Subgroups — C₁₃×#26426 #15712765

Order 3328.

840 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2439	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2361	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1895	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1875	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1736	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₃	—	2	1	no	—
20	C₂×C₄×D₄×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	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₁₃×#396	—	2	1	no	—
33	C₁₃×#393	—	2	1	no	—
34	C₁₃×#391	—	2	1	no	—
35	C₁₃×#390	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#388	—	2	1	no	—
40	C₁₃×#387	—	2	1	no	—
41	C₁₃×#386	—	2	1	no	—
42	C₁₃×#385	—	2	1	no	—
43	C₁₃×#382	C₂²	1	1	yes	characteristic
44	C₁₃×#380	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#340	C₂²	1	1	yes	characteristic
48	C₁₃×#340	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	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×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	—	2	1	no	—
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	—	4	1	no	—
67	C₂×C₁₃×M₁₆	—	4	1	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×#121	—	2	2	no	—
75	C₁₃×#121	Q₈	1	4	yes	complemented
76	C₄×D₄×C₁₃	—	2	2	no	—
77	C₄×D₄×C₁₃	—	4	1	no	—
78	C₄×D₄×C₁₃	—	4	4	no	—
79	C₁₃×#117	—	2	2	no	—
80	C₁₃×#117	—	4	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	2	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	—	4	1	no	—
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
102	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	—	2	1	no	—
104	C₂×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
107	C₁₃×#107	—	2	2	no	—
108	C₁₃×#107	—	4	1	no	—
109	C₁₃×C₄⋊C₈	—	4	1	no	—
110	C₁₃×C₄⋊C₈	—	4	1	no	—
111	C₁₃×#102	—	2	2	no	—
112	C₁₃×#102	—	4	1	no	—
113	C₁₃×#102	—	4	1	no	—
114	C₁₃×#102	—	4	1	no	—
115	C₁₃×C₂²⋊C₈	—	2	2	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	D₄	1	1	yes	characteristic
124	C₁₃×#95	D₄	1	1	yes	characteristic
125	#26426	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
126	C₂⁴×C₁₃	—	2	1	no	—
127	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	—	4	2	no	—
129	C₂×Q₈×C₁₃	—	4	2	no	—
130	C₂×Q₈×C₁₃	—	8	1	no	—
131	C₂×D₄×C₁₃	—	2	4	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂×D₄×C₁₃	—	2	1	no	—
136	C₂×D₄×C₁₃	—	2	1	no	—
137	C₂×D₄×C₁₃	—	4	2	no	—
138	C₂×D₄×C₁₃	—	4	2	no	—
139	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
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	—	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	—	4	2	no	—
152	C₂²×C₄×C₁₃	—	4	2	no	—
153	C₂²×C₄×C₁₃	—	4	2	no	—
154	C₂²×C₄×C₁₃	—	4	2	no	—
155	C₂²×C₄×C₁₃	—	8	1	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	—	4	4	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	—	2	1	no	—
177	C₂×C₈×C₁₃	—	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	—	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	—	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	C₂×Q₈	1	2	yes	—
195	C₁₃×C₄⋊C₄	#41	1	2	yes	—
196	C₁₃×C₄⋊C₄	#41	1	2	yes	—
197	C₁₃×C₂²⋊C₄	—	2	4	no	—
198	C₁₃×C₂²⋊C₄	—	2	2	no	—
199	C₁₃×C₂²⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	2	no	—
201	C₁₃×C₂²⋊C₄	—	4	2	no	—
202	C₁₃×C₂²⋊C₄	—	4	2	no	—
203	C₁₃×C₂²⋊C₄	—	8	1	no	—
204	C₁₃×C₂²⋊C₄	—	8	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	2	1	no	—
209	C₄²×C₁₃	—	4	2	no	—
210	C₄²×C₁₃	—	4	2	no	—
211	#2439	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#2361	C₂×C₁₃	1	1	yes	characteristic
213	#2101	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2087	C₂×C₁₃	1	1	yes	characteristic, complemented
215	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
217	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
218	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
219	#1895	C₂×C₁₃	1	1	yes	characteristic
220	#1875	C₂×C₁₃	1	1	yes	characteristic
221	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#1851	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#1736	C₂×C₁₃	1	1	yes	characteristic, complemented
226	C₂³×C₁₃	—	2	1	no	—
227	C₂³×C₁₃	—	2	1	no	—
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	2	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	4	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	—	4	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
240	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
241	Q₈×C₁₃	—	8	4	no	—
242	D₄×C₁₃	—	2	2	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	4	8	no	—
245	D₄×C₁₃	—	4	1	no	—
246	D₄×C₁₃	—	4	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	—	2	1	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	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	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	8	4	no	—
286	C₂×C₄×C₁₃	—	8	4	no	—
287	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
288	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
289	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
293	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
294	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
295	C₈×C₁₃	—	4	1	no	—
296	C₈×C₁₃	—	4	1	no	—
297	C₈×C₁₃	—	4	1	no	—
298	C₈×C₁₃	—	4	1	no	—
299	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄×D₄	—	2	1	no	—
303	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
315	#396	—	2	1	no	—
316	#393	—	2	1	no	—
317	#391	—	2	1	no	—
318	#390	C₂²×C₁₃	1	1	yes	characteristic
319	#389	C₂²×C₁₃	1	1	yes	characteristic
320	#389	C₂²×C₁₃	1	1	yes	characteristic
321	#389	C₂²×C₁₃	1	1	yes	characteristic
322	#388	—	2	1	no	—
323	#387	—	2	1	no	—
324	#386	—	2	1	no	—
325	#385	—	2	1	no	—
326	#382	C₂²×C₁₃	1	1	yes	characteristic
327	#380	C₂²×C₁₃	1	1	yes	characteristic
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
329	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
330	#340	C₂²×C₁₃	1	1	yes	characteristic
331	#340	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	#340	C₂²×C₁₃	1	1	yes	characteristic
339	#340	C₂²×C₁₃	1	1	yes	characteristic
340	#336	C₂²×C₁₃	1	1	yes	characteristic
341	#336	C₂²×C₁₃	1	1	yes	characteristic
342	C₂²×C₁₃	—	2	2	no	—
343	C₂²×C₁₃	—	2	2	no	—
344	C₂²×C₁₃	—	2	2	no	—
345	C₂²×C₁₃	—	4	1	no	—
346	C₂²×C₁₃	—	4	1	no	—
347	C₂²×C₁₃	—	4	1	no	—
348	C₂²×C₁₃	—	4	1	no	—
349	C₂²×C₁₃	—	4	2	no	—
350	C₂²×C₁₃	—	4	2	no	—
351	C₂²×C₁₃	—	4	2	no	—
352	C₂²×C₁₃	—	8	1	no	—
353	C₂²×C₁₃	—	8	1	no	—
354	C₂²×C₁₃	—	8	1	no	—
355	C₂²×C₁₃	—	8	1	no	—
356	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
357	C₂²×C₁₃	#546	1	1	yes	characteristic
358	C₂²×C₁₃	#546	1	1	yes	characteristic
359	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₂²×C₁₃	#575	1	1	yes	characteristic
361	C₂²×C₁₃	#576	1	1	yes	characteristic
362	C₂²×C₁₃	#578	1	1	yes	characteristic
363	C₄×C₁₃	—	2	2	no	—
364	C₄×C₁₃	—	2	2	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	2	no	—
369	C₄×C₁₃	—	4	1	no	—
370	C₄×C₁₃	—	4	2	no	—
371	C₄×C₁₃	—	8	1	no	—
372	C₄×C₁₃	—	8	1	no	—
373	C₄×C₁₃	—	8	1	no	—
374	C₄×C₁₃	—	8	1	no	—
375	C₄×C₁₃	#529	1	1	yes	characteristic
376	C₄×C₁₃	#538	1	1	yes	characteristic
377	C₄×C₁₃	#554	1	1	yes	characteristic
378	C₄×C₁₃	#554	1	1	yes	characteristic
379	C₂²×Q₈	—	2	1	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
382	C₂³×C₄	—	2	1	no	—
383	C₂³×C₄	—	2	1	no	—
384	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×M₁₆	—	2	2	no	—
386	C₂×M₁₆	—	4	1	no	—
387	C₂×M₁₆	—	4	1	no	—
388	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
392	C₄⋊Q₈	—	2	2	no	—
393	C₄⋊Q₈	—	4	1	no	—
394	#121	—	2	2	no	—
395	#121	Q₈×C₁₃	1	4	yes	complemented
396	C₄×D₄	—	2	2	no	—
397	C₄×D₄	—	4	1	no	—
398	C₄×D₄	—	4	4	no	—
399	#117	—	2	2	no	—
400	#117	—	4	1	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	4	1	no	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
410	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	—	2	1	no	—
416	C₂×C₂²⋊C₄	—	2	1	no	—
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	#107	—	2	2	no	—
428	#107	—	4	1	no	—
429	C₄⋊C₈	—	4	1	no	—
430	C₄⋊C₈	—	4	1	no	—
431	#102	—	2	2	no	—
432	#102	—	4	1	no	—
433	#102	—	4	1	no	—
434	#102	—	4	1	no	—
435	C₂²⋊C₈	—	2	2	no	—
436	#95	—	2	1	no	—
437	#95	—	2	1	no	—
438	#95	—	2	1	no	—
439	#95	—	2	1	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	D₄×C₁₃	1	1	yes	characteristic
444	#95	D₄×C₁₃	1	1	yes	characteristic
445	C₂×C₁₃	—	4	2	no	—
446	C₂×C₁₃	—	8	2	no	—
447	C₂×C₁₃	#2450	1	1	yes	characteristic
448	C₂×C₁₃	#3077	1	1	yes	characteristic
449	C₂×C₁₃	#3083	1	1	yes	characteristic
450	C₂×C₁₃	#3308	1	1	yes	characteristic
451	C₂×C₁₃	#3313	1	1	yes	characteristic
452	C₂×C₁₃	#3322	1	1	yes	characteristic
453	C₂×C₁₃	#3325	1	1	yes	characteristic
454	C₂⁴	—	2	1	no	—
455	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
456	C₂×Q₈	—	4	2	no	—
457	C₂×Q₈	—	4	2	no	—
458	C₂×Q₈	—	8	1	no	—
459	C₂×D₄	—	2	4	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	4	2	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	8	1	no	—
484	C₂²×C₄	—	8	1	no	—
485	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
486	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
491	C₂²×C₄	C₁₃×#41	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
493	M₁₆	—	4	4	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	1	no	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	4	2	no	—
518	C₄⋊C₄	—	4	2	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₄⋊C₄	—	8	1	no	—
522	C₄⋊C₄	C₂×Q₈×C₁₃	1	2	yes	—
523	C₄⋊C₄	C₁₃×#41	1	2	yes	—
524	C₄⋊C₄	C₁₃×#41	1	2	yes	—
525	C₂²⋊C₄	—	2	4	no	—
526	C₂²⋊C₄	—	2	2	no	—
527	C₂²⋊C₄	—	4	1	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	8	1	no	—
532	C₂²⋊C₄	—	8	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	4	2	no	—
538	C₄²	—	4	2	no	—
539	C₁₃	#26426	1	1	yes	characteristic, direct product factor, Sylow
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	1	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	C₁₃×C₂²⋊Q₈	1	2	yes	—
554	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	Q₈	—	8	4	no	—
556	D₄	—	2	2	no	—
557	D₄	—	2	2	no	—
558	D₄	—	4	8	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	4	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	8	4	no	—
600	C₂×C₄	—	8	4	no	—
601	C₂×C₄	C₁₃×C₂²⋊Q₈	1	2	yes	—
602	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
603	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
604	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
605	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
606	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
607	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	4	1	no	—
612	C₈	—	4	1	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	4	1	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	4	2	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	8	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
628	C₂²	C₁₃×#546	1	1	yes	characteristic
629	C₂²	C₁₃×#546	1	1	yes	characteristic
630	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
631	C₂²	C₁₃×#575	1	1	yes	characteristic
632	C₂²	C₁₃×#576	1	1	yes	characteristic
633	C₂²	C₁₃×#578	1	1	yes	characteristic
634	C₄	—	2	2	no	—
635	C₄	—	2	2	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	1	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	2	no	—
642	C₄	—	8	1	no	—
643	C₄	—	8	1	no	—
644	C₄	—	8	1	no	—
645	C₄	—	8	1	no	—
646	C₄	C₁₃×#529	1	1	yes	characteristic
647	C₄	C₁₃×#538	1	1	yes	characteristic
648	C₄	C₁₃×#554	1	1	yes	characteristic
649	C₄	C₁₃×#554	1	1	yes	characteristic
650	C₂	—	4	2	no	—
651	C₂	—	8	2	no	—
652	C₂	C₁₃×#2450	1	1	yes	characteristic
653	C₂	C₁₃×#3077	1	1	yes	characteristic
654	C₂	C₁₃×#3083	1	1	yes	characteristic
655	C₂	C₁₃×#3308	1	1	yes	characteristic
656	C₂	C₁₃×#3313	1	1	yes	characteristic
657	C₂	C₁₃×#3322	1	1	yes	characteristic
658	C₂	C₁₃×#3325	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#121	C₂²
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. C₁₃×#2439	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
4. C₁₃×#2087	C₂	semidirect
5. C₁₃×#2067	C₂	semidirect
6. C₁₃×#2023	C₂	semidirect
7. C₁₃×#1987	C₂	semidirect
8. C₁₃×#1918	C₂	semidirect
11. C₁₃×#1862	C₂	semidirect
12. C₁₃×#1852	C₂	semidirect
13. C₁₃×#1851	C₂	semidirect
14. C₁₃×#1804	C₂	semidirect
15. C₁₃×#1736	C₂	semidirect
75. C₁₃×#121	Q₈	semidirect
125. #26426	C₁₃	direct (N × H)
211. #2439	C₂×C₁₃	semidirect
213. #2101	C₂×C₁₃	semidirect
214. #2087	C₂×C₁₃	semidirect
215. #2067	C₂×C₁₃	semidirect
216. #2023	C₂×C₁₃	semidirect
217. #1987	C₂×C₁₃	semidirect
218. #1918	C₂×C₁₃	semidirect
221. #1862	C₂×C₁₃	semidirect
222. #1852	C₂×C₁₃	semidirect
223. #1851	C₂×C₁₃	semidirect
224. #1804	C₂×C₁₃	semidirect
225. #1736	C₂×C₁₃	semidirect
395. #121	Q₈×C₁₃	semidirect
539. C₁₃	#26426	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×#2439	2
C₁₃×#2361	2
C₁₃×#2101	2
C₁₃×#2087	2
C₁₃×#2067	2
C₁₃×#2023	2
C₁₃×#1987	2
C₁₃×#1918	2
C₁₃×#1895	2
C₁₃×#1875	2
C₁₃×#1862	2
C₁₃×#1852	2
C₁₃×#1851	2
C₁₃×#1804	2
C₁₃×#1736	2
#26426	13

Subgroups — C13×#26426 #15712765

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26426 #15712765