Finite Group Databasebeta

← C3×#10600211 #14280209

Subgroups — C3×#10600211 #14280209

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#95C211yesmaximal, characteristic
2C2×C3×#3963C211yesmaximal, characteristic
3C2×C3×#3963C211yesmaximal, characteristic
4C2×C3×#3963C211yesmaximal, characteristic
5C2×C3×#3963C211yesmaximal, characteristic
6C2×C3×#3963C211yesmaximal, characteristic
7C2×C3×#3963C211yesmaximal, characteristic
8#10600211C311yesmaximal, 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
16C3×C5×#95—22no—
17C3×#3963—22no—
18C3×#3963—22no—
19C3×#3963—22no—
20C3×#3963—22no—
21C3×#3963—22no—
22C3×#3963C414yescomplemented
23C3×#1443—51nomaximal, Hall
24C2×C5×#95C2×C311yescharacteristic
25C2×#3963C2×C311yescharacteristic
26C2×#3963C2×C311yescharacteristic
27C2×#3963C2×C311yescharacteristic
28C2×#3963C2×C311yescharacteristic
29C2×#3963C2×C311yescharacteristic
30C2×#3963C2×C311yescharacteristic
31C24×C3×C5C2311yescharacteristic
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
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×C5C2×C412yes—
51C22×C3×C4×C5D412yes—
52C22×C3×C4×C5D412yes—
53C22×C3×Dic5—21no—
54C22×C3×Dic5—21no—
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×Dic5Q812yes—
81C2×C3×#95—51no—
82C2×C3×#95—51no—
83C2×C3×#95—51no—
84C2×C3×#95—51no—
85C2×C3×#95—51no—
86C2×C3×#95—51no—
87C2×C3×#95D511yescharacteristic
88C23×C4×C5C22×C311yescharacteristic
89C23×C4×C5C22×C311yescharacteristic
90C23×C4×C5C22×C311yescharacteristic
91C23×Dic5C22×C311yescharacteristic
92C23×Dic5C22×C311yescharacteristic
93C23×Dic5C22×C311yescharacteristic
94C23×Dic5C22×C311yescharacteristic
95C5×#95—22no—
96#3963—22no—
97#3963—22no—
98#3963—22no—
99#3963—22no—
100#3963—22no—
101#3963C3×C414yescomplemented
102#1443—51noSylow
103C23×C3×C5C22×C411yescharacteristic
104C23×C3×C5C2×D411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×Q811yescharacteristic
108C23×C3×C5#4111yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C23×C3×C5#4111yescharacteristic
112C23×C3×C5#4111yescharacteristic
113C23×C3×C5#4111yescharacteristic
114C23×C3×C5#4111yescharacteristic
115C23×C3×C5#4111yescharacteristic
116C23×C3×C5#4111yescharacteristic
117C23×C3×C5#4111yescharacteristic
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—41no—
128C2×C3×C4×C5—41no—
129C2×C3×C4×C5—41no—
130C2×C3×C4×C5—41no—
131C2×C3×C4×C5—41no—
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×Dic5—22no—
140C2×C3×Dic5—22no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
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—41no—
152C2×C3×Dic5—41no—
153C2×C3×Dic5—41no—
154C2×C3×Dic5—41no—
155C2×C3×Dic5—41no—
156C2×C3×Dic5—41no—
157C2×C3×Dic5—41no—
158C2×C3×Dic5—41no—
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—
167C23×C3×C4—51no—
168C23×C3×C4—51no—
169C23×C3×C4—51no—
170C23×C3×C4—51no—
171C23×C3×C4C2×D511yescharacteristic
172C23×C3×C4C2×D511yescharacteristic
173C23×C3×C4C2×D511yescharacteristic
174C3×#95—22no—
175C3×#95—54no—
176C3×#95—102no—
177C3×#95—102no—
178C3×#95—102no—
179C3×#95—102no—
180C3×#95—102no—
181C24×C5C23×C311yescharacteristic
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
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×C5C2×C3×C412yes—
201C22×C4×C5C3×D412yes—
202C22×C4×C5C3×D412yes—
203C22×Dic5—21no—
204C22×Dic5—21no—
205C22×Dic5—21no—
206C22×Dic5—21no—
207C22×Dic5—21no—
208C22×Dic5—21no—
209C22×Dic5—21no—
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×Dic5C2×C3×C412yes—
228C22×Dic5C2×C3×C412yes—
229C22×Dic5C3×D412yes—
230C22×Dic5C3×Q812yes—
231C2×#95—51no—
232C2×#95—51no—
233C2×#95—51no—
234C2×#95—51no—
235C2×#95—51no—
236C2×#95—51no—
237C2×#95C3×D511yescharacteristic
238C22×C3×C5#11711yescharacteristic
239C22×C3×C5#11711yescharacteristic
240C22×C3×C5#11711yescharacteristic
241C22×C3×C5C4×D411yescharacteristic
242C22×C3×C5C4×D411yescharacteristic
243C22×C3×C5C4×D411yescharacteristic
244C22×C3×C5C4×Q811yescharacteristic
245C22×C3×C5#12111yescharacteristic
246C22×C3×C5#12111yescharacteristic
247C22×C3×C5#12111yescharacteristic
248C22×C3×C5C22⋊Q811yescharacteristic
249C22×C3×C5C22⋊Q811yescharacteristic
250C22×C3×C5C22⋊Q811yescharacteristic
251C22×C3×C5#12311yescharacteristic
252C22×C3×C5#12311yescharacteristic
253C22×C3×C5#12311yescharacteristic
254C22×C3×C5#12311yescharacteristic
255C22×C3×C5#12311yescharacteristic
256C22×C3×C5#12311yescharacteristic
257C22×C3×C5#12411yescharacteristic
258C22×C3×C5#12411yescharacteristic
259C22×C3×C5#12411yescharacteristic
260C22×C3×C5#12511yescharacteristic
261C22×C3×C5#12511yescharacteristic
262C22×C3×C5#12511yescharacteristic
263C22×C3×C5#12611yescharacteristic
264C22×C3×C5#12611yescharacteristic
265C22×C3×C5#12611yescharacteristic
266C22×C3×C5#12611yescharacteristic
267C22×C3×C5#12611yescharacteristic
268C22×C3×C5#12611yescharacteristic
269C22×C3×C5#12611yescharacteristic
270C22×C3×C5#12611yescharacteristic
271C22×C3×C5#12611yescharacteristic
272C22×C3×C5#12611yescharacteristic
273C3×C4×C5—42no—
274C3×C4×C5—42no—
275C3×C4×C5—42no—
276C3×Dic5—42no—
277C3×Dic5—42no—
278C3×Dic5—42no—
279C3×Dic5—42no—
280C24×C3C22×D511yescharacteristic
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
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—52no—
300C22×C3×C4—52no—
301C22×C3×C4—52no—
302C22×C3×C4—52no—
303C22×C3×C4—101no—
304C22×C3×C4—101no—
305C22×C3×C4—101no—
306C22×C3×C4—101no—
307C22×C3×C4—101no—
308C22×C3×C4—101no—
309C22×C3×C4—101no—
310C22×C3×C4—101no—
311C22×C3×C4—101no—
312C22×C3×C4—101no—
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×C4C4×D512yes—
328C22×C3×C4D2012yes—
329C22×C3×C4C22⋊D512yes—
330C23×C5C22×C3×C411yescharacteristic
331C23×C5C2×C3×D411yescharacteristic
332C23×C5C2×C3×D411yescharacteristic
333C23×C5C2×C3×D411yescharacteristic
334C23×C5C2×C3×Q811yescharacteristic
335C23×C5C3×#4111yescharacteristic
336C23×C5C3×#4111yescharacteristic
337C23×C5C3×#4111yescharacteristic
338C23×C5C3×#4111yescharacteristic
339C23×C5C3×#4111yescharacteristic
340C23×C5C3×#4111yescharacteristic
341C23×C5C3×#4111yescharacteristic
342C23×C5C3×#4111yescharacteristic
343C23×C5C3×#4111yescharacteristic
344C23×C5C3×#4111yescharacteristic
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—22no—
369C2×Dic5—22no—
370C2×Dic5—22no—
371C2×Dic5—22no—
372C2×Dic5—22no—
373C2×Dic5—22no—
374C2×Dic5—22no—
375C2×Dic5—22no—
376C2×Dic5—22no—
377C2×Dic5—22no—
378C2×Dic5—41no—
379C2×Dic5—41no—
380C2×Dic5—41no—
381C2×Dic5—41no—
382C2×Dic5—41no—
383C2×Dic5—41no—
384C2×Dic5—41no—
385C2×Dic5—41no—
386C2×Dic5—41no—
387C2×Dic5—41no—
388C2×Dic5—41no—
389C2×Dic5—41no—
390C2×Dic5—41no—
391C2×Dic5—41no—
392C2×Dic5—41no—
393C2×Dic5—41no—
394C23×C4—51no—
395C23×C4—51no—
396C23×C4—51no—
397C23×C4—51no—
398C23×C4C2×C3×D511yescharacteristic
399C23×C4C2×C3×D511yescharacteristic
400C23×C4C2×C3×D511yescharacteristic
401#95—22no—
402#95—54no—
403#95—102no—
404#95—102no—
405#95—102no—
406#95—102no—
407#95—102no—
408C2×C3×C5#38311yescharacteristic
409C2×C3×C5#38711yescharacteristic
410C2×C3×C5#38711yescharacteristic
411C2×C3×C5#38711yescharacteristic
412C2×C3×C5#38811yescharacteristic
413C2×C3×C5#38811yescharacteristic
414C2×C3×C5#38811yescharacteristic
415C2×C3×C5#39611yescharacteristic
416C2×C3×C5#39711yescharacteristic
417C2×C3×C5#39711yescharacteristic
418C2×C3×C5#39711yescharacteristic
419C2×C3×C5#40011yescharacteristic
420C2×C3×C5#40011yescharacteristic
421C2×C3×C5#40011yescharacteristic
422C2×C3×C5#40111yescharacteristic
423C23×C3C2×C4×D511yescharacteristic
424C23×C3C2×D2011yescharacteristic
425C23×C3#70911yescharacteristic
426C23×C3#70911yescharacteristic
427C23×C3#70911yescharacteristic
428C23×C3#70911yescharacteristic
429C23×C3D4×D511yescharacteristic
430C23×C3#71111yescharacteristic
431C23×C3#71111yescharacteristic
432C23×C3#71111yescharacteristic
433C23×C3#71111yescharacteristic
434C23×C3#71111yescharacteristic
435C23×C3Q8×D511yescharacteristic
436C23×C3#71311yescharacteristic
437C23×C3C2×C22⋊D511yescharacteristic
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—102no—
460C2×C3×C4—102no—
461C2×C3×C4—102no—
462C2×C3×C4—102no—
463C2×C3×C4—102no—
464C2×C3×C4—102no—
465C2×C3×C4—102no—
466C2×C3×C4—102no—
467C2×C3×C4—102no—
468C2×C3×C4—102no—
469C2×C3×C4—102no—
470C2×C3×C4—102no—
471C2×C3×C4—201no—
472C2×C3×C4—201no—
473C2×C3×C4—201no—
474C2×C3×C4—201no—
475C2×C3×C4—201no—
476C2×C3×C4—201no—
477C2×C3×C4—201no—
478C2×C3×C4—201no—
479C2×C3×C4—201no—
480C2×C3×C4—201no—
481C2×C3×C4—201no—
482C2×C3×C4—201no—
483C2×C3×C4—201no—
484C2×C3×C4—201no—
485C2×C3×C4—201no—
486C2×C3×C4—201no—
487C22×C5C3×#11711yescharacteristic
488C22×C5C3×#11711yescharacteristic
489C22×C5C3×#11711yescharacteristic
490C22×C5C3×C4×D411yescharacteristic
491C22×C5C3×C4×D411yescharacteristic
492C22×C5C3×C4×D411yescharacteristic
493C22×C5C3×C4×Q811yescharacteristic
494C22×C5C3×#12111yescharacteristic
495C22×C5C3×#12111yescharacteristic
496C22×C5C3×#12111yescharacteristic
497C22×C5C3×C22⋊Q811yescharacteristic
498C22×C5C3×C22⋊Q811yescharacteristic
499C22×C5C3×C22⋊Q811yescharacteristic
500C22×C5C3×#12311yescharacteristic
501C22×C5C3×#12311yescharacteristic
502C22×C5C3×#12311yescharacteristic
503C22×C5C3×#12311yescharacteristic
504C22×C5C3×#12311yescharacteristic
505C22×C5C3×#12311yescharacteristic
506C22×C5C3×#12411yescharacteristic
507C22×C5C3×#12411yescharacteristic
508C22×C5C3×#12411yescharacteristic
509C22×C5C3×#12511yescharacteristic
510C22×C5C3×#12511yescharacteristic
511C22×C5C3×#12511yescharacteristic
512C22×C5C3×#12611yescharacteristic
513C22×C5C3×#12611yescharacteristic
514C22×C5C3×#12611yescharacteristic
515C22×C5C3×#12611yescharacteristic
516C22×C5C3×#12611yescharacteristic
517C22×C5C3×#12611yescharacteristic
518C22×C5C3×#12611yescharacteristic
519C22×C5C3×#12611yescharacteristic
520C22×C5C3×#12611yescharacteristic
521C22×C5C3×#12611yescharacteristic
522C4×C5—42no—
523C4×C5—42no—
524C4×C5—42no—
525Dic5—42no—
526Dic5—42no—
527Dic5—42no—
528Dic5—42no—
529C24C22×C3×D511yescharacteristic
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—52no—
549C22×C4—52no—
550C22×C4—52no—
551C22×C4—52no—
552C22×C4—101no—
553C22×C4—101no—
554C22×C4—101no—
555C22×C4—101no—
556C22×C4—101no—
557C22×C4—101no—
558C22×C4—101no—
559C22×C4—101no—
560C22×C4—101no—
561C22×C4—101no—
562C22×C4—101no—
563C22×C4—101no—
564C22×C4—101no—
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×C4C3×C4×D512yes—
577C22×C4C3×D2012yes—
578C22×C4C3×C22⋊D512yes—
579C3×C5#144311yescharacteristic, complemented, Hall
580C22×C3#401811yescharacteristic
581C22×C3C4×D2011yescharacteristic
582C22×C3#402111yescharacteristic
583C22×C3#402211yescharacteristic
584C22×C3#402311yescharacteristic
585C22×C3#402511yescharacteristic
586C22×C3#402511yescharacteristic
587C22×C3#402511yescharacteristic
588C22×C3#402511yescharacteristic
589C22×C3#402511yescharacteristic
590C22×C3#402711yescharacteristic
591C22×C3#402911yescharacteristic
592C22×C3#402911yescharacteristic
593C22×C3#403111yescharacteristic
594C22×C3#403211yescharacteristic
595C22×C3#403211yescharacteristic
596C22×C3#403311yescharacteristic
597C22×C3#403511yescharacteristic
598C22×C3#403511yescharacteristic
599C22×C3#403511yescharacteristic
600C22×C3#403811yescharacteristic
601C22×C3#404111yescharacteristic
602C22×C3#404211yescharacteristic
603C22×C3#404311yescharacteristic
604C22×C3#404411yescharacteristic
605C22×C3#404411yescharacteristic
606C22×C3#404411yescharacteristic
607C22×C3#404411yescharacteristic
608C22×C3C4×C22⋊D511yescharacteristic
609C22×C3#407511yescharacteristic
610C22×C3#407611yescharacteristic
611C22×C3#408111yescharacteristic
612C22×C3#408211yescharacteristic
613C22×C3#408511yescharacteristic
614C22×C3#409211yescharacteristic
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—42no—
618C3×C4—202no—
619C3×C4—202no—
620C3×C4—202no—
621C3×C4—202no—
622C2×C5C3×#38311yescharacteristic
623C2×C5C3×#38711yescharacteristic
624C2×C5C3×#38711yescharacteristic
625C2×C5C3×#38711yescharacteristic
626C2×C5C3×#38811yescharacteristic
627C2×C5C3×#38811yescharacteristic
628C2×C5C3×#38811yescharacteristic
629C2×C5C3×#39611yescharacteristic
630C2×C5C3×#39711yescharacteristic
631C2×C5C3×#39711yescharacteristic
632C2×C5C3×#39711yescharacteristic
633C2×C5C3×#40011yescharacteristic
634C2×C5C3×#40011yescharacteristic
635C2×C5C3×#40011yescharacteristic
636C2×C5C3×#40111yescharacteristic
637C23C2×C3×C4×D511yescharacteristic
638C23C2×C3×D2011yescharacteristic
639C23C3×#70911yescharacteristic
640C23C3×#70911yescharacteristic
641C23C3×#70911yescharacteristic
642C23C3×#70911yescharacteristic
643C23C3×D4×D511yescharacteristic
644C23C3×#71111yescharacteristic
645C23C3×#71111yescharacteristic
646C23C3×#71111yescharacteristic
647C23C3×#71111yescharacteristic
648C23C3×#71111yescharacteristic
649C23C3×Q8×D511yescharacteristic
650C23C3×#71311yescharacteristic
651C23C2×C3×C22⋊D511yescharacteristic
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—102no—
674C2×C4—102no—
675C2×C4—102no—
676C2×C4—102no—
677C2×C4—102no—
678C2×C4—102no—
679C2×C4—102no—
680C2×C4—102no—
681C2×C4—102no—
682C2×C4—102no—
683C2×C4—102no—
684C2×C4—102no—
685C2×C4—201no—
686C2×C4—201no—
687C2×C4—201no—
688C2×C4—201no—
689C2×C4—201no—
690C2×C4—201no—
691C2×C4—201no—
692C2×C4—201no—
693C2×C4—201no—
694C2×C4—201no—
695C2×C4—201no—
696C2×C4—201no—
697C2×C4—201no—
698C2×C4—201no—
699C2×C4—201no—
700C2×C4—201no—
701C2×C3#6494011yescharacteristic
702C2×C3#6494111yescharacteristic
703C2×C3#6494211yescharacteristic
704C2×C3#6494711yescharacteristic
705C2×C3#6494811yescharacteristic
706C2×C3C5⋊#40111yescharacteristic
707C2×C3#6495911yescharacteristic
708C2×C3#6496311yescharacteristic
709C2×C3#6522911yescharacteristic
710C2×C3#6523411yescharacteristic
711C2×C3#6524111yescharacteristic
712C2×C3#6524211yescharacteristic
713C2×C3#6526711yescharacteristic
714C2×C3#6527111yescharacteristic
715C2×C3#6528311yescharacteristic
716C5C3×#144311yescharacteristic, complemented, Sylow
717C22C3×#401811yescharacteristic
718C22C3×C4×D2011yescharacteristic
719C22C3×#402111yescharacteristic
720C22C3×#402211yescharacteristic
721C22C3×#402311yescharacteristic
722C22C3×#402511yescharacteristic
723C22C3×#402511yescharacteristic
724C22C3×#402511yescharacteristic
725C22C3×#402511yescharacteristic
726C22C3×#402511yescharacteristic
727C22C3×#402711yescharacteristic
728C22C3×#402911yescharacteristic
729C22C3×#402911yescharacteristic
730C22C3×#403111yescharacteristic
731C22C3×#403211yescharacteristic
732C22C3×#403211yescharacteristic
733C22C3×#403311yescharacteristic
734C22C3×#403511yescharacteristic
735C22C3×#403511yescharacteristic
736C22C3×#403511yescharacteristic
737C22C3×#403811yescharacteristic
738C22C3×#404111yescharacteristic
739C22C3×#404211yescharacteristic
740C22C3×#404311yescharacteristic
741C22C3×#404411yescharacteristic
742C22C3×#404411yescharacteristic
743C22C3×#404411yescharacteristic
744C22C3×#404411yescharacteristic
745C22C3×C4×C22⋊D511yescharacteristic
746C22C3×#407511yescharacteristic
747C22C3×#407611yescharacteristic
748C22C3×#408111yescharacteristic
749C22C3×#408211yescharacteristic
750C22C3×#408511yescharacteristic
751C22C3×#409211yescharacteristic
752C4—42no—
753C4—42no—
754C4—42no—
755C4—202no—
756C4—202no—
757C4—202no—
758C4—202no—
759C3#1060021111yescharacteristic, direct product factor, Sylow
760C2C3×#6494011yescharacteristic
761C2C3×#6494111yescharacteristic
762C2C3×#6494211yescharacteristic
763C2C3×#6494711yescharacteristic
764C2C3×#6494811yescharacteristic
765C2C3×C5⋊#40111yescharacteristic
766C2C3×#6495911yescharacteristic
767C2C3×#6496311yescharacteristic
768C2C3×#6522911yescharacteristic
769C2C3×#6523411yescharacteristic
770C2C3×#6524111yescharacteristic
771C2C3×#6524211yescharacteristic
772C2C3×#6526711yescharacteristic
773C2C3×#6527111yescharacteristic
774C2C3×#6528311yescharacteristic
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×#1443
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. #10600211C3direct (N × H)
22. C3×#3963C4semidirect
101. #3963C3×C4semidirect
579. C3×C5#1443semidirect
716. C5C3×#1443semidirect
759. C3#10600211direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×#952
C2×C3×#39632
#106002113
C3×#14435