Subgroups — C₅×#9819 #11932539

Order 1280.

526 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#498	C₂	1	1	yes	maximal, characteristic
2	C₅×#1990	C₂	1	2	yes	maximal
3	C₅×#1956	C₂	1	2	yes	maximal
4	C₅×#1844	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×C₈²	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
7	C₅×#498	—	2	2	no	—
8	C₅×#498	C₄	1	4	yes	complemented
9	C₂×C₅×#106	—	2	2	no	—
10	C₂×C₅×#106	—	2	2	no	—
11	C₂×C₅×#103	—	2	4	no	—
12	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
14	C₅×#384	C₂²	1	1	yes	characteristic
15	C₅×#384	C₂²	1	1	yes	characteristic
16	C₅×#340	—	2	4	no	—
17	C₅×C₈²	—	2	2	no	—
18	#9819	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
19	C₂²×C₅×Q₈	—	2	2	no	—
20	C₂²×C₅×C₈	D₄	1	4	yes	—
21	C₂²×C₅×C₈	D₄	1	2	yes	—
22	C₅×C₄⋊Q₈	—	2	2	no	—
23	C₅×C₄⋊Q₈	—	2	2	no	—
24	C₅×C₄⋊Q₈	—	2	2	no	—
25	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
26	C₂×C₅×C₄⋊C₄	—	2	2	no	—
27	C₂×C₅×C₄⋊C₄	—	2	2	no	—
28	C₂×C₅×C₄⋊C₄	—	2	2	no	—
29	C₂×C₅×C₄⋊C₄	—	2	2	no	—
30	C₂×C₅×C₄⋊C₄	—	2	1	no	—
31	C₂×C₅×C₄⋊C₄	—	2	1	no	—
32	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
33	C₅×#106	—	2	8	no	—
34	C₅×#106	—	4	4	no	—
35	C₅×#103	—	4	8	no	—
36	C₄×C₅×C₈	—	2	2	no	—
37	C₄×C₅×C₈	—	2	2	no	—
38	C₄×C₅×C₈	C₂×C₄	1	2	yes	—
39	C₄×C₅×C₈	D₄	1	2	yes	—
40	C₂×#498	C₂×C₅	1	1	yes	characteristic
41	#1990	C₂×C₅	1	2	yes	—
42	#1956	C₂×C₅	1	2	yes	—
43	#1844	C₂×C₅	1	1	yes	characteristic
44	C₂×C₈²	C₂×C₅	1	1	yes	characteristic
45	C₂×C₅×Q₈	—	2	4	no	—
46	C₂×C₅×Q₈	—	4	2	no	—
47	C₂×C₅×Q₈	—	4	4	no	—
48	C₂×C₅×Q₈	—	4	4	no	—
49	C₂²×C₄×C₅	—	4	2	no	—
50	C₂²×C₄×C₅	—	4	1	no	—
51	C₂²×C₄×C₅	—	4	1	no	—
52	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
53	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
54	C₂×C₅×C₈	—	2	4	no	—
55	C₂×C₅×C₈	—	2	4	no	—
56	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
57	C₂×C₅×C₈	SD₁₆	1	8	yes	—
58	C₂×C₅×C₈	SD₁₆	1	4	yes	—
59	C₂×C₅×C₈	Q₁₆	1	4	yes	—
60	C₅×C₄⋊C₄	—	2	4	no	—
61	C₅×C₄⋊C₄	—	2	4	no	—
62	C₅×C₄⋊C₄	—	4	2	no	—
63	C₅×C₄⋊C₄	—	4	2	no	—
64	C₅×C₄⋊C₄	—	4	4	no	—
65	C₅×C₄⋊C₄	—	4	2	no	—
66	C₅×C₄⋊C₄	—	4	2	no	—
67	C₅×C₄⋊C₄	—	4	4	no	—
68	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
69	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
70	C₄²×C₅	#41	1	2	yes	—
71	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
72	#498	—	2	2	no	—
73	#498	C₄×C₅	1	4	yes	complemented
74	C₂×#106	—	2	2	no	—
75	C₂×#106	—	2	2	no	—
76	C₂×#103	—	2	4	no	—
77	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
78	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
79	#384	C₂²×C₅	1	1	yes	characteristic
80	#384	C₂²×C₅	1	1	yes	characteristic
81	#340	—	2	4	no	—
82	C₈²	—	2	2	no	—
83	C₂³×C₅	#127	1	1	yes	characteristic
84	C₅×Q₈	—	4	8	no	—
85	C₅×Q₈	—	8	4	no	—
86	C₂×C₄×C₅	—	4	4	no	—
87	C₂×C₄×C₅	—	8	2	no	—
88	C₂×C₄×C₅	—	8	2	no	—
89	C₂×C₄×C₅	—	8	1	no	—
90	C₂×C₄×C₅	—	8	2	no	—
91	C₂×C₄×C₅	—	8	1	no	—
92	C₂×C₄×C₅	—	8	2	no	—
93	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
95	C₂×C₄×C₅	#121	1	2	yes	—
96	C₂×C₄×C₅	#124	1	1	yes	characteristic
97	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
98	C₂×C₄×C₅	C₂×SD₁₆	1	4	yes	—
99	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
100	C₂×C₄×C₅	#135	1	4	yes	—
101	C₅×C₈	—	2	8	no	—
102	C₅×C₈	#103	1	8	yes	complemented
103	C₂²×Q₈	—	2	2	no	—
104	C₂²×C₈	C₅×D₄	1	4	yes	—
105	C₂²×C₈	C₅×D₄	1	2	yes	—
106	C₄⋊Q₈	—	2	2	no	—
107	C₄⋊Q₈	—	2	2	no	—
108	C₄⋊Q₈	—	2	2	no	—
109	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
110	C₂×C₄⋊C₄	—	2	2	no	—
111	C₂×C₄⋊C₄	—	2	2	no	—
112	C₂×C₄⋊C₄	—	2	2	no	—
113	C₂×C₄⋊C₄	—	2	2	no	—
114	C₂×C₄⋊C₄	—	2	1	no	—
115	C₂×C₄⋊C₄	—	2	1	no	—
116	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
117	#106	—	2	8	no	—
118	#106	—	4	4	no	—
119	#103	—	4	8	no	—
120	C₄×C₈	—	2	2	no	—
121	C₄×C₈	—	2	2	no	—
122	C₄×C₈	C₂×C₄×C₅	1	2	yes	—
123	C₄×C₈	C₅×D₄	1	2	yes	—
124	C₂²×C₅	#390	1	1	yes	characteristic
125	C₂²×C₅	#492	1	1	yes	characteristic
126	C₂²×C₅	#492	1	2	yes	—
127	C₂²×C₅	#494	1	1	yes	characteristic
128	C₂²×C₅	#495	1	2	yes	—
129	C₄×C₅	—	8	4	no	—
130	C₄×C₅	—	16	1	no	—
131	C₄×C₅	—	16	1	no	—
132	C₄×C₅	C₂×#103	1	2	yes	—
133	C₄×C₅	C₄×SD₁₆	1	4	yes	—
134	C₄×C₅	#465	1	4	yes	—
135	C₄×C₅	#487	1	2	yes	—
136	C₂×Q₈	—	2	4	no	—
137	C₂×Q₈	—	4	2	no	—
138	C₂×Q₈	—	4	4	no	—
139	C₂×Q₈	—	4	4	no	—
140	C₂²×C₄	—	4	2	no	—
141	C₂²×C₄	—	4	1	no	—
142	C₂²×C₄	—	4	1	no	—
143	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
144	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
145	C₂×C₈	—	2	4	no	—
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
148	C₂×C₈	C₅×SD₁₆	1	8	yes	—
149	C₂×C₈	C₅×SD₁₆	1	4	yes	—
150	C₂×C₈	C₅×Q₁₆	1	4	yes	—
151	C₄⋊C₄	—	2	4	no	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	4	2	no	—
154	C₄⋊C₄	—	4	2	no	—
155	C₄⋊C₄	—	4	4	no	—
156	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	—	4	4	no	—
159	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
160	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
161	C₄²	C₅×#41	1	2	yes	—
162	C₂×C₅	#1705	1	1	yes	characteristic
163	C₂×C₅	#1707	1	2	yes	—
164	C₂×C₅	#1708	1	1	yes	characteristic
165	C₂×C₅	#1956	1	1	yes	characteristic
166	C₂×C₅	#1968	1	2	yes	—
167	C₂³	C₅×#127	1	1	yes	characteristic
168	Q₈	—	4	8	no	—
169	Q₈	—	8	4	no	—
170	C₂×C₄	—	4	4	no	—
171	C₂×C₄	—	8	2	no	—
172	C₂×C₄	—	8	2	no	—
173	C₂×C₄	—	8	1	no	—
174	C₂×C₄	—	8	2	no	—
175	C₂×C₄	—	8	1	no	—
176	C₂×C₄	—	8	2	no	—
177	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
179	C₂×C₄	C₅×#121	1	2	yes	—
180	C₂×C₄	C₅×#124	1	1	yes	characteristic
181	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
182	C₂×C₄	C₂×C₅×SD₁₆	1	4	yes	—
183	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
184	C₂×C₄	C₅×#135	1	4	yes	—
185	C₈	—	2	8	no	—
186	C₈	C₅×#103	1	8	yes	complemented
187	C₅	#9819	1	1	yes	characteristic, direct product factor, Sylow
188	C₂²	C₅×#390	1	1	yes	characteristic
189	C₂²	C₅×#492	1	1	yes	characteristic
190	C₂²	C₅×#492	1	2	yes	—
191	C₂²	C₅×#494	1	1	yes	characteristic
192	C₂²	C₅×#495	1	2	yes	—
193	C₄	—	8	4	no	—
194	C₄	—	16	1	no	—
195	C₄	—	16	1	no	—
196	C₄	C₂×C₅×#103	1	2	yes	—
197	C₄	C₄×C₅×SD₁₆	1	4	yes	—
198	C₄	C₅×#465	1	4	yes	—
199	C₄	C₅×#487	1	2	yes	—
200	C₂	C₅×#1705	1	1	yes	characteristic
201	C₂	C₅×#1707	1	2	yes	—
202	C₂	C₅×#1708	1	1	yes	characteristic
203	C₂	C₅×#1956	1	1	yes	characteristic
204	C₂	C₅×#1968	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	#127
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₅×#498	C₄	semidirect
18. #9819	C₅	direct (N × H)
73. #498	C₄×C₅	semidirect
102. C₅×C₈	#103	semidirect
186. C₈	C₅×#103	semidirect
187. C₅	#9819	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#498	2
C₅×#1990	2
C₅×#1956	2
C₅×#1844	2
C₂×C₅×C₈²	2
#9819	5

Subgroups — C5×#9819 #11932539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#9819 #11932539