Subgroups — C₁₃×#22651 #15708990

Order 3328.

992 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#436	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#424	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2293	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1851	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1850	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1798	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×M₁₆	C₂²	1	2	yes	—
13	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#117	C₂²	1	2	yes	—
16	C₁₃×#436	—	2	4	no	—
17	C₈×D₄×C₁₃	—	2	4	no	—
18	C₁₃×#424	—	2	8	no	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₁₃×#390	C₄	1	1	yes	characteristic
32	C₁₃×#390	C₄	1	1	yes	characteristic
33	C₁₃×#389	C₄	1	1	yes	characteristic
34	C₁₃×#389	C₄	1	1	yes	characteristic
35	C₁₃×#388	C₄	1	2	yes	—
36	C₁₃×#388	C₄	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₄³×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₁₃×#336	C₂²	1	1	yes	characteristic
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂×C₁₃×M₁₆	—	2	4	no	—
47	C₂×C₁₃×M₁₆	—	2	4	no	—
48	C₂×C₁₃×M₁₆	—	4	2	no	—
49	C₂²×C₈×C₁₃	—	2	4	no	—
50	C₂²×C₈×C₁₃	—	2	4	no	—
51	C₂²×C₈×C₁₃	—	4	2	no	—
52	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₄×D₄×C₁₃	D₄	1	4	yes	—
59	C₄×D₄×C₁₃	Q₈	1	4	yes	—
60	C₁₃×#117	—	2	4	no	—
61	C₁₃×#117	—	2	4	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
66	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
67	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
68	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×C₁₃×C₂²⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×C₄⋊C₈	—	2	4	no	—
81	C₁₃×C₄⋊C₈	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	4	no	—
83	C₁₃×C₄⋊C₈	—	2	2	no	—
84	C₁₃×C₄⋊C₈	—	2	2	no	—
85	C₁₃×C₄⋊C₈	—	2	2	no	—
86	C₁₃×C₄⋊C₈	—	4	2	no	—
87	C₁₃×C₄⋊C₈	D₄	1	4	yes	complemented
88	C₁₃×C₂²⋊C₈	—	2	4	no	—
89	C₁₃×C₂²⋊C₈	—	2	4	no	—
90	C₄×C₈×C₁₃	—	2	2	no	—
91	C₄×C₈×C₁₃	—	2	2	no	—
92	C₁₃×#95	C₂×C₄	1	2	yes	—
93	C₁₃×#95	C₂×C₄	1	2	yes	—
94	C₁₃×#95	C₂×C₄	1	2	yes	—
95	#22651	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
97	C₂×D₄×C₁₃	—	2	2	no	—
98	C₂×D₄×C₁₃	—	2	2	no	—
99	C₂×D₄×C₁₃	C₄⋊C₄	1	4	yes	—
100	C₂²×C₄×C₁₃	—	2	2	no	—
101	C₂²×C₄×C₁₃	—	2	2	no	—
102	C₂²×C₄×C₁₃	—	2	2	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
114	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
115	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
116	C₁₃×M₁₆	—	4	8	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	1	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	1	no	—
129	C₂×C₈×C₁₃	—	2	2	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	4	8	no	—
134	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
136	C₁₃×C₄⋊C₄	—	2	4	no	—
137	C₁₃×C₄⋊C₄	—	2	4	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	2	2	no	—
140	C₁₃×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
141	C₁₃×C₂²⋊C₄	—	2	4	no	—
142	C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₁₃×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
146	C₄²×C₁₃	—	2	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	2	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	4	1	no	—
154	C₄²×C₁₃	C₂×D₄	1	2	yes	—
155	C₄²×C₁₃	C₂×D₄	1	2	yes	—
156	C₄²×C₁₃	C₂×Q₈	1	2	yes	—
157	C₄²×C₁₃	#41	1	2	yes	—
158	C₂×#436	C₂×C₁₃	1	1	yes	characteristic
159	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
160	C₂×#424	C₂×C₁₃	1	2	yes	complemented
161	#2293	C₂×C₁₃	1	1	yes	characteristic
162	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1939	C₂×C₁₃	1	1	yes	characteristic, complemented
164	#1851	C₂×C₁₃	1	2	yes	complemented
165	#1850	C₂×C₁₃	1	2	yes	complemented
166	#1842	C₂×C₁₃	1	1	yes	characteristic, complemented
167	#1798	C₂×C₁₃	1	2	yes	complemented
168	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
176	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
177	D₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	1	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	1	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	4	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	4	no	—
191	C₂×C₄×C₁₃	—	2	4	no	—
192	C₂×C₄×C₁₃	—	2	2	no	—
193	C₂×C₄×C₁₃	—	2	2	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	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	1	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
202	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
203	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
204	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
205	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
206	C₂×C₄×C₁₃	#131	1	2	yes	—
207	C₂×C₄×C₁₃	#131	1	2	yes	—
208	C₂×C₄×C₁₃	#131	1	2	yes	—
209	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
214	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
215	C₈×C₁₃	—	2	2	no	—
216	C₈×C₁₃	—	2	2	no	—
217	C₈×C₁₃	—	4	2	no	—
218	C₈×C₁₃	—	4	2	no	—
219	C₈×C₁₃	—	4	1	no	—
220	C₈×C₁₃	—	4	1	no	—
221	C₂²×M₁₆	C₂²×C₁₃	1	2	yes	—
222	C₂³×C₈	C₂²×C₁₃	1	2	yes	—
223	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#117	C₂²×C₁₃	1	2	yes	—
225	#436	—	2	4	no	—
226	C₈×D₄	—	2	4	no	—
227	#424	—	2	8	no	—
228	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
233	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
234	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
235	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
237	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
238	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
239	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
240	#390	C₄×C₁₃	1	1	yes	characteristic
241	#390	C₄×C₁₃	1	1	yes	characteristic
242	#389	C₄×C₁₃	1	1	yes	characteristic
243	#389	C₄×C₁₃	1	1	yes	characteristic
244	#388	C₄×C₁₃	1	2	yes	—
245	#388	C₄×C₁₃	1	2	yes	—
246	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
247	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
248	C₄³	C₂²×C₁₃	1	1	yes	characteristic
249	#336	C₂²×C₁₃	1	2	yes	—
250	#336	C₂²×C₁₃	1	2	yes	—
251	#336	C₂²×C₁₃	1	1	yes	characteristic
252	#336	C₂²×C₁₃	1	1	yes	characteristic
253	C₂²×C₁₃	—	2	4	no	—
254	C₂²×C₁₃	—	2	4	no	—
255	C₂²×C₁₃	—	2	4	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
261	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂²×C₁₃	#520	1	1	yes	characteristic
263	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
264	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
265	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
266	C₂²×C₁₃	#568	1	1	yes	characteristic
267	C₄×C₁₃	—	2	4	no	—
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	2	2	no	—
270	C₄×C₁₃	—	2	2	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	#424	1	4	yes	complemented
276	C₄×C₁₃	D₄²	1	1	yes	characteristic
277	C₄×C₁₃	#547	1	1	yes	characteristic
278	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
279	C₄×C₁₃	#554	1	1	yes	characteristic
280	C₂²×D₄	C₂×C₄×C₁₃	1	1	yes	characteristic
281	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
282	C₂×M₁₆	—	2	4	no	—
283	C₂×M₁₆	—	2	4	no	—
284	C₂×M₁₆	—	4	2	no	—
285	C₂²×C₈	—	2	4	no	—
286	C₂²×C₈	—	2	4	no	—
287	C₂²×C₈	—	4	2	no	—
288	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
289	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
290	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
291	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
294	C₄×D₄	D₄×C₁₃	1	4	yes	—
295	C₄×D₄	Q₈×C₁₃	1	4	yes	—
296	#117	—	2	4	no	—
297	#117	—	2	4	no	—
298	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
300	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
303	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
305	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
306	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
307	C₂×C₂²⋊C₄	C₂×C₄×C₁₃	1	2	yes	—
308	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
309	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
310	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
311	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
312	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
313	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
315	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
316	C₄⋊C₈	—	2	4	no	—
317	C₄⋊C₈	—	2	4	no	—
318	C₄⋊C₈	—	2	4	no	—
319	C₄⋊C₈	—	2	2	no	—
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	2	2	no	—
322	C₄⋊C₈	—	4	2	no	—
323	C₄⋊C₈	D₄×C₁₃	1	4	yes	complemented
324	C₂²⋊C₈	—	2	4	no	—
325	C₂²⋊C₈	—	2	4	no	—
326	C₄×C₈	—	2	2	no	—
327	C₄×C₈	—	2	2	no	—
328	#95	C₂×C₄×C₁₃	1	2	yes	—
329	#95	C₂×C₄×C₁₃	1	2	yes	—
330	#95	C₂×C₄×C₁₃	1	2	yes	—
331	C₂×C₁₃	—	4	4	no	—
332	C₂×C₁₃	D₄×C₄⋊C₄	1	1	yes	characteristic
333	C₂×C₁₃	C₂×#424	1	1	yes	characteristic
334	C₂×C₁₃	#2906	1	1	yes	characteristic
335	C₂×C₁₃	#2931	1	1	yes	characteristic
336	C₂×C₁₃	#2935	1	1	yes	characteristic
337	C₂×C₁₃	#2993	1	1	yes	characteristic
338	C₂×C₁₃	#2994	1	1	yes	characteristic
339	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₁₃×C₄⋊C₄	1	4	yes	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
350	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
351	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
352	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
353	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
355	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
357	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
359	M₁₆	—	4	8	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	4	8	no	—
377	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	C₁₃×C₄⋊C₄	1	4	yes	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	4	2	no	—
388	C₂²⋊C₄	C₁₃×C₄⋊C₄	1	8	yes	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	2	1	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	4	1	no	—
397	C₄²	C₂×D₄×C₁₃	1	2	yes	—
398	C₄²	C₂×D₄×C₁₃	1	2	yes	—
399	C₄²	C₂×Q₈×C₁₃	1	2	yes	—
400	C₄²	C₁₃×#41	1	2	yes	—
401	C₁₃	#22651	1	1	yes	characteristic, direct product factor, Sylow
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
409	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
410	D₄	—	2	8	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
435	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
436	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	2	yes	—
437	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
438	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
439	C₂×C₄	C₁₃×#131	1	2	yes	—
440	C₂×C₄	C₁₃×#131	1	2	yes	—
441	C₂×C₄	C₁₃×#131	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
443	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
445	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
446	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
447	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
448	C₈	—	2	2	no	—
449	C₈	—	2	2	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	2	no	—
452	C₈	—	4	1	no	—
453	C₈	—	4	1	no	—
454	C₂²	—	2	4	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
462	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
463	C₂²	C₁₃×#520	1	1	yes	characteristic
464	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
465	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
466	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
467	C₂²	C₁₃×#568	1	1	yes	characteristic
468	C₄	—	2	4	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	1	no	—
476	C₄	C₁₃×#424	1	4	yes	complemented
477	C₄	D₄²×C₁₃	1	1	yes	characteristic
478	C₄	C₁₃×#547	1	1	yes	characteristic
479	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
480	C₄	C₁₃×#554	1	1	yes	characteristic
481	C₂	—	4	4	no	—
482	C₂	D₄×C₁₃×C₄⋊C₄	1	1	yes	characteristic
483	C₂	C₂×C₁₃×#424	1	1	yes	characteristic
484	C₂	C₁₃×#2906	1	1	yes	characteristic
485	C₂	C₁₃×#2931	1	1	yes	characteristic
486	C₂	C₁₃×#2935	1	1	yes	characteristic
487	C₂	C₁₃×#2993	1	1	yes	characteristic
488	C₂	C₁₃×#2994	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₃×#424	C₂	semidirect
5. C₁₃×#1939	C₂	semidirect
6. C₁₃×#1939	C₂	semidirect
7. C₁₃×#1851	C₂	semidirect
8. C₁₃×#1850	C₂	semidirect
9. C₁₃×#1842	C₂	semidirect
10. C₁₃×#1798	C₂	semidirect
11. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
87. C₁₃×C₄⋊C₈	D₄	semidirect
95. #22651	C₁₃	direct (N × H)
160. C₂×#424	C₂×C₁₃	semidirect
162. #1939	C₂×C₁₃	semidirect
163. #1939	C₂×C₁₃	semidirect
164. #1851	C₂×C₁₃	semidirect
165. #1850	C₂×C₁₃	semidirect
166. #1842	C₂×C₁₃	semidirect
167. #1798	C₂×C₁₃	semidirect
168. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
275. C₄×C₁₃	#424	semidirect
323. C₄⋊C₈	D₄×C₁₃	semidirect
401. C₁₃	#22651	direct (N × H)
476. C₄	C₁₃×#424	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#436	2
C₂×C₈×D₄×C₁₃	2
C₂×C₁₃×#424	2
C₁₃×#2293	2
C₁₃×#1939	2
C₁₃×#1851	2
C₁₃×#1850	2
C₁₃×#1842	2
C₁₃×#1798	2
C₄×C₁₃×C₄⋊C₈	2
#22651	13

Subgroups — C13×#22651 #15708990

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22651 #15708990