Subgroups — C₁₃×#26481 #15712820

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2454	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2453	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2026	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1941	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic
15	C₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
21	C₁₃×#499	—	2	4	no	—
22	C₄×C₁₃×SD₁₆	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#400	—	2	1	no	—
39	C₁₃×#399	—	2	1	no	—
40	C₁₃×#398	—	2	1	no	—
41	C₁₃×#396	—	2	1	no	—
42	C₁₃×#391	C₂²	1	1	yes	characteristic
43	C₁₃×#391	C₂²	1	1	yes	characteristic
44	C₁₃×#390	C₂²	1	1	yes	characteristic
45	C₁₃×#390	C₂²	1	1	yes	characteristic
46	C₁₃×#389	—	2	1	no	—
47	C₁₃×#389	C₂²	1	1	yes	characteristic
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#389	C₂²	1	1	yes	characteristic
51	C₁₃×#387	—	2	1	no	—
52	C₁₃×#385	—	2	1	no	—
53	C₁₃×#380	—	2	1	no	—
54	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₃	—	2	1	no	—
64	C₂×C₁₃×SD₁₆	—	2	2	no	—
65	C₂×C₁₃×SD₁₆	—	2	2	no	—
66	C₂×C₁₃×SD₁₆	Q₈	1	4	yes	—
67	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#125	—	2	2	no	—
72	C₁₃×#125	—	2	2	no	—
73	C₁₃×#125	—	4	1	no	—
74	C₁₃×#125	—	4	1	no	—
75	C₄×Q₈×C₁₃	—	2	2	no	—
76	C₄×Q₈×C₁₃	—	4	1	no	—
77	C₄×D₄×C₁₃	—	2	2	no	—
78	C₄×D₄×C₁₃	—	4	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	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	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
89	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃	—	2	1	no	—
102	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
105	C₁₃×#107	—	2	2	no	—
106	C₁₃×#107	—	2	2	no	—
107	C₁₃×#106	—	2	2	no	—
108	C₁₃×#106	—	2	2	no	—
109	C₁₃×#106	D₄	1	4	yes	—
110	C₁₃×C₄⋊C₈	—	2	2	no	—
111	C₁₃×#103	—	2	2	no	—
112	C₁₃×#103	—	2	2	no	—
113	C₁₃×#103	—	4	1	no	—
114	C₁₃×#102	—	2	2	no	—
115	C₁₃×#102	—	2	2	no	—
116	C₁₃×#102	—	4	1	no	—
117	C₄×C₈×C₁₃	—	2	2	no	—
118	C₄×C₈×C₁₃	—	2	2	no	—
119	C₄×C₈×C₁₃	—	2	2	no	—
120	C₁₃×#95	—	2	1	no	—
121	C₁₃×#95	—	2	1	no	—
122	C₁₃×#95	—	2	1	no	—
123	C₁₃×#95	—	2	1	no	—
124	C₁₃×#95	—	2	1	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	D₄	1	1	yes	characteristic
129	C₁₃×#95	D₄	1	1	yes	characteristic
130	#26481	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂⁴×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	1	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
138	C₂×D₄×C₁₃	—	2	1	no	—
139	C₂×D₄×C₁₃	—	2	1	no	—
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
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	—	8	1	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
161	C₁₃×SD₁₆	—	2	8	no	—
162	C₂×C₈×C₁₃	—	2	1	no	—
163	C₂×C₈×C₁₃	—	2	1	no	—
164	C₂×C₈×C₁₃	—	2	1	no	—
165	C₂×C₈×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
172	C₂×C₈×C₁₃	#41	1	2	yes	—
173	C₂×C₈×C₁₃	#41	1	2	yes	—
174	C₁₃×C₄⋊C₄	—	2	2	no	—
175	C₁₃×C₄⋊C₄	—	2	2	no	—
176	C₁₃×C₄⋊C₄	—	2	1	no	—
177	C₁₃×C₄⋊C₄	—	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	—	4	2	no	—
187	C₁₃×C₄⋊C₄	—	4	2	no	—
188	C₁₃×C₄⋊C₄	—	4	2	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	—	8	1	no	—
195	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
196	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
197	C₁₃×C₂²⋊C₄	—	4	2	no	—
198	C₁₃×C₂²⋊C₄	—	4	2	no	—
199	C₁₃×C₂²⋊C₄	—	8	1	no	—
200	C₁₃×C₂²⋊C₄	—	8	1	no	—
201	C₁₃×C₂²⋊C₄	—	8	1	no	—
202	C₄²×C₁₃	—	2	1	no	—
203	C₄²×C₁₃	—	2	1	no	—
204	C₄²×C₁₃	—	2	1	no	—
205	C₄²×C₁₃	—	2	1	no	—
206	C₄²×C₁₃	—	2	1	no	—
207	C₄²×C₁₃	—	2	1	no	—
208	C₄²×C₁₃	—	4	2	no	—
209	C₂×#499	C₂×C₁₃	1	1	yes	characteristic, complemented
210	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
211	#2454	C₂×C₁₃	1	1	yes	characteristic
212	#2453	C₂×C₁₃	1	1	yes	characteristic, complemented
213	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
214	#2067	C₂×C₁₃	1	1	yes	characteristic
215	#2026	C₂×C₁₃	1	1	yes	characteristic, complemented
216	#2025	C₂×C₁₃	1	1	yes	characteristic
217	#1968	C₂×C₁₃	1	1	yes	characteristic
218	#1968	C₂×C₁₃	1	1	yes	characteristic
219	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
220	#1941	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#1862	C₂×C₁₃	1	1	yes	characteristic
223	C₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂³×C₁₃	—	2	2	no	—
225	C₂³×C₁₃	—	4	1	no	—
226	C₂³×C₁₃	—	4	1	no	—
227	C₂³×C₁₃	—	4	1	no	—
228	C₂³×C₁₃	—	4	1	no	—
229	C₂³×C₁₃	—	4	1	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
232	Q₈×C₁₃	—	2	2	no	—
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	4	1	no	—
235	Q₈×C₁₃	—	4	1	no	—
236	D₄×C₁₃	—	2	2	no	—
237	D₄×C₁₃	—	2	2	no	—
238	D₄×C₁₃	—	4	1	no	—
239	D₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	2	no	—
251	C₂×C₄×C₁₃	—	2	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	1	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	1	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	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	—	4	1	no	—
265	C₂×C₄×C₁₃	—	4	1	no	—
266	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
278	C₂×C₄×C₁₃	#135	1	2	yes	—
279	C₂×C₄×C₁₃	#135	1	2	yes	—
280	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
284	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
285	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
286	C₈×C₁₃	—	2	2	no	—
287	C₈×C₁₃	—	4	1	no	—
288	C₈×C₁₃	—	4	1	no	—
289	C₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
290	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
295	#499	—	2	4	no	—
296	C₄×SD₁₆	—	2	4	no	—
297	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
298	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
299	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
301	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
302	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
303	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
309	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
310	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
311	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
312	#400	—	2	1	no	—
313	#399	—	2	1	no	—
314	#398	—	2	1	no	—
315	#396	—	2	1	no	—
316	#391	C₂²×C₁₃	1	1	yes	characteristic
317	#391	C₂²×C₁₃	1	1	yes	characteristic
318	#390	C₂²×C₁₃	1	1	yes	characteristic
319	#390	C₂²×C₁₃	1	1	yes	characteristic
320	#389	—	2	1	no	—
321	#389	C₂²×C₁₃	1	1	yes	characteristic
322	#389	C₂²×C₁₃	1	1	yes	characteristic
323	#389	C₂²×C₁₃	1	1	yes	characteristic
324	#389	C₂²×C₁₃	1	1	yes	characteristic
325	#387	—	2	1	no	—
326	#385	—	2	1	no	—
327	#380	—	2	1	no	—
328	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
329	#340	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	#336	C₂²×C₁₃	1	1	yes	characteristic
334	#336	C₂²×C₁₃	1	1	yes	characteristic
335	C₂²×C₁₃	—	4	2	no	—
336	C₂²×C₁₃	—	4	2	no	—
337	C₂²×C₁₃	—	4	2	no	—
338	C₂²×C₁₃	—	8	1	no	—
339	C₂²×C₁₃	—	8	1	no	—
340	C₂²×C₁₃	—	8	1	no	—
341	C₂²×C₁₃	—	8	1	no	—
342	C₂²×C₁₃	#532	1	1	yes	characteristic
343	C₂²×C₁₃	D₄²	1	1	yes	characteristic
344	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
345	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
346	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
347	C₂²×C₁₃	#577	1	1	yes	characteristic
348	C₂²×C₁₃	#577	1	1	yes	characteristic
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	—	2	2	no	—
351	C₄×C₁₃	—	4	1	no	—
352	C₄×C₁₃	—	4	2	no	—
353	C₄×C₁₃	—	4	1	no	—
354	C₄×C₁₃	—	4	2	no	—
355	C₄×C₁₃	—	4	1	no	—
356	C₄×C₁₃	—	4	1	no	—
357	C₄×C₁₃	—	4	2	no	—
358	C₄×C₁₃	—	8	1	no	—
359	C₄×C₁₃	—	8	1	no	—
360	C₄×C₁₃	—	8	1	no	—
361	C₄×C₁₃	—	8	1	no	—
362	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
363	C₄×C₁₃	#542	1	1	yes	characteristic
364	C₄×C₁₃	#548	1	1	yes	characteristic
365	C₄×C₁₃	#554	1	1	yes	characteristic
366	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
367	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
368	C₂³×C₄	—	2	1	no	—
369	C₂×SD₁₆	—	2	2	no	—
370	C₂×SD₁₆	—	2	2	no	—
371	C₂×SD₁₆	Q₈×C₁₃	1	4	yes	—
372	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
376	#125	—	2	2	no	—
377	#125	—	2	2	no	—
378	#125	—	4	1	no	—
379	#125	—	4	1	no	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	4	1	no	—
382	C₄×D₄	—	2	2	no	—
383	C₄×D₄	—	4	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	—	2	1	no	—
392	C₂×C₄⋊C₄	—	2	1	no	—
393	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₂²⋊C₄	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
408	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
410	#107	—	2	2	no	—
411	#107	—	2	2	no	—
412	#106	—	2	2	no	—
413	#106	—	2	2	no	—
414	#106	D₄×C₁₃	1	4	yes	—
415	C₄⋊C₈	—	2	2	no	—
416	#103	—	2	2	no	—
417	#103	—	2	2	no	—
418	#103	—	4	1	no	—
419	#102	—	2	2	no	—
420	#102	—	2	2	no	—
421	#102	—	4	1	no	—
422	C₄×C₈	—	2	2	no	—
423	C₄×C₈	—	2	2	no	—
424	C₄×C₈	—	2	2	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	—	2	1	no	—
431	#95	—	2	1	no	—
432	#95	—	2	1	no	—
433	#95	D₄×C₁₃	1	1	yes	characteristic
434	#95	D₄×C₁₃	1	1	yes	characteristic
435	C₂×C₁₃	—	8	2	no	—
436	C₂×C₁₃	#2452	1	1	yes	characteristic
437	C₂×C₁₃	#3168	1	1	yes	characteristic
438	C₂×C₁₃	#3174	1	1	yes	characteristic
439	C₂×C₁₃	#3282	1	1	yes	characteristic
440	C₂×C₁₃	#3284	1	1	yes	characteristic
441	C₂×C₁₃	#3381	1	1	yes	characteristic
442	C₂×C₁₃	#3381	1	1	yes	characteristic
443	C₂⁴	—	2	1	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	8	1	no	—
466	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
468	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
469	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
470	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
472	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
473	SD₁₆	—	2	8	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
483	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
484	C₂×C₈	C₁₃×#41	1	2	yes	—
485	C₂×C₈	C₁₃×#41	1	2	yes	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	4	2	no	—
499	C₄⋊C₄	—	4	2	no	—
500	C₄⋊C₄	—	4	2	no	—
501	C₄⋊C₄	—	4	2	no	—
502	C₄⋊C₄	—	4	2	no	—
503	C₄⋊C₄	—	4	2	no	—
504	C₄⋊C₄	—	4	2	no	—
505	C₄⋊C₄	—	8	1	no	—
506	C₄⋊C₄	—	8	1	no	—
507	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
508	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
509	C₂²⋊C₄	—	4	2	no	—
510	C₂²⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	—	8	1	no	—
512	C₂²⋊C₄	—	8	1	no	—
513	C₂²⋊C₄	—	8	1	no	—
514	C₄²	—	2	1	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	4	2	no	—
521	C₁₃	#26481	1	1	yes	characteristic, direct product factor, Sylow
522	C₂³	—	2	2	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	4	1	no	—
526	C₂³	—	4	1	no	—
527	C₂³	—	4	1	no	—
528	C₂³	—	4	1	no	—
529	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	1	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	4	1	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	4	1	no	—
564	C₂×C₄	—	4	1	no	—
565	C₂×C₄	—	4	1	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	—	4	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	4	1	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	8	4	no	—
576	C₂×C₄	C₁₃×#135	1	2	yes	—
577	C₂×C₄	C₁₃×#135	1	2	yes	—
578	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
579	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
581	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
582	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
583	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
584	C₈	—	2	2	no	—
585	C₈	—	4	1	no	—
586	C₈	—	4	1	no	—
587	C₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	8	1	no	—
592	C₂²	—	8	1	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	C₁₃×#532	1	1	yes	characteristic
596	C₂²	D₄²×C₁₃	1	1	yes	characteristic
597	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
598	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
599	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
600	C₂²	C₁₃×#577	1	1	yes	characteristic
601	C₂²	C₁₃×#577	1	1	yes	characteristic
602	C₄	—	2	2	no	—
603	C₄	—	2	2	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	1	no	—
607	C₄	—	4	1	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	1	no	—
610	C₄	—	4	2	no	—
611	C₄	—	8	1	no	—
612	C₄	—	8	1	no	—
613	C₄	—	8	1	no	—
614	C₄	—	8	1	no	—
615	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
616	C₄	C₁₃×#542	1	1	yes	characteristic
617	C₄	C₁₃×#548	1	1	yes	characteristic
618	C₄	C₁₃×#554	1	1	yes	characteristic
619	C₂	—	8	2	no	—
620	C₂	C₁₃×#2452	1	1	yes	characteristic
621	C₂	C₁₃×#3168	1	1	yes	characteristic
622	C₂	C₁₃×#3174	1	1	yes	characteristic
623	C₂	C₁₃×#3282	1	1	yes	characteristic
624	C₂	C₁₃×#3284	1	1	yes	characteristic
625	C₂	C₁₃×#3381	1	1	yes	characteristic
626	C₂	C₁₃×#3381	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	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#499	C₂	semidirect
4. C₁₃×#2453	C₂	semidirect
5. C₁₃×#2068	C₂	semidirect
7. C₁₃×#2026	C₂	semidirect
11. C₁₃×#1941	C₂	semidirect
12. C₁₃×#1941	C₂	semidirect
13. C₁₃×#1863	C₂	semidirect
15. C₈×C₁₃×C₄⋊C₄	C₂	semidirect
130. #26481	C₁₃	direct (N × H)
209. C₂×#499	C₂×C₁₃	semidirect
212. #2453	C₂×C₁₃	semidirect
213. #2068	C₂×C₁₃	semidirect
215. #2026	C₂×C₁₃	semidirect
219. #1941	C₂×C₁₃	semidirect
220. #1941	C₂×C₁₃	semidirect
221. #1863	C₂×C₁₃	semidirect
223. C₈×C₄⋊C₄	C₂×C₁₃	semidirect
521. C₁₃	#26481	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#499	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2454	2
C₁₃×#2453	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#2026	2
C₁₃×#2025	2
C₁₃×#1968	2
C₁₃×#1941	2
C₁₃×#1863	2
C₁₃×#1862	2
C₈×C₁₃×C₄⋊C₄	2
#26481	13

Subgroups — C13×#26481 #15712820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26481 #15712820