Subgroups — C₁₃×#26161 #15712500

Order 3328.

840 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#464	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2447	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2096	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2071	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1878	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1865	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
23	C₁₃×#464	—	2	4	no	—
24	C₄×C₁₃×SD₁₆	—	2	4	no	—
25	C₂×C₁₃×#106	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×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	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×#397	—	2	1	no	—
38	C₁₃×#397	—	2	1	no	—
39	C₁₃×#391	C₂²	1	1	yes	characteristic
40	C₁₃×#391	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#389	—	2	1	no	—
43	C₁₃×#389	—	2	1	no	—
44	C₁₃×#389	C₂²	1	1	yes	characteristic
45	C₁₃×#389	C₂²	1	1	yes	characteristic
46	C₁₃×#389	C₂²	1	1	yes	characteristic
47	C₁₃×#385	—	2	1	no	—
48	C₁₃×#384	—	2	1	no	—
49	C₁₃×#384	C₂²	1	1	yes	characteristic
50	C₁₃×#381	—	2	1	no	—
51	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
52	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×Q₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂×C₁₃×Q₁₆	—	2	2	no	—
66	C₂×C₁₃×Q₁₆	—	2	2	no	—
67	C₂×C₁₃×Q₁₆	—	2	2	no	—
68	C₂×C₁₃×SD₁₆	—	2	2	no	—
69	C₂×C₁₃×SD₁₆	—	2	2	no	—
70	C₂×C₁₃×SD₁₆	D₄	1	4	yes	—
71	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
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	C₁₃×#124	—	2	2	no	—
76	C₁₃×#124	—	4	1	no	—
77	C₄×Q₈×C₁₃	—	2	2	no	—
78	C₄×Q₈×C₁₃	—	2	2	no	—
79	C₄×Q₈×C₁₃	—	2	2	no	—
80	C₄×Q₈×C₁₃	—	2	2	no	—
81	C₄×Q₈×C₁₃	—	4	1	no	—
82	C₄×Q₈×C₁₃	—	4	1	no	—
83	C₄×D₄×C₁₃	—	2	2	no	—
84	C₄×D₄×C₁₃	—	4	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	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
93	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
94	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	2	1	no	—
107	C₂×C₄²×C₁₃	—	2	1	no	—
108	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₁₃×#106	—	2	2	no	—
112	C₁₃×#106	—	4	1	no	—
113	C₁₃×C₄⋊C₈	—	2	2	no	—
114	C₁₃×#103	—	2	2	no	—
115	C₁₃×#103	—	2	2	no	—
116	C₁₃×#103	—	2	2	no	—
117	C₁₃×#103	—	2	2	no	—
118	C₁₃×#103	—	4	1	no	—
119	C₁₃×#102	—	2	2	no	—
120	C₁₃×#102	—	2	2	no	—
121	C₁₃×#102	—	2	2	no	—
122	C₄×C₈×C₁₃	—	2	2	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	—	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	#26161	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
133	C₂⁴×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	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×Q₈×C₁₃	#41	1	2	yes	—
145	C₂×Q₈×C₁₃	#41	1	2	yes	—
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	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
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	—	8	1	no	—
162	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
169	C₁₃×Q₁₆	—	4	4	no	—
170	C₁₃×SD₁₆	—	2	8	no	—
171	C₂×C₈×C₁₃	—	2	1	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	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	C₂×D₄	1	2	yes	—
183	C₁₃×C₄⋊C₄	—	2	4	no	—
184	C₁₃×C₄⋊C₄	—	2	2	no	—
185	C₁₃×C₄⋊C₄	—	2	2	no	—
186	C₁₃×C₄⋊C₄	—	2	1	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	2	no	—
196	C₁₃×C₄⋊C₄	—	4	2	no	—
197	C₁₃×C₄⋊C₄	—	4	2	no	—
198	C₁₃×C₄⋊C₄	—	8	1	no	—
199	C₁₃×C₄⋊C₄	—	8	1	no	—
200	C₁₃×C₄⋊C₄	—	8	1	no	—
201	C₁₃×C₄⋊C₄	—	8	1	no	—
202	C₁₃×C₄⋊C₄	#41	1	2	yes	—
203	C₁₃×C₂²⋊C₄	—	4	2	no	—
204	C₁₃×C₂²⋊C₄	—	4	2	no	—
205	C₁₃×C₂²⋊C₄	—	4	2	no	—
206	C₁₃×C₂²⋊C₄	—	4	2	no	—
207	C₁₃×C₂²⋊C₄	—	8	1	no	—
208	C₄²×C₁₃	—	2	4	no	—
209	C₄²×C₁₃	—	2	1	no	—
210	C₄²×C₁₃	—	2	1	no	—
211	C₄²×C₁₃	—	2	1	no	—
212	C₄²×C₁₃	—	2	1	no	—
213	C₄²×C₁₃	—	2	1	no	—
214	C₄²×C₁₃	—	2	1	no	—
215	C₄²×C₁₃	—	4	2	no	—
216	C₄²×C₁₃	—	4	2	no	—
217	C₂×#464	C₂×C₁₃	1	1	yes	characteristic
218	C₂×C₄×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
219	#2447	C₂×C₁₃	1	1	yes	characteristic
220	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
221	#2096	C₂×C₁₃	1	1	yes	characteristic, complemented
222	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
223	#2071	C₂×C₁₃	1	1	yes	characteristic
224	#2042	C₂×C₁₃	1	1	yes	characteristic
225	#1933	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1916	C₂×C₁₃	1	1	yes	characteristic, complemented
227	#1880	C₂×C₁₃	1	1	yes	characteristic
228	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1878	C₂×C₁₃	1	1	yes	characteristic, complemented
230	#1865	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#1864	C₂×C₁₃	1	1	yes	characteristic
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	4	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	—	4	1	no	—
238	C₂³×C₁₃	—	4	1	no	—
239	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
240	Q₈×C₁₃	—	2	2	no	—
241	Q₈×C₁₃	—	2	2	no	—
242	Q₈×C₁₃	—	2	2	no	—
243	Q₈×C₁₃	—	4	1	no	—
244	Q₈×C₁₃	—	4	1	no	—
245	Q₈×C₁₃	—	4	1	no	—
246	Q₈×C₁₃	—	4	1	no	—
247	Q₈×C₁₃	#123	1	4	yes	—
248	D₄×C₁₃	—	2	2	no	—
249	D₄×C₁₃	—	2	2	no	—
250	D₄×C₁₃	—	4	1	no	—
251	D₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	—	2	1	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	1	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	1	no	—
258	C₂×C₄×C₁₃	—	2	1	no	—
259	C₂×C₄×C₁₃	—	2	1	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	1	no	—
262	C₂×C₄×C₁₃	—	2	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	1	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	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	—	4	1	no	—
278	C₂×C₄×C₁₃	—	4	1	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	4	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	—	8	4	no	—
290	C₂×C₄×C₁₃	#135	1	2	yes	—
291	C₂×C₄×C₁₃	#137	1	2	yes	—
292	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
297	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
298	C₈×C₁₃	—	2	2	no	—
299	C₈×C₁₃	—	4	1	no	—
300	C₈×C₁₃	—	4	1	no	—
301	C₈×C₁₃	—	4	1	no	—
302	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
304	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
308	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
309	#464	—	2	4	no	—
310	C₄×SD₁₆	—	2	4	no	—
311	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
312	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
314	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
315	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
316	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
317	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
318	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
319	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
320	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
322	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
323	#397	—	2	1	no	—
324	#397	—	2	1	no	—
325	#391	C₂²×C₁₃	1	1	yes	characteristic
326	#391	C₂²×C₁₃	1	1	yes	characteristic
327	#390	C₂²×C₁₃	1	1	yes	characteristic
328	#389	—	2	1	no	—
329	#389	—	2	1	no	—
330	#389	C₂²×C₁₃	1	1	yes	characteristic
331	#389	C₂²×C₁₃	1	1	yes	characteristic
332	#389	C₂²×C₁₃	1	1	yes	characteristic
333	#385	—	2	1	no	—
334	#384	—	2	1	no	—
335	#384	C₂²×C₁₃	1	1	yes	characteristic
336	#381	—	2	1	no	—
337	C₄×C₄⋊C₄	—	2	1	no	—
338	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
339	#340	C₂²×C₁₃	1	1	yes	characteristic
340	#340	C₂²×C₁₃	1	1	yes	characteristic
341	#340	C₂²×C₁₃	1	1	yes	characteristic
342	#340	C₂²×C₁₃	1	1	yes	characteristic
343	#336	C₂²×C₁₃	1	1	yes	characteristic
344	#336	C₂²×C₁₃	1	1	yes	characteristic
345	#336	C₂²×C₁₃	1	1	yes	characteristic
346	#336	C₂²×C₁₃	1	1	yes	characteristic
347	C₂²×C₁₃	—	4	2	no	—
348	C₂²×C₁₃	—	4	2	no	—
349	C₂²×C₁₃	—	4	2	no	—
350	C₂²×C₁₃	—	8	1	no	—
351	C₂²×C₁₃	—	8	1	no	—
352	C₂²×C₁₃	—	8	1	no	—
353	C₂²×C₁₃	—	8	1	no	—
354	C₂²×C₁₃	#525	1	1	yes	characteristic
355	C₂²×C₁₃	D₄²	1	1	yes	characteristic
356	C₂²×C₁₃	#548	1	1	yes	characteristic
357	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
358	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
359	C₂²×C₁₃	#577	1	1	yes	characteristic
360	C₂²×C₁₃	#577	1	1	yes	characteristic
361	C₄×C₁₃	—	2	2	no	—
362	C₄×C₁₃	—	2	4	no	—
363	C₄×C₁₃	—	2	2	no	—
364	C₄×C₁₃	—	4	1	no	—
365	C₄×C₁₃	—	4	2	no	—
366	C₄×C₁₃	—	4	1	no	—
367	C₄×C₁₃	—	4	1	no	—
368	C₄×C₁₃	—	4	1	no	—
369	C₄×C₁₃	—	8	1	no	—
370	C₄×C₁₃	—	8	1	no	—
371	C₄×C₁₃	—	8	1	no	—
372	C₄×C₁₃	—	8	1	no	—
373	C₄×C₁₃	—	8	1	no	—
374	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
375	C₄×C₁₃	#539	1	1	yes	characteristic
376	C₄×C₁₃	#547	1	1	yes	characteristic
377	C₄×C₁₃	#553	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
379	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
380	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
381	C₂³×C₄	—	2	1	no	—
382	C₂×Q₁₆	—	2	2	no	—
383	C₂×Q₁₆	—	2	2	no	—
384	C₂×Q₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	2	2	no	—
386	C₂×SD₁₆	—	2	2	no	—
387	C₂×SD₁₆	D₄×C₁₃	1	4	yes	—
388	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
389	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
390	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
391	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
392	#124	—	2	2	no	—
393	#124	—	4	1	no	—
394	C₄×Q₈	—	2	2	no	—
395	C₄×Q₈	—	2	2	no	—
396	C₄×Q₈	—	2	2	no	—
397	C₄×Q₈	—	2	2	no	—
398	C₄×Q₈	—	4	1	no	—
399	C₄×Q₈	—	4	1	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	4	1	no	—
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	1	no	—
404	C₂×C₄⋊C₄	—	2	1	no	—
405	C₂×C₄⋊C₄	—	2	1	no	—
406	C₂×C₄⋊C₄	—	2	1	no	—
407	C₂×C₄⋊C₄	—	2	1	no	—
408	C₂×C₄⋊C₄	—	2	1	no	—
409	C₂×C₄⋊C₄	—	2	1	no	—
410	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
411	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
414	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
417	C₂×C₂²⋊C₄	—	2	1	no	—
418	C₂×C₂²⋊C₄	—	2	1	no	—
419	C₂×C₂²⋊C₄	—	2	1	no	—
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₄²	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
428	#106	—	2	2	no	—
429	#106	—	4	1	no	—
430	C₄⋊C₈	—	2	2	no	—
431	#103	—	2	2	no	—
432	#103	—	2	2	no	—
433	#103	—	2	2	no	—
434	#103	—	2	2	no	—
435	#103	—	4	1	no	—
436	#102	—	2	2	no	—
437	#102	—	2	2	no	—
438	#102	—	2	2	no	—
439	C₄×C₈	—	2	2	no	—
440	#95	—	2	1	no	—
441	#95	—	2	1	no	—
442	#95	—	2	1	no	—
443	#95	—	2	1	no	—
444	#95	—	2	1	no	—
445	#95	—	2	1	no	—
446	#95	—	2	1	no	—
447	#95	D₄×C₁₃	1	1	yes	characteristic
448	#95	D₄×C₁₃	1	1	yes	characteristic
449	C₂×C₁₃	—	8	2	no	—
450	C₂×C₁₃	#2443	1	1	yes	characteristic
451	C₂×C₁₃	#3108	1	1	yes	characteristic
452	C₂×C₁₃	#3125	1	1	yes	characteristic
453	C₂×C₁₃	#3266	1	1	yes	characteristic
454	C₂×C₁₃	#3284	1	1	yes	characteristic
455	C₂×C₁₃	#3365	1	1	yes	characteristic
456	C₂×C₁₃	#3369	1	1	yes	characteristic
457	C₂⁴	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	1	no	—
460	C₂×Q₈	—	2	1	no	—
461	C₂×Q₈	—	2	1	no	—
462	C₂×Q₈	—	2	1	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	1	no	—
465	C₂×Q₈	—	2	1	no	—
466	C₂×Q₈	—	2	1	no	—
467	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
468	C₂×Q₈	C₁₃×#41	1	2	yes	—
469	C₂×Q₈	C₁₃×#41	1	2	yes	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	1	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	1	no	—
475	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
476	C₂²×C₄	—	2	1	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	2	1	no	—
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	4	2	no	—
485	C₂²×C₄	—	8	1	no	—
486	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
487	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
488	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
489	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
493	Q₁₆	—	4	4	no	—
494	SD₁₆	—	2	8	no	—
495	C₂×C₈	—	2	1	no	—
496	C₂×C₈	—	2	1	no	—
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
507	C₄⋊C₄	—	2	4	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	4	2	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	—	8	1	no	—
523	C₄⋊C₄	—	8	1	no	—
524	C₄⋊C₄	—	8	1	no	—
525	C₄⋊C₄	—	8	1	no	—
526	C₄⋊C₄	C₁₃×#41	1	2	yes	—
527	C₂²⋊C₄	—	4	2	no	—
528	C₂²⋊C₄	—	4	2	no	—
529	C₂²⋊C₄	—	4	2	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	8	1	no	—
532	C₄²	—	2	4	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	4	2	no	—
540	C₄²	—	4	2	no	—
541	C₁₃	#26161	1	1	yes	characteristic, direct product factor, Sylow
542	C₂³	—	2	2	no	—
543	C₂³	—	4	1	no	—
544	C₂³	—	4	1	no	—
545	C₂³	—	4	1	no	—
546	C₂³	—	4	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
550	Q₈	—	2	2	no	—
551	Q₈	—	2	2	no	—
552	Q₈	—	2	2	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	4	1	no	—
555	Q₈	—	4	1	no	—
556	Q₈	—	4	1	no	—
557	Q₈	C₁₃×#123	1	4	yes	—
558	D₄	—	2	2	no	—
559	D₄	—	2	2	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	1	no	—
583	C₂×C₄	—	4	1	no	—
584	C₂×C₄	—	4	1	no	—
585	C₂×C₄	—	4	1	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	8	4	no	—
600	C₂×C₄	C₁₃×#135	1	2	yes	—
601	C₂×C₄	C₁₃×#137	1	2	yes	—
602	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
603	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
604	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
605	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
606	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
607	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
608	C₈	—	2	2	no	—
609	C₈	—	4	1	no	—
610	C₈	—	4	1	no	—
611	C₈	—	4	1	no	—
612	C₂²	—	4	2	no	—
613	C₂²	—	4	2	no	—
614	C₂²	—	4	2	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	C₁₃×#525	1	1	yes	characteristic
620	C₂²	D₄²×C₁₃	1	1	yes	characteristic
621	C₂²	C₁₃×#548	1	1	yes	characteristic
622	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
623	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
624	C₂²	C₁₃×#577	1	1	yes	characteristic
625	C₂²	C₁₃×#577	1	1	yes	characteristic
626	C₄	—	2	2	no	—
627	C₄	—	2	2	no	—
628	C₄	—	2	4	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	1	no	—
633	C₄	—	4	2	no	—
634	C₄	—	8	1	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	—	8	1	no	—
638	C₄	—	8	1	no	—
639	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
640	C₄	C₁₃×#539	1	1	yes	characteristic
641	C₄	C₁₃×#547	1	1	yes	characteristic
642	C₄	C₁₃×#553	1	1	yes	characteristic
643	C₂	—	8	2	no	—
644	C₂	C₁₃×#2443	1	1	yes	characteristic
645	C₂	C₁₃×#3108	1	1	yes	characteristic
646	C₂	C₁₃×#3125	1	1	yes	characteristic
647	C₂	C₁₃×#3266	1	1	yes	characteristic
648	C₂	C₁₃×#3284	1	1	yes	characteristic
649	C₂	C₁₃×#3365	1	1	yes	characteristic
650	C₂	C₁₃×#3369	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
4. Q₈×C₁₃×C₄⋊C₄	C₂	semidirect
5. C₁₃×#2096	C₂	semidirect
6. C₁₃×#2088	C₂	semidirect
9. C₁₃×#1933	C₂	semidirect
10. C₁₃×#1916	C₂	semidirect
12. C₁₃×#1878	C₂	semidirect
13. C₁₃×#1878	C₂	semidirect
14. C₁₃×#1865	C₂	semidirect
132. #26161	C₁₃	direct (N × H)
220. Q₈×C₄⋊C₄	C₂×C₁₃	semidirect
221. #2096	C₂×C₁₃	semidirect
222. #2088	C₂×C₁₃	semidirect
225. #1933	C₂×C₁₃	semidirect
226. #1916	C₂×C₁₃	semidirect
228. #1878	C₂×C₁₃	semidirect
229. #1878	C₂×C₁₃	semidirect
230. #1865	C₂×C₁₃	semidirect
541. C₁₃	#26161	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×#464	2
C₂×C₄×C₁₃×SD₁₆	2
C₁₃×#2447	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#2096	2
C₁₃×#2088	2
C₁₃×#2071	2
C₁₃×#2042	2
C₁₃×#1933	2
C₁₃×#1916	2
C₁₃×#1880	2
C₁₃×#1878	2
C₁₃×#1865	2
C₁₃×#1864	2
#26161	13

Subgroups — C13×#26161 #15712500

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#26161 #15712500