Subgroups — C₂×C₅×#1366 #11934675

Order 1280.

294 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#499	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#364	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#364	C₂	1	1	yes	maximal, characteristic
4	C₅×#1366	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₅×#125	C₄	1	2	yes	—
6	C₂×C₅×M₃₂	—	2	1	no	—
7	C₂×C₅×M₃₂	—	2	1	no	—
8	C₅×#499	—	2	1	no	—
9	C₅×#499	—	2	1	no	—
10	C₅×#499	C₄	1	2	yes	—
11	C₅×#499	C₂²	1	2	yes	—
12	C₂×C₅×#107	—	2	1	no	—
13	C₂×C₅×#106	—	2	1	no	—
14	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#364	—	2	1	no	—
16	C₅×#364	—	2	1	no	—
17	C₅×#364	C₂²	1	2	yes	—
18	C₅×#364	C₂²	1	2	yes	—
19	C₂×#1366	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
20	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
21	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
22	C₅×#125	—	2	2	no	—
23	C₅×#125	—	4	2	no	—
24	C₅×#125	C₂×C₄	1	4	yes	—
25	C₂×C₅×C₄⋊C₄	—	2	2	no	—
26	C₂×C₅×C₄⋊C₄	—	4	2	no	—
27	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
28	C₅×M₃₂	—	2	2	no	—
29	C₅×M₃₂	—	2	2	no	—
30	C₅×M₃₂	—	4	1	no	—
31	C₅×M₃₂	—	4	1	no	—
32	C₂×C₅×C₁₆	—	4	1	no	—
33	C₂×C₅×C₁₆	—	4	1	no	—
34	C₅×#107	—	2	2	no	—
35	C₅×#107	—	2	2	no	—
36	C₅×#106	—	2	2	no	—
37	C₅×#106	—	2	2	no	—
38	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
39	C₄×C₅×C₈	D₄	1	1	yes	characteristic
40	C₄×C₅×C₈	D₄	1	1	yes	characteristic
41	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
42	C₂×#499	C₂×C₅	1	1	yes	characteristic
43	C₂×#364	C₂×C₅	1	1	yes	characteristic
44	C₂×#364	C₂×C₅	1	1	yes	characteristic
45	#1366	C₂×C₅	1	4	yes	direct product factor
46	C₂²×C₄×C₅	—	2	1	no	—
47	C₂²×C₄×C₅	—	4	2	no	—
48	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₅×C₈	SD₁₆	1	1	yes	characteristic
52	C₂×C₅×C₈	SD₁₆	1	1	yes	characteristic
53	C₂×C₅×C₈	SD₁₆	1	1	yes	characteristic
54	C₂×C₅×C₈	SD₁₆	1	1	yes	characteristic
55	C₂×C₅×C₈	Q₁₆	1	1	yes	characteristic
56	C₂×C₅×C₈	Q₁₆	1	1	yes	characteristic
57	C₂×C₅×C₈	Q₁₆	1	1	yes	characteristic
58	C₂×C₅×C₈	Q₁₆	1	1	yes	characteristic
59	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
60	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
61	C₅×C₄⋊C₄	—	2	4	no	—
62	C₅×C₄⋊C₄	—	4	4	no	—
63	C₅×C₄⋊C₄	—	4	4	no	—
64	C₅×C₄⋊C₄	—	4	2	no	—
65	C₄²×C₅	—	2	1	no	—
66	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
67	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
68	C₅×C₁₆	—	4	2	no	—
69	C₅×C₁₆	—	4	2	no	—
70	C₂×#125	C₄×C₅	1	2	yes	—
71	C₂×M₃₂	—	2	1	no	—
72	C₂×M₃₂	—	2	1	no	—
73	#499	—	2	1	no	—
74	#499	—	2	1	no	—
75	#499	C₄×C₅	1	2	yes	—
76	#499	C₂²×C₅	1	2	yes	—
77	C₂×#107	—	2	1	no	—
78	C₂×#106	—	2	1	no	—
79	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
80	#364	—	2	1	no	—
81	#364	—	2	1	no	—
82	#364	C₂²×C₅	1	2	yes	—
83	#364	C₂²×C₅	1	2	yes	—
84	C₂³×C₅	#100	1	1	yes	characteristic
85	C₂×C₄×C₅	—	2	1	no	—
86	C₂×C₄×C₅	—	2	1	no	—
87	C₂×C₄×C₅	—	4	2	no	—
88	C₂×C₄×C₅	—	4	4	no	—
89	C₂×C₄×C₅	—	8	4	no	—
90	C₂×C₄×C₅	#100	1	1	yes	characteristic
91	C₂×C₄×C₅	#103	1	1	yes	characteristic
92	C₂×C₄×C₅	#103	1	1	yes	characteristic
93	C₂×C₄×C₅	#103	1	1	yes	characteristic
94	C₂×C₄×C₅	#103	1	1	yes	characteristic
95	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₅×C₈	#103	1	1	yes	characteristic
97	C₅×C₈	#103	1	1	yes	characteristic
98	C₅×C₈	#103	1	1	yes	characteristic
99	C₅×C₈	#103	1	1	yes	characteristic
100	C₅×C₈	C₂×SD₁₆	1	1	yes	characteristic
101	C₅×C₈	C₂×SD₁₆	1	1	yes	characteristic
102	C₅×C₈	C₂×Q₁₆	1	1	yes	characteristic
103	C₅×C₈	C₂×Q₁₆	1	1	yes	characteristic
104	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
105	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
106	#125	—	2	2	no	—
107	#125	—	4	2	no	—
108	#125	C₂×C₄×C₅	1	4	yes	—
109	C₂×C₄⋊C₄	—	2	2	no	—
110	C₂×C₄⋊C₄	—	4	2	no	—
111	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
112	M₃₂	—	2	2	no	—
113	M₃₂	—	2	2	no	—
114	M₃₂	—	4	1	no	—
115	M₃₂	—	4	1	no	—
116	C₂×C₁₆	—	4	1	no	—
117	C₂×C₁₆	—	4	1	no	—
118	#107	—	2	2	no	—
119	#107	—	2	2	no	—
120	#106	—	2	2	no	—
121	#106	—	2	2	no	—
122	C₄×C₈	C₂×C₄×C₅	1	1	yes	characteristic
123	C₄×C₈	C₅×D₄	1	1	yes	characteristic
124	C₄×C₈	C₅×D₄	1	1	yes	characteristic
125	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
126	C₂²×C₅	—	2	2	no	—
127	C₂²×C₅	#333	1	1	yes	characteristic
128	C₂²×C₅	#333	1	1	yes	characteristic
129	C₂²×C₅	C₂×#100	1	1	yes	characteristic
130	C₄×C₅	—	4	1	no	—
131	C₄×C₅	—	4	1	no	—
132	C₄×C₅	—	8	4	no	—
133	C₄×C₅	#333	1	1	yes	characteristic
134	C₄×C₅	#333	1	1	yes	characteristic
135	C₄×C₅	C₂×#103	1	1	yes	characteristic
136	C₄×C₅	C₂×#103	1	1	yes	characteristic
137	C₂²×C₄	—	2	1	no	—
138	C₂²×C₄	—	4	2	no	—
139	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₈	C₅×SD₁₆	1	1	yes	characteristic
143	C₂×C₈	C₅×SD₁₆	1	1	yes	characteristic
144	C₂×C₈	C₅×SD₁₆	1	1	yes	characteristic
145	C₂×C₈	C₅×SD₁₆	1	1	yes	characteristic
146	C₂×C₈	C₅×Q₁₆	1	1	yes	characteristic
147	C₂×C₈	C₅×Q₁₆	1	1	yes	characteristic
148	C₂×C₈	C₅×Q₁₆	1	1	yes	characteristic
149	C₂×C₈	C₅×Q₁₆	1	1	yes	characteristic
150	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
151	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	4	4	no	—
154	C₄⋊C₄	—	4	4	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₄²	—	2	1	no	—
157	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
158	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
159	C₁₆	—	4	2	no	—
160	C₁₆	—	4	2	no	—
161	C₂×C₅	—	2	1	no	—
162	C₂×C₅	—	2	1	no	—
163	C₂×C₅	#1366	1	2	yes	direct product factor
164	C₂×C₅	C₂×#333	1	1	yes	characteristic
165	C₂³	C₅×#100	1	1	yes	characteristic
166	C₂×C₄	—	2	1	no	—
167	C₂×C₄	—	2	1	no	—
168	C₂×C₄	—	4	2	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	8	4	no	—
171	C₂×C₄	C₅×#100	1	1	yes	characteristic
172	C₂×C₄	C₅×#103	1	1	yes	characteristic
173	C₂×C₄	C₅×#103	1	1	yes	characteristic
174	C₂×C₄	C₅×#103	1	1	yes	characteristic
175	C₂×C₄	C₅×#103	1	1	yes	characteristic
176	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
177	C₈	C₅×#103	1	1	yes	characteristic
178	C₈	C₅×#103	1	1	yes	characteristic
179	C₈	C₅×#103	1	1	yes	characteristic
180	C₈	C₅×#103	1	1	yes	characteristic
181	C₈	C₂×C₅×SD₁₆	1	1	yes	characteristic
182	C₈	C₂×C₅×SD₁₆	1	1	yes	characteristic
183	C₈	C₂×C₅×Q₁₆	1	1	yes	characteristic
184	C₈	C₂×C₅×Q₁₆	1	1	yes	characteristic
185	C₅	C₂×#1366	1	1	yes	characteristic, direct product factor, Sylow
186	C₂²	—	2	2	no	—
187	C₂²	C₅×#333	1	1	yes	characteristic
188	C₂²	C₅×#333	1	1	yes	characteristic
189	C₂²	C₂×C₅×#100	1	1	yes	characteristic
190	C₄	—	4	1	no	—
191	C₄	—	4	1	no	—
192	C₄	—	8	4	no	—
193	C₄	C₅×#333	1	1	yes	characteristic
194	C₄	C₅×#333	1	1	yes	characteristic
195	C₄	C₂×C₅×#103	1	1	yes	characteristic
196	C₄	C₂×C₅×#103	1	1	yes	characteristic
197	C₂	—	2	1	no	—
198	C₂	—	2	1	no	—
199	C₂	C₅×#1366	1	2	yes	direct product factor
200	C₂	C₂×C₅×#333	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	#333
commutator	C₄²	C₂²×C₄×C₅
Frattini, cosocle	C₄×C₈	C₂³×C₅
prime radical	C₂³×C₅	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂²×C₄×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1366	C₂	direct (N × H)
19. C₂×#1366	C₅	direct (N × H)
45. #1366	C₂×C₅	direct (N × H)
163. C₂×C₅	#1366	direct (N × H)
185. C₅	C₂×#1366	direct (N × H)
199. C₂	C₅×#1366	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×#499	2
C₂×C₅×#364	2
C₅×#1366	2
C₂×#1366	5

Subgroups — C2×C5×#1366 #11934675

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1366 #11934675