Finite Group Databasebeta

← #14324386

Subgroups — #14324386

Order 1920.

1480 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91770C211yesmaximal, characteristic, complemented
2C2×#91567C211yesmaximal, characteristic
3C2×C4×#1201C211yesmaximal, characteristic, complemented
4C5×#4956C211yesmaximal, characteristic, complemented
5C3×#65245C211yesmaximal, characteristic, complemented
6#11749501C211yesmaximal, characteristic, complemented
7#11749500C211yesmaximal, characteristic, complemented
8#11749483C211yesmaximal, characteristic, complemented
9#11748918C211yesmaximal, characteristic, complemented
10#11748917C211yesmaximal, characteristic, complemented
11#11748916C211yesmaximal, characteristic, complemented
12#11748914C211yesmaximal, characteristic, complemented
13#11748907C211yesmaximal, characteristic, complemented
14#11748653C211yesmaximal, characteristic, complemented
15#11748644C211yesmaximal, characteristic, complemented
16#10606398—31nomaximal, Hall
17C22×#1220C2211yescharacteristic
18C23×Dic15C2211yescharacteristic
19C22×C4×D15C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×C3×C22⋊D5C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1203C2211yescharacteristic
25C22×#1202C2211yescharacteristic
26C22×#1201C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31#91770—24no—
32C2×C5×#217C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×#685C2211yescharacteristic
36#91567C418yescomplemented
37C2×#6669C2211yescharacteristic
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×#6665C2211yescharacteristic
43C2×#6665C2211yescharacteristic
44C2×Dic3×Dic5C2211yescharacteristic
45C2×Dic3×Dic5C2211yescharacteristic
46C4×#1201—24no—
47C5×C3⋊#95C2211yescharacteristic
48C5×C3⋊#95C2211yescharacteristic
49C3×#3963C2211yescharacteristic
50C3×#3963C2211yescharacteristic
51#90994C2211yescharacteristic
52#90994C2211yescharacteristic
53#90994C2211yescharacteristic
54#90994C2211yescharacteristic
55#74667—51nomaximal, Hall
56C2×#4086—31no—
57C2×C4×C22⋊D5—31no—
58C2×#4027—31no—
59C5×#386—31no—
60#65509—31no—
61#65502—31no—
62#65247—31no—
63#65246—31no—
64#65246—31no—
65#65245—31no—
66#65245D311yescharacteristic, complemented
67#64954—31no—
68#64954—31no—
69#64939—31no—
70#64937—31no—
71C24×C3×C5C2311yescharacteristic
72C23×D15C2311yescharacteristic
73C23×C5×D3C2311yescharacteristic
74C23×C3×D5C2311yescharacteristic
75C22×C3×C4×C5C2311yescharacteristic
76C22×C3×C4×C5C2311yescharacteristic
77C2×#1220—22no—
78C2×#1220—22no—
79C2×#1220C2×C414yescomplemented
80C22×Dic15—22no—
81C22×Dic15—41no—
82C22×Dic15—41no—
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C2×C4×D15—22no—
87C2×C4×D15—41no—
88C2×C4×D15—41no—
89C2×C5×#67—41no—
90C2×C5×#67—41no—
91C2×C5×#67C2×C414yescomplemented
92C22×C5×Dic3C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C2×C4×C5×D3—22no—
96C2×C4×C5×D3—41no—
97C2×C4×C5×D3—41no—
98C2×C3×C22⋊D5—41no—
99C2×C3×C22⋊D5—41no—
100C2×C3×C22⋊D5C2×C414yescomplemented
101C22×C3×Dic5C2311yescharacteristic
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C2×C3×C4×D5—22no—
105C2×C3×C4×D5—41no—
106C2×C3×C4×D5—41no—
107C2×#1203—41no—
108C2×#1203—41no—
109C2×#1203C2×C414yescomplemented
110C2×#1202—41no—
111C2×#1202—41no—
112C2×#1202C2×C414yescomplemented
113C2×#1201—22no—
114C2×#1201—22no—
115C2×#1201C2×C414yescomplemented
116C3×C5×C22⋊C4—22no—
117#6714—22no—
118#6712—22no—
119C4×Dic15D414yescomplemented
120C5×#217—41no—
121C5×(C2×D3)⋊C4—41no—
122C3×C22⋊Dic5—41no—
123C3×#685—41no—
124#6669—22no—
125#6667—41no—
126#6667—41no—
127(C2×D3)⋊Dic5—22no—
128(C2×D3)⋊Dic5—41no—
129#6665—22no—
130#6665—41no—
131Dic3×Dic5—22no—
132Dic3×Dic5C2×C414yescomplemented
133C2×#940—51no—
134C2×C4×#67—51no—
135C2×#67⋊C4—51no—
136C3×#386—51no—
137#5220—51no—
138#5213—51no—
139#4958—51no—
140#4957—51no—
141#4957—51no—
142#4956—51no—
143#4956D511yescharacteristic, complemented
144#4665—51no—
145#4665—51no—
146#4650—51no—
147#4648—51no—
148C22×C5×D4—31no—
149C23×C4×C5—31no—
150C22×C22⋊D5—31no—
151C22×C22⋊D5—31no—
152C22×C22⋊D5—31no—
153C22×C22⋊D5C2×D311yescharacteristic
154C23×Dic5—31no—
155C22×D20—31no—
156C22×C4×D5—31no—
157C22×C4×D5C2×D311yescharacteristic
158C2×C5×C22⋊C4—31no—
159C2×C5×C22⋊C4—31no—
160C2×C5×C22⋊C4C2×D311yescharacteristic
161C2×C22⋊Dic5—31no—
162C2×C22⋊Dic5—31no—
163C2×C22⋊Dic5C2×D311yescharacteristic
164#4086—38no—
165C4×C22⋊D5—64no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685—31no—
170C2×#685—31no—
171C2×#685C2×D311yescharacteristic
172C2×#683—31no—
173C2×#683—31no—
174C2×C4×Dic5—31no—
175C2×C4×Dic5—31no—
176C2×C4×Dic5—31no—
177#4027—64no—
178C5×#95—31no—
179C5×#95—31no—
180#3963—31no—
181#3963—31no—
182#3963—31no—
183#3963—31no—
184#3963C2×D311yescharacteristic
185#3963C2×D311yescharacteristic
186#2328—151noSylow
187C23×C3×C5—21no—
188C23×C3×C5—21no—
189C23×C3×C5—21no—
190C23×C3×C5—21no—
191C23×C3×C5—21no—
192C23×C3×C5—21no—
193C23×C3×C5C22×C412yes—
194C23×C3×C5C2411yescharacteristic
195C22×D15—21no—
196C22×D15—21no—
197C22×D15—21no—
198C22×D15—21no—
199C22×D15—21no—
200C22×D15—21no—
201C22×D15C22×C412yes—
202C22×C5×D3—21no—
203C22×C5×D3—21no—
204C22×C5×D3—21no—
205C22×C5×D3—21no—
206C22×C5×D3—21no—
207C22×C5×D3—21no—
208C22×C5×D3C22×C412yes—
209C22×C3×D5—21no—
210C22×C3×D5—21no—
211C22×C3×D5—21no—
212C22×C3×D5—21no—
213C22×C3×D5—21no—
214C22×C3×D5—21no—
215C22×C3×D5C22×C412yes—
216C2×C3×C4×C5—21no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5C2×D412yes—
222#1220—28no—
223C2×Dic15—21no—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—44no—
229C2×Dic15C22×C412yes—
230C2×Dic15C2×D412yes—
231C2×Dic15C2×D412yes—
232C2×Dic15#4112yes—
233C4×D15—44no—
234C5×#67—44no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C2×C5×Dic3—21no—
240C2×C5×Dic3—21no—
241C2×C5×Dic3—21no—
242C2×C5×Dic3—21no—
243C2×C5×Dic3C22×C412yes—
244C4×C5×D3—44no—
245C3×C22⋊D5—44no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5—21no—
249C2×C3×Dic5—21no—
250C2×C3×Dic5—21no—
251C2×C3×Dic5—21no—
252C2×C3×Dic5—21no—
253C2×C3×Dic5—21no—
254C2×C3×Dic5C22×C412yes—
255C3×C4×D5—44no—
256#1203—44no—
257#1202—44no—
258#1201—28no—
259C22×C3×D4—51no—
260C23×C3×C4—51no—
261C22×#67—51no—
262C22×#67—51no—
263C22×#67—51no—
264C22×#67C2×D511yescharacteristic
265C23×Dic3—51no—
266C22×D12—51no—
267C22×C4×D3—51no—
268C22×C4×D3C2×D511yescharacteristic
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4C2×D511yescharacteristic
272C2×#217—51no—
273C2×#217—51no—
274C2×#217C2×D511yescharacteristic
275#940—58no—
276C4×#67—104no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4C2×D511yescharacteristic
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288#67⋊C4—104no—
289C3×#95—51no—
290C3×#95—51no—
291C3⋊#95—51no—
292C3⋊#95—51no—
293C3⋊#95—51no—
294C3⋊#95—51no—
295C3⋊#95C2×D511yescharacteristic
296C3⋊#95C2×D511yescharacteristic
297C24×C5—31no—
298C24×C5C22×D311yescharacteristic
299C23×D5—31no—
300C23×D5C22×D311yescharacteristic
301C2×C5×D4—34no—
302C2×C5×D4—121no—
303C2×C5×D4—121no—
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—62no—
308C22×C4×C5—121no—
309C22×C4×C5—121no—
310C22×C4×C5C22×D311yescharacteristic
311C22×C4×C5C22×D311yescharacteristic
312C2×C22⋊D5—34no—
313C2×C22⋊D5—34no—
314C2×C22⋊D5—34no—
315C2×C22⋊D5—41no—
316C2×C22⋊D5—41no—
317C2×C22⋊D5—62no—
318C2×C22⋊D5—62no—
319C2×C22⋊D5—62no—
320C2×C22⋊D5—62no—
321C2×C22⋊D5—121no—
322C2×C22⋊D5—121no—
323C2×C22⋊D5C4×D314yescomplemented
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—62no—
328C22×Dic5—121no—
329C22×Dic5—121no—
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C22×Dic5C22×D311yescharacteristic
333C2×D20—34no—
334C2×D20—121no—
335C2×D20—121no—
336C2×C4×D5—22no—
337C2×C4×D5—41no—
338C2×C4×D5—41no—
339C2×C4×D5—62no—
340C2×C4×D5—121no—
341C2×C4×D5—121no—
342C5×C22⋊C4—22no—
343C5×C22⋊C4—121no—
344C5×C22⋊C4—121no—
345C22⋊Dic5—41no—
346C22⋊Dic5—62no—
347C22⋊Dic5—121no—
348#685—41no—
349#685—62no—
350#685—62no—
351#685—121no—
352#685—121no—
353#685—121no—
354#683—62no—
355#683—62no—
356C4×Dic5—34no—
357C4×Dic5—34no—
358C4×Dic5—62no—
359C2×#127—151no—
360C2×C4×D4—151no—
361C2×C4×D4—151no—
362#390—151no—
363#390—151no—
364#386—31no—
365#386—51no—
366#386—151no—
367#386—151no—
368#386—151no—
369#386—151no—
370#386—151no—
371#386—151no—
372#382—151no—
373#376—151no—
374C22×C3×C5—22no—
375C22×C3×C5—22no—
376C22×C3×C5—22no—
377C22×C3×C5—41no—
378C22×C3×C5—41no—
379C22×C3×C5—41no—
380C22×C3×C5—41no—
381C22×C3×C5C23×C411yescharacteristic
382C22×C3×C5C22×D411yescharacteristic
383C22×C3×C5C2×#4111yescharacteristic
384C22×C3×C5H(5,𝔽2)11yescharacteristic
385C22×C3×C5H(5,𝔽2)11yescharacteristic
386C22×C3×C5H(5,𝔽2)11yescharacteristic
387C22×C3×C5H(5,𝔽2)11yescharacteristic
388C2×D15—22no—
389C2×D15—22no—
390C2×D15—22no—
391C2×D15—41no—
392C2×D15—41no—
393C2×D15—41no—
394C2×D15—41no—
395C2×C5×D3—22no—
396C2×C5×D3—22no—
397C2×C5×D3—22no—
398C2×C5×D3—41no—
399C2×C5×D3—41no—
400C2×C5×D3—41no—
401C2×C5×D3—41no—
402C2×C3×D5—22no—
403C2×C3×D5—22no—
404C2×C3×D5—22no—
405C2×C3×D5—41no—
406C2×C3×D5—41no—
407C2×C3×D5—41no—
408C2×C3×D5—41no—
409C3×C4×C5—22no—
410C3×C4×C5—41no—
411Dic15—22no—
412Dic15—41no—
413Dic15C4×D414yes—
414C3×Dic5—22no—
415C3×Dic5—41no—
416C3×Dic5—41no—
417C5×Dic3—22no—
418C5×Dic3—41no—
419C5×Dic3—41no—
420C24×C3—51no—
421C24×C3C22×D511yescharacteristic
422C23×D3—51no—
423C23×D3C22×D511yescharacteristic
424C2×C3×D4—54no—
425C2×C3×D4—201no—
426C2×C3×D4—201no—
427C22×C3×C4—51no—
428C22×C3×C4—51no—
429C22×C3×C4—51no—
430C22×C3×C4—102no—
431C22×C3×C4—201no—
432C22×C3×C4—201no—
433C22×C3×C4C22×D511yescharacteristic
434C22×C3×C4C22×D511yescharacteristic
435C2×#67—41no—
436C2×#67—41no—
437C2×#67—54no—
438C2×#67—54no—
439C2×#67—54no—
440C2×#67—102no—
441C2×#67—102no—
442C2×#67—102no—
443C2×#67—102no—
444C2×#67—201no—
445C2×#67—201no—
446C2×#67C4×D514yescomplemented
447C22×Dic3—51no—
448C22×Dic3—51no—
449C22×Dic3—51no—
450C22×Dic3—102no—
451C22×Dic3—201no—
452C22×Dic3—201no—
453C22×Dic3C22×D511yescharacteristic
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
456C2×D12—54no—
457C2×D12—201no—
458C2×D12—201no—
459C2×C4×D3—22no—
460C2×C4×D3—41no—
461C2×C4×D3—41no—
462C2×C4×D3—102no—
463C2×C4×D3—201no—
464C2×C4×D3—201no—
465C3×C22⋊C4—22no—
466C3×C22⋊C4—201no—
467C3×C22⋊C4—201no—
468#217—41no—
469#217—102no—
470#217—201no—
471(C2×D3)⋊C4—41no—
472(C2×D3)⋊C4—102no—
473(C2×D3)⋊C4—102no—
474(C2×D3)⋊C4—201no—
475(C2×D3)⋊C4—201no—
476(C2×D3)⋊C4—201no—
477Dic3⋊C4—102no—
478Dic3⋊C4—102no—
479C4×Dic3—54no—
480C4×Dic3—54no—
481C4×Dic3—102no—
482C23×C5—21no—
483C23×C5—21no—
484C23×C5—21no—
485C23×C5—21no—
486C23×C5—21no—
487C23×C5—21no—
488C23×C5—32no—
489C23×C5—61no—
490C23×C5—61no—
491C23×C5—61no—
492C23×C5—61no—
493C23×C5—61no—
494C23×C5—61no—
495C23×C5C2×C4×D312yes—
496C23×C5C23×D311yescharacteristic
497C22×D5—21no—
498C22×D5—21no—
499C22×D5—21no—
500C22×D5—21no—
501C22×D5—21no—
502C22×D5—21no—
503C22×D5—32no—
504C22×D5—61no—
505C22×D5—61no—
506C22×D5—61no—
507C22×D5—61no—
508C22×D5—61no—
509C22×D5—61no—
510C22×D5C2×C4×D312yes—
511C5×D4—124no—
512C2×C4×C5—21no—
513C2×C4×C5—21no—
514C2×C4×C5—21no—
515C2×C4×C5—21no—
516C2×C4×C5—21no—
517C2×C4×C5—32no—
518C2×C4×C5—61no—
519C2×C4×C5—61no—
520C2×C4×C5—61no—
521C2×C4×C5—61no—
522C2×C4×C5—61no—
523C2×C4×C5—61no—
524C2×C4×C5—61no—
525C2×C4×C5—61no—
526C2×C4×C5—124no—
527C2×C4×C5D3×D412yes—
528C22⋊D5—44no—
529C22⋊D5—68no—
530C22⋊D5—68no—
531C22⋊D5—124no—
532C2×Dic5—21no—
533C2×Dic5—21no—
534C2×Dic5—21no—
535C2×Dic5—21no—
536C2×Dic5—21no—
537C2×Dic5—21no—
538C2×Dic5—21no—
539C2×Dic5—21no—
540C2×Dic5—32no—
541C2×Dic5—32no—
542C2×Dic5—32no—
543C2×Dic5—32no—
544C2×Dic5—61no—
545C2×Dic5—61no—
546C2×Dic5—61no—
547C2×Dic5—61no—
548C2×Dic5—61no—
549C2×Dic5—124no—
550C2×Dic5C2×C4×D312yes—
551D20—124no—
552C4×D5—44no—
553C4×D5—124no—
554C22×D4—31no—
555C22×D4—51no—
556C22×D4—151no—
557C22×D4—151no—
558C22×D4—151no—
559C22×D4—151no—
560C23×C4—31no—
561C23×C4—51no—
562C23×C4—151no—
563C23×C4—151no—
564#127—158no—
565C4×D4—304no—
566C4×D4—304no—
567C2×C4⋊C4—151no—
568C2×C4⋊C4—151no—
569C2×C22⋊C4—31no—
570C2×C22⋊C4—31no—
571C2×C22⋊C4—51no—
572C2×C22⋊C4—51no—
573C2×C22⋊C4—151no—
574C2×C22⋊C4—151no—
575C2×C22⋊C4—151no—
576C2×C22⋊C4—151no—
577C2×C22⋊C4—151no—
578C2×C22⋊C4—151no—
579C2×C22⋊C4—151no—
580C2×C22⋊C4D3×D511yescharacteristic
581C2×C42—151no—
582C2×C42—151no—
583C2×C42—151no—
584#95—31no—
585#95—31no—
586#95—51no—
587#95—51no—
588#95—151no—
589#95—151no—
590#95—151no—
591#95—151no—
592C2×C3×C5—42no—
593C2×C3×C5C2×C4×D411yescharacteristic
594C2×C3×C5#51811yescharacteristic
595C2×C3×C5#51811yescharacteristic
596C2×C3×C5#53511yescharacteristic
597C2×C3×C5#53511yescharacteristic
598C2×C3×C5#54011yescharacteristic
599C2×C3×C5#54011yescharacteristic
600D15—42no—
601C3×D5—42no—
602C5×D3—42no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—21no—
609C23×C3—52no—
610C23×C3—101no—
611C23×C3—101no—
612C23×C3—101no—
613C23×C3—101no—
614C23×C3—101no—
615C23×C3—101no—
616C23×C3C2×C4×D512yes—
617C23×C3C23×D511yescharacteristic
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—52no—
625C22×D3—101no—
626C22×D3—101no—
627C22×D3—101no—
628C22×D3—101no—
629C22×D3—101no—
630C22×D3—101no—
631C22×D3C2×C4×D512yes—
632C3×D4—204no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—21no—
636C2×C3×C4—21no—
637C2×C3×C4—21no—
638C2×C3×C4—52no—
639C2×C3×C4—101no—
640C2×C3×C4—101no—
641C2×C3×C4—101no—
642C2×C3×C4—101no—
643C2×C3×C4—101no—
644C2×C3×C4—101no—
645C2×C3×C4—101no—
646C2×C3×C4—101no—
647C2×C3×C4—204no—
648C2×C3×C4D4×D512yes—
649#67—44no—
650#67—108no—
651#67—108no—
652#67—204no—
653C2×Dic3—21no—
654C2×Dic3—21no—
655C2×Dic3—21no—
656C2×Dic3—21no—
657C2×Dic3—21no—
658C2×Dic3—21no—
659C2×Dic3—21no—
660C2×Dic3—21no—
661C2×Dic3—52no—
662C2×Dic3—52no—
663C2×Dic3—52no—
664C2×Dic3—52no—
665C2×Dic3—101no—
666C2×Dic3—101no—
667C2×Dic3—101no—
668C2×Dic3—101no—
669C2×Dic3—101no—
670C2×Dic3—204no—
671C2×Dic3C2×C4×D512yes—
672D12—204no—
673C4×D3—44no—
674C4×D3—204no—
675C22×C5—22no—
676C22×C5—22no—
677C22×C5—22no—
678C22×C5—41no—
679C22×C5—41no—
680C22×C5—41no—
681C22×C5—41no—
682C22×C5—62no—
683C22×C5—62no—
684C22×C5—62no—
685C22×C5—121no—
686C22×C5—121no—
687C22×C5—121no—
688C22×C5—121no—
689C22×C5C22×C4×D311yescharacteristic
690C22×C5C2×D3×D411yescharacteristic
691C22×C5#100411yescharacteristic
692C22×C5#100411yescharacteristic
693C22×C5#100411yescharacteristic
694C22×C5D3×#4111yescharacteristic
695C22×C5#100911yescharacteristic
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—22no—
699C2×D5—41no—
700C2×D5—41no—
701C2×D5—41no—
702C2×D5—41no—
703C2×D5—62no—
704C2×D5—62no—
705C2×D5—62no—
706C2×D5—121no—
707C2×D5—121no—
708C2×D5—121no—
709C2×D5—121no—
710C4×C5—22no—
711C4×C5—41no—
712C4×C5—62no—
713C4×C5—121no—
714C4×C5—121no—
715Dic5—22no—
716Dic5—34no—
717Dic5—41no—
718Dic5—41no—
719Dic5—62no—
720Dic5—121no—
721C24—31no—
722C24—51no—
723C24—151no—
724C24C2×D3×D511yescharacteristic
725C2×D4—34no—
726C2×D4—54no—
727C2×D4—121no—
728C2×D4—121no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—201no—
734C2×D4—201no—
735C2×D4—302no—
736C2×D4—302no—
737C2×D4—302no—
738C2×D4—302no—
739C2×D4—601no—
740C2×D4—601no—
741C2×D4—601no—
742C2×D4—601no—
743C22×C4—31no—
744C22×C4—31no—
745C22×C4—31no—
746C22×C4—51no—
747C22×C4—51no—
748C22×C4—51no—
749C22×C4—62no—
750C22×C4—102no—
751C22×C4—121no—
752C22×C4—121no—
753C22×C4—151no—
754C22×C4—151no—
755C22×C4—151no—
756C22×C4—201no—
757C22×C4—201no—
758C22×C4—302no—
759C22×C4—302no—
760C22×C4—601no—
761C22×C4—601no—
762C22×C4—601no—
763C22×C4—601no—
764C22×C4C2×D3×D511yescharacteristic
765C22×C4C2×D3×D511yescharacteristic
766C4⋊C4—302no—
767C4⋊C4—302no—
768C22⋊C4—22no—
769C22⋊C4—121no—
770C22⋊C4—121no—
771C22⋊C4—201no—
772C22⋊C4—201no—
773C22⋊C4—302no—
774C22⋊C4—302no—
775C22⋊C4—302no—
776C22⋊C4—601no—
777C22⋊C4—601no—
778C22⋊C4—601no—
779C22⋊C4—601no—
780C42—154no—
781C42—154no—
782C42—302no—
783C3×C5#232811yescharacteristic, complemented, Hall
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—41no—
788C22×C3—41no—
789C22×C3—41no—
790C22×C3—41no—
791C22×C3—102no—
792C22×C3—102no—
793C22×C3—102no—
794C22×C3—201no—
795C22×C3—201no—
796C22×C3—201no—
797C22×C3—201no—
798C22×C3C22×C4×D511yescharacteristic
799C22×C3C2×D4×D511yescharacteristic
800C22×C3#414411yescharacteristic
801C22×C3#414411yescharacteristic
802C22×C3#414411yescharacteristic
803C22×C3D5×#4111yescharacteristic
804C22×C3#414911yescharacteristic
805C2×D3—22no—
806C2×D3—22no—
807C2×D3—22no—
808C2×D3—41no—
809C2×D3—41no—
810C2×D3—41no—
811C2×D3—41no—
812C2×D3—102no—
813C2×D3—102no—
814C2×D3—102no—
815C2×D3—201no—
816C2×D3—201no—
817C2×D3—201no—
818C2×D3—201no—
819C3×C4—22no—
820C3×C4—41no—
821C3×C4—102no—
822C3×C4—201no—
823C3×C4—201no—
824Dic3—22no—
825Dic3—41no—
826Dic3—41no—
827Dic3—54no—
828Dic3—102no—
829Dic3—201no—
830C2×C5—42no—
831C2×C5—122no—
832C2×C5#548611yescharacteristic
833C2×C5C4×D3×D411yescharacteristic
834C2×C5#554511yescharacteristic
835C2×C5#559211yescharacteristic
836C2×C5#560711yescharacteristic
837C2×C5#561511yescharacteristic
838C2×C5#566311yescharacteristic
839D5—42no—
840D5—122no—
841C23—21no—
842C23—21no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—32no—
848C23—52no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—101no—
856C23—101no—
857C23—101no—
858C23—101no—
859C23—101no—
860C23—101no—
861C23—152no—
862C23—301no—
863C23—301no—
864C23—301no—
865C23—301no—
866C23—301no—
867C23—301no—
868C23C4×D3×D512yes—
869C23C22×D3×D511yescharacteristic
870D4—124no—
871D4—204no—
872D4—308no—
873D4—308no—
874D4—604no—
875D4—604no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—32no—
882C2×C4—52no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—101no—
892C2×C4—101no—
893C2×C4—101no—
894C2×C4—101no—
895C2×C4—101no—
896C2×C4—101no—
897C2×C4—101no—
898C2×C4—101no—
899C2×C4—124no—
900C2×C4—152no—
901C2×C4—152no—
902C2×C4—152no—
903C2×C4—152no—
904C2×C4—204no—
905C2×C4—301no—
906C2×C4—301no—
907C2×C4—301no—
908C2×C4—301no—
909C2×C4—301no—
910C2×C4—604no—
911C2×C4—604no—
912C2×C4#679012yes—
913C2×C3—42no—
914C2×C3—202no—
915C2×C3#6582011yescharacteristic
916C2×C3C4×D4×D511yescharacteristic
917C2×C3#6587911yescharacteristic
918C2×C3#6592611yescharacteristic
919C2×C3#6594111yescharacteristic
920C2×C3#6594911yescharacteristic
921C2×C3#6599711yescharacteristic
922D3—42no—
923D3—202no—
924C5#7466711yescharacteristic, complemented, Sylow
925C22—22no—
926C22—22no—
927C22—22no—
928C22—41no—
929C22—41no—
930C22—41no—
931C22—41no—
932C22—62no—
933C22—62no—
934C22—62no—
935C22—102no—
936C22—102no—
937C22—102no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—201no—
943C22—201no—
944C22—201no—
945C22—201no—
946C22—302no—
947C22—302no—
948C22—302no—
949C22—601no—
950C22—601no—
951C22—601no—
952C22—601no—
953C22C2×C4×D3×D511yescharacteristic
954C22#9201611yescharacteristic
955C22#9202511yescharacteristic
956C22#9202511yescharacteristic
957C22#9202611yescharacteristic
958C22#9202711yescharacteristic
959C22C2×#679011yescharacteristic
960C4—22no—
961C4—41no—
962C4—62no—
963C4—102no—
964C4—121no—
965C4—121no—
966C4—154no—
967C4—201no—
968C4—201no—
969C4—302no—
970C4—601no—
971C3#1060639811yescharacteristic, complemented, Sylow
972C2—42no—
973C2—122no—
974C2—202no—
975C2—602no—
976C2#1175301311yescharacteristic
977C2#1175314511yescharacteristic
978C2#1175320011yescharacteristic
979C2#1175320211yescharacteristic
980C2C4×#679011yescharacteristic
981C2#1175495311yescharacteristic
982C2#1175495511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91567C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2328
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91770C2semidirect
3. C2×C4×#1201C2semidirect
4. C5×#4956C2semidirect
5. C3×#65245C2semidirect
6. #11749501C2semidirect
7. #11749500C2semidirect
8. #11749483C2semidirect
9. #11748918C2semidirect
10. #11748917C2semidirect
11. #11748916C2semidirect
12. #11748914C2semidirect
13. #11748907C2semidirect
14. #11748653C2semidirect
15. #11748644C2semidirect
36. #91567C4semidirect
66. #65245D3semidirect
79. C2×#1220C2×C4semidirect
91. C2×C5×#67C2×C4semidirect
100. C2×C3×C22⋊D5C2×C4semidirect
109. C2×#1203C2×C4semidirect
112. C2×#1202C2×C4semidirect
115. C2×#1201C2×C4semidirect
119. C4×Dic15D4semidirect
132. Dic3×Dic5C2×C4semidirect
143. #4956D5semidirect
323. C2×C22⋊D5C4×D3semidirect
446. C2×#67C4×D5semidirect
783. C3×C5#2328semidirect
924. C5#74667semidirect
971. C3#10606398semidirect

Maximal subgroups

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

subgroupindex
C2×#917702
C2×#915672
C2×C4×#12012
C5×#49562
C3×#652452
#117495012
#117495002
#117494832
#117489182
#117489172
#117489162
#117489142
#117489072
#117486532
#117486442
#106063983
#746675