Finite Group Databasebeta

← #14285320

Subgroups — #14285320

Order 1920.

492 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 98 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
1#11752556C211yesmaximal, characteristic
2#11750936C211yesmaximal, characteristic, complemented
3#11747015C211yesmaximal, characteristic, complemented
4C5×#4482C211yesmaximal, characteristic, complemented
5C3×#64705C211yesmaximal, characteristic, complemented
6#11745857C211yesmaximal, characteristic, complemented
7#11745852C211yesmaximal, characteristic, complemented
8#10599222—31nomaximal, Hall
9C2×#6766—21no—
10C42×D15C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4020C2211yescharacteristic
13#91465—21no—
14#91465C412yes—
15#91434—21no—
16#91434C412yes—
17#91368—21no—
18C2×#6651—21no—
19C3×C5×C4⋊C8C2211yescharacteristic
20#91104—21no—
21#91099—21no—
22C4⋊(C3⋊#168)C2211yescharacteristic
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×C4⋊#168C2211yescharacteristic
25#90983—21no—
26#68388—51nomaximal, Hall
27#66059—31no—
28#65126—31no—
29#65124—31no—
30C5×#332—31no—
31#64767—31no—
32#64705—31no—
33#64705D311yescharacteristic, complemented
34C2×C4×D15C2×C411yescharacteristic
35C2×C4×D15D411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C5×Dic6—21no—
38C2×C3×D20—21no—
39C2×C3×D20—21no—
40C2×C3×D20C2×C412yes—
41C2×#1202—22no—
42C2×D5×Dic3—22no—
43#6766—42no—
44#6766—42no—
45C2×C3×C5×C8—21no—
46C3×C42×C5C2311yescharacteristic
47C4×Dic15C2×C411yescharacteristic
48C4×Dic15D411yescharacteristic
49C4×Dic15D411yescharacteristic
50C2×C3⋊#168—21no—
51C5×C4⋊Dic3—21no—
52C5×C4⋊Dic3C2×C412yes—
53C2×C5×C3⋊C8—21no—
54C2×C3×#168—21no—
55#6665—22no—
56#6665—22no—
57#6651—42no—
58#5716—51no—
59#4837—51no—
60#4835—51no—
61C3×#331—51no—
62#4544—51no—
63#4486—51no—
64#4482D511yescharacteristic, complemented
65C2×#713—61no—
66C5×C4⋊Q8—31no—
67#4093—61no—
68C2×#676—61no—
69#4041—32no—
70#4041—61no—
71#4039—32no—
72#4039—61no—
73#4020C2×D311yescharacteristic
74C42×D5—31no—
75C5×C4⋊C8—31no—
76C5×C4⋊C8C2×D311yescharacteristic
77#3952—61no—
78#3947—61no—
79#3946—61no—
80C4⋊#168—31no—
81C4⋊#168C2×D311yescharacteristic
82#1557—151noSylow
83C22×D15C22⋊C411yescharacteristic
84C22×C3×D5—22no—
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15C22⋊C411yescharacteristic
89C2×Dic15C22⋊C411yescharacteristic
90C2×Dic15C22⋊C411yescharacteristic
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—21no—
94C4×D15—21no—
95C4×D15—41no—
96C2×C5×Dic3—22no—
97C5×Dic6—41no—
98C5×Dic6—41no—
99C3×D20—42no—
100C3×D20—41no—
101C3×D20—41no—
102C3×D20—41no—
103C3×D20—41no—
104#1202—44no—
105D5×Dic3—44no—
106C3×C5×C8—41no—
107C3⋊#168—41no—
108C3×#168—41no—
109C5×C3⋊C8—41no—
110C2×#237—101no—
111C3×#127—51no—
112#938—52no—
113#938—101no—
114#936—101no—
115D4×Dic3—52no—
116D4×Dic3—101no—
117C2×ΓL(1,𝔽25)—101no—
118C42×D3—51no—
119#869C2×D511yescharacteristic
120C3×C4⋊C8—51no—
121C3×C4⋊C8C2×D511yescharacteristic
122(C2×D3)⋊C8—101no—
123#815—101no—
124Dic3⋊C8—101no—
125C4⋊(C3⋊C8)—51no—
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C2×C5×Q8—61no—
128#713—122no—
129#713—122no—
130C2×D20—21no—
131C2×D20—21no—
132C2×D20—62no—
133C2×D20C4×D312yes—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×C4×D5—62no—
138C2×C5×C8—21no—
139C2×C5×C8—61no—
140C5×C4⋊C4—32no—
141C5×C4⋊C4—61no—
142C42×C5C22×D311yescharacteristic
143#685—62no—
144#685—62no—
145C4×Dic5—31no—
146C4×Dic5—31no—
147C4×Dic5—31no—
148C2×#168—21no—
149C2×#168—61no—
150#676—122no—
151#532—151no—
152#432—151no—
153#423—151no—
154#332—31no—
155#332—151no—
156#331—51no—
157#331—151no—
158C22×C3×C5C2×C22⋊C411yescharacteristic
159C2×D15—21no—
160C2×D15—21no—
161C2×D15—21no—
162C2×C3×D5—42no—
163C2×C3×D5—42no—
164C2×C3×D5—42no—
165C3×C4×C5—21no—
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C3×C4×C5#13711yescharacteristic
170Dic15—21no—
171Dic15—21no—
172Dic15—21no—
173C5×Dic3—42no—
174C2×C3×D4—52no—
175C2×C3×D4—101no—
176C2×C3×D4—101no—
177C2×#67—102no—
178C22×Dic3—102no—
179#237—202no—
180#237—202no—
181C2×C4×D3—51no—
182C2×C4×D3—51no—
183C2×C4×D3—51no—
184C2×Dic6—21no—
185C2×C3×C8—21no—
186C2×C3×C8—101no—
187C3×C42C22×D511yescharacteristic
188#217—102no—
189#217—102no—
190C4⋊Dic3—21no—
191C4⋊Dic3C4×D512yes—
192C4×Dic3—51no—
193C4×Dic3—51no—
194C4×Dic3—51no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—101no—
197ΓL(1,𝔽25)—202no—
198C22×D5—22no—
199C22×D5—31no—
200C5×Q8—121no—
201C5×Q8—121no—
202C2×C4×C5—62no—
203C2×C4×C5C2×C4×D311yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C2×C4×C5D3×D411yescharacteristic
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5—31no—
209D20—42no—
210D20—41no—
211D20—41no—
212D20—41no—
213D20—41no—
214D20—124no—
215C4×D5—61no—
216C4×D5—61no—
217C4×D5—61no—
218C4×D5—61no—
219C4×D5—121no—
220C4×D5—124no—
221C5×C8—41no—
222C5×C8—121no—
223#168—41no—
224#168—121no—
225C2×#41—301no—
226C2×M16—301no—
227C4⋊Q8—31no—
228#127—51no—
229#124—301no—
230#121—152no—
231#121—301no—
232C4×D4—152no—
233C4×D4—301no—
234C2×C42—151no—
235C4⋊C8—31no—
236C4⋊C8—51no—
237C4⋊C8—151no—
238C4⋊C8—301no—
239C4⋊C8D3×D511yescharacteristic
240C22⋊C8—301no—
241#97—301no—
242C2×C3×C5#41311yescharacteristic
243C2×C3×C5#41711yescharacteristic
244C2×C3×C5#41811yescharacteristic
245D15—41no—
246C3×D5—82no—
247C23×C3—102no—
248C22×D3—51no—
249C3×D4—202no—
250C3×D4—201no—
251C3×D4—201no—
252C3×D4—201no—
253C3×D4—201no—
254C2×C3×C4C2×C4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257#67—204no—
258C2×Dic3—22no—
259C2×Dic3—51no—
260C2×Dic3—51no—
261C2×Dic3—51no—
262C2×Dic3—204no—
263C4×D3—101no—
264C4×D3—101no—
265C4×D3—101no—
266C4×D3—101no—
267C4×D3—201no—
268Dic6—41no—
269Dic6—41no—
270C3×C8—41no—
271C3×C8—201no—
272C3⋊C8—41no—
273C3⋊C8—201no—
274C22×C5D3×C22⋊C411yescharacteristic
275C2×D5—42no—
276C2×D5—42no—
277C2×D5—42no—
278C2×D5—61no—
279C2×D5—61no—
280C2×D5—61no—
281C4×C5—21no—
282C4×C5—122no—
283C4×C5#91111yescharacteristic
284C4×C5#91111yescharacteristic
285C4×C5#91411yescharacteristic
286C4×C5#91511yescharacteristic
287Dic5—61no—
288Dic5—61no—
289Dic5—61no—
290#41—602no—
291#41—602no—
292C2×Q8—61no—
293C2×D4—52no—
294C2×D4—101no—
295C2×D4—101no—
296C2×D4—302no—
297C22×C4—151no—
298C22×C4—151no—
299C22×C4—151no—
300C22×C4—302no—
301M16—602no—
302C2×C8—21no—
303C2×C8—61no—
304C2×C8—101no—
305C2×C8—301no—
306C4⋊C4—32no—
307C4⋊C4—61no—
308C22⋊C4—302no—
309C22⋊C4—302no—
310C42—151no—
311C42—151no—
312C42—151no—
313C42C2×D3×D511yescharacteristic
314C3×C5#155711yescharacteristic, complemented, Hall
315C22×C3—202no—
316C22×C3—202no—
317C22×C3—202no—
318C22×C3D5×C22⋊C411yescharacteristic
319C2×D3—101no—
320C2×D3—101no—
321C2×D3—101no—
322C3×C4—21no—
323C3×C4#405711yescharacteristic
324C3×C4#406011yescharacteristic
325C3×C4#406011yescharacteristic
326C3×C4#406411yescharacteristic
327Dic3—42no—
328Dic3—101no—
329Dic3—101no—
330Dic3—101no—
331C2×C5#474511yescharacteristic
332C2×C5#477011yescharacteristic
333C2×C5#477111yescharacteristic
334D5—82no—
335D5—121no—
336C23—102no—
337C23—151no—
338Q8—121no—
339Q8—121no—
340D4—202no—
341D4—201no—
342D4—201no—
343D4—201no—
344D4—201no—
345D4—604no—
346C2×C4—62no—
347C2×C4—151no—
348C2×C4—151no—
349C2×C4—151no—
350C2×C4—301no—
351C2×C4—301no—
352C2×C4—301no—
353C2×C4—301no—
354C2×C4—601no—
355C2×C4—604no—
356C2×C4C4×D3×D511yescharacteristic
357C2×C4#677711yescharacteristic
358C2×C4#679011yescharacteristic
359C8—41no—
360C8—121no—
361C8—201no—
362C8—601no—
363C2×C3—402no—
364C2×C3#6504011yescharacteristic
365C2×C3#6505911yescharacteristic
366C2×C3#6509211yescharacteristic
367D3—201no—
368C5#6838811yescharacteristic, complemented, Sylow
369C22—202no—
370C22—202no—
371C22—202no—
372C22—301no—
373C22—301no—
374C22—301no—
375C22#9147311yescharacteristic
376C4—21no—
377C4—122no—
378C4—301no—
379C4—301no—
380C4—301no—
381C4#9125811yescharacteristic
382C4#9127811yescharacteristic
383C4#9148211yescharacteristic
384C4#9150611yescharacteristic
385C3#1059922211yescharacteristic, complemented, Sylow
386C2—402no—
387C2—601no—
388C2#1174747911yescharacteristic
389C2#1174814211yescharacteristic
390C2#1174823811yescharacteristic
subgroupG/H
centerC22#91473
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11752556C2
cosocleC3×C42×C5C23
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1557
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11750936C2semidirect
3. #11747015C2semidirect
4. C5×#4482C2semidirect
5. C3×#64705C2semidirect
6. #11745857C2semidirect
7. #11745852C2semidirect
33. #64705D3semidirect
64. #4482D5semidirect
314. C3×C5#1557semidirect
368. C5#68388semidirect
385. C3#10599222semidirect

Maximal subgroups

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

subgroupindex
#117525562
#117509362
#117470152
C5×#44822
C3×#647052
#117458572
#117458522
#105992223
#683885