Subgroups — C₁₃×#10845 #15697184

Order 3328.

774 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#423	C₂	1	2	yes	maximal
2	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#341	C₂	1	4	yes	maximal
4	C₂²×C₁₃×M₁₆	C₂²	1	4	yes	—
5	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₁₃×#423	—	2	4	no	—
8	C₁₃×#423	C₄	1	8	yes	—
9	C₂×C₁₃×C₄⋊C₈	—	2	4	no	—
10	C₂×C₁₃×#97	—	2	4	no	—
11	C₂×C₁₃×#97	C₄	1	4	yes	—
12	C₁₃×#341	—	2	8	no	—
13	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
14	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×C₁₃×M₁₆	—	2	4	no	—
16	C₂×C₁₃×M₁₆	—	2	8	no	—
17	C₂×C₁₃×M₁₆	—	2	8	no	—
18	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
19	C₂²×C₈×C₁₃	—	2	4	no	—
20	C₂²×C₈×C₁₃	—	2	4	no	—
21	C₂²×C₈×C₁₃	—	2	4	no	—
22	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
23	C₂²×C₈×C₁₃	D₄	1	4	yes	—
24	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
25	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
27	C₂×C₄²×C₁₃	D₄	1	4	yes	—
28	C₂×C₄²×C₁₃	D₄	1	2	yes	—
29	C₁₃×C₄⋊C₈	—	2	16	no	—
30	C₁₃×#97	—	2	8	no	—
31	#10845	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	—	4	4	no	—
34	C₂²×C₄×C₁₃	C₄⋊C₄	1	4	yes	—
35	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
38	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
39	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
42	C₂²×C₄×C₁₃	#41	1	4	yes	—
43	C₁₃×M₁₆	—	2	16	no	—
44	C₁₃×M₁₆	—	4	8	no	—
45	C₂×C₈×C₁₃	—	2	4	no	—
46	C₂×C₈×C₁₃	—	2	4	no	—
47	C₂×C₈×C₁₃	—	2	8	no	—
48	C₂×C₈×C₁₃	—	2	8	no	—
49	C₂×C₈×C₁₃	—	2	8	no	—
50	C₂×C₈×C₁₃	—	4	4	no	—
51	C₂×C₈×C₁₃	—	4	4	no	—
52	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
53	C₄²×C₁₃	C₄²	1	4	yes	—
54	C₄²×C₁₃	C₂²⋊C₄	1	4	yes	—
55	C₄²×C₁₃	C₂²⋊C₄	1	8	yes	—
56	C₂×#423	C₂×C₁₃	1	2	yes	—
57	C₂²×#97	C₂×C₁₃	1	1	yes	characteristic
58	C₂×#341	C₂×C₁₃	1	4	yes	—
59	C₂³×C₁₃	—	2	4	no	—
60	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
61	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂³×C₁₃	#125	1	2	yes	—
63	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
64	C₂×C₄×C₁₃	—	2	8	no	—
65	C₂×C₄×C₁₃	—	4	8	no	—
66	C₂×C₄×C₁₃	#95	1	8	yes	—
67	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
68	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
70	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
71	C₂×C₄×C₁₃	#117	1	2	yes	—
72	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
73	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
74	C₂×C₄×C₁₃	#121	1	4	yes	—
75	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
76	C₂×C₄×C₁₃	#124	1	2	yes	—
77	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
79	C₈×C₁₃	—	2	8	no	—
80	C₈×C₁₃	—	4	8	no	—
81	C₂²×M₁₆	C₂²×C₁₃	1	4	yes	—
82	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
83	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
84	#423	—	2	4	no	—
85	#423	C₄×C₁₃	1	8	yes	—
86	C₂×C₄⋊C₈	—	2	4	no	—
87	C₂×#97	—	2	4	no	—
88	C₂×#97	C₄×C₁₃	1	4	yes	—
89	#341	—	2	8	no	—
90	C₂²×C₁₃	—	2	4	no	—
91	C₂²×C₁₃	—	2	4	no	—
92	C₂²×C₁₃	—	2	4	no	—
93	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
94	C₂²×C₁₃	#382	1	1	yes	characteristic
95	C₂²×C₁₃	#384	1	1	yes	characteristic
96	C₂²×C₁₃	#389	1	4	yes	—
97	C₂²×C₁₃	#430	1	4	yes	—
98	C₄×C₁₃	—	2	8	no	—
99	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
100	C₄×C₁₃	#380	1	2	yes	—
101	C₄×C₁₃	#390	1	2	yes	—
102	C₄×C₁₃	#391	1	2	yes	—
103	C₂³×C₄	Q₈×C₁₃	1	2	yes	—
104	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
105	C₂×M₁₆	—	2	4	no	—
106	C₂×M₁₆	—	2	8	no	—
107	C₂×M₁₆	—	2	8	no	—
108	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
109	C₂²×C₈	—	2	4	no	—
110	C₂²×C₈	—	2	4	no	—
111	C₂²×C₈	—	2	4	no	—
112	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
113	C₂²×C₈	D₄×C₁₃	1	4	yes	—
114	C₂²×C₈	Q₈×C₁₃	1	4	yes	—
115	C₂×C₄²	C₂×C₄×C₁₃	1	2	yes	—
116	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
117	C₂×C₄²	D₄×C₁₃	1	4	yes	—
118	C₂×C₄²	D₄×C₁₃	1	2	yes	—
119	C₄⋊C₈	—	2	16	no	—
120	#97	—	2	8	no	—
121	C₂×C₁₃	—	2	4	no	—
122	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
123	C₂×C₁₃	#1738	1	2	yes	—
124	C₂×C₁₃	#1838	1	2	yes	—
125	C₂×C₁₃	#1849	1	2	yes	—
126	C₂⁴	C₂×Q₈×C₁₃	1	1	yes	characteristic
127	C₂²×C₄	—	4	4	no	—
128	C₂²×C₄	C₁₃×C₄⋊C₄	1	4	yes	—
129	C₂²×C₄	C₁₃×C₄⋊C₄	1	8	yes	—
130	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
131	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
132	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
133	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
134	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
135	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
136	C₂²×C₄	C₁₃×#41	1	4	yes	—
137	M₁₆	—	2	16	no	—
138	M₁₆	—	4	8	no	—
139	C₂×C₈	—	2	4	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	2	8	no	—
142	C₂×C₈	—	2	8	no	—
143	C₂×C₈	—	2	8	no	—
144	C₂×C₈	—	4	4	no	—
145	C₂×C₈	—	4	4	no	—
146	C₂×C₈	C₁₃×C₄⋊C₄	1	8	yes	—
147	C₄²	C₄²×C₁₃	1	4	yes	—
148	C₄²	C₁₃×C₂²⋊C₄	1	4	yes	—
149	C₄²	C₁₃×C₂²⋊C₄	1	8	yes	—
150	C₁₃	#10845	1	1	yes	characteristic, direct product factor, Sylow
151	C₂³	—	2	4	no	—
152	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
153	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
154	C₂³	C₁₃×#125	1	2	yes	—
155	C₂³	C₁₃×C₄⋊Q₈	1	2	yes	—
156	C₂×C₄	—	2	8	no	—
157	C₂×C₄	—	4	8	no	—
158	C₂×C₄	C₁₃×#95	1	8	yes	—
159	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
160	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
163	C₂×C₄	C₁₃×#117	1	2	yes	—
164	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
165	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
166	C₂×C₄	C₁₃×#121	1	4	yes	—
167	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
168	C₂×C₄	C₁₃×#124	1	2	yes	—
169	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
170	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
171	C₈	—	2	8	no	—
172	C₈	—	4	8	no	—
173	C₂²	—	2	4	no	—
174	C₂²	—	2	4	no	—
175	C₂²	—	2	4	no	—
176	C₂²	C₂×C₁₃×#95	1	1	yes	characteristic
177	C₂²	C₁₃×#382	1	1	yes	characteristic
178	C₂²	C₁₃×#384	1	1	yes	characteristic
179	C₂²	C₁₃×#389	1	4	yes	—
180	C₂²	C₁₃×#430	1	4	yes	—
181	C₄	—	2	8	no	—
182	C₄	C₄×C₁₃×C₄⋊C₄	1	2	yes	—
183	C₄	C₁₃×#380	1	2	yes	—
184	C₄	C₁₃×#390	1	2	yes	—
185	C₄	C₁₃×#391	1	2	yes	—
186	C₂	—	2	4	no	—
187	C₂	C₁₃×C₄⋊#95	1	1	yes	characteristic
188	C₂	C₁₃×#1738	1	2	yes	—
189	C₂	C₁₃×#1838	1	2	yes	—
190	C₂	C₁₃×#1849	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
31. #10845	C₁₃	direct (N × H)
150. C₁₃	#10845	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×#423	2
C₂²×C₁₃×#97	2
C₂×C₁₃×#341	2
#10845	13

Subgroups — C13×#10845 #15697184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10845 #15697184