Finite Group Databasebeta

← C2×#11752918 #14483571

Subgroups — C2×#11752918 #14483571

Order 1920.

2248 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91768C211yesmaximal, characteristic, complemented
2C2×C5×#878C211yesmaximal, characteristic, complemented
3C2×C3×#4029C211yesmaximal, characteristic
4C2×Dic3×C22⋊D5C211yesmaximal, characteristic
5C2×#91548C211yesmaximal, characteristic
6C2×#91531C211yesmaximal, characteristic, complemented
7C2×#91529C211yesmaximal, characteristic, complemented
8C2×#91421C211yesmaximal, characteristic, complemented
9C2×#91394C211yesmaximal, characteristic, complemented
10C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
11C2×#91358C211yesmaximal, characteristic, complemented
12C2×#91344C211yesmaximal, characteristic, complemented
13C2×#91343C211yesmaximal, characteristic, complemented
14C2×#91339C211yesmaximal, characteristic, complemented
15C2×#91335C211yesmaximal, characteristic, complemented
16#11752918C2116yesmaximal, direct product factor
17C2×#65973—31nomaximal, Hall
18C23×C5×Dic3C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C4×D5C2211yescharacteristic
22C22×D5×Dic3C2211yescharacteristic
23C22×D5×Dic3C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×#6712C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31#91768C2218yescomplemented
32C2×C5×#217C2211yescharacteristic
33C2×C5×C4⋊Dic3C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C5×#878C2218yescomplemented
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×#685C2211yescharacteristic
39C2×C3×C4⋊Dic5C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C3×#4029C2218yes—
42Dic3×C22⋊D5C2218yes—
43#91548C2218yes—
44C2×Dic3⋊Dic5C2211yescharacteristic
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×Dic3⋊Dic5C2211yescharacteristic
47C2×Dic3⋊Dic5C2211yescharacteristic
48C2×#6669C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6668C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6665C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54#91531C2218yescomplemented
55#91529C2218yescomplemented
56C2×Dic3×Dic5C2211yescharacteristic
57C2×Dic3×Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91421C2218yescomplemented
61#91394C2218yescomplemented
62D5×Dic3⋊C4C2218yescomplemented
63#91358C2218yescomplemented
64#91344C2218yescomplemented
65#91343C2218yescomplemented
66#91339C2218yescomplemented
67#91335C2218yescomplemented
68C2×#5650—51nomaximal, Hall
69C2×C5×C22⋊Q8—31no—
70C2×#4092—31no—
71C2×Q8×Dic5—31no—
72C2×C4×C22⋊D5—31no—
73C2×#4072—31no—
74#65973—316no—
75C2×#4038—31no—
76C2×#4038—31no—
77C2×D5×C4⋊C4—31no—
78C2×#4036—31no—
79C2×#4035—31no—
80C2×#4035—31no—
81C2×#4029—31no—
82C2×#4029D311yescharacteristic
83C2×#4025—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×C5×Dic3—24no—
94C22×C5×Dic3C2314yes—
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C2×C5×Dic6—24no—
100C2×C5×Dic6C2314yes—
101C2×C3×C22⋊D5—24no—
102C2×C3×C22⋊D5C2314yes—
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×C3×C4×D5—24no—
107C2×C3×C4×D5C2314yes—
108C2×D5×Dic3—24no—
109C2×D5×Dic3—24no—
110C2×D5×Dic3C2314yes—
111C2×D5×Dic3C2314yes—
112C3×C5×C22⋊C4C2314yes—
113#6719C2314yes—
114#6719C2314yes—
115C4⋊Dic15C2314yes—
116#6712C2314yes—
117#6712C2314yes—
118C4×Dic15C2314yes—
119C5×#217C2314yes—
120C5×C4⋊Dic3C2314yes—
121C5×Dic3⋊C4C2314yes—
122C5×Dic3⋊C4C2314yes—
123C3×C22⋊Dic5C2314yes—
124C3×#685C2314yes—
125C3×C4⋊Dic5C2314yes—
126C3×#683C2314yes—
127Dic3⋊Dic5C2314yes—
128Dic3⋊Dic5C2314yes—
129Dic3⋊Dic5C2314yes—
130Dic3⋊Dic5C2314yes—
131#6669C2314yes—
132#6669C2314yes—
133#6668C2314yes—
134#6668C2314yes—
135#6665C2314yes—
136#6665C2314yes—
137Dic3×Dic5C2314yes—
138Dic3×Dic5C2314yes—
139Dic3×Dic5C2314yes—
140Dic3×Dic5C2314yes—
141C2×C3×#123—51no—
142C2×#935—51no—
143C2×D4×Dic3—51no—
144C2×#926—51no—
145C22×Dic3⋊C4—51no—
146#5650—516no—
147C2×#890—51no—
148C2×#889—51no—
149C2×#889—51no—
150C2×#887—51no—
151C2×#879—51no—
152C2×#879—51no—
153C2×#878—51no—
154C2×#878D511yescharacteristic, complemented
155C2×#877—51no—
156C2×#877—51no—
157C22×C5×Q8—31no—
158C23×C4×C5—31no—
159C22×C22⋊D5C2×D311yescharacteristic
160C22×C4×D5—31no—
161C22×C4×D5—31no—
162C22×C4×D5C2×D311yescharacteristic
163C5×C22⋊Q8—38no—
164C2×C5×C4⋊C4—31no—
165C2×C5×C4⋊C4—31no—
166C2×C5×C4⋊C4—31no—
167C2×C5×C22⋊C4—31no—
168C2×C5×C22⋊C4C2×D311yescharacteristic
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5C2×D311yescharacteristic
172#4092—38no—
173Q8×Dic5—38no—
174C4×C22⋊D5—38no—
175C2×#685—31no—
176C2×#685—31no—
177C2×#685C2×D311yescharacteristic
178#4072—38no—
179C2×C4⋊Dic5—31no—
180C2×C4⋊Dic5—31no—
181C2×C4⋊Dic5—31no—
182C2×C4⋊Dic5—31no—
183C2×C4⋊Dic5—31no—
184C2×C4⋊Dic5C2×D311yescharacteristic
185C2×#683—31no—
186C2×#683—31no—
187C2×#683—31no—
188C2×#683—31no—
189C2×#683—31no—
190C2×#683—31no—
191C2×#683C2×D311yescharacteristic
192C2×C4×Dic5—31no—
193C2×C4×Dic5—31no—
194C2×C4×Dic5—31no—
195C2×C4×Dic5—31no—
196C2×C4×Dic5—31no—
197#4038—38no—
198#4038—38no—
199D5×C4⋊C4—38no—
200#4036—38no—
201#4035—38no—
202#4035—38no—
203#4029—38no—
204#4029C2×D318yes—
205#4025—38no—
206#4025—38no—
207C2×#552—151noSylow
208C23×C3×C5—22no—
209C23×C3×C5—22no—
210C23×C3×C5—22no—
211C23×C3×C5C2412yes—
212C23×C3×C5C2411yescharacteristic
213C22×C3×D5—22no—
214C22×C3×D5—22no—
215C22×C3×D5#4114yes—
216C22×C3×D5C2412yes—
217C2×C3×C4×C5—22no—
218C2×C3×C4×C5—22no—
219C2×C3×C4×C5C2412yes—
220C2×C3×C4×C5C2412yes—
221C2×Dic15—22no—
222C2×Dic15—22no—
223C2×Dic15—22no—
224C2×Dic15—22no—
225C2×Dic15C2412yes—
226C2×Dic15C2412yes—
227C2×Dic15C2412yes—
228C2×Dic15C2412yes—
229C2×C5×Dic3—22no—
230C2×C5×Dic3—22no—
231C2×C5×Dic3—22no—
232C2×C5×Dic3—28no—
233C2×C5×Dic3#4114yes—
234C2×C5×Dic3C2412yes—
235C2×C5×Dic3C2412yes—
236C2×C5×Dic3C2412yes—
237C2×C5×Dic3C2412yes—
238C5×Dic6—28no—
239C3×C22⋊D5—28no—
240C2×C3×Dic5—22no—
241C2×C3×Dic5—22no—
242C2×C3×Dic5—22no—
243C2×C3×Dic5C2412yes—
244C2×C3×Dic5C2412yes—
245C2×C3×Dic5C2412yes—
246C3×C4×D5—28no—
247D5×Dic3—28no—
248D5×Dic3—28no—
249C22×C3×D4—51no—
250C23×C3×C4—51no—
251C23×Dic3—51no—
252C23×Dic3—51no—
253C23×Dic3C2×D511yescharacteristic
254C22×Dic6C2×D511yescharacteristic
255C3×#123—58no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C22⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4C2×D511yescharacteristic
261C2×#217—51no—
262C2×#217—51no—
263C2×#217—51no—
264C2×#217—51no—
265C2×#217C2×D511yescharacteristic
266#935—58no—
267D4×Dic3—58no—
268#926—58no—
269C2×C4⋊Dic3—51no—
270C2×C4⋊Dic3—51no—
271C2×C4⋊Dic3—51no—
272C2×C4⋊Dic3C2×D511yescharacteristic
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×Dic3⋊C4—51no—
280C2×Dic3⋊C4—51no—
281C2×Dic3⋊C4—58no—
282C2×Dic3⋊C4C2×D511yescharacteristic
283C2×Dic3⋊C4C2×D511yescharacteristic
284C2×C4×Dic3—51no—
285C2×C4×Dic3—51no—
286C2×C4×Dic3—51no—
287C2×C4×Dic3—51no—
288C2×C4×Dic3—51no—
289#890—58no—
290#889—58no—
291#889—58no—
292#887—58no—
293#879—58no—
294#879—58no—
295#878—58no—
296#878C2×D518yescomplemented
297#877—58no—
298#877—58no—
299C24×C5C22×D311yescharacteristic
300C23×D5C22×D311yescharacteristic
301C2×C5×Q8—34no—
302C2×C5×Q8—64no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—34no—
308C22×C4×C5—64no—
309C22×C4×C5C22×D311yescharacteristic
310C22×C4×C5C22×D311yescharacteristic
311C2×C22⋊D5—24no—
312C2×C22⋊D5C22×D314yes—
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—31no—
317C22×Dic5C22×D311yescharacteristic
318C22×Dic5C22×D311yescharacteristic
319C22×Dic5C22×D311yescharacteristic
320C2×C4×D5—24no—
321C2×C4×D5—34no—
322C2×C4×D5—34no—
323C2×C4×D5—64no—
324C2×C4×D5—64no—
325C2×C4×D5C22×D314yes—
326C5×C4⋊C4—34no—
327C5×C4⋊C4—34no—
328C5×C4⋊C4—34no—
329C5×C22⋊C4—34no—
330C5×C22⋊C4C22×D314yes—
331C22⋊Dic5—34no—
332C22⋊Dic5—34no—
333C22⋊Dic5C22×D314yes—
334#685—34no—
335#685—34no—
336#685C22×D314yes—
337C4⋊Dic5—34no—
338C4⋊Dic5—34no—
339C4⋊Dic5—34no—
340C4⋊Dic5—34no—
341C4⋊Dic5—34no—
342C4⋊Dic5C22×D314yes—
343#683—34no—
344#683—34no—
345#683—34no—
346#683—34no—
347#683—34no—
348#683—34no—
349#683C22×D314yes—
350C4×Dic5—34no—
351C4×Dic5—34no—
352C4×Dic5—34no—
353C4×Dic5—34no—
354C4×Dic5—34no—
355#552—1516no—
356C2×#126—151no—
357C2×#126—151no—
358C2×#125—151no—
359C2×#125—151no—
360C2×#125—151no—
361C2×#123—51no—
362C2×#123—151no—
363C2×C22⋊Q8—31no—
364C2×C22⋊Q8—151no—
365C2×C4×Q8—151no—
366C2×C4×D4—151no—
367C2×#117—151no—
368C2×#117—151no—
369C2×#117—151no—
370C22×C4⋊C4—151no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—44no—
375C22×C3×C5C2×#4112yes—
376C22×C3×C5C2×#4112yes—
377C22×C3×C52−1+412yes—
378C22×C3×C5C2511yescharacteristic
379C2×C3×D5—28no—
380C2×C3×D5—22no—
381C2×C3×D5—22no—
382C2×C3×D5C2×#4114yes—
383C3×C4×C5—22no—
384C3×C4×C5—22no—
385Dic15—22no—
386Dic15—22no—
387Dic15—22no—
388Dic15—22no—
389C3×Dic5—22no—
390C3×Dic5—22no—
391C3×Dic5—22no—
392C5×Dic3—22no—
393C5×Dic3—22no—
394C5×Dic3—22no—
395C5×Dic3C2×#4114yes—
396C24×C3—51no—
397C24×C3C22×D511yescharacteristic
398C2×C3×D4—54no—
399C2×C3×D4—104no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4—51no—
403C22×C3×C4—54no—
404C22×C3×C4—104no—
405C22×C3×C4C22×D511yescharacteristic
406C22×C3×C4C22×D511yescharacteristic
407C22×Dic3—24no—
408C22×Dic3—51no—
409C22×Dic3—51no—
410C22×Dic3—51no—
411C22×Dic3—51no—
412C22×Dic3—54no—
413C22×Dic3—54no—
414C22×Dic3—104no—
415C22×Dic3—104no—
416C22×Dic3C22×D514yes—
417C22×Dic3C22×D511yescharacteristic
418C22×Dic3C22×D511yescharacteristic
419C22×Dic3C22×D511yescharacteristic
420C22×Dic3C22×D511yescharacteristic
421C2×Dic6—24no—
422C2×Dic6C22×D514yes—
423C3×C4⋊C4—54no—
424C3×C4⋊C4—54no—
425C3×C22⋊C4—54no—
426C3×C22⋊C4—54no—
427C3×C22⋊C4C22×D514yes—
428#217—54no—
429#217—54no—
430#217—54no—
431#217—54no—
432#217C22×D514yes—
433C4⋊Dic3—54no—
434C4⋊Dic3—54no—
435C4⋊Dic3—54no—
436C4⋊Dic3C22×D514yes—
437Dic3⋊C4—54no—
438Dic3⋊C4—54no—
439Dic3⋊C4—54no—
440Dic3⋊C4—54no—
441Dic3⋊C4—54no—
442Dic3⋊C4—54no—
443Dic3⋊C4—54no—
444Dic3⋊C4—54no—
445Dic3⋊C4C22×D514yes—
446Dic3⋊C4C22×D514yes—
447C4×Dic3—54no—
448C4×Dic3—54no—
449C4×Dic3—54no—
450C4×Dic3—54no—
451C4×Dic3—54no—
452C23×C5—22no—
453C23×C5—22no—
454C23×C5—22no—
455C23×C5C23×D312yes—
456C23×C5C23×D311yescharacteristic
457C22×D5—22no—
458C22×D5—22no—
459C22×D5#23714yes—
460C22×D5C23×D312yes—
461C5×Q8—68no—
462C2×C4×C5—22no—
463C2×C4×C5—22no—
464C2×C4×C5—34no—
465C2×C4×C5—32no—
466C2×C4×C5—32no—
467C2×C4×C5—32no—
468C2×C4×C5—32no—
469C2×C4×C5—68no—
470C2×C4×C5—62no—
471C2×C4×C5—62no—
472C2×C4×C5—62no—
473C2×C4×C5C23×D312yes—
474C2×C4×C5C23×D312yes—
475C22⋊D5—28no—
476C2×Dic5—22no—
477C2×Dic5—22no—
478C2×Dic5—22no—
479C2×Dic5—32no—
480C2×Dic5—32no—
481C2×Dic5—32no—
482C2×Dic5—32no—
483C2×Dic5—62no—
484C2×Dic5—62no—
485C2×Dic5—62no—
486C2×Dic5—62no—
487C2×Dic5C23×D312yes—
488C2×Dic5C23×D312yes—
489C2×Dic5C23×D312yes—
490C4×D5—28no—
491C4×D5—68no—
492C4×D5—68no—
493C22×Q8—31no—
494C22×D4—51no—
495C23×C4—31no—
496C23×C4—51no—
497C23×C4—151no—
498C23×C4—151no—
499#126—158no—
500#126—158no—
501#125—158no—
502#125—158no—
503#125—158no—
504#123—58no—
505#123—158no—
506C22⋊Q8—38no—
507C22⋊Q8—158no—
508C4×Q8—158no—
509C4×D4—158no—
510#117—158no—
511#117—158no—
512#117—158no—
513C2×C4⋊C4—31no—
514C2×C4⋊C4—31no—
515C2×C4⋊C4—31no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—158no—
519C2×C4⋊C4—151no—
520C2×C4⋊C4—151no—
521C2×C4⋊C4—151no—
522C2×C4⋊C4—151no—
523C2×C4⋊C4—151no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C4⋊C4—151no—
527C2×C4⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C22⋊C4—31no—
531C2×C22⋊C4—51no—
532C2×C22⋊C4—51no—
533C2×C22⋊C4—151no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C22⋊C4D3×D511yescharacteristic
538C2×C42—151no—
539C2×C42—151no—
540C2×C42—151no—
541C2×C42—151no—
542C2×C42—151no—
543C2×C3×C5—42no—
544C2×C3×C5#55214yescomplemented
545C2×C3×C5C22×#4111yescharacteristic
546C2×C3×C5C22×#4111yescharacteristic
547C2×C3×C5C2×2−1+411yescharacteristic
548C3×D5—24no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3—54no—
553C23×C3—52no—
554C23×C3—102no—
555C23×C3—102no—
556C23×C3C23×D512yes—
557C23×C3C23×D511yescharacteristic
558C3×D4—108no—
559C2×C3×C4—22no—
560C2×C3×C4—22no—
561C2×C3×C4—52no—
562C2×C3×C4—52no—
563C2×C3×C4—52no—
564C2×C3×C4—108no—
565C2×C3×C4—102no—
566C2×C3×C4—102no—
567C2×C3×C4—102no—
568C2×C3×C4C23×D512yes—
569C2×C3×C4C23×D512yes—
570C2×Dic3—22no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—28no—
574C2×Dic3—52no—
575C2×Dic3—52no—
576C2×Dic3—52no—
577C2×Dic3—52no—
578C2×Dic3—108no—
579C2×Dic3—102no—
580C2×Dic3—102no—
581C2×Dic3—102no—
582C2×Dic3—102no—
583C2×Dic3—108no—
584C2×Dic3#71114yes—
585C2×Dic3C23×D512yes—
586C2×Dic3C23×D512yes—
587C2×Dic3C23×D512yes—
588C2×Dic3C23×D512yes—
589Dic6—28no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—22no—
593C22×C5—44no—
594C22×C5C2×#23712yes—
595C22×C5D3×#4112yes—
596C22×C5#101012yes—
597C22×C5C24×D311yescharacteristic
598C2×D5—28no—
599C2×D5—22no—
600C2×D5—22no—
601C2×D5C2×#23714yes—
602C4×C5—22no—
603C4×C5—22no—
604C4×C5—34no—
605C4×C5—62no—
606C4×C5—62no—
607C4×C5—62no—
608Dic5—22no—
609Dic5—22no—
610Dic5—22no—
611Dic5—62no—
612Dic5—62no—
613Dic5—62no—
614Dic5—62no—
615C24—51no—
616C24C2×D3×D511yescharacteristic
617C2×Q8—34no—
618C2×Q8—64no—
619C2×D4—54no—
620C2×D4—104no—
621C22×C4—31no—
622C22×C4—34no—
623C22×C4—31no—
624C22×C4—31no—
625C22×C4—31no—
626C22×C4—51no—
627C22×C4—51no—
628C22×C4—51no—
629C22×C4—54no—
630C22×C4—64no—
631C22×C4—104no—
632C22×C4—154no—
633C22×C4—154no—
634C22×C4—151no—
635C22×C4—151no—
636C22×C4—151no—
637C22×C4—151no—
638C22×C4—304no—
639C22×C4—304no—
640C22×C4C2×D3×D511yescharacteristic
641C22×C4C2×D3×D511yescharacteristic
642C4⋊C4—34no—
643C4⋊C4—34no—
644C4⋊C4—34no—
645C4⋊C4—54no—
646C4⋊C4—54no—
647C4⋊C4—154no—
648C4⋊C4—154no—
649C4⋊C4—154no—
650C4⋊C4—154no—
651C4⋊C4—154no—
652C4⋊C4—154no—
653C4⋊C4—154no—
654C4⋊C4—154no—
655C4⋊C4—154no—
656C4⋊C4—154no—
657C4⋊C4—154no—
658C22⋊C4—34no—
659C22⋊C4—54no—
660C22⋊C4—54no—
661C22⋊C4—154no—
662C22⋊C4—154no—
663C22⋊C4—154no—
664C22⋊C4—154no—
665C22⋊C4C2×D3×D514yes—
666C42—154no—
667C42—154no—
668C42—154no—
669C42—154no—
670C42—154no—
671C3×C5C2×#55211yescharacteristic, complemented, Hall
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—44no—
676C22×C3—54no—
677C22×C3—108no—
678C22×C3—102no—
679C22×C3—102no—
680C22×C3C2×#71112yes—
681C22×C3#414712yes—
682C22×C3D5×#4112yes—
683C22×C3C24×D511yescharacteristic
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—102no—
687C3×C4—102no—
688C3×C4—102no—
689Dic3—22no—
690Dic3—22no—
691Dic3—22no—
692Dic3—102no—
693Dic3—102no—
694Dic3—102no—
695Dic3—102no—
696Dic3C2×#71114yes—
697C2×C5—42no—
698C2×C5#565014yescomplemented
699C2×C5C22×#23711yescharacteristic
700C2×C5C2×D3×#4111yescharacteristic
701C2×C5C2×#101011yescharacteristic
702D5—24no—
703C23—22no—
704C23—22no—
705C23—22no—
706C23—54no—
707C23—52no—
708C23—102no—
709C23—102no—
710C23C22×D3×D512yes—
711C23C22×D3×D511yescharacteristic
712Q8—68no—
713D4—108no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—34no—
717C2×C4—32no—
718C2×C4—32no—
719C2×C4—32no—
720C2×C4—32no—
721C2×C4—52no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—68no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—108no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—152no—
733C2×C4—152no—
734C2×C4—152no—
735C2×C4—152no—
736C2×C4—308no—
737C2×C4—308no—
738C2×C4—302no—
739C2×C4—302no—
740C2×C4—302no—
741C2×C4—302no—
742C2×C4C22×D3×D512yes—
743C2×C4C22×D3×D512yes—
744C2×C3—42no—
745C2×C3—104no—
746C2×C3#6597314yescomplemented
747C2×C3C22×#71111yescharacteristic
748C2×C3C2×#414711yescharacteristic
749C2×C3C2×D5×#4111yescharacteristic
750C5C2×#565011yescharacteristic, complemented, Sylow
751C22—22no—
752C22—22no—
753C22—22no—
754C22—44no—
755C22—54no—
756C22—102no—
757C22—108no—
758C22—102no—
759C22#9200012yes—
760C22D5×#23712yes—
761C22D3×#71112yes—
762C22C23×D3×D511yescharacteristic
763C4—22no—
764C4—22no—
765C4—34no—
766C4—62no—
767C4—62no—
768C4—62no—
769C4—102no—
770C4—102no—
771C4—102no—
772C4—302no—
773C4—302no—
774C4—302no—
775C4—302no—
776C3C2×#6597311yescharacteristic, complemented, Sylow
777C2—42no—
778C2—104no—
779C2#1175291814yesdirect product factor
780C2C2×#9200011yescharacteristic
781C2C2×D5×#23711yescharacteristic
782C2C2×D3×#71111yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC22×C3×C22⋊D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#552
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×#91768C2semidirect
2. C2×C5×#878C2semidirect
6. C2×#91531C2semidirect
7. C2×#91529C2semidirect
8. C2×#91421C2semidirect
9. C2×#91394C2semidirect
10. C2×D5×Dic3⋊C4C2semidirect
11. C2×#91358C2semidirect
12. C2×#91344C2semidirect
13. C2×#91343C2semidirect
14. C2×#91339C2semidirect
15. C2×#91335C2semidirect
16. #11752918C2direct (N × H)
31. #91768C22semidirect
36. C5×#878C22semidirect
54. #91531C22semidirect
55. #91529C22semidirect
60. #91421C22semidirect
61. #91394C22semidirect
62. D5×Dic3⋊C4C22semidirect
63. #91358C22semidirect
64. #91344C22semidirect
65. #91343C22semidirect
66. #91339C22semidirect
67. #91335C22semidirect
154. C2×#878D5semidirect
296. #878C2×D5semidirect
544. C2×C3×C5#552semidirect
671. C3×C5C2×#552semidirect
698. C2×C5#5650semidirect
746. C2×C3#65973semidirect
750. C5C2×#5650semidirect
776. C3C2×#65973semidirect
779. C2#11752918direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917682
C2×C5×#8782
C2×C3×#40292
C2×Dic3×C22⋊D52
C2×#915482
C2×#915312
C2×#915292
C2×#914212
C2×#913942
C2×D5×Dic3⋊C42
C2×#913582
C2×#913442
C2×#913432
C2×#913392
C2×#913352
#117529182
C2×#659733
C2×#56505