Subgroups — C₂×C₁₃×#2486 #15721094

Order 3328.

3678 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#123	C₂	1	2	yes	maximal
2	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2486	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#398	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₃×#397	C₂	1	2	yes	maximal, complemented
7	C₂×C₁₃×#389	C₂	1	2	yes	maximal, complemented
8	C₂×C₁₃×#381	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₃×#380	C₂	1	2	yes	maximal, complemented
11	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#123	—	2	16	no	—
16	C₂×C₁₃×#123	C₂²	1	16	yes	—
17	C₂×C₄×D₄×C₁₃	—	2	8	no	—
18	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	—
19	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
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	4	yes	—
23	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	8	yes	complemented
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#398	C₂²	1	16	yes	complemented
32	C₁₃×#397	C₂²	1	16	yes	complemented
33	C₁₃×#389	C₂²	1	16	yes	complemented
34	C₁₃×#381	C₂²	1	16	yes	complemented
35	C₁₃×#380	C₂²	1	16	yes	complemented
36	C₁₃×#380	C₂²	1	8	yes	complemented
37	C₂×C₁₃×#95	C₂²	1	4	yes	—
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	4	yes	—
40	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
41	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₁₃	—	2	4	no	—
43	C₂²×D₄×C₁₃	—	2	4	no	—
44	C₂²×D₄×C₁₃	D₄	1	8	yes	—
45	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₃	—	2	8	no	—
47	C₂³×C₄×C₁₃	—	2	8	no	—
48	C₂³×C₄×C₁₃	—	2	8	no	—
49	C₂³×C₄×C₁₃	—	2	8	no	—
50	C₂³×C₄×C₁₃	—	2	4	no	—
51	C₂³×C₄×C₁₃	—	2	8	no	—
52	C₂³×C₄×C₁₃	D₄	1	8	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
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×#123	—	2	64	no	—
64	C₄×D₄×C₁₃	—	2	32	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	16	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	16	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
80	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
81	C₂×C₁₃×C₂²⋊C₄	C₂³	1	16	yes	—
82	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₃	—	2	4	no	—
85	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
86	C₁₃×#95	C₂³	1	16	yes	—
87	C₁₃×#95	C₂³	1	8	yes	—
88	C₁₃×#95	C₂³	1	16	yes	—
89	C₂×#2486	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂⁴×C₁₃	—	2	4	no	—
91	C₂⁴×C₁₃	—	2	4	no	—
92	C₂⁴×C₁₃	—	2	2	no	—
93	C₂⁴×C₁₃	—	2	4	no	—
94	C₂⁴×C₁₃	—	2	2	no	—
95	C₂⁴×C₁₃	—	2	4	no	—
96	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
97	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
98	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
99	C₂⁴×C₁₃	#41	1	4	yes	—
100	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
101	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
102	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂×D₄×C₁₃	—	2	32	no	—
104	C₂×D₄×C₁₃	—	2	8	no	—
105	C₂×D₄×C₁₃	—	2	8	no	—
106	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	32	no	—
111	C₂²×C₄×C₁₃	—	2	16	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	8	no	—
114	C₂²×C₄×C₁₃	—	2	8	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	16	no	—
117	C₂²×C₄×C₁₃	—	2	8	no	—
118	C₂²×C₄×C₁₃	—	2	16	no	—
119	C₂²×C₄×C₁₃	—	2	8	no	—
120	C₂²×C₄×C₁₃	—	2	16	no	—
121	C₂²×C₄×C₁₃	—	2	8	no	—
122	C₂²×C₄×C₁₃	—	2	4	no	—
123	C₂²×C₄×C₁₃	—	2	4	no	—
124	C₂²×C₄×C₁₃	—	2	8	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	16	no	—
127	C₂²×C₄×C₁₃	—	4	32	no	—
128	C₂²×C₄×C₁₃	—	4	16	no	—
129	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₁₃	#41	1	8	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
137	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
138	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
141	C₁₃×C₄⋊C₄	—	2	16	no	—
142	C₁₃×C₄⋊C₄	—	2	16	no	—
143	C₁₃×C₄⋊C₄	—	2	8	no	—
144	C₁₃×C₄⋊C₄	—	2	32	no	—
145	C₁₃×C₄⋊C₄	—	2	16	no	—
146	C₁₃×C₂²⋊C₄	—	2	8	no	—
147	C₁₃×C₂²⋊C₄	—	2	16	no	—
148	C₁₃×C₂²⋊C₄	—	2	32	no	—
149	C₁₃×C₂²⋊C₄	—	2	8	no	—
150	C₄²×C₁₃	—	2	8	no	—
151	C₂²×#123	C₂×C₁₃	1	2	yes	—
152	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic
153	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#2486	C₂×C₁₃	1	16	yes	direct product factor
155	C₂×#398	C₂×C₁₃	1	2	yes	complemented
156	C₂×#397	C₂×C₁₃	1	2	yes	complemented
157	C₂×#389	C₂×C₁₃	1	2	yes	complemented
158	C₂×#381	C₂×C₁₃	1	2	yes	complemented
159	C₂×#380	C₂×C₁₃	1	2	yes	complemented
160	C₂×#380	C₂×C₁₃	1	1	yes	characteristic, complemented
161	C₂³×C₁₃	—	2	8	no	—
162	C₂³×C₁₃	—	2	8	no	—
163	C₂³×C₁₃	—	2	16	no	—
164	C₂³×C₁₃	—	2	16	no	—
165	C₂³×C₁₃	—	2	4	no	—
166	C₂³×C₁₃	—	2	4	no	—
167	C₂³×C₁₃	—	2	8	no	—
168	C₂³×C₁₃	—	2	16	no	—
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	4	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	4	no	—
173	C₂³×C₁₃	—	4	4	no	—
174	C₂³×C₁₃	—	4	4	no	—
175	C₂³×C₁₃	—	4	8	no	—
176	C₂³×C₁₃	#121	1	16	yes	—
177	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
178	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
179	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
180	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
181	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
182	C₂³×C₁₃	C₂×#41	1	4	yes	—
183	C₂³×C₁₃	C₂×#41	1	2	yes	—
184	C₂³×C₁₃	C₂×#41	1	4	yes	—
185	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
186	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
187	D₄×C₁₃	—	2	32	no	—
188	C₂×C₄×C₁₃	—	2	8	no	—
189	C₂×C₄×C₁₃	—	2	8	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	32	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	8	no	—
199	C₂×C₄×C₁₃	—	2	8	no	—
200	C₂×C₄×C₁₃	—	2	8	no	—
201	C₂×C₄×C₁₃	—	2	4	no	—
202	C₂×C₄×C₁₃	—	2	4	no	—
203	C₂×C₄×C₁₃	—	2	8	no	—
204	C₂×C₄×C₁₃	—	4	32	no	—
205	C₂×C₄×C₁₃	—	4	16	no	—
206	C₂×C₄×C₁₃	—	4	4	no	—
207	C₂×C₄×C₁₃	—	4	4	no	—
208	C₂×C₄×C₁₃	—	4	16	no	—
209	C₂×C₄×C₁₃	—	4	16	no	—
210	C₂×C₄×C₁₃	#123	1	16	yes	complemented
211	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
214	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
215	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
217	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
218	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×#123	—	2	16	no	—
220	C₂×#123	C₂²×C₁₃	1	16	yes	—
221	C₂×C₄×D₄	—	2	8	no	—
222	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	—
223	C₂²×C₄⋊C₄	—	2	8	no	—
224	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
225	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
227	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
229	C₂²×C₄⋊C₄	C₂²×C₁₃	1	8	yes	complemented
230	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
232	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
234	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
235	#398	C₂²×C₁₃	1	16	yes	complemented
236	#397	C₂²×C₁₃	1	16	yes	complemented
237	#389	C₂²×C₁₃	1	16	yes	complemented
238	#381	C₂²×C₁₃	1	16	yes	complemented
239	#380	C₂²×C₁₃	1	16	yes	complemented
240	#380	C₂²×C₁₃	1	8	yes	complemented
241	C₂×#95	C₂²×C₁₃	1	2	yes	—
242	C₂×#95	C₂²×C₁₃	1	4	yes	—
243	C₂×#95	C₂²×C₁₃	1	4	yes	—
244	C₂²×C₁₃	—	2	4	no	—
245	C₂²×C₁₃	—	2	4	no	—
246	C₂²×C₁₃	—	2	8	no	—
247	C₂²×C₁₃	—	2	8	no	—
248	C₂²×C₁₃	—	2	32	no	—
249	C₂²×C₁₃	—	2	4	no	—
250	C₂²×C₁₃	—	2	8	no	—
251	C₂²×C₁₃	—	4	2	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	—	4	4	no	—
254	C₂²×C₁₃	—	4	16	no	—
255	C₂²×C₁₃	C₂×#121	1	8	yes	—
256	C₂²×C₁₃	C₂×#121	1	4	yes	—
257	C₂²×C₁₃	C₂×#123	1	4	yes	—
258	C₂²×C₁₃	#536	1	4	yes	—
259	C₂²×C₁₃	#547	1	8	yes	—
260	C₂²×C₁₃	#552	1	8	yes	—
261	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
262	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
263	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
264	C₂²×C₁₃	C₂²×#41	1	2	yes	—
265	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
266	C₄×C₁₃	—	2	4	no	—
267	C₄×C₁₃	—	2	4	no	—
268	C₄×C₁₃	—	4	8	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	4	8	no	—
272	C₄×C₁₃	C₂×#123	1	8	yes	complemented
273	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
274	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
275	C₂²×D₄	—	2	4	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	D₄×C₁₃	1	8	yes	—
278	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
279	C₂³×C₄	—	2	8	no	—
280	C₂³×C₄	—	2	8	no	—
281	C₂³×C₄	—	2	8	no	—
282	C₂³×C₄	—	2	8	no	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	—	2	8	no	—
285	C₂³×C₄	D₄×C₁₃	1	8	yes	—
286	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
287	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
289	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
291	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
292	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
293	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
294	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
295	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
296	#123	—	2	64	no	—
297	C₄×D₄	—	2	32	no	—
298	C₂×C₄⋊C₄	—	2	8	no	—
299	C₂×C₄⋊C₄	—	2	8	no	—
300	C₂×C₄⋊C₄	—	2	32	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	—	2	16	no	—
303	C₂×C₄⋊C₄	—	2	8	no	—
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
305	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	16	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
309	C₂×C₂²⋊C₄	—	2	4	no	—
310	C₂×C₂²⋊C₄	—	2	8	no	—
311	C₂×C₂²⋊C₄	—	2	16	no	—
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
314	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
315	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₁₃	1	16	yes	—
317	C₂×C₄²	—	2	4	no	—
318	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
319	#95	C₂³×C₁₃	1	16	yes	—
320	#95	C₂³×C₁₃	1	8	yes	—
321	#95	C₂³×C₁₃	1	16	yes	—
322	C₂×C₁₃	—	2	8	no	—
323	C₂×C₁₃	—	4	4	no	—
324	C₂×C₁₃	#2486	1	8	yes	direct product factor
325	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
326	C₂×C₁₃	C₂²×#123	1	1	yes	characteristic
327	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
328	C₂×C₁₃	C₂×#547	1	2	yes	—
329	C₂×C₁₃	C₂×#552	1	2	yes	—
330	C₂⁴	—	2	4	no	—
331	C₂⁴	—	2	4	no	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	2	4	no	—
334	C₂⁴	—	2	2	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
337	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
338	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
339	C₂⁴	C₁₃×#41	1	4	yes	—
340	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
341	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
342	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
343	C₂×D₄	—	2	32	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	8	no	—
346	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	32	no	—
351	C₂²×C₄	—	2	16	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	8	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	16	no	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	2	16	no	—
359	C₂²×C₄	—	2	8	no	—
360	C₂²×C₄	—	2	16	no	—
361	C₂²×C₄	—	2	8	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	8	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	16	no	—
367	C₂²×C₄	—	4	32	no	—
368	C₂²×C₄	—	4	16	no	—
369	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
370	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	—
372	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
373	C₂²×C₄	C₁₃×#41	1	8	yes	—
374	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
375	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
376	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
377	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
378	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
379	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
380	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
381	C₄⋊C₄	—	2	16	no	—
382	C₄⋊C₄	—	2	16	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	32	no	—
385	C₄⋊C₄	—	2	16	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	16	no	—
388	C₂²⋊C₄	—	2	32	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₄²	—	2	8	no	—
391	C₁₃	C₂×#2486	1	1	yes	characteristic, direct product factor, Sylow
392	C₂³	—	2	8	no	—
393	C₂³	—	2	8	no	—
394	C₂³	—	2	16	no	—
395	C₂³	—	2	16	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	2	8	no	—
399	C₂³	—	2	16	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	4	no	—
404	C₂³	—	4	4	no	—
405	C₂³	—	4	4	no	—
406	C₂³	—	4	8	no	—
407	C₂³	C₁₃×#121	1	16	yes	—
408	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
409	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
410	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
411	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
412	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
413	C₂³	C₂×C₁₃×#41	1	4	yes	—
414	C₂³	C₂×C₁₃×#41	1	2	yes	—
415	C₂³	C₂×C₁₃×#41	1	4	yes	—
416	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
417	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
418	D₄	—	2	32	no	—
419	C₂×C₄	—	2	8	no	—
420	C₂×C₄	—	2	8	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	32	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	4	32	no	—
436	C₂×C₄	—	4	16	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	16	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	C₁₃×#123	1	16	yes	complemented
442	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
443	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
444	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
445	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	4	no	—
448	C₂²	—	2	8	no	—
449	C₂²	—	2	8	no	—
450	C₂²	—	2	32	no	—
451	C₂²	—	2	4	no	—
452	C₂²	—	2	8	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	16	no	—
457	C₂²	C₂×C₁₃×#121	1	8	yes	—
458	C₂²	C₂×C₁₃×#121	1	4	yes	—
459	C₂²	C₂×C₁₃×#123	1	4	yes	—
460	C₂²	C₁₃×#536	1	4	yes	—
461	C₂²	C₁₃×#547	1	8	yes	—
462	C₂²	C₁₃×#552	1	8	yes	—
463	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
464	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
465	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
466	C₂²	C₂²×C₁₃×#41	1	2	yes	—
467	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
468	C₄	—	2	4	no	—
469	C₄	—	2	4	no	—
470	C₄	—	4	8	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	8	no	—
474	C₄	C₂×C₁₃×#123	1	8	yes	complemented
475	C₂	—	2	8	no	—
476	C₂	—	4	4	no	—
477	C₂	C₁₃×#2486	1	8	yes	direct product factor
478	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
479	C₂	C₂²×C₁₃×#123	1	1	yes	characteristic
480	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
481	C₂	C₂×C₁₃×#547	1	2	yes	—
482	C₂	C₂×C₁₃×#552	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
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
3. C₂³×C₁₃×C₄⋊C₄	C₂	semidirect
4. C₁₃×#2486	C₂	direct (N × H)
5. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#397	C₂	semidirect
7. C₂×C₁₃×#389	C₂	semidirect
8. C₂×C₁₃×#381	C₂	semidirect
9. C₂×C₁₃×#380	C₂	semidirect
10. C₂×C₁₃×#380	C₂	semidirect
25. C₂²×C₁₃×C₄⋊C₄	C₂²	semidirect
31. C₁₃×#398	C₂²	semidirect
32. C₁₃×#397	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
34. C₁₃×#381	C₂²	semidirect
35. C₁₃×#380	C₂²	semidirect
36. C₁₃×#380	C₂²	semidirect
89. C₂×#2486	C₁₃	direct (N × H)
153. C₂³×C₄⋊C₄	C₂×C₁₃	semidirect
154. #2486	C₂×C₁₃	direct (N × H)
155. C₂×#398	C₂×C₁₃	semidirect
156. C₂×#397	C₂×C₁₃	semidirect
157. C₂×#389	C₂×C₁₃	semidirect
158. C₂×#381	C₂×C₁₃	semidirect
159. C₂×#380	C₂×C₁₃	semidirect
160. C₂×#380	C₂×C₁₃	semidirect
210. C₂×C₄×C₁₃	#123	semidirect
229. C₂²×C₄⋊C₄	C₂²×C₁₃	semidirect
235. #398	C₂²×C₁₃	semidirect
236. #397	C₂²×C₁₃	semidirect
237. #389	C₂²×C₁₃	semidirect
238. #381	C₂²×C₁₃	semidirect
239. #380	C₂²×C₁₃	semidirect
240. #380	C₂²×C₁₃	semidirect
272. C₄×C₁₃	C₂×#123	semidirect
324. C₂×C₁₃	#2486	direct (N × H)
391. C₁₃	C₂×#2486	direct (N × H)
441. C₂×C₄	C₁₃×#123	semidirect
474. C₄	C₂×C₁₃×#123	semidirect
477. C₂	C₁₃×#2486	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×#123	2
C₂²×C₄×D₄×C₁₃	2
C₂³×C₁₃×C₄⋊C₄	2
C₁₃×#2486	2
C₂×C₁₃×#398	2
C₂×C₁₃×#397	2
C₂×C₁₃×#389	2
C₂×C₁₃×#381	2
C₂×C₁₃×#380	2
C₂×#2486	13

Subgroups — C2×C13×#2486 #15721094

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2486 #15721094