Subgroups — C₁₃×#29131 #15715470

Order 3328.

742 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₁₃×#124	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₁₃×#2042	C₂	1	2	yes	maximal
5	C₁₃×#1936	C₂	1	2	yes	maximal
6	C₁₃×#1935	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1802	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1767	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₃×#125	—	2	1	no	—
13	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#103	C₂²	1	2	yes	—
19	C₂×C₁₃×#103	C₂²	1	2	yes	—
20	C₂×C₁₃×#102	C₂²	1	2	yes	—
21	C₂×C₁₃×#102	C₂²	1	2	yes	—
22	C₂×C₁₃×#97	C₂²	1	2	yes	—
23	C₁₃×#391	C₂²	1	1	yes	characteristic
24	C₁₃×#390	C₂²	1	1	yes	characteristic
25	C₁₃×#389	—	2	1	no	—
26	C₁₃×#389	—	2	1	no	—
27	C₁₃×#389	C₂²	1	2	yes	—
28	C₁₃×#389	C₂²	1	2	yes	—
29	C₁₃×#388	—	2	1	no	—
30	C₁₃×#388	—	2	1	no	—
31	C₁₃×#384	C₂²	1	1	yes	characteristic
32	C₁₃×#384	C₂²	1	1	yes	characteristic
33	C₁₃×#382	—	2	1	no	—
34	C₁₃×#382	C₂²	1	1	yes	characteristic
35	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
36	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
37	C₄³×C₁₃	C₂²	1	1	yes	characteristic
38	C₁₃×#340	C₂²	1	2	yes	—
39	C₁₃×#340	C₂²	1	2	yes	—
40	C₁₃×#340	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	—	2	1	no	—
46	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
48	C₁₃×#125	—	4	4	no	—
49	C₁₃×#124	—	2	2	no	—
50	C₁₃×#124	—	2	2	no	—
51	C₄×Q₈×C₁₃	—	2	2	no	—
52	C₄×Q₈×C₁₃	—	2	2	no	—
53	C₄×D₄×C₁₃	—	2	2	no	—
54	C₄×D₄×C₁₃	—	2	2	no	—
55	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
56	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
57	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
58	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
59	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
60	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
62	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
63	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
64	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
65	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
71	C₂×C₄²×C₁₃	—	2	1	no	—
72	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
79	C₁₃×C₄⋊C₈	—	2	2	no	—
80	C₁₃×C₄⋊C₈	—	2	2	no	—
81	C₁₃×#103	—	2	4	no	—
82	C₁₃×#103	—	4	2	no	—
83	C₁₃×#102	—	2	4	no	—
84	C₁₃×#102	—	4	2	no	—
85	C₁₃×#97	—	4	2	no	—
86	C₁₃×#95	—	2	1	no	—
87	C₁₃×#95	—	2	1	no	—
88	C₁₃×#95	—	2	1	no	—
89	C₁₃×#95	—	2	1	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	#29131	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
93	C₂⁴×C₁₃	—	2	1	no	—
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×Q₈×C₁₃	—	2	1	no	—
96	C₂×Q₈×C₁₃	—	2	1	no	—
97	C₂×Q₈×C₁₃	—	2	1	no	—
98	C₂×Q₈×C₁₃	—	2	1	no	—
99	C₂×Q₈×C₁₃	#41	1	2	yes	—
100	C₂×D₄×C₁₃	—	2	1	no	—
101	C₂×D₄×C₁₃	—	2	1	no	—
102	C₂×D₄×C₁₃	—	2	1	no	—
103	C₂×D₄×C₁₃	—	2	1	no	—
104	C₂×D₄×C₁₃	—	2	1	no	—
105	C₂×D₄×C₁₃	#41	1	2	yes	—
106	C₂²×C₄×C₁₃	—	2	1	no	—
107	C₂²×C₄×C₁₃	—	2	1	no	—
108	C₂²×C₄×C₁₃	—	2	1	no	—
109	C₂²×C₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	2	no	—
111	C₂²×C₄×C₁₃	—	4	2	no	—
112	C₂²×C₄×C₁₃	—	4	2	no	—
113	C₂²×C₄×C₁₃	—	4	2	no	—
114	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₁₃	—	2	2	no	—
122	C₂×C₈×C₁₃	—	2	2	no	—
123	C₂×C₈×C₁₃	—	2	2	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	2	no	—
127	C₁₃×C₄⋊C₄	—	2	2	no	—
128	C₁₃×C₄⋊C₄	—	2	2	no	—
129	C₁₃×C₄⋊C₄	—	2	1	no	—
130	C₁₃×C₄⋊C₄	—	2	1	no	—
131	C₁₃×C₄⋊C₄	—	2	1	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	2	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	4	2	no	—
136	C₁₃×C₄⋊C₄	—	4	2	no	—
137	C₁₃×C₄⋊C₄	—	4	4	no	—
138	C₁₃×C₄⋊C₄	—	4	4	no	—
139	C₁₃×C₄⋊C₄	—	4	2	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₂²⋊C₄	—	2	4	no	—
143	C₁₃×C₂²⋊C₄	—	2	4	no	—
144	C₁₃×C₂²⋊C₄	—	4	2	no	—
145	C₁₃×C₂²⋊C₄	—	4	2	no	—
146	C₁₃×C₂²⋊C₄	—	4	2	no	—
147	C₄²×C₁₃	—	2	2	no	—
148	C₄²×C₁₃	—	2	2	no	—
149	C₄²×C₁₃	—	2	1	no	—
150	C₄²×C₁₃	—	2	1	no	—
151	C₄²×C₁₃	—	2	1	no	—
152	C₄²×C₁₃	—	2	1	no	—
153	C₄²×C₁₃	—	4	1	no	—
154	C₄²×C₁₃	—	4	1	no	—
155	C₄²×C₁₃	—	4	2	no	—
156	C₄²×C₁₃	#41	1	2	yes	—
157	C₄²×C₁₃	#41	1	2	yes	—
158	#2859	C₂×C₁₃	1	1	yes	characteristic, complemented
159	C₄×#124	C₂×C₁₃	1	1	yes	characteristic
160	#2101	C₂×C₁₃	1	2	yes	complemented
161	#2042	C₂×C₁₃	1	2	yes	—
162	#1936	C₂×C₁₃	1	2	yes	—
163	#1935	C₂×C₁₃	1	2	yes	complemented
164	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
165	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
166	#1802	C₂×C₁₃	1	1	yes	characteristic
167	#1802	C₂×C₁₃	1	1	yes	characteristic
168	#1767	C₂×C₁₃	1	1	yes	characteristic, complemented
169	C₂³×C₁₃	—	2	2	no	—
170	C₂³×C₁₃	—	4	1	no	—
171	C₂³×C₁₃	—	4	1	no	—
172	C₂³×C₁₃	—	4	1	no	—
173	C₂³×C₁₃	—	4	1	no	—
174	C₂³×C₁₃	—	4	1	no	—
175	C₂³×C₁₃	—	4	1	no	—
176	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
177	Q₈×C₁₃	—	2	2	no	—
178	Q₈×C₁₃	—	2	2	no	—
179	Q₈×C₁₃	—	4	1	no	—
180	Q₈×C₁₃	—	4	1	no	—
181	D₄×C₁₃	—	2	2	no	—
182	D₄×C₁₃	—	2	2	no	—
183	D₄×C₁₃	—	4	1	no	—
184	D₄×C₁₃	—	4	1	no	—
185	C₂×C₄×C₁₃	—	2	1	no	—
186	C₂×C₄×C₁₃	—	2	1	no	—
187	C₂×C₄×C₁₃	—	2	1	no	—
188	C₂×C₄×C₁₃	—	2	1	no	—
189	C₂×C₄×C₁₃	—	2	2	no	—
190	C₂×C₄×C₁₃	—	2	1	no	—
191	C₂×C₄×C₁₃	—	2	1	no	—
192	C₂×C₄×C₁₃	—	2	1	no	—
193	C₂×C₄×C₁₃	—	2	1	no	—
194	C₂×C₄×C₁₃	—	2	1	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	1	no	—
202	C₂×C₄×C₁₃	—	4	2	no	—
203	C₂×C₄×C₁₃	—	4	1	no	—
204	C₂×C₄×C₁₃	—	4	1	no	—
205	C₂×C₄×C₁₃	—	4	2	no	—
206	C₂×C₄×C₁₃	—	4	2	no	—
207	C₂×C₄×C₁₃	—	4	2	no	—
208	C₂×C₄×C₁₃	—	4	1	no	—
209	C₂×C₄×C₁₃	—	4	1	no	—
210	C₂×C₄×C₁₃	—	4	1	no	—
211	C₂×C₄×C₁₃	—	4	1	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	2	no	—
214	C₂×C₄×C₁₃	—	8	4	no	—
215	C₂×C₄×C₁₃	#124	1	2	yes	—
216	C₂×C₄×C₁₃	#124	1	2	yes	—
217	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
218	C₂×C₄×C₁₃	#137	1	2	yes	—
219	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
220	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
223	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
225	C₈×C₁₃	—	4	2	no	—
226	C₈×C₁₃	—	4	2	no	—
227	C₂×#125	—	2	1	no	—
228	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
233	C₂×#103	C₂²×C₁₃	1	2	yes	—
234	C₂×#103	C₂²×C₁₃	1	2	yes	—
235	C₂×#102	C₂²×C₁₃	1	2	yes	—
236	C₂×#102	C₂²×C₁₃	1	2	yes	—
237	C₂×#97	C₂²×C₁₃	1	2	yes	—
238	#391	C₂²×C₁₃	1	1	yes	characteristic
239	#390	C₂²×C₁₃	1	1	yes	characteristic
240	#389	—	2	1	no	—
241	#389	—	2	1	no	—
242	#389	C₂²×C₁₃	1	2	yes	—
243	#389	C₂²×C₁₃	1	2	yes	—
244	#388	—	2	1	no	—
245	#388	—	2	1	no	—
246	#384	C₂²×C₁₃	1	1	yes	characteristic
247	#384	C₂²×C₁₃	1	1	yes	characteristic
248	#382	—	2	1	no	—
249	#382	C₂²×C₁₃	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	—	2	1	no	—
251	C₄×C₂²⋊C₄	—	2	1	no	—
252	C₄³	C₂²×C₁₃	1	1	yes	characteristic
253	#340	C₂²×C₁₃	1	2	yes	—
254	#340	C₂²×C₁₃	1	2	yes	—
255	#340	C₂²×C₁₃	1	2	yes	—
256	#340	C₂²×C₁₃	1	2	yes	—
257	#336	C₂²×C₁₃	1	2	yes	—
258	C₂²×C₁₃	—	4	2	no	—
259	C₂²×C₁₃	—	4	2	no	—
260	C₂²×C₁₃	—	4	2	no	—
261	C₂²×C₁₃	—	8	1	no	—
262	C₂²×C₁₃	—	8	1	no	—
263	C₂²×C₁₃	—	8	1	no	—
264	C₂²×C₁₃	—	8	1	no	—
265	C₂²×C₁₃	#525	1	1	yes	characteristic
266	C₂²×C₁₃	C₂×#124	1	1	yes	characteristic
267	C₂²×C₁₃	#537	1	1	yes	characteristic
268	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
270	C₂²×C₁₃	#575	1	1	yes	characteristic
271	C₂²×C₁₃	#575	1	1	yes	characteristic
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	4	2	no	—
274	C₄×C₁₃	—	4	1	no	—
275	C₄×C₁₃	—	4	1	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	4	1	no	—
278	C₄×C₁₃	—	8	2	no	—
279	C₄×C₁₃	—	8	1	no	—
280	C₄×C₁₃	—	8	1	no	—
281	C₄×C₁₃	—	8	2	no	—
282	C₄×C₁₃	#489	1	4	yes	—
283	C₄×C₁₃	#552	1	1	yes	characteristic
284	C₄×C₁₃	#552	1	1	yes	characteristic
285	C₄×C₁₃	#553	1	1	yes	characteristic
286	C₄×C₁₃	#553	1	1	yes	characteristic
287	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
288	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
289	C₂³×C₄	—	2	1	no	—
290	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
291	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
292	#125	—	4	4	no	—
293	#124	—	2	2	no	—
294	#124	—	2	2	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	—	2	2	no	—
297	C₄×D₄	—	2	2	no	—
298	C₄×D₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	2	1	no	—
306	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
307	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
310	C₂×C₂²⋊C₄	—	2	1	no	—
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₂²⋊C₄	—	2	1	no	—
315	C₂×C₄²	—	2	1	no	—
316	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
317	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
318	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
319	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
320	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
322	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
323	C₄⋊C₈	—	2	2	no	—
324	C₄⋊C₈	—	2	2	no	—
325	#103	—	2	4	no	—
326	#103	—	4	2	no	—
327	#102	—	2	4	no	—
328	#102	—	4	2	no	—
329	#97	—	4	2	no	—
330	#95	—	2	1	no	—
331	#95	—	2	1	no	—
332	#95	—	2	1	no	—
333	#95	—	2	1	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	C₂×C₁₃	—	8	2	no	—
337	C₂×C₁₃	#2562	1	1	yes	characteristic
338	C₂×C₁₃	#3115	1	1	yes	characteristic
339	C₂×C₁₃	#3116	1	1	yes	characteristic
340	C₂×C₁₃	C₂×#489	1	1	yes	characteristic
341	C₂×C₁₃	#3142	1	1	yes	characteristic
342	C₂×C₁₃	#3251	1	1	yes	characteristic
343	C₂×C₁₃	#3252	1	1	yes	characteristic
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	C₁₃×#41	1	2	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	C₁₃×#41	1	2	yes	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	4	2	no	—
363	C₂²×C₄	—	4	2	no	—
364	C₂²×C₄	—	4	2	no	—
365	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	4	4	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	4	2	no	—
390	C₄⋊C₄	—	4	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	2	4	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₂²⋊C₄	—	4	2	no	—
397	C₂²⋊C₄	—	4	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	1	no	—
401	C₄²	—	2	1	no	—
402	C₄²	—	2	1	no	—
403	C₄²	—	2	1	no	—
404	C₄²	—	4	1	no	—
405	C₄²	—	4	1	no	—
406	C₄²	—	4	2	no	—
407	C₄²	C₁₃×#41	1	2	yes	—
408	C₄²	C₁₃×#41	1	2	yes	—
409	C₁₃	#29131	1	1	yes	characteristic, direct product factor, Sylow
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	1	no	—
417	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	D₄	—	2	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	4	1	no	—
425	D₄	—	4	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	8	4	no	—
456	C₂×C₄	C₁₃×#124	1	2	yes	—
457	C₂×C₄	C₁₃×#124	1	2	yes	—
458	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
459	C₂×C₄	C₁₃×#137	1	2	yes	—
460	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
461	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
462	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
463	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
464	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
465	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₁₃×#525	1	1	yes	characteristic
476	C₂²	C₂×C₁₃×#124	1	1	yes	characteristic
477	C₂²	C₁₃×#537	1	1	yes	characteristic
478	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
479	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
480	C₂²	C₁₃×#575	1	1	yes	characteristic
481	C₂²	C₁₃×#575	1	1	yes	characteristic
482	C₄	—	2	2	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	1	no	—
487	C₄	—	4	1	no	—
488	C₄	—	8	2	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	2	no	—
492	C₄	C₁₃×#489	1	4	yes	—
493	C₄	C₁₃×#552	1	1	yes	characteristic
494	C₄	C₁₃×#552	1	1	yes	characteristic
495	C₄	C₁₃×#553	1	1	yes	characteristic
496	C₄	C₁₃×#553	1	1	yes	characteristic
497	C₂	—	8	2	no	—
498	C₂	C₁₃×#2562	1	1	yes	characteristic
499	C₂	C₁₃×#3115	1	1	yes	characteristic
500	C₂	C₁₃×#3116	1	1	yes	characteristic
501	C₂	C₂×C₁₃×#489	1	1	yes	characteristic
502	C₂	C₁₃×#3142	1	1	yes	characteristic
503	C₂	C₁₃×#3251	1	1	yes	characteristic
504	C₂	C₁₃×#3252	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 ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₃×#2859	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
6. C₁₃×#1935	C₂	semidirect
7. C₁₃×#1803	C₂	semidirect
8. C₁₃×#1803	C₂	semidirect
11. C₁₃×#1767	C₂	semidirect
92. #29131	C₁₃	direct (N × H)
158. #2859	C₂×C₁₃	semidirect
160. #2101	C₂×C₁₃	semidirect
163. #1935	C₂×C₁₃	semidirect
164. #1803	C₂×C₁₃	semidirect
165. #1803	C₂×C₁₃	semidirect
168. #1767	C₂×C₁₃	semidirect
409. C₁₃	#29131	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2859	2
C₄×C₁₃×#124	2
C₁₃×#2101	2
C₁₃×#2042	2
C₁₃×#1936	2
C₁₃×#1935	2
C₁₃×#1803	2
C₁₃×#1802	2
C₁₃×#1767	2
#29131	13

Subgroups — C13×#29131 #15715470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29131 #15715470