Subgroups — C₁₃×#24817 #15711156

Order 3328.

806 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#477	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2567	C₂	1	1	yes	maximal, characteristic
4	Q₈×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2083	C₂	1	2	yes	maximal
6	C₁₃×#2068	C₂	1	2	yes	maximal
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1939	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1878	C₂	1	2	yes	maximal
10	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1803	C₂	1	2	yes	maximal
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
17	C₁₃×#477	—	2	4	no	—
18	C₄×C₁₃×Q₁₆	—	2	4	no	—
19	C₂×C₁₃×#107	C₂²	1	2	yes	—
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂×C₁₃×#103	C₂²	1	2	yes	—
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	2	yes	—
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#395	—	2	2	no	—
29	C₁₃×#391	C₂²	1	2	yes	—
30	C₁₃×#389	—	2	1	no	—
31	C₁₃×#389	—	2	1	no	—
32	C₁₃×#389	—	2	2	no	—
33	C₁₃×#389	C₂²	1	2	yes	—
34	C₁₃×#384	—	2	1	no	—
35	C₁₃×#384	C₂²	1	1	yes	characteristic
36	C₁₃×#384	C₂²	1	2	yes	—
37	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
38	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
44	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
45	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
46	C₂×C₁₃×Q₁₆	—	2	2	no	—
47	C₂×C₁₃×Q₁₆	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	Q₈	1	4	yes	complemented
49	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
51	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	—	2	2	no	—
53	C₁₃×C₄⋊Q₈	—	2	2	no	—
54	C₄×Q₈×C₁₃	—	2	2	no	—
55	C₄×Q₈×C₁₃	—	2	4	no	—
56	C₄×Q₈×C₁₃	—	2	2	no	—
57	C₄×Q₈×C₁₃	—	2	2	no	—
58	C₄×Q₈×C₁₃	—	4	2	no	—
59	C₄×Q₈×C₁₃	D₄	1	4	yes	—
60	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
61	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
62	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₃	—	2	1	no	—
76	C₂×C₄²×C₁₃	—	2	2	no	—
77	C₂×C₄²×C₁₃	—	2	1	no	—
78	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
80	C₁₃×#107	—	2	2	no	—
81	C₁₃×#107	—	2	4	no	—
82	C₁₃×C₄⋊C₈	—	2	2	no	—
83	C₁₃×C₄⋊C₈	—	4	2	no	—
84	C₁₃×#103	—	2	2	no	—
85	C₁₃×#103	—	2	4	no	—
86	C₁₃×#103	—	2	2	no	—
87	C₁₃×#103	—	4	2	no	—
88	C₄×C₈×C₁₃	—	2	2	no	—
89	C₁₃×#95	—	2	2	no	—
90	C₁₃×#95	—	2	2	no	—
91	C₁₃×#95	—	2	2	no	—
92	C₁₃×#95	D₄	1	2	yes	—
93	#24817	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	1	no	—
100	C₂×Q₈×C₁₃	—	2	1	no	—
101	C₂×Q₈×C₁₃	—	2	1	no	—
102	C₂×Q₈×C₁₃	—	4	2	no	—
103	C₂×Q₈×C₁₃	—	8	1	no	—
104	C₂×Q₈×C₁₃	—	8	1	no	—
105	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
106	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
107	C₂×Q₈×C₁₃	C₂×Q₈	1	2	yes	—
108	C₂×Q₈×C₁₃	#41	1	2	yes	—
109	C₂²×C₄×C₁₃	—	2	1	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	2	no	—
113	C₂²×C₄×C₁₃	—	2	2	no	—
114	C₂²×C₄×C₁₃	—	2	1	no	—
115	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₁₃×Q₁₆	—	2	8	no	—
121	C₂×C₈×C₁₃	—	2	1	no	—
122	C₂×C₈×C₁₃	—	2	1	no	—
123	C₂×C₈×C₁₃	—	2	1	no	—
124	C₂×C₈×C₁₃	—	2	2	no	—
125	C₂×C₈×C₁₃	—	2	2	no	—
126	C₂×C₈×C₁₃	—	2	1	no	—
127	C₂×C₈×C₁₃	—	2	1	no	—
128	C₂×C₈×C₁₃	—	2	2	no	—
129	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
130	C₁₃×C₄⋊C₄	—	2	4	no	—
131	C₁₃×C₄⋊C₄	—	2	2	no	—
132	C₁₃×C₄⋊C₄	—	2	1	no	—
133	C₁₃×C₄⋊C₄	—	2	1	no	—
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₄⋊C₄	—	2	1	no	—
136	C₁₃×C₄⋊C₄	—	2	2	no	—
137	C₁₃×C₄⋊C₄	—	2	2	no	—
138	C₁₃×C₄⋊C₄	—	2	2	no	—
139	C₁₃×C₄⋊C₄	—	4	4	no	—
140	C₁₃×C₄⋊C₄	—	4	2	no	—
141	C₁₃×C₄⋊C₄	—	4	2	no	—
142	C₁₃×C₄⋊C₄	—	4	2	no	—
143	C₁₃×C₄⋊C₄	—	8	1	no	—
144	C₁₃×C₄⋊C₄	—	8	2	no	—
145	C₁₃×C₄⋊C₄	—	8	2	no	—
146	C₁₃×C₄⋊C₄	—	8	2	no	—
147	C₁₃×C₄⋊C₄	Q₁₆	1	4	yes	complemented
148	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
149	C₄²×C₁₃	—	2	4	no	—
150	C₄²×C₁₃	—	2	2	no	—
151	C₄²×C₁₃	—	2	2	no	—
152	C₄²×C₁₃	—	4	4	no	—
153	C₄²×C₁₃	—	4	2	no	—
154	C₄²×C₁₃	C₂×D₄	1	2	yes	—
155	C₄²×C₁₃	#41	1	2	yes	—
156	C₂×#477	C₂×C₁₃	1	1	yes	characteristic
157	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic
158	#2567	C₂×C₁₃	1	1	yes	characteristic
159	Q₈×C₄⋊C₄	C₂×C₁₃	1	1	yes	characteristic
160	#2083	C₂×C₁₃	1	2	yes	—
161	#2068	C₂×C₁₃	1	2	yes	—
162	#1990	C₂×C₁₃	1	1	yes	characteristic
163	#1939	C₂×C₁₃	1	1	yes	characteristic
164	#1878	C₂×C₁₃	1	2	yes	—
165	#1803	C₂×C₁₃	1	1	yes	characteristic
166	#1803	C₂×C₁₃	1	2	yes	—
167	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₁₃	—	2	2	no	—
169	Q₈×C₁₃	—	2	2	no	—
170	Q₈×C₁₃	—	2	2	no	—
171	Q₈×C₁₃	—	2	2	no	—
172	Q₈×C₁₃	—	2	2	no	—
173	Q₈×C₁₃	—	4	1	no	—
174	Q₈×C₁₃	—	4	1	no	—
175	Q₈×C₁₃	—	8	4	no	—
176	Q₈×C₁₃	C₂²⋊Q₈	1	4	yes	—
177	C₂×C₄×C₁₃	—	2	2	no	—
178	C₂×C₄×C₁₃	—	2	2	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	2	1	no	—
182	C₂×C₄×C₁₃	—	2	2	no	—
183	C₂×C₄×C₁₃	—	2	1	no	—
184	C₂×C₄×C₁₃	—	2	2	no	—
185	C₂×C₄×C₁₃	—	2	2	no	—
186	C₂×C₄×C₁₃	—	2	2	no	—
187	C₂×C₄×C₁₃	—	2	2	no	—
188	C₂×C₄×C₁₃	—	2	2	no	—
189	C₂×C₄×C₁₃	—	4	1	no	—
190	C₂×C₄×C₁₃	—	4	1	no	—
191	C₂×C₄×C₁₃	—	4	1	no	—
192	C₂×C₄×C₁₃	—	4	1	no	—
193	C₂×C₄×C₁₃	—	4	1	no	—
194	C₂×C₄×C₁₃	—	4	2	no	—
195	C₂×C₄×C₁₃	—	4	2	no	—
196	C₂×C₄×C₁₃	—	4	2	no	—
197	C₂×C₄×C₁₃	—	4	2	no	—
198	C₂×C₄×C₁₃	—	4	1	no	—
199	C₂×C₄×C₁₃	—	4	2	no	—
200	C₂×C₄×C₁₃	—	4	1	no	—
201	C₂×C₄×C₁₃	—	4	2	no	—
202	C₂×C₄×C₁₃	#121	1	2	yes	—
203	C₂×C₄×C₁₃	#121	1	2	yes	—
204	C₂×C₄×C₁₃	C₂×Q₁₆	1	4	yes	—
205	C₂×C₄×C₁₃	C₂×Q₁₆	1	2	yes	—
206	C₂×C₄×C₁₃	#137	1	2	yes	—
207	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
209	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
212	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
213	C₈×C₁₃	—	2	2	no	—
214	C₈×C₁₃	—	4	1	no	—
215	C₈×C₁₃	—	4	2	no	—
216	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
217	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
218	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	—
220	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
221	#477	—	2	4	no	—
222	C₄×Q₁₆	—	2	4	no	—
223	C₂×#107	C₂²×C₁₃	1	2	yes	—
224	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₁₃	1	2	yes	—
227	C₂×#103	C₂²×C₁₃	1	2	yes	—
228	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
229	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
230	C₂×#103	C₂²×C₁₃	1	2	yes	—
231	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
232	#395	—	2	2	no	—
233	#391	C₂²×C₁₃	1	2	yes	—
234	#389	—	2	1	no	—
235	#389	—	2	1	no	—
236	#389	—	2	2	no	—
237	#389	C₂²×C₁₃	1	2	yes	—
238	#384	—	2	1	no	—
239	#384	C₂²×C₁₃	1	2	yes	—
240	#384	C₂²×C₁₃	1	1	yes	characteristic
241	C₄×C₄⋊C₄	—	2	1	no	—
242	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
243	#340	C₂²×C₁₃	1	2	yes	—
244	#340	C₂²×C₁₃	1	2	yes	—
245	#340	C₂²×C₁₃	1	2	yes	—
246	#336	C₂²×C₁₃	1	2	yes	—
247	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
248	C₂²×C₁₃	#546	1	1	yes	characteristic
249	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
250	C₂²×C₁₃	C₂²×Q₁₆	1	1	yes	characteristic
251	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
252	C₂²×C₁₃	#576	1	1	yes	characteristic
253	C₂²×C₁₃	#577	1	1	yes	characteristic
254	C₄×C₁₃	—	2	4	no	—
255	C₄×C₁₃	—	2	4	no	—
256	C₄×C₁₃	—	2	2	no	—
257	C₄×C₁₃	—	4	2	no	—
258	C₄×C₁₃	—	4	2	no	—
259	C₄×C₁₃	—	4	2	no	—
260	C₄×C₁₃	—	8	2	no	—
261	C₄×C₁₃	—	8	1	no	—
262	C₄×C₁₃	—	8	2	no	—
263	C₄×C₁₃	#462	1	4	yes	—
264	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
265	C₄×C₁₃	#537	1	1	yes	characteristic
266	C₄×C₁₃	#552	1	1	yes	characteristic
267	C₄×C₁₃	#554	1	1	yes	characteristic
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
270	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
271	C₂×Q₁₆	—	2	2	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×Q₁₆	Q₈×C₁₃	1	4	yes	complemented
274	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
275	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄×Q₈	—	2	2	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	—	2	2	no	—
282	C₄×Q₈	—	2	2	no	—
283	C₄×Q₈	—	4	2	no	—
284	C₄×Q₈	D₄×C₁₃	1	4	yes	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	2	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
295	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	2	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
304	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
305	#107	—	2	2	no	—
306	#107	—	2	4	no	—
307	C₄⋊C₈	—	2	2	no	—
308	C₄⋊C₈	—	4	2	no	—
309	#103	—	2	2	no	—
310	#103	—	2	4	no	—
311	#103	—	2	2	no	—
312	#103	—	4	2	no	—
313	C₄×C₈	—	2	2	no	—
314	#95	—	2	2	no	—
315	#95	—	2	2	no	—
316	#95	—	2	2	no	—
317	#95	D₄×C₁₃	1	2	yes	—
318	C₂×C₁₃	#2417	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#462	1	1	yes	characteristic
320	C₂×C₁₃	#3045	1	1	yes	characteristic
321	C₂×C₁₃	#3299	1	1	yes	characteristic
322	C₂×C₁₃	#3333	1	1	yes	characteristic
323	C₂×C₁₃	Q₈×Q₁₆	1	1	yes	characteristic
324	C₂×C₁₃	#3387	1	1	yes	characteristic
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	4	2	no	—
334	C₂×Q₈	—	8	1	no	—
335	C₂×Q₈	—	8	1	no	—
336	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
337	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
338	C₂×Q₈	C₂×Q₈×C₁₃	1	2	yes	—
339	C₂×Q₈	C₁₃×#41	1	2	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
351	Q₁₆	—	2	8	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	1	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	1	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₄⋊C₄	—	4	2	no	—
373	C₄⋊C₄	—	4	2	no	—
374	C₄⋊C₄	—	8	1	no	—
375	C₄⋊C₄	—	8	2	no	—
376	C₄⋊C₄	—	8	2	no	—
377	C₄⋊C₄	—	8	2	no	—
378	C₄⋊C₄	C₁₃×Q₁₆	1	4	yes	complemented
379	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
380	C₄²	—	2	4	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	2	no	—
383	C₄²	—	4	4	no	—
384	C₄²	—	4	2	no	—
385	C₄²	C₂×D₄×C₁₃	1	2	yes	—
386	C₄²	C₁₃×#41	1	2	yes	—
387	C₁₃	#24817	1	1	yes	characteristic, direct product factor, Sylow
388	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
389	Q₈	—	2	2	no	—
390	Q₈	—	2	2	no	—
391	Q₈	—	2	2	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	2	2	no	—
394	Q₈	—	4	1	no	—
395	Q₈	—	4	1	no	—
396	Q₈	—	8	4	no	—
397	Q₈	C₁₃×C₂²⋊Q₈	1	4	yes	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	C₁₃×#121	1	2	yes	—
424	C₂×C₄	C₁₃×#121	1	2	yes	—
425	C₂×C₄	C₂×C₁₃×Q₁₆	1	4	yes	—
426	C₂×C₄	C₂×C₁₃×Q₁₆	1	2	yes	—
427	C₂×C₄	C₁₃×#137	1	2	yes	—
428	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
429	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
431	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
432	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
433	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	2	no	—
437	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
438	C₂²	C₁₃×#546	1	1	yes	characteristic
439	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
440	C₂²	C₂²×C₁₃×Q₁₆	1	1	yes	characteristic
441	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
442	C₂²	C₁₃×#576	1	1	yes	characteristic
443	C₂²	C₁₃×#577	1	1	yes	characteristic
444	C₄	—	2	4	no	—
445	C₄	—	2	2	no	—
446	C₄	—	2	4	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	2	no	—
449	C₄	—	4	2	no	—
450	C₄	—	8	1	no	—
451	C₄	—	8	2	no	—
452	C₄	—	8	2	no	—
453	C₄	C₁₃×#462	1	4	yes	—
454	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
455	C₄	C₁₃×#537	1	1	yes	characteristic
456	C₄	C₁₃×#552	1	1	yes	characteristic
457	C₄	C₁₃×#554	1	1	yes	characteristic
458	C₂	C₁₃×#2417	1	1	yes	characteristic
459	C₂	C₂×C₁₃×#462	1	1	yes	characteristic
460	C₂	C₁₃×#3045	1	1	yes	characteristic
461	C₂	C₁₃×#3299	1	1	yes	characteristic
462	C₂	C₁₃×#3333	1	1	yes	characteristic
463	C₂	Q₈×C₁₃×Q₁₆	1	1	yes	characteristic
464	C₂	C₁₃×#3387	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 ◁ C₄×C₁₃×C₄⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
48. C₂×C₁₃×Q₁₆	Q₈	semidirect
93. #24817	C₁₃	direct (N × H)
147. C₁₃×C₄⋊C₄	Q₁₆	semidirect
273. C₂×Q₁₆	Q₈×C₁₃	semidirect
378. C₄⋊C₄	C₁₃×Q₁₆	semidirect
387. C₁₃	#24817	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×#477	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2567	2
Q₈×C₁₃×C₄⋊C₄	2
C₁₃×#2083	2
C₁₃×#2068	2
C₁₃×#1990	2
C₁₃×#1939	2
C₁₃×#1878	2
C₁₃×#1803	2
#24817	13

Subgroups — C13×#24817 #15711156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24817 #15711156