Subgroups — C₁₃×#13286 #15699625

Order 3328.

342 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3160	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1848	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1382	C₂	1	4	yes	maximal
5	C₁₃×#533	—	2	1	no	—
6	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
7	C₁₃×#500	C₄	1	2	yes	—
8	C₁₃×#499	—	2	1	no	—
9	C₁₃×#499	C₄	1	2	yes	—
10	C₁₃×#498	—	2	1	no	—
11	C₂×C₁₃×#108	—	2	1	no	—
12	C₂×C₁₃×#108	C₂²	1	2	yes	—
13	C₁₃×#427	—	2	1	no	—
14	C₁₃×#427	C₂²	1	2	yes	—
15	C₁₃×#423	—	2	1	no	—
16	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#346	—	2	1	no	—
18	C₁₃×#346	—	2	1	no	—
19	C₂×C₁₃×M₁₆	—	2	2	no	—
20	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₁₃×C₄⋊Q₈	—	2	2	no	—
23	C₁₃×#125	—	2	2	no	—
24	C₁₃×C₂²⋊Q₈	—	4	2	no	—
25	C₄×Q₈×C₁₃	—	4	2	no	—
26	C₁₃×#117	—	2	2	no	—
27	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
28	C₂×C₁₃×C₁₆	—	2	2	no	—
29	C₂×C₁₃×C₁₆	—	2	2	no	—
30	C₂×C₁₃×C₁₆	Q₈	1	4	yes	complemented
31	C₁₃×#108	—	2	4	no	—
32	C₁₃×#108	—	4	2	no	—
33	C₁₃×#107	—	2	2	no	—
34	C₁₃×#107	C₂×C₄	1	4	yes	—
35	C₁₃×#106	—	2	2	no	—
36	C₁₃×#106	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	4	2	no	—
38	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
41	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
42	#13286	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×Q₈×C₁₃	—	4	2	no	—
44	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
45	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₁₃×M₁₆	—	4	2	no	—
47	C₁₃×M₁₆	—	4	2	no	—
48	C₂×C₈×C₁₃	—	4	2	no	—
49	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
52	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
53	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
56	C₂×C₈×C₁₃	#41	1	2	yes	—
57	C₁₃×C₄⋊C₄	—	2	4	no	—
58	C₁₃×C₄⋊C₄	—	4	4	no	—
59	C₁₃×C₄⋊C₄	—	4	2	no	—
60	C₁₃×C₂²⋊C₄	—	4	2	no	—
61	C₄²×C₁₃	—	4	2	no	—
62	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
63	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
64	C₄²×C₁₃	D₈	1	2	yes	—
65	C₁₃×C₁₆	—	2	4	no	—
66	#3160	C₂×C₁₃	1	1	yes	characteristic
67	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
68	#1848	C₂×C₁₃	1	1	yes	characteristic
69	#1382	C₂×C₁₃	1	4	yes	—
70	C₂³×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
71	Q₈×C₁₃	—	8	4	no	—
72	C₂×C₄×C₁₃	—	4	2	no	—
73	C₂×C₄×C₁₃	—	4	4	no	—
74	C₂×C₄×C₁₃	#102	1	2	yes	—
75	C₂×C₄×C₁₃	#102	1	2	yes	—
76	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
82	C₈×C₁₃	—	8	2	no	—
83	C₈×C₁₃	#103	1	2	yes	—
84	C₈×C₁₃	#103	1	2	yes	—
85	C₈×C₁₃	C₄×Q₈	1	2	yes	—
86	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
87	#533	—	2	1	no	—
88	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
89	#500	C₄×C₁₃	1	2	yes	—
90	#499	—	2	1	no	—
91	#499	C₄×C₁₃	1	2	yes	—
92	#498	—	2	1	no	—
93	C₂×#108	—	2	1	no	—
94	C₂×#108	C₂²×C₁₃	1	2	yes	—
95	#427	—	2	1	no	—
96	#427	C₂²×C₁₃	1	2	yes	—
97	#423	—	2	1	no	—
98	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
99	#346	—	2	1	no	—
100	#346	—	2	1	no	—
101	C₂²×C₁₃	—	2	2	no	—
102	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
103	C₂²×C₁₃	#487	1	1	yes	characteristic
104	C₂²×C₁₃	#498	1	1	yes	characteristic
105	C₄×C₁₃	—	2	2	no	—
106	C₄×C₁₃	—	2	2	no	—
107	C₄×C₁₃	—	8	4	no	—
108	C₄×C₁₃	#391	1	1	yes	characteristic
109	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
110	C₄×C₁₃	#486	1	1	yes	characteristic
111	C₄×C₁₃	#500	1	1	yes	characteristic
112	C₂×M₁₆	—	2	2	no	—
113	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
114	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
115	C₄⋊Q₈	—	2	2	no	—
116	#125	—	2	2	no	—
117	C₂²⋊Q₈	—	4	2	no	—
118	C₄×Q₈	—	4	2	no	—
119	#117	—	2	2	no	—
120	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
121	C₂×C₁₆	—	2	2	no	—
122	C₂×C₁₆	—	2	2	no	—
123	C₂×C₁₆	Q₈×C₁₃	1	4	yes	complemented
124	#108	—	2	4	no	—
125	#108	—	4	2	no	—
126	#107	—	2	2	no	—
127	#107	C₂×C₄×C₁₃	1	4	yes	—
128	#106	—	2	2	no	—
129	#106	—	2	2	no	—
130	C₄⋊C₈	—	4	2	no	—
131	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
132	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
133	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
134	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
135	C₂×C₁₃	—	2	1	no	—
136	C₂×C₁₃	—	2	1	no	—
137	C₂×C₁₃	#1990	1	1	yes	characteristic
138	C₂×C₁₃	#2143	1	2	yes	—
139	C₂×Q₈	—	4	2	no	—
140	C₂²×C₄	C₁₃×SD₁₆	1	2	yes	—
141	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
142	M₁₆	—	4	2	no	—
143	M₁₆	—	4	2	no	—
144	C₂×C₈	—	4	2	no	—
145	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₈	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₈	C₁₃×SD₁₆	1	2	yes	—
148	C₂×C₈	C₁₃×Q₁₆	1	2	yes	—
149	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
150	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
151	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
152	C₂×C₈	C₁₃×#41	1	2	yes	—
153	C₄⋊C₄	—	2	4	no	—
154	C₄⋊C₄	—	4	4	no	—
155	C₄⋊C₄	—	4	2	no	—
156	C₂²⋊C₄	—	4	2	no	—
157	C₄²	—	4	2	no	—
158	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
159	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
160	C₄²	C₁₃×D₈	1	2	yes	—
161	C₁₆	—	2	4	no	—
162	C₁₃	#13286	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
164	Q₈	—	8	4	no	—
165	C₂×C₄	—	4	2	no	—
166	C₂×C₄	—	4	4	no	—
167	C₂×C₄	C₁₃×#102	1	2	yes	—
168	C₂×C₄	C₁₃×#102	1	2	yes	—
169	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
170	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
171	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
172	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
173	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
174	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
175	C₈	—	8	2	no	—
176	C₈	C₁₃×#103	1	2	yes	—
177	C₈	C₁₃×#103	1	2	yes	—
178	C₈	C₄×Q₈×C₁₃	1	2	yes	—
179	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
180	C₂²	—	2	2	no	—
181	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
182	C₂²	C₁₃×#487	1	1	yes	characteristic
183	C₂²	C₁₃×#498	1	1	yes	characteristic
184	C₄	—	2	2	no	—
185	C₄	—	2	2	no	—
186	C₄	—	8	4	no	—
187	C₄	C₁₃×#391	1	1	yes	characteristic
188	C₄	C₂×C₁₃×#103	1	1	yes	characteristic
189	C₄	C₁₃×#486	1	1	yes	characteristic
190	C₄	C₁₃×#500	1	1	yes	characteristic
191	C₂	—	2	1	no	—
192	C₂	—	2	1	no	—
193	C₂	C₁₃×#1990	1	1	yes	characteristic
194	C₂	C₁₃×#2143	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	C₂×#102
prime radical	C₂³×C₁₃	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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
30. C₂×C₁₃×C₁₆	Q₈	semidirect
42. #13286	C₁₃	direct (N × H)
123. C₂×C₁₆	Q₈×C₁₃	semidirect
162. C₁₃	#13286	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#3160	2
C₂×C₁₃×#346	2
C₁₃×#1848	2
C₁₃×#1382	2
#13286	13

Subgroups — C13×#13286 #15699625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13286 #15699625