Subgroups — C₂×C₁₃×#2496 #15721099

Order 3328.

2574 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#126	C₂	1	2	yes	maximal
2	C₁₃×#2496	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₃×#400	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₃×#397	C₂	1	2	yes	maximal
5	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#387	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
10	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#126	—	2	16	no	—
15	C₂×C₁₃×#126	C₂²	1	16	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
31	C₁₃×#400	C₂²	1	16	yes	complemented
32	C₁₃×#397	C₂²	1	16	yes	—
33	C₁₃×#389	C₂²	1	8	yes	complemented
34	C₁₃×#389	C₂²	1	8	yes	complemented
35	C₁₃×#387	C₂²	1	16	yes	complemented
36	C₁₃×#384	C₂²	1	8	yes	complemented
37	C₁₃×#380	C₂²	1	8	yes	—
38	C₁₃×#380	C₂²	1	8	yes	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
40	C₄×C₁₃×C₂²⋊C₄	C₂²	1	8	yes	—
41	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×#95	C₂²	1	2	yes	—
44	C₂×C₁₃×#95	C₂²	1	2	yes	—
45	C₂×C₁₃×#95	C₂²	1	2	yes	—
46	C₂×C₁₃×#95	C₂²	1	2	yes	—
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	—	2	4	no	—
50	C₂³×C₄×C₁₃	—	2	4	no	—
51	C₂³×C₄×C₁₃	—	2	4	no	—
52	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#126	—	2	64	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
83	C₂×C₁₃×C₂²⋊C₄	D₄	1	8	yes	—
84	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
86	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₃	—	2	8	no	—
89	C₂×C₄²×C₁₃	—	2	4	no	—
90	C₂×C₄²×C₁₃	—	2	4	no	—
91	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
93	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
94	C₁₃×#95	C₂³	1	4	yes	—
95	C₁₃×#95	C₂³	1	4	yes	—
96	C₁₃×#95	C₂³	1	8	yes	—
97	C₁₃×#95	C₂³	1	8	yes	—
98	C₁₃×#95	C₂³	1	8	yes	—
99	C₁₃×#95	C₂³	1	8	yes	—
100	C₁₃×#95	C₂³	1	8	yes	—
101	C₂×#2496	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	2	no	—
103	C₂⁴×C₁₃	—	2	2	no	—
104	C₂⁴×C₁₃	—	2	2	no	—
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	—	2	2	no	—
107	C₂⁴×C₁₃	—	2	2	no	—
108	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
109	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
110	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	4	no	—
118	C₂²×C₄×C₁₃	—	2	4	no	—
119	C₂²×C₄×C₁₃	—	2	4	no	—
120	C₂²×C₄×C₁₃	—	2	4	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	4	no	—
133	C₂²×C₄×C₁₃	—	2	4	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	8	no	—
136	C₂²×C₄×C₁₃	—	2	8	no	—
137	C₂²×C₄×C₁₃	—	2	8	no	—
138	C₂²×C₄×C₁₃	—	4	16	no	—
139	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	#41	1	4	yes	—
142	C₂²×C₄×C₁₃	#41	1	4	yes	—
143	C₂²×C₄×C₁₃	#41	1	4	yes	—
144	C₂²×C₄×C₁₃	#41	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
155	C₁₃×C₄⋊C₄	—	2	16	no	—
156	C₁₃×C₄⋊C₄	—	2	16	no	—
157	C₁₃×C₄⋊C₄	—	2	16	no	—
158	C₁₃×C₄⋊C₄	—	2	16	no	—
159	C₁₃×C₄⋊C₄	—	2	8	no	—
160	C₁₃×C₄⋊C₄	—	2	8	no	—
161	C₁₃×C₄⋊C₄	—	2	8	no	—
162	C₁₃×C₄⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	16	no	—
164	C₁₃×C₂²⋊C₄	—	2	16	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	C₂×D₄	1	16	yes	—
167	C₄²×C₁₃	—	2	16	no	—
168	C₄²×C₁₃	—	2	8	no	—
169	C₄²×C₁₃	—	2	8	no	—
170	C₂²×#126	C₂×C₁₃	1	2	yes	—
171	#2496	C₂×C₁₃	1	16	yes	direct product factor
172	C₂×#400	C₂×C₁₃	1	2	yes	complemented
173	C₂×#397	C₂×C₁₃	1	2	yes	—
174	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
175	C₂×#389	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂×#387	C₂×C₁₃	1	2	yes	complemented
177	C₂×#384	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
179	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
180	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂×C₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
182	C₂³×C₁₃	—	2	8	no	—
183	C₂³×C₁₃	—	2	8	no	—
184	C₂³×C₁₃	—	2	8	no	—
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	2	2	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	4	4	no	—
192	C₂³×C₁₃	—	4	4	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	4	4	no	—
195	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
196	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
197	C₂³×C₁₃	C₂×#41	1	2	yes	—
198	C₂³×C₁₃	C₂×#41	1	2	yes	—
199	C₂³×C₁₃	C₂×#41	1	2	yes	—
200	C₂³×C₁₃	C₂×#41	1	2	yes	—
201	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
202	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
203	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
204	C₂×C₄×C₁₃	—	2	8	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	8	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	2	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	4	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	4	4	no	—
232	C₂×C₄×C₁₃	—	4	8	no	—
233	C₂×C₄×C₁₃	—	4	8	no	—
234	C₂×C₄×C₁₃	—	4	8	no	—
235	C₂×C₄×C₁₃	—	4	8	no	—
236	C₂×C₄×C₁₃	—	4	4	no	—
237	C₂×C₄×C₁₃	—	4	16	no	—
238	C₂×C₄×C₁₃	#126	1	16	yes	complemented
239	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
240	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
241	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
242	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
243	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
244	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
245	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#126	—	2	16	no	—
247	C₂×#126	C₂²×C₁₃	1	16	yes	—
248	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
249	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
250	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
252	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
254	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
258	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
259	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
260	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
261	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
263	#400	C₂²×C₁₃	1	16	yes	complemented
264	#397	C₂²×C₁₃	1	16	yes	—
265	#389	C₂²×C₁₃	1	8	yes	complemented
266	#389	C₂²×C₁₃	1	8	yes	complemented
267	#387	C₂²×C₁₃	1	16	yes	complemented
268	#384	C₂²×C₁₃	1	8	yes	complemented
269	#380	C₂²×C₁₃	1	8	yes	—
270	#380	C₂²×C₁₃	1	8	yes	—
271	C₄×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
272	C₄×C₂²⋊C₄	C₂²×C₁₃	1	8	yes	—
273	C₂×#95	C₂²×C₁₃	1	2	yes	—
274	C₂×#95	C₂²×C₁₃	1	2	yes	—
275	C₂×#95	C₂²×C₁₃	1	2	yes	—
276	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#95	C₂²×C₁₃	1	2	yes	—
278	C₂×#95	C₂²×C₁₃	1	2	yes	—
279	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
280	C₂²×C₁₃	—	2	4	no	—
281	C₂²×C₁₃	—	2	4	no	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	16	no	—
288	C₂²×C₁₃	C₂×#126	1	4	yes	—
289	C₂²×C₁₃	#532	1	4	yes	—
290	C₂²×C₁₃	#541	1	4	yes	—
291	C₂²×C₁₃	#547	1	4	yes	—
292	C₂²×C₁₃	#547	1	4	yes	—
293	C₂²×C₁₃	#552	1	4	yes	—
294	C₂²×C₁₃	#556	1	4	yes	—
295	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
296	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
297	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
298	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
299	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
300	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
301	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
302	C₄×C₁₃	—	2	4	no	—
303	C₄×C₁₃	—	2	4	no	—
304	C₄×C₁₃	—	2	4	no	—
305	C₄×C₁₃	—	4	2	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	—	4	4	no	—
308	C₄×C₁₃	—	4	4	no	—
309	C₄×C₁₃	—	4	4	no	—
310	C₄×C₁₃	—	4	2	no	—
311	C₄×C₁₃	C₂×#126	1	8	yes	complemented
312	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
313	C₂³×C₄	—	2	4	no	—
314	C₂³×C₄	—	2	4	no	—
315	C₂³×C₄	—	2	4	no	—
316	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
317	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
319	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
320	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
323	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
327	#126	—	2	64	no	—
328	C₂×C₄⋊C₄	—	2	8	no	—
329	C₂×C₄⋊C₄	—	2	8	no	—
330	C₂×C₄⋊C₄	—	2	8	no	—
331	C₂×C₄⋊C₄	—	2	8	no	—
332	C₂×C₄⋊C₄	—	2	4	no	—
333	C₂×C₄⋊C₄	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	4	no	—
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
339	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
344	C₂×C₂²⋊C₄	—	2	8	no	—
345	C₂×C₂²⋊C₄	—	2	8	no	—
346	C₂×C₂²⋊C₄	—	2	4	no	—
347	C₂×C₂²⋊C₄	D₄×C₁₃	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
350	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
352	C₂×C₄²	—	2	8	no	—
353	C₂×C₄²	—	2	4	no	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	C₂³×C₁₃	1	8	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
357	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
358	#95	C₂³×C₁₃	1	4	yes	—
359	#95	C₂³×C₁₃	1	4	yes	—
360	#95	C₂³×C₁₃	1	8	yes	—
361	#95	C₂³×C₁₃	1	8	yes	—
362	#95	C₂³×C₁₃	1	8	yes	—
363	#95	C₂³×C₁₃	1	8	yes	—
364	#95	C₂³×C₁₃	1	8	yes	—
365	C₂×C₁₃	—	4	4	no	—
366	C₂×C₁₃	#2496	1	8	yes	direct product factor
367	C₂×C₁₃	C₂²×#126	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
369	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
370	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
371	C₂×C₁₃	C₂×#547	1	1	yes	characteristic
372	C₂×C₁₃	C₂×#552	1	1	yes	characteristic
373	C₂×C₁₃	C₂×#556	1	1	yes	characteristic
374	C₂⁴	—	2	2	no	—
375	C₂⁴	—	2	2	no	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
381	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
382	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	8	no	—
408	C₂²×C₄	—	2	8	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	4	16	no	—
411	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
412	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
413	C₂²×C₄	C₁₃×#41	1	4	yes	—
414	C₂²×C₄	C₁₃×#41	1	4	yes	—
415	C₂²×C₄	C₁₃×#41	1	4	yes	—
416	C₂²×C₄	C₁₃×#41	1	4	yes	—
417	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
418	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
420	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
424	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
427	C₄⋊C₄	—	2	16	no	—
428	C₄⋊C₄	—	2	16	no	—
429	C₄⋊C₄	—	2	16	no	—
430	C₄⋊C₄	—	2	16	no	—
431	C₄⋊C₄	—	2	8	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₂²⋊C₄	—	2	16	no	—
436	C₂²⋊C₄	—	2	16	no	—
437	C₂²⋊C₄	—	2	8	no	—
438	C₂²⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
439	C₄²	—	2	16	no	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	8	no	—
442	C₁₃	C₂×#2496	1	1	yes	characteristic, direct product factor, Sylow
443	C₂³	—	2	8	no	—
444	C₂³	—	2	8	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
457	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
458	C₂³	C₂×C₁₃×#41	1	2	yes	—
459	C₂³	C₂×C₁₃×#41	1	2	yes	—
460	C₂³	C₂×C₁₃×#41	1	2	yes	—
461	C₂³	C₂×C₁₃×#41	1	2	yes	—
462	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
463	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
464	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	8	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	16	no	—
499	C₂×C₄	C₁₃×#126	1	16	yes	complemented
500	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
502	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
503	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
504	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
505	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	4	16	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	C₂×C₁₃×#126	1	4	yes	—
515	C₂²	C₁₃×#532	1	4	yes	—
516	C₂²	C₁₃×#541	1	4	yes	—
517	C₂²	C₁₃×#547	1	4	yes	—
518	C₂²	C₁₃×#547	1	4	yes	—
519	C₂²	C₁₃×#552	1	4	yes	—
520	C₂²	C₁₃×#556	1	4	yes	—
521	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
522	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
523	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
524	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
525	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
526	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
527	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
528	C₄	—	2	4	no	—
529	C₄	—	2	4	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	4	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	C₂×C₁₃×#126	1	8	yes	complemented
538	C₂	—	4	4	no	—
539	C₂	C₁₃×#2496	1	8	yes	direct product factor
540	C₂	C₂²×C₁₃×#126	1	1	yes	characteristic
541	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
542	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
543	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
544	C₂	C₂×C₁₃×#547	1	1	yes	characteristic
545	C₂	C₂×C₁₃×#552	1	1	yes	characteristic
546	C₂	C₂×C₁₃×#556	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2496	C₂	direct (N × H)
3. C₂×C₁₃×#400	C₂	semidirect
5. C₂×C₁₃×#389	C₂	semidirect
6. C₂×C₁₃×#389	C₂	semidirect
7. C₂×C₁₃×#387	C₂	semidirect
8. C₂×C₁₃×#384	C₂	semidirect
11. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
31. C₁₃×#400	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
34. C₁₃×#389	C₂²	semidirect
35. C₁₃×#387	C₂²	semidirect
36. C₁₃×#384	C₂²	semidirect
39. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
101. C₂×#2496	C₁₃	direct (N × H)
171. #2496	C₂×C₁₃	direct (N × H)
172. C₂×#400	C₂×C₁₃	semidirect
174. C₂×#389	C₂×C₁₃	semidirect
175. C₂×#389	C₂×C₁₃	semidirect
176. C₂×#387	C₂×C₁₃	semidirect
177. C₂×#384	C₂×C₁₃	semidirect
180. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
238. C₂×C₄×C₁₃	#126	semidirect
263. #400	C₂²×C₁₃	semidirect
265. #389	C₂²×C₁₃	semidirect
266. #389	C₂²×C₁₃	semidirect
267. #387	C₂²×C₁₃	semidirect
268. #384	C₂²×C₁₃	semidirect
271. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
311. C₄×C₁₃	C₂×#126	semidirect
366. C₂×C₁₃	#2496	direct (N × H)
442. C₁₃	C₂×#2496	direct (N × H)
499. C₂×C₄	C₁₃×#126	semidirect
537. C₄	C₂×C₁₃×#126	semidirect
539. C₂	C₁₃×#2496	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#126	2
C₁₃×#2496	2
C₂×C₁₃×#400	2
C₂×C₁₃×#397	2
C₂×C₁₃×#389	2
C₂×C₁₃×#387	2
C₂×C₁₃×#384	2
C₂×C₁₃×#380	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₂×C₄×C₁₃×C₂²⋊C₄	2
C₂×#2496	13

Subgroups — C2×C13×#2496 #15721099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2496 #15721099