Subgroups — C₁₃×#10844 #15697183

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 210 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×C₄×C₈×C₁₃	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×C₄×C₈×C₁₃	—	2	4	no	—
11	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
12	C₂×C₄×C₈×C₁₃	C₄	1	2	yes	—
13	C₁₃×#341	—	2	8	no	—
14	C₂³×C₄×C₁₃	Q₈	1	2	yes	—
15	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
16	C₂×C₁₃×M₁₆	—	2	4	no	—
17	C₂×C₁₃×M₁₆	—	2	8	no	—
18	C₂×C₁₃×M₁₆	—	2	8	no	—
19	C₂×C₁₃×M₁₆	C₂×C₄	1	8	yes	—
20	C₂²×C₈×C₁₃	—	2	4	no	—
21	C₂²×C₈×C₁₃	—	2	4	no	—
22	C₂²×C₈×C₁₃	—	2	4	no	—
23	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	—
24	C₂²×C₈×C₁₃	D₄	1	4	yes	—
25	C₂²×C₈×C₁₃	Q₈	1	4	yes	—
26	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₁₃	D₄	1	4	yes	—
30	C₂×C₄²×C₁₃	D₄	1	2	yes	—
31	C₁₃×C₄⋊C₈	—	2	16	no	—
32	C₄×C₈×C₁₃	—	2	4	no	—
33	C₄×C₈×C₁₃	—	2	4	no	—
34	#10844	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂⁴×C₁₃	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₃	—	2	8	no	—
37	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
38	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
39	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
42	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
43	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
44	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
46	C₂²×C₄×C₁₃	#41	1	4	yes	—
47	C₁₃×M₁₆	—	2	16	no	—
48	C₁₃×M₁₆	—	4	8	no	—
49	C₂×C₈×C₁₃	—	2	4	no	—
50	C₂×C₈×C₁₃	—	2	4	no	—
51	C₂×C₈×C₁₃	—	2	8	no	—
52	C₂×C₈×C₁₃	—	2	8	no	—
53	C₂×C₈×C₁₃	—	2	8	no	—
54	C₂×C₈×C₁₃	—	4	4	no	—
55	C₂×C₈×C₁₃	—	4	4	no	—
56	C₂×C₈×C₁₃	C₄⋊C₄	1	8	yes	—
57	C₄²×C₁₃	C₄²	1	2	yes	—
58	C₄²×C₁₃	C₄²	1	2	yes	—
59	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
60	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
61	C₄²×C₁₃	C₂²⋊C₄	1	8	yes	—
62	C₂×#423	C₂×C₁₃	1	2	yes	—
63	C₂²×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic
64	C₂×#341	C₂×C₁₃	1	4	yes	—
65	C₂³×C₁₃	—	2	4	no	—
66	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
67	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂³×C₁₃	#125	1	2	yes	—
69	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
70	C₂×C₄×C₁₃	—	2	4	no	—
71	C₂×C₄×C₁₃	—	2	16	no	—
72	C₂×C₄×C₁₃	#95	1	4	yes	—
73	C₂×C₄×C₁₃	#95	1	4	yes	—
74	C₂×C₄×C₁₃	#108	1	8	yes	—
75	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
78	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
79	C₂×C₄×C₁₃	#117	1	2	yes	—
80	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
81	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
82	C₂×C₄×C₁₃	#121	1	4	yes	—
83	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
84	C₂×C₄×C₁₃	#124	1	2	yes	—
85	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
86	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
87	C₈×C₁₃	—	2	8	no	—
88	C₈×C₁₃	—	4	8	no	—
89	C₂²×M₁₆	C₂²×C₁₃	1	4	yes	—
90	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
91	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
92	#423	—	2	4	no	—
93	#423	C₄×C₁₃	1	8	yes	—
94	C₂×C₄⋊C₈	—	2	4	no	—
95	C₂×C₄×C₈	—	2	4	no	—
96	C₂×C₄×C₈	C₄×C₁₃	1	2	yes	—
97	C₂×C₄×C₈	C₄×C₁₃	1	2	yes	—
98	#341	—	2	8	no	—
99	C₂²×C₁₃	—	2	4	no	—
100	C₂²×C₁₃	—	2	4	no	—
101	C₂²×C₁₃	—	2	4	no	—
102	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
103	C₂²×C₁₃	#382	1	1	yes	characteristic
104	C₂²×C₁₃	#384	1	1	yes	characteristic
105	C₂²×C₁₃	#389	1	4	yes	—
106	C₂²×C₁₃	C₂×#108	1	4	yes	—
107	C₄×C₁₃	—	2	4	no	—
108	C₄×C₁₃	#341	1	8	yes	complemented
109	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
110	C₄×C₁₃	#380	1	2	yes	—
111	C₄×C₁₃	#390	1	2	yes	—
112	C₄×C₁₃	#391	1	2	yes	—
113	C₂³×C₄	Q₈×C₁₃	1	2	yes	—
114	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
115	C₂×M₁₆	—	2	4	no	—
116	C₂×M₁₆	—	2	8	no	—
117	C₂×M₁₆	—	2	8	no	—
118	C₂×M₁₆	C₂×C₄×C₁₃	1	8	yes	—
119	C₂²×C₈	—	2	4	no	—
120	C₂²×C₈	—	2	4	no	—
121	C₂²×C₈	—	2	4	no	—
122	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	—
123	C₂²×C₈	D₄×C₁₃	1	4	yes	—
124	C₂²×C₈	Q₈×C₁₃	1	4	yes	—
125	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
126	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
127	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
128	C₂×C₄²	D₄×C₁₃	1	4	yes	—
129	C₂×C₄²	D₄×C₁₃	1	2	yes	—
130	C₄⋊C₈	—	2	16	no	—
131	C₄×C₈	—	2	4	no	—
132	C₄×C₈	—	2	4	no	—
133	C₂×C₁₃	—	2	4	no	—
134	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
135	C₂×C₁₃	C₂×#341	1	2	yes	—
136	C₂×C₁₃	#1837	1	2	yes	—
137	C₂×C₁₃	#1848	1	2	yes	—
138	C₂⁴	C₂×Q₈×C₁₃	1	1	yes	characteristic
139	C₂²×C₄	—	2	8	no	—
140	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
141	C₂²×C₄	C₁₃×C₄⋊C₄	1	8	yes	—
142	C₂²×C₄	C₁₃×C₄⋊C₄	1	2	yes	—
143	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
144	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
145	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
146	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
147	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
148	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
149	C₂²×C₄	C₁₃×#41	1	4	yes	—
150	M₁₆	—	2	16	no	—
151	M₁₆	—	4	8	no	—
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	2	4	no	—
154	C₂×C₈	—	2	8	no	—
155	C₂×C₈	—	2	8	no	—
156	C₂×C₈	—	2	8	no	—
157	C₂×C₈	—	4	4	no	—
158	C₂×C₈	—	4	4	no	—
159	C₂×C₈	C₁₃×C₄⋊C₄	1	8	yes	—
160	C₄²	C₄²×C₁₃	1	2	yes	—
161	C₄²	C₄²×C₁₃	1	2	yes	—
162	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
163	C₄²	C₁₃×C₂²⋊C₄	1	2	yes	—
164	C₄²	C₁₃×C₂²⋊C₄	1	8	yes	—
165	C₁₃	#10844	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³	—	2	4	no	—
167	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
168	C₂³	C₂×C₁₃×C₄⋊C₄	1	1	yes	characteristic
169	C₂³	C₁₃×#125	1	2	yes	—
170	C₂³	C₁₃×C₄⋊Q₈	1	2	yes	—
171	C₂×C₄	—	2	4	no	—
172	C₂×C₄	—	2	16	no	—
173	C₂×C₄	C₁₃×#95	1	4	yes	—
174	C₂×C₄	C₁₃×#95	1	4	yes	—
175	C₂×C₄	C₁₃×#108	1	8	yes	—
176	C₂×C₄	C₂×C₄²×C₁₃	1	1	yes	characteristic
177	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
178	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
180	C₂×C₄	C₁₃×#117	1	2	yes	—
181	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
182	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
183	C₂×C₄	C₁₃×#121	1	4	yes	—
184	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
185	C₂×C₄	C₁₃×#124	1	2	yes	—
186	C₂×C₄	C₁₃×#127	1	1	yes	characteristic
187	C₂×C₄	C₁₃×C₄⋊Q₈	1	1	yes	characteristic
188	C₈	—	2	8	no	—
189	C₈	—	4	8	no	—
190	C₂²	—	2	4	no	—
191	C₂²	—	2	4	no	—
192	C₂²	—	2	4	no	—
193	C₂²	C₂×C₁₃×#95	1	1	yes	characteristic
194	C₂²	C₁₃×#382	1	1	yes	characteristic
195	C₂²	C₁₃×#384	1	1	yes	characteristic
196	C₂²	C₁₃×#389	1	4	yes	—
197	C₂²	C₂×C₁₃×#108	1	4	yes	—
198	C₄	—	2	4	no	—
199	C₄	C₁₃×#341	1	8	yes	complemented
200	C₄	C₄×C₁₃×C₄⋊C₄	1	2	yes	—
201	C₄	C₁₃×#380	1	2	yes	—
202	C₄	C₁₃×#390	1	2	yes	—
203	C₄	C₁₃×#391	1	2	yes	—
204	C₂	—	2	4	no	—
205	C₂	C₁₃×C₄⋊#95	1	1	yes	characteristic
206	C₂	C₂×C₁₃×#341	1	2	yes	—
207	C₂	C₁₃×#1837	1	2	yes	—
208	C₂	C₁₃×#1848	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
34. #10844	C₁₃	direct (N × H)
108. C₄×C₁₃	#341	semidirect
165. C₁₃	#10844	direct (N × H)
199. C₄	C₁₃×#341	semidirect

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×C₄×C₈×C₁₃	2
C₂×C₁₃×#341	2
#10844	13

Subgroups — C13×#10844 #15697183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#10844 #15697183