Subgroups — C₁₃×#13167 #15699506

Order 3328.

318 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#367	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#366	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1942	C₂	1	2	yes	maximal
5	C₁₃×#1380	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×#107	C₂²	1	2	yes	—
9	C₂×C₁₃×#107	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₁₃×#389	—	2	2	no	—
12	C₁₃×#367	C₄	1	4	yes	complemented
13	C₁₃×#366	—	2	2	no	—
14	C₁₃×#346	—	2	2	no	—
15	C₁₃×#340	—	2	2	no	—
16	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
19	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
20	C₂×C₁₃×C₄⋊C₄	—	4	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	2	yes	—
25	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
26	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
27	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
28	C₁₃×#107	—	2	2	no	—
29	C₁₃×#107	—	2	2	no	—
30	C₁₃×#107	—	2	2	no	—
31	C₁₃×#107	C₂×C₄	1	4	yes	—
32	C₄×C₈×C₁₃	—	2	1	no	—
33	C₄×C₈×C₁₃	—	2	1	no	—
34	C₁₃×#95	—	4	2	no	—
35	#13167	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₄×C₁₃	—	4	2	no	—
37	C₂²×C₄×C₁₃	—	4	2	no	—
38	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
39	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	—	2	1	no	—
42	C₂×C₈×C₁₃	—	2	1	no	—
43	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
49	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
50	C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₁₃×C₄⋊C₄	—	4	2	no	—
52	C₁₃×C₄⋊C₄	—	4	2	no	—
53	C₁₃×C₄⋊C₄	—	4	2	no	—
54	C₁₃×C₄⋊C₄	—	8	4	no	—
55	C₄²×C₁₃	—	2	1	no	—
56	C₄²×C₁₃	—	2	1	no	—
57	C₁₃×C₁₆	—	2	2	no	—
58	C₁₃×C₁₆	C₄⋊C₄	1	4	yes	complemented
59	C₂×#367	C₂×C₁₃	1	1	yes	characteristic
60	C₂×#366	C₂×C₁₃	1	1	yes	characteristic
61	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
62	#1942	C₂×C₁₃	1	2	yes	—
63	#1380	C₂×C₁₃	1	2	yes	—
64	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
65	C₂×C₄×C₁₃	—	2	1	no	—
66	C₂×C₄×C₁₃	—	2	1	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	2	no	—
69	C₂×C₄×C₁₃	—	4	4	no	—
70	C₂×C₄×C₁₃	—	8	2	no	—
71	C₂×C₄×C₁₃	—	8	2	no	—
72	C₂×C₄×C₁₃	—	8	2	no	—
73	C₂×C₄×C₁₃	—	8	2	no	—
74	C₂×C₄×C₁₃	—	8	2	no	—
75	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
79	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
80	C₂×C₄×C₁₃	#135	1	1	yes	characteristic
81	C₈×C₁₃	—	2	2	no	—
82	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
83	C₈×C₁₃	C₄×Q₈	1	1	yes	characteristic
84	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
85	C₈×C₁₃	#125	1	1	yes	characteristic
86	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
87	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
88	C₂×#107	C₂²×C₁₃	1	2	yes	—
89	C₂×#107	C₂²×C₁₃	1	2	yes	—
90	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
91	#389	—	2	2	no	—
92	#367	C₄×C₁₃	1	4	yes	complemented
93	#366	—	2	2	no	—
94	#346	—	2	2	no	—
95	#340	—	2	2	no	—
96	C₂²×C₁₃	C₄×D₈	1	1	yes	characteristic
97	C₂²×C₁₃	#466	1	1	yes	characteristic
98	C₂²×C₁₃	#500	1	1	yes	characteristic
99	C₂²×C₁₃	#509	1	2	yes	—
100	C₂²×C₁₃	#510	1	2	yes	—
101	C₄×C₁₃	—	4	1	no	—
102	C₄×C₁₃	—	4	1	no	—
103	C₄×C₁₃	—	8	4	no	—
104	C₄×C₁₃	—	16	2	no	—
105	C₄×C₁₃	#389	1	1	yes	characteristic
106	C₄×C₁₃	C₄×Q₁₆	1	1	yes	characteristic
107	C₄×C₁₃	#467	1	1	yes	characteristic
108	C₄×C₁₃	#499	1	1	yes	characteristic
109	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
110	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
111	C₂×C₄⋊C₄	—	2	2	no	—
112	C₂×C₄⋊C₄	—	2	2	no	—
113	C₂×C₄⋊C₄	—	4	2	no	—
114	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
115	C₂×C₁₆	—	2	1	no	—
116	C₂×C₁₆	—	2	1	no	—
117	C₂×C₁₆	C₂×C₄×C₁₃	1	2	yes	—
118	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
119	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
120	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
121	#107	—	2	2	no	—
122	#107	—	2	2	no	—
123	#107	—	2	2	no	—
124	#107	C₂×C₄×C₁₃	1	4	yes	—
125	C₄×C₈	—	2	1	no	—
126	C₄×C₈	—	2	1	no	—
127	#95	—	4	2	no	—
128	C₂×C₁₃	#1942	1	1	yes	characteristic
129	C₂×C₁₃	#2175	1	2	yes	—
130	C₂×C₁₃	#2218	1	1	yes	characteristic
131	C₂×C₁₃	#2219	1	1	yes	characteristic
132	C₂×C₁₃	#2255	1	2	yes	—
133	C₂²×C₄	—	4	2	no	—
134	C₂²×C₄	—	4	2	no	—
135	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
136	C₂²×C₄	C₁₃×D₈	1	1	yes	characteristic
137	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
138	C₂×C₈	—	2	1	no	—
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
141	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
142	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
143	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
144	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
145	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
146	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
147	C₄⋊C₄	—	2	4	no	—
148	C₄⋊C₄	—	4	2	no	—
149	C₄⋊C₄	—	4	2	no	—
150	C₄⋊C₄	—	4	2	no	—
151	C₄⋊C₄	—	8	4	no	—
152	C₄²	—	2	1	no	—
153	C₄²	—	2	1	no	—
154	C₁₆	—	2	2	no	—
155	C₁₆	C₁₃×C₄⋊C₄	1	4	yes	complemented
156	C₁₃	#13167	1	1	yes	characteristic, direct product factor, Sylow
157	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	—	8	2	no	—
164	C₂×C₄	—	8	2	no	—
165	C₂×C₄	—	8	2	no	—
166	C₂×C₄	—	8	2	no	—
167	C₂×C₄	—	8	2	no	—
168	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
169	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
170	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
171	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
172	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
173	C₂×C₄	C₁₃×#135	1	1	yes	characteristic
174	C₈	—	2	2	no	—
175	C₈	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
176	C₈	C₄×Q₈×C₁₃	1	1	yes	characteristic
177	C₈	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
178	C₈	C₁₃×#125	1	1	yes	characteristic
179	C₂²	C₄×C₁₃×D₈	1	1	yes	characteristic
180	C₂²	C₁₃×#466	1	1	yes	characteristic
181	C₂²	C₁₃×#500	1	1	yes	characteristic
182	C₂²	C₁₃×#509	1	2	yes	—
183	C₂²	C₁₃×#510	1	2	yes	—
184	C₄	—	4	1	no	—
185	C₄	—	4	1	no	—
186	C₄	—	8	4	no	—
187	C₄	—	16	2	no	—
188	C₄	C₁₃×#389	1	1	yes	characteristic
189	C₄	C₄×C₁₃×Q₁₆	1	1	yes	characteristic
190	C₄	C₁₃×#467	1	1	yes	characteristic
191	C₄	C₁₃×#499	1	1	yes	characteristic
192	C₂	C₁₃×#1942	1	1	yes	characteristic
193	C₂	C₁₃×#2175	1	2	yes	—
194	C₂	C₁₃×#2218	1	1	yes	characteristic
195	C₂	C₁₃×#2219	1	1	yes	characteristic
196	C₂	C₁₃×#2255	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
12. C₁₃×#367	C₄	semidirect
35. #13167	C₁₃	direct (N × H)
58. C₁₃×C₁₆	C₄⋊C₄	semidirect
92. #367	C₄×C₁₃	semidirect
155. C₁₆	C₁₃×C₄⋊C₄	semidirect
156. C₁₃	#13167	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×#367	2
C₂×C₁₃×#366	2
C₂×C₁₃×#346	2
C₁₃×#1942	2
C₁₃×#1380	2
#13167	13

Subgroups — C13×#13167 #15699506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13167 #15699506