Subgroups — C₁₃×#12908 #15699247

Order 3328.

350 conjugacy classes of subgroups.

The subgroup lattice has 194 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	2	yes	maximal
2	C₂×C₁₃×#366	C₂	1	2	yes	maximal
3	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
7	C₂×C₁₃×#107	—	2	1	no	—
8	C₂×C₁₃×#107	C₂²	1	2	yes	—
9	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
10	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×#106	—	2	1	no	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#384	—	2	1	no	—
14	C₁₃×#382	—	2	1	no	—
15	C₁₃×#367	—	2	4	no	—
16	C₁₃×#366	—	2	4	no	—
17	C₁₃×#346	C₄	1	4	yes	complemented
18	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
21	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
22	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
23	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
24	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
25	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
26	C₂×C₁₃×C₁₆	D₄	1	4	yes	—
27	C₂×C₁₃×C₁₆	Q₈	1	4	yes	—
28	C₁₃×#107	—	2	2	no	—
29	C₁₃×#107	—	2	2	no	—
30	C₁₃×#107	—	2	2	no	—
31	C₁₃×#107	—	2	2	no	—
32	C₁₃×#107	—	4	2	no	—
33	C₁₃×#106	—	4	2	no	—
34	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₃	Q₈	1	2	yes	—
36	C₁₃×#95	—	4	2	no	—
37	#12908	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂²×C₄×C₁₃	—	4	1	no	—
39	C₂²×C₄×C₁₃	—	4	1	no	—
40	C₂²×C₄×C₁₃	—	4	2	no	—
41	C₂²×C₄×C₁₃	D₈	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₃	D₈	1	2	yes	—
45	C₂×C₈×C₁₃	Q₁₆	1	2	yes	—
46	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
48	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
49	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
50	C₁₃×C₄⋊C₄	—	4	1	no	—
51	C₁₃×C₄⋊C₄	—	4	2	no	—
52	C₁₃×C₄⋊C₄	—	4	1	no	—
53	C₁₃×C₄⋊C₄	—	4	1	no	—
54	C₁₃×C₄⋊C₄	—	4	1	no	—
55	C₁₃×C₄⋊C₄	—	4	2	no	—
56	C₁₃×C₄⋊C₄	—	8	4	no	—
57	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
58	C₄²×C₁₃	Q₁₆	1	2	yes	—
59	C₁₃×C₁₆	C₄⋊C₄	1	8	yes	complemented
60	C₂×#367	C₂×C₁₃	1	2	yes	—
61	C₂×#366	C₂×C₁₃	1	2	yes	—
62	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
63	#1846	C₂×C₁₃	1	1	yes	characteristic
64	#1845	C₂×C₁₃	1	1	yes	characteristic
65	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	8	1	no	—
69	C₂×C₄×C₁₃	—	8	2	no	—
70	C₂×C₄×C₁₃	—	8	1	no	—
71	C₂×C₄×C₁₃	—	8	4	no	—
72	C₂×C₄×C₁₃	—	8	2	no	—
73	C₂×C₄×C₁₃	—	8	2	no	—
74	C₂×C₄×C₁₃	#107	1	4	yes	—
75	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
81	C₈×C₁₃	#107	1	4	yes	—
82	C₈×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
83	C₈×C₁₃	C₄⋊Q₈	1	2	yes	—
84	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
85	C₂×#107	—	2	1	no	—
86	C₂×#107	C₂²×C₁₃	1	2	yes	—
87	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
88	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
89	C₂×#106	—	2	1	no	—
90	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
91	#384	—	2	1	no	—
92	#382	—	2	1	no	—
93	#367	—	2	4	no	—
94	#366	—	2	4	no	—
95	#346	C₄×C₁₃	1	4	yes	complemented
96	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
97	C₂²×C₁₃	#493	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	—	2	4	no	—
102	C₄×C₁₃	—	16	2	no	—
103	C₄×C₁₃	—	16	1	no	—
104	C₄×C₁₃	—	16	1	no	—
105	C₄×C₁₃	#384	1	1	yes	characteristic
106	C₄×C₁₃	C₂×#107	1	1	yes	characteristic
107	C₄×C₁₃	#494	1	1	yes	characteristic
108	C₄×C₁₃	#500	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	1	no	—
112	C₂×C₄⋊C₄	—	2	1	no	—
113	C₂×C₄⋊C₄	—	2	2	no	—
114	C₂×C₄⋊C₄	—	4	2	no	—
115	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
116	C₂×C₁₆	C₂×C₄×C₁₃	1	4	yes	—
117	C₂×C₁₆	D₄×C₁₃	1	4	yes	—
118	C₂×C₁₆	Q₈×C₁₃	1	4	yes	—
119	#107	—	2	2	no	—
120	#107	—	2	2	no	—
121	#107	—	2	2	no	—
122	#107	—	2	2	no	—
123	#107	—	4	2	no	—
124	#106	—	4	2	no	—
125	C₄×C₈	C₂×C₄×C₁₃	1	2	yes	—
126	C₄×C₈	Q₈×C₁₃	1	2	yes	—
127	#95	—	4	2	no	—
128	C₂×C₁₃	#1845	1	1	yes	characteristic
129	C₂×C₁₃	#2159	1	2	yes	—
130	C₂×C₁₃	#2250	1	1	yes	characteristic
131	C₂×C₁₃	#2251	1	1	yes	characteristic
132	C₂×C₁₃	#2255	1	2	yes	—
133	C₂²×C₄	—	4	1	no	—
134	C₂²×C₄	—	4	1	no	—
135	C₂²×C₄	—	4	2	no	—
136	C₂²×C₄	C₁₃×D₈	1	2	yes	—
137	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
138	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
139	C₂×C₈	C₁₃×D₈	1	2	yes	—
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	2	yes	—
143	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
144	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
145	C₄⋊C₄	—	4	1	no	—
146	C₄⋊C₄	—	4	2	no	—
147	C₄⋊C₄	—	4	1	no	—
148	C₄⋊C₄	—	4	1	no	—
149	C₄⋊C₄	—	4	1	no	—
150	C₄⋊C₄	—	4	2	no	—
151	C₄⋊C₄	—	8	4	no	—
152	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
153	C₄²	C₁₃×Q₁₆	1	2	yes	—
154	C₁₆	C₁₃×C₄⋊C₄	1	8	yes	complemented
155	C₁₃	#12908	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³	C₂×C₁₃×D₈	1	1	yes	characteristic
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	8	1	no	—
160	C₂×C₄	—	8	2	no	—
161	C₂×C₄	—	8	1	no	—
162	C₂×C₄	—	8	4	no	—
163	C₂×C₄	—	8	2	no	—
164	C₂×C₄	—	8	2	no	—
165	C₂×C₄	C₁₃×#107	1	4	yes	—
166	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
167	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
168	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
169	C₂×C₄	C₂×C₁₃×D₈	1	1	yes	characteristic
170	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
171	C₂×C₄	C₂×C₁₃×Q₁₆	1	1	yes	characteristic
172	C₈	C₁₃×#107	1	4	yes	—
173	C₈	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
174	C₈	C₁₃×C₄⋊Q₈	1	2	yes	—
175	C₂²	C₂×C₁₃×#107	1	1	yes	characteristic
176	C₂²	C₁₃×#493	1	1	yes	characteristic
177	C₂²	C₁₃×#500	1	1	yes	characteristic
178	C₂²	C₁₃×#509	1	2	yes	—
179	C₂²	C₁₃×#510	1	2	yes	—
180	C₄	—	2	4	no	—
181	C₄	—	16	2	no	—
182	C₄	—	16	1	no	—
183	C₄	—	16	1	no	—
184	C₄	C₁₃×#384	1	1	yes	characteristic
185	C₄	C₂×C₁₃×#107	1	1	yes	characteristic
186	C₄	C₁₃×#494	1	1	yes	characteristic
187	C₄	C₁₃×#500	1	1	yes	characteristic
188	C₂	C₁₃×#1845	1	1	yes	characteristic
189	C₂	C₁₃×#2159	1	2	yes	—
190	C₂	C₁₃×#2250	1	1	yes	characteristic
191	C₂	C₁₃×#2251	1	1	yes	characteristic
192	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
17. C₁₃×#346	C₄	semidirect
37. #12908	C₁₃	direct (N × H)
59. C₁₃×C₁₆	C₄⋊C₄	semidirect
95. #346	C₄×C₁₃	semidirect
154. C₁₆	C₁₃×C₄⋊C₄	semidirect
155. C₁₃	#12908	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×#1846	2
C₁₃×#1845	2
#12908	13

Subgroups — C13×#12908 #15699247

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#12908 #15699247