Subgroups — C₁₃×#24501 #15710840

Order 3328.

1208 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2065	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1968	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1934	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1853	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
17	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
18	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
19	C₁₃×#450	—	2	4	no	—
20	C₁₃×#431	—	2	4	no	—
21	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×#102	C₂²	1	2	yes	—
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₃	C₂²	1	2	yes	complemented
30	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#390	—	2	1	no	—
33	C₁₃×#390	—	2	1	no	—
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#390	C₂²	1	2	yes	—
36	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#387	—	2	1	no	—
39	C₁₃×#387	—	2	1	no	—
40	C₁₃×#385	—	2	1	no	—
41	C₁₃×#381	—	2	1	no	—
42	C₁₃×#380	C₂²	1	1	yes	characteristic
43	C₁₃×#340	C₂²	1	2	yes	complemented
44	C₁₃×#340	C₂²	1	2	yes	complemented
45	C₂⁵×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×D₄×C₁₃	—	2	4	no	—
48	C₂²×D₄×C₁₃	—	2	1	no	—
49	C₂²×D₄×C₁₃	—	2	2	no	—
50	C₂²×D₄×C₁₃	—	2	2	no	—
51	C₂²×D₄×C₁₃	—	4	2	no	—
52	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₃	—	2	1	no	—
54	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₁₃×SD₁₆	—	2	4	no	—
58	C₂×C₁₃×SD₁₆	—	2	4	no	—
59	C₂×C₁₃×SD₁₆	—	4	2	no	—
60	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
61	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
62	C₁₃×C₂²⋊Q₈	—	2	2	no	—
63	C₁₃×C₂²⋊Q₈	—	2	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	—	2	2	no	—
83	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#106	—	4	2	no	—
88	C₁₃×C₄⋊C₈	—	2	4	no	—
89	C₁₃×#103	—	4	2	no	—
90	C₁₃×#102	—	2	4	no	—
91	C₁₃×#102	—	2	4	no	—
92	C₁₃×#102	—	4	2	no	—
93	C₁₃×C₂²⋊C₈	—	2	2	no	—
94	C₁₃×C₂²⋊C₈	D₄	1	4	yes	—
95	C₄×C₈×C₁₃	—	2	4	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	1	no	—
103	#24501	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂⁴×C₁₃	—	2	4	no	—
105	C₂⁴×C₁₃	—	2	2	no	—
106	C₂⁴×C₁₃	—	4	2	no	—
107	C₂⁴×C₁₃	—	4	2	no	—
108	C₂⁴×C₁₃	—	4	2	no	—
109	C₂⁴×C₁₃	—	4	2	no	—
110	C₂⁴×C₁₃	—	4	2	no	—
111	C₂⁴×C₁₃	—	4	2	no	—
112	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	4	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	2	2	no	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	4	8	no	—
124	C₂×D₄×C₁₃	—	4	8	no	—
125	C₂×D₄×C₁₃	—	4	2	no	—
126	C₂×D₄×C₁₃	—	4	2	no	—
127	C₂×D₄×C₁₃	#41	1	4	yes	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	2	no	—
139	C₂²×C₄×C₁₃	—	4	1	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	—	4	2	no	—
143	C₂²×C₄×C₁₃	SD₁₆	1	4	yes	complemented
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	#41	1	2	yes	—
151	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
152	C₁₃×SD₁₆	—	4	8	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	—	2	2	no	—
157	C₂×C₈×C₁₃	—	2	2	no	—
158	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	2	2	no	—
164	C₁₃×C₄⋊C₄	—	2	2	no	—
165	C₁₃×C₄⋊C₄	—	4	2	no	—
166	C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₄⋊C₄	—	4	2	no	—
169	C₁₃×C₂²⋊C₄	—	4	4	no	—
170	C₁₃×C₂²⋊C₄	—	4	2	no	—
171	C₁₃×C₂²⋊C₄	—	4	2	no	—
172	C₁₃×C₂²⋊C₄	—	4	4	no	—
173	C₁₃×C₂²⋊C₄	—	4	4	no	—
174	C₁₃×C₂²⋊C₄	—	4	4	no	—
175	C₄²×C₁₃	—	2	2	no	—
176	C₄²×C₁₃	—	2	2	no	—
177	C₄²×C₁₃	—	2	1	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
182	C₂×#431	C₂×C₁₃	1	1	yes	characteristic, complemented
183	#2855	C₂×C₁₃	1	1	yes	characteristic, complemented
184	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
185	#2065	C₂×C₁₃	1	2	yes	complemented
186	#2055	C₂×C₁₃	1	2	yes	complemented
187	#1968	C₂×C₁₃	1	2	yes	complemented
188	#1934	C₂×C₁₃	1	2	yes	complemented
189	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#1853	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#1786	C₂×C₁₃	1	1	yes	characteristic
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	2	1	no	—
195	C₂³×C₁₃	—	2	1	no	—
196	C₂³×C₁₃	—	2	4	no	—
197	C₂³×C₁₃	—	4	8	no	—
198	C₂³×C₁₃	—	4	8	no	—
199	C₂³×C₁₃	—	4	8	no	—
200	C₂³×C₁₃	—	4	2	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	—	4	2	no	—
203	C₂³×C₁₃	—	4	2	no	—
204	C₂³×C₁₃	—	4	2	no	—
205	C₂³×C₁₃	—	4	2	no	—
206	C₂³×C₁₃	—	8	4	no	—
207	C₂³×C₁₃	—	8	4	no	—
208	C₂³×C₁₃	—	8	4	no	—
209	C₂³×C₁₃	—	8	4	no	—
210	C₂³×C₁₃	#121	1	2	yes	—
211	C₂³×C₁₃	C₂×SD₁₆	1	2	yes	—
212	C₂³×C₁₃	#135	1	2	yes	—
213	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
214	Q₈×C₁₃	—	4	2	no	—
215	Q₈×C₁₃	—	4	2	no	—
216	D₄×C₁₃	—	2	4	no	—
217	D₄×C₁₃	—	2	4	no	—
218	D₄×C₁₃	—	4	8	no	—
219	D₄×C₁₃	—	4	2	no	—
220	D₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	1	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	8	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	4	4	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	8	4	no	—
252	C₂×C₄×C₁₃	#121	1	2	yes	—
253	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
254	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
255	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
256	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
260	C₈×C₁₃	—	2	4	no	—
261	C₈×C₁₃	—	4	2	no	—
262	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
263	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
264	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	—	2	1	no	—
267	C₂²×C₂²⋊C₄	—	2	1	no	—
268	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
269	#450	—	2	4	no	—
270	#431	—	2	4	no	—
271	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
272	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	complemented
273	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
274	C₂×#102	C₂²×C₁₃	1	2	yes	—
275	C₂×#102	C₂²×C₁₃	1	2	yes	—
276	C₂×#102	C₂²×C₁₃	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×C₄×C₈	C₂²×C₁₃	1	2	yes	complemented
280	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
281	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
282	#390	—	2	1	no	—
283	#390	—	2	1	no	—
284	#390	C₂²×C₁₃	1	2	yes	—
285	#390	C₂²×C₁₃	1	2	yes	—
286	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
287	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
288	#387	—	2	1	no	—
289	#387	—	2	1	no	—
290	#385	—	2	1	no	—
291	#381	—	2	1	no	—
292	#380	C₂²×C₁₃	1	1	yes	characteristic
293	#340	C₂²×C₁₃	1	2	yes	complemented
294	#340	C₂²×C₁₃	1	2	yes	complemented
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	2	2	no	—
299	C₂²×C₁₃	—	2	2	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	4	4	no	—
302	C₂²×C₁₃	—	4	4	no	—
303	C₂²×C₁₃	—	4	4	no	—
304	C₂²×C₁₃	—	8	16	no	—
305	C₂²×C₁₃	—	8	2	no	—
306	C₂²×C₁₃	—	8	2	no	—
307	C₂²×C₁₃	—	8	2	no	—
308	C₂²×C₁₃	—	8	2	no	—
309	C₂²×C₁₃	#465	1	4	yes	—
310	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
311	C₂²×C₁₃	#525	1	1	yes	characteristic
312	C₂²×C₁₃	#535	1	1	yes	characteristic
313	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
314	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
315	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
316	C₂²×C₁₃	#575	1	1	yes	characteristic
317	C₄×C₁₃	—	2	2	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	—	2	2	no	—
321	C₄×C₁₃	—	4	1	no	—
322	C₄×C₁₃	—	8	1	no	—
323	C₄×C₁₃	—	8	1	no	—
324	C₄×C₁₃	—	8	2	no	—
325	C₄×C₁₃	—	8	1	no	—
326	C₄×C₁₃	—	8	1	no	—
327	C₄×C₁₃	#546	1	2	yes	—
328	C₄×C₁₃	#551	1	2	yes	—
329	C₂⁵	—	2	1	no	—
330	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×D₄	—	2	4	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	—	4	2	no	—
336	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
339	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
340	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	2	4	no	—
343	C₂×SD₁₆	—	4	2	no	—
344	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
345	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	4	2	no	—
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	2	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	4	4	no	—
364	C₂×C₂²⋊C₄	—	4	4	no	—
365	C₂×C₄²	—	2	2	no	—
366	C₂×C₄²	—	2	2	no	—
367	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
371	#106	—	4	2	no	—
372	C₄⋊C₈	—	2	4	no	—
373	#103	—	4	2	no	—
374	#102	—	2	4	no	—
375	#102	—	2	4	no	—
376	#102	—	4	2	no	—
377	C₂²⋊C₈	—	2	2	no	—
378	C₂²⋊C₈	D₄×C₁₃	1	4	yes	—
379	C₄×C₈	—	2	4	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	C₂×C₁₃	—	2	4	no	—
388	C₂×C₁₃	—	8	4	no	—
389	C₂×C₁₃	#2411	1	1	yes	characteristic
390	C₂×C₁₃	C₂×#465	1	1	yes	characteristic
391	C₂×C₁₃	#3055	1	1	yes	characteristic
392	C₂×C₁₃	#3101	1	1	yes	characteristic
393	C₂×C₁₃	#3105	1	1	yes	characteristic
394	C₂×C₁₃	#3208	1	1	yes	characteristic
395	C₂×C₁₃	#3211	1	1	yes	characteristic
396	C₂⁴	—	2	4	no	—
397	C₂⁴	—	2	2	no	—
398	C₂⁴	—	4	2	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	—	4	2	no	—
401	C₂⁴	—	4	2	no	—
402	C₂⁴	—	4	2	no	—
403	C₂⁴	—	4	2	no	—
404	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	2	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	4	8	no	—
416	C₂×D₄	—	4	8	no	—
417	C₂×D₄	—	4	2	no	—
418	C₂×D₄	—	4	2	no	—
419	C₂×D₄	C₁₃×#41	1	4	yes	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	C₁₃×SD₁₆	1	4	yes	complemented
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
440	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
442	C₂²×C₄	C₁₃×#41	1	2	yes	—
443	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
444	SD₁₆	—	4	8	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	2	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	4	2	no	—
458	C₄⋊C₄	—	4	2	no	—
459	C₄⋊C₄	—	4	2	no	—
460	C₄⋊C₄	—	4	2	no	—
461	C₂²⋊C₄	—	4	4	no	—
462	C₂²⋊C₄	—	4	2	no	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	4	no	—
465	C₂²⋊C₄	—	4	4	no	—
466	C₂²⋊C₄	—	4	4	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₁₃	#24501	1	1	yes	characteristic, direct product factor, Sylow
474	C₂³	—	2	1	no	—
475	C₂³	—	2	1	no	—
476	C₂³	—	2	1	no	—
477	C₂³	—	2	1	no	—
478	C₂³	—	2	4	no	—
479	C₂³	—	4	8	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	8	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	4	2	no	—
486	C₂³	—	4	2	no	—
487	C₂³	—	4	2	no	—
488	C₂³	—	8	4	no	—
489	C₂³	—	8	4	no	—
490	C₂³	—	8	4	no	—
491	C₂³	—	8	4	no	—
492	C₂³	C₁₃×#121	1	2	yes	—
493	C₂³	C₂×C₁₃×SD₁₆	1	2	yes	—
494	C₂³	C₁₃×#135	1	2	yes	—
495	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
496	Q₈	—	4	2	no	—
497	Q₈	—	4	2	no	—
498	D₄	—	2	4	no	—
499	D₄	—	2	4	no	—
500	D₄	—	4	8	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	C₂×C₄	—	2	8	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	4	no	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	C₁₃×#121	1	2	yes	—
535	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
536	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
537	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
539	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
540	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
541	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
542	C₈	—	2	4	no	—
543	C₈	—	4	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	2	2	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	2	no	—
549	C₂²	—	2	2	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	4	4	no	—
553	C₂²	—	8	16	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	2	no	—
557	C₂²	—	8	2	no	—
558	C₂²	C₁₃×#465	1	4	yes	—
559	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
560	C₂²	C₁₃×#525	1	1	yes	characteristic
561	C₂²	C₁₃×#535	1	1	yes	characteristic
562	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
563	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
564	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
565	C₂²	C₁₃×#575	1	1	yes	characteristic
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	4	1	no	—
571	C₄	—	8	1	no	—
572	C₄	—	8	1	no	—
573	C₄	—	8	1	no	—
574	C₄	—	8	2	no	—
575	C₄	—	8	1	no	—
576	C₄	C₁₃×#546	1	2	yes	—
577	C₄	C₁₃×#551	1	2	yes	—
578	C₂	—	2	4	no	—
579	C₂	—	8	4	no	—
580	C₂	C₁₃×#2411	1	1	yes	characteristic
581	C₂	C₂×C₁₃×#465	1	1	yes	characteristic
582	C₂	C₁₃×#3055	1	1	yes	characteristic
583	C₂	C₁₃×#3101	1	1	yes	characteristic
584	C₂	C₁₃×#3105	1	1	yes	characteristic
585	C₂	C₁₃×#3208	1	1	yes	characteristic
586	C₂	C₁₃×#3211	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂³×D₄×C₁₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#431	C₂	semidirect
3. C₁₃×#2855	C₂	semidirect
5. C₁₃×#2065	C₂	semidirect
6. C₁₃×#2055	C₂	semidirect
7. C₁₃×#1968	C₂	semidirect
8. C₁₃×#1934	C₂	semidirect
9. C₁₃×#1872	C₂	semidirect
10. C₁₃×#1853	C₂	semidirect
21. C₂×C₁₃×#106	C₂²	semidirect
22. C₂×C₁₃×C₄⋊C₈	C₂²	semidirect
23. C₂×C₁₃×#103	C₂²	semidirect
29. C₂×C₄×C₈×C₁₃	C₂²	semidirect
30. C₁₃×#391	C₂²	semidirect
31. C₁₃×#391	C₂²	semidirect
36. C₁₃×#389	C₂²	semidirect
37. C₁₃×#389	C₂²	semidirect
43. C₁₃×#340	C₂²	semidirect
44. C₁₃×#340	C₂²	semidirect
103. #24501	C₁₃	direct (N × H)
143. C₂²×C₄×C₁₃	SD₁₆	semidirect
182. C₂×#431	C₂×C₁₃	semidirect
183. #2855	C₂×C₁₃	semidirect
185. #2065	C₂×C₁₃	semidirect
186. #2055	C₂×C₁₃	semidirect
187. #1968	C₂×C₁₃	semidirect
188. #1934	C₂×C₁₃	semidirect
189. #1872	C₂×C₁₃	semidirect
190. #1853	C₂×C₁₃	semidirect
271. C₂×#106	C₂²×C₁₃	semidirect
272. C₂×C₄⋊C₈	C₂²×C₁₃	semidirect
273. C₂×#103	C₂²×C₁₃	semidirect
279. C₂×C₄×C₈	C₂²×C₁₃	semidirect
280. #391	C₂²×C₁₃	semidirect
281. #391	C₂²×C₁₃	semidirect
286. #389	C₂²×C₁₃	semidirect
287. #389	C₂²×C₁₃	semidirect
293. #340	C₂²×C₁₃	semidirect
294. #340	C₂²×C₁₃	semidirect
435. C₂²×C₄	C₁₃×SD₁₆	semidirect
473. C₁₃	#24501	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×#450	2
C₂×C₁₃×#431	2
C₁₃×#2855	2
C₂×C₁₃×#390	2
C₁₃×#2065	2
C₁₃×#2055	2
C₁₃×#1968	2
C₁₃×#1934	2
C₁₃×#1872	2
C₁₃×#1853	2
C₁₃×#1786	2
#24501	13

Subgroups — C13×#24501 #15710840

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24501 #15710840