Subgroups — C₁₃×#36711 #15723050

Order 3328.

2422 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#123	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2848	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2694	C₂	1	8	yes	maximal, complemented
5	C₁₃×#2674	C₂	1	8	yes	maximal, complemented
6	C₁₃×#2626	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2583	C₂	1	2	yes	maximal, complemented
8	C₁₃×#2482	C₂	1	2	yes	maximal, complemented
9	C₁₃×#2482	C₂	1	2	yes	maximal, complemented
10	C₁₃×#2435	C₂	1	2	yes	maximal
11	C₁₃×#2313	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₁₃×#544	—	2	8	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	4	yes	complemented
16	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
17	C₂×C₁₃×#124	C₂²	1	4	yes	—
18	C₂×C₁₃×#123	—	2	8	no	—
19	C₂×C₁₃×#123	C₂²	1	8	yes	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
23	C₂×C₁₃×#117	C₂²	1	2	yes	—
24	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#399	C₂²	1	4	yes	complemented
30	C₁₃×#399	C₂²	1	4	yes	complemented
31	C₁₃×#399	C₂²	1	4	yes	complemented
32	C₁₃×#398	C₂²	1	4	yes	complemented
33	C₁₃×#397	C₂²	1	4	yes	complemented
34	C₁₃×#397	C₂²	1	4	yes	complemented
35	C₁₃×#396	C₂²	1	8	yes	complemented
36	C₁₃×#395	C₂²	1	4	yes	complemented
37	C₁₃×#394	C₂²	1	8	yes	—
38	C₁₃×#393	C₂²	1	4	yes	complemented
39	C₁₃×#390	C₂²	1	4	yes	—
40	C₁₃×#389	C₂²	1	8	yes	complemented
41	C₁₃×#388	C₂²	1	8	yes	complemented
42	C₁₃×#388	C₂²	1	8	yes	complemented
43	C₁₃×#387	C₂²	1	8	yes	complemented
44	C₁₃×#385	C₂²	1	4	yes	—
45	C₁₃×#385	C₂²	1	4	yes	—
46	C₁₃×#385	C₂²	1	8	yes	complemented
47	C₁₃×#381	C₂²	1	2	yes	—
48	C₁₃×#380	C₂²	1	2	yes	—
49	C₁₃×#380	C₂²	1	4	yes	complemented
50	C₁₃×#379	C₂²	1	4	yes	—
51	C₁₃×#379	C₂²	1	4	yes	—
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
53	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
54	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
55	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×D₄×C₁₃	—	2	4	no	—
58	C₂²×D₄×C₁₃	—	4	4	no	—
59	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₃	—	2	4	no	—
61	C₂³×C₄×C₁₃	—	4	4	no	—
62	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×C₄⋊Q₈	—	2	16	no	—
69	C₁₃×#125	—	2	16	no	—
70	C₁₃×#124	—	4	8	no	—
71	C₁₃×#123	—	2	32	no	—
72	C₁₃×C₂²⋊Q₈	—	2	8	no	—
73	C₁₃×C₂²⋊Q₈	—	2	8	no	—
74	C₁₃×C₂²⋊Q₈	—	4	8	no	—
75	C₁₃×#117	—	2	8	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
77	C₂×C₁₃×C₄⋊C₄	D₄	1	8	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	8	yes	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
97	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
98	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
101	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	4	yes	—
104	C₁₃×#95	C₂³	1	4	yes	—
105	C₁₃×#95	C₂³	1	8	yes	—
106	C₁₃×#95	C₂³	1	4	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	8	yes	—
109	#36711	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₂⁴×C₁₃	—	2	4	no	—
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	—	2	4	no	—
114	C₂⁴×C₁₃	—	2	4	no	—
115	C₂⁴×C₁₃	—	4	2	no	—
116	C₂⁴×C₁₃	—	4	2	no	—
117	C₂⁴×C₁₃	—	4	2	no	—
118	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
119	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
120	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×Q₈×C₁₃	—	2	4	no	—
122	C₂×Q₈×C₁₃	—	2	4	no	—
123	C₂×Q₈×C₁₃	—	4	4	no	—
124	C₂×Q₈×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	2	8	no	—
126	C₂×D₄×C₁₃	—	2	8	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	—	4	16	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	8	no	—
133	C₂²×C₄×C₁₃	—	2	8	no	—
134	C₂²×C₄×C₁₃	—	4	2	no	—
135	C₂²×C₄×C₁₃	—	4	4	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	2	no	—
139	C₂²×C₄×C₁₃	—	4	16	no	—
140	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	8	no	—
157	C₁₃×C₄⋊C₄	—	2	8	no	—
158	C₁₃×C₄⋊C₄	—	4	8	no	—
159	C₁₃×C₄⋊C₄	—	4	4	no	—
160	C₁₃×C₄⋊C₄	—	4	8	no	—
161	C₁₃×C₄⋊C₄	C₂×D₄	1	16	yes	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	16	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	2	8	no	—
168	C₁₃×C₂²⋊C₄	—	4	8	no	—
169	C₁₃×C₂²⋊C₄	—	4	8	no	—
170	C₁₃×C₂²⋊C₄	—	4	8	no	—
171	C₄²×C₁₃	—	2	8	no	—
172	C₄²×C₁₃	—	4	4	no	—
173	C₂×#544	C₂×C₁₃	1	1	yes	characteristic, complemented
174	C₂²×#123	C₂×C₁₃	1	1	yes	characteristic
175	#2848	C₂×C₁₃	1	2	yes	complemented
176	#2694	C₂×C₁₃	1	8	yes	complemented
177	#2674	C₂×C₁₃	1	8	yes	complemented
178	#2626	C₂×C₁₃	1	2	yes	complemented
179	#2583	C₂×C₁₃	1	2	yes	complemented
180	#2482	C₂×C₁₃	1	2	yes	complemented
181	#2482	C₂×C₁₃	1	2	yes	complemented
182	#2435	C₂×C₁₃	1	2	yes	—
183	#2313	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂³×C₁₃	—	2	2	no	—
185	C₂³×C₁₃	—	2	2	no	—
186	C₂³×C₁₃	—	2	8	no	—
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	4	no	—
190	C₂³×C₁₃	—	2	4	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	4	no	—
193	C₂³×C₁₃	—	2	4	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	—	4	16	no	—
196	C₂³×C₁₃	—	4	4	no	—
197	C₂³×C₁₃	—	4	4	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	—	4	4	no	—
200	C₂³×C₁₃	—	4	4	no	—
201	C₂³×C₁₃	—	8	8	no	—
202	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
203	C₂³×C₁₃	H(5,𝔽₂)	1	4	yes	—
204	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
205	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
206	Q₈×C₁₃	—	8	4	no	—
207	Q₈×C₁₃	—	8	4	no	—
208	D₄×C₁₃	—	4	16	no	—
209	C₂×C₄×C₁₃	—	2	8	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	2	no	—
216	C₂×C₄×C₁₃	—	2	2	no	—
217	C₂×C₄×C₁₃	—	2	8	no	—
218	C₂×C₄×C₁₃	—	2	8	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	8	no	—
221	C₂×C₄×C₁₃	—	2	8	no	—
222	C₂×C₄×C₁₃	—	2	8	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	—	4	4	no	—
226	C₂×C₄×C₁₃	—	4	16	no	—
227	C₂×C₄×C₁₃	—	4	4	no	—
228	C₂×C₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
230	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
231	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
232	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
233	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
234	#544	—	2	8	no	—
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
236	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
237	C₂×#124	C₂²×C₁₃	1	4	yes	—
238	C₂×#123	—	2	8	no	—
239	C₂×#123	C₂²×C₁₃	1	8	yes	—
240	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
241	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
242	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	4	yes	complemented
243	C₂×#117	C₂²×C₁₃	1	2	yes	—
244	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
245	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
248	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
249	#399	C₂²×C₁₃	1	4	yes	complemented
250	#399	C₂²×C₁₃	1	4	yes	complemented
251	#399	C₂²×C₁₃	1	4	yes	complemented
252	#398	C₂²×C₁₃	1	4	yes	complemented
253	#397	C₂²×C₁₃	1	4	yes	complemented
254	#397	C₂²×C₁₃	1	4	yes	complemented
255	#396	C₂²×C₁₃	1	8	yes	complemented
256	#395	C₂²×C₁₃	1	4	yes	complemented
257	#394	C₂²×C₁₃	1	8	yes	—
258	#393	C₂²×C₁₃	1	4	yes	complemented
259	#390	C₂²×C₁₃	1	4	yes	—
260	#389	C₂²×C₁₃	1	8	yes	complemented
261	#388	C₂²×C₁₃	1	8	yes	complemented
262	#388	C₂²×C₁₃	1	8	yes	complemented
263	#387	C₂²×C₁₃	1	8	yes	complemented
264	#385	C₂²×C₁₃	1	4	yes	—
265	#385	C₂²×C₁₃	1	4	yes	—
266	#385	C₂²×C₁₃	1	8	yes	complemented
267	#381	C₂²×C₁₃	1	2	yes	—
268	#380	C₂²×C₁₃	1	2	yes	—
269	#380	C₂²×C₁₃	1	4	yes	complemented
270	#379	C₂²×C₁₃	1	4	yes	—
271	#379	C₂²×C₁₃	1	4	yes	—
272	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	8	no	—
276	C₂²×C₁₃	—	2	4	no	—
277	C₂²×C₁₃	—	2	8	no	—
278	C₂²×C₁₃	—	4	16	no	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	4	4	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	8	no	—
286	C₂²×C₁₃	—	8	8	no	—
287	C₂²×C₁₃	#536	1	4	yes	—
288	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
289	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
290	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
291	C₂²×C₁₃	#585	1	2	yes	—
292	C₄×C₁₃	—	2	4	no	—
293	C₄×C₁₃	—	2	4	no	—
294	C₄×C₁₃	—	2	4	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	4	no	—
297	C₄×C₁₃	—	4	4	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	4	8	no	—
300	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
301	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
302	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
303	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
304	C₂²×D₄	—	2	4	no	—
305	C₂²×D₄	—	4	4	no	—
306	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
307	C₂³×C₄	—	2	4	no	—
308	C₂³×C₄	—	4	4	no	—
309	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
310	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
313	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
315	C₄⋊Q₈	—	2	16	no	—
316	#125	—	2	16	no	—
317	#124	—	4	8	no	—
318	#123	—	2	32	no	—
319	C₂²⋊Q₈	—	2	8	no	—
320	C₂²⋊Q₈	—	2	8	no	—
321	C₂²⋊Q₈	—	4	8	no	—
322	#117	—	2	8	no	—
323	C₂×C₄⋊C₄	—	2	4	no	—
324	C₂×C₄⋊C₄	D₄×C₁₃	1	8	yes	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	8	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
336	C₂×C₂²⋊C₄	—	2	4	no	—
337	C₂×C₂²⋊C₄	—	2	4	no	—
338	C₂×C₂²⋊C₄	—	2	4	no	—
339	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	8	yes	—
348	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
349	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
350	#95	C₂³×C₁₃	1	4	yes	—
351	#95	C₂³×C₁₃	1	4	yes	—
352	#95	C₂³×C₁₃	1	8	yes	—
353	#95	C₂³×C₁₃	1	4	yes	—
354	#95	C₂³×C₁₃	1	4	yes	—
355	#95	C₂³×C₁₃	1	8	yes	—
356	C₂×C₁₃	—	2	4	no	—
357	C₂×C₁₃	—	4	4	no	—
358	C₂×C₁₃	—	8	2	no	—
359	C₂×C₁₃	C₂×#536	1	1	yes	characteristic
360	C₂×C₁₃	#3484	1	1	yes	characteristic
361	C₂×C₁₃	#3487	1	1	yes	characteristic
362	C₂×C₁₃	#3535	1	4	yes	—
363	C₂⁴	—	2	2	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	2	2	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	4	2	no	—
369	C₂⁴	—	4	2	no	—
370	C₂⁴	—	4	2	no	—
371	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
372	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
373	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×D₄	—	2	8	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	4	4	no	—
381	C₂×D₄	—	4	16	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	2	8	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	4	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	16	no	—
393	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
394	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
396	C₂²×C₄	C₂⁴×C₁₃	1	8	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
403	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	4	4	no	—
412	C₄⋊C₄	—	4	8	no	—
413	C₄⋊C₄	—	4	8	no	—
414	C₄⋊C₄	C₂×D₄×C₁₃	1	16	yes	—
415	C₂²⋊C₄	—	2	8	no	—
416	C₂²⋊C₄	—	2	16	no	—
417	C₂²⋊C₄	—	2	8	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	4	8	no	—
422	C₂²⋊C₄	—	4	8	no	—
423	C₂²⋊C₄	—	4	8	no	—
424	C₄²	—	2	8	no	—
425	C₄²	—	4	4	no	—
426	C₁₃	#36711	1	1	yes	characteristic, direct product factor, Sylow
427	C₂³	—	2	2	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	8	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	4	no	—
436	C₂³	—	2	4	no	—
437	C₂³	—	2	4	no	—
438	C₂³	—	4	16	no	—
439	C₂³	—	4	4	no	—
440	C₂³	—	4	4	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	4	no	—
444	C₂³	—	8	8	no	—
445	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
446	C₂³	C₁₃×H(5,𝔽₂)	1	4	yes	—
447	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
448	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
449	Q₈	—	8	4	no	—
450	Q₈	—	8	4	no	—
451	D₄	—	4	16	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	4	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	16	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
473	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
474	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
475	C₂²	—	2	8	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	16	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	8	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	8	8	no	—
489	C₂²	C₁₃×#536	1	4	yes	—
490	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
491	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
492	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
493	C₂²	C₁₃×#585	1	2	yes	—
494	C₄	—	2	4	no	—
495	C₄	—	2	4	no	—
496	C₄	—	2	4	no	—
497	C₄	—	4	8	no	—
498	C₄	—	4	2	no	—
499	C₄	—	4	4	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	2	no	—
502	C₂	—	2	4	no	—
503	C₂	—	4	4	no	—
504	C₂	—	8	2	no	—
505	C₂	C₂×C₁₃×#536	1	1	yes	characteristic
506	C₂	C₁₃×#3484	1	1	yes	characteristic
507	C₂	C₁₃×#3487	1	1	yes	characteristic
508	C₂	C₁₃×#3535	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#544	C₂	semidirect
3. C₁₃×#2848	C₂	semidirect
4. C₁₃×#2694	C₂	semidirect
5. C₁₃×#2674	C₂	semidirect
6. C₁₃×#2626	C₂	semidirect
7. C₁₃×#2583	C₂	semidirect
8. C₁₃×#2482	C₂	semidirect
9. C₁₃×#2482	C₂	semidirect
11. C₁₃×#2313	C₂	semidirect
15. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
16. C₂×C₁₃×#125	C₂²	semidirect
22. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
29. C₁₃×#399	C₂²	semidirect
30. C₁₃×#399	C₂²	semidirect
31. C₁₃×#399	C₂²	semidirect
32. C₁₃×#398	C₂²	semidirect
33. C₁₃×#397	C₂²	semidirect
34. C₁₃×#397	C₂²	semidirect
35. C₁₃×#396	C₂²	semidirect
36. C₁₃×#395	C₂²	semidirect
38. C₁₃×#393	C₂²	semidirect
40. C₁₃×#389	C₂²	semidirect
41. C₁₃×#388	C₂²	semidirect
42. C₁₃×#388	C₂²	semidirect
43. C₁₃×#387	C₂²	semidirect
46. C₁₃×#385	C₂²	semidirect
49. C₁₃×#380	C₂²	semidirect
109. #36711	C₁₃	direct (N × H)
173. C₂×#544	C₂×C₁₃	semidirect
175. #2848	C₂×C₁₃	semidirect
176. #2694	C₂×C₁₃	semidirect
177. #2674	C₂×C₁₃	semidirect
178. #2626	C₂×C₁₃	semidirect
179. #2583	C₂×C₁₃	semidirect
180. #2482	C₂×C₁₃	semidirect
181. #2482	C₂×C₁₃	semidirect
183. #2313	C₂×C₁₃	semidirect
235. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
236. C₂×#125	C₂²×C₁₃	semidirect
242. C₂×C₂²⋊Q₈	C₂²×C₁₃	semidirect
249. #399	C₂²×C₁₃	semidirect
250. #399	C₂²×C₁₃	semidirect
251. #399	C₂²×C₁₃	semidirect
252. #398	C₂²×C₁₃	semidirect
253. #397	C₂²×C₁₃	semidirect
254. #397	C₂²×C₁₃	semidirect
255. #396	C₂²×C₁₃	semidirect
256. #395	C₂²×C₁₃	semidirect
258. #393	C₂²×C₁₃	semidirect
260. #389	C₂²×C₁₃	semidirect
261. #388	C₂²×C₁₃	semidirect
262. #388	C₂²×C₁₃	semidirect
263. #387	C₂²×C₁₃	semidirect
266. #385	C₂²×C₁₃	semidirect
269. #380	C₂²×C₁₃	semidirect
426. C₁₃	#36711	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×#544	2
C₂²×C₁₃×#123	2
C₁₃×#2848	2
C₁₃×#2694	2
C₁₃×#2674	2
C₁₃×#2626	2
C₁₃×#2583	2
C₁₃×#2482	2
C₁₃×#2435	2
C₁₃×#2313	2
#36711	13

Subgroups — C13×#36711 #15723050

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36711 #15723050