Subgroups — C₁₃×#26078 #15712417

Order 3328.

818 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2441	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2440	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1943	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1844	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1753	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
22	C₁₃×#501	—	2	4	no	—
23	C₁₃×#428	—	2	4	no	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#399	—	2	1	no	—
38	C₁₃×#398	—	2	1	no	—
39	C₁₃×#396	—	2	1	no	—
40	C₁₃×#395	—	2	1	no	—
41	C₁₃×#389	—	2	1	no	—
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#387	—	2	1	no	—
47	C₁₃×#385	—	2	1	no	—
48	C₁₃×#384	C₂²	1	1	yes	characteristic
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₁₃×#380	C₂²	1	1	yes	characteristic
51	C₁₃×#380	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×M₁₆	—	2	2	no	—
65	C₂×C₁₃×M₁₆	—	2	2	no	—
66	C₂×C₁₃×M₁₆	Q₈	1	4	yes	complemented
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×C₄⋊Q₈	—	2	2	no	—
72	C₁₃×C₄⋊Q₈	—	4	1	no	—
73	C₁₃×#125	—	2	2	no	—
74	C₁₃×#125	—	4	1	no	—
75	C₁₃×C₂²⋊Q₈	—	4	4	no	—
76	C₁₃×#117	—	2	2	no	—
77	C₁₃×#117	—	4	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	4	1	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₁₃×#107	—	2	2	no	—
109	C₁₃×#107	—	2	2	no	—
110	C₁₃×#107	—	2	2	no	—
111	C₁₃×#107	D₄	1	4	yes	—
112	C₁₃×#106	—	2	2	no	—
113	C₁₃×#106	—	2	2	no	—
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×#106	—	2	2	no	—
116	C₁₃×#106	—	4	1	no	—
117	C₁₃×#106	—	4	1	no	—
118	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	complemented
119	C₁₃×#97	—	2	2	no	—
120	C₄×C₈×C₁₃	—	2	2	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	—	2	1	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	D₄	1	1	yes	characteristic
128	C₁₃×#95	D₄	1	1	yes	characteristic
129	#26078	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×Q₈×C₁₃	—	4	2	no	—
132	C₂×Q₈×C₁₃	—	4	2	no	—
133	C₂×Q₈×C₁₃	—	8	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	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	—	4	2	no	—
147	C₂²×C₄×C₁₃	—	4	2	no	—
148	C₂²×C₄×C₁₃	—	8	1	no	—
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
155	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×M₁₆	—	2	8	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	—	2	1	no	—
161	C₂×C₈×C₁₃	—	2	1	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
165	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
166	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
167	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
168	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
169	C₂×C₈×C₁₃	#41	1	2	yes	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	2	1	no	—
175	C₁₃×C₄⋊C₄	—	2	1	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	2	1	no	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	—	2	1	no	—
183	C₁₃×C₄⋊C₄	—	2	1	no	—
184	C₁₃×C₄⋊C₄	—	4	2	no	—
185	C₁₃×C₄⋊C₄	—	4	2	no	—
186	C₁₃×C₄⋊C₄	—	4	2	no	—
187	C₁₃×C₄⋊C₄	—	4	2	no	—
188	C₁₃×C₄⋊C₄	—	4	2	no	—
189	C₁₃×C₄⋊C₄	—	4	2	no	—
190	C₁₃×C₄⋊C₄	—	4	2	no	—
191	C₁₃×C₄⋊C₄	—	4	2	no	—
192	C₁₃×C₄⋊C₄	—	4	2	no	—
193	C₁₃×C₄⋊C₄	—	8	1	no	—
194	C₁₃×C₄⋊C₄	—	8	1	no	—
195	C₁₃×C₄⋊C₄	—	8	1	no	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
197	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	2	2	no	—
200	C₁₃×C₂²⋊C₄	—	4	2	no	—
201	C₁₃×C₂²⋊C₄	—	4	2	no	—
202	C₁₃×C₂²⋊C₄	—	8	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	4	2	no	—
208	C₂×#501	C₂×C₁₃	1	1	yes	characteristic, complemented
209	C₂×#428	C₂×C₁₃	1	1	yes	characteristic
210	#2441	C₂×C₁₃	1	1	yes	characteristic
211	#2440	C₂×C₁₃	1	1	yes	characteristic
212	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2083	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2059	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#1943	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1854	C₂×C₁₃	1	1	yes	characteristic
219	#1853	C₂×C₁₃	1	1	yes	characteristic
220	#1844	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1809	C₂×C₁₃	1	1	yes	characteristic
222	#1753	C₂×C₁₃	1	1	yes	characteristic
223	C₂³×C₁₃	—	2	1	no	—
224	C₂³×C₁₃	—	2	1	no	—
225	C₂³×C₁₃	—	2	1	no	—
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
230	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	Q₈×C₁₃	—	8	4	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	1	no	—
267	C₂×C₄×C₁₃	—	4	1	no	—
268	C₂×C₄×C₁₃	—	4	1	no	—
269	C₂×C₄×C₁₃	—	4	1	no	—
270	C₂×C₄×C₁₃	—	4	1	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	8	4	no	—
273	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
274	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
275	C₂×C₄×C₁₃	#137	1	2	yes	—
276	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
278	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
279	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
280	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
281	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
282	C₈×C₁₃	—	2	2	no	—
283	C₈×C₁₃	—	2	2	no	—
284	C₈×C₁₃	—	2	2	no	—
285	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
286	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊Q₈	—	2	1	no	—
290	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
291	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
292	#501	—	2	4	no	—
293	#428	—	2	4	no	—
294	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
295	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
307	#399	—	2	1	no	—
308	#398	—	2	1	no	—
309	#396	—	2	1	no	—
310	#395	—	2	1	no	—
311	#389	—	2	1	no	—
312	#389	C₂²×C₁₃	1	1	yes	characteristic
313	#389	C₂²×C₁₃	1	1	yes	characteristic
314	#389	C₂²×C₁₃	1	1	yes	characteristic
315	#389	C₂²×C₁₃	1	1	yes	characteristic
316	#387	—	2	1	no	—
317	#385	—	2	1	no	—
318	#384	C₂²×C₁₃	1	1	yes	characteristic
319	#384	C₂²×C₁₃	1	1	yes	characteristic
320	#380	C₂²×C₁₃	1	1	yes	characteristic
321	#380	C₂²×C₁₃	1	1	yes	characteristic
322	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
323	#340	C₂²×C₁₃	1	1	yes	characteristic
324	#340	C₂²×C₁₃	1	1	yes	characteristic
325	#340	C₂²×C₁₃	1	1	yes	characteristic
326	#340	C₂²×C₁₃	1	1	yes	characteristic
327	#340	C₂²×C₁₃	1	1	yes	characteristic
328	#340	C₂²×C₁₃	1	1	yes	characteristic
329	#336	C₂²×C₁₃	1	1	yes	characteristic
330	#336	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	2	no	—
333	C₂²×C₁₃	—	2	2	no	—
334	C₂²×C₁₃	—	4	1	no	—
335	C₂²×C₁₃	—	4	1	no	—
336	C₂²×C₁₃	—	4	1	no	—
337	C₂²×C₁₃	—	4	1	no	—
338	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
339	C₂²×C₁₃	D₄²	1	1	yes	characteristic
340	C₂²×C₁₃	#547	1	1	yes	characteristic
341	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
343	C₂²×C₁₃	#577	1	1	yes	characteristic
344	C₂²×C₁₃	#577	1	1	yes	characteristic
345	C₄×C₁₃	—	2	2	no	—
346	C₄×C₁₃	—	2	2	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	—	4	1	no	—
349	C₄×C₁₃	—	4	2	no	—
350	C₄×C₁₃	—	4	2	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	8	1	no	—
353	C₄×C₁₃	—	8	1	no	—
354	C₄×C₁₃	—	8	1	no	—
355	C₄×C₁₃	—	8	1	no	—
356	C₄×C₁₃	—	8	1	no	—
357	C₄×C₁₃	—	8	1	no	—
358	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
359	C₄×C₁₃	#544	1	1	yes	characteristic
360	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
361	C₄×C₁₃	#554	1	1	yes	characteristic
362	C₂²×Q₈	—	2	1	no	—
363	C₂³×C₄	—	2	1	no	—
364	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	2	no	—
367	C₂×M₁₆	Q₈×C₁₃	1	4	yes	complemented
368	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
369	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
372	C₄⋊Q₈	—	2	2	no	—
373	C₄⋊Q₈	—	4	1	no	—
374	#125	—	2	2	no	—
375	#125	—	4	1	no	—
376	C₂²⋊Q₈	—	4	4	no	—
377	#117	—	2	2	no	—
378	#117	—	4	1	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	4	1	no	—
393	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
405	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
409	#107	—	2	2	no	—
410	#107	—	2	2	no	—
411	#107	—	2	2	no	—
412	#107	D₄×C₁₃	1	4	yes	—
413	#106	—	2	2	no	—
414	#106	—	2	2	no	—
415	#106	—	2	2	no	—
416	#106	—	2	2	no	—
417	#106	—	4	1	no	—
418	#106	—	4	1	no	—
419	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	complemented
420	#97	—	2	2	no	—
421	C₄×C₈	—	2	2	no	—
422	#95	—	2	1	no	—
423	#95	—	2	1	no	—
424	#95	—	2	1	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	D₄×C₁₃	1	1	yes	characteristic
429	#95	D₄×C₁₃	1	1	yes	characteristic
430	C₂×C₁₃	—	4	2	no	—
431	C₂×C₁₃	#2440	1	1	yes	characteristic
432	C₂×C₁₃	#3163	1	1	yes	characteristic
433	C₂×C₁₃	#3165	1	1	yes	characteristic
434	C₂×C₁₃	#3272	1	1	yes	characteristic
435	C₂×C₁₃	#3278	1	1	yes	characteristic
436	C₂×C₁₃	#3344	1	1	yes	characteristic
437	C₂×C₁₃	#3345	1	1	yes	characteristic
438	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
439	C₂×Q₈	—	4	2	no	—
440	C₂×Q₈	—	4	2	no	—
441	C₂×Q₈	—	8	1	no	—
442	C₂²×C₄	—	2	1	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	8	1	no	—
457	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
463	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
465	M₁₆	—	2	8	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
473	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
474	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
475	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
476	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
477	C₂×C₈	C₁₃×#41	1	2	yes	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	4	2	no	—
494	C₄⋊C₄	—	4	2	no	—
495	C₄⋊C₄	—	4	2	no	—
496	C₄⋊C₄	—	4	2	no	—
497	C₄⋊C₄	—	4	2	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	8	1	no	—
502	C₄⋊C₄	—	8	1	no	—
503	C₄⋊C₄	—	8	1	no	—
504	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
505	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	4	2	no	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₂²⋊C₄	—	8	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	1	no	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	4	2	no	—
516	C₁₃	#26078	1	1	yes	characteristic, direct product factor, Sylow
517	C₂³	—	2	1	no	—
518	C₂³	—	2	1	no	—
519	C₂³	—	2	1	no	—
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	—	2	1	no	—
523	C₂³	C₁₃×C₄⋊Q₈	1	2	yes	—
524	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
525	Q₈	—	8	4	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	8	4	no	—
567	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
568	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
569	C₂×C₄	C₁₃×#137	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
571	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
572	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
573	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
574	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
575	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
576	C₈	—	2	2	no	—
577	C₈	—	2	2	no	—
578	C₈	—	2	2	no	—
579	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
580	C₂²	—	2	2	no	—
581	C₂²	—	2	2	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	4	1	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
588	C₂²	D₄²×C₁₃	1	1	yes	characteristic
589	C₂²	C₁₃×#547	1	1	yes	characteristic
590	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
591	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
592	C₂²	C₁₃×#577	1	1	yes	characteristic
593	C₂²	C₁₃×#577	1	1	yes	characteristic
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	1	no	—
601	C₄	—	8	1	no	—
602	C₄	—	8	1	no	—
603	C₄	—	8	1	no	—
604	C₄	—	8	1	no	—
605	C₄	—	8	1	no	—
606	C₄	—	8	1	no	—
607	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
608	C₄	C₁₃×#544	1	1	yes	characteristic
609	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
610	C₄	C₁₃×#554	1	1	yes	characteristic
611	C₂	—	4	2	no	—
612	C₂	C₁₃×#2440	1	1	yes	characteristic
613	C₂	C₁₃×#3163	1	1	yes	characteristic
614	C₂	C₁₃×#3165	1	1	yes	characteristic
615	C₂	C₁₃×#3272	1	1	yes	characteristic
616	C₂	C₁₃×#3278	1	1	yes	characteristic
617	C₂	C₁₃×#3344	1	1	yes	characteristic
618	C₂	C₁₃×#3345	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#501	C₂	semidirect
5. C₁₃×#2084	C₂	semidirect
6. C₁₃×#2083	C₂	semidirect
7. C₁₃×#2059	C₂	semidirect
8. C₁₃×#2058	C₂	semidirect
9. C₁₃×#1943	C₂	semidirect
10. C₁₃×#1942	C₂	semidirect
13. C₁₃×#1844	C₂	semidirect
66. C₂×C₁₃×M₁₆	Q₈	semidirect
118. C₁₃×C₂²⋊C₈	Q₈	semidirect
129. #26078	C₁₃	direct (N × H)
208. C₂×#501	C₂×C₁₃	semidirect
212. #2084	C₂×C₁₃	semidirect
213. #2083	C₂×C₁₃	semidirect
214. #2059	C₂×C₁₃	semidirect
215. #2058	C₂×C₁₃	semidirect
216. #1943	C₂×C₁₃	semidirect
217. #1942	C₂×C₁₃	semidirect
220. #1844	C₂×C₁₃	semidirect
285. C₈×C₁₃	C₂²⋊Q₈	semidirect
367. C₂×M₁₆	Q₈×C₁₃	semidirect
419. C₂²⋊C₈	Q₈×C₁₃	semidirect
516. C₁₃	#26078	direct (N × H)
579. C₈	C₁₃×C₂²⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#501	2
C₂×C₁₃×#428	2
C₁₃×#2441	2
C₁₃×#2440	2
C₁₃×#2084	2
C₁₃×#2083	2
C₁₃×#2059	2
C₁₃×#2058	2
C₁₃×#1943	2
C₁₃×#1942	2
C₁₃×#1854	2
C₁₃×#1853	2
C₁₃×#1844	2
C₁₃×#1809	2
C₁₃×#1753	2
#26078	13

Subgroups — C13×#26078 #15712417

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26078 #15712417