Subgroups — C₁₃×#34816 #15721155

Order 3328.

1918 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2514	C₂	1	2	yes	maximal, complemented
2	C₁₃×#2513	C₂	1	2	yes	maximal, complemented
3	C₁₃×#2512	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2511	C₂	1	2	yes	maximal, complemented
5	C₁₃×#2510	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2481	C₂	1	4	yes	maximal, complemented
7	C₁₃×#2401	C₂	1	4	yes	maximal, complemented
8	C₄×C₁₃×#126	C₂	1	4	yes	maximal, complemented
9	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#2297	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2285	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#126	C₂²	1	4	yes	—
18	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#401	C₂²	1	4	yes	—
26	C₁₃×#400	C₂²	1	4	yes	—
27	C₁₃×#400	C₂²	1	4	yes	—
28	C₁₃×#400	C₂²	1	4	yes	—
29	C₁₃×#397	C₂²	1	4	yes	—
30	C₁₃×#397	C₂²	1	4	yes	—
31	C₁₃×#397	C₂²	1	4	yes	—
32	C₁₃×#396	C₂²	1	4	yes	—
33	C₁₃×#391	C₂²	1	1	yes	characteristic
34	C₁₃×#391	C₂²	1	2	yes	—
35	C₁₃×#391	C₂²	1	2	yes	—
36	C₁₃×#391	C₂²	1	1	yes	characteristic
37	C₁₃×#390	C₂²	1	1	yes	characteristic
38	C₁₃×#390	C₂²	1	2	yes	—
39	C₁₃×#390	C₂²	1	2	yes	—
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	2	yes	—
42	C₁₃×#389	C₂²	1	2	yes	—
43	C₁₃×#388	C₂²	1	4	yes	—
44	C₁₃×#388	C₂²	1	4	yes	—
45	C₁₃×#388	C₂²	1	4	yes	—
46	C₁₃×#387	C₂²	1	4	yes	—
47	C₁₃×#387	C₂²	1	4	yes	—
48	C₁₃×#387	C₂²	1	4	yes	—
49	C₁₃×#386	C₂²	1	2	yes	—
50	C₁₃×#386	C₂²	1	4	yes	—
51	C₁₃×#386	C₂²	1	4	yes	—
52	C₁₃×#386	C₂²	1	2	yes	—
53	C₁₃×#385	C₂²	1	2	yes	—
54	C₁₃×#385	C₂²	1	2	yes	—
55	C₁₃×#384	C₂²	1	2	yes	—
56	C₁₃×#383	C₂²	1	4	yes	—
57	C₁₃×#382	C₂²	1	2	yes	—
58	C₁₃×#380	C₂²	1	4	yes	—
59	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
60	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
61	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
62	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
63	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
64	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
65	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
66	C₄×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
67	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
68	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
69	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
70	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
71	C₄×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
72	C₁₃×#376	C₂²	1	2	yes	—
73	C₂×C₁₃×#95	C₂²	1	2	yes	—
74	C₄³×C₁₃	C₂²	1	2	yes	—
75	C₂×C₁₃×#41	—	2	4	no	—
76	C₂×C₁₃×#41	—	2	4	no	—
77	C₂×C₁₃×#41	—	2	4	no	—
78	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₁₃×#126	—	2	16	no	—
88	C₁₃×#117	—	2	4	no	—
89	C₁₃×#117	—	2	4	no	—
90	C₁₃×#117	—	2	4	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
102	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
103	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
104	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
113	C₂×C₄²×C₁₃	—	2	4	no	—
114	C₂×C₄²×C₁₃	—	2	4	no	—
115	C₂×C₄²×C₁₃	—	2	4	no	—
116	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
117	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
118	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
121	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
122	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
123	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
128	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
129	C₁₃×#95	C₂³	1	4	yes	—
130	C₁₃×#95	C₂³	1	4	yes	—
131	C₁₃×#95	C₂³	1	4	yes	—
132	C₁₃×#95	C₂³	1	4	yes	—
133	C₁₃×#95	C₂³	1	4	yes	—
134	C₁₃×#95	C₂³	1	4	yes	—
135	C₁₃×#95	C₂³	1	4	yes	—
136	C₁₃×#95	C₂³	1	4	yes	—
137	C₁₃×#95	C₂³	1	2	yes	—
138	C₁₃×#95	C₂³	1	2	yes	—
139	C₁₃×#95	C₂³	1	2	yes	—
140	C₁₃×#95	C₂³	1	2	yes	—
141	C₁₃×#95	C₂³	1	4	yes	—
142	C₁₃×#95	C₂³	1	4	yes	—
143	C₁₃×#95	C₂³	1	4	yes	—
144	C₁₃×#95	C₂³	1	4	yes	—
145	#34816	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
147	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
148	C₁₃×#41	—	4	16	no	—
149	C₂×Q₈×C₁₃	—	2	2	no	—
150	C₂×Q₈×C₁₃	—	2	2	no	—
151	C₂×Q₈×C₁₃	—	2	2	no	—
152	C₂×D₄×C₁₃	—	2	4	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	4	no	—
155	C₂×D₄×C₁₃	—	2	2	no	—
156	C₂×D₄×C₁₃	—	2	2	no	—
157	C₂×D₄×C₁₃	—	2	2	no	—
158	C₂²×C₄×C₁₃	—	2	2	no	—
159	C₂²×C₄×C₁₃	—	2	4	no	—
160	C₂²×C₄×C₁₃	—	2	4	no	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	4	no	—
164	C₂²×C₄×C₁₃	—	2	4	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	4	no	—
168	C₂²×C₄×C₁₃	—	4	2	no	—
169	C₂²×C₄×C₁₃	—	4	2	no	—
170	C₂²×C₄×C₁₃	—	4	2	no	—
171	C₂²×C₄×C₁₃	#41	1	4	yes	—
172	C₂²×C₄×C₁₃	#41	1	4	yes	—
173	C₂²×C₄×C₁₃	#41	1	4	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
180	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
187	C₁₃×C₄⋊C₄	—	2	4	no	—
188	C₁₃×C₄⋊C₄	—	2	4	no	—
189	C₁₃×C₄⋊C₄	—	2	4	no	—
190	C₁₃×C₄⋊C₄	—	2	2	no	—
191	C₁₃×C₄⋊C₄	—	2	2	no	—
192	C₁₃×C₄⋊C₄	—	2	4	no	—
193	C₁₃×C₄⋊C₄	—	2	4	no	—
194	C₁₃×C₄⋊C₄	—	2	8	no	—
195	C₁₃×C₄⋊C₄	—	2	8	no	—
196	C₁₃×C₄⋊C₄	—	4	4	no	—
197	C₁₃×C₄⋊C₄	—	4	4	no	—
198	C₁₃×C₄⋊C₄	#41	1	8	yes	complemented
199	C₁₃×C₂²⋊C₄	—	2	4	no	—
200	C₁₃×C₂²⋊C₄	—	2	4	no	—
201	C₁₃×C₂²⋊C₄	—	2	4	no	—
202	C₁₃×C₂²⋊C₄	—	2	8	no	—
203	C₁₃×C₂²⋊C₄	—	2	8	no	—
204	C₁₃×C₂²⋊C₄	—	2	8	no	—
205	C₁₃×C₂²⋊C₄	—	4	4	no	—
206	C₁₃×C₂²⋊C₄	—	4	4	no	—
207	C₁₃×C₂²⋊C₄	—	4	4	no	—
208	C₄²×C₁₃	—	2	2	no	—
209	C₄²×C₁₃	—	2	2	no	—
210	C₄²×C₁₃	—	2	4	no	—
211	C₄²×C₁₃	—	2	4	no	—
212	C₄²×C₁₃	—	2	4	no	—
213	C₄²×C₁₃	—	2	4	no	—
214	C₄²×C₁₃	—	2	2	no	—
215	C₄²×C₁₃	—	2	2	no	—
216	C₄²×C₁₃	—	2	4	no	—
217	C₄²×C₁₃	—	2	4	no	—
218	C₄²×C₁₃	—	2	4	no	—
219	C₄²×C₁₃	—	2	8	no	—
220	C₄²×C₁₃	—	4	4	no	—
221	#2514	C₂×C₁₃	1	2	yes	complemented
222	#2513	C₂×C₁₃	1	2	yes	complemented
223	#2512	C₂×C₁₃	1	2	yes	complemented
224	#2511	C₂×C₁₃	1	2	yes	complemented
225	#2510	C₂×C₁₃	1	4	yes	complemented
226	#2481	C₂×C₁₃	1	4	yes	complemented
227	#2401	C₂×C₁₃	1	4	yes	complemented
228	C₄×#126	C₂×C₁₃	1	4	yes	complemented
229	#2297	C₂×C₁₃	1	1	yes	characteristic
230	#2297	C₂×C₁₃	1	1	yes	characteristic
231	#2297	C₂×C₁₃	1	1	yes	characteristic
232	#2296	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#2285	C₂×C₁₃	1	1	yes	characteristic, complemented
234	C₄×#117	C₂×C₁₃	1	1	yes	characteristic, complemented
235	C₂×C₄×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂³×C₁₃	—	2	2	no	—
237	C₂³×C₁₃	—	2	2	no	—
238	C₂³×C₁₃	—	2	4	no	—
239	C₂³×C₁₃	—	2	2	no	—
240	C₂³×C₁₃	—	2	2	no	—
241	C₂³×C₁₃	—	2	2	no	—
242	C₂³×C₁₃	—	2	4	no	—
243	C₂³×C₁₃	C₂×#41	1	2	yes	—
244	C₂³×C₁₃	C₂×#41	1	2	yes	—
245	C₂³×C₁₃	C₂×#41	1	2	yes	—
246	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
247	Q₈×C₁₃	—	4	4	no	—
248	D₄×C₁₃	—	4	8	no	—
249	D₄×C₁₃	—	4	4	no	—
250	C₂×C₄×C₁₃	—	2	8	no	—
251	C₂×C₄×C₁₃	—	2	2	no	—
252	C₂×C₄×C₁₃	—	2	2	no	—
253	C₂×C₄×C₁₃	—	2	2	no	—
254	C₂×C₄×C₁₃	—	2	2	no	—
255	C₂×C₄×C₁₃	—	2	2	no	—
256	C₂×C₄×C₁₃	—	2	2	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	2	no	—
259	C₂×C₄×C₁₃	—	2	2	no	—
260	C₂×C₄×C₁₃	—	2	2	no	—
261	C₂×C₄×C₁₃	—	2	4	no	—
262	C₂×C₄×C₁₃	—	2	2	no	—
263	C₂×C₄×C₁₃	—	2	4	no	—
264	C₂×C₄×C₁₃	—	2	4	no	—
265	C₂×C₄×C₁₃	—	2	4	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	2	no	—
268	C₂×C₄×C₁₃	—	2	2	no	—
269	C₂×C₄×C₁₃	—	2	2	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	2	2	no	—
272	C₂×C₄×C₁₃	—	2	4	no	—
273	C₂×C₄×C₁₃	—	2	4	no	—
274	C₂×C₄×C₁₃	—	2	2	no	—
275	C₂×C₄×C₁₃	—	2	2	no	—
276	C₂×C₄×C₁₃	—	2	2	no	—
277	C₂×C₄×C₁₃	—	2	4	no	—
278	C₂×C₄×C₁₃	—	2	2	no	—
279	C₂×C₄×C₁₃	—	4	8	no	—
280	C₂×C₄×C₁₃	—	4	8	no	—
281	C₂×C₄×C₁₃	—	4	4	no	—
282	C₂×C₄×C₁₃	—	4	8	no	—
283	C₂×C₄×C₁₃	#126	1	16	yes	complemented
284	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
285	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
286	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
287	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
288	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
289	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
290	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
291	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
292	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
293	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
294	C₂×#126	C₂²×C₁₃	1	4	yes	—
295	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
296	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
298	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
299	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
300	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
301	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
302	#401	C₂²×C₁₃	1	4	yes	—
303	#400	C₂²×C₁₃	1	4	yes	—
304	#400	C₂²×C₁₃	1	4	yes	—
305	#400	C₂²×C₁₃	1	4	yes	—
306	#397	C₂²×C₁₃	1	4	yes	—
307	#397	C₂²×C₁₃	1	4	yes	—
308	#397	C₂²×C₁₃	1	4	yes	—
309	#396	C₂²×C₁₃	1	4	yes	—
310	#391	C₂²×C₁₃	1	1	yes	characteristic
311	#391	C₂²×C₁₃	1	2	yes	—
312	#391	C₂²×C₁₃	1	2	yes	—
313	#391	C₂²×C₁₃	1	1	yes	characteristic
314	#390	C₂²×C₁₃	1	1	yes	characteristic
315	#390	C₂²×C₁₃	1	2	yes	—
316	#390	C₂²×C₁₃	1	2	yes	—
317	#390	C₂²×C₁₃	1	1	yes	characteristic
318	#389	C₂²×C₁₃	1	2	yes	—
319	#389	C₂²×C₁₃	1	2	yes	—
320	#388	C₂²×C₁₃	1	4	yes	—
321	#388	C₂²×C₁₃	1	4	yes	—
322	#388	C₂²×C₁₃	1	4	yes	—
323	#387	C₂²×C₁₃	1	4	yes	—
324	#387	C₂²×C₁₃	1	4	yes	—
325	#387	C₂²×C₁₃	1	4	yes	—
326	#386	C₂²×C₁₃	1	2	yes	—
327	#386	C₂²×C₁₃	1	4	yes	—
328	#386	C₂²×C₁₃	1	4	yes	—
329	#386	C₂²×C₁₃	1	2	yes	—
330	#385	C₂²×C₁₃	1	2	yes	—
331	#385	C₂²×C₁₃	1	2	yes	—
332	#384	C₂²×C₁₃	1	2	yes	—
333	#383	C₂²×C₁₃	1	4	yes	—
334	#382	C₂²×C₁₃	1	2	yes	—
335	#380	C₂²×C₁₃	1	4	yes	—
336	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
337	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
338	C₄×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
339	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
340	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
341	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
342	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
343	C₄×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
344	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
345	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
346	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
347	C₄×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
348	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
349	#376	C₂²×C₁₃	1	2	yes	—
350	C₂×#95	C₂²×C₁₃	1	2	yes	—
351	C₄³	C₂²×C₁₃	1	2	yes	—
352	C₂²×C₁₃	—	2	2	no	—
353	C₂²×C₁₃	—	2	2	no	—
354	C₂²×C₁₃	—	2	4	no	—
355	C₂²×C₁₃	—	2	4	no	—
356	C₂²×C₁₃	—	4	2	no	—
357	C₂²×C₁₃	—	4	2	no	—
358	C₂²×C₁₃	—	4	2	no	—
359	C₂²×C₁₃	—	4	4	no	—
360	C₂²×C₁₃	—	4	4	no	—
361	C₂²×C₁₃	C₂×#126	1	4	yes	—
362	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
363	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
364	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₁₃	C₂²×#41	1	2	yes	—
366	C₂²×C₁₃	#585	1	2	yes	—
367	C₄×C₁₃	—	2	4	no	—
368	C₄×C₁₃	—	2	4	no	—
369	C₄×C₁₃	—	2	4	no	—
370	C₄×C₁₃	—	4	2	no	—
371	C₄×C₁₃	—	4	2	no	—
372	C₄×C₁₃	—	4	2	no	—
373	C₄×C₁₃	—	4	2	no	—
374	C₄×C₁₃	—	4	2	no	—
375	C₄×C₁₃	—	4	2	no	—
376	C₄×C₁₃	—	4	4	no	—
377	C₄×C₁₃	—	4	4	no	—
378	C₄×C₁₃	C₂×#126	1	4	yes	—
379	C₄×C₁₃	C₂×#126	1	4	yes	—
380	C₂×#41	—	2	4	no	—
381	C₂×#41	—	2	4	no	—
382	C₂×#41	—	2	4	no	—
383	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
384	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
385	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
388	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
389	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
390	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
391	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
392	#126	—	2	16	no	—
393	#117	—	2	4	no	—
394	#117	—	2	4	no	—
395	#117	—	2	4	no	—
396	C₂×C₄⋊C₄	—	2	8	no	—
397	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
399	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
401	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
402	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
403	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
404	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
405	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
406	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
408	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₁₃	1	2	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
418	C₂×C₄²	—	2	4	no	—
419	C₂×C₄²	—	2	4	no	—
420	C₂×C₄²	—	2	4	no	—
421	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
422	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
423	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
424	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
425	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
426	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
427	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
428	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
429	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
430	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
433	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
434	#95	C₂³×C₁₃	1	2	yes	—
435	#95	C₂³×C₁₃	1	2	yes	—
436	#95	C₂³×C₁₃	1	2	yes	—
437	#95	C₂³×C₁₃	1	2	yes	—
438	#95	C₂³×C₁₃	1	4	yes	—
439	#95	C₂³×C₁₃	1	4	yes	—
440	#95	C₂³×C₁₃	1	4	yes	—
441	#95	C₂³×C₁₃	1	4	yes	—
442	#95	C₂³×C₁₃	1	4	yes	—
443	#95	C₂³×C₁₃	1	4	yes	—
444	#95	C₂³×C₁₃	1	4	yes	—
445	#95	C₂³×C₁₃	1	4	yes	—
446	#95	C₂³×C₁₃	1	4	yes	—
447	#95	C₂³×C₁₃	1	4	yes	—
448	#95	C₂³×C₁₃	1	4	yes	—
449	#95	C₂³×C₁₃	1	4	yes	—
450	C₂×C₁₃	—	2	4	no	—
451	C₂×C₁₃	—	8	2	no	—
452	C₂×C₁₃	C₂²×#126	1	1	yes	characteristic
453	C₂×C₁₃	#3444	1	1	yes	characteristic
454	C₂×C₁₃	#3455	1	1	yes	characteristic
455	C₂×C₁₃	#3475	1	2	yes	—
456	C₂×C₁₃	#3480	1	2	yes	—
457	C₂⁴	C₂⁴×C₁₃	1	2	yes	—
458	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
459	#41	—	4	16	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	2	2	no	—
462	C₂×Q₈	—	2	2	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	2	4	no	—
466	C₂×D₄	—	2	2	no	—
467	C₂×D₄	—	2	2	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	2	4	no	—
475	C₂²×C₄	—	2	4	no	—
476	C₂²×C₄	—	2	4	no	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	2	4	no	—
479	C₂²×C₄	—	4	2	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	2	no	—
482	C₂²×C₄	C₁₃×#41	1	4	yes	—
483	C₂²×C₄	C₁₃×#41	1	4	yes	—
484	C₂²×C₄	C₁₃×#41	1	4	yes	—
485	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
491	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
493	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
494	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
495	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
498	C₄⋊C₄	—	2	4	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	4	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	8	no	—
506	C₄⋊C₄	—	2	8	no	—
507	C₄⋊C₄	—	4	4	no	—
508	C₄⋊C₄	—	4	4	no	—
509	C₄⋊C₄	C₁₃×#41	1	8	yes	complemented
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	8	no	—
514	C₂²⋊C₄	—	2	8	no	—
515	C₂²⋊C₄	—	2	8	no	—
516	C₂²⋊C₄	—	4	4	no	—
517	C₂²⋊C₄	—	4	4	no	—
518	C₂²⋊C₄	—	4	4	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	2	4	no	—
524	C₄²	—	2	4	no	—
525	C₄²	—	2	2	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	4	no	—
528	C₄²	—	2	4	no	—
529	C₄²	—	2	4	no	—
530	C₄²	—	2	8	no	—
531	C₄²	—	4	4	no	—
532	C₁₃	#34816	1	1	yes	characteristic, direct product factor, Sylow
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	2	2	no	—
539	C₂³	—	2	4	no	—
540	C₂³	C₂×C₁₃×#41	1	2	yes	—
541	C₂³	C₂×C₁₃×#41	1	2	yes	—
542	C₂³	C₂×C₁₃×#41	1	2	yes	—
543	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
544	Q₈	—	4	4	no	—
545	D₄	—	4	8	no	—
546	D₄	—	4	4	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	4	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	4	8	no	—
577	C₂×C₄	—	4	8	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	8	no	—
580	C₂×C₄	C₁₃×#126	1	16	yes	complemented
581	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
582	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
583	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
584	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
585	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
586	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
587	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
588	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
589	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
590	C₂²	—	2	2	no	—
591	C₂²	—	2	2	no	—
592	C₂²	—	2	4	no	—
593	C₂²	—	2	4	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	—	4	2	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	4	no	—
599	C₂²	C₂×C₁₃×#126	1	4	yes	—
600	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
601	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
602	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
603	C₂²	C₂²×C₁₃×#41	1	2	yes	—
604	C₂²	C₁₃×#585	1	2	yes	—
605	C₄	—	2	4	no	—
606	C₄	—	2	4	no	—
607	C₄	—	2	4	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	4	2	no	—
614	C₄	—	4	4	no	—
615	C₄	—	4	4	no	—
616	C₄	C₂×C₁₃×#126	1	4	yes	—
617	C₄	C₂×C₁₃×#126	1	4	yes	—
618	C₂	—	2	4	no	—
619	C₂	—	8	2	no	—
620	C₂	C₂²×C₁₃×#126	1	1	yes	characteristic
621	C₂	C₁₃×#3444	1	1	yes	characteristic
622	C₂	C₁₃×#3455	1	1	yes	characteristic
623	C₂	C₁₃×#3475	1	2	yes	—
624	C₂	C₁₃×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
socle	C₂³×C₁₃	C₂⁵
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2514	C₂	semidirect
2. C₁₃×#2513	C₂	semidirect
3. C₁₃×#2512	C₂	semidirect
4. C₁₃×#2511	C₂	semidirect
5. C₁₃×#2510	C₂	semidirect
6. C₁₃×#2481	C₂	semidirect
7. C₁₃×#2401	C₂	semidirect
8. C₄×C₁₃×#126	C₂	semidirect
12. C₁₃×#2296	C₂	semidirect
13. C₁₃×#2285	C₂	semidirect
14. C₄×C₁₃×#117	C₂	semidirect
15. C₂×C₄×C₁₃×C₄⋊C₄	C₂	semidirect
145. #34816	C₁₃	direct (N × H)
198. C₁₃×C₄⋊C₄	#41	semidirect
221. #2514	C₂×C₁₃	semidirect
222. #2513	C₂×C₁₃	semidirect
223. #2512	C₂×C₁₃	semidirect
224. #2511	C₂×C₁₃	semidirect
225. #2510	C₂×C₁₃	semidirect
226. #2481	C₂×C₁₃	semidirect
227. #2401	C₂×C₁₃	semidirect
228. C₄×#126	C₂×C₁₃	semidirect
232. #2296	C₂×C₁₃	semidirect
233. #2285	C₂×C₁₃	semidirect
234. C₄×#117	C₂×C₁₃	semidirect
235. C₂×C₄×C₄⋊C₄	C₂×C₁₃	semidirect
283. C₂×C₄×C₁₃	#126	semidirect
509. C₄⋊C₄	C₁₃×#41	semidirect
532. C₁₃	#34816	direct (N × H)
580. C₂×C₄	C₁₃×#126	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#2514	2
C₁₃×#2513	2
C₁₃×#2512	2
C₁₃×#2511	2
C₁₃×#2510	2
C₁₃×#2481	2
C₁₃×#2401	2
C₄×C₁₃×#126	2
C₁₃×#2297	2
C₁₃×#2296	2
C₁₃×#2285	2
C₄×C₁₃×#117	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#34816	13

Subgroups — C13×#34816 #15721155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#34816 #15721155