Subgroups — C₂×C₁₃×#1452 #15703657

Order 3328.

902 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#431	C₂	1	2	yes	maximal
2	C₂²×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1452	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₁₃×#322	C₂	1	4	yes	maximal, complemented
5	C₂³×C₈×C₁₃	C₄	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#431	C₄	1	8	yes	—
8	C₁₃×#431	C₂²	1	8	yes	—
9	C₂×C₁₃×C₄⋊C₈	C₄	1	4	yes	—
10	C₂×C₁₃×C₂²⋊C₈	C₄	1	4	yes	—
11	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	C₄	1	4	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
16	C₁₃×#322	C₂²	1	16	yes	complemented
17	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
18	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	—	2	8	no	—
20	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
21	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
29	C₁₃×C₄⋊C₈	C₂×C₄	1	16	yes	—
30	C₁₃×C₂²⋊C₈	C₂×C₄	1	16	yes	—
31	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
32	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
33	C₄×C₈×C₁₃	C₂×C₄	1	8	yes	—
34	C₄×C₈×C₁₃	C₂³	1	4	yes	—
35	C₄×C₈×C₁₃	C₂³	1	8	yes	—
36	C₂×#1452	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂⁴×C₁₃	C₄²	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	—	2	8	no	—
39	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
40	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
41	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
42	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	M₁₆	1	8	yes	—
44	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂×C₈×C₁₃	—	2	16	no	—
49	C₂×C₈×C₁₃	—	2	8	no	—
50	C₂×C₈×C₁₃	—	2	16	no	—
51	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
52	C₂×C₈×C₁₃	C₂²×C₄	1	16	yes	—
53	C₄²×C₁₃	C₄²	1	2	yes	—
54	C₄²×C₁₃	C₄²	1	4	yes	—
55	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
56	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
57	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
59	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
60	C₂×#431	C₂×C₁₃	1	2	yes	—
61	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic
62	#1452	C₂×C₁₃	1	8	yes	direct product factor
63	C₂×#322	C₂×C₁₃	1	4	yes	complemented
64	C₂³×C₁₃	—	2	4	no	—
65	C₂³×C₁₃	#97	1	4	yes	—
66	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
67	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₃	—	2	4	no	—
69	C₂×C₄×C₁₃	—	2	8	no	—
70	C₂×C₄×C₁₃	—	2	8	no	—
71	C₂×C₄×C₁₃	#97	1	8	yes	—
72	C₂×C₄×C₁₃	#97	1	4	yes	—
73	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
74	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
76	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
77	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
78	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
79	C₂×C₄×C₁₃	#131	1	8	yes	—
80	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
82	C₈×C₁₃	—	2	8	no	—
83	C₈×C₁₃	—	2	16	no	—
84	C₂³×C₈	C₄×C₁₃	1	2	yes	—
85	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
86	#431	C₄×C₁₃	1	8	yes	—
87	#431	C₂²×C₁₃	1	8	yes	—
88	C₂×C₄⋊C₈	C₄×C₁₃	1	4	yes	—
89	C₂×C₂²⋊C₈	C₄×C₁₃	1	4	yes	—
90	C₂×C₄×C₈	C₄×C₁₃	1	4	yes	—
91	C₂×C₄×C₈	C₄×C₁₃	1	2	yes	—
92	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
93	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
94	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
95	#322	C₂²×C₁₃	1	16	yes	complemented
96	C₂²×C₁₃	—	2	4	no	—
97	C₂²×C₁₃	—	2	8	no	—
98	C₂²×C₁₃	C₂×#97	1	4	yes	—
99	C₂²×C₁₃	C₂×#97	1	2	yes	—
100	C₂²×C₁₃	#405	1	4	yes	—
101	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
102	C₄×C₁₃	—	2	4	no	—
103	C₄×C₁₃	C₂×#97	1	2	yes	—
104	C₄×C₁₃	C₂×#97	1	4	yes	—
105	C₄×C₁₃	#405	1	4	yes	—
106	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
107	C₄×C₁₃	C₂×#131	1	4	yes	—
108	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
109	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
110	C₂²×C₈	—	2	8	no	—
111	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
112	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	—
113	C₂²×C₈	C₂×C₄×C₁₃	1	8	yes	—
114	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
115	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
116	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
117	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
118	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
119	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
120	C₄⋊C₈	C₂×C₄×C₁₃	1	16	yes	—
121	C₂²⋊C₈	C₂×C₄×C₁₃	1	16	yes	—
122	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	—
123	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	—
124	C₄×C₈	C₂×C₄×C₁₃	1	8	yes	—
125	C₄×C₈	C₂³×C₁₃	1	4	yes	—
126	C₄×C₈	C₂³×C₁₃	1	8	yes	—
127	C₂×C₁₃	—	2	4	no	—
128	C₂×C₁₃	#1452	1	4	yes	direct product factor
129	C₂×C₁₃	C₂²×#97	1	1	yes	characteristic
130	C₂×C₁₃	C₂×#405	1	2	yes	—
131	C₂⁴	C₄²×C₁₃	1	1	yes	characteristic
132	C₂²×C₄	—	2	8	no	—
133	C₂²×C₄	C₄²×C₁₃	1	2	yes	—
134	C₂²×C₄	C₄²×C₁₃	1	4	yes	—
135	C₂²×C₄	C₄²×C₁₃	1	2	yes	—
136	C₂²×C₄	C₄²×C₁₃	1	1	yes	characteristic
137	C₂²×C₄	C₁₃×M₁₆	1	8	yes	—
138	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
139	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
140	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
141	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
142	C₂×C₈	—	2	16	no	—
143	C₂×C₈	—	2	8	no	—
144	C₂×C₈	—	2	16	no	—
145	C₂×C₈	C₂²×C₄×C₁₃	1	8	yes	—
146	C₂×C₈	C₂²×C₄×C₁₃	1	16	yes	—
147	C₄²	C₄²×C₁₃	1	2	yes	—
148	C₄²	C₄²×C₁₃	1	4	yes	—
149	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
150	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
151	C₄²	C₂²×C₄×C₁₃	1	1	yes	characteristic
152	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
153	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
154	C₁₃	C₂×#1452	1	1	yes	characteristic, direct product factor, Sylow
155	C₂³	—	2	4	no	—
156	C₂³	C₁₃×#97	1	4	yes	—
157	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
158	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	2	8	no	—
162	C₂×C₄	C₁₃×#97	1	8	yes	—
163	C₂×C₄	C₁₃×#97	1	4	yes	—
164	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
165	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
166	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
167	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
168	C₂×C₄	C₂×C₁₃×M₁₆	1	8	yes	—
169	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
170	C₂×C₄	C₁₃×#131	1	8	yes	—
171	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
172	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
173	C₈	—	2	8	no	—
174	C₈	—	2	16	no	—
175	C₂²	—	2	4	no	—
176	C₂²	—	2	8	no	—
177	C₂²	C₂×C₁₃×#97	1	4	yes	—
178	C₂²	C₂×C₁₃×#97	1	2	yes	—
179	C₂²	C₁₃×#405	1	4	yes	—
180	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
181	C₄	—	2	4	no	—
182	C₄	C₂×C₁₃×#97	1	2	yes	—
183	C₄	C₂×C₁₃×#97	1	4	yes	—
184	C₄	C₁₃×#405	1	4	yes	—
185	C₄	C₂²×C₁₃×M₁₆	1	2	yes	—
186	C₄	C₂×C₁₃×#131	1	4	yes	—
187	C₂	—	2	4	no	—
188	C₂	C₁₃×#1452	1	4	yes	direct product factor
189	C₂	C₂²×C₁₃×#97	1	1	yes	characteristic
190	C₂	C₂×C₁₃×#405	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₄²	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂⁴×C₁₃	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1452	C₂	direct (N × H)
4. C₂×C₁₃×#322	C₂	semidirect
16. C₁₃×#322	C₂²	semidirect
36. C₂×#1452	C₁₃	direct (N × H)
62. #1452	C₂×C₁₃	direct (N × H)
63. C₂×#322	C₂×C₁₃	semidirect
95. #322	C₂²×C₁₃	semidirect
128. C₂×C₁₃	#1452	direct (N × H)
154. C₁₃	C₂×#1452	direct (N × H)
188. C₂	C₁₃×#1452	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×C₁₃×#431	2
C₂²×C₄×C₈×C₁₃	2
C₁₃×#1452	2
C₂×C₁₃×#322	2
C₂×#1452	13

Subgroups — C2×C13×#1452 #15703657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1452 #15703657