Subgroups — C₁₃×#26231 #15712570

Order 3328.

862 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#485	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2542	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2354	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2036	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×#1873	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₃×#107	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	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	2	yes	—
17	C₁₃×#485	—	2	8	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	C₂²	1	2	yes	—
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#103	C₂²	1	2	yes	—
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×C₂²⋊C₈	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#399	—	2	2	no	—
30	C₁₃×#390	—	2	1	no	—
31	C₁₃×#390	—	2	1	no	—
32	C₁₃×#388	—	2	2	no	—
33	C₁₃×#384	—	2	1	no	—
34	C₁₃×#384	C₂²	1	1	yes	characteristic
35	C₁₃×#380	C₂²	1	2	yes	—
36	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
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	C₂³	1	2	yes	—
45	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₁₃×C₄⋊Q₈	—	2	2	no	—
49	C₁₃×C₄⋊Q₈	—	2	2	no	—
50	C₁₃×C₂²⋊Q₈	—	2	4	no	—
51	C₁₃×C₂²⋊Q₈	—	2	4	no	—
52	C₁₃×C₂²⋊Q₈	—	4	2	no	—
53	C₁₃×C₂²⋊Q₈	—	4	2	no	—
54	C₄×D₄×C₁₃	—	2	2	no	—
55	C₄×D₄×C₁₃	—	2	2	no	—
56	C₁₃×#117	—	2	4	no	—
57	C₁₃×#117	—	4	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	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	1	no	—
64	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×#107	—	2	2	no	—
80	C₁₃×#107	D₄	1	4	yes	complemented
81	C₁₃×#106	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×#103	—	2	4	no	—
84	C₁₃×#103	—	2	4	no	—
85	C₁₃×#103	—	4	2	no	—
86	C₁₃×#103	—	4	2	no	—
87	C₁₃×C₂²⋊C₈	—	2	4	no	—
88	C₁₃×C₂²⋊C₈	—	4	2	no	—
89	C₄×C₈×C₁₃	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	1	no	—
92	C₁₃×#95	—	2	1	no	—
93	#26231	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
95	C₂×Q₈×C₁₃	—	2	2	no	—
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×D₄×C₁₃	—	2	2	no	—
102	C₂×D₄×C₁₃	—	2	2	no	—
103	C₂×D₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	1	no	—
105	C₂²×C₄×C₁₃	—	2	1	no	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	2	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	1	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	2	no	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₁₃	—	2	1	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	2	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	C₂×D₄	1	2	yes	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
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	2	no	—
137	C₁₃×C₄⋊C₄	—	4	4	no	—
138	C₁₃×C₄⋊C₄	—	4	4	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	8	1	no	—
143	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
145	C₁₃×C₄⋊C₄	#41	1	2	yes	—
146	C₁₃×C₂²⋊C₄	—	2	4	no	—
147	C₁₃×C₂²⋊C₄	—	4	4	no	—
148	C₁₃×C₂²⋊C₄	—	4	4	no	—
149	C₁₃×C₂²⋊C₄	—	4	4	no	—
150	C₁₃×C₂²⋊C₄	—	8	2	no	—
151	C₄²×C₁₃	—	4	4	no	—
152	C₄²×C₁₃	—	4	2	no	—
153	C₄²×C₁₃	—	4	2	no	—
154	C₄²×C₁₃	#41	1	2	yes	—
155	C₄²×C₁₃	#41	1	2	yes	—
156	C₂×#485	C₂×C₁₃	1	2	yes	complemented
157	#2542	C₂×C₁₃	1	1	yes	characteristic
158	#2354	C₂×C₁₃	1	1	yes	characteristic
159	#2036	C₂×C₁₃	1	2	yes	complemented
160	#2035	C₂×C₁₃	1	2	yes	complemented
161	#1981	C₂×C₁₃	1	1	yes	characteristic, complemented
162	#1956	C₂×C₁₃	1	1	yes	characteristic, complemented
163	#1954	C₂×C₁₃	1	1	yes	characteristic
164	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1873	C₂×C₁₃	1	2	yes	complemented
166	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂³×C₁₃	—	2	2	no	—
168	C₂³×C₁₃	—	2	2	no	—
169	C₂³×C₁₃	—	2	2	no	—
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	C₂²×D₄	1	1	yes	characteristic
175	Q₈×C₁₃	—	4	2	no	—
176	Q₈×C₁₃	—	4	2	no	—
177	Q₈×C₁₃	—	4	2	no	—
178	Q₈×C₁₃	—	4	2	no	—
179	D₄×C₁₃	—	4	4	no	—
180	C₂×C₄×C₁₃	—	2	1	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	2	no	—
184	C₂×C₄×C₁₃	—	2	2	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	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	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	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	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	1	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	2	no	—
205	C₂×C₄×C₁₃	—	4	1	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	#123	1	2	yes	—
208	C₂×C₄×C₁₃	#123	1	2	yes	—
209	C₂×C₄×C₁₃	#135	1	2	yes	—
210	C₂×C₄×C₁₃	#137	1	2	yes	—
211	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
217	C₈×C₁₃	—	2	2	no	—
218	C₈×C₁₃	—	4	1	no	—
219	C₈×C₁₃	—	4	2	no	—
220	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
222	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
223	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
224	C₂×#117	C₂²×C₁₃	1	2	yes	—
225	#485	—	2	8	no	—
226	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
227	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
228	C₂×#106	C₂²×C₁₃	1	2	yes	—
229	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#103	C₂²×C₁₃	1	2	yes	—
231	C₂×#103	C₂²×C₁₃	1	2	yes	—
232	C₂×#103	C₂²×C₁₃	1	2	yes	—
233	C₂×#103	C₂²×C₁₃	1	2	yes	—
234	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
236	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
237	#399	—	2	2	no	—
238	#390	—	2	1	no	—
239	#390	—	2	1	no	—
240	#388	—	2	2	no	—
241	#384	—	2	1	no	—
242	#384	C₂²×C₁₃	1	1	yes	characteristic
243	#380	C₂²×C₁₃	1	2	yes	—
244	C₄×C₄⋊C₄	—	2	1	no	—
245	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
246	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
247	#340	C₂²×C₁₃	1	1	yes	characteristic
248	#340	C₂²×C₁₃	1	2	yes	—
249	#340	C₂²×C₁₃	1	1	yes	characteristic
250	C₂²×C₁₃	—	4	2	no	—
251	C₂²×C₁₃	—	4	2	no	—
252	C₂²×C₁₃	—	4	2	no	—
253	C₂²×C₁₃	—	4	2	no	—
254	C₂²×C₁₃	—	4	2	no	—
255	C₂²×C₁₃	—	4	2	no	—
256	C₂²×C₁₃	—	4	2	no	—
257	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
258	C₂²×C₁₃	D₄²	1	1	yes	characteristic
259	C₂²×C₁₃	#546	1	1	yes	characteristic
260	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
261	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
262	C₂²×C₁₃	#577	1	1	yes	characteristic
263	C₂²×C₁₃	#578	1	1	yes	characteristic
264	C₄×C₁₃	—	2	2	no	—
265	C₄×C₁₃	—	4	2	no	—
266	C₄×C₁₃	—	4	2	no	—
267	C₄×C₁₃	—	4	2	no	—
268	C₄×C₁₃	—	4	2	no	—
269	C₄×C₁₃	—	8	2	no	—
270	C₄×C₁₃	—	8	2	no	—
271	C₄×C₁₃	—	8	1	no	—
272	C₄×C₁₃	#485	1	4	yes	complemented
273	C₄×C₁₃	#532	1	1	yes	characteristic
274	C₄×C₁₃	#540	1	1	yes	characteristic
275	C₄×C₁₃	#550	1	1	yes	characteristic
276	C₄×C₁₃	#559	1	1	yes	characteristic
277	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
278	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
279	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
280	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
282	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
283	C₄⋊Q₈	—	2	2	no	—
284	C₄⋊Q₈	—	2	2	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	C₂²⋊Q₈	—	2	4	no	—
287	C₂²⋊Q₈	—	4	2	no	—
288	C₂²⋊Q₈	—	4	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	—	2	2	no	—
291	#117	—	2	4	no	—
292	#117	—	4	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
300	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	—	2	1	no	—
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
314	#107	—	2	2	no	—
315	#107	D₄×C₁₃	1	4	yes	complemented
316	#106	—	2	4	no	—
317	C₄⋊C₈	—	2	2	no	—
318	#103	—	2	4	no	—
319	#103	—	2	4	no	—
320	#103	—	4	2	no	—
321	#103	—	4	2	no	—
322	C₂²⋊C₈	—	2	4	no	—
323	C₂²⋊C₈	—	4	2	no	—
324	C₄×C₈	—	2	2	no	—
325	#95	—	2	2	no	—
326	#95	—	2	1	no	—
327	#95	—	2	1	no	—
328	C₂×C₁₃	—	8	2	no	—
329	C₂×C₁₃	#2445	1	1	yes	characteristic
330	C₂×C₁₃	C₂×#485	1	1	yes	characteristic
331	C₂×C₁₃	#3097	1	1	yes	characteristic
332	C₂×C₁₃	#3278	1	1	yes	characteristic
333	C₂×C₁₃	#3283	1	1	yes	characteristic
334	C₂×C₁₃	#3303	1	1	yes	characteristic
335	C₂×C₁₃	#3328	1	1	yes	characteristic
336	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
360	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
361	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	2	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	4	2	no	—
384	C₄⋊C₄	—	8	1	no	—
385	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
386	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
387	C₄⋊C₄	C₁₃×#41	1	2	yes	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	4	4	no	—
390	C₂²⋊C₄	—	4	4	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	8	2	no	—
393	C₄²	—	4	4	no	—
394	C₄²	—	4	2	no	—
395	C₄²	—	4	2	no	—
396	C₄²	C₁₃×#41	1	2	yes	—
397	C₄²	C₁₃×#41	1	2	yes	—
398	C₁₃	#26231	1	1	yes	characteristic, direct product factor, Sylow
399	C₂³	—	2	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
407	Q₈	—	4	2	no	—
408	Q₈	—	4	2	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	D₄	—	4	4	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	C₁₃×#123	1	2	yes	—
440	C₂×C₄	C₁₃×#123	1	2	yes	—
441	C₂×C₄	C₁₃×#135	1	2	yes	—
442	C₂×C₄	C₁₃×#137	1	2	yes	—
443	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
444	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
445	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
446	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
447	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
449	C₈	—	2	2	no	—
450	C₈	—	4	1	no	—
451	C₈	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
460	C₂²	D₄²×C₁₃	1	1	yes	characteristic
461	C₂²	C₁₃×#546	1	1	yes	characteristic
462	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
463	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
464	C₂²	C₁₃×#577	1	1	yes	characteristic
465	C₂²	C₁₃×#578	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	8	2	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	2	no	—
474	C₄	C₁₃×#485	1	4	yes	complemented
475	C₄	C₁₃×#532	1	1	yes	characteristic
476	C₄	C₁₃×#540	1	1	yes	characteristic
477	C₄	C₁₃×#550	1	1	yes	characteristic
478	C₄	C₁₃×#559	1	1	yes	characteristic
479	C₂	—	8	2	no	—
480	C₂	C₁₃×#2445	1	1	yes	characteristic
481	C₂	C₂×C₁₃×#485	1	1	yes	characteristic
482	C₂	C₁₃×#3097	1	1	yes	characteristic
483	C₂	C₁₃×#3278	1	1	yes	characteristic
484	C₂	C₁₃×#3283	1	1	yes	characteristic
485	C₂	C₁₃×#3303	1	1	yes	characteristic
486	C₂	C₁₃×#3328	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×#485	C₂	semidirect
4. C₁₃×#2036	C₂	semidirect
5. C₁₃×#2035	C₂	semidirect
6. C₁₃×#1981	C₂	semidirect
7. C₁₃×#1956	C₂	semidirect
9. C₁₃×#1948	C₂	semidirect
10. C₁₃×#1873	C₂	semidirect
11. C₄×C₁₃×#107	C₂	semidirect
80. C₁₃×#107	D₄	semidirect
93. #26231	C₁₃	direct (N × H)
156. C₂×#485	C₂×C₁₃	semidirect
159. #2036	C₂×C₁₃	semidirect
160. #2035	C₂×C₁₃	semidirect
161. #1981	C₂×C₁₃	semidirect
162. #1956	C₂×C₁₃	semidirect
164. #1948	C₂×C₁₃	semidirect
165. #1873	C₂×C₁₃	semidirect
166. C₄×#107	C₂×C₁₃	semidirect
272. C₄×C₁₃	#485	semidirect
315. #107	D₄×C₁₃	semidirect
398. C₁₃	#26231	direct (N × H)
474. C₄	C₁₃×#485	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#485	2
C₁₃×#2542	2
C₁₃×#2354	2
C₁₃×#2036	2
C₁₃×#2035	2
C₁₃×#1981	2
C₁₃×#1956	2
C₁₃×#1954	2
C₁₃×#1948	2
C₁₃×#1873	2
C₄×C₁₃×#107	2
#26231	13

Subgroups — C13×#26231 #15712570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26231 #15712570