Finite Group Databasebeta

← #14327631

Subgroups — #14327631

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91441C211yesmaximal, characteristic
2#11751079C211yesmaximal, characteristic, complemented
3C5×#4987C211yesmaximal, characteristic, complemented
4C3×#65279C211yesmaximal, characteristic, complemented
5#11748911C211yesmaximal, characteristic
6#11748911C211yesmaximal, characteristic
7#11748886C211yesmaximal, characteristic, complemented
8#11748884C211yesmaximal, characteristic, complemented
9D3×#3963C211yesmaximal, characteristic, complemented
10Dic5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11#11748871C211yesmaximal, characteristic, complemented
12#11748771C211yesmaximal, characteristic, complemented
13#11748687C211yesmaximal, characteristic, complemented
14#11748646C211yesmaximal, characteristic, complemented
15#11748635C211yesmaximal, characteristic, complemented
16#10605615—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×#1201C2211yescharacteristic
19C22×D3×Dic5C2211yescharacteristic
20C22×D3×Dic5C2211yescharacteristic
21C22×D5×Dic3C2211yescharacteristic
22C2×C3×C5×C4⋊C4C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×C4×Dic15C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C5×C4⋊Dic3C2211yescharacteristic
28C2×C3×#685C2211yescharacteristic
29C2×C3×#685C2211yescharacteristic
30C2×C3×#685C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×(C2×D3)⋊Dic5C2211yescharacteristic
33C2×#6665C2211yescharacteristic
34C2×#6665C2211yescharacteristic
35C2×Dic3×Dic5C2211yescharacteristic
36C2×Dic3×Dic5C2211yescharacteristic
37C2×Dic3×Dic5C2211yescharacteristic
38#91441C418yescomplemented
39#91115C2211yescharacteristic
40#91115C2211yescharacteristic
41#91115C2211yescharacteristic
42#91115C2211yescharacteristic
43C5×C3⋊#95C2211yescharacteristic
44C5×C3⋊#95C2211yescharacteristic
45C3×#3963C2211yescharacteristic
46C3×#3963C2211yescharacteristic
47#90994C2211yescharacteristic
48#90994C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#75835—51nomaximal, Hall
54C2×C4×C22⋊D5—31no—
55C5×#380—31no—
56C2×#3963—31no—
57#65279—31no—
58#65279D311yescharacteristic, complemented
59#65267—31no—
60#65267—31no—
61#65247—31no—
62#65247—31no—
63C22⋊C4×Dic5—31no—
64C22⋊C4×Dic5—31no—
65#64955—31no—
66#64953—31no—
67#64940—31no—
68#64937—31no—
69C23×C5×D3C2311yescharacteristic
70C23×C3×D5C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×Dic15C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C22×C5×Dic3C2311yescharacteristic
81C2×C4×C5×D3—41no—
82C2×C4×C5×D3—41no—
83C2×C4×C5×D3C2×C414yes—
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×#1201—22no—
88C2×#1201—22no—
89C2×#1201C2×C414yes—
90C2×D3×Dic5—22no—
91C2×D3×Dic5—22no—
92C2×D3×Dic5—22no—
93C2×D3×Dic5—22no—
94C2×D3×Dic5—41no—
95C2×D3×Dic5—41no—
96C2×D5×Dic3—41no—
97C2×D5×Dic3—41no—
98C2×D5×Dic3C2×C414yescomplemented
99C3×C5×C4⋊C4—41no—
100#6712C2×C414yescomplemented
101C4×Dic15—41no—
102C5×(C2×D3)⋊C4—22no—
103C5×(C2×D3)⋊C4—22no—
104C5×C4⋊Dic3—41no—
105C3×#685—22no—
106C3×#685—41no—
107C3×#685C2×C414yescomplemented
108C3×C4×Dic5—22no—
109(C2×D3)⋊Dic5C2×C414yes—
110#6665—22no—
111#6665—41no—
112Dic3×Dic5—22no—
113Dic3×Dic5—41no—
114Dic3×Dic5C2×C414yescomplemented
115C2×#67⋊C4—51no—
116C3×#388—51no—
117#4987D511yescharacteristic, complemented
118#4978—51no—
119#4956—51no—
120#4956—51no—
121#4951—51no—
122#4943—51no—
123Dic3×C22⋊C4—51no—
124C4×(C2×D3)⋊C4—51no—
125#4932—51no—
126#4666—51no—
127D3×#95—51no—
128#4655—51no—
129#4651—51no—
130C23×C4×C5—31no—
131C22×C22⋊D5—31no—
132C23×Dic5—31no—
133C23×Dic5—31no—
134C22×C4×D5—31no—
135C2×C5×C4⋊C4—31no—
136C2×C5×C4⋊C4C2×D311yescharacteristic
137C2×C5×C22⋊C4—31no—
138C2×C5×C22⋊C4—31no—
139C2×C22⋊Dic5—31no—
140C4×C22⋊D5—38no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685C2×D311yescharacteristic
144C2×#685C2×D311yescharacteristic
145C2×#685C2×D311yescharacteristic
146C2×#683—31no—
147C2×C4×Dic5—31no—
148C2×C4×Dic5—31no—
149C2×C4×Dic5—31no—
150C2×C4×Dic5—31no—
151C2×C4×Dic5C2×D311yescharacteristic
152C5×#95—31no—
153C5×#95—31no—
154#3963—31no—
155#3963—31no—
156#3963—31no—
157#3963—31no—
158#3963—31no—
159#3963—31no—
160#3963—31no—
161#3963—31no—
162#3963—31no—
163#3963—31no—
164#3963C2×D311yescharacteristic
165#3963C2×D311yescharacteristic
166#2353—151noSylow
167C23×C3×C5C2411yescharacteristic
168C22×C5×D3—21no—
169C22×C5×D3—21no—
170C22×C5×D3—21no—
171C22×C5×D3—21no—
172C22×C5×D3C22×C412yes—
173C22×C5×D3#4112yes—
174C22×C5×D3#4112yes—
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—21no—
178C22×C3×D5—21no—
179C22×C3×D5—21no—
180C22×C3×D5—21no—
181C22×C3×D5C22×C412yes—
182C2×C3×C4×C5—21no—
183C2×C3×C4×C5—21no—
184C2×C3×C4×C5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C22×C412yes—
191C2×Dic15—21no—
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—21no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—21no—
199C2×Dic15—21no—
200C2×Dic15C22×C412yes—
201C2×Dic15C22×C412yes—
202C2×Dic15#4112yes—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—21no—
208C2×C5×Dic3—21no—
209C2×C5×Dic3—21no—
210C2×C5×Dic3—21no—
211C2×C5×Dic3C22×C412yes—
212C4×C5×D3—44no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5—21no—
219C2×C3×Dic5—21no—
220C2×C3×Dic5C22×C412yes—
221C2×C3×Dic5#4112yes—
222#1201—28no—
223D3×Dic5—44no—
224D3×Dic5—44no—
225D5×Dic3—44no—
226C22×#67—51no—
227C23×Dic3—51no—
228C22×C4×D3—51no—
229C22×C4×D3—51no—
230C22×C4×D3C2×D511yescharacteristic
231C2×C3×C4⋊C4C2×D511yescharacteristic
232C2×C3×C22⋊C4—51no—
233C2×C3×C22⋊C4—51no—
234C2×C3×C22⋊C4—51no—
235C2×C3×C42—51no—
236C2×#217—51no—
237C2×#217—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4C2×D511yescharacteristic
240C2×(C2×D3)⋊C4C2×D511yescharacteristic
241C2×C4⋊Dic3C2×D511yescharacteristic
242C2×Dic3⋊C4—51no—
243C2×C4×Dic3—51no—
244C2×C4×Dic3—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247#67⋊C4—58no—
248C3×#95—51no—
249C3×#95—51no—
250C3⋊#95—51no—
251C3⋊#95—51no—
252C3⋊#95—51no—
253C3⋊#95—51no—
254C3⋊#95—51no—
255C3⋊#95—51no—
256C3⋊#95—51no—
257C3⋊#95—51no—
258C3⋊#95—51no—
259C3⋊#95—51no—
260C3⋊#95C2×D511yescharacteristic
261C3⋊#95C2×D511yescharacteristic
262C24×C5—31no—
263C23×D5C22×D311yescharacteristic
264C22×C4×C5—31no—
265C22×C4×C5—34no—
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—121no—
269C22×C4×C5—121no—
270C22×C4×C5C22×D311yescharacteristic
271C22×C4×C5C22×D311yescharacteristic
272C22×C4×C5C22×D311yescharacteristic
273C2×C22⋊D5—34no—
274C2×C22⋊D5—62no—
275C2×C22⋊D5—62no—
276C22×Dic5—31no—
277C22×Dic5—31no—
278C22×Dic5—31no—
279C22×Dic5—31no—
280C22×Dic5—62no—
281C22×Dic5—62no—
282C22×Dic5—62no—
283C22×Dic5—62no—
284C22×Dic5—121no—
285C22×Dic5—121no—
286C22×Dic5C22×D311yescharacteristic
287C22×Dic5C22×D311yescharacteristic
288C22×Dic5C22×D311yescharacteristic
289C2×C4×D5—34no—
290C2×C4×D5—121no—
291C2×C4×D5—121no—
292C5×C4⋊C4—41no—
293C5×C4⋊C4—121no—
294C5×C22⋊C4—62no—
295C5×C22⋊C4—62no—
296C22⋊Dic5—34no—
297#685—22no—
298#685—41no—
299#685—62no—
300#685—121no—
301#685C4×D314yescomplemented
302#683—34no—
303C4×Dic5—22no—
304C4×Dic5—34no—
305C4×Dic5—62no—
306C4×Dic5—121no—
307C4×Dic5—121no—
308C2×C4×D4—151no—
309#388—51no—
310#388—151no—
311#387—151no—
312#387—151no—
313#386—151no—
314#386—151no—
315#383—151no—
316#381—151no—
317#380—31no—
318C4×C22⋊C4—151no—
319C4×C22⋊C4—151no—
320C4×C22⋊C4—151no—
321#376—151no—
322C2×#95—151no—
323C22×C3×C5C23×C411yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5C2×#4111yescharacteristic
326C22×C3×C5C2×#4111yescharacteristic
327C22×C3×C5C2×#4111yescharacteristic
328C22×C3×C5H(5,𝔽2)11yescharacteristic
329C22×C3×C5H(5,𝔽2)11yescharacteristic
330C2×C5×D3—22no—
331C2×C5×D3—22no—
332C2×C5×D3—22no—
333C2×C5×D3—22no—
334C2×C5×D3—22no—
335C2×C5×D3—22no—
336C2×C5×D3#11714yes—
337C2×C3×D5—22no—
338C2×C3×D5—22no—
339C2×C3×D5—22no—
340C2×C3×D5—41no—
341C2×C3×D5—41no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C3×C4×C5—22no—
345C3×C4×C5—41no—
346C3×C4×C5—41no—
347Dic15—22no—
348Dic15—22no—
349Dic15—22no—
350Dic15—41no—
351C3×Dic5—22no—
352C3×Dic5—22no—
353C3×Dic5—41no—
354C5×Dic3—22no—
355C5×Dic3—41no—
356C5×Dic3—41no—
357C24×C3—51no—
358C23×D3C22×D511yescharacteristic
359C22×C3×C4—51no—
360C22×C3×C4—51no—
361C22×C3×C4—51no—
362C22×C3×C4C22×D511yescharacteristic
363C22×C3×C4C22×D511yescharacteristic
364C22×C3×C4C22×D511yescharacteristic
365C2×#67—54no—
366C2×#67—102no—
367C2×#67—102no—
368C22×Dic3—51no—
369C22×Dic3—51no—
370C22×Dic3—51no—
371C22×Dic3—54no—
372C22×Dic3—51no—
373C22×Dic3—201no—
374C22×Dic3—201no—
375C22×Dic3C22×D511yescharacteristic
376C22×Dic3C22×D511yescharacteristic
377C22×Dic3C22×D511yescharacteristic
378C2×C4×D3—41no—
379C2×C4×D3—41no—
380C2×C4×D3—102no—
381C2×C4×D3—102no—
382C2×C4×D3—102no—
383C2×C4×D3—102no—
384C2×C4×D3—201no—
385C2×C4×D3—201no—
386C2×C4×D3C4×D514yes—
387C3×C4⋊C4—41no—
388C3×C22⋊C4—54no—
389C3×C22⋊C4—102no—
390C3×C22⋊C4—201no—
391C3×C42—102no—
392#217—102no—
393#217—201no—
394(C2×D3)⋊C4—22no—
395(C2×D3)⋊C4—22no—
396(C2×D3)⋊C4—54no—
397C4⋊Dic3—41no—
398Dic3⋊C4—54no—
399C4×Dic3—54no—
400C4×Dic3—102no—
401C4×Dic3—201no—
402C4×Dic3—201no—
403C23×C5—32no—
404C23×C5—32no—
405C23×C5—32no—
406C23×C5—61no—
407C23×C5—61no—
408C23×C5—61no—
409C23×C5—61no—
410C23×C5C23×D311yescharacteristic
411C22×D5—21no—
412C22×D5—21no—
413C22×D5—21no—
414C22×D5—21no—
415C22×D5—21no—
416C22×D5—21no—
417C22×D5C2×C4×D312yes—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—21no—
424C2×C4×C5—21no—
425C2×C4×C5—21no—
426C2×C4×C5—32no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—61no—
433C2×C4×C5—61no—
434C2×C4×C5—61no—
435C2×C4×C5—124no—
436C2×C4×C5C2×C4×D312yes—
437C22⋊D5—68no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—21no—
445C2×Dic5—32no—
446C2×Dic5—32no—
447C2×Dic5—32no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5—61no—
454C2×Dic5—61no—
455C2×Dic5—61no—
456C2×Dic5—61no—
457C2×Dic5—124no—
458C2×Dic5—124no—
459C2×Dic5C2×C4×D312yes—
460C2×Dic5#23712yes—
461C4×D5—124no—
462C22×D4—151no—
463C23×C4—31no—
464C23×C4—151no—
465C23×C4—151no—
466C23×C4—151no—
467C4×D4—158no—
468C2×C4⋊C4—31no—
469C2×C4⋊C4—151no—
470C2×C4⋊C4D3×D511yescharacteristic
471C2×C22⋊C4—31no—
472C2×C22⋊C4—31no—
473C2×C22⋊C4—51no—
474C2×C22⋊C4—51no—
475C2×C22⋊C4—51no—
476C2×C22⋊C4—151no—
477C2×C22⋊C4—151no—
478C2×C22⋊C4—151no—
479C2×C42—51no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42—151no—
484#95—31no—
485#95—31no—
486#95—51no—
487#95—51no—
488#95—151no—
489#95—151no—
490#95—151no—
491#95—151no—
492#95—151no—
493#95—151no—
494#95—151no—
495#95—151no—
496#95—151no—
497#95—151no—
498C2×C3×C5C2×#11711yescharacteristic
499C2×C3×C5C4×#4111yescharacteristic
500C2×C3×C5#51811yescharacteristic
501C2×C3×C5#55111yescharacteristic
502C2×C3×C5#55111yescharacteristic
503C2×C3×C5#55311yescharacteristic
504C2×C3×C5#55311yescharacteristic
505C3×D5—42no—
506C5×D3—24no—
507C23×C3—52no—
508C23×C3—101no—
509C23×C3—101no—
510C23×C3—101no—
511C23×C3—101no—
512C23×C3—101no—
513C23×C3—101no—
514C23×C3C23×D511yescharacteristic
515C22×D3—21no—
516C22×D3—21no—
517C22×D3—21no—
518C22×D3—21no—
519C22×D3C2×C4×D512yes—
520C22×D3#71112yes—
521C22×D3#71312yes—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—52no—
531C2×C3×C4—52no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4—101no—
538C2×C3×C4—101no—
539C2×C3×C4C2×C4×D512yes—
540#67—108no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—52no—
550C2×Dic3—52no—
551C2×Dic3—52no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3—101no—
556C2×Dic3—101no—
557C2×Dic3—101no—
558C2×Dic3—101no—
559C2×Dic3—101no—
560C2×Dic3—101no—
561C2×Dic3—204no—
562C2×Dic3C2×C4×D512yes—
563C4×D3—44no—
564C4×D3—204no—
565C4×D3—204no—
566C22×C5—34no—
567C22×C5—62no—
568C22×C5—62no—
569C22×C5—62no—
570C22×C5—62no—
571C22×C5—62no—
572C22×C5—62no—
573C22×C5C22×C4×D311yescharacteristic
574C22×C5C2×#23711yescharacteristic
575C22×C5#100411yescharacteristic
576C22×C5D3×#4111yescharacteristic
577C22×C5D3×#4111yescharacteristic
578C22×C5D3×#4111yescharacteristic
579C22×C5#100911yescharacteristic
580C2×D5—22no—
581C2×D5—22no—
582C2×D5—22no—
583C2×D5—41no—
584C2×D5—41no—
585C2×D5—41no—
586C2×D5—41no—
587C4×C5—22no—
588C4×C5—41no—
589C4×C5—41no—
590C4×C5—62no—
591C4×C5—121no—
592C4×C5—121no—
593Dic5—22no—
594Dic5—22no—
595Dic5—41no—
596Dic5—62no—
597Dic5—62no—
598Dic5—62no—
599Dic5—121no—
600C24—31no—
601C24—51no—
602C2×D4—154no—
603C2×D4—302no—
604C2×D4—302no—
605C22×C4—31no—
606C22×C4—34no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—51no—
610C22×C4—51no—
611C22×C4—51no—
612C22×C4—121no—
613C22×C4—121no—
614C22×C4—154no—
615C22×C4—151no—
616C22×C4—151no—
617C22×C4—151no—
618C22×C4—151no—
619C22×C4—302no—
620C22×C4—302no—
621C22×C4—302no—
622C22×C4—302no—
623C22×C4—601no—
624C22×C4—601no—
625C22×C4—601no—
626C22×C4—601no—
627C22×C4C2×D3×D511yescharacteristic
628C22×C4C2×D3×D511yescharacteristic
629C22×C4C2×D3×D511yescharacteristic
630C4⋊C4—41no—
631C4⋊C4—121no—
632C4⋊C4—154no—
633C22⋊C4—54no—
634C22⋊C4—62no—
635C22⋊C4—62no—
636C22⋊C4—102no—
637C22⋊C4—154no—
638C22⋊C4—201no—
639C22⋊C4—302no—
640C22⋊C4—601no—
641C42—102no—
642C42—154no—
643C42—302no—
644C42—601no—
645C42—601no—
646C3×C5#235311yescharacteristic, complemented, Hall
647C22×C3—102no—
648C22×C3—102no—
649C22×C3—102no—
650C22×C3—201no—
651C22×C3—201no—
652C22×C3—201no—
653C22×C3—201no—
654C22×C3C22×C4×D511yescharacteristic
655C22×C3C2×#71111yescharacteristic
656C22×C3#414411yescharacteristic
657C22×C3#414411yescharacteristic
658C22×C3C2×#71311yescharacteristic
659C22×C3D5×#4111yescharacteristic
660C22×C3D5×#4111yescharacteristic
661C2×D3—22no—
662C2×D3—22no—
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—22no—
666C2×D3—22no—
667C2×D3#403814yes—
668C3×C4—22no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—102no—
672C3×C4—102no—
673C3×C4—201no—
674Dic3—22no—
675Dic3—41no—
676Dic3—41no—
677Dic3—102no—
678Dic3—102no—
679Dic3—102no—
680Dic3—201no—
681C2×C5—64no—
682C2×C5D3×#11711yescharacteristic
683C2×C5C4×#23711yescharacteristic
684C2×C5#554511yescharacteristic
685C2×C5#561411yescharacteristic
686C2×C5#565811yescharacteristic
687C2×C5#567911yescharacteristic
688C2×C5#570911yescharacteristic
689D5—42no—
690C23—32no—
691C23—32no—
692C23—32no—
693C23—52no—
694C23—61no—
695C23—61no—
696C23—61no—
697C23—61no—
698C23—101no—
699C23—101no—
700C23—101no—
701C23—101no—
702C23—101no—
703C23—101no—
704C23C22×D3×D511yescharacteristic
705D4—308no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—32no—
715C2×C4—52no—
716C2×C4—52no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—101no—
729C2×C4—101no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—124no—
733C2×C4—152no—
734C2×C4—152no—
735C2×C4—152no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—301no—
739C2×C4—301no—
740C2×C4—301no—
741C2×C4—301no—
742C2×C4—301no—
743C2×C4—301no—
744C2×C4—301no—
745C2×C4—604no—
746C2×C4—604no—
747C2×C4—604no—
748C2×C4C4×D3×D512yes—
749C2×C3—202no—
750C2×C3#6582011yescharacteristic
751C2×C3C2×#403811yescharacteristic
752C2×C3#6585611yescharacteristic
753C2×C3#6593511yescharacteristic
754C2×C3#6593511yescharacteristic
755C2×C3#6597111yescharacteristic
756C2×C3#6597111yescharacteristic
757D3—24no—
758C5#7583511yescharacteristic, complemented, Sylow
759C22—34no—
760C22—62no—
761C22—62no—
762C22—62no—
763C22—62no—
764C22—62no—
765C22—62no—
766C22—102no—
767C22—102no—
768C22—102no—
769C22—201no—
770C22—201no—
771C22—201no—
772C22—201no—
773C22C2×C4×D3×D511yescharacteristic
774C22#9201811yescharacteristic
775C22D5×#23711yescharacteristic
776C22D3×#71111yescharacteristic
777C22D3×#71311yescharacteristic
778C22#9203411yescharacteristic
779C22#9204911yescharacteristic
780C4—22no—
781C4—41no—
782C4—41no—
783C4—62no—
784C4—102no—
785C4—102no—
786C4—121no—
787C4—121no—
788C4—201no—
789C4—302no—
790C4—302no—
791C4—302no—
792C4—601no—
793C3#1060561511yescharacteristic, complemented, Sylow
794C2—64no—
795C2—202no—
796C2#1175339811yescharacteristic
797C2#1175357211yescharacteristic
798C2D3×#403811yescharacteristic
799C2#1175390411yescharacteristic
800C2#1175462711yescharacteristic
801C2#1175485111yescharacteristic
802C2#1175529211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #11751079C2semidirect
3. C5×#4987C2semidirect
4. C3×#65279C2semidirect
7. #11748886C2semidirect
8. #11748884C2semidirect
9. D3×#3963C2semidirect
10. Dic5×(C2×D3)⋊C4C2semidirect
11. #11748871C2semidirect
12. #11748771C2semidirect
13. #11748687C2semidirect
14. #11748646C2semidirect
15. #11748635C2semidirect
38. #91441C4semidirect
58. #65279D3semidirect
98. C2×D5×Dic3C2×C4semidirect
100. #6712C2×C4semidirect
107. C3×#685C2×C4semidirect
114. Dic3×Dic5C2×C4semidirect
117. #4987D5semidirect
301. #685C4×D3semidirect
646. C3×C5#2353semidirect
758. C5#75835semidirect
793. C3#10605615semidirect

Maximal subgroups

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

subgroupindex
C2×#914412
#117510792
C5×#49872
C3×#652792
#117489112
#117488862
#117488842
D3×#39632
Dic5×(C2×D3)⋊C42
#117488712
#117487712
#117486872
#117486462
#117486352
#106056153
#758355