Subgroups — C₂×C₅×#1295 #11930747

Order 1280.

830 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#97	C₂	1	2	yes	maximal
2	C₂×C₅×#382	C₂	1	1	yes	maximal, characteristic
3	C₅×#1295	C₂	1	4	yes	maximal, direct product factor
4	C₂³×C₅×C₈	—	2	2	no	—
5	C₂²×C₅×C₄⋊C₄	C₄	1	2	yes	—
6	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₅×#97	—	2	2	no	—
8	C₂×C₅×#97	—	2	4	no	—
9	C₂×C₅×#97	C₄	1	8	yes	complemented
10	C₂×C₅×#97	C₂²	1	4	yes	—
11	C₅×#382	—	2	2	no	—
12	C₅×#382	C₄	1	2	yes	—
13	C₅×#382	C₂²	1	2	yes	—
14	C₂×C₅×#95	—	2	2	no	—
15	C₂×#1295	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
16	C₂³×C₄×C₅	—	2	2	no	—
17	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₅	D₄	1	2	yes	—
19	C₂²×C₅×C₈	—	2	16	no	—
20	C₂²×C₅×C₈	—	2	8	no	—
21	C₂²×C₅×C₈	—	2	4	no	—
22	C₂×C₅×C₄⋊C₄	—	2	2	no	—
23	C₂×C₅×C₄⋊C₄	—	4	4	no	—
24	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
25	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₅	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₅	D₄	1	2	yes	—
28	C₂×C₄²×C₅	D₄	1	2	yes	—
29	C₂×C₄²×C₅	Q₈	1	2	yes	—
30	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
31	C₅×#97	—	2	8	no	—
32	C₅×#97	—	2	4	no	—
33	C₅×#97	C₂×C₄	1	8	yes	complemented
34	C₅×#95	—	2	4	no	—
35	C₅×#95	—	2	4	no	—
36	C₂²×#97	C₂×C₅	1	2	yes	—
37	C₂×#382	C₂×C₅	1	1	yes	characteristic
38	#1295	C₂×C₅	1	4	yes	direct product factor
39	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
40	C₂²×C₄×C₅	—	2	2	no	—
41	C₂²×C₄×C₅	—	2	2	no	—
42	C₂²×C₄×C₅	—	2	8	no	—
43	C₂²×C₄×C₅	—	2	4	no	—
44	C₂²×C₄×C₅	—	4	4	no	—
45	C₂²×C₄×C₅	—	4	8	no	—
46	C₂²×C₄×C₅	C₄²	1	2	yes	—
47	C₂²×C₄×C₅	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₅	C₂²⋊C₄	1	4	yes	—
50	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
51	C₂²×C₄×C₅	C₄⋊C₄	1	2	yes	—
52	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
54	C₂×C₅×C₈	—	2	32	no	—
55	C₂×C₅×C₈	—	2	16	no	—
56	C₂×C₅×C₈	—	2	8	no	—
57	C₅×C₄⋊C₄	—	4	4	no	—
58	C₅×C₄⋊C₄	—	4	4	no	—
59	C₄²×C₅	C₄²	1	2	yes	—
60	C₄²×C₅	C₂²⋊C₄	1	4	yes	—
61	C₄²×C₅	C₄⋊C₄	1	2	yes	—
62	C₄²×C₅	C₄⋊C₄	1	4	yes	—
63	C₄²×C₅	C₂²×C₄	1	2	yes	—
64	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
66	C₂³×C₈	—	2	2	no	—
67	C₂²×C₄⋊C₄	C₄×C₅	1	2	yes	—
68	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
69	C₂×#97	—	2	2	no	—
70	C₂×#97	—	2	4	no	—
71	C₂×#97	C₄×C₅	1	8	yes	complemented
72	C₂×#97	C₂²×C₅	1	4	yes	—
73	#382	—	2	2	no	—
74	#382	C₄×C₅	1	2	yes	—
75	#382	C₂²×C₅	1	2	yes	—
76	C₂×#95	—	2	2	no	—
77	C₂³×C₅	#95	1	2	yes	—
78	C₂³×C₅	#100	1	2	yes	—
79	C₂³×C₅	#101	1	2	yes	—
80	C₂³×C₅	#104	1	8	yes	—
81	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₅	—	2	8	no	—
83	C₂×C₄×C₅	—	2	8	no	—
84	C₂×C₄×C₅	—	2	4	no	—
85	C₂×C₄×C₅	—	2	4	no	—
86	C₂×C₄×C₅	—	2	1	no	—
87	C₂×C₄×C₅	—	2	1	no	—
88	C₂×C₄×C₅	—	2	1	no	—
89	C₂×C₄×C₅	—	2	1	no	—
90	C₂×C₄×C₅	—	2	4	no	—
91	C₂×C₄×C₅	—	2	4	no	—
92	C₂×C₄×C₅	—	4	4	no	—
93	C₂×C₄×C₅	—	4	8	no	—
94	C₂×C₄×C₅	—	8	8	no	—
95	C₂×C₄×C₅	#95	1	4	yes	—
96	C₂×C₄×C₅	#95	1	2	yes	—
97	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
98	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
99	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
100	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
101	C₅×C₈	—	2	16	no	—
102	C₂³×C₄	—	2	2	no	—
103	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
104	C₂³×C₄	C₅×D₄	1	2	yes	—
105	C₂²×C₈	—	2	16	no	—
106	C₂²×C₈	—	2	8	no	—
107	C₂²×C₈	—	2	4	no	—
108	C₂×C₄⋊C₄	—	2	2	no	—
109	C₂×C₄⋊C₄	—	4	4	no	—
110	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
111	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
112	C₂×C₄²	C₂×C₄×C₅	1	4	yes	—
113	C₂×C₄²	C₅×D₄	1	2	yes	—
114	C₂×C₄²	C₅×D₄	1	2	yes	—
115	C₂×C₄²	C₅×Q₈	1	2	yes	—
116	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
117	#97	—	2	8	no	—
118	#97	—	2	4	no	—
119	#97	C₂×C₄×C₅	1	8	yes	complemented
120	#95	—	2	4	no	—
121	#95	—	2	4	no	—
122	C₂²×C₅	#329	1	8	yes	—
123	C₂²×C₅	#330	1	8	yes	—
124	C₂²×C₅	#339	1	8	yes	—
125	C₂²×C₅	#343	1	4	yes	—
126	C₂²×C₅	C₂×#95	1	1	yes	characteristic
127	C₂²×C₅	C₂×#100	1	1	yes	characteristic
128	C₂²×C₅	C₂×#101	1	1	yes	characteristic
129	C₂²×C₅	C₂×#104	1	4	yes	—
130	C₄×C₅	—	2	2	no	—
131	C₄×C₅	—	2	4	no	—
132	C₄×C₅	—	2	2	no	—
133	C₄×C₅	—	2	2	no	—
134	C₄×C₅	—	2	1	no	—
135	C₄×C₅	—	2	1	no	—
136	C₄×C₅	—	8	4	no	—
137	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
138	C₂²×C₄	—	2	2	no	—
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	—	2	8	no	—
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	—	4	4	no	—
143	C₂²×C₄	—	4	8	no	—
144	C₂²×C₄	C₄²×C₅	1	2	yes	—
145	C₂²×C₄	C₅×C₂²⋊C₄	1	4	yes	—
146	C₂²×C₄	C₅×C₂²⋊C₄	1	2	yes	—
147	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
149	C₂²×C₄	C₅×C₄⋊C₄	1	2	yes	—
150	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
152	C₂×C₈	—	2	32	no	—
153	C₂×C₈	—	2	16	no	—
154	C₂×C₈	—	2	8	no	—
155	C₄⋊C₄	—	4	4	no	—
156	C₄⋊C₄	—	4	4	no	—
157	C₄²	C₄²×C₅	1	2	yes	—
158	C₄²	C₅×C₂²⋊C₄	1	4	yes	—
159	C₄²	C₅×C₄⋊C₄	1	4	yes	—
160	C₄²	C₅×C₄⋊C₄	1	2	yes	—
161	C₄²	C₂²×C₄×C₅	1	2	yes	—
162	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
163	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
164	C₂×C₅	#1295	1	8	yes	direct product factor
165	C₂×C₅	C₂×#329	1	2	yes	—
166	C₂×C₅	C₂×#330	1	2	yes	—
167	C₂×C₅	C₂×#339	1	2	yes	—
168	C₂×C₅	C₂×#343	1	1	yes	characteristic
169	C₂³	C₅×#95	1	2	yes	—
170	C₂³	C₅×#100	1	2	yes	—
171	C₂³	C₅×#101	1	2	yes	—
172	C₂³	C₅×#104	1	8	yes	—
173	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	8	no	—
177	C₂×C₄	—	2	8	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	4	4	no	—
185	C₂×C₄	—	4	8	no	—
186	C₂×C₄	—	8	8	no	—
187	C₂×C₄	C₅×#95	1	4	yes	—
188	C₂×C₄	C₅×#95	1	2	yes	—
189	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
190	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
191	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
192	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
193	C₈	—	2	16	no	—
194	C₅	C₂×#1295	1	1	yes	characteristic, direct product factor, Sylow
195	C₂²	C₅×#329	1	8	yes	—
196	C₂²	C₅×#330	1	8	yes	—
197	C₂²	C₅×#339	1	8	yes	—
198	C₂²	C₅×#343	1	4	yes	—
199	C₂²	C₂×C₅×#95	1	1	yes	characteristic
200	C₂²	C₂×C₅×#100	1	1	yes	characteristic
201	C₂²	C₂×C₅×#101	1	1	yes	characteristic
202	C₂²	C₂×C₅×#104	1	4	yes	—
203	C₄	—	2	2	no	—
204	C₄	—	2	2	no	—
205	C₄	—	2	4	no	—
206	C₄	—	2	1	no	—
207	C₄	—	2	1	no	—
208	C₄	—	2	2	no	—
209	C₄	—	8	4	no	—
210	C₂	C₅×#1295	1	8	yes	direct product factor
211	C₂	C₂×C₅×#329	1	2	yes	—
212	C₂	C₂×C₅×#330	1	2	yes	—
213	C₂	C₂×C₅×#339	1	2	yes	—
214	C₂	C₂×C₅×#343	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₅	C₂²⋊C₄
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₅×#1295	C₂	direct (N × H)
9. C₂×C₅×#97	C₄	semidirect
15. C₂×#1295	C₅	direct (N × H)
33. C₅×#97	C₂×C₄	semidirect
38. #1295	C₂×C₅	direct (N × H)
71. C₂×#97	C₄×C₅	semidirect
119. #97	C₂×C₄×C₅	semidirect
164. C₂×C₅	#1295	direct (N × H)
194. C₅	C₂×#1295	direct (N × H)
210. C₂	C₅×#1295	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₅×#97	2
C₂×C₅×#382	2
C₅×#1295	2
C₂×#1295	5

Subgroups — C2×C5×#1295 #11930747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1295 #11930747