Subgroups — C₁₃×#8263 #15694602

Order 3328.

470 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	C₄×C₁₃×C₄⋊C₈	C₂	1	2	yes	maximal
2	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#322	C₂	1	2	yes	maximal
4	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1273	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊C₈	C₄	1	4	yes	—
7	C₂×C₁₃×#97	C₄	1	2	yes	—
8	C₂×C₁₃×#97	C₄	1	2	yes	—
9	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₄³×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#336	C₄	1	4	yes	—
15	C₁₃×#322	—	2	4	no	—
16	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
20	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
22	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
25	C₁₃×C₄⋊C₈	—	2	8	no	—
26	C₁₃×#97	—	2	4	no	—
27	C₁₃×#97	—	2	4	no	—
28	C₄×C₈×C₁₃	—	2	2	no	—
29	C₄×C₈×C₁₃	—	2	2	no	—
30	C₄×C₈×C₁₃	—	2	2	no	—
31	C₄×C₈×C₁₃	—	2	2	no	—
32	C₄×C₈×C₁₃	—	2	2	no	—
33	C₄×C₈×C₁₃	D₄	1	2	yes	—
34	C₄×C₈×C₁₃	Q₈	1	2	yes	—
35	#8263	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	C₄²	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
40	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
41	C₂×C₈×C₁₃	—	2	2	no	—
42	C₂×C₈×C₁₃	—	2	4	no	—
43	C₂×C₈×C₁₃	—	2	2	no	—
44	C₂×C₈×C₁₃	—	2	2	no	—
45	C₂×C₈×C₁₃	—	2	2	no	—
46	C₂×C₈×C₁₃	—	2	4	no	—
47	C₂×C₈×C₁₃	—	2	4	no	—
48	C₂×C₈×C₁₃	—	2	4	no	—
49	C₂×C₈×C₁₃	—	2	4	no	—
50	C₂×C₈×C₁₃	C₄⋊C₄	1	4	yes	—
51	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
52	C₂×C₈×C₁₃	M₁₆	1	8	yes	—
53	C₄²×C₁₃	—	2	2	no	—
54	C₄²×C₁₃	—	2	4	no	—
55	C₄²×C₁₃	—	2	4	no	—
56	C₄²×C₁₃	M₁₆	1	4	yes	—
57	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₄²×C₁₃	C₂×Q₈	1	1	yes	characteristic
59	C₄²×C₁₃	#41	1	2	yes	—
60	C₄×C₄⋊C₈	C₂×C₁₃	1	2	yes	—
61	C₄×#97	C₂×C₁₃	1	1	yes	characteristic
62	C₂×#322	C₂×C₁₃	1	2	yes	—
63	#1273	C₂×C₁₃	1	1	yes	characteristic
64	#1273	C₂×C₁₃	1	1	yes	characteristic
65	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
66	C₂×C₄×C₁₃	—	2	2	no	—
67	C₂×C₄×C₁₃	—	2	2	no	—
68	C₂×C₄×C₁₃	—	2	1	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	2	1	no	—
71	C₂×C₄×C₁₃	—	2	2	no	—
72	C₂×C₄×C₁₃	#97	1	4	yes	—
73	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
75	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
76	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
77	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
79	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
80	C₂×C₄×C₁₃	#131	1	4	yes	—
81	C₈×C₁₃	—	2	4	no	—
82	C₈×C₁₃	—	2	4	no	—
83	C₈×C₁₃	—	2	8	no	—
84	C₈×C₁₃	—	4	4	no	—
85	C₂×C₄⋊C₈	C₄×C₁₃	1	4	yes	—
86	C₂×#97	C₄×C₁₃	1	2	yes	—
87	C₂×#97	C₄×C₁₃	1	2	yes	—
88	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
89	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
90	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
91	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
92	C₄³	C₂²×C₁₃	1	1	yes	characteristic
93	#336	C₄×C₁₃	1	4	yes	—
94	#322	—	2	4	no	—
95	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
96	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
97	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
98	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
99	C₂²×C₁₃	#405	1	2	yes	—
100	C₄×C₁₃	—	2	4	no	—
101	C₄×C₁₃	—	4	1	no	—
102	C₄×C₁₃	—	4	1	no	—
103	C₄×C₁₃	#423	1	2	yes	—
104	C₄×C₁₃	#432	1	2	yes	—
105	C₄×C₁₃	#435	1	4	yes	—
106	C₄×C₁₃	#446	1	4	yes	—
107	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
108	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
109	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
110	C₂²×C₈	C₂×C₄×C₁₃	1	2	yes	—
111	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
112	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
113	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
114	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
115	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
116	C₄⋊C₈	—	2	8	no	—
117	#97	—	2	4	no	—
118	#97	—	2	4	no	—
119	C₄×C₈	—	2	2	no	—
120	C₄×C₈	—	2	2	no	—
121	C₄×C₈	—	2	2	no	—
122	C₄×C₈	—	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	#1451	1	2	yes	—
127	C₂×C₁₃	#1453	1	1	yes	characteristic
128	C₂×C₁₃	#1455	1	1	yes	characteristic
129	C₂×C₁₃	#1767	1	1	yes	characteristic
130	C₂×C₁₃	#1771	1	2	yes	—
131	C₂²×C₄	C₄²×C₁₃	1	1	yes	characteristic
132	C₂²×C₄	C₄²×C₁₃	1	1	yes	characteristic
133	C₂²×C₄	C₄²×C₁₃	1	2	yes	—
134	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
135	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
136	C₂×C₈	—	2	2	no	—
137	C₂×C₈	—	2	4	no	—
138	C₂×C₈	—	2	2	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	—	2	4	no	—
145	C₂×C₈	C₁₃×C₄⋊C₄	1	4	yes	—
146	C₂×C₈	C₁₃×M₁₆	1	4	yes	—
147	C₂×C₈	C₁₃×M₁₆	1	8	yes	—
148	C₄²	—	2	2	no	—
149	C₄²	—	2	4	no	—
150	C₄²	—	2	4	no	—
151	C₄²	C₁₃×M₁₆	1	4	yes	—
152	C₄²	C₂×D₄×C₁₃	1	1	yes	characteristic
153	C₄²	C₂×Q₈×C₁₃	1	1	yes	characteristic
154	C₄²	C₁₃×#41	1	2	yes	—
155	C₁₃	#8263	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³	C₂×C₄²×C₁₃	1	1	yes	characteristic
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	2	1	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	C₁₃×#97	1	4	yes	—
164	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄	C₁₃×#117	1	1	yes	characteristic
166	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
167	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
168	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
169	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
170	C₂×C₄	C₂×C₁₃×M₁₆	1	4	yes	—
171	C₂×C₄	C₁₃×#131	1	4	yes	—
172	C₈	—	2	4	no	—
173	C₈	—	2	4	no	—
174	C₈	—	2	8	no	—
175	C₈	—	4	4	no	—
176	C₂²	C₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
177	C₂²	C₂×C₁₃×#97	1	1	yes	characteristic
178	C₂²	C₄×C₁₃×M₁₆	1	1	yes	characteristic
179	C₂²	C₄×C₁₃×M₁₆	1	2	yes	—
180	C₂²	C₁₃×#405	1	2	yes	—
181	C₄	—	2	4	no	—
182	C₄	—	4	1	no	—
183	C₄	—	4	1	no	—
184	C₄	C₁₃×#423	1	2	yes	—
185	C₄	C₁₃×#432	1	2	yes	—
186	C₄	C₁₃×#435	1	4	yes	—
187	C₄	C₁₃×#446	1	4	yes	—
188	C₂	C₁₃×#1451	1	2	yes	—
189	C₂	C₁₃×#1453	1	1	yes	characteristic
190	C₂	C₁₃×#1455	1	1	yes	characteristic
191	C₂	C₁₃×#1767	1	1	yes	characteristic
192	C₂	C₁₃×#1771	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²×C₁₃	C₂³
commutator	C₂³	C₂×C₄²×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle, prime radical	C₂³×C₁₃	C₂×C₄²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
35. #8263	C₁₃	direct (N × H)
155. C₁₃	#8263	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₄×C₁₃×C₄⋊C₈	2
C₄×C₁₃×#97	2
C₂×C₁₃×#322	2
C₁₃×#1273	2
#8263	13

Subgroups — C13×#8263 #15694602

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#8263 #15694602