Subgroups — C₂×D₁₃⋊M₆₄ #16807432

Order 3328.

502 conjugacy classes of subgroups.

The subgroup lattice has 222 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718214	C₂	1	2	yes	maximal, complemented
2	D₁₃⋊M₆₄	C₂	1	8	yes	maximal, direct product factor
3	C₂×#11718249	C₂	1	2	yes	maximal, complemented
4	C₂×D₁₃⋊C₃₂	C₂	1	2	yes	maximal, complemented
5	C₂²×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₈×D₁₃	C₄	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
8	C₂²×#6090	C₂²	1	1	yes	characteristic
9	C₂×C₁₆×D₁₃	C₄	1	4	yes	—
10	C₂×C₁₆×D₁₃	C₄	1	1	yes	characteristic
11	C₂×C₁₆×D₁₃	C₄	1	1	yes	characteristic
12	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₆×D₁₃	C₂²	1	4	yes	—
14	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
15	#11718249	C₂²	1	8	yes	complemented
16	C₂×#88036	C₂²	1	4	yes	complemented
17	#11718214	C₂²	1	8	yes	complemented
18	D₁₃⋊C₃₂	C₂²	1	8	yes	complemented
19	C₂²×C₄×D₁₃	C₈	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×#1055	C₈	1	1	yes	characteristic
22	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
23	C₂×C₈×D₁₃	C₈	1	4	yes	—
24	C₂×C₈×D₁₃	C₈	1	1	yes	characteristic
25	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₈×D₁₃	C₂×C₄	1	4	yes	—
27	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
29	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
30	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
31	C₂×#6090	C₂×C₄	1	2	yes	—
32	C₂×#6090	C₂×C₄	1	1	yes	characteristic
33	C₂×#6090	C₂³	1	1	yes	characteristic
34	C₂×#6090	C₂³	1	2	yes	—
35	C₁₆×D₁₃	C₂×C₄	1	2	yes	—
36	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
37	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
38	C₁₆×D₁₃	C₂×C₄	1	2	yes	—
39	C₁₆×D₁₃	C₂³	1	2	yes	—
40	C₁₆×D₁₃	C₂³	1	2	yes	—
41	#88036	C₂³	1	8	yes	complemented
42	C₂²×M₆₄	—	13	1	no	maximal, Sylow
43	C₂³×D₁₃	C₁₆	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
45	C₂²×Dic₁₃	C₁₆	1	1	yes	characteristic
46	C₂×C₄×D₁₃	C₁₆	1	1	yes	characteristic
47	C₂×C₄×D₁₃	C₁₆	1	4	yes	—
48	C₂×C₄×D₁₃	C₁₆	1	1	yes	characteristic
49	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
50	C₂×C₄×D₁₃	C₂×C₈	1	4	yes	—
51	C₂×C₄×D₁₃	C₂×C₈	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
53	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
54	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
55	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
56	C₂×#1055	C₂×C₈	1	4	yes	—
57	C₂×#1055	C₂×C₈	1	1	yes	characteristic
58	C₂×#1055	C₂×C₈	1	1	yes	characteristic
59	C₈×D₁₃	C₂×C₈	1	4	yes	—
60	C₈×D₁₃	C₂×C₈	1	2	yes	—
61	C₈×D₁₃	C₂×C₈	1	2	yes	—
62	C₈×D₁₃	C₂×C₈	1	4	yes	—
63	C₈×D₁₃	C₂²×C₄	1	2	yes	—
64	C₈×D₁₃	C₂²×C₄	1	2	yes	—
65	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
66	C₁₃×C₁₆	C₂²×C₄	1	2	yes	—
67	#6090	C₂²×C₄	1	1	yes	characteristic
68	#6090	C₂²×C₄	1	2	yes	—
69	#6090	C₂⁴	1	1	yes	characteristic
70	C₂³×C₁₆	—	13	1	no	—
71	C₂×M₆₄	—	13	2	no	—
72	C₂×M₆₄	—	13	8	no	—
73	C₂×M₆₄	—	13	2	no	—
74	C₂²×C₃₂	—	13	2	no	—
75	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
76	C₂²×D₁₃	—	2	4	no	—
77	C₂²×D₁₃	C₂×C₁₆	1	1	yes	characteristic
78	C₂²×D₁₃	C₂×C₁₆	1	4	yes	—
79	C₂²×D₁₃	C₂×C₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
81	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
83	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
84	C₂×Dic₁₃	C₂×C₁₆	1	4	yes	—
85	C₂×Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
86	C₂×Dic₁₃	C₂×C₁₆	1	1	yes	characteristic
87	C₄×D₁₃	C₂×C₁₆	1	4	yes	—
88	C₄×D₁₃	C₂×C₁₆	1	2	yes	—
89	C₄×D₁₃	C₂×C₁₆	1	2	yes	—
90	C₄×D₁₃	C₂×C₁₆	1	4	yes	—
91	C₄×D₁₃	C₂²×C₈	1	2	yes	—
92	C₄×D₁₃	C₂²×C₈	1	2	yes	—
93	C₈×C₁₃	C₂²×C₈	1	2	yes	—
94	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
95	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
96	#1055	C₂²×C₈	1	2	yes	—
97	#1055	C₂²×C₈	1	2	yes	—
98	C₂³×C₈	—	13	1	no	—
99	C₂²×C₁₆	—	13	1	no	—
100	C₂²×C₁₆	—	13	4	no	—
101	C₂²×C₁₆	—	13	1	no	—
102	C₂²×C₁₆	—	13	1	no	—
103	C₂²×C₁₆	—	13	4	no	—
104	C₂²×C₁₆	—	13	1	no	—
105	C₂²×C₁₆	—	13	1	no	—
106	C₂²×C₁₆	#261	1	1	yes	characteristic
107	M₆₄	—	13	8	no	—
108	M₆₄	—	13	8	no	—
109	C₂×C₃₂	—	13	8	no	—
110	C₂×C₃₂	—	13	4	no	—
111	C₂²×C₁₃	—	2	2	no	—
112	C₂²×C₁₃	C₂²×C₁₆	1	2	yes	—
113	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
114	C₂×D₁₃	—	2	2	no	—
115	C₂×D₁₃	—	2	8	no	—
116	C₂×D₁₃	M₆₄	1	4	yes	complemented
117	C₂×D₁₃	C₂²×C₁₆	1	2	yes	—
118	C₂×D₁₃	C₂²×C₁₆	1	2	yes	—
119	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
120	C₄×C₁₃	C₂²×C₁₆	1	2	yes	—
121	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
122	Dic₁₃	C₂²×C₁₆	1	2	yes	—
123	Dic₁₃	C₂²×C₁₆	1	2	yes	—
124	C₂³×C₄	—	13	1	no	—
125	C₂²×C₈	—	13	1	no	—
126	C₂²×C₈	—	13	1	no	—
127	C₂²×C₈	—	13	4	no	—
128	C₂²×C₈	—	13	1	no	—
129	C₂²×C₈	—	13	4	no	—
130	C₂²×C₈	—	13	1	no	—
131	C₂²×C₈	—	13	1	no	—
132	C₂²×C₈	C₂×#261	1	1	yes	characteristic
133	C₂×C₁₆	—	13	1	no	—
134	C₂×C₁₆	—	13	2	no	—
135	C₂×C₁₆	—	13	2	no	—
136	C₂×C₁₆	—	13	1	no	—
137	C₂×C₁₆	—	13	2	no	—
138	C₂×C₁₆	—	13	2	no	—
139	C₂×C₁₆	—	13	2	no	—
140	C₂×C₁₆	—	13	4	no	—
141	C₂×C₁₆	—	13	2	no	—
142	C₂×C₁₆	—	13	4	no	—
143	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
144	C₂×C₁₆	C₂×#261	1	4	yes	—
145	C₂×C₁₆	C₂×#261	1	1	yes	characteristic
146	C₃₂	—	13	8	no	—
147	C₂×C₁₃	—	2	2	no	—
148	C₂×C₁₃	C₂×M₆₄	1	2	yes	complemented
149	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
150	D₁₃	—	2	2	no	—
151	D₁₃	C₂×M₆₄	1	4	yes	complemented
152	C₂⁴	—	13	1	no	—
153	C₂²×C₄	—	13	1	no	—
154	C₂²×C₄	—	13	1	no	—
155	C₂²×C₄	—	13	4	no	—
156	C₂²×C₄	—	13	1	no	—
157	C₂²×C₄	—	13	1	no	—
158	C₂²×C₄	—	13	4	no	—
159	C₂²×C₄	—	13	1	no	—
160	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
161	C₂×C₈	—	13	4	no	—
162	C₂×C₈	—	13	1	no	—
163	C₂×C₈	—	13	1	no	—
164	C₂×C₈	—	13	4	no	—
165	C₂×C₈	—	13	4	no	—
166	C₂×C₈	—	13	2	no	—
167	C₂×C₈	—	13	2	no	—
168	C₂×C₈	—	13	2	no	—
169	C₂×C₈	—	13	2	no	—
170	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
171	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
172	C₂×C₈	C₂²×#261	1	2	yes	—
173	C₂×C₈	C₂²×#261	1	1	yes	characteristic
174	C₁₆	—	13	1	no	—
175	C₁₆	—	13	1	no	—
176	C₁₆	—	13	2	no	—
177	C₁₆	C₂²×#261	1	2	yes	—
178	C₁₆	C₂²×#261	1	2	yes	—
179	C₁₃	C₂²×M₆₄	1	1	yes	characteristic, complemented, Sylow
180	C₂³	—	13	1	no	—
181	C₂³	—	13	4	no	—
182	C₂³	—	13	1	no	—
183	C₂³	—	26	4	no	—
184	C₂³	D₁₃⋊C₁₆	1	1	yes	characteristic
185	C₂×C₄	—	13	4	no	—
186	C₂×C₄	—	13	1	no	—
187	C₂×C₄	—	13	1	no	—
188	C₂×C₄	—	13	4	no	—
189	C₂×C₄	—	13	2	no	—
190	C₂×C₄	—	13	2	no	—
191	C₂×C₄	—	13	4	no	—
192	C₂×C₄	—	13	2	no	—
193	C₂×C₄	—	13	2	no	—
194	C₂×C₄	D₁₃⋊C₁₆	1	2	yes	—
195	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
196	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
197	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
198	C₈	—	13	2	no	—
199	C₈	—	13	2	no	—
200	C₈	C₂×D₁₃⋊C₈	1	2	yes	—
201	C₈	C₂×D₁₃⋊C₈	1	1	yes	characteristic
202	C₈	C₂³×#261	1	1	yes	characteristic
203	C₂²	—	2	2	no	—
204	C₂²	—	13	2	no	—
205	C₂²	—	13	4	no	—
206	C₂²	—	13	2	no	—
207	C₂²	—	26	8	no	—
208	C₂²	—	26	2	no	—
209	C₂²	C₂×D₁₃⋊C₁₆	1	2	yes	—
210	C₂²	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
211	C₄	—	13	2	no	—
212	C₄	—	13	2	no	—
213	C₄	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
214	C₄	C₂×D₁₃⋊C₁₆	1	2	yes	—
215	C₄	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
216	C₂	—	2	2	no	—
217	C₂	—	13	4	no	—
218	C₂	—	26	2	no	—
219	C₂	D₁₃⋊M₆₄	1	2	yes	direct product factor
220	C₂	C₂²×D₁₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂×#261
commutator	C₂×C₁₃	C₂³×C₁₆
Frattini	C₈	C₂³×#261
Fitting	C₂²×C₁₃×C₁₆	C₄
socle	C₂²×C₁₃	C₂²×C₁₆
prime radical	C₂³×D₁₃	C₁₆
cosocle	#6090	C₂⁴
hypercenter	C₂²×C₁₆	#261
hypocenter	C₁₃	C₂²×M₆₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#11718214	C₂	semidirect
2. D₁₃⋊M₆₄	C₂	direct (N × H)
3. C₂×#11718249	C₂	semidirect
4. C₂×D₁₃⋊C₃₂	C₂	semidirect
15. #11718249	C₂²	semidirect
16. C₂×#88036	C₂²	semidirect
17. #11718214	C₂²	semidirect
18. D₁₃⋊C₃₂	C₂²	semidirect
41. #88036	C₂³	semidirect
116. C₂×D₁₃	M₆₄	semidirect
148. C₂×C₁₃	C₂×M₆₄	semidirect
151. D₁₃	C₂×M₆₄	semidirect
179. C₁₃	C₂²×M₆₄	semidirect
219. C₂	D₁₃⋊M₆₄	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×#11718214	2
D₁₃⋊M₆₄	2
C₂×#11718249	2
C₂×D₁₃⋊C₃₂	2
C₂²×C₁₆×D₁₃	2
C₂²×M₆₄	13

Subgroups — C2×D13⋊M64 #16807432

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃⋊M₆₄ #16807432