Finite Group Databasebeta

← #14285308

Subgroups — #14285308

Order 1920.

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

normal subgroups only

This group has 492 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#11747015C211yesmaximal, characteristic, complemented
3#11746867C211yesmaximal, characteristic, complemented
4C5×#4544C211yesmaximal, characteristic, complemented
5C3×#64764C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10599181—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
18C2×#6651—21no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90983—21no—
24#90957—21no—
25#90954—21no—
26#68388—51nomaximal, Hall
27#66050—31no—
28#65126—31no—
29#65124—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#6651—42no—
58#5716—51no—
59#4837—51no—
60#4835—51no—
61C3×#331—51no—
62#4544D511yescharacteristic, complemented
63#4486—51no—
64#4482—51no—
65C2×#711—61no—
66C5×#127C2×D311yescharacteristic
67#4084—32no—
68#4084—61no—
69#4082—61no—
70D4×Dic5—32no—
71D4×Dic5—61no—
72C2×#676—61no—
73C42×D5—31no—
74#4015—31no—
75C5×C4⋊C8—31no—
76C5×C4⋊C8—31no—
77#3952—61no—
78#3947—61no—
79#3946—61no—
80C4⋊#168C2×D311yescharacteristic
81C4⋊#168C2×D311yescharacteristic
82#1557—151noSylow
83C23×C3×C5—22no—
84C22×D15C22⋊C411yescharacteristic
85C3×C5×D4—42no—
86C3×C5×D4—41no—
87C3×C5×D4—41no—
88C3×C5×D4—41no—
89C3×C5×D4—41no—
90C2×C3×C4×C5C22×C411yescharacteristic
91C2×C3×C4×C5C2×D411yescharacteristic
92C2×C3×C4×C5C2×D411yescharacteristic
93#1220—44no—
94C2×Dic15—22no—
95C2×Dic15—44no—
96C2×Dic15C22⋊C411yescharacteristic
97C2×Dic15C22⋊C411yescharacteristic
98C2×Dic15C22⋊C411yescharacteristic
99C4×D15—21no—
100C4×D15—21no—
101C4×D15—21no—
102C4×D15—21no—
103C4×D15—41no—
104Dic30—41no—
105Dic30—41no—
106C3×#168—41no—
107C3×#168—41no—
108C5×C3⋊C8—41no—
109C5×C3⋊C8—41no—
110C2×#237—101no—
111C3×#127C2×D511yescharacteristic
112#938—52no—
113#938—101no—
114#936—101no—
115D4×Dic3—52no—
116D4×Dic3—101no—
117C2×ΓL(1,𝔽25)—101no—
118C42×D3—51no—
119#869—51no—
120C3×C4⋊C8—51no—
121C3×C4⋊C8—51no—
122(C2×D3)⋊C8—101no—
123#815—101no—
124Dic3⋊C8—101no—
125C4⋊(C3⋊C8)C2×D511yescharacteristic
126C4⋊(C3⋊C8)C2×D511yescharacteristic
127C2×C5×D4—21no—
128C2×C5×D4—21no—
129C2×C5×D4C4×D312yes—
130C2×C22⋊D5—62no—
131C22×Dic5—62no—
132#711—122no—
133#711—122no—
134C2×C4×D5—31no—
135C2×C4×D5—31no—
136C2×C4×D5—31no—
137C2×Dic10—61no—
138C2×C5×C8—61no—
139C2×C5×C8—61no—
140C42×C5C22×D311yescharacteristic
141C22⋊Dic5—62no—
142C22⋊Dic5—62no—
143C4⋊Dic5—32no—
144C4⋊Dic5—61no—
145C4×Dic5—31no—
146C4×Dic5—31no—
147C4×Dic5—31no—
148C2×#168—21no—
149C2×#168—21no—
150#676—122no—
151#532—151no—
152#432—151no—
153#423—151no—
154#332—151no—
155#332—151no—
156#331—31no—
157#331—51no—
158C22×C3×C5—42no—
159C22×C3×C5—42no—
160C22×C3×C5—42no—
161C22×C3×C5C2×C22⋊C411yescharacteristic
162C2×D15—21no—
163C2×D15—21no—
164C2×D15—21no—
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—
173Dic15—42no—
174C2×C3×D4—21no—
175C2×C3×D4—21no—
176C2×C3×D4C4×D512yes—
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—101no—
185C2×C3×C8—101no—
186C2×C3×C8—101no—
187C3×C42C22×D511yescharacteristic
188#217—102no—
189#217—102no—
190C4⋊Dic3—52no—
191C4⋊Dic3—101no—
192C4×Dic3—51no—
193C4×Dic3—51no—
194C4×Dic3—51no—
195C2×C3⋊C8—21no—
196C2×C3⋊C8—21no—
197ΓL(1,𝔽25)—202no—
198C23×C5—22no—
199C22×D5—31no—
200C5×D4—42no—
201C5×D4—41no—
202C5×D4—41no—
203C5×D4—41no—
204C5×D4—41no—
205C2×C4×C5C2×C4×D311yescharacteristic
206C2×C4×C5D3×D411yescharacteristic
207C2×C4×C5D3×D411yescharacteristic
208C22⋊D5—124no—
209C2×Dic5—31no—
210C2×Dic5—31no—
211C2×Dic5—31no—
212C2×Dic5—62no—
213C2×Dic5—124no—
214C4×D5—61no—
215C4×D5—61no—
216C4×D5—61no—
217C4×D5—61no—
218C4×D5—121no—
219Dic10—121no—
220Dic10—121no—
221C5×C8—121no—
222C5×C8—121no—
223#168—41no—
224#168—41no—
225C2×#41—301no—
226C2×M16—301no—
227C4⋊Q8—151no—
228#127D3×D511yescharacteristic
229#124—301no—
230#121—152no—
231#121—301no—
232C4×D4—152no—
233C4×D4—301no—
234C2×C42—151no—
235C4⋊C8—31no—
236C4⋊C8—31no—
237C4⋊C8—51no—
238C4⋊C8—51no—
239C4⋊C8—301no—
240C22⋊C8—301no—
241#97—301no—
242C2×C3×C5—82no—
243C2×C3×C5#41311yescharacteristic
244C2×C3×C5#41711yescharacteristic
245C2×C3×C5#41811yescharacteristic
246D15—41no—
247C23×C3—22no—
248C22×D3—51no—
249C3×D4—42no—
250C3×D4—41no—
251C3×D4—41no—
252C3×D4—41no—
253C3×D4—41no—
254C2×C3×C4C2×C4×D511yescharacteristic
255C2×C3×C4D4×D511yescharacteristic
256C2×C3×C4D4×D511yescharacteristic
257#67—204no—
258C2×Dic3—51no—
259C2×Dic3—51no—
260C2×Dic3—51no—
261C2×Dic3—102no—
262C2×Dic3—204no—
263C4×D3—101no—
264C4×D3—101no—
265C4×D3—101no—
266C4×D3—101no—
267C4×D3—201no—
268Dic6—201no—
269Dic6—201no—
270C3×C8—201no—
271C3×C8—201no—
272C3⋊C8—41no—
273C3⋊C8—41no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—42no—
277C22×C5D3×C22⋊C411yescharacteristic
278C2×D5—61no—
279C2×D5—61no—
280C2×D5—61no—
281C4×C5—21no—
282C4×C5#91111yescharacteristic
283C4×C5#91111yescharacteristic
284C4×C5#91411yescharacteristic
285C4×C5#91511yescharacteristic
286Dic5—61no—
287Dic5—61no—
288Dic5—61no—
289Dic5—122no—
290#41—602no—
291#41—602no—
292C2×Q8—301no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—302no—
296C2×D4#120012yes—
297C22×C4—151no—
298C22×C4—151no—
299C22×C4—151no—
300C22×C4—302no—
301M16—602no—
302C2×C8—61no—
303C2×C8—61no—
304C2×C8—101no—
305C2×C8—101no—
306C4⋊C4—152no—
307C4⋊C4—301no—
308C22⋊C4—302no—
309C22⋊C4—302no—
310C42—151no—
311C42—151no—
312C42—151no—
313C42C2×D3×D511yescharacteristic
314C3×C5#155711yescharacteristic, complemented, Hall
315C22×C3—42no—
316C22×C3—42no—
317C22×C3—42no—
318C22×C3D5×C22⋊C411yescharacteristic
319C2×D3—101no—
320C2×D3—101no—
321C2×D3—101no—
322C3×C4—21no—
323C3×C4#405711yescharacteristic
324C3×C4#405711yescharacteristic
325C3×C4#406011yescharacteristic
326C3×C4#406111yescharacteristic
327Dic3—101no—
328Dic3—101no—
329Dic3—101no—
330Dic3—202no—
331C2×C5—82no—
332C2×C5#474511yescharacteristic
333C2×C5#477011yescharacteristic
334C2×C5#477111yescharacteristic
335D5—121no—
336C23—22no—
337C23—151no—
338Q8—601no—
339Q8—601no—
340D4—42no—
341D4—41no—
342D4—41no—
343D4—41no—
344D4—41no—
345D4—604no—
346C2×C4—151no—
347C2×C4—151no—
348C2×C4—151no—
349C2×C4—301no—
350C2×C4—301no—
351C2×C4—301no—
352C2×C4—301no—
353C2×C4—302no—
354C2×C4—601no—
355C2×C4—604no—
356C2×C4C2×#120011yescharacteristic
357C2×C4#679011yescharacteristic
358C2×C4#679011yescharacteristic
359C8—121no—
360C8—121no—
361C8—201no—
362C8—201no—
363C2×C3—82no—
364C2×C3#6503411yescharacteristic
365C2×C3#6505911yescharacteristic
366C2×C3#6506011yescharacteristic
367D3—201no—
368C5#6838811yescharacteristic, complemented, Sylow
369C22—42no—
370C22—42no—
371C22—42no—
372C22—301no—
373C22—301no—
374C22—301no—
375C22#9156111yescharacteristic
376C4—21no—
377C4—301no—
378C4—301no—
379C4—301no—
380C4—602no—
381C4#9148211yescharacteristic
382C4#9148811yescharacteristic
383C4#9149811yescharacteristic
384C4#9150011yescharacteristic
385C3#1059918111yescharacteristic, complemented, Sylow
386C2—82no—
387C2—601no—
388C2#1174895911yescharacteristic
389C2#1174897211yescharacteristic
390C2#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#1557
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. #11747015C2semidirect
3. #11746867C2semidirect
4. C5×#4544C2semidirect
5. C3×#64764C2semidirect
6. #11745860C2semidirect
7. #11745859C2semidirect
31. #64764D3semidirect
62. #4544D5semidirect
314. C3×C5#1557semidirect
368. C5#68388semidirect
385. C3#10599181semidirect

Maximal subgroups

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

subgroupindex
#117564752
#117470152
#117468672
C5×#45442
C3×#647642
#117458602
#117458592
#105991813
#683885