Subgroups — C₁₃×#20467 #15706806

Order 3328.

930 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#432	C₂	1	2	yes	maximal
2	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1768	C₂	1	4	yes	maximal, complemented
4	C₁₃×#1750	C₂	1	4	yes	maximal
5	C₁₃×#1745	C₂	1	2	yes	maximal, complemented
6	C₄×C₁₃×#97	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#117	C₂²	1	2	yes	—
8	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
9	C₁₃×#432	C₄	1	16	yes	complemented
10	C₂×C₁₃×C₄⋊C₈	C₂²	1	4	yes	—
11	C₂×C₁₃×C₂²⋊C₈	C₂²	1	4	yes	—
12	C₂×C₁₃×#97	C₂²	1	4	yes	—
13	C₂×C₁₃×#97	C₂²	1	4	yes	—
14	C₂×C₄×C₈×C₁₃	C₂²	1	4	yes	—
15	C₄×C₁₃×C₄⋊C₄	C₄	1	4	yes	—
16	C₄×C₁₃×C₂²⋊C₄	C₄	1	4	yes	—
17	C₁₃×#376	C₂²	1	2	yes	—
18	C₄³×C₁₃	C₂²	1	1	yes	characteristic
19	C₄³×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#336	C₂²	1	8	yes	—
21	C₂³×C₄×C₁₃	C₂×C₄	1	2	yes	—
22	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂³	1	8	yes	—
24	C₁₃×#117	—	2	8	no	—
25	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
26	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
28	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂×C₄	1	8	yes	—
31	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
35	C₁₃×C₄⋊C₈	C₂×C₄	1	16	yes	—
36	C₁₃×C₂²⋊C₈	C₂×C₄	1	16	yes	—
37	C₁₃×#97	—	2	8	no	—
38	C₁₃×#97	C₂×C₄	1	16	yes	—
39	C₄×C₈×C₁₃	—	2	8	no	—
40	C₁₃×#95	C₂×C₄	1	8	yes	—
41	#20467	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	—	2	4	no	—
44	C₂²×C₄×C₁₃	—	4	4	no	—
45	C₂²×C₄×C₁₃	C₄²	1	8	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
51	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
52	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
53	C₂×C₈×C₁₃	—	2	8	no	—
54	C₂×C₈×C₁₃	—	2	8	no	—
55	C₂×C₈×C₁₃	C₂²×C₄	1	16	yes	—
56	C₁₃×C₄⋊C₄	—	2	8	no	—
57	C₁₃×C₂²⋊C₄	—	2	8	no	—
58	C₄²×C₁₃	—	2	4	no	—
59	C₄²×C₁₃	—	4	4	no	—
60	C₄²×C₁₃	—	4	4	no	—
61	C₄²×C₁₃	C₄²	1	8	yes	—
62	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
63	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
64	C₄²×C₁₃	#41	1	8	yes	—
65	C₂×#432	C₂×C₁₃	1	2	yes	—
66	C₄×#117	C₂×C₁₃	1	1	yes	characteristic
67	#1768	C₂×C₁₃	1	4	yes	complemented
68	#1750	C₂×C₁₃	1	4	yes	—
69	#1745	C₂×C₁₃	1	2	yes	complemented
70	C₄×#97	C₂×C₁₃	1	2	yes	complemented
71	C₂³×C₁₃	—	2	2	no	—
72	C₂³×C₁₃	—	2	4	no	—
73	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
74	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
75	C₂×C₄×C₁₃	—	2	2	no	—
76	C₂×C₄×C₁₃	—	2	4	no	—
77	C₂×C₄×C₁₃	—	2	8	no	—
78	C₂×C₄×C₁₃	—	2	4	no	—
79	C₂×C₄×C₁₃	—	2	8	no	—
80	C₂×C₄×C₁₃	—	2	4	no	—
81	C₂×C₄×C₁₃	—	2	8	no	—
82	C₂×C₄×C₁₃	—	4	8	no	—
83	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
84	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
85	C₂×C₄×C₁₃	C₂×C₄²	1	4	yes	—
86	C₂×C₄×C₁₃	#117	1	8	yes	—
87	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
89	C₈×C₁₃	—	2	16	no	—
90	C₂×#117	C₂²×C₁₃	1	2	yes	—
91	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
92	#432	C₄×C₁₃	1	16	yes	complemented
93	C₂×C₄⋊C₈	C₂²×C₁₃	1	4	yes	—
94	C₂×C₂²⋊C₈	C₂²×C₁₃	1	4	yes	—
95	C₂×#97	C₂²×C₁₃	1	4	yes	—
96	C₂×#97	C₂²×C₁₃	1	4	yes	—
97	C₂×C₄×C₈	C₂²×C₁₃	1	4	yes	—
98	C₄×C₄⋊C₄	C₄×C₁₃	1	4	yes	—
99	C₄×C₂²⋊C₄	C₄×C₁₃	1	4	yes	—
100	#376	C₂²×C₁₃	1	2	yes	—
101	C₄³	C₂²×C₁₃	1	1	yes	characteristic
102	C₄³	C₂²×C₁₃	1	1	yes	characteristic
103	#336	C₂²×C₁₃	1	8	yes	—
104	C₂²×C₁₃	—	2	4	no	—
105	C₂²×C₁₃	—	2	2	no	—
106	C₂²×C₁₃	—	4	4	no	—
107	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
108	C₂²×C₁₃	C₂×#117	1	2	yes	—
109	C₂²×C₁₃	#568	1	4	yes	—
110	C₄×C₁₃	—	2	4	no	—
111	C₄×C₁₃	—	2	4	no	—
112	C₄×C₁₃	—	2	8	no	—
113	C₄×C₁₃	—	2	2	no	—
114	C₄×C₁₃	—	4	4	no	—
115	C₄×C₁₃	C₄×#41	1	4	yes	—
116	C₂³×C₄	C₂×C₄×C₁₃	1	2	yes	—
117	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
118	C₂²×C₈	C₂³×C₁₃	1	8	yes	—
119	#117	—	2	8	no	—
120	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
121	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
122	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
123	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
124	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
125	C₂×C₄²	C₂×C₄×C₁₃	1	8	yes	—
126	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
127	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
128	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
129	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
130	C₄⋊C₈	C₂×C₄×C₁₃	1	16	yes	—
131	C₂²⋊C₈	C₂×C₄×C₁₃	1	16	yes	—
132	#97	—	2	8	no	—
133	#97	C₂×C₄×C₁₃	1	16	yes	—
134	C₄×C₈	—	2	8	no	—
135	#95	C₂×C₄×C₁₃	1	8	yes	—
136	C₂×C₁₃	—	4	2	no	—
137	C₂×C₁₃	C₄×#117	1	1	yes	characteristic
138	C₂×C₁₃	#2873	1	2	yes	—
139	C₂×C₁₃	#2923	1	4	yes	—
140	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
141	C₂²×C₄	—	2	4	no	—
142	C₂²×C₄	—	4	4	no	—
143	C₂²×C₄	C₄²×C₁₃	1	8	yes	—
144	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
145	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
146	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
147	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
148	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
149	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
150	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
151	C₂×C₈	—	2	8	no	—
152	C₂×C₈	—	2	8	no	—
153	C₂×C₈	C₂²×C₄×C₁₃	1	16	yes	—
154	C₄⋊C₄	—	2	8	no	—
155	C₂²⋊C₄	—	2	8	no	—
156	C₄²	—	2	4	no	—
157	C₄²	—	4	4	no	—
158	C₄²	—	4	4	no	—
159	C₄²	C₄²×C₁₃	1	8	yes	—
160	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
161	C₄²	C₂²×C₄×C₁₃	1	4	yes	—
162	C₄²	C₁₃×#41	1	8	yes	—
163	C₁₃	#20467	1	1	yes	characteristic, direct product factor, Sylow
164	C₂³	—	2	2	no	—
165	C₂³	—	2	4	no	—
166	C₂³	C₂×C₄²×C₁₃	1	2	yes	—
167	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	2	8	no	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	8	no	—
173	C₂×C₄	—	2	4	no	—
174	C₂×C₄	—	2	8	no	—
175	C₂×C₄	—	4	8	no	—
176	C₂×C₄	C₂×C₄²×C₁₃	1	2	yes	—
177	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
178	C₂×C₄	C₂×C₄²×C₁₃	1	4	yes	—
179	C₂×C₄	C₁₃×#117	1	8	yes	—
180	C₂×C₄	C₂³×C₄×C₁₃	1	2	yes	—
181	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
182	C₈	—	2	16	no	—
183	C₂²	—	2	2	no	—
184	C₂²	—	2	4	no	—
185	C₂²	—	4	4	no	—
186	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
187	C₂²	C₂×C₁₃×#117	1	2	yes	—
188	C₂²	C₁₃×#568	1	4	yes	—
189	C₄	—	2	2	no	—
190	C₄	—	2	4	no	—
191	C₄	—	2	4	no	—
192	C₄	—	2	8	no	—
193	C₄	—	4	4	no	—
194	C₄	C₄×C₁₃×#41	1	4	yes	—
195	C₂	—	4	2	no	—
196	C₂	C₄×C₁₃×#117	1	1	yes	characteristic
197	C₂	C₁₃×#2873	1	2	yes	—
198	C₂	C₁₃×#2923	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#1768	C₂	semidirect
5. C₁₃×#1745	C₂	semidirect
6. C₄×C₁₃×#97	C₂	semidirect
9. C₁₃×#432	C₄	semidirect
41. #20467	C₁₃	direct (N × H)
67. #1768	C₂×C₁₃	semidirect
69. #1745	C₂×C₁₃	semidirect
70. C₄×#97	C₂×C₁₃	semidirect
92. #432	C₄×C₁₃	semidirect
163. C₁₃	#20467	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×#432	2
C₄×C₁₃×#117	2
C₁₃×#1768	2
C₁₃×#1750	2
C₁₃×#1745	2
C₄×C₁₃×#97	2
#20467	13

Subgroups — C13×#20467 #15706806

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#20467 #15706806