Subgroups — C₁₃×#26355 #15712694

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#428	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2440	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2362	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1894	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1854	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1851	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×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₁₃×#477	—	2	4	no	—
24	C₁₃×#428	—	2	4	no	—
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×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₃×#398	—	2	1	no	—
39	C₁₃×#395	—	2	1	no	—
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#388	—	2	1	no	—
45	C₁₃×#388	—	2	1	no	—
46	C₁₃×#387	—	2	1	no	—
47	C₁₃×#385	—	2	1	no	—
48	C₁₃×#384	C₂²	1	1	yes	characteristic
49	C₁₃×#380	C₂²	1	1	yes	characteristic
50	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
51	C₄×C₁₃×C₄⋊C₄	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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
65	C₂×C₁₃×M₁₆	—	2	2	no	—
66	C₂×C₁₃×M₁₆	—	2	2	no	—
67	C₂×C₁₃×M₁₆	—	2	2	no	—
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
72	C₁₃×C₄⋊Q₈	—	2	2	no	—
73	C₁₃×C₄⋊Q₈	—	4	1	no	—
74	C₁₃×C₂²⋊Q₈	—	2	2	no	—
75	C₁₃×C₂²⋊Q₈	—	4	4	no	—
76	C₁₃×C₂²⋊Q₈	Q₈	1	4	yes	complemented
77	C₄×Q₈×C₁₃	—	2	2	no	—
78	C₄×Q₈×C₁₃	—	4	1	no	—
79	C₁₃×#117	—	2	2	no	—
80	C₁₃×#117	—	4	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	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×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
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	—	4	1	no	—
115	C₁₃×C₄⋊C₈	—	2	2	no	—
116	C₁₃×C₄⋊C₈	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#103	—	2	2	no	—
120	C₁₃×#103	—	4	1	no	—
121	C₁₃×C₂²⋊C₈	—	2	2	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	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	D₄	1	1	yes	characteristic
130	C₁₃×#95	D₄	1	1	yes	characteristic
131	#26355	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
132	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	4	2	no	—
139	C₂×Q₈×C₁₃	—	4	2	no	—
140	C₂×Q₈×C₁₃	—	8	1	no	—
141	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
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	—	2	1	no	—
147	C₂²×C₄×C₁₃	—	2	1	no	—
148	C₂²×C₄×C₁₃	—	2	1	no	—
149	C₂²×C₄×C₁₃	—	2	1	no	—
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₃	—	4	2	no	—
156	C₂²×C₄×C₁₃	—	8	1	no	—
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
163	C₂²×C₄×C₁₃	#41	1	2	yes	—
164	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₁₃×M₁₆	—	2	8	no	—
166	C₂×C₈×C₁₃	—	2	1	no	—
167	C₂×C₈×C₁₃	—	2	1	no	—
168	C₂×C₈×C₁₃	—	2	1	no	—
169	C₂×C₈×C₁₃	—	2	1	no	—
170	C₂×C₈×C₁₃	—	2	1	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₁₃	#41	1	2	yes	—
178	C₁₃×C₄⋊C₄	—	2	4	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	—	2	1	no	—
185	C₁₃×C₄⋊C₄	—	2	1	no	—
186	C₁₃×C₄⋊C₄	—	2	1	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	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	—	4	2	no	—
194	C₁₃×C₄⋊C₄	—	4	2	no	—
195	C₁₃×C₄⋊C₄	—	4	2	no	—
196	C₁₃×C₄⋊C₄	—	4	2	no	—
197	C₁₃×C₄⋊C₄	—	8	1	no	—
198	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
199	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
200	C₁₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	2	no	—
203	C₁₃×C₂²⋊C₄	—	2	2	no	—
204	C₁₃×C₂²⋊C₄	—	4	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	4	2	no	—
211	C₄²×C₁₃	—	4	2	no	—
212	C₄²×C₁₃	—	4	2	no	—
213	C₂×#477	C₂×C₁₃	1	1	yes	characteristic, complemented
214	C₂×#428	C₂×C₁₃	1	1	yes	characteristic
215	#2440	C₂×C₁₃	1	1	yes	characteristic
216	#2362	C₂×C₁₃	1	1	yes	characteristic
217	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1894	C₂×C₁₃	1	1	yes	characteristic
224	#1872	C₂×C₁₃	1	1	yes	characteristic
225	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1854	C₂×C₁₃	1	1	yes	characteristic
227	#1851	C₂×C₁₃	1	1	yes	characteristic
228	C₂³×C₁₃	—	2	1	no	—
229	C₂³×C₁₃	—	2	1	no	—
230	C₂³×C₁₃	—	2	1	no	—
231	C₂³×C₁₃	—	2	1	no	—
232	C₂³×C₁₃	—	2	1	no	—
233	C₂³×C₁₃	—	2	1	no	—
234	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
235	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
236	Q₈×C₁₃	—	2	2	no	—
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	4	1	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	Q₈×C₁₃	—	8	4	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	1	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	1	no	—
274	C₂×C₄×C₁₃	—	4	1	no	—
275	C₂×C₄×C₁₃	—	4	1	no	—
276	C₂×C₄×C₁₃	—	4	1	no	—
277	C₂×C₄×C₁₃	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	8	4	no	—
282	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
283	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
284	C₂×C₄×C₁₃	#137	1	2	yes	—
285	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
287	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
291	C₈×C₁₃	—	2	2	no	—
292	C₈×C₁₃	—	2	2	no	—
293	C₈×C₁₃	—	4	1	no	—
294	C₈×C₁₃	—	4	1	no	—
295	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×C₂²⋊Q₈	—	2	1	no	—
298	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
302	#477	—	2	4	no	—
303	#428	—	2	4	no	—
304	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
317	#398	—	2	1	no	—
318	#395	—	2	1	no	—
319	#391	C₂²×C₁₃	1	1	yes	characteristic
320	#389	C₂²×C₁₃	1	1	yes	characteristic
321	#389	C₂²×C₁₃	1	1	yes	characteristic
322	#389	C₂²×C₁₃	1	1	yes	characteristic
323	#388	—	2	1	no	—
324	#388	—	2	1	no	—
325	#387	—	2	1	no	—
326	#385	—	2	1	no	—
327	#384	C₂²×C₁₃	1	1	yes	characteristic
328	#380	C₂²×C₁₃	1	1	yes	characteristic
329	C₄×C₄⋊C₄	—	2	1	no	—
330	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
331	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
332	#340	C₂²×C₁₃	1	1	yes	characteristic
333	#340	C₂²×C₁₃	1	1	yes	characteristic
334	#340	C₂²×C₁₃	1	1	yes	characteristic
335	#340	C₂²×C₁₃	1	1	yes	characteristic
336	#340	C₂²×C₁₃	1	1	yes	characteristic
337	#340	C₂²×C₁₃	1	1	yes	characteristic
338	#336	C₂²×C₁₃	1	1	yes	characteristic
339	#336	C₂²×C₁₃	1	1	yes	characteristic
340	C₂²×C₁₃	—	2	2	no	—
341	C₂²×C₁₃	—	2	2	no	—
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	4	1	no	—
344	C₂²×C₁₃	—	4	1	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
348	C₂²×C₁₃	D₄²	1	1	yes	characteristic
349	C₂²×C₁₃	#547	1	1	yes	characteristic
350	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
351	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
352	C₂²×C₁₃	#577	1	1	yes	characteristic
353	C₂²×C₁₃	#578	1	1	yes	characteristic
354	C₄×C₁₃	—	2	2	no	—
355	C₄×C₁₃	—	2	2	no	—
356	C₄×C₁₃	—	2	2	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	4	1	no	—
359	C₄×C₁₃	—	4	2	no	—
360	C₄×C₁₃	—	4	1	no	—
361	C₄×C₁₃	—	4	2	no	—
362	C₄×C₁₃	—	4	2	no	—
363	C₄×C₁₃	—	8	1	no	—
364	C₄×C₁₃	—	8	1	no	—
365	C₄×C₁₃	—	8	1	no	—
366	C₄×C₁₃	—	8	1	no	—
367	C₄×C₁₃	#525	1	1	yes	characteristic
368	C₄×C₁₃	#539	1	1	yes	characteristic
369	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
370	C₄×C₁₃	#554	1	1	yes	characteristic
371	C₂²×Q₈	—	2	1	no	—
372	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₂³×C₄	—	2	1	no	—
374	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×M₁₆	—	2	2	no	—
376	C₂×M₁₆	—	2	2	no	—
377	C₂×M₁₆	—	2	2	no	—
378	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
381	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₄⋊Q₈	—	2	2	no	—
383	C₄⋊Q₈	—	4	1	no	—
384	C₂²⋊Q₈	—	2	2	no	—
385	C₂²⋊Q₈	—	4	4	no	—
386	C₂²⋊Q₈	Q₈×C₁₃	1	4	yes	complemented
387	C₄×Q₈	—	2	2	no	—
388	C₄×Q₈	—	4	1	no	—
389	#117	—	2	2	no	—
390	#117	—	4	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	2	no	—
393	C₂×C₄⋊C₄	—	2	1	no	—
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
396	C₂×C₄⋊C₄	—	2	1	no	—
397	C₂×C₄⋊C₄	—	2	1	no	—
398	C₂×C₄⋊C₄	—	2	1	no	—
399	C₂×C₄⋊C₄	—	2	1	no	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	4	1	no	—
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	2	1	no	—
410	C₂×C₂²⋊C₄	—	2	1	no	—
411	C₂×C₂²⋊C₄	—	2	1	no	—
412	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	—	2	1	no	—
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
419	#107	—	2	2	no	—
420	#107	—	2	2	no	—
421	#107	D₄×C₁₃	1	4	yes	—
422	#106	—	2	2	no	—
423	#106	—	2	2	no	—
424	#106	—	4	1	no	—
425	C₄⋊C₈	—	2	2	no	—
426	C₄⋊C₈	—	2	2	no	—
427	#103	—	2	2	no	—
428	#103	—	2	2	no	—
429	#103	—	2	2	no	—
430	#103	—	4	1	no	—
431	C₂²⋊C₈	—	2	2	no	—
432	#95	—	2	1	no	—
433	#95	—	2	1	no	—
434	#95	—	2	1	no	—
435	#95	—	2	1	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	D₄×C₁₃	1	1	yes	characteristic
440	#95	D₄×C₁₃	1	1	yes	characteristic
441	C₂×C₁₃	—	4	2	no	—
442	C₂×C₁₃	#2449	1	1	yes	characteristic
443	C₂×C₁₃	#3079	1	1	yes	characteristic
444	C₂×C₁₃	#3082	1	1	yes	characteristic
445	C₂×C₁₃	#3270	1	1	yes	characteristic
446	C₂×C₁₃	#3272	1	1	yes	characteristic
447	C₂×C₁₃	#3343	1	1	yes	characteristic
448	C₂×C₁₃	#3356	1	1	yes	characteristic
449	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₂×Q₈	—	2	1	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	4	2	no	—
456	C₂×Q₈	—	4	2	no	—
457	C₂×Q₈	—	8	1	no	—
458	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	4	2	no	—
472	C₂²×C₄	—	4	2	no	—
473	C₂²×C₄	—	8	1	no	—
474	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
475	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
480	C₂²×C₄	C₁₃×#41	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
482	M₁₆	—	2	8	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
494	C₂×C₈	C₁₃×#41	1	2	yes	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	4	2	no	—
508	C₄⋊C₄	—	4	2	no	—
509	C₄⋊C₄	—	4	2	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₄⋊C₄	—	4	2	no	—
512	C₄⋊C₄	—	4	2	no	—
513	C₄⋊C₄	—	4	2	no	—
514	C₄⋊C₄	—	8	1	no	—
515	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
516	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
517	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
518	C₂²⋊C₄	—	2	4	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	4	2	no	—
522	C₂²⋊C₄	—	4	2	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	1	no	—
527	C₄²	—	4	2	no	—
528	C₄²	—	4	2	no	—
529	C₄²	—	4	2	no	—
530	C₁₃	#26355	1	1	yes	characteristic, direct product factor, Sylow
531	C₂³	—	2	1	no	—
532	C₂³	—	2	1	no	—
533	C₂³	—	2	1	no	—
534	C₂³	—	2	1	no	—
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
538	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
539	Q₈	—	2	2	no	—
540	Q₈	—	2	2	no	—
541	Q₈	—	4	1	no	—
542	Q₈	—	4	1	no	—
543	Q₈	—	8	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	8	4	no	—
585	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
586	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
587	C₂×C₄	C₁₃×#137	1	2	yes	—
588	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
590	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
591	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
592	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	2	no	—
596	C₈	—	4	1	no	—
597	C₈	—	4	1	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	2	2	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	1	no	—
605	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
606	C₂²	D₄²×C₁₃	1	1	yes	characteristic
607	C₂²	C₁₃×#547	1	1	yes	characteristic
608	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
609	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
610	C₂²	C₁₃×#577	1	1	yes	characteristic
611	C₂²	C₁₃×#578	1	1	yes	characteristic
612	C₄	—	2	2	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	2	no	—
615	C₄	—	4	1	no	—
616	C₄	—	4	2	no	—
617	C₄	—	4	2	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	2	no	—
621	C₄	—	8	1	no	—
622	C₄	—	8	1	no	—
623	C₄	—	8	1	no	—
624	C₄	—	8	1	no	—
625	C₄	C₁₃×#525	1	1	yes	characteristic
626	C₄	C₁₃×#539	1	1	yes	characteristic
627	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
628	C₄	C₁₃×#554	1	1	yes	characteristic
629	C₂	—	4	2	no	—
630	C₂	C₁₃×#2449	1	1	yes	characteristic
631	C₂	C₁₃×#3079	1	1	yes	characteristic
632	C₂	C₁₃×#3082	1	1	yes	characteristic
633	C₂	C₁₃×#3270	1	1	yes	characteristic
634	C₂	C₁₃×#3272	1	1	yes	characteristic
635	C₂	C₁₃×#3343	1	1	yes	characteristic
636	C₂	C₁₃×#3356	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×#477	C₂	semidirect
5. C₁₃×#2096	C₂	semidirect
6. C₁₃×#2088	C₂	semidirect
7. C₁₃×#2066	C₂	semidirect
8. C₁₃×#2058	C₂	semidirect
9. C₁₃×#1947	C₂	semidirect
10. C₁₃×#1918	C₂	semidirect
13. C₁₃×#1863	C₂	semidirect
76. C₁₃×C₂²⋊Q₈	Q₈	semidirect
131. #26355	C₁₃	direct (N × H)
213. C₂×#477	C₂×C₁₃	semidirect
217. #2096	C₂×C₁₃	semidirect
218. #2088	C₂×C₁₃	semidirect
219. #2066	C₂×C₁₃	semidirect
220. #2058	C₂×C₁₃	semidirect
221. #1947	C₂×C₁₃	semidirect
222. #1918	C₂×C₁₃	semidirect
225. #1863	C₂×C₁₃	semidirect
386. C₂²⋊Q₈	Q₈×C₁₃	semidirect
530. C₁₃	#26355	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#477	2
C₂×C₁₃×#428	2
C₁₃×#2440	2
C₁₃×#2362	2
C₁₃×#2096	2
C₁₃×#2088	2
C₁₃×#2066	2
C₁₃×#2058	2
C₁₃×#1947	2
C₁₃×#1918	2
C₁₃×#1894	2
C₁₃×#1872	2
C₁₃×#1863	2
C₁₃×#1854	2
C₁₃×#1851	2
#26355	13

Subgroups — C13×#26355 #15712694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26355 #15712694