Subgroups — C₁₃×#14441 #15700780

Order 3328.

1390 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#389	C₂	1	2	yes	maximal
2	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#387	C₂	1	2	yes	maximal
4	C₁₃×#1444	C₂	1	2	yes	maximal
5	C₁₃×#1441	C₂	1	2	yes	maximal
6	C₁₃×#1441	C₂	1	2	yes	maximal
7	C₁₃×#1436	C₂	1	2	yes	maximal
8	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
11	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
20	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#389	—	2	8	no	—
22	C₁₃×#389	C₄	1	8	yes	complemented
23	C₁₃×#387	—	2	8	no	—
24	C₂×C₁₃×#95	C₂²	1	2	yes	—
25	C₂×C₁₃×#95	C₂²	1	2	yes	—
26	C₂×C₁₃×#95	C₂²	1	2	yes	—
27	C₂×C₁₃×#95	C₂²	1	2	yes	—
28	C₂×C₁₃×#95	C₂²	1	2	yes	—
29	C₂×C₁₃×#95	C₂²	1	2	yes	—
30	C₂×C₁₃×#95	C₂²	1	2	yes	—
31	C₂×C₁₃×#95	C₂²	1	2	yes	—
32	C₂×C₁₃×#95	C₂²	1	2	yes	—
33	C₂×C₁₃×#95	C₂²	1	2	yes	—
34	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
35	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
36	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
37	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
39	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
43	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
44	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
45	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
46	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
47	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
48	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
49	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
50	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
51	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
52	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
53	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
54	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
66	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
68	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
69	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
70	C₂×C₄²×C₁₃	—	2	4	no	—
71	C₂×C₄²×C₁₃	—	2	4	no	—
72	C₂×C₄²×C₁₃	—	4	1	no	—
73	C₂×C₄²×C₁₃	—	4	1	no	—
74	C₂×C₄²×C₁₃	—	4	2	no	—
75	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
76	C₁₃×#95	—	2	4	no	—
77	C₁₃×#95	—	2	4	no	—
78	C₁₃×#95	—	2	4	no	—
79	C₁₃×#95	—	2	4	no	—
80	C₁₃×#95	—	2	4	no	—
81	C₁₃×#95	—	2	4	no	—
82	C₁₃×#95	—	2	4	no	—
83	C₁₃×#95	—	4	2	no	—
84	C₁₃×#95	—	4	2	no	—
85	C₁₃×#95	C₂×C₄	1	8	yes	—
86	#14441	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	—	2	2	no	—
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	1	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	no	—
95	C₂²×C₄×C₁₃	—	2	1	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	1	no	—
98	C₂²×C₄×C₁₃	—	2	1	no	—
99	C₂²×C₄×C₁₃	—	2	1	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	2	no	—
118	C₂²×C₄×C₁₃	—	2	2	no	—
119	C₂²×C₄×C₁₃	—	2	2	no	—
120	C₂²×C₄×C₁₃	—	2	2	no	—
121	C₂²×C₄×C₁₃	—	2	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	2	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
137	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
138	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
139	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
140	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
148	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
149	C₂²×C₄×C₁₃	#41	1	2	yes	—
150	C₂²×C₄×C₁₃	#41	1	2	yes	—
151	C₁₃×C₄⋊C₄	—	2	16	no	—
152	C₁₃×C₄⋊C₄	—	4	4	no	—
153	C₁₃×C₄⋊C₄	—	4	4	no	—
154	C₁₃×C₄⋊C₄	—	4	4	no	—
155	C₁₃×C₄⋊C₄	—	4	8	no	—
156	C₁₃×C₄⋊C₄	—	4	4	no	—
157	C₁₃×C₄⋊C₄	—	4	4	no	—
158	C₁₃×C₄⋊C₄	—	4	8	no	—
159	C₁₃×C₄⋊C₄	C₄⋊C₄	1	16	yes	complemented
160	C₄²×C₁₃	—	4	4	no	—
161	C₄²×C₁₃	—	4	8	no	—
162	C₂×#389	C₂×C₁₃	1	2	yes	—
163	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
164	C₂×#387	C₂×C₁₃	1	2	yes	—
165	#1444	C₂×C₁₃	1	2	yes	—
166	#1441	C₂×C₁₃	1	2	yes	—
167	#1441	C₂×C₁₃	1	2	yes	—
168	#1436	C₂×C₁₃	1	2	yes	—
169	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
170	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
171	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
172	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
173	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
174	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
175	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
176	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
177	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
178	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
179	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
180	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
181	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
182	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
183	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
184	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
185	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
186	C₂×C₄×C₁₃	—	2	4	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	2	2	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	4	no	—
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	—	2	2	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	2	no	—
199	C₂×C₄×C₁₃	—	2	2	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	2	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	4	no	—
209	C₂×C₄×C₁₃	—	2	4	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	4	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	2	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	4	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	—	4	2	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
246	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
247	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
248	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
249	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
250	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
251	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
252	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
254	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
258	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
259	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
260	#389	—	2	8	no	—
261	#389	C₄×C₁₃	1	8	yes	complemented
262	#387	—	2	8	no	—
263	C₂×#95	C₂²×C₁₃	1	2	yes	—
264	C₂×#95	C₂²×C₁₃	1	2	yes	—
265	C₂×#95	C₂²×C₁₃	1	2	yes	—
266	C₂×#95	C₂²×C₁₃	1	2	yes	—
267	C₂×#95	C₂²×C₁₃	1	2	yes	—
268	C₂×#95	C₂²×C₁₃	1	2	yes	—
269	C₂×#95	C₂²×C₁₃	1	2	yes	—
270	C₂×#95	C₂²×C₁₃	1	2	yes	—
271	C₂×#95	C₂²×C₁₃	1	2	yes	—
272	C₂×#95	C₂²×C₁₃	1	2	yes	—
273	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
274	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
275	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
276	C₂²×C₁₃	#518	1	1	yes	characteristic
277	C₂²×C₁₃	#519	1	1	yes	characteristic
278	C₂²×C₁₃	#520	1	1	yes	characteristic
279	C₂²×C₁₃	#520	1	1	yes	characteristic
280	C₂²×C₁₃	#534	1	1	yes	characteristic
281	C₂²×C₁₃	#537	1	1	yes	characteristic
282	C₂²×C₁₃	#537	1	1	yes	characteristic
283	C₂²×C₁₃	#537	1	1	yes	characteristic
284	C₂²×C₁₃	#538	1	1	yes	characteristic
285	C₂²×C₁₃	#538	1	1	yes	characteristic
286	C₂²×C₁₃	#539	1	1	yes	characteristic
287	C₂²×C₁₃	#539	1	1	yes	characteristic
288	C₂²×C₁₃	#543	1	1	yes	characteristic
289	C₂²×C₁₃	#544	1	1	yes	characteristic
290	C₂²×C₁₃	#544	1	1	yes	characteristic
291	C₂²×C₁₃	#544	1	1	yes	characteristic
292	C₂²×C₁₃	D₄²	1	1	yes	characteristic
293	C₂²×C₁₃	#547	1	1	yes	characteristic
294	C₂²×C₁₃	#547	1	1	yes	characteristic
295	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
296	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
297	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
298	C₂²×C₁₃	#550	1	1	yes	characteristic
299	C₂²×C₁₃	#554	1	1	yes	characteristic
300	C₂²×C₁₃	#556	1	1	yes	characteristic
301	C₂²×C₁₃	#557	1	1	yes	characteristic
302	C₂²×C₁₃	#557	1	1	yes	characteristic
303	C₂²×C₁₃	Q₈²	1	1	yes	characteristic
304	C₂²×C₁₃	#562	1	1	yes	characteristic
305	C₂²×C₁₃	#563	1	1	yes	characteristic
306	C₂²×C₁₃	#563	1	1	yes	characteristic
307	C₂²×C₁₃	#564	1	1	yes	characteristic
308	C₄×C₁₃	—	2	4	no	—
309	C₄×C₁₃	—	2	4	no	—
310	C₄×C₁₃	—	2	4	no	—
311	C₄×C₁₃	—	2	8	no	—
312	C₄×C₁₃	—	4	4	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	—	4	4	no	—
315	C₄×C₁₃	—	8	2	no	—
316	C₄×C₁₃	—	8	2	no	—
317	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
319	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
320	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
321	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
322	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
323	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	—	2	4	no	—
327	C₂×C₄⋊C₄	—	2	4	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	—	2	4	no	—
330	C₂×C₄⋊C₄	—	2	4	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	2	no	—
333	C₂×C₄⋊C₄	—	4	1	no	—
334	C₂×C₄⋊C₄	—	4	1	no	—
335	C₂×C₄⋊C₄	—	4	1	no	—
336	C₂×C₄⋊C₄	—	4	1	no	—
337	C₂×C₄⋊C₄	—	4	1	no	—
338	C₂×C₄⋊C₄	—	4	1	no	—
339	C₂×C₄⋊C₄	—	4	2	no	—
340	C₂×C₄⋊C₄	—	4	1	no	—
341	C₂×C₄⋊C₄	—	4	1	no	—
342	C₂×C₄⋊C₄	—	4	1	no	—
343	C₂×C₄⋊C₄	—	4	1	no	—
344	C₂×C₄⋊C₄	—	4	2	no	—
345	C₂×C₄⋊C₄	—	4	2	no	—
346	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
347	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
348	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
349	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
350	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
351	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
352	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
353	C₂×C₄²	—	2	4	no	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	—	4	1	no	—
356	C₂×C₄²	—	4	1	no	—
357	C₂×C₄²	—	4	2	no	—
358	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
359	#95	—	2	4	no	—
360	#95	—	2	4	no	—
361	#95	—	2	4	no	—
362	#95	—	2	4	no	—
363	#95	—	2	4	no	—
364	#95	—	2	4	no	—
365	#95	—	2	4	no	—
366	#95	—	4	2	no	—
367	#95	—	4	2	no	—
368	#95	C₂×C₄×C₁₃	1	8	yes	—
369	C₂×C₁₃	#2316	1	1	yes	characteristic
370	C₂×C₁₃	#2325	1	1	yes	characteristic
371	C₂×C₁₃	#2329	1	1	yes	characteristic
372	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
373	C₂×C₁₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
374	C₂×C₁₃	#2365	1	1	yes	characteristic
375	C₂×C₁₃	#2382	1	1	yes	characteristic
376	C₂×C₁₃	#2682	1	1	yes	characteristic
377	C₂×C₁₃	#2683	1	1	yes	characteristic
378	C₂×C₁₃	#2726	1	1	yes	characteristic
379	C₂×C₁₃	#2726	1	1	yes	characteristic
380	C₂×C₁₃	#2727	1	1	yes	characteristic
381	C₂×C₁₃	#2734	1	1	yes	characteristic
382	C₂×C₁₃	#2805	1	1	yes	characteristic
383	C₂×C₁₃	#2806	1	1	yes	characteristic
384	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
434	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
435	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
436	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
437	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
441	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
442	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
443	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
444	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
445	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
446	C₂²×C₄	C₁₃×#41	1	2	yes	—
447	C₂²×C₄	C₁₃×#41	1	2	yes	—
448	C₄⋊C₄	—	2	16	no	—
449	C₄⋊C₄	—	4	4	no	—
450	C₄⋊C₄	—	4	4	no	—
451	C₄⋊C₄	—	4	4	no	—
452	C₄⋊C₄	—	4	8	no	—
453	C₄⋊C₄	—	4	4	no	—
454	C₄⋊C₄	—	4	4	no	—
455	C₄⋊C₄	—	4	8	no	—
456	C₄⋊C₄	C₁₃×C₄⋊C₄	1	16	yes	complemented
457	C₄²	—	4	4	no	—
458	C₄²	—	4	8	no	—
459	C₁₃	#14441	1	1	yes	characteristic, direct product factor, Sylow
460	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
461	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
462	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
463	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
464	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
465	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
466	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
467	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
468	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
471	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
472	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
473	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
474	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	2	4	no	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	4	no	—
506	C₂×C₄	—	2	4	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
535	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	8	yes	—
536	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
537	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
538	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
539	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
540	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
541	C₂²	C₁₃×#518	1	1	yes	characteristic
542	C₂²	C₁₃×#519	1	1	yes	characteristic
543	C₂²	C₁₃×#520	1	1	yes	characteristic
544	C₂²	C₁₃×#520	1	1	yes	characteristic
545	C₂²	C₁₃×#534	1	1	yes	characteristic
546	C₂²	C₁₃×#537	1	1	yes	characteristic
547	C₂²	C₁₃×#537	1	1	yes	characteristic
548	C₂²	C₁₃×#537	1	1	yes	characteristic
549	C₂²	C₁₃×#538	1	1	yes	characteristic
550	C₂²	C₁₃×#538	1	1	yes	characteristic
551	C₂²	C₁₃×#539	1	1	yes	characteristic
552	C₂²	C₁₃×#539	1	1	yes	characteristic
553	C₂²	C₁₃×#543	1	1	yes	characteristic
554	C₂²	C₁₃×#544	1	1	yes	characteristic
555	C₂²	C₁₃×#544	1	1	yes	characteristic
556	C₂²	C₁₃×#544	1	1	yes	characteristic
557	C₂²	D₄²×C₁₃	1	1	yes	characteristic
558	C₂²	C₁₃×#547	1	1	yes	characteristic
559	C₂²	C₁₃×#547	1	1	yes	characteristic
560	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
561	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
562	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
563	C₂²	C₁₃×#550	1	1	yes	characteristic
564	C₂²	C₁₃×#554	1	1	yes	characteristic
565	C₂²	C₁₃×#556	1	1	yes	characteristic
566	C₂²	C₁₃×#557	1	1	yes	characteristic
567	C₂²	C₁₃×#557	1	1	yes	characteristic
568	C₂²	Q₈²×C₁₃	1	1	yes	characteristic
569	C₂²	C₁₃×#562	1	1	yes	characteristic
570	C₂²	C₁₃×#563	1	1	yes	characteristic
571	C₂²	C₁₃×#563	1	1	yes	characteristic
572	C₂²	C₁₃×#564	1	1	yes	characteristic
573	C₄	—	2	4	no	—
574	C₄	—	2	4	no	—
575	C₄	—	2	4	no	—
576	C₄	—	2	8	no	—
577	C₄	—	4	4	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	4	no	—
580	C₄	—	8	2	no	—
581	C₄	—	8	2	no	—
582	C₂	C₁₃×#2316	1	1	yes	characteristic
583	C₂	C₁₃×#2325	1	1	yes	characteristic
584	C₂	C₁₃×#2329	1	1	yes	characteristic
585	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
586	C₂	Q₈×C₁₃×C₄⋊C₄	1	1	yes	characteristic
587	C₂	C₁₃×#2365	1	1	yes	characteristic
588	C₂	C₁₃×#2382	1	1	yes	characteristic
589	C₂	C₁₃×#2682	1	1	yes	characteristic
590	C₂	C₁₃×#2683	1	1	yes	characteristic
591	C₂	C₁₃×#2726	1	1	yes	characteristic
592	C₂	C₁₃×#2726	1	1	yes	characteristic
593	C₂	C₁₃×#2727	1	1	yes	characteristic
594	C₂	C₁₃×#2734	1	1	yes	characteristic
595	C₂	C₁₃×#2805	1	1	yes	characteristic
596	C₂	C₁₃×#2806	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×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
22. C₁₃×#389	C₄	semidirect
86. #14441	C₁₃	direct (N × H)
159. C₁₃×C₄⋊C₄	C₄⋊C₄	semidirect
261. #389	C₄×C₁₃	semidirect
456. C₄⋊C₄	C₁₃×C₄⋊C₄	semidirect
459. C₁₃	#14441	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×#389	2
C₂×C₁₃×#387	2
C₁₃×#1444	2
C₁₃×#1441	2
C₁₃×#1436	2
C₁₃×C₄⋊#95	2
#14441	13

Subgroups — C13×#14441 #15700780

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14441 #15700780