Subgroups — C₅×#11963 #11934683

Order 1280.

396 conjugacy classes of subgroups.

The subgroup lattice has 256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3147	C₂	1	1	yes	maximal, characteristic
2	C₅×#2162	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#1568	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1362	C₂	1	2	yes	maximal, complemented
5	C₅×#1361	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#135	—	2	1	no	—
7	C₂×C₅×#135	C₄	1	2	yes	—
8	C₅×#532	—	2	1	no	—
9	C₅×#495	—	2	1	no	—
10	C₅×#495	C₄	1	2	yes	—
11	C₅×#494	C₂²	1	1	yes	characteristic
12	C₅×#493	C₂²	1	1	yes	characteristic
13	C₅×#492	—	2	1	no	—
14	C₅×#432	—	2	1	no	—
15	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
17	C₅×C₂²⋊C₁₆	—	2	1	no	—
18	C₄×C₅×C₁₆	—	2	1	no	—
19	C₅×#335	C₂²	1	2	yes	—
20	C₅×#334	—	2	1	no	—
21	#11963	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂×C₅×#41	—	2	2	no	—
23	C₅×#135	—	4	4	no	—
24	C₅×#135	—	4	4	no	—
25	C₂×C₅×Q₁₆	—	2	1	no	—
26	C₂×C₅×Q₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₅×SD₁₆	—	2	2	no	—
28	C₂×C₅×SD₁₆	—	2	2	no	—
29	C₂×C₅×D₈	—	2	1	no	—
30	C₂×C₅×D₈	C₂×C₄	1	2	yes	—
31	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
33	C₅×C₄⋊Q₈	—	2	1	no	—
34	C₅×#127	—	2	1	no	—
35	C₅×#124	—	2	2	no	—
36	C₅×#121	—	4	1	no	—
37	C₅×#121	—	4	1	no	—
38	C₄×C₅×D₄	—	4	1	no	—
39	C₄×C₅×D₄	—	4	1	no	—
40	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₂×C₅×C₁₆	—	2	2	no	—
42	C₅×C₄⋊C₈	—	2	2	no	—
43	C₅×C₂²⋊C₈	—	4	1	no	—
44	C₅×#97	—	4	1	no	—
45	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
46	C₄×C₅×C₈	D₄	1	1	yes	characteristic
47	C₄×C₅×C₈	D₄	1	1	yes	characteristic
48	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
49	#3147	C₂×C₅	1	1	yes	characteristic
50	#2162	C₂×C₅	1	1	yes	characteristic, complemented
51	#1568	C₂×C₅	1	1	yes	characteristic, complemented
52	#1362	C₂×C₅	1	2	yes	complemented
53	#1361	C₂×C₅	1	2	yes	complemented
54	C₅×#41	—	4	4	no	—
55	C₅×#41	—	4	4	no	—
56	C₂×C₅×Q₈	—	2	2	no	—
57	C₂×C₅×D₄	—	2	2	no	—
58	C₂×C₅×D₄	—	4	2	no	—
59	C₂×C₅×D₄	—	4	1	no	—
60	C₂×C₅×D₄	—	4	1	no	—
61	C₂²×C₄×C₅	—	4	2	no	—
62	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
64	C₂²×C₄×C₅	SD₁₆	1	1	yes	characteristic
65	C₅×Q₁₆	—	4	2	no	—
66	C₅×Q₁₆	—	4	2	no	—
67	C₅×SD₁₆	—	4	4	no	—
68	C₅×SD₁₆	—	4	4	no	—
69	C₅×D₈	—	4	2	no	—
70	C₅×D₈	—	4	2	no	—
71	C₂×C₅×C₈	—	2	2	no	—
72	C₂×C₅×C₈	—	2	2	no	—
73	C₂×C₅×C₈	—	4	2	no	—
74	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
77	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
78	C₅×C₄⋊C₄	—	4	1	no	—
79	C₅×C₄⋊C₄	—	4	1	no	—
80	C₅×C₂²⋊C₄	—	4	2	no	—
81	C₅×C₂²⋊C₄	—	4	2	no	—
82	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
83	C₄²×C₅	D₈	1	1	yes	characteristic
84	C₄²×C₅	SD₁₆	1	1	yes	characteristic
85	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
86	C₅×C₁₆	—	4	2	no	—
87	C₂×#135	—	2	1	no	—
88	C₂×#135	C₄×C₅	1	2	yes	—
89	#532	—	2	1	no	—
90	#495	—	2	1	no	—
91	#495	C₄×C₅	1	2	yes	—
92	#494	C₂²×C₅	1	1	yes	characteristic
93	#493	C₂²×C₅	1	1	yes	characteristic
94	#492	—	2	1	no	—
95	#432	—	2	1	no	—
96	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
97	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
98	C₂²⋊C₁₆	—	2	1	no	—
99	C₄×C₁₆	—	2	1	no	—
100	#335	C₂²×C₅	1	2	yes	—
101	#334	—	2	1	no	—
102	C₂³×C₅	—	4	2	no	—
103	C₂³×C₅	#102	1	1	yes	characteristic
104	C₅×Q₈	—	4	2	no	—
105	C₅×Q₈	—	4	2	no	—
106	C₅×D₄	—	4	2	no	—
107	C₅×D₄	—	4	2	no	—
108	C₅×D₄	—	8	2	no	—
109	C₅×D₄	—	8	4	no	—
110	C₅×D₄	—	8	2	no	—
111	C₂×C₄×C₅	—	2	1	no	—
112	C₂×C₄×C₅	—	2	1	no	—
113	C₂×C₄×C₅	—	2	2	no	—
114	C₂×C₄×C₅	—	4	1	no	—
115	C₂×C₄×C₅	—	4	2	no	—
116	C₂×C₄×C₅	—	8	4	no	—
117	C₂×C₄×C₅	#102	1	1	yes	characteristic
118	C₂×C₄×C₅	#102	1	1	yes	characteristic
119	C₂×C₄×C₅	#102	1	1	yes	characteristic
120	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
122	C₂×C₄×C₅	C₂×SD₁₆	1	1	yes	characteristic
123	C₅×C₈	—	2	1	no	—
124	C₅×C₈	—	2	1	no	—
125	C₅×C₈	—	8	2	no	—
126	C₅×C₈	#100	1	2	yes	—
127	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
128	C₂×#41	—	2	2	no	—
129	#135	—	4	4	no	—
130	#135	—	4	4	no	—
131	C₂×Q₁₆	—	2	1	no	—
132	C₂×Q₁₆	C₂×C₄×C₅	1	2	yes	—
133	C₂×SD₁₆	—	2	2	no	—
134	C₂×SD₁₆	—	2	2	no	—
135	C₂×D₈	—	2	1	no	—
136	C₂×D₈	C₂×C₄×C₅	1	2	yes	—
137	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
138	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
139	C₄⋊Q₈	—	2	1	no	—
140	#127	—	2	1	no	—
141	#124	—	2	2	no	—
142	#121	—	4	1	no	—
143	#121	—	4	1	no	—
144	C₄×D₄	—	4	1	no	—
145	C₄×D₄	—	4	1	no	—
146	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
147	C₂×C₁₆	—	2	2	no	—
148	C₄⋊C₈	—	2	2	no	—
149	C₂²⋊C₈	—	4	1	no	—
150	#97	—	4	1	no	—
151	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
152	C₄×C₈	C₅×D₄	1	1	yes	characteristic
153	C₄×C₈	C₅×D₄	1	1	yes	characteristic
154	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
155	C₂²×C₅	—	2	1	no	—
156	C₂²×C₅	—	2	1	no	—
157	C₂²×C₅	—	2	1	no	—
158	C₂²×C₅	—	8	2	no	—
159	C₂²×C₅	—	8	2	no	—
160	C₂²×C₅	—	8	2	no	—
161	C₂²×C₅	C₂×#102	1	1	yes	characteristic
162	C₄×C₅	—	2	1	no	—
163	C₄×C₅	—	2	1	no	—
164	C₄×C₅	—	2	1	no	—
165	C₄×C₅	—	2	1	no	—
166	C₄×C₅	—	8	2	no	—
167	C₄×C₅	C₂×#100	1	1	yes	characteristic
168	C₄×C₅	#418	1	1	yes	characteristic
169	C₄×C₅	#508	1	2	yes	—
170	#41	—	4	4	no	—
171	#41	—	4	4	no	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	—	4	2	no	—
175	C₂×D₄	—	4	1	no	—
176	C₂×D₄	—	4	1	no	—
177	C₂²×C₄	—	4	2	no	—
178	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
180	C₂²×C₄	C₅×SD₁₆	1	1	yes	characteristic
181	Q₁₆	—	4	2	no	—
182	Q₁₆	—	4	2	no	—
183	SD₁₆	—	4	4	no	—
184	SD₁₆	—	4	4	no	—
185	D₈	—	4	2	no	—
186	D₈	—	4	2	no	—
187	C₂×C₈	—	2	2	no	—
188	C₂×C₈	—	2	2	no	—
189	C₂×C₈	—	4	2	no	—
190	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
193	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
194	C₄⋊C₄	—	4	1	no	—
195	C₄⋊C₄	—	4	1	no	—
196	C₂²⋊C₄	—	4	2	no	—
197	C₂²⋊C₄	—	4	2	no	—
198	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
199	C₄²	C₅×D₈	1	1	yes	characteristic
200	C₄²	C₅×SD₁₆	1	1	yes	characteristic
201	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
202	C₁₆	—	4	2	no	—
203	C₂×C₅	—	4	1	no	—
204	C₂×C₅	—	16	2	no	—
205	C₂×C₅	#1545	1	1	yes	characteristic
206	C₂×C₅	#2138	1	1	yes	characteristic
207	C₂×C₅	#2148	1	1	yes	characteristic
208	C₂³	—	4	2	no	—
209	C₂³	C₅×#102	1	1	yes	characteristic
210	Q₈	—	4	2	no	—
211	Q₈	—	4	2	no	—
212	D₄	—	4	2	no	—
213	D₄	—	4	2	no	—
214	D₄	—	8	2	no	—
215	D₄	—	8	4	no	—
216	D₄	—	8	2	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	2	2	no	—
220	C₂×C₄	—	4	1	no	—
221	C₂×C₄	—	4	2	no	—
222	C₂×C₄	—	8	4	no	—
223	C₂×C₄	C₅×#102	1	1	yes	characteristic
224	C₂×C₄	C₅×#102	1	1	yes	characteristic
225	C₂×C₄	C₅×#102	1	1	yes	characteristic
226	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
228	C₂×C₄	C₂×C₅×SD₁₆	1	1	yes	characteristic
229	C₈	—	2	1	no	—
230	C₈	—	2	1	no	—
231	C₈	—	8	2	no	—
232	C₈	C₅×#100	1	2	yes	—
233	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
234	C₅	#11963	1	1	yes	characteristic, direct product factor, Sylow
235	C₂²	—	2	1	no	—
236	C₂²	—	2	1	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	8	2	no	—
239	C₂²	—	8	2	no	—
240	C₂²	—	8	2	no	—
241	C₂²	C₂×C₅×#102	1	1	yes	characteristic
242	C₄	—	2	1	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	1	no	—
246	C₄	—	8	2	no	—
247	C₄	C₂×C₅×#100	1	1	yes	characteristic
248	C₄	C₅×#418	1	1	yes	characteristic
249	C₄	C₅×#508	1	2	yes	—
250	C₂	—	4	1	no	—
251	C₂	—	16	2	no	—
252	C₂	C₅×#1545	1	1	yes	characteristic
253	C₂	C₅×#2138	1	1	yes	characteristic
254	C₂	C₅×#2148	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₅
Frattini, cosocle	C₄×C₈	C₂³×C₅
prime radical	C₅×#3147	C₂
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2162	C₂	semidirect
3. C₅×#1568	C₂	semidirect
4. C₅×#1362	C₂	semidirect
5. C₅×#1361	C₂	semidirect
21. #11963	C₅	direct (N × H)
50. #2162	C₂×C₅	semidirect
51. #1568	C₂×C₅	semidirect
52. #1362	C₂×C₅	semidirect
53. #1361	C₂×C₅	semidirect
234. C₅	#11963	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3147	2
C₅×#2162	2
C₅×#1568	2
C₅×#1362	2
C₅×#1361	2
#11963	5

Subgroups — C5×#11963 #11934683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11963 #11934683