Subgroups — C₂×D₁₃×#366 #16015938

Order 3328.

782 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃×#107	C₂	1	2	yes	maximal
3	C₂×#11718096	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11718081	C₂	1	2	yes	maximal, complemented
5	D₁₃×#366	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₁₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊C₄×D₁₃	—	2	2	no	—
9	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#107	C₂²	1	2	yes	—
11	C₂×#88058	C₂²	1	2	yes	—
12	C₂²×#6090	C₂²	1	1	yes	characteristic
13	C₂×#88047	—	2	2	no	—
14	C₂×C₁₆×D₁₃	C₄	1	8	yes	complemented
15	C₂×C₁₆×D₁₃	C₂²	1	4	yes	—
16	D₁₃×#107	—	2	4	no	—
17	D₁₃×#107	C₂²	1	8	yes	—
18	C₁₃×#366	C₂²	1	4	yes	complemented
19	#11718096	C₂²	1	4	yes	complemented
20	#11718081	C₂²	1	8	yes	complemented
21	C₂²×C₄×D₁₃	—	4	2	no	—
22	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
25	C₂×C₄⋊Dic₁₃	—	2	2	no	—
26	C₂×#6101	—	4	2	no	—
27	C₂²×#1055	D₄	1	1	yes	characteristic
28	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
29	C₂×C₈×D₁₃	D₄	1	2	yes	—
30	C₂×C₈×D₁₃	Q₈	1	4	yes	—
31	C₂×C₈×D₁₃	C₂³	1	2	yes	—
32	C₄⋊C₄×D₁₃	—	2	8	no	—
33	C₄⋊C₄×D₁₃	—	4	4	no	—
34	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	complemented
35	C₂×C₁₃×C₁₆	C₂³	1	2	yes	—
36	C₁₃×#107	—	2	2	no	—
37	C₁₃×#107	C₂³	1	4	yes	—
38	#88058	—	2	2	no	—
39	#88058	C₂³	1	4	yes	—
40	C₂×#6090	C₂×C₄	1	4	yes	complemented
41	C₂×#6090	C₂³	1	2	yes	—
42	#88047	—	2	8	no	—
43	C₁₆×D₁₃	C₂×C₄	1	16	yes	complemented
44	C₂²×#366	—	13	1	no	maximal, Sylow
45	C₂³×D₁₃	D₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₃	—	4	2	no	—
47	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×Dic₁₃	—	4	2	no	—
49	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
50	C₂×C₄×D₁₃	—	4	8	no	—
51	C₂×C₄×D₁₃	—	8	8	no	—
52	C₂×C₄×D₁₃	C₄⋊C₄	1	4	yes	—
53	C₂×C₄×D₁₃	D₈	1	2	yes	—
54	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
55	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
57	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
59	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
60	C₁₃×C₄⋊C₄	—	2	4	no	—
61	C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₄⋊Dic₁₃	—	2	4	no	—
63	C₄⋊Dic₁₃	—	4	2	no	—
64	#6101	—	4	8	no	—
65	C₂×#1055	C₄⋊C₄	1	4	yes	—
66	C₂×#1055	C₂×D₄	1	2	yes	—
67	C₈×D₁₃	C₄⋊C₄	1	8	yes	—
68	C₈×D₁₃	C₂²×C₄	1	4	yes	—
69	C₈×D₁₃	C₂×Q₈	1	4	yes	—
70	C₁₃×C₁₆	C₂²×C₄	1	4	yes	complemented
71	#6090	C₂²×C₄	1	4	yes	complemented
72	C₂³×C₁₆	—	13	1	no	—
73	C₂²×#107	—	13	2	no	—
74	C₂×#366	—	13	1	no	—
75	C₂×#366	—	13	2	no	—
76	C₂×#366	—	13	8	no	—
77	C₂×#366	D₁₃	1	1	yes	characteristic, direct product factor
78	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
79	C₂²×D₁₃	#107	1	4	yes	—
80	C₂²×D₁₃	D₁₆	1	4	yes	—
81	C₂²×D₁₃	Q₃₂	1	4	yes	—
82	C₂²×D₁₃	C₂×D₈	1	2	yes	—
83	C₂×C₄×C₁₃	—	4	4	no	—
84	C₂×C₄×C₁₃	—	8	4	no	—
85	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
86	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
88	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
89	C₂×Dic₁₃	—	4	4	no	—
90	C₂×Dic₁₃	—	8	4	no	—
91	C₂×Dic₁₃	#107	1	4	yes	—
92	C₂×Dic₁₃	C₂×D₈	1	2	yes	—
93	C₄×D₁₃	—	8	16	no	—
94	C₄×D₁₃	#107	1	8	yes	—
95	C₄×D₁₃	C₂×C₄⋊C₄	1	4	yes	—
96	C₄×D₁₃	C₂×Q₁₆	1	4	yes	—
97	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
98	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
99	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
100	#1055	C₂×C₄⋊C₄	1	4	yes	—
101	C₂³×C₈	—	13	1	no	—
102	C₂²×C₄⋊C₄	—	26	2	no	—
103	C₂²×C₁₆	—	13	1	no	—
104	C₂²×C₁₆	—	13	8	no	—
105	C₂²×C₁₆	—	13	4	no	—
106	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
107	C₂×#107	—	13	2	no	—
108	C₂×#107	—	13	8	no	—
109	C₂×#107	—	26	4	no	—
110	C₂×#107	—	26	2	no	—
111	C₂×#107	C₂×D₁₃	1	2	yes	—
112	#366	—	13	4	no	—
113	#366	—	13	8	no	—
114	#366	C₂×D₁₃	1	4	yes	direct product factor
115	C₂²×C₁₃	C₂×#107	1	2	yes	—
116	C₂²×C₁₃	C₂×D₁₆	1	2	yes	—
117	C₂²×C₁₃	C₂×Q₃₂	1	2	yes	—
118	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
119	C₂×D₁₃	#366	1	16	yes	direct product factor
120	C₂×D₁₃	C₂×#107	1	4	yes	—
121	C₂×D₁₃	C₂×D₁₆	1	4	yes	—
122	C₂×D₁₃	C₂×Q₃₂	1	4	yes	—
123	C₄×C₁₃	—	8	4	no	—
124	C₄×C₁₃	C₂×#107	1	2	yes	—
125	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
126	C₄×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
127	Dic₁₃	—	8	4	no	—
128	Dic₁₃	C₂×#107	1	4	yes	—
129	C₂³×C₄	—	13	1	no	—
130	C₂³×C₄	—	52	2	no	—
131	C₂²×C₈	—	13	1	no	—
132	C₂²×C₈	—	13	4	no	—
133	C₂²×C₈	—	13	2	no	—
134	C₂²×C₈	—	13	4	no	—
135	C₂²×C₈	—	13	2	no	—
136	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	—	26	8	no	—
139	C₂×C₄⋊C₄	—	26	2	no	—
140	C₂×C₄⋊C₄	—	52	4	no	—
141	C₂×C₄⋊C₄	—	52	2	no	—
142	C₂×C₁₆	—	13	4	no	—
143	C₂×C₁₆	—	13	2	no	—
144	C₂×C₁₆	—	13	16	no	—
145	C₂×C₁₆	C₄×D₁₃	1	4	yes	complemented
146	C₂×C₁₆	C₂²×D₁₃	1	2	yes	—
147	#107	—	2	2	no	—
148	#107	—	13	4	no	—
149	#107	—	26	8	no	—
150	#107	—	26	2	no	—
151	#107	C₂²×D₁₃	1	4	yes	—
152	C₂×C₁₃	C₂×#366	1	4	yes	complemented
153	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
154	C₂×C₁₃	C₂²×D₁₆	1	1	yes	characteristic
155	C₂×C₁₃	C₂²×Q₃₂	1	1	yes	characteristic
156	D₁₃	C₂×#366	1	8	yes	direct product factor
157	C₂⁴	—	13	1	no	—
158	C₂²×C₄	—	4	2	no	—
159	C₂²×C₄	—	13	1	no	—
160	C₂²×C₄	—	13	4	no	—
161	C₂²×C₄	—	13	2	no	—
162	C₂²×C₄	—	13	4	no	—
163	C₂²×C₄	—	13	2	no	—
164	C₂²×C₄	—	52	8	no	—
165	C₂²×C₄	—	52	2	no	—
166	C₂²×C₄	—	104	8	no	—
167	C₂²×C₄	D₄×D₁₃	1	1	yes	characteristic
168	C₂×C₈	—	13	4	no	—
169	C₂×C₈	—	13	2	no	—
170	C₂×C₈	—	13	8	no	—
171	C₂×C₈	—	13	4	no	—
172	C₂×C₈	—	13	4	no	—
173	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
174	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
175	C₂×C₈	Q₈×D₁₃	1	2	yes	—
176	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
177	C₄⋊C₄	—	2	4	no	—
178	C₄⋊C₄	—	4	2	no	—
179	C₄⋊C₄	—	26	4	no	—
180	C₄⋊C₄	—	52	8	no	—
181	C₄⋊C₄	—	52	2	no	—
182	C₁₆	—	13	4	no	—
183	C₁₆	C₂×C₄×D₁₃	1	4	yes	complemented
184	C₁₃	C₂²×#366	1	1	yes	characteristic, complemented, Sylow
185	C₂³	—	13	2	no	—
186	C₂³	—	13	4	no	—
187	C₂³	—	13	4	no	—
188	C₂³	—	13	4	no	—
189	C₂³	D₈×D₁₃	1	1	yes	characteristic
190	C₂×C₄	—	4	4	no	—
191	C₂×C₄	—	8	4	no	—
192	C₂×C₄	—	13	2	no	—
193	C₂×C₄	—	13	4	no	—
194	C₂×C₄	—	13	4	no	—
195	C₂×C₄	—	13	4	no	—
196	C₂×C₄	—	13	8	no	—
197	C₂×C₄	—	52	4	no	—
198	C₂×C₄	—	104	16	no	—
199	C₂×C₄	—	104	4	no	—
200	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
201	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
202	C₂×C₄	Q₁₆×D₁₃	1	2	yes	—
203	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
204	C₈	—	13	4	no	—
205	C₈	C₄⋊C₄×D₁₃	1	2	yes	—
206	C₈	C₂²×C₄×D₁₃	1	1	yes	characteristic
207	C₈	C₂×Q₈×D₁₃	1	1	yes	characteristic
208	C₂²	—	13	4	no	—
209	C₂²	—	13	4	no	—
210	C₂²	—	13	4	no	—
211	C₂²	—	13	16	no	—
212	C₂²	D₁₃×#107	1	2	yes	—
213	C₂²	D₁₃×D₁₆	1	2	yes	—
214	C₂²	D₁₃×Q₃₂	1	2	yes	—
215	C₂²	C₂×D₈×D₁₃	1	1	yes	characteristic
216	C₄	—	8	4	no	—
217	C₄	—	13	4	no	—
218	C₄	—	104	4	no	—
219	C₄	D₁₃×#107	1	2	yes	—
220	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
221	C₄	C₂×Q₁₆×D₁₃	1	1	yes	characteristic
222	C₂	—	13	8	no	—
223	C₂	D₁₃×#366	1	4	yes	direct product factor
224	C₂	C₂×D₁₃×#107	1	1	yes	characteristic
225	C₂	C₂×D₁₃×D₁₆	1	1	yes	characteristic
226	C₂	C₂×D₁₃×Q₃₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₃
commutator	C₈×C₁₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂×C₁₃×#366	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂³×D₁₃	D₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂×#366	D₁₃
hypocenter	C₁₃	C₂²×#366
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
3. C₂×#11718096	C₂	semidirect
4. C₂×#11718081	C₂	semidirect
5. D₁₃×#366	C₂	direct (N × H)
6. C₂×C₁₃×#366	C₂	semidirect
14. C₂×C₁₆×D₁₃	C₄	semidirect
18. C₁₃×#366	C₂²	semidirect
19. #11718096	C₂²	semidirect
20. #11718081	C₂²	semidirect
34. C₂×C₁₃×C₁₆	C₂×C₄	semidirect
40. C₂×#6090	C₂×C₄	semidirect
43. C₁₆×D₁₃	C₂×C₄	semidirect
70. C₁₃×C₁₆	C₂²×C₄	semidirect
71. #6090	C₂²×C₄	semidirect
77. C₂×#366	D₁₃	direct (N × H)
114. #366	C₂×D₁₃	direct (N × H)
119. C₂×D₁₃	#366	direct (N × H)
145. C₂×C₁₆	C₄×D₁₃	semidirect
152. C₂×C₁₃	C₂×#366	semidirect
156. D₁₃	C₂×#366	direct (N × H)
183. C₁₆	C₂×C₄×D₁₃	semidirect
184. C₁₃	C₂²×#366	semidirect
223. C₂	D₁₃×#366	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₁₆×D₁₃	2
C₂×D₁₃×#107	2
C₂×#11718096	2
C₂×#11718081	2
D₁₃×#366	2
C₂×C₁₃×#366	2
C₂²×#366	13

Subgroups — C2×D13×#366 #16015938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#366 #16015938