Finite Group Databasebeta

← C5×#11843 #11934563

Subgroups — C5×#11843 #11934563

Order 1280.

620 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2539C211yesmaximal, characteristic
2C5×#1819C211yesmaximal, characteristic, complemented
3C2×C5×#323C211yesmaximal, characteristic, complemented
4C5×#1352C212yesmaximal, complemented
5C5×#1343C212yesmaximal, complemented
6C2×C5×#123—21no—
7C2×C5×#121C411yescharacteristic, complemented
8C2×C5×#120—21no—
9C22×C5×C22⋊C4C2211yescharacteristic
10C2×C5×C22⋊C8—21no—
11C5×#399C411yescharacteristic, complemented
12C5×#399C2211yescharacteristic
13C5×#392C411yescharacteristic, complemented
14C5×#392C2211yescharacteristic
15C5×#390—21no—
16C5×#390—21no—
17C5×#379—21no—
18C4×C5×C22⋊C4C411yescharacteristic, complemented
19C5×#342—21no—
20C5×#342C2212yes—
21C5×#323—21no—
22C5×#323C2212yes—
23#11843C511yesmaximal, characteristic, direct product factor, Sylow
24C25×C5D411yescharacteristic
25C22×C5×D4—21no—
26C22×C5×D4—21no—
27C22×C5×D4—21no—
28C22×C5×D4C2×C411yescharacteristic
29C23×C4×C5C2×C411yescharacteristic
30C23×C4×C5D411yescharacteristic
31C22×C5×C8—41no—
32C5×#123—44no—
33C5×#121—41no—
34C5×#121—41no—
35C5×#120—44no—
36C2×C5×C4⋊C4—21no—
37C2×C5×C4⋊C4—21no—
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C5×C22⋊C4—21no—
45C2×C5×C22⋊C4—22no—
46C2×C5×C22⋊C4—41no—
47C2×C5×C22⋊C4—41no—
48C2×C5×C22⋊C4—41no—
49C2×C5×C22⋊C4—41no—
50C2×C5×C22⋊C4C2×C411yescharacteristic
51C2×C5×C22⋊C4D411yescharacteristic
52C2×C5×C22⋊C4D411yescharacteristic
53C2×C5×C22⋊C4C2311yescharacteristic
54C2×C42×C5—21no—
55C5×C22⋊C8—22no—
56C5×C22⋊C8—41no—
57C5×#95C2×C411yescharacteristic
58C5×#95C2×C411yescharacteristic
59#2539C2×C511yescharacteristic
60#1819C2×C511yescharacteristic, complemented
61C2×#323C2×C511yescharacteristic, complemented
62#1352C2×C512yescomplemented
63#1343C2×C512yescomplemented
64C24×C5—21no—
65C24×C5—21no—
66C24×C5—22no—
67C24×C5—21no—
68C24×C5—41no—
69C24×C5—42no—
70C24×C5—81no—
71C24×C5C22⋊C411yescharacteristic
72C24×C5C22⋊C411yescharacteristic
73C24×C5C2×D411yescharacteristic
74C2×C5×D4—41no—
75C2×C5×D4—42no—
76C2×C5×D4—42no—
77C2×C5×D4—42no—
78C2×C5×D4—42no—
79C2×C5×D4—42no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—42no—
83C2×C5×D4—81no—
84C2×C5×D4—81no—
85C2×C5×D4—81no—
86C22×C4×C5—21no—
87C22×C4×C5—21no—
88C22×C4×C5—21no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5—21no—
92C22×C4×C5—21no—
93C22×C4×C5—42no—
94C22×C4×C5—42no—
95C22×C4×C5—81no—
96C22×C4×C5C22⋊C411yescharacteristic
97C22×C4×C5C22⋊C411yescharacteristic
98C22×C4×C5C22×C411yescharacteristic
99C22×C4×C5C2×D411yescharacteristic
100C2×C5×C8—42no—
101C2×C5×C8—82no—
102C5×C4⋊C4—41no—
103C5×C4⋊C4—42no—
104C5×C4⋊C4—42no—
105C5×C22⋊C4—24no—
106C5×C22⋊C4—41no—
107C5×C22⋊C4—41no—
108C5×C22⋊C4—41no—
109C5×C22⋊C4—41no—
110C5×C22⋊C4—42no—
111C5×C22⋊C4—42no—
112C5×C22⋊C4—42no—
113C5×C22⋊C4—42no—
114C5×C22⋊C4—42no—
115C5×C22⋊C4—42no—
116C5×C22⋊C4—42no—
117C5×C22⋊C4—82no—
118C5×C22⋊C4—82no—
119C42×C5—81no—
120C2×#123—21no—
121C2×#121C4×C511yescharacteristic, complemented
122C2×#120—21no—
123C22×C22⋊C4C22×C511yescharacteristic
124C2×C22⋊C8—21no—
125#399C4×C511yescharacteristic, complemented
126#399C22×C511yescharacteristic
127#392C4×C511yescharacteristic, complemented
128#392C22×C511yescharacteristic
129#390—21no—
130#390—21no—
131#379—21no—
132C4×C22⋊C4C4×C511yescharacteristic, complemented
133#342—21no—
134#342C22×C512yes—
135#323—21no—
136#323C22×C512yes—
137C23×C5—22no—
138C23×C5—21no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—21no—
142C23×C5—21no—
143C23×C5—21no—
144C23×C5—21no—
145C23×C5—41no—
146C23×C5—42no—
147C23×C5—42no—
148C23×C5—41no—
149C23×C5—41no—
150C23×C5—41no—
151C23×C5—41no—
152C23×C5—42no—
153C23×C5—41no—
154C23×C5—41no—
155C23×C5—41no—
156C23×C5—41no—
157C23×C5—42no—
158C23×C5—41no—
159C23×C5—41no—
160C23×C5—41no—
161C23×C5—81no—
162C23×C5—81no—
163C23×C5—84no—
164C23×C5—84no—
165C23×C5#9911yescharacteristic
166C23×C5#9911yescharacteristic
167C23×C5C2×C22⋊C411yescharacteristic
168C23×C5#13512yes—
169C5×D4—84no—
170C5×D4—84no—
171C5×D4—82no—
172C5×D4—82no—
173C5×D4—82no—
174C2×C4×C5—22no—
175C2×C4×C5—22no—
176C2×C4×C5—21no—
177C2×C4×C5—21no—
178C2×C4×C5—21no—
179C2×C4×C5—21no—
180C2×C4×C5—41no—
181C2×C4×C5—41no—
182C2×C4×C5—42no—
183C2×C4×C5—41no—
184C2×C4×C5—41no—
185C2×C4×C5—41no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—81no—
193C2×C4×C5—81no—
194C2×C4×C5—81no—
195C2×C4×C5—82no—
196C2×C4×C5—82no—
197C2×C4×C5—82no—
198C5×C8—82no—
199C25C5×D411yescharacteristic
200C22×D4—21no—
201C22×D4—21no—
202C22×D4—21no—
203C22×D4C2×C4×C511yescharacteristic
204C23×C4C2×C4×C511yescharacteristic
205C23×C4C5×D411yescharacteristic
206C22×C8—41no—
207#123—44no—
208#121—41no—
209#121—41no—
210#120—44no—
211C2×C4⋊C4—21no—
212C2×C4⋊C4—21no—
213C2×C4⋊C4C2×C4×C511yescharacteristic
214C2×C22⋊C4—21no—
215C2×C22⋊C4—21no—
216C2×C22⋊C4—21no—
217C2×C22⋊C4—21no—
218C2×C22⋊C4—21no—
219C2×C22⋊C4—21no—
220C2×C22⋊C4—22no—
221C2×C22⋊C4—41no—
222C2×C22⋊C4—41no—
223C2×C22⋊C4—41no—
224C2×C22⋊C4—41no—
225C2×C22⋊C4C2×C4×C511yescharacteristic
226C2×C22⋊C4C5×D411yescharacteristic
227C2×C22⋊C4C5×D411yescharacteristic
228C2×C22⋊C4C23×C511yescharacteristic
229C2×C42—21no—
230C22⋊C8—22no—
231C22⋊C8—41no—
232#95C2×C4×C511yescharacteristic
233#95C2×C4×C511yescharacteristic
234C22×C5—21no—
235C22×C5—21no—
236C22×C5—21no—
237C22×C5—21no—
238C22×C5—21no—
239C22×C5—21no—
240C22×C5—22no—
241C22×C5—21no—
242C22×C5—42no—
243C22×C5—42no—
244C22×C5—42no—
245C22×C5—42no—
246C22×C5—41no—
247C22×C5—41no—
248C22×C5—41no—
249C22×C5—41no—
250C22×C5—41no—
251C22×C5—81no—
252C22×C5—84no—
253C22×C5—81no—
254C22×C5—81no—
255C22×C5—81no—
256C22×C5—81no—
257C22×C5—81no—
258C22×C5—84no—
259C22×C5—81no—
260C22×C5—81no—
261C22×C5—81no—
262C22×C5#35312yes—
263C22×C5C2×#9911yescharacteristic
264C22×C5#41611yescharacteristic
265C22×C5#42111yescharacteristic
266C4×C5—42no—
267C4×C5—42no—
268C4×C5—41no—
269C4×C5—41no—
270C4×C5—41no—
271C4×C5—41no—
272C4×C5—81no—
273C4×C5—162no—
274C24—21no—
275C24—21no—
276C24—22no—
277C24—21no—
278C24—41no—
279C24—42no—
280C24—81no—
281C24C5×C22⋊C411yescharacteristic
282C24C5×C22⋊C411yescharacteristic
283C24C2×C5×D411yescharacteristic
284C2×D4—41no—
285C2×D4—42no—
286C2×D4—42no—
287C2×D4—42no—
288C2×D4—42no—
289C2×D4—42no—
290C2×D4—42no—
291C2×D4—41no—
292C2×D4—41no—
293C2×D4—81no—
294C2×D4—81no—
295C2×D4—81no—
296C22×C4—21no—
297C22×C4—21no—
298C22×C4—21no—
299C22×C4—21no—
300C22×C4—21no—
301C22×C4—21no—
302C22×C4—21no—
303C22×C4—42no—
304C22×C4—42no—
305C22×C4—81no—
306C22×C4C5×C22⋊C411yescharacteristic
307C22×C4C5×C22⋊C411yescharacteristic
308C22×C4C22×C4×C511yescharacteristic
309C22×C4C2×C5×D411yescharacteristic
310C2×C8—42no—
311C2×C8—82no—
312C4⋊C4—41no—
313C4⋊C4—42no—
314C4⋊C4—42no—
315C22⋊C4—24no—
316C22⋊C4—41no—
317C22⋊C4—41no—
318C22⋊C4—41no—
319C22⋊C4—41no—
320C22⋊C4—42no—
321C22⋊C4—42no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—42no—
325C22⋊C4—42no—
326C22⋊C4—42no—
327C22⋊C4—82no—
328C22⋊C4—82no—
329C42—81no—
330C2×C5—21no—
331C2×C5—21no—
332C2×C5—22no—
333C2×C5—42no—
334C2×C5—41no—
335C2×C5—81no—
336C2×C5—161no—
337C2×C5#151611yescharacteristic
338C2×C5#212111yescharacteristic
339C2×C5C2×#35311yescharacteristic
340C23—21no—
341C23—21no—
342C23—21no—
343C23—22no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—41no—
349C23—42no—
350C23—42no—
351C23—41no—
352C23—41no—
353C23—41no—
354C23—41no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—41no—
359C23—41no—
360C23—42no—
361C23—41no—
362C23—41no—
363C23—41no—
364C23—81no—
365C23—81no—
366C23—84no—
367C23—84no—
368C23C5×#9911yescharacteristic
369C23C5×#9911yescharacteristic
370C23C2×C5×C22⋊C411yescharacteristic
371C23C5×#13512yes—
372D4—84no—
373D4—84no—
374D4—82no—
375D4—82no—
376D4—82no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—42no—
388C2×C4—41no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—41no—
394C2×C4—41no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4—81no—
398C2×C4—82no—
399C2×C4—82no—
400C2×C4—82no—
401C8—82no—
402C5#1184311yescharacteristic, direct product factor, Sylow
403C22—21no—
404C22—21no—
405C22—21no—
406C22—21no—
407C22—22no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—42no—
412C22—42no—
413C22—42no—
414C22—42no—
415C22—41no—
416C22—41no—
417C22—41no—
418C22—41no—
419C22—41no—
420C22—81no—
421C22—84no—
422C22—81no—
423C22—81no—
424C22—81no—
425C22—81no—
426C22—81no—
427C22—84no—
428C22—81no—
429C22—81no—
430C22—81no—
431C22C5×#35312yes—
432C22C2×C5×#9911yescharacteristic
433C22C5×#41611yescharacteristic
434C22C5×#42111yescharacteristic
435C4—42no—
436C4—42no—
437C4—41no—
438C4—41no—
439C4—41no—
440C4—41no—
441C4—81no—
442C4—162no—
443C2—21no—
444C2—21no—
445C2—22no—
446C2—42no—
447C2—41no—
448C2—81no—
449C2—161no—
450C2C5×#151611yescharacteristic
451C2C5×#212111yescharacteristic
452C2C2×C5×#35311yescharacteristic
subgroupG/H
center, socleC22×C5C2×#99
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C22⋊C4C23×C5
prime radicalC5×#2539C2
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C24×C5 ◁ C22×C5×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1819C2semidirect
3. C2×C5×#323C2semidirect
4. C5×#1352C2semidirect
5. C5×#1343C2semidirect
7. C2×C5×#121C4semidirect
11. C5×#399C4semidirect
13. C5×#392C4semidirect
18. C4×C5×C22⋊C4C4semidirect
23. #11843C5direct (N × H)
60. #1819C2×C5semidirect
61. C2×#323C2×C5semidirect
62. #1352C2×C5semidirect
63. #1343C2×C5semidirect
121. C2×#121C4×C5semidirect
125. #399C4×C5semidirect
127. #392C4×C5semidirect
132. C4×C22⋊C4C4×C5semidirect
402. C5#11843direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#25392
C5×#18192
C2×C5×#3232
C5×#13522
C5×#13432
#118435