Subgroups — C₁₃×#36701 #15723040

Order 3328.

1304 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2845	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2839	C₂	1	12	yes	maximal
3	C₁₃×#2822	C₂	1	3	yes	maximal
4	C₁₃×#2402	C₂	1	12	yes	maximal
5	C₄×C₁₃×#125	C₂	1	3	yes	maximal
6	C₂×C₁₃×#125	C₂²	1	3	yes	—
7	C₁₃×#400	C₂²	1	12	yes	—
8	C₁₃×#400	C₂²	1	12	yes	—
9	C₁₃×#400	C₂²	1	12	yes	—
10	C₁₃×#400	C₂²	1	12	yes	—
11	C₁₃×#398	C₂²	1	12	yes	—
12	C₁₃×#398	C₂²	1	12	yes	—
13	C₁₃×#398	C₂²	1	12	yes	—
14	C₁₃×#398	C₂²	1	12	yes	—
15	C₁₃×#389	C₂²	1	6	yes	—
16	C₁₃×#387	C₂²	1	12	yes	—
17	C₁₃×#382	C₂²	1	3	yes	—
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	12	yes	—
19	C₄×C₁₃×C₄⋊C₄	C₂²	1	6	yes	—
20	C₄×C₁₃×C₄⋊C₄	C₂²	1	12	yes	—
21	C₁₃×#376	C₂²	1	4	yes	—
22	C₄³×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#125	—	2	12	no	—
24	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
25	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
26	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	—
27	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
28	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
29	C₂×C₁₃×C₄⋊C₄	C₂³	1	12	yes	—
30	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
31	C₂×C₄²×C₁₃	C₂³	1	12	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
34	C₁₃×#95	C₂³	1	12	yes	—
35	C₁₃×#95	C₂³	1	12	yes	—
36	C₁₃×#95	C₂³	1	12	yes	—
37	C₁₃×#95	C₂³	1	12	yes	—
38	C₁₃×#95	C₂³	1	12	yes	—
39	C₁₃×#95	C₂³	1	12	yes	—
40	C₁₃×#95	C₂³	1	4	yes	—
41	#36701	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
43	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
44	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	—
45	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
46	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₁₃×C₄⋊C₄	—	2	24	no	—
48	C₁₃×C₄⋊C₄	—	2	12	no	—
49	C₁₃×C₄⋊C₄	—	4	6	no	—
50	C₁₃×C₄⋊C₄	—	4	12	no	—
51	C₁₃×C₄⋊C₄	—	4	12	no	—
52	C₁₃×C₄⋊C₄	—	4	12	no	—
53	C₄²×C₁₃	—	2	6	no	—
54	C₄²×C₁₃	—	2	24	no	—
55	C₄²×C₁₃	—	4	3	no	—
56	C₄²×C₁₃	#41	1	4	yes	—
57	#2845	C₂×C₁₃	1	1	yes	characteristic
58	#2839	C₂×C₁₃	1	12	yes	—
59	#2822	C₂×C₁₃	1	3	yes	—
60	#2402	C₂×C₁₃	1	12	yes	—
61	C₄×#125	C₂×C₁₃	1	3	yes	—
62	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
63	C₂×C₄×C₁₃	—	2	3	no	—
64	C₂×C₄×C₁₃	—	2	3	no	—
65	C₂×C₄×C₁₃	—	2	12	no	—
66	C₂×C₄×C₁₃	—	2	12	no	—
67	C₂×C₄×C₁₃	—	2	3	no	—
68	C₂×C₄×C₁₃	—	2	12	no	—
69	C₂×C₄×C₁₃	—	2	6	no	—
70	C₂×C₄×C₁₃	—	2	12	no	—
71	C₂×C₄×C₁₃	—	2	12	no	—
72	C₂×C₄×C₁₃	—	2	12	no	—
73	C₂×C₄×C₁₃	C₂×#41	1	6	yes	—
74	C₂×C₄×C₁₃	2₋¹⁺⁴	1	6	yes	—
75	C₂×#125	C₂²×C₁₃	1	3	yes	—
76	#400	C₂²×C₁₃	1	12	yes	—
77	#400	C₂²×C₁₃	1	12	yes	—
78	#400	C₂²×C₁₃	1	12	yes	—
79	#400	C₂²×C₁₃	1	12	yes	—
80	#398	C₂²×C₁₃	1	12	yes	—
81	#398	C₂²×C₁₃	1	12	yes	—
82	#398	C₂²×C₁₃	1	12	yes	—
83	#398	C₂²×C₁₃	1	12	yes	—
84	#389	C₂²×C₁₃	1	6	yes	—
85	#387	C₂²×C₁₃	1	12	yes	—
86	#382	C₂²×C₁₃	1	3	yes	—
87	C₄×C₄⋊C₄	C₂²×C₁₃	1	12	yes	—
88	C₄×C₄⋊C₄	C₂²×C₁₃	1	6	yes	—
89	C₄×C₄⋊C₄	C₂²×C₁₃	1	12	yes	—
90	#376	C₂²×C₁₃	1	4	yes	—
91	C₄³	C₂²×C₁₃	1	1	yes	characteristic
92	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
93	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	3	yes	—
94	C₂²×C₁₃	#585	1	3	yes	—
95	C₄×C₁₃	—	2	6	no	—
96	C₄×C₁₃	—	4	12	no	—
97	C₄×C₁₃	—	4	3	no	—
98	C₄×C₁₃	—	4	12	no	—
99	C₄×C₁₃	#564	1	4	yes	—
100	#125	—	2	12	no	—
101	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
102	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
103	C₂×C₄⋊C₄	C₂³×C₁₃	1	6	yes	—
104	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
105	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
106	C₂×C₄⋊C₄	C₂³×C₁₃	1	12	yes	—
107	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
108	C₂×C₄²	C₂³×C₁₃	1	12	yes	—
109	C₂×C₄²	C₂³×C₁₃	1	3	yes	—
110	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
111	#95	C₂³×C₁₃	1	12	yes	—
112	#95	C₂³×C₁₃	1	4	yes	—
113	#95	C₂³×C₁₃	1	12	yes	—
114	#95	C₂³×C₁₃	1	12	yes	—
115	#95	C₂³×C₁₃	1	12	yes	—
116	#95	C₂³×C₁₃	1	12	yes	—
117	#95	C₂³×C₁₃	1	12	yes	—
118	C₂×C₁₃	#3461	1	3	yes	—
119	C₂×C₁₃	C₂×#564	1	1	yes	characteristic
120	C₂×C₁₃	#3531	1	3	yes	—
121	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
122	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
123	C₂²×C₄	C₂⁴×C₁₃	1	12	yes	—
124	C₂²×C₄	C₂⁴×C₁₃	1	3	yes	—
125	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
126	C₄⋊C₄	—	2	24	no	—
127	C₄⋊C₄	—	2	12	no	—
128	C₄⋊C₄	—	4	6	no	—
129	C₄⋊C₄	—	4	12	no	—
130	C₄⋊C₄	—	4	12	no	—
131	C₄⋊C₄	—	4	12	no	—
132	C₄²	—	2	6	no	—
133	C₄²	—	2	24	no	—
134	C₄²	—	4	3	no	—
135	C₄²	C₁₃×#41	1	4	yes	—
136	C₁₃	#36701	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
138	C₂×C₄	—	2	3	no	—
139	C₂×C₄	—	2	3	no	—
140	C₂×C₄	—	2	12	no	—
141	C₂×C₄	—	2	3	no	—
142	C₂×C₄	—	2	12	no	—
143	C₂×C₄	—	2	12	no	—
144	C₂×C₄	—	2	6	no	—
145	C₂×C₄	—	2	12	no	—
146	C₂×C₄	—	2	12	no	—
147	C₂×C₄	—	2	12	no	—
148	C₂×C₄	C₂×C₁₃×#41	1	6	yes	—
149	C₂×C₄	C₁₃×2₋¹⁺⁴	1	6	yes	—
150	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
151	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	3	yes	—
152	C₂²	C₁₃×#585	1	3	yes	—
153	C₄	—	2	6	no	—
154	C₄	—	4	3	no	—
155	C₄	—	4	12	no	—
156	C₄	—	4	12	no	—
157	C₄	C₁₃×#564	1	4	yes	—
158	C₂	C₁₃×#3461	1	3	yes	—
159	C₂	C₂×C₁₃×#564	1	1	yes	characteristic
160	C₂	C₁₃×#3531	1	3	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle, prime radical	C₂³×C₁₃	C₂⁵
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
41. #36701	C₁₃	direct (N × H)
136. C₁₃	#36701	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×#2845	2
C₁₃×#2839	2
C₁₃×#2822	2
C₁₃×#2402	2
C₄×C₁₃×#125	2
#36701	13

Subgroups — C13×#36701 #15723040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36701 #15723040