Subgroups — C₁₃×#25849 #15712188

Order 3328.

1000 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#501	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2546	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2059	C₂	1	2	yes	maximal
6	C₁₃×#2057	C₂	1	2	yes	maximal
7	C₁₃×#1989	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1985	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1865	C₂	1	2	yes	maximal
10	C₁₃×#1863	C₂	1	2	yes	maximal
11	C₁₃×#1763	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#557	—	2	4	no	—
13	C₁₃×#557	—	2	4	no	—
14	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₁₃×C₄⋊Q₈	—	2	1	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	—	2	1	no	—
19	C₂×C₁₃×#125	—	2	1	no	—
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#501	—	2	4	no	—
28	C₁₃×#477	—	2	4	no	—
29	C₂×C₁₃×#107	C₂²	1	2	yes	—
30	C₂×C₁₃×#107	C₂²	1	2	yes	—
31	C₂×C₁₃×#106	C₂²	1	2	yes	—
32	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×#103	C₂²	1	2	yes	—
35	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
36	C₁₃×#398	—	2	1	no	—
37	C₁₃×#398	—	2	1	no	—
38	C₁₃×#391	—	2	1	no	—
39	C₁₃×#389	C₂²	1	2	yes	—
40	C₁₃×#389	C₂²	1	2	yes	—
41	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₁₃×#336	C₂²	1	2	yes	—
46	C₁₃×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₁₃	—	2	1	no	—
48	C₂²×Q₈×C₁₃	—	2	1	no	—
49	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
50	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
53	C₁₃×C₄⋊Q₈	—	2	8	no	—
54	C₁₃×C₄⋊Q₈	—	2	2	no	—
55	C₁₃×C₄⋊Q₈	—	2	2	no	—
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	—	2	2	no	—
58	C₁₃×C₄⋊Q₈	—	4	4	no	—
59	C₁₃×#125	—	2	8	no	—
60	C₁₃×#125	—	2	8	no	—
61	C₁₃×#125	—	2	2	no	—
62	C₁₃×#125	—	2	2	no	—
63	C₁₃×#125	—	2	2	no	—
64	C₁₃×#125	D₄	1	4	yes	—
65	C₄×Q₈×C₁₃	—	2	8	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	—	2	2	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	no	—
71	C₄×Q₈×C₁₃	—	2	2	no	—
72	C₄×Q₈×C₁₃	—	2	2	no	—
73	C₄×Q₈×C₁₃	D₄	1	4	yes	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
81	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
82	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
83	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
84	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₄²×C₁₃	—	2	1	no	—
94	C₂×C₄²×C₁₃	—	2	1	no	—
95	C₂×C₄²×C₁₃	—	2	1	no	—
96	C₂×C₄²×C₁₃	—	2	1	no	—
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
100	C₁₃×#107	—	2	4	no	—
101	C₁₃×#107	—	2	4	no	—
102	C₁₃×#106	—	2	4	no	—
103	C₁₃×C₄⋊C₈	—	2	2	no	—
104	C₁₃×#103	—	2	4	no	—
105	C₁₃×#103	Q₈	1	8	yes	complemented
106	C₁₃×#97	—	2	2	no	—
107	C₁₃×#95	—	2	1	no	—
108	C₁₃×#95	—	2	2	no	—
109	C₁₃×#95	—	2	2	no	—
110	#25849	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
111	C₂×Q₈×C₁₃	—	2	4	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	2	no	—
116	C₂×Q₈×C₁₃	—	4	1	no	—
117	C₂×Q₈×C₁₃	—	4	2	no	—
118	C₂×Q₈×C₁₃	—	4	2	no	—
119	C₂×Q₈×C₁₃	—	4	2	no	—
120	C₂×Q₈×C₁₃	—	4	2	no	—
121	C₂×Q₈×C₁₃	—	4	2	no	—
122	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
123	C₂×Q₈×C₁₃	C₂×Q₈	1	4	yes	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	2	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₂×C₈×C₁₃	—	2	2	no	—
138	C₂×C₈×C₁₃	—	2	2	no	—
139	C₂×C₈×C₁₃	—	2	2	no	—
140	C₂×C₈×C₁₃	—	2	4	no	—
141	C₂×C₈×C₁₃	C₂×Q₈	1	4	yes	—
142	C₁₃×C₄⋊C₄	—	2	4	no	—
143	C₁₃×C₄⋊C₄	—	2	4	no	—
144	C₁₃×C₄⋊C₄	—	2	4	no	—
145	C₁₃×C₄⋊C₄	—	2	4	no	—
146	C₁₃×C₄⋊C₄	—	2	4	no	—
147	C₁₃×C₄⋊C₄	—	2	4	no	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	2	no	—
158	C₁₃×C₄⋊C₄	—	2	2	no	—
159	C₁₃×C₄⋊C₄	—	4	4	no	—
160	C₁₃×C₄⋊C₄	—	4	2	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂×Q₈	1	4	yes	—
166	C₄²×C₁₃	—	2	4	no	—
167	C₄²×C₁₃	—	2	4	no	—
168	C₄²×C₁₃	—	2	4	no	—
169	C₄²×C₁₃	—	2	1	no	—
170	C₄²×C₁₃	—	2	1	no	—
171	C₄²×C₁₃	—	2	1	no	—
172	C₄²×C₁₃	—	2	1	no	—
173	C₄²×C₁₃	—	4	2	no	—
174	C₄²×C₁₃	C₂×D₄	1	2	yes	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₂×#557	C₂×C₁₃	1	1	yes	characteristic
177	C₂×#501	C₂×C₁₃	1	1	yes	characteristic
178	C₂×#477	C₂×C₁₃	1	1	yes	characteristic
179	#2546	C₂×C₁₃	1	1	yes	characteristic
180	#2059	C₂×C₁₃	1	2	yes	—
181	#2057	C₂×C₁₃	1	2	yes	—
182	#1989	C₂×C₁₃	1	1	yes	characteristic
183	#1985	C₂×C₁₃	1	1	yes	characteristic
184	#1865	C₂×C₁₃	1	2	yes	—
185	#1863	C₂×C₁₃	1	2	yes	—
186	#1763	C₂×C₁₃	1	1	yes	characteristic
187	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	2	4	no	—
190	Q₈×C₁₃	—	4	4	no	—
191	Q₈×C₁₃	—	4	8	no	—
192	Q₈×C₁₃	—	8	4	no	—
193	Q₈×C₁₃	C₄⋊Q₈	1	4	yes	complemented
194	C₂×C₄×C₁₃	—	2	2	no	—
195	C₂×C₄×C₁₃	—	2	1	no	—
196	C₂×C₄×C₁₃	—	2	4	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	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	1	no	—
202	C₂×C₄×C₁₃	—	2	1	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	2	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	4	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	#120	1	2	yes	—
223	C₂×C₄×C₁₃	#120	1	2	yes	—
224	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
225	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
228	C₂×C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
229	C₈×C₁₃	—	2	4	no	—
230	C₈×C₁₃	—	4	2	no	—
231	#557	—	2	4	no	—
232	#557	—	2	4	no	—
233	C₂×C₄⋊Q₈	—	2	1	no	—
234	C₂×C₄⋊Q₈	—	2	1	no	—
235	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
237	C₂×#125	—	2	1	no	—
238	C₂×#125	—	2	1	no	—
239	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
240	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₄×Q₈	—	2	1	no	—
242	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
243	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
245	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
246	#501	—	2	4	no	—
247	#477	—	2	4	no	—
248	C₂×#107	C₂²×C₁₃	1	2	yes	—
249	C₂×#107	C₂²×C₁₃	1	2	yes	—
250	C₂×#106	C₂²×C₁₃	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#103	C₂²×C₁₃	1	2	yes	—
253	C₂×#103	C₂²×C₁₃	1	2	yes	—
254	C₂×#97	C₂²×C₁₃	1	1	yes	characteristic
255	#398	—	2	1	no	—
256	#398	—	2	1	no	—
257	#391	—	2	1	no	—
258	#389	C₂²×C₁₃	1	2	yes	—
259	#389	C₂²×C₁₃	1	2	yes	—
260	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
261	#340	C₂²×C₁₃	1	2	yes	—
262	#340	C₂²×C₁₃	1	2	yes	—
263	#340	C₂²×C₁₃	1	2	yes	—
264	#336	C₂²×C₁₃	1	2	yes	—
265	#336	C₂²×C₁₃	1	2	yes	—
266	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
267	C₂²×C₁₃	D₄×Q₈	1	2	yes	—
268	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
269	C₂²×C₁₃	#575	1	1	yes	characteristic
270	C₂²×C₁₃	#578	1	2	yes	—
271	C₄×C₁₃	—	2	4	no	—
272	C₄×C₁₃	—	2	2	no	—
273	C₄×C₁₃	—	2	2	no	—
274	C₄×C₁₃	—	2	2	no	—
275	C₄×C₁₃	—	4	4	no	—
276	C₄×C₁₃	—	4	1	no	—
277	C₄×C₁₃	—	4	2	no	—
278	C₄×C₁₃	—	4	2	no	—
279	C₄×C₁₃	—	4	1	no	—
280	C₄×C₁₃	—	4	1	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	—	8	2	no	—
283	C₄×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
284	C₄×C₁₃	#536	1	1	yes	characteristic
285	C₄×C₁₃	D₄×Q₈	1	2	yes	—
286	C₂²×Q₈	—	2	1	no	—
287	C₂²×Q₈	—	2	1	no	—
288	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
291	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
292	C₄⋊Q₈	—	2	8	no	—
293	C₄⋊Q₈	—	2	2	no	—
294	C₄⋊Q₈	—	2	2	no	—
295	C₄⋊Q₈	—	2	2	no	—
296	C₄⋊Q₈	—	2	2	no	—
297	C₄⋊Q₈	—	4	4	no	—
298	#125	—	2	8	no	—
299	#125	—	2	8	no	—
300	#125	—	2	2	no	—
301	#125	—	2	2	no	—
302	#125	—	2	2	no	—
303	#125	D₄×C₁₃	1	4	yes	—
304	C₄×Q₈	—	2	8	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	2	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₄×Q₈	—	2	2	no	—
312	C₄×Q₈	D₄×C₁₃	1	4	yes	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
325	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
326	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
337	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
339	#107	—	2	4	no	—
340	#107	—	2	4	no	—
341	#106	—	2	4	no	—
342	C₄⋊C₈	—	2	2	no	—
343	#103	—	2	4	no	—
344	#103	Q₈×C₁₃	1	8	yes	complemented
345	#97	—	2	2	no	—
346	#95	—	2	1	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	C₂×C₁₃	#2434	1	1	yes	characteristic
350	C₂×C₁₃	#3006	1	1	yes	characteristic
351	C₂×C₁₃	#3011	1	1	yes	characteristic
352	C₂×C₁₃	#3386	1	2	yes	—
353	C₂×C₁₃	#3390	1	2	yes	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	2	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	4	1	no	—
360	C₂×Q₈	—	4	2	no	—
361	C₂×Q₈	—	4	2	no	—
362	C₂×Q₈	—	4	2	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	—	4	2	no	—
365	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
366	C₂×Q₈	C₂×Q₈×C₁₃	1	4	yes	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
377	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	4	no	—
384	C₂×C₈	C₂×Q₈×C₁₃	1	4	yes	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	4	4	no	—
403	C₄⋊C₄	—	4	2	no	—
404	C₄⋊C₄	—	4	4	no	—
405	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
406	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
407	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
408	C₄⋊C₄	C₂×Q₈×C₁₃	1	4	yes	—
409	C₄²	—	2	4	no	—
410	C₄²	—	2	4	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	4	2	no	—
417	C₄²	C₂×D₄×C₁₃	1	2	yes	—
418	C₄²	C₂×D₄×C₁₃	1	2	yes	—
419	C₁₃	#25849	1	1	yes	characteristic, direct product factor, Sylow
420	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
421	Q₈	—	2	2	no	—
422	Q₈	—	2	4	no	—
423	Q₈	—	4	4	no	—
424	Q₈	—	4	8	no	—
425	Q₈	—	8	4	no	—
426	Q₈	C₁₃×C₄⋊Q₈	1	4	yes	complemented
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	C₁₃×#120	1	2	yes	—
456	C₂×C₄	C₁₃×#120	1	2	yes	—
457	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
460	C₂×C₄	C₂²×Q₈×C₁₃	1	2	yes	—
461	C₂×C₄	C₁₃×2₋¹⁺⁴	1	2	yes	—
462	C₈	—	2	4	no	—
463	C₈	—	4	2	no	—
464	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
465	C₂²	D₄×Q₈×C₁₃	1	2	yes	—
466	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
467	C₂²	C₁₃×#575	1	1	yes	characteristic
468	C₂²	C₁₃×#578	1	2	yes	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	2	4	no	—
473	C₄	—	4	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	4	2	no	—
476	C₄	—	4	1	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	4	no	—
480	C₄	—	8	2	no	—
481	C₄	C₂×C₁₃×C₄⋊Q₈	1	1	yes	characteristic
482	C₄	C₁₃×#536	1	1	yes	characteristic
483	C₄	D₄×Q₈×C₁₃	1	2	yes	—
484	C₂	C₁₃×#2434	1	1	yes	characteristic
485	C₂	C₁₃×#3006	1	1	yes	characteristic
486	C₂	C₁₃×#3011	1	1	yes	characteristic
487	C₂	C₁₃×#3386	1	2	yes	—
488	C₂	C₁₃×#3390	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
105. C₁₃×#103	Q₈	semidirect
110. #25849	C₁₃	direct (N × H)
193. Q₈×C₁₃	C₄⋊Q₈	semidirect
344. #103	Q₈×C₁₃	semidirect
419. C₁₃	#25849	direct (N × H)
426. Q₈	C₁₃×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#557	2
C₂×C₁₃×#501	2
C₂×C₁₃×#477	2
C₁₃×#2546	2
C₁₃×#2059	2
C₁₃×#2057	2
C₁₃×#1989	2
C₁₃×#1985	2
C₁₃×#1865	2
C₁₃×#1863	2
C₁₃×#1763	2
#25849	13

Subgroups — C13×#25849 #15712188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#25849 #15712188