Subgroups — C₁₃×#13269 #15699608

Order 3328.

308 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2961	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2153	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2110	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1378	C₂	1	2	yes	maximal
5	C₁₃×#1375	C₂	1	2	yes	maximal
6	C₁₃×#533	C₄	1	1	yes	characteristic
7	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
8	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
9	C₁₃×#446	—	2	2	no	—
10	C₁₃×#446	—	2	2	no	—
11	C₁₃×#424	C₄	1	1	yes	characteristic
12	C₁₃×#424	C₄	1	1	yes	characteristic
13	C₁₃×#423	C₄	1	1	yes	characteristic
14	C₁₃×#405	C₂²	1	1	yes	characteristic
15	C₁₃×#405	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
17	C₁₃×#364	—	2	2	no	—
18	C₁₃×#347	—	2	2	no	—
19	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
20	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	—	2	1	no	—
24	C₁₃×#125	—	2	1	no	—
25	C₁₃×C₂²⋊Q₈	—	2	2	no	—
26	C₄×Q₈×C₁₃	—	2	2	no	—
27	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
28	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
30	C₁₃×M₃₂	—	2	2	no	—
31	C₁₃×M₃₂	—	2	2	no	—
32	C₁₃×M₃₂	—	2	2	no	—
33	C₁₃×M₃₂	—	2	2	no	—
34	C₂×C₁₃×C₁₆	—	2	2	no	—
35	C₂×C₁₃×C₁₆	Q₈	1	4	yes	complemented
36	C₁₃×C₄⋊C₈	—	2	2	no	—
37	C₁₃×C₄⋊C₈	—	2	2	no	—
38	C₁₃×C₄⋊C₈	—	2	2	no	—
39	C₁₃×#97	—	2	1	no	—
40	C₁₃×#97	—	2	1	no	—
41	C₁₃×#97	—	2	1	no	—
42	C₁₃×#97	D₄	1	2	yes	—
43	C₄×C₈×C₁₃	—	2	1	no	—
44	C₄×C₈×C₁₃	D₄	1	2	yes	—
45	#13269	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×Q₈×C₁₃	—	2	2	no	—
47	C₂²×C₄×C₁₃	—	2	1	no	—
48	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
49	C₁₃×M₁₆	—	2	2	no	—
50	C₁₃×M₁₆	—	2	2	no	—
51	C₂×C₈×C₁₃	—	2	1	no	—
52	C₂×C₈×C₁₃	—	2	1	no	—
53	C₂×C₈×C₁₃	—	2	2	no	—
54	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
55	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
58	C₂×C₈×C₁₃	#41	1	2	yes	—
59	C₁₃×C₄⋊C₄	—	2	4	no	—
60	C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₁₃×C₂²⋊C₄	—	2	1	no	—
64	C₁₃×C₂²⋊C₄	M₁₆	1	2	yes	—
65	C₄²×C₁₃	—	2	1	no	—
66	C₄²×C₁₃	—	2	1	no	—
67	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
69	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
70	C₁₃×C₁₆	—	2	4	no	—
71	C₁₃×C₁₆	—	4	2	no	—
72	#2961	C₂×C₁₃	1	1	yes	characteristic
73	#2153	C₂×C₁₃	1	1	yes	characteristic
74	#2110	C₂×C₁₃	1	1	yes	characteristic
75	#1378	C₂×C₁₃	1	2	yes	—
76	#1375	C₂×C₁₃	1	2	yes	—
77	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
78	Q₈×C₁₃	—	8	2	no	—
79	C₂×C₄×C₁₃	—	2	1	no	—
80	C₂×C₄×C₁₃	—	2	1	no	—
81	C₂×C₄×C₁₃	—	2	2	no	—
82	C₂×C₄×C₁₃	—	2	2	no	—
83	C₂×C₄×C₁₃	—	8	1	no	—
84	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
86	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
87	C₂×C₄×C₁₃	#131	1	2	yes	—
88	C₈×C₁₃	—	2	2	no	—
89	C₈×C₁₃	—	4	1	no	—
90	C₈×C₁₃	—	4	1	no	—
91	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
92	C₈×C₁₃	#124	1	1	yes	characteristic
93	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
94	#533	C₄×C₁₃	1	1	yes	characteristic
95	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
96	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
97	#446	—	2	2	no	—
98	#446	—	2	2	no	—
99	#424	C₄×C₁₃	1	1	yes	characteristic
100	#424	C₄×C₁₃	1	1	yes	characteristic
101	#423	C₄×C₁₃	1	1	yes	characteristic
102	#405	C₂²×C₁₃	1	1	yes	characteristic
103	#405	C₂²×C₁₃	1	1	yes	characteristic
104	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
105	#364	—	2	2	no	—
106	#347	—	2	2	no	—
107	C₂²×C₁₃	—	4	1	no	—
108	C₂²×C₁₃	#407	1	1	yes	characteristic
109	C₂²×C₁₃	#446	1	2	yes	—
110	C₄×C₁₃	—	4	1	no	—
111	C₄×C₁₃	—	4	1	no	—
112	C₄×C₁₃	—	4	2	no	—
113	C₄×C₁₃	—	4	2	no	—
114	C₄×C₁₃	#391	1	1	yes	characteristic
115	C₄×C₁₃	#408	1	1	yes	characteristic
116	C₄×C₁₃	#446	1	2	yes	—
117	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
118	C₂×M₁₆	C₂×C₄×C₁₃	1	1	yes	characteristic
119	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
120	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
121	C₄⋊Q₈	—	2	1	no	—
122	#125	—	2	1	no	—
123	C₂²⋊Q₈	—	2	2	no	—
124	C₄×Q₈	—	2	2	no	—
125	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
126	#117	C₂×C₄×C₁₃	1	1	yes	characteristic
127	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
128	M₃₂	—	2	2	no	—
129	M₃₂	—	2	2	no	—
130	M₃₂	—	2	2	no	—
131	M₃₂	—	2	2	no	—
132	C₂×C₁₆	—	2	2	no	—
133	C₂×C₁₆	Q₈×C₁₃	1	4	yes	complemented
134	C₄⋊C₈	—	2	2	no	—
135	C₄⋊C₈	—	2	2	no	—
136	C₄⋊C₈	—	2	2	no	—
137	#97	—	2	1	no	—
138	#97	—	2	1	no	—
139	#97	—	2	1	no	—
140	#97	D₄×C₁₃	1	2	yes	—
141	C₄×C₈	—	2	1	no	—
142	C₄×C₈	D₄×C₁₃	1	2	yes	—
143	C₂×C₁₃	—	2	1	no	—
144	C₂×C₁₃	—	2	2	no	—
145	C₂×C₁₃	#1985	1	1	yes	characteristic
146	C₂×Q₈	—	2	2	no	—
147	C₂²×C₄	—	2	1	no	—
148	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
149	M₁₆	—	2	2	no	—
150	M₁₆	—	2	2	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	2	1	no	—
153	C₂×C₈	—	2	2	no	—
154	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
155	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
156	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
157	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
158	C₂×C₈	C₁₃×#41	1	2	yes	—
159	C₄⋊C₄	—	2	4	no	—
160	C₄⋊C₄	—	2	2	no	—
161	C₄⋊C₄	—	2	1	no	—
162	C₄⋊C₄	—	2	1	no	—
163	C₂²⋊C₄	—	2	1	no	—
164	C₂²⋊C₄	C₁₃×M₁₆	1	2	yes	—
165	C₄²	—	2	1	no	—
166	C₄²	—	2	1	no	—
167	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
168	C₄²	C₁₃×M₁₆	1	1	yes	characteristic
169	C₄²	C₁₃×M₁₆	1	1	yes	characteristic
170	C₁₆	—	2	4	no	—
171	C₁₆	—	4	2	no	—
172	C₁₃	#13269	1	1	yes	characteristic, direct product factor, Sylow
173	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
174	Q₈	—	8	2	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	1	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	8	1	no	—
180	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
181	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
182	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
183	C₂×C₄	C₁₃×#131	1	2	yes	—
184	C₈	—	2	2	no	—
185	C₈	—	4	1	no	—
186	C₈	—	4	1	no	—
187	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
188	C₈	C₁₃×#124	1	1	yes	characteristic
189	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
190	C₂²	—	4	1	no	—
191	C₂²	C₁₃×#407	1	1	yes	characteristic
192	C₂²	C₁₃×#446	1	2	yes	—
193	C₄	—	4	1	no	—
194	C₄	—	4	1	no	—
195	C₄	—	4	2	no	—
196	C₄	—	4	2	no	—
197	C₄	C₁₃×#391	1	1	yes	characteristic
198	C₄	C₁₃×#408	1	1	yes	characteristic
199	C₄	C₁₃×#446	1	2	yes	—
200	C₂	—	2	1	no	—
201	C₂	—	2	2	no	—
202	C₂	C₁₃×#1985	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₃	#391
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂×C₁₃	#1985
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
35. C₂×C₁₃×C₁₆	Q₈	semidirect
45. #13269	C₁₃	direct (N × H)
133. C₂×C₁₆	Q₈×C₁₃	semidirect
172. C₁₃	#13269	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×#2961	2
C₁₃×#2153	2
C₁₃×#2110	2
C₁₃×#1378	2
C₁₃×#1375	2
#13269	13

Subgroups — C13×#13269 #15699608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13269 #15699608