Subgroups — C₁₃×#60820 #15747159

Order 3328.

2122 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	C₁₃×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3221	C₂	1	8	yes	maximal, complemented
4	C₁₃×#3207	C₂	1	4	yes	maximal, complemented
5	C₁₃×#3206	C₂	1	4	yes	maximal, complemented
6	C₁₃×#3151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₃×#492	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#3139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#3042	C₂	1	4	yes	maximal, complemented
11	C₁₃×#3010	C₂	1	4	yes	maximal, complemented
12	C₁₃×#2922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₁₃×2₋¹⁺⁴	C₂²	1	2	yes	—
14	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	4	yes	—
15	C₂²×C₁₃×SD₁₆	C₂²	1	4	yes	—
16	C₁₃×#559	—	2	2	no	—
17	C₁₃×#550	—	2	2	no	—
18	D₄×Q₈×C₁₃	—	2	2	no	—
19	C₁₃×#547	—	2	4	no	—
20	C₁₃×#547	—	2	2	no	—
21	C₁₃×#546	—	2	4	no	—
22	C₁₃×#540	C₂²	1	4	yes	—
23	C₁₃×#536	C₂²	1	2	yes	—
24	C₁₃×#536	C₂²	1	4	yes	complemented
25	C₁₃×#535	C₂²	1	2	yes	—
26	C₁₃×#533	C₂²	1	1	yes	characteristic
27	C₁₃×#532	C₂²	1	1	yes	characteristic
28	C₁₃×#532	C₂²	1	4	yes	—
29	C₁₃×#532	C₂²	1	2	yes	complemented
30	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
33	C₁₃×#518	C₂²	1	2	yes	—
34	C₄×C₁₃×#41	C₂²	1	1	yes	characteristic
35	C₁₃×#496	C₂²	1	4	yes	—
36	C₁₃×#493	C₂²	1	2	yes	—
37	C₁₃×#492	C₂²	1	4	yes	—
38	C₁₃×#492	C₂²	1	4	yes	—
39	C₁₃×#492	C₂²	1	2	yes	—
40	C₁₃×#491	C₂²	1	4	yes	complemented
41	C₁₃×#488	C₂²	1	4	yes	complemented
42	C₁₃×#487	C₂²	1	2	yes	complemented
43	C₁₃×#487	C₂²	1	4	yes	complemented
44	C₁₃×#486	C₂²	1	2	yes	complemented
45	C₁₃×#463	C₂²	1	16	yes	complemented
46	C₁₃×#461	C₂²	1	16	yes	complemented
47	C₁₃×#449	C₂²	1	16	yes	complemented
48	C₁₃×#448	C₂²	1	16	yes	complemented
49	C₁₃×#433	C₂²	1	4	yes	complemented
50	C₁₃×#431	C₂²	1	4	yes	complemented
51	C₁₃×#424	C₂²	1	2	yes	—
52	C₁₃×#419	C₂²	1	4	yes	—
53	C₁₃×#416	C₂²	1	4	yes	—
54	C₁₃×#408	C₂²	1	2	yes	—
55	C₄×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
57	C₁₃×2₋¹⁺⁴	—	4	8	no	—
58	C₂×C₁₃×#41	—	2	4	no	—
59	C₂×C₁₃×#41	—	2	2	no	—
60	C₂×C₁₃×#41	—	2	4	no	—
61	C₂×C₁₃×#41	C₂³	1	2	yes	—
62	C₂×C₁₃×#41	C₂³	1	4	yes	—
63	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₁₃	—	2	2	no	—
65	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
66	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
67	C₂²×D₄×C₁₃	—	2	2	no	—
68	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
69	C₁₃×AGL(1,ℤ/8)	—	4	8	no	—
70	C₂×C₁₃×SD₁₆	—	4	8	no	—
71	C₂×C₁₃×SD₁₆	C₂³	1	8	yes	—
72	C₂×C₁₃×SD₁₆	C₂³	1	16	yes	—
73	C₂×C₁₃×D₈	C₂³	1	8	yes	—
74	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
76	C₁₃×C₄⋊Q₈	—	2	2	no	—
77	C₁₃×C₄⋊Q₈	—	2	4	no	—
78	C₁₃×C₄⋊Q₈	C₂³	1	4	yes	—
79	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
80	C₁₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
82	C₁₃×C₄⋊Q₈	C₂³	1	2	yes	—
83	C₁₃×#127	—	2	2	no	—
84	C₁₃×#127	—	2	2	no	—
85	C₁₃×#127	C₂³	1	1	yes	characteristic
86	C₁₃×#127	C₂³	1	2	yes	—
87	C₁₃×#127	C₂³	1	2	yes	—
88	C₁₃×#125	C₂³	1	2	yes	—
89	C₁₃×#124	—	2	2	no	—
90	C₁₃×#124	—	2	4	no	—
91	C₁₃×#124	C₂³	1	4	yes	—
92	C₁₃×#124	C₂³	1	2	yes	—
93	C₁₃×#123	—	2	8	no	—
94	C₁₃×#123	—	2	4	no	—
95	C₁₃×#123	—	2	8	no	—
96	C₁₃×C₂²⋊Q₈	—	2	2	no	—
97	C₁₃×C₂²⋊Q₈	—	2	4	no	—
98	C₁₃×C₂²⋊Q₈	—	2	8	no	—
99	C₁₃×#121	—	2	4	no	—
100	C₁₃×#121	—	2	2	no	—
101	C₁₃×#121	—	2	4	no	—
102	C₁₃×#121	—	2	8	no	—
103	C₁₃×#121	C₂³	1	8	yes	—
104	C₁₃×#120	—	2	4	no	—
105	C₄×Q₈×C₁₃	—	2	2	no	—
106	C₄×Q₈×C₁₃	D₄	1	2	yes	—
107	C₄×D₄×C₁₃	—	2	4	no	—
108	C₄×D₄×C₁₃	—	2	4	no	—
109	C₄×D₄×C₁₃	—	2	2	no	—
110	C₄×D₄×C₁₃	—	2	4	no	—
111	C₄×D₄×C₁₃	D₄	1	4	yes	—
112	C₄×D₄×C₁₃	D₄	1	2	yes	—
113	C₄×D₄×C₁₃	C₂³	1	8	yes	—
114	C₁₃×#117	C₂³	1	2	yes	—
115	C₁₃×#117	C₂³	1	1	yes	characteristic
116	C₁₃×#117	C₂³	1	2	yes	—
117	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
118	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
120	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₁₃×C₄⋊C₈	C₂³	1	8	yes	—
123	C₁₃×#103	C₂³	1	8	yes	—
124	C₁₃×#103	C₂³	1	16	yes	—
125	C₁₃×#102	C₂³	1	8	yes	—
126	C₁₃×C₂²⋊C₈	C₂³	1	8	yes	—
127	C₁₃×#97	C₂³	1	2	yes	—
128	C₄×C₈×C₁₃	C₂³	1	2	yes	—
129	C₄×C₈×C₁₃	C₂³	1	2	yes	—
130	C₄×C₈×C₁₃	C₂³	1	2	yes	—
131	#60820	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	—	2	2	no	—
133	C₁₃×#41	—	2	4	no	—
134	C₁₃×#41	—	2	8	no	—
135	C₁₃×#41	—	4	8	no	—
136	C₁₃×#41	—	4	16	no	—
137	C₁₃×#41	—	4	8	no	—
138	C₁₃×#41	—	8	8	no	—
139	C₂×Q₈×C₁₃	—	2	2	no	—
140	C₂×Q₈×C₁₃	—	2	4	no	—
141	C₂×Q₈×C₁₃	—	2	2	no	—
142	C₂×Q₈×C₁₃	—	2	8	no	—
143	C₂×Q₈×C₁₃	—	4	8	no	—
144	C₂×Q₈×C₁₃	—	4	8	no	—
145	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
147	C₂×Q₈×C₁₃	C₂⁴	1	2	yes	—
148	C₂×D₄×C₁₃	—	2	4	no	—
149	C₂×D₄×C₁₃	—	2	2	no	—
150	C₂×D₄×C₁₃	—	2	8	no	—
151	C₂×D₄×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	8	no	—
156	C₂×D₄×C₁₃	—	8	4	no	—
157	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	2	no	—
165	C₂²×C₄×C₁₃	—	2	8	no	—
166	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
167	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×SD₁₆	—	4	16	no	—
171	C₁₃×SD₁₆	—	4	8	no	—
172	C₁₃×D₈	—	4	8	no	—
173	C₁₃×M₁₆	—	2	4	no	—
174	C₂×C₈×C₁₃	—	2	4	no	—
175	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
176	C₂×C₈×C₁₃	C₂⁴	1	4	yes	—
177	C₁₃×C₄⋊C₄	—	2	4	no	—
178	C₁₃×C₄⋊C₄	—	2	2	no	—
179	C₁₃×C₄⋊C₄	—	2	8	no	—
180	C₁₃×C₄⋊C₄	—	2	4	no	—
181	C₁₃×C₄⋊C₄	—	2	2	no	—
182	C₁₃×C₄⋊C₄	—	2	4	no	—
183	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
184	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
185	C₁₃×C₄⋊C₄	C₂⁴	1	4	yes	—
186	C₁₃×C₂²⋊C₄	—	2	2	no	—
187	C₁₃×C₂²⋊C₄	—	2	8	no	—
188	C₁₃×C₂²⋊C₄	—	2	8	no	—
189	C₁₃×C₂²⋊C₄	—	2	8	no	—
190	C₁₃×C₂²⋊C₄	—	2	4	no	—
191	C₁₃×C₂²⋊C₄	C₂×D₄	1	2	yes	—
192	C₁₃×C₂²⋊C₄	C₂×D₄	1	4	yes	—
193	C₄²×C₁₃	—	2	2	no	—
194	C₄²×C₁₃	C₂×D₄	1	4	yes	—
195	C₄²×C₁₃	C₂×D₄	1	2	yes	—
196	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
197	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₄²×C₁₃	C₂⁴	1	2	yes	—
199	#3508	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#3499	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#3221	C₂×C₁₃	1	8	yes	complemented
202	#3207	C₂×C₁₃	1	4	yes	complemented
203	#3206	C₂×C₁₃	1	4	yes	complemented
204	#3151	C₂×C₁₃	1	1	yes	characteristic, complemented
205	C₂×#492	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#3139	C₂×C₁₃	1	1	yes	characteristic, complemented
207	#3131	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#3042	C₂×C₁₃	1	4	yes	complemented
209	#3010	C₂×C₁₃	1	4	yes	complemented
210	#2922	C₂×C₁₃	1	1	yes	characteristic, complemented
211	C₂³×C₁₃	—	2	2	no	—
212	C₂³×C₁₃	—	2	4	no	—
213	C₂³×C₁₃	—	4	4	no	—
214	C₂³×C₁₃	—	8	4	no	—
215	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
216	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
217	Q₈×C₁₃	—	2	2	no	—
218	Q₈×C₁₃	—	2	8	no	—
219	Q₈×C₁₃	—	2	4	no	—
220	Q₈×C₁₃	—	4	8	no	—
221	Q₈×C₁₃	—	4	4	no	—
222	Q₈×C₁₃	—	4	4	no	—
223	D₄×C₁₃	—	2	4	no	—
224	D₄×C₁₃	—	2	2	no	—
225	D₄×C₁₃	—	2	4	no	—
226	D₄×C₁₃	—	2	8	no	—
227	D₄×C₁₃	—	4	8	no	—
228	D₄×C₁₃	—	4	4	no	—
229	D₄×C₁₃	—	4	4	no	—
230	D₄×C₁₃	—	4	4	no	—
231	D₄×C₁₃	—	4	8	no	—
232	D₄×C₁₃	—	8	4	no	—
233	D₄×C₁₃	—	8	8	no	—
234	C₂×C₄×C₁₃	—	2	4	no	—
235	C₂×C₄×C₁₃	—	2	8	no	—
236	C₂×C₄×C₁₃	—	2	4	no	—
237	C₂×C₄×C₁₃	—	2	4	no	—
238	C₂×C₄×C₁₃	—	2	4	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	4	8	no	—
241	C₂×C₄×C₁₃	—	4	8	no	—
242	C₂×C₄×C₁₃	—	4	4	no	—
243	C₂×C₄×C₁₃	—	4	4	no	—
244	C₂×C₄×C₁₃	—	8	8	no	—
245	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₁₃	C₂²×D₄	1	4	yes	—
247	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
251	C₂×C₄×C₁₃	C₂⁵	1	1	yes	characteristic
252	C₈×C₁₃	—	2	4	no	—
253	C₈×C₁₃	—	2	4	no	—
254	C₂×2₋¹⁺⁴	C₂²×C₁₃	1	2	yes	—
255	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	4	yes	—
256	C₂²×SD₁₆	C₂²×C₁₃	1	4	yes	—
257	#559	—	2	2	no	—
258	#550	—	2	2	no	—
259	D₄×Q₈	—	2	2	no	—
260	#547	—	2	4	no	—
261	#547	—	2	2	no	—
262	#546	—	2	4	no	—
263	#540	C₂²×C₁₃	1	4	yes	—
264	#536	C₂²×C₁₃	1	2	yes	—
265	#536	C₂²×C₁₃	1	4	yes	complemented
266	#535	C₂²×C₁₃	1	2	yes	—
267	#533	C₂²×C₁₃	1	1	yes	characteristic
268	#532	C₂²×C₁₃	1	1	yes	characteristic
269	#532	C₂²×C₁₃	1	4	yes	—
270	#532	C₂²×C₁₃	1	2	yes	complemented
271	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	complemented
273	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
274	#518	C₂²×C₁₃	1	2	yes	—
275	C₄×#41	C₂²×C₁₃	1	1	yes	characteristic
276	#496	C₂²×C₁₃	1	4	yes	—
277	#493	C₂²×C₁₃	1	2	yes	—
278	#492	C₂²×C₁₃	1	4	yes	—
279	#492	C₂²×C₁₃	1	4	yes	—
280	#492	C₂²×C₁₃	1	2	yes	—
281	#491	C₂²×C₁₃	1	4	yes	complemented
282	#488	C₂²×C₁₃	1	4	yes	complemented
283	#487	C₂²×C₁₃	1	2	yes	complemented
284	#487	C₂²×C₁₃	1	4	yes	complemented
285	#486	C₂²×C₁₃	1	2	yes	complemented
286	#463	C₂²×C₁₃	1	16	yes	complemented
287	#461	C₂²×C₁₃	1	16	yes	complemented
288	#449	C₂²×C₁₃	1	16	yes	complemented
289	#448	C₂²×C₁₃	1	16	yes	complemented
290	#433	C₂²×C₁₃	1	4	yes	complemented
291	#431	C₂²×C₁₃	1	4	yes	complemented
292	#424	C₂²×C₁₃	1	2	yes	—
293	#419	C₂²×C₁₃	1	4	yes	—
294	#416	C₂²×C₁₃	1	4	yes	—
295	#408	C₂²×C₁₃	1	2	yes	—
296	C₄×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	4	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	4	no	—
303	C₂²×C₁₃	—	4	8	no	—
304	C₂²×C₁₃	—	4	4	no	—
305	C₂²×C₁₃	—	16	4	no	—
306	C₂²×C₁₃	#535	1	2	yes	—
307	C₂²×C₁₃	C₂³×D₄	1	1	yes	characteristic
308	C₄×C₁₃	—	2	2	no	—
309	C₄×C₁₃	—	2	4	no	—
310	C₄×C₁₃	—	2	2	no	—
311	C₄×C₁₃	—	4	4	no	—
312	C₄×C₁₃	—	4	2	no	—
313	C₄×C₁₃	—	4	4	no	—
314	C₄×C₁₃	#535	1	2	yes	—
315	C₄×C₁₃	#577	1	4	yes	—
316	C₄×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
317	2₋¹⁺⁴	—	4	8	no	—
318	C₂×#41	—	2	4	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	4	no	—
321	C₂×#41	C₂³×C₁₃	1	2	yes	—
322	C₂×#41	C₂³×C₁₃	1	4	yes	—
323	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
326	C₂²×Q₈	C₂³×C₁₃	1	4	yes	—
327	C₂²×D₄	—	2	2	no	—
328	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
329	AGL(1,ℤ/8)	—	4	8	no	—
330	C₂×SD₁₆	—	4	8	no	—
331	C₂×SD₁₆	C₂³×C₁₃	1	16	yes	—
332	C₂×SD₁₆	C₂³×C₁₃	1	8	yes	—
333	C₂×D₈	C₂³×C₁₃	1	8	yes	—
334	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
335	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	4	no	—
338	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
339	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
340	C₄⋊Q₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₄⋊Q₈	C₂³×C₁₃	1	4	yes	—
342	C₄⋊Q₈	C₂³×C₁₃	1	2	yes	—
343	#127	—	2	2	no	—
344	#127	—	2	2	no	—
345	#127	C₂³×C₁₃	1	2	yes	—
346	#127	C₂³×C₁₃	1	2	yes	—
347	#127	C₂³×C₁₃	1	1	yes	characteristic
348	#125	C₂³×C₁₃	1	2	yes	—
349	#124	—	2	2	no	—
350	#124	—	2	4	no	—
351	#124	C₂³×C₁₃	1	2	yes	—
352	#124	C₂³×C₁₃	1	4	yes	—
353	#123	—	2	8	no	—
354	#123	—	2	4	no	—
355	#123	—	2	8	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	4	no	—
358	C₂²⋊Q₈	—	2	8	no	—
359	#121	—	2	4	no	—
360	#121	—	2	2	no	—
361	#121	—	2	4	no	—
362	#121	—	2	8	no	—
363	#121	C₂³×C₁₃	1	8	yes	—
364	#120	—	2	4	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	D₄×C₁₃	1	2	yes	—
367	C₄×D₄	—	2	4	no	—
368	C₄×D₄	—	2	4	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	4	no	—
371	C₄×D₄	D₄×C₁₃	1	4	yes	—
372	C₄×D₄	D₄×C₁₃	1	2	yes	—
373	C₄×D₄	C₂³×C₁₃	1	8	yes	—
374	#117	C₂³×C₁₃	1	2	yes	—
375	#117	C₂³×C₁₃	1	1	yes	characteristic
376	#117	C₂³×C₁₃	1	2	yes	—
377	C₂×C₄⋊C₄	—	2	2	no	—
378	C₂×C₄⋊C₄	—	2	4	no	—
379	C₂×C₂²⋊C₄	—	2	4	no	—
380	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
382	C₄⋊C₈	C₂³×C₁₃	1	8	yes	—
383	#103	C₂³×C₁₃	1	8	yes	—
384	#103	C₂³×C₁₃	1	16	yes	—
385	#102	C₂³×C₁₃	1	8	yes	—
386	C₂²⋊C₈	C₂³×C₁₃	1	8	yes	—
387	#97	C₂³×C₁₃	1	2	yes	—
388	C₄×C₈	C₂³×C₁₃	1	2	yes	—
389	C₄×C₈	C₂³×C₁₃	1	2	yes	—
390	C₄×C₈	C₂³×C₁₃	1	2	yes	—
391	C₂×C₁₃	—	2	2	no	—
392	C₂×C₁₃	—	4	2	no	—
393	C₂×C₁₃	—	8	2	no	—
394	C₂×C₁₃	—	8	4	no	—
395	C₂×C₁₃	C₂×#535	1	1	yes	characteristic
396	C₂×C₁₃	C₂×#577	1	2	yes	—
397	C₂⁴	—	2	2	no	—
398	#41	—	2	4	no	—
399	#41	—	2	8	no	—
400	#41	—	4	8	no	—
401	#41	—	4	16	no	—
402	#41	—	4	8	no	—
403	#41	—	8	8	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	4	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	2	8	no	—
408	C₂×Q₈	—	4	8	no	—
409	C₂×Q₈	—	4	8	no	—
410	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
411	C₂×Q₈	C₂⁴×C₁₃	1	4	yes	—
412	C₂×Q₈	C₂⁴×C₁₃	1	2	yes	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	8	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	4	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	8	no	—
421	C₂×D₄	—	8	4	no	—
422	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
423	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₂×D₄	C₂⁴×C₁₃	1	2	yes	—
425	C₂×D₄	C₂⁴×C₁₃	1	4	yes	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	8	no	—
431	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
432	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
435	SD₁₆	—	4	16	no	—
436	SD₁₆	—	4	8	no	—
437	D₈	—	4	8	no	—
438	M₁₆	—	2	4	no	—
439	C₂×C₈	—	2	4	no	—
440	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
441	C₂×C₈	C₂⁴×C₁₃	1	4	yes	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	2	4	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
449	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
450	C₄⋊C₄	C₂⁴×C₁₃	1	4	yes	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	8	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	4	no	—
456	C₂²⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
457	C₂²⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
458	C₄²	—	2	2	no	—
459	C₄²	C₂×D₄×C₁₃	1	4	yes	—
460	C₄²	C₂×D₄×C₁₃	1	2	yes	—
461	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
462	C₄²	C₂⁴×C₁₃	1	1	yes	characteristic
463	C₄²	C₂⁴×C₁₃	1	2	yes	—
464	C₁₃	#60820	1	1	yes	characteristic, direct product factor, Sylow
465	C₂³	—	2	2	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	8	4	no	—
469	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
470	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
471	Q₈	—	2	2	no	—
472	Q₈	—	2	8	no	—
473	Q₈	—	2	4	no	—
474	Q₈	—	4	8	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	8	no	—
481	D₄	—	4	8	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	8	no	—
485	D₄	—	4	4	no	—
486	D₄	—	8	4	no	—
487	D₄	—	8	8	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	8	8	no	—
499	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₁₃	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
504	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
505	C₂×C₄	C₂⁵×C₁₃	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₈	—	2	4	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	16	4	no	—
516	C₂²	C₁₃×#535	1	2	yes	—
517	C₂²	C₂³×D₄×C₁₃	1	1	yes	characteristic
518	C₄	—	2	4	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	2	no	—
524	C₄	C₁₃×#535	1	2	yes	—
525	C₄	C₁₃×#577	1	4	yes	—
526	C₄	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
527	C₂	—	2	2	no	—
528	C₂	—	4	2	no	—
529	C₂	—	8	4	no	—
530	C₂	—	8	2	no	—
531	C₂	C₂×C₁₃×#535	1	1	yes	characteristic
532	C₂	C₂×C₁₃×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄×C₁₃×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3508	C₂	semidirect
2. C₁₃×#3499	C₂	semidirect
3. C₁₃×#3221	C₂	semidirect
4. C₁₃×#3207	C₂	semidirect
5. C₁₃×#3206	C₂	semidirect
6. C₁₃×#3151	C₂	semidirect
7. C₂×C₁₃×#492	C₂	semidirect
8. C₁₃×#3139	C₂	semidirect
9. C₁₃×#3131	C₂	semidirect
10. C₁₃×#3042	C₂	semidirect
11. C₁₃×#3010	C₂	semidirect
12. C₁₃×#2922	C₂	semidirect
24. C₁₃×#536	C₂²	semidirect
29. C₁₃×#532	C₂²	semidirect
31. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
40. C₁₃×#491	C₂²	semidirect
41. C₁₃×#488	C₂²	semidirect
42. C₁₃×#487	C₂²	semidirect
43. C₁₃×#487	C₂²	semidirect
44. C₁₃×#486	C₂²	semidirect
45. C₁₃×#463	C₂²	semidirect
46. C₁₃×#461	C₂²	semidirect
47. C₁₃×#449	C₂²	semidirect
48. C₁₃×#448	C₂²	semidirect
49. C₁₃×#433	C₂²	semidirect
50. C₁₃×#431	C₂²	semidirect
131. #60820	C₁₃	direct (N × H)
199. #3508	C₂×C₁₃	semidirect
200. #3499	C₂×C₁₃	semidirect
201. #3221	C₂×C₁₃	semidirect
202. #3207	C₂×C₁₃	semidirect
203. #3206	C₂×C₁₃	semidirect
204. #3151	C₂×C₁₃	semidirect
205. C₂×#492	C₂×C₁₃	semidirect
206. #3139	C₂×C₁₃	semidirect
207. #3131	C₂×C₁₃	semidirect
208. #3042	C₂×C₁₃	semidirect
209. #3010	C₂×C₁₃	semidirect
210. #2922	C₂×C₁₃	semidirect
265. #536	C₂²×C₁₃	semidirect
270. #532	C₂²×C₁₃	semidirect
272. C₂×C₄⋊Q₈	C₂²×C₁₃	semidirect
281. #491	C₂²×C₁₃	semidirect
282. #488	C₂²×C₁₃	semidirect
283. #487	C₂²×C₁₃	semidirect
284. #487	C₂²×C₁₃	semidirect
285. #486	C₂²×C₁₃	semidirect
286. #463	C₂²×C₁₃	semidirect
287. #461	C₂²×C₁₃	semidirect
288. #449	C₂²×C₁₃	semidirect
289. #448	C₂²×C₁₃	semidirect
290. #433	C₂²×C₁₃	semidirect
291. #431	C₂²×C₁₃	semidirect
464. C₁₃	#60820	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×#3508	2
C₁₃×#3499	2
C₁₃×#3221	2
C₁₃×#3207	2
C₁₃×#3206	2
C₁₃×#3151	2
C₂×C₁₃×#492	2
C₁₃×#3139	2
C₁₃×#3131	2
C₁₃×#3042	2
C₁₃×#3010	2
C₁₃×#2922	2
#60820	13

Subgroups — C13×#60820 #15747159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#60820 #15747159