Subgroups — C₁₃×#13267 #15699606

Order 3328.

334 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2150	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#346	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1379	C₂	1	4	yes	maximal
5	C₁₃×#533	C₄	1	1	yes	characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂²×C₁₃×C₁₆	C₂²	1	2	yes	—
8	C₁₃×#446	—	2	2	no	—
9	C₈×Q₈×C₁₃	—	2	2	no	—
10	C₁₃×#424	C₄	1	2	yes	—
11	C₁₃×#423	C₄	1	1	yes	characteristic
12	C₁₃×#405	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×C₄⋊C₁₆	—	2	2	no	—
15	C₁₃×#346	—	2	2	no	—
16	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₁₃×C₄⋊Q₈	C₈	1	2	yes	—
20	C₁₃×#125	C₈	1	2	yes	—
21	C₁₃×C₂²⋊Q₈	—	2	2	no	—
22	C₄×Q₈×C₁₃	—	2	2	no	—
23	C₁₃×#117	C₂×C₄	1	2	yes	—
24	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₁₃×M₃₂	—	2	4	no	—
26	C₂×C₁₃×C₁₆	—	2	2	no	—
27	C₂×C₁₃×C₁₆	—	2	2	no	—
28	C₂×C₁₃×C₁₆	—	2	2	no	—
29	C₂×C₁₃×C₁₆	Q₈	1	4	yes	complemented
30	C₁₃×C₄⋊C₈	—	2	4	no	—
31	C₁₃×C₄⋊C₈	—	2	2	no	—
32	C₁₃×#97	—	2	2	no	—
33	C₄×C₈×C₁₃	—	2	2	no	—
34	C₄×C₈×C₁₃	D₄	1	2	yes	—
35	C₄×C₈×C₁₃	D₄	1	2	yes	—
36	#13267	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂×Q₈×C₁₃	—	2	2	no	—
38	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₁₃×M₁₆	—	2	4	no	—
41	C₂×C₈×C₁₃	—	2	2	no	—
42	C₂×C₈×C₁₃	—	2	2	no	—
43	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
44	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
47	C₂×C₈×C₁₃	#41	1	2	yes	—
48	C₁₃×C₄⋊C₄	—	2	4	no	—
49	C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
51	C₁₃×C₂²⋊C₄	—	2	2	no	—
52	C₄²×C₁₃	—	2	2	no	—
53	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
54	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
55	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
56	C₁₃×C₁₆	—	2	4	no	—
57	C₁₃×C₁₆	—	4	2	no	—
58	#2960	C₂×C₁₃	1	1	yes	characteristic
59	#2150	C₂×C₁₃	1	1	yes	characteristic
60	C₂×#346	C₂×C₁₃	1	1	yes	characteristic
61	#1379	C₂×C₁₃	1	4	yes	—
62	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
63	Q₈×C₁₃	—	4	4	no	—
64	C₂×C₄×C₁₃	—	2	4	no	—
65	C₂×C₄×C₁₃	—	4	2	no	—
66	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
67	C₂×C₄×C₁₃	C₂²⋊C₈	1	2	yes	—
68	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
70	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₃	#131	1	2	yes	—
72	C₈×C₁₃	—	2	2	no	—
73	C₈×C₁₃	—	4	2	no	—
74	C₈×C₁₃	C₂²⋊Q₈	1	2	yes	—
75	C₈×C₁₃	#124	1	1	yes	characteristic
76	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
77	#533	C₄×C₁₃	1	1	yes	characteristic
78	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
79	C₂²×C₁₆	C₂²×C₁₃	1	2	yes	—
80	#446	—	2	2	no	—
81	C₈×Q₈	—	2	2	no	—
82	#424	C₄×C₁₃	1	2	yes	—
83	#423	C₄×C₁₃	1	1	yes	characteristic
84	#405	C₂²×C₁₃	1	2	yes	—
85	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
86	C₄⋊C₁₆	—	2	2	no	—
87	#346	—	2	2	no	—
88	C₂²×C₁₃	—	2	2	no	—
89	C₂²×C₁₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
90	C₂²×C₁₃	#446	1	2	yes	—
91	C₄×C₁₃	—	2	2	no	—
92	C₄×C₁₃	—	2	2	no	—
93	C₄×C₁₃	—	4	4	no	—
94	C₄×C₁₃	#391	1	1	yes	characteristic
95	C₄×C₁₃	#408	1	1	yes	characteristic
96	C₄×C₁₃	C₈×Q₈	1	2	yes	—
97	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
98	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
99	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
100	C₄⋊Q₈	C₈×C₁₃	1	2	yes	—
101	#125	C₈×C₁₃	1	2	yes	—
102	C₂²⋊Q₈	—	2	2	no	—
103	C₄×Q₈	—	2	2	no	—
104	#117	C₂×C₄×C₁₃	1	2	yes	—
105	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
106	M₃₂	—	2	4	no	—
107	C₂×C₁₆	—	2	2	no	—
108	C₂×C₁₆	—	2	2	no	—
109	C₂×C₁₆	—	2	2	no	—
110	C₂×C₁₆	Q₈×C₁₃	1	4	yes	complemented
111	C₄⋊C₈	—	2	4	no	—
112	C₄⋊C₈	—	2	2	no	—
113	#97	—	2	2	no	—
114	C₄×C₈	—	2	2	no	—
115	C₄×C₈	D₄×C₁₃	1	2	yes	—
116	C₄×C₈	D₄×C₁₃	1	2	yes	—
117	C₂×C₁₃	—	2	2	no	—
118	C₂×C₁₃	#1984	1	1	yes	characteristic
119	C₂×C₁₃	#2117	1	2	yes	—
120	C₂×Q₈	—	2	2	no	—
121	C₂²×C₄	C₁₃×M₁₆	1	2	yes	—
122	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
123	M₁₆	—	2	4	no	—
124	C₂×C₈	—	2	2	no	—
125	C₂×C₈	—	2	2	no	—
126	C₂×C₈	C₁₃×C₂²⋊C₄	1	2	yes	—
127	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
128	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
129	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
130	C₂×C₈	C₁₃×#41	1	2	yes	—
131	C₄⋊C₄	—	2	4	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
134	C₂²⋊C₄	—	2	2	no	—
135	C₄²	—	2	2	no	—
136	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
137	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
138	C₄²	C₂×C₈×C₁₃	1	1	yes	characteristic
139	C₁₆	—	2	4	no	—
140	C₁₆	—	4	2	no	—
141	C₁₃	#13267	1	1	yes	characteristic, direct product factor, Sylow
142	C₂³	C₂×C₁₃×M₁₆	1	1	yes	characteristic
143	Q₈	—	4	4	no	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	4	2	no	—
146	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
147	C₂×C₄	C₁₃×C₂²⋊C₈	1	2	yes	—
148	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
150	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
151	C₂×C₄	C₁₃×#131	1	2	yes	—
152	C₈	—	2	2	no	—
153	C₈	—	4	2	no	—
154	C₈	C₁₃×C₂²⋊Q₈	1	2	yes	—
155	C₈	C₁₃×#124	1	1	yes	characteristic
156	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
157	C₂²	—	2	2	no	—
158	C₂²	C₂×C₁₃×C₂²⋊C₈	1	1	yes	characteristic
159	C₂²	C₁₃×#446	1	2	yes	—
160	C₄	—	2	2	no	—
161	C₄	—	2	2	no	—
162	C₄	—	4	4	no	—
163	C₄	C₁₃×#391	1	1	yes	characteristic
164	C₄	C₁₃×#408	1	1	yes	characteristic
165	C₄	C₈×Q₈×C₁₃	1	2	yes	—
166	C₂	—	2	2	no	—
167	C₂	C₁₃×#1984	1	1	yes	characteristic
168	C₂	C₁₃×#2117	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂²×C₁₃	C₂×C₂²⋊C₈
prime radical	C₂³×C₁₃	C₂×M₁₆
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
29. C₂×C₁₃×C₁₆	Q₈	semidirect
36. #13267	C₁₃	direct (N × H)
110. C₂×C₁₆	Q₈×C₁₃	semidirect
141. C₁₃	#13267	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×#2960	2
C₁₃×#2150	2
C₂×C₁₃×#346	2
C₁₃×#1379	2
#13267	13

Subgroups — C13×#13267 #15699606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13267 #15699606