Subgroups — C₁₃×#26850 #15713189

Order 3328.

776 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3136	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3096	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#3081	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2946	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2060	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2051	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2002	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1957	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1937	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1887	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1859	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1772	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
17	C₁₃×#544	C₂²	1	1	yes	characteristic
18	C₁₃×#535	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
20	C₁₃×#520	C₂²	1	1	yes	characteristic
21	C₁₃×#518	C₂²	1	1	yes	characteristic
22	C₁₃×#490	—	2	1	no	—
23	C₁₃×#489	—	2	1	no	—
24	C₁₃×#488	—	2	1	no	—
25	C₁₃×#486	—	2	1	no	—
26	C₁₃×#482	—	2	1	no	—
27	C₁₃×#482	—	2	1	no	—
28	C₁₃×#481	—	2	1	no	—
29	C₁₃×#480	—	2	1	no	—
30	C₁₃×#478	—	2	1	no	—
31	C₁₃×#478	—	2	1	no	—
32	C₁₃×#476	—	2	1	no	—
33	C₁₃×#474	—	2	1	no	—
34	C₁₃×#442	—	2	1	no	—
35	C₁₃×#440	—	2	1	no	—
36	C₄×C₁₃×SD₁₆	—	2	1	no	—
37	C₄×C₁₃×D₈	—	2	1	no	—
38	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#427	C₂²	1	1	yes	characteristic
43	C₁₃×#424	C₂²	1	1	yes	characteristic
44	C₂×C₁₃×#104	C₂²	1	1	yes	characteristic
45	C₁₃×#418	C₂²	1	1	yes	characteristic
46	C₁₃×#418	C₂²	1	1	yes	characteristic
47	C₁₃×#418	C₂²	1	1	yes	characteristic
48	C₁₃×#417	C₂²	1	1	yes	characteristic
49	C₁₃×#416	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₁₃×#408	C₂²	1	1	yes	characteristic
57	C₁₃×#405	C₂²	1	1	yes	characteristic
58	C₁₃×#405	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
60	C₁₃×#384	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	C₂²	1	1	yes	characteristic
63	C₁₃×#341	C₂²	1	1	yes	characteristic
64	C₁₃×#339	C₂²	1	1	yes	characteristic
65	C₁₃×#339	C₂²	1	1	yes	characteristic
66	C₁₃×#339	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
68	C₂²×D₄×C₁₃	—	4	1	no	—
69	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
72	C₁₃×AGL(1,ℤ/8)	—	2	2	no	—
73	C₂×C₁₃×SD₁₆	—	2	1	no	—
74	C₂×C₁₃×D₈	—	2	1	no	—
75	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₁₃×C₄⋊Q₈	—	2	1	no	—
82	C₁₃×C₄⋊Q₈	—	2	1	no	—
83	C₁₃×#127	—	2	1	no	—
84	C₁₃×#127	—	2	2	no	—
85	C₁₃×#127	—	2	2	no	—
86	C₁₃×#125	—	2	1	no	—
87	C₁₃×#125	—	2	1	no	—
88	C₁₃×#124	—	2	1	no	—
89	C₁₃×C₂²⋊Q₈	—	4	1	no	—
90	C₁₃×#121	—	2	1	no	—
91	C₁₃×#121	—	2	1	no	—
92	C₁₃×#120	—	4	1	no	—
93	C₄×Q₈×C₁₃	—	2	1	no	—
94	C₄×D₄×C₁₃	—	2	1	no	—
95	C₄×D₄×C₁₃	—	2	1	no	—
96	C₄×D₄×C₁₃	—	2	1	no	—
97	C₄×D₄×C₁₃	—	2	1	no	—
98	C₄×D₄×C₁₃	—	2	1	no	—
99	C₄×D₄×C₁₃	—	4	1	no	—
100	C₁₃×#117	—	2	1	no	—
101	C₁₃×#117	C₂³	1	1	yes	characteristic
102	C₁₃×#117	C₂³	1	1	yes	characteristic
103	C₁₃×#117	C₂³	1	1	yes	characteristic
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
106	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₁₃×#108	—	2	2	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	—	2	1	no	—
114	C₁₃×#107	D₄	1	1	yes	characteristic, complemented
115	C₁₃×#107	D₄	1	1	yes	characteristic, complemented
116	C₁₃×#106	—	2	1	no	—
117	C₁₃×#106	—	2	1	no	—
118	C₁₃×#106	—	2	1	no	—
119	C₁₃×#106	D₄	1	1	yes	characteristic, complemented
120	C₁₃×#106	D₄	1	1	yes	characteristic, complemented
121	C₁₃×C₄⋊C₈	—	2	1	no	—
122	C₁₃×C₄⋊C₈	—	2	1	no	—
123	C₁₃×#104	—	2	2	no	—
124	C₁₃×#103	—	2	1	no	—
125	C₁₃×#103	D₄	1	1	yes	characteristic, complemented
126	C₁₃×#103	D₄	1	1	yes	characteristic, complemented
127	C₁₃×#102	—	2	1	no	—
128	C₁₃×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#102	—	2	1	no	—
137	C₁₃×#102	—	2	1	no	—
138	C₁₃×#102	—	2	1	no	—
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	2	1	no	—
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	D₄	1	1	yes	characteristic, complemented
143	C₁₃×#102	D₄	1	1	yes	characteristic, complemented
144	C₁₃×#100	—	2	2	no	—
145	C₁₃×#100	—	2	2	no	—
146	C₁₃×C₂²⋊C₈	—	2	1	no	—
147	C₁₃×C₂²⋊C₈	—	2	1	no	—
148	C₁₃×#97	—	2	1	no	—
149	C₁₃×#97	—	2	1	no	—
150	C₄×C₈×C₁₃	—	2	1	no	—
151	C₄×C₈×C₁₃	—	2	1	no	—
152	C₄×C₈×C₁₃	—	2	2	no	—
153	#26850	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
154	C₂⁴×C₁₃	—	2	1	no	—
155	C₂⁴×C₁₃	—	2	1	no	—
156	C₁₃×#41	—	2	1	no	—
157	C₁₃×#41	—	2	1	no	—
158	C₁₃×#41	—	2	1	no	—
159	C₁₃×#41	—	2	1	no	—
160	C₂×Q₈×C₁₃	—	4	1	no	—
161	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₃	—	2	1	no	—
163	C₂×D₄×C₁₃	—	2	1	no	—
164	C₂×D₄×C₁₃	—	2	1	no	—
165	C₂×D₄×C₁₃	—	2	1	no	—
166	C₂×D₄×C₁₃	—	2	1	no	—
167	C₂×D₄×C₁₃	—	2	1	no	—
168	C₂×D₄×C₁₃	—	2	1	no	—
169	C₂×D₄×C₁₃	—	2	1	no	—
170	C₂×D₄×C₁₃	—	2	1	no	—
171	C₂×D₄×C₁₃	—	2	1	no	—
172	C₂×D₄×C₁₃	—	2	1	no	—
173	C₂×D₄×C₁₃	—	2	1	no	—
174	C₂×D₄×C₁₃	—	4	4	no	—
175	C₂×D₄×C₁₃	—	4	1	no	—
176	C₂×D₄×C₁₃	—	4	1	no	—
177	C₂×D₄×C₁₃	—	8	2	no	—
178	C₂×D₄×C₁₃	—	8	2	no	—
179	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂×D₄×C₁₃	#41	1	2	yes	—
181	C₂²×C₄×C₁₃	—	2	1	no	—
182	C₂²×C₄×C₁₃	—	2	1	no	—
183	C₂²×C₄×C₁₃	—	2	1	no	—
184	C₂²×C₄×C₁₃	—	2	1	no	—
185	C₂²×C₄×C₁₃	—	4	1	no	—
186	C₂²×C₄×C₁₃	—	4	1	no	—
187	C₂²×C₄×C₁₃	—	4	1	no	—
188	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
189	C₁₃×SD₁₆	—	2	4	no	—
190	C₁₃×D₈	—	2	4	no	—
191	C₁₃×M₁₆	—	2	1	no	—
192	C₁₃×M₁₆	—	2	1	no	—
193	C₁₃×M₁₆	—	2	1	no	—
194	C₁₃×M₁₆	—	2	1	no	—
195	C₁₃×M₁₆	—	2	1	no	—
196	C₁₃×M₁₆	—	2	1	no	—
197	C₁₃×M₁₆	—	2	1	no	—
198	C₁₃×M₁₆	#41	1	2	yes	—
199	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	—	2	1	no	—
202	C₂×C₈×C₁₃	—	2	1	no	—
203	C₂×C₈×C₁₃	—	2	1	no	—
204	C₂×C₈×C₁₃	—	2	1	no	—
205	C₂×C₈×C₁₃	—	2	1	no	—
206	C₂×C₈×C₁₃	—	2	1	no	—
207	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
208	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
209	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
210	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	4	1	no	—
216	C₁₃×C₄⋊C₄	—	4	1	no	—
217	C₁₃×C₄⋊C₄	—	4	1	no	—
218	C₁₃×C₄⋊C₄	—	4	1	no	—
219	C₁₃×C₄⋊C₄	—	8	2	no	—
220	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
221	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
222	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
223	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
224	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
225	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
226	C₁₃×C₂²⋊C₄	—	2	1	no	—
227	C₁₃×C₂²⋊C₄	—	2	1	no	—
228	C₁₃×C₂²⋊C₄	—	2	1	no	—
229	C₁₃×C₂²⋊C₄	—	4	1	no	—
230	C₁₃×C₂²⋊C₄	—	4	1	no	—
231	C₁₃×C₂²⋊C₄	—	4	1	no	—
232	C₁₃×C₂²⋊C₄	—	4	1	no	—
233	C₁₃×C₂²⋊C₄	—	4	1	no	—
234	C₄²×C₁₃	—	2	1	no	—
235	C₄²×C₁₃	—	2	1	no	—
236	C₄²×C₁₃	—	2	1	no	—
237	C₄²×C₁₃	—	2	1	no	—
238	C₄²×C₁₃	—	4	1	no	—
239	C₄²×C₁₃	#41	1	2	yes	—
240	#3136	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#3096	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#3081	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#2946	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#2060	C₂×C₁₃	1	1	yes	characteristic, complemented
246	#2051	C₂×C₁₃	1	1	yes	characteristic, complemented
247	#2002	C₂×C₁₃	1	1	yes	characteristic
248	#1957	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1937	C₂×C₁₃	1	1	yes	characteristic, complemented
250	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
251	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
252	#1887	C₂×C₁₃	1	1	yes	characteristic, complemented
253	#1859	C₂×C₁₃	1	1	yes	characteristic, complemented
254	#1772	C₂×C₁₃	1	1	yes	characteristic, complemented
255	C₂³×C₁₃	—	2	1	no	—
256	C₂³×C₁₃	—	2	2	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	8	1	no	—
263	C₂³×C₁₃	—	8	1	no	—
264	C₂³×C₁₃	—	8	1	no	—
265	C₂³×C₁₃	—	8	1	no	—
266	C₂³×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
267	Q₈×C₁₃	—	2	1	no	—
268	Q₈×C₁₃	—	2	1	no	—
269	Q₈×C₁₃	—	16	1	no	—
270	D₄×C₁₃	—	2	1	no	—
271	D₄×C₁₃	—	2	2	no	—
272	D₄×C₁₃	—	2	1	no	—
273	D₄×C₁₃	—	2	2	no	—
274	D₄×C₁₃	—	4	1	no	—
275	D₄×C₁₃	—	4	1	no	—
276	D₄×C₁₃	—	4	1	no	—
277	D₄×C₁₃	—	4	1	no	—
278	D₄×C₁₃	—	4	1	no	—
279	D₄×C₁₃	—	4	1	no	—
280	D₄×C₁₃	—	4	1	no	—
281	D₄×C₁₃	—	4	1	no	—
282	D₄×C₁₃	—	8	8	no	—
283	D₄×C₁₃	—	16	1	no	—
284	D₄×C₁₃	—	16	1	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	2	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	8	1	no	—
300	C₂×C₄×C₁₃	—	8	1	no	—
301	C₂×C₄×C₁₃	—	16	1	no	—
302	C₂×C₄×C₁₃	—	16	1	no	—
303	C₂×C₄×C₁₃	—	16	1	no	—
304	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
307	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
308	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
309	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
310	C₈×C₁₃	—	2	2	no	—
311	C₈×C₁₃	—	2	1	no	—
312	C₈×C₁₃	—	2	1	no	—
313	C₈×C₁₃	—	2	1	no	—
314	C₈×C₁₃	—	2	1	no	—
315	C₈×C₁₃	—	4	1	no	—
316	C₈×C₁₃	—	4	1	no	—
317	C₈×C₁₃	—	4	1	no	—
318	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	1	yes	characteristic
319	#544	C₂²×C₁₃	1	1	yes	characteristic
320	#535	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#127	C₂²×C₁₃	1	1	yes	characteristic
322	#520	C₂²×C₁₃	1	1	yes	characteristic
323	#518	C₂²×C₁₃	1	1	yes	characteristic
324	#490	—	2	1	no	—
325	#489	—	2	1	no	—
326	#488	—	2	1	no	—
327	#486	—	2	1	no	—
328	#482	—	2	1	no	—
329	#482	—	2	1	no	—
330	#481	—	2	1	no	—
331	#480	—	2	1	no	—
332	#478	—	2	1	no	—
333	#478	—	2	1	no	—
334	#476	—	2	1	no	—
335	#474	—	2	1	no	—
336	#442	—	2	1	no	—
337	#440	—	2	1	no	—
338	C₄×SD₁₆	—	2	1	no	—
339	C₄×D₈	—	2	1	no	—
340	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
341	#428	C₂²×C₁₃	1	1	yes	characteristic
342	#428	C₂²×C₁₃	1	1	yes	characteristic
343	#428	C₂²×C₁₃	1	1	yes	characteristic
344	#427	C₂²×C₁₃	1	1	yes	characteristic
345	#424	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#104	C₂²×C₁₃	1	1	yes	characteristic
347	#418	C₂²×C₁₃	1	1	yes	characteristic
348	#418	C₂²×C₁₃	1	1	yes	characteristic
349	#418	C₂²×C₁₃	1	1	yes	characteristic
350	#417	C₂²×C₁₃	1	1	yes	characteristic
351	#416	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
353	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
354	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
355	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
356	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
357	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
358	#408	C₂²×C₁₃	1	1	yes	characteristic
359	#405	C₂²×C₁₃	1	1	yes	characteristic
360	#405	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
362	#384	C₂²×C₁₃	1	1	yes	characteristic
363	#343	C₂²×C₁₃	1	1	yes	characteristic
364	#343	C₂²×C₁₃	1	1	yes	characteristic
365	#341	C₂²×C₁₃	1	1	yes	characteristic
366	#339	C₂²×C₁₃	1	1	yes	characteristic
367	#339	C₂²×C₁₃	1	1	yes	characteristic
368	#339	C₂²×C₁₃	1	1	yes	characteristic
369	C₂²×C₁₃	—	2	1	no	—
370	C₂²×C₁₃	—	2	1	no	—
371	C₂²×C₁₃	—	4	1	no	—
372	C₂²×C₁₃	—	4	2	no	—
373	C₂²×C₁₃	—	4	1	no	—
374	C₂²×C₁₃	—	4	1	no	—
375	C₂²×C₁₃	—	8	2	no	—
376	C₂²×C₁₃	—	8	2	no	—
377	C₂²×C₁₃	—	8	1	no	—
378	C₂²×C₁₃	—	8	1	no	—
379	C₂²×C₁₃	—	8	1	no	—
380	C₂²×C₁₃	—	8	1	no	—
381	C₂²×C₁₃	—	8	1	no	—
382	C₂²×C₁₃	—	16	1	no	—
383	C₂²×C₁₃	—	16	1	no	—
384	C₂²×C₁₃	#542	1	1	yes	characteristic
385	C₂²×C₁₃	D₄²	1	1	yes	characteristic
386	C₂²×C₁₃	#551	1	1	yes	characteristic
387	C₄×C₁₃	—	2	4	no	—
388	C₄×C₁₃	—	4	1	no	—
389	C₄×C₁₃	—	4	1	no	—
390	C₄×C₁₃	—	4	1	no	—
391	C₄×C₁₃	—	4	1	no	—
392	C₄×C₁₃	—	4	1	no	—
393	C₄×C₁₃	—	4	1	no	—
394	C₄×C₁₃	—	4	1	no	—
395	C₄×C₁₃	—	8	1	no	—
396	C₄×C₁₃	—	8	1	no	—
397	C₄×C₁₃	#525	1	1	yes	characteristic
398	C₄×C₁₃	#532	1	1	yes	characteristic
399	C₄×C₁₃	#547	1	1	yes	characteristic
400	C₄×C₁₃	#548	1	1	yes	characteristic
401	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
402	C₂²×D₄	—	4	1	no	—
403	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
405	AGL(1,ℤ/8)	—	2	2	no	—
406	AGL(1,ℤ/8)	—	2	2	no	—
407	C₂×SD₁₆	—	2	1	no	—
408	C₂×D₈	—	2	1	no	—
409	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
413	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
414	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
415	C₄⋊Q₈	—	2	1	no	—
416	C₄⋊Q₈	—	2	1	no	—
417	#127	—	2	1	no	—
418	#127	—	2	2	no	—
419	#127	—	2	2	no	—
420	#125	—	2	1	no	—
421	#125	—	2	1	no	—
422	#124	—	2	1	no	—
423	C₂²⋊Q₈	—	4	1	no	—
424	#121	—	2	1	no	—
425	#121	—	2	1	no	—
426	#120	—	4	1	no	—
427	C₄×Q₈	—	2	1	no	—
428	C₄×D₄	—	2	1	no	—
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	—	2	1	no	—
433	C₄×D₄	—	4	1	no	—
434	#117	—	2	1	no	—
435	#117	C₂³×C₁₃	1	1	yes	characteristic
436	#117	C₂³×C₁₃	1	1	yes	characteristic
437	#117	C₂³×C₁₃	1	1	yes	characteristic
438	C₂×C₄⋊C₄	—	2	1	no	—
439	C₂×C₄⋊C₄	—	4	1	no	—
440	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
441	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
442	C₂×C₂²⋊C₄	—	4	1	no	—
443	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
444	#108	—	2	2	no	—
445	#107	—	2	1	no	—
446	#107	—	2	1	no	—
447	#107	—	2	1	no	—
448	#107	D₄×C₁₃	1	1	yes	characteristic, complemented
449	#107	D₄×C₁₃	1	1	yes	characteristic, complemented
450	#106	—	2	1	no	—
451	#106	—	2	1	no	—
452	#106	—	2	1	no	—
453	#106	D₄×C₁₃	1	1	yes	characteristic, complemented
454	#106	D₄×C₁₃	1	1	yes	characteristic, complemented
455	C₄⋊C₈	—	2	1	no	—
456	C₄⋊C₈	—	2	1	no	—
457	#104	—	2	2	no	—
458	#103	—	2	1	no	—
459	#103	D₄×C₁₃	1	1	yes	characteristic, complemented
460	#103	D₄×C₁₃	1	1	yes	characteristic, complemented
461	#102	—	2	1	no	—
462	#102	—	2	1	no	—
463	#102	—	2	1	no	—
464	#102	—	2	1	no	—
465	#102	—	2	1	no	—
466	#102	—	2	1	no	—
467	#102	—	2	1	no	—
468	#102	—	2	1	no	—
469	#102	—	2	1	no	—
470	#102	—	2	1	no	—
471	#102	—	2	1	no	—
472	#102	—	2	1	no	—
473	#102	—	2	1	no	—
474	#102	—	2	1	no	—
475	#102	—	2	1	no	—
476	#102	D₄×C₁₃	1	1	yes	characteristic, complemented
477	#102	D₄×C₁₃	1	1	yes	characteristic, complemented
478	#100	—	2	2	no	—
479	#100	—	2	2	no	—
480	C₂²⋊C₈	—	2	1	no	—
481	C₂²⋊C₈	—	2	1	no	—
482	#97	—	2	1	no	—
483	#97	—	2	1	no	—
484	C₄×C₈	—	2	1	no	—
485	C₄×C₈	—	2	1	no	—
486	C₄×C₈	—	2	2	no	—
487	C₂×C₁₃	—	2	1	no	—
488	C₂×C₁₃	—	2	1	no	—
489	C₂×C₁₃	—	8	1	no	—
490	C₂×C₁₃	—	8	2	no	—
491	C₂×C₁₃	—	16	1	no	—
492	C₂×C₁₃	#2461	1	1	yes	characteristic
493	C₂×C₁₃	#3291	1	1	yes	characteristic
494	C₂×C₁₃	#3292	1	1	yes	characteristic
495	C₂⁴	—	2	1	no	—
496	C₂⁴	—	2	1	no	—
497	#41	—	2	1	no	—
498	#41	—	2	1	no	—
499	#41	—	2	1	no	—
500	#41	—	2	1	no	—
501	C₂×Q₈	—	4	1	no	—
502	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	4	4	no	—
516	C₂×D₄	—	4	1	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂×D₄	—	8	2	no	—
519	C₂×D₄	—	8	2	no	—
520	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
521	C₂×D₄	C₁₃×#41	1	2	yes	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	4	1	no	—
527	C₂²×C₄	—	4	1	no	—
528	C₂²×C₄	—	4	1	no	—
529	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
530	SD₁₆	—	2	4	no	—
531	D₈	—	2	4	no	—
532	M₁₆	—	2	1	no	—
533	M₁₆	—	2	1	no	—
534	M₁₆	—	2	1	no	—
535	M₁₆	—	2	1	no	—
536	M₁₆	—	2	1	no	—
537	M₁₆	—	2	1	no	—
538	M₁₆	—	2	1	no	—
539	M₁₆	C₁₃×#41	1	2	yes	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
551	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	4	1	no	—
557	C₄⋊C₄	—	4	1	no	—
558	C₄⋊C₄	—	4	1	no	—
559	C₄⋊C₄	—	4	1	no	—
560	C₄⋊C₄	—	8	2	no	—
561	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
562	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
563	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
564	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
565	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
566	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	—	4	1	no	—
572	C₂²⋊C₄	—	4	1	no	—
573	C₂²⋊C₄	—	4	1	no	—
574	C₂²⋊C₄	—	4	1	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	4	1	no	—
580	C₄²	C₁₃×#41	1	2	yes	—
581	C₁₃	#26850	1	1	yes	characteristic, direct product factor, Sylow
582	C₂³	—	2	1	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	4	1	no	—
585	C₂³	—	4	1	no	—
586	C₂³	—	4	1	no	—
587	C₂³	—	4	1	no	—
588	C₂³	—	4	1	no	—
589	C₂³	—	8	1	no	—
590	C₂³	—	8	1	no	—
591	C₂³	—	8	1	no	—
592	C₂³	—	8	1	no	—
593	C₂³	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
594	Q₈	—	2	1	no	—
595	Q₈	—	2	1	no	—
596	Q₈	—	16	1	no	—
597	D₄	—	2	1	no	—
598	D₄	—	2	2	no	—
599	D₄	—	2	1	no	—
600	D₄	—	2	2	no	—
601	D₄	—	4	1	no	—
602	D₄	—	4	1	no	—
603	D₄	—	4	1	no	—
604	D₄	—	4	1	no	—
605	D₄	—	4	1	no	—
606	D₄	—	4	1	no	—
607	D₄	—	4	1	no	—
608	D₄	—	4	1	no	—
609	D₄	—	8	8	no	—
610	D₄	—	16	1	no	—
611	D₄	—	16	1	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	4	1	no	—
626	C₂×C₄	—	8	1	no	—
627	C₂×C₄	—	8	1	no	—
628	C₂×C₄	—	16	1	no	—
629	C₂×C₄	—	16	1	no	—
630	C₂×C₄	—	16	1	no	—
631	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
632	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
633	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
634	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
635	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
636	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
637	C₈	—	2	2	no	—
638	C₈	—	2	1	no	—
639	C₈	—	2	1	no	—
640	C₈	—	2	1	no	—
641	C₈	—	2	1	no	—
642	C₈	—	4	1	no	—
643	C₈	—	4	1	no	—
644	C₈	—	4	1	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	4	1	no	—
648	C₂²	—	4	1	no	—
649	C₂²	—	4	1	no	—
650	C₂²	—	4	2	no	—
651	C₂²	—	8	2	no	—
652	C₂²	—	8	2	no	—
653	C₂²	—	8	1	no	—
654	C₂²	—	8	1	no	—
655	C₂²	—	8	1	no	—
656	C₂²	—	8	1	no	—
657	C₂²	—	8	1	no	—
658	C₂²	—	16	1	no	—
659	C₂²	—	16	1	no	—
660	C₂²	C₁₃×#542	1	1	yes	characteristic
661	C₂²	D₄²×C₁₃	1	1	yes	characteristic
662	C₂²	C₁₃×#551	1	1	yes	characteristic
663	C₄	—	2	4	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	1	no	—
671	C₄	—	8	1	no	—
672	C₄	—	8	1	no	—
673	C₄	C₁₃×#525	1	1	yes	characteristic
674	C₄	C₁₃×#532	1	1	yes	characteristic
675	C₄	C₁₃×#547	1	1	yes	characteristic
676	C₄	C₁₃×#548	1	1	yes	characteristic
677	C₂	—	2	1	no	—
678	C₂	—	2	1	no	—
679	C₂	—	8	1	no	—
680	C₂	—	8	2	no	—
681	C₂	—	16	1	no	—
682	C₂	C₁₃×#2461	1	1	yes	characteristic
683	C₂	C₁₃×#3291	1	1	yes	characteristic
684	C₂	C₁₃×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#2002	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#3136	C₂	semidirect
2. C₁₃×#3096	C₂	semidirect
3. C₁₃×#3081	C₂	semidirect
4. C₁₃×#2946	C₂	semidirect
5. C₁₃×#2063	C₂	semidirect
6. C₁₃×#2060	C₂	semidirect
7. C₁₃×#2051	C₂	semidirect
9. C₁₃×#1957	C₂	semidirect
10. C₁₃×#1937	C₂	semidirect
11. C₁₃×#1931	C₂	semidirect
12. C₁₃×#1931	C₂	semidirect
13. C₁₃×#1887	C₂	semidirect
14. C₁₃×#1859	C₂	semidirect
15. C₁₃×#1772	C₂	semidirect
114. C₁₃×#107	D₄	semidirect
115. C₁₃×#107	D₄	semidirect
119. C₁₃×#106	D₄	semidirect
120. C₁₃×#106	D₄	semidirect
125. C₁₃×#103	D₄	semidirect
126. C₁₃×#103	D₄	semidirect
142. C₁₃×#102	D₄	semidirect
143. C₁₃×#102	D₄	semidirect
153. #26850	C₁₃	direct (N × H)
240. #3136	C₂×C₁₃	semidirect
241. #3096	C₂×C₁₃	semidirect
242. #3081	C₂×C₁₃	semidirect
243. #2946	C₂×C₁₃	semidirect
244. #2063	C₂×C₁₃	semidirect
245. #2060	C₂×C₁₃	semidirect
246. #2051	C₂×C₁₃	semidirect
248. #1957	C₂×C₁₃	semidirect
249. #1937	C₂×C₁₃	semidirect
250. #1931	C₂×C₁₃	semidirect
251. #1931	C₂×C₁₃	semidirect
252. #1887	C₂×C₁₃	semidirect
253. #1859	C₂×C₁₃	semidirect
254. #1772	C₂×C₁₃	semidirect
448. #107	D₄×C₁₃	semidirect
449. #107	D₄×C₁₃	semidirect
453. #106	D₄×C₁₃	semidirect
454. #106	D₄×C₁₃	semidirect
459. #103	D₄×C₁₃	semidirect
460. #103	D₄×C₁₃	semidirect
476. #102	D₄×C₁₃	semidirect
477. #102	D₄×C₁₃	semidirect
581. C₁₃	#26850	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×#3136	2
C₁₃×#3096	2
C₁₃×#3081	2
C₁₃×#2946	2
C₁₃×#2063	2
C₁₃×#2060	2
C₁₃×#2051	2
C₁₃×#2002	2
C₁₃×#1957	2
C₁₃×#1937	2
C₁₃×#1931	2
C₁₃×#1887	2
C₁₃×#1859	2
C₁₃×#1772	2
#26850	13

Subgroups — C13×#26850 #15713189

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26850 #15713189