Subgroups — C₁₃×#1934 #13110992

Order 1664.

292 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#102	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#390	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#340	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₁₃	C₂²	1	1	yes	characteristic
11	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
12	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
16	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
17	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
18	C₁₃×#102	—	2	2	no	—
19	C₁₃×#102	C₄	1	4	yes	complemented
20	C₄×C₈×C₁₃	—	2	2	no	—
21	C₁₃×#95	—	2	1	no	—
22	C₂⁴×C₁₃	—	2	1	no	—
23	C₂×D₄×C₁₃	—	2	1	no	—
24	C₂×D₄×C₁₃	—	2	1	no	—
25	C₂×D₄×C₁₃	—	2	1	no	—
26	C₂×D₄×C₁₃	—	2	1	no	—
27	C₂×D₄×C₁₃	—	2	1	no	—
28	C₂×D₄×C₁₃	C₂×C₄	1	2	yes	—
29	C₂²×C₄×C₁₃	—	2	1	no	—
30	C₂²×C₄×C₁₃	—	2	1	no	—
31	C₂²×C₄×C₁₃	—	2	1	no	—
32	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
33	C₂²×C₄×C₁₃	D₄	1	1	yes	characteristic
34	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
35	C₂×C₈×C₁₃	—	2	1	no	—
36	C₂×C₈×C₁₃	—	2	1	no	—
37	C₂×C₈×C₁₃	—	2	1	no	—
38	C₂×C₈×C₁₃	—	2	1	no	—
39	C₂×C₈×C₁₃	C₂×C₄	1	2	yes	—
40	C₂×C₈×C₁₃	D₄	1	2	yes	—
41	C₁₃×C₄⋊C₄	—	2	1	no	—
42	C₁₃×C₄⋊C₄	—	2	1	no	—
43	C₁₃×C₄⋊C₄	—	2	1	no	—
44	C₁₃×C₄⋊C₄	—	2	1	no	—
45	C₁₃×C₄⋊C₄	—	2	1	no	—
46	C₁₃×C₄⋊C₄	—	4	2	no	—
47	C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₁₃×C₂²⋊C₄	—	4	2	no	—
49	C₁₃×C₂²⋊C₄	—	4	2	no	—
50	C₄²×C₁₃	—	2	1	no	—
51	C₄²×C₁₃	—	2	1	no	—
52	#1934	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂³×C₁₃	—	2	2	no	—
54	C₂³×C₁₃	—	4	1	no	—
55	C₂³×C₁₃	—	4	1	no	—
56	C₂³×C₁₃	—	4	1	no	—
57	C₂³×C₁₃	—	4	1	no	—
58	C₂³×C₁₃	—	4	1	no	—
59	C₂³×C₁₃	—	4	1	no	—
60	C₂³×C₁₃	C₂×D₄	1	1	yes	characteristic
61	D₄×C₁₃	—	2	2	no	—
62	D₄×C₁₃	—	2	2	no	—
63	D₄×C₁₃	—	4	1	no	—
64	D₄×C₁₃	—	4	1	no	—
65	C₂×C₄×C₁₃	—	2	1	no	—
66	C₂×C₄×C₁₃	—	2	1	no	—
67	C₂×C₄×C₁₃	—	2	1	no	—
68	C₂×C₄×C₁₃	—	2	1	no	—
69	C₂×C₄×C₁₃	—	2	2	no	—
70	C₂×C₄×C₁₃	—	4	1	no	—
71	C₂×C₄×C₁₃	—	4	1	no	—
72	C₂×C₄×C₁₃	—	4	1	no	—
73	C₂×C₄×C₁₃	—	4	1	no	—
74	C₂×C₄×C₁₃	—	4	1	no	—
75	C₂×C₄×C₁₃	—	4	1	no	—
76	C₂×C₄×C₁₃	—	4	1	no	—
77	C₂×C₄×C₁₃	—	4	1	no	—
78	C₂×C₄×C₁₃	D₈	1	2	yes	—
79	C₂×C₄×C₁₃	SD₁₆	1	2	yes	—
80	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
83	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
84	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
85	C₂×C₄×C₁₃	#41	1	1	yes	characteristic
86	C₈×C₁₃	—	2	2	no	—
87	C₈×C₁₃	—	2	2	no	—
88	C₂×#102	C₂×C₁₃	1	1	yes	characteristic
89	C₂×#102	C₂×C₁₃	1	1	yes	characteristic
90	C₂×C₄×C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
91	#390	C₂×C₁₃	1	1	yes	characteristic
92	#389	C₂×C₁₃	1	1	yes	characteristic, complemented
93	#340	C₂×C₁₃	1	1	yes	characteristic, complemented
94	#340	C₂×C₁₃	1	1	yes	characteristic, complemented
95	C₂²×C₁₃	—	4	2	no	—
96	C₂²×C₁₃	—	4	2	no	—
97	C₂²×C₁₃	—	4	2	no	—
98	C₂²×C₁₃	—	8	1	no	—
99	C₂²×C₁₃	—	8	1	no	—
100	C₂²×C₁₃	—	8	1	no	—
101	C₂²×C₁₃	—	8	1	no	—
102	C₂²×C₁₃	C₄×D₄	1	1	yes	characteristic
103	C₂²×C₁₃	#121	1	1	yes	characteristic
104	C₂²×C₁₃	#124	1	1	yes	characteristic
105	C₂²×C₁₃	C₂×D₈	1	1	yes	characteristic
106	C₂²×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
107	C₂²×C₁₃	#135	1	1	yes	characteristic
108	C₂²×C₁₃	#135	1	1	yes	characteristic
109	C₄×C₁₃	—	2	2	no	—
110	C₄×C₁₃	—	2	2	no	—
111	C₄×C₁₃	—	4	2	no	—
112	C₄×C₁₃	—	8	1	no	—
113	C₄×C₁₃	—	8	1	no	—
114	C₄×C₁₃	#117	1	1	yes	characteristic
115	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
116	C₄×C₁₃	#123	1	1	yes	characteristic
117	C₄×C₁₃	#126	1	1	yes	characteristic
118	C₂²×D₄	C₂²×C₁₃	1	1	yes	characteristic
119	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
120	C₂²×C₈	C₂²×C₁₃	1	1	yes	characteristic
121	C₂×C₄⋊C₄	—	2	1	no	—
122	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
123	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
124	C₂×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
125	C₂×C₂²⋊C₄	—	2	1	no	—
126	C₂×C₂²⋊C₄	—	2	1	no	—
127	C₂×C₄²	C₂²×C₁₃	1	1	yes	characteristic
128	#102	—	2	2	no	—
129	#102	C₄×C₁₃	1	4	yes	complemented
130	C₄×C₈	—	2	2	no	—
131	#95	—	2	1	no	—
132	C₂×C₁₃	—	8	2	no	—
133	C₂×C₁₃	#388	1	1	yes	characteristic
134	C₂×C₁₃	C₄×D₈	1	1	yes	characteristic
135	C₂×C₁₃	C₄×SD₁₆	1	1	yes	characteristic
136	C₂×C₁₃	#465	1	1	yes	characteristic
137	C₂×C₁₃	#466	1	1	yes	characteristic
138	C₂×C₁₃	#486	1	1	yes	characteristic
139	C₂×C₁₃	#488	1	1	yes	characteristic
140	C₂⁴	—	2	1	no	—
141	C₂×D₄	—	2	1	no	—
142	C₂×D₄	—	2	1	no	—
143	C₂×D₄	—	2	1	no	—
144	C₂×D₄	—	2	1	no	—
145	C₂×D₄	—	2	1	no	—
146	C₂×D₄	C₂×C₄×C₁₃	1	2	yes	—
147	C₂²×C₄	—	2	1	no	—
148	C₂²×C₄	—	2	1	no	—
149	C₂²×C₄	—	2	1	no	—
150	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
151	C₂²×C₄	D₄×C₁₃	1	1	yes	characteristic
152	C₂²×C₄	C₂³×C₁₃	1	1	yes	characteristic
153	C₂×C₈	—	2	1	no	—
154	C₂×C₈	—	2	1	no	—
155	C₂×C₈	—	2	1	no	—
156	C₂×C₈	—	2	1	no	—
157	C₂×C₈	C₂×C₄×C₁₃	1	2	yes	—
158	C₂×C₈	D₄×C₁₃	1	2	yes	—
159	C₄⋊C₄	—	2	1	no	—
160	C₄⋊C₄	—	2	1	no	—
161	C₄⋊C₄	—	2	1	no	—
162	C₄⋊C₄	—	2	1	no	—
163	C₄⋊C₄	—	2	1	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
166	C₂²⋊C₄	—	4	2	no	—
167	C₂²⋊C₄	—	4	2	no	—
168	C₄²	—	2	1	no	—
169	C₄²	—	2	1	no	—
170	C₁₃	#1934	1	1	yes	characteristic, direct product factor, Sylow
171	C₂³	—	2	2	no	—
172	C₂³	—	4	1	no	—
173	C₂³	—	4	1	no	—
174	C₂³	—	4	1	no	—
175	C₂³	—	4	1	no	—
176	C₂³	—	4	1	no	—
177	C₂³	—	4	1	no	—
178	C₂³	C₂×D₄×C₁₃	1	1	yes	characteristic
179	D₄	—	2	2	no	—
180	D₄	—	2	2	no	—
181	D₄	—	4	1	no	—
182	D₄	—	4	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	1	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	4	1	no	—
189	C₂×C₄	—	4	1	no	—
190	C₂×C₄	—	4	1	no	—
191	C₂×C₄	—	4	1	no	—
192	C₂×C₄	—	4	1	no	—
193	C₂×C₄	—	4	1	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	C₁₃×D₈	1	2	yes	—
197	C₂×C₄	C₁₃×SD₁₆	1	2	yes	—
198	C₂×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
199	C₂×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
200	C₂×C₄	C₁₃×#41	1	1	yes	characteristic
201	C₂×C₄	C₁₃×#41	1	1	yes	characteristic
202	C₂×C₄	C₁₃×#41	1	1	yes	characteristic
203	C₂×C₄	C₁₃×#41	1	1	yes	characteristic
204	C₈	—	2	2	no	—
205	C₈	—	2	2	no	—
206	C₂²	—	4	2	no	—
207	C₂²	—	4	2	no	—
208	C₂²	—	4	2	no	—
209	C₂²	—	8	1	no	—
210	C₂²	—	8	1	no	—
211	C₂²	—	8	1	no	—
212	C₂²	—	8	1	no	—
213	C₂²	C₄×D₄×C₁₃	1	1	yes	characteristic
214	C₂²	C₁₃×#121	1	1	yes	characteristic
215	C₂²	C₁₃×#124	1	1	yes	characteristic
216	C₂²	C₂×C₁₃×D₈	1	1	yes	characteristic
217	C₂²	C₂×C₁₃×SD₁₆	1	1	yes	characteristic
218	C₂²	C₁₃×#135	1	1	yes	characteristic
219	C₂²	C₁₃×#135	1	1	yes	characteristic
220	C₄	—	2	2	no	—
221	C₄	—	2	2	no	—
222	C₄	—	4	2	no	—
223	C₄	—	8	1	no	—
224	C₄	—	8	1	no	—
225	C₄	C₁₃×#117	1	1	yes	characteristic
226	C₄	C₄×D₄×C₁₃	1	1	yes	characteristic
227	C₄	C₁₃×#123	1	1	yes	characteristic
228	C₄	C₁₃×#126	1	1	yes	characteristic
229	C₂	—	8	2	no	—
230	C₂	C₁₃×#388	1	1	yes	characteristic
231	C₂	C₄×C₁₃×D₈	1	1	yes	characteristic
232	C₂	C₄×C₁₃×SD₁₆	1	1	yes	characteristic
233	C₂	C₁₃×#465	1	1	yes	characteristic
234	C₂	C₁₃×#466	1	1	yes	characteristic
235	C₂	C₁₃×#486	1	1	yes	characteristic
236	C₂	C₁₃×#488	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₈×C₁₃	C₂	semidirect
5. C₁₃×#389	C₂	semidirect
6. C₁₃×#340	C₂	semidirect
7. C₁₃×#340	C₂	semidirect
19. C₁₃×#102	C₄	semidirect
52. #1934	C₁₃	direct (N × H)
90. C₂×C₄×C₈	C₂×C₁₃	semidirect
92. #389	C₂×C₁₃	semidirect
93. #340	C₂×C₁₃	semidirect
94. #340	C₂×C₁₃	semidirect
129. #102	C₄×C₁₃	semidirect
170. C₁₃	#1934	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×#102	2
C₂×C₄×C₈×C₁₃	2
C₁₃×#390	2
C₁₃×#389	2
C₁₃×#340	2
#1934	13

Subgroups — C13×#1934 #13110992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#1934 #13110992