3×Dic5—41no—
166C2×C3×Dic5—41no—
167C2×C3×Dic5—41no—
168C2×C3×Dic5—41no—
169C2×C3×Dic5—41no—
170C2×C3×Dic5—41no—
171C2×C3×Dic5C22⋊C414yes—
172C23×C3×C4—51no—
173C23×C3×C4—51no—
174C23×C3×C4—51no—
175C23×C3×C4—51no—
176C23×C3×C4C2×D511yescharacteristic
177C23×C3×C4C2×D511yescharacteristic
178C23×C3×C4C2×D511yescharacteristic
179C2×C3×C4⋊C4—54no—
180C2×C3×C4⋊C4—102no—
181C2×C3×C4⋊C4—102no—
182C3×#95—22no—
183C3×#95—102no—
184C3×#95—102no—
185C3×#95—102no—
186C3×#95—102no—
187C3×#95—102no—
188C24×C5C23×C311yescharacteristic
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—21no—
201C22×C4×C5—21no—
202C22×C4×C5—21no—
203C22×C4×C5—21no—
204C22×C4×C5—21no—
205C22×C4×C5—21no—
206C22×C4×C5—21no—
207C22×C4×C5C2×C3×C412yes—
208C22×C4×C5C3×D412yes—
209C22×C4×C5C3×Q812yes—
210C22×Dic5—21no—
211C22×Dic5—21no—
212C22×Dic5—21no—
213C22×Dic5—21no—
214C22×Dic5—21no—
215C22×Dic5—21no—
216C22×Dic5—21no—
217C22×Dic5—21no—
218C22×Dic5—21no—
219C22×Dic5—21no—
220C22×Dic5—21no—
221C22×Dic5—21no—
222C22×Dic5—21no—
223C22×Dic5—21no—
224C22×Dic5—21no—
225C22×Dic5—21no—
226C22×Dic5—21no—
227C22×Dic5—21no—
228C22×Dic5—21no—
229C22×Dic5—21no—
230C22×Dic5—21no—
231C22×Dic5—21no—
232C22×Dic5C2×C3×C412yes—
233C22×Dic5C2×C3×C412yes—
234C22×Dic5C3×D412yes—
235C22×Dic5C3×D412yes—
236C22×Dic5C3×D412yes—
237C22×Dic5C3×Q812yes—
238#683—28no—
239C22×C4⋊C4—51no—
240C2×#95—51no—
241C2×#95—51no—
242C2×#95—51no—
243C2×#95—51no—
244C2×#95—51no—
245C2×#95C3×D511yescharacteristic
246C22×C3×C5C2×C22⋊C411yescharacteristic
247C22×C3×C5#11711yescharacteristic
248C22×C3×C5#11711yescharacteristic
249C22×C3×C5C4×D411yescharacteristic
250C22×C3×C5C4×D411yescharacteristic
251C22×C3×C5C4×Q811yescharacteristic
252C22×C3×C5C4×Q811yescharacteristic
253C22×C3×C5#12111yescharacteristic
254C22×C3×C5#12111yescharacteristic
255C22×C3×C5C22⋊Q811yescharacteristic
256C22×C3×C5C22⋊Q811yescharacteristic
257C22×C3×C5C22⋊Q811yescharacteristic
258C22×C3×C5C22⋊Q811yescharacteristic
259C22×C3×C5C22⋊Q811yescharacteristic
260C22×C3×C5C22⋊Q811yescharacteristic
261C22×C3×C5#12311yescharacteristic
262C22×C3×C5#12311yescharacteristic
263C22×C3×C5#12311yescharacteristic
264C22×C3×C5#12311yescharacteristic
265C22×C3×C5#12311yescharacteristic
266C22×C3×C5#12311yescharacteristic
267C22×C3×C5#12311yescharacteristic
268C22×C3×C5#12311yescharacteristic
269C22×C3×C5#12411yescharacteristic
270C22×C3×C5#12411yescharacteristic
271C22×C3×C5#12511yescharacteristic
272C22×C3×C5#12511yescharacteristic
273C22×C3×C5#12511yescharacteristic
274C22×C3×C5#12511yescharacteristic
275C22×C3×C5#12611yescharacteristic
276C22×C3×C5#12611yescharacteristic
277C22×C3×C5#12611yescharacteristic
278C22×C3×C5#12611yescharacteristic
279C22×C3×C5#12711yescharacteristic
280C22×C3×C5C4⋊Q811yescharacteristic
281C3×C4×C5—42no—
282C3×C4×C5—42no—
283C3×C4×C5—42no—
284C3×Dic5—24no—
285C3×Dic5—42no—
286C3×Dic5—42no—
287C3×Dic5—42no—
288C24×C3C22×D511yescharacteristic
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4—21no—
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—21no—
304C22×C3×C4—21no—
305C22×C3×C4—21no—
306C22×C3×C4—21no—
307C22×C3×C4—52no—
308C22×C3×C4—52no—
309C22×C3×C4—52no—
310C22×C3×C4—52no—
311C22×C3×C4—52no—
312C22×C3×C4—52no—
313C22×C3×C4—101no—
314C22×C3×C4—101no—
315C22×C3×C4—101no—
316C22×C3×C4—101no—
317C22×C3×C4—101no—
318C22×C3×C4—101no—
319C22×C3×C4—101no—
320C22×C3×C4—101no—
321C22×C3×C4—101no—
322C22×C3×C4—101no—
323C22×C3×C4—101no—
324C22×C3×C4—101no—
325C22×C3×C4—101no—
326C22×C3×C4—101no—
327C22×C3×C4—101no—
328C22×C3×C4—101no—
329C22×C3×C4—101no—
330C22×C3×C4—101no—
331C22×C3×C4—101no—
332C22×C3×C4—101no—
333C22×C3×C4—101no—
334C22×C3×C4—101no—
335C22×C3×C4Dic1012yes—
336C22×C3×C4C4×D512yes—
337C22×C3×C4C22⋊D512yes—
338C3×C4⋊C4—108no—
339C23×C5C22×C3×C411yescharacteristic
340C23×C5C2×C3×D411yescharacteristic
341C23×C5C2×C3×D411yescharacteristic
342C23×C5C2×C3×D411yescharacteristic
343C23×C5C2×C3×D411yescharacteristic
344C23×C5C2×C3×Q811yescharacteristic
345C23×C5C2×C3×Q811yescharacteristic
346C23×C5C3×#4111yescharacteristic
347C23×C5C3×#4111yescharacteristic
348C23×C5C3×#4111yescharacteristic
349C23×C5C3×#4111yescharacteristic
350C23×C5C3×#4111yescharacteristic
351C23×C5C3×#4111yescharacteristic
352C23×C5C3×#4111yescharacteristic
353C23×C5C3×#4111yescharacteristic
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—22no—
357C2×C4×C5—22no—
358C2×C4×C5—22no—
359C2×C4×C5—22no—
360C2×C4×C5—22no—
361C2×C4×C5—22no—
362C2×C4×C5—22no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—41no—
367C2×C4×C5—41no—
368C2×C4×C5—41no—
369C2×C4×C5—41no—
370C2×C4×C5—41no—
371C2×C4×C5—41no—
372C2×C4×C5—41no—
373C2×C4×C5—41no—
374C2×C4×C5—41no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—22no—
379C2×Dic5—22no—
380C2×Dic5—22no—
381C2×Dic5—22no—
382C2×Dic5—22no—
383C2×Dic5—22no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—22no—
390C2×Dic5—41no—
391C2×Dic5—41no—
392C2×Dic5—41no—
393C2×Dic5—41no—
394C2×Dic5—41no—
395C2×Dic5—41no—
396C2×Dic5—41no—
397C2×Dic5—41no—
398C2×Dic5—41no—
399C2×Dic5—41no—
400C2×Dic5—41no—
401C2×Dic5—41no—
402C2×Dic5C3×C22⋊C414yes—
403C23×C4—51no—
404C23×C4—51no—
405C23×C4—51no—
406C23×C4—51no—
407C23×C4C2×C3×D511yescharacteristic
408C23×C4C2×C3×D511yescharacteristic
409C23×C4C2×C3×D511yescharacteristic
410C2×C4⋊C4—54no—
411C2×C4⋊C4—102no—
412C2×C4⋊C4—102no—
413#95—22no—
414#95—102no—
415#95—102no—
416#95—102no—
417#95—102no—
418#95—102no—
419C2×C3×C5#38111yescharacteristic
420C2×C3×C5#38711yescharacteristic
421C2×C3×C5#38711yescharacteristic
422C2×C3×C5#38711yescharacteristic
423C2×C3×C5#38711yescharacteristic
424C2×C3×C5#39011yescharacteristic
425C2×C3×C5#39111yescharacteristic
426C2×C3×C5#39711yescharacteristic
427C2×C3×C5#39711yescharacteristic
428C2×C3×C5#39811yescharacteristic
429C2×C3×C5#39811yescharacteristic
430C2×C3×C5#39911yescharacteristic
431C2×C3×C5#39911yescharacteristic
432C2×C3×C5#40011yescharacteristic
433C2×C3×C5#40011yescharacteristic
434C23×C3C2×Dic1011yescharacteristic
435C23×C3C2×C4×D511yescharacteristic
436C23×C3#70911yescharacteristic
437C23×C3#70911yescharacteristic
438C23×C3#70911yescharacteristic
439C23×C3#70911yescharacteristic
440C23×C3D4×D511yescharacteristic
441C23×C3D4×D511yescharacteristic
442C23×C3D4×D511yescharacteristic
443C23×C3#71111yescharacteristic
444C23×C3#71111yescharacteristic
445C23×C3#71111yescharacteristic
446C23×C3Q8×D511yescharacteristic
447C23×C3#71311yescharacteristic
448C23×C3C2×C22⋊D511yescharacteristic
449C2×C3×C4—22no—
450C2×C3×C4—22no—
451C2×C3×C4—22no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—22no—
455C2×C3×C4—22no—
456C2×C3×C4—22no—
457C2×C3×C4—22no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—41no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—41no—
464C2×C3×C4—41no—
465C2×C3×C4—41no—
466C2×C3×C4—41no—
467C2×C3×C4—41no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—54no—
471C2×C3×C4—102no—
472C2×C3×C4—102no—
473C2×C3×C4—102no—
474C2×C3×C4—102no—
475C2×C3×C4—102no—
476C2×C3×C4—102no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—102no—
480C2×C3×C4—102no—
481C2×C3×C4—102no—
482C2×C3×C4—102no—
483C2×C3×C4—102no—
484C2×C3×C4—102no—
485C2×C3×C4—102no—
486C2×C3×C4—201no—
487C2×C3×C4—201no—
488C2×C3×C4—201no—
489C2×C3×C4—201no—
490C2×C3×C4—201no—
491C2×C3×C4—201no—
492C2×C3×C4—201no—
493C2×C3×C4—201no—
494C2×C3×C4—201no—
495C2×C3×C4—201no—
496C2×C3×C4—201no—
497C2×C3×C4—201no—
498C22×C5C2×C3×C22⋊C411yescharacteristic
499C22×C5C3×#11711yescharacteristic
500C22×C5C3×#11711yescharacteristic
501C22×C5C3×C4×D411yescharacteristic
502C22×C5C3×C4×D411yescharacteristic
503C22×C5C3×C4×Q811yescharacteristic
504C22×C5C3×C4×Q811yescharacteristic
505C22×C5C3×#12111yescharacteristic
506C22×C5C3×#12111yescharacteristic
507C22×C5C3×C22⋊Q811yescharacteristic
508C22×C5C3×C22⋊Q811yescharacteristic
509C22×C5C3×C22⋊Q811yescharacteristic
510C22×C5C3×C22⋊Q811yescharacteristic
511C22×C5C3×C22⋊Q811yescharacteristic
512C22×C5C3×C22⋊Q811yescharacteristic
513C22×C5C3×#12311yescharacteristic
514C22×C5C3×#12311yescharacteristic
515C22×C5C3×#12311yescharacteristic
516C22×C5C3×#12311yescharacteristic
517C22×C5C3×#12311yescharacteristic
518C22×C5C3×#12311yescharacteristic
519C22×C5C3×#12311yescharacteristic
520C22×C5C3×#12311yescharacteristic
521C22×C5C3×#12411yescharacteristic
522C22×C5C3×#12411yescharacteristic
523C22×C5C3×#12511yescharacteristic
524C22×C5C3×#12511yescharacteristic
525C22×C5C3×#12511yescharacteristic
526C22×C5C3×#12511yescharacteristic
527C22×C5C3×#12611yescharacteristic
528C22×C5C3×#12611yescharacteristic
529C22×C5C3×#12611yescharacteristic
530C22×C5C3×#12611yescharacteristic
531C22×C5C3×#12711yescharacteristic
532C22×C5C3×C4⋊Q811yescharacteristic
533C4×C5—42no—
534C4×C5—42no—
535C4×C5—42no—
536Dic5—24no—
537Dic5—42no—
538Dic5—42no—
539Dic5—42no—
540C24C22×C3×D511yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—52no—
560C22×C4—52no—
561C22×C4—52no—
562C22×C4—52no—
563C22×C4—52no—
564C22×C4—52no—
565C22×C4—101no—
566C22×C4—101no—
567C22×C4—101no—
568C22×C4—101no—
569C22×C4—101no—
570C22×C4—101no—
571C22×C4—101no—
572C22×C4—101no—
573C22×C4—101no—
574C22×C4—101no—
575C22×C4—101no—
576C22×C4—101no—
577C22×C4—101no—
578C22×C4—101no—
579C22×C4—101no—
580C22×C4—101no—
581C22×C4—101no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—101no—
587C22×C4C3×Dic1012yes—
588C22×C4C3×C4×D512yes—
589C22×C4C3×C22⋊D512yes—
590C4⋊C4—108no—
591C3×C5#144511yescharacteristic, complemented, Hall
592C22×C3C4×Dic1011yescharacteristic
593C22×C3#401611yescharacteristic
594C22×C3#401811yescharacteristic
595C22×C3#402211yescharacteristic
596C22×C3#402411yescharacteristic
597C22×C3#402411yescharacteristic
598C22×C3#402511yescharacteristic
599C22×C3#402511yescharacteristic
600C22×C3D5×C22⋊C411yescharacteristic
601C22×C3#402711yescharacteristic
602C22×C3#402911yescharacteristic
603C22×C3#402911yescharacteristic
604C22×C3#402911yescharacteristic
605C22×C3#403011yescharacteristic
606C22×C3#403111yescharacteristic
607C22×C3#403111yescharacteristic
608C22×C3#403311yescharacteristic
609C22×C3#403411yescharacteristic
610C22×C3#403511yescharacteristic
611C22×C3#403511yescharacteristic
612C22×C3#403611yescharacteristic
613C22×C3#403811yescharacteristic
614C22×C3#404011yescharacteristic
615C22×C3#404011yescharacteristic
616C22×C3#404011yescharacteristic
617C22×C3#404211yescharacteristic
618C22×C3#404211yescharacteristic
619C22×C3#404411yescharacteristic
620C22×C3#407011yescharacteristic
621C22×C3C4×C22⋊D511yescharacteristic
622C22×C3#407511yescharacteristic
623C22×C3#408111yescharacteristic
624C22×C3#408511yescharacteristic
625C22×C3#408611yescharacteristic
626C22×C3#409211yescharacteristic
627C3×C4—42no—
628C3×C4—42no—
629C3×C4—42no—
630C3×C4—104no—
631C3×C4—202no—
632C3×C4—202no—
633C3×C4—202no—
634C2×C5C3×#38111yescharacteristic
635C2×C5C3×#38711yescharacteristic
636C2×C5C3×#38711yescharacteristic
637C2×C5C3×#38711yescharacteristic
638C2×C5C3×#38711yescharacteristic
639C2×C5C3×#39011yescharacteristic
640C2×C5C3×#39111yescharacteristic
641C2×C5C3×#39711yescharacteristic
642C2×C5C3×#39711yescharacteristic
643C2×C5C3×#39811yescharacteristic
644C2×C5C3×#39811yescharacteristic
645C2×C5C3×#39911yescharacteristic
646C2×C5C3×#39911yescharacteristic
647C2×C5C3×#40011yescharacteristic
648C2×C5C3×#40011yescharacteristic
649C23C2×C3×Dic1011yescharacteristic
650C23C2×C3×C4×D511yescharacteristic
651C23C3×#70911yescharacteristic
652C23C3×#70911yescharacteristic
653C23C3×#70911yescharacteristic
654C23C3×#70911yescharacteristic
655C23C3×D4×D511yescharacteristic
656C23C3×D4×D511yescharacteristic
657C23C3×D4×D511yescharacteristic
658C23C3×#71111yescharacteristic
659C23C3×#71111yescharacteristic
660C23C3×#71111yescharacteristic
661C23C3×Q8×D511yescharacteristic
662C23C3×#71311yescharacteristic
663C23C2×C3×C22⋊D511yescharacteristic
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—54no—
686C2×C4—102no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—102no—
692C2×C4—102no—
693C2×C4—102no—
694C2×C4—102no—
695C2×C4—102no—
696C2×C4—102no—
697C2×C4—102no—
698C2×C4—102no—
699C2×C4—102no—
700C2×C4—102no—
701C2×C4—201no—
702C2×C4—201no—
703C2×C4—201no—
704C2×C4—201no—
705C2×C4—201no—
706C2×C4—201no—
707C2×C4—201no—
708C2×C4—201no—
709C2×C4—201no—
710C2×C4—201no—
711C2×C4—201no—
712C2×C4—201no—
713C2×C3#6493511yescharacteristic
714C2×C3#6494111yescharacteristic
715C2×C3#6494411yescharacteristic
716C2×C3#6494611yescharacteristic
717C2×C3#6494711yescharacteristic
718C2×C3#6494911yescharacteristic
719C2×C3#6495311yescharacteristic
720C2×C3#6496411yescharacteristic
721C2×C3#6522211yescharacteristic
722C2×C3#6523811yescharacteristic
723C2×C3#6524111yescharacteristic
724C2×C3#6524611yescharacteristic
725C2×C3#6526711yescharacteristic
726C2×C3#6527311yescharacteristic
727C2×C3#6528111yescharacteristic
728C5C3×#144511yescharacteristic, complemented, Sylow
729C22C3×C4×Dic1011yescharacteristic
730C22C3×#401611yescharacteristic
731C22C3×#401811yescharacteristic
732C22C3×#402211yescharacteristic
733C22C3×#402411yescharacteristic
734C22C3×#402411yescharacteristic
735C22C3×#402511yescharacteristic
736C22C3×#402511yescharacteristic
737C22C3×D5×C22⋊C411yescharacteristic
738C22C3×#402711yescharacteristic
739C22C3×#402911yescharacteristic
740C22C3×#402911yescharacteristic
741C22C3×#402911yescharacteristic
742C22C3×#403011yescharacteristic
743C22C3×#403111yescharacteristic
744C22C3×#403111yescharacteristic
745C22C3×#403311yescharacteristic
746C22C3×#403411yescharacteristic
747C22C3×#403511yescharacteristic
748C22C3×#403511yescharacteristic
749C22C3×#403611yescharacteristic
750C22C3×#403811yescharacteristic
751C22C3×#404011yescharacteristic
752C22C3×#404011yescharacteristic
753C22C3×#404011yescharacteristic
754C22C3×#404211yescharacteristic
755C22C3×#404211yescharacteristic
756C22C3×#404411yescharacteristic
757C22C3×#407011yescharacteristic
758C22C3×C4×C22⋊D511yescharacteristic
759C22C3×#407511yescharacteristic
760C22C3×#408111yescharacteristic
761C22C3×#408511yescharacteristic
762C22C3×#408611yescharacteristic
763C22C3×#409211yescharacteristic
764C4—42no—
765C4—42no—
766C4—42no—
767C4—104no—
768C4—202no—
769C4—202no—
770C4—202no—
771C3#1060021411yescharacteristic, direct product factor, Sylow
772C2C3×#6493511yescharacteristic
773C2C3×#6494111yescharacteristic
774C2C3×#6494411yescharacteristic
775C2C3×#6494611yescharacteristic
776C2C3×#6494711yescharacteristic
777C2C3×#6494911yescharacteristic
778C2C3×#6495311yescharacteristic
779C2C3×#6496411yescharacteristic
780C2C3×#6522211yescharacteristic
781C2C3×#6523811yescharacteristic
782C2C3×#6524111yescharacteristic
783C2C3×#6524611yescharacteristic
784C2C3×#6526711yescharacteristic
785C2C3×#6527311yescharacteristic
786C2C3×#6528111yescharacteristic
subgroupG/H
centerC24×C3C22×D5
commutatorC23×C5C22×C3×C4
FrattiniC24C22×C3×D5
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
cosocleC24×C5C23×C3
hypercenterC2×C3×#95D5
hypocenterC5C3×#1445
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C2×C3×#95

Complements

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

NH ≅ G/Ntype
8. #10600214C3direct (N × H)
18. C2×C3×#683C4semidirect
100. C2×#683C3×C4semidirect
591. C3×C5#1445semidirect
728. C5C3×#1445semidirect
771. C3#10600214direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#6832
C2×C3×C5×#952
C2×C3×#39632
#106002143
C3×#14455