Subgroups — C₁₃×#13276 #15699615

Order 3328.

398 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1380	C₂	1	4	yes	maximal
5	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
6	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
7	C₁₃×#500	—	2	2	no	—
8	C₁₃×#500	C₄	1	4	yes	complemented
9	C₂×C₁₃×#107	—	2	1	no	—
10	C₂×C₁₃×#107	C₂²	1	2	yes	—
11	C₂×C₁₃×#107	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
14	C₁₃×C₄⋊C₁₆	—	2	2	no	—
15	C₁₃×#340	—	2	1	no	—
16	C₂²×Q₈×C₁₃	—	4	1	no	—
17	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₁₃×C₄⋊Q₈	—	2	4	no	—
20	C₁₃×C₄⋊Q₈	—	4	2	no	—
21	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
24	C₂×C₄²×C₁₃	—	4	1	no	—
25	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
26	C₂×C₁₃×C₁₆	—	2	2	no	—
27	C₂×C₁₃×C₁₆	—	2	4	no	—
28	C₁₃×#107	—	2	4	no	—
29	C₁₃×#107	—	2	2	no	—
30	C₁₃×#107	—	2	2	no	—
31	C₁₃×#107	C₂×C₄	1	4	yes	—
32	C₁₃×#107	Q₈	1	4	yes	complemented
33	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
34	C₄×C₈×C₁₃	D₄	1	2	yes	—
35	C₁₃×#95	—	4	1	no	—
36	#13276	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×Q₈×C₁₃	—	4	4	no	—
38	C₂×Q₈×C₁₃	—	8	4	no	—
39	C₂²×C₄×C₁₃	—	4	2	no	—
40	C₂²×C₄×C₁₃	—	4	2	no	—
41	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂×C₈×C₁₃	—	2	2	no	—
45	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
46	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
48	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
49	C₂×C₈×C₁₃	#41	1	2	yes	—
50	C₁₃×C₄⋊C₄	—	2	4	no	—
51	C₁₃×C₄⋊C₄	—	2	4	no	—
52	C₁₃×C₄⋊C₄	—	4	4	no	—
53	C₁₃×C₄⋊C₄	—	4	2	no	—
54	C₁₃×C₄⋊C₄	—	4	2	no	—
55	C₄²×C₁₃	—	8	2	no	—
56	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
57	C₄²×C₁₃	SD₁₆	1	2	yes	—
58	C₁₃×C₁₆	—	4	2	no	—
59	C₂×#500	C₂×C₁₃	1	1	yes	characteristic
60	C₂×C₄⋊C₁₆	C₂×C₁₃	1	1	yes	characteristic
61	C₄×#107	C₂×C₁₃	1	1	yes	characteristic
62	#1380	C₂×C₁₃	1	4	yes	—
63	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
64	Q₈×C₁₃	—	8	8	no	—
65	C₂×C₄×C₁₃	—	2	2	no	—
66	C₂×C₄×C₁₃	—	4	4	no	—
67	C₂×C₄×C₁₃	—	4	4	no	—
68	C₂×C₄×C₁₃	—	8	2	no	—
69	C₂×C₄×C₁₃	—	8	2	no	—
70	C₂×C₄×C₁₃	—	8	4	no	—
71	C₂×C₄×C₁₃	#102	1	2	yes	—
72	C₂×C₄×C₁₃	#102	1	2	yes	—
73	C₂×C₄×C₁₃	SD₃₂	1	2	yes	—
74	C₂×C₄×C₁₃	Q₃₂	1	2	yes	—
75	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
77	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
78	C₂×C₄×C₁₃	#137	1	2	yes	—
79	C₈×C₁₃	—	2	2	no	—
80	C₈×C₁₃	C₄×Q₈	1	2	yes	—
81	C₈×C₁₃	#124	1	1	yes	characteristic
82	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
83	C₂×C₄⋊Q₈	—	2	1	no	—
84	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
85	#500	—	2	2	no	—
86	#500	C₄×C₁₃	1	4	yes	complemented
87	C₂×#107	—	2	1	no	—
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	C₄×C₄⋊C₄	—	2	1	no	—
92	C₄⋊C₁₆	—	2	2	no	—
93	#340	—	2	1	no	—
94	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
95	C₂²×C₁₃	#474	1	2	yes	—
96	C₂²×C₁₃	C₂×SD₃₂	1	1	yes	characteristic
97	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
98	C₂²×C₁₃	#509	1	2	yes	—
99	C₄×C₁₃	—	2	2	no	—
100	C₄×C₁₃	—	8	4	no	—
101	C₄×C₁₃	—	8	4	no	—
102	C₄×C₁₃	#358	1	4	yes	—
103	C₄×C₁₃	#391	1	1	yes	characteristic
104	C₄×C₁₃	#419	1	1	yes	characteristic
105	C₄×C₁₃	#475	1	2	yes	—
106	C₂²×Q₈	—	4	1	no	—
107	C₂²×C₈	D₄×C₁₃	1	1	yes	characteristic
108	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
109	C₄⋊Q₈	—	2	4	no	—
110	C₄⋊Q₈	—	4	2	no	—
111	C₂×C₄⋊C₄	—	2	2	no	—
112	C₂×C₄⋊C₄	—	2	2	no	—
113	C₂×C₄⋊C₄	—	4	1	no	—
114	C₂×C₄²	—	4	1	no	—
115	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
116	C₂×C₁₆	—	2	2	no	—
117	C₂×C₁₆	—	2	4	no	—
118	#107	—	2	4	no	—
119	#107	—	2	2	no	—
120	#107	—	2	2	no	—
121	#107	C₂×C₄×C₁₃	1	4	yes	—
122	#107	Q₈×C₁₃	1	4	yes	complemented
123	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
124	C₄×C₈	D₄×C₁₃	1	2	yes	—
125	#95	—	4	1	no	—
126	C₂×C₁₃	#1988	1	1	yes	characteristic
127	C₂×C₁₃	C₂×#358	1	1	yes	characteristic
128	C₂×C₁₃	#2140	1	1	yes	characteristic
129	C₂×C₁₃	#2226	1	2	yes	—
130	C₂×C₁₃	#2227	1	2	yes	—
131	C₂×Q₈	—	4	4	no	—
132	C₂×Q₈	—	8	4	no	—
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	2	no	—
139	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
140	C₂×C₈	C₂²×C₄×C₁₃	1	1	yes	characteristic
141	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
142	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
143	C₂×C₈	C₁₃×#41	1	2	yes	—
144	C₄⋊C₄	—	2	4	no	—
145	C₄⋊C₄	—	2	4	no	—
146	C₄⋊C₄	—	4	4	no	—
147	C₄⋊C₄	—	4	2	no	—
148	C₄⋊C₄	—	4	2	no	—
149	C₄²	—	8	2	no	—
150	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
151	C₄²	C₁₃×SD₁₆	1	2	yes	—
152	C₁₆	—	4	2	no	—
153	C₁₃	#13276	1	1	yes	characteristic, direct product factor, Sylow
154	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
155	Q₈	—	8	8	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	4	4	no	—
158	C₂×C₄	—	4	4	no	—
159	C₂×C₄	—	8	2	no	—
160	C₂×C₄	—	8	2	no	—
161	C₂×C₄	—	8	4	no	—
162	C₂×C₄	C₁₃×#102	1	2	yes	—
163	C₂×C₄	C₁₃×#102	1	2	yes	—
164	C₂×C₄	C₁₃×SD₃₂	1	2	yes	—
165	C₂×C₄	C₁₃×Q₃₂	1	2	yes	—
166	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
167	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
168	C₂×C₄	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
169	C₂×C₄	C₁₃×#137	1	2	yes	—
170	C₈	—	2	2	no	—
171	C₈	C₄×Q₈×C₁₃	1	2	yes	—
172	C₈	C₁₃×#124	1	1	yes	characteristic
173	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
174	C₂²	C₂×C₁₃×#102	1	1	yes	characteristic
175	C₂²	C₁₃×#474	1	2	yes	—
176	C₂²	C₂×C₁₃×SD₃₂	1	1	yes	characteristic
177	C₂²	C₂×C₁₃×Q₃₂	1	1	yes	characteristic
178	C₂²	C₁₃×#509	1	2	yes	—
179	C₄	—	2	2	no	—
180	C₄	—	8	4	no	—
181	C₄	—	8	4	no	—
182	C₄	C₁₃×#358	1	4	yes	—
183	C₄	C₁₃×#391	1	1	yes	characteristic
184	C₄	C₁₃×#419	1	1	yes	characteristic
185	C₄	C₁₃×#475	1	2	yes	—
186	C₂	C₁₃×#1988	1	1	yes	characteristic
187	C₂	C₂×C₁₃×#358	1	1	yes	characteristic
188	C₂	C₁₃×#2140	1	1	yes	characteristic
189	C₂	C₁₃×#2226	1	2	yes	—
190	C₂	C₁₃×#2227	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
8. C₁₃×#500	C₄	semidirect
32. C₁₃×#107	Q₈	semidirect
36. #13276	C₁₃	direct (N × H)
86. #500	C₄×C₁₃	semidirect
122. #107	Q₈×C₁₃	semidirect
153. C₁₃	#13276	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×#500	2
C₂×C₁₃×C₄⋊C₁₆	2
C₄×C₁₃×#107	2
C₁₃×#1380	2
#13276	13

Subgroups — C13×#13276 #15699615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13276 #15699615