Subgroups — C₁₃×#26891 #15713230

Order 3328.

876 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2454	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2012	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1877	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#479	—	2	4	no	—
24	C₄×C₁₃×D₈	—	2	4	no	—
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	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×#102	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×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#399	—	2	1	no	—
38	C₁₃×#396	—	2	1	no	—
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#390	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#388	—	2	1	no	—
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#385	—	2	1	no	—
48	C₁₃×#385	—	2	1	no	—
49	C₁₃×#380	—	2	1	no	—
50	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
51	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
52	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	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	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂×C₁₃×SD₁₆	—	2	2	no	—
67	C₂×C₁₃×SD₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	4	1	no	—
69	C₂×C₁₃×D₈	—	2	2	no	—
70	C₂×C₁₃×D₈	—	2	2	no	—
71	C₂×C₁₃×D₈	—	2	2	no	—
72	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₁₃×#125	—	2	2	no	—
77	C₁₃×#125	—	4	1	no	—
78	C₁₃×#124	—	2	2	no	—
79	C₁₃×#124	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	4	1	no	—
82	C₄×D₄×C₁₃	—	2	2	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	4	1	no	—
85	C₄×D₄×C₁₃	—	4	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
108	C₂×C₄²×C₁₃	—	2	1	no	—
109	C₂×C₄²×C₁₃	—	2	1	no	—
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₁₃×#107	D₄	1	4	yes	—
114	C₁₃×#106	—	2	2	no	—
115	C₁₃×C₄⋊C₈	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	2	2	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₁₃×#102	—	2	2	no	—
123	C₁₃×#102	—	4	1	no	—
124	C₄×C₈×C₁₃	—	2	2	no	—
125	C₁₃×#95	—	2	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	D₄	1	1	yes	characteristic
131	C₁₃×#95	D₄	1	1	yes	characteristic
132	#26891	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×C₁₃	—	2	1	no	—
134	C₂⁴×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	1	no	—
136	C₂×Q₈×C₁₃	—	2	1	no	—
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	#41	1	2	yes	—
141	C₂×D₄×C₁₃	—	2	1	no	—
142	C₂×D₄×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	#41	1	2	yes	—
152	C₂×D₄×C₁₃	#41	1	2	yes	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	4	2	no	—
160	C₂²×C₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	4	2	no	—
162	C₂²×C₄×C₁₃	—	4	2	no	—
163	C₂²×C₄×C₁₃	—	8	1	no	—
164	C₂²×C₄×C₁₃	—	8	1	no	—
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₁₃×SD₁₆	—	4	4	no	—
173	C₁₃×D₈	—	2	8	no	—
174	C₂×C₈×C₁₃	—	2	1	no	—
175	C₂×C₈×C₁₃	—	2	1	no	—
176	C₂×C₈×C₁₃	—	2	1	no	—
177	C₂×C₈×C₁₃	—	2	1	no	—
178	C₂×C₈×C₁₃	—	2	1	no	—
179	C₂×C₈×C₁₃	—	2	1	no	—
180	C₂×C₈×C₁₃	—	2	1	no	—
181	C₂×C₈×C₁₃	—	2	1	no	—
182	C₂×C₈×C₁₃	—	2	1	no	—
183	C₂×C₈×C₁₃	—	2	1	no	—
184	C₂×C₈×C₁₃	—	2	1	no	—
185	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
186	C₁₃×C₄⋊C₄	—	2	2	no	—
187	C₁₃×C₄⋊C₄	—	2	1	no	—
188	C₁₃×C₄⋊C₄	—	2	1	no	—
189	C₁₃×C₄⋊C₄	—	2	1	no	—
190	C₁₃×C₄⋊C₄	—	2	1	no	—
191	C₁₃×C₄⋊C₄	—	2	1	no	—
192	C₁₃×C₄⋊C₄	—	2	1	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	1	no	—
195	C₁₃×C₄⋊C₄	—	4	1	no	—
196	C₁₃×C₄⋊C₄	—	4	2	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	—	4	2	no	—
199	C₁₃×C₄⋊C₄	—	8	1	no	—
200	C₁₃×C₄⋊C₄	—	8	1	no	—
201	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
202	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
203	C₁₃×C₂²⋊C₄	—	2	4	no	—
204	C₁₃×C₂²⋊C₄	—	2	4	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	4	2	no	—
208	C₁₃×C₂²⋊C₄	—	4	2	no	—
209	C₁₃×C₂²⋊C₄	—	8	1	no	—
210	C₁₃×C₂²⋊C₄	—	8	1	no	—
211	C₁₃×C₂²⋊C₄	—	8	1	no	—
212	C₁₃×C₂²⋊C₄	—	8	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	2	1	no	—
216	C₄²×C₁₃	—	2	1	no	—
217	C₄²×C₁₃	—	2	1	no	—
218	C₄²×C₁₃	—	2	1	no	—
219	C₄²×C₁₃	—	4	2	no	—
220	C₄²×C₁₃	—	8	1	no	—
221	C₂×#479	C₂×C₁₃	1	1	yes	characteristic, complemented
222	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
223	#2454	C₂×C₁₃	1	1	yes	characteristic, complemented
224	#2367	C₂×C₁₃	1	1	yes	characteristic, complemented
225	#2054	C₂×C₁₃	1	1	yes	characteristic
226	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
228	#2012	C₂×C₁₃	1	1	yes	characteristic
229	#1933	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1926	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#1916	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#1880	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#1877	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	—	4	1	no	—
240	C₂³×C₁₃	—	4	1	no	—
241	C₂³×C₁₃	—	4	1	no	—
242	C₂³×C₁₃	—	4	1	no	—
243	C₂³×C₁₃	—	4	1	no	—
244	C₂³×C₁₃	—	4	1	no	—
245	C₂³×C₁₃	—	4	1	no	—
246	C₂³×C₁₃	—	4	1	no	—
247	C₂³×C₁₃	—	4	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
251	Q₈×C₁₃	—	2	2	no	—
252	Q₈×C₁₃	—	2	2	no	—
253	Q₈×C₁₃	—	4	1	no	—
254	Q₈×C₁₃	—	4	1	no	—
255	D₄×C₁₃	—	2	2	no	—
256	D₄×C₁₃	—	2	2	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	4	1	no	—
260	D₄×C₁₃	—	4	1	no	—
261	D₄×C₁₃	—	4	1	no	—
262	D₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	2	1	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	2	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	4	1	no	—
284	C₂×C₄×C₁₃	—	4	1	no	—
285	C₂×C₄×C₁₃	—	4	1	no	—
286	C₂×C₄×C₁₃	—	4	1	no	—
287	C₂×C₄×C₁₃	—	4	1	no	—
288	C₂×C₄×C₁₃	—	4	1	no	—
289	C₂×C₄×C₁₃	—	4	1	no	—
290	C₂×C₄×C₁₃	—	4	1	no	—
291	C₂×C₄×C₁₃	—	4	1	no	—
292	C₂×C₄×C₁₃	—	4	1	no	—
293	C₂×C₄×C₁₃	—	4	1	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	8	4	no	—
299	C₂×C₄×C₁₃	—	8	4	no	—
300	C₂×C₄×C₁₃	#135	1	2	yes	—
301	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
303	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
304	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
305	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
306	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
307	C₈×C₁₃	—	2	2	no	—
308	C₈×C₁₃	—	4	1	no	—
309	C₈×C₁₃	—	4	1	no	—
310	C₈×C₁₃	—	4	1	no	—
311	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
312	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
318	#479	—	2	4	no	—
319	C₄×D₈	—	2	4	no	—
320	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
323	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
324	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
325	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
326	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
327	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
328	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
332	#399	—	2	1	no	—
333	#396	—	2	1	no	—
334	#391	C₂²×C₁₃	1	1	yes	characteristic
335	#390	C₂²×C₁₃	1	1	yes	characteristic
336	#390	C₂²×C₁₃	1	1	yes	characteristic
337	#390	C₂²×C₁₃	1	1	yes	characteristic
338	#389	C₂²×C₁₃	1	1	yes	characteristic
339	#389	C₂²×C₁₃	1	1	yes	characteristic
340	#388	—	2	1	no	—
341	#388	—	2	1	no	—
342	#385	—	2	1	no	—
343	#385	—	2	1	no	—
344	#380	—	2	1	no	—
345	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
346	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
347	C₄×C₂²⋊C₄	—	2	1	no	—
348	#340	C₂²×C₁₃	1	1	yes	characteristic
349	#340	C₂²×C₁₃	1	1	yes	characteristic
350	#340	C₂²×C₁₃	1	1	yes	characteristic
351	#340	C₂²×C₁₃	1	1	yes	characteristic
352	#336	C₂²×C₁₃	1	1	yes	characteristic
353	#336	C₂²×C₁₃	1	1	yes	characteristic
354	#336	C₂²×C₁₃	1	1	yes	characteristic
355	#336	C₂²×C₁₃	1	1	yes	characteristic
356	C₂²×C₁₃	—	4	2	no	—
357	C₂²×C₁₃	—	4	2	no	—
358	C₂²×C₁₃	—	4	2	no	—
359	C₂²×C₁₃	—	4	2	no	—
360	C₂²×C₁₃	—	4	2	no	—
361	C₂²×C₁₃	—	4	2	no	—
362	C₂²×C₁₃	—	8	1	no	—
363	C₂²×C₁₃	—	8	1	no	—
364	C₂²×C₁₃	—	8	1	no	—
365	C₂²×C₁₃	—	8	1	no	—
366	C₂²×C₁₃	—	8	1	no	—
367	C₂²×C₁₃	—	8	1	no	—
368	C₂²×C₁₃	—	8	1	no	—
369	C₂²×C₁₃	—	8	1	no	—
370	C₂²×C₁₃	#525	1	1	yes	characteristic
371	C₂²×C₁₃	D₄²	1	1	yes	characteristic
372	C₂²×C₁₃	#548	1	1	yes	characteristic
373	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
374	C₂²×C₁₃	#575	1	1	yes	characteristic
375	C₂²×C₁₃	#576	1	1	yes	characteristic
376	C₂²×C₁₃	#577	1	1	yes	characteristic
377	C₄×C₁₃	—	2	2	no	—
378	C₄×C₁₃	—	4	1	no	—
379	C₄×C₁₃	—	4	1	no	—
380	C₄×C₁₃	—	4	2	no	—
381	C₄×C₁₃	—	4	1	no	—
382	C₄×C₁₃	—	4	1	no	—
383	C₄×C₁₃	—	4	1	no	—
384	C₄×C₁₃	—	4	2	no	—
385	C₄×C₁₃	—	4	2	no	—
386	C₄×C₁₃	—	8	1	no	—
387	C₄×C₁₃	—	8	1	no	—
388	C₄×C₁₃	—	8	1	no	—
389	C₄×C₁₃	#525	1	1	yes	characteristic
390	C₄×C₁₃	#539	1	1	yes	characteristic
391	C₄×C₁₃	#548	1	1	yes	characteristic
392	C₄×C₁₃	#551	1	1	yes	characteristic
393	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
394	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
395	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
396	C₂³×C₄	—	2	1	no	—
397	C₂³×C₄	—	2	1	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	4	1	no	—
401	C₂×D₈	—	2	2	no	—
402	C₂×D₈	—	2	2	no	—
403	C₂×D₈	—	2	2	no	—
404	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
405	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
406	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
407	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
408	#125	—	2	2	no	—
409	#125	—	4	1	no	—
410	#124	—	2	2	no	—
411	#124	—	2	2	no	—
412	C₄×Q₈	—	2	2	no	—
413	C₄×Q₈	—	4	1	no	—
414	C₄×D₄	—	2	2	no	—
415	C₄×D₄	—	2	2	no	—
416	C₄×D₄	—	4	1	no	—
417	C₄×D₄	—	4	1	no	—
418	C₂×C₄⋊C₄	—	2	1	no	—
419	C₂×C₄⋊C₄	—	2	1	no	—
420	C₂×C₄⋊C₄	—	2	1	no	—
421	C₂×C₄⋊C₄	—	2	1	no	—
422	C₂×C₄⋊C₄	—	2	1	no	—
423	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
425	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
428	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
429	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	1	no	—
432	C₂×C₂²⋊C₄	—	2	1	no	—
433	C₂×C₂²⋊C₄	—	2	1	no	—
434	C₂×C₂²⋊C₄	—	2	1	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	1	no	—
437	C₂×C₂²⋊C₄	—	2	1	no	—
438	C₂×C₂²⋊C₄	—	2	1	no	—
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₄²	—	2	1	no	—
441	C₂×C₄²	—	2	1	no	—
442	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
444	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
445	#107	D₄×C₁₃	1	4	yes	—
446	#106	—	2	2	no	—
447	C₄⋊C₈	—	2	2	no	—
448	#103	—	2	2	no	—
449	#103	—	2	2	no	—
450	#103	—	2	2	no	—
451	#102	—	2	2	no	—
452	#102	—	2	2	no	—
453	#102	—	2	2	no	—
454	#102	—	2	2	no	—
455	#102	—	4	1	no	—
456	C₄×C₈	—	2	2	no	—
457	#95	—	2	1	no	—
458	#95	—	2	1	no	—
459	#95	—	2	1	no	—
460	#95	—	2	1	no	—
461	#95	—	2	1	no	—
462	#95	D₄×C₁₃	1	1	yes	characteristic
463	#95	D₄×C₁₃	1	1	yes	characteristic
464	C₂×C₁₃	—	8	2	no	—
465	C₂×C₁₃	—	8	2	no	—
466	C₂×C₁₃	#2463	1	1	yes	characteristic
467	C₂×C₁₃	#3102	1	1	yes	characteristic
468	C₂×C₁₃	#3119	1	1	yes	characteristic
469	C₂×C₁₃	#3271	1	1	yes	characteristic
470	C₂×C₁₃	#3280	1	1	yes	characteristic
471	C₂×C₁₃	#3360	1	1	yes	characteristic
472	C₂×C₁₃	#3370	1	1	yes	characteristic
473	C₂⁴	—	2	1	no	—
474	C₂⁴	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	C₁₃×#41	1	2	yes	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	1	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	C₁₃×#41	1	2	yes	—
492	C₂×D₄	C₁₃×#41	1	2	yes	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	4	2	no	—
500	C₂²×C₄	—	4	2	no	—
501	C₂²×C₄	—	4	2	no	—
502	C₂²×C₄	—	4	2	no	—
503	C₂²×C₄	—	8	1	no	—
504	C₂²×C₄	—	8	1	no	—
505	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
506	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
507	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
508	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
509	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
511	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
512	SD₁₆	—	4	4	no	—
513	D₈	—	2	8	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	4	1	no	—
536	C₄⋊C₄	—	4	2	no	—
537	C₄⋊C₄	—	4	2	no	—
538	C₄⋊C₄	—	4	2	no	—
539	C₄⋊C₄	—	8	1	no	—
540	C₄⋊C₄	—	8	1	no	—
541	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
542	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
543	C₂²⋊C₄	—	2	4	no	—
544	C₂²⋊C₄	—	2	4	no	—
545	C₂²⋊C₄	—	4	2	no	—
546	C₂²⋊C₄	—	4	2	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	8	1	no	—
550	C₂²⋊C₄	—	8	1	no	—
551	C₂²⋊C₄	—	8	1	no	—
552	C₂²⋊C₄	—	8	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	4	2	no	—
560	C₄²	—	8	1	no	—
561	C₁₃	#26891	1	1	yes	characteristic, direct product factor, Sylow
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
577	Q₈	—	2	2	no	—
578	Q₈	—	2	2	no	—
579	Q₈	—	4	1	no	—
580	Q₈	—	4	1	no	—
581	D₄	—	2	2	no	—
582	D₄	—	2	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	4	1	no	—
586	D₄	—	4	1	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	8	4	no	—
625	C₂×C₄	—	8	4	no	—
626	C₂×C₄	C₁₃×#135	1	2	yes	—
627	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
628	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
629	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
630	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
631	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
632	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
633	C₈	—	2	2	no	—
634	C₈	—	4	1	no	—
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	4	2	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	8	1	no	—
644	C₂²	—	8	1	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	C₁₃×#525	1	1	yes	characteristic
652	C₂²	D₄²×C₁₃	1	1	yes	characteristic
653	C₂²	C₁₃×#548	1	1	yes	characteristic
654	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
655	C₂²	C₁₃×#575	1	1	yes	characteristic
656	C₂²	C₁₃×#576	1	1	yes	characteristic
657	C₂²	C₁₃×#577	1	1	yes	characteristic
658	C₄	—	2	2	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	1	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	1	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	2	no	—
667	C₄	—	8	1	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	C₁₃×#525	1	1	yes	characteristic
671	C₄	C₁₃×#539	1	1	yes	characteristic
672	C₄	C₁₃×#548	1	1	yes	characteristic
673	C₄	C₁₃×#551	1	1	yes	characteristic
674	C₂	—	8	2	no	—
675	C₂	—	8	2	no	—
676	C₂	C₁₃×#2463	1	1	yes	characteristic
677	C₂	C₁₃×#3102	1	1	yes	characteristic
678	C₂	C₁₃×#3119	1	1	yes	characteristic
679	C₂	C₁₃×#3271	1	1	yes	characteristic
680	C₂	C₁₃×#3280	1	1	yes	characteristic
681	C₂	C₁₃×#3360	1	1	yes	characteristic
682	C₂	C₁₃×#3370	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
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×#479	C₂	semidirect
3. C₁₃×#2454	C₂	semidirect
4. C₁₃×#2367	C₂	semidirect
6. C₁₃×#2042	C₂	semidirect
7. C₁₃×#2025	C₂	semidirect
9. C₁₃×#1933	C₂	semidirect
10. C₁₃×#1926	C₂	semidirect
11. C₁₃×#1918	C₂	semidirect
12. C₁₃×#1916	C₂	semidirect
13. C₁₃×#1880	C₂	semidirect
14. C₁₃×#1877	C₂	semidirect
15. C₁₃×#1864	C₂	semidirect
132. #26891	C₁₃	direct (N × H)
221. C₂×#479	C₂×C₁₃	semidirect
223. #2454	C₂×C₁₃	semidirect
224. #2367	C₂×C₁₃	semidirect
226. #2042	C₂×C₁₃	semidirect
227. #2025	C₂×C₁₃	semidirect
229. #1933	C₂×C₁₃	semidirect
230. #1926	C₂×C₁₃	semidirect
231. #1918	C₂×C₁₃	semidirect
232. #1916	C₂×C₁₃	semidirect
233. #1880	C₂×C₁₃	semidirect
234. #1877	C₂×C₁₃	semidirect
235. #1864	C₂×C₁₃	semidirect
561. C₁₃	#26891	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×#479	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2454	2
C₁₃×#2367	2
C₁₃×#2054	2
C₁₃×#2042	2
C₁₃×#2025	2
C₁₃×#2012	2
C₁₃×#1933	2
C₁₃×#1926	2
C₁₃×#1918	2
C₁₃×#1916	2
C₁₃×#1880	2
C₁₃×#1877	2
C₁₃×#1864	2
#26891	13

Subgroups — C13×#26891 #15713230

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26891 #15713230