Finite Group Databasebeta

← C5×#8993 #11931713

Subgroups — C5×#8993 #11931713

Order 1280.

476 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3076C211yesmaximal, characteristic
2C5×#2906C211yesmaximal, characteristic
3C5×#1493C211yesmaximal, characteristic, complemented
4C5×#1481C211yesmaximal, characteristic, complemented
5C5×#1476C211yesmaximal, characteristic
6C5×#1301C211yesmaximal, characteristic, complemented
7C5×#1277C211yesmaximal, characteristic, complemented
8C2×C5×#131—21no—
9C5×#533C2211yescharacteristic
10C4×C5×#41C2211yescharacteristic
11C5×#479—21no—
12C5×#478—21no—
13C5×#477C411yescharacteristic
14C5×#476C411yescharacteristic
15C5×#475C411yescharacteristic
16C5×#474C411yescharacteristic
17C5×#431C2211yescharacteristic
18C5×#427—21no—
19C5×#424—22no—
20C5×#424—21no—
21C5×#423—21no—
22C5×#423C2211yescharacteristic
23C2×C5×C4⋊C8—21no—
24C2×C5×C4⋊C8C2211yescharacteristic
25C2×C5×C4⋊C8C2211yescharacteristic
26C5×#416—21no—
27C2×C4×C5×C8C2211yescharacteristic
28C5×Q8⋊C8—21no—
29C5×Q8⋊C8—21no—
30C5×Q8⋊C8—22no—
31C5×Q8⋊C8—21no—
32C5×D4⋊C8—21no—
33#8993C511yesmaximal, characteristic, direct product factor, Sylow
34C2×C5×#41D411yescharacteristic
35C5×#131—42no—
36C5×#131—42no—
37C2×C5×M16—22no—
38C2×C5×M16—21no—
39C22×C5×C8—22no—
40C22×C5×C8—21no—
41C22×C5×C8—21no—
42C22×C5×C8—21no—
43C5×C4⋊Q8C2×C411yescharacteristic
44C5×C4⋊Q8C2×C411yescharacteristic
45C5×#125—21no—
46C5×C22⋊Q8—21no—
47C5×C22⋊Q8—21no—
48C4×C5×Q8—21no—
49C4×C5×Q8—21no—
50C4×C5×Q8C2×C411yescharacteristic
51C4×C5×Q8D411yescharacteristic
52C4×C5×D4—21no—
53C4×C5×D4—21no—
54C4×C5×D4C2×C411yescharacteristic
55C4×C5×D4D411yescharacteristic
56C5×#117—21no—
57C5×#117—21no—
58C5×#117D411yescharacteristic
59C2×C42×C5—21no—
60C2×C42×C5C2311yescharacteristic
61C5×#107—21no—
62C5×#107—21no—
63C5×#106—21no—
64C5×#106—21no—
65C5×C4⋊C8—22no—
66C5×C4⋊C8—22no—
67C5×C4⋊C8—21no—
68C5×C4⋊C8—21no—
69C5×C4⋊C8—21no—
70C5×C4⋊C8—21no—
71C5×C4⋊C8C2×C411yescharacteristic
72C5×C4⋊C8C2×C411yescharacteristic
73C5×C4⋊C8D411yescharacteristic
74C5×C4⋊C8D411yescharacteristic
75C5×C4⋊C8D412yes—
76C5×#103—21no—
77C5×#103—21no—
78C5×#102—21no—
79C5×#102—21no—
80C5×C22⋊C8—21no—
81C4×C5×C8—21no—
82C4×C5×C8—21no—
83C4×C5×C8—21no—
84#3076C2×C511yescharacteristic
85#2906C2×C511yescharacteristic
86#1493C2×C511yescharacteristic, complemented
87#1481C2×C511yescharacteristic, complemented
88#1476C2×C511yescharacteristic
89#1301C2×C511yescharacteristic, complemented
90#1277C2×C511yescharacteristic, complemented
91C5×#41—21no—
92C5×#41—21no—
93C5×#41SD1612yes—
94C5×#41Q1612yes—
95C2×C5×Q8—21no—
96C2×C5×Q8—21no—
97C2×C5×Q8C22⋊C411yescharacteristic
98C2×C5×D4—21no—
99C2×C5×D4C22⋊C411yescharacteristic
100C22×C4×C5—21no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5C2×D411yescharacteristic
104C22×C4×C5#4111yescharacteristic
105C22×C4×C5#4111yescharacteristic
106C5×M16—44no—
107C5×M16—41no—
108C5×M16—41no—
109C2×C5×C8—22no—
110C2×C5×C8—21no—
111C2×C5×C8—21no—
112C2×C5×C8—21no—
113C2×C5×C8—22no—
114C2×C5×C8—21no—
115C2×C5×C8—41no—
116C2×C5×C8—44no—
117C2×C5×C8—41no—
118C2×C5×C8—41no—
119C2×C5×C8—41no—
120C2×C5×C8—41no—
121C2×C5×C8—41no—
122C2×C5×C8—41no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—21no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4—21no—
129C5×C4⋊C4—41no—
130C5×C4⋊C4—41no—
131C5×C4⋊C4C22⋊C411yescharacteristic
132C5×C4⋊C4C22⋊C411yescharacteristic
133C5×C22⋊C4—21no—
134C5×C22⋊C4—21no—
135C5×C22⋊C4—21no—
136C5×C22⋊C4—41no—
137C42×C5—21no—
138C42×C5—21no—
139C42×C5—21no—
140C42×C5—41no—
141C42×C5C22×C411yescharacteristic
142C42×C5C2×D411yescharacteristic
143C42×C5C2×D411yescharacteristic
144C42×C5C2×D411yescharacteristic
145C2×#131—21no—
146#533C22×C511yescharacteristic
147C4×#41C22×C511yescharacteristic
148#479—21no—
149#478—21no—
150#477C4×C511yescharacteristic
151#476C4×C511yescharacteristic
152#475C4×C511yescharacteristic
153#474C4×C511yescharacteristic
154#431C22×C511yescharacteristic
155#427—21no—
156#424—21no—
157#424—22no—
158#423—21no—
159#423C22×C511yescharacteristic
160C2×C4⋊C8—21no—
161C2×C4⋊C8C22×C511yescharacteristic
162C2×C4⋊C8C22×C511yescharacteristic
163#416—21no—
164C2×C4×C8C22×C511yescharacteristic
165Q8⋊C8—21no—
166Q8⋊C8—21no—
167Q8⋊C8—21no—
168Q8⋊C8—22no—
169D4⋊C8—21no—
170C23×C5—21no—
171C23×C5#12311yescharacteristic
172C5×Q8—21no—
173C5×Q8—42no—
174C5×Q8—41no—
175C5×Q8—41no—
176C5×Q8#10312yes—
177C5×D4—22no—
178C5×D4—22no—
179C5×D4—21no—
180C5×D4#10312yes—
181C2×C4×C5—21no—
182C2×C4×C5—21no—
183C2×C4×C5—21no—
184C2×C4×C5—22no—
185C2×C4×C5—22no—
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—41no—
189C2×C4×C5—41no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—81no—
194C2×C4×C5C2×C22⋊C411yescharacteristic
195C2×C4×C5C4×D411yescharacteristic
196C2×C4×C5C4×D411yescharacteristic
197C2×C4×C5#12011yescharacteristic
198C2×C4×C5#12111yescharacteristic
199C2×C4×C5#12111yescharacteristic
200C2×C4×C5C2×SD1611yescharacteristic
201C2×C4×C5C2×Q1611yescharacteristic
202C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
203C2×C4×C5#13711yescharacteristic
204C5×C8—42no—
205C5×C8—41no—
206C5×C8—41no—
207C5×C8—41no—
208C5×C8—42no—
209C5×C8—41no—
210C5×C8—81no—
211C2×#41C5×D411yescharacteristic
212#131—42no—
213#131—42no—
214C2×M16—22no—
215C2×M16—21no—
216C22×C8—22no—
217C22×C8—21no—
218C22×C8—21no—
219C22×C8—21no—
220C4⋊Q8C2×C4×C511yescharacteristic
221C4⋊Q8C2×C4×C511yescharacteristic
222#125—21no—
223C22⋊Q8—21no—
224C22⋊Q8—21no—
225C4×Q8—21no—
226C4×Q8—21no—
227C4×Q8C2×C4×C511yescharacteristic
228C4×Q8C5×D411yescharacteristic
229C4×D4—21no—
230C4×D4—21no—
231C4×D4C2×C4×C511yescharacteristic
232C4×D4C5×D411yescharacteristic
233#117—21no—
234#117—21no—
235#117C5×D411yescharacteristic
236C2×C42—21no—
237C2×C42C23×C511yescharacteristic
238#107—21no—
239#107—21no—
240#106—21no—
241#106—21no—
242C4⋊C8—22no—
243C4⋊C8—22no—
244C4⋊C8—21no—
245C4⋊C8—21no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8C2×C4×C511yescharacteristic
249C4⋊C8C2×C4×C511yescharacteristic
250C4⋊C8C5×D411yescharacteristic
251C4⋊C8C5×D411yescharacteristic
252C4⋊C8C5×D412yes—
253#103—21no—
254#103—21no—
255#102—21no—
256#102—21no—
257C22⋊C8—21no—
258C4×C8—21no—
259C4×C8—21no—
260C4×C8—21no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—22no—
264C22×C5—41no—
265C22×C5—41no—
266C22×C5#38611yescharacteristic
267C22×C5#48311yescharacteristic
268C22×C5#48411yescharacteristic
269C4×C5—22no—
270C4×C5—21no—
271C4×C5—21no—
272C4×C5—21no—
273C4×C5—41no—
274C4×C5—41no—
275C4×C5—81no—
276C4×C5—81no—
277C4×C5C2×#10311yescharacteristic
278C4×C5#41711yescharacteristic
279C4×C5#44311yescharacteristic
280C4×C5#44411yescharacteristic
281C4×C5#45011yescharacteristic
282C4×C5#45111yescharacteristic
283#41—21no—
284#41—21no—
285#41C5×SD1612yes—
286#41C5×Q1612yes—
287C2×Q8—21no—
288C2×Q8—21no—
289C2×Q8C5×C22⋊C411yescharacteristic
290C2×D4—21no—
291C2×D4C5×C22⋊C411yescharacteristic
292C22×C4—21no—
293C22×C4—21no—
294C22×C4—21no—
295C22×C4C2×C5×D411yescharacteristic
296C22×C4C5×#4111yescharacteristic
297C22×C4C5×#4111yescharacteristic
298M16—44no—
299M16—41no—
300M16—41no—
301C2×C8—22no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—22no—
306C2×C8—21no—
307C2×C8—44no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8—41no—
312C2×C8—41no—
313C2×C8—41no—
314C2×C8—41no—
315C4⋊C4—21no—
316C4⋊C4—21no—
317C4⋊C4—21no—
318C4⋊C4—21no—
319C4⋊C4—21no—
320C4⋊C4—21no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4C5×C22⋊C411yescharacteristic
324C4⋊C4C5×C22⋊C411yescharacteristic
325C22⋊C4—21no—
326C22⋊C4—21no—
327C22⋊C4—21no—
328C22⋊C4—41no—
329C42—21no—
330C42—21no—
331C42—21no—
332C42—41no—
333C42C22×C4×C511yescharacteristic
334C42C2×C5×D411yescharacteristic
335C42C2×C5×D411yescharacteristic
336C42C2×C5×D411yescharacteristic
337C2×C5—21no—
338C2×C5—21no—
339C2×C5—42no—
340C2×C5#187211yescharacteristic
341C2×C5#187611yescharacteristic
342C2×C5#188111yescharacteristic
343C23—21no—
344C23C5×#12311yescharacteristic
345Q8—21no—
346Q8—42no—
347Q8—41no—
348Q8—41no—
349Q8C5×#10312yes—
350D4—22no—
351D4—22no—
352D4—21no—
353D4C5×#10312yes—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—22no—
358C2×C4—22no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—41no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—81no—
367C2×C4C2×C5×C22⋊C411yescharacteristic
368C2×C4C4×C5×D411yescharacteristic
369C2×C4C4×C5×D411yescharacteristic
370C2×C4C5×#12011yescharacteristic
371C2×C4C5×#12111yescharacteristic
372C2×C4C5×#12111yescharacteristic
373C2×C4C2×C5×SD1611yescharacteristic
374C2×C4C2×C5×Q1611yescharacteristic
375C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
376C2×C4C5×#13711yescharacteristic
377C8—42no—
378C8—41no—
379C8—41no—
380C8—41no—
381C8—42no—
382C8—41no—
383C8—81no—
384C5#899311yescharacteristic, direct product factor, Sylow
385C22—21no—
386C22—21no—
387C22—22no—
388C22—41no—
389C22—41no—
390C22C5×#38611yescharacteristic
391C22C5×#48311yescharacteristic
392C22C5×#48411yescharacteristic
393C4—22no—
394C4—21no—
395C4—21no—
396C4—21no—
397C4—41no—
398C4—41no—
399C4—81no—
400C4—81no—
401C4C2×C5×#10311yescharacteristic
402C4C5×#41711yescharacteristic
403C4C5×#44311yescharacteristic
404C4C5×#44411yescharacteristic
405C4C5×#45011yescharacteristic
406C4C5×#45111yescharacteristic
407C2—21no—
408C2—21no—
409C2—42no—
410C2C5×#187211yescharacteristic
411C2C5×#187611yescharacteristic
412C2C5×#188111yescharacteristic
subgroupG/H
centerC2×C4×C5#120
commutatorC42C22×C4×C5
Frattini, cosocleC2×C42C23×C5
socleC22×C5#386
prime radicalC2×C5×#41D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C2×C4×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1493C2semidirect
4. C5×#1481C2semidirect
6. C5×#1301C2semidirect
7. C5×#1277C2semidirect
33. #8993C5direct (N × H)
86. #1493C2×C5semidirect
87. #1481C2×C5semidirect
89. #1301C2×C5semidirect
90. #1277C2×C5semidirect
384. C5#8993direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30762
C5×#29062
C5×#14932
C5×#14812
C5×#14762
C5×#13012
C5×#12772
#89935