Subgroups — C₁₃×#13263 #15699602

Order 3328.

398 conjugacy classes of subgroups.

The subgroup lattice has 200 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×C₄×C₁₃×C₁₆	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	C₄×C₁₃×C₁₆	—	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	#13263	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×Q₈×C₁₃	—	2	2	no	—
39	C₂×Q₈×C₁₃	—	2	2	no	—
40	C₂×Q₈×C₁₃	C₁₆	1	4	yes	complemented
41	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×C₈	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	—	2	2	no	—
47	C₂×C₈×C₁₃	—	2	2	no	—
48	C₂×C₈×C₁₃	—	2	4	no	—
49	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
50	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
53	C₂×C₈×C₁₃	#41	1	2	yes	—
54	C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₄²×C₁₃	—	2	2	no	—
58	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
59	C₄²×C₁₃	M₁₆	1	2	yes	—
60	C₁₃×C₁₆	—	2	4	no	—
61	C₁₃×C₁₆	—	4	2	no	—
62	C₂×C₈×Q₈	C₂×C₁₃	1	1	yes	characteristic
63	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic
64	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
65	#1374	C₂×C₁₃	1	4	yes	—
66	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
67	Q₈×C₁₃	—	2	8	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	C₂×C₁₆	1	4	yes	—
76	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
77	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
80	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₃	#131	1	2	yes	—
82	C₈×C₁₃	—	2	2	no	—
83	C₈×C₁₃	—	4	2	no	—
84	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
85	C₈×C₁₃	#124	1	1	yes	characteristic
86	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
87	C₂×C₄×Q₈	C₄×C₁₃	1	1	yes	characteristic
88	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
89	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
90	C₈×Q₈	—	2	2	no	—
91	C₈×Q₈	—	2	2	no	—
92	C₂×C₄⋊C₈	C₄×C₁₃	1	2	yes	—
93	C₂×C₄⋊C₈	C₄×C₁₃	1	1	yes	characteristic
94	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
95	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
96	C₄⋊C₁₆	—	2	2	no	—
97	C₄×C₁₆	—	2	2	no	—
98	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
99	C₂²×C₁₃	C₈×Q₈	1	2	yes	—
100	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
101	C₂²×C₁₃	C₂×M₃₂	1	1	yes	characteristic
102	C₂²×C₁₃	#504	1	2	yes	—
103	C₄×C₁₃	—	2	4	no	—
104	C₄×C₁₃	—	2	2	no	—
105	C₄×C₁₃	—	4	2	no	—
106	C₄×C₁₃	C₂²⋊C₁₆	1	4	yes	—
107	C₄×C₁₃	#391	1	1	yes	characteristic
108	C₄×C₁₃	#408	1	1	yes	characteristic
109	C₄×C₁₃	#446	1	2	yes	—
110	C₂²×Q₈	C₈×C₁₃	1	1	yes	characteristic
111	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
112	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
113	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
114	C₄×Q₈	—	2	2	no	—
115	C₄×Q₈	—	2	2	no	—
116	C₂×C₄⋊C₄	C₈×C₁₃	1	1	yes	characteristic
117	C₂×C₄⋊C₄	C₈×C₁₃	1	2	yes	—
118	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
119	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
120	C₂×C₁₆	—	2	2	no	—
121	C₂×C₁₆	—	2	2	no	—
122	C₂×C₁₆	—	2	2	no	—
123	C₂×C₁₆	—	2	4	no	—
124	C₂×C₁₆	Q₈×C₁₃	1	4	yes	complemented
125	C₄⋊C₈	—	2	4	no	—
126	C₄⋊C₈	—	2	2	no	—
127	C₄×C₈	—	2	2	no	—
128	C₄×C₈	—	2	2	no	—
129	C₄×C₈	D₄×C₁₃	1	2	yes	—
130	C₄×C₈	D₄×C₁₃	1	2	yes	—
131	C₂×C₁₃	#1984	1	1	yes	characteristic
132	C₂×C₁₃	C₂×C₂²⋊C₁₆	1	1	yes	characteristic
133	C₂×C₁₃	#2113	1	1	yes	characteristic
134	C₂×C₁₃	Q₈×C₁₆	1	2	yes	—
135	C₂×C₁₃	#2183	1	2	yes	—
136	C₂×Q₈	—	2	2	no	—
137	C₂×Q₈	—	2	2	no	—
138	C₂×Q₈	C₁₃×C₁₆	1	4	yes	complemented
139	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
140	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
141	C₂²×C₄	C₂×C₈×C₁₃	1	2	yes	—
142	C₂²×C₄	C₂×C₈×C₁₃	1	1	yes	characteristic
143	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
144	C₂×C₈	—	2	2	no	—
145	C₂×C₈	—	2	2	no	—
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
148	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
149	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
150	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
151	C₂×C₈	C₁₃×#41	1	2	yes	—
152	C₄⋊C₄	—	2	4	no	—
153	C₄⋊C₄	—	2	2	no	—
154	C₄²	—	2	2	no	—
155	C₄²	—	2	2	no	—
156	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
157	C₄²	C₁₃×M₁₆	1	2	yes	—
158	C₁₆	—	2	4	no	—
159	C₁₆	—	4	2	no	—
160	C₁₃	#13263	1	1	yes	characteristic, direct product factor, Sylow
161	C₂³	C₂²×C₈×C₁₃	1	1	yes	characteristic
162	Q₈	—	2	8	no	—
163	C₂×C₄	—	2	2	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	4	no	—
168	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
169	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
170	C₂×C₄	C₂×C₁₃×C₁₆	1	4	yes	—
171	C₂×C₄	C₂×C₁₃×C₁₆	1	2	yes	—
172	C₂×C₄	C₁₃×M₃₂	1	2	yes	—
173	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
175	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
176	C₂×C₄	C₁₃×#131	1	2	yes	—
177	C₈	—	2	2	no	—
178	C₈	—	4	2	no	—
179	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
180	C₈	C₁₃×#124	1	1	yes	characteristic
181	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
182	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
183	C₂²	C₈×Q₈×C₁₃	1	2	yes	—
184	C₂²	C₂²×C₁₃×C₁₆	1	1	yes	characteristic
185	C₂²	C₂×C₁₃×M₃₂	1	1	yes	characteristic
186	C₂²	C₁₃×#504	1	2	yes	—
187	C₄	—	2	4	no	—
188	C₄	—	2	2	no	—
189	C₄	—	4	2	no	—
190	C₄	C₁₃×C₂²⋊C₁₆	1	4	yes	—
191	C₄	C₁₃×#391	1	1	yes	characteristic
192	C₄	C₁₃×#408	1	1	yes	characteristic
193	C₄	C₁₃×#446	1	2	yes	—
194	C₂	C₁₃×#1984	1	1	yes	characteristic
195	C₂	C₂×C₁₃×C₂²⋊C₁₆	1	1	yes	characteristic
196	C₂	C₁₃×#2113	1	1	yes	characteristic
197	C₂	Q₈×C₁₃×C₁₆	1	2	yes	—
198	C₂	C₁₃×#2183	1	2	yes	—

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂²	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂²×C₈
LCS	G ▷ C₂² ▷ 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. #13263	C₁₃	direct (N × H)
40. C₂×Q₈×C₁₃	C₁₆	semidirect
124. C₂×C₁₆	Q₈×C₁₃	semidirect
138. C₂×Q₈	C₁₃×C₁₆	semidirect
160. C₁₃	#13263	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×C₄×C₁₃×C₁₆	2
C₁₃×#1374	2
#13263	13

Subgroups — C13×#13263 #15699602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13263 #15699602