Subgroups — C₁₃×#13826 #15700165

Order 3328.

1606 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#391	C₂	1	3	yes	maximal
2	C₁₃×#1436	C₂	1	6	yes	maximal
3	C₄×C₁₃×#95	C₂	1	6	yes	maximal
4	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
5	C₂²×C₁₃×C₄⋊C₄	C₂²	1	3	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	6	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	3	yes	—
8	C₁₃×#391	C₄	1	24	yes	complemented
9	C₂×C₁₃×#95	C₂²	1	6	yes	—
10	C₂×C₁₃×#95	C₂²	1	2	yes	—
11	C₂×C₁₃×#95	C₂²	1	12	yes	—
12	C₂×C₁₃×#95	C₂²	1	2	yes	—
13	C₂²×Q₈×C₁₃	—	4	3	no	—
14	C₂²×Q₈×C₁₃	—	4	1	no	—
15	C₂²×Q₈×C₁₃	C₂×C₄	1	12	yes	—
16	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
17	C₂³×C₄×C₁₃	C₂³	1	3	yes	—
18	C₂³×C₄×C₁₃	C₂³	1	6	yes	—
19	C₂×C₁₃×C₄⋊C₄	—	4	3	no	—
20	C₂×C₁₃×C₄⋊C₄	—	4	3	no	—
21	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	12	yes	—
22	C₂×C₄²×C₁₃	—	2	24	no	—
23	C₂×C₄²×C₁₃	—	4	6	no	—
24	C₂×C₄²×C₁₃	—	4	6	no	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	12	yes	—
26	C₁₃×#95	—	2	12	no	—
27	C₁₃×#95	—	4	2	no	—
28	C₁₃×#95	C₂×C₄	1	48	yes	—
29	C₁₃×#95	Q₈	1	8	yes	complemented
30	#13826	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
32	C₂×Q₈×C₁₃	—	4	12	no	—
33	C₂×Q₈×C₁₃	—	4	12	no	—
34	C₂×Q₈×C₁₃	C₄²	1	16	yes	complemented
35	C₂²×C₄×C₁₃	—	2	12	no	—
36	C₂²×C₄×C₁₃	—	2	12	no	—
37	C₂²×C₄×C₁₃	—	2	6	no	—
38	C₂²×C₄×C₁₃	—	2	3	no	—
39	C₂²×C₄×C₁₃	—	2	3	no	—
40	C₂²×C₄×C₁₃	—	2	12	no	—
41	C₂²×C₄×C₁₃	—	2	12	no	—
42	C₂²×C₄×C₁₃	—	2	6	no	—
43	C₂²×C₄×C₁₃	—	2	6	no	—
44	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
45	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
46	C₂²×C₄×C₁₃	C₂²×C₄	1	6	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	12	yes	—
48	C₂²×C₄×C₁₃	C₂×Q₈	1	12	yes	—
49	C₂²×C₄×C₁₃	#41	1	12	yes	—
50	C₁₃×C₄⋊C₄	—	4	12	no	—
51	C₄²×C₁₃	—	4	12	no	—
52	C₄²×C₁₃	—	4	24	no	—
53	C₂×#391	C₂×C₁₃	1	3	yes	—
54	#1436	C₂×C₁₃	1	6	yes	—
55	C₄×#95	C₂×C₁₃	1	6	yes	—
56	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
57	C₂³×C₁₃	C₂²×Q₈	1	2	yes	—
58	C₂³×C₁₃	C₂×#41	1	6	yes	—
59	C₂³×C₁₃	H(5,𝔽₂)	1	3	yes	—
60	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
61	Q₈×C₁₃	—	4	16	no	—
62	C₂×C₄×C₁₃	—	2	12	no	—
63	C₂×C₄×C₁₃	—	2	12	no	—
64	C₂×C₄×C₁₃	—	2	6	no	—
65	C₂×C₄×C₁₃	—	2	6	no	—
66	C₂×C₄×C₁₃	—	2	12	no	—
67	C₂×C₄×C₁₃	—	2	12	no	—
68	C₂×C₄×C₁₃	—	2	24	no	—
69	C₂×C₄×C₁₃	—	2	24	no	—
70	C₂×C₄×C₁₃	—	2	24	no	—
71	C₂×C₄×C₁₃	—	2	12	no	—
72	C₂×C₄×C₁₃	—	4	6	no	—
73	C₂×C₄×C₁₃	—	4	6	no	—
74	C₂×C₄×C₁₃	—	4	12	no	—
75	C₂×C₄×C₁₃	C₂×C₄²	1	12	yes	—
76	C₂×C₄×C₁₃	C₄×Q₈	1	24	yes	—
77	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
78	C₂²×C₄⋊C₄	C₂²×C₁₃	1	3	yes	—
79	C₂²×C₄²	C₂²×C₁₃	1	6	yes	—
80	C₂²×C₄²	C₂²×C₁₃	1	3	yes	—
81	#391	C₄×C₁₃	1	24	yes	complemented
82	C₂×#95	C₂²×C₁₃	1	6	yes	—
83	C₂×#95	C₂²×C₁₃	1	2	yes	—
84	C₂×#95	C₂²×C₁₃	1	12	yes	—
85	C₂×#95	C₂²×C₁₃	1	2	yes	—
86	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
87	C₂²×C₁₃	C₂×C₄×Q₈	1	6	yes	—
88	C₂²×C₁₃	C₄×#41	1	6	yes	—
89	C₂²×C₁₃	#518	1	3	yes	—
90	C₂²×C₁₃	#518	1	3	yes	—
91	C₂²×C₁₃	#551	1	6	yes	—
92	C₂²×C₁₃	#554	1	6	yes	—
93	C₂²×C₁₃	#555	1	3	yes	—
94	C₂²×C₁₃	Q₈²	1	1	yes	characteristic
95	C₄×C₁₃	—	2	24	no	—
96	C₄×C₁₃	—	2	12	no	—
97	C₄×C₁₃	—	4	12	no	—
98	C₂²×Q₈	—	4	3	no	—
99	C₂²×Q₈	—	4	1	no	—
100	C₂²×Q₈	C₂×C₄×C₁₃	1	12	yes	—
101	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
102	C₂³×C₄	C₂³×C₁₃	1	3	yes	—
103	C₂³×C₄	C₂³×C₁₃	1	6	yes	—
104	C₂×C₄⋊C₄	—	4	3	no	—
105	C₂×C₄⋊C₄	—	4	3	no	—
106	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	12	yes	—
107	C₂×C₄²	—	2	24	no	—
108	C₂×C₄²	—	4	6	no	—
109	C₂×C₄²	—	4	6	no	—
110	C₂×C₄²	C₂×C₄×C₁₃	1	12	yes	—
111	#95	—	2	12	no	—
112	#95	—	4	2	no	—
113	#95	C₂×C₄×C₁₃	1	48	yes	—
114	#95	Q₈×C₁₃	1	8	yes	complemented
115	C₂×C₁₃	C₄²×Q₈	1	2	yes	—
116	C₂×C₁₃	#2273	1	1	yes	characteristic
117	C₂×C₁₃	#2368	1	6	yes	—
118	C₂×C₁₃	#2369	1	3	yes	—
119	C₂×C₁₃	#2372	1	3	yes	—
120	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
121	C₂×Q₈	—	4	12	no	—
122	C₂×Q₈	—	4	12	no	—
123	C₂×Q₈	C₄²×C₁₃	1	16	yes	complemented
124	C₂²×C₄	—	2	12	no	—
125	C₂²×C₄	—	2	12	no	—
126	C₂²×C₄	—	2	6	no	—
127	C₂²×C₄	—	2	3	no	—
128	C₂²×C₄	—	2	3	no	—
129	C₂²×C₄	—	2	12	no	—
130	C₂²×C₄	—	2	12	no	—
131	C₂²×C₄	—	2	6	no	—
132	C₂²×C₄	—	2	6	no	—
133	C₂²×C₄	C₂²×C₄×C₁₃	1	12	yes	—
134	C₂²×C₄	C₂²×C₄×C₁₃	1	12	yes	—
135	C₂²×C₄	C₂²×C₄×C₁₃	1	6	yes	—
136	C₂²×C₄	C₂²×C₄×C₁₃	1	12	yes	—
137	C₂²×C₄	C₂×Q₈×C₁₃	1	12	yes	—
138	C₂²×C₄	C₁₃×#41	1	12	yes	—
139	C₄⋊C₄	—	4	12	no	—
140	C₄²	—	4	12	no	—
141	C₄²	—	4	24	no	—
142	C₁₃	#13826	1	1	yes	characteristic, direct product factor, Sylow
143	C₂³	C₂³×C₄×C₁₃	1	3	yes	—
144	C₂³	C₂²×Q₈×C₁₃	1	2	yes	—
145	C₂³	C₂×C₁₃×#41	1	6	yes	—
146	C₂³	C₁₃×H(5,𝔽₂)	1	3	yes	—
147	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
148	Q₈	—	4	16	no	—
149	C₂×C₄	—	2	12	no	—
150	C₂×C₄	—	2	12	no	—
151	C₂×C₄	—	2	6	no	—
152	C₂×C₄	—	2	6	no	—
153	C₂×C₄	—	2	12	no	—
154	C₂×C₄	—	2	12	no	—
155	C₂×C₄	—	2	24	no	—
156	C₂×C₄	—	2	24	no	—
157	C₂×C₄	—	2	24	no	—
158	C₂×C₄	—	2	12	no	—
159	C₂×C₄	—	4	6	no	—
160	C₂×C₄	—	4	6	no	—
161	C₂×C₄	—	4	12	no	—
162	C₂×C₄	C₂×C₄²×C₁₃	1	12	yes	—
163	C₂×C₄	C₄×Q₈×C₁₃	1	24	yes	—
164	C₂²	C₂²×C₄²×C₁₃	1	1	yes	characteristic
165	C₂²	C₂×C₄×Q₈×C₁₃	1	6	yes	—
166	C₂²	C₄×C₁₃×#41	1	6	yes	—
167	C₂²	C₁₃×#518	1	3	yes	—
168	C₂²	C₁₃×#518	1	3	yes	—
169	C₂²	C₁₃×#551	1	6	yes	—
170	C₂²	C₁₃×#554	1	6	yes	—
171	C₂²	C₁₃×#555	1	3	yes	—
172	C₂²	Q₈²×C₁₃	1	1	yes	characteristic
173	C₄	—	2	12	no	—
174	C₄	—	2	24	no	—
175	C₄	—	4	12	no	—
176	C₂	C₄²×Q₈×C₁₃	1	2	yes	—
177	C₂	C₁₃×#2273	1	1	yes	characteristic
178	C₂	C₁₃×#2368	1	6	yes	—
179	C₂	C₁₃×#2369	1	3	yes	—
180	C₂	C₁₃×#2372	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₃×#391	C₄	semidirect
29. C₁₃×#95	Q₈	semidirect
30. #13826	C₁₃	direct (N × H)
34. C₂×Q₈×C₁₃	C₄²	semidirect
81. #391	C₄×C₁₃	semidirect
114. #95	Q₈×C₁₃	semidirect
123. C₂×Q₈	C₄²×C₁₃	semidirect
142. C₁₃	#13826	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×C₁₃×#391	2
C₁₃×#1436	2
C₄×C₁₃×#95	2
#13826	13

Subgroups — C13×#13826 #15700165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13826 #15700165