Subgroups — C₁₃×#13288 #15699627

Order 3328.

354 conjugacy classes of subgroups.

The subgroup lattice has 200 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	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1386	C₂	1	4	yes	maximal
5	C₁₃×#533	—	2	1	no	—
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₁₃×#500	C₄	1	2	yes	complemented
8	C₁₃×#499	—	2	1	no	—
9	C₁₃×#499	C₄	1	2	yes	complemented
10	C₁₃×#498	—	2	1	no	—
11	C₁₃×#427	—	2	1	no	—
12	C₁₃×#427	C₂²	1	2	yes	—
13	C₂×C₁₃×#107	—	2	1	no	—
14	C₂×C₁₃×#106	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
16	C₁₃×#382	—	2	1	no	—
17	C₁₃×#346	—	2	1	no	—
18	C₄×C₁₃×C₁₆	—	2	1	no	—
19	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
21	C₁₃×C₄⋊Q₈	—	2	2	no	—
22	C₁₃×#125	—	2	2	no	—
23	C₁₃×C₂²⋊Q₈	—	4	2	no	—
24	C₄×Q₈×C₁₃	—	4	2	no	—
25	C₁₃×#117	—	2	2	no	—
26	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
27	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
28	C₁₃×M₃₂	—	2	2	no	—
29	C₁₃×M₃₂	Q₈	1	4	yes	complemented
30	C₂×C₁₃×C₁₆	—	2	2	no	—
31	C₁₃×#107	—	2	2	no	—
32	C₁₃×#107	—	4	2	no	—
33	C₁₃×#107	C₂×C₄	1	4	yes	—
34	C₁₃×#106	—	2	2	no	—
35	C₁₃×#106	—	2	2	no	—
36	C₁₃×#106	—	2	4	no	—
37	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
38	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
39	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
40	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
41	C₁₃×#95	—	4	2	no	—
42	#13288	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂×Q₈×C₁₃	—	4	2	no	—
44	C₂²×C₄×C₁₃	—	4	2	no	—
45	C₂²×C₄×C₁₃	D₈	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₃	SD₁₆	1	2	yes	—
50	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
51	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
53	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
54	C₂×C₈×C₁₃	#41	1	2	yes	—
55	C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₁₃×C₄⋊C₄	—	4	4	no	—
57	C₁₃×C₄⋊C₄	—	4	2	no	—
58	C₁₃×C₄⋊C₄	—	4	2	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	SD₁₆	1	2	yes	—
65	C₁₃×C₁₆	—	2	4	no	—
66	#3160	C₂×C₁₃	1	1	yes	characteristic
67	C₄×M₃₂	C₂×C₁₃	1	1	yes	characteristic
68	#1846	C₂×C₁₃	1	1	yes	characteristic
69	#1386	C₂×C₁₃	1	4	yes	—
70	C₂³×C₁₃	C₂×D₈	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	—	8	4	no	—
75	C₂×C₄×C₁₃	—	8	2	no	—
76	C₂×C₄×C₁₃	#102	1	2	yes	—
77	C₂×C₄×C₁₃	#102	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
83	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
84	C₈×C₁₃	#103	1	2	yes	—
85	C₈×C₁₃	#103	1	2	yes	—
86	C₈×C₁₃	C₄×Q₈	1	2	yes	—
87	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
88	#533	—	2	1	no	—
89	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
90	#500	C₄×C₁₃	1	2	yes	complemented
91	#499	—	2	1	no	—
92	#499	C₄×C₁₃	1	2	yes	complemented
93	#498	—	2	1	no	—
94	#427	—	2	1	no	—
95	#427	C₂²×C₁₃	1	2	yes	—
96	C₂×#107	—	2	1	no	—
97	C₂×#106	C₂²×C₁₃	1	2	yes	—
98	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
99	#382	—	2	1	no	—
100	#346	—	2	1	no	—
101	C₄×C₁₆	—	2	1	no	—
102	C₂²×C₁₃	—	2	2	no	—
103	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
104	C₂²×C₁₃	#486	1	1	yes	characteristic
105	C₂²×C₁₃	#500	1	1	yes	characteristic
106	C₄×C₁₃	—	2	2	no	—
107	C₄×C₁₃	—	2	2	no	—
108	C₄×C₁₃	—	8	4	no	—
109	C₄×C₁₃	—	16	2	no	—
110	C₄×C₁₃	#391	1	1	yes	characteristic
111	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
112	C₄×C₁₃	#487	1	1	yes	characteristic
113	C₄×C₁₃	#498	1	1	yes	characteristic
114	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
115	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
116	C₄⋊Q₈	—	2	2	no	—
117	#125	—	2	2	no	—
118	C₂²⋊Q₈	—	4	2	no	—
119	C₄×Q₈	—	4	2	no	—
120	#117	—	2	2	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
123	M₃₂	—	2	2	no	—
124	M₃₂	Q₈×C₁₃	1	4	yes	complemented
125	C₂×C₁₆	—	2	2	no	—
126	#107	—	2	2	no	—
127	#107	—	4	2	no	—
128	#107	C₂×C₄×C₁₃	1	4	yes	—
129	#106	—	2	2	no	—
130	#106	—	2	2	no	—
131	#106	—	2	4	no	—
132	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
133	C₄×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
134	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
135	C₄×C₈	D₄×C₁₃	1	1	yes	characteristic
136	#95	—	4	2	no	—
137	C₂×C₁₃	—	2	1	no	—
138	C₂×C₁₃	—	2	1	no	—
139	C₂×C₁₃	#1990	1	1	yes	characteristic
140	C₂×C₁₃	#2145	1	2	yes	—
141	C₂×Q₈	—	4	2	no	—
142	C₂²×C₄	—	4	2	no	—
143	C₂²×C₄	C₁₃×D₈	1	2	yes	—
144	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
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	C₄⋊C₄	—	4	2	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₂²⋊C₄	—	4	2	no	—
159	C₄²	—	4	2	no	—
160	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
161	C₄²	C₁₃×C₂²⋊C₄	1	1	yes	characteristic
162	C₄²	C₁₃×SD₁₆	1	2	yes	—
163	C₁₆	—	2	4	no	—
164	C₁₃	#13288	1	1	yes	characteristic, direct product factor, Sylow
165	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
166	Q₈	—	8	4	no	—
167	C₂×C₄	—	4	2	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	8	4	no	—
170	C₂×C₄	—	8	2	no	—
171	C₂×C₄	C₁₃×#102	1	2	yes	—
172	C₂×C₄	C₁₃×#102	1	2	yes	—
173	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
174	C₂×C₄	C₁₃×#124	1	1	yes	characteristic
175	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
176	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
177	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
178	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
179	C₈	C₁₃×#103	1	2	yes	—
180	C₈	C₁₃×#103	1	2	yes	—
181	C₈	C₄×Q₈×C₁₃	1	2	yes	—
182	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
183	C₂²	—	2	2	no	—
184	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
185	C₂²	C₁₃×#486	1	1	yes	characteristic
186	C₂²	C₁₃×#500	1	1	yes	characteristic
187	C₄	—	2	2	no	—
188	C₄	—	2	2	no	—
189	C₄	—	8	4	no	—
190	C₄	—	16	2	no	—
191	C₄	C₁₃×#391	1	1	yes	characteristic
192	C₄	C₂×C₁₃×#103	1	1	yes	characteristic
193	C₄	C₁₃×#487	1	1	yes	characteristic
194	C₄	C₁₃×#498	1	1	yes	characteristic
195	C₂	—	2	1	no	—
196	C₂	—	2	1	no	—
197	C₂	C₁₃×#1990	1	1	yes	characteristic
198	C₂	C₁₃×#2145	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	C₂×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×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
7. C₁₃×#500	C₄	semidirect
9. C₁₃×#499	C₄	semidirect
29. C₁₃×M₃₂	Q₈	semidirect
42. #13288	C₁₃	direct (N × H)
90. #500	C₄×C₁₃	semidirect
92. #499	C₄×C₁₃	semidirect
124. M₃₂	Q₈×C₁₃	semidirect
164. C₁₃	#13288	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
C₄×C₁₃×M₃₂	2
C₁₃×#1846	2
C₁₃×#1386	2
#13288	13

Subgroups — C13×#13288 #15699627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13288 #15699627