Subgroups — C₂×C₁₃×#1442 #15700179

Order 3328.

2942 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₃×#95	C₂	1	2	yes	maximal
3	C₂²×C₁₃×#95	C₂	1	2	yes	maximal
4	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×#95	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#1442	C₂	1	8	yes	maximal, direct product factor
7	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
8	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₃	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
11	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×C₁₃×C₄⋊C₄	—	2	8	no	—
13	C₂²×C₁₃×C₄⋊C₄	—	2	4	no	—
14	C₂²×C₁₃×C₄⋊C₄	C₂²	1	4	yes	—
15	C₂×C₁₃×#95	—	2	8	no	—
16	C₂×C₁₃×#95	—	2	8	no	—
17	C₂×C₁₃×#95	—	2	4	no	—
18	C₂×C₁₃×#95	C₄	1	8	yes	complemented
19	C₂×C₁₃×#95	C₂²	1	8	yes	—
20	C₂×C₁₃×#95	C₂²	1	8	yes	—
21	C₂×C₁₃×#95	C₂²	1	4	yes	—
22	C₂×C₁₃×#95	C₂²	1	4	yes	—
23	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
24	C₂³×C₄×C₁₃	—	2	4	no	—
25	C₂³×C₄×C₁₃	—	2	4	no	—
26	C₂³×C₄×C₁₃	—	2	4	no	—
27	C₂³×C₄×C₁₃	—	2	4	no	—
28	C₂³×C₄×C₁₃	—	2	4	no	—
29	C₂³×C₄×C₁₃	—	2	4	no	—
30	C₂³×C₄×C₁₃	—	2	4	no	—
31	C₂³×C₄×C₁₃	—	2	2	no	—
32	C₂³×C₄×C₁₃	—	2	2	no	—
33	C₂³×C₄×C₁₃	—	2	4	no	—
34	C₂³×C₄×C₁₃	—	2	4	no	—
35	C₂³×C₄×C₁₃	—	2	4	no	—
36	C₂³×C₄×C₁₃	—	2	4	no	—
37	C₂³×C₄×C₁₃	—	2	4	no	—
38	C₂³×C₄×C₁₃	—	2	4	no	—
39	C₂³×C₄×C₁₃	—	2	2	no	—
40	C₂³×C₄×C₁₃	—	2	4	no	—
41	C₂³×C₄×C₁₃	—	2	2	no	—
42	C₂³×C₄×C₁₃	—	2	4	no	—
43	C₂³×C₄×C₁₃	—	2	4	no	—
44	C₂³×C₄×C₁₃	—	2	4	no	—
45	C₂³×C₄×C₁₃	—	2	4	no	—
46	C₂³×C₄×C₁₃	C₂×C₄	1	8	yes	—
47	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₁₃	D₄	1	8	yes	—
49	C₂³×C₄×C₁₃	D₄	1	4	yes	—
50	C₂³×C₄×C₁₃	D₄	1	4	yes	—
51	C₂³×C₄×C₁₃	Q₈	1	4	yes	—
52	C₂³×C₄×C₁₃	Q₈	1	4	yes	—
53	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
54	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂×C₁₃×C₄⋊C₄	—	2	32	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	16	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
61	C₁₃×#95	—	2	16	no	—
62	C₁₃×#95	—	2	16	no	—
63	C₁₃×#95	—	2	8	no	—
64	C₁₃×#95	C₂×C₄	1	16	yes	complemented
65	C₂×#1442	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂⁴×C₁₃	C₂²×C₄	1	2	yes	—
67	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
68	C₂⁴×C₁₃	C₂×D₄	1	4	yes	—
69	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
70	C₂⁴×C₁₃	C₂×Q₈	1	2	yes	—
71	C₂⁴×C₁₃	C₂×Q₈	1	2	yes	—
72	C₂⁴×C₁₃	#41	1	4	yes	—
73	C₂⁴×C₁₃	#41	1	4	yes	—
74	C₂⁴×C₁₃	#41	1	4	yes	—
75	C₂⁴×C₁₃	#41	1	2	yes	—
76	C₂⁴×C₁₃	#41	1	2	yes	—
77	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	—	2	16	no	—
79	C₂²×C₄×C₁₃	—	2	8	no	—
80	C₂²×C₄×C₁₃	—	2	16	no	—
81	C₂²×C₄×C₁₃	—	2	8	no	—
82	C₂²×C₄×C₁₃	—	2	4	no	—
83	C₂²×C₄×C₁₃	—	2	4	no	—
84	C₂²×C₄×C₁₃	—	2	16	no	—
85	C₂²×C₄×C₁₃	—	2	16	no	—
86	C₂²×C₄×C₁₃	—	2	16	no	—
87	C₂²×C₄×C₁₃	—	2	16	no	—
88	C₂²×C₄×C₁₃	—	2	16	no	—
89	C₂²×C₄×C₁₃	—	2	8	no	—
90	C₂²×C₄×C₁₃	—	2	16	no	—
91	C₂²×C₄×C₁₃	—	2	8	no	—
92	C₂²×C₄×C₁₃	—	2	16	no	—
93	C₂²×C₄×C₁₃	—	2	16	no	—
94	C₂²×C₄×C₁₃	—	2	4	no	—
95	C₂²×C₄×C₁₃	—	2	4	no	—
96	C₂²×C₄×C₁₃	—	2	4	no	—
97	C₂²×C₄×C₁₃	—	2	2	no	—
98	C₂²×C₄×C₁₃	—	2	2	no	—
99	C₂²×C₄×C₁₃	—	2	4	no	—
100	C₂²×C₄×C₁₃	—	2	4	no	—
101	C₂²×C₄×C₁₃	—	2	4	no	—
102	C₂²×C₄×C₁₃	—	2	4	no	—
103	C₂²×C₄×C₁₃	—	2	4	no	—
104	C₂²×C₄×C₁₃	—	2	4	no	—
105	C₂²×C₄×C₁₃	—	2	4	no	—
106	C₂²×C₄×C₁₃	—	2	4	no	—
107	C₂²×C₄×C₁₃	—	2	2	no	—
108	C₂²×C₄×C₁₃	—	2	4	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	4	no	—
111	C₂²×C₄×C₁₃	—	2	4	no	—
112	C₂²×C₄×C₁₃	—	2	4	no	—
113	C₂²×C₄×C₁₃	—	2	4	no	—
114	C₂²×C₄×C₁₃	—	4	4	no	—
115	C₂²×C₄×C₁₃	—	4	8	no	—
116	C₂²×C₄×C₁₃	—	4	8	no	—
117	C₂²×C₄×C₁₃	—	4	8	no	—
118	C₂²×C₄×C₁₃	—	4	8	no	—
119	C₂²×C₄×C₁₃	—	4	8	no	—
120	C₂²×C₄×C₁₃	—	4	4	no	—
121	C₂²×C₄×C₁₃	—	4	8	no	—
122	C₂²×C₄×C₁₃	—	4	4	no	—
123	C₂²×C₄×C₁₃	—	4	8	no	—
124	C₂²×C₄×C₁₃	—	4	8	no	—
125	C₂²×C₄×C₁₃	—	4	4	no	—
126	C₂²×C₄×C₁₃	—	4	8	no	—
127	C₂²×C₄×C₁₃	—	4	8	no	—
128	C₂²×C₄×C₁₃	C₄⋊C₄	1	16	yes	—
129	C₂²×C₄×C₁₃	C₂²×C₄	1	8	yes	—
130	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂×D₄	1	8	yes	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
135	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
136	C₁₃×C₄⋊C₄	—	2	32	no	—
137	C₂³×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
138	C₂²×#95	C₂×C₁₃	1	2	yes	—
139	C₂²×#95	C₂×C₁₃	1	2	yes	—
140	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic
141	C₂²×#95	C₂×C₁₃	1	1	yes	characteristic
142	#1442	C₂×C₁₃	1	8	yes	direct product factor
143	C₂³×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
144	C₂³×C₁₃	#117	1	8	yes	—
145	C₂³×C₁₃	C₄×D₄	1	8	yes	—
146	C₂³×C₁₃	C₄×D₄	1	4	yes	—
147	C₂³×C₁₃	C₄×Q₈	1	4	yes	—
148	C₂³×C₁₃	#120	1	4	yes	—
149	C₂³×C₁₃	#121	1	8	yes	—
150	C₂³×C₁₃	#121	1	4	yes	—
151	C₂³×C₁₃	C₂²⋊Q₈	1	8	yes	—
152	C₂³×C₁₃	C₂²⋊Q₈	1	8	yes	—
153	C₂³×C₁₃	C₂²⋊Q₈	1	4	yes	—
154	C₂³×C₁₃	#123	1	4	yes	—
155	C₂³×C₁₃	#123	1	8	yes	—
156	C₂³×C₁₃	#123	1	8	yes	—
157	C₂³×C₁₃	#124	1	4	yes	—
158	C₂³×C₁₃	#124	1	4	yes	—
159	C₂³×C₁₃	#124	1	8	yes	—
160	C₂³×C₁₃	#125	1	8	yes	—
161	C₂³×C₁₃	#125	1	8	yes	—
162	C₂³×C₁₃	#125	1	4	yes	—
163	C₂³×C₁₃	#126	1	8	yes	—
164	C₂³×C₁₃	#126	1	8	yes	—
165	C₂³×C₁₃	C₄⋊Q₈	1	4	yes	—
166	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
167	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	C₂³×C₁₃	C₂²×D₄	1	2	yes	—
169	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
170	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
171	C₂³×C₁₃	C₂²×Q₈	1	1	yes	characteristic
172	C₂³×C₁₃	C₂×#41	1	2	yes	—
173	C₂³×C₁₃	C₂×#41	1	2	yes	—
174	C₂³×C₁₃	C₂×#41	1	2	yes	—
175	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
176	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₁₃	—	2	8	no	—
178	C₂×C₄×C₁₃	—	2	4	no	—
179	C₂×C₄×C₁₃	—	2	8	no	—
180	C₂×C₄×C₁₃	—	2	4	no	—
181	C₂×C₄×C₁₃	—	2	32	no	—
182	C₂×C₄×C₁₃	—	2	8	no	—
183	C₂×C₄×C₁₃	—	2	8	no	—
184	C₂×C₄×C₁₃	—	2	8	no	—
185	C₂×C₄×C₁₃	—	2	8	no	—
186	C₂×C₄×C₁₃	—	2	8	no	—
187	C₂×C₄×C₁₃	—	2	4	no	—
188	C₂×C₄×C₁₃	—	2	8	no	—
189	C₂×C₄×C₁₃	—	2	4	no	—
190	C₂×C₄×C₁₃	—	2	8	no	—
191	C₂×C₄×C₁₃	—	2	8	no	—
192	C₂×C₄×C₁₃	—	4	2	no	—
193	C₂×C₄×C₁₃	—	4	4	no	—
194	C₂×C₄×C₁₃	—	4	4	no	—
195	C₂×C₄×C₁₃	—	4	4	no	—
196	C₂×C₄×C₁₃	—	4	4	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	4	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	4	no	—
201	C₂×C₄×C₁₃	—	4	4	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	4	no	—
204	C₂×C₄×C₁₃	—	4	4	no	—
205	C₂×C₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	4	32	no	—
207	C₂×C₄×C₁₃	—	4	16	no	—
208	C₂×C₄×C₁₃	—	4	32	no	—
209	C₂×C₄×C₁₃	—	4	16	no	—
210	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
211	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
212	C₂⁴×C₄	C₂²×C₁₃	1	2	yes	—
213	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
214	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
215	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
216	C₂²×C₄⋊C₄	—	2	8	no	—
217	C₂²×C₄⋊C₄	—	2	4	no	—
218	C₂²×C₄⋊C₄	C₂²×C₁₃	1	4	yes	—
219	C₂×#95	—	2	8	no	—
220	C₂×#95	—	2	8	no	—
221	C₂×#95	—	2	4	no	—
222	C₂×#95	C₄×C₁₃	1	8	yes	complemented
223	C₂×#95	C₂²×C₁₃	1	8	yes	—
224	C₂×#95	C₂²×C₁₃	1	8	yes	—
225	C₂×#95	C₂²×C₁₃	1	4	yes	—
226	C₂×#95	C₂²×C₁₃	1	4	yes	—
227	C₂²×C₁₃	#382	1	8	yes	—
228	C₂²×C₁₃	#385	1	8	yes	—
229	C₂²×C₁₃	#387	1	16	yes	—
230	C₂²×C₁₃	#388	1	16	yes	—
231	C₂²×C₁₃	#389	1	8	yes	—
232	C₂²×C₁₃	#393	1	8	yes	—
233	C₂²×C₁₃	#394	1	8	yes	—
234	C₂²×C₁₃	#397	1	8	yes	—
235	C₂²×C₁₃	#398	1	16	yes	—
236	C₂²×C₁₃	#400	1	16	yes	—
237	C₂²×C₁₃	#400	1	8	yes	—
238	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
239	C₂²×C₁₃	C₂×#117	1	2	yes	—
240	C₂²×C₁₃	C₂×C₄×D₄	1	2	yes	—
241	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
242	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
243	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
244	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
245	C₂²×C₁₃	C₂×#121	1	2	yes	—
246	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
247	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
248	C₂²×C₁₃	C₂×C₂²⋊Q₈	1	2	yes	—
249	C₂²×C₁₃	C₂×#123	1	2	yes	—
250	C₂²×C₁₃	C₂×#123	1	2	yes	—
251	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
252	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
253	C₂²×C₁₃	C₂×#124	1	2	yes	—
254	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
255	C₂²×C₁₃	C₂×#125	1	2	yes	—
256	C₂²×C₁₃	C₂×#125	1	2	yes	—
257	C₂²×C₁₃	C₂×#125	1	1	yes	characteristic
258	C₂²×C₁₃	C₂×#126	1	2	yes	—
259	C₂²×C₁₃	C₂×#126	1	2	yes	—
260	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
261	C₄×C₁₃	—	2	8	no	—
262	C₄×C₁₃	—	4	4	no	—
263	C₄×C₁₃	—	4	8	no	—
264	C₄×C₁₃	—	4	4	no	—
265	C₄×C₁₃	—	4	8	no	—
266	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
267	C₂³×C₄	—	2	4	no	—
268	C₂³×C₄	—	2	4	no	—
269	C₂³×C₄	—	2	4	no	—
270	C₂³×C₄	—	2	4	no	—
271	C₂³×C₄	—	2	4	no	—
272	C₂³×C₄	—	2	4	no	—
273	C₂³×C₄	—	2	4	no	—
274	C₂³×C₄	—	2	2	no	—
275	C₂³×C₄	—	2	2	no	—
276	C₂³×C₄	—	2	4	no	—
277	C₂³×C₄	—	2	4	no	—
278	C₂³×C₄	—	2	4	no	—
279	C₂³×C₄	—	2	4	no	—
280	C₂³×C₄	—	2	4	no	—
281	C₂³×C₄	—	2	4	no	—
282	C₂³×C₄	—	2	2	no	—
283	C₂³×C₄	—	2	4	no	—
284	C₂³×C₄	—	2	2	no	—
285	C₂³×C₄	—	2	4	no	—
286	C₂³×C₄	—	2	4	no	—
287	C₂³×C₄	—	2	4	no	—
288	C₂³×C₄	—	2	4	no	—
289	C₂³×C₄	C₂×C₄×C₁₃	1	8	yes	—
290	C₂³×C₄	C₂×C₄×C₁₃	1	4	yes	—
291	C₂³×C₄	D₄×C₁₃	1	8	yes	—
292	C₂³×C₄	D₄×C₁₃	1	4	yes	—
293	C₂³×C₄	D₄×C₁₃	1	4	yes	—
294	C₂³×C₄	Q₈×C₁₃	1	4	yes	—
295	C₂³×C₄	Q₈×C₁₃	1	4	yes	—
296	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
297	C₂³×C₄	C₂³×C₁₃	1	4	yes	—
298	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
299	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
300	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
301	C₂×C₄⋊C₄	—	2	32	no	—
302	C₂×C₄⋊C₄	—	2	16	no	—
303	C₂×C₄⋊C₄	—	2	8	no	—
304	#95	—	2	16	no	—
305	#95	—	2	16	no	—
306	#95	—	2	8	no	—
307	#95	C₂×C₄×C₁₃	1	16	yes	complemented
308	C₂×C₁₃	#1442	1	16	yes	direct product factor
309	C₂×C₁₃	C₂×#382	1	1	yes	characteristic
310	C₂×C₁₃	C₂×#385	1	1	yes	characteristic
311	C₂×C₁₃	C₂×#387	1	2	yes	—
312	C₂×C₁₃	C₂×#388	1	2	yes	—
313	C₂×C₁₃	C₂×#389	1	1	yes	characteristic
314	C₂×C₁₃	C₂×#393	1	1	yes	characteristic
315	C₂×C₁₃	C₂×#394	1	1	yes	characteristic
316	C₂×C₁₃	C₂×#397	1	1	yes	characteristic
317	C₂×C₁₃	C₂×#398	1	2	yes	—
318	C₂×C₁₃	C₂×#400	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#400	1	2	yes	—
320	C₂⁴	C₂²×C₄×C₁₃	1	2	yes	—
321	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
322	C₂⁴	C₂×D₄×C₁₃	1	4	yes	—
323	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
324	C₂⁴	C₂×Q₈×C₁₃	1	2	yes	—
325	C₂⁴	C₂×Q₈×C₁₃	1	2	yes	—
326	C₂⁴	C₁₃×#41	1	4	yes	—
327	C₂⁴	C₁₃×#41	1	4	yes	—
328	C₂⁴	C₁₃×#41	1	4	yes	—
329	C₂⁴	C₁₃×#41	1	2	yes	—
330	C₂⁴	C₁₃×#41	1	2	yes	—
331	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
332	C₂²×C₄	—	2	16	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	16	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	16	no	—
339	C₂²×C₄	—	2	16	no	—
340	C₂²×C₄	—	2	16	no	—
341	C₂²×C₄	—	2	16	no	—
342	C₂²×C₄	—	2	16	no	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	16	no	—
345	C₂²×C₄	—	2	8	no	—
346	C₂²×C₄	—	2	16	no	—
347	C₂²×C₄	—	2	16	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	4	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	4	8	no	—
370	C₂²×C₄	—	4	8	no	—
371	C₂²×C₄	—	4	8	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	8	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	8	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	8	no	—
378	C₂²×C₄	—	4	8	no	—
379	C₂²×C₄	—	4	4	no	—
380	C₂²×C₄	—	4	8	no	—
381	C₂²×C₄	—	4	8	no	—
382	C₂²×C₄	C₁₃×C₄⋊C₄	1	16	yes	—
383	C₂²×C₄	C₂²×C₄×C₁₃	1	8	yes	—
384	C₂²×C₄	C₂²×C₄×C₁₃	1	4	yes	—
385	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	8	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	4	yes	—
388	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
389	C₂²×C₄	C₂×Q₈×C₁₃	1	4	yes	—
390	C₄⋊C₄	—	2	32	no	—
391	C₁₃	C₂×#1442	1	1	yes	characteristic, direct product factor, Sylow
392	C₂³	C₂×C₁₃×C₄⋊C₄	1	4	yes	—
393	C₂³	C₁₃×#117	1	8	yes	—
394	C₂³	C₄×D₄×C₁₃	1	8	yes	—
395	C₂³	C₄×D₄×C₁₃	1	4	yes	—
396	C₂³	C₄×Q₈×C₁₃	1	4	yes	—
397	C₂³	C₁₃×#120	1	4	yes	—
398	C₂³	C₁₃×#121	1	8	yes	—
399	C₂³	C₁₃×#121	1	4	yes	—
400	C₂³	C₁₃×C₂²⋊Q₈	1	8	yes	—
401	C₂³	C₁₃×C₂²⋊Q₈	1	8	yes	—
402	C₂³	C₁₃×C₂²⋊Q₈	1	4	yes	—
403	C₂³	C₁₃×#123	1	4	yes	—
404	C₂³	C₁₃×#123	1	8	yes	—
405	C₂³	C₁₃×#123	1	8	yes	—
406	C₂³	C₁₃×#124	1	4	yes	—
407	C₂³	C₁₃×#124	1	4	yes	—
408	C₂³	C₁₃×#124	1	8	yes	—
409	C₂³	C₁₃×#125	1	8	yes	—
410	C₂³	C₁₃×#125	1	8	yes	—
411	C₂³	C₁₃×#125	1	4	yes	—
412	C₂³	C₁₃×#126	1	8	yes	—
413	C₂³	C₁₃×#126	1	8	yes	—
414	C₂³	C₁₃×C₄⋊Q₈	1	4	yes	—
415	C₂³	C₂³×C₄×C₁₃	1	1	yes	characteristic
416	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
417	C₂³	C₂²×D₄×C₁₃	1	2	yes	—
418	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
419	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
420	C₂³	C₂²×Q₈×C₁₃	1	1	yes	characteristic
421	C₂³	C₂×C₁₃×#41	1	2	yes	—
422	C₂³	C₂×C₁₃×#41	1	2	yes	—
423	C₂³	C₂×C₁₃×#41	1	2	yes	—
424	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
425	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
426	C₂×C₄	—	2	32	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	4	32	no	—
442	C₂×C₄	—	4	16	no	—
443	C₂×C₄	—	4	32	no	—
444	C₂×C₄	—	4	16	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	4	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	4	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	4	4	no	—
459	C₂×C₄	C₂×C₁₃×C₄⋊C₄	1	8	yes	—
460	C₂²	C₁₃×#382	1	8	yes	—
461	C₂²	C₁₃×#385	1	8	yes	—
462	C₂²	C₁₃×#387	1	16	yes	—
463	C₂²	C₁₃×#388	1	16	yes	—
464	C₂²	C₁₃×#389	1	8	yes	—
465	C₂²	C₁₃×#393	1	8	yes	—
466	C₂²	C₁₃×#394	1	8	yes	—
467	C₂²	C₁₃×#397	1	8	yes	—
468	C₂²	C₁₃×#398	1	16	yes	—
469	C₂²	C₁₃×#400	1	16	yes	—
470	C₂²	C₁₃×#400	1	8	yes	—
471	C₂²	C₂²×C₁₃×C₄⋊C₄	1	1	yes	characteristic
472	C₂²	C₂×C₁₃×#117	1	2	yes	—
473	C₂²	C₂×C₄×D₄×C₁₃	1	2	yes	—
474	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
475	C₂²	C₂×C₄×Q₈×C₁₃	1	1	yes	characteristic
476	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
477	C₂²	C₂×C₁₃×#121	1	2	yes	—
478	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
479	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
480	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	2	yes	—
481	C₂²	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
482	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
483	C₂²	C₂×C₁₃×#123	1	2	yes	—
484	C₂²	C₂×C₁₃×#123	1	2	yes	—
485	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
486	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
487	C₂²	C₂×C₁₃×#124	1	2	yes	—
488	C₂²	C₂×C₁₃×#125	1	2	yes	—
489	C₂²	C₂×C₁₃×#125	1	2	yes	—
490	C₂²	C₂×C₁₃×#125	1	1	yes	characteristic
491	C₂²	C₂×C₁₃×#126	1	2	yes	—
492	C₂²	C₂×C₁₃×#126	1	2	yes	—
493	C₂²	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
494	C₄	—	2	8	no	—
495	C₄	—	4	8	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	8	no	—
498	C₄	—	4	4	no	—
499	C₂	C₁₃×#1442	1	16	yes	direct product factor
500	C₂	C₂×C₁₃×#382	1	1	yes	characteristic
501	C₂	C₂×C₁₃×#385	1	1	yes	characteristic
502	C₂	C₂×C₁₃×#387	1	2	yes	—
503	C₂	C₂×C₁₃×#388	1	2	yes	—
504	C₂	C₂×C₁₃×#389	1	1	yes	characteristic
505	C₂	C₂×C₁₃×#393	1	1	yes	characteristic
506	C₂	C₂×C₁₃×#394	1	1	yes	characteristic
507	C₂	C₂×C₁₃×#397	1	1	yes	characteristic
508	C₂	C₂×C₁₃×#398	1	2	yes	—
509	C₂	C₂×C₁₃×#400	1	2	yes	—
510	C₂	C₂×C₁₃×#400	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. C₁₃×#1442	C₂	direct (N × H)
18. C₂×C₁₃×#95	C₄	semidirect
64. C₁₃×#95	C₂×C₄	semidirect
65. C₂×#1442	C₁₃	direct (N × H)
142. #1442	C₂×C₁₃	direct (N × H)
222. C₂×#95	C₄×C₁₃	semidirect
307. #95	C₂×C₄×C₁₃	semidirect
308. C₂×C₁₃	#1442	direct (N × H)
391. C₁₃	C₂×#1442	direct (N × H)
499. C₂	C₁₃×#1442	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×C₄⋊C₄	2
C₂²×C₁₃×#95	2
C₁₃×#1442	2
C₂×#1442	13

Subgroups — C2×C13×#1442 #15700179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₃×#1442 #15700179