Subgroups — C₁₃×#22627 #15708966

Order 3328.

868 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#1940	C₂	1	2	yes	maximal, complemented
3	C₁₃×#1917	C₂	1	2	yes	maximal, complemented
4	C₁₃×#1916	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1771	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic
11	C₄×C₁₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
13	C₂²×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#97	C₂²	1	2	yes	—
25	C₂×C₁₃×#97	C₂²	1	2	yes	—
26	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	—
27	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
28	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
29	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
30	C₄×C₁₃×C₄⋊C₄	C₄	1	1	yes	characteristic
31	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#95	C₄	1	1	yes	characteristic
36	C₂×C₁₃×#95	C₄	1	1	yes	characteristic
37	C₁₃×#336	C₂²	1	2	yes	—
38	C₁₃×#336	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	2	yes	—
40	C₁₃×#336	C₂²	1	2	yes	—
41	C₁₃×#336	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
56	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₁₃	—	2	4	no	—
65	C₂×C₄²×C₁₃	—	4	2	no	—
66	C₂×C₄²×C₁₃	—	4	2	no	—
67	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	—	2	4	no	—
80	C₁₃×C₄⋊C₈	—	4	2	no	—
81	C₁₃×C₄⋊C₈	—	4	2	no	—
82	C₁₃×C₂²⋊C₈	—	2	2	no	—
83	C₁₃×C₂²⋊C₈	—	2	2	no	—
84	C₁₃×C₂²⋊C₈	—	2	2	no	—
85	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	—
86	C₁₃×#97	—	2	4	no	—
87	C₁₃×#97	—	4	2	no	—
88	C₄×C₈×C₁₃	—	4	2	no	—
89	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
90	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
91	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
92	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
93	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
94	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
95	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
96	C₁₃×#95	C₂×C₄	1	1	yes	characteristic
97	#22627	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
98	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	—	2	2	no	—
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	—	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	—	4	1	no	—
112	C₂²×C₄×C₁₃	—	4	1	no	—
113	C₂²×C₄×C₁₃	—	4	1	no	—
114	C₂²×C₄×C₁₃	—	4	1	no	—
115	C₂²×C₄×C₁₃	—	4	1	no	—
116	C₂²×C₄×C₁₃	—	4	1	no	—
117	C₂²×C₄×C₁₃	—	4	1	no	—
118	C₂²×C₄×C₁₃	M₁₆	1	4	yes	—
119	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
133	C₂²×C₄×C₁₃	#41	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	—	2	2	no	—
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	2	no	—
141	C₂×C₈×C₁₃	—	2	2	no	—
142	C₂×C₈×C₁₃	—	2	2	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	2	no	—
146	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	2	no	—
154	C₁₃×C₄⋊C₄	M₁₆	1	4	yes	—
155	C₄²×C₁₃	—	2	2	no	—
156	C₄²×C₁₃	—	2	2	no	—
157	C₄²×C₁₃	—	2	2	no	—
158	C₄²×C₁₃	—	2	2	no	—
159	C₄²×C₁₃	—	2	2	no	—
160	C₄²×C₁₃	—	2	2	no	—
161	C₄²×C₁₃	—	2	2	no	—
162	C₄²×C₁₃	—	4	1	no	—
163	C₄²×C₁₃	—	4	1	no	—
164	C₄²×C₁₃	—	4	1	no	—
165	C₄²×C₁₃	—	4	1	no	—
166	C₄²×C₁₃	#41	1	4	yes	—
167	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
168	#1940	C₂×C₁₃	1	2	yes	complemented
169	#1917	C₂×C₁₃	1	2	yes	complemented
170	#1916	C₂×C₁₃	1	2	yes	complemented
171	#1797	C₂×C₁₃	1	1	yes	characteristic
172	#1797	C₂×C₁₃	1	1	yes	characteristic
173	#1797	C₂×C₁₃	1	1	yes	characteristic
174	#1771	C₂×C₁₃	1	2	yes	complemented
175	#1749	C₂×C₁₃	1	1	yes	characteristic
176	#1749	C₂×C₁₃	1	1	yes	characteristic
177	C₄×C₂²⋊C₈	C₂×C₁₃	1	1	yes	characteristic
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
183	C₂³×C₁₃	C₂×M₁₆	1	2	yes	—
184	C₂³×C₁₃	#131	1	2	yes	—
185	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	—	2	8	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	1	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	1	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	4	no	—
204	C₂×C₄×C₁₃	—	2	4	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	4	4	no	—
221	C₂×C₄×C₁₃	—	4	4	no	—
222	C₂×C₄×C₁₃	—	4	4	no	—
223	C₂×C₄×C₁₃	—	4	4	no	—
224	C₂×C₄×C₁₃	—	4	4	no	—
225	C₂×C₄×C₁₃	#117	1	2	yes	—
226	C₂×C₄×C₁₃	#117	1	2	yes	—
227	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
228	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
229	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
230	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
231	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
232	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
233	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
237	C₈×C₁₃	—	2	4	no	—
238	C₈×C₁₃	—	4	2	no	—
239	C₈×C₁₃	—	4	2	no	—
240	C₈×C₁₃	—	4	2	no	—
241	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
243	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
244	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
247	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
249	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#97	C₂²×C₁₃	1	2	yes	—
254	C₂×#97	C₂²×C₁₃	1	2	yes	—
255	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	—
256	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
257	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
258	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
259	C₄×C₄⋊C₄	C₄×C₁₃	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#95	C₄×C₁₃	1	1	yes	characteristic
265	C₂×#95	C₄×C₁₃	1	1	yes	characteristic
266	#336	C₂²×C₁₃	1	2	yes	—
267	#336	C₂²×C₁₃	1	2	yes	—
268	#336	C₂²×C₁₃	1	2	yes	—
269	#336	C₂²×C₁₃	1	2	yes	—
270	#336	C₂²×C₁₃	1	2	yes	—
271	#336	C₂²×C₁₃	1	2	yes	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	2	2	no	—
276	C₂²×C₁₃	—	2	2	no	—
277	C₂²×C₁₃	—	2	2	no	—
278	C₂²×C₁₃	#446	1	4	yes	—
279	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
280	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
281	C₂²×C₁₃	#518	1	1	yes	characteristic
282	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
283	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
284	C₂²×C₁₃	C₂×#131	1	1	yes	characteristic
285	C₂²×C₁₃	#568	1	1	yes	characteristic
286	C₄×C₁₃	—	2	2	no	—
287	C₄×C₁₃	—	2	2	no	—
288	C₄×C₁₃	—	2	2	no	—
289	C₄×C₁₃	—	2	2	no	—
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	2	2	no	—
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	—	4	1	no	—
296	C₄×C₁₃	—	4	1	no	—
297	C₄×C₁₃	—	4	1	no	—
298	C₄×C₁₃	—	4	1	no	—
299	C₄×C₁₃	#553	1	2	yes	—
300	C₄×C₁₃	#554	1	2	yes	—
301	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
302	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
303	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
304	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
306	C₂³×C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
309	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
310	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
311	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	4	no	—
314	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
316	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂×C₄×C₁₃	1	1	yes	characteristic
322	C₂×C₄²	—	2	4	no	—
323	C₂×C₄²	—	4	2	no	—
324	C₂×C₄²	—	4	2	no	—
325	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
328	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
329	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
330	C₂×C₄²	C₂×C₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
332	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
336	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
337	C₄⋊C₈	—	2	4	no	—
338	C₄⋊C₈	—	4	2	no	—
339	C₄⋊C₈	—	4	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	C₂²⋊C₈	—	2	2	no	—
342	C₂²⋊C₈	—	2	2	no	—
343	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	—
344	#97	—	2	4	no	—
345	#97	—	4	2	no	—
346	C₄×C₈	—	4	2	no	—
347	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
348	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
349	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
350	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
351	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
352	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
353	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
354	#95	C₂×C₄×C₁₃	1	1	yes	characteristic
355	C₂×C₁₃	—	2	4	no	—
356	C₂×C₁₃	#2345	1	1	yes	characteristic
357	C₂×C₁₃	#2920	1	1	yes	characteristic
358	C₂×C₁₃	#2924	1	1	yes	characteristic
359	C₂×C₁₃	C₂×#446	1	1	yes	characteristic
360	C₂×C₁₃	Q₈×M₁₆	1	1	yes	characteristic
361	C₂×C₁₃	#2973	1	1	yes	characteristic
362	C₂×C₁₃	#2974	1	1	yes	characteristic
363	C₂⁴	C₂²×C₄×C₁₃	1	1	yes	characteristic
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	1	no	—
377	C₂²×C₄	—	4	1	no	—
378	C₂²×C₄	—	4	1	no	—
379	C₂²×C₄	—	4	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	—	4	1	no	—
382	C₂²×C₄	—	4	1	no	—
383	C₂²×C₄	C₁₃×M₁₆	1	4	yes	—
384	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
385	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
387	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
389	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
391	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
395	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₂²×C₄×C₁₃	1	1	yes	characteristic
397	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
398	C₂²×C₄	C₁₃×#41	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	—	2	2	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	C₁₃×M₁₆	1	4	yes	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	2	2	no	—
425	C₄²	—	2	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	4	1	no	—
428	C₄²	—	4	1	no	—
429	C₄²	—	4	1	no	—
430	C₄²	—	4	1	no	—
431	C₄²	C₁₃×#41	1	4	yes	—
432	C₁₃	#22627	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	C₄×Q₈×C₁₃	1	2	yes	—
438	C₂³	C₂×C₁₃×M₁₆	1	2	yes	—
439	C₂³	C₁₃×#131	1	2	yes	—
440	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
441	C₂×C₄	—	2	8	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	4	4	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	4	no	—
480	C₂×C₄	C₁₃×#117	1	2	yes	—
481	C₂×C₄	C₁₃×#117	1	2	yes	—
482	C₂×C₄	C₄×Q₈×C₁₃	1	2	yes	—
483	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
484	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
485	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
486	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
487	C₂×C₄	C₂×C₁₃×M₁₆	1	2	yes	—
488	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
489	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
490	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
491	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
492	C₈	—	2	4	no	—
493	C₈	—	4	2	no	—
494	C₈	—	4	2	no	—
495	C₈	—	4	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	C₁₃×#446	1	4	yes	—
503	C₂²	C₂×C₁₃×#117	1	1	yes	characteristic
504	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
505	C₂²	C₁₃×#518	1	1	yes	characteristic
506	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
507	C₂²	C₂²×C₁₃×M₁₆	1	1	yes	characteristic
508	C₂²	C₂×C₁₃×#131	1	1	yes	characteristic
509	C₂²	C₁₃×#568	1	1	yes	characteristic
510	C₄	—	2	2	no	—
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	2	2	no	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	4	1	no	—
522	C₄	—	4	1	no	—
523	C₄	C₁₃×#553	1	2	yes	—
524	C₄	C₁₃×#554	1	2	yes	—
525	C₂	—	2	4	no	—
526	C₂	C₁₃×#2345	1	1	yes	characteristic
527	C₂	C₁₃×#2920	1	1	yes	characteristic
528	C₂	C₁₃×#2924	1	1	yes	characteristic
529	C₂	C₂×C₁₃×#446	1	1	yes	characteristic
530	C₂	Q₈×C₁₃×M₁₆	1	1	yes	characteristic
531	C₂	C₁₃×#2973	1	1	yes	characteristic
532	C₂	C₁₃×#2974	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	C₂⁴×C₁₃	C₂²×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
2. C₁₃×#1940	C₂	semidirect
3. C₁₃×#1917	C₂	semidirect
4. C₁₃×#1916	C₂	semidirect
8. C₁₃×#1771	C₂	semidirect
97. #22627	C₁₃	direct (N × H)
168. #1940	C₂×C₁₃	semidirect
169. #1917	C₂×C₁₃	semidirect
170. #1916	C₂×C₁₃	semidirect
174. #1771	C₂×C₁₃	semidirect
432. C₁₃	#22627	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×C₄×C₁₃×C₄⋊C₄	2
C₁₃×#1940	2
C₁₃×#1917	2
C₁₃×#1916	2
C₁₃×#1797	2
C₁₃×#1771	2
C₁₃×#1749	2
C₄×C₁₃×C₂²⋊C₈	2
#22627	13

Subgroups — C13×#22627 #15708966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22627 #15708966