Subgroups — C₁₃×#13264 #15699603

Order 3328.

386 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Q₈×C₁₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1374	C₂	1	4	yes	maximal
5	C₂×C₄×Q₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
7	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
8	C₈×Q₈×C₁₃	—	2	2	no	—
9	C₈×Q₈×C₁₃	—	2	2	no	—
10	C₂×C₁₃×C₄⋊C₈	C₄	1	2	yes	—
11	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×C₄⋊C₁₆	—	2	2	no	—
15	C₁₃×#346	—	2	2	no	—
16	C₂²×Q₈×C₁₃	C₈	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₄×Q₈×C₁₃	—	2	2	no	—
21	C₄×Q₈×C₁₃	—	2	2	no	—
22	C₂×C₁₃×C₄⋊C₄	C₈	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₄	C₈	1	2	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₃×C₁₆	—	2	2	no	—
27	C₂×C₁₃×C₁₆	—	2	2	no	—
28	C₂×C₁₃×C₁₆	—	2	2	no	—
29	C₂×C₁₃×C₁₆	—	2	4	no	—
30	C₂×C₁₃×C₁₆	Q₈	1	4	yes	complemented
31	C₁₃×C₄⋊C₈	—	2	4	no	—
32	C₁₃×C₄⋊C₈	—	2	2	no	—
33	C₄×C₈×C₁₃	—	2	2	no	—
34	C₄×C₈×C₁₃	—	2	2	no	—
35	C₄×C₈×C₁₃	D₄	1	2	yes	—
36	C₄×C₈×C₁₃	D₄	1	2	yes	—
37	#13264	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×Q₈×C₁₃	—	2	2	no	—
39	C₂×Q₈×C₁₃	—	2	4	no	—
40	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
41	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	—	2	2	no	—
46	C₂×C₈×C₁₃	—	2	2	no	—
47	C₂×C₈×C₁₃	—	2	4	no	—
48	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
49	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
52	C₂×C₈×C₁₃	#41	1	2	yes	—
53	C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₄²×C₁₃	—	2	2	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
58	C₄²×C₁₃	M₁₆	1	2	yes	—
59	C₁₃×C₁₆	—	2	4	no	—
60	C₁₃×C₁₆	—	4	2	no	—
61	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
62	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic
63	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
64	#1374	C₂×C₁₃	1	4	yes	—
65	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
66	Q₈×C₁₃	—	2	8	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	2	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	—	2	4	no	—
73	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
74	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
75	C₂×C₄×C₁₃	M₃₂	1	4	yes	—
76	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
79	C₂×C₄×C₁₃	#131	1	2	yes	—
80	C₈×C₁₃	—	2	2	no	—
81	C₈×C₁₃	—	4	2	no	—
82	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
83	C₈×C₁₃	#124	1	1	yes	characteristic
84	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
85	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
86	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
87	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
88	C₈×Q₈	—	2	2	no	—
89	C₈×Q₈	—	2	2	no	—
90	C₂×C₄⋊C₈	C₄×C₁₃	1	2	yes	—
91	C₂×C₄⋊C₈	C₄×C₁₃	1	1	yes	characteristic
92	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
93	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
94	C₄⋊C₁₆	—	2	2	no	—
95	#346	—	2	2	no	—
96	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
97	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
98	C₂²×C₁₃	C₂×M₃₂	1	2	yes	—
99	C₂²×C₁₃	#504	1	2	yes	—
100	C₄×C₁₃	—	2	2	no	—
101	C₄×C₁₃	—	2	4	no	—
102	C₄×C₁₃	—	2	2	no	—
103	C₄×C₁₃	—	4	2	no	—
104	C₄×C₁₃	#391	1	1	yes	characteristic
105	C₄×C₁₃	#408	1	1	yes	characteristic
106	C₄×C₁₃	#446	1	2	yes	—
107	C₂²×Q₈	C₈×C₁₃	1	1	yes	characteristic
108	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
109	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
110	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
111	C₄×Q₈	—	2	2	no	—
112	C₄×Q₈	—	2	2	no	—
113	C₂×C₄⋊C₄	C₈×C₁₃	1	1	yes	characteristic
114	C₂×C₄⋊C₄	C₈×C₁₃	1	2	yes	—
115	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
116	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
117	C₂×C₁₆	—	2	2	no	—
118	C₂×C₁₆	—	2	2	no	—
119	C₂×C₁₆	—	2	2	no	—
120	C₂×C₁₆	—	2	4	no	—
121	C₂×C₁₆	Q₈×C₁₃	1	4	yes	complemented
122	C₄⋊C₈	—	2	4	no	—
123	C₄⋊C₈	—	2	2	no	—
124	C₄×C₈	—	2	2	no	—
125	C₄×C₈	—	2	2	no	—
126	C₄×C₈	D₄×C₁₃	1	2	yes	—
127	C₄×C₈	D₄×C₁₃	1	2	yes	—
128	C₂×C₁₃	#1984	1	1	yes	characteristic
129	C₂×C₁₃	#2112	1	1	yes	characteristic
130	C₂×C₁₃	#2113	1	1	yes	characteristic
131	C₂×C₁₃	#2183	1	4	yes	—
132	C₂×Q₈	—	2	2	no	—
133	C₂×Q₈	—	2	4	no	—
134	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
135	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
136	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
137	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
138	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
143	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
144	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
145	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
146	C₂×C₈	C₁₃×#41	1	2	yes	—
147	C₄⋊C₄	—	2	4	no	—
148	C₄⋊C₄	—	2	2	no	—
149	C₄²	—	2	2	no	—
150	C₄²	—	2	2	no	—
151	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
152	C₄²	C₁₃×M₁₆	1	2	yes	—
153	C₁₆	—	2	4	no	—
154	C₁₆	—	4	2	no	—
155	C₁₃	#13264	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
157	Q₈	—	2	8	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
165	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
166	C₂×C₄	C₁₃×M₃₂	1	4	yes	—
167	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
169	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
170	C₂×C₄	C₁₃×#131	1	2	yes	—
171	C₈	—	2	2	no	—
172	C₈	—	4	2	no	—
173	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
174	C₈	C₁₃×#124	1	1	yes	characteristic
175	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
176	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
177	C₂²	C₈×Q₈×C₁₃	1	2	yes	—
178	C₂²	C₂×C₁₃×M₃₂	1	2	yes	—
179	C₂²	C₁₃×#504	1	2	yes	—
180	C₄	—	2	2	no	—
181	C₄	—	2	4	no	—
182	C₄	—	2	2	no	—
183	C₄	—	4	2	no	—
184	C₄	C₁₃×#391	1	1	yes	characteristic
185	C₄	C₁₃×#408	1	1	yes	characteristic
186	C₄	C₁₃×#446	1	2	yes	—
187	C₂	C₁₃×#1984	1	1	yes	characteristic
188	C₂	C₁₃×#2112	1	1	yes	characteristic
189	C₂	C₁₃×#2113	1	1	yes	characteristic
190	C₂	C₁₃×#2183	1	4	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂³	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
30. C₂×C₁₃×C₁₆	Q₈	semidirect
37. #13264	C₁₃	direct (N × H)
121. C₂×C₁₆	Q₈×C₁₃	semidirect
155. C₁₃	#13264	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×C₈×Q₈×C₁₃	2
C₂×C₁₃×C₄⋊C₁₆	2
C₂×C₁₃×#346	2
C₁₃×#1374	2
#13264	13

Subgroups — C13×#13264 #15699603

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13264 #15699603