Subgroups — C₂×#13112979 #15783127

Order 3328.

294 conjugacy classes of subgroups.

The subgroup lattice has 220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718562	C₂	1	1	yes	maximal, characteristic
2	C₂²×#88034	C₂	1	1	yes	maximal, characteristic, complemented
3	#13112979	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₁₃×M₆₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88155	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×#88052	C₄	1	1	yes	characteristic
8	#11718562	—	2	1	no	—
9	#11718562	—	2	1	no	—
10	#11718562	C₄	1	2	yes	—
11	#11718562	C₂²	1	2	yes	—
12	C₂×#88038	—	2	1	no	—
13	C₂×C₁₆×D₁₃	—	2	1	no	—
14	C₁₃×M₆₄	—	2	1	no	—
15	C₁₃×M₆₄	C₂²	1	2	yes	complemented
16	C₂×C₁₃×C₃₂	—	2	1	no	—
17	C₂×#88034	—	2	1	no	—
18	C₂×#88034	—	2	1	no	—
19	C₂×#88034	C₂²	1	2	yes	complemented
20	C₂×#6127	C₈	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×#6099	C₈	1	1	yes	characteristic
23	#88155	—	2	1	no	—
24	#88155	—	2	1	no	—
25	#88155	C₈	1	2	yes	—
26	#88155	C₂×C₄	1	2	yes	—
27	C₂×#6094	—	2	1	no	—
28	C₂×C₈×D₁₃	—	2	1	no	—
29	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
31	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
32	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
33	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
34	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
35	#88052	—	2	1	no	—
36	#88052	C₂×C₄	1	2	yes	—
37	C₂×#6090	—	2	1	no	—
38	#88038	—	2	2	no	—
39	#88038	—	2	2	no	—
40	C₁₆×D₁₃	—	2	2	no	—
41	C₁₆×D₁₃	—	2	2	no	—
42	C₁₃×C₃₂	—	2	2	no	—
43	#88034	—	2	2	no	—
44	C₂×#1401	—	13	1	no	maximal, Sylow
45	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
46	C₂×C₂²⋊D₁₃	—	2	1	no	—
47	#6127	—	2	1	no	—
48	#6127	—	2	1	no	—
49	#6127	C₁₆	1	2	yes	—
50	#6127	C₂×C₈	1	2	yes	—
51	C₂×D₅₂	C₁₆	1	1	yes	characteristic
52	C₂×C₄×D₁₃	—	2	1	no	—
53	C₂×Dic₂₆	C₁₆	1	1	yes	characteristic
54	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
57	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
58	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
59	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
60	#6099	—	2	1	no	—
61	#6099	C₂×C₈	1	2	yes	—
62	C₂×#1055	—	2	1	no	—
63	#6094	—	2	2	no	—
64	#6094	—	2	2	no	—
65	C₈×D₁₃	—	2	2	no	—
66	C₈×D₁₃	—	2	2	no	—
67	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
68	C₁₃×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
69	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
70	C₁₃×C₁₆	C₂×D₄	1	1	yes	characteristic
71	#6090	—	2	2	no	—
72	C₂×#504	—	13	1	no	—
73	C₂×M₆₄	D₁₃	1	1	yes	characteristic, complemented
74	C₂²×C₃₂	—	13	1	no	—
75	#1401	—	13	4	no	—
76	C₂³×C₁₃	M₃₂	1	1	yes	characteristic
77	C₂²×D₁₃	—	2	1	no	—
78	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
84	C₂²⋊D₁₃	—	2	2	no	—
85	C₂²⋊D₁₃	—	2	2	no	—
86	C₂×Dic₁₃	—	2	1	no	—
87	D₅₂	—	2	1	no	—
88	D₅₂	C₂×C₁₆	1	2	yes	—
89	C₄×D₁₃	—	2	2	no	—
90	C₄×D₁₃	—	2	2	no	—
91	Dic₂₆	—	2	1	no	—
92	Dic₂₆	C₂×C₁₆	1	2	yes	—
93	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
94	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
95	C₈×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
96	C₈×C₁₃	C₂×M₁₆	1	1	yes	characteristic
97	#1055	—	2	2	no	—
98	C₂×#131	—	13	1	no	—
99	#504	—	13	2	no	—
100	#504	—	13	2	no	—
101	#504	—	26	1	no	—
102	#504	—	26	1	no	—
103	C₂×M₃₂	—	13	1	no	—
104	C₂×M₃₂	—	26	1	no	—
105	C₂²×C₁₆	—	26	1	no	—
106	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
107	M₆₄	—	2	1	no	—
108	M₆₄	C₂×D₁₃	1	2	yes	complemented
109	C₂×C₃₂	—	2	1	no	—
110	C₂×C₃₂	—	13	2	no	—
111	C₂×C₃₂	—	26	1	no	—
112	C₂×C₃₂	—	26	1	no	—
113	C₂²×C₁₃	—	2	2	no	—
114	C₂²×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
115	C₂²×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
116	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
117	C₂×D₁₃	—	2	2	no	—
118	C₂×D₁₃	—	4	2	no	—
119	C₄×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
120	C₄×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
121	C₄×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
122	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
123	Dic₁₃	—	2	2	no	—
124	C₂×#41	—	13	1	no	—
125	#131	—	13	2	no	—
126	#131	—	13	2	no	—
127	#131	—	26	1	no	—
128	#131	—	26	1	no	—
129	C₂×M₁₆	—	13	1	no	—
130	C₂×M₁₆	—	26	1	no	—
131	C₂²×C₈	—	26	1	no	—
132	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
133	M₃₂	—	13	2	no	—
134	M₃₂	—	26	1	no	—
135	M₃₂	—	26	2	no	—
136	M₃₂	—	26	2	no	—
137	C₂×C₁₆	—	26	1	no	—
138	C₂×C₁₆	—	26	2	no	—
139	C₂×C₁₆	—	26	2	no	—
140	C₂×C₁₆	C₄×D₁₃	1	1	yes	characteristic
141	C₂×C₁₆	D₅₂	1	1	yes	characteristic
142	C₂×C₁₆	D₅₂	1	1	yes	characteristic
143	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
144	C₂×C₁₆	C₂²⋊D₁₃	1	1	yes	characteristic
145	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
146	C₃₂	—	2	2	no	—
147	C₃₂	—	26	2	no	—
148	C₂×C₁₃	—	2	1	no	—
149	C₂×C₁₃	—	2	1	no	—
150	C₂×C₁₃	#1401	1	2	yes	complemented
151	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
152	D₁₃	—	4	2	no	—
153	#41	—	13	2	no	—
154	#41	—	13	2	no	—
155	#41	—	26	1	no	—
156	#41	—	26	1	no	—
157	C₂×Q₈	—	13	1	no	—
158	C₂×D₄	—	13	1	no	—
159	C₂×D₄	—	26	1	no	—
160	C₂²×C₄	—	26	1	no	—
161	C₂²×C₄	C₈×D₁₃	1	1	yes	characteristic
162	M₁₆	—	13	2	no	—
163	M₁₆	—	26	1	no	—
164	M₁₆	—	26	2	no	—
165	M₁₆	—	26	2	no	—
166	C₂×C₈	—	26	1	no	—
167	C₂×C₈	—	26	2	no	—
168	C₂×C₈	—	26	2	no	—
169	C₂×C₈	C₈×D₁₃	1	1	yes	characteristic
170	C₂×C₈	#6094	1	1	yes	characteristic
171	C₂×C₈	#6094	1	1	yes	characteristic
172	C₂×C₈	#6103	1	1	yes	characteristic
173	C₂×C₈	#6103	1	1	yes	characteristic
174	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
175	C₁₆	—	26	2	no	—
176	C₁₆	#6103	1	1	yes	characteristic
177	C₁₆	#6103	1	1	yes	characteristic
178	C₁₆	C₂×D₅₂	1	1	yes	characteristic
179	C₁₆	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
180	C₁₃	C₂×#1401	1	1	yes	characteristic, complemented, Sylow
181	C₂³	—	26	1	no	—
182	C₂³	#88038	1	1	yes	characteristic
183	Q₈	—	13	2	no	—
184	Q₈	—	26	1	no	—
185	D₄	—	13	2	no	—
186	D₄	—	26	2	no	—
187	D₄	—	26	2	no	—
188	D₄	—	26	1	no	—
189	C₂×C₄	—	26	1	no	—
190	C₂×C₄	—	26	2	no	—
191	C₂×C₄	—	26	2	no	—
192	C₂×C₄	C₁₆×D₁₃	1	1	yes	characteristic
193	C₂×C₄	C₁₆×D₁₃	1	1	yes	characteristic
194	C₂×C₄	#88038	1	1	yes	characteristic
195	C₂×C₄	#88060	1	1	yes	characteristic
196	C₂×C₄	#88060	1	1	yes	characteristic
197	C₂×C₄	C₂×C₈×D₁₃	1	1	yes	characteristic
198	C₈	—	26	2	no	—
199	C₈	#88060	1	1	yes	characteristic
200	C₈	#88060	1	1	yes	characteristic
201	C₈	C₂×#6094	1	1	yes	characteristic
202	C₈	C₂×#6103	1	1	yes	characteristic
203	C₂²	—	2	2	no	—
204	C₂²	—	26	2	no	—
205	C₂²	—	52	2	no	—
206	C₂²	#11718099	1	1	yes	characteristic
207	C₂²	#11718099	1	1	yes	characteristic
208	C₂²	C₂×#88038	1	1	yes	characteristic
209	C₄	—	26	2	no	—
210	C₄	#11718099	1	1	yes	characteristic
211	C₄	#11718099	1	1	yes	characteristic
212	C₄	C₂×C₁₆×D₁₃	1	1	yes	characteristic
213	C₄	C₂×#88060	1	1	yes	characteristic
214	C₂	—	2	1	no	—
215	C₂	—	2	1	no	—
216	C₂	—	52	2	no	—
217	C₂	#13112979	1	2	yes	direct product factor
218	C₂	C₂×#11718099	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₂×C₁₃×M₆₄	C₂
socle	C₂²×C₁₃	C₂²⋊C₁₆
prime radical	C₂×#6127	C₈
cosocle	C₂×C₁₃×C₁₆	C₂³
hypercenter	C₂×M₆₄	D₁₃
hypocenter	C₁₃	C₂×#1401
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
2. C₂²×#88034	C₂	semidirect
3. #13112979	C₂	direct (N × H)
4. C₂×C₁₃×M₆₄	C₂	semidirect
15. C₁₃×M₆₄	C₂²	semidirect
19. C₂×#88034	C₂²	semidirect
73. C₂×M₆₄	D₁₃	semidirect
108. M₆₄	C₂×D₁₃	semidirect
150. C₂×C₁₃	#1401	semidirect
180. C₁₃	C₂×#1401	semidirect
217. C₂	#13112979	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×#11718562	2
C₂²×#88034	2
#13112979	2
C₂×C₁₃×M₆₄	2
C₂×#1401	13

Subgroups — C2×#13112979 #15783127

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13112979 #15783127