Subgroups — C₂×#13116591 #16015897

Order 3328.

798 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×#88052	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#13116591	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718093	C₂	1	4	yes	maximal, complemented
5	C₂²×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂²×C₄×Dic₁₃	C₄	1	1	yes	characteristic
8	C₂³×#1055	C₄	1	1	yes	characteristic
9	C₂×C₁₃×M₃₂	—	2	4	no	—
10	C₂×C₁₃×M₃₂	C₂²	1	4	yes	—
11	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
12	C₂×C₈×Dic₁₃	C₄	1	2	yes	—
13	C₂×C₈×Dic₁₃	C₄	1	4	yes	—
14	C₂×C₈×Dic₁₃	C₂²	1	2	yes	—
15	C₂×C₈×Dic₁₃	C₂²	1	4	yes	—
16	C₂×#88052	—	2	4	no	—
17	C₂×#88052	C₂²	1	4	yes	—
18	C₂²×#6090	C₂²	1	2	yes	—
19	#11718093	C₂²	1	16	yes	complemented
20	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂³×Dic₁₃	C₈	1	2	yes	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
24	C₂²×C₈×C₁₃	D₄	1	4	yes	—
25	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
26	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₄×Dic₁₃	C₈	1	1	yes	characteristic
29	C₂×C₄×Dic₁₃	C₈	1	4	yes	—
30	C₂×C₄×Dic₁₃	C₈	1	1	yes	characteristic
31	C₂×C₄×Dic₁₃	C₂×C₄	1	4	yes	—
32	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
33	C₂²×#1055	—	2	4	no	—
34	C₂²×#1055	C₂×C₄	1	2	yes	—
35	C₂²×#1055	C₂×C₄	1	4	yes	—
36	C₁₃×M₃₂	—	2	8	no	—
37	C₂×C₁₃×C₁₆	—	2	4	no	—
38	C₂×C₁₃×C₁₆	C₂³	1	4	yes	—
39	C₈×Dic₁₃	C₂×C₄	1	4	yes	—
40	C₈×Dic₁₃	C₂×C₄	1	8	yes	—
41	C₈×Dic₁₃	C₂³	1	4	yes	—
42	#88052	—	2	8	no	—
43	C₂×#6090	—	2	4	no	—
44	C₂×#6090	C₂³	1	4	yes	—
45	C₂×#2150	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	C₂×C₈	1	1	yes	characteristic
47	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
48	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
49	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
51	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
52	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
53	C₂²×Dic₁₃	—	2	8	no	—
54	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
55	C₂²×Dic₁₃	C₂×C₈	1	8	yes	—
56	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
57	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
58	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
59	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
60	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
62	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
63	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
64	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
65	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
66	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
67	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
68	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
69	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
70	C₂×#1055	—	2	8	no	—
71	C₂×#1055	—	2	4	no	—
72	C₂×#1055	C₂²×C₄	1	4	yes	—
73	C₁₃×C₁₆	—	2	4	no	—
74	#6090	—	2	4	no	—
75	C₂²×M₃₂	—	13	1	no	—
76	C₂²×M₃₂	D₁₃	1	1	yes	characteristic
77	C₂²×C₄×C₈	—	13	1	no	—
78	#2150	—	13	8	no	—
79	C₂×C₄⋊C₁₆	—	13	4	no	—
80	C₂³×C₁₃	—	2	4	no	—
81	C₂³×C₁₃	C₄⋊C₈	1	4	yes	—
82	C₂³×C₁₃	C₂²×C₈	1	2	yes	—
83	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₃	C₄⋊C₈	1	8	yes	—
85	C₂×C₄×C₁₃	C₄⋊C₈	1	4	yes	—
86	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
87	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
88	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
89	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
90	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
91	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
92	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
93	C₂×Dic₁₃	—	2	4	no	—
94	C₂×Dic₁₃	—	2	16	no	—
95	C₂×Dic₁₃	M₃₂	1	8	yes	complemented
96	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
97	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
98	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
99	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
100	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
101	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
102	#1055	—	2	4	no	—
103	C₂³×C₈	—	13	1	no	—
104	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
105	C₂²×C₄²	—	13	1	no	—
106	C₂×M₃₂	—	2	4	no	—
107	C₂×M₃₂	—	13	4	no	—
108	C₂×M₃₂	—	26	4	no	—
109	C₂×M₃₂	C₂×D₁₃	1	4	yes	—
110	C₂²×C₁₆	—	13	2	no	—
111	C₂²×C₁₆	C₂×D₁₃	1	2	yes	—
112	C₂×C₄×C₈	—	13	2	no	—
113	C₂×C₄×C₈	—	13	4	no	—
114	C₂×C₄×C₈	—	13	4	no	—
115	C₂×C₄×C₈	—	13	2	no	—
116	C₄⋊C₁₆	—	13	16	no	—
117	C₂²×C₁₃	—	2	4	no	—
118	C₂²×C₁₃	—	2	8	no	—
119	C₂²×C₁₃	C₂×C₄⋊C₈	1	4	yes	—
120	C₂²×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
121	C₂²×C₁₃	C₂×M₃₂	1	4	yes	—
122	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
123	C₄×C₁₃	C₂×C₄⋊C₈	1	2	yes	—
124	C₄×C₁₃	C₂×C₄⋊C₈	1	4	yes	—
125	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
126	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
127	Dic₁₃	—	2	4	no	—
128	Dic₁₃	C₂×M₃₂	1	8	yes	complemented
129	C₂³×C₄	—	13	2	no	—
130	C₂³×C₄	C₄×D₁₃	1	1	yes	characteristic
131	C₂²×C₈	—	13	4	no	—
132	C₂²×C₈	—	13	2	no	—
133	C₂²×C₈	—	26	4	no	—
134	C₂²×C₈	Dic₂₆	1	4	yes	—
135	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
136	C₂²×C₈	C₄×D₁₃	1	2	yes	—
137	C₂²×C₈	C₂²⋊D₁₃	1	4	yes	—
138	C₂²×C₈	C₂²×D₁₃	1	2	yes	—
139	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
140	C₂×C₄²	—	13	1	no	—
141	C₂×C₄²	—	13	4	no	—
142	C₂×C₄²	—	13	1	no	—
143	C₂×C₄²	—	13	2	no	—
144	C₂×C₄²	—	13	4	no	—
145	M₃₂	—	2	8	no	—
146	M₃₂	—	26	8	no	—
147	C₂×C₁₆	—	2	4	no	—
148	C₂×C₁₆	—	13	4	no	—
149	C₂×C₁₆	—	26	4	no	—
150	C₂×C₁₆	C₂²×D₁₃	1	4	yes	—
151	C₄×C₈	—	13	8	no	—
152	C₄×C₈	—	13	4	no	—
153	C₄×C₈	—	13	4	no	—
154	C₂×C₁₃	—	2	4	no	—
155	C₂×C₁₃	#2150	1	4	yes	complemented
156	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
157	C₂×C₁₃	C₂²×M₃₂	1	2	yes	—
158	C₂⁴	C₈×D₁₃	1	1	yes	characteristic
159	C₂²×C₄	—	13	2	no	—
160	C₂²×C₄	—	13	8	no	—
161	C₂²×C₄	—	13	2	no	—
162	C₂²×C₄	—	26	8	no	—
163	C₂²×C₄	C₈×D₁₃	1	2	yes	—
164	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
165	C₂²×C₄	#6094	1	4	yes	—
166	C₂²×C₄	#6101	1	4	yes	—
167	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
168	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
169	C₂×C₈	—	13	4	no	—
170	C₂×C₈	—	26	8	no	—
171	C₂×C₈	—	26	4	no	—
172	C₂×C₈	#6101	1	4	yes	—
173	C₂×C₈	#6101	1	8	yes	—
174	C₂×C₈	C₂×Dic₂₆	1	4	yes	—
175	C₂×C₈	C₂×Dic₂₆	1	2	yes	—
176	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
177	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
178	C₂×C₈	C₂×C₂²⋊D₁₃	1	2	yes	—
179	C₂×C₈	C₂×C₂²⋊D₁₃	1	4	yes	—
180	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
181	C₄²	—	13	4	no	—
182	C₄²	—	13	4	no	—
183	C₄²	—	13	4	no	—
184	C₄²	—	13	4	no	—
185	C₁₆	—	2	4	no	—
186	C₁₆	—	26	4	no	—
187	C₁₃	C₂×#2150	1	1	yes	characteristic, complemented, Sylow
188	C₂³	—	2	4	no	—
189	C₂³	#88054	1	4	yes	—
190	C₂³	C₂×C₈×D₁₃	1	2	yes	—
191	C₂³	C₂×C₈×D₁₃	1	1	yes	characteristic
192	C₂×C₄	—	13	4	no	—
193	C₂×C₄	—	13	8	no	—
194	C₂×C₄	—	13	4	no	—
195	C₂×C₄	—	26	16	no	—
196	C₂×C₄	—	26	4	no	—
197	C₂×C₄	#88054	1	8	yes	—
198	C₂×C₄	#88054	1	4	yes	—
199	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
200	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
201	C₂×C₄	C₂×#6094	1	4	yes	—
202	C₂×C₄	C₂×#6094	1	2	yes	—
203	C₂×C₄	C₂×#6101	1	4	yes	—
204	C₂×C₄	C₂×#6101	1	2	yes	—
205	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
206	C₈	—	26	4	no	—
207	C₈	C₂×#6101	1	4	yes	—
208	C₈	C₂×#6101	1	2	yes	—
209	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
210	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
211	C₂²	—	2	8	no	—
212	C₂²	—	2	4	no	—
213	C₂²	D₁₃×M₃₂	1	4	yes	—
214	C₂²	C₂×#88054	1	4	yes	—
215	C₂²	C₂×#88054	1	2	yes	—
216	C₂²	C₂²×C₈×D₁₃	1	1	yes	characteristic
217	C₄	—	13	8	no	—
218	C₄	—	26	4	no	—
219	C₄	C₂×#88054	1	4	yes	—
220	C₄	C₂×#88054	1	2	yes	—
221	C₄	C₂²×#6094	1	1	yes	characteristic
222	C₄	C₂²×#6101	1	1	yes	characteristic
223	C₂	—	2	4	no	—
224	C₂	#13116591	1	4	yes	direct product factor
225	C₂	C₂²×#88054	1	1	yes	characteristic
226	C₂	C₂×D₁₃×M₃₂	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₂²×C₁₃×M₃₂	C₂
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	C₂²×M₃₂	D₁₃
hypocenter	C₁₃	C₂×#2150
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₈ ◁ C₂²×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13116591	C₂	direct (N × H)
4. C₂×#11718093	C₂	semidirect
19. #11718093	C₂²	semidirect
95. C₂×Dic₁₃	M₃₂	semidirect
128. Dic₁₃	C₂×M₃₂	semidirect
155. C₂×C₁₃	#2150	semidirect
187. C₁₃	C₂×#2150	semidirect
224. C₂	#13116591	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×#88052	2
C₂²×C₈×Dic₁₃	2
#13116591	2
C₂×#11718093	2
C₂²×C₁₃×M₃₂	2
C₂×#2150	13

Subgroups — C2×#13116591 #16015897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13116591 #16015897