Finite Group Databasebeta

← #14285143

Subgroups — #14285143

Order 1920.

484 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 100 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#11756475C211yesmaximal, characteristic
2#11746867C211yesmaximal, characteristic, complemented
3#11746859C211yesmaximal, characteristic, complemented
4C5×#4544C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10599179—31nomaximal, Hall
9C2×#6819—21no—
10C3×C5×#127C2211yescharacteristic
11#91827—21no—
12#91827C412yes—
13#91825—21no—
14D4×Dic15—21no—
15D4×Dic15C412yes—
16C42×D15C2211yescharacteristic
17#91758C2211yescharacteristic
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90957—21no—
23#90957—21no—
24#90954—21no—
25#90951—21no—
26#68386—51nomaximal, Hall
27#66050—31no—
28#65124—31no—
29#65122—31no—
30C5×#331—31no—
31#64764D311yescharacteristic, complemented
32#64706—31no—
33#64702—31no—
34C2×C3×C5×D4—21no—
35C2×C3×C5×D4—21no—
36C2×C3×C5×D4C2×C412yes—
37C2×#1220—22no—
38C22×Dic15—22no—
39#6819—42no—
40#6819—42no—
41C2×C4×D15C2×C411yescharacteristic
42C2×C4×D15D411yescharacteristic
43C2×C4×D15D411yescharacteristic
44C2×Dic30—21no—
45C3×C42×C5C2311yescharacteristic
46#6719—22no—
47#6719—22no—
48C4⋊Dic15—21no—
49C4⋊Dic15C2×C412yes—
50C4×Dic15C2×C411yescharacteristic
51C4×Dic15D411yescharacteristic
52C4×Dic15D411yescharacteristic
53C2×C5×C3⋊C8—21no—
54C2×C5×C3⋊C8—21no—
55C2×C3×#168—21no—
56C2×C3×#168—21no—
57#5716—51no—
58#4835—51no—
59#4833—51no—
60C3×#331—51no—
61#4544D511yescharacteristic, complemented
62#4486—51no—
63#4482—51no—
64C2×#711—61no—
65C5×#127C2×D311yescharacteristic
66#4084—32no—
67#4084—61no—
68#4082—61no—
69D4×Dic5—32no—
70D4×Dic5—61no—
71C42×D5—31no—
72#4015—31no—
73C5×C4⋊C8—31no—
74C5×C4⋊C8—31no—
75#3952—61no—
76#3952—61no—
77#3947—61no—
78C8×Dic5—61no—
79C4⋊#168C2×D311yescharacteristic
80C4⋊#168C2×D311yescharacteristic
81#1553—151noSylow
82C23×C3×C5—22no—
83C22×D15C22⋊C411yescharacteristic
84C3×C5×D4—42no—
85C3×C5×D4—41no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C2×C3×C4×C5C22×C411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92#1220—44no—
93C2×Dic15—22no—
94C2×Dic15—44no—
95C2×Dic15C22⋊C411yescharacteristic
96C2×Dic15C22⋊C411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C4×D15—21no—
99C4×D15—21no—
100C4×D15—21no—
101C4×D15—21no—
102C4×D15—41no—
103Dic30—41no—
104Dic30—41no—
105C3×#168—41no—
106C3×#168—41no—
107C5×C3⋊C8—41no—
108C5×C3⋊C8—41no—
109C2×#237—101no—
110C3×#127C2×D511yescharacteristic
111#938—52no—
112#938—101no—
113#936—101no—
114D4×Dic3—52no—
115D4×Dic3—101no—
116C42×D3—51no—
117#869—51no—
118C3×C4⋊C8—51no—
119C3×C4⋊C8—51no—
120(C2×D3)⋊C8—101no—
121(C2×D3)⋊C8—101no—
122#815—101no—
123C8×Dic3—101no—
124C4⋊(C3⋊C8)C2×D511yescharacteristic
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C2×C5×D4—21no—
127C2×C5×D4—21no—
128C2×C5×D4C4×D312yes—
129C2×C22⋊D5—62no—
130C22×Dic5—62no—
131#711—122no—
132#711—122no—
133C2×C4×D5—31no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×Dic10—61no—
137C2×C5×C8—61no—
138C2×C5×C8—61no—
139C42×C5C22×D311yescharacteristic
140C22⋊Dic5—62no—
141C22⋊Dic5—62no—
142C4⋊Dic5—32no—
143C4⋊Dic5—61no—
144C4×Dic5—31no—
145C4×Dic5—31no—
146C4×Dic5—31no—
147C2×#168—21no—
148C2×#168—21no—
149#532—151no—
150#432—151no—
151#431—151no—
152#332—151no—
153#332—151no—
154#331—31no—
155#331—51no—
156C22×C3×C5—42no—
157C22×C3×C5—42no—
158C22×C3×C5—42no—
159C22×C3×C5C2×C22⋊C411yescharacteristic
160C2×D15—21no—
161C2×D15—21no—
162C2×D15—21no—
163C3×C4×C5—21no—
164C3×C4×C5#13511yescharacteristic
165C3×C4×C5#13511yescharacteristic
166C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
168Dic15—21no—
169Dic15—21no—
170Dic15—21no—
171Dic15—42no—
172C2×C3×D4—21no—
173C2×C3×D4—21no—
174C2×C3×D4C4×D512yes—
175C2×#67—102no—
176C22×Dic3—102no—
177#237—202no—
178#237—202no—
179C2×C4×D3—51no—
180C2×C4×D3—51no—
181C2×C4×D3—51no—
182C2×Dic6—101no—
183C2×C3×C8—101no—
184C2×C3×C8—101no—
185C3×C42C22×D511yescharacteristic
186#217—102no—
187#217—102no—
188C4⋊Dic3—52no—
189C4⋊Dic3—101no—
190C4×Dic3—51no—
191C4×Dic3—51no—
192C4×Dic3—51no—
193C2×C3⋊C8—21no—
194C2×C3⋊C8—21no—
195C23×C5—22no—
196C22×D5—31no—
197C5×D4—42no—
198C5×D4—41no—
199C5×D4—41no—
200C5×D4—41no—
201C5×D4—41no—
202C2×C4×C5C2×C4×D311yescharacteristic
203C2×C4×C5D3×D411yescharacteristic
204C2×C4×C5D3×D411yescharacteristic
205C22⋊D5—124no—
206C2×Dic5—31no—
207C2×Dic5—31no—
208C2×Dic5—31no—
209C2×Dic5—62no—
210C2×Dic5—124no—
211C4×D5—61no—
212C4×D5—61no—
213C4×D5—61no—
214C4×D5—61no—
215C4×D5—121no—
216Dic10—121no—
217Dic10—121no—
218C5×C8—121no—
219C5×C8—121no—
220#168—41no—
221#168—41no—
222C2×#41—301no—
223C4⋊Q8—151no—
224#127D3×D511yescharacteristic
225#124—301no—
226#121—152no—
227#121—301no—
228C4×D4—152no—
229C4×D4—301no—
230C2×C42—151no—
231C4⋊C8—31no—
232C4⋊C8—31no—
233C4⋊C8—51no—
234C4⋊C8—51no—
235C22⋊C8—301no—
236C22⋊C8—301no—
237#97—301no—
238C4×C8—301no—
239C2×C3×C5—82no—
240C2×C3×C5#41311yescharacteristic
241C2×C3×C5#41611yescharacteristic
242C2×C3×C5#41811yescharacteristic
243D15—41no—
244C23×C3—22no—
245C22×D3—51no—
246C3×D4—42no—
247C3×D4—41no—
248C3×D4—41no—
249C3×D4—41no—
250C3×D4—41no—
251C2×C3×C4C2×C4×D511yescharacteristic
252C2×C3×C4D4×D511yescharacteristic
253C2×C3×C4D4×D511yescharacteristic
254#67—204no—
255C2×Dic3—51no—
256C2×Dic3—51no—
257C2×Dic3—51no—
258C2×Dic3—102no—
259C2×Dic3—204no—
260C4×D3—101no—
261C4×D3—101no—
262C4×D3—101no—
263C4×D3—101no—
264C4×D3—201no—
265Dic6—201no—
266Dic6—201no—
267C3×C8—201no—
268C3×C8—201no—
269C3⋊C8—41no—
270C3⋊C8—41no—
271C22×C5—42no—
272C22×C5—42no—
273C22×C5—42no—
274C22×C5D3×C22⋊C411yescharacteristic
275C2×D5—61no—
276C2×D5—61no—
277C2×D5—61no—
278C4×C5—21no—
279C4×C5#91111yescharacteristic
280C4×C5#91211yescharacteristic
281C4×C5#91411yescharacteristic
282C4×C5#91611yescharacteristic
283Dic5—61no—
284Dic5—61no—
285Dic5—61no—
286Dic5—122no—
287#41—602no—
288#41—602no—
289C2×Q8—301no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—302no—
293C2×D4#120012yes—
294C22×C4—151no—
295C22×C4—151no—
296C22×C4—151no—
297C22×C4—302no—
298C2×C8—61no—
299C2×C8—61no—
300C2×C8—101no—
301C2×C8—101no—
302C4⋊C4—152no—
303C4⋊C4—301no—
304C22⋊C4—302no—
305C22⋊C4—302no—
306C42—151no—
307C42—151no—
308C42—151no—
309C42C2×D3×D511yescharacteristic
310C3×C5#155311yescharacteristic, complemented, Hall
311C22×C3—42no—
312C22×C3—42no—
313C22×C3—42no—
314C22×C3D5×C22⋊C411yescharacteristic
315C2×D3—101no—
316C2×D3—101no—
317C2×D3—101no—
318C3×C4—21no—
319C3×C4#405711yescharacteristic
320C3×C4#405811yescharacteristic
321C3×C4#406011yescharacteristic
322C3×C4#406211yescharacteristic
323Dic3—101no—
324Dic3—101no—
325Dic3—101no—
326Dic3—202no—
327C2×C5—82no—
328C2×C5#474511yescharacteristic
329C2×C5#477011yescharacteristic
330C2×C5#477211yescharacteristic
331D5—121no—
332C23—22no—
333C23—151no—
334Q8—601no—
335Q8—601no—
336D4—42no—
337D4—41no—
338D4—41no—
339D4—41no—
340D4—41no—
341D4—604no—
342C2×C4—151no—
343C2×C4—151no—
344C2×C4—151no—
345C2×C4—301no—
346C2×C4—301no—
347C2×C4—301no—
348C2×C4—301no—
349C2×C4—302no—
350C2×C4—601no—
351C2×C4—604no—
352C2×C4C2×#120011yescharacteristic
353C2×C4#679011yescharacteristic
354C2×C4#679011yescharacteristic
355C8—121no—
356C8—121no—
357C8—201no—
358C8—201no—
359C2×C3—82no—
360C2×C3#6503411yescharacteristic
361C2×C3#6505911yescharacteristic
362C2×C3#6506111yescharacteristic
363D3—201no—
364C5#6838611yescharacteristic, complemented, Sylow
365C22—42no—
366C22—42no—
367C22—42no—
368C22—301no—
369C22—301no—
370C22—301no—
371C22#9156111yescharacteristic
372C4—21no—
373C4—301no—
374C4—301no—
375C4—301no—
376C4—602no—
377C4#9149711yescharacteristic
378C4#9149811yescharacteristic
379C4#9149911yescharacteristic
380C4#9150011yescharacteristic
381C3#1059917911yescharacteristic, complemented, Sylow
382C2—82no—
383C2—601no—
384C2#1174896911yescharacteristic
385C2#1174897211yescharacteristic
386C2#1174912811yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756475C2
cosocleC3×C42×C5C23
hypercenter#127D3×D5
hypocenterC3×C5#1553
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11746867C2semidirect
3. #11746859C2semidirect
4. C5×#4544C2semidirect
5. C3×#64764C2semidirect
6. #11745860C2semidirect
7. #11745859C2semidirect
31. #64764D3semidirect
61. #4544D5semidirect
310. C3×C5#1553semidirect
364. C5#68386semidirect
381. C3#10599179semidirect

Maximal subgroups

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

subgroupindex
#117564752
#117468672
#117468592
C5×#45442
C3×#647642
#117458602
#117458592
#105991793
#683865