Finite Group Databasebeta

← C2×#11753710 #14483839

Subgroups — C2×#11753710 #14483839

Order 1920.

2400 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91776C211yesmaximal, characteristic, complemented
2C2×C5×#896C211yesmaximal, characteristic, complemented
3C2×C3×#4042C211yesmaximal, characteristic, complemented
4C2×#91442C211yesmaximal, characteristic
5C2×#91442C211yesmaximal, characteristic
6C2×C4×#1201C211yesmaximal, characteristic
7C2×#91432C211yesmaximal, characteristic, complemented
8C2×#91431C211yesmaximal, characteristic, complemented
9C2×#91421C211yesmaximal, characteristic, complemented
10C2×#91410C211yesmaximal, characteristic, complemented
11C2×D3×#683C211yesmaximal, characteristic, complemented
12C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
13C2×#91385C211yesmaximal, characteristic, complemented
14C2×#91382C211yesmaximal, characteristic, complemented
15C2×#91382C211yesmaximal, characteristic, complemented
16#11753710C2116yesmaximal, direct product factor
17C2×#65970—31nomaximal, Hall
18C22×Dic30C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C5×Dic6C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×C3×Dic10C2211yescharacteristic
23C22×#1201C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C22×D5×Dic3C2211yescharacteristic
28C2×C3×C5×C4⋊C4C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×C4×Dic15C2211yescharacteristic
32C2×C4×Dic15C2211yescharacteristic
33C2×C4×Dic15C2211yescharacteristic
34#91776C2218yescomplemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C2×C5×Dic3⋊C4C2211yescharacteristic
38C2×C5×Dic3⋊C4C2211yescharacteristic
39C5×#896C2218yescomplemented
40C2×C3×#685C2211yescharacteristic
41C2×C3×#685C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×#683C2211yescharacteristic
44C3×#4042C2218yescomplemented
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×Dic3⋊Dic5C2211yescharacteristic
47C2×#6669C2211yescharacteristic
48C2×#6669C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6669C2211yescharacteristic
51C2×#6669C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53C2×#6668C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56#91442C2218yes—
57#91442C2218yes—
58C4×#1201C2218yes—
59#91432C2218yescomplemented
60#91431C2218yescomplemented
61#91421C2218yescomplemented
62#91410C2218yescomplemented
63D3×#683C2218yescomplemented
64D5×Dic3⋊C4C2218yescomplemented
65#91385C2218yescomplemented
66#91382C2218yescomplemented
67#91382C2218yescomplemented
68C2×#5636—51nomaximal, Hall
69C2×C5×C22⋊Q8—31no—
70C2×#4092—31no—
71C2×#4090—31no—
72C2×C4×C22⋊D5—31no—
73C22×#683—31no—
74#65970—316no—
75C2×#4042—31no—
76C2×#4042D311yescharacteristic, complemented
77C2×D5×C4⋊C4—31no—
78C2×#4035—31no—
79C2×#4035—31no—
80C2×#4033—31no—
81C2×#4027—31no—
82C2×#4027—31no—
83C2×#4024—31no—
84C2×#4024—31no—
85C23×C5×D3C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C2×Dic30—24no—
95C2×Dic30C2314yes—
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C2×C4×C5×D3—42no—
100C2×C4×C5×D3C2314yes—
101C2×C5×Dic6—42no—
102C2×C5×Dic6C2314yes—
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×C3×C4×D5—42no—
107C2×C3×C4×D5C2314yes—
108C2×C3×Dic10—42no—
109C2×C3×Dic10C2314yes—
110C2×#1201Q818yescomplemented
111C2×#1201C2314yes—
112C2×D3×Dic5—24no—
113C2×D3×Dic5—42no—
114C2×D3×Dic5C2314yes—
115C2×D3×Dic5C2314yes—
116C2×D5×Dic3—24no—
117C2×D5×Dic3—42no—
118C2×D5×Dic3C2314yes—
119C2×D5×Dic3C2314yes—
120C3×C5×C4⋊C4C2314yes—
121#6712C2314yes—
122#6712C2314yes—
123C4×Dic15C2314yes—
124C4×Dic15C2314yes—
125C4×Dic15C2314yes—
126C5×(C2×D3)⋊C4C2314yes—
127C5×(C2×D3)⋊C4C2314yes—
128C5×Dic3⋊C4C2314yes—
129C5×Dic3⋊C4C2314yes—
130C3×#685C2314yes—
131C3×#685C2314yes—
132C3×#683C2314yes—
133C3×#683C2314yes—
134Dic3⋊Dic5C2314yes—
135Dic3⋊Dic5C2314yes—
136#6669C2314yes—
137#6669C2314yes—
138#6669C2314yes—
139#6669C2314yes—
140#6669C2314yes—
141#6668C2314yes—
142#6668C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144#6665C2314yes—
145C2×C3×C22⋊Q8—51no—
146C2×#946—51no—
147C2×#944—51no—
148C2×C4×#67—51no—
149C22×Dic3⋊C4—51no—
150#5636—516no—
151C2×#896—51no—
152C2×#896D511yescharacteristic, complemented
153C2×D3×C4⋊C4—51no—
154C2×#889—51no—
155C2×#889—51no—
156C2×#887—51no—
157C2×#67⋊C4—51no—
158C2×#67⋊C4—51no—
159C2×#878—51no—
160C2×#878—51no—
161C22×C5×Q8—31no—
162C23×C4×C5—31no—
163C22×C22⋊D5—31no—
164C23×Dic5—31no—
165C23×Dic5—31no—
166C22×C4×D5—31no—
167C22×C4×D5—31no—
168C22×C4×D5C2×D311yescharacteristic
169C22×Dic10—31no—
170C22×Dic10C2×D311yescharacteristic
171C5×C22⋊Q8—38no—
172C2×C5×C4⋊C4—31no—
173C2×C5×C4⋊C4—31no—
174C2×C5×C4⋊C4C2×D311yescharacteristic
175C2×C5×C22⋊C4—31no—
176C2×C5×C22⋊C4—31no—
177C2×C22⋊Dic5—31no—
178#4092—38no—
179#4090—38no—
180C4×C22⋊D5—38no—
181C2×#685—31no—
182C2×#685C2×D311yescharacteristic
183C2×#685C2×D311yescharacteristic
184C2×C4⋊Dic5—31no—
185C2×C4⋊Dic5—31no—
186C2×#683—31no—
187C2×#683—31no—
188C2×#683—31no—
189C2×#683—31no—
190C2×#683—31no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—38no—
196C2×#683C2×D311yescharacteristic
197C2×#683C2×D311yescharacteristic
198C2×C4×Dic5—31no—
199C2×C4×Dic5—31no—
200C2×C4×Dic5—31no—
201#4042—38no—
202#4042C2×D318yescomplemented
203D5×C4⋊C4—38no—
204#4035—38no—
205#4035—38no—
206#4033—38no—
207#4027—38no—
208#4027—38no—
209#4024—38no—
210#4024—38no—
211C2×#554—151noSylow
212C23×C3×C5C2411yescharacteristic
213C22×C5×D3—22no—
214C22×C5×D3—22no—
215C22×C5×D3C2×Q814yes—
216C22×C5×D3C2412yes—
217C22×C3×D5—22no—
218C22×C3×D5—22no—
219C22×C3×D5C2×Q814yes—
220C22×C3×D5C2412yes—
221C2×C3×C4×C5—22no—
222C2×C3×C4×C5—22no—
223C2×C3×C4×C5—22no—
224C2×C3×C4×C5C2412yes—
225C2×C3×C4×C5C2412yes—
226C2×C3×C4×C5C2412yes—
227C2×Dic15—22no—
228C2×Dic15—22no—
229C2×Dic15C2×Q814yes—
230C2×Dic15#4114yes—
231C2×Dic15C2412yes—
232C2×Dic15C2412yes—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235Dic30—28no—
236C2×C5×Dic3—22no—
237C2×C5×Dic3—22no—
238C2×C5×Dic3—22no—
239C2×C5×Dic3C2412yes—
240C2×C5×Dic3C2412yes—
241C2×C5×Dic3C2412yes—
242C4×C5×D3—44no—
243C5×Dic6—44no—
244C2×C3×Dic5—22no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5C2412yes—
248C2×C3×Dic5C2412yes—
249C2×C3×Dic5C2412yes—
250C3×C4×D5—44no—
251C3×Dic10—44no—
252#1201C2×Q8116yescomplemented
253D3×Dic5—28no—
254D3×Dic5—44no—
255D5×Dic3—28no—
256D5×Dic3—44no—
257C22×C3×Q8—51no—
258C23×C3×C4—51no—
259C22×#67—51no—
260C23×Dic3—51no—
261C23×Dic3—51no—
262C22×C4×D3—51no—
263C22×C4×D3—51no—
264C22×C4×D3C2×D511yescharacteristic
265C22×Dic6—51no—
266C22×Dic6C2×D511yescharacteristic
267C3×C22⋊Q8—58no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C4⋊C4C2×D511yescharacteristic
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4—51no—
273C2×#217—51no—
274#946—58no—
275#944—58no—
276C4×#67—58no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4C2×D511yescharacteristic
279C2×(C2×D3)⋊C4C2×D511yescharacteristic
280C2×C4⋊Dic3—51no—
281C2×C4⋊Dic3—51no—
282C2×Dic3⋊C4—51no—
283C2×Dic3⋊C4—51no—
284C2×Dic3⋊C4—51no—
285C2×Dic3⋊C4—51no—
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—58no—
292C2×Dic3⋊C4C2×D511yescharacteristic
293C2×Dic3⋊C4C2×D511yescharacteristic
294C2×C4×Dic3—51no—
295C2×C4×Dic3—51no—
296C2×C4×Dic3—51no—
297#896—58no—
298#896C2×D518yescomplemented
299D3×C4⋊C4—58no—
300#889—58no—
301#889—58no—
302#887—58no—
303#67⋊C4—58no—
304#67⋊C4—58no—
305#878—58no—
306#878—58no—
307C24×C5—31no—
308C23×D5C22×D311yescharacteristic
309C2×C5×Q8—34no—
310C2×C5×Q8—122no—
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5—34no—
315C22×C4×C5—122no—
316C22×C4×C5C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C22×C4×C5C22×D311yescharacteristic
319C2×C22⋊D5—38no—
320C2×C22⋊D5—34no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—34no—
326C22×Dic5—34no—
327C22×Dic5—64no—
328C22×Dic5—122no—
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C2×C4×D5—34no—
333C2×C4×D5—34no—
334C2×C4×D5—42no—
335C2×C4×D5—64no—
336C2×C4×D5—122no—
337C2×C4×D5C22×D314yes—
338C2×Dic10—34no—
339C2×Dic10—42no—
340C2×Dic10—64no—
341C2×Dic10C22×D314yes—
342C5×C4⋊C4—34no—
343C5×C4⋊C4—34no—
344C5×C4⋊C4C22×D314yes—
345C5×C22⋊C4—34no—
346C5×C22⋊C4—34no—
347C22⋊Dic5—34no—
348#685—34no—
349#685C22×D314yes—
350#685C22×D314yes—
351C4⋊Dic5—34no—
352C4⋊Dic5—34no—
353#683—34no—
354#683—34no—
355#683—34no—
356#683—34no—
357#683—34no—
358#683—34no—
359#683—34no—
360#683—34no—
361#683—34no—
362#683C22×D314yes—
363#683C22×D314yes—
364C4×Dic5—34no—
365C4×Dic5—34no—
366C4×Dic5—34no—
367#554—1516no—
368C2×C4⋊Q8—151no—
369C2×#125—151no—
370C2×#125—151no—
371C2×C22⋊Q8—31no—
372C2×C22⋊Q8—51no—
373C2×C22⋊Q8—151no—
374C2×C22⋊Q8—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C4×Q8—151no—
378C2×C4×D4—151no—
379C2×C4×D4—151no—
380C2×C4×D4—151no—
381C22×C4⋊C4—151no—
382C22×C4⋊C4—151no—
383C22×C3×C5C22×Q812yes—
384C22×C3×C5C2×#4112yes—
385C22×C3×C5H(5,𝔽2)12yes—
386C22×C3×C5C2511yescharacteristic
387C2×C5×D3—28no—
388C2×C5×D3—22no—
389C2×C5×D3—22no—
390C2×C5×D3C22×Q814yes—
391C2×C3×D5—28no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5C22×Q814yes—
395C3×C4×C5—22no—
396C3×C4×C5—22no—
397C3×C4×C5—22no—
398Dic15—22no—
399Dic15—22no—
400Dic15C22×Q814yes—
401Dic15C2×#4114yes—
402C3×Dic5—22no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C5×Dic3—22no—
406C5×Dic3—22no—
407C5×Dic3—22no—
408C24×C3—51no—
409C23×D3C22×D511yescharacteristic
410C2×C3×Q8—54no—
411C2×C3×Q8—202no—
412C22×C3×C4—51no—
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—54no—
416C22×C3×C4—202no—
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C22×C3×C4C22×D511yescharacteristic
420C2×#67—58no—
421C2×#67—54no—
422C22×Dic3—51no—
423C22×Dic3—51no—
424C22×Dic3—51no—
425C22×Dic3—51no—
426C22×Dic3—54no—
427C22×Dic3—54no—
428C22×Dic3—104no—
429C22×Dic3—202no—
430C22×Dic3C22×D511yescharacteristic
431C22×Dic3C22×D511yescharacteristic
432C22×Dic3C22×D511yescharacteristic
433C2×C4×D3—42no—
434C2×C4×D3—54no—
435C2×C4×D3—54no—
436C2×C4×D3—104no—
437C2×C4×D3—202no—
438C2×C4×D3C22×D514yes—
439C2×Dic6—42no—
440C2×Dic6—54no—
441C2×Dic6—104no—
442C2×Dic6C22×D514yes—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C4⋊C4C22×D514yes—
446C3×C22⋊C4—54no—
447C3×C22⋊C4—54no—
448#217—54no—
449(C2×D3)⋊C4—54no—
450(C2×D3)⋊C4C22×D514yes—
451(C2×D3)⋊C4C22×D514yes—
452C4⋊Dic3—54no—
453C4⋊Dic3—54no—
454Dic3⋊C4—54no—
455Dic3⋊C4—54no—
456Dic3⋊C4—54no—
457Dic3⋊C4—54no—
458Dic3⋊C4—54no—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4C22×D514yes—
464Dic3⋊C4C22×D514yes—
465C4×Dic3—54no—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C23×C5—34no—
469C23×C5—32no—
470C23×C5—62no—
471C23×C5—62no—
472C23×C5C23×D311yescharacteristic
473C22×D5—22no—
474C22×D5—22no—
475C22×D5D3×Q814yes—
476C22×D5C23×D312yes—
477C5×Q8—124no—
478C2×C4×C5—22no—
479C2×C4×C5—22no—
480C2×C4×C5—22no—
481C2×C4×C5—32no—
482C2×C4×C5—32no—
483C2×C4×C5—32no—
484C2×C4×C5—62no—
485C2×C4×C5—62no—
486C2×C4×C5—62no—
487C2×C4×C5—124no—
488C2×C4×C5C23×D312yes—
489C2×C4×C5C23×D312yes—
490C2×C4×C5C23×D312yes—
491C22⋊D5—316no—
492C2×Dic5—22no—
493C2×Dic5—22no—
494C2×Dic5—22no—
495C2×Dic5—34no—
496C2×Dic5—34no—
497C2×Dic5—32no—
498C2×Dic5—32no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—68no—
502C2×Dic5—62no—
503C2×Dic5—62no—
504C2×Dic5—124no—
505C2×Dic5C23×D312yes—
506C2×Dic5C23×D312yes—
507C2×Dic5C23×D312yes—
508C4×D5—44no—
509C4×D5—68no—
510C4×D5—124no—
511Dic10—44no—
512Dic10—68no—
513C22×Q8—31no—
514C22×Q8—51no—
515C22×Q8—151no—
516C22×D4—151no—
517C23×C4—31no—
518C23×C4—51no—
519C23×C4—151no—
520C23×C4—151no—
521C23×C4—151no—
522C23×C4—151no—
523C4⋊Q8—158no—
524#125—158no—
525#125—158no—
526C22⋊Q8—38no—
527C22⋊Q8—58no—
528C22⋊Q8—158no—
529C22⋊Q8—158no—
530C22⋊Q8—158no—
531C22⋊Q8—158no—
532C4×Q8—158no—
533C4×D4—158no—
534C4×D4—158no—
535C4×D4—158no—
536C2×C4⋊C4—31no—
537C2×C4⋊C4—31no—
538C2×C4⋊C4—51no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—158no—
541C2×C4⋊C4—158no—
542C2×C4⋊C4—151no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C4⋊C4—151no—
549C2×C4⋊C4—151no—
550C2×C4⋊C4—151no—
551C2×C4⋊C4—151no—
552C2×C4⋊C4—151no—
553C2×C4⋊C4D3×D511yescharacteristic
554C2×C22⋊C4—31no—
555C2×C22⋊C4—31no—
556C2×C22⋊C4—51no—
557C2×C22⋊C4—51no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C42—151no—
561C2×C42—151no—
562C2×C42—151no—
563C2×C3×C5#55414yescomplemented
564C2×C3×C5C23×Q811yescharacteristic
565C2×C3×C5C22×#4111yescharacteristic
566C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
567C3×D5—24no—
568C5×D3—24no—
569C23×C3—54no—
570C23×C3—52no—
571C23×C3—102no—
572C23×C3—102no—
573C23×C3C23×D511yescharacteristic
574C22×D3—22no—
575C22×D3—22no—
576C22×D3Q8×D514yes—
577C22×D3C23×D512yes—
578C3×Q8—204no—
579C2×C3×C4—22no—
580C2×C3×C4—22no—
581C2×C3×C4—22no—
582C2×C3×C4—52no—
583C2×C3×C4—52no—
584C2×C3×C4—52no—
585C2×C3×C4—102no—
586C2×C3×C4—102no—
587C2×C3×C4—102no—
588C2×C3×C4—204no—
589C2×C3×C4C23×D512yes—
590C2×C3×C4C23×D512yes—
591C2×C3×C4C23×D512yes—
592#67—516no—
593C2×Dic3—22no—
594C2×Dic3—22no—
595C2×Dic3—22no—
596C2×Dic3—54no—
597C2×Dic3—54no—
598C2×Dic3—52no—
599C2×Dic3—52no—
600C2×Dic3—52no—
601C2×Dic3—52no—
602C2×Dic3—108no—
603C2×Dic3—102no—
604C2×Dic3—102no—
605C2×Dic3—204no—
606C2×Dic3C23×D512yes—
607C2×Dic3C23×D512yes—
608C2×Dic3C23×D512yes—
609C4×D3—44no—
610C4×D3—108no—
611C4×D3—204no—
612Dic6—44no—
613Dic6—108no—
614C22×C5—34no—
615C22×C5—68no—
616C22×C5—62no—
617C22×C5—62no—
618C22×C5#100412yes—
619C22×C5C2×D3×Q812yes—
620C22×C5D3×#4112yes—
621C22×C5C24×D311yescharacteristic
622C2×D5—28no—
623C2×D5—22no—
624C2×D5—22no—
625C2×D5C2×D3×Q814yes—
626C4×C5—22no—
627C4×C5—22no—
628C4×C5—22no—
629C4×C5—62no—
630C4×C5—62no—
631C4×C5—62no—
632Dic5—22no—
633Dic5—22no—
634Dic5—22no—
635Dic5—34no—
636Dic5—34no—
637Dic5—62no—
638Dic5—62no—
639C24—31no—
640C24—51no—
641C2×Q8—34no—
642C2×Q8—54no—
643C2×Q8—122no—
644C2×Q8—154no—
645C2×Q8—202no—
646C2×Q8—304no—
647C2×D4—154no—
648C2×D4—158no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—31no—
652C22×C4—34no—
653C22×C4—51no—
654C22×C4—51no—
655C22×C4—51no—
656C22×C4—54no—
657C22×C4—122no—
658C22×C4—154no—
659C22×C4—154no—
660C22×C4—154no—
661C22×C4—154no—
662C22×C4—151no—
663C22×C4—151no—
664C22×C4—151no—
665C22×C4—151no—
666C22×C4—202no—
667C22×C4—304no—
668C22×C4—304no—
669C22×C4—602no—
670C22×C4—602no—
671C22×C4C2×D3×D511yescharacteristic
672C22×C4C2×D3×D511yescharacteristic
673C22×C4C2×D3×D511yescharacteristic
674C4⋊C4—34no—
675C4⋊C4—34no—
676C4⋊C4—54no—
677C4⋊C4—54no—
678C4⋊C4—154no—
679C4⋊C4—154no—
680C4⋊C4—154no—
681C4⋊C4—154no—
682C4⋊C4—154no—
683C4⋊C4—154no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C4⋊C4C2×D3×D514yes—
690C22⋊C4—34no—
691C22⋊C4—34no—
692C22⋊C4—54no—
693C22⋊C4—54no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C42—154no—
697C42—154no—
698C42—154no—
699C3×C5C2×#55411yescharacteristic, complemented, Hall
700C22×C3—54no—
701C22×C3—108no—
702C22×C3—102no—
703C22×C3—102no—
704C22×C3#414412yes—
705C22×C3C2×Q8×D512yes—
706C22×C3D5×#4112yes—
707C22×C3C24×D511yescharacteristic
708C2×D3—28no—
709C2×D3—22no—
710C2×D3—22no—
711C2×D3C2×Q8×D514yes—
712C3×C4—22no—
713C3×C4—22no—
714C3×C4—22no—
715C3×C4—102no—
716C3×C4—102no—
717C3×C4—102no—
718Dic3—22no—
719Dic3—22no—
720Dic3—22no—
721Dic3—54no—
722Dic3—54no—
723Dic3—102no—
724Dic3—102no—
725C2×C5—64no—
726C2×C5#563614yescomplemented
727C2×C5C2×#100411yescharacteristic
728C2×C5C22×D3×Q811yescharacteristic
729C2×C5C2×D3×#4111yescharacteristic
730D5—24no—
731C23—34no—
732C23—32no—
733C23—54no—
734C23—52no—
735C23—62no—
736C23—62no—
737C23—102no—
738C23—102no—
739C23C22×D3×D511yescharacteristic
740Q8—124no—
741Q8—204no—
742Q8—308no—
743D4—1516no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—32no—
748C2×C4—32no—
749C2×C4—32no—
750C2×C4—52no—
751C2×C4—52no—
752C2×C4—52no—
753C2×C4—62no—
754C2×C4—62no—
755C2×C4—62no—
756C2×C4—102no—
757C2×C4—102no—
758C2×C4—102no—
759C2×C4—124no—
760C2×C4—154no—
761C2×C4—154no—
762C2×C4—152no—
763C2×C4—152no—
764C2×C4—152no—
765C2×C4—152no—
766C2×C4—204no—
767C2×C4—308no—
768C2×C4—308no—
769C2×C4—302no—
770C2×C4—302no—
771C2×C4—604no—
772C2×C4—604no—
773C2×C4C22×D3×D512yes—
774C2×C4C22×D3×D512yes—
775C2×C4C22×D3×D512yes—
776C2×C3—104no—
777C2×C3#6597014yescomplemented
778C2×C3C2×#414411yescharacteristic
779C2×C3C22×Q8×D511yescharacteristic
780C2×C3C2×D5×#4111yescharacteristic
781D3—24no—
782C5C2×#563611yescharacteristic, complemented, Sylow
783C22—34no—
784C22—54no—
785C22—62no—
786C22—62no—
787C22—68no—
788C22—102no—
789C22—102no—
790C22—108no—
791C22#9201612yes—
792C22#9202512yes—
793C22D3×Q8×D512yes—
794C22C23×D3×D511yescharacteristic
795C4—22no—
796C4—22no—
797C4—22no—
798C4—62no—
799C4—62no—
800C4—62no—
801C4—102no—
802C4—102no—
803C4—102no—
804C4—154no—
805C4—154no—
806C4—302no—
807C4—302no—
808C3C2×#6597011yescharacteristic, complemented, Sylow
809C2—64no—
810C2—104no—
811C2#1175371014yesdirect product factor
812C2C2×#9201611yescharacteristic
813C2C2×#9202511yescharacteristic
814C2C2×D3×Q8×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC22×#1201C22
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#554
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
1. C2×#91776C2semidirect
2. C2×C5×#896C2semidirect
3. C2×C3×#4042C2semidirect
7. C2×#91432C2semidirect
8. C2×#91431C2semidirect
9. C2×#91421C2semidirect
10. C2×#91410C2semidirect
11. C2×D3×#683C2semidirect
12. C2×D5×Dic3⋊C4C2semidirect
13. C2×#91385C2semidirect
14. C2×#91382C2semidirect
15. C2×#91382C2semidirect
16. #11753710C2direct (N × H)
34. #91776C22semidirect
39. C5×#896C22semidirect
44. C3×#4042C22semidirect
59. #91432C22semidirect
60. #91431C22semidirect
61. #91421C22semidirect
62. #91410C22semidirect
63. D3×#683C22semidirect
64. D5×Dic3⋊C4C22semidirect
65. #91385C22semidirect
66. #91382C22semidirect
67. #91382C22semidirect
76. C2×#4042D3semidirect
110. C2×#1201Q8semidirect
152. C2×#896D5semidirect
202. #4042C2×D3semidirect
252. #1201C2×Q8semidirect
298. #896C2×D5semidirect
563. C2×C3×C5#554semidirect
699. C3×C5C2×#554semidirect
726. C2×C5#5636semidirect
777. C2×C3#65970semidirect
782. C5C2×#5636semidirect
808. C3C2×#65970semidirect
811. C2#11753710direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917762
C2×C5×#8962
C2×C3×#40422
C2×#914422
C2×C4×#12012
C2×#914322
C2×#914312
C2×#914212
C2×#914102
C2×D3×#6832
C2×D5×Dic3⋊C42
C2×#913852
C2×#913822
#117537102
C2×#659703
C2×#56365