Subgroups — C₁₃×#13169 #15699508

Order 3328.

286 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#368	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2158	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1945	C₂	1	2	yes	maximal
5	C₁₃×#1382	C₂	1	2	yes	maximal
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#108	C₂²	1	2	yes	—
9	C₁₃×#427	C₂²	1	2	yes	—
10	C₁₃×#424	—	2	2	no	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₁₃×#368	—	2	2	no	—
13	C₁₃×#367	C₄	1	2	yes	complemented
14	C₁₃×#366	C₄	1	2	yes	complemented
15	C₄×C₁₃×C₁₆	—	2	2	no	—
16	C₁₃×#339	—	2	2	no	—
17	C₂×C₁₃×M₁₆	—	2	2	no	—
18	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₁₃×#117	—	2	2	no	—
21	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
22	C₂×C₁₃×C₁₆	—	2	1	no	—
23	C₂×C₁₃×C₁₆	—	2	1	no	—
24	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
25	C₂×C₁₃×C₁₆	C₂×C₄	1	1	yes	characteristic
26	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
27	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
28	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
29	C₁₃×#108	—	2	2	no	—
30	C₁₃×#108	—	2	2	no	—
31	C₁₃×#107	C₂×C₄	1	4	yes	—
32	C₁₃×#106	—	2	2	no	—
33	C₁₃×C₄⋊C₈	—	4	4	no	—
34	C₄×C₈×C₁₃	—	2	1	no	—
35	C₄×C₈×C₁₃	—	2	1	no	—
36	#13169	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₄×C₁₃	—	2	1	no	—
38	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
39	C₁₃×M₁₆	—	4	2	no	—
40	C₁₃×M₁₆	—	4	2	no	—
41	C₂×C₈×C₁₃	—	2	1	no	—
42	C₂×C₈×C₁₃	—	2	1	no	—
43	C₂×C₈×C₁₃	—	4	2	no	—
44	C₂×C₈×C₁₃	D₈	1	2	yes	—
45	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
49	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
50	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
51	C₁₃×C₄⋊C₄	—	2	4	no	—
52	C₁₃×C₂²⋊C₄	—	4	2	no	—
53	C₄²×C₁₃	—	2	1	no	—
54	C₄²×C₁₃	—	4	2	no	—
55	C₄²×C₁₃	Q₁₆	1	2	yes	—
56	C₁₃×C₁₆	—	2	2	no	—
57	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
58	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
59	C₂×#368	C₂×C₁₃	1	1	yes	characteristic
60	#2158	C₂×C₁₃	1	1	yes	characteristic
61	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
62	#1945	C₂×C₁₃	1	2	yes	—
63	#1382	C₂×C₁₃	1	2	yes	—
64	C₂³×C₁₃	#135	1	1	yes	characteristic
65	C₂×C₄×C₁₃	—	2	4	no	—
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	4	4	no	—
68	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
70	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
74	C₈×C₁₃	—	2	2	no	—
75	C₈×C₁₃	—	8	2	no	—
76	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
78	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
79	C₈×C₁₃	#125	1	1	yes	characteristic
80	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
81	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
82	C₂×#108	C₂²×C₁₃	1	2	yes	—
83	#427	C₂²×C₁₃	1	2	yes	—
84	#424	—	2	2	no	—
85	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
86	#368	—	2	2	no	—
87	#367	C₄×C₁₃	1	2	yes	complemented
88	#366	C₄×C₁₃	1	2	yes	complemented
89	C₄×C₁₆	—	2	2	no	—
90	#339	—	2	2	no	—
91	C₂²×C₁₃	—	2	2	no	—
92	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
93	C₂²×C₁₃	#467	1	1	yes	characteristic
94	C₂²×C₁₃	#499	1	1	yes	characteristic
95	C₄×C₁₃	—	2	4	no	—
96	C₄×C₁₃	—	8	4	no	—
97	C₄×C₁₃	#389	1	1	yes	characteristic
98	C₄×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
99	C₄×C₁₃	#466	1	1	yes	characteristic
100	C₄×C₁₃	#500	1	1	yes	characteristic
101	C₂×M₁₆	—	2	2	no	—
102	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
103	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
104	#117	—	2	2	no	—
105	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
106	C₂×C₁₆	—	2	1	no	—
107	C₂×C₁₆	—	2	1	no	—
108	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
109	C₂×C₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
110	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
111	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
112	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
113	#108	—	2	2	no	—
114	#108	—	2	2	no	—
115	#107	C₂×C₄×C₁₃	1	4	yes	—
116	#106	—	2	2	no	—
117	C₄⋊C₈	—	4	4	no	—
118	C₄×C₈	—	2	1	no	—
119	C₄×C₈	—	2	1	no	—
120	C₂×C₁₃	—	2	1	no	—
121	C₂×C₁₃	—	2	1	no	—
122	C₂×C₁₃	#1942	1	1	yes	characteristic
123	C₂×C₁₃	#2178	1	2	yes	—
124	C₂²×C₄	—	2	1	no	—
125	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
126	M₁₆	—	4	2	no	—
127	M₁₆	—	4	2	no	—
128	C₂×C₈	—	2	1	no	—
129	C₂×C₈	—	2	1	no	—
130	C₂×C₈	—	4	2	no	—
131	C₂×C₈	C₁₃×D₈	1	2	yes	—
132	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
133	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
134	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
135	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
136	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
137	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
138	C₄⋊C₄	—	2	4	no	—
139	C₂²⋊C₄	—	4	2	no	—
140	C₄²	—	2	1	no	—
141	C₄²	—	4	2	no	—
142	C₄²	C₁₃×Q₁₆	1	2	yes	—
143	C₁₆	—	2	2	no	—
144	C₁₆	C₁₃×C₄⋊C₄	1	2	yes	—
145	C₁₆	C₁₃×C₄⋊C₄	1	2	yes	—
146	C₁₃	#13169	1	1	yes	characteristic, direct product factor, Sylow
147	C₂³	C₁₃×#135	1	1	yes	characteristic
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	4	4	no	—
151	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
152	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
153	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
154	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
155	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
156	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
157	C₈	—	2	2	no	—
158	C₈	—	8	2	no	—
159	C₈	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
160	C₈	C₄×Q₈×C₁₃	1	1	yes	characteristic
161	C₈	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
162	C₈	C₁₃×#125	1	1	yes	characteristic
163	C₂²	—	2	2	no	—
164	C₂²	C₄×C₁₃×D₈	1	1	yes	characteristic
165	C₂²	C₁₃×#467	1	1	yes	characteristic
166	C₂²	C₁₃×#499	1	1	yes	characteristic
167	C₄	—	2	4	no	—
168	C₄	—	8	4	no	—
169	C₄	C₁₃×#389	1	1	yes	characteristic
170	C₄	C₄×C₁₃×Q₁₆	1	1	yes	characteristic
171	C₄	C₁₃×#466	1	1	yes	characteristic
172	C₄	C₁₃×#500	1	1	yes	characteristic
173	C₂	—	2	1	no	—
174	C₂	—	2	1	no	—
175	C₂	C₁₃×#1942	1	1	yes	characteristic
176	C₂	C₁₃×#2178	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₄×D₈
prime radical	C₂³×C₁₃	#135
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₁₃×#367	C₄	semidirect
14. C₁₃×#366	C₄	semidirect
36. #13169	C₁₃	direct (N × H)
87. #367	C₄×C₁₃	semidirect
88. #366	C₄×C₁₃	semidirect
146. C₁₃	#13169	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×#368	2
C₁₃×#2158	2
C₂×C₄×C₁₃×C₁₆	2
C₁₃×#1945	2
C₁₃×#1382	2
#13169	13

Subgroups — C13×#13169 #15699508

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13169 #15699508