Subgroups — C₂×D₁₃⋊#108 #13131493

Order 1664.

480 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₁₆	C₂	1	2	yes	maximal
2	C₂²×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
3	D₁₃⋊#108	C₂	1	8	yes	maximal, direct product factor
4	C₂×#88104	C₂	1	2	yes	maximal, complemented
5	C₂×#88103	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
7	C₂×#6122	—	2	2	no	—
8	D₁₃⋊M₁₆	—	2	4	no	—
9	D₁₃⋊M₁₆	C₂²	1	8	yes	—
10	C₂×#6118	C₂²	1	4	yes	—
11	C₂×D₁₃⋊C₈	—	2	2	no	—
12	C₂²×C₈×C₁₃	C₄	1	1	yes	characteristic
13	C₂²×#1055	C₄	1	1	yes	characteristic
14	C₂×C₈×D₁₃	C₄	1	4	yes	—
15	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
16	C₂×C₈×D₁₃	C₄	1	1	yes	characteristic
17	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₈×D₁₃	C₂²	1	4	yes	—
20	#88104	C₂²	1	8	yes	complemented
21	#88103	C₂²	1	8	yes	complemented
22	C₂³×D₁₃	Q₈	1	1	yes	characteristic
23	C₂²×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×Dic₁₃	D₄	1	1	yes	characteristic
25	C₂×C₄×D₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄×D₁₃	D₄	1	1	yes	characteristic
28	C₂×C₄×D₁₃	D₄	1	2	yes	—
29	C₂×C₄×D₁₃	Q₈	1	2	yes	—
30	C₂×C₄×D₁₃	Q₈	1	1	yes	characteristic
31	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
32	C₂×C₄×D₁₃	C₂³	1	2	yes	—
33	#6122	—	2	8	no	—
34	C₂×#1057	—	2	4	no	—
35	#6118	—	2	4	no	—
36	#6118	C₂³	1	8	yes	—
37	D₁₃⋊C₈	—	2	8	no	—
38	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₈×C₁₃	C₂×C₄	1	4	yes	—
41	C₂×#1055	C₂×C₄	1	1	yes	characteristic
42	C₂×#1055	C₂×C₄	1	1	yes	characteristic
43	C₂×#1055	C₂×C₄	1	4	yes	—
44	C₈×D₁₃	C₂×C₄	1	2	yes	—
45	C₈×D₁₃	C₂×C₄	1	2	yes	—
46	C₈×D₁₃	C₂×C₄	1	4	yes	—
47	C₈×D₁₃	C₂×C₄	1	4	yes	—
48	C₈×D₁₃	C₂³	1	2	yes	—
49	C₈×D₁₃	C₂³	1	2	yes	—
50	C₂²×#108	—	13	1	no	maximal, Sylow
51	C₂³×C₁₃	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×D₁₃	—	2	4	no	—
53	C₂²×D₁₃	C₄⋊C₄	1	2	yes	—
54	C₂²×D₁₃	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
56	C₂²×D₁₃	C₂×Q₈	1	2	yes	—
57	C₂×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
58	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂×Dic₁₃	C₄⋊C₄	1	2	yes	—
62	C₂×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
63	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
64	C₂×Dic₁₃	C₂×D₄	1	2	yes	—
65	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
66	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
67	C₄×D₁₃	C₄⋊C₄	1	2	yes	—
68	C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
69	C₄×D₁₃	C₂²×C₄	1	2	yes	—
70	C₄×D₁₃	C₂×D₄	1	2	yes	—
71	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
72	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
73	C₄×D₁₃	C₂×Q₈	1	2	yes	—
74	C₄×D₁₃	C₂⁴	1	1	yes	characteristic
75	#1057	—	2	8	no	—
76	C₈×C₁₃	C₂²×C₄	1	2	yes	—
77	C₈×C₁₃	C₂²×C₄	1	2	yes	—
78	#1055	C₂²×C₄	1	2	yes	—
79	#1055	C₂²×C₄	1	2	yes	—
80	C₂²×M₁₆	—	13	2	no	—
81	C₂³×C₈	—	13	1	no	—
82	C₂×#108	—	13	2	no	—
83	C₂×#108	—	13	2	no	—
84	C₂×#108	—	13	8	no	—
85	C₂²×C₁₃	—	2	2	no	—
86	C₂²×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
87	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
88	C₂×D₁₃	—	2	2	no	—
89	C₂×D₁₃	—	2	4	no	—
90	C₂×D₁₃	—	2	4	no	—
91	C₂×D₁₃	#108	1	4	yes	complemented
92	C₂×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂×D₁₃	C₂×C₄⋊C₄	1	2	yes	—
94	C₂×D₁₃	C₂²×Q₈	1	1	yes	characteristic
95	C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
96	C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
97	C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
98	Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
99	Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
100	Dic₁₃	C₂²×D₄	1	1	yes	characteristic
101	C₂³×C₄	—	13	1	no	—
102	C₂×M₁₆	—	13	4	no	—
103	C₂×M₁₆	—	13	8	no	—
104	C₂×M₁₆	—	26	4	no	—
105	C₂×M₁₆	—	26	2	no	—
106	C₂²×C₈	—	13	1	no	—
107	C₂²×C₈	—	13	1	no	—
108	C₂²×C₈	—	13	1	no	—
109	C₂²×C₈	—	13	4	no	—
110	C₂²×C₈	—	13	1	no	—
111	C₂²×C₈	—	13	1	no	—
112	C₂²×C₈	—	13	4	no	—
113	C₂²×C₈	—	26	2	no	—
114	C₂²×C₈	#261	1	1	yes	characteristic
115	#108	—	13	8	no	—
116	#108	—	13	8	no	—
117	C₂×C₁₃	—	2	2	no	—
118	C₂×C₁₃	C₂×#108	1	2	yes	complemented
119	C₂×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
120	D₁₃	—	2	1	no	—
121	D₁₃	—	2	1	no	—
122	D₁₃	C₂×#108	1	4	yes	complemented
123	C₂⁴	—	13	1	no	—
124	C₂²×C₄	—	13	1	no	—
125	C₂²×C₄	—	13	2	no	—
126	C₂²×C₄	—	13	2	no	—
127	C₂²×C₄	—	13	1	no	—
128	C₂²×C₄	—	13	1	no	—
129	C₂²×C₄	—	13	1	no	—
130	C₂²×C₄	—	13	2	no	—
131	C₂²×C₄	—	13	1	no	—
132	C₂²×C₄	—	13	2	no	—
133	C₂²×C₄	C₂×#261	1	1	yes	characteristic
134	M₁₆	—	13	8	no	—
135	M₁₆	—	26	4	no	—
136	M₁₆	—	26	8	no	—
137	C₂×C₈	—	13	1	no	—
138	C₂×C₈	—	13	1	no	—
139	C₂×C₈	—	13	4	no	—
140	C₂×C₈	—	13	2	no	—
141	C₂×C₈	—	13	2	no	—
142	C₂×C₈	—	13	4	no	—
143	C₂×C₈	—	13	4	no	—
144	C₂×C₈	—	13	2	no	—
145	C₂×C₈	—	13	2	no	—
146	C₂×C₈	—	26	8	no	—
147	C₂×C₈	—	26	4	no	—
148	C₂×C₈	C₂×#261	1	1	yes	characteristic
149	C₂×C₈	C₂×#261	1	1	yes	characteristic
150	C₂×C₈	C₂×#261	1	4	yes	—
151	C₁₃	C₂²×#108	1	1	yes	characteristic, complemented, Sylow
152	C₂³	—	13	1	no	—
153	C₂³	—	13	2	no	—
154	C₂³	—	13	2	no	—
155	C₂³	—	13	1	no	—
156	C₂³	—	26	4	no	—
157	C₂³	C₄⋊#261	1	1	yes	characteristic
158	C₂×C₄	—	13	1	no	—
159	C₂×C₄	—	13	2	no	—
160	C₂×C₄	—	13	2	no	—
161	C₂×C₄	—	13	1	no	—
162	C₂×C₄	—	13	2	no	—
163	C₂×C₄	—	13	1	no	—
164	C₂×C₄	—	13	2	no	—
165	C₂×C₄	—	13	2	no	—
166	C₂×C₄	—	13	2	no	—
167	C₂×C₄	—	13	1	no	—
168	C₂×C₄	—	13	2	no	—
169	C₂×C₄	—	13	1	no	—
170	C₂×C₄	—	13	2	no	—
171	C₂×C₄	—	13	1	no	—
172	C₂×C₄	C₄⋊#261	1	2	yes	—
173	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
174	C₂×C₄	C₂²×#261	1	1	yes	characteristic
175	C₂×C₄	C₂²×#261	1	2	yes	—
176	C₈	—	13	2	no	—
177	C₈	—	13	2	no	—
178	C₈	—	26	8	no	—
179	C₈	C₂²×#261	1	2	yes	—
180	C₈	C₂²×#261	1	2	yes	—
181	C₂²	—	2	2	no	—
182	C₂²	—	13	4	no	—
183	C₂²	—	13	2	no	—
184	C₂²	—	13	1	no	—
185	C₂²	—	13	1	no	—
186	C₂²	—	26	4	no	—
187	C₂²	—	26	4	no	—
188	C₂²	—	26	2	no	—
189	C₂²	C₂×C₄⋊#261	1	2	yes	—
190	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
191	C₄	—	13	1	no	—
192	C₄	—	13	2	no	—
193	C₄	—	13	1	no	—
194	C₄	C₂×C₄⋊#261	1	1	yes	characteristic
195	C₄	C₂×C₄⋊#261	1	2	yes	—
196	C₄	C₂³×#261	1	1	yes	characteristic
197	C₂	—	2	2	no	—
198	C₂	—	13	4	no	—
199	C₂	—	26	1	no	—
200	C₂	—	26	1	no	—
201	C₂	D₁₃⋊#108	1	2	yes	direct product factor
202	C₂	C₂²×C₄⋊#261	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#261
commutator	C₄×C₁₃	C₂³×C₄
Frattini	C₄	C₂³×#261
Fitting	C₂²×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×D₁₃	Q₈
cosocle	C₄×D₁₃	C₂⁴
hypercenter	C₂²×C₈	#261
hypocenter	C₁₃	C₂²×#108
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. D₁₃⋊#108	C₂	direct (N × H)
4. C₂×#88104	C₂	semidirect
5. C₂×#88103	C₂	semidirect
20. #88104	C₂²	semidirect
21. #88103	C₂²	semidirect
91. C₂×D₁₃	#108	semidirect
118. C₂×C₁₃	C₂×#108	semidirect
122. D₁₃	C₂×#108	semidirect
151. C₁₃	C₂²×#108	semidirect
201. 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×D₁₃⋊M₁₆	2
C₂²×C₈×D₁₃	2
D₁₃⋊#108	2
C₂×#88104	2
C₂×#88103	2
C₂²×#108	13

Subgroups — C2×D13⋊#108 #13131493

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃⋊#108 #13131493