Finite Group Databasebeta

← C2×#11756835 #14478945

Subgroups — C2×#11756835 #14478945

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D5×#235C211yesmaximal, characteristic
2C22×C4×ΓL(1,𝔽16)C211yesmaximal, characteristic, complemented
3C2×C3×#4130C211yesmaximal, characteristic, complemented
4C2×#67⋊AGL(1,𝔽5)C214yesmaximal, complemented
5#11756835C2116yesmaximal, direct product factor
6C2×#91921C212yesmaximal, complemented
7C2×C4×D3×AGL(1,𝔽5)C212yesmaximal, complemented
8C2×#91909C212yesmaximal, complemented
9C2×ΓL(1,𝔽16)⋊Q8C212yesmaximal, complemented
10C2×#41×AGL(1,𝔽5)—31nomaximal, Hall
11C23×ΓL(1,𝔽16)C2212yes—
12C22×D3×AGL(1,𝔽5)C2214yes—
13C2×#6817C411yescharacteristic, complemented
14C2×C5×#235C411yescharacteristic, complemented
15C22×C3×C4×D5C2211yescharacteristic
16C2×D5×#67C2212yes—
17C2×#6782C412yescomplemented
18D5×#235C418yescomplemented
19D5×#235C2218yes—
20C2×D5×D12C2211yescharacteristic
21C2×C4×D3×D5C2212yes—
22C2×#6773C411yescharacteristic, complemented
23C2×#6772C411yescharacteristic, complemented
24C2×#6771C412yescomplemented
25C2×D5×Dic6C2211yescharacteristic
26C2×C4×ΓL(1,𝔽16)C2212yes—
27C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
28C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
29C2×C4×ΓL(1,𝔽16)C2218yescomplemented
30C2×C3×C22⋊AGL(1,𝔽5)C2212yes—
31C3×#4130C2218yescomplemented
32C2×C3×C4⋊AGL(1,𝔽5)C2212yes—
33C2×C3×C4×AGL(1,𝔽5)C2212yes—
34#67⋊AGL(1,𝔽5)C22132yescomplemented
35C2×Dic3⋊AGL(1,𝔽5)C2214yes—
36C2×(C2×D3)⋊AGL(1,𝔽5)C2214yes—
37C2×Dic3×AGL(1,𝔽5)C2214yes—
38#91921C22116yescomplemented
39C4×D3×AGL(1,𝔽5)C22116yescomplemented
40#91909C22116yescomplemented
41ΓL(1,𝔽16)⋊Q8C22116yescomplemented
42C2×#5522—51nomaximal, Hall
43C2×D5×#41—31no—
44#41×AGL(1,𝔽5)—316no—
45C2×Q8×AGL(1,𝔽5)—32no—
46C2×D4×AGL(1,𝔽5)—34no—
47C2×D4×AGL(1,𝔽5)—32no—
48C2×#4130—32no—
49C2×#4130D311yescharacteristic, complemented
50C22×C4×AGL(1,𝔽5)—31no—
51C22×C4×AGL(1,𝔽5)—32no—
52C23×C3×D5C2311yescharacteristic
53C22×D3×D5C2312yes—
54C22×ΓL(1,𝔽16)—28no—
55C22×ΓL(1,𝔽16)C2312yes—
56C22×ΓL(1,𝔽16)C2318yes—
57C22×ΓL(1,𝔽16)C2312yes—
58C22×C3×AGL(1,𝔽5)C2314yes—
59C2×D3×AGL(1,𝔽5)—216no—
60C2×D3×AGL(1,𝔽5)C23116yes—
61C22×C3×C4×C5C2×C411yescharacteristic, complemented
62C2×#1220C2×C412yescomplemented
63#6817C2×C418yescomplemented
64C2×D60C2×C411yescharacteristic, complemented
65C2×C4×D15C2×C412yescomplemented
66C2×Dic30C2×C411yescharacteristic, complemented
67C2×C5×#67C2×C412yescomplemented
68C5×#235C2×C418yescomplemented
69C2×C5×D12C2×C411yescharacteristic, complemented
70C2×C4×C5×D3C2×C412yescomplemented
71C2×C5×Dic6C2×C411yescharacteristic, complemented
72C22×C3×Dic5C2×C411yescharacteristic, complemented
73C2×C3×C4×D5C2×C414yescomplemented
74C2×C3×C4×D5C2×C411yescharacteristic, complemented
75C2×C3×C4×D5C2×C411yescharacteristic, complemented
76C2×C3×C4×D5C2311yescharacteristic
77C2×C3×C4×D5C2311yescharacteristic
78C2×C3×C4×D5C2314yes—
79D5×#67C2×C418yescomplemented
80D5×#67C2318yes—
81C2×#1204C2×C412yescomplemented
82C2×#1203C2×C412yescomplemented
83C2×#1202C2×C412yescomplemented
84C2×#1201C2×C412yescomplemented
85C2×#1200C2×C412yescomplemented
86#6782C2×C4116yescomplemented
87C2×D3×Dic5C2×C412yescomplemented
88C2×D5×Dic3C2312yes—
89D5×D12C2×C414yescomplemented
90D5×D12C2314yes—
91C4×D3×D5C2×C418yescomplemented
92C4×D3×D5C2318yes—
93#6773C2×C418yescomplemented
94#6772C2×C418yescomplemented
95#6771C2×C4116yescomplemented
96D5×Dic6C2×C414yescomplemented
97D5×Dic6C2314yes—
98C4×ΓL(1,𝔽16)C2318yes—
99C4×ΓL(1,𝔽16)C2314yes—
100C4×ΓL(1,𝔽16)C2314yes—
101C3×C22⋊AGL(1,𝔽5)C2318yes—
102C3×C4⋊AGL(1,𝔽5)C2318yes—
103C3×C4×AGL(1,𝔽5)C2318yes—
104Dic3⋊AGL(1,𝔽5)C23116yes—
105(C2×D3)⋊AGL(1,𝔽5)C23116yes—
106Dic3×AGL(1,𝔽5)C23116yes—
107C22×#235—51no—
108C2×C3×#117—51no—
109C22×C4×Dic3—51no—
110#5522—516no—
111C2×#893—52no—
112C2×#887—52no—
113C2×#67⋊C4—54no—
114C2×#872—52no—
115C2×C42×D3—52no—
116C23×AGL(1,𝔽5)—32no—
117C23×AGL(1,𝔽5)—34no—
118C2×C5×#41—31no—
119D5×#41—38no—
120D5×#41—38no—
121C2×#713—31no—
122C2×Q8×D5—31no—
123C2×#711—32no—
124C2×#711—31no—
125C2×D4×D5—32no—
126C2×D4×D5—31no—
127C2×#709—31no—
128C2×#709—32no—
129C22×C4×D5—32no—
130C22×C4×D5C2×D311yescharacteristic
131C2×C22⋊AGL(1,𝔽5)—34no—
132C2×C22⋊AGL(1,𝔽5)C2×D312yes—
133Q8×AGL(1,𝔽5)—316no—
134D4×AGL(1,𝔽5)—332no—
135D4×AGL(1,𝔽5)—316no—
136#4130—316no—
137#4130C2×D318yescomplemented
138C2×C4⋊AGL(1,𝔽5)—34no—
139C2×C4⋊AGL(1,𝔽5)C2×D312yes—
140C2×C4×AGL(1,𝔽5)—34no—
141C2×C4×AGL(1,𝔽5)—31no—
142C2×C4×AGL(1,𝔽5)—31no—
143C2×C4×AGL(1,𝔽5)—32no—
144C2×C4×AGL(1,𝔽5)—38no—
145C2×C4×AGL(1,𝔽5)—316no—
146C2×C4×AGL(1,𝔽5)C2×D312yes—
147C2×C4×#41—151noSylow
148C23×C3×C5C22×C411yescharacteristic
149C22×D15C22×C412yes—
150C22×C5×D3C22×C412yes—
151C22×C3×D5—24no—
152C22×C3×D5C22×C411yescharacteristic
153C22×C3×D5C22×C412yes—
154C22×C3×D5C2412yes—
155C22×C3×D5C2411yescharacteristic
156C2×D3×D5—28no—
157C2×D3×D5C22×C414yes—
158C2×D3×D5C2414yes—
159C2×ΓL(1,𝔽16)—24no—
160C2×ΓL(1,𝔽16)—216no—
161C2×ΓL(1,𝔽16)#4118yescomplemented
162C2×ΓL(1,𝔽16)C2414yes—
163C2×ΓL(1,𝔽16)C2414yes—
164C2×C3×AGL(1,𝔽5)—28no—
165C2×C3×AGL(1,𝔽5)C2418yes—
166D3×AGL(1,𝔽5)—232no—
167C2×C3×C4×C5C22×C411yescharacteristic
168C2×C3×C4×C5C22×C411yescharacteristic
169C2×C3×C4×C5C22×C414yescomplemented
170#1220C22×C418yescomplemented
171C2×Dic15C22×C412yes—
172D60C22×C414yescomplemented
173C4×D15C22×C418yescomplemented
174Dic30C22×C414yescomplemented
175C5×#67C22×C418yescomplemented
176C2×C5×Dic3C22×C412yes—
177C5×D12C22×C414yescomplemented
178C4×C5×D3C22×C418yescomplemented
179C5×Dic6C22×C414yescomplemented
180C2×C3×Dic5C22×C411yescharacteristic
181C2×C3×Dic5C22×C411yescharacteristic
182C2×C3×Dic5C22×C414yescomplemented
183C3×C4×D5C22×C412yes—
184C3×C4×D5C22×C412yes—
185C3×C4×D5C22×C414yescomplemented
186C3×C4×D5C22×C414yescomplemented
187C3×C4×D5C2412yes—
188C3×C4×D5C2412yes—
189#1204C22×C418yescomplemented
190#1203C22×C418yescomplemented
191#1202C22×C418yescomplemented
192#1201C22×C418yescomplemented
193#1200C22×C418yescomplemented
194D3×Dic5C22×C418yescomplemented
195D5×Dic3C22×C414yes—
196D5×Dic3C2414yes—
197C23×C3×C4—51no—
198C22×#67—52no—
199C23×Dic3—52no—
200C2×#235—51no—
201C2×#235—52no—
202C2×#235—58no—
203C2×#235—58no—
204C2×#235—51no—
205C2×#235—52no—
206C2×#235—51no—
207C2×#235AGL(1,𝔽5)11yescharacteristic, complemented
208C22×D12—51no—
209C22×C4×D3—52no—
210C22×C4×D3—54no—
211C22×Dic6—51no—
212C3×#117—58no—
213C2×C3×C4⋊C4—52no—
214C2×C3×C22⋊C4—52no—
215C2×C3×C42—52no—
216C2×(C2×D3)⋊C4—54no—
217C2×Dic3⋊C4—54no—
218C2×C4×Dic3—54no—
219C2×C4×Dic3—51no—
220C2×C4×Dic3—51no—
221C2×C4×Dic3—52no—
222C2×C4×Dic3—58no—
223#893—516no—
224#887—516no—
225#67⋊C4—532no—
226#872—516no—
227C42×D3—516no—
228C23×D5—32no—
229C23×D5C22×D311yescharacteristic
230C22×AGL(1,𝔽5)—32no—
231C22×AGL(1,𝔽5)—32no—
232C22×AGL(1,𝔽5)—38no—
233C22×AGL(1,𝔽5)—316no—
234C22×AGL(1,𝔽5)—616no—
235C22×AGL(1,𝔽5)—68no—
236C22×AGL(1,𝔽5)C22×D314yes—
237C5×#41—38no—
238C2×C5×Q8—31no—
239C2×C5×D4—32no—
240C2×C5×D4—31no—
241C22×C4×C5—32no—
242C22×C4×C5C4×D311yescharacteristic, complemented
243C2×C22⋊D5—32no—
244C2×C22⋊D5—32no—
245C2×C22⋊D5—32no—
246C22×Dic5—32no—
247C22×Dic5C4×D311yescharacteristic, complemented
248#713—38no—
249Q8×D5—34no—
250Q8×D5—34no—
251#711—316no—
252#711—38no—
253D4×D5—38no—
254D4×D5—38no—
255D4×D5—34no—
256D4×D5—34no—
257#709—38no—
258#709—316no—
259C2×D20—32no—
260C2×D20—31no—
261C2×C4×D5—32no—
262C2×C4×D5—32no—
263C2×C4×D5—32no—
264C2×C4×D5—38no—
265C2×C4×D5—38no—
266C2×C4×D5C4×D314yescomplemented
267C2×C4×D5C4×D311yescharacteristic, complemented
268C2×C4×D5C4×D311yescharacteristic, complemented
269C2×C4×D5C22×D311yescharacteristic
270C2×C4×D5C22×D311yescharacteristic
271C2×C4×D5C22×D314yes—
272C2×Dic10—31no—
273C2×Dic10—32no—
274C22⋊AGL(1,𝔽5)—316no—
275C22⋊AGL(1,𝔽5)C22×D318yes—
276C4⋊AGL(1,𝔽5)—316no—
277C4⋊AGL(1,𝔽5)C22×D318yes—
278C4×AGL(1,𝔽5)—316no—
279C4×AGL(1,𝔽5)—34no—
280C4×AGL(1,𝔽5)—34no—
281C4×AGL(1,𝔽5)—38no—
282C4×AGL(1,𝔽5)C22×D318yes—
283C22×#41—151no—
284C4×#41—1516no—
285C2×C4×Q8—152no—
286C2×C4×D4—154no—
287C2×C4×D4—152no—
288C2×#117—51no—
289C2×#117—152no—
290C22×C42—152no—
291C22×C42—151no—
292C22×C3×C5—22no—
293C22×C3×C5C23×C412yes—
294C22×C3×C5C23×C411yescharacteristic
295C2×D15—24no—
296C2×D15C23×C414yes—
297C2×C5×D3—24no—
298C2×C5×D3C23×C414yes—
299C2×C3×D5—22no—
300C2×C3×D5—24no—
301C2×C3×D5—24no—
302C2×C3×D5C23×C412yes—
303C2×C3×D5C23×C411yescharacteristic
304C2×C3×D5C2×#4114yes—
305C2×C3×D5C2511yescharacteristic
306D3×D5—28no—
307D3×D5—28no—
308ΓL(1,𝔽16)—24no—
309ΓL(1,𝔽16)C2×#4118yescomplemented
310C3×AGL(1,𝔽5)—28no—
311C3×C4×C5C23×C412yes—
312C3×C4×C5C23×C412yes—
313Dic15C23×C414yes—
314C3×Dic5C23×C412yes—
315C3×Dic5C23×C412yes—
316C5×Dic3C23×C414yes—
317C24×C3—51no—
318C23×D3—52no—
319C22×C3×C4—51no—
320C22×C3×C4—51no—
321C22×C3×C4—51no—
322C22×C3×C4—51no—
323C22×C3×C4—51no—
324C22×C3×C4—54no—
325C22×C3×C4—54no—
326C22×C3×C4—54no—
327C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
328C2×#67—52no—
329C2×#67—52no—
330C2×#67—58no—
331C2×#67—58no—
332C2×#67—52no—
333C2×#67C2×AGL(1,𝔽5)12yescomplemented
334C22×Dic3—52no—
335C22×Dic3—52no—
336C22×Dic3—58no—
337C22×Dic3—52no—
338C22×Dic3—108no—
339#235—58no—
340#235—516no—
341#235—58no—
342#235—516no—
343#235—58no—
344#235C2×AGL(1,𝔽5)18yescomplemented
345C2×D12—52no—
346C2×D12—51no—
347C2×D12—54no—
348C2×D12—54no—
349C2×D12C2×AGL(1,𝔽5)11yescharacteristic, complemented
350C2×C4×D3—52no—
351C2×C4×D3—52no—
352C2×C4×D3—52no—
353C2×C4×D3—58no—
354C2×C4×D3—58no—
355C2×C4×D3—516no—
356C2×C4×D3—1016no—
357C2×C4×D3C2×AGL(1,𝔽5)12yescomplemented
358C2×Dic6—51no—
359C2×Dic6—52no—
360C2×Dic6—54no—
361C2×Dic6—54no—
362C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic, complemented
363C3×C4⋊C4—58no—
364C3×C22⋊C4—58no—
365C3×C42—58no—
366(C2×D3)⋊C4—516no—
367Dic3⋊C4—516no—
368C4×Dic3—516no—
369C4×Dic3—54no—
370C4×Dic3—54no—
371C4×Dic3—58no—
372C23×C5—32no—
373C23×C5C2×C4×D311yescharacteristic
374C22×D5—24no—
375C22×D5—32no—
376C22×D5—34no—
377C22×D5—34no—
378C22×D5—68no—
379C22×D5C2×C4×D311yescharacteristic
380C22×D5C2×C4×D312yes—
381C22×D5C23×D312yes—
382C22×D5C23×D311yescharacteristic
383C2×AGL(1,𝔽5)—28no—
384C2×AGL(1,𝔽5)—38no—
385C2×AGL(1,𝔽5)—34no—
386C2×AGL(1,𝔽5)—34no—
387C2×AGL(1,𝔽5)—632no—
388C2×AGL(1,𝔽5)—616no—
389C2×AGL(1,𝔽5)—64no—
390C2×AGL(1,𝔽5)C23×D318yes—
391C5×Q8—34no—
392C5×D4—38no—
393C5×D4—34no—
394C2×C4×C5—32no—
395C2×C4×C5—38no—
396C2×C4×C5C2×C4×D311yescharacteristic
397C2×C4×C5C2×C4×D311yescharacteristic
398C2×C4×C5C2×C4×D314yescomplemented
399C22⋊D5—38no—
400C22⋊D5—38no—
401C22⋊D5—38no—
402C2×Dic5—32no—
403C2×Dic5—38no—
404C2×Dic5C2×C4×D311yescharacteristic
405C2×Dic5C2×C4×D311yescharacteristic
406C2×Dic5C2×C4×D314yescomplemented
407D20—38no—
408D20—34no—
409C4×D5—34no—
410C4×D5—34no—
411C4×D5—38no—
412C4×D5—38no—
413C4×D5C2×C4×D312yes—
414C4×D5C2×C4×D312yes—
415C4×D5C2×C4×D314yescomplemented
416C4×D5C2×C4×D314yescomplemented
417C4×D5C23×D312yes—
418C4×D5C23×D312yes—
419Dic10—34no—
420Dic10—38no—
421C2×#41—31no—
422C2×#41—152no—
423C2×#41—152no—
424C2×#41—151no—
425C2×#41—151no—
426C2×#41—158no—
427C2×#41—158no—
428C2×#41—151no—
429C22×Q8—151no—
430C22×D4—151no—
431C22×D4—152no—
432C23×C4—51no—
433C23×C4—152no—
434C23×C4—154no—
435C23×C4—152no—
436C4×Q8—1516no—
437C4×D4—1532no—
438C4×D4—1516no—
439#117—58no—
440#117—1516no—
441C2×C4⋊C4—52no—
442C2×C4⋊C4—154no—
443C2×C22⋊C4—52no—
444C2×C22⋊C4—154no—
445C2×C42—52no—
446C2×C42—1516no—
447C2×C42—151no—
448C2×C42—152no—
449C2×C42—154no—
450C2×C42—158no—
451C2×C42—151no—
452C2×C3×C5—22no—
453C2×C3×C5C4×#4112yescomplemented
454C2×C3×C5C24×C411yescharacteristic
455D15—24no—
456C3×D5—22no—
457C3×D5C4×#4112yescomplemented
458C3×D5C22×#4112yes—
459C5×D3—24no—
460C23×C3—51no—
461C23×C3—52no—
462C23×C3—51no—
463C23×C3—52no—
464C23×C3—104no—
465C23×C3C22×AGL(1,𝔽5)11yescharacteristic
466C22×D3—52no—
467C22×D3—54no—
468C22×D3—54no—
469C22×D3—108no—
470C22×D3C22×AGL(1,𝔽5)12yes—
471C2×C3×C4—51no—
472C2×C3×C4—51no—
473C2×C3×C4—54no—
474C2×C3×C4—52no—
475C2×C3×C4—52no—
476C2×C3×C4—54no—
477C2×C3×C4—54no—
478C2×C3×C4—52no—
479C2×C3×C4—52no—
480C2×C3×C4—58no—
481C2×C3×C4—108no—
482C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
483C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
484C2×C3×C4C22×AGL(1,𝔽5)14yescomplemented
485#67—58no—
486#67—58no—
487#67—58no—
488#67C22×AGL(1,𝔽5)18yescomplemented
489C2×Dic3—58no—
490C2×Dic3—54no—
491C2×Dic3—52no—
492C2×Dic3—54no—
493C2×Dic3—54no—
494C2×Dic3—54no—
495C2×Dic3—1016no—
496C2×Dic3—104no—
497C2×Dic3C22×AGL(1,𝔽5)12yes—
498D12—58no—
499D12—54no—
500D12C22×AGL(1,𝔽5)14yescomplemented
501C4×D3—58no—
502C4×D3—58no—
503C4×D3—58no—
504C4×D3—1032no—
505C4×D3C22×AGL(1,𝔽5)18yescomplemented
506Dic6—54no—
507Dic6—58no—
508Dic6C22×AGL(1,𝔽5)14yescomplemented
509C22×C5—22no—
510C22×C5—34no—
511C22×C5—64no—
512C22×C5C22×C4×D312yes—
513C22×C5C22×C4×D311yescharacteristic
514C2×D5—22no—
515C2×D5—24no—
516C2×D5—24no—
517C2×D5—34no—
518C2×D5—64no—
519C2×D5—68no—
520C2×D5—68no—
521C2×D5C22×C4×D312yes—
522C2×D5C22×C4×D311yescharacteristic
523C2×D5D3×#4114yes—
524C2×D5C24×D311yescharacteristic
525AGL(1,𝔽5)—28no—
526AGL(1,𝔽5)—38no—
527AGL(1,𝔽5)—64no—
528C4×C5—34no—
529C4×C5C22×C4×D312yes—
530C4×C5C22×C4×D312yes—
531Dic5—34no—
532Dic5C22×C4×D312yes—
533Dic5C22×C4×D312yes—
534C24—51no—
535C24—152no—
536#41—38no—
537#41—1516no—
538#41—1516no—
539#41—158no—
540#41—158no—
541#41—158no—
542C2×Q8—31no—
543C2×Q8—152no—
544C2×Q8—154no—
545C2×Q8—154no—
546C2×Q8—151no—
547C2×D4—32no—
548C2×D4—31no—
549C2×D4—152no—
550C2×D4—154no—
551C2×D4—154no—
552C2×D4—152no—
553C2×D4—158no—
554C2×D4—158no—
555C2×D4—152no—
556C2×D4—152no—
557C2×D4—151no—
558C22×C4—32no—
559C22×C4—51no—
560C22×C4—51no—
561C22×C4—51no—
562C22×C4—51no—
563C22×C4—51no—
564C22×C4—54no—
565C22×C4—54no—
566C22×C4—54no—
567C22×C4—158no—
568C22×C4—152no—
569C22×C4—158no—
570C22×C4—152no—
571C22×C4—152no—
572C22×C4—1516no—
573C22×C4—152no—
574C22×C4—152no—
575C22×C4—152no—
576C22×C4—158no—
577C22×C4—3016no—
578C22×C4—308no—
579C22×C4D3×AGL(1,𝔽5)11yescharacteristic, complemented
580C4⋊C4—58no—
581C4⋊C4—1516no—
582C22⋊C4—58no—
583C22⋊C4—1516no—
584C42—58no—
585C42—154no—
586C42—154no—
587C42—158no—
588C42—1516no—
589C3×C5C2×C4×#4111yescharacteristic, complemented, Hall
590C22×C3—22no—
591C22×C3—54no—
592C22×C3—51no—
593C22×C3—51no—
594C22×C3—52no—
595C22×C3—104no—
596C22×C3—104no—
597C22×C3—102no—
598C22×C3C23×AGL(1,𝔽5)12yes—
599C22×C3C23×AGL(1,𝔽5)11yescharacteristic
600C2×D3—24no—
601C2×D3—54no—
602C2×D3—108no—
603C2×D3—108no—
604C2×D3—104no—
605C2×D3C23×AGL(1,𝔽5)14yes—
606C3×C4—52no—
607C3×C4—52no—
608C3×C4—108no—
609C3×C4C23×AGL(1,𝔽5)12yes—
610C3×C4C23×AGL(1,𝔽5)12yes—
611Dic3—58no—
612Dic3—54no—
613Dic3—104no—
614Dic3C23×AGL(1,𝔽5)14yes—
615C2×C5—22no—
616C2×C5—64no—
617C2×C5#552212yescomplemented
618C2×C5C23×C4×D311yescharacteristic
619D5—22no—
620D5—64no—
621D5#552212yescomplemented
622D5C2×D3×#4112yes—
623C23—32no—
624C23—51no—
625C23—52no—
626C23—52no—
627C23—51no—
628C23—104no—
629C23—154no—
630C23—154no—
631C23—152no—
632C23—308no—
633C23C2×D3×AGL(1,𝔽5)11yescharacteristic
634Q8—34no—
635Q8—158no—
636Q8—154no—
637D4—38no—
638D4—34no—
639D4—158no—
640D4—158no—
641D4—158no—
642D4—158no—
643D4—154no—
644C2×C4—32no—
645C2×C4—38no—
646C2×C4—51no—
647C2×C4—51no—
648C2×C4—54no—
649C2×C4—52no—
650C2×C4—52no—
651C2×C4—52no—
652C2×C4—52no—
653C2×C4—54no—
654C2×C4—54no—
655C2×C4—58no—
656C2×C4—108no—
657C2×C4—158no—
658C2×C4—154no—
659C2×C4—154no—
660C2×C4—158no—
661C2×C4—154no—
662C2×C4—158no—
663C2×C4—152no—
664C2×C4—158no—
665C2×C4—154no—
666C2×C4—3032no—
667C2×C4—3016no—
668C2×C4—304no—
669C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
670C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
671C2×C4C2×D3×AGL(1,𝔽5)14yescomplemented
672C2×C3—22no—
673C2×C3—52no—
674C2×C3—52no—
675C2×C3—102no—
676C2×C3#41×AGL(1,𝔽5)12yescomplemented
677C2×C3C24×AGL(1,𝔽5)11yescharacteristic
678D3—24no—
679D3—104no—
680C5C2×#552211yescharacteristic, complemented, Sylow
681C22—22no—
682C22—34no—
683C22—54no—
684C22—51no—
685C22—51no—
686C22—52no—
687C22—64no—
688C22—104no—
689C22—104no—
690C22—102no—
691C22—154no—
692C22—308no—
693C22—308no—
694C22—304no—
695C22C22×D3×AGL(1,𝔽5)12yes—
696C22C22×D3×AGL(1,𝔽5)11yescharacteristic
697C4—34no—
698C4—52no—
699C4—52no—
700C4—108no—
701C4—158no—
702C4—154no—
703C4—304no—
704C4C22×D3×AGL(1,𝔽5)12yes—
705C4C22×D3×AGL(1,𝔽5)12yes—
706C3C2×#41×AGL(1,𝔽5)11yescharacteristic, complemented, Sylow
707C2—22no—
708C2—52no—
709C2—52no—
710C2—64no—
711C2—102no—
712C2—304no—
713C2#1175683512yesdirect product factor
714C2C23×D3×AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC2×C4C2×D3×AGL(1,𝔽5)
commutatorC2×C3×C5C24×C4
FrattiniC2C23×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C23×C4
prime radicalC2×D5×#235C2
cosocleC2×C3×D5C25
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×C4×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×ΓL(1,𝔽16)C2semidirect
3. C2×C3×#4130C2semidirect
4. C2×#67⋊AGL(1,𝔽5)C2semidirect
5. #11756835C2direct (N × H)
6. C2×#91921C2semidirect
7. C2×C4×D3×AGL(1,𝔽5)C2semidirect
8. C2×#91909C2semidirect
9. C2×ΓL(1,𝔽16)⋊Q8C2semidirect
13. C2×#6817C4semidirect
14. C2×C5×#235C4semidirect
17. C2×#6782C4semidirect
18. D5×#235C4semidirect
22. C2×#6773C4semidirect
23. C2×#6772C4semidirect
24. C2×#6771C4semidirect
29. C2×C4×ΓL(1,𝔽16)C22semidirect
31. C3×#4130C22semidirect
34. #67⋊AGL(1,𝔽5)C22semidirect
38. #91921C22semidirect
39. C4×D3×AGL(1,𝔽5)C22semidirect
40. #91909C22semidirect
41. ΓL(1,𝔽16)⋊Q8C22semidirect
49. C2×#4130D3semidirect
61. C22×C3×C4×C5C2×C4semidirect
62. C2×#1220C2×C4semidirect
63. #6817C2×C4semidirect
64. C2×D60C2×C4semidirect
65. C2×C4×D15C2×C4semidirect
66. C2×Dic30C2×C4semidirect
67. C2×C5×#67C2×C4semidirect
68. C5×#235C2×C4semidirect
69. C2×C5×D12C2×C4semidirect
70. C2×C4×C5×D3C2×C4semidirect
71. C2×C5×Dic6C2×C4semidirect
72. C22×C3×Dic5C2×C4semidirect
73. C2×C3×C4×D5C2×C4semidirect
74. C2×C3×C4×D5C2×C4semidirect
75. C2×C3×C4×D5C2×C4semidirect
79. D5×#67C2×C4semidirect
81. C2×#1204C2×C4semidirect
82. C2×#1203C2×C4semidirect
83. C2×#1202C2×C4semidirect
84. C2×#1201C2×C4semidirect
85. C2×#1200C2×C4semidirect
86. #6782C2×C4semidirect
87. C2×D3×Dic5C2×C4semidirect
89. D5×D12C2×C4semidirect
91. C4×D3×D5C2×C4semidirect
93. #6773C2×C4semidirect
94. #6772C2×C4semidirect
95. #6771C2×C4semidirect
96. D5×Dic6C2×C4semidirect
137. #4130C2×D3semidirect
161. C2×ΓL(1,𝔽16)#41semidirect
169. C2×C3×C4×C5C22×C4semidirect
170. #1220C22×C4semidirect
172. D60C22×C4semidirect
173. C4×D15C22×C4semidirect
174. Dic30C22×C4semidirect
175. C5×#67C22×C4semidirect
177. C5×D12C22×C4semidirect
178. C4×C5×D3C22×C4semidirect
179. C5×Dic6C22×C4semidirect
182. C2×C3×Dic5C22×C4semidirect
185. C3×C4×D5C22×C4semidirect
186. C3×C4×D5C22×C4semidirect
189. #1204C22×C4semidirect
190. #1203C22×C4semidirect
191. #1202C22×C4semidirect
192. #1201C22×C4semidirect
193. #1200C22×C4semidirect
194. D3×Dic5C22×C4semidirect
207. C2×#235AGL(1,𝔽5)semidirect
242. C22×C4×C5C4×D3semidirect
247. C22×Dic5C4×D3semidirect
266. C2×C4×D5C4×D3semidirect
267. C2×C4×D5C4×D3semidirect
268. C2×C4×D5C4×D3semidirect
309. ΓL(1,𝔽16)C2×#41semidirect
327. C22×C3×C4C2×AGL(1,𝔽5)semidirect
333. C2×#67C2×AGL(1,𝔽5)semidirect
344. #235C2×AGL(1,𝔽5)semidirect
349. C2×D12C2×AGL(1,𝔽5)semidirect
357. C2×C4×D3C2×AGL(1,𝔽5)semidirect
362. C2×Dic6C2×AGL(1,𝔽5)semidirect
398. C2×C4×C5C2×C4×D3semidirect
406. C2×Dic5C2×C4×D3semidirect
415. C4×D5C2×C4×D3semidirect
416. C4×D5C2×C4×D3semidirect
453. C2×C3×C5C4×#41semidirect
457. C3×D5C4×#41semidirect
484. C2×C3×C4C22×AGL(1,𝔽5)semidirect
488. #67C22×AGL(1,𝔽5)semidirect
500. D12C22×AGL(1,𝔽5)semidirect
505. C4×D3C22×AGL(1,𝔽5)semidirect
508. Dic6C22×AGL(1,𝔽5)semidirect
579. C22×C4D3×AGL(1,𝔽5)semidirect
589. C3×C5C2×C4×#41semidirect
617. C2×C5#5522semidirect
621. D5#5522semidirect
671. C2×C4C2×D3×AGL(1,𝔽5)semidirect
676. C2×C3#41×AGL(1,𝔽5)semidirect
680. C5C2×#5522semidirect
706. C3C2×#41×AGL(1,𝔽5)semidirect
713. C2#11756835direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D5×#2352
C22×C4×ΓL(1,𝔽16)2
C2×C3×#41302
C2×#67⋊AGL(1,𝔽5)2
#117568352
C2×#919212
C2×C4×D3×AGL(1,𝔽5)2
C2×#919092
C2×ΓL(1,𝔽16)⋊Q82
C2×#41×AGL(1,𝔽5)3
C2×#55225