Subgroups — C₁₃×#13161 #15699500

Order 3328.

298 conjugacy classes of subgroups.

The subgroup lattice has 186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#364	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2151	C₂	1	2	yes	maximal
3	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1379	C₂	1	2	yes	maximal
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#108	C₄	1	1	yes	characteristic
10	C₁₃×#427	C₄	1	1	yes	characteristic
11	C₁₃×#405	C₂²	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₁₃×#364	—	2	2	no	—
14	C₁₃×C₄⋊C₁₆	—	2	4	no	—
15	C₄×C₁₃×C₁₆	—	2	2	no	—
16	C₁₃×#339	C₄	1	2	yes	—
17	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
20	C₁₃×#117	C₂×C₄	1	2	yes	—
21	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
22	C₁₃×M₃₂	—	2	2	no	—
23	C₁₃×M₃₂	—	2	2	no	—
24	C₂×C₁₃×C₁₆	—	2	1	no	—
25	C₂×C₁₃×C₁₆	—	2	1	no	—
26	C₂×C₁₃×C₁₆	—	2	1	no	—
27	C₂×C₁₃×C₁₆	—	2	1	no	—
28	C₂×C₁₃×C₁₆	—	2	2	no	—
29	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
30	C₂×C₁₃×C₁₆	Q₈	1	2	yes	—
31	C₁₃×#108	—	2	2	no	—
32	C₁₃×#107	C₈	1	2	yes	—
33	C₁₃×#106	C₈	1	2	yes	—
34	C₁₃×#97	—	2	2	no	—
35	C₄×C₈×C₁₃	—	2	2	no	—
36	C₄×C₈×C₁₃	D₄	1	2	yes	—
37	C₄×C₈×C₁₃	Q₈	1	2	yes	—
38	#13161	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂²×C₄×C₁₃	—	2	1	no	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₁₃×M₁₆	—	2	2	no	—
42	C₁₃×M₁₆	—	2	2	no	—
43	C₂×C₈×C₁₃	—	2	2	no	—
44	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
45	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
46	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
47	C₂×C₈×C₁₃	M₁₆	1	2	yes	—
48	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
49	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
52	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
53	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
54	C₁₃×C₄⋊C₄	C₂×C₈	1	4	yes	—
55	C₁₃×C₂²⋊C₄	—	2	2	no	—
56	C₄²×C₁₃	—	2	2	no	—
57	C₄²×C₁₃	—	2	1	no	—
58	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
59	C₁₃×C₁₆	—	2	2	no	—
60	C₁₃×C₁₆	—	2	2	no	—
61	C₁₃×C₁₆	—	4	2	no	—
62	C₂×#364	C₂×C₁₃	1	1	yes	characteristic
63	#2151	C₂×C₁₃	1	2	yes	—
64	C₂×C₄×C₁₆	C₂×C₁₃	1	1	yes	characteristic
65	#1772	C₂×C₁₃	1	1	yes	characteristic
66	#1379	C₂×C₁₃	1	2	yes	—
67	C₂³×C₁₃	#131	1	1	yes	characteristic
68	C₂×C₄×C₁₃	—	2	4	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	4	no	—
71	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
74	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
76	C₂×C₄×C₁₃	#131	1	1	yes	characteristic
77	C₈×C₁₃	—	4	2	no	—
78	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
79	C₈×C₁₃	C₄⋊C₈	1	2	yes	—
80	C₈×C₁₃	#121	1	1	yes	characteristic
81	C₈×C₁₃	C₂²⋊Q₈	1	1	yes	characteristic
82	C₈×C₁₃	#125	1	1	yes	characteristic
83	C₈×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
84	C₂×M₃₂	C₂²×C₁₃	1	2	yes	—
85	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
86	C₂²×C₁₆	C₂²×C₁₃	1	1	yes	characteristic
87	C₂×#108	C₄×C₁₃	1	1	yes	characteristic
88	#427	C₄×C₁₃	1	1	yes	characteristic
89	#405	C₂²×C₁₃	1	2	yes	—
90	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
91	#364	—	2	2	no	—
92	C₄⋊C₁₆	—	2	4	no	—
93	C₄×C₁₆	—	2	2	no	—
94	#339	C₄×C₁₃	1	2	yes	—
95	C₂²×C₁₃	—	2	2	no	—
96	C₂²×C₁₃	#424	1	1	yes	characteristic
97	C₂²×C₁₃	C₈×D₄	1	1	yes	characteristic
98	C₂²×C₁₃	#446	1	1	yes	characteristic
99	C₄×C₁₃	—	2	4	no	—
100	C₄×C₁₃	—	4	4	no	—
101	C₄×C₁₃	#389	1	1	yes	characteristic
102	C₄×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
103	C₄×C₁₃	#436	1	1	yes	characteristic
104	C₄×C₁₃	C₈×Q₈	1	1	yes	characteristic
105	C₂×M₁₆	C₂×C₄×C₁₃	1	2	yes	—
106	C₂²×C₈	C₂×C₄×C₁₃	1	1	yes	characteristic
107	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
108	#117	C₂×C₄×C₁₃	1	2	yes	—
109	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
110	M₃₂	—	2	2	no	—
111	M₃₂	—	2	2	no	—
112	C₂×C₁₆	—	2	1	no	—
113	C₂×C₁₆	—	2	1	no	—
114	C₂×C₁₆	—	2	1	no	—
115	C₂×C₁₆	—	2	1	no	—
116	C₂×C₁₆	—	2	2	no	—
117	C₂×C₁₆	D₄×C₁₃	1	2	yes	—
118	C₂×C₁₆	Q₈×C₁₃	1	2	yes	—
119	#108	—	2	2	no	—
120	#107	C₈×C₁₃	1	2	yes	—
121	#106	C₈×C₁₃	1	2	yes	—
122	#97	—	2	2	no	—
123	C₄×C₈	—	2	2	no	—
124	C₄×C₈	D₄×C₁₃	1	2	yes	—
125	C₄×C₈	Q₈×C₁₃	1	2	yes	—
126	C₂×C₁₃	—	2	1	no	—
127	C₂×C₁₃	—	2	1	no	—
128	C₂×C₁₃	#1939	1	1	yes	characteristic
129	C₂×C₁₃	#2170	1	2	yes	—
130	C₂²×C₄	—	2	1	no	—
131	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
132	M₁₆	—	2	2	no	—
133	M₁₆	—	2	2	no	—
134	C₂×C₈	—	2	2	no	—
135	C₂×C₈	C₁₃×C₄⋊C₄	1	2	yes	—
136	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
137	C₂×C₈	C₂×C₈×C₁₃	1	1	yes	characteristic
138	C₂×C₈	C₁₃×M₁₆	1	2	yes	—
139	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
140	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
141	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
142	C₂×C₈	C₂×Q₈×C₁₃	1	1	yes	characteristic
143	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
144	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
145	C₄⋊C₄	C₂×C₈×C₁₃	1	4	yes	—
146	C₂²⋊C₄	—	2	2	no	—
147	C₄²	—	2	2	no	—
148	C₄²	—	2	1	no	—
149	C₄²	C₁₃×C₄⋊C₄	1	2	yes	—
150	C₁₆	—	2	2	no	—
151	C₁₆	—	2	2	no	—
152	C₁₆	—	4	2	no	—
153	C₁₃	#13161	1	1	yes	characteristic, direct product factor, Sylow
154	C₂³	C₁₃×#131	1	1	yes	characteristic
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
160	C₂×C₄	C₄×Q₈×C₁₃	1	1	yes	characteristic
161	C₂×C₄	C₂²×C₈×C₁₃	1	1	yes	characteristic
162	C₂×C₄	C₂×C₁₃×M₁₆	1	1	yes	characteristic
163	C₂×C₄	C₁₃×#131	1	1	yes	characteristic
164	C₈	—	4	2	no	—
165	C₈	C₁₃×C₄⋊C₈	1	2	yes	—
166	C₈	C₁₃×C₄⋊C₈	1	2	yes	—
167	C₈	C₁₃×#121	1	1	yes	characteristic
168	C₈	C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
169	C₈	C₁₃×#125	1	1	yes	characteristic
170	C₈	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
171	C₂²	—	2	2	no	—
172	C₂²	C₁₃×#424	1	1	yes	characteristic
173	C₂²	C₈×D₄×C₁₃	1	1	yes	characteristic
174	C₂²	C₁₃×#446	1	1	yes	characteristic
175	C₄	—	2	4	no	—
176	C₄	—	4	4	no	—
177	C₄	C₁₃×#389	1	1	yes	characteristic
178	C₄	C₂×C₁₃×C₄⋊C₈	1	1	yes	characteristic
179	C₄	C₁₃×#436	1	1	yes	characteristic
180	C₄	C₈×Q₈×C₁₃	1	1	yes	characteristic
181	C₂	—	2	1	no	—
182	C₂	—	2	1	no	—
183	C₂	C₁₃×#1939	1	1	yes	characteristic
184	C₂	C₁₃×#2170	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	C₈×D₄
prime radical	C₂³×C₁₃	#131
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₃ ◁ C₂²×C₁₃×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
38. #13161	C₁₃	direct (N × H)
153. C₁₃	#13161	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×#364	2
C₁₃×#2151	2
C₂×C₄×C₁₃×C₁₆	2
C₁₃×#1772	2
C₁₃×#1379	2
#13161	13

Subgroups — C13×#13161 #15699500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#13161 #15699500