Subgroups — C₂×D₁₃×#560 #16769784

Order 3328.

9606 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719416	C₂	1	2	yes	maximal, complemented
2	C₂×#11719371	C₂	1	3	yes	maximal, complemented
3	C₂×#11719300	C₂	1	3	yes	maximal, complemented
4	C₂×#11719325	C₂	1	6	yes	maximal, complemented
5	C₂×#11719425	C₂	1	1	yes	maximal, characteristic, complemented
6	D₁₃×#560	C₂	1	32	yes	maximal, direct product factor
7	C₂×D₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₁₃×#126	C₂	1	2	yes	maximal, complemented
9	C₂×D₁₃×#123	C₂	1	3	yes	maximal, complemented
10	C₂×D₁₃×#121	C₂	1	6	yes	maximal, complemented
11	C₂×D₁₃×#120	C₂	1	3	yes	maximal, complemented
12	C₂×C₁₃×#560	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁵×D₁₃	C₂²	1	1	yes	characteristic
14	C₂²×D₄×D₁₃	C₂²	1	6	yes	—
15	C₂²×D₄×D₁₃	C₂²	1	3	yes	—
16	C₂²×D₄×D₁₃	C₂²	1	3	yes	complemented
17	C₂³×C₄×D₁₃	C₂²	1	3	yes	complemented
18	C₁₃×#560	C₂²	1	16	yes	complemented
19	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₃×#126	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#123	C₂²	1	3	yes	complemented
22	C₂×C₁₃×#121	C₂²	1	6	yes	complemented
23	C₂×C₁₃×#120	C₂²	1	3	yes	complemented
24	C₂×#88207	C₂²	1	3	yes	complemented
25	C₂×#88194	C₂²	1	3	yes	complemented
26	C₂×#88194	C₂²	1	3	yes	complemented
27	C₂×#88193	C₂²	1	6	yes	complemented
28	C₂×#88193	C₂²	1	6	yes	complemented
29	C₂×#88192	C₂²	1	6	yes	complemented
30	C₂×#88191	C₂²	1	3	yes	complemented
31	C₂×#88191	C₂²	1	6	yes	complemented
32	C₂×#88189	C₂²	1	3	yes	complemented
33	C₂×#88184	C₂²	1	6	yes	complemented
34	C₂×#88183	C₂²	1	3	yes	complemented
35	#11719425	C₂²	1	16	yes	complemented
36	D₁₃×#127	C₂²	1	16	yes	complemented
37	#11719416	C₂²	1	32	yes	complemented
38	D₁₃×#126	C₂²	1	32	yes	complemented
39	#11719371	C₂²	1	48	yes	complemented
40	D₁₃×#123	C₂²	1	48	yes	complemented
41	#11719325	C₂²	1	96	yes	complemented
42	D₁₃×#121	C₂²	1	96	yes	complemented
43	#11719300	C₂²	1	48	yes	complemented
44	D₁₃×#120	C₂²	1	48	yes	complemented
45	C₂×#88152	C₂²	1	6	yes	complemented
46	C₂×#88149	C₂²	1	6	yes	complemented
47	C₂×#88148	C₂²	1	6	yes	complemented
48	C₂×C₄⋊C₄×D₁₃	C₂²	1	6	yes	complemented
49	C₂×#88140	C₂²	1	3	yes	complemented
50	C₂×#88138	C₂²	1	6	yes	complemented
51	C₂×#88138	C₂²	1	6	yes	complemented
52	C₂×#88137	C₂²	1	6	yes	complemented
53	C₂×#88136	C₂²	1	6	yes	complemented
54	C₂×#88136	C₂²	1	3	yes	complemented
55	C₂×C₂²⋊C₄×D₁₃	C₂²	1	6	yes	—
56	C₂×C₂²⋊C₄×D₁₃	C₂²	1	3	yes	—
57	C₂×C₂²⋊C₄×D₁₃	C₂²	1	3	yes	complemented
58	C₂×#88133	C₂²	1	6	yes	complemented
59	C₂×#88130	C₂²	1	2	yes	complemented
60	C₂×#88128	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic, complemented
62	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
63	C₂⁴×D₁₃	—	4	12	no	—
64	C₂⁴×D₁₃	C₂³	1	2	yes	—
65	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
66	C₂⁴×D₁₃	C₂³	1	3	yes	—
67	C₂⁴×D₁₃	C₂³	1	2	yes	—
68	C₂⁴×D₁₃	C₂³	1	1	yes	characteristic
69	C₂⁴×D₁₃	C₂³	1	8	yes	—
70	C₂²×D₄×C₁₃	C₂³	1	3	yes	—
71	C₂²×D₄×C₁₃	C₂³	1	6	yes	—
72	C₂²×D₄×C₁₃	C₂³	1	3	yes	complemented
73	C₂³×C₄×C₁₃	C₂³	1	3	yes	complemented
74	C₂²×C₂²⋊D₁₃	C₂³	1	3	yes	—
75	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
76	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	—
77	C₂²×C₂²⋊D₁₃	C₂³	1	3	yes	—
78	C₂²×C₂²⋊D₁₃	C₂³	1	6	yes	complemented
79	C₂³×Dic₁₃	C₂³	1	3	yes	complemented
80	C₂×D₄×D₁₃	—	4	24	no	—
81	C₂×D₄×D₁₃	—	4	12	no	—
82	C₂×D₄×D₁₃	—	4	12	no	—
83	C₂×D₄×D₁₃	C₂³	1	48	yes	—
84	C₂×D₄×D₁₃	C₂³	1	24	yes	—
85	C₂×D₄×D₁₃	C₂³	1	24	yes	complemented
86	C₂²×D₅₂	C₂³	1	3	yes	—
87	C₂²×D₅₂	C₂³	1	6	yes	—
88	C₂²×D₅₂	C₂³	1	3	yes	complemented
89	C₂²×C₄×D₁₃	—	4	12	no	—
90	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
91	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
92	C₂²×C₄×D₁₃	C₂³	1	24	yes	complemented
93	C₂²×C₄×D₁₃	C₂³	1	6	yes	complemented
94	C₁₃×#127	C₂³	1	8	yes	complemented
95	C₁₃×#126	C₂³	1	16	yes	complemented
96	C₁₃×#123	C₂³	1	24	yes	complemented
97	C₁₃×#121	C₂³	1	48	yes	complemented
98	C₁₃×#120	C₂³	1	24	yes	complemented
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	6	yes	complemented
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	6	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	—
102	C₂×C₁₃×C₂²⋊C₄	C₂³	1	3	yes	complemented
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic, complemented
104	#88207	C₂³	1	24	yes	complemented
105	C₂×C₂²⋊Dic₁₃	C₂³	1	6	yes	—
106	C₂×C₂²⋊Dic₁₃	C₂³	1	3	yes	—
107	C₂×C₂²⋊Dic₁₃	C₂³	1	3	yes	complemented
108	#88194	C₂³	1	24	yes	complemented
109	#88194	C₂³	1	24	yes	complemented
110	#88193	C₂³	1	48	yes	complemented
111	#88193	C₂³	1	48	yes	complemented
112	#88192	C₂³	1	48	yes	complemented
113	#88191	C₂³	1	24	yes	complemented
114	#88191	C₂³	1	48	yes	complemented
115	#88189	C₂³	1	24	yes	complemented
116	#88184	C₂³	1	48	yes	complemented
117	#88183	C₂³	1	24	yes	complemented
118	C₂×#6103	C₂³	1	6	yes	—
119	C₂×#6103	C₂³	1	6	yes	—
120	C₂×#6103	C₂³	1	6	yes	—
121	C₂×#6103	C₂³	1	6	yes	complemented
122	C₂×C₄⋊Dic₁₃	C₂³	1	6	yes	complemented
123	C₂×#6101	C₂³	1	6	yes	complemented
124	C₂×#6101	C₂³	1	6	yes	complemented
125	C₂×C₄×Dic₁₃	C₂³	1	3	yes	complemented
126	#88152	C₂³	1	48	yes	complemented
127	#88149	C₂³	1	48	yes	complemented
128	#88148	C₂³	1	48	yes	complemented
129	C₄⋊C₄×D₁₃	C₂³	1	48	yes	complemented
130	#88140	C₂³	1	24	yes	complemented
131	#88138	C₂³	1	48	yes	complemented
132	#88138	C₂³	1	48	yes	complemented
133	#88137	C₂³	1	48	yes	complemented
134	#88136	C₂³	1	48	yes	complemented
135	#88136	C₂³	1	24	yes	complemented
136	C₂²⋊C₄×D₁₃	C₂³	1	48	yes	—
137	C₂²⋊C₄×D₁₃	C₂³	1	24	yes	—
138	C₂²⋊C₄×D₁₃	C₂³	1	24	yes	complemented
139	#88133	C₂³	1	48	yes	complemented
140	#88130	C₂³	1	16	yes	complemented
141	#88128	C₂³	1	8	yes	complemented
142	C₄²×D₁₃	C₂³	1	8	yes	complemented
143	C₂²×#560	—	13	1	no	maximal, Sylow
144	C₂⁴×C₁₃	—	4	6	no	—
145	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
146	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
147	C₂⁴×C₁₃	C₂⁴	1	3	yes	—
148	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
149	C₂³×D₁₃	—	2	12	no	—
150	C₂³×D₁₃	—	2	24	no	—
151	C₂³×D₁₃	—	2	24	no	—
152	C₂³×D₁₃	—	2	12	no	—
153	C₂³×D₁₃	—	4	48	no	—
154	C₂³×D₁₃	—	4	12	no	—
155	C₂³×D₁₃	—	4	6	no	—
156	C₂³×D₁₃	—	4	64	no	—
157	C₂³×D₁₃	C₂⁴	1	8	yes	—
158	C₂³×D₁₃	C₂⁴	1	4	yes	—
159	C₂³×D₁₃	C₂⁴	1	12	yes	—
160	C₂³×D₁₃	C₂⁴	1	2	yes	—
161	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
162	C₂³×D₁₃	C₂⁴	1	3	yes	—
163	C₂³×D₁₃	C₂⁴	1	8	yes	—
164	C₂³×D₁₃	C₂⁴	1	4	yes	—
165	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×D₄×C₁₃	—	4	12	no	—
167	C₂×D₄×C₁₃	—	4	6	no	—
168	C₂×D₄×C₁₃	—	4	6	no	—
169	C₂×D₄×C₁₃	C₂⁴	1	12	yes	—
170	C₂×D₄×C₁₃	C₂⁴	1	24	yes	—
171	C₂×D₄×C₁₃	C₂⁴	1	12	yes	complemented
172	C₂²×C₄×C₁₃	—	4	6	no	—
173	C₂²×C₄×C₁₃	C₂⁴	1	3	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	12	yes	complemented
176	C₂×C₂²⋊D₁₃	—	4	12	no	—
177	C₂×C₂²⋊D₁₃	—	4	12	no	—
178	C₂×C₂²⋊D₁₃	—	4	6	no	—
179	C₂×C₂²⋊D₁₃	—	4	6	no	—
180	C₂×C₂²⋊D₁₃	—	4	12	no	—
181	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
182	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
183	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	—
184	C₂×C₂²⋊D₁₃	C₂⁴	1	12	yes	—
185	C₂×C₂²⋊D₁₃	C₂⁴	1	24	yes	complemented
186	C₂²×Dic₁₃	—	4	6	no	—
187	C₂²×Dic₁₃	C₂⁴	1	3	yes	—
188	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
189	C₂²×Dic₁₃	C₂⁴	1	12	yes	complemented
190	D₄×D₁₃	—	4	96	no	—
191	D₄×D₁₃	—	4	48	no	—
192	D₄×D₁₃	—	4	48	no	—
193	C₂×D₅₂	—	4	12	no	—
194	C₂×D₅₂	—	4	6	no	—
195	C₂×D₅₂	—	4	6	no	—
196	C₂×D₅₂	C₂⁴	1	12	yes	—
197	C₂×D₅₂	C₂⁴	1	24	yes	—
198	C₂×D₅₂	C₂⁴	1	12	yes	complemented
199	C₂×C₄×D₁₃	—	2	24	no	—
200	C₂×C₄×D₁₃	—	2	12	no	—
201	C₂×C₄×D₁₃	—	4	48	no	—
202	C₂×C₄×D₁₃	—	4	12	no	—
203	C₂×C₄×D₁₃	C₂⁴	1	12	yes	—
204	C₂×C₄×D₁₃	C₂⁴	1	24	yes	—
205	C₂×C₄×D₁₃	C₂⁴	1	24	yes	complemented
206	C₁₃×C₄⋊C₄	C₂⁴	1	24	yes	complemented
207	C₁₃×C₂²⋊C₄	C₂⁴	1	24	yes	—
208	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	—
209	C₁₃×C₂²⋊C₄	C₂⁴	1	12	yes	complemented
210	C₄²×C₁₃	C₂⁴	1	4	yes	complemented
211	C₂²⋊Dic₁₃	C₂⁴	1	24	yes	—
212	C₂²⋊Dic₁₃	C₂⁴	1	12	yes	—
213	C₂²⋊Dic₁₃	C₂⁴	1	12	yes	complemented
214	#6103	C₂⁴	1	24	yes	—
215	#6103	C₂⁴	1	24	yes	—
216	#6103	C₂⁴	1	24	yes	—
217	#6103	C₂⁴	1	24	yes	complemented
218	C₄⋊Dic₁₃	C₂⁴	1	24	yes	complemented
219	#6101	C₂⁴	1	24	yes	complemented
220	#6101	C₂⁴	1	24	yes	complemented
221	C₄×Dic₁₃	C₂⁴	1	12	yes	complemented
222	C₂×#560	—	13	32	no	—
223	C₂×#560	—	13	1	no	—
224	C₂×#560	—	13	2	no	—
225	C₂×#560	—	13	3	no	—
226	C₂×#560	—	13	6	no	—
227	C₂×#560	—	13	3	no	—
228	C₂×#560	D₁₃	1	1	yes	characteristic, direct product factor
229	C₂²×#127	—	13	1	no	—
230	C₂²×#126	—	13	2	no	—
231	C₂²×#123	—	13	3	no	—
232	C₂²×#121	—	13	6	no	—
233	C₂²×#120	—	13	3	no	—
234	C₂³×C₁₃	—	2	6	no	—
235	C₂³×C₁₃	—	2	12	no	—
236	C₂³×C₁₃	—	2	12	no	—
237	C₂³×C₁₃	—	2	6	no	—
238	C₂³×C₁₃	—	4	12	no	—
239	C₂³×C₁₃	—	4	16	no	—
240	C₂³×C₁₃	C₂⁵	1	4	yes	—
241	C₂³×C₁₃	C₂⁵	1	2	yes	—
242	C₂³×C₁₃	C₂⁵	1	6	yes	—
243	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
244	C₂²×D₁₃	—	2	6	no	—
245	C₂²×D₁₃	—	2	12	no	—
246	C₂²×D₁₃	—	2	12	no	—
247	C₂²×D₁₃	—	2	6	no	—
248	C₂²×D₁₃	—	2	24	no	—
249	C₂²×D₁₃	—	2	48	no	—
250	C₂²×D₁₃	—	2	48	no	—
251	C₂²×D₁₃	—	2	24	no	—
252	C₂²×D₁₃	—	4	24	no	—
253	C₂²×D₁₃	—	4	12	no	—
254	C₂²×D₁₃	—	4	32	no	—
255	C₂²×D₁₃	—	4	16	no	—
256	C₂²×D₁₃	—	4	128	no	—
257	C₂²×D₁₃	—	4	48	no	—
258	C₂²×D₁₃	—	4	32	no	—
259	C₂²×D₁₃	—	4	16	no	—
260	C₂²×D₁₃	H(5,𝔽₂)	1	12	yes	—
261	C₂²×D₁₃	C₂⁵	1	4	yes	—
262	C₂²×D₁₃	C₂⁵	1	2	yes	—
263	C₂²×D₁₃	C₂⁵	1	6	yes	—
264	C₂²×D₁₃	C₂⁵	1	2	yes	—
265	D₄×C₁₃	—	4	24	no	—
266	D₄×C₁₃	—	4	12	no	—
267	D₄×C₁₃	—	4	12	no	—
268	C₂×C₄×C₁₃	—	2	12	no	—
269	C₂×C₄×C₁₃	—	2	6	no	—
270	C₂×C₄×C₁₃	—	4	12	no	—
271	C₂×C₄×C₁₃	C₂⁵	1	6	yes	—
272	C₂×C₄×C₁₃	C₂⁵	1	12	yes	—
273	C₂²⋊D₁₃	—	4	24	no	—
274	C₂²⋊D₁₃	—	4	24	no	—
275	C₂²⋊D₁₃	—	4	12	no	—
276	C₂²⋊D₁₃	—	4	12	no	—
277	C₂²⋊D₁₃	—	4	24	no	—
278	C₂×Dic₁₃	—	2	12	no	—
279	C₂×Dic₁₃	—	2	6	no	—
280	C₂×Dic₁₃	—	4	12	no	—
281	C₂×Dic₁₃	C₂⁵	1	6	yes	—
282	C₂×Dic₁₃	C₂⁵	1	12	yes	—
283	D₅₂	—	4	24	no	—
284	D₅₂	—	4	12	no	—
285	D₅₂	—	4	12	no	—
286	C₄×D₁₃	—	2	48	no	—
287	C₄×D₁₃	—	2	24	no	—
288	C₄×D₁₃	—	4	24	no	—
289	C₂⁶	—	13	1	no	—
290	C₂³×D₄	—	13	6	no	—
291	C₂³×D₄	—	13	3	no	—
292	C₂³×D₄	—	13	3	no	—
293	C₂⁴×C₄	—	13	3	no	—
294	#560	—	13	16	no	—
295	#560	—	13	32	no	—
296	#560	—	13	48	no	—
297	#560	—	13	96	no	—
298	#560	—	13	48	no	—
299	#560	C₂×D₁₃	1	16	yes	direct product factor
300	C₂×#127	—	13	3	no	—
301	C₂×#127	—	13	3	no	—
302	C₂×#127	—	13	16	no	—
303	C₂×#127	—	13	1	no	—
304	C₂×#127	C₂×D₁₃	1	1	yes	characteristic, complemented
305	C₂×#126	—	13	32	no	—
306	C₂×#126	—	13	6	no	—
307	C₂×#126	—	13	6	no	—
308	C₂×#126	—	13	2	no	—
309	C₂×#126	C₂×D₁₃	1	2	yes	complemented
310	C₂×#123	—	13	3	no	—
311	C₂×#123	—	13	3	no	—
312	C₂×#123	—	13	48	no	—
313	C₂×#123	—	13	6	no	—
314	C₂×#123	—	13	6	no	—
315	C₂×#123	—	13	3	no	—
316	C₂×#123	C₂×D₁₃	1	3	yes	complemented
317	C₂×#121	—	13	6	no	—
318	C₂×#121	—	13	6	no	—
319	C₂×#121	—	13	6	no	—
320	C₂×#121	—	13	6	no	—
321	C₂×#121	—	13	96	no	—
322	C₂×#121	—	13	6	no	—
323	C₂×#121	—	13	6	no	—
324	C₂×#121	—	13	6	no	—
325	C₂×#121	C₂×D₁₃	1	6	yes	complemented
326	C₂×#120	—	13	3	no	—
327	C₂×#120	—	13	6	no	—
328	C₂×#120	—	13	3	no	—
329	C₂×#120	—	13	48	no	—
330	C₂×#120	—	13	3	no	—
331	C₂×#120	—	13	6	no	—
332	C₂×#120	C₂×D₁₃	1	3	yes	complemented
333	C₂²×C₄⋊C₄	—	13	6	no	—
334	C₂²×C₂²⋊C₄	—	13	6	no	—
335	C₂²×C₂²⋊C₄	—	13	3	no	—
336	C₂²×C₂²⋊C₄	—	13	3	no	—
337	C₂²×C₄²	—	13	1	no	—
338	C₂²×C₁₃	—	2	6	no	—
339	C₂²×C₁₃	—	2	12	no	—
340	C₂²×C₁₃	—	2	12	no	—
341	C₂²×C₁₃	—	2	6	no	—
342	C₂²×C₁₃	—	4	16	no	—
343	C₂²×C₁₃	—	4	8	no	—
344	C₂²×C₁₃	—	4	4	no	—
345	C₂²×C₁₃	—	4	12	no	—
346	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	6	yes	—
347	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
348	C₂×D₁₃	—	2	6	no	—
349	C₂×D₁₃	—	2	12	no	—
350	C₂×D₁₃	—	2	12	no	—
351	C₂×D₁₃	—	2	6	no	—
352	C₂×D₁₃	—	4	32	no	—
353	C₂×D₁₃	—	4	16	no	—
354	C₂×D₁₃	—	4	12	no	—
355	C₂×D₁₃	—	4	8	no	—
356	C₂×D₁₃	—	4	4	no	—
357	C₂×D₁₃	—	4	48	no	—
358	C₂×D₁₃	—	4	32	no	—
359	C₂×D₁₃	—	4	16	no	—
360	C₂×D₁₃	#560	1	16	yes	direct product factor
361	C₂×D₁₃	C₂×H(5,𝔽₂)	1	12	yes	—
362	C₄×C₁₃	—	2	12	no	—
363	C₄×C₁₃	—	2	6	no	—
364	Dic₁₃	—	2	12	no	—
365	Dic₁₃	—	2	6	no	—
366	C₂⁵	—	13	2	no	—
367	C₂⁵	—	13	1	no	—
368	C₂⁵	—	13	3	no	—
369	C₂⁵	—	13	8	no	—
370	C₂⁵	—	13	1	no	—
371	C₂⁵	—	13	2	no	—
372	C₂⁵	—	52	12	no	—
373	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
374	C₂²×D₄	—	13	6	no	—
375	C₂²×D₄	—	13	6	no	—
376	C₂²×D₄	—	13	3	no	—
377	C₂²×D₄	—	13	3	no	—
378	C₂²×D₄	—	13	6	no	—
379	C₂²×D₄	—	13	48	no	—
380	C₂²×D₄	—	13	24	no	—
381	C₂²×D₄	—	13	24	no	—
382	C₂²×D₄	—	13	6	no	—
383	C₂²×D₄	—	13	3	no	—
384	C₂²×D₄	—	13	3	no	—
385	C₂²×D₄	—	52	24	no	—
386	C₂²×D₄	—	52	12	no	—
387	C₂²×D₄	—	52	12	no	—
388	C₂²×D₄	C₂²×D₁₃	1	6	yes	—
389	C₂²×D₄	C₂²×D₁₃	1	3	yes	—
390	C₂²×D₄	C₂²×D₁₃	1	3	yes	complemented
391	C₂³×C₄	—	13	3	no	—
392	C₂³×C₄	—	13	6	no	—
393	C₂³×C₄	—	13	3	no	—
394	C₂³×C₄	—	13	6	no	—
395	C₂³×C₄	—	13	24	no	—
396	C₂³×C₄	—	52	12	no	—
397	C₂³×C₄	C₂²×D₁₃	1	3	yes	complemented
398	#127	—	13	24	no	—
399	#127	—	13	24	no	—
400	#127	—	13	8	no	—
401	#127	C₂²×D₁₃	1	8	yes	complemented
402	#126	—	13	48	no	—
403	#126	—	13	48	no	—
404	#126	—	13	16	no	—
405	#126	C₂²×D₁₃	1	16	yes	complemented
406	#123	—	13	24	no	—
407	#123	—	13	24	no	—
408	#123	—	13	48	no	—
409	#123	—	13	48	no	—
410	#123	—	13	24	no	—
411	#123	C₂²×D₁₃	1	24	yes	complemented
412	#121	—	13	48	no	—
413	#121	—	13	48	no	—
414	#121	—	13	48	no	—
415	#121	—	13	48	no	—
416	#121	—	13	48	no	—
417	#121	—	13	48	no	—
418	#121	—	13	48	no	—
419	#121	C₂²×D₁₃	1	48	yes	complemented
420	#120	—	13	24	no	—
421	#120	—	13	48	no	—
422	#120	—	13	24	no	—
423	#120	—	13	24	no	—
424	#120	—	13	48	no	—
425	#120	C₂²×D₁₃	1	24	yes	complemented
426	C₂×C₄⋊C₄	—	13	6	no	—
427	C₂×C₄⋊C₄	—	13	6	no	—
428	C₂×C₄⋊C₄	—	13	6	no	—
429	C₂×C₄⋊C₄	—	13	48	no	—
430	C₂×C₄⋊C₄	C₂²×D₁₃	1	6	yes	complemented
431	C₂×C₂²⋊C₄	—	13	6	no	—
432	C₂×C₂²⋊C₄	—	13	3	no	—
433	C₂×C₂²⋊C₄	—	13	3	no	—
434	C₂×C₂²⋊C₄	—	13	6	no	—
435	C₂×C₂²⋊C₄	—	13	6	no	—
436	C₂×C₂²⋊C₄	—	13	6	no	—
437	C₂×C₂²⋊C₄	—	13	6	no	—
438	C₂×C₂²⋊C₄	—	13	48	no	—
439	C₂×C₂²⋊C₄	—	13	24	no	—
440	C₂×C₂²⋊C₄	—	13	24	no	—
441	C₂×C₂²⋊C₄	C₂²×D₁₃	1	6	yes	—
442	C₂×C₂²⋊C₄	C₂²×D₁₃	1	3	yes	—
443	C₂×C₂²⋊C₄	C₂²×D₁₃	1	3	yes	complemented
444	C₂×C₄²	—	13	3	no	—
445	C₂×C₄²	—	13	8	no	—
446	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic, complemented
447	C₂×C₁₃	—	4	4	no	—
448	C₂×C₁₃	—	4	2	no	—
449	C₂×C₁₃	—	4	6	no	—
450	C₂×C₁₃	C₂×#560	1	4	yes	complemented
451	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	3	yes	—
452	D₁₃	—	4	6	no	—
453	D₁₃	—	4	4	no	—
454	D₁₃	—	4	2	no	—
455	D₁₃	C₂×#560	1	8	yes	direct product factor
456	C₂⁴	—	4	6	no	—
457	C₂⁴	—	13	1	no	—
458	C₂⁴	—	13	8	no	—
459	C₂⁴	—	13	4	no	—
460	C₂⁴	—	13	12	no	—
461	C₂⁴	—	13	2	no	—
462	C₂⁴	—	13	1	no	—
463	C₂⁴	—	13	3	no	—
464	C₂⁴	—	13	4	no	—
465	C₂⁴	—	13	8	no	—
466	C₂⁴	—	26	12	no	—
467	C₂⁴	—	26	24	no	—
468	C₂⁴	—	26	24	no	—
469	C₂⁴	—	26	12	no	—
470	C₂⁴	—	52	12	no	—
471	C₂⁴	—	52	6	no	—
472	C₂⁴	—	52	48	no	—
473	C₂⁴	—	52	64	no	—
474	C₂⁴	C₂³×D₁₃	1	2	yes	—
475	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
476	C₂⁴	C₂³×D₁₃	1	3	yes	—
477	C₂⁴	C₂³×D₁₃	1	4	yes	—
478	C₂×D₄	—	4	12	no	—
479	C₂×D₄	—	4	6	no	—
480	C₂×D₄	—	4	6	no	—
481	C₂×D₄	—	13	24	no	—
482	C₂×D₄	—	13	24	no	—
483	C₂×D₄	—	13	12	no	—
484	C₂×D₄	—	13	12	no	—
485	C₂×D₄	—	13	24	no	—
486	C₂×D₄	—	13	24	no	—
487	C₂×D₄	—	13	12	no	—
488	C₂×D₄	—	13	12	no	—
489	C₂×D₄	—	52	12	no	—
490	C₂×D₄	—	52	6	no	—
491	C₂×D₄	—	52	6	no	—
492	C₂×D₄	—	52	96	no	—
493	C₂×D₄	—	52	48	no	—
494	C₂×D₄	—	52	48	no	—
495	C₂×D₄	—	52	12	no	—
496	C₂×D₄	—	52	12	no	—
497	C₂×D₄	—	52	6	no	—
498	C₂×D₄	—	52	12	no	—
499	C₂×D₄	—	52	6	no	—
500	C₂×D₄	C₂³×D₁₃	1	24	yes	—
501	C₂×D₄	C₂³×D₁₃	1	12	yes	—
502	C₂×D₄	C₂³×D₁₃	1	12	yes	complemented
503	C₂²×C₄	—	4	6	no	—
504	C₂²×C₄	—	13	3	no	—
505	C₂²×C₄	—	13	6	no	—
506	C₂²×C₄	—	13	12	no	—
507	C₂²×C₄	—	13	12	no	—
508	C₂²×C₄	—	13	24	no	—
509	C₂²×C₄	—	13	24	no	—
510	C₂²×C₄	—	26	24	no	—
511	C₂²×C₄	—	26	12	no	—
512	C₂²×C₄	—	52	12	no	—
513	C₂²×C₄	—	52	48	no	—
514	C₂²×C₄	—	52	6	no	—
515	C₂²×C₄	C₂³×D₁₃	1	3	yes	—
516	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
517	C₂²×C₄	C₂³×D₁₃	1	12	yes	complemented
518	C₄⋊C₄	—	13	24	no	—
519	C₄⋊C₄	—	13	24	no	—
520	C₄⋊C₄	—	13	24	no	—
521	C₄⋊C₄	C₂³×D₁₃	1	24	yes	complemented
522	C₂²⋊C₄	—	13	24	no	—
523	C₂²⋊C₄	—	13	12	no	—
524	C₂²⋊C₄	—	13	12	no	—
525	C₂²⋊C₄	—	13	24	no	—
526	C₂²⋊C₄	—	13	24	no	—
527	C₂²⋊C₄	—	13	24	no	—
528	C₂²⋊C₄	—	13	24	no	—
529	C₂²⋊C₄	C₂³×D₁₃	1	24	yes	—
530	C₂²⋊C₄	C₂³×D₁₃	1	12	yes	—
531	C₂²⋊C₄	C₂³×D₁₃	1	12	yes	complemented
532	C₄²	—	13	12	no	—
533	C₄²	C₂³×D₁₃	1	4	yes	complemented
534	C₁₃	C₂²×#560	1	1	yes	characteristic, complemented, Sylow
535	C₂³	—	2	6	no	—
536	C₂³	—	2	12	no	—
537	C₂³	—	2	12	no	—
538	C₂³	—	2	6	no	—
539	C₂³	—	4	12	no	—
540	C₂³	—	4	16	no	—
541	C₂³	—	13	12	no	—
542	C₂³	—	13	2	no	—
543	C₂³	—	13	4	no	—
544	C₂³	—	13	2	no	—
545	C₂³	—	13	6	no	—
546	C₂³	—	26	24	no	—
547	C₂³	—	26	48	no	—
548	C₂³	—	26	48	no	—
549	C₂³	—	26	24	no	—
550	C₂³	—	26	6	no	—
551	C₂³	—	26	12	no	—
552	C₂³	—	26	12	no	—
553	C₂³	—	26	6	no	—
554	C₂³	—	52	24	no	—
555	C₂³	—	52	12	no	—
556	C₂³	—	52	32	no	—
557	C₂³	—	52	16	no	—
558	C₂³	—	52	48	no	—
559	C₂³	—	52	128	no	—
560	C₂³	—	52	32	no	—
561	C₂³	—	52	16	no	—
562	C₂³	C₂⁴×D₁₃	1	4	yes	—
563	C₂³	C₂⁴×D₁₃	1	2	yes	—
564	C₂³	C₂⁴×D₁₃	1	6	yes	—
565	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
566	D₄	—	4	24	no	—
567	D₄	—	4	12	no	—
568	D₄	—	4	12	no	—
569	D₄	—	52	24	no	—
570	D₄	—	52	12	no	—
571	D₄	—	52	12	no	—
572	D₄	—	52	24	no	—
573	D₄	—	52	24	no	—
574	D₄	—	52	12	no	—
575	D₄	—	52	24	no	—
576	D₄	—	52	12	no	—
577	C₂×C₄	—	2	12	no	—
578	C₂×C₄	—	2	6	no	—
579	C₂×C₄	—	4	12	no	—
580	C₂×C₄	—	13	6	no	—
581	C₂×C₄	—	13	12	no	—
582	C₂×C₄	—	26	48	no	—
583	C₂×C₄	—	26	24	no	—
584	C₂×C₄	—	26	12	no	—
585	C₂×C₄	—	26	6	no	—
586	C₂×C₄	—	52	24	no	—
587	C₂×C₄	—	52	12	no	—
588	C₂×C₄	C₂⁴×D₁₃	1	6	yes	—
589	C₂×C₄	C₂⁴×D₁₃	1	12	yes	—
590	C₂²	—	2	6	no	—
591	C₂²	—	2	12	no	—
592	C₂²	—	2	12	no	—
593	C₂²	—	2	6	no	—
594	C₂²	—	4	16	no	—
595	C₂²	—	4	8	no	—
596	C₂²	—	4	4	no	—
597	C₂²	—	4	12	no	—
598	C₂²	—	13	12	no	—
599	C₂²	—	13	16	no	—
600	C₂²	—	26	6	no	—
601	C₂²	—	26	12	no	—
602	C₂²	—	26	12	no	—
603	C₂²	—	26	6	no	—
604	C₂²	—	52	48	no	—
605	C₂²	—	52	32	no	—
606	C₂²	—	52	16	no	—
607	C₂²	—	52	32	no	—
608	C₂²	—	52	16	no	—
609	C₂²	—	52	12	no	—
610	C₂²	—	52	8	no	—
611	C₂²	—	52	4	no	—
612	C₂²	D₁₃×H(5,𝔽₂)	1	6	yes	—
613	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
614	C₄	—	2	12	no	—
615	C₄	—	2	6	no	—
616	C₄	—	26	12	no	—
617	C₄	—	26	6	no	—
618	C₂	—	4	4	no	—
619	C₂	—	4	2	no	—
620	C₂	—	4	6	no	—
621	C₂	—	13	8	no	—
622	C₂	—	52	4	no	—
623	C₂	—	52	2	no	—
624	C₂	—	52	6	no	—
625	C₂	D₁₃×#560	1	4	yes	direct product factor
626	C₂	C₂×D₁₃×H(5,𝔽₂)	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#560	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#560	D₁₃
hypocenter	C₁₃	C₂²×#560
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#560

Complements

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

N	H ≅ G/N	type
1. C₂×#11719416	C₂	semidirect
2. C₂×#11719371	C₂	semidirect
3. C₂×#11719300	C₂	semidirect
4. C₂×#11719325	C₂	semidirect
5. C₂×#11719425	C₂	semidirect
6. D₁₃×#560	C₂	direct (N × H)
7. C₂×D₁₃×#127	C₂	semidirect
8. C₂×D₁₃×#126	C₂	semidirect
9. C₂×D₁₃×#123	C₂	semidirect
10. C₂×D₁₃×#121	C₂	semidirect
11. C₂×D₁₃×#120	C₂	semidirect
12. C₂×C₁₃×#560	C₂	semidirect
16. C₂²×D₄×D₁₃	C₂²	semidirect
17. C₂³×C₄×D₁₃	C₂²	semidirect
18. C₁₃×#560	C₂²	semidirect
19. C₂×C₁₃×#127	C₂²	semidirect
20. C₂×C₁₃×#126	C₂²	semidirect
21. C₂×C₁₃×#123	C₂²	semidirect
22. C₂×C₁₃×#121	C₂²	semidirect
23. C₂×C₁₃×#120	C₂²	semidirect
24. C₂×#88207	C₂²	semidirect
25. C₂×#88194	C₂²	semidirect
26. C₂×#88194	C₂²	semidirect
27. C₂×#88193	C₂²	semidirect
28. C₂×#88193	C₂²	semidirect
29. C₂×#88192	C₂²	semidirect
30. C₂×#88191	C₂²	semidirect
31. C₂×#88191	C₂²	semidirect
32. C₂×#88189	C₂²	semidirect
33. C₂×#88184	C₂²	semidirect
34. C₂×#88183	C₂²	semidirect
35. #11719425	C₂²	semidirect
36. D₁₃×#127	C₂²	semidirect
37. #11719416	C₂²	semidirect
38. D₁₃×#126	C₂²	semidirect
39. #11719371	C₂²	semidirect
40. D₁₃×#123	C₂²	semidirect
41. #11719325	C₂²	semidirect
42. D₁₃×#121	C₂²	semidirect
43. #11719300	C₂²	semidirect
44. D₁₃×#120	C₂²	semidirect
45. C₂×#88152	C₂²	semidirect
46. C₂×#88149	C₂²	semidirect
47. C₂×#88148	C₂²	semidirect
48. C₂×C₄⋊C₄×D₁₃	C₂²	semidirect
49. C₂×#88140	C₂²	semidirect
50. C₂×#88138	C₂²	semidirect
51. C₂×#88138	C₂²	semidirect
52. C₂×#88137	C₂²	semidirect
53. C₂×#88136	C₂²	semidirect
54. C₂×#88136	C₂²	semidirect
57. C₂×C₂²⋊C₄×D₁₃	C₂²	semidirect
58. C₂×#88133	C₂²	semidirect
59. C₂×#88130	C₂²	semidirect
60. C₂×#88128	C₂²	semidirect
61. C₂×C₄²×D₁₃	C₂²	semidirect
72. C₂²×D₄×C₁₃	C₂³	semidirect
73. C₂³×C₄×C₁₃	C₂³	semidirect
78. C₂²×C₂²⋊D₁₃	C₂³	semidirect
79. C₂³×Dic₁₃	C₂³	semidirect
85. C₂×D₄×D₁₃	C₂³	semidirect
88. C₂²×D₅₂	C₂³	semidirect
92. C₂²×C₄×D₁₃	C₂³	semidirect
93. C₂²×C₄×D₁₃	C₂³	semidirect
94. C₁₃×#127	C₂³	semidirect
95. C₁₃×#126	C₂³	semidirect
96. C₁₃×#123	C₂³	semidirect
97. C₁₃×#121	C₂³	semidirect
98. C₁₃×#120	C₂³	semidirect
99. C₂×C₁₃×C₄⋊C₄	C₂³	semidirect
102. C₂×C₁₃×C₂²⋊C₄	C₂³	semidirect
103. C₂×C₄²×C₁₃	C₂³	semidirect
104. #88207	C₂³	semidirect
107. C₂×C₂²⋊Dic₁₃	C₂³	semidirect
108. #88194	C₂³	semidirect
109. #88194	C₂³	semidirect
110. #88193	C₂³	semidirect
111. #88193	C₂³	semidirect
112. #88192	C₂³	semidirect
113. #88191	C₂³	semidirect
114. #88191	C₂³	semidirect
115. #88189	C₂³	semidirect
116. #88184	C₂³	semidirect
117. #88183	C₂³	semidirect
121. C₂×#6103	C₂³	semidirect
122. C₂×C₄⋊Dic₁₃	C₂³	semidirect
123. C₂×#6101	C₂³	semidirect
124. C₂×#6101	C₂³	semidirect
125. C₂×C₄×Dic₁₃	C₂³	semidirect
126. #88152	C₂³	semidirect
127. #88149	C₂³	semidirect
128. #88148	C₂³	semidirect
129. C₄⋊C₄×D₁₃	C₂³	semidirect
130. #88140	C₂³	semidirect
131. #88138	C₂³	semidirect
132. #88138	C₂³	semidirect
133. #88137	C₂³	semidirect
134. #88136	C₂³	semidirect
135. #88136	C₂³	semidirect
138. C₂²⋊C₄×D₁₃	C₂³	semidirect
139. #88133	C₂³	semidirect
140. #88130	C₂³	semidirect
141. #88128	C₂³	semidirect
142. C₄²×D₁₃	C₂³	semidirect
171. C₂×D₄×C₁₃	C₂⁴	semidirect
175. C₂²×C₄×C₁₃	C₂⁴	semidirect
185. C₂×C₂²⋊D₁₃	C₂⁴	semidirect
189. C₂²×Dic₁₃	C₂⁴	semidirect
198. C₂×D₅₂	C₂⁴	semidirect
205. C₂×C₄×D₁₃	C₂⁴	semidirect
206. C₁₃×C₄⋊C₄	C₂⁴	semidirect
209. C₁₃×C₂²⋊C₄	C₂⁴	semidirect
210. C₄²×C₁₃	C₂⁴	semidirect
213. C₂²⋊Dic₁₃	C₂⁴	semidirect
217. #6103	C₂⁴	semidirect
218. C₄⋊Dic₁₃	C₂⁴	semidirect
219. #6101	C₂⁴	semidirect
220. #6101	C₂⁴	semidirect
221. C₄×Dic₁₃	C₂⁴	semidirect
228. C₂×#560	D₁₃	direct (N × H)
299. #560	C₂×D₁₃	direct (N × H)
304. C₂×#127	C₂×D₁₃	semidirect
309. C₂×#126	C₂×D₁₃	semidirect
316. C₂×#123	C₂×D₁₃	semidirect
325. C₂×#121	C₂×D₁₃	semidirect
332. C₂×#120	C₂×D₁₃	semidirect
360. C₂×D₁₃	#560	direct (N × H)
390. C₂²×D₄	C₂²×D₁₃	semidirect
397. C₂³×C₄	C₂²×D₁₃	semidirect
401. #127	C₂²×D₁₃	semidirect
405. #126	C₂²×D₁₃	semidirect
411. #123	C₂²×D₁₃	semidirect
419. #121	C₂²×D₁₃	semidirect
425. #120	C₂²×D₁₃	semidirect
430. C₂×C₄⋊C₄	C₂²×D₁₃	semidirect
443. C₂×C₂²⋊C₄	C₂²×D₁₃	semidirect
446. C₂×C₄²	C₂²×D₁₃	semidirect
450. C₂×C₁₃	C₂×#560	semidirect
455. D₁₃	C₂×#560	direct (N × H)
502. C₂×D₄	C₂³×D₁₃	semidirect
517. C₂²×C₄	C₂³×D₁₃	semidirect
521. C₄⋊C₄	C₂³×D₁₃	semidirect
531. C₂²⋊C₄	C₂³×D₁₃	semidirect
533. C₄²	C₂³×D₁₃	semidirect
534. C₁₃	C₂²×#560	semidirect
625. C₂	D₁₃×#560	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×#11719416	2
C₂×#11719371	2
C₂×#11719300	2
C₂×#11719325	2
C₂×#11719425	2
D₁₃×#560	2
C₂×D₁₃×#127	2
C₂×D₁₃×#126	2
C₂×D₁₃×#123	2
C₂×D₁₃×#121	2
C₂×D₁₃×#120	2
C₂×C₁₃×#560	2
C₂²×#560	13

Subgroups — C2×D13×#560 #16769784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×#560 #16769784