Subgroups — C₁₃×#24809 #15711148

Order 3328.

830 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3068	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#472	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2916	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2069	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2048	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1953	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1903	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1813	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#575	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
16	C₁₃×#568	C₂²	1	2	yes	—
17	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
19	C₁₃×#472	—	2	4	no	—
20	C₁₃×#472	—	2	2	no	—
21	C₁₃×#472	—	2	2	no	—
22	C₁₃×#472	—	2	2	no	—
23	C₁₃×#472	—	2	2	no	—
24	C₁₃×#471	—	2	4	no	—
25	C₁₃×#444	—	2	2	no	—
26	C₁₃×#443	—	2	2	no	—
27	C₁₃×#430	—	2	2	no	—
28	C₁₃×#430	C₂²	1	2	yes	—
29	C₁₃×#430	C₂²	1	2	yes	—
30	C₁₃×#430	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#108	—	2	2	no	—
32	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₁₃×#421	C₂²	1	1	yes	characteristic
36	C₁₃×#421	C₂²	1	1	yes	characteristic
37	C₁₃×#418	C₂²	1	2	yes	—
38	C₁₃×#413	C₂²	1	2	yes	—
39	C₂×C₁₃×#100	C₂²	1	2	yes	—
40	C₂×C₁₃×#100	C₂²	1	2	yes	—
41	C₂×C₁₃×#100	C₂²	1	2	yes	—
42	C₁₃×#405	C₂²	1	1	yes	characteristic
43	C₁₃×#344	C₂²	1	2	yes	—
44	C₁₃×#338	C₂²	1	2	yes	—
45	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
48	C₁₃×#137	—	2	1	no	—
49	C₁₃×#137	D₄	1	2	yes	—
50	C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
51	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
52	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
53	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
54	C₁₃×AGL(1,ℤ/8)	—	4	2	no	—
55	C₁₃×AGL(1,ℤ/8)	D₄	1	2	yes	—
56	C₁₃×#135	—	2	2	no	—
57	C₂×C₁₃×SD₁₆	—	2	2	no	—
58	C₂×C₁₃×SD₁₆	—	2	2	no	—
59	C₂×C₁₃×D₈	—	2	2	no	—
60	C₂×C₁₃×D₈	—	2	2	no	—
61	C₂×C₁₃×D₈	—	2	1	no	—
62	C₂×C₁₃×D₈	—	2	1	no	—
63	C₂×C₁₃×D₈	—	2	1	no	—
64	C₂×C₁₃×D₈	—	2	1	no	—
65	C₂×C₁₃×D₈	—	2	1	no	—
66	C₂×C₁₃×D₈	—	2	1	no	—
67	C₁₃×#131	—	2	1	no	—
68	C₁₃×#131	—	2	1	no	—
69	C₁₃×#131	—	2	4	no	—
70	C₁₃×#131	—	2	1	no	—
71	C₁₃×#131	—	2	1	no	—
72	C₁₃×#131	—	2	1	no	—
73	C₁₃×#131	—	2	1	no	—
74	C₁₃×#131	—	4	2	no	—
75	C₁₃×#131	D₄	1	2	yes	—
76	C₁₃×#131	D₄	1	2	yes	—
77	C₂×C₁₃×M₁₆	—	2	1	no	—
78	C₂×C₁₃×M₁₆	—	2	1	no	—
79	C₂×C₁₃×M₁₆	—	2	4	no	—
80	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
82	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
83	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
84	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
86	C₂²×C₈×C₁₃	—	2	1	no	—
87	C₂²×C₈×C₁₃	—	2	1	no	—
88	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
89	C₁₃×#117	C₂³	1	1	yes	characteristic
90	C₁₃×#108	—	2	4	no	—
91	C₁₃×#108	—	2	2	no	—
92	C₁₃×#108	—	2	4	no	—
93	C₁₃×#108	—	2	1	no	—
94	C₁₃×#108	—	2	1	no	—
95	C₁₃×#108	—	2	1	no	—
96	C₁₃×#108	—	2	1	no	—
97	C₁₃×#108	D₄	1	2	yes	—
98	C₁₃×#108	D₄	1	2	yes	—
99	C₁₃×#104	—	2	2	no	—
100	C₁₃×#104	—	2	2	no	—
101	C₁₃×#102	—	4	2	no	—
102	C₁₃×#101	—	2	2	no	—
103	C₁₃×#100	—	2	2	no	—
104	C₁₃×#100	—	2	4	no	—
105	C₁₃×#100	—	2	4	no	—
106	C₁₃×#100	—	2	4	no	—
107	C₁₃×#97	—	2	1	no	—
108	C₄×C₈×C₁₃	—	2	1	no	—
109	#24809	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
110	C₂⁴×C₁₃	—	2	2	no	—
111	C₁₃×#41	—	2	1	no	—
112	C₁₃×#41	—	2	1	no	—
113	C₁₃×#41	—	2	1	no	—
114	C₁₃×#41	—	2	1	no	—
115	C₁₃×#41	—	2	1	no	—
116	C₁₃×#41	—	2	1	no	—
117	C₁₃×#41	C₂×D₄	1	2	yes	—
118	C₁₃×#41	C₂×D₄	1	2	yes	—
119	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×Q₈×C₁₃	#41	1	1	yes	characteristic
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	2	no	—
125	C₂×D₄×C₁₃	—	2	2	no	—
126	C₂×D₄×C₁₃	—	2	2	no	—
127	C₂×D₄×C₁₃	—	2	2	no	—
128	C₂×D₄×C₁₃	—	2	2	no	—
129	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
130	C₂×D₄×C₁₃	#41	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₁₃×Q₁₆	—	2	2	no	—
135	C₁₃×SD₁₆	—	2	2	no	—
136	C₁₃×SD₁₆	—	2	2	no	—
137	C₁₃×SD₁₆	—	4	4	no	—
138	C₁₃×SD₁₆	—	4	4	no	—
139	C₁₃×D₈	—	2	2	no	—
140	C₁₃×D₈	—	4	4	no	—
141	C₁₃×D₈	—	4	4	no	—
142	C₁₃×D₈	—	4	1	no	—
143	C₁₃×D₈	—	4	1	no	—
144	C₁₃×D₈	—	4	1	no	—
145	C₁₃×D₈	—	4	1	no	—
146	C₁₃×M₁₆	—	2	1	no	—
147	C₁₃×M₁₆	—	2	1	no	—
148	C₁₃×M₁₆	—	2	2	no	—
149	C₁₃×M₁₆	—	2	2	no	—
150	C₁₃×M₁₆	—	2	2	no	—
151	C₁₃×M₁₆	—	2	1	no	—
152	C₁₃×M₁₆	—	2	2	no	—
153	C₁₃×M₁₆	—	2	2	no	—
154	C₁₃×M₁₆	—	2	2	no	—
155	C₁₃×M₁₆	—	2	1	no	—
156	C₁₃×M₁₆	—	2	2	no	—
157	C₁₃×M₁₆	—	4	4	no	—
158	C₁₃×M₁₆	—	4	1	no	—
159	C₁₃×M₁₆	—	4	1	no	—
160	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
161	C₁₃×M₁₆	C₂×D₄	1	2	yes	—
162	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	—	2	2	no	—
167	C₂×C₈×C₁₃	—	2	2	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	4	4	no	—
172	C₂×C₈×C₁₃	—	4	1	no	—
173	C₂×C₈×C₁₃	—	4	1	no	—
174	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
176	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
177	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
179	C₂×C₈×C₁₃	#41	1	1	yes	characteristic
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₂²⋊C₄	—	2	1	no	—
182	C₄²×C₁₃	—	2	1	no	—
183	#3068	C₂×C₁₃	1	2	yes	complemented
184	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
185	C₂×#472	C₂×C₁₃	1	1	yes	characteristic, complemented
186	#2955	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#2916	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#2069	C₂×C₁₃	1	2	yes	complemented
189	#2048	C₂×C₁₃	1	2	yes	complemented
190	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1953	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1903	C₂×C₁₃	1	2	yes	complemented
193	#1813	C₂×C₁₃	1	1	yes	characteristic, complemented
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	4	2	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	16	2	no	—
200	C₂³×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
201	Q₈×C₁₃	—	2	1	no	—
202	Q₈×C₁₃	—	2	1	no	—
203	Q₈×C₁₃	—	2	1	no	—
204	Q₈×C₁₃	#121	1	2	yes	—
205	D₄×C₁₃	—	2	2	no	—
206	D₄×C₁₃	—	2	2	no	—
207	D₄×C₁₃	—	2	1	no	—
208	D₄×C₁₃	—	2	1	no	—
209	D₄×C₁₃	—	2	1	no	—
210	D₄×C₁₃	—	4	1	no	—
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	—	4	2	no	—
213	D₄×C₁₃	—	4	2	no	—
214	D₄×C₁₃	—	4	2	no	—
215	D₄×C₁₃	—	4	2	no	—
216	D₄×C₁₃	#121	1	2	yes	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	2	no	—
219	C₂×C₄×C₁₃	—	2	2	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
228	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
230	C₈×C₁₃	—	2	2	no	—
231	C₈×C₁₃	—	2	2	no	—
232	C₈×C₁₃	—	2	4	no	—
233	C₈×C₁₃	—	4	1	no	—
234	C₈×C₁₃	—	4	2	no	—
235	C₈×C₁₃	—	4	2	no	—
236	C₈×C₁₃	#121	1	1	yes	characteristic
237	C₈×C₁₃	#121	1	1	yes	characteristic
238	C₈×C₁₃	#121	1	1	yes	characteristic
239	C₈×C₁₃	#121	1	1	yes	characteristic
240	#575	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
242	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
243	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
244	#568	C₂²×C₁₃	1	2	yes	—
245	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
246	C₂×#131	C₂²×C₁₃	1	1	yes	characteristic
247	#472	—	2	4	no	—
248	#472	—	2	2	no	—
249	#472	—	2	2	no	—
250	#472	—	2	2	no	—
251	#472	—	2	2	no	—
252	#471	—	2	4	no	—
253	#444	—	2	2	no	—
254	#443	—	2	2	no	—
255	#430	—	2	2	no	—
256	#430	C₂²×C₁₃	1	2	yes	—
257	#430	C₂²×C₁₃	1	1	yes	characteristic
258	#430	C₂²×C₁₃	1	2	yes	—
259	C₂×#108	—	2	2	no	—
260	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
263	#421	C₂²×C₁₃	1	1	yes	characteristic
264	#421	C₂²×C₁₃	1	1	yes	characteristic
265	#418	C₂²×C₁₃	1	2	yes	—
266	#413	C₂²×C₁₃	1	2	yes	—
267	C₂×#100	C₂²×C₁₃	1	2	yes	—
268	C₂×#100	C₂²×C₁₃	1	2	yes	—
269	C₂×#100	C₂²×C₁₃	1	2	yes	—
270	#405	C₂²×C₁₃	1	1	yes	characteristic
271	#344	C₂²×C₁₃	1	2	yes	—
272	#338	C₂²×C₁₃	1	2	yes	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	4	1	no	—
275	C₂²×C₁₃	—	4	1	no	—
276	C₂²×C₁₃	—	8	1	no	—
277	C₂²×C₁₃	—	8	1	no	—
278	C₂²×C₁₃	—	8	2	no	—
279	C₂²×C₁₃	—	16	2	no	—
280	C₂²×C₁₃	—	16	2	no	—
281	C₂²×C₁₃	—	16	2	no	—
282	C₂²×C₁₃	#537	1	1	yes	characteristic
283	C₂²×C₁₃	#547	1	1	yes	characteristic
284	C₂²×C₁₃	#548	1	1	yes	characteristic
285	C₄×C₁₃	—	2	2	no	—
286	C₄×C₁₃	—	4	1	no	—
287	C₄×C₁₃	—	8	1	no	—
288	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
289	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
290	C₄×C₁₃	D₄²	1	1	yes	characteristic
291	C₄×C₁₃	#553	1	1	yes	characteristic
292	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
293	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
294	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
295	#137	—	2	1	no	—
296	#137	D₄×C₁₃	1	2	yes	—
297	AGL(1,ℤ/8)	—	2	1	no	—
298	AGL(1,ℤ/8)	—	2	4	no	—
299	AGL(1,ℤ/8)	—	2	4	no	—
300	AGL(1,ℤ/8)	—	2	4	no	—
301	AGL(1,ℤ/8)	—	4	2	no	—
302	AGL(1,ℤ/8)	D₄×C₁₃	1	2	yes	—
303	#135	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×D₈	—	2	2	no	—
307	C₂×D₈	—	2	2	no	—
308	C₂×D₈	—	2	1	no	—
309	C₂×D₈	—	2	1	no	—
310	C₂×D₈	—	2	1	no	—
311	C₂×D₈	—	2	1	no	—
312	C₂×D₈	—	2	1	no	—
313	C₂×D₈	—	2	1	no	—
314	#131	—	2	1	no	—
315	#131	—	2	1	no	—
316	#131	—	2	4	no	—
317	#131	—	2	1	no	—
318	#131	—	2	1	no	—
319	#131	—	2	1	no	—
320	#131	—	2	1	no	—
321	#131	—	4	2	no	—
322	#131	D₄×C₁₃	1	2	yes	—
323	#131	D₄×C₁₃	1	2	yes	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	4	no	—
327	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
328	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
329	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
330	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
332	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
336	#117	C₂³×C₁₃	1	1	yes	characteristic
337	#108	—	2	4	no	—
338	#108	—	2	2	no	—
339	#108	—	2	4	no	—
340	#108	—	2	1	no	—
341	#108	—	2	1	no	—
342	#108	—	2	1	no	—
343	#108	—	2	1	no	—
344	#108	D₄×C₁₃	1	2	yes	—
345	#108	D₄×C₁₃	1	2	yes	—
346	#104	—	2	2	no	—
347	#104	—	2	2	no	—
348	#102	—	4	2	no	—
349	#101	—	2	2	no	—
350	#100	—	2	2	no	—
351	#100	—	2	4	no	—
352	#100	—	2	4	no	—
353	#100	—	2	4	no	—
354	#97	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	C₂×C₁₃	—	2	1	no	—
357	C₂×C₁₃	—	2	1	no	—
358	C₂×C₁₃	—	2	1	no	—
359	C₂×C₁₃	—	4	2	no	—
360	C₂×C₁₃	—	8	1	no	—
361	C₂×C₁₃	—	16	2	no	—
362	C₂×C₁₃	#2416	1	1	yes	characteristic
363	C₂⁴	—	2	2	no	—
364	#41	—	2	1	no	—
365	#41	—	2	1	no	—
366	#41	—	2	1	no	—
367	#41	—	2	1	no	—
368	#41	—	2	1	no	—
369	#41	—	2	1	no	—
370	#41	C₂×D₄×C₁₃	1	2	yes	—
371	#41	C₂×D₄×C₁₃	1	2	yes	—
372	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
373	C₂×Q₈	C₁₃×#41	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
383	C₂×D₄	C₁₃×#41	1	1	yes	characteristic
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
387	Q₁₆	—	2	2	no	—
388	SD₁₆	—	2	2	no	—
389	SD₁₆	—	2	2	no	—
390	SD₁₆	—	4	4	no	—
391	SD₁₆	—	4	4	no	—
392	D₈	—	2	2	no	—
393	D₈	—	4	4	no	—
394	D₈	—	4	4	no	—
395	D₈	—	4	1	no	—
396	D₈	—	4	1	no	—
397	D₈	—	4	1	no	—
398	D₈	—	4	1	no	—
399	M₁₆	—	2	1	no	—
400	M₁₆	—	2	1	no	—
401	M₁₆	—	2	2	no	—
402	M₁₆	—	2	2	no	—
403	M₁₆	—	2	2	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	2	2	no	—
406	M₁₆	—	2	2	no	—
407	M₁₆	—	2	2	no	—
408	M₁₆	—	2	1	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	4	4	no	—
411	M₁₆	—	4	1	no	—
412	M₁₆	—	4	1	no	—
413	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
414	M₁₆	C₂×D₄×C₁₃	1	2	yes	—
415	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	2	no	—
423	C₂×C₈	—	2	2	no	—
424	C₂×C₈	—	4	4	no	—
425	C₂×C₈	—	4	1	no	—
426	C₂×C₈	—	4	1	no	—
427	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
431	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
432	C₂×C₈	C₁₃×#41	1	1	yes	characteristic
433	C₄⋊C₄	—	2	1	no	—
434	C₂²⋊C₄	—	2	1	no	—
435	C₄²	—	2	1	no	—
436	C₁₃	#24809	1	1	yes	characteristic, direct product factor, Sylow
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	16	2	no	—
443	C₂³	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	2	1	no	—
447	Q₈	C₁₃×#121	1	2	yes	—
448	D₄	—	2	2	no	—
449	D₄	—	2	2	no	—
450	D₄	—	2	1	no	—
451	D₄	—	2	1	no	—
452	D₄	—	2	1	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	4	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	2	no	—
459	D₄	C₁₃×#121	1	2	yes	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
468	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
469	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
470	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
471	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
472	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	2	2	no	—
475	C₈	—	2	4	no	—
476	C₈	—	4	1	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	2	no	—
479	C₈	C₁₃×#121	1	1	yes	characteristic
480	C₈	C₁₃×#121	1	1	yes	characteristic
481	C₈	C₁₃×#121	1	1	yes	characteristic
482	C₈	C₁₃×#121	1	1	yes	characteristic
483	C₂²	—	2	2	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	1	no	—
486	C₂²	—	8	1	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	16	2	no	—
490	C₂²	—	16	2	no	—
491	C₂²	—	16	2	no	—
492	C₂²	C₁₃×#537	1	1	yes	characteristic
493	C₂²	C₁₃×#547	1	1	yes	characteristic
494	C₂²	C₁₃×#548	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	4	1	no	—
497	C₄	—	8	1	no	—
498	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
499	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
500	C₄	D₄²×C₁₃	1	1	yes	characteristic
501	C₄	C₁₃×#553	1	1	yes	characteristic
502	C₂	—	2	1	no	—
503	C₂	—	2	1	no	—
504	C₂	—	2	1	no	—
505	C₂	—	4	2	no	—
506	C₂	—	8	1	no	—
507	C₂	—	16	2	no	—
508	C₂	C₁₃×#2416	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₃	#2416
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3068	C₂	semidirect
2. C₂×C₁₃×#472	C₂	semidirect
3. C₂×C₁₃×#472	C₂	semidirect
4. C₁₃×#2955	C₂	semidirect
5. C₁₃×#2916	C₂	semidirect
6. C₁₃×#2069	C₂	semidirect
7. C₁₃×#2048	C₂	semidirect
8. C₁₃×#1978	C₂	semidirect
9. C₁₃×#1953	C₂	semidirect
10. C₁₃×#1903	C₂	semidirect
11. C₁₃×#1813	C₂	semidirect
109. #24809	C₁₃	direct (N × H)
183. #3068	C₂×C₁₃	semidirect
184. C₂×#472	C₂×C₁₃	semidirect
185. C₂×#472	C₂×C₁₃	semidirect
186. #2955	C₂×C₁₃	semidirect
187. #2916	C₂×C₁₃	semidirect
188. #2069	C₂×C₁₃	semidirect
189. #2048	C₂×C₁₃	semidirect
190. #1978	C₂×C₁₃	semidirect
191. #1953	C₂×C₁₃	semidirect
192. #1903	C₂×C₁₃	semidirect
193. #1813	C₂×C₁₃	semidirect
436. C₁₃	#24809	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#3068	2
C₂×C₁₃×#472	2
C₁₃×#2955	2
C₁₃×#2916	2
C₁₃×#2069	2
C₁₃×#2048	2
C₁₃×#1978	2
C₁₃×#1953	2
C₁₃×#1903	2
C₁₃×#1813	2
#24809	13

Subgroups — C13×#24809 #15711148

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24809 #15711148