Finite Group Databasebeta

← C2×#11752453 #14412326

Subgroups — C2×#11752453 #14412326

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D5×#41C211yesmaximal, characteristic
2C2×#91989C211yesmaximal, characteristic, complemented
3C22×D5⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#11752453C218yesmaximal, direct product factor
5C2×#91238C212yesmaximal, complemented
6C2×#91236C212yesmaximal, complemented
7C2×#65794—31nomaximal, Hall
8C2×C3×C5×#41C411yescharacteristic, complemented
9C3×D5×#41—22no—
10C3×D5×#41—22no—
11C3×D5×#41C414yescomplemented
12C3×D5×#41C2214yes—
13C2×C3×#713C411yescharacteristic, complemented
14C2×C3×Q8×D5C2211yescharacteristic
15C2×C3×#711—21no—
16C2×C3×#711C411yescharacteristic, complemented
17C2×C3×D4×D5—21no—
18C2×C3×D4×D5C2211yescharacteristic
19C2×C3×#709—21no—
20C2×C3×#709C411yescharacteristic, complemented
21C22×C3×C4×D5—21no—
22C22×C3×C4×D5C2211yescharacteristic
23C2×#6763—21no—
24C22×C3⋊#170—21no—
25#91989—22no—
26#91989C2214yescomplemented
27C2×C4⋊ΓL(1,𝔽16)C2212yes—
28C2×C4×ΓL(1,𝔽16)—21no—
29C2×D5⋊(C3⋊C8)—22no—
30C2×D5⋊(C3⋊C8)—21no—
31C2×D5⋊(C3⋊C8)C2212yes—
32C2×D5⋊(C3⋊C8)C2214yescomplemented
33#91238C2218yescomplemented
34#91236C2218yescomplemented
35C2×#5233—51nomaximal, Hall
36C2×D5×#41D311yescharacteristic
37C2×#4130—31no—
38C22×D5⋊C8—31no—
39#65794—38no—
40C2×#4009—32no—
41C2×#4007—32no—
42C23×C3×D5—21no—
43C23×C3×D5D411yescharacteristic
44C22×ΓL(1,𝔽16)—22no—
45C3×C5×#41—22no—
46C3×C5×#41C2×C414yescomplemented
47C2×C3×C5×Q8C2×C411yescharacteristic
48C2×C3×C5×D4—21no—
49C2×C3×C5×D4C2×C411yescharacteristic
50C22×C3×C4×C5—21no—
51C22×C3×C4×C5C2×C411yescharacteristic
52C2×C3×C22⋊D5—21no—
53C2×C3×C22⋊D5—21no—
54C2×C3×C22⋊D5—21no—
55C22×C3×Dic5—21no—
56C22×C3×Dic5D411yescharacteristic
57C3×#713—22no—
58C3×#713C2×C414yescomplemented
59C3×Q8×D5—21no—
60C3×Q8×D5—21no—
61C3×Q8×D5C2×C412yes—
62C3×Q8×D5C2312yes—
63C3×#711—24no—
64C3×#711—24no—
65C3×#711—22no—
66C3×#711C2×C414yescomplemented
67C3×D4×D5—24no—
68C3×D4×D5—24no—
69C3×D4×D5—21no—
70C3×D4×D5—21no—
71C3×D4×D5C2×C412yes—
72C3×D4×D5C2312yes—
73C3×#709—22no—
74C3×#709—24no—
75C3×#709—24no—
76C3×#709C2×C414yescomplemented
77C2×C3×D20—21no—
78C2×C3×D20C2×C411yescharacteristic
79C2×C3×C4×D5—21no—
80C2×C3×C4×D5—21no—
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5—24no—
83C2×C3×C4×D5—24no—
84C2×C3×C4×D5C2×C411yescharacteristic
85C2×C3×C4×D5C2×C412yes—
86C2×C3×C4×D5D411yescharacteristic
87C2×C3×C4×D5D412yes—
88C2×C3×C4×D5D411yescharacteristic
89C2×C3×C4×D5D412yes—
90C2×C3×C4×D5C2311yescharacteristic
91C2×C3×C4×D5C2312yes—
92C2×C3×Dic10—21no—
93C2×C3×Dic10C2×C411yescharacteristic
94#6763—24no—
95C2×C3⋊#170—22no—
96C2×C3⋊#170—24no—
97C4⋊ΓL(1,𝔽16)—22no—
98C4⋊ΓL(1,𝔽16)C2314yes—
99C4×ΓL(1,𝔽16)—24no—
100D5⋊(C3⋊C8)—22no—
101D5⋊(C3⋊C8)—24no—
102D5⋊(C3⋊C8)C2314yes—
103C22×C3×#41—51no—
104C2×#926—51no—
105C23×C3⋊C8—51no—
106#5233—58no—
107C2×#835—52no—
108C2×#832—52no—
109C2×C5×#41Dic311yescharacteristic, complemented
110D5×#41—22no—
111D5×#41—22no—
112D5×#41Dic314yescomplemented
113D5×#41C2×D314yes—
114C2×#713Dic311yescharacteristic, complemented
115C2×Q8×D5C2×D311yescharacteristic
116C2×#711—21no—
117C2×#711Dic311yescharacteristic, complemented
118C2×D4×D5—21no—
119C2×D4×D5C2×D311yescharacteristic
120C2×#709—21no—
121C2×#709Dic311yescharacteristic, complemented
122C22×C4×D5—21no—
123C22×C4×D5C2×D311yescharacteristic
124C2×C22⋊AGL(1,𝔽5)—61no—
125C22×#170—61no—
126#4130—34no—
127#4130—62no—
128C2×C4⋊AGL(1,𝔽5)—32no—
129C2×C4×AGL(1,𝔽5)—61no—
130C2×D5⋊C8—34no—
131C2×D5⋊C8—32no—
132C2×D5⋊C8—61no—
133C2×D5⋊C8—62no—
134#4009—38no—
135#4007—38no—
136C2×#416—151noSylow
137C23×C3×C5—21no—
138C23×C3×C5C22⋊C411yescharacteristic
139C22×C3×D5—24no—
140C22×C3×D5—21no—
141C22×C3×D5—22no—
142C22×C3×D5—22no—
143C22×C3×D5—44no—
144C22×C3×D5C22⋊C411yescharacteristic
145C22×C3×D5C22⋊C412yes—
146C22×C3×D5C2×D412yes—
147C22×C3×D5C2×D411yescharacteristic
148C2×ΓL(1,𝔽16)—24no—
149C2×ΓL(1,𝔽16)—44no—
150C3×C5×Q8—21no—
151C3×C5×Q8C22×C412yes—
152C3×C5×D4—24no—
153C3×C5×D4—21no—
154C3×C5×D4C22×C412yes—
155C2×C3×C4×C5—21no—
156C2×C3×C4×C5—24no—
157C2×C3×C4×C5C22⋊C411yescharacteristic
158C2×C3×C4×C5C22⋊C412yes—
159C2×C3×C4×C5C22×C411yescharacteristic
160C2×C3×C4×C5C22×C412yes—
161C3×C22⋊D5—24no—
162C3×C22⋊D5—24no—
163C3×C22⋊D5—22no—
164C3×C22⋊D5—22no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—24no—
167C2×C3×Dic5C22⋊C411yescharacteristic
168C2×C3×Dic5C22⋊C412yes—
169C2×C3×Dic5C2×D411yescharacteristic
170C2×C3×Dic5C2×D412yes—
171C3×D20—24no—
172C3×D20—21no—
173C3×D20C22×C412yes—
174C3×C4×D5—22no—
175C3×C4×D5—22no—
176C3×C4×D5—24no—
177C3×C4×D5—24no—
178C3×C4×D5C22⋊C412yes—
179C3×C4×D5C22⋊C412yes—
180C3×C4×D5C22⋊C412yes—
181C3×C4×D5C22×C411yescharacteristic
182C3×C4×D5C22×C412yes—
183C3×C4×D5C2×D412yes—
184C3×C4×D5C2×D411yescharacteristic
185C3×C4×D5C2×D412yes—
186C3×C4×D5C2×D411yescharacteristic
187C3×C4×D5C2411yescharacteristic
188C3×Dic10—21no—
189C3×Dic10—22no—
190C3×Dic10—22no—
191C3×Dic10C22×C412yes—
192C3⋊#170—24no—
193C2×C3×#41—54no—
194C2×C3×#41—54no—
195C2×C3×#41—51no—
196C2×C3×#41—51no—
197C2×C3×#41—51no—
198C2×C3×#41—101no—
199C2×C3×#41—101no—
200C2×C3×#41—102no—
201C2×C3×#41—102no—
202C2×C3×#41AGL(1,𝔽5)11yescharacteristic, complemented
203C22×C3×Q8—51no—
204C22×C3×D4—51no—
205C22×C3×D4—101no—
206C23×C3×C4—51no—
207C23×C3×C4—101no—
208C2×#217—101no—
209#926—54no—
210#926—102no—
211C2×C4⋊Dic3—52no—
212C2×C4×Dic3—101no—
213C22×C3⋊C8—52no—
214C22×C3⋊C8—54no—
215C22×C3⋊C8—102no—
216C22×C3⋊C8—101no—
217C22×C3⋊C8—101no—
218#835—58no—
219#832—58no—
220C23×D5—21no—
221C23×D5#6711yescharacteristic
222C22×AGL(1,𝔽5)—62no—
223C5×#41—22no—
224C5×#41C2×Dic314yescomplemented
225C2×C5×Q8C2×Dic311yescharacteristic
226C2×C5×D4—21no—
227C2×C5×D4C2×Dic311yescharacteristic
228C22×C4×C5—21no—
229C22×C4×C5C2×Dic311yescharacteristic
230C2×C22⋊D5—21no—
231C2×C22⋊D5—21no—
232C2×C22⋊D5—21no—
233C22×Dic5—21no—
234C22×Dic5#6711yescharacteristic
235#713—22no—
236#713C2×Dic314yescomplemented
237Q8×D5—21no—
238Q8×D5—21no—
239Q8×D5C2×Dic312yes—
240Q8×D5C22×D312yes—
241#711—24no—
242#711—24no—
243#711—22no—
244#711C2×Dic314yescomplemented
245D4×D5—24no—
246D4×D5—24no—
247D4×D5—21no—
248D4×D5—21no—
249D4×D5C2×Dic312yes—
250D4×D5C22×D312yes—
251#709—22no—
252#709—24no—
253#709—24no—
254#709C2×Dic314yescomplemented
255C2×D20—21no—
256C2×D20C2×Dic311yescharacteristic
257C2×C4×D5—21no—
258C2×C4×D5—21no—
259C2×C4×D5—21no—
260C2×C4×D5—24no—
261C2×C4×D5—24no—
262C2×C4×D5C2×Dic311yescharacteristic
263C2×C4×D5C2×Dic312yes—
264C2×C4×D5#6711yescharacteristic
265C2×C4×D5#6712yes—
266C2×C4×D5#6711yescharacteristic
267C2×C4×D5#6712yes—
268C2×C4×D5C22×D311yescharacteristic
269C2×C4×D5C22×D312yes—
270C2×Dic10—21no—
271C2×Dic10C2×Dic311yescharacteristic
272C22⋊AGL(1,𝔽5)—64no—
273C2×#170—62no—
274C2×#170—64no—
275C4⋊AGL(1,𝔽5)—34no—
276C4⋊AGL(1,𝔽5)—62no—
277C4×AGL(1,𝔽5)—64no—
278D5⋊C8—34no—
279D5⋊C8—64no—
280D5⋊C8—62no—
281C22×#41—51no—
282C23×C8—151no—
283C2×#117—151no—
284#416—158no—
285C2×#103—152no—
286C2×#102—152no—
287C22×C3×C5—22no—
288C22×C3×C5—22no—
289C22×C3×C5—42no—
290C22×C3×C5C2×C22⋊C412yes—
291C22×C3×C5C2×C22⋊C411yescharacteristic
292C2×C3×D5—22no—
293C2×C3×D5—24no—
294C2×C3×D5—24no—
295C2×C3×D5—22no—
296C2×C3×D5—42no—
297C2×C3×D5—44no—
298C2×C3×D5—44no—
299C2×C3×D5C2×C22⋊C412yes—
300C2×C3×D5C2×C22⋊C411yescharacteristic
301C2×C3×D5#13514yes—
302C2×C3×D5C22×D411yescharacteristic
303ΓL(1,𝔽16)—44no—
304C3×C4×C5—22no—
305C3×C4×C5C2×C22⋊C411yescharacteristic
306C3×C4×C5C2×C22⋊C412yes—
307C3×C4×C5C23×C411yescharacteristic
308C3×Dic5—22no—
309C3×Dic5C2×C22⋊C411yescharacteristic
310C3×Dic5C2×C22⋊C412yes—
311C3×Dic5C22×D411yescharacteristic
312C24×C3—51no—
313C24×C3—101no—
314C3×#41—22no—
315C3×#41—54no—
316C3×#41—54no—
317C3×#41—54no—
318C3×#41—104no—
319C3×#41—104no—
320C3×#41—104no—
321C3×#41—104no—
322C3×#41—102no—
323C3×#41—102no—
324C3×#41—102no—
325C3×#41C2×AGL(1,𝔽5)14yescomplemented
326C2×C3×Q8—52no—
327C2×C3×Q8—52no—
328C2×C3×Q8—51no—
329C2×C3×Q8—101no—
330C2×C3×Q8—101no—
331C2×C3×Q8—101no—
332C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
333C2×C3×D4—21no—
334C2×C3×D4—52no—
335C2×C3×D4—52no—
336C2×C3×D4—51no—
337C2×C3×D4—101no—
338C2×C3×D4—101no—
339C2×C3×D4—101no—
340C2×C3×D4—101no—
341C2×C3×D4—104no—
342C2×C3×D4—104no—
343C2×C3×D4—101no—
344C2×C3×D4—101no—
345C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—51no—
348C22×C3×C4—52no—
349C22×C3×C4—51no—
350C22×C3×C4—51no—
351C22×C3×C4—52no—
352C22×C3×C4—51no—
353C22×C3×C4—52no—
354C22×C3×C4—51no—
355C22×C3×C4—52no—
356C22×C3×C4—101no—
357C22×C3×C4—104no—
358C22×C3×C4—104no—
359C22×C3×C4—101no—
360C22×C3×C4—101no—
361C22×C3×C4—101no—
362C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
363C22×Dic3—102no—
364#217—104no—
365C4⋊Dic3—54no—
366C4⋊Dic3—102no—
367C4×Dic3—104no—
368C2×C3⋊C8—54no—
369C2×C3⋊C8—102no—
370C2×C3⋊C8—104no—
371C2×C3⋊C8—102no—
372C2×C3⋊C8—104no—
373C23×C5—21no—
374C23×C5#21711yescharacteristic
375C22×D5—24no—
376C22×D5—21no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—44no—
380C22×D5#21711yescharacteristic
381C22×D5#21712yes—
382C22×D5C2×#6712yes—
383C22×D5C2×#6711yescharacteristic
384C2×AGL(1,𝔽5)—64no—
385C2×AGL(1,𝔽5)—124no—
386C5×Q8—21no—
387C5×Q8C22×Dic312yes—
388C5×D4—24no—
389C5×D4—21no—
390C5×D4C22×Dic312yes—
391C2×C4×C5—21no—
392C2×C4×C5—24no—
393C2×C4×C5#21712yes—
394C2×C4×C5#21711yescharacteristic
395C2×C4×C5C22×Dic311yescharacteristic
396C2×C4×C5C22×Dic312yes—
397C22⋊D5—24no—
398C22⋊D5—24no—
399C22⋊D5—22no—
400C22⋊D5—22no—
401C2×Dic5—21no—
402C2×Dic5—24no—
403C2×Dic5#21711yescharacteristic
404C2×Dic5#21712yes—
405C2×Dic5C2×#6711yescharacteristic
406C2×Dic5C2×#6712yes—
407D20—24no—
408D20—21no—
409D20C22×Dic312yes—
410C4×D5—22no—
411C4×D5—22no—
412C4×D5—24no—
413C4×D5—24no—
414C4×D5#21712yes—
415C4×D5#21712yes—
416C4×D5#21712yes—
417C4×D5C22×Dic311yescharacteristic
418C4×D5C22×Dic312yes—
419C4×D5C2×#6712yes—
420C4×D5C2×#6711yescharacteristic
421C4×D5C2×#6712yes—
422C4×D5C2×#6711yescharacteristic
423C4×D5C23×D311yescharacteristic
424Dic10—21no—
425Dic10—22no—
426Dic10—22no—
427Dic10C22×Dic312yes—
428#170—64no—
429C2×#41—54no—
430C2×#41—54no—
431C2×#41—51no—
432C2×#41—51no—
433C2×#41—51no—
434C2×#41—101no—
435C2×#41—101no—
436C2×#41—102no—
437C2×#41—102no—
438C2×#41ΓL(1,𝔽16)11yescharacteristic, complemented
439C22×Q8—51no—
440C22×D4—51no—
441C22×D4—101no—
442C23×C4—51no—
443C23×C4—101no—
444C22×C8—152no—
445C22×C8—154no—
446C22×C8—302no—
447C22×C8—301no—
448C22×C8—301no—
449#117—154no—
450#117—302no—
451C2×C4⋊C4—152no—
452C2×C22⋊C4—301no—
453C2×C42—301no—
454#103—158no—
455#102—158no—
456C2×C3×C5—22no—
457C2×C3×C5—42no—
458C2×C3×C5#41612yescomplemented
459C2×C3×C5C22×C22⋊C411yescharacteristic
460C3×D5—22no—
461C3×D5—42no—
462C3×D5#41612yescomplemented
463C3×D5C2×#13512yes—
464C23×C3—21no—
465C23×C3—51no—
466C23×C3—52no—
467C23×C3—51no—
468C23×C3—52no—
469C23×C3—104no—
470C23×C3—102no—
471C23×C3—102no—
472C23×C3—101no—
473C23×C3—204no—
474C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
475C3×Q8—21no—
476C3×Q8—52no—
477C3×Q8—102no—
478C3×Q8—102no—
479C3×Q8—101no—
480C3×Q8C22×AGL(1,𝔽5)12yes—
481C3×D4—24no—
482C3×D4—21no—
483C3×D4—52no—
484C3×D4—104no—
485C3×D4—102no—
486C3×D4—102no—
487C3×D4—104no—
488C3×D4—104no—
489C3×D4—101no—
490C3×D4C22×AGL(1,𝔽5)12yes—
491C2×C3×C4—21no—
492C2×C3×C4—24no—
493C2×C3×C4—51no—
494C2×C3×C4—52no—
495C2×C3×C4—51no—
496C2×C3×C4—52no—
497C2×C3×C4—52no—
498C2×C3×C4—52no—
499C2×C3×C4—52no—
500C2×C3×C4—51no—
501C2×C3×C4—52no—
502C2×C3×C4—52no—
503C2×C3×C4—51no—
504C2×C3×C4—51no—
505C2×C3×C4—52no—
506C2×C3×C4—51no—
507C2×C3×C4—104no—
508C2×C3×C4—102no—
509C2×C3×C4—102no—
510C2×C3×C4—104no—
511C2×C3×C4—101no—
512C2×C3×C4—104no—
513C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
514C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
515C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
516C2×C3×C4C22×AGL(1,𝔽5)12yes—
517C2×Dic3—104no—
518C2×Dic3—204no—
519C3⋊C8—104no—
520C22×C5—22no—
521C22×C5—22no—
522C22×C5—42no—
523C22×C5C2×#21712yes—
524C22×C5C2×#21711yescharacteristic
525C2×D5—22no—
526C2×D5—24no—
527C2×D5—24no—
528C2×D5—22no—
529C2×D5—42no—
530C2×D5—44no—
531C2×D5—44no—
532C2×D5#95014yes—
533C2×D5C2×#21712yes—
534C2×D5C2×#21711yescharacteristic
535C2×D5C22×#6711yescharacteristic
536AGL(1,𝔽5)—124no—
537C4×C5—22no—
538C4×C5C2×#21711yescharacteristic
539C4×C5C2×#21712yes—
540C4×C5C23×Dic311yescharacteristic
541Dic5—22no—
542Dic5C2×#21711yescharacteristic
543Dic5C2×#21712yes—
544Dic5C22×#6711yescharacteristic
545C24—51no—
546C24—101no—
547#41—22no—
548#41—54no—
549#41—54no—
550#41—54no—
551#41—104no—
552#41—104no—
553#41—104no—
554#41—104no—
555#41—102no—
556#41—102no—
557#41—102no—
558#41C2×ΓL(1,𝔽16)14yescomplemented
559C2×Q8—52no—
560C2×Q8—52no—
561C2×Q8—51no—
562C2×Q8—101no—
563C2×Q8—101no—
564C2×Q8—101no—
565C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
566C2×D4—21no—
567C2×D4—52no—
568C2×D4—52no—
569C2×D4—51no—
570C2×D4—101no—
571C2×D4—101no—
572C2×D4—101no—
573C2×D4—101no—
574C2×D4—104no—
575C2×D4—104no—
576C2×D4—101no—
577C2×D4—101no—
578C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
579C22×C4—21no—
580C22×C4—51no—
581C22×C4—52no—
582C22×C4—52no—
583C22×C4—51no—
584C22×C4—51no—
585C22×C4—51no—
586C22×C4—52no—
587C22×C4—51no—
588C22×C4—52no—
589C22×C4—101no—
590C22×C4—104no—
591C22×C4—104no—
592C22×C4—101no—
593C22×C4—101no—
594C22×C4—101no—
595C22×C4—302no—
596C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
597C2×C8—154no—
598C2×C8—302no—
599C2×C8—304no—
600C2×C8—302no—
601C2×C8—304no—
602C4⋊C4—154no—
603C4⋊C4—302no—
604C22⋊C4—304no—
605C42—304no—
606C3×C5C2×#41611yescharacteristic, complemented, Hall
607C22×C3—22no—
608C22×C3—22no—
609C22×C3—42no—
610C22×C3—54no—
611C22×C3—51no—
612C22×C3—51no—
613C22×C3—52no—
614C22×C3—104no—
615C22×C3—104no—
616C22×C3—102no—
617C22×C3—102no—
618C22×C3—204no—
619C22×C3—204no—
620C22×C3—202no—
621C22×C3C2×C22⋊AGL(1,𝔽5)12yes—
622C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
623C3×C4—22no—
624C3×C4—52no—
625C3×C4—51no—
626C3×C4—51no—
627C3×C4—102no—
628C3×C4C2×C22⋊AGL(1,𝔽5)12yes—
629C3×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
630C3×C4C23×AGL(1,𝔽5)11yescharacteristic
631Dic3—204no—
632C2×C5—22no—
633C2×C5—42no—
634C2×C5#523312yescomplemented
635C2×C5C22×#21711yescharacteristic
636D5—22no—
637D5—42no—
638D5#523312yescomplemented
639D5C2×#95012yes—
640C23—21no—
641C23—51no—
642C23—52no—
643C23—52no—
644C23—51no—
645C23—104no—
646C23—102no—
647C23—102no—
648C23—101no—
649C23—204no—
650C23#676311yescharacteristic
651Q8—21no—
652Q8—52no—
653Q8—102no—
654Q8—102no—
655Q8—101no—
656Q8C22×ΓL(1,𝔽16)12yes—
657D4—24no—
658D4—21no—
659D4—52no—
660D4—104no—
661D4—102no—
662D4—102no—
663D4—104no—
664D4—104no—
665D4—101no—
666D4C22×ΓL(1,𝔽16)12yes—
667C2×C4—21no—
668C2×C4—24no—
669C2×C4—51no—
670C2×C4—52no—
671C2×C4—51no—
672C2×C4—52no—
673C2×C4—52no—
674C2×C4—51no—
675C2×C4—51no—
676C2×C4—52no—
677C2×C4—52no—
678C2×C4—52no—
679C2×C4—52no—
680C2×C4—51no—
681C2×C4—51no—
682C2×C4—52no—
683C2×C4—104no—
684C2×C4—102no—
685C2×C4—102no—
686C2×C4—104no—
687C2×C4—101no—
688C2×C4—104no—
689C2×C4—304no—
690C2×C4—604no—
691C2×C4#676312yes—
692C2×C4#676311yescharacteristic
693C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
694C2×C4C22×ΓL(1,𝔽16)12yes—
695C8—304no—
696C2×C3—22no—
697C2×C3—42no—
698C2×C3—52no—
699C2×C3—52no—
700C2×C3—102no—
701C2×C3—202no—
702C2×C3#6579412yescomplemented
703C2×C3C22×C22⋊AGL(1,𝔽5)11yescharacteristic
704C5C2×#523311yescharacteristic, complemented, Sylow
705C22—22no—
706C22—22no—
707C22—42no—
708C22—54no—
709C22—51no—
710C22—51no—
711C22—52no—
712C22—104no—
713C22—104no—
714C22—102no—
715C22—102no—
716C22—204no—
717C22—204no—
718C22—202no—
719C22C2×#676312yes—
720C22C2×#676311yescharacteristic
721C4—22no—
722C4—51no—
723C4—52no—
724C4—51no—
725C4—102no—
726C4—604no—
727C4C2×#676312yes—
728C4C2×#676311yescharacteristic
729C4C23×ΓL(1,𝔽16)11yescharacteristic
730C3C2×#6579411yescharacteristic, complemented, Sylow
731C2—22no—
732C2—42no—
733C2—52no—
734C2—52no—
735C2—102no—
736C2—202no—
737C2#1175245312yesdirect product factor
738C2C22×#676311yescharacteristic
subgroupG/H
centerC2×C4#6763
commutatorC3×C4×C5C23×C4
FrattiniC4C23×ΓL(1,𝔽16)
FittingC2×C3×C5×#41C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C3×D5×#41C2
cosocleC3×C4×D5C24
hypercenterC2×#41ΓL(1,𝔽16)
hypocenterC3×C5C2×#416
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91989C2semidirect
3. C22×D5⋊(C3⋊C8)C2semidirect
4. #11752453C2direct (N × H)
5. C2×#91238C2semidirect
6. C2×#91236C2semidirect
8. C2×C3×C5×#41C4semidirect
11. C3×D5×#41C4semidirect
13. C2×C3×#713C4semidirect
16. C2×C3×#711C4semidirect
20. C2×C3×#709C4semidirect
26. #91989C22semidirect
32. C2×D5⋊(C3⋊C8)C22semidirect
33. #91238C22semidirect
34. #91236C22semidirect
46. C3×C5×#41C2×C4semidirect
58. C3×#713C2×C4semidirect
66. C3×#711C2×C4semidirect
76. C3×#709C2×C4semidirect
109. C2×C5×#41Dic3semidirect
112. D5×#41Dic3semidirect
114. C2×#713Dic3semidirect
117. C2×#711Dic3semidirect
121. C2×#709Dic3semidirect
202. C2×C3×#41AGL(1,𝔽5)semidirect
224. C5×#41C2×Dic3semidirect
236. #713C2×Dic3semidirect
244. #711C2×Dic3semidirect
254. #709C2×Dic3semidirect
325. C3×#41C2×AGL(1,𝔽5)semidirect
438. C2×#41ΓL(1,𝔽16)semidirect
458. C2×C3×C5#416semidirect
462. C3×D5#416semidirect
558. #41C2×ΓL(1,𝔽16)semidirect
606. C3×C5C2×#416semidirect
634. C2×C5#5233semidirect
638. D5#5233semidirect
702. C2×C3#65794semidirect
704. C5C2×#5233semidirect
730. C3C2×#65794semidirect
737. C2#11752453direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×D5×#412
C2×#919892
C22×D5⋊(C3⋊C8)2
#117524532
C2×#912382
C2×#912362
C2×#657943
C2×#52335