Subgroups — C₁₃×#22437 #15708776

Order 3328.

1602 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₁₃×SD₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#440	C₂	1	2	yes	maximal, complemented
3	Q₈×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₃×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#1973	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1880	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1877	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1787	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₃	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
14	C₂²×C₁₃×SD₁₆	—	2	8	no	—
15	C₂²×C₁₃×SD₁₆	C₄	1	8	yes	complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
21	C₂×C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
22	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	—
23	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
24	C₁₃×#440	—	2	8	no	—
25	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
26	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
28	C₂×C₁₃×#102	C₂²	1	2	yes	—
29	C₂×C₁₃×#102	C₂²	1	2	yes	—
30	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
32	C₁₃×#391	—	2	2	no	—
33	C₁₃×#391	C₂²	1	2	yes	complemented
34	C₁₃×#390	C₂²	1	2	yes	—
35	C₁₃×#386	—	2	2	no	—
36	C₁₃×#380	—	2	1	no	—
37	C₁₃×#380	C₂²	1	1	yes	characteristic
38	C₁₃×#380	C₂²	1	1	yes	characteristic
39	C₁₃×#379	—	2	1	no	—
40	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
41	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
42	C₁₃×#340	C₂²	1	2	yes	complemented
43	C₁₃×#336	C₂²	1	2	yes	complemented
44	C₂⁵×C₁₃	—	2	1	no	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	—	2	2	no	—
47	C₂²×Q₈×C₁₃	—	2	4	no	—
48	C₂²×Q₈×C₁₃	—	4	2	no	—
49	C₂²×Q₈×C₁₃	C₂×C₄	1	4	yes	complemented
50	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
51	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₁₃	—	2	4	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	2	2	no	—
55	C₂²×D₄×C₁₃	—	4	2	no	—
56	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	—
57	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	—	2	1	no	—
60	C₂³×C₄×C₁₃	—	2	2	no	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂×C₁₃×SD₁₆	—	2	4	no	—
63	C₂×C₁₃×SD₁₆	—	2	4	no	—
64	C₂×C₁₃×SD₁₆	—	2	32	no	—
65	C₂×C₁₃×SD₁₆	—	2	4	no	—
66	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
67	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	—
68	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	complemented
69	C₂×C₁₃×SD₁₆	C₂×C₄	1	4	yes	complemented
70	C₂×C₁₃×SD₁₆	D₄	1	8	yes	—
71	C₂²×C₈×C₁₃	—	2	4	no	—
72	C₂²×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
73	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₄×Q₈×C₁₃	—	2	4	no	—
77	C₄×Q₈×C₁₃	—	4	2	no	—
78	C₄×D₄×C₁₃	—	2	4	no	—
79	C₄×D₄×C₁₃	—	4	2	no	—
80	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
89	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
90	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	—	2	2	no	—
92	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
93	C₁₃×#107	—	2	4	no	—
94	C₁₃×#103	—	2	4	no	—
95	C₁₃×#103	—	4	2	no	—
96	C₁₃×#102	—	2	4	no	—
97	C₁₃×#102	—	4	2	no	—
98	C₁₃×C₂²⋊C₈	—	2	2	no	—
99	C₁₃×#97	—	2	4	no	—
100	C₁₃×#95	—	2	2	no	—
101	C₁₃×#95	—	2	2	no	—
102	C₁₃×#95	—	2	1	no	—
103	C₁₃×#95	—	2	1	no	—
104	C₁₃×#95	D₄	1	2	yes	—
105	#22437	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	—	2	1	no	—
107	C₂⁴×C₁₃	—	2	1	no	—
108	C₂⁴×C₁₃	—	2	4	no	—
109	C₂⁴×C₁₃	—	4	4	no	—
110	C₂⁴×C₁₃	—	4	2	no	—
111	C₂⁴×C₁₃	—	4	2	no	—
112	C₂⁴×C₁₃	—	8	2	no	—
113	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
114	C₂×Q₈×C₁₃	—	2	4	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	2	no	—
118	C₂×Q₈×C₁₃	—	2	8	no	—
119	C₂×Q₈×C₁₃	—	2	2	no	—
120	C₂×Q₈×C₁₃	—	2	2	no	—
121	C₂×Q₈×C₁₃	—	4	4	no	—
122	C₂×Q₈×C₁₃	—	4	4	no	—
123	C₂×Q₈×C₁₃	—	4	8	no	—
124	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
125	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
126	C₂×Q₈×C₁₃	C₂×D₄	1	4	yes	—
127	C₂×D₄×C₁₃	—	2	8	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	2	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	4	4	no	—
135	C₂×D₄×C₁₃	—	4	8	no	—
136	C₂×D₄×C₁₃	—	4	4	no	—
137	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
138	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
139	C₂×D₄×C₁₃	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	2	no	—
142	C₂²×C₄×C₁₃	—	2	2	no	—
143	C₂²×C₄×C₁₃	—	2	4	no	—
144	C₂²×C₄×C₁₃	—	2	1	no	—
145	C₂²×C₄×C₁₃	—	2	2	no	—
146	C₂²×C₄×C₁₃	—	2	2	no	—
147	C₂²×C₄×C₁₃	—	4	4	no	—
148	C₂²×C₄×C₁₃	—	4	4	no	—
149	C₂²×C₄×C₁₃	—	4	4	no	—
150	C₂²×C₄×C₁₃	—	8	2	no	—
151	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	#41	1	2	yes	—
156	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
157	C₁₃×SD₁₆	—	2	8	no	—
158	C₁₃×SD₁₆	—	2	8	no	—
159	C₁₃×SD₁₆	—	2	8	no	—
160	C₁₃×SD₁₆	C₂²⋊C₄	1	16	yes	complemented
161	C₂×C₈×C₁₃	—	2	2	no	—
162	C₂×C₈×C₁₃	—	2	8	no	—
163	C₂×C₈×C₁₃	—	2	2	no	—
164	C₂×C₈×C₁₃	—	2	2	no	—
165	C₂×C₈×C₁₃	—	2	2	no	—
166	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
169	C₁₃×C₄⋊C₄	—	2	2	no	—
170	C₁₃×C₄⋊C₄	—	2	2	no	—
171	C₁₃×C₄⋊C₄	—	2	2	no	—
172	C₁₃×C₄⋊C₄	—	2	2	no	—
173	C₁₃×C₄⋊C₄	—	4	4	no	—
174	C₁₃×C₂²⋊C₄	—	2	2	no	—
175	C₁₃×C₂²⋊C₄	—	2	2	no	—
176	C₁₃×C₂²⋊C₄	—	4	4	no	—
177	C₁₃×C₂²⋊C₄	—	4	4	no	—
178	C₁₃×C₂²⋊C₄	—	4	2	no	—
179	C₁₃×C₂²⋊C₄	—	4	2	no	—
180	C₁₃×C₂²⋊C₄	—	8	2	no	—
181	C₄²×C₁₃	—	2	2	no	—
182	C₄²×C₁₃	—	2	2	no	—
183	C₄²×C₁₃	—	4	4	no	—
184	C₂³×SD₁₆	C₂×C₁₃	1	1	yes	characteristic
185	C₂×#440	C₂×C₁₃	1	2	yes	complemented
186	Q₈×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic, complemented
187	D₄×C₂²⋊C₄	C₂×C₁₃	1	1	yes	characteristic
188	#1973	C₂×C₁₃	1	2	yes	complemented
189	#1880	C₂×C₁₃	1	2	yes	complemented
190	#1877	C₂×C₁₃	1	2	yes	complemented
191	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#1787	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1786	C₂×C₁₃	1	1	yes	characteristic
194	#1752	C₂×C₁₃	1	1	yes	characteristic, complemented
195	C₂³×C₁₃	—	2	2	no	—
196	C₂³×C₁₃	—	2	2	no	—
197	C₂³×C₁₃	—	2	2	no	—
198	C₂³×C₁₃	—	2	4	no	—
199	C₂³×C₁₃	—	2	2	no	—
200	C₂³×C₁₃	—	4	8	no	—
201	C₂³×C₁₃	—	4	1	no	—
202	C₂³×C₁₃	—	4	1	no	—
203	C₂³×C₁₃	—	4	2	no	—
204	C₂³×C₁₃	—	4	2	no	—
205	C₂³×C₁₃	—	4	1	no	—
206	C₂³×C₁₃	—	4	1	no	—
207	C₂³×C₁₃	—	4	2	no	—
208	C₂³×C₁₃	—	4	8	no	—
209	C₂³×C₁₃	—	8	4	no	—
210	C₂³×C₁₃	—	8	8	no	—
211	C₂³×C₁₃	—	8	8	no	—
212	C₂³×C₁₃	C₄×D₄	1	2	yes	—
213	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
214	C₂³×C₁₃	#137	1	2	yes	—
215	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
216	Q₈×C₁₃	—	2	2	no	—
217	Q₈×C₁₃	—	2	4	no	—
218	Q₈×C₁₃	—	2	2	no	—
219	Q₈×C₁₃	—	2	2	no	—
220	Q₈×C₁₃	—	4	8	no	—
221	Q₈×C₁₃	—	4	2	no	—
222	Q₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	complemented
223	D₄×C₁₃	—	2	2	no	—
224	D₄×C₁₃	—	2	2	no	—
225	D₄×C₁₃	—	2	2	no	—
226	D₄×C₁₃	—	2	4	no	—
227	D₄×C₁₃	—	4	8	no	—
228	D₄×C₁₃	—	4	2	no	—
229	D₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	—	2	4	no	—
232	C₂×C₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	2	2	no	—
234	C₂×C₄×C₁₃	—	2	2	no	—
235	C₂×C₄×C₁₃	—	2	4	no	—
236	C₂×C₄×C₁₃	—	2	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	4	8	no	—
244	C₂×C₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	4	2	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	—	4	2	no	—
250	C₂×C₄×C₁₃	—	4	2	no	—
251	C₂×C₄×C₁₃	—	8	8	no	—
252	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
257	C₈×C₁₃	—	2	2	no	—
258	C₈×C₁₃	—	4	2	no	—
259	C₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	complemented
260	C₂³×Q₈	C₂²×C₁₃	1	1	yes	characteristic
261	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
262	C₂²×SD₁₆	—	2	8	no	—
263	C₂²×SD₁₆	C₄×C₁₃	1	8	yes	complemented
264	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
266	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
267	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
268	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₄×Q₈	C₂²×C₁₃	1	2	yes	complemented
270	C₂×C₄×D₄	C₂²×C₁₃	1	2	yes	—
271	C₂²×C₂²⋊C₄	—	2	1	no	—
272	#440	—	2	8	no	—
273	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
274	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
275	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
276	C₂×#102	C₂²×C₁₃	1	2	yes	—
277	C₂×#102	C₂²×C₁₃	1	2	yes	—
278	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
280	#391	—	2	2	no	—
281	#391	C₂²×C₁₃	1	2	yes	complemented
282	#390	C₂²×C₁₃	1	2	yes	—
283	#386	—	2	2	no	—
284	#380	—	2	1	no	—
285	#380	C₂²×C₁₃	1	1	yes	characteristic
286	#380	C₂²×C₁₃	1	1	yes	characteristic
287	#379	—	2	1	no	—
288	C₄×C₂²⋊C₄	—	2	1	no	—
289	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
290	#340	C₂²×C₁₃	1	2	yes	complemented
291	#336	C₂²×C₁₃	1	2	yes	complemented
292	C₂²×C₁₃	—	2	2	no	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	2	4	no	—
295	C₂²×C₁₃	—	2	4	no	—
296	C₂²×C₁₃	—	2	4	no	—
297	C₂²×C₁₃	—	4	2	no	—
298	C₂²×C₁₃	—	4	2	no	—
299	C₂²×C₁₃	—	4	4	no	—
300	C₂²×C₁₃	—	4	4	no	—
301	C₂²×C₁₃	—	4	2	no	—
302	C₂²×C₁₃	—	4	2	no	—
303	C₂²×C₁₃	—	4	2	no	—
304	C₂²×C₁₃	—	8	16	no	—
305	C₂²×C₁₃	—	8	2	no	—
306	C₂²×C₁₃	—	8	2	no	—
307	C₂²×C₁₃	#440	1	4	yes	complemented
308	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₁₃	D₄²	1	2	yes	—
310	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
311	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
312	C₂²×C₁₃	#577	1	2	yes	—
313	C₄×C₁₃	—	2	2	no	—
314	C₄×C₁₃	—	2	4	no	—
315	C₄×C₁₃	—	4	2	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	2	no	—
318	C₄×C₁₃	—	8	2	no	—
319	C₄×C₁₃	—	8	2	no	—
320	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
321	C₄×C₁₃	#518	1	1	yes	characteristic
322	C₄×C₁₃	#546	1	2	yes	—
323	C₂⁵	—	2	1	no	—
324	C₂²×Q₈	—	2	1	no	—
325	C₂²×Q₈	—	2	2	no	—
326	C₂²×Q₈	—	2	4	no	—
327	C₂²×Q₈	—	4	2	no	—
328	C₂²×Q₈	C₂×C₄×C₁₃	1	4	yes	complemented
329	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
330	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
331	C₂²×D₄	—	2	4	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	—	2	2	no	—
334	C₂²×D₄	—	4	2	no	—
335	C₂²×D₄	C₂×C₄×C₁₃	1	4	yes	—
336	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
337	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂³×C₄	—	2	1	no	—
339	C₂³×C₄	—	2	2	no	—
340	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	2	4	no	—
343	C₂×SD₁₆	—	2	32	no	—
344	C₂×SD₁₆	—	2	4	no	—
345	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
346	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	—
347	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
348	C₂×SD₁₆	C₂×C₄×C₁₃	1	4	yes	complemented
349	C₂×SD₁₆	D₄×C₁₃	1	8	yes	—
350	C₂²×C₈	—	2	4	no	—
351	C₂²×C₈	C₂×C₄×C₁₃	1	4	yes	complemented
352	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
353	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
355	C₄×Q₈	—	2	4	no	—
356	C₄×Q₈	—	4	2	no	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	—	4	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₂²⋊C₄	—	2	2	no	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	4	4	no	—
368	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
370	C₂×C₄²	—	2	2	no	—
371	C₂×C₄²	C₂³×C₁₃	1	2	yes	—
372	#107	—	2	4	no	—
373	#103	—	2	4	no	—
374	#103	—	4	2	no	—
375	#102	—	2	4	no	—
376	#102	—	4	2	no	—
377	C₂²⋊C₈	—	2	2	no	—
378	#97	—	2	4	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	D₄×C₁₃	1	2	yes	—
384	C₂×C₁₃	—	2	4	no	—
385	C₂×C₁₃	—	4	4	no	—
386	C₂×C₁₃	—	8	2	no	—
387	C₂×C₁₃	D₄×C₂²⋊C₄	1	1	yes	characteristic
388	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
389	C₂×C₁₃	#2949	1	1	yes	characteristic
390	C₂×C₁₃	#3265	1	2	yes	—
391	C₂×C₁₃	#3266	1	2	yes	—
392	C₂⁴	—	2	1	no	—
393	C₂⁴	—	2	1	no	—
394	C₂⁴	—	2	4	no	—
395	C₂⁴	—	4	4	no	—
396	C₂⁴	—	4	2	no	—
397	C₂⁴	—	4	2	no	—
398	C₂⁴	—	8	2	no	—
399	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
400	C₂×Q₈	—	2	4	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	—	4	4	no	—
408	C₂×Q₈	—	4	4	no	—
409	C₂×Q₈	—	4	8	no	—
410	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
411	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
412	C₂×Q₈	C₂×D₄×C₁₃	1	4	yes	—
413	C₂×D₄	—	2	8	no	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	—	4	8	no	—
422	C₂×D₄	—	4	4	no	—
423	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
424	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
425	C₂×D₄	C₂×D₄×C₁₃	1	4	yes	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	2	no	—
433	C₂²×C₄	—	4	4	no	—
434	C₂²×C₄	—	4	4	no	—
435	C₂²×C₄	—	4	4	no	—
436	C₂²×C₄	—	8	2	no	—
437	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
438	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
439	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
440	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
441	C₂²×C₄	C₁₃×#41	1	2	yes	—
442	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
443	SD₁₆	—	2	8	no	—
444	SD₁₆	—	2	8	no	—
445	SD₁₆	—	2	8	no	—
446	SD₁₆	C₁₃×C₂²⋊C₄	1	16	yes	complemented
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	2	8	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
453	C₂×C₈	C₂²×C₄×C₁₃	1	2	yes	—
454	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
455	C₄⋊C₄	—	2	2	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	4	4	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₂²⋊C₄	—	4	4	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	8	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	—	2	2	no	—
469	C₄²	—	4	4	no	—
470	C₁₃	#22437	1	1	yes	characteristic, direct product factor, Sylow
471	C₂³	—	2	2	no	—
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	4	8	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	8	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	2	no	—
485	C₂³	—	8	4	no	—
486	C₂³	—	8	8	no	—
487	C₂³	—	8	8	no	—
488	C₂³	C₄×D₄×C₁₃	1	2	yes	—
489	C₂³	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
490	C₂³	C₁₃×#137	1	2	yes	—
491	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
492	Q₈	—	2	2	no	—
493	Q₈	—	2	4	no	—
494	Q₈	—	2	2	no	—
495	Q₈	—	2	2	no	—
496	Q₈	—	4	8	no	—
497	Q₈	—	4	2	no	—
498	Q₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	complemented
499	D₄	—	2	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	2	no	—
502	D₄	—	2	4	no	—
503	D₄	—	4	8	no	—
504	D₄	—	4	2	no	—
505	D₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	4	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	4	8	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	2	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	8	8	no	—
528	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
529	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
530	C₂×C₄	C₂²×D₄×C₁₃	1	2	yes	—
531	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
532	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
533	C₈	—	2	2	no	—
534	C₈	—	4	2	no	—
535	C₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	complemented
536	C₂²	—	2	4	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	2	no	—
539	C₂²	—	2	2	no	—
540	C₂²	—	2	4	no	—
541	C₂²	—	4	4	no	—
542	C₂²	—	4	4	no	—
543	C₂²	—	4	2	no	—
544	C₂²	—	4	2	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	8	16	no	—
549	C₂²	—	8	2	no	—
550	C₂²	—	8	2	no	—
551	C₂²	C₁₃×#440	1	4	yes	complemented
552	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
553	C₂²	D₄²×C₁₃	1	2	yes	—
554	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
555	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
556	C₂²	C₁₃×#577	1	2	yes	—
557	C₄	—	2	2	no	—
558	C₄	—	2	4	no	—
559	C₄	—	4	2	no	—
560	C₄	—	4	2	no	—
561	C₄	—	4	2	no	—
562	C₄	—	8	2	no	—
563	C₄	—	8	2	no	—
564	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
565	C₄	C₁₃×#518	1	1	yes	characteristic
566	C₄	C₁₃×#546	1	2	yes	—
567	C₂	—	2	4	no	—
568	C₂	—	4	4	no	—
569	C₂	—	8	2	no	—
570	C₂	D₄×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
571	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
572	C₂	C₁₃×#2949	1	1	yes	characteristic
573	C₂	C₁₃×#3265	1	2	yes	—
574	C₂	C₁₃×#3266	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#440	C₂	semidirect
3. Q₈×C₁₃×C₂²⋊C₄	C₂	semidirect
5. C₁₃×#1973	C₂	semidirect
6. C₁₃×#1880	C₂	semidirect
7. C₁₃×#1877	C₂	semidirect
8. C₁₃×#1808	C₂	semidirect
9. C₁₃×#1787	C₂	semidirect
11. C₁₃×#1752	C₂	semidirect
15. C₂²×C₁₃×SD₁₆	C₄	semidirect
21. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
25. C₂×C₁₃×#107	C₂²	semidirect
26. C₂×C₁₃×#103	C₂²	semidirect
27. C₂×C₁₃×#103	C₂²	semidirect
31. C₂×C₁₃×#97	C₂²	semidirect
33. C₁₃×#391	C₂²	semidirect
42. C₁₃×#340	C₂²	semidirect
43. C₁₃×#336	C₂²	semidirect
49. C₂²×Q₈×C₁₃	C₂×C₄	semidirect
68. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
69. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
72. C₂²×C₈×C₁₃	C₂×C₄	semidirect
105. #22437	C₁₃	direct (N × H)
160. C₁₃×SD₁₆	C₂²⋊C₄	semidirect
185. C₂×#440	C₂×C₁₃	semidirect
186. Q₈×C₂²⋊C₄	C₂×C₁₃	semidirect
188. #1973	C₂×C₁₃	semidirect
189. #1880	C₂×C₁₃	semidirect
190. #1877	C₂×C₁₃	semidirect
191. #1808	C₂×C₁₃	semidirect
192. #1787	C₂×C₁₃	semidirect
194. #1752	C₂×C₁₃	semidirect
222. Q₈×C₁₃	C₂×C₂²⋊C₄	semidirect
259. C₈×C₁₃	C₂×C₂²⋊C₄	semidirect
263. C₂²×SD₁₆	C₄×C₁₃	semidirect
269. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
273. C₂×#107	C₂²×C₁₃	semidirect
274. C₂×#103	C₂²×C₁₃	semidirect
275. C₂×#103	C₂²×C₁₃	semidirect
279. C₂×#97	C₂²×C₁₃	semidirect
281. #391	C₂²×C₁₃	semidirect
290. #340	C₂²×C₁₃	semidirect
291. #336	C₂²×C₁₃	semidirect
307. C₂²×C₁₃	#440	semidirect
328. C₂²×Q₈	C₂×C₄×C₁₃	semidirect
347. C₂×SD₁₆	C₂×C₄×C₁₃	semidirect
348. C₂×SD₁₆	C₂×C₄×C₁₃	semidirect
351. C₂²×C₈	C₂×C₄×C₁₃	semidirect
446. SD₁₆	C₁₃×C₂²⋊C₄	semidirect
470. C₁₃	#22437	direct (N × H)
498. Q₈	C₂×C₁₃×C₂²⋊C₄	semidirect
535. C₈	C₂×C₁₃×C₂²⋊C₄	semidirect
551. C₂²	C₁₃×#440	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₁₃×SD₁₆	2
C₂×C₁₃×#440	2
Q₈×C₁₃×C₂²⋊C₄	2
D₄×C₁₃×C₂²⋊C₄	2
C₁₃×#1973	2
C₁₃×#1880	2
C₁₃×#1877	2
C₁₃×#1808	2
C₁₃×#1787	2
C₁₃×#1786	2
C₁₃×#1752	2
#22437	13

Subgroups — C13×#22437 #15708776

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22437 #15708776