Subgroups — C₁₃×#24744 #15711083

Order 3328.

1180 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#459	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#459	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2541	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2349	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2041	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1961	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1879	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
13	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#127	C₂²	1	2	yes	—
16	C₂×C₁₃×#121	—	2	2	no	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
19	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#459	—	2	8	no	—
21	C₁₃×#459	—	2	4	no	—
22	C₁₃×#442	—	2	4	no	—
23	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×#102	C₂²	1	2	yes	—
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	2	yes	—
32	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
33	C₁₃×#392	—	2	1	no	—
34	C₁₃×#392	—	2	1	no	—
35	C₁₃×#390	C₂²	1	2	yes	—
36	C₁₃×#389	C₂²	1	2	yes	—
37	C₁₃×#385	—	2	2	no	—
38	C₁₃×#382	C₂²	1	1	yes	characteristic
39	C₁₃×#380	—	2	1	no	—
40	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#95	—	2	1	no	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₂²×D₄×C₁₃	—	2	1	no	—
45	C₂²×D₄×C₁₃	—	2	2	no	—
46	C₂²×D₄×C₁₃	—	2	2	no	—
47	C₂²×D₄×C₁₃	—	2	1	no	—
48	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
49	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₃	—	2	1	no	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	—	2	2	no	—
54	C₂×C₁₃×D₈	—	2	2	no	—
55	C₂×C₁₃×D₈	—	2	2	no	—
56	C₂×C₁₃×D₈	—	2	4	no	—
57	C₂×C₁₃×D₈	—	2	4	no	—
58	C₂×C₁₃×D₈	—	2	4	no	—
59	C₂×C₁₃×D₈	D₄	1	4	yes	complemented
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₁₃×#127	—	2	4	no	—
64	C₁₃×#127	—	2	2	no	—
65	C₁₃×#127	—	2	2	no	—
66	C₁₃×#127	—	4	2	no	—
67	C₁₃×#121	—	4	8	no	—
68	C₄×D₄×C₁₃	—	2	4	no	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₄×D₄×C₁₃	—	2	2	no	—
72	C₄×D₄×C₁₃	—	4	2	no	—
73	C₄×D₄×C₁₃	D₄	1	4	yes	complemented
74	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
82	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₁₃×#106	—	2	2	no	—
87	C₁₃×C₄⋊C₈	—	2	4	no	—
88	C₁₃×C₄⋊C₈	—	2	2	no	—
89	C₁₃×#102	—	2	2	no	—
90	C₁₃×#102	—	2	4	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	2	2	no	—
93	C₁₃×#102	—	2	4	no	—
94	C₁₃×#102	—	4	2	no	—
95	C₁₃×#97	—	2	2	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	2	no	—
99	C₁₃×#95	D₄	1	1	yes	characteristic
100	C₁₃×#95	D₄	1	1	yes	characteristic
101	#24744	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	1	no	—
103	C₂⁴×C₁₃	—	2	1	no	—
104	C₂⁴×C₁₃	—	2	2	no	—
105	C₂×D₄×C₁₃	—	2	1	no	—
106	C₂×D₄×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	1	no	—
109	C₂×D₄×C₁₃	—	2	1	no	—
110	C₂×D₄×C₁₃	—	2	1	no	—
111	C₂×D₄×C₁₃	—	2	2	no	—
112	C₂×D₄×C₁₃	—	2	2	no	—
113	C₂×D₄×C₁₃	—	2	1	no	—
114	C₂×D₄×C₁₃	—	2	1	no	—
115	C₂×D₄×C₁₃	—	2	2	no	—
116	C₂×D₄×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	4	4	no	—
120	C₂×D₄×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	—	4	4	no	—
122	C₂×D₄×C₁₃	—	4	4	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	4	2	no	—
125	C₂×D₄×C₁₃	—	4	4	no	—
126	C₂×D₄×C₁₃	—	8	2	no	—
127	C₂×D₄×C₁₃	—	8	2	no	—
128	C₂×D₄×C₁₃	—	8	2	no	—
129	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
131	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
132	C₂×D₄×C₁₃	#41	1	2	yes	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	4	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	4	4	no	—
138	C₂²×C₄×C₁₃	—	4	4	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	4	no	—
141	C₂²×C₄×C₁₃	—	8	2	no	—
142	C₂²×C₄×C₁₃	—	8	2	no	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×D₈	—	2	8	no	—
149	C₁₃×D₈	—	4	8	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
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	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	8	2	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	4	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₁₃×C₂²⋊C₄	—	4	4	no	—
172	C₄²×C₁₃	—	2	2	no	—
173	C₄²×C₁₃	—	2	2	no	—
174	C₄²×C₁₃	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃	#41	1	2	yes	—
176	C₂×#459	C₂×C₁₃	1	2	yes	complemented
177	C₂×#459	C₂×C₁₃	1	1	yes	characteristic, complemented
178	C₂×#442	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2541	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2349	C₂×C₁₃	1	1	yes	characteristic, complemented
181	#2065	C₂×C₁₃	1	2	yes	complemented
182	#2041	C₂×C₁₃	1	2	yes	complemented
183	#1961	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1940	C₂×C₁₃	1	1	yes	characteristic, complemented
185	#1879	C₂×C₁₃	1	2	yes	complemented
186	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
187	C₂³×C₁₃	—	2	2	no	—
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	4	2	no	—
192	C₂³×C₁₃	—	4	2	no	—
193	C₂³×C₁₃	—	4	1	no	—
194	C₂³×C₁₃	—	4	1	no	—
195	C₂³×C₁₃	—	4	2	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	2	no	—
200	C₂³×C₁₃	—	4	2	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	—	4	2	no	—
203	C₂³×C₁₃	—	4	2	no	—
204	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	2	no	—
208	D₄×C₁₃	—	2	2	no	—
209	D₄×C₁₃	—	2	2	no	—
210	D₄×C₁₃	—	4	2	no	—
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	—	4	2	no	—
213	D₄×C₁₃	—	4	2	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	4	2	no	—
216	D₄×C₁₃	—	8	8	no	—
217	D₄×C₁₃	—	8	4	no	—
218	D₄×C₁₃	—	8	4	no	—
219	D₄×C₁₃	—	8	8	no	—
220	D₄×C₁₃	#121	1	4	yes	complemented
221	C₂×C₄×C₁₃	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	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	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	1	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	—	8	4	no	—
236	C₂×C₄×C₁₃	—	8	8	no	—
237	C₂×C₄×C₁₃	—	8	4	no	—
238	C₂×C₄×C₁₃	#121	1	2	yes	—
239	C₂×C₄×C₁₃	#121	1	2	yes	—
240	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
241	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
247	C₈×C₁₃	—	2	2	no	—
248	C₈×C₁₃	—	4	2	no	—
249	C₈×C₁₃	—	4	1	no	—
250	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
251	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
253	C₂×#127	C₂²×C₁₃	1	2	yes	—
254	C₂×#121	—	2	2	no	—
255	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
257	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
258	#459	—	2	8	no	—
259	#459	—	2	4	no	—
260	#442	—	2	4	no	—
261	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
264	C₂×#102	C₂²×C₁₃	1	2	yes	—
265	C₂×#102	C₂²×C₁₃	1	2	yes	—
266	C₂×#102	C₂²×C₁₃	1	2	yes	—
267	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#102	C₂²×C₁₃	1	2	yes	—
270	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
271	#392	—	2	1	no	—
272	#392	—	2	1	no	—
273	#390	C₂²×C₁₃	1	2	yes	—
274	#389	C₂²×C₁₃	1	2	yes	—
275	#385	—	2	2	no	—
276	#382	C₂²×C₁₃	1	1	yes	characteristic
277	#380	—	2	1	no	—
278	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#95	—	2	1	no	—
280	#340	C₂²×C₁₃	1	2	yes	—
281	#336	C₂²×C₁₃	1	2	yes	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	4	4	no	—
284	C₂²×C₁₃	—	4	4	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	—	4	2	no	—
287	C₂²×C₁₃	—	4	2	no	—
288	C₂²×C₁₃	—	4	4	no	—
289	C₂²×C₁₃	—	8	2	no	—
290	C₂²×C₁₃	—	8	1	no	—
291	C₂²×C₁₃	—	8	1	no	—
292	C₂²×C₁₃	—	8	2	no	—
293	C₂²×C₁₃	—	8	2	no	—
294	C₂²×C₁₃	—	8	2	no	—
295	C₂²×C₁₃	—	8	2	no	—
296	C₂²×C₁₃	—	8	2	no	—
297	C₂²×C₁₃	—	8	2	no	—
298	C₂²×C₁₃	—	8	2	no	—
299	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
300	C₂²×C₁₃	D₄²	1	1	yes	characteristic
301	C₂²×C₁₃	#548	1	1	yes	characteristic
302	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
303	C₂²×C₁₃	#576	1	2	yes	—
304	C₄×C₁₃	—	2	4	no	—
305	C₄×C₁₃	—	2	2	no	—
306	C₄×C₁₃	—	2	2	no	—
307	C₄×C₁₃	—	4	2	no	—
308	C₄×C₁₃	—	4	2	no	—
309	C₄×C₁₃	—	8	2	no	—
310	C₄×C₁₃	—	8	1	no	—
311	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
312	C₄×C₁₃	#537	1	1	yes	characteristic
313	C₄×C₁₃	#547	1	1	yes	characteristic
314	C₄×C₁₃	#553	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	—	2	1	no	—
319	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
320	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
321	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	—	2	2	no	—
325	C₂×D₈	—	2	2	no	—
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	4	no	—
328	C₂×D₈	—	2	4	no	—
329	C₂×D₈	—	2	4	no	—
330	C₂×D₈	D₄×C₁₃	1	4	yes	complemented
331	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
332	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
334	#127	—	2	4	no	—
335	#127	—	2	2	no	—
336	#127	—	2	2	no	—
337	#127	—	4	2	no	—
338	#121	—	4	8	no	—
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	2	no	—
341	C₄×D₄	—	2	2	no	—
342	C₄×D₄	—	2	2	no	—
343	C₄×D₄	—	4	2	no	—
344	C₄×D₄	D₄×C₁₃	1	4	yes	complemented
345	C₂×C₄⋊C₄	—	2	2	no	—
346	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	1	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
356	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
357	#106	—	2	2	no	—
358	C₄⋊C₈	—	2	4	no	—
359	C₄⋊C₈	—	2	2	no	—
360	#102	—	2	2	no	—
361	#102	—	2	4	no	—
362	#102	—	2	4	no	—
363	#102	—	2	2	no	—
364	#102	—	2	4	no	—
365	#102	—	4	2	no	—
366	#97	—	2	2	no	—
367	#95	—	2	1	no	—
368	#95	—	2	2	no	—
369	#95	—	2	1	no	—
370	#95	D₄×C₁₃	1	1	yes	characteristic
371	#95	D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₁₃	—	4	4	no	—
373	C₂×C₁₃	—	8	2	no	—
374	C₂×C₁₃	—	16	2	no	—
375	C₂×C₁₃	#2416	1	1	yes	characteristic
376	C₂×C₁₃	#3038	1	1	yes	characteristic
377	C₂×C₁₃	#3041	1	1	yes	characteristic
378	C₂×C₁₃	#3264	1	2	yes	—
379	C₂×C₁₃	#3366	1	2	yes	—
380	C₂⁴	—	2	1	no	—
381	C₂⁴	—	2	1	no	—
382	C₂⁴	—	2	2	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	2	2	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	4	4	no	—
398	C₂×D₄	—	4	4	no	—
399	C₂×D₄	—	4	4	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	2	no	—
402	C₂×D₄	—	4	2	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	—	8	2	no	—
405	C₂×D₄	—	8	2	no	—
406	C₂×D₄	—	8	2	no	—
407	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
409	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
410	C₂×D₄	C₁₃×#41	1	2	yes	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	4	no	—
417	C₂²×C₄	—	4	2	no	—
418	C₂²×C₄	—	4	4	no	—
419	C₂²×C₄	—	8	2	no	—
420	C₂²×C₄	—	8	2	no	—
421	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
426	D₈	—	2	8	no	—
427	D₈	—	4	8	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
437	C₄⋊C₄	—	2	4	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	8	2	no	—
444	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
445	C₂²⋊C₄	—	2	4	no	—
446	C₂²⋊C₄	—	4	4	no	—
447	C₂²⋊C₄	—	4	4	no	—
448	C₂²⋊C₄	—	4	2	no	—
449	C₂²⋊C₄	—	4	4	no	—
450	C₄²	—	2	2	no	—
451	C₄²	—	2	2	no	—
452	C₄²	C₂×D₄×C₁₃	1	2	yes	—
453	C₄²	C₁₃×#41	1	2	yes	—
454	C₁₃	#24744	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	2	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	1	no	—
462	C₂³	—	4	1	no	—
463	C₂³	—	4	2	no	—
464	C₂³	—	4	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	4	2	no	—
469	C₂³	—	4	2	no	—
470	C₂³	—	4	2	no	—
471	C₂³	—	4	2	no	—
472	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	2	no	—
477	D₄	—	2	2	no	—
478	D₄	—	4	2	no	—
479	D₄	—	4	1	no	—
480	D₄	—	4	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	2	no	—
484	D₄	—	8	8	no	—
485	D₄	—	8	4	no	—
486	D₄	—	8	4	no	—
487	D₄	—	8	8	no	—
488	D₄	C₁₃×#121	1	4	yes	complemented
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	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	8	4	no	—
504	C₂×C₄	—	8	8	no	—
505	C₂×C₄	—	8	4	no	—
506	C₂×C₄	C₁₃×#121	1	2	yes	—
507	C₂×C₄	C₁₃×#121	1	2	yes	—
508	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	4	yes	—
509	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
511	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
512	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
513	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
514	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	4	2	no	—
517	C₈	—	4	1	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	4	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	8	1	no	—
526	C₂²	—	8	1	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
536	C₂²	D₄²×C₁₃	1	1	yes	characteristic
537	C₂²	C₁₃×#548	1	1	yes	characteristic
538	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	2	yes	—
539	C₂²	C₁₃×#576	1	2	yes	—
540	C₄	—	2	4	no	—
541	C₄	—	2	2	no	—
542	C₄	—	2	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	8	2	no	—
546	C₄	—	8	1	no	—
547	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
548	C₄	C₁₃×#537	1	1	yes	characteristic
549	C₄	C₁₃×#547	1	1	yes	characteristic
550	C₄	C₁₃×#553	1	1	yes	characteristic
551	C₂	—	4	4	no	—
552	C₂	—	8	2	no	—
553	C₂	—	16	2	no	—
554	C₂	C₁₃×#2416	1	1	yes	characteristic
555	C₂	C₁₃×#3038	1	1	yes	characteristic
556	C₂	C₁₃×#3041	1	1	yes	characteristic
557	C₂	C₁₃×#3264	1	2	yes	—
558	C₂	C₁₃×#3366	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#459	C₂	semidirect
2. C₂×C₁₃×#459	C₂	semidirect
3. C₂×C₁₃×#442	C₂	semidirect
4. C₁₃×#2541	C₂	semidirect
5. C₁₃×#2349	C₂	semidirect
6. C₁₃×#2065	C₂	semidirect
7. C₁₃×#2041	C₂	semidirect
8. C₁₃×#1961	C₂	semidirect
9. C₁₃×#1940	C₂	semidirect
10. C₁₃×#1879	C₂	semidirect
11. C₁₃×#1804	C₂	semidirect
59. C₂×C₁₃×D₈	D₄	semidirect
73. C₄×D₄×C₁₃	D₄	semidirect
101. #24744	C₁₃	direct (N × H)
176. C₂×#459	C₂×C₁₃	semidirect
177. C₂×#459	C₂×C₁₃	semidirect
178. C₂×#442	C₂×C₁₃	semidirect
179. #2541	C₂×C₁₃	semidirect
180. #2349	C₂×C₁₃	semidirect
181. #2065	C₂×C₁₃	semidirect
182. #2041	C₂×C₁₃	semidirect
183. #1961	C₂×C₁₃	semidirect
184. #1940	C₂×C₁₃	semidirect
185. #1879	C₂×C₁₃	semidirect
186. #1804	C₂×C₁₃	semidirect
220. D₄×C₁₃	#121	semidirect
330. C₂×D₈	D₄×C₁₃	semidirect
344. C₄×D₄	D₄×C₁₃	semidirect
454. C₁₃	#24744	direct (N × H)
488. D₄	C₁₃×#121	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#459	2
C₂×C₁₃×#442	2
C₁₃×#2541	2
C₁₃×#2349	2
C₁₃×#2065	2
C₁₃×#2041	2
C₁₃×#1961	2
C₁₃×#1940	2
C₁₃×#1879	2
C₁₃×#1804	2
#24744	13

Subgroups — C13×#24744 #15711083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24744 #15711083