Finite Group Databasebeta

← C2×#11753580 #14481075

Subgroups — C2×#11753580 #14481075

Order 1920.

2288 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91778C211yesmaximal, characteristic, complemented
2C2×C5×#895C211yesmaximal, characteristic
3C2×C3×#4035C211yesmaximal, characteristic, complemented
4C2×#91436C211yesmaximal, characteristic, complemented
5C2×#91435C211yesmaximal, characteristic, complemented
6C2×#91423C211yesmaximal, characteristic, complemented
7C2×#91423C211yesmaximal, characteristic, complemented
8C2×#91423C211yesmaximal, characteristic, complemented
9C2×#91423C211yesmaximal, characteristic, complemented
10C2×#91417C211yesmaximal, characteristic, complemented
11C2×Dic5×D12C211yesmaximal, characteristic, complemented
12C2×D3×#683C211yesmaximal, characteristic, complemented
13C2×#91372C211yesmaximal, characteristic, complemented
14C2×#91367C211yesmaximal, characteristic, complemented
15C2×#91352C211yesmaximal, characteristic, complemented
16#11753580C2116yesmaximal, direct product factor
17C2×#65936—31nomaximal, Hall
18C22×C5×D12C2211yescharacteristic
19C22×C5×D12C2211yescharacteristic
20C22×C5×D12C2211yescharacteristic
21C22×C4×C5×D3C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C22×D3×Dic5C2211yescharacteristic
26C22×D3×Dic5C2211yescharacteristic
27C2×C3×C5×C4⋊C4C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×#6712C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×C4×Dic15C2211yescharacteristic
34#91778C2218yescomplemented
35C2×C5×(C2×D3)⋊C4C2211yescharacteristic
36C2×C5×(C2×D3)⋊C4C2211yescharacteristic
37C5×#895C2218yes—
38C2×C3×C4⋊Dic5C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×#683C2211yescharacteristic
43C2×C3×C4×Dic5C2211yescharacteristic
44C3×#4035C2218yescomplemented
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×#6669C2211yescharacteristic
47C2×#6668C2211yescharacteristic
48C2×(C2×D3)⋊Dic5C2211yescharacteristic
49C2×(C2×D3)⋊Dic5C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×(C2×D3)⋊Dic5C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56#91436C2218yescomplemented
57#91435C2218yescomplemented
58#91423C2218yescomplemented
59#91423C2218yescomplemented
60#91423C2218yescomplemented
61#91423C2218yescomplemented
62#91417C2218yescomplemented
63Dic5×D12C2218yescomplemented
64D3×#683C2218yescomplemented
65#91372C2218yescomplemented
66#91367C2218yescomplemented
67#91352C2218yescomplemented
68C2×#5692—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4081—31no—
71C2×#4081—31no—
72C2×#4081—31no—
73C2×#4081—31no—
74C2×D4×Dic5—31no—
75C2×D4×Dic5—31no—
76C2×#4070—31no—
77C22×#683—31no—
78#65936—316no—
79C2×#4035—31no—
80C2×#4035D311yescharacteristic, complemented
81C2×#4025—31no—
82C2×#4025—31no—
83C2×#4024—31no—
84C2×#4024—31no—
85C23×C5×D3C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C2×C5×D12—24no—
97C2×C5×D12—24no—
98C2×C5×D12—42no—
99C2×C5×D12C2314yes—
100C2×C5×D12C2314yes—
101C2×C5×D12C2314yes—
102C2×C4×C5×D3—42no—
103C2×C4×C5×D3C2314yes—
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×#1204—42no—
109C2×#1204C2314yes—
110C2×D3×Dic5—24no—
111C2×D3×Dic5—42no—
112C2×D3×Dic5—42no—
113C2×D3×Dic5—42no—
114C2×D3×Dic5C2314yes—
115C2×D3×Dic5C2314yes—
116C2×D3×Dic5C2314yes—
117C2×D3×Dic5C2314yes—
118C3×C5×C4⋊C4C2314yes—
119C4⋊Dic15C2314yes—
120#6712C2314yes—
121#6712C2314yes—
122#6712C2314yes—
123#6712C2314yes—
124C4×Dic15C2314yes—
125C5×(C2×D3)⋊C4C2314yes—
126C5×(C2×D3)⋊C4C2314yes—
127C3×C4⋊Dic5C2314yes—
128C3×#683C2314yes—
129C3×#683C2314yes—
130C3×#683C2314yes—
131C3×#683C2314yes—
132C3×C4×Dic5C2314yes—
133Dic3⋊Dic5C2314yes—
134#6669C2314yes—
135#6668C2314yes—
136(C2×D3)⋊Dic5C2314yes—
137(C2×D3)⋊Dic5C2314yes—
138(C2×D3)⋊Dic5C2314yes—
139(C2×D3)⋊Dic5C2314yes—
140(C2×D3)⋊Dic5C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143(C2×D3)⋊Dic5C2314yes—
144C2×C3×#125—51no—
145#5692—516no—
146C2×#898—51no—
147C2×#897—51no—
148C2×#896—51no—
149C2×#896—51no—
150C2×#895D511yescharacteristic
151C2×#894—51no—
152C2×#894—51no—
153C2×#894—51no—
154C2×#894—51no—
155C2×#893—51no—
156C2×D3×C4⋊C4—51no—
157C2×#889—51no—
158C2×#876—51no—
159C2×C4×D12—51no—
160C22×C5×D4—31no—
161C22×C5×D4—31no—
162C22×C5×D4—31no—
163C23×C4×C5—31no—
164C23×Dic5—31no—
165C23×Dic5—31no—
166C23×Dic5—31no—
167C23×Dic5—31no—
168C22×Dic10—31no—
169C5×#121—38no—
170C2×C5×C4⋊C4C2×D311yescharacteristic
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4—31no—
173C2×C22⋊Dic5—31no—
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5—31no—
179C2×C22⋊Dic5—31no—
180C2×C22⋊Dic5—31no—
181#4081—38no—
182#4081—38no—
183#4081—38no—
184#4081—38no—
185D4×Dic5—38no—
186D4×Dic5—38no—
187C2×C4⋊Dic5—31no—
188C2×C4⋊Dic5—31no—
189C2×C4⋊Dic5C2×D311yescharacteristic
190#4070—38no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683—38no—
198C2×#683C2×D311yescharacteristic
199C2×#683C2×D311yescharacteristic
200C2×#683C2×D311yescharacteristic
201C2×#683C2×D311yescharacteristic
202C2×C4×Dic5—31no—
203C2×C4×Dic5C2×D311yescharacteristic
204#4035—38no—
205#4035C2×D318yescomplemented
206#4025—38no—
207#4025—38no—
208#4024—38no—
209#4024—38no—
210C2×#539—151noSylow
211C23×C3×C5C2411yescharacteristic
212C22×C5×D3—22no—
213C22×C5×D3—22no—
214C22×C5×D3—22no—
215C22×C5×D3—22no—
216C22×C5×D3—22no—
217C22×C5×D3—22no—
218C22×C5×D3—22no—
219C22×C5×D3—22no—
220C22×C5×D3#4114yes—
221C22×C5×D3C2412yes—
222C22×C5×D3C2412yes—
223C22×C5×D3C2412yes—
224C2×C3×C4×C5—22no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5—22no—
227C2×C3×C4×C5C2412yes—
228C2×C3×C4×C5C2412yes—
229C2×C3×C4×C5C2412yes—
230C2×Dic15—22no—
231C2×Dic15—22no—
232C2×Dic15—22no—
233C2×Dic15—22no—
234C2×Dic15C2412yes—
235C2×Dic15C2412yes—
236C2×Dic15C2412yes—
237C2×Dic15C2412yes—
238C2×C5×Dic3—22no—
239C2×C5×Dic3C2412yes—
240C5×D12—28no—
241C5×D12—28no—
242C5×D12—44no—
243C4×C5×D3—44no—
244C2×C3×Dic5—22no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5—22no—
248C2×C3×Dic5C2412yes—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252#1204—44no—
253D3×Dic5—28no—
254D3×Dic5—44no—
255D3×Dic5—44no—
256D3×Dic5—44no—
257C22×D12C2×D511yescharacteristic
258C22×D12C2×D511yescharacteristic
259C22×D12C2×D511yescharacteristic
260C22×C4×D3—51no—
261C22×C4×D3—51no—
262C22×C4×D3—51no—
263C22×C4×D3—51no—
264C22×C4×D3C2×D511yescharacteristic
265C22×Dic6—51no—
266C3×#125—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C4⋊C4—51no—
271C2×C3×C4⋊C4—51no—
272C2×C3×C4⋊C4C2×D511yescharacteristic
273C2×C3×C42—51no—
274C2×(C2×D3)⋊C4—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
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×(C2×D3)⋊C4C2×D511yescharacteristic
284C2×C4⋊Dic3—51no—
285C2×C4⋊Dic3—51no—
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×C4×Dic3—51no—
293#898—58no—
294#897—58no—
295#896—58no—
296#896—58no—
297#895C2×D518yes—
298#894—58no—
299#894—58no—
300#894—58no—
301#894—58no—
302#893—58no—
303D3×C4⋊C4—58no—
304#889—58no—
305#876—58no—
306C4×D12—58no—
307C24×C5—31no—
308C24×C5—31no—
309C24×C5—31no—
310C2×C5×D4—34no—
311C2×C5×D4—34no—
312C2×C5×D4—34no—
313C2×C5×D4—64no—
314C2×C5×D4—64no—
315C2×C5×D4—122no—
316C22×C4×C5—31no—
317C22×C4×C5—34no—
318C22×C4×C5—122no—
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C22×C4×C5C22×D311yescharacteristic
322C22×Dic5—31no—
323C22×Dic5—31no—
324C22×Dic5—31no—
325C22×Dic5—31no—
326C22×Dic5—34no—
327C22×Dic5—34no—
328C22×Dic5—34no—
329C22×Dic5—34no—
330C22×Dic5—64no—
331C22×Dic5—122no—
332C22×Dic5—122no—
333C22×Dic5—122no—
334C22×Dic5C22×D311yescharacteristic
335C22×Dic5C22×D311yescharacteristic
336C22×Dic5C22×D311yescharacteristic
337C22×Dic5C22×D311yescharacteristic
338C2×Dic10—34no—
339C2×Dic10—122no—
340C5×C4⋊C4C22×D314yes—
341C5×C22⋊C4—34no—
342C5×C22⋊C4—34no—
343C22⋊Dic5—34no—
344C22⋊Dic5—34no—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5—34no—
349C22⋊Dic5—34no—
350C22⋊Dic5—34no—
351C4⋊Dic5—34no—
352C4⋊Dic5—34no—
353C4⋊Dic5C22×D314yes—
354#683—34no—
355#683—34no—
356#683—34no—
357#683—34no—
358#683—34no—
359#683—34no—
360#683C22×D314yes—
361#683C22×D314yes—
362#683C22×D314yes—
363#683C22×D314yes—
364C4×Dic5—34no—
365C4×Dic5C22×D314yes—
366#539—1516no—
367C2×#126—151no—
368C2×#126—151no—
369C2×#125—51no—
370C2×#125—151no—
371C2×#123—151no—
372C2×#123—151no—
373C2×#123—151no—
374C2×#123—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8—151no—
378C2×#121—31no—
379C2×C4×D4—151no—
380C2×C4×D4—151no—
381C22×C4⋊C4—151no—
382C22×C3×C5C2×#4112yes—
383C22×C3×C5H(5,𝔽2)12yes—
384C22×C3×C52−1+412yes—
385C22×C3×C5C2511yescharacteristic
386C2×C5×D3—28no—
387C2×C5×D3—22no—
388C2×C5×D3—22no—
389C2×C5×D3—22no—
390C2×C5×D3—22no—
391C2×C5×D3—22no—
392C2×C5×D3—22no—
393C2×C5×D3—22no—
394C2×C5×D3—22no—
395C2×C5×D3—44no—
396C2×C5×D3—44no—
397C2×C5×D3C2×#4114yes—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401Dic15—22no—
402Dic15—22no—
403Dic15—22no—
404Dic15—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C3×Dic5—22no—
408C3×Dic5—22no—
409C5×Dic3—22no—
410C23×D3C22×D511yescharacteristic
411C23×D3C22×D511yescharacteristic
412C23×D3C22×D511yescharacteristic
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C22×C3×C4C22×D511yescharacteristic
420C22×Dic3—51no—
421C22×Dic3—51no—
422C22×Dic3—51no—
423C22×Dic3—51no—
424C22×Dic3C22×D511yescharacteristic
425C2×D12—24no—
426C2×D12—24no—
427C2×D12—42no—
428C2×D12C22×D514yes—
429C2×D12C22×D514yes—
430C2×D12C22×D514yes—
431C2×C4×D3—42no—
432C2×C4×D3—54no—
433C2×C4×D3—54no—
434C2×C4×D3—54no—
435C2×C4×D3—54no—
436C2×C4×D3—104no—
437C2×C4×D3—202no—
438C2×C4×D3—202no—
439C2×C4×D3—202no—
440C2×C4×D3C22×D514yes—
441C2×Dic6—54no—
442C2×Dic6—202no—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C4⋊C4—54no—
446C3×C4⋊C4—54no—
447C3×C4⋊C4—54no—
448C3×C4⋊C4C22×D514yes—
449C3×C42—54no—
450(C2×D3)⋊C4—54no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—54no—
457(C2×D3)⋊C4—54no—
458(C2×D3)⋊C4C22×D514yes—
459(C2×D3)⋊C4C22×D514yes—
460C4⋊Dic3—54no—
461C4⋊Dic3—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4—54no—
465Dic3⋊C4—54no—
466Dic3⋊C4—54no—
467Dic3⋊C4—54no—
468C4×Dic3—54no—
469C23×C5—34no—
470C23×C5—32no—
471C23×C5—32no—
472C23×C5—32no—
473C23×C5—62no—
474C23×C5—62no—
475C23×C5—62no—
476C23×C5—62no—
477C23×C5—62no—
478C23×C5—62no—
479C23×C5—62no—
480C23×C5—62no—
481C23×C5C23×D311yescharacteristic
482C5×D4—68no—
483C5×D4—68no—
484C5×D4—124no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—32no—
489C2×C4×C5—62no—
490C2×C4×C5—124no—
491C2×C4×C5C23×D312yes—
492C2×C4×C5C23×D312yes—
493C2×C4×C5C23×D312yes—
494C2×Dic5—22no—
495C2×Dic5—22no—
496C2×Dic5—22no—
497C2×Dic5—22no—
498C2×Dic5—32no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—68no—
503C2×Dic5—62no—
504C2×Dic5—62no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5—124no—
508C2×Dic5—124no—
509C2×Dic5—124no—
510C2×Dic5C23×D312yes—
511C2×Dic5C23×D312yes—
512C2×Dic5C23×D312yes—
513C2×Dic5C23×D312yes—
514Dic10—124no—
515C22×Q8—151no—
516C22×D4—31no—
517C22×D4—31no—
518C22×D4—31no—
519C23×C4—31no—
520C23×C4—151no—
521C23×C4—151no—
522C23×C4—151no—
523C23×C4—151no—
524#126—158no—
525#126—158no—
526#125—58no—
527#125—158no—
528#123—158no—
529#123—158no—
530#123—158no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
535#121—38no—
536C4×D4—158no—
537C4×D4—158no—
538C2×C4⋊C4—51no—
539C2×C4⋊C4—51no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—51no—
542C2×C4⋊C4—51no—
543C2×C4⋊C4—158no—
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⋊C4D3×D511yescharacteristic
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
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×C42—51no—
564C2×C42—151no—
565C2×C3×C5#53914yescomplemented
566C2×C3×C5C22×#4111yescharacteristic
567C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
568C2×C3×C5C2×2−1+411yescharacteristic
569C5×D3—24no—
570C5×D3—42no—
571C5×D3—42no—
572C23×C3C23×D511yescharacteristic
573C22×D3—22no—
574C22×D3—22no—
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3#71114yes—
582C22×D3C23×D512yes—
583C22×D3C23×D512yes—
584C22×D3C23×D512yes—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—22no—
588C2×C3×C4—52no—
589C2×C3×C4—52no—
590C2×C3×C4—52no—
591C2×C3×C4—52no—
592C2×C3×C4—102no—
593C2×C3×C4—102no—
594C2×C3×C4—102no—
595C2×C3×C4—102no—
596C2×C3×C4C23×D512yes—
597C2×C3×C4C23×D512yes—
598C2×C3×C4C23×D512yes—
599C2×Dic3—22no—
600C2×Dic3—52no—
601C2×Dic3—52no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—102no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3C23×D512yes—
609D12—28no—
610D12—28no—
611D12—44no—
612C4×D3—44no—
613C4×D3—108no—
614C4×D3—204no—
615C4×D3—204no—
616C4×D3—204no—
617Dic6—204no—
618C22×C5—34no—
619C22×C5—68no—
620C22×C5—62no—
621C22×C5—62no—
622C22×C5—62no—
623C22×C5—62no—
624C22×C5—62no—
625C22×C5—62no—
626C22×C5—62no—
627C22×C5—62no—
628C22×C5—124no—
629C22×C5—124no—
630C22×C5#100712yes—
631C22×C5D3×#4112yes—
632C22×C5#100912yes—
633C22×C5C24×D311yescharacteristic
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—22no—
637C4×C5—62no—
638Dic5—22no—
639Dic5—22no—
640Dic5—22no—
641Dic5—22no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—31no—
647C24—31no—
648C24—31no—
649C2×Q8—154no—
650C2×Q8—602no—
651C2×D4—34no—
652C2×D4—34no—
653C2×D4—34no—
654C2×D4—64no—
655C2×D4—64no—
656C2×D4—122no—
657C22×C4—31no—
658C22×C4—34no—
659C22×C4—51no—
660C22×C4—51no—
661C22×C4—51no—
662C22×C4—51no—
663C22×C4—122no—
664C22×C4—154no—
665C22×C4—154no—
666C22×C4—154no—
667C22×C4—154no—
668C22×C4—151no—
669C22×C4—151no—
670C22×C4—151no—
671C22×C4—151no—
672C22×C4—304no—
673C22×C4—602no—
674C22×C4—602no—
675C22×C4—602no—
676C22×C4C2×D3×D511yescharacteristic
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—54no—
680C4⋊C4—54no—
681C4⋊C4—54no—
682C4⋊C4—54no—
683C4⋊C4—54no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C4⋊C4—154no—
690C4⋊C4—154no—
691C4⋊C4—154no—
692C4⋊C4C2×D3×D514yes—
693C22⋊C4—34no—
694C22⋊C4—34no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—154no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C22⋊C4—154no—
702C22⋊C4—154no—
703C42—54no—
704C42—154no—
705C3×C5C2×#53911yescharacteristic, complemented, Hall
706C22×C3C2×#71112yes—
707C22×C3#414412yes—
708C22×C3#415012yes—
709C22×C3C24×D511yescharacteristic
710C2×D3—28no—
711C2×D3—22no—
712C2×D3—22no—
713C2×D3—22no—
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—22no—
718C2×D3—22no—
719C2×D3—44no—
720C2×D3—44no—
721C2×D3C2×#71114yes—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—102no—
726C3×C4—102no—
727C3×C4—102no—
728C3×C4—102no—
729Dic3—22no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3—102no—
734C2×C5—64no—
735C2×C5—122no—
736C2×C5—122no—
737C2×C5#569214yescomplemented
738C2×C5C2×#100711yescharacteristic
739C2×C5C2×D3×#4111yescharacteristic
740C2×C5C2×#100911yescharacteristic
741C23—34no—
742C23—32no—
743C23—32no—
744C23—32no—
745C23—62no—
746C23—62no—
747C23—62no—
748C23—62no—
749C23—62no—
750C23—62no—
751C23—62no—
752C23—62no—
753C23C22×D3×D511yescharacteristic
754Q8—604no—
755D4—68no—
756D4—68no—
757D4—124no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—32no—
762C2×C4—52no—
763C2×C4—52no—
764C2×C4—52no—
765C2×C4—52no—
766C2×C4—62no—
767C2×C4—102no—
768C2×C4—102no—
769C2×C4—102no—
770C2×C4—102no—
771C2×C4—124no—
772C2×C4—152no—
773C2×C4—152no—
774C2×C4—152no—
775C2×C4—152no—
776C2×C4—308no—
777C2×C4—302no—
778C2×C4—302no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—604no—
782C2×C4—604no—
783C2×C4—604no—
784C2×C4C22×D3×D512yes—
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D512yes—
787C2×C3#6593614yescomplemented
788C2×C3C22×#71111yescharacteristic
789C2×C3C2×#414411yescharacteristic
790C2×C3C2×#415011yescharacteristic
791D3—24no—
792D3—42no—
793D3—42no—
794C5C2×#569211yescharacteristic, complemented, Sylow
795C22—34no—
796C22—68no—
797C22—62no—
798C22—62no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—62no—
803C22—62no—
804C22—62no—
805C22—124no—
806C22—124no—
807C22#9201812yes—
808C22D3×#71112yes—
809C22#9203012yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—62no—
815C4—102no—
816C4—102no—
817C4—102no—
818C4—102no—
819C4—302no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6593611yescharacteristic, complemented, Sylow
824C2—64no—
825C2—122no—
826C2—122no—
827C2#1175358014yesdirect product factor
828C2C2×#9201811yescharacteristic
829C2C2×D3×#71111yescharacteristic
830C2C2×#9203011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC2×C5×#895C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#539
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×#91778C2semidirect
3. C2×C3×#4035C2semidirect
4. C2×#91436C2semidirect
5. C2×#91435C2semidirect
6. C2×#91423C2semidirect
7. C2×#91423C2semidirect
8. C2×#91423C2semidirect
9. C2×#91423C2semidirect
10. C2×#91417C2semidirect
11. C2×Dic5×D12C2semidirect
12. C2×D3×#683C2semidirect
13. C2×#91372C2semidirect
14. C2×#91367C2semidirect
15. C2×#91352C2semidirect
16. #11753580C2direct (N × H)
34. #91778C22semidirect
44. C3×#4035C22semidirect
56. #91436C22semidirect
57. #91435C22semidirect
58. #91423C22semidirect
59. #91423C22semidirect
60. #91423C22semidirect
61. #91423C22semidirect
62. #91417C22semidirect
63. Dic5×D12C22semidirect
64. D3×#683C22semidirect
65. #91372C22semidirect
66. #91367C22semidirect
67. #91352C22semidirect
80. C2×#4035D3semidirect
205. #4035C2×D3semidirect
565. C2×C3×C5#539semidirect
705. C3×C5C2×#539semidirect
737. C2×C5#5692semidirect
787. C2×C3#65936semidirect
794. C5C2×#5692semidirect
823. C3C2×#65936semidirect
827. C2#11753580direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917782
C2×C5×#8952
C2×C3×#40352
C2×#914362
C2×#914352
C2×#914232
C2×#914172
C2×Dic5×D122
C2×D3×#6832
C2×#913722
C2×#913672
C2×#913522
#117535802
C2×#659363
C2×#56925