Subgroups — C₂×D₁₃⋊#131 #13131825

Order 1664.

1504 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×#41×D₁₃	C₂	1	1	yes	maximal, characteristic
2	D₁₃⋊#131	C₂	1	16	yes	maximal, direct product factor
3	C₂×#88240	C₂	1	2	yes	maximal, complemented
4	C₂×#88238	C₂	1	6	yes	maximal, complemented
5	C₂×D₁₃⋊M₁₆	C₂	1	3	yes	maximal, complemented
6	C₂²×D₁₃⋊C₈	C₂	1	3	yes	maximal, complemented
7	C₂×C₁₃×#41	C₄	1	1	yes	characteristic
8	#41×D₁₃	C₄	1	8	yes	—
9	#41×D₁₃	C₂²	1	8	yes	—
10	C₂×#6131	C₂²	1	1	yes	characteristic
11	C₂×Q₈×D₁₃	C₄	1	1	yes	characteristic
12	C₂×#6129	C₂²	1	3	yes	—
13	C₂×D₄×D₁₃	C₄	1	3	yes	—
14	C₂×#6127	C₄	1	3	yes	—
15	C₂²×C₄×D₁₃	C₂²	1	3	yes	—
16	C₂×#6122	C₂²	1	6	yes	complemented
17	C₂²×#1057	C₂²	1	6	yes	complemented
18	#88240	C₂²	1	16	yes	complemented
19	#88238	C₂²	1	48	yes	complemented
20	D₁₃⋊M₁₆	C₂²	1	24	yes	complemented
21	C₂×#6118	C₂²	1	6	yes	complemented
22	C₂×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×D₁₃⋊C₈	C₂²	1	3	yes	—
24	C₂×D₁₃⋊C₈	C₂²	1	24	yes	complemented
25	C₂×D₁₃⋊C₈	C₂²	1	6	yes	complemented
26	C₂³×D₁₃	C₂×C₄	1	3	yes	—
27	C₁₃×#41	C₂×C₄	1	8	yes	—
28	C₂×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×D₄×C₁₃	C₂×C₄	1	3	yes	—
30	C₂²×C₄×C₁₃	C₂×C₄	1	3	yes	—
31	C₂×C₂²⋊D₁₃	C₂×C₄	1	6	yes	—
32	C₂²×Dic₁₃	C₂³	1	3	yes	—
33	#6131	C₂×C₄	1	4	yes	—
34	#6131	C₂³	1	4	yes	—
35	Q₈×D₁₃	C₂×C₄	1	8	yes	—
36	#6129	C₂×C₄	1	12	yes	—
37	#6129	C₂³	1	12	yes	—
38	D₄×D₁₃	C₂×C₄	1	24	yes	—
39	#6127	C₂×C₄	1	24	yes	—
40	C₂×D₅₂	C₂×C₄	1	3	yes	—
41	C₂×C₄×D₁₃	C₂×C₄	1	3	yes	—
42	C₂×C₄×D₁₃	C₂×C₄	1	3	yes	—
43	C₂×C₄×D₁₃	C₂×C₄	1	12	yes	—
44	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
45	C₂×C₄×D₁₃	C₂³	1	3	yes	—
46	C₂×C₄×D₁₃	C₂³	1	12	yes	—
47	C₂×Dic₂₆	C₂×C₄	1	3	yes	—
48	#6122	C₂³	1	24	yes	complemented
49	C₂×#1057	C₂³	1	2	yes	—
50	C₂×#1057	C₂³	1	6	yes	—
51	C₂×#1057	C₂³	1	24	yes	complemented
52	#6118	C₂³	1	24	yes	complemented
53	D₁₃⋊C₈	C₂³	1	4	yes	—
54	D₁₃⋊C₈	C₂³	1	12	yes	—
55	D₁₃⋊C₈	C₂³	1	24	yes	complemented
56	C₂²×#131	—	13	1	no	maximal, Sylow
57	C₂³×C₁₃	C₂²×C₄	1	3	yes	—
58	C₂²×D₁₃	—	2	12	no	—
59	C₂²×D₁₃	C₂²×C₄	1	3	yes	—
60	C₂²×D₁₃	C₂²×C₄	1	12	yes	—
61	C₂²×D₁₃	C₂²×C₄	1	1	yes	characteristic
62	Q₈×C₁₃	C₂²×C₄	1	4	yes	—
63	D₄×C₁₃	C₂²×C₄	1	12	yes	—
64	C₂×C₄×C₁₃	C₂²×C₄	1	3	yes	—
65	C₂×C₄×C₁₃	C₂²×C₄	1	12	yes	—
66	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
67	C₂²⋊D₁₃	C₂²×C₄	1	24	yes	—
68	C₂×Dic₁₃	C₂²×C₄	1	3	yes	—
69	C₂×Dic₁₃	C₂²×C₄	1	6	yes	—
70	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
71	C₂×Dic₁₃	C₂⁴	1	6	yes	—
72	D₅₂	C₂²×C₄	1	12	yes	—
73	C₄×D₁₃	C₂²×C₄	1	2	yes	—
74	C₄×D₁₃	C₂²×C₄	1	12	yes	—
75	C₄×D₁₃	C₂²×C₄	1	12	yes	—
76	C₄×D₁₃	C₂²×C₄	1	6	yes	—
77	C₄×D₁₃	C₂⁴	1	2	yes	—
78	C₄×D₁₃	C₂⁴	1	6	yes	—
79	Dic₂₆	C₂²×C₄	1	12	yes	—
80	#1057	C₂⁴	1	4	yes	—
81	#1057	C₂⁴	1	12	yes	—
82	C₂²×#41	—	13	1	no	—
83	C₂×#131	—	13	6	no	—
84	C₂×#131	—	13	2	no	—
85	C₂×#131	—	13	16	no	—
86	C₂²×M₁₆	—	13	3	no	—
87	C₂³×C₈	—	13	3	no	—
88	C₂²×C₁₃	—	2	6	no	—
89	C₂²×C₁₃	C₂³×C₄	1	6	yes	—
90	C₂²×C₁₃	C₂³×C₄	1	1	yes	characteristic
91	C₂×D₁₃	—	2	6	no	—
92	C₂×D₁₃	—	2	24	no	—
93	C₂×D₁₃	#131	1	4	yes	complemented
94	C₂×D₁₃	C₂³×C₄	1	6	yes	—
95	C₂×D₁₃	C₂³×C₄	1	2	yes	—
96	C₄×C₁₃	C₂³×C₄	1	6	yes	—
97	C₄×C₁₃	C₂³×C₄	1	2	yes	—
98	Dic₁₃	C₂³×C₄	1	6	yes	—
99	Dic₁₃	C₂³×C₄	1	1	yes	characteristic
100	Dic₁₃	C₂⁵	1	1	yes	characteristic
101	C₂×#41	—	13	8	no	—
102	C₂×#41	—	13	8	no	—
103	C₂×#41	—	13	1	no	—
104	C₂×#41	—	13	3	no	—
105	C₂×#41	—	13	3	no	—
106	C₂×#41	#261	1	1	yes	characteristic
107	C₂²×Q₈	—	13	1	no	—
108	C₂²×D₄	—	13	3	no	—
109	C₂³×C₄	—	13	3	no	—
110	#131	—	13	48	no	—
111	#131	—	13	16	no	—
112	C₂×M₁₆	—	13	6	no	—
113	C₂×M₁₆	—	13	24	no	—
114	C₂×M₁₆	—	13	6	no	—
115	C₂²×C₈	—	13	1	no	—
116	C₂²×C₈	—	13	3	no	—
117	C₂²×C₈	—	13	24	no	—
118	C₂²×C₈	—	13	6	no	—
119	C₂²×C₈	—	13	6	no	—
120	C₂×C₁₃	—	2	6	no	—
121	C₂×C₁₃	C₂×#131	1	2	yes	complemented
122	C₂×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
123	D₁₃	—	2	6	no	—
124	D₁₃	C₂×#131	1	4	yes	complemented
125	C₂⁴	—	13	3	no	—
126	#41	—	13	4	no	—
127	#41	—	13	4	no	—
128	#41	—	13	12	no	—
129	#41	—	13	12	no	—
130	#41	—	13	24	no	—
131	#41	C₂×#261	1	8	yes	—
132	C₂×Q₈	—	13	8	no	—
133	C₂×Q₈	—	13	3	no	—
134	C₂×Q₈	C₂×#261	1	1	yes	characteristic
135	C₂×D₄	—	13	6	no	—
136	C₂×D₄	—	13	24	no	—
137	C₂×D₄	—	13	3	no	—
138	C₂×D₄	C₂×#261	1	3	yes	—
139	C₂²×C₄	—	13	3	no	—
140	C₂²×C₄	—	13	3	no	—
141	C₂²×C₄	—	13	12	no	—
142	C₂²×C₄	—	13	3	no	—
143	C₂²×C₄	—	13	12	no	—
144	C₂²×C₄	—	13	1	no	—
145	C₂²×C₄	—	13	3	no	—
146	C₂²×C₄	C₂×#261	1	3	yes	—
147	M₁₆	—	13	24	no	—
148	M₁₆	—	13	24	no	—
149	C₂×C₈	—	13	4	no	—
150	C₂×C₈	—	13	2	no	—
151	C₂×C₈	—	13	12	no	—
152	C₂×C₈	—	13	6	no	—
153	C₂×C₈	—	13	24	no	—
154	C₂×C₈	—	13	24	no	—
155	C₁₃	C₂²×#131	1	1	yes	characteristic, complemented, Sylow
156	C₂³	—	13	1	no	—
157	C₂³	—	13	12	no	—
158	C₂³	—	13	3	no	—
159	C₂³	—	26	12	no	—
160	C₂³	C₂²×#261	1	3	yes	—
161	Q₈	—	13	12	no	—
162	Q₈	C₂²×#261	1	4	yes	—
163	D₄	—	13	24	no	—
164	D₄	—	13	12	no	—
165	D₄	C₂²×#261	1	12	yes	—
166	C₂×C₄	—	13	1	no	—
167	C₂×C₄	—	13	6	no	—
168	C₂×C₄	—	13	3	no	—
169	C₂×C₄	—	13	6	no	—
170	C₂×C₄	—	13	2	no	—
171	C₂×C₄	—	13	6	no	—
172	C₂×C₄	—	13	2	no	—
173	C₂×C₄	—	13	12	no	—
174	C₂×C₄	—	13	6	no	—
175	C₂×C₄	—	13	12	no	—
176	C₂×C₄	C₂²×#261	1	3	yes	—
177	C₂×C₄	C₂²×#261	1	12	yes	—
178	C₂×C₄	C₂²×#261	1	1	yes	characteristic
179	C₈	—	13	4	no	—
180	C₈	—	13	12	no	—
181	C₂²	—	2	6	no	—
182	C₂²	—	13	4	no	—
183	C₂²	—	13	2	no	—
184	C₂²	—	13	6	no	—
185	C₂²	—	26	24	no	—
186	C₂²	—	26	6	no	—
187	C₂²	C₂³×#261	1	6	yes	—
188	C₂²	C₂³×#261	1	1	yes	characteristic
189	C₄	—	13	1	no	—
190	C₄	—	13	6	no	—
191	C₄	—	13	1	no	—
192	C₄	C₂³×#261	1	2	yes	—
193	C₄	C₂³×#261	1	6	yes	—
194	C₂	—	2	6	no	—
195	C₂	—	13	4	no	—
196	C₂	—	26	6	no	—
197	C₂	D₁₃⋊#131	1	2	yes	direct product factor
198	C₂	C₂⁴×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#261
commutator	C₂×C₁₃	C₂⁴×C₄
Frattini	C₂	C₂⁴×#261
Fitting	C₂×C₁₃×#41	C₄
socle	C₂²×C₁₃	C₂³×C₄
prime radical	C₂×#41×D₁₃	C₂
cosocle	Dic₁₃	C₂⁵
hypercenter	C₂×#41	#261
hypocenter	C₁₃	C₂²×#131
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. D₁₃⋊#131	C₂	direct (N × H)
3. C₂×#88240	C₂	semidirect
4. C₂×#88238	C₂	semidirect
5. C₂×D₁₃⋊M₁₆	C₂	semidirect
6. C₂²×D₁₃⋊C₈	C₂	semidirect
16. C₂×#6122	C₂²	semidirect
17. C₂²×#1057	C₂²	semidirect
18. #88240	C₂²	semidirect
19. #88238	C₂²	semidirect
20. D₁₃⋊M₁₆	C₂²	semidirect
21. C₂×#6118	C₂²	semidirect
24. C₂×D₁₃⋊C₈	C₂²	semidirect
25. C₂×D₁₃⋊C₈	C₂²	semidirect
48. #6122	C₂³	semidirect
51. C₂×#1057	C₂³	semidirect
52. #6118	C₂³	semidirect
55. D₁₃⋊C₈	C₂³	semidirect
93. C₂×D₁₃	#131	semidirect
121. C₂×C₁₃	C₂×#131	semidirect
124. D₁₃	C₂×#131	semidirect
155. C₁₃	C₂²×#131	semidirect
197. C₂	D₁₃⋊#131	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×#41×D₁₃	2
D₁₃⋊#131	2
C₂×#88240	2
C₂×#88238	2
C₂×D₁₃⋊M₁₆	2
C₂²×D₁₃⋊C₈	2
C₂²×#131	13

Subgroups — C2×D13⋊#131 #13131825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃⋊#131 #13131825