Finite Group Databasebeta

← #14328016

Subgroups — #14328016

Order 1920.

1120 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91446C211yesmaximal, characteristic
2#11751041C211yesmaximal, characteristic, complemented
3C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C3×C4×#683C211yesmaximal, characteristic, complemented
5#11748909C211yesmaximal, characteristic
6#11748908C211yesmaximal, characteristic
7#11748889C211yesmaximal, characteristic, complemented
8#11748875C211yesmaximal, characteristic, complemented
9#11748854C211yesmaximal, characteristic, complemented
10#11748777C211yesmaximal, characteristic, complemented
11#11748721C211yesmaximal, characteristic, complemented
12#11748715C211yesmaximal, characteristic, complemented
13#11748642C211yesmaximal, characteristic, complemented
14#11748640C211yesmaximal, characteristic, complemented
15Dic3×#683C211yesmaximal, characteristic, complemented
16#10605194—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C22×#1203C2211yescharacteristic
19C22×#1200C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6714C2211yescharacteristic
22C2×#6714C2211yescharacteristic
23C2×#6714C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2211yescharacteristic
26C2×C5×(C2×D3)⋊C4C2211yescharacteristic
27C2×C4×C5×Dic3C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C2×C3×C4×Dic5C2211yescharacteristic
32C2×#6669C2211yescharacteristic
33C2×#6668C2211yescharacteristic
34C2×#6667C2211yescharacteristic
35C2×#6667C2211yescharacteristic
36C2×(C2×D3)⋊Dic5C2211yescharacteristic
37C2×(C2×D3)⋊Dic5C2211yescharacteristic
38C2×(C2×D3)⋊Dic5C2211yescharacteristic
39C2×Dic3×Dic5C2211yescharacteristic
40C2×Dic3×Dic5C2211yescharacteristic
41C2×Dic3×Dic5C2211yescharacteristic
42#91446C418yescomplemented
43#91115C2211yescharacteristic
44#91115C2211yescharacteristic
45C5×C3⋊#95C2211yescharacteristic
46C5×C3⋊#95C2211yescharacteristic
47C3×#3963C2211yescharacteristic
48C3×#3963C2211yescharacteristic
49#90994C2211yescharacteristic
50#90994C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#73646—51nomaximal, Hall
54C2×C4×C22⋊D5—31no—
55C4×C5×C22⋊C4—31no—
56#65500—31no—
57#65246—31no—
58#65246—31no—
59#65234—31no—
60#65234—31no—
61#65229—31no—
62#65229—31no—
63C4×#683—31no—
64C4×#683D311yescharacteristic, complemented
65#64955—31no—
66#64953—31no—
67#64939—31no—
68#64938—31no—
69C23×D15C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
71C22×C3×C4×C5C2311yescharacteristic
72C22×C3×C4×C5C2311yescharacteristic
73C22×C3×C4×C5C2311yescharacteristic
74C22×Dic15C2311yescharacteristic
75C22×Dic15C2311yescharacteristic
76C22×Dic15C2311yescharacteristic
77C22×C5×Dic3C2311yescharacteristic
78C22×C5×Dic3C2311yescharacteristic
79C22×C5×Dic3C2311yescharacteristic
80C2×C4×C5×D3—41no—
81C2×C4×C5×D3—41no—
82C2×C4×C5×D3C2×C414yes—
83C22×C3×Dic5C2311yescharacteristic
84C22×C3×Dic5C2311yescharacteristic
85C22×C3×Dic5C2311yescharacteristic
86C22×C3×Dic5C2311yescharacteristic
87C2×#1203—22no—
88C2×#1203—22no—
89C2×#1203C2×C414yes—
90C2×#1200—41no—
91C2×#1200—41no—
92C2×#1200C2×C414yes—
93C3×C42×C5—41no—
94#6714—22no—
95#6714—41no—
96#6714C2×C414yes—
97#6712—22no—
98C5×(C2×D3)⋊C4—22no—
99C5×(C2×D3)⋊C4—22no—
100C4×C5×Dic3—41no—
101C3×#683—22no—
102C3×#683C2×C414yes—
103C3×C4×Dic5—22no—
104C3×C4×Dic5—41no—
105#6669—22no—
106#6668—22no—
107#6667—22no—
108#6667—41no—
109(C2×D3)⋊Dic5—41no—
110(C2×D3)⋊Dic5—41no—
111(C2×D3)⋊Dic5C2×C414yes—
112Dic3×Dic5—22no—
113Dic3×Dic5—41no—
114Dic3×Dic5C2×C414yes—
115C2×#893—51no—
116C3×C4×C4⋊C4—51no—
117#4988—51no—
118#4977—51no—
119Dic3×C4⋊C4—51no—
120#4940—51no—
121#4940—51no—
122#4939—51no—
123C4×(C2×D3)⋊C4—51no—
124C4×(C2×D3)⋊C4D511yescharacteristic, complemented
125C4×Dic3⋊C4—51no—
126#4669—51no—
127#4669—51no—
128#4664—51no—
129#4664—51no—
130C23×C4×C5—31no—
131C22×C22⋊D5—31no—
132C22×C4×D5—31no—
133C2×C5×C22⋊C4—31no—
134C2×C5×C22⋊C4—31no—
135C2×C42×C5—31no—
136C2×C42×C5C2×D311yescharacteristic
137C2×C22⋊Dic5—31no—
138C2×C22⋊Dic5—31no—
139C2×C22⋊Dic5—31no—
140C4×C22⋊D5—38no—
141C2×#685—31no—
142C2×#685—31no—
143C2×#685—31no—
144C2×#685—31no—
145C2×#685—31no—
146C2×#683—31no—
147C2×#683—31no—
148C2×#683—31no—
149C2×#683C2×D311yescharacteristic
150C2×#683C2×D311yescharacteristic
151C2×C4×Dic5—31no—
152C2×C4×Dic5—31no—
153C2×C4×Dic5—31no—
154C2×C4×Dic5C2×D311yescharacteristic
155C2×C4×Dic5C2×D311yescharacteristic
156C5×#95—31no—
157C5×#95—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#2357—151noSylow
167C23×C3×C5C2411yescharacteristic
168C22×D15—21no—
169C22×D15—21no—
170C22×D15—21no—
171C22×D15—21no—
172C22×D15—21no—
173C22×D15—21no—
174C22×D15C22×C412yes—
175C22×C5×D3—21no—
176C22×C5×D3—21no—
177C22×C5×D3—21no—
178C22×C5×D3—21no—
179C22×C5×D3—21no—
180C22×C5×D3—21no—
181C22×C5×D3C22×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×C5C22×C412yes—
190C2×C3×C4×C5#4112yes—
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×Dic15C22×C412yes—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3C22×C412yes—
208C2×C5×Dic3#4112yes—
209C4×C5×D3—44no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—21no—
215C2×C3×Dic5—21no—
216C2×C3×Dic5—21no—
217C2×C3×Dic5—21no—
218C2×C3×Dic5C22×C412yes—
219C2×C3×Dic5C22×C412yes—
220C2×C3×Dic5#4112yes—
221C2×C3×Dic5#4112yes—
222#1203—28no—
223#1200—44no—
224C22×D12—51no—
225C22×C4×D3—51no—
226C22×C4×D3C2×D511yescharacteristic
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—51no—
229C2×C3×C42—51no—
230C2×C3×C42—51no—
231C2×C3×C42C2×D511yescharacteristic
232C2×(C2×D3)⋊C4—51no—
233C2×(C2×D3)⋊C4—51no—
234C2×(C2×D3)⋊C4—51no—
235C2×(C2×D3)⋊C4—51no—
236C2×(C2×D3)⋊C4—51no—
237C2×(C2×D3)⋊C4—51no—
238C2×(C2×D3)⋊C4—51no—
239C2×(C2×D3)⋊C4—51no—
240C2×(C2×D3)⋊C4C2×D511yescharacteristic
241C2×(C2×D3)⋊C4C2×D511yescharacteristic
242C2×C4⋊Dic3—51no—
243C2×Dic3⋊C4—51no—
244C2×Dic3⋊C4—51no—
245C2×C4×Dic3—51no—
246C2×C4×Dic3—51no—
247C2×C4×Dic3—51no—
248C2×C4×Dic3C2×D511yescharacteristic
249#893—58no—
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⋊#95C2×D511yescharacteristic
259C3⋊#95C2×D511yescharacteristic
260C24×C5—31no—
261C23×D5—31no—
262C22×C4×C5—31no—
263C22×C4×C5—31no—
264C22×C4×C5—34no—
265C22×C4×C5—31no—
266C22×C4×C5—121no—
267C22×C4×C5—121no—
268C22×C4×C5C22×D311yescharacteristic
269C22×C4×C5C22×D311yescharacteristic
270C22×C4×C5C22×D311yescharacteristic
271C2×C22⋊D5—34no—
272C2×C22⋊D5—62no—
273C2×C22⋊D5—62no—
274C22×Dic5—31no—
275C22×Dic5—31no—
276C22×Dic5—31no—
277C22×Dic5C22×D311yescharacteristic
278C22×Dic5C22×D311yescharacteristic
279C22×Dic5C22×D311yescharacteristic
280C22×Dic5C22×D311yescharacteristic
281C2×C4×D5—34no—
282C2×C4×D5—121no—
283C2×C4×D5—121no—
284C5×C22⋊C4—62no—
285C5×C22⋊C4—62no—
286C42×C5—41no—
287C42×C5—121no—
288C22⋊Dic5—34no—
289C22⋊Dic5—121no—
290C22⋊Dic5—121no—
291#685—34no—
292#685—62no—
293#685—62no—
294#685—121no—
295#685—121no—
296#683—22no—
297#683—62no—
298#683—62no—
299#683—62no—
300#683C4×D314yes—
301C4×Dic5—22no—
302C4×Dic5—34no—
303C4×Dic5—41no—
304C4×Dic5—62no—
305C4×Dic5—121no—
306C2×C4×D4—151no—
307#390—151no—
308#390—151no—
309#388—151no—
310#388—151no—
311#388—151no—
312#388—151no—
313#382—151no—
314#381—151no—
315#381—151no—
316C4×C4⋊C4—51no—
317C4×C4⋊C4—151no—
318C4×C4⋊C4—151no—
319C4×C22⋊C4—31no—
320C4×C22⋊C4—151no—
321C22×C3×C5C23×C411yescharacteristic
322C22×C3×C5C2×#4111yescharacteristic
323C22×C3×C5C2×#4111yescharacteristic
324C22×C3×C5C2×#4111yescharacteristic
325C22×C3×C5C2×#4111yescharacteristic
326C22×C3×C5H(5,𝔽2)11yescharacteristic
327C22×C3×C5H(5,𝔽2)11yescharacteristic
328C2×D15—22no—
329C2×D15—22no—
330C2×D15—22no—
331C2×D15—41no—
332C2×D15—41no—
333C2×D15—41no—
334C2×D15—41no—
335C2×C5×D3—22no—
336C2×C5×D3—22no—
337C2×C5×D3—22no—
338C2×C5×D3—41no—
339C2×C5×D3—41no—
340C2×C5×D3—41no—
341C2×C5×D3—41no—
342C3×C4×C5—22no—
343C3×C4×C5—22no—
344C3×C4×C5—41no—
345Dic15—22no—
346Dic15—41no—
347Dic15—41no—
348C3×Dic5—22no—
349C3×Dic5—41no—
350C3×Dic5—41no—
351C3×Dic5#11714yes—
352C5×Dic3—22no—
353C5×Dic3—22no—
354C5×Dic3—41no—
355C23×D3—51no—
356C23×D3C22×D511yescharacteristic
357C22×C3×C4—51no—
358C22×C3×C4—51no—
359C22×C3×C4—51no—
360C22×C3×C4—51no—
361C22×C3×C4C22×D511yescharacteristic
362C22×C3×C4C22×D511yescharacteristic
363C22×C3×C4C22×D511yescharacteristic
364C22×Dic3—51no—
365C22×Dic3—51no—
366C22×Dic3—51no—
367C22×Dic3C22×D511yescharacteristic
368C22×Dic3C22×D511yescharacteristic
369C22×Dic3C22×D511yescharacteristic
370C2×D12—54no—
371C2×D12—102no—
372C2×D12—102no—
373C2×C4×D3—41no—
374C2×C4×D3—41no—
375C2×C4×D3—54no—
376C2×C4×D3—201no—
377C2×C4×D3—201no—
378C2×C4×D3C4×D514yes—
379C3×C4⋊C4—54no—
380C3×C4⋊C4—102no—
381C3×C42—41no—
382C3×C42—102no—
383C3×C42—201no—
384(C2×D3)⋊C4—22no—
385(C2×D3)⋊C4—22no—
386(C2×D3)⋊C4—54no—
387(C2×D3)⋊C4—54no—
388(C2×D3)⋊C4—102no—
389(C2×D3)⋊C4—102no—
390(C2×D3)⋊C4—201no—
391(C2×D3)⋊C4—201no—
392(C2×D3)⋊C4—201no—
393(C2×D3)⋊C4—201no—
394C4⋊Dic3—102no—
395Dic3⋊C4—102no—
396Dic3⋊C4—102no—
397C4×Dic3—41no—
398C4×Dic3—54no—
399C4×Dic3—102no—
400C4×Dic3—201no—
401C23×C5—32no—
402C23×C5—61no—
403C23×C5—61no—
404C23×C5—61no—
405C23×C5—61no—
406C23×C5—61no—
407C23×C5—61no—
408C23×C5C23×D311yescharacteristic
409C22×D5—32no—
410C22×D5—61no—
411C22×D5—61no—
412C22×D5—61no—
413C22×D5—61no—
414C22×D5—61no—
415C22×D5—61no—
416C2×C4×C5—21no—
417C2×C4×C5—21no—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—21no—
421C2×C4×C5—21no—
422C2×C4×C5—21no—
423C2×C4×C5—32no—
424C2×C4×C5—32no—
425C2×C4×C5—61no—
426C2×C4×C5—61no—
427C2×C4×C5—61no—
428C2×C4×C5—61no—
429C2×C4×C5—61no—
430C2×C4×C5—61no—
431C2×C4×C5—61no—
432C2×C4×C5—124no—
433C2×C4×C5C2×C4×D312yes—
434C2×C4×C5#23912yes—
435C22⋊D5—68no—
436C2×Dic5—21no—
437C2×Dic5—21no—
438C2×Dic5—21no—
439C2×Dic5—21no—
440C2×Dic5—21no—
441C2×Dic5—21no—
442C2×Dic5—21no—
443C2×Dic5—21no—
444C2×Dic5—32no—
445C2×Dic5—61no—
446C2×Dic5—61no—
447C2×Dic5—61no—
448C2×Dic5—61no—
449C2×Dic5—61no—
450C2×Dic5—61no—
451C2×Dic5—61no—
452C2×Dic5—61no—
453C2×Dic5C2×C4×D312yes—
454C2×Dic5C2×C4×D312yes—
455C2×Dic5#23512yes—
456C2×Dic5#23512yes—
457C4×D5—124no—
458C22×D4—151no—
459C23×C4—31no—
460C23×C4—151no—
461C4×D4—158no—
462C2×C4⋊C4—51no—
463C2×C4⋊C4—51no—
464C2×C4⋊C4—151no—
465C2×C4⋊C4—151no—
466C2×C4⋊C4—151no—
467C2×C22⋊C4—31no—
468C2×C22⋊C4—31no—
469C2×C22⋊C4—151no—
470C2×C22⋊C4—151no—
471C2×C22⋊C4—151no—
472C2×C22⋊C4—151no—
473C2×C22⋊C4—151no—
474C2×C22⋊C4—151no—
475C2×C22⋊C4—151no—
476C2×C22⋊C4—151no—
477C2×C42—31no—
478C2×C42—51no—
479C2×C42—51no—
480C2×C42—151no—
481C2×C42—151no—
482C2×C42—151no—
483C2×C42D3×D511yescharacteristic
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—
494C2×C3×C5C2×#11711yescharacteristic
495C2×C3×C5C4×#4111yescharacteristic
496C2×C3×C5#51811yescharacteristic
497C2×C3×C5#55311yescharacteristic
498C2×C3×C5#55311yescharacteristic
499C2×C3×C5#55911yescharacteristic
500C2×C3×C5#55911yescharacteristic
501D15—42no—
502C5×D3—42no—
503C23×C3C23×D511yescharacteristic
504C22×D3—21no—
505C22×D3—21no—
506C22×D3—21no—
507C22×D3—21no—
508C22×D3—21no—
509C22×D3—21no—
510C22×D3—52no—
511C22×D3—101no—
512C22×D3—101no—
513C22×D3—101no—
514C22×D3—101no—
515C22×D3—101no—
516C22×D3—101no—
517C22×D3C2×C4×D512yes—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—52no—
526C2×C3×C4—52no—
527C2×C3×C4—52no—
528C2×C3×C4—52no—
529C2×C3×C4—101no—
530C2×C3×C4—101no—
531C2×C3×C4—101no—
532C2×C3×C4—101no—
533C2×C3×C4—101no—
534C2×C3×C4—101no—
535C2×C3×C4—101no—
536C2×C3×C4—101no—
537C2×C3×C4C2×C4×D512yes—
538C2×C3×C4#70912yes—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—52no—
547C2×Dic3—101no—
548C2×Dic3—101no—
549C2×Dic3—101no—
550C2×Dic3—101no—
551C2×Dic3—101no—
552C2×Dic3—101no—
553C2×Dic3—101no—
554C2×Dic3—101no—
555C2×Dic3C2×C4×D512yes—
556C2×Dic3#70912yes—
557D12—108no—
558C4×D3—44no—
559C4×D3—204no—
560C22×C5—62no—
561C22×C5—62no—
562C22×C5—62no—
563C22×C5—121no—
564C22×C5—121no—
565C22×C5—121no—
566C22×C5—121no—
567C22×C5C22×C4×D311yescharacteristic
568C22×C5C2×#23511yescharacteristic
569C22×C5C2×#23511yescharacteristic
570C22×C5#100411yescharacteristic
571C22×C5C2×#23911yescharacteristic
572C22×C5D3×#4111yescharacteristic
573C22×C5#100911yescharacteristic
574C2×D5—62no—
575C2×D5—62no—
576C2×D5—62no—
577C2×D5—121no—
578C2×D5—121no—
579C2×D5—121no—
580C2×D5—121no—
581C4×C5—22no—
582C4×C5—22no—
583C4×C5—41no—
584C4×C5—62no—
585C4×C5—62no—
586C4×C5—121no—
587Dic5—22no—
588Dic5—41no—
589Dic5—41no—
590Dic5—62no—
591Dic5—121no—
592Dic5—121no—
593Dic5#87214yes—
594C24—31no—
595C24—151no—
596C2×D4—154no—
597C2×D4—302no—
598C2×D4—302no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—34no—
602C22×C4—31no—
603C22×C4—51no—
604C22×C4—51no—
605C22×C4—51no—
606C22×C4—51no—
607C22×C4—121no—
608C22×C4—121no—
609C22×C4—154no—
610C22×C4—151no—
611C22×C4—151no—
612C22×C4—151no—
613C22×C4—601no—
614C22×C4—601no—
615C22×C4C2×D3×D511yescharacteristic
616C22×C4C2×D3×D511yescharacteristic
617C22×C4C2×D3×D511yescharacteristic
618C4⋊C4—54no—
619C4⋊C4—102no—
620C4⋊C4—302no—
621C4⋊C4—302no—
622C4⋊C4—302no—
623C22⋊C4—62no—
624C22⋊C4—62no—
625C22⋊C4—154no—
626C22⋊C4—154no—
627C22⋊C4—302no—
628C22⋊C4—302no—
629C22⋊C4—601no—
630C22⋊C4—601no—
631C22⋊C4—601no—
632C22⋊C4—601no—
633C42—41no—
634C42—102no—
635C42—121no—
636C42—154no—
637C42—201no—
638C42—302no—
639C42—601no—
640C3×C5#235711yescharacteristic, complemented, Hall
641C22×C3C22×C4×D511yescharacteristic
642C22×C3C2×#70911yescharacteristic
643C22×C3C2×#70911yescharacteristic
644C22×C3#414411yescharacteristic
645C22×C3#414411yescharacteristic
646C22×C3D5×#4111yescharacteristic
647C22×C3D5×#4111yescharacteristic
648C2×D3—22no—
649C2×D3—22no—
650C2×D3—22no—
651C2×D3—41no—
652C2×D3—41no—
653C2×D3—41no—
654C2×D3—41no—
655C2×D3—102no—
656C2×D3—102no—
657C2×D3—102no—
658C2×D3—201no—
659C2×D3—201no—
660C2×D3—201no—
661C2×D3—201no—
662C3×C4—22no—
663C3×C4—22no—
664C3×C4—41no—
665C3×C4—54no—
666C3×C4—102no—
667C3×C4—201no—
668C3×C4—201no—
669Dic3—22no—
670Dic3—22no—
671Dic3—41no—
672Dic3—102no—
673Dic3—201no—
674Dic3—201no—
675C2×C5—122no—
676C2×C5C2×#87211yescharacteristic
677C2×C5#551411yescharacteristic
678C2×C5#553011yescharacteristic
679C2×C5#554511yescharacteristic
680C2×C5#555911yescharacteristic
681C2×C5C4×#23911yescharacteristic
682C2×C5#558511yescharacteristic
683D5—122no—
684C23—32no—
685C23—61no—
686C23—61no—
687C23—61no—
688C23—61no—
689C23—61no—
690C23—61no—
691C23—152no—
692C23—301no—
693C23—301no—
694C23—301no—
695C23—301no—
696C23—301no—
697C23—301no—
698C23C22×D3×D511yescharacteristic
699D4—308no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—52no—
710C2×C4—52no—
711C2×C4—52no—
712C2×C4—52no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—101no—
721C2×C4—101no—
722C2×C4—101no—
723C2×C4—101no—
724C2×C4—101no—
725C2×C4—101no—
726C2×C4—101no—
727C2×C4—101no—
728C2×C4—124no—
729C2×C4—152no—
730C2×C4—301no—
731C2×C4—301no—
732C2×C4—301no—
733C2×C4—301no—
734C2×C4—301no—
735C2×C4—301no—
736C2×C4—301no—
737C2×C4—301no—
738C2×C4—604no—
739C2×C4#676912yes—
740C2×C4C4×D3×D512yes—
741C2×C3C4×#70911yescharacteristic
742C2×C3#6582011yescharacteristic
743C2×C3D5×#11711yescharacteristic
744C2×C3#6587411yescharacteristic
745C2×C3#6587411yescharacteristic
746C2×C3#6589311yescharacteristic
747C2×C3#6589311yescharacteristic
748D3—42no—
749D3—202no—
750C5#7364611yescharacteristic, complemented, Sylow
751C22—62no—
752C22—62no—
753C22—62no—
754C22—121no—
755C22—121no—
756C22—121no—
757C22—121no—
758C22—302no—
759C22—302no—
760C22—302no—
761C22—601no—
762C22—601no—
763C22—601no—
764C22—601no—
765C22C2×#676911yescharacteristic
766C22C2×C4×D3×D511yescharacteristic
767C22D5×#23511yescharacteristic
768C22D5×#23511yescharacteristic
769C22D3×#70911yescharacteristic
770C22#9201811yescharacteristic
771C22#9204911yescharacteristic
772C4—22no—
773C4—22no—
774C4—41no—
775C4—54no—
776C4—62no—
777C4—62no—
778C4—102no—
779C4—121no—
780C4—201no—
781C4—201no—
782C4—302no—
783C4—601no—
784C4—601no—
785C3#1060519411yescharacteristic, complemented, Sylow
786C2—122no—
787C2—602no—
788C2C4×#676911yescharacteristic
789C2#1175259311yescharacteristic
790C2#1175268711yescharacteristic
791C2D5×#87211yescharacteristic
792C2#1175441611yescharacteristic
793C2#1175457311yescharacteristic
794C2#1175462711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×#1203C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2357
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. #11751041C2semidirect
3. C4×C5×(C2×D3)⋊C4C2semidirect
4. C3×C4×#683C2semidirect
7. #11748889C2semidirect
8. #11748875C2semidirect
9. #11748854C2semidirect
10. #11748777C2semidirect
11. #11748721C2semidirect
12. #11748715C2semidirect
13. #11748642C2semidirect
14. #11748640C2semidirect
15. Dic3×#683C2semidirect
42. #91446C4semidirect
64. C4×#683D3semidirect
124. C4×(C2×D3)⋊C4D5semidirect
640. C3×C5#2357semidirect
750. C5#73646semidirect
785. C3#10605194semidirect

Maximal subgroups

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

subgroupindex
C2×#914462
#117510412
C4×C5×(C2×D3)⋊C42
C3×C4×#6832
#117489092
#117489082
#117488892
#117488752
#117488542
#117487772
#117487212
#117487152
#117486422
#117486402
Dic3×#6832
#106051943
#736465