Subgroups — C₁₃×#26300 #15712639

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2563	C₂	1	1	yes	maximal, characteristic
2	D₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2077	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2077	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1948	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1853	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1823	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×C₄×D₄×C₁₃	—	2	1	no	—
14	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#106	C₂²	1	2	yes	—
19	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#393	—	2	2	no	—
24	C₁₃×#390	—	2	1	no	—
25	C₁₃×#389	—	2	1	no	—
26	C₁₃×#385	—	2	2	no	—
27	C₁₃×#384	C₂²	1	1	yes	characteristic
28	C₁₃×#382	—	2	1	no	—
29	C₁₃×#380	C₂²	1	2	yes	—
30	C₁₃×#380	C₂²	1	2	yes	—
31	C₁₃×#380	C₂²	1	2	yes	—
32	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₁₃×#340	C₂²	1	2	yes	—
35	C₁₃×#340	C₂²	1	2	yes	—
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	1	yes	characteristic
39	C₁₃×#340	C₂²	1	1	yes	characteristic
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₁₃	—	2	1	no	—
42	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₁₃	—	2	2	no	—
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	C₄×D₄×C₁₃	—	2	2	no	—
51	C₄×D₄×C₁₃	—	2	2	no	—
52	C₄×D₄×C₁₃	—	4	4	no	—
53	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
59	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
60	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
70	C₂×C₄²×C₁₃	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
73	C₁₃×#106	—	2	2	no	—
74	C₁₃×#106	—	2	2	no	—
75	C₁₃×#106	—	4	2	no	—
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₂²⋊C₈	—	2	4	no	—
78	C₁₃×C₂²⋊C₈	—	4	2	no	—
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₁₃×#95	—	2	1	no	—
81	C₁₃×#95	—	2	1	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	—	2	2	no	—
85	#26300	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
86	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
87	C₂×Q₈×C₁₃	—	4	2	no	—
88	C₂×Q₈×C₁₃	—	8	1	no	—
89	C₂×Q₈×C₁₃	—	8	1	no	—
90	C₂×D₄×C₁₃	—	2	2	no	—
91	C₂×D₄×C₁₃	—	2	2	no	—
92	C₂×D₄×C₁₃	SD₁₆	1	4	yes	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	2	no	—
95	C₂²×C₄×C₁₃	—	2	2	no	—
96	C₂²×C₄×C₁₃	—	2	2	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	2	no	—
100	C₂²×C₄×C₁₃	—	2	1	no	—
101	C₂²×C₄×C₁₃	—	2	1	no	—
102	C₂²×C₄×C₁₃	—	2	1	no	—
103	C₂²×C₄×C₁₃	—	2	2	no	—
104	C₂²×C₄×C₁₃	—	2	2	no	—
105	C₂²×C₄×C₁₃	—	4	4	no	—
106	C₂²×C₄×C₁₃	—	4	4	no	—
107	C₂²×C₄×C₁₃	—	8	2	no	—
108	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₁₃	—	2	1	no	—
113	C₂×C₈×C₁₃	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	1	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	1	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	1	no	—
120	C₂×C₈×C₁₃	#41	1	2	yes	—
121	C₁₃×C₄⋊C₄	—	2	2	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	2	1	no	—
124	C₁₃×C₄⋊C₄	—	2	1	no	—
125	C₁₃×C₄⋊C₄	—	2	1	no	—
126	C₁₃×C₄⋊C₄	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	8	1	no	—
137	C₁₃×C₄⋊C₄	#41	1	2	yes	—
138	C₁₃×C₂²⋊C₄	—	2	4	no	—
139	C₁₃×C₂²⋊C₄	—	4	4	no	—
140	C₁₃×C₂²⋊C₄	—	8	2	no	—
141	C₁₃×C₂²⋊C₄	—	8	2	no	—
142	C₄²×C₁₃	—	4	2	no	—
143	C₄²×C₁₃	—	4	2	no	—
144	C₄²×C₁₃	#41	1	2	yes	—
145	C₄²×C₁₃	#41	1	2	yes	—
146	#2563	C₂×C₁₃	1	1	yes	characteristic
147	D₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
148	#2077	C₂×C₁₃	1	2	yes	complemented
149	#2077	C₂×C₁₃	1	2	yes	complemented
150	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1987	C₂×C₁₃	1	1	yes	characteristic, complemented
152	#1954	C₂×C₁₃	1	1	yes	characteristic
153	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
154	#1853	C₂×C₁₃	1	2	yes	complemented
155	#1823	C₂×C₁₃	1	2	yes	complemented
156	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	—	2	2	no	—
161	C₂³×C₁₃	—	2	2	no	—
162	C₂³×C₁₃	—	2	2	no	—
163	C₂³×C₁₃	C₂×SD₁₆	1	4	yes	—
164	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
165	Q₈×C₁₃	—	8	4	no	—
166	D₄×C₁₃	—	2	8	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	4	2	no	—
177	C₂×C₄×C₁₃	—	4	2	no	—
178	C₂×C₄×C₁₃	—	4	2	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	—	4	1	no	—
183	C₂×C₄×C₁₃	—	4	1	no	—
184	C₂×C₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	1	no	—
187	C₂×C₄×C₁₃	—	4	1	no	—
188	C₂×C₄×C₁₃	—	4	1	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	4	2	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	8	8	no	—
195	C₂×C₄×C₁₃	#123	1	2	yes	—
196	C₂×C₄×C₁₃	#123	1	2	yes	—
197	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
198	C₂×C₄×C₁₃	#137	1	2	yes	—
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
202	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
205	C₈×C₁₃	—	2	2	no	—
206	C₈×C₁₃	—	4	1	no	—
207	C₈×C₁₃	—	4	2	no	—
208	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
209	C₂×C₄×D₄	—	2	1	no	—
210	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
211	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
212	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
213	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#106	C₂²×C₁₃	1	2	yes	—
215	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
216	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
217	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
218	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
219	#393	—	2	2	no	—
220	#390	—	2	1	no	—
221	#389	—	2	1	no	—
222	#385	—	2	2	no	—
223	#384	C₂²×C₁₃	1	1	yes	characteristic
224	#382	—	2	1	no	—
225	#380	C₂²×C₁₃	1	2	yes	—
226	#380	C₂²×C₁₃	1	2	yes	—
227	#380	C₂²×C₁₃	1	2	yes	—
228	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
229	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
230	#340	C₂²×C₁₃	1	2	yes	—
231	#340	C₂²×C₁₃	1	1	yes	characteristic
232	#340	C₂²×C₁₃	1	2	yes	—
233	#340	C₂²×C₁₃	1	2	yes	—
234	#340	C₂²×C₁₃	1	2	yes	—
235	#340	C₂²×C₁₃	1	1	yes	characteristic
236	#340	C₂²×C₁₃	1	2	yes	—
237	C₂²×C₁₃	—	2	4	no	—
238	C₂²×C₁₃	—	2	4	no	—
239	C₂²×C₁₃	—	2	4	no	—
240	C₂²×C₁₃	—	4	2	no	—
241	C₂²×C₁₃	—	4	2	no	—
242	C₂²×C₁₃	—	4	2	no	—
243	C₂²×C₁₃	—	4	2	no	—
244	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
245	C₂²×C₁₃	#546	1	1	yes	characteristic
246	C₂²×C₁₃	#547	1	1	yes	characteristic
247	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
249	C₂²×C₁₃	#576	1	1	yes	characteristic
250	C₂²×C₁₃	#577	1	1	yes	characteristic
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	4	2	no	—
253	C₄×C₁₃	—	4	2	no	—
254	C₄×C₁₃	—	8	1	no	—
255	C₄×C₁₃	—	8	1	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	—	8	1	no	—
258	C₄×C₁₃	—	8	2	no	—
259	C₄×C₁₃	#483	1	4	yes	—
260	C₄×C₁₃	#529	1	1	yes	characteristic
261	C₄×C₁₃	#542	1	1	yes	characteristic
262	C₄×C₁₃	#556	1	1	yes	characteristic
263	C₄×C₁₃	#559	1	1	yes	characteristic
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
266	C₂³×C₄	—	2	2	no	—
267	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	2	2	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	—	4	4	no	—
276	C₂×C₄⋊C₄	—	2	4	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	4	2	no	—
282	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	—	2	2	no	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
293	C₂×C₄²	—	2	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
296	#106	—	2	2	no	—
297	#106	—	2	2	no	—
298	#106	—	4	2	no	—
299	C₄⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	2	4	no	—
301	C₂²⋊C₈	—	4	2	no	—
302	C₄×C₈	—	2	2	no	—
303	#95	—	2	1	no	—
304	#95	—	2	1	no	—
305	#95	—	2	2	no	—
306	#95	—	2	2	no	—
307	#95	—	2	2	no	—
308	C₂×C₁₃	—	4	4	no	—
309	C₂×C₁₃	#2447	1	1	yes	characteristic
310	C₂×C₁₃	C₂×#483	1	1	yes	characteristic
311	C₂×C₁₃	#3096	1	1	yes	characteristic
312	C₂×C₁₃	#3295	1	1	yes	characteristic
313	C₂×C₁₃	#3329	1	1	yes	characteristic
314	C₂×C₁₃	#3335	1	1	yes	characteristic
315	C₂×C₁₃	#3357	1	1	yes	characteristic
316	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
317	C₂×Q₈	—	4	2	no	—
318	C₂×Q₈	—	8	1	no	—
319	C₂×Q₈	—	8	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	C₁₃×SD₁₆	1	4	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	8	2	no	—
338	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
339	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
341	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	C₁₃×#41	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	1	no	—
363	C₄⋊C₄	—	4	4	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	—	4	2	no	—
366	C₄⋊C₄	—	8	1	no	—
367	C₄⋊C₄	C₁₃×#41	1	2	yes	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	4	4	no	—
370	C₂²⋊C₄	—	8	2	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₄²	—	4	2	no	—
373	C₄²	—	4	2	no	—
374	C₄²	C₁₃×#41	1	2	yes	—
375	C₄²	C₁₃×#41	1	2	yes	—
376	C₁₃	#26300	1	1	yes	characteristic, direct product factor, Sylow
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₂×C₁₃×SD₁₆	1	4	yes	—
384	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
385	Q₈	—	8	4	no	—
386	D₄	—	2	8	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	8	8	no	—
415	C₂×C₄	C₁₃×#123	1	2	yes	—
416	C₂×C₄	C₁₃×#123	1	2	yes	—
417	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
418	C₂×C₄	C₁₃×#137	1	2	yes	—
419	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
421	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
422	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
423	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
424	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
425	C₈	—	2	2	no	—
426	C₈	—	4	1	no	—
427	C₈	—	4	2	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
436	C₂²	C₁₃×#546	1	1	yes	characteristic
437	C₂²	C₁₃×#547	1	1	yes	characteristic
438	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
439	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
440	C₂²	C₁₃×#576	1	1	yes	characteristic
441	C₂²	C₁₃×#577	1	1	yes	characteristic
442	C₄	—	2	2	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	2	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	8	2	no	—
449	C₄	—	8	1	no	—
450	C₄	C₁₃×#483	1	4	yes	—
451	C₄	C₁₃×#529	1	1	yes	characteristic
452	C₄	C₁₃×#542	1	1	yes	characteristic
453	C₄	C₁₃×#556	1	1	yes	characteristic
454	C₄	C₁₃×#559	1	1	yes	characteristic
455	C₂	—	4	4	no	—
456	C₂	C₁₃×#2447	1	1	yes	characteristic
457	C₂	C₂×C₁₃×#483	1	1	yes	characteristic
458	C₂	C₁₃×#3096	1	1	yes	characteristic
459	C₂	C₁₃×#3295	1	1	yes	characteristic
460	C₂	C₁₃×#3329	1	1	yes	characteristic
461	C₂	C₁₃×#3335	1	1	yes	characteristic
462	C₂	C₁₃×#3357	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
3. C₁₃×#2077	C₂	semidirect
4. C₁₃×#2077	C₂	semidirect
5. C₁₃×#1990	C₂	semidirect
6. C₁₃×#1987	C₂	semidirect
8. C₁₃×#1948	C₂	semidirect
9. C₁₃×#1853	C₂	semidirect
10. C₁₃×#1823	C₂	semidirect
11. C₄×C₁₃×#106	C₂	semidirect
85. #26300	C₁₃	direct (N × H)
148. #2077	C₂×C₁₃	semidirect
149. #2077	C₂×C₁₃	semidirect
150. #1990	C₂×C₁₃	semidirect
151. #1987	C₂×C₁₃	semidirect
153. #1948	C₂×C₁₃	semidirect
154. #1853	C₂×C₁₃	semidirect
155. #1823	C₂×C₁₃	semidirect
156. C₄×#106	C₂×C₁₃	semidirect
376. C₁₃	#26300	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×#2563	2
D₄×C₁₃×C₄⋊C₄	2
C₁₃×#2077	2
C₁₃×#1990	2
C₁₃×#1987	2
C₁₃×#1954	2
C₁₃×#1948	2
C₁₃×#1853	2
C₁₃×#1823	2
C₄×C₁₃×#106	2
#26300	13

Subgroups — C13×#26300 #15712639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26300 #15712639