Subgroups — C₁₃×#26065 #15712404

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#500	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₃×#107	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2440	C₂	1	2	yes	maximal
4	C₁₃×#2083	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2057	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1852	C₂	1	2	yes	maximal
9	C₁₃×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
11	C₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊Q₈	—	2	2	no	—
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
16	C₁₃×#500	—	2	4	no	—
17	C₂×C₁₃×#107	—	2	4	no	—
18	C₂×C₁₃×#107	C₂²	1	2	yes	—
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#107	C₂²	1	2	yes	—
22	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#107	C₂²	1	2	yes	—
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#398	—	2	2	no	—
29	C₁₃×#395	—	2	2	no	—
30	C₁₃×#389	C₂²	1	2	yes	—
31	C₁₃×#389	C₂²	1	2	yes	—
32	C₁₃×#385	—	2	2	no	—
33	C₁₃×#384	C₂²	1	2	yes	—
34	C₁₃×#380	C₂²	1	2	yes	—
35	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
36	C₁₃×#340	C₂²	1	2	yes	—
37	C₁₃×#340	C₂²	1	2	yes	—
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#336	C₂²	1	1	yes	characteristic
40	C₁₃×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₁₃	—	2	2	no	—
42	C₂³×C₄×C₁₃	—	2	2	no	—
43	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	—	2	2	no	—
45	C₂²×C₈×C₁₃	—	2	2	no	—
46	C₂²×C₈×C₁₃	Q₈	1	4	yes	complemented
47	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₁₃×C₄⋊Q₈	—	2	4	no	—
52	C₁₃×C₄⋊Q₈	—	4	2	no	—
53	C₁₃×C₂²⋊Q₈	—	4	8	no	—
54	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
68	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
71	C₁₃×#107	—	2	2	no	—
72	C₁₃×#107	—	2	2	no	—
73	C₁₃×#107	—	2	2	no	—
74	C₁₃×#107	—	2	4	no	—
75	C₁₃×#107	—	2	4	no	—
76	C₁₃×#107	—	4	2	no	—
77	C₁₃×#107	D₄	1	4	yes	—
78	C₁₃×C₂²⋊C₈	Q₈	1	4	yes	complemented
79	C₄×C₈×C₁₃	—	2	2	no	—
80	C₄×C₈×C₁₃	—	2	2	no	—
81	C₁₃×#95	—	2	2	no	—
82	C₁₃×#95	—	2	2	no	—
83	C₁₃×#95	—	2	2	no	—
84	C₁₃×#95	D₄	1	1	yes	characteristic
85	C₁₃×#95	D₄	1	1	yes	characteristic
86	#26065	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
87	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₁₃	—	4	4	no	—
89	C₂×Q₈×C₁₃	—	4	4	no	—
90	C₂×Q₈×C₁₃	—	8	2	no	—
91	C₂²×C₄×C₁₃	—	2	1	no	—
92	C₂²×C₄×C₁₃	—	2	1	no	—
93	C₂²×C₄×C₁₃	—	2	1	no	—
94	C₂²×C₄×C₁₃	—	2	1	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	—	4	4	no	—
100	C₂²×C₄×C₁₃	—	4	4	no	—
101	C₂²×C₄×C₁₃	—	8	2	no	—
102	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
108	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
109	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₁₃	—	2	1	no	—
111	C₂×C₈×C₁₃	—	2	1	no	—
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	1	no	—
116	C₂×C₈×C₁₃	—	2	8	no	—
117	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
119	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
120	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
121	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
122	C₂×C₈×C₁₃	#41	1	2	yes	—
123	C₁₃×C₄⋊C₄	—	2	2	no	—
124	C₁₃×C₄⋊C₄	—	2	2	no	—
125	C₁₃×C₄⋊C₄	—	2	2	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	2	no	—
130	C₁₃×C₄⋊C₄	—	4	4	no	—
131	C₁₃×C₄⋊C₄	—	4	4	no	—
132	C₁₃×C₄⋊C₄	—	4	4	no	—
133	C₁₃×C₄⋊C₄	—	4	4	no	—
134	C₁₃×C₄⋊C₄	—	4	4	no	—
135	C₁₃×C₄⋊C₄	—	8	2	no	—
136	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
137	C₁₃×C₂²⋊C₄	—	4	4	no	—
138	C₁₃×C₂²⋊C₄	D₈	1	4	yes	—
139	C₁₃×C₂²⋊C₄	Q₁₆	1	4	yes	—
140	C₄²×C₁₃	—	2	1	no	—
141	C₄²×C₁₃	—	2	1	no	—
142	C₄²×C₁₃	—	2	1	no	—
143	C₄²×C₁₃	—	2	1	no	—
144	C₂×#500	C₂×C₁₃	1	1	yes	characteristic, complemented
145	C₂²×#107	C₂×C₁₃	1	1	yes	characteristic
146	#2440	C₂×C₁₃	1	2	yes	—
147	#2083	C₂×C₁₃	1	2	yes	complemented
148	#2057	C₂×C₁₃	1	2	yes	complemented
149	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
150	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
151	#1852	C₂×C₁₃	1	2	yes	—
152	#1845	C₂×C₁₃	1	1	yes	characteristic, complemented
153	#1808	C₂×C₁₃	1	1	yes	characteristic
154	C₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
155	C₂³×C₁₃	—	2	1	no	—
156	C₂³×C₁₃	—	2	1	no	—
157	C₂³×C₁₃	—	2	1	no	—
158	C₂³×C₁₃	—	2	1	no	—
159	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
160	C₂³×C₁₃	C₂×D₈	1	2	yes	—
161	C₂³×C₁₃	C₂×Q₁₆	1	2	yes	—
162	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₁₃	—	8	8	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	no	—
169	C₂×C₄×C₁₃	—	2	1	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	—	2	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	4	2	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	—	4	2	no	—
182	C₂×C₄×C₁₃	—	4	2	no	—
183	C₂×C₄×C₁₃	—	4	2	no	—
184	C₂×C₄×C₁₃	—	4	2	no	—
185	C₂×C₄×C₁₃	—	4	2	no	—
186	C₂×C₄×C₁₃	—	4	2	no	—
187	C₂×C₄×C₁₃	—	4	2	no	—
188	C₂×C₄×C₁₃	—	4	2	no	—
189	C₂×C₄×C₁₃	—	4	2	no	—
190	C₂×C₄×C₁₃	—	8	8	no	—
191	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
192	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
193	C₂×C₄×C₁₃	C₂×D₈	1	2	yes	—
194	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
195	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
196	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
202	C₈×C₁₃	—	2	2	no	—
203	C₈×C₁₃	—	2	2	no	—
204	C₈×C₁₃	—	2	2	no	—
205	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	complemented
206	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
207	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
208	C₂×C₂²⋊Q₈	—	2	2	no	—
209	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
210	#500	—	2	4	no	—
211	C₂×#107	—	2	4	no	—
212	C₂×#107	C₂²×C₁₃	1	2	yes	—
213	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
214	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
215	C₂×#107	C₂²×C₁₃	1	2	yes	—
216	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×#107	C₂²×C₁₃	1	2	yes	—
218	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
221	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
222	#398	—	2	2	no	—
223	#395	—	2	2	no	—
224	#389	C₂²×C₁₃	1	2	yes	—
225	#389	C₂²×C₁₃	1	2	yes	—
226	#385	—	2	2	no	—
227	#384	C₂²×C₁₃	1	2	yes	—
228	#380	C₂²×C₁₃	1	2	yes	—
229	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
230	#340	C₂²×C₁₃	1	2	yes	—
231	#340	C₂²×C₁₃	1	2	yes	—
232	#340	C₂²×C₁₃	1	2	yes	—
233	#336	C₂²×C₁₃	1	1	yes	characteristic
234	#336	C₂²×C₁₃	1	1	yes	characteristic
235	C₂²×C₁₃	—	2	2	no	—
236	C₂²×C₁₃	—	2	2	no	—
237	C₂²×C₁₃	—	2	2	no	—
238	C₂²×C₁₃	—	2	2	no	—
239	C₂²×C₁₃	—	2	2	no	—
240	C₂²×C₁₃	—	2	2	no	—
241	C₂²×C₁₃	#500	1	4	yes	complemented
242	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
243	C₂²×C₁₃	D₄²	1	1	yes	characteristic
244	C₂²×C₁₃	#547	1	1	yes	characteristic
245	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
246	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
247	C₂²×C₁₃	#576	1	1	yes	characteristic
248	C₂²×C₁₃	#578	1	1	yes	characteristic
249	C₄×C₁₃	—	2	2	no	—
250	C₄×C₁₃	—	2	2	no	—
251	C₄×C₁₃	—	2	2	no	—
252	C₄×C₁₃	—	2	2	no	—
253	C₄×C₁₃	—	2	2	no	—
254	C₄×C₁₃	—	4	4	no	—
255	C₄×C₁₃	—	8	2	no	—
256	C₄×C₁₃	—	8	2	no	—
257	C₄×C₁₃	—	8	2	no	—
258	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
259	C₄×C₁₃	#544	1	1	yes	characteristic
260	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
261	C₄×C₁₃	#554	1	1	yes	characteristic
262	C₂²×Q₈	—	2	2	no	—
263	C₂³×C₄	—	2	2	no	—
264	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
265	C₂²×C₈	—	2	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	Q₈×C₁₃	1	4	yes	complemented
268	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
272	C₄⋊Q₈	—	2	4	no	—
273	C₄⋊Q₈	—	4	2	no	—
274	C₂²⋊Q₈	—	4	8	no	—
275	C₂×C₄⋊C₄	—	2	4	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	4	2	no	—
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	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
289	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#107	—	2	2	no	—
294	#107	—	2	2	no	—
295	#107	—	2	4	no	—
296	#107	—	2	4	no	—
297	#107	—	4	2	no	—
298	#107	D₄×C₁₃	1	4	yes	—
299	C₂²⋊C₈	Q₈×C₁₃	1	4	yes	complemented
300	C₄×C₈	—	2	2	no	—
301	C₄×C₈	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	D₄×C₁₃	1	1	yes	characteristic
306	#95	D₄×C₁₃	1	1	yes	characteristic
307	C₂×C₁₃	—	2	4	no	—
308	C₂×C₁₃	#2440	1	1	yes	characteristic
309	C₂×C₁₃	C₂×#500	1	1	yes	characteristic
310	C₂×C₁₃	#3164	1	1	yes	characteristic
311	C₂×C₁₃	D₄×D₈	1	1	yes	characteristic
312	C₂×C₁₃	D₄×Q₁₆	1	1	yes	characteristic
313	C₂×C₁₃	#3334	1	1	yes	characteristic
314	C₂×C₁₃	#3338	1	1	yes	characteristic
315	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
316	C₂×Q₈	—	4	4	no	—
317	C₂×Q₈	—	4	4	no	—
318	C₂×Q₈	—	8	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	4	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	8	2	no	—
330	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
333	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
335	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
336	C₂²×C₄	C₂×Q₈×C₁₃	1	2	yes	—
337	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	8	no	—
345	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
346	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
347	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
348	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
349	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
350	C₂×C₈	C₁₃×#41	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	4	no	—
359	C₄⋊C₄	—	4	4	no	—
360	C₄⋊C₄	—	4	4	no	—
361	C₄⋊C₄	—	4	4	no	—
362	C₄⋊C₄	—	4	4	no	—
363	C₄⋊C₄	—	8	2	no	—
364	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
365	C₂²⋊C₄	—	4	4	no	—
366	C₂²⋊C₄	C₁₃×D₈	1	4	yes	—
367	C₂²⋊C₄	C₁₃×Q₁₆	1	4	yes	—
368	C₄²	—	2	1	no	—
369	C₄²	—	2	1	no	—
370	C₄²	—	2	1	no	—
371	C₄²	—	2	1	no	—
372	C₁₃	#26065	1	1	yes	characteristic, direct product factor, Sylow
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	C₁₃×C₄⋊Q₈	1	2	yes	—
378	C₂³	C₂×C₁₃×D₈	1	2	yes	—
379	C₂³	C₂×C₁₃×Q₁₆	1	2	yes	—
380	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
381	Q₈	—	8	8	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	4	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	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	8	no	—
409	C₂×C₄	C₁₃×C₄⋊Q₈	1	2	yes	—
410	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
411	C₂×C₄	C₂×C₁₃×D₈	1	2	yes	—
412	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
413	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
414	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
417	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
418	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
419	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	2	2	no	—
423	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	complemented
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	C₁₃×#500	1	4	yes	complemented
431	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
432	C₂²	D₄²×C₁₃	1	1	yes	characteristic
433	C₂²	C₁₃×#547	1	1	yes	characteristic
434	C₂²	C₂²×C₁₃×D₈	1	1	yes	characteristic
435	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
436	C₂²	C₁₃×#576	1	1	yes	characteristic
437	C₂²	C₁₃×#578	1	1	yes	characteristic
438	C₄	—	2	2	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	4	no	—
444	C₄	—	8	2	no	—
445	C₄	—	8	2	no	—
446	C₄	—	8	2	no	—
447	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
448	C₄	C₁₃×#544	1	1	yes	characteristic
449	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
450	C₄	C₁₃×#554	1	1	yes	characteristic
451	C₂	—	2	4	no	—
452	C₂	C₁₃×#2440	1	1	yes	characteristic
453	C₂	C₂×C₁₃×#500	1	1	yes	characteristic
454	C₂	C₁₃×#3164	1	1	yes	characteristic
455	C₂	D₄×C₁₃×D₈	1	1	yes	characteristic
456	C₂	D₄×C₁₃×Q₁₆	1	1	yes	characteristic
457	C₂	C₁₃×#3334	1	1	yes	characteristic
458	C₂	C₁₃×#3338	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×#500	C₂	semidirect
4. C₁₃×#2083	C₂	semidirect
5. C₁₃×#2057	C₂	semidirect
6. C₁₃×#1942	C₂	semidirect
7. C₁₃×#1942	C₂	semidirect
9. C₁₃×#1845	C₂	semidirect
46. C₂²×C₈×C₁₃	Q₈	semidirect
78. C₁₃×C₂²⋊C₈	Q₈	semidirect
86. #26065	C₁₃	direct (N × H)
144. C₂×#500	C₂×C₁₃	semidirect
147. #2083	C₂×C₁₃	semidirect
148. #2057	C₂×C₁₃	semidirect
149. #1942	C₂×C₁₃	semidirect
150. #1942	C₂×C₁₃	semidirect
152. #1845	C₂×C₁₃	semidirect
205. C₈×C₁₃	C₂²⋊Q₈	semidirect
241. C₂²×C₁₃	#500	semidirect
267. C₂²×C₈	Q₈×C₁₃	semidirect
299. C₂²⋊C₈	Q₈×C₁₃	semidirect
372. C₁₃	#26065	direct (N × H)
423. C₈	C₁₃×C₂²⋊Q₈	semidirect
430. C₂²	C₁₃×#500	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#500	2
C₂²×C₁₃×#107	2
C₁₃×#2440	2
C₁₃×#2083	2
C₁₃×#2057	2
C₁₃×#1942	2
C₁₃×#1852	2
C₁₃×#1845	2
C₁₃×#1808	2
C₈×C₁₃×C₂²⋊C₄	2
#26065	13

Subgroups — C13×#26065 #15712404

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26065 #15712404