Subgroups — C₂×#13113130 #15828536

Order 3328.

866 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	C₂×#11718346	C₂	1	2	yes	maximal
2	C₂×C₄×#6094	C₂	1	1	yes	maximal, characteristic
3	#13113130	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718046	C₂	1	2	yes	maximal, complemented
5	C₂×#11718047	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#6094	C₄	1	2	yes	—
8	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂×#88060	C₄	1	4	yes	—
12	C₂×#88055	C₄	1	2	yes	—
13	C₂×#88054	C₄	1	4	yes	—
14	C₂×C₄×#1055	C₂²	1	2	yes	—
15	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
16	C₄×#6094	C₄	1	4	yes	—
17	C₄×#6094	C₂²	1	4	yes	—
18	#11718346	C₄	1	8	yes	—
19	#11718346	C₂²	1	8	yes	—
20	C₈²×C₁₃	C₂²	1	4	yes	complemented
21	#11718047	C₂²	1	4	yes	complemented
22	#11718046	C₂²	1	8	yes	complemented
23	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄×D₁₃	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
26	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
29	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₂²×#1055	C₂×C₄	1	2	yes	—
31	C₂²×#1055	C₂×C₄	1	4	yes	—
32	C₂×#6094	—	2	8	no	—
33	C₂×#6094	C₂×C₄	1	8	yes	—
34	C₄²×D₁₃	C₂×C₄	1	4	yes	—
35	C₄²×D₁₃	C₂×C₄	1	2	yes	—
36	C₄²×D₁₃	C₂³	1	2	yes	—
37	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
38	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₁₃	C₂³	1	4	yes	—
40	C₄×C₈×C₁₃	C₂³	1	2	yes	—
41	#88060	C₂×C₄	1	16	yes	—
42	#88055	C₂×C₄	1	8	yes	—
43	#88054	C₂×C₄	1	16	yes	—
44	C₄×#1055	C₂×C₄	1	4	yes	—
45	C₄×#1055	C₂×C₄	1	2	yes	—
46	C₄×#1055	C₂³	1	2	yes	—
47	C₄×#1055	C₂³	1	4	yes	—
48	C₂×#1453	—	13	1	no	maximal, Sylow
49	C₂³×D₁₃	C₄²	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
52	C₂²×Dic₁₃	C₄²	1	1	yes	characteristic
53	C₂²×Dic₁₃	C₄²	1	2	yes	—
54	C₂×C₄×D₁₃	—	2	4	no	—
55	C₂×C₄×D₁₃	—	2	8	no	—
56	C₂×C₄×D₁₃	C₄²	1	2	yes	—
57	C₂×C₄×D₁₃	C₄²	1	4	yes	—
58	C₂×C₄×D₁₃	C₂²×C₄	1	2	yes	—
59	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
60	C₂×C₈×C₁₃	—	2	8	no	—
61	C₂×C₈×C₁₃	M₁₆	1	8	yes	—
62	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
63	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
64	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
65	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
67	C₄×Dic₁₃	C₄²	1	2	yes	—
68	C₄×Dic₁₃	C₄²	1	4	yes	—
69	C₄×Dic₁₃	C₂²×C₄	1	4	yes	—
70	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
71	C₂×#1055	—	2	4	no	—
72	C₂×#1055	—	2	8	no	—
73	C₂×#1055	C₂²×C₄	1	4	yes	—
74	C₂×#1055	C₂²×C₄	1	8	yes	—
75	#6094	—	2	16	no	—
76	C₂×#431	—	13	2	no	—
77	C₂×C₄×M₁₆	—	13	1	no	—
78	#1453	—	13	8	no	—
79	C₂×#322	—	13	1	no	—
80	C₂×#322	—	13	2	no	—
81	C₂×C₈²	D₁₃	1	1	yes	characteristic, complemented
82	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
83	C₂²×D₁₃	—	2	2	no	—
84	C₂²×D₁₃	—	2	4	no	—
85	C₂²×D₁₃	C₂×C₄²	1	2	yes	—
86	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
87	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
88	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
89	C₂×C₄×C₁₃	#131	1	8	yes	—
90	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
91	C₂×C₄×C₁₃	C₂³×C₄	1	2	yes	—
92	C₂×Dic₁₃	—	2	2	no	—
93	C₂×Dic₁₃	—	2	4	no	—
94	C₂×Dic₁₃	C₂×C₄²	1	2	yes	—
95	C₂×Dic₁₃	C₂×C₄²	1	4	yes	—
96	C₄×D₁₃	—	2	4	no	—
97	C₄×D₁₃	—	2	8	no	—
98	C₄×D₁₃	—	2	4	no	—
99	C₄×D₁₃	—	2	8	no	—
100	C₈×C₁₃	—	2	8	no	—
101	C₈×C₁₃	C₂×M₁₆	1	8	yes	—
102	#1055	—	2	4	no	—
103	#1055	—	2	8	no	—
104	C₂²×M₁₆	—	13	2	no	—
105	C₂²×C₄²	—	13	1	no	—
106	#431	—	13	8	no	—
107	#431	—	13	8	no	—
108	C₂×C₄⋊C₈	—	13	4	no	—
109	C₂×C₂²⋊C₈	—	13	4	no	—
110	C₄×M₁₆	—	13	4	no	—
111	C₄×M₁₆	—	13	4	no	—
112	C₂×#97	—	13	2	no	—
113	C₂×C₄×C₈	—	13	1	no	—
114	C₂×C₄×C₈	—	13	2	no	—
115	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
116	C₂×C₄×C₈	C₂×D₁₃	1	2	yes	—
117	#322	—	13	8	no	—
118	#322	—	13	4	no	—
119	C₈²	C₂×D₁₃	1	4	yes	complemented
120	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
121	C₂²×C₁₃	#405	1	4	yes	—
122	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
123	C₂×D₁₃	—	2	2	no	—
124	C₂×D₁₃	—	2	4	no	—
125	C₂×D₁₃	—	4	4	no	—
126	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
127	C₄×C₁₃	#405	1	4	yes	—
128	C₄×C₁₃	C₂²×M₁₆	1	2	yes	—
129	C₄×C₁₃	C₂×#131	1	4	yes	—
130	Dic₁₃	—	2	2	no	—
131	Dic₁₃	—	2	4	no	—
132	C₂³×C₄	—	13	1	no	—
133	C₂³×C₄	—	13	2	no	—
134	C₂×M₁₆	—	13	8	no	—
135	C₂×M₁₆	—	26	8	no	—
136	C₂²×C₈	—	13	2	no	—
137	C₂²×C₈	—	13	4	no	—
138	C₂²×C₈	C₄×D₁₃	1	4	yes	—
139	C₂²×C₈	C₄×D₁₃	1	2	yes	—
140	C₂×C₄²	—	13	1	no	—
141	C₂×C₄²	—	13	2	no	—
142	C₂×C₄²	—	13	2	no	—
143	C₂×C₄²	—	13	4	no	—
144	C₂×C₄²	—	13	2	no	—
145	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
146	C₄⋊C₈	—	13	16	no	—
147	C₂²⋊C₈	—	13	16	no	—
148	#97	—	13	8	no	—
149	C₄×C₈	—	13	2	no	—
150	C₄×C₈	—	13	4	no	—
151	C₄×C₈	—	13	2	no	—
152	C₄×C₈	—	13	4	no	—
153	C₄×C₈	C₄×D₁₃	1	2	yes	—
154	C₄×C₈	C₄×D₁₃	1	4	yes	—
155	C₄×C₈	C₂²×D₁₃	1	2	yes	—
156	C₄×C₈	C₂²×D₁₃	1	4	yes	—
157	C₂×C₁₃	#1453	1	4	yes	complemented
158	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
159	C₂×C₁₃	C₂×#405	1	2	yes	—
160	D₁₃	—	4	2	no	—
161	C₂⁴	—	13	1	no	—
162	C₂²×C₄	—	13	1	no	—
163	C₂²×C₄	—	13	2	no	—
164	C₂²×C₄	—	13	2	no	—
165	C₂²×C₄	—	13	4	no	—
166	C₂²×C₄	—	13	4	no	—
167	C₂²×C₄	—	13	2	no	—
168	C₂²×C₄	—	26	4	no	—
169	C₂²×C₄	—	26	8	no	—
170	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
171	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
172	M₁₆	—	26	16	no	—
173	C₂×C₈	—	2	8	no	—
174	C₂×C₈	—	13	4	no	—
175	C₂×C₈	—	13	8	no	—
176	C₂×C₈	—	26	4	no	—
177	C₂×C₈	—	26	8	no	—
178	C₂×C₈	#6094	1	8	yes	—
179	C₂×C₈	C₂×C₄×D₁₃	1	8	yes	—
180	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
181	C₄²	—	13	2	no	—
182	C₄²	—	13	4	no	—
183	C₄²	—	13	2	no	—
184	C₄²	—	13	4	no	—
185	C₄²	C₂×C₄×D₁₃	1	2	yes	—
186	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
187	C₄²	C₂³×D₁₃	1	1	yes	characteristic
188	C₁₃	C₂×#1453	1	1	yes	characteristic, complemented, Sylow
189	C₂³	—	13	2	no	—
190	C₂³	—	26	2	no	—
191	C₂³	—	26	4	no	—
192	C₂³	C₄²×D₁₃	1	1	yes	characteristic
193	C₂×C₄	—	13	2	no	—
194	C₂×C₄	—	13	4	no	—
195	C₂×C₄	—	26	2	no	—
196	C₂×C₄	—	26	4	no	—
197	C₂×C₄	—	26	4	no	—
198	C₂×C₄	—	26	8	no	—
199	C₂×C₄	—	26	4	no	—
200	C₂×C₄	—	26	8	no	—
201	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
202	C₂×C₄	C₄²×D₁₃	1	2	yes	—
203	C₂×C₄	C₂×#6094	1	4	yes	—
204	C₂×C₄	#88155	1	8	yes	—
205	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
206	C₂×C₄	C₂²×C₄×D₁₃	1	2	yes	—
207	C₈	—	2	8	no	—
208	C₈	—	26	4	no	—
209	C₈	—	26	8	no	—
210	C₈	C₂×#6094	1	8	yes	—
211	C₂²	—	26	2	no	—
212	C₂²	—	26	4	no	—
213	C₂²	—	52	4	no	—
214	C₂²	C₄×#6094	1	2	yes	—
215	C₂²	#11718350	1	4	yes	—
216	C₂²	C₂×C₄²×D₁₃	1	1	yes	characteristic
217	C₄	—	26	2	no	—
218	C₄	—	26	4	no	—
219	C₄	C₄×#6094	1	2	yes	—
220	C₄	#11718350	1	4	yes	—
221	C₄	C₂²×#6094	1	2	yes	—
222	C₄	C₂×#88155	1	4	yes	—
223	C₂	—	52	2	no	—
224	C₂	#13113130	1	4	yes	direct product factor
225	C₂	C₂×C₄×#6094	1	1	yes	characteristic
226	C₂	C₂×#11718350	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	C₂²×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Frattini	C₄²	C₂³×D₁₃
Fitting	C₂×C₈²×C₁₃	C₂
socle	C₂³×C₁₃	C₂×C₄²
prime radical	C₂³×D₁₃	C₄²
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	C₂×C₈²	D₁₃
hypocenter	C₁₃	C₂×#1453
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
3. #13113130	C₂	direct (N × H)
4. C₂×#11718046	C₂	semidirect
5. C₂×#11718047	C₂	semidirect
6. C₂×C₈²×C₁₃	C₂	semidirect
20. C₈²×C₁₃	C₂²	semidirect
21. #11718047	C₂²	semidirect
22. #11718046	C₂²	semidirect
81. C₂×C₈²	D₁₃	semidirect
119. C₈²	C₂×D₁₃	semidirect
157. C₂×C₁₃	#1453	semidirect
188. C₁₃	C₂×#1453	semidirect
224. C₂	#13113130	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×#11718346	2
C₂×C₄×#6094	2
#13113130	2
C₂×#11718046	2
C₂×#11718047	2
C₂×C₈²×C₁₃	2
C₂×#1453	13

Subgroups — C2×#13113130 #15828536

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13113130 #15828536