Subgroups — C₁₃×#14005 #15700344

Order 3328.

1614 conjugacy classes of subgroups.

The subgroup lattice has 692 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	1	yes	maximal, characteristic
2	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#389	C₂	1	2	yes	maximal
4	C₂×C₁₃×#389	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#384	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1444	C₂	1	2	yes	maximal
8	C₁₃×#1441	C₂	1	2	yes	maximal
9	C₁₃×#1436	C₂	1	2	yes	maximal
10	C₁₃×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#389	—	2	4	no	—
26	C₁₃×#389	—	2	4	no	—
27	C₁₃×#389	—	2	8	no	—
28	C₁₃×#389	C₄	1	8	yes	complemented
29	C₁₃×#384	—	2	4	no	—
30	C₄×C₁₃×C₄⋊C₄	—	2	4	no	—
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	C₂×C₁₃×#95	C₂²	1	2	yes	—
35	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#95	C₂²	1	2	yes	—
38	C₂×C₁₃×#95	C₂²	1	2	yes	—
39	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
41	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
42	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
52	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
71	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
72	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	8	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
77	C₂×C₁₃×C₄⋊C₄	D₄	1	4	yes	—
78	C₂×C₁₃×C₄⋊C₄	Q₈	1	4	yes	—
79	C₂×C₄²×C₁₃	—	2	2	no	—
80	C₂×C₄²×C₁₃	—	2	2	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	—	2	4	no	—
84	C₂×C₄²×C₁₃	—	2	4	no	—
85	C₂×C₄²×C₁₃	—	2	2	no	—
86	C₂×C₄²×C₁₃	—	2	2	no	—
87	C₂×C₄²×C₁₃	—	2	2	no	—
88	C₂×C₄²×C₁₃	—	4	2	no	—
89	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
90	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
91	C₁₃×#95	—	2	4	no	—
92	C₁₃×#95	—	2	4	no	—
93	C₁₃×#95	—	2	4	no	—
94	C₁₃×#95	—	2	4	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	4	2	no	—
98	C₁₃×#95	C₂×C₄	1	8	yes	—
99	C₁₃×#95	D₄	1	4	yes	—
100	C₁₃×#95	Q₈	1	4	yes	—
101	#14005	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	—	2	1	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	2	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	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	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	2	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	2	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	—	2	2	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	2	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	1	no	—
143	C₂²×C₄×C₁₃	—	2	2	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	2	no	—
154	C₂²×C₄×C₁₃	—	2	2	no	—
155	C₂²×C₄×C₁₃	—	2	2	no	—
156	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
157	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
158	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
159	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
161	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
163	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
170	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
171	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
172	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
173	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
174	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
176	C₂²×C₄×C₁₃	#41	1	2	yes	—
177	C₂²×C₄×C₁₃	#41	1	2	yes	—
178	C₂²×C₄×C₁₃	#41	1	2	yes	—
179	C₂²×C₄×C₁₃	#41	1	2	yes	—
180	C₁₃×C₄⋊C₄	—	2	16	no	—
181	C₁₃×C₄⋊C₄	—	2	8	no	—
182	C₁₃×C₄⋊C₄	—	2	8	no	—
183	C₁₃×C₄⋊C₄	—	4	8	no	—
184	C₁₃×C₄⋊C₄	—	4	8	no	—
185	C₁₃×C₄⋊C₄	—	4	8	no	—
186	C₁₃×C₄⋊C₄	—	4	8	no	—
187	C₁₃×C₄⋊C₄	—	4	4	no	—
188	C₁₃×C₄⋊C₄	C₄⋊C₄	1	16	yes	complemented
189	C₄²×C₁₃	—	2	8	no	—
190	C₄²×C₁₃	—	2	8	no	—
191	C₄²×C₁₃	—	4	8	no	—
192	C₄²×C₁₃	—	4	4	no	—
193	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
194	C₂×#389	C₂×C₁₃	1	2	yes	—
195	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
196	C₂×#389	C₂×C₁₃	1	1	yes	characteristic
197	C₂×#384	C₂×C₁₃	1	1	yes	characteristic
198	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
199	#1444	C₂×C₁₃	1	2	yes	—
200	#1441	C₂×C₁₃	1	2	yes	—
201	#1436	C₂×C₁₃	1	2	yes	—
202	C₄⋊#95	C₂×C₁₃	1	1	yes	characteristic
203	C₄×#95	C₂×C₁₃	1	1	yes	characteristic
204	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
205	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
206	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
209	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
210	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
211	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
212	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
218	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	2	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	2	no	—
224	C₂×C₄×C₁₃	—	2	2	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	2	no	—
228	C₂×C₄×C₁₃	—	2	4	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	4	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	4	no	—
244	C₂×C₄×C₁₃	—	2	4	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	4	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	4	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	2	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	2	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	2	no	—
265	C₂×C₄×C₁₃	—	4	2	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	2	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	2	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	2	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	2	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	—	4	2	no	—
280	C₂×C₄×C₁₃	—	4	2	no	—
281	C₂×C₄×C₁₃	—	4	2	no	—
282	C₂×C₄×C₁₃	—	4	2	no	—
283	C₂×C₄×C₁₃	—	4	2	no	—
284	C₂×C₄×C₁₃	—	4	2	no	—
285	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
286	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
287	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
288	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
289	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
290	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
291	C₂×C₄×C₁₃	#121	1	4	yes	—
292	C₂×C₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
293	C₂×C₄×C₁₃	#125	1	4	yes	—
294	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
295	C₂×C₄×C₁₃	C₄⋊Q₈	1	4	yes	—
296	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
298	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
299	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
300	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
301	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
303	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
305	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
306	C₂²×C₄²	C₂²×C₁₃	1	2	yes	—
307	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
308	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
309	#389	—	2	4	no	—
310	#389	—	2	4	no	—
311	#389	—	2	8	no	—
312	#389	C₄×C₁₃	1	8	yes	complemented
313	#384	—	2	4	no	—
314	C₄×C₄⋊C₄	—	2	4	no	—
315	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#95	C₂²×C₁₃	1	2	yes	—
318	C₂×#95	C₂²×C₁₃	1	2	yes	—
319	C₂×#95	C₂²×C₁₃	1	2	yes	—
320	C₂×#95	C₂²×C₁₃	1	2	yes	—
321	C₂×#95	C₂²×C₁₃	1	2	yes	—
322	C₂×#95	C₂²×C₁₃	1	2	yes	—
323	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
325	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
326	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
327	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
328	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
329	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
330	C₂²×C₁₃	#520	1	1	yes	characteristic
331	C₂²×C₁₃	#520	1	1	yes	characteristic
332	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
333	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
334	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
335	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
336	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
337	C₂²×C₁₃	#532	1	1	yes	characteristic
338	C₂²×C₁₃	#533	1	1	yes	characteristic
339	C₂²×C₁₃	#533	1	1	yes	characteristic
340	C₂²×C₁₃	#540	1	1	yes	characteristic
341	C₂²×C₁₃	#541	1	1	yes	characteristic
342	C₂²×C₁₃	#544	1	1	yes	characteristic
343	C₂²×C₁₃	#544	1	1	yes	characteristic
344	C₂²×C₁₃	D₄²	1	1	yes	characteristic
345	C₂²×C₁₃	D₄²	1	1	yes	characteristic
346	C₂²×C₁₃	#546	1	1	yes	characteristic
347	C₂²×C₁₃	#547	1	1	yes	characteristic
348	C₂²×C₁₃	#547	1	1	yes	characteristic
349	C₂²×C₁₃	#548	1	1	yes	characteristic
350	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
351	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
352	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
353	C₂²×C₁₃	#550	1	1	yes	characteristic
354	C₂²×C₁₃	#552	1	1	yes	characteristic
355	C₂²×C₁₃	#553	1	1	yes	characteristic
356	C₂²×C₁₃	#554	1	1	yes	characteristic
357	C₂²×C₁₃	#554	1	1	yes	characteristic
358	C₂²×C₁₃	#557	1	1	yes	characteristic
359	C₂²×C₁₃	Q₈²	1	1	yes	characteristic
360	C₄×C₁₃	—	2	8	no	—
361	C₄×C₁₃	—	2	4	no	—
362	C₄×C₁₃	—	2	4	no	—
363	C₄×C₁₃	—	2	4	no	—
364	C₄×C₁₃	—	4	4	no	—
365	C₄×C₁₃	—	4	4	no	—
366	C₄×C₁₃	—	4	2	no	—
367	C₄×C₁₃	—	4	2	no	—
368	C₄×C₁₃	—	4	2	no	—
369	C₄×C₁₃	—	8	2	no	—
370	C₄×C₁₃	#389	1	8	yes	complemented
371	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
372	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
373	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
377	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
378	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
379	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
380	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂×C₄⋊C₄	—	2	2	no	—
383	C₂×C₄⋊C₄	—	2	4	no	—
384	C₂×C₄⋊C₄	—	2	2	no	—
385	C₂×C₄⋊C₄	—	2	4	no	—
386	C₂×C₄⋊C₄	—	2	2	no	—
387	C₂×C₄⋊C₄	—	2	2	no	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	—	2	4	no	—
390	C₂×C₄⋊C₄	—	2	2	no	—
391	C₂×C₄⋊C₄	—	2	4	no	—
392	C₂×C₄⋊C₄	—	2	4	no	—
393	C₂×C₄⋊C₄	—	2	4	no	—
394	C₂×C₄⋊C₄	—	2	4	no	—
395	C₂×C₄⋊C₄	—	2	4	no	—
396	C₂×C₄⋊C₄	—	2	2	no	—
397	C₂×C₄⋊C₄	—	2	4	no	—
398	C₂×C₄⋊C₄	—	2	2	no	—
399	C₂×C₄⋊C₄	—	4	2	no	—
400	C₂×C₄⋊C₄	—	4	2	no	—
401	C₂×C₄⋊C₄	—	4	2	no	—
402	C₂×C₄⋊C₄	—	4	2	no	—
403	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
404	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	8	yes	—
405	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	4	yes	—
406	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
407	C₂×C₄⋊C₄	D₄×C₁₃	1	4	yes	—
408	C₂×C₄⋊C₄	Q₈×C₁₃	1	4	yes	—
409	C₂×C₄²	—	2	2	no	—
410	C₂×C₄²	—	2	2	no	—
411	C₂×C₄²	—	2	2	no	—
412	C₂×C₄²	—	2	2	no	—
413	C₂×C₄²	—	2	4	no	—
414	C₂×C₄²	—	2	4	no	—
415	C₂×C₄²	—	2	2	no	—
416	C₂×C₄²	—	2	2	no	—
417	C₂×C₄²	—	2	2	no	—
418	C₂×C₄²	—	4	2	no	—
419	C₂×C₄²	C₂×C₄×C₁₃	1	4	yes	—
420	C₂×C₄²	Q₈×C₁₃	1	4	yes	—
421	#95	—	2	4	no	—
422	#95	—	2	4	no	—
423	#95	—	2	4	no	—
424	#95	—	2	4	no	—
425	#95	—	2	2	no	—
426	#95	—	2	2	no	—
427	#95	—	4	2	no	—
428	#95	C₂×C₄×C₁₃	1	8	yes	—
429	#95	D₄×C₁₃	1	4	yes	—
430	#95	Q₈×C₁₃	1	4	yes	—
431	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
432	C₂×C₁₃	C₄×C₄⋊Q₈	1	1	yes	characteristic
433	C₂×C₁₃	#2330	1	1	yes	characteristic
434	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
435	C₂×C₁₃	Q₈×C₄⋊C₄	1	1	yes	characteristic
436	C₂×C₁₃	#2360	1	1	yes	characteristic
437	C₂×C₁₃	#2361	1	1	yes	characteristic
438	C₂×C₁₃	#2428	1	1	yes	characteristic
439	C₂×C₁₃	#2429	1	1	yes	characteristic
440	C₂×C₁₃	#2440	1	1	yes	characteristic
441	C₂×C₁₃	#2441	1	1	yes	characteristic
442	C₂×C₁₃	#2506	1	1	yes	characteristic
443	C₂×C₁₃	#2507	1	1	yes	characteristic
444	C₂×C₁₃	#2550	1	1	yes	characteristic
445	C₂×C₁₃	#2551	1	1	yes	characteristic
446	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	2	no	—
480	C₂²×C₄	—	2	2	no	—
481	C₂²×C₄	—	2	2	no	—
482	C₂²×C₄	—	2	2	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	2	no	—
485	C₂²×C₄	—	2	2	no	—
486	C₂²×C₄	—	2	1	no	—
487	C₂²×C₄	—	2	2	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	2	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	2	no	—
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	2	no	—
496	C₂²×C₄	—	2	2	no	—
497	C₂²×C₄	—	2	2	no	—
498	C₂²×C₄	—	2	2	no	—
499	C₂²×C₄	—	2	2	no	—
500	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
501	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
502	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
503	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
504	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
505	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
506	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
507	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
508	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
509	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
510	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
511	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
512	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
513	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
514	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
515	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
516	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
517	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
518	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
519	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
520	C₂²×C₄	C₁₃×#41	1	2	yes	—
521	C₂²×C₄	C₁₃×#41	1	2	yes	—
522	C₂²×C₄	C₁₃×#41	1	2	yes	—
523	C₂²×C₄	C₁₃×#41	1	2	yes	—
524	C₄⋊C₄	—	2	16	no	—
525	C₄⋊C₄	—	2	8	no	—
526	C₄⋊C₄	—	2	8	no	—
527	C₄⋊C₄	—	4	8	no	—
528	C₄⋊C₄	—	4	8	no	—
529	C₄⋊C₄	—	4	8	no	—
530	C₄⋊C₄	—	4	8	no	—
531	C₄⋊C₄	—	4	4	no	—
532	C₄⋊C₄	C₁₃×C₄⋊C₄	1	16	yes	complemented
533	C₄²	—	2	8	no	—
534	C₄²	—	2	8	no	—
535	C₄²	—	4	8	no	—
536	C₄²	—	4	4	no	—
537	C₁₃	#14005	1	1	yes	characteristic, direct product factor, Sylow
538	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
539	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
540	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
541	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
542	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
543	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
544	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
545	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
546	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
547	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
548	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
549	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
550	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
551	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
552	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	4	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	4	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	4	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	2	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	2	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	2	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	4	2	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	2	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	4	2	no	—
614	C₂×C₄	—	4	2	no	—
615	C₂×C₄	—	4	2	no	—
616	C₂×C₄	—	4	2	no	—
617	C₂×C₄	—	4	2	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	8	yes	—
620	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
621	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
622	C₂×C₄	C₄×D₄×C₁₃	1	4	yes	—
623	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
624	C₂×C₄	C₄×Q₈×C₁₃	1	4	yes	—
625	C₂×C₄	C₁₃×#121	1	4	yes	—
626	C₂×C₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
627	C₂×C₄	C₁₃×#125	1	4	yes	—
628	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
629	C₂×C₄	C₁₃×C₄⋊Q₈	1	4	yes	—
630	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
631	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
632	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
633	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
634	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
635	C₂²	C₁₃×#520	1	1	yes	characteristic
636	C₂²	C₁₃×#520	1	1	yes	characteristic
637	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
638	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
639	C₂²	C₂×C₁₃×#125	1	1	yes	characteristic
640	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
641	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
642	C₂²	C₁₃×#532	1	1	yes	characteristic
643	C₂²	C₁₃×#533	1	1	yes	characteristic
644	C₂²	C₁₃×#533	1	1	yes	characteristic
645	C₂²	C₁₃×#540	1	1	yes	characteristic
646	C₂²	C₁₃×#541	1	1	yes	characteristic
647	C₂²	C₁₃×#544	1	1	yes	characteristic
648	C₂²	C₁₃×#544	1	1	yes	characteristic
649	C₂²	D₄²×C₁₃	1	1	yes	characteristic
650	C₂²	D₄²×C₁₃	1	1	yes	characteristic
651	C₂²	C₁₃×#546	1	1	yes	characteristic
652	C₂²	C₁₃×#547	1	1	yes	characteristic
653	C₂²	C₁₃×#547	1	1	yes	characteristic
654	C₂²	C₁₃×#548	1	1	yes	characteristic
655	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
656	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
657	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
658	C₂²	C₁₃×#550	1	1	yes	characteristic
659	C₂²	C₁₃×#552	1	1	yes	characteristic
660	C₂²	C₁₃×#553	1	1	yes	characteristic
661	C₂²	C₁₃×#554	1	1	yes	characteristic
662	C₂²	C₁₃×#554	1	1	yes	characteristic
663	C₂²	C₁₃×#557	1	1	yes	characteristic
664	C₂²	Q₈²×C₁₃	1	1	yes	characteristic
665	C₄	—	2	8	no	—
666	C₄	—	2	4	no	—
667	C₄	—	2	4	no	—
668	C₄	—	2	4	no	—
669	C₄	—	4	4	no	—
670	C₄	—	4	4	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	2	no	—
673	C₄	—	4	2	no	—
674	C₄	—	8	2	no	—
675	C₄	C₁₃×#389	1	8	yes	complemented
676	C₂	C₂×C₁₃×#389	1	1	yes	characteristic
677	C₂	C₄×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
678	C₂	C₁₃×#2330	1	1	yes	characteristic
679	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
680	C₂	Q₈×C₁₃×C₄⋊C₄	1	1	yes	characteristic
681	C₂	C₁₃×#2360	1	1	yes	characteristic
682	C₂	C₁₃×#2361	1	1	yes	characteristic
683	C₂	C₁₃×#2428	1	1	yes	characteristic
684	C₂	C₁₃×#2429	1	1	yes	characteristic
685	C₂	C₁₃×#2440	1	1	yes	characteristic
686	C₂	C₁₃×#2441	1	1	yes	characteristic
687	C₂	C₁₃×#2506	1	1	yes	characteristic
688	C₂	C₁₃×#2507	1	1	yes	characteristic
689	C₂	C₁₃×#2550	1	1	yes	characteristic
690	C₂	C₁₃×#2551	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
28. C₁₃×#389	C₄	semidirect
101. #14005	C₁₃	direct (N × H)
188. C₁₃×C₄⋊C₄	C₄⋊C₄	semidirect
312. #389	C₄×C₁₃	semidirect
370. C₄×C₁₃	#389	semidirect
532. C₄⋊C₄	C₁₃×C₄⋊C₄	semidirect
537. C₁₃	#14005	direct (N × H)
675. C₄	C₁₃×#389	semidirect

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×#384	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₁₃×#1444	2
C₁₃×#1441	2
C₁₃×#1436	2
C₁₃×C₄⋊#95	2
C₄×C₁₃×#95	2
#14005	13

Subgroups — C13×#14005 #15700344

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#14005 #15700344