Subgroups — C₂×D₁₃×#108 #13123437

Order 1664.

480 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×M₁₆×D₁₃	C₂	1	2	yes	maximal
2	C₂²×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#108	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#88062	C₂	1	2	yes	maximal, complemented
5	C₂×#88059	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₃×#108	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#6099	C₂²	1	2	yes	—
11	C₂²×#1055	C₂²	1	1	yes	characteristic
12	M₁₆×D₁₃	—	2	4	no	—
13	M₁₆×D₁₃	C₂²	1	8	yes	—
14	C₂×#6094	—	2	2	no	—
15	C₂×C₈×D₁₃	—	2	2	no	—
16	C₂×C₈×D₁₃	C₄	1	2	yes	—
17	C₂×C₈×D₁₃	C₄	1	4	yes	—
18	C₂×C₈×D₁₃	C₄	1	2	yes	—
19	C₂×C₈×D₁₃	C₂²	1	4	yes	—
20	C₁₃×#108	C₂²	1	4	yes	complemented
21	#88062	C₂²	1	8	yes	complemented
22	#88059	C₂²	1	4	yes	complemented
23	C₂³×D₁₃	Q₈	1	1	yes	characteristic
24	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
25	C₂²×Dic₁₃	Q₈	1	1	yes	characteristic
26	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
30	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
31	C₂×C₄×D₁₃	D₄	1	2	yes	—
32	C₂×C₄×D₁₃	Q₈	1	2	yes	—
33	C₂×C₄×D₁₃	C₂³	1	2	yes	—
34	C₁₃×M₁₆	—	2	2	no	—
35	C₁₃×M₁₆	C₂³	1	4	yes	—
36	C₂×C₈×C₁₃	—	2	2	no	—
37	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
39	C₂×C₈×C₁₃	C₂³	1	2	yes	—
40	#6099	—	2	2	no	—
41	#6099	C₂³	1	4	yes	—
42	C₂×#1055	—	2	2	no	—
43	C₂×#1055	C₂×C₄	1	2	yes	—
44	C₂×#1055	C₂×C₄	1	2	yes	—
45	C₂×#1055	C₂³	1	2	yes	—
46	#6094	—	2	8	no	—
47	C₈×D₁₃	—	2	8	no	—
48	C₈×D₁₃	C₂×C₄	1	8	yes	—
49	C₈×D₁₃	C₂×C₄	1	8	yes	—
50	C₂²×#108	—	13	1	no	maximal, Sylow
51	C₂³×C₁₃	C₂×Q₈	1	1	yes	characteristic
52	C₂²×D₁₃	—	2	4	no	—
53	C₂²×D₁₃	C₄⋊C₄	1	1	yes	characteristic
54	C₂²×D₁₃	C₄⋊C₄	1	2	yes	—
55	C₂²×D₁₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×D₁₃	C₂×Q₈	1	2	yes	—
57	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
63	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
64	C₂×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
65	C₂×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
66	C₂×Dic₁₃	C₂×Q₈	1	2	yes	—
67	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
68	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
69	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
70	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
71	C₄×D₁₃	C₂²×C₄	1	2	yes	—
72	C₄×D₁₃	C₂²×C₄	1	2	yes	—
73	C₄×D₁₃	C₂×D₄	1	2	yes	—
74	C₄×D₁₃	C₂×D₄	1	2	yes	—
75	C₈×C₁₃	—	2	4	no	—
76	C₈×C₁₃	C₂²×C₄	1	4	yes	—
77	#1055	—	2	4	no	—
78	#1055	C₂²×C₄	1	4	yes	—
79	C₂²×M₁₆	—	13	2	no	—
80	C₂³×C₈	—	13	1	no	—
81	C₂×#108	—	13	2	no	—
82	C₂×#108	—	13	1	no	—
83	C₂×#108	—	13	8	no	—
84	C₂×#108	D₁₃	1	1	yes	characteristic, direct product factor
85	C₂²×C₁₃	—	2	2	no	—
86	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
87	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
89	C₂×D₁₃	—	2	2	no	—
90	C₂×D₁₃	—	2	4	no	—
91	C₂×D₁₃	—	2	4	no	—
92	C₂×D₁₃	#108	1	4	yes	direct product factor
93	C₂×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
94	C₂×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
95	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
97	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
98	C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
99	Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
100	Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
101	C₂³×C₄	—	13	1	no	—
102	C₂×M₁₆	—	13	2	no	—
103	C₂×M₁₆	—	13	8	no	—
104	C₂×M₁₆	—	26	2	no	—
105	C₂×M₁₆	—	26	4	no	—
106	C₂×M₁₆	C₂×D₁₃	1	2	yes	—
107	C₂²×C₈	—	13	1	no	—
108	C₂²×C₈	—	13	2	no	—
109	C₂²×C₈	—	13	2	no	—
110	C₂²×C₈	—	13	4	no	—
111	C₂²×C₈	—	13	4	no	—
112	C₂²×C₈	—	26	2	no	—
113	C₂²×C₈	C₂×D₁₃	1	1	yes	characteristic
114	#108	—	13	8	no	—
115	#108	—	13	4	no	—
116	#108	C₂×D₁₃	1	4	yes	direct product factor
117	C₂×C₁₃	—	2	1	no	—
118	C₂×C₁₃	—	2	1	no	—
119	C₂×C₁₃	C₂×#108	1	2	yes	complemented
120	C₂×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
121	D₁₃	—	2	2	no	—
122	D₁₃	C₂×#108	1	4	yes	direct product factor
123	C₂⁴	—	13	1	no	—
124	C₂²×C₄	—	13	1	no	—
125	C₂²×C₄	—	13	1	no	—
126	C₂²×C₄	—	13	2	no	—
127	C₂²×C₄	—	13	1	no	—
128	C₂²×C₄	—	13	2	no	—
129	C₂²×C₄	—	13	1	no	—
130	C₂²×C₄	—	13	1	no	—
131	C₂²×C₄	—	13	2	no	—
132	C₂²×C₄	—	13	2	no	—
133	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
134	M₁₆	—	2	2	no	—
135	M₁₆	—	13	4	no	—
136	M₁₆	—	26	8	no	—
137	M₁₆	—	26	2	no	—
138	M₁₆	C₂²×D₁₃	1	4	yes	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	13	2	no	—
141	C₂×C₈	—	13	2	no	—
142	C₂×C₈	—	13	2	no	—
143	C₂×C₈	—	13	8	no	—
144	C₂×C₈	—	13	8	no	—
145	C₂×C₈	—	26	8	no	—
146	C₂×C₈	—	26	2	no	—
147	C₂×C₈	C₄×D₁₃	1	2	yes	—
148	C₂×C₈	C₄×D₁₃	1	2	yes	—
149	C₂×C₈	C₂²×D₁₃	1	2	yes	—
150	C₁₃	C₂²×#108	1	1	yes	characteristic, complemented, Sylow
151	C₂³	—	13	1	no	—
152	C₂³	—	13	2	no	—
153	C₂³	—	13	1	no	—
154	C₂³	—	13	2	no	—
155	C₂³	—	26	4	no	—
156	C₂³	Q₈×D₁₃	1	1	yes	characteristic
157	C₂×C₄	—	13	2	no	—
158	C₂×C₄	—	13	1	no	—
159	C₂×C₄	—	13	1	no	—
160	C₂×C₄	—	13	2	no	—
161	C₂×C₄	—	13	2	no	—
162	C₂×C₄	—	13	2	no	—
163	C₂×C₄	—	13	2	no	—
164	C₂×C₄	—	13	2	no	—
165	C₂×C₄	—	13	2	no	—
166	C₂×C₄	—	13	2	no	—
167	C₂×C₄	—	13	2	no	—
168	C₂×C₄	—	13	2	no	—
169	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
170	C₂×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
171	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
172	C₂×C₄	D₄×D₁₃	1	1	yes	characteristic
173	C₂×C₄	Q₈×D₁₃	1	1	yes	characteristic
174	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
175	C₈	—	2	4	no	—
176	C₈	—	13	4	no	—
177	C₈	—	26	4	no	—
178	C₈	C₂×C₄×D₁₃	1	4	yes	—
179	C₂²	—	2	2	no	—
180	C₂²	—	13	2	no	—
181	C₂²	—	13	4	no	—
182	C₂²	—	13	2	no	—
183	C₂²	—	26	4	no	—
184	C₂²	—	26	4	no	—
185	C₂²	—	26	2	no	—
186	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
187	C₂²	C₄⋊C₄×D₁₃	1	1	yes	characteristic
188	C₂²	C₂×Q₈×D₁₃	1	1	yes	characteristic
189	C₄	—	13	2	no	—
190	C₄	—	13	2	no	—
191	C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
192	C₄	C₄⋊C₄×D₁₃	1	1	yes	characteristic
193	C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
194	C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
195	C₂	—	2	1	no	—
196	C₂	—	2	1	no	—
197	C₂	—	13	4	no	—
198	C₂	—	26	2	no	—
199	C₂	D₁₃×#108	1	2	yes	direct product factor
200	C₂	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₃
commutator	C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₃
Fitting	C₂×C₁₃×#108	C₂
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×D₁₃	Q₈
cosocle	C₂×C₄×C₁₃	C₂⁴
hypercenter	C₂×#108	D₁₃
hypocenter	C₁₃	C₂²×#108
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#108	C₂	semidirect
4. C₂×#88062	C₂	semidirect
5. C₂×#88059	C₂	semidirect
6. D₁₃×#108	C₂	direct (N × H)
20. C₁₃×#108	C₂²	semidirect
21. #88062	C₂²	semidirect
22. #88059	C₂²	semidirect
84. C₂×#108	D₁₃	direct (N × H)
92. C₂×D₁₃	#108	direct (N × H)
116. #108	C₂×D₁₃	direct (N × H)
119. C₂×C₁₃	C₂×#108	semidirect
122. D₁₃	C₂×#108	direct (N × H)
150. C₁₃	C₂²×#108	semidirect
199. C₂	D₁₃×#108	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×M₁₆×D₁₃	2
C₂²×C₈×D₁₃	2
C₂×C₁₃×#108	2
C₂×#88062	2
C₂×#88059	2
D₁₃×#108	2
C₂²×#108	13

Subgroups — C2×D13×#108 #13123437

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#108 #13123437