Subgroups — C₁₃×#24191 #15710530

Order 3328.

1050 conjugacy classes of subgroups.

The subgroup lattice has 510 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×#462	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2582	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2043	C₂	1	2	yes	maximal
6	C₁₃×#2016	C₂	1	2	yes	maximal
7	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1956	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1878	C₂	1	2	yes	maximal
10	C₁₃×#1863	C₂	1	2	yes	maximal
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×Q₁₆	C₂²	1	2	yes	—
14	C₁₃×#557	—	2	4	no	—
15	C₁₃×#557	—	2	4	no	—
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#125	—	2	1	no	—
19	C₂×C₁₃×#125	—	2	2	no	—
20	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₁₃×#462	—	2	4	no	—
26	C₄×C₁₃×Q₁₆	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×#103	C₂²	1	2	yes	—
35	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
36	C₁₃×#398	—	2	2	no	—
37	C₁₃×#391	—	2	1	no	—
38	C₁₃×#391	C₂²	1	2	yes	—
39	C₁₃×#389	—	2	1	no	—
40	C₁₃×#389	C₂²	1	2	yes	—
41	C₁₃×#384	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#336	C₂²	1	2	yes	—
44	C₁₃×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	4	no	—
52	C₂×C₁₃×Q₁₆	—	2	4	no	—
53	C₂×C₁₃×Q₁₆	—	2	2	no	—
54	C₂×C₁₃×Q₁₆	—	4	2	no	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₁₃×C₄⋊Q₈	—	2	4	no	—
59	C₁₃×C₄⋊Q₈	—	2	4	no	—
60	C₁₃×C₄⋊Q₈	—	2	2	no	—
61	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
62	C₁₃×#125	—	2	16	no	—
63	C₁₃×#125	—	2	8	no	—
64	C₄×Q₈×C₁₃	—	2	8	no	—
65	C₄×Q₈×C₁₃	—	2	4	no	—
66	C₄×Q₈×C₁₃	—	2	4	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	D₄	1	4	yes	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
77	C₂×C₁₃×C₄⋊C₄	—	2	2	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	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	D₄	1	2	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
87	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	—	2	2	no	—
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
92	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
93	C₁₃×#107	—	2	2	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×#103	—	2	2	no	—
96	C₁₃×#103	—	2	4	no	—
97	C₁₃×#103	—	2	4	no	—
98	C₁₃×#103	—	2	2	no	—
99	C₁₃×#103	—	4	2	no	—
100	C₁₃×#103	—	4	2	no	—
101	C₄×C₈×C₁₃	—	2	2	no	—
102	C₁₃×#95	—	2	2	no	—
103	C₁₃×#95	—	2	2	no	—
104	C₁₃×#95	—	2	2	no	—
105	#24191	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×Q₈×C₁₃	—	2	2	no	—
108	C₂×Q₈×C₁₃	—	2	2	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	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	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	2	1	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	1	no	—
121	C₂×Q₈×C₁₃	—	2	1	no	—
122	C₂×Q₈×C₁₃	—	2	2	no	—
123	C₂×Q₈×C₁₃	Q₁₆	1	4	yes	complemented
124	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
125	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
126	C₂×Q₈×C₁₃	#41	1	2	yes	—
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	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
133	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
136	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₁₃×Q₁₆	—	2	8	no	—
139	C₁₃×Q₁₆	—	4	8	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	2	no	—
144	C₂×C₈×C₁₃	—	2	2	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	#41	1	2	yes	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	4	no	—
155	C₁₃×C₄⋊C₄	—	2	4	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	4	2	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	8	1	no	—
165	C₁₃×C₄⋊C₄	—	8	2	no	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₄²×C₁₃	—	2	8	no	—
168	C₄²×C₁₃	—	2	4	no	—
169	C₄²×C₁₃	—	2	2	no	—
170	C₄²×C₁₃	—	2	2	no	—
171	C₄²×C₁₃	—	4	2	no	—
172	C₄²×C₁₃	C₂×D₄	1	2	yes	—
173	C₄²×C₁₃	C₂×D₄	1	2	yes	—
174	C₂×#557	C₂×C₁₃	1	1	yes	characteristic
175	C₂×#462	C₂×C₁₃	1	1	yes	characteristic
176	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
177	#2582	C₂×C₁₃	1	1	yes	characteristic
178	#2043	C₂×C₁₃	1	2	yes	—
179	#2016	C₂×C₁₃	1	2	yes	—
180	#1984	C₂×C₁₃	1	1	yes	characteristic
181	#1956	C₂×C₁₃	1	1	yes	characteristic
182	#1878	C₂×C₁₃	1	2	yes	—
183	#1863	C₂×C₁₃	1	2	yes	—
184	#1803	C₂×C₁₃	1	1	yes	characteristic
185	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
186	Q₈×C₁₃	—	2	8	no	—
187	Q₈×C₁₃	—	2	2	no	—
188	Q₈×C₁₃	—	2	2	no	—
189	Q₈×C₁₃	—	2	2	no	—
190	Q₈×C₁₃	—	2	2	no	—
191	Q₈×C₁₃	—	2	4	no	—
192	Q₈×C₁₃	—	2	4	no	—
193	Q₈×C₁₃	—	4	2	no	—
194	Q₈×C₁₃	—	4	2	no	—
195	Q₈×C₁₃	—	4	1	no	—
196	Q₈×C₁₃	—	4	1	no	—
197	Q₈×C₁₃	—	4	1	no	—
198	Q₈×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	2	2	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	2	no	—
205	C₂×C₄×C₁₃	—	2	4	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	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	1	no	—
214	C₂×C₄×C₁₃	—	4	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	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	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	#120	1	2	yes	—
225	C₂×C₄×C₁₃	#120	1	2	yes	—
226	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
227	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
228	C₂×C₄×C₁₃	#137	1	2	yes	—
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
235	C₈×C₁₃	—	2	2	no	—
236	C₈×C₁₃	—	4	1	no	—
237	C₈×C₁₃	—	4	2	no	—
238	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
239	C₂²×Q₁₆	C₂²×C₁₃	1	2	yes	—
240	#557	—	2	4	no	—
241	#557	—	2	4	no	—
242	C₂×C₄⋊Q₈	C₂²×C₁₃	1	2	yes	—
243	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#125	—	2	1	no	—
245	C₂×#125	—	2	2	no	—
246	C₂×C₄×Q₈	—	2	1	no	—
247	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
248	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
249	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
251	#462	—	2	4	no	—
252	C₄×Q₁₆	—	2	4	no	—
253	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
255	C₂×#103	C₂²×C₁₃	1	2	yes	—
256	C₂×#103	C₂²×C₁₃	1	2	yes	—
257	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×#103	C₂²×C₁₃	1	2	yes	—
260	C₂×#103	C₂²×C₁₃	1	2	yes	—
261	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
262	#398	—	2	2	no	—
263	#391	—	2	1	no	—
264	#391	C₂²×C₁₃	1	2	yes	—
265	#389	—	2	1	no	—
266	#389	C₂²×C₁₃	1	2	yes	—
267	#384	C₂²×C₁₃	1	1	yes	characteristic
268	#340	C₂²×C₁₃	1	2	yes	—
269	#336	C₂²×C₁₃	1	2	yes	—
270	#336	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
272	C₂²×C₁₃	#548	1	1	yes	characteristic
273	C₂²×C₁₃	#550	1	1	yes	characteristic
274	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
275	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
276	C₂²×C₁₃	#577	1	1	yes	characteristic
277	C₂²×C₁₃	#578	1	1	yes	characteristic
278	C₄×C₁₃	—	2	4	no	—
279	C₄×C₁₃	—	2	2	no	—
280	C₄×C₁₃	—	4	2	no	—
281	C₄×C₁₃	—	4	4	no	—
282	C₄×C₁₃	—	4	2	no	—
283	C₄×C₁₃	—	4	2	no	—
284	C₄×C₁₃	—	4	2	no	—
285	C₄×C₁₃	—	8	2	no	—
286	C₄×C₁₃	—	8	1	no	—
287	C₄×C₁₃	#451	1	4	yes	—
288	C₄×C₁₃	#525	1	1	yes	characteristic
289	C₄×C₁₃	#537	1	1	yes	characteristic
290	C₄×C₁₃	#546	1	1	yes	characteristic
291	C₄×C₁₃	#547	1	1	yes	characteristic
292	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
293	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
294	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
295	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
296	C₂×Q₁₆	—	2	2	no	—
297	C₂×Q₁₆	—	2	2	no	—
298	C₂×Q₁₆	—	2	4	no	—
299	C₂×Q₁₆	—	2	4	no	—
300	C₂×Q₁₆	—	2	2	no	—
301	C₂×Q₁₆	—	4	2	no	—
302	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
303	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
304	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
305	C₄⋊Q₈	—	2	4	no	—
306	C₄⋊Q₈	—	2	4	no	—
307	C₄⋊Q₈	—	2	2	no	—
308	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
309	#125	—	2	16	no	—
310	#125	—	2	8	no	—
311	C₄×Q₈	—	2	8	no	—
312	C₄×Q₈	—	2	4	no	—
313	C₄×Q₈	—	2	4	no	—
314	C₄×Q₈	—	2	2	no	—
315	C₄×Q₈	—	2	2	no	—
316	C₄×Q₈	—	2	2	no	—
317	C₄×Q₈	—	2	2	no	—
318	C₄×Q₈	—	2	2	no	—
319	C₄×Q₈	D₄×C₁₃	1	4	yes	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	2	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
331	C₂×C₄⋊C₄	D₄×C₁₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
339	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
340	#107	—	2	2	no	—
341	C₄⋊C₈	—	2	2	no	—
342	#103	—	2	2	no	—
343	#103	—	2	4	no	—
344	#103	—	2	4	no	—
345	#103	—	2	2	no	—
346	#103	—	4	2	no	—
347	#103	—	4	2	no	—
348	C₄×C₈	—	2	2	no	—
349	#95	—	2	2	no	—
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	C₂×C₁₃	#2407	1	1	yes	characteristic
353	C₂×C₁₃	C₂×#451	1	1	yes	characteristic
354	C₂×C₁₃	#3013	1	1	yes	characteristic
355	C₂×C₁₃	#3363	1	1	yes	characteristic
356	C₂×C₁₃	#3374	1	1	yes	characteristic
357	C₂×C₁₃	#3395	1	1	yes	characteristic
358	C₂×C₁₃	#3400	1	1	yes	characteristic
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	1	no	—
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	C₁₃×Q₁₆	1	4	yes	complemented
377	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
378	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
379	C₂×Q₈	C₁₃×#41	1	2	yes	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
388	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
390	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
391	Q₁₆	—	2	8	no	—
392	Q₁₆	—	4	8	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	C₁₃×#41	1	2	yes	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	8	1	no	—
418	C₄⋊C₄	—	8	2	no	—
419	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
420	C₄²	—	2	8	no	—
421	C₄²	—	2	4	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	—	4	2	no	—
425	C₄²	C₂×D₄×C₁₃	1	2	yes	—
426	C₄²	C₂×D₄×C₁₃	1	2	yes	—
427	C₁₃	#24191	1	1	yes	characteristic, direct product factor, Sylow
428	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	Q₈	—	2	8	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	2	2	no	—
433	Q₈	—	2	2	no	—
434	Q₈	—	2	4	no	—
435	Q₈	—	2	4	no	—
436	Q₈	—	4	2	no	—
437	Q₈	—	4	2	no	—
438	Q₈	—	4	1	no	—
439	Q₈	—	4	1	no	—
440	Q₈	—	4	1	no	—
441	Q₈	—	4	1	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	C₁₃×#120	1	2	yes	—
468	C₂×C₄	C₁₃×#120	1	2	yes	—
469	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
470	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
471	C₂×C₄	C₁₃×#137	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
474	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
475	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
476	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
478	C₈	—	2	2	no	—
479	C₈	—	4	1	no	—
480	C₈	—	4	2	no	—
481	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
482	C₂²	C₁₃×#548	1	1	yes	characteristic
483	C₂²	C₁₃×#550	1	1	yes	characteristic
484	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
485	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
486	C₂²	C₁₃×#577	1	1	yes	characteristic
487	C₂²	C₁₃×#578	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	2	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	2	no	—
497	C₄	C₁₃×#451	1	4	yes	—
498	C₄	C₁₃×#525	1	1	yes	characteristic
499	C₄	C₁₃×#537	1	1	yes	characteristic
500	C₄	C₁₃×#546	1	1	yes	characteristic
501	C₄	C₁₃×#547	1	1	yes	characteristic
502	C₂	C₁₃×#2407	1	1	yes	characteristic
503	C₂	C₂×C₁₃×#451	1	1	yes	characteristic
504	C₂	C₁₃×#3013	1	1	yes	characteristic
505	C₂	C₁₃×#3363	1	1	yes	characteristic
506	C₂	C₁₃×#3374	1	1	yes	characteristic
507	C₂	C₁₃×#3395	1	1	yes	characteristic
508	C₂	C₁₃×#3400	1	1	yes	characteristic

	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. #24191	C₁₃	direct (N × H)
123. C₂×Q₈×C₁₃	Q₁₆	semidirect
376. C₂×Q₈	C₁₃×Q₁₆	semidirect
427. C₁₃	#24191	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×#557	2
C₂×C₁₃×#462	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2582	2
C₁₃×#2043	2
C₁₃×#2016	2
C₁₃×#1984	2
C₁₃×#1956	2
C₁₃×#1878	2
C₁₃×#1863	2
C₁₃×#1803	2
#24191	13

Subgroups — C13×#24191 #15710530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24191 #15710530