Subgroups — C₂×C₁₃×#2543 #15721157

Order 3328.

4326 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#121	C₂	1	2	yes	maximal, complemented
3	C₂²×C₄×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2543	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₁₃×#398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₃×#397	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×#392	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₃×#388	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#386	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
14	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
15	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#121	—	2	16	no	—
21	C₂×C₁₃×#121	—	2	8	no	—
22	C₂×C₁₃×#121	C₂²	1	8	yes	complemented
23	C₂×C₁₃×#121	C₂²	1	16	yes	complemented
24	C₂×C₄×D₄×C₁₃	—	2	8	no	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	8	yes	complemented
26	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
33	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
34	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
35	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
36	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#398	C₂²	1	8	yes	complemented
38	C₁₃×#397	C₂²	1	8	yes	complemented
39	C₁₃×#394	C₂²	1	8	yes	complemented
40	C₁₃×#392	C₂²	1	8	yes	complemented
41	C₁₃×#388	C₂²	1	16	yes	complemented
42	C₁₃×#386	C₂²	1	16	yes	complemented
43	C₁₃×#386	C₂²	1	16	yes	complemented
44	C₂×C₁₃×#95	C₂²	1	2	yes	—
45	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
46	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
47	C₂×C₁₃×#95	C₂²	1	2	yes	—
48	C₂×C₁₃×#95	C₂²	1	2	yes	—
49	C₂×C₁₃×#95	C₂²	1	8	yes	complemented
50	C₂⁵×C₁₃	C₂³	1	2	yes	—
51	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
52	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₁₃	—	2	4	no	—
54	C₂²×D₄×C₁₃	—	2	4	no	—
55	C₂²×D₄×C₁₃	—	2	8	no	—
56	C₂²×D₄×C₁₃	—	2	8	no	—
57	C₂²×D₄×C₁₃	—	2	8	no	—
58	C₂²×D₄×C₁₃	—	2	8	no	—
59	C₂²×D₄×C₁₃	—	2	4	no	—
60	C₂²×D₄×C₁₃	—	2	8	no	—
61	C₂²×D₄×C₁₃	—	4	4	no	—
62	C₂²×D₄×C₁₃	—	4	4	no	—
63	C₂²×D₄×C₁₃	D₄	1	8	yes	complemented
64	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	8	yes	—
66	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
68	C₂³×C₄×C₁₃	—	2	8	no	—
69	C₂³×C₄×C₁₃	—	2	4	no	—
70	C₂³×C₄×C₁₃	—	2	8	no	—
71	C₂³×C₄×C₁₃	—	4	4	no	—
72	C₂³×C₄×C₁₃	—	4	4	no	—
73	C₂³×C₄×C₁₃	—	4	4	no	—
74	C₂³×C₄×C₁₃	D₄	1	8	yes	complemented
75	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
76	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
78	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
79	C₂³×C₄×C₁₃	C₂³	1	8	yes	—
80	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
86	C₁₃×#121	—	2	64	no	—
87	C₁₃×#121	—	2	32	no	—
88	C₄×D₄×C₁₃	—	2	32	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	8	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
109	C₂×C₄²×C₁₃	—	2	4	no	—
110	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
111	C₁₃×#95	C₂³	1	8	yes	—
112	C₁₃×#95	C₂³	1	8	yes	—
113	C₁₃×#95	C₂³	1	8	yes	—
114	C₁₃×#95	C₂³	1	4	yes	—
115	C₁₃×#95	C₂³	1	4	yes	—
116	C₂×#2543	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
117	C₂⁴×C₁₃	—	2	4	no	—
118	C₂⁴×C₁₃	—	2	4	no	—
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	—	2	2	no	—
121	C₂⁴×C₁₃	—	2	4	no	—
122	C₂⁴×C₁₃	—	2	4	no	—
123	C₂⁴×C₁₃	—	2	4	no	—
124	C₂⁴×C₁₃	—	2	4	no	—
125	C₂⁴×C₁₃	—	2	4	no	—
126	C₂⁴×C₁₃	—	2	4	no	—
127	C₂⁴×C₁₃	—	2	4	no	—
128	C₂⁴×C₁₃	—	2	4	no	—
129	C₂⁴×C₁₃	—	2	4	no	—
130	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
131	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
132	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
133	C₂⁴×C₁₃	#41	1	4	yes	—
134	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
135	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
136	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
137	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂×D₄×C₁₃	—	2	32	no	—
139	C₂×D₄×C₁₃	—	2	8	no	—
140	C₂×D₄×C₁₃	—	2	8	no	—
141	C₂×D₄×C₁₃	—	2	16	no	—
142	C₂×D₄×C₁₃	—	2	16	no	—
143	C₂×D₄×C₁₃	—	2	16	no	—
144	C₂×D₄×C₁₃	—	2	16	no	—
145	C₂×D₄×C₁₃	—	2	8	no	—
146	C₂×D₄×C₁₃	—	2	16	no	—
147	C₂×D₄×C₁₃	—	4	8	no	—
148	C₂×D₄×C₁₃	—	4	8	no	—
149	C₂×D₄×C₁₃	—	4	32	no	—
150	C₂×D₄×C₁₃	—	4	16	no	—
151	C₂×D₄×C₁₃	—	4	32	no	—
152	C₂×D₄×C₁₃	C₂×D₄	1	16	yes	complemented
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	4	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	—	2	4	no	—
157	C₂²×C₄×C₁₃	—	2	4	no	—
158	C₂²×C₄×C₁₃	—	2	4	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	16	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	8	no	—
171	C₂²×C₄×C₁₃	—	2	16	no	—
172	C₂²×C₄×C₁₃	—	4	16	no	—
173	C₂²×C₄×C₁₃	—	4	8	no	—
174	C₂²×C₄×C₁₃	—	4	8	no	—
175	C₂²×C₄×C₁₃	—	4	8	no	—
176	C₂²×C₄×C₁₃	—	4	32	no	—
177	C₂²×C₄×C₁₃	—	4	16	no	—
178	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₁₃	C₂×D₄	1	16	yes	complemented
182	C₂²×C₄×C₁₃	#41	1	8	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
187	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
191	C₁₃×C₄⋊C₄	—	2	8	no	—
192	C₁₃×C₄⋊C₄	—	2	16	no	—
193	C₁₃×C₄⋊C₄	—	2	8	no	—
194	C₁₃×C₂²⋊C₄	—	2	8	no	—
195	C₁₃×C₂²⋊C₄	—	2	16	no	—
196	C₁₃×C₂²⋊C₄	—	2	8	no	—
197	C₁₃×C₂²⋊C₄	—	2	16	no	—
198	C₁₃×C₂²⋊C₄	—	2	16	no	—
199	C₁₃×C₂²⋊C₄	—	2	16	no	—
200	C₁₃×C₂²⋊C₄	—	4	8	no	—
201	C₄²×C₁₃	—	2	8	no	—
202	C₂²×#121	C₂×C₁₃	1	2	yes	complemented
203	C₂²×#121	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₂²×C₄×D₄	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#2543	C₂×C₁₃	1	16	yes	direct product factor
206	C₂×#398	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂×#397	C₂×C₁₃	1	1	yes	characteristic, complemented
208	C₂×#394	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×#392	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂×#388	C₂×C₁₃	1	2	yes	complemented
211	C₂×#386	C₂×C₁₃	1	2	yes	complemented
212	C₂×#386	C₂×C₁₃	1	2	yes	complemented
213	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂³×C₁₃	—	2	8	no	—
215	C₂³×C₁₃	—	2	8	no	—
216	C₂³×C₁₃	—	2	16	no	—
217	C₂³×C₁₃	—	2	16	no	—
218	C₂³×C₁₃	—	2	4	no	—
219	C₂³×C₁₃	—	2	4	no	—
220	C₂³×C₁₃	—	2	8	no	—
221	C₂³×C₁₃	—	2	16	no	—
222	C₂³×C₁₃	—	2	2	no	—
223	C₂³×C₁₃	—	2	2	no	—
224	C₂³×C₁₃	—	2	4	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	2	4	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	4	no	—
230	C₂³×C₁₃	—	2	4	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	4	no	—
233	C₂³×C₁₃	—	4	4	no	—
234	C₂³×C₁₃	—	4	4	no	—
235	C₂³×C₁₃	—	4	8	no	—
236	C₂³×C₁₃	—	4	8	no	—
237	C₂³×C₁₃	—	4	8	no	—
238	C₂³×C₁₃	—	4	8	no	—
239	C₂³×C₁₃	—	4	8	no	—
240	C₂³×C₁₃	—	4	8	no	—
241	C₂³×C₁₃	—	4	8	no	—
242	C₂³×C₁₃	—	4	8	no	—
243	C₂³×C₁₃	#121	1	16	yes	—
244	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
245	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
246	C₂³×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
249	C₂³×C₁₃	C₂×#41	1	4	yes	—
250	C₂³×C₁₃	C₂×#41	1	2	yes	—
251	C₂³×C₁₃	C₂×#41	1	4	yes	—
252	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
253	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
254	D₄×C₁₃	—	2	32	no	—
255	D₄×C₁₃	—	4	32	no	—
256	D₄×C₁₃	—	4	16	no	—
257	D₄×C₁₃	—	4	32	no	—
258	C₂×C₄×C₁₃	—	2	8	no	—
259	C₂×C₄×C₁₃	—	2	8	no	—
260	C₂×C₄×C₁₃	—	2	8	no	—
261	C₂×C₄×C₁₃	—	2	16	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	2	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	4	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	4	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	4	no	—
275	C₂×C₄×C₁₃	—	2	4	no	—
276	C₂×C₄×C₁₃	—	2	4	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	4	16	no	—
279	C₂×C₄×C₁₃	—	4	32	no	—
280	C₂×C₄×C₁₃	—	4	16	no	—
281	C₂×C₄×C₁₃	—	4	8	no	—
282	C₂×C₄×C₁₃	—	4	4	no	—
283	C₂×C₄×C₁₃	—	4	4	no	—
284	C₂×C₄×C₁₃	—	4	8	no	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
287	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
288	C₂×C₄×C₁₃	C₂×#41	1	8	yes	—
289	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
290	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
291	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
292	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
293	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
294	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
295	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#121	—	2	16	no	—
297	C₂×#121	—	2	8	no	—
298	C₂×#121	C₂²×C₁₃	1	8	yes	complemented
299	C₂×#121	C₂²×C₁₃	1	16	yes	complemented
300	C₂×C₄×D₄	—	2	8	no	—
301	C₂×C₄×D₄	C₂²×C₁₃	1	8	yes	complemented
302	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
305	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
307	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
308	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
309	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
310	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
311	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
312	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
313	#398	C₂²×C₁₃	1	8	yes	complemented
314	#397	C₂²×C₁₃	1	8	yes	complemented
315	#394	C₂²×C₁₃	1	8	yes	complemented
316	#392	C₂²×C₁₃	1	8	yes	complemented
317	#388	C₂²×C₁₃	1	16	yes	complemented
318	#386	C₂²×C₁₃	1	16	yes	complemented
319	#386	C₂²×C₁₃	1	16	yes	complemented
320	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×#95	C₂²×C₁₃	1	2	yes	—
323	C₂×#95	C₂²×C₁₃	1	2	yes	—
324	C₂×#95	C₂²×C₁₃	1	2	yes	—
325	C₂×#95	C₂²×C₁₃	1	8	yes	complemented
326	C₂²×C₁₃	—	2	4	no	—
327	C₂²×C₁₃	—	2	4	no	—
328	C₂²×C₁₃	—	2	8	no	—
329	C₂²×C₁₃	—	2	8	no	—
330	C₂²×C₁₃	—	2	32	no	—
331	C₂²×C₁₃	—	2	4	no	—
332	C₂²×C₁₃	—	2	8	no	—
333	C₂²×C₁₃	—	4	2	no	—
334	C₂²×C₁₃	—	4	2	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	—	4	16	no	—
337	C₂²×C₁₃	—	4	4	no	—
338	C₂²×C₁₃	—	4	4	no	—
339	C₂²×C₁₃	—	4	4	no	—
340	C₂²×C₁₃	—	4	4	no	—
341	C₂²×C₁₃	—	4	4	no	—
342	C₂²×C₁₃	—	4	4	no	—
343	C₂²×C₁₃	—	4	4	no	—
344	C₂²×C₁₃	—	8	16	no	—
345	C₂²×C₁₃	C₂×#121	1	8	yes	—
346	C₂²×C₁₃	C₂×#121	1	4	yes	—
347	C₂²×C₁₃	#532	1	4	yes	—
348	C₂²×C₁₃	#534	1	4	yes	—
349	C₂²×C₁₃	#546	1	8	yes	—
350	C₂²×C₁₃	#553	1	8	yes	—
351	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
352	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
353	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
354	C₂²×C₁₃	C₂²×#41	1	2	yes	—
355	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
356	C₄×C₁₃	—	2	4	no	—
357	C₄×C₁₃	—	2	4	no	—
358	C₄×C₁₃	—	2	4	no	—
359	C₄×C₁₃	—	2	8	no	—
360	C₄×C₁₃	—	4	4	no	—
361	C₄×C₁₃	—	4	2	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	4	4	no	—
364	C₂⁵	C₂³×C₁₃	1	2	yes	—
365	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
366	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×D₄	—	2	4	no	—
368	C₂²×D₄	—	2	4	no	—
369	C₂²×D₄	—	2	8	no	—
370	C₂²×D₄	—	2	8	no	—
371	C₂²×D₄	—	2	8	no	—
372	C₂²×D₄	—	2	8	no	—
373	C₂²×D₄	—	2	4	no	—
374	C₂²×D₄	—	2	8	no	—
375	C₂²×D₄	—	4	4	no	—
376	C₂²×D₄	—	4	4	no	—
377	C₂²×D₄	D₄×C₁₃	1	8	yes	complemented
378	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
379	C₂²×D₄	C₂³×C₁₃	1	8	yes	—
380	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
381	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
382	C₂³×C₄	—	2	8	no	—
383	C₂³×C₄	—	2	4	no	—
384	C₂³×C₄	—	2	8	no	—
385	C₂³×C₄	—	4	4	no	—
386	C₂³×C₄	—	4	4	no	—
387	C₂³×C₄	—	4	4	no	—
388	C₂³×C₄	D₄×C₁₃	1	8	yes	complemented
389	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
392	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
393	C₂³×C₄	C₂³×C₁₃	1	8	yes	—
394	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
398	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
399	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
400	#121	—	2	64	no	—
401	#121	—	2	32	no	—
402	C₄×D₄	—	2	32	no	—
403	C₂×C₄⋊C₄	—	2	4	no	—
404	C₂×C₄⋊C₄	—	2	8	no	—
405	C₂×C₄⋊C₄	—	2	4	no	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
409	C₂×C₂²⋊C₄	—	2	4	no	—
410	C₂×C₂²⋊C₄	—	2	8	no	—
411	C₂×C₂²⋊C₄	—	2	4	no	—
412	C₂×C₂²⋊C₄	—	2	8	no	—
413	C₂×C₂²⋊C₄	—	2	8	no	—
414	C₂×C₂²⋊C₄	—	2	8	no	—
415	C₂×C₂²⋊C₄	—	4	4	no	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
423	C₂×C₄²	—	2	4	no	—
424	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
425	#95	C₂³×C₁₃	1	8	yes	—
426	#95	C₂³×C₁₃	1	4	yes	—
427	#95	C₂³×C₁₃	1	4	yes	—
428	#95	C₂³×C₁₃	1	8	yes	—
429	#95	C₂³×C₁₃	1	8	yes	—
430	C₂×C₁₃	—	2	8	no	—
431	C₂×C₁₃	—	4	4	no	—
432	C₂×C₁₃	—	8	4	no	—
433	C₂×C₁₃	#2543	1	8	yes	direct product factor
434	C₂×C₁₃	C₂²×#121	1	1	yes	characteristic
435	C₂×C₁₃	C₂×#532	1	1	yes	characteristic
436	C₂×C₁₃	C₂×#534	1	1	yes	characteristic
437	C₂×C₁₃	C₂×#546	1	2	yes	—
438	C₂×C₁₃	C₂×#553	1	2	yes	—
439	C₂⁴	—	2	4	no	—
440	C₂⁴	—	2	4	no	—
441	C₂⁴	—	2	2	no	—
442	C₂⁴	—	2	2	no	—
443	C₂⁴	—	2	4	no	—
444	C₂⁴	—	2	4	no	—
445	C₂⁴	—	2	4	no	—
446	C₂⁴	—	2	4	no	—
447	C₂⁴	—	2	4	no	—
448	C₂⁴	—	2	4	no	—
449	C₂⁴	—	2	4	no	—
450	C₂⁴	—	2	4	no	—
451	C₂⁴	—	2	4	no	—
452	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
453	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
454	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
455	C₂⁴	C₁₃×#41	1	4	yes	—
456	C₂⁴	C₂⁴×C₁₃	1	4	yes	—
457	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
458	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
459	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
460	C₂×D₄	—	2	32	no	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	16	no	—
464	C₂×D₄	—	2	16	no	—
465	C₂×D₄	—	2	16	no	—
466	C₂×D₄	—	2	16	no	—
467	C₂×D₄	—	2	8	no	—
468	C₂×D₄	—	2	16	no	—
469	C₂×D₄	—	4	8	no	—
470	C₂×D₄	—	4	8	no	—
471	C₂×D₄	—	4	32	no	—
472	C₂×D₄	—	4	16	no	—
473	C₂×D₄	—	4	32	no	—
474	C₂×D₄	C₂×D₄×C₁₃	1	16	yes	complemented
475	C₂²×C₄	—	2	2	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	2	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	4	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	4	no	—
483	C₂²×C₄	—	2	2	no	—
484	C₂²×C₄	—	2	4	no	—
485	C₂²×C₄	—	2	4	no	—
486	C₂²×C₄	—	2	16	no	—
487	C₂²×C₄	—	2	4	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	8	no	—
493	C₂²×C₄	—	2	16	no	—
494	C₂²×C₄	—	4	16	no	—
495	C₂²×C₄	—	4	8	no	—
496	C₂²×C₄	—	4	8	no	—
497	C₂²×C₄	—	4	8	no	—
498	C₂²×C₄	—	4	32	no	—
499	C₂²×C₄	—	4	16	no	—
500	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
501	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
502	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
503	C₂²×C₄	C₂×D₄×C₁₃	1	16	yes	complemented
504	C₂²×C₄	C₁₃×#41	1	8	yes	—
505	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
506	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
507	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
508	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
509	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
511	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
513	C₄⋊C₄	—	2	8	no	—
514	C₄⋊C₄	—	2	16	no	—
515	C₄⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	2	8	no	—
517	C₂²⋊C₄	—	2	16	no	—
518	C₂²⋊C₄	—	2	8	no	—
519	C₂²⋊C₄	—	2	16	no	—
520	C₂²⋊C₄	—	2	16	no	—
521	C₂²⋊C₄	—	2	16	no	—
522	C₂²⋊C₄	—	4	8	no	—
523	C₄²	—	2	8	no	—
524	C₁₃	C₂×#2543	1	1	yes	characteristic, direct product factor, Sylow
525	C₂³	—	2	8	no	—
526	C₂³	—	2	8	no	—
527	C₂³	—	2	16	no	—
528	C₂³	—	2	16	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	8	no	—
532	C₂³	—	2	16	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	—	2	4	no	—
540	C₂³	—	2	4	no	—
541	C₂³	—	2	4	no	—
542	C₂³	—	2	4	no	—
543	C₂³	—	2	4	no	—
544	C₂³	—	4	4	no	—
545	C₂³	—	4	4	no	—
546	C₂³	—	4	8	no	—
547	C₂³	—	4	8	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	4	8	no	—
550	C₂³	—	4	8	no	—
551	C₂³	—	4	8	no	—
552	C₂³	—	4	8	no	—
553	C₂³	—	4	8	no	—
554	C₂³	C₁₃×#121	1	16	yes	—
555	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
556	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
557	C₂³	C₂²×D₄×C₁₃	1	4	yes	—
558	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
559	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
560	C₂³	C₂×C₁₃×#41	1	4	yes	—
561	C₂³	C₂×C₁₃×#41	1	2	yes	—
562	C₂³	C₂×C₁₃×#41	1	4	yes	—
563	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
564	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
565	D₄	—	2	32	no	—
566	D₄	—	4	32	no	—
567	D₄	—	4	16	no	—
568	D₄	—	4	32	no	—
569	C₂×C₄	—	2	8	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	8	no	—
572	C₂×C₄	—	2	16	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	4	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	2	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	4	16	no	—
590	C₂×C₄	—	4	32	no	—
591	C₂×C₄	—	4	16	no	—
592	C₂×C₄	—	4	8	no	—
593	C₂×C₄	—	4	4	no	—
594	C₂×C₄	—	4	4	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
597	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
598	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
599	C₂×C₄	C₂×C₁₃×#41	1	8	yes	—
600	C₂²	—	2	32	no	—
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	8	no	—
604	C₂²	—	2	8	no	—
605	C₂²	—	2	4	no	—
606	C₂²	—	2	8	no	—
607	C₂²	—	4	16	no	—
608	C₂²	—	4	2	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	4	no	—
611	C₂²	—	4	4	no	—
612	C₂²	—	4	4	no	—
613	C₂²	—	4	4	no	—
614	C₂²	—	4	4	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	4	4	no	—
617	C₂²	—	4	4	no	—
618	C₂²	—	8	16	no	—
619	C₂²	C₂×C₁₃×#121	1	8	yes	—
620	C₂²	C₂×C₁₃×#121	1	4	yes	—
621	C₂²	C₁₃×#532	1	4	yes	—
622	C₂²	C₁₃×#534	1	4	yes	—
623	C₂²	C₁₃×#546	1	8	yes	—
624	C₂²	C₁₃×#553	1	8	yes	—
625	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
626	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
627	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
628	C₂²	C₂²×C₁₃×#41	1	2	yes	—
629	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
630	C₄	—	2	4	no	—
631	C₄	—	2	4	no	—
632	C₄	—	2	4	no	—
633	C₄	—	2	8	no	—
634	C₄	—	4	4	no	—
635	C₄	—	4	2	no	—
636	C₄	—	4	2	no	—
637	C₄	—	4	4	no	—
638	C₂	—	2	8	no	—
639	C₂	—	4	4	no	—
640	C₂	—	8	4	no	—
641	C₂	C₁₃×#2543	1	8	yes	direct product factor
642	C₂	C₂²×C₁₃×#121	1	1	yes	characteristic
643	C₂	C₂×C₁₃×#532	1	1	yes	characteristic
644	C₂	C₂×C₁₃×#534	1	1	yes	characteristic
645	C₂	C₂×C₁₃×#546	1	2	yes	—
646	C₂	C₂×C₁₃×#553	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
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
1. C₂²×C₁₃×#121	C₂	semidirect
2. C₂²×C₁₃×#121	C₂	semidirect
3. C₂²×C₄×D₄×C₁₃	C₂	semidirect
4. C₁₃×#2543	C₂	direct (N × H)
5. C₂×C₁₃×#398	C₂	semidirect
6. C₂×C₁₃×#397	C₂	semidirect
7. C₂×C₁₃×#394	C₂	semidirect
8. C₂×C₁₃×#392	C₂	semidirect
9. C₂×C₁₃×#388	C₂	semidirect
10. C₂×C₁₃×#386	C₂	semidirect
11. C₂×C₁₃×#386	C₂	semidirect
12. C₂²×C₁₃×#95	C₂	semidirect
22. C₂×C₁₃×#121	C₂²	semidirect
23. C₂×C₁₃×#121	C₂²	semidirect
25. C₂×C₄×D₄×C₁₃	C₂²	semidirect
37. C₁₃×#398	C₂²	semidirect
38. C₁₃×#397	C₂²	semidirect
39. C₁₃×#394	C₂²	semidirect
40. C₁₃×#392	C₂²	semidirect
41. C₁₃×#388	C₂²	semidirect
42. C₁₃×#386	C₂²	semidirect
43. C₁₃×#386	C₂²	semidirect
49. C₂×C₁₃×#95	C₂²	semidirect
63. C₂²×D₄×C₁₃	D₄	semidirect
74. C₂³×C₄×C₁₃	D₄	semidirect
116. C₂×#2543	C₁₃	direct (N × H)
152. C₂×D₄×C₁₃	C₂×D₄	semidirect
181. C₂²×C₄×C₁₃	C₂×D₄	semidirect
202. C₂²×#121	C₂×C₁₃	semidirect
203. C₂²×#121	C₂×C₁₃	semidirect
204. C₂²×C₄×D₄	C₂×C₁₃	semidirect
205. #2543	C₂×C₁₃	direct (N × H)
206. C₂×#398	C₂×C₁₃	semidirect
207. C₂×#397	C₂×C₁₃	semidirect
208. C₂×#394	C₂×C₁₃	semidirect
209. C₂×#392	C₂×C₁₃	semidirect
210. C₂×#388	C₂×C₁₃	semidirect
211. C₂×#386	C₂×C₁₃	semidirect
212. C₂×#386	C₂×C₁₃	semidirect
213. C₂²×#95	C₂×C₁₃	semidirect
298. C₂×#121	C₂²×C₁₃	semidirect
299. C₂×#121	C₂²×C₁₃	semidirect
301. C₂×C₄×D₄	C₂²×C₁₃	semidirect
313. #398	C₂²×C₁₃	semidirect
314. #397	C₂²×C₁₃	semidirect
315. #394	C₂²×C₁₃	semidirect
316. #392	C₂²×C₁₃	semidirect
317. #388	C₂²×C₁₃	semidirect
318. #386	C₂²×C₁₃	semidirect
319. #386	C₂²×C₁₃	semidirect
325. C₂×#95	C₂²×C₁₃	semidirect
377. C₂²×D₄	D₄×C₁₃	semidirect
388. C₂³×C₄	D₄×C₁₃	semidirect
433. C₂×C₁₃	#2543	direct (N × H)
474. C₂×D₄	C₂×D₄×C₁₃	semidirect
503. C₂²×C₄	C₂×D₄×C₁₃	semidirect
524. C₁₃	C₂×#2543	direct (N × H)
641. C₂	C₁₃×#2543	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×#121	2
C₂²×C₄×D₄×C₁₃	2
C₁₃×#2543	2
C₂×C₁₃×#398	2
C₂×C₁₃×#397	2
C₂×C₁₃×#394	2
C₂×C₁₃×#392	2
C₂×C₁₃×#388	2
C₂×C₁₃×#386	2
C₂²×C₁₃×#95	2
C₂×#2543	13

Subgroups — C2×C13×#2543 #15721157

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#2543 #15721157