Subgroups — C₁₃×#26234 #15712573

Order 3328.

934 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#483	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic
3	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1981	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1872	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₁₃	—	2	1	no	—
16	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₁₃×#483	—	2	8	no	—
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	2	yes	—
25	C₂×C₁₃×#103	C₂²	1	2	yes	—
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#399	—	2	2	no	—
31	C₁₃×#390	—	2	1	no	—
32	C₁₃×#389	—	2	1	no	—
33	C₁₃×#385	—	2	2	no	—
34	C₁₃×#384	—	2	1	no	—
35	C₁₃×#384	C₂²	1	1	yes	characteristic
36	C₁₃×#380	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	1	yes	characteristic
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₃	—	2	2	no	—
45	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
46	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₄⋊Q₈	—	2	2	no	—
51	C₁₃×C₂²⋊Q₈	—	2	4	no	—
52	C₁₃×C₂²⋊Q₈	—	2	4	no	—
53	C₁₃×C₂²⋊Q₈	—	4	2	no	—
54	C₁₃×C₂²⋊Q₈	—	4	2	no	—
55	C₄×D₄×C₁₃	—	2	2	no	—
56	C₄×D₄×C₁₃	—	2	2	no	—
57	C₄×D₄×C₁₃	—	4	4	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	—	2	1	no	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#106	—	2	4	no	—
81	C₁₃×#106	—	2	2	no	—
82	C₁₃×#106	D₄	1	4	yes	complemented
83	C₁₃×C₄⋊C₈	—	2	2	no	—
84	C₁₃×#103	—	2	4	no	—
85	C₁₃×#103	—	2	4	no	—
86	C₁₃×#103	—	4	2	no	—
87	C₁₃×#103	—	4	2	no	—
88	C₁₃×C₂²⋊C₈	—	2	4	no	—
89	C₁₃×C₂²⋊C₈	—	4	2	no	—
90	C₄×C₈×C₁₃	—	2	2	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	C₁₃×#95	—	2	2	no	—
94	#26234	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
95	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
96	C₂×Q₈×C₁₃	—	2	2	no	—
97	C₂×Q₈×C₁₃	—	2	2	no	—
98	C₂×Q₈×C₁₃	—	2	2	no	—
99	C₂×Q₈×C₁₃	—	2	2	no	—
100	C₂×Q₈×C₁₃	—	2	2	no	—
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂×D₄×C₁₃	SD₁₆	1	4	yes	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	2	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	2	2	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	—	2	2	no	—
117	C₂²×C₄×C₁₃	—	4	4	no	—
118	C₂²×C₄×C₁₃	—	4	4	no	—
119	C₂²×C₄×C₁₃	—	8	2	no	—
120	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₁₃	—	2	1	no	—
125	C₂×C₈×C₁₃	—	2	1	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	—	2	1	no	—
130	C₂×C₈×C₁₃	—	2	2	no	—
131	C₂×C₈×C₁₃	—	2	1	no	—
132	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	1	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	1	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	1	no	—
139	C₁₃×C₄⋊C₄	—	2	1	no	—
140	C₁₃×C₄⋊C₄	—	2	2	no	—
141	C₁₃×C₄⋊C₄	—	4	4	no	—
142	C₁₃×C₄⋊C₄	—	4	4	no	—
143	C₁₃×C₄⋊C₄	—	4	4	no	—
144	C₁₃×C₄⋊C₄	—	4	2	no	—
145	C₁₃×C₄⋊C₄	—	4	2	no	—
146	C₁₃×C₄⋊C₄	—	4	2	no	—
147	C₁₃×C₄⋊C₄	—	8	1	no	—
148	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
150	C₁₃×C₄⋊C₄	#41	1	2	yes	—
151	C₁₃×C₂²⋊C₄	—	2	4	no	—
152	C₁₃×C₂²⋊C₄	—	4	4	no	—
153	C₁₃×C₂²⋊C₄	—	4	4	no	—
154	C₁₃×C₂²⋊C₄	—	4	4	no	—
155	C₄²×C₁₃	—	4	2	no	—
156	C₄²×C₁₃	—	4	2	no	—
157	C₄²×C₁₃	#41	1	2	yes	—
158	C₄²×C₁₃	#41	1	2	yes	—
159	C₂×#483	C₂×C₁₃	1	2	yes	complemented
160	#2542	C₂×C₁₃	1	1	yes	characteristic
161	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
162	#2035	C₂×C₁₃	1	2	yes	complemented
163	#2035	C₂×C₁₃	1	2	yes	complemented
164	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1956	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1954	C₂×C₁₃	1	1	yes	characteristic
167	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
168	#1872	C₂×C₁₃	1	2	yes	complemented
169	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
170	C₂³×C₁₃	—	2	2	no	—
171	C₂³×C₁₃	—	2	2	no	—
172	C₂³×C₁₃	—	2	2	no	—
173	C₂³×C₁₃	—	2	2	no	—
174	C₂³×C₁₃	—	2	2	no	—
175	C₂³×C₁₃	—	2	2	no	—
176	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
177	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
178	Q₈×C₁₃	—	4	2	no	—
179	Q₈×C₁₃	—	4	2	no	—
180	Q₈×C₁₃	—	4	2	no	—
181	Q₈×C₁₃	—	4	2	no	—
182	D₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	1	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	1	no	—
195	C₂×C₄×C₁₃	—	4	1	no	—
196	C₂×C₄×C₁₃	—	4	1	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	2	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	2	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	2	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	1	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	2	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	8	8	no	—
211	C₂×C₄×C₁₃	#123	1	2	yes	—
212	C₂×C₄×C₁₃	#123	1	2	yes	—
213	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
214	C₂×C₄×C₁₃	#137	1	2	yes	—
215	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
221	C₈×C₁₃	—	2	2	no	—
222	C₈×C₁₃	—	4	1	no	—
223	C₈×C₁₃	—	4	2	no	—
224	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
226	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
227	C₂×C₄×D₄	—	2	1	no	—
228	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
230	#483	—	2	8	no	—
231	C₂×#106	C₂²×C₁₃	1	2	yes	—
232	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
234	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
235	C₂×#103	C₂²×C₁₃	1	2	yes	—
236	C₂×#103	C₂²×C₁₃	1	2	yes	—
237	C₂×#103	C₂²×C₁₃	1	2	yes	—
238	C₂×#103	C₂²×C₁₃	1	2	yes	—
239	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
241	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
242	#399	—	2	2	no	—
243	#390	—	2	1	no	—
244	#389	—	2	1	no	—
245	#385	—	2	2	no	—
246	#384	—	2	1	no	—
247	#384	C₂²×C₁₃	1	1	yes	characteristic
248	#380	C₂²×C₁₃	1	2	yes	—
249	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
250	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
251	#340	C₂²×C₁₃	1	1	yes	characteristic
252	#340	C₂²×C₁₃	1	2	yes	—
253	#340	C₂²×C₁₃	1	1	yes	characteristic
254	C₂²×C₁₃	—	2	4	no	—
255	C₂²×C₁₃	—	2	4	no	—
256	C₂²×C₁₃	—	2	4	no	—
257	C₂²×C₁₃	—	4	2	no	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
262	C₂²×C₁₃	D₄²	1	1	yes	characteristic
263	C₂²×C₁₃	#546	1	1	yes	characteristic
264	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
265	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
266	C₂²×C₁₃	#577	1	1	yes	characteristic
267	C₂²×C₁₃	#578	1	1	yes	characteristic
268	C₄×C₁₃	—	2	2	no	—
269	C₄×C₁₃	—	4	2	no	—
270	C₄×C₁₃	—	4	2	no	—
271	C₄×C₁₃	—	4	2	no	—
272	C₄×C₁₃	—	4	2	no	—
273	C₄×C₁₃	—	8	2	no	—
274	C₄×C₁₃	—	8	2	no	—
275	C₄×C₁₃	—	8	1	no	—
276	C₄×C₁₃	#483	1	4	yes	complemented
277	C₄×C₁₃	#532	1	1	yes	characteristic
278	C₄×C₁₃	#540	1	1	yes	characteristic
279	C₄×C₁₃	#550	1	1	yes	characteristic
280	C₄×C₁₃	#559	1	1	yes	characteristic
281	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
282	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
285	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
287	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₄⋊Q₈	—	2	2	no	—
289	C₄⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	—	2	4	no	—
291	C₂²⋊Q₈	—	2	4	no	—
292	C₂²⋊Q₈	—	4	2	no	—
293	C₂²⋊Q₈	—	4	2	no	—
294	C₄×D₄	—	2	2	no	—
295	C₄×D₄	—	2	2	no	—
296	C₄×D₄	—	4	4	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	2	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	4	2	no	—
306	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
316	C₂×C₄²	—	2	1	no	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
319	#106	—	2	4	no	—
320	#106	—	2	2	no	—
321	#106	D₄×C₁₃	1	4	yes	complemented
322	C₄⋊C₈	—	2	2	no	—
323	#103	—	2	4	no	—
324	#103	—	2	4	no	—
325	#103	—	4	2	no	—
326	#103	—	4	2	no	—
327	C₂²⋊C₈	—	2	4	no	—
328	C₂²⋊C₈	—	4	2	no	—
329	C₄×C₈	—	2	2	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	C₂×C₁₃	—	4	4	no	—
334	C₂×C₁₃	#2445	1	1	yes	characteristic
335	C₂×C₁₃	C₂×#483	1	1	yes	characteristic
336	C₂×C₁₃	#3097	1	1	yes	characteristic
337	C₂×C₁₃	#3276	1	1	yes	characteristic
338	C₂×C₁₃	D₄×SD₁₆	1	1	yes	characteristic
339	C₂×C₁₃	#3298	1	1	yes	characteristic
340	C₂×C₁₃	#3331	1	1	yes	characteristic
341	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	C₁₃×SD₁₆	1	4	yes	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	4	4	no	—
364	C₂²×C₄	—	4	4	no	—
365	C₂²×C₄	—	8	2	no	—
366	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	4	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	8	1	no	—
394	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
395	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
396	C₄⋊C₄	C₁₃×#41	1	2	yes	—
397	C₂²⋊C₄	—	2	4	no	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	4	no	—
401	C₄²	—	4	2	no	—
402	C₄²	—	4	2	no	—
403	C₄²	C₁₃×#41	1	2	yes	—
404	C₄²	C₁₃×#41	1	2	yes	—
405	C₁₃	#26234	1	1	yes	characteristic, direct product factor, Sylow
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
413	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	D₄	—	2	8	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	8	8	no	—
447	C₂×C₄	C₁₃×#123	1	2	yes	—
448	C₂×C₄	C₁₃×#123	1	2	yes	—
449	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
450	C₂×C₄	C₁₃×#137	1	2	yes	—
451	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
453	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
454	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
455	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
456	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	4	1	no	—
459	C₈	—	4	2	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
468	C₂²	D₄²×C₁₃	1	1	yes	characteristic
469	C₂²	C₁₃×#546	1	1	yes	characteristic
470	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
471	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
472	C₂²	C₁₃×#577	1	1	yes	characteristic
473	C₂²	C₁₃×#578	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	2	no	—
480	C₄	—	8	1	no	—
481	C₄	—	8	2	no	—
482	C₄	C₁₃×#483	1	4	yes	complemented
483	C₄	C₁₃×#532	1	1	yes	characteristic
484	C₄	C₁₃×#540	1	1	yes	characteristic
485	C₄	C₁₃×#550	1	1	yes	characteristic
486	C₄	C₁₃×#559	1	1	yes	characteristic
487	C₂	—	4	4	no	—
488	C₂	C₁₃×#2445	1	1	yes	characteristic
489	C₂	C₂×C₁₃×#483	1	1	yes	characteristic
490	C₂	C₁₃×#3097	1	1	yes	characteristic
491	C₂	C₁₃×#3276	1	1	yes	characteristic
492	C₂	D₄×C₁₃×SD₁₆	1	1	yes	characteristic
493	C₂	C₁₃×#3298	1	1	yes	characteristic
494	C₂	C₁₃×#3331	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#483	C₂	semidirect
4. C₁₃×#2035	C₂	semidirect
5. C₁₃×#2035	C₂	semidirect
6. C₁₃×#1981	C₂	semidirect
7. C₁₃×#1956	C₂	semidirect
9. C₁₃×#1948	C₂	semidirect
10. C₁₃×#1872	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
82. C₁₃×#106	D₄	semidirect
94. #26234	C₁₃	direct (N × H)
159. C₂×#483	C₂×C₁₃	semidirect
162. #2035	C₂×C₁₃	semidirect
163. #2035	C₂×C₁₃	semidirect
164. #1981	C₂×C₁₃	semidirect
165. #1956	C₂×C₁₃	semidirect
167. #1948	C₂×C₁₃	semidirect
168. #1872	C₂×C₁₃	semidirect
169. C₄×#106	C₂×C₁₃	semidirect
276. C₄×C₁₃	#483	semidirect
321. #106	D₄×C₁₃	semidirect
405. C₁₃	#26234	direct (N × H)
482. C₄	C₁₃×#483	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#483	2
C₁₃×#2542	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2035	2
C₁₃×#1981	2
C₁₃×#1956	2
C₁₃×#1954	2
C₁₃×#1948	2
C₁₃×#1872	2
C₄×C₁₃×#106	2
#26234	13

Subgroups — C13×#26234 #15712573

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26234 #15712573