Subgroups — C₁₃×#2851 #13111909

Order 1664.

556 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×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄²×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#389	C₂	1	2	yes	maximal, complemented
4	C₁₃×#387	C₂	1	4	yes	maximal, complemented
5	C₁₃×#385	C₂	1	4	yes	maximal
6	C₁₃×#382	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#380	C₂	1	2	yes	maximal
8	C₂³×C₄×C₁₃	C₂²	1	2	yes	—
9	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
10	C₁₃×#125	—	2	4	no	—
11	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
15	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
16	C₂×C₄²×C₁₃	—	2	4	no	—
17	C₂×C₄²×C₁₃	C₂²	1	2	yes	—
18	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#95	C₂²	1	4	yes	—
21	C₁₃×#95	C₂²	1	4	yes	—
22	C₁₃×#95	C₂²	1	4	yes	—
23	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
24	C₂²×C₄×C₁₃	—	2	4	no	—
25	C₂²×C₄×C₁₃	—	2	4	no	—
26	C₂²×C₄×C₁₃	—	2	2	no	—
27	C₂²×C₄×C₁₃	—	2	4	no	—
28	C₂²×C₄×C₁₃	—	2	2	no	—
29	C₂²×C₄×C₁₃	Q₈	1	4	yes	—
30	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
31	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
32	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
33	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₁₃×C₄⋊C₄	—	2	8	no	—
37	C₁₃×C₄⋊C₄	—	2	4	no	—
38	C₁₃×C₄⋊C₄	—	2	8	no	—
39	C₁₃×C₄⋊C₄	—	2	4	no	—
40	C₁₃×C₂²⋊C₄	—	2	8	no	—
41	C₄²×C₁₃	—	2	4	no	—
42	C₄²×C₁₃	—	2	2	no	—
43	C₄²×C₁₃	D₄	1	4	yes	—
44	#2851	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂³×C₁₃	—	2	1	no	—
46	C₂³×C₁₃	—	2	1	no	—
47	C₂³×C₁₃	—	2	2	no	—
48	C₂³×C₁₃	C₂×Q₈	1	2	yes	—
49	C₂³×C₁₃	#41	1	4	yes	—
50	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
51	C₂×C₄×C₁₃	—	2	16	no	—
52	C₂×C₄×C₁₃	—	2	1	no	—
53	C₂×C₄×C₁₃	—	2	2	no	—
54	C₂×C₄×C₁₃	—	2	1	no	—
55	C₂×C₄×C₁₃	—	2	2	no	—
56	C₂×C₄×C₁₃	—	2	2	no	—
57	C₂×C₄×C₁₃	—	2	2	no	—
58	C₂×C₄×C₁₃	—	2	8	no	—
59	C₂×C₄×C₁₃	—	2	4	no	—
60	C₂×C₄×C₁₃	—	2	4	no	—
61	C₂×C₄×C₁₃	—	2	4	no	—
62	C₂×C₄×C₁₃	—	2	4	no	—
63	C₂×C₄×C₁₃	—	2	4	no	—
64	C₂×C₄×C₁₃	—	2	4	no	—
65	C₂×C₄×C₁₃	C₂×D₄	1	4	yes	—
66	C₂×C₄×C₁₃	C₂×D₄	1	2	yes	—
67	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
68	C₂×C₄×C₁₃	C₂×Q₈	1	2	yes	—
69	C₂×C₄×C₁₃	#41	1	4	yes	—
70	C₂×C₄×C₁₃	#41	1	2	yes	—
71	C₂×#125	C₂×C₁₃	1	1	yes	characteristic, complemented
72	C₂²×C₄²	C₂×C₁₃	1	1	yes	characteristic
73	#389	C₂×C₁₃	1	2	yes	complemented
74	#387	C₂×C₁₃	1	4	yes	complemented
75	#385	C₂×C₁₃	1	4	yes	—
76	#382	C₂×C₁₃	1	1	yes	characteristic, complemented
77	#380	C₂×C₁₃	1	2	yes	—
78	C₂²×C₁₃	—	2	2	no	—
79	C₂²×C₁₃	—	2	4	no	—
80	C₂²×C₁₃	—	2	4	no	—
81	C₂²×C₁₃	—	2	2	no	—
82	C₂²×C₁₃	#125	1	4	yes	complemented
83	C₂²×C₁₃	C₂²×D₄	1	1	yes	characteristic
84	C₂²×C₁₃	C₂²×Q₈	1	1	yes	characteristic
85	C₂²×C₁₃	C₂×#41	1	1	yes	characteristic
86	C₂²×C₁₃	C₂×#41	1	2	yes	—
87	C₂²×C₁₃	C₂×#41	1	2	yes	—
88	C₄×C₁₃	—	2	2	no	—
89	C₄×C₁₃	—	2	4	no	—
90	C₄×C₁₃	—	2	4	no	—
91	C₄×C₁₃	—	4	4	no	—
92	C₄×C₁₃	—	4	4	no	—
93	C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
94	C₂³×C₄	C₂²×C₁₃	1	2	yes	—
95	C₂³×C₄	C₂²×C₁₃	1	1	yes	characteristic
96	#125	—	2	4	no	—
97	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
98	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
99	C₂×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
100	C₂×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
101	C₂×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
102	C₂×C₄²	—	2	4	no	—
103	C₂×C₄²	C₂²×C₁₃	1	2	yes	—
104	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
105	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
106	#95	C₂²×C₁₃	1	4	yes	—
107	#95	C₂²×C₁₃	1	4	yes	—
108	#95	C₂²×C₁₃	1	4	yes	—
109	C₂×C₁₃	—	2	4	no	—
110	C₂×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
111	C₂×C₁₃	#525	1	2	yes	—
112	C₂×C₁₃	C₂×#125	1	1	yes	characteristic
113	C₂×C₁₃	#529	1	2	yes	—
114	C₂×C₁₃	#533	1	1	yes	characteristic
115	C₂⁴	C₂³×C₁₃	1	1	yes	characteristic
116	C₂²×C₄	—	2	4	no	—
117	C₂²×C₄	—	2	4	no	—
118	C₂²×C₄	—	2	2	no	—
119	C₂²×C₄	—	2	4	no	—
120	C₂²×C₄	—	2	2	no	—
121	C₂²×C₄	Q₈×C₁₃	1	4	yes	—
122	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
123	C₂²×C₄	C₂³×C₁₃	1	4	yes	—
124	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
125	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
126	C₂²×C₄	C₂³×C₁₃	1	2	yes	—
127	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
128	C₄⋊C₄	—	2	8	no	—
129	C₄⋊C₄	—	2	4	no	—
130	C₄⋊C₄	—	2	8	no	—
131	C₄⋊C₄	—	2	4	no	—
132	C₂²⋊C₄	—	2	8	no	—
133	C₄²	—	2	4	no	—
134	C₄²	—	2	2	no	—
135	C₄²	D₄×C₁₃	1	4	yes	—
136	C₁₃	#2851	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³	—	2	1	no	—
138	C₂³	—	2	1	no	—
139	C₂³	—	2	2	no	—
140	C₂³	C₂×Q₈×C₁₃	1	2	yes	—
141	C₂³	C₁₃×#41	1	4	yes	—
142	C₂³	C₂⁴×C₁₃	1	1	yes	characteristic
143	C₂×C₄	—	2	16	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	—	2	2	no	—
146	C₂×C₄	—	2	1	no	—
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	2	2	no	—
150	C₂×C₄	—	2	8	no	—
151	C₂×C₄	—	2	4	no	—
152	C₂×C₄	—	2	4	no	—
153	C₂×C₄	—	2	4	no	—
154	C₂×C₄	—	2	4	no	—
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	C₂×D₄×C₁₃	1	4	yes	—
158	C₂×C₄	C₂×D₄×C₁₃	1	2	yes	—
159	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
160	C₂×C₄	C₂×Q₈×C₁₃	1	2	yes	—
161	C₂×C₄	C₁₃×#41	1	4	yes	—
162	C₂×C₄	C₁₃×#41	1	2	yes	—
163	C₂²	—	2	2	no	—
164	C₂²	—	2	4	no	—
165	C₂²	—	2	4	no	—
166	C₂²	—	2	2	no	—
167	C₂²	C₁₃×#125	1	4	yes	complemented
168	C₂²	C₂²×D₄×C₁₃	1	1	yes	characteristic
169	C₂²	C₂²×Q₈×C₁₃	1	1	yes	characteristic
170	C₂²	C₂×C₁₃×#41	1	1	yes	characteristic
171	C₂²	C₂×C₁₃×#41	1	2	yes	—
172	C₂²	C₂×C₁₃×#41	1	2	yes	—
173	C₄	—	2	2	no	—
174	C₄	—	2	4	no	—
175	C₄	—	2	4	no	—
176	C₄	—	4	4	no	—
177	C₄	—	4	4	no	—
178	C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
179	C₂	—	2	4	no	—
180	C₂	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
181	C₂	C₁₃×#525	1	2	yes	—
182	C₂	C₂×C₁₃×#125	1	1	yes	characteristic
183	C₂	C₁₃×#529	1	2	yes	—
184	C₂	C₁₃×#533	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#125	C₂	semidirect
3. C₁₃×#389	C₂	semidirect
4. C₁₃×#387	C₂	semidirect
6. C₁₃×#382	C₂	semidirect
44. #2851	C₁₃	direct (N × H)
71. C₂×#125	C₂×C₁₃	semidirect
73. #389	C₂×C₁₃	semidirect
74. #387	C₂×C₁₃	semidirect
76. #382	C₂×C₁₃	semidirect
82. C₂²×C₁₃	#125	semidirect
136. C₁₃	#2851	direct (N × H)
167. C₂²	C₁₃×#125	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#125	2
C₂²×C₄²×C₁₃	2
C₁₃×#389	2
C₁₃×#387	2
C₁₃×#385	2
C₁₃×#382	2
C₁₃×#380	2
#2851	13

Subgroups — C13×#2851 #13111909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#2851 #13111909