Subgroups — C₁₃×#24211 #15710550

Order 3328.

2118 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₃×#127	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#460	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₃×#450	C₂	1	2	yes	maximal, complemented
4	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2041	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2014	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1982	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1786	C₂	1	2	yes	maximal, complemented
10	C₂³×D₄×C₁₃	—	2	1	no	—
11	C₂³×D₄×C₁₃	—	2	1	no	—
12	C₂³×D₄×C₁₃	C₂²	1	2	yes	—
13	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	complemented
14	C₂×C₁₃×#127	—	2	8	no	—
15	C₂×C₁₃×#127	—	2	1	no	—
16	C₂×C₁₃×#127	—	2	1	no	—
17	C₂×C₁₃×#127	C₂²	1	2	yes	—
18	C₂×C₁₃×#127	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
22	C₁₃×#460	—	2	8	no	—
23	C₁₃×#450	—	2	8	no	—
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
25	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
26	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
27	C₂×C₁₃×#102	C₂²	1	4	yes	complemented
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#387	—	2	1	no	—
32	C₁₃×#385	—	2	1	no	—
33	C₁₃×#380	C₂²	1	1	yes	characteristic
34	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
35	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
36	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
37	C₁₃×#336	C₂²	1	2	yes	complemented
38	C₂⁵×C₁₃	—	2	2	no	—
39	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₁₃	—	2	8	no	—
41	C₂²×D₄×C₁₃	—	2	8	no	—
42	C₂²×D₄×C₁₃	—	2	8	no	—
43	C₂²×D₄×C₁₃	—	2	2	no	—
44	C₂²×D₄×C₁₃	—	2	2	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	2	4	no	—
49	C₂²×D₄×C₁₃	—	2	4	no	—
50	C₂²×D₄×C₁₃	—	4	4	no	—
51	C₂²×D₄×C₁₃	—	4	4	no	—
52	C₂²×D₄×C₁₃	—	4	4	no	—
53	C₂²×D₄×C₁₃	—	4	4	no	—
54	C₂²×D₄×C₁₃	—	4	4	no	—
55	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
58	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂×C₁₃×SD₁₆	—	2	8	no	—
60	C₂×C₁₃×SD₁₆	—	2	8	no	—
61	C₂×C₁₃×SD₁₆	—	4	4	no	—
62	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
63	C₁₃×#127	—	2	8	no	—
64	C₁₃×#127	—	2	8	no	—
65	C₁₃×#127	—	2	8	no	—
66	C₁₃×#127	—	2	4	no	—
67	C₁₃×#127	D₄	1	8	yes	—
68	C₁₃×C₂²⋊Q₈	—	2	2	no	—
69	C₁₃×C₂²⋊Q₈	D₄	1	4	yes	complemented
70	C₄×Q₈×C₁₃	—	2	4	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	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
79	C₂×C₄²×C₁₃	—	2	4	no	—
80	C₂×C₄²×C₁₃	—	2	1	no	—
81	C₂×C₄²×C₁₃	—	2	1	no	—
82	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×C₄⋊C₈	—	2	4	no	—
87	C₁₃×#102	—	2	8	no	—
88	C₁₃×#102	—	2	8	no	—
89	C₁₃×#102	—	4	4	no	—
90	C₁₃×C₂²⋊C₈	—	2	4	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	1	no	—
94	C₁₃×#95	—	2	1	no	—
95	C₁₃×#95	—	2	1	no	—
96	#24211	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
97	C₂⁴×C₁₃	—	2	8	no	—
98	C₂⁴×C₁₃	—	2	4	no	—
99	C₂⁴×C₁₃	—	4	4	no	—
100	C₂⁴×C₁₃	—	4	4	no	—
101	C₂⁴×C₁₃	—	4	4	no	—
102	C₂⁴×C₁₃	—	4	4	no	—
103	C₂⁴×C₁₃	—	4	4	no	—
104	C₂⁴×C₁₃	—	4	4	no	—
105	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂×Q₈×C₁₃	—	2	1	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	complemented
110	C₂×D₄×C₁₃	—	2	8	no	—
111	C₂×D₄×C₁₃	—	2	8	no	—
112	C₂×D₄×C₁₃	—	2	8	no	—
113	C₂×D₄×C₁₃	—	2	8	no	—
114	C₂×D₄×C₁₃	—	2	8	no	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	4	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	4	no	—
119	C₂×D₄×C₁₃	—	2	4	no	—
120	C₂×D₄×C₁₃	—	4	16	no	—
121	C₂×D₄×C₁₃	—	4	16	no	—
122	C₂×D₄×C₁₃	—	4	32	no	—
123	C₂×D₄×C₁₃	—	4	4	no	—
124	C₂×D₄×C₁₃	—	4	4	no	—
125	C₂×D₄×C₁₃	—	4	4	no	—
126	C₂×D₄×C₁₃	—	4	4	no	—
127	C₂×D₄×C₁₃	—	4	4	no	—
128	C₂×D₄×C₁₃	—	4	32	no	—
129	C₂×D₄×C₁₃	—	4	4	no	—
130	C₂×D₄×C₁₃	—	4	4	no	—
131	C₂×D₄×C₁₃	—	4	4	no	—
132	C₂×D₄×C₁₃	—	4	4	no	—
133	C₂×D₄×C₁₃	—	4	4	no	—
134	C₂×D₄×C₁₃	C₂×D₄	1	8	yes	—
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	2	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	1	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	1	no	—
146	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	complemented
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
150	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₃	#41	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
155	C₁₃×SD₁₆	—	4	16	no	—
156	C₂×C₈×C₁₃	—	2	4	no	—
157	C₂×C₈×C₁₃	—	2	4	no	—
158	C₂×C₈×C₁₃	—	2	4	no	—
159	C₁₃×C₄⋊C₄	—	2	4	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	4	2	no	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	complemented
166	C₁₃×C₂²⋊C₄	—	2	4	no	—
167	C₁₃×C₂²⋊C₄	—	4	2	no	—
168	C₄²×C₁₃	—	2	2	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	4	2	no	—
172	C₄²×C₁₃	—	4	2	no	—
173	C₄²×C₁₃	C₂×D₄	1	4	yes	—
174	C₂²×#127	C₂×C₁₃	1	1	yes	characteristic
175	C₂×#460	C₂×C₁₃	1	2	yes	complemented
176	C₂×#450	C₂×C₁₃	1	2	yes	complemented
177	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2041	C₂×C₁₃	1	2	yes	complemented
179	#2014	C₂×C₁₃	1	2	yes	complemented
180	#1982	C₂×C₁₃	1	2	yes	complemented
181	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
182	#1786	C₂×C₁₃	1	2	yes	complemented
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	8	no	—
188	C₂³×C₁₃	—	4	16	no	—
189	C₂³×C₁₃	—	4	16	no	—
190	C₂³×C₁₃	—	4	16	no	—
191	C₂³×C₁₃	—	4	4	no	—
192	C₂³×C₁₃	—	4	4	no	—
193	C₂³×C₁₃	—	4	4	no	—
194	C₂³×C₁₃	—	4	4	no	—
195	C₂³×C₁₃	—	4	4	no	—
196	C₂³×C₁₃	—	4	4	no	—
197	C₂³×C₁₃	—	8	8	no	—
198	C₂³×C₁₃	—	8	8	no	—
199	C₂³×C₁₃	—	8	8	no	—
200	C₂³×C₁₃	—	8	8	no	—
201	C₂³×C₁₃	#121	1	2	yes	—
202	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
203	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
204	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	Q₈×C₁₃	—	2	4	no	—
206	Q₈×C₁₃	—	4	2	no	—
207	D₄×C₁₃	—	2	8	no	—
208	D₄×C₁₃	—	2	8	no	—
209	D₄×C₁₃	—	4	16	no	—
210	D₄×C₁₃	—	4	16	no	—
211	D₄×C₁₃	—	4	16	no	—
212	D₄×C₁₃	—	4	16	no	—
213	D₄×C₁₃	—	4	4	no	—
214	D₄×C₁₃	—	4	4	no	—
215	D₄×C₁₃	—	4	16	no	—
216	C₂×C₄×C₁₃	—	2	8	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	—	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	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	8	no	—
228	C₂×C₄×C₁₃	—	2	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	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	#120	1	2	yes	—
241	C₂×C₄×C₁₃	#120	1	2	yes	—
242	C₂×C₄×C₁₃	#121	1	2	yes	—
243	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
244	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
245	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
246	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
251	C₈×C₁₃	—	4	4	no	—
252	C₂³×D₄	—	2	1	no	—
253	C₂³×D₄	—	2	1	no	—
254	C₂³×D₄	C₂²×C₁₃	1	2	yes	—
255	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	complemented
256	C₂×#127	—	2	8	no	—
257	C₂×#127	—	2	1	no	—
258	C₂×#127	—	2	1	no	—
259	C₂×#127	C₂²×C₁₃	1	2	yes	—
260	C₂×#127	C₂²×C₁₃	1	2	yes	—
261	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
263	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
264	#460	—	2	8	no	—
265	#450	—	2	8	no	—
266	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
267	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
268	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
269	C₂×#102	C₂²×C₁₃	1	4	yes	complemented
270	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
271	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
272	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
273	#387	—	2	1	no	—
274	#385	—	2	1	no	—
275	#380	C₂²×C₁₃	1	1	yes	characteristic
276	C₄×C₄⋊C₄	—	2	1	no	—
277	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
278	C₄×C₂²⋊C₄	—	2	1	no	—
279	#336	C₂²×C₁₃	1	2	yes	complemented
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	2	no	—
283	C₂²×C₁₃	—	2	2	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	4	8	no	—
287	C₂²×C₁₃	—	4	8	no	—
288	C₂²×C₁₃	—	4	8	no	—
289	C₂²×C₁₃	—	8	32	no	—
290	C₂²×C₁₃	—	8	4	no	—
291	C₂²×C₁₃	—	8	4	no	—
292	C₂²×C₁₃	—	8	4	no	—
293	C₂²×C₁₃	—	8	4	no	—
294	C₂²×C₁₃	#460	1	4	yes	complemented
295	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
296	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
297	C₂²×C₁₃	#535	1	1	yes	characteristic
298	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
299	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
300	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
301	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	2	2	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	4	2	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	8	1	no	—
309	C₄×C₁₃	—	8	1	no	—
310	C₄×C₁₃	#450	1	4	yes	complemented
311	C₄×C₁₃	D₄²	1	2	yes	—
312	C₄×C₁₃	#546	1	2	yes	—
313	C₂⁵	—	2	2	no	—
314	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×D₄	—	2	8	no	—
316	C₂²×D₄	—	2	8	no	—
317	C₂²×D₄	—	2	8	no	—
318	C₂²×D₄	—	2	2	no	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	—	2	2	no	—
322	C₂²×D₄	—	2	2	no	—
323	C₂²×D₄	—	2	4	no	—
324	C₂²×D₄	—	2	4	no	—
325	C₂²×D₄	—	4	4	no	—
326	C₂²×D₄	—	4	4	no	—
327	C₂²×D₄	—	4	4	no	—
328	C₂²×D₄	—	4	4	no	—
329	C₂²×D₄	—	4	4	no	—
330	C₂²×D₄	C₂³×C₁₃	1	4	yes	—
331	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
332	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
333	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
334	C₂×SD₁₆	—	2	8	no	—
335	C₂×SD₁₆	—	2	8	no	—
336	C₂×SD₁₆	—	4	4	no	—
337	C₂²×C₈	C₂³×C₁₃	1	4	yes	—
338	#127	—	2	8	no	—
339	#127	—	2	8	no	—
340	#127	—	2	8	no	—
341	#127	—	2	4	no	—
342	#127	D₄×C₁₃	1	8	yes	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	D₄×C₁₃	1	4	yes	complemented
345	C₄×Q₈	—	2	4	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₄²	—	2	4	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
358	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
361	C₄⋊C₈	—	2	4	no	—
362	#102	—	2	8	no	—
363	#102	—	2	8	no	—
364	#102	—	4	4	no	—
365	C₂²⋊C₈	—	2	4	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	C₂×C₁₃	—	2	4	no	—
372	C₂×C₁₃	—	8	8	no	—
373	C₂×C₁₃	#2408	1	1	yes	characteristic
374	C₂×C₁₃	C₂×#450	1	1	yes	characteristic
375	C₂×C₁₃	#3003	1	1	yes	characteristic
376	C₂×C₁₃	C₂×#460	1	1	yes	characteristic
377	C₂×C₁₃	#3038	1	1	yes	characteristic
378	C₂×C₁₃	#3208	1	1	yes	characteristic
379	C₂×C₁₃	#3217	1	1	yes	characteristic
380	C₂⁴	—	2	8	no	—
381	C₂⁴	—	2	4	no	—
382	C₂⁴	—	4	4	no	—
383	C₂⁴	—	4	4	no	—
384	C₂⁴	—	4	4	no	—
385	C₂⁴	—	4	4	no	—
386	C₂⁴	—	4	4	no	—
387	C₂⁴	—	4	4	no	—
388	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	complemented
393	C₂×D₄	—	2	8	no	—
394	C₂×D₄	—	2	8	no	—
395	C₂×D₄	—	2	8	no	—
396	C₂×D₄	—	2	8	no	—
397	C₂×D₄	—	2	8	no	—
398	C₂×D₄	—	2	4	no	—
399	C₂×D₄	—	2	4	no	—
400	C₂×D₄	—	2	4	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	4	16	no	—
404	C₂×D₄	—	4	16	no	—
405	C₂×D₄	—	4	32	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	4	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	—	4	4	no	—
410	C₂×D₄	—	4	4	no	—
411	C₂×D₄	—	4	32	no	—
412	C₂×D₄	—	4	4	no	—
413	C₂×D₄	—	4	4	no	—
414	C₂×D₄	—	4	4	no	—
415	C₂×D₄	—	4	4	no	—
416	C₂×D₄	—	4	4	no	—
417	C₂×D₄	C₂×D₄×C₁₃	1	8	yes	—
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	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	complemented
430	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
432	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₁₃×#41	1	2	yes	—
437	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
438	SD₁₆	—	4	16	no	—
439	C₂×C₈	—	2	4	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	4	2	no	—
447	C₄⋊C₄	—	4	2	no	—
448	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	complemented
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	4	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	2	2	no	—
453	C₄²	—	2	2	no	—
454	C₄²	—	4	2	no	—
455	C₄²	—	4	2	no	—
456	C₄²	C₂×D₄×C₁₃	1	4	yes	—
457	C₁₃	#24211	1	1	yes	characteristic, direct product factor, Sylow
458	C₂³	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	2	1	no	—
461	C₂³	—	2	1	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	4	16	no	—
464	C₂³	—	4	16	no	—
465	C₂³	—	4	16	no	—
466	C₂³	—	4	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	4	4	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	8	8	no	—
473	C₂³	—	8	8	no	—
474	C₂³	—	8	8	no	—
475	C₂³	—	8	8	no	—
476	C₂³	C₁₃×#121	1	2	yes	—
477	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
478	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
479	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
480	Q₈	—	2	4	no	—
481	Q₈	—	4	2	no	—
482	D₄	—	2	8	no	—
483	D₄	—	2	8	no	—
484	D₄	—	4	16	no	—
485	D₄	—	4	16	no	—
486	D₄	—	4	16	no	—
487	D₄	—	4	16	no	—
488	D₄	—	4	16	no	—
489	D₄	—	4	4	no	—
490	D₄	—	4	4	no	—
491	C₂×C₄	—	2	8	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	4	no	—
502	C₂×C₄	—	2	4	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	C₁₃×#120	1	2	yes	—
516	C₂×C₄	C₁₃×#120	1	2	yes	—
517	C₂×C₄	C₁₃×#121	1	2	yes	—
518	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
519	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
520	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
521	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
522	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
523	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
524	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
525	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
526	C₈	—	4	4	no	—
527	C₂²	—	2	2	no	—
528	C₂²	—	2	2	no	—
529	C₂²	—	2	2	no	—
530	C₂²	—	2	2	no	—
531	C₂²	—	2	2	no	—
532	C₂²	—	2	2	no	—
533	C₂²	—	4	8	no	—
534	C₂²	—	4	8	no	—
535	C₂²	—	4	8	no	—
536	C₂²	—	8	32	no	—
537	C₂²	—	8	4	no	—
538	C₂²	—	8	4	no	—
539	C₂²	—	8	4	no	—
540	C₂²	—	8	4	no	—
541	C₂²	C₁₃×#460	1	4	yes	complemented
542	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
543	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
544	C₂²	C₁₃×#535	1	1	yes	characteristic
545	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
546	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
547	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
548	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
549	C₄	—	2	2	no	—
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	C₁₃×#450	1	4	yes	complemented
558	C₄	D₄²×C₁₃	1	2	yes	—
559	C₄	C₁₃×#546	1	2	yes	—
560	C₂	—	2	4	no	—
561	C₂	—	8	8	no	—
562	C₂	C₁₃×#2408	1	1	yes	characteristic
563	C₂	C₂×C₁₃×#450	1	1	yes	characteristic
564	C₂	C₁₃×#3003	1	1	yes	characteristic
565	C₂	C₂×C₁₃×#460	1	1	yes	characteristic
566	C₂	C₁₃×#3038	1	1	yes	characteristic
567	C₂	C₁₃×#3208	1	1	yes	characteristic
568	C₂	C₁₃×#3217	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#127	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#460	C₂	semidirect
3. C₂×C₁₃×#450	C₂	semidirect
4. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
5. C₁₃×#2041	C₂	semidirect
6. C₁₃×#2014	C₂	semidirect
7. C₁₃×#1982	C₂	semidirect
8. C₁₃×#1797	C₂	semidirect
9. C₁₃×#1786	C₂	semidirect
13. C₂²×C₁₃×SD₁₆	C₂²	semidirect
20. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
24. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
25. C₂×C₁₃×#102	C₂²	semidirect
26. C₂×C₁₃×#102	C₂²	semidirect
27. C₂×C₁₃×#102	C₂²	semidirect
29. C₁₃×#391	C₂²	semidirect
30. C₁₃×#389	C₂²	semidirect
35. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
37. C₁₃×#336	C₂²	semidirect
69. C₁₃×C₂²⋊Q₈	D₄	semidirect
96. #24211	C₁₃	direct (N × H)
109. C₂×Q₈×C₁₃	C₂×D₄	semidirect
146. C₂²×C₄×C₁₃	SD₁₆	semidirect
165. C₁₃×C₄⋊C₄	C₂×D₄	semidirect
175. C₂×#460	C₂×C₁₃	semidirect
176. C₂×#450	C₂×C₁₃	semidirect
177. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
178. #2041	C₂×C₁₃	semidirect
179. #2014	C₂×C₁₃	semidirect
180. #1982	C₂×C₁₃	semidirect
181. #1797	C₂×C₁₃	semidirect
182. #1786	C₂×C₁₃	semidirect
255. C₂²×SD₁₆	C₂²×C₁₃	semidirect
262. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
266. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
267. C₂×#102	C₂²×C₁₃	semidirect
268. C₂×#102	C₂²×C₁₃	semidirect
269. C₂×#102	C₂²×C₁₃	semidirect
271. #391	C₂²×C₁₃	semidirect
272. #389	C₂²×C₁₃	semidirect
277. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
279. #336	C₂²×C₁₃	semidirect
294. C₂²×C₁₃	#460	semidirect
310. C₄×C₁₃	#450	semidirect
344. C₂²⋊Q₈	D₄×C₁₃	semidirect
392. C₂×Q₈	C₂×D₄×C₁₃	semidirect
429. C₂²×C₄	C₁₃×SD₁₆	semidirect
448. C₄⋊C₄	C₂×D₄×C₁₃	semidirect
457. C₁₃	#24211	direct (N × H)
541. C₂²	C₁₃×#460	semidirect
557. C₄	C₁₃×#450	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₃×#127	2
C₂×C₁₃×#460	2
C₂×C₁₃×#450	2
C₄×C₁₃×C₂²⋊Q₈	2
C₁₃×#2041	2
C₁₃×#2014	2
C₁₃×#1982	2
C₁₃×#1797	2
C₁₃×#1786	2
#24211	13

Subgroups — C13×#24211 #15710550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24211 #15710550