Subgroups — C₁₃×#21992 #15708331

Order 3328.

762 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#433	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2317	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2314	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1847	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1834	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#433	C₄	1	8	yes	complemented
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#389	—	2	1	no	—
35	C₁₃×#389	—	2	1	no	—
36	C₁₃×#388	—	2	1	no	—
37	C₁₃×#388	—	2	1	no	—
38	C₁₃×#387	—	2	1	no	—
39	C₁₃×#387	—	2	1	no	—
40	C₁₃×#385	—	2	1	no	—
41	C₁₃×#385	—	2	1	no	—
42	C₁₃×#384	C₂²	1	1	yes	characteristic
43	C₁₃×#384	C₂²	1	1	yes	characteristic
44	C₁₃×#384	C₂²	1	1	yes	characteristic
45	C₁₃×#382	C₂²	1	1	yes	characteristic
46	C₁₃×#382	C₂²	1	1	yes	characteristic
47	C₁₃×#382	C₂²	1	1	yes	characteristic
48	C₁₃×#380	C₂²	1	1	yes	characteristic
49	C₁₃×#380	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#340	C₂²	1	1	yes	characteristic
60	C₂³×C₄×C₁₃	—	2	1	no	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₁₃×#117	—	4	1	no	—
67	C₁₃×#117	—	4	1	no	—
68	C₁₃×#117	C₂×C₄	1	4	yes	—
69	C₁₃×#117	Q₈	1	4	yes	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
79	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
93	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₁₃×#107	—	4	1	no	—
100	C₁₃×#107	—	4	1	no	—
101	C₁₃×#107	—	4	1	no	—
102	C₁₃×#107	—	4	1	no	—
103	C₁₃×#106	—	4	1	no	—
104	C₁₃×#106	—	4	1	no	—
105	C₁₃×#106	—	4	1	no	—
106	C₁₃×#106	—	4	1	no	—
107	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
108	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	complemented
109	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
110	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
111	C₁₃×#97	C₂×C₄	1	4	yes	complemented
112	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	#21992	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	8	1	no	—
139	C₂²×C₄×C₁₃	—	8	1	no	—
140	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₂×C₈×C₁₃	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
157	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
158	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
159	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	4	2	no	—
177	C₁₃×C₄⋊C₄	—	8	1	no	—
178	C₁₃×C₄⋊C₄	—	8	1	no	—
179	C₁₃×C₄⋊C₄	—	8	1	no	—
180	C₁₃×C₄⋊C₄	—	8	1	no	—
181	C₁₃×C₄⋊C₄	—	8	1	no	—
182	C₁₃×C₄⋊C₄	—	8	1	no	—
183	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
184	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
185	C₁₃×C₂²⋊C₄	—	4	2	no	—
186	C₁₃×C₂²⋊C₄	—	8	1	no	—
187	C₁₃×C₂²⋊C₄	—	8	1	no	—
188	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
189	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	4	yes	—
190	C₄²×C₁₃	—	4	2	no	—
191	C₄²×C₁₃	—	8	1	no	—
192	C₄²×C₁₃	—	8	1	no	—
193	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
194	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
195	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
196	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
197	C₂×#433	C₂×C₁₃	1	1	yes	characteristic
198	#2317	C₂×C₁₃	1	1	yes	characteristic
199	#2314	C₂×C₁₃	1	1	yes	characteristic
200	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
204	#1854	C₂×C₁₃	1	1	yes	characteristic
205	#1854	C₂×C₁₃	1	1	yes	characteristic
206	#1853	C₂×C₁₃	1	1	yes	characteristic
207	#1852	C₂×C₁₃	1	1	yes	characteristic
208	#1847	C₂×C₁₃	1	1	yes	characteristic, complemented
209	#1846	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1836	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1834	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₂³×C₁₃	—	2	1	no	—
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	1	no	—
215	C₂³×C₁₃	—	2	1	no	—
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	2	1	no	—
218	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
219	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	8	4	no	—
259	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
260	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
261	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
262	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
263	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
264	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
266	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
267	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
268	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
269	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
270	C₈×C₁₃	—	2	2	no	—
271	C₈×C₁₃	—	2	2	no	—
272	C₈×C₁₃	—	2	2	no	—
273	C₈×C₁₃	—	2	2	no	—
274	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
276	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
277	#433	C₄×C₁₃	1	8	yes	complemented
278	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
292	#389	—	2	1	no	—
293	#389	—	2	1	no	—
294	#388	—	2	1	no	—
295	#388	—	2	1	no	—
296	#387	—	2	1	no	—
297	#387	—	2	1	no	—
298	#385	—	2	1	no	—
299	#385	—	2	1	no	—
300	#384	C₂²×C₁₃	1	1	yes	characteristic
301	#384	C₂²×C₁₃	1	1	yes	characteristic
302	#384	C₂²×C₁₃	1	1	yes	characteristic
303	#382	C₂²×C₁₃	1	1	yes	characteristic
304	#382	C₂²×C₁₃	1	1	yes	characteristic
305	#382	C₂²×C₁₃	1	1	yes	characteristic
306	#380	C₂²×C₁₃	1	1	yes	characteristic
307	#380	C₂²×C₁₃	1	1	yes	characteristic
308	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
309	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
310	#340	C₂²×C₁₃	1	1	yes	characteristic
311	#340	C₂²×C₁₃	1	1	yes	characteristic
312	#340	C₂²×C₁₃	1	1	yes	characteristic
313	#340	C₂²×C₁₃	1	1	yes	characteristic
314	#340	C₂²×C₁₃	1	1	yes	characteristic
315	#340	C₂²×C₁₃	1	1	yes	characteristic
316	#340	C₂²×C₁₃	1	1	yes	characteristic
317	#340	C₂²×C₁₃	1	1	yes	characteristic
318	C₂²×C₁₃	—	2	2	no	—
319	C₂²×C₁₃	—	2	2	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
326	C₂²×C₁₃	#535	1	1	yes	characteristic
327	C₂²×C₁₃	#536	1	1	yes	characteristic
328	C₂²×C₁₃	#576	1	1	yes	characteristic
329	C₂²×C₁₃	#577	1	1	yes	characteristic
330	C₂²×C₁₃	#577	1	1	yes	characteristic
331	C₂²×C₁₃	#578	1	1	yes	characteristic
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	8	1	no	—
338	C₄×C₁₃	—	8	1	no	—
339	C₄×C₁₃	—	8	1	no	—
340	C₄×C₁₃	—	8	1	no	—
341	C₄×C₁₃	—	8	1	no	—
342	C₄×C₁₃	—	8	1	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	#520	1	1	yes	characteristic
346	C₄×C₁₃	#520	1	1	yes	characteristic
347	C₄×C₁₃	#544	1	1	yes	characteristic
348	C₄×C₁₃	#544	1	1	yes	characteristic
349	C₂³×C₄	—	2	1	no	—
350	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
352	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
355	#117	—	4	1	no	—
356	#117	—	4	1	no	—
357	#117	C₂×C₄×C₁₃	1	4	yes	—
358	#117	Q₈×C₁₃	1	4	yes	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	4	1	no	—
367	C₂×C₄⋊C₄	—	4	1	no	—
368	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
387	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
388	#107	—	4	1	no	—
389	#107	—	4	1	no	—
390	#107	—	4	1	no	—
391	#107	—	4	1	no	—
392	#106	—	4	1	no	—
393	#106	—	4	1	no	—
394	#106	—	4	1	no	—
395	#106	—	4	1	no	—
396	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
397	C₄⋊C₈	C₂×C₄×C₁₃	1	4	yes	complemented
398	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
399	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
400	#97	C₂×C₄×C₁₃	1	4	yes	complemented
401	C₄×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
402	#95	—	2	1	no	—
403	#95	—	2	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	C₂×C₁₃	—	4	2	no	—
413	C₂×C₁₃	#2317	1	1	yes	characteristic
414	C₂×C₁₃	#2912	1	1	yes	characteristic
415	C₂×C₁₃	#2913	1	1	yes	characteristic
416	C₂×C₁₃	#3224	1	1	yes	characteristic
417	C₂×C₁₃	#3225	1	1	yes	characteristic
418	C₂×C₁₃	#3241	1	1	yes	characteristic
419	C₂×C₁₃	#3242	1	1	yes	characteristic
420	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	1	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	8	1	no	—
435	C₂²×C₄	—	8	1	no	—
436	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
453	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
454	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
455	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	4	2	no	—
473	C₄⋊C₄	—	8	1	no	—
474	C₄⋊C₄	—	8	1	no	—
475	C₄⋊C₄	—	8	1	no	—
476	C₄⋊C₄	—	8	1	no	—
477	C₄⋊C₄	—	8	1	no	—
478	C₄⋊C₄	—	8	1	no	—
479	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
480	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
481	C₂²⋊C₄	—	4	2	no	—
482	C₂²⋊C₄	—	8	1	no	—
483	C₂²⋊C₄	—	8	1	no	—
484	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
485	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
486	C₄²	—	4	2	no	—
487	C₄²	—	8	1	no	—
488	C₄²	—	8	1	no	—
489	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
490	C₄²	C₂²×C₄×C₁₃	1	2	yes	—
491	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
492	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
493	C₁₃	#21992	1	1	yes	characteristic, direct product factor, Sylow
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
501	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	8	4	no	—
541	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
542	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
543	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
544	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
545	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
546	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
547	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
548	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
549	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
551	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
552	C₈	—	2	2	no	—
553	C₈	—	2	2	no	—
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
564	C₂²	C₁₃×#535	1	1	yes	characteristic
565	C₂²	C₁₃×#536	1	1	yes	characteristic
566	C₂²	C₁₃×#576	1	1	yes	characteristic
567	C₂²	C₁₃×#577	1	1	yes	characteristic
568	C₂²	C₁₃×#577	1	1	yes	characteristic
569	C₂²	C₁₃×#578	1	1	yes	characteristic
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	2	2	no	—
575	C₄	—	8	1	no	—
576	C₄	—	8	1	no	—
577	C₄	—	8	1	no	—
578	C₄	—	8	1	no	—
579	C₄	—	8	1	no	—
580	C₄	—	8	1	no	—
581	C₄	—	8	1	no	—
582	C₄	—	8	1	no	—
583	C₄	C₁₃×#520	1	1	yes	characteristic
584	C₄	C₁₃×#520	1	1	yes	characteristic
585	C₄	C₁₃×#544	1	1	yes	characteristic
586	C₄	C₁₃×#544	1	1	yes	characteristic
587	C₂	—	4	2	no	—
588	C₂	C₁₃×#2317	1	1	yes	characteristic
589	C₂	C₁₃×#2912	1	1	yes	characteristic
590	C₂	C₁₃×#2913	1	1	yes	characteristic
591	C₂	C₁₃×#3224	1	1	yes	characteristic
592	C₂	C₁₃×#3225	1	1	yes	characteristic
593	C₂	C₁₃×#3241	1	1	yes	characteristic
594	C₂	C₁₃×#3242	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₁₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₃×#1949	C₂	semidirect
5. C₁₃×#1949	C₂	semidirect
6. C₁₃×#1948	C₂	semidirect
7. C₁₃×#1947	C₂	semidirect
12. C₁₃×#1847	C₂	semidirect
13. C₁₃×#1846	C₂	semidirect
14. C₁₃×#1836	C₂	semidirect
15. C₁₃×#1834	C₂	semidirect
19. C₁₃×#433	C₄	semidirect
107. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
108. C₁₃×C₄⋊C₈	C₂×C₄	semidirect
111. C₁₃×#97	C₂×C₄	semidirect
112. C₄×C₈×C₁₃	C₂×C₄	semidirect
123. #21992	C₁₃	direct (N × H)
200. #1949	C₂×C₁₃	semidirect
201. #1949	C₂×C₁₃	semidirect
202. #1948	C₂×C₁₃	semidirect
203. #1947	C₂×C₁₃	semidirect
208. #1847	C₂×C₁₃	semidirect
209. #1846	C₂×C₁₃	semidirect
210. #1836	C₂×C₁₃	semidirect
211. #1834	C₂×C₁₃	semidirect
277. #433	C₄×C₁₃	semidirect
396. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
397. C₄⋊C₈	C₂×C₄×C₁₃	semidirect
400. #97	C₂×C₄×C₁₃	semidirect
401. C₄×C₈	C₂×C₄×C₁₃	semidirect
493. C₁₃	#21992	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×#433	2
C₁₃×#2317	2
C₁₃×#2314	2
C₁₃×#1949	2
C₁₃×#1948	2
C₁₃×#1947	2
C₁₃×#1854	2
C₁₃×#1853	2
C₁₃×#1852	2
C₁₃×#1847	2
C₁₃×#1846	2
C₁₃×#1836	2
C₁₃×#1834	2
#21992	13

Subgroups — C13×#21992 #15708331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21992 #15708331