Finite Group Databasebeta

← #14330670

Subgroups — #14330670

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91475C211yesmaximal, characteristic
2#11751091C211yesmaximal, characteristic, complemented
3C5×#4988C211yesmaximal, characteristic, complemented
4C3×#65279C211yesmaximal, characteristic, complemented
5#11748940C211yesmaximal, characteristic, complemented
6#11748940C211yesmaximal, characteristic, complemented
7#11748915C211yesmaximal, characteristic, complemented
8#11748911C211yesmaximal, characteristic, complemented
9#11748908C211yesmaximal, characteristic, complemented
10#11748901C211yesmaximal, characteristic, complemented
11#11748883C211yesmaximal, characteristic, complemented
12#11748854C211yesmaximal, characteristic, complemented
13#11748770C211yesmaximal, characteristic, complemented
14#11748724C211yesmaximal, characteristic, complemented
15#11748714C211yesmaximal, characteristic, complemented
16#10608165—31nomaximal, Hall
17C23×D3×D5C2211yescharacteristic
18C22×C5×D12C2211yescharacteristic
19C22×#1203C2211yescharacteristic
20C22×#1201C2211yescharacteristic
21C22×D3×Dic5C2211yescharacteristic, complemented
22C2×C3×C5×C4⋊C4C2211yescharacteristic, complemented
23C2×#6714C2211yescharacteristic
24C2×#6714C2211yescharacteristic
25C2×#6714C2211yescharacteristic
26C2×C4×Dic15C2211yescharacteristic, complemented
27C2×C5×(C2×D3)⋊C4C2211yescharacteristic
28C2×C5×(C2×D3)⋊C4C2211yescharacteristic
29C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
30C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
31C2×C4×C5×Dic3C2211yescharacteristic, complemented
32C2×C3×#685C2211yescharacteristic
33C2×C3×#685C2211yescharacteristic
34C2×C3×#685C2211yescharacteristic
35C2×C3×C4×Dic5C2211yescharacteristic, complemented
36C2×#6669C2211yescharacteristic, complemented
37C2×#6668C2211yescharacteristic, complemented
38C2×#6667C2211yescharacteristic
39C2×#6667C2211yescharacteristic
40C2×(C2×D3)⋊Dic5C2211yescharacteristic
41C2×(C2×D3)⋊Dic5C2211yescharacteristic
42C2×(C2×D3)⋊Dic5C2211yescharacteristic
43C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
44C2×#6665C2211yescharacteristic
45C2×#6665C2211yescharacteristic
46#91475C418yescomplemented
47#91115C2211yescharacteristic, complemented
48#91115C2211yescharacteristic, complemented
49C3×#3963C2211yescharacteristic, complemented
50C3×#3963C2211yescharacteristic, complemented
51#90994C2211yescharacteristic, complemented
52#90994C2211yescharacteristic, complemented
53#75840—51nomaximal, Hall
54C2×#4083—31no—
55C5×#390—31no—
56#65509—31no—
57#65279—31no—
58#65279D311yescharacteristic, complemented
59#65247—31no—
60#65247—31no—
61#65246—31no—
62#65246—31no—
63#65244—31no—
64#65244—31no—
65#65233—31no—
66#65233—31no—
67#65229—31no—
68#65229—31no—
69C23×D15C2311yescharacteristic
70C23×C5×D3C2311yescharacteristic
71C23×C5×D3C2311yescharacteristic
72C23×C3×D5C2311yescharacteristic
73C22×D3×D5—41no—
74C22×D3×D5—41no—
75C22×D3×D5—41no—
76C22×D3×D5—41no—
77C22×D3×D5—41no—
78C22×D3×D5—41no—
79C22×D3×D5C2×C414yescomplemented
80C22×C3×C4×C5C2311yescharacteristic
81C22×C3×C4×C5C2311yescharacteristic
82C22×C3×C4×C5C2311yescharacteristic
83C22×Dic15C2311yescharacteristic
84C22×Dic15C2311yescharacteristic
85C22×Dic15C2311yescharacteristic
86C22×C5×Dic3C2311yescharacteristic
87C22×C5×Dic3C2311yescharacteristic
88C2×C5×D12—41no—
89C2×C5×D12—41no—
90C2×C5×D12C2×C414yes—
91C22×C3×Dic5C2311yescharacteristic
92C22×C3×Dic5C2311yescharacteristic
93C22×C3×Dic5C2311yescharacteristic
94C2×#1203—41no—
95C2×#1203—41no—
96C2×#1203C2×C414yes—
97C2×#1201—41no—
98C2×#1201—41no—
99C2×#1201C2×C414yes—
100C2×D3×Dic5—41no—
101C2×D3×Dic5—41no—
102C2×D3×Dic5—41no—
103C3×C5×C4⋊C4—41no—
104#6714—41no—
105#6714—41no—
106#6714C2×C414yescomplemented
107C4×Dic15—41no—
108C5×(C2×D3)⋊C4—41no—
109C5×(C2×D3)⋊C4—41no—
110C5×(C2×D3)⋊C4—41no—
111C5×(C2×D3)⋊C4—41no—
112C4×C5×Dic3—41no—
113C3×#685—41no—
114C3×#685—41no—
115C3×#685C2×C414yescomplemented
116C3×C4×Dic5—41no—
117#6669—41no—
118#6668—41no—
119#6667—41no—
120#6667—41no—
121(C2×D3)⋊Dic5—41no—
122(C2×D3)⋊Dic5—41no—
123(C2×D3)⋊Dic5—41no—
124(C2×D3)⋊Dic5C2×C414yescomplemented
125#6665—41no—
126#6665—41no—
127C2×#882—51no—
128C3×#388—51no—
129#4990—51no—
130#4988D511yescharacteristic, complemented
131#4957—51no—
132#4956—51no—
133#4955—51no—
134#4955—51no—
135#4951—51no—
136#4940—51no—
137#4939—51no—
138#4670—51no—
139#4669—51no—
140#4665—51no—
141#4665—51no—
142C24×D5—31no—
143C22×C5×D4—31no—
144C22×C22⋊D5—31no—
145C22×C22⋊D5—31no—
146C23×Dic5—31no—
147C2×C5×C4⋊C4C2×D311yescharacteristic, complemented
148C2×C5×C22⋊C4—31no—
149C2×C5×C22⋊C4—31no—
150C2×C5×C22⋊C4—31no—
151C2×C5×C22⋊C4—31no—
152C2×C42×C5—31no—
153C2×C22⋊Dic5—31no—
154C2×C22⋊Dic5—31no—
155C2×C22⋊Dic5—31no—
156C2×C22⋊Dic5—31no—
157#4083—38no—
158C2×#685—31no—
159C2×#685—31no—
160C2×#685—31no—
161C2×#685—31no—
162C2×#685—31no—
163C2×#685—31no—
164C2×#685—31no—
165C2×#685C2×D311yescharacteristic
166C2×#685C2×D311yescharacteristic
167C2×#685C2×D311yescharacteristic
168C2×#683—31no—
169C2×#683—31no—
170C2×C4×Dic5—31no—
171C2×C4×Dic5C2×D311yescharacteristic, complemented
172#3963—31no—
173#3963—31no—
174#3963—31no—
175#3963—31no—
176#3963C2×D311yescharacteristic, complemented
177#3963C2×D311yescharacteristic, complemented
178#2375—151noSylow
179C23×C3×C5C2411yescharacteristic
180C22×D15—21no—
181C22×D15—21no—
182C22×D15—21no—
183C22×D15—21no—
184C22×D15—21no—
185C22×D15—21no—
186C22×D15C22×C412yes—
187C22×C5×D3—21no—
188C22×C5×D3—21no—
189C22×C5×D3—21no—
190C22×C5×D3—21no—
191C22×C5×D3—21no—
192C22×C5×D3—21no—
193C22×C5×D3—21no—
194C22×C5×D3—21no—
195C22×C5×D3—21no—
196C22×C5×D3—21no—
197C22×C5×D3—21no—
198C22×C5×D3—21no—
199C22×C5×D3C22×C412yes—
200C22×C5×D3C22×C412yes—
201C22×C3×D5—21no—
202C22×C3×D5—21no—
203C22×C3×D5—21no—
204C22×C3×D5—21no—
205C22×C3×D5—21no—
206C22×C3×D5—21no—
207C22×C3×D5C22×C412yes—
208C2×D3×D5—44no—
209C2×D3×D5—44no—
210C2×D3×D5—44no—
211C2×D3×D5—44no—
212C2×D3×D5—44no—
213C2×D3×D5—44no—
214C2×D3×D5—44no—
215C2×C3×C4×C5—21no—
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×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5C22×C412yes—
224C2×Dic15—21no—
225C2×Dic15—21no—
226C2×Dic15—21no—
227C2×Dic15—21no—
228C2×Dic15—21no—
229C2×Dic15—21no—
230C2×Dic15—21no—
231C2×Dic15—21no—
232C2×Dic15C22×C412yes—
233C2×C5×Dic3—21no—
234C2×C5×Dic3—21no—
235C2×C5×Dic3—21no—
236C2×C5×Dic3—21no—
237C2×C5×Dic3—21no—
238C2×C5×Dic3—21no—
239C5×D12—44no—
240C2×C3×Dic5—21no—
241C2×C3×Dic5—21no—
242C2×C3×Dic5—21no—
243C2×C3×Dic5—21no—
244C2×C3×Dic5—21no—
245C2×C3×Dic5—21no—
246C2×C3×Dic5—21no—
247C2×C3×Dic5—21no—
248C2×C3×Dic5C22×C412yes—
249#1203—44no—
250#1201—44no—
251D3×Dic5—44no—
252C24×D3—51no—
253C22×#67—51no—
254C22×D12—51no—
255C22×D12C2×D511yescharacteristic
256C22×C4×D3—51no—
257C2×C3×C4⋊C4C2×D511yescharacteristic, complemented
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C42—51no—
262C2×#217—51no—
263C2×#217—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4—51no—
269C2×(C2×D3)⋊C4—51no—
270C2×(C2×D3)⋊C4—51no—
271C2×(C2×D3)⋊C4—51no—
272C2×(C2×D3)⋊C4—51no—
273C2×(C2×D3)⋊C4C2×D511yescharacteristic
274C2×(C2×D3)⋊C4C2×D511yescharacteristic
275C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
276C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
277C2×C4⋊Dic3—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3C2×D511yescharacteristic, complemented
281#882—58no—
282C3×#95—51no—
283C3×#95—51no—
284C3⋊#95—51no—
285C3⋊#95—51no—
286C3⋊#95—51no—
287C3⋊#95—51no—
288C24×C5—31no—
289C24×C5—31no—
290C23×D5—31no—
291C23×D5—34no—
292C23×D5—121no—
293C23×D5—121no—
294C23×D5—121no—
295C23×D5—121no—
296C23×D5—121no—
297C23×D5—121no—
298C23×D5C22×D311yescharacteristic
299C2×C5×D4—34no—
300C2×C5×D4—121no—
301C2×C5×D4—121no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5C22×D311yescharacteristic
305C22×C4×C5C22×D311yescharacteristic
306C22×C4×C5C22×D311yescharacteristic
307C2×C22⋊D5—34no—
308C2×C22⋊D5—34no—
309C2×C22⋊D5—121no—
310C2×C22⋊D5—121no—
311C2×C22⋊D5—121no—
312C2×C22⋊D5—121no—
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—121no—
317C22×Dic5—121no—
318C22×Dic5—121no—
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C5×C4⋊C4—41no—
323C5×C22⋊C4—121no—
324C5×C22⋊C4—121no—
325C5×C22⋊C4—121no—
326C5×C22⋊C4—121no—
327C42×C5—121no—
328C22⋊Dic5—34no—
329C22⋊Dic5—121no—
330C22⋊Dic5—121no—
331C22⋊Dic5—121no—
332#685—34no—
333#685—41no—
334#685—41no—
335#685—121no—
336#685—121no—
337#685—121no—
338#685—121no—
339#685—121no—
340#685—121no—
341#685C4×D314yescomplemented
342#683—121no—
343#683—121no—
344C4×Dic5—41no—
345C4×Dic5—121no—
346C2×#120—151no—
347#390—31no—
348#390—151no—
349#390—151no—
350#388—51no—
351#388—151no—
352#388—151no—
353#388—151no—
354#388—151no—
355#388—151no—
356#386—151no—
357#386—151no—
358#386—151no—
359#379—151no—
360#379—151no—
361C22×C3×C5C23×C411yescharacteristic
362C22×C3×C5H(5,𝔽2)11yescharacteristic
363C22×C3×C5H(5,𝔽2)11yescharacteristic
364C22×C3×C5H(5,𝔽2)11yescharacteristic
365C22×C3×C5H(5,𝔽2)11yescharacteristic
366C22×C3×C5H(5,𝔽2)11yescharacteristic
367C22×C3×C5H(5,𝔽2)11yescharacteristic
368C2×D15—22no—
369C2×D15—22no—
370C2×D15—22no—
371C2×D15—41no—
372C2×D15—41no—
373C2×D15—41no—
374C2×D15—41no—
375C2×C5×D3—22no—
376C2×C5×D3—22no—
377C2×C5×D3—22no—
378C2×C5×D3—22no—
379C2×C5×D3—22no—
380C2×C5×D3—22no—
381C2×C5×D3—41no—
382C2×C5×D3—41no—
383C2×C5×D3—41no—
384C2×C5×D3—41no—
385C2×C5×D3—41no—
386C2×C5×D3—41no—
387C2×C5×D3—41no—
388C2×C5×D3—41no—
389C2×C3×D5—22no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—41no—
393C2×C3×D5—41no—
394C2×C3×D5—41no—
395C2×C3×D5—41no—
396D3×D5—416no—
397C3×C4×C5—22no—
398C3×C4×C5—41no—
399C3×C4×C5—41no—
400Dic15—22no—
401Dic15—41no—
402Dic15—41no—
403C3×Dic5—22no—
404C3×Dic5—41no—
405C3×Dic5—41no—
406C5×Dic3—41no—
407C5×Dic3—41no—
408C24×C3—51no—
409C23×D3—51no—
410C23×D3—54no—
411C23×D3—201no—
412C23×D3—201no—
413C23×D3—201no—
414C23×D3—201no—
415C23×D3—201no—
416C23×D3—201no—
417C23×D3C22×D511yescharacteristic
418C23×D3C22×D511yescharacteristic
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—51no—
422C22×C3×C4C22×D511yescharacteristic
423C22×C3×C4C22×D511yescharacteristic
424C22×C3×C4C22×D511yescharacteristic
425C2×#67—54no—
426C2×#67—201no—
427C2×#67—201no—
428C22×Dic3—51no—
429C22×Dic3—51no—
430C22×Dic3—51no—
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C2×D12—41no—
434C2×D12—41no—
435C2×D12—54no—
436C2×D12—201no—
437C2×D12—201no—
438C2×D12C4×D514yes—
439C2×C4×D3—201no—
440C2×C4×D3—201no—
441C2×C4×D3—201no—
442C3×C4⋊C4—41no—
443C3×C22⋊C4—54no—
444C3×C22⋊C4—201no—
445C3×C22⋊C4—201no—
446C3×C42—201no—
447#217—201no—
448#217—201no—
449(C2×D3)⋊C4—41no—
450(C2×D3)⋊C4—41no—
451(C2×D3)⋊C4—41no—
452(C2×D3)⋊C4—41no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—201no—
456(C2×D3)⋊C4—201no—
457(C2×D3)⋊C4—201no—
458(C2×D3)⋊C4—201no—
459(C2×D3)⋊C4—201no—
460(C2×D3)⋊C4—201no—
461(C2×D3)⋊C4—201no—
462C4⋊Dic3—201no—
463Dic3⋊C4—201no—
464C4×Dic3—41no—
465C4×Dic3—201no—
466C23×C5—32no—
467C23×C5—32no—
468C23×C5—61no—
469C23×C5—61no—
470C23×C5—61no—
471C23×C5—61no—
472C23×C5—61no—
473C23×C5—61no—
474C23×C5—61no—
475C23×C5—61no—
476C23×C5—61no—
477C23×C5—61no—
478C23×C5—61no—
479C23×C5—61no—
480C23×C5C23×D311yescharacteristic
481C22×D5—21no—
482C22×D5—21no—
483C22×D5—21no—
484C22×D5—21no—
485C22×D5—21no—
486C22×D5—21no—
487C22×D5—32no—
488C22×D5—61no—
489C22×D5—61no—
490C22×D5—61no—
491C22×D5—61no—
492C22×D5—61no—
493C22×D5—61no—
494C22×D5—124no—
495C22×D5—124no—
496C22×D5—124no—
497C22×D5—124no—
498C22×D5—124no—
499C22×D5—124no—
500C22×D5—124no—
501C22×D5C2×C4×D312yes—
502C5×D4—124no—
503C2×C4×C5—21no—
504C2×C4×C5—21no—
505C2×C4×C5—21no—
506C2×C4×C5—21no—
507C2×C4×C5—21no—
508C2×C4×C5—21no—
509C2×C4×C5—21no—
510C2×C4×C5—21no—
511C2×C4×C5—61no—
512C2×C4×C5—61no—
513C2×C4×C5—61no—
514C2×C4×C5—61no—
515C2×C4×C5—61no—
516C2×C4×C5—61no—
517C2×C4×C5C2×C4×D312yes—
518C22⋊D5—124no—
519C22⋊D5—124no—
520C2×Dic5—21no—
521C2×Dic5—21no—
522C2×Dic5—21no—
523C2×Dic5—21no—
524C2×Dic5—21no—
525C2×Dic5—21no—
526C2×Dic5—21no—
527C2×Dic5—21no—
528C2×Dic5—32no—
529C2×Dic5—61no—
530C2×Dic5—61no—
531C2×Dic5—61no—
532C2×Dic5—61no—
533C2×Dic5—61no—
534C2×Dic5—61no—
535C2×Dic5—61no—
536C2×Dic5—61no—
537C2×Dic5—124no—
538C2×Dic5C2×C4×D312yes—
539C25—151no—
540C22×D4—31no—
541C22×D4—151no—
542C22×D4—151no—
543C23×C4—151no—
544#120—158no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4D3×D511yescharacteristic, complemented
548C2×C22⋊C4—31no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—31no—
552C2×C22⋊C4—51no—
553C2×C22⋊C4—51no—
554C2×C22⋊C4—51no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C22⋊C4—151no—
562C2×C22⋊C4—151no—
563C2×C22⋊C4—151no—
564C2×C22⋊C4—151no—
565C2×C22⋊C4—151no—
566C2×C42—31no—
567C2×C42—51no—
568C2×C42—151no—
569#95—51no—
570#95—51no—
571#95—151no—
572#95—151no—
573#95—151no—
574#95—151no—
575C2×C3×C5#51811yescharacteristic
576C2×C3×C5#51811yescharacteristic
577C2×C3×C5#51811yescharacteristic
578C2×C3×C5#56011yescharacteristic
579C2×C3×C5#56011yescharacteristic
580C2×C3×C5#56011yescharacteristic
581C2×C3×C5H(3,𝔽4)11yescharacteristic
582D15—42no—
583C3×D5—42no—
584C5×D3—42no—
585C5×D3—42no—
586C23×C3—52no—
587C23×C3—101no—
588C23×C3—101no—
589C23×C3—101no—
590C23×C3—101no—
591C23×C3—101no—
592C23×C3—101no—
593C23×C3C23×D511yescharacteristic
594C22×D3—21no—
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—52no—
607C22×D3—101no—
608C22×D3—101no—
609C22×D3—101no—
610C22×D3—101no—
611C22×D3—101no—
612C22×D3—101no—
613C22×D3—204no—
614C22×D3—204no—
615C22×D3—204no—
616C22×D3—204no—
617C22×D3—204no—
618C22×D3—204no—
619C22×D3—204no—
620C22×D3C2×C4×D512yes—
621C22×D3C2×C4×D512yes—
622C2×C3×C4—21no—
623C2×C3×C4—21no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—21no—
628C2×C3×C4—21no—
629C2×C3×C4—21no—
630C2×C3×C4—52no—
631C2×C3×C4—101no—
632C2×C3×C4—101no—
633C2×C3×C4—101no—
634C2×C3×C4—101no—
635C2×C3×C4—101no—
636C2×C3×C4—101no—
637C2×C3×C4—101no—
638C2×C3×C4—101no—
639C2×C3×C4C2×C4×D512yes—
640#67—204no—
641C2×Dic3—21no—
642C2×Dic3—21no—
643C2×Dic3—21no—
644C2×Dic3—21no—
645C2×Dic3—21no—
646C2×Dic3—21no—
647C2×Dic3—52no—
648C2×Dic3—101no—
649C2×Dic3—101no—
650C2×Dic3—101no—
651C2×Dic3—101no—
652C2×Dic3—101no—
653C2×Dic3—101no—
654C2×Dic3—101no—
655C2×Dic3—101no—
656D12—44no—
657D12—204no—
658C4×D3—204no—
659C22×C5—62no—
660C22×C5—62no—
661C22×C5—62no—
662C22×C5—62no—
663C22×C5—62no—
664C22×C5—62no—
665C22×C5—121no—
666C22×C5—121no—
667C22×C5—121no—
668C22×C5—121no—
669C22×C5—121no—
670C22×C5—121no—
671C22×C5—121no—
672C22×C5—121no—
673C22×C5C22×C4×D311yescharacteristic
674C22×C5#100411yescharacteristic
675C22×C5#100411yescharacteristic
676C22×C5#100911yescharacteristic
677C22×C5#100911yescharacteristic
678C22×C5#100911yescharacteristic
679C22×C5#100911yescharacteristic
680C2×D5—22no—
681C2×D5—22no—
682C2×D5—22no—
683C2×D5—41no—
684C2×D5—41no—
685C2×D5—41no—
686C2×D5—41no—
687C2×D5—62no—
688C2×D5—62no—
689C2×D5—62no—
690C2×D5—1216no—
691C2×D5—121no—
692C2×D5—121no—
693C2×D5—121no—
694C2×D5—121no—
695C4×C5—22no—
696C4×C5—41no—
697C4×C5—41no—
698C4×C5—121no—
699C4×C5—121no—
700Dic5—22no—
701Dic5—41no—
702Dic5—41no—
703Dic5—62no—
704Dic5—121no—
705Dic5—121no—
706C24—31no—
707C24—31no—
708C24—51no—
709C24—154no—
710C24—151no—
711C24—601no—
712C24—601no—
713C24—601no—
714C24—601no—
715C24—601no—
716C24—601no—
717C2×D4—34no—
718C2×D4—121no—
719C2×D4—121no—
720C2×D4—154no—
721C2×D4—154no—
722C2×D4—601no—
723C2×D4—601no—
724C2×D4—601no—
725C2×D4—601no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—51no—
729C22×C4—51no—
730C22×C4—51no—
731C22×C4—151no—
732C22×C4—151no—
733C22×C4—151no—
734C22×C4—601no—
735C22×C4—601no—
736C22×C4—601no—
737C22×C4C2×D3×D511yescharacteristic
738C22×C4C2×D3×D511yescharacteristic
739C22×C4C2×D3×D511yescharacteristic
740C4⋊C4—41no—
741C4⋊C4—601no—
742C4⋊C4—601no—
743C22⋊C4—54no—
744C22⋊C4—121no—
745C22⋊C4—121no—
746C22⋊C4—121no—
747C22⋊C4—121no—
748C22⋊C4—154no—
749C22⋊C4—154no—
750C22⋊C4—201no—
751C22⋊C4—201no—
752C22⋊C4—601no—
753C22⋊C4—601no—
754C22⋊C4—601no—
755C22⋊C4—601no—
756C22⋊C4—601no—
757C22⋊C4—601no—
758C22⋊C4—601no—
759C22⋊C4—601no—
760C22⋊C4—601no—
761C42—121no—
762C42—201no—
763C42—601no—
764C3×C5#237511yescharacteristic, complemented, Hall
765C22×C3—102no—
766C22×C3—102no—
767C22×C3—102no—
768C22×C3—201no—
769C22×C3—201no—
770C22×C3—201no—
771C22×C3—201no—
772C22×C3C22×C4×D511yescharacteristic
773C22×C3#414411yescharacteristic
774C22×C3#414411yescharacteristic
775C22×C3#414411yescharacteristic
776C22×C3#414411yescharacteristic
777C22×C3#414911yescharacteristic
778C22×C3#414911yescharacteristic
779C2×D3—22no—
780C2×D3—22no—
781C2×D3—22no—
782C2×D3—22no—
783C2×D3—22no—
784C2×D3—22no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—41no—
790C2×D3—41no—
791C2×D3—41no—
792C2×D3—41no—
793C2×D3—102no—
794C2×D3—102no—
795C2×D3—102no—
796C2×D3—2016no—
797C2×D3—201no—
798C2×D3—201no—
799C2×D3—201no—
800C2×D3—201no—
801C3×C4—22no—
802C3×C4—41no—
803C3×C4—41no—
804C3×C4—102no—
805C3×C4—201no—
806C3×C4—201no—
807Dic3—41no—
808Dic3—41no—
809Dic3—102no—
810Dic3—201no—
811Dic3—201no—
812C2×C5—122no—
813C2×C5—122no—
814C2×C5#552111yescharacteristic
815C2×C5#554511yescharacteristic
816C2×C5#554511yescharacteristic
817C2×C5#562011yescharacteristic
818C2×C5#566611yescharacteristic
819C2×C5#568311yescharacteristic
820C2×C5#571111yescharacteristic
821D5—42no—
822D5—122no—
823C23—32no—
824C23—32no—
825C23—52no—
826C23—61no—
827C23—61no—
828C23—61no—
829C23—61no—
830C23—61no—
831C23—61no—
832C23—61no—
833C23—61no—
834C23—61no—
835C23—61no—
836C23—61no—
837C23—61no—
838C23—101no—
839C23—101no—
840C23—101no—
841C23—101no—
842C23—101no—
843C23—101no—
844C23—152no—
845C23—301no—
846C23—301no—
847C23—301no—
848C23—301no—
849C23—301no—
850C23—301no—
851C23—604no—
852C23—604no—
853C23—604no—
854C23—604no—
855C23—604no—
856C23—604no—
857C23—604no—
858C23C22×D3×D511yescharacteristic
859D4—124no—
860D4—604no—
861D4—604no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—52no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—101no—
878C2×C4—101no—
879C2×C4—101no—
880C2×C4—101no—
881C2×C4—101no—
882C2×C4—101no—
883C2×C4—101no—
884C2×C4—101no—
885C2×C4—152no—
886C2×C4—301no—
887C2×C4—301no—
888C2×C4—301no—
889C2×C4—301no—
890C2×C4—301no—
891C2×C4—301no—
892C2×C4—301no—
893C2×C4—301no—
894C2×C4—604no—
895C2×C4C4×D3×D512yes—
896C2×C3—202no—
897C2×C3#6582011yescharacteristic
898C2×C3#6587911yescharacteristic
899C2×C3#6587911yescharacteristic
900C2×C3#6595411yescharacteristic
901C2×C3#6595411yescharacteristic
902C2×C3#6601711yescharacteristic
903C2×C3#6605411yescharacteristic
904D3—42no—
905D3—42no—
906D3—202no—
907C5#7584011yescharacteristic, complemented, Sylow
908C22—62no—
909C22—62no—
910C22—62no—
911C22—62no—
912C22—62no—
913C22—62no—
914C22—102no—
915C22—102no—
916C22—102no—
917C22—121no—
918C22—121no—
919C22—121no—
920C22—121no—
921C22—121no—
922C22—121no—
923C22—121no—
924C22—121no—
925C22—201no—
926C22—201no—
927C22—201no—
928C22—201no—
929C22—302no—
930C22—302no—
931C22—302no—
932C22—6016no—
933C22—601no—
934C22—601no—
935C22—601no—
936C22—601no—
937C22C2×C4×D3×D511yescharacteristic
938C22#9201811yescharacteristic
939C22#9202511yescharacteristic
940C22#9202711yescharacteristic
941C22#9203511yescharacteristic
942C22#9203511yescharacteristic
943C22#9204911yescharacteristic
944C4—22no—
945C4—41no—
946C4—41no—
947C4—102no—
948C4—121no—
949C4—121no—
950C4—201no—
951C4—201no—
952C4—302no—
953C4—601no—
954C4—601no—
955C3#1060816511yescharacteristic, complemented, Sylow
956C2—122no—
957C2—122no—
958C2—202no—
959C2—602no—
960C2#1175383711yescharacteristic
961C2#1175384111yescharacteristic
962C2#1175394011yescharacteristic
963C2#1175394211yescharacteristic
964C2#1175462711yescharacteristic
965C2#1175507911yescharacteristic
966C2#1175529411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91475C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2375
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. #11751091C2semidirect
3. C5×#4988C2semidirect
4. C3×#65279C2semidirect
5. #11748940C2semidirect
6. #11748940C2semidirect
7. #11748915C2semidirect
8. #11748911C2semidirect
9. #11748908C2semidirect
10. #11748901C2semidirect
11. #11748883C2semidirect
12. #11748854C2semidirect
13. #11748770C2semidirect
14. #11748724C2semidirect
15. #11748714C2semidirect
21. C22×D3×Dic5C22semidirect
22. C2×C3×C5×C4⋊C4C22semidirect
26. C2×C4×Dic15C22semidirect
29. C2×C5×(C2×D3)⋊C4C22semidirect
30. C2×C5×(C2×D3)⋊C4C22semidirect
31. C2×C4×C5×Dic3C22semidirect
35. C2×C3×C4×Dic5C22semidirect
36. C2×#6669C22semidirect
37. C2×#6668C22semidirect
43. C2×(C2×D3)⋊Dic5C22semidirect
46. #91475C4semidirect
47. #91115C22semidirect
48. #91115C22semidirect
49. C3×#3963C22semidirect
50. C3×#3963C22semidirect
51. #90994C22semidirect
52. #90994C22semidirect
58. #65279D3semidirect
79. C22×D3×D5C2×C4semidirect
106. #6714C2×C4semidirect
115. C3×#685C2×C4semidirect
124. (C2×D3)⋊Dic5C2×C4semidirect
130. #4988D5semidirect
147. C2×C5×C4⋊C4C2×D3semidirect
171. C2×C4×Dic5C2×D3semidirect
176. #3963C2×D3semidirect
177. #3963C2×D3semidirect
257. C2×C3×C4⋊C4C2×D5semidirect
275. C2×(C2×D3)⋊C4C2×D5semidirect
276. C2×(C2×D3)⋊C4C2×D5semidirect
280. C2×C4×Dic3C2×D5semidirect
341. #685C4×D3semidirect
547. C2×C4⋊C4D3×D5semidirect
764. C3×C5#2375semidirect
907. C5#75840semidirect
955. C3#10608165semidirect

Maximal subgroups

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

subgroupindex
C2×#914752
#117510912
C5×#49882
C3×#652792
#117489402
#117489152
#117489112
#117489082
#117489012
#117488832
#117488542
#117487702
#117487242
#117487142
#106081653
#758405