Subgroups — C₁₃×#22049 #15708388

Order 3328.

1212 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#450	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#390	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#1973	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1936	C₂	1	2	yes	maximal, complemented
6	C₁₃×#1925	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1880	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1872	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1852	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1786	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
18	C₂²×C₁₃×C₂²⋊C₄	—	2	1	no	—
19	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
20	C₁₃×#450	C₄	1	8	yes	complemented
21	C₂×C₁₃×#107	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#102	C₂²	1	2	yes	—
24	C₂×C₁₃×#102	C₂²	1	2	yes	—
25	C₂×C₁₃×#102	C₂²	1	2	yes	—
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#97	C₂²	1	2	yes	complemented
29	C₁₃×#391	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#390	—	2	1	no	—
31	C₁₃×#390	—	2	1	no	—
32	C₁₃×#390	C₂²	1	2	yes	—
33	C₁₃×#390	C₂²	1	2	yes	—
34	C₁₃×#389	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#387	—	2	1	no	—
36	C₁₃×#385	—	2	1	no	—
37	C₁₃×#380	C₂²	1	1	yes	characteristic
38	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
39	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
40	C₄×C₁₃×C₂²⋊C₄	—	2	1	no	—
41	C₁₃×#340	C₂²	1	2	yes	complemented
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	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₁₃	—	2	1	no	—
47	C₂²×D₄×C₁₃	—	2	2	no	—
48	C₂²×D₄×C₁₃	—	4	2	no	—
49	C₂²×D₄×C₁₃	—	4	2	no	—
50	C₂²×D₄×C₁₃	C₂×C₄	1	4	yes	—
51	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
52	C₂³×C₄×C₁₃	—	2	1	no	—
53	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×SD₁₆	—	4	2	no	—
57	C₂×C₁₃×SD₁₆	—	4	2	no	—
58	C₂×C₁₃×SD₁₆	C₂×C₄	1	8	yes	complemented
59	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
60	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
61	C₁₃×C₂²⋊Q₈	—	2	2	no	—
62	C₁₃×C₂²⋊Q₈	C₂×C₄	1	4	yes	—
63	C₄×Q₈×C₁₃	—	4	2	no	—
64	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
65	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₃×C₄⋊C₄	—	4	2	no	—
69	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
71	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
73	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
80	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
81	C₂×C₄²×C₁₃	—	2	1	no	—
82	C₂×C₄²×C₁₃	—	2	1	no	—
83	C₂×C₄²×C₁₃	—	4	2	no	—
84	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
86	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
88	C₁₃×#107	—	4	2	no	—
89	C₁₃×#103	—	4	2	no	—
90	C₁₃×#102	—	4	2	no	—
91	C₁₃×#102	—	4	2	no	—
92	C₁₃×#102	C₂×C₄	1	8	yes	complemented
93	C₁₃×C₂²⋊C₈	—	2	2	no	—
94	C₁₃×C₂²⋊C₈	C₂×C₄	1	4	yes	—
95	C₁₃×#97	—	4	2	no	—
96	C₁₃×#95	—	2	1	no	—
97	C₁₃×#95	—	2	1	no	—
98	C₁₃×#95	—	2	1	no	—
99	C₁₃×#95	—	2	1	no	—
100	C₁₃×#95	—	2	1	no	—
101	#22049	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
102	C₂⁴×C₁₃	—	2	4	no	—
103	C₂⁴×C₁₃	—	2	2	no	—
104	C₂⁴×C₁₃	—	4	2	no	—
105	C₂⁴×C₁₃	—	4	2	no	—
106	C₂⁴×C₁₃	—	4	2	no	—
107	C₂⁴×C₁₃	—	4	2	no	—
108	C₂⁴×C₁₃	—	4	2	no	—
109	C₂⁴×C₁₃	—	4	2	no	—
110	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	2	no	—
113	C₂×Q₈×C₁₃	—	2	2	no	—
114	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₁₃	—	2	4	no	—
116	C₂×D₄×C₁₃	—	2	2	no	—
117	C₂×D₄×C₁₃	—	2	2	no	—
118	C₂×D₄×C₁₃	—	2	2	no	—
119	C₂×D₄×C₁₃	—	2	2	no	—
120	C₂×D₄×C₁₃	—	2	2	no	—
121	C₂×D₄×C₁₃	—	4	8	no	—
122	C₂×D₄×C₁₃	—	4	2	no	—
123	C₂×D₄×C₁₃	—	4	2	no	—
124	C₂×D₄×C₁₃	—	4	8	no	—
125	C₂×D₄×C₁₃	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₁₃	—	2	2	no	—
127	C₂²×C₄×C₁₃	—	2	2	no	—
128	C₂²×C₄×C₁₃	—	2	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	1	no	—
134	C₂²×C₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	2	no	—
136	C₂²×C₄×C₁₃	—	4	1	no	—
137	C₂²×C₄×C₁₃	—	4	1	no	—
138	C₂²×C₄×C₁₃	—	4	1	no	—
139	C₂²×C₄×C₁₃	—	4	2	no	—
140	C₂²×C₄×C₁₃	—	4	2	no	—
141	C₂²×C₄×C₁₃	—	4	2	no	—
142	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	#41	1	2	yes	—
149	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₁₃×SD₁₆	—	4	8	no	—
151	C₂×C₈×C₁₃	—	2	2	no	—
152	C₂×C₈×C₁₃	—	2	2	no	—
153	C₂×C₈×C₁₃	—	2	2	no	—
154	C₂×C₈×C₁₃	—	2	2	no	—
155	C₂×C₈×C₁₃	—	2	2	no	—
156	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
157	C₁₃×C₄⋊C₄	—	2	4	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	2	2	no	—
162	C₁₃×C₄⋊C₄	—	2	2	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	4	2	no	—
165	C₁₃×C₄⋊C₄	—	4	2	no	—
166	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
167	C₁₃×C₂²⋊C₄	—	2	4	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	4	no	—
170	C₁₃×C₂²⋊C₄	—	4	4	no	—
171	C₁₃×C₂²⋊C₄	—	4	2	no	—
172	C₁₃×C₂²⋊C₄	—	4	4	no	—
173	C₄²×C₁₃	—	2	2	no	—
174	C₄²×C₁₃	—	2	2	no	—
175	C₄²×C₁₃	—	4	1	no	—
176	C₄²×C₁₃	—	4	1	no	—
177	C₄²×C₁₃	—	4	2	no	—
178	C₄²×C₁₃	—	4	2	no	—
179	C₂×#450	C₂×C₁₃	1	1	yes	characteristic
180	C₄×C₂²⋊Q₈	C₂×C₁₃	1	1	yes	characteristic, complemented
181	C₂×#390	C₂×C₁₃	1	1	yes	characteristic
182	#1973	C₂×C₁₃	1	2	yes	complemented
183	#1936	C₂×C₁₃	1	2	yes	complemented
184	#1925	C₂×C₁₃	1	2	yes	complemented
185	#1880	C₂×C₁₃	1	2	yes	complemented
186	#1872	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#1852	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#1786	C₂×C₁₃	1	1	yes	characteristic
189	#1749	C₂×C₁₃	1	1	yes	characteristic, complemented
190	C₂³×C₁₃	—	2	1	no	—
191	C₂³×C₁₃	—	2	1	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	1	no	—
194	C₂³×C₁₃	—	2	4	no	—
195	C₂³×C₁₃	—	4	8	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	—	4	2	no	—
198	C₂³×C₁₃	—	4	2	no	—
199	C₂³×C₁₃	—	4	2	no	—
200	C₂³×C₁₃	—	4	2	no	—
201	C₂³×C₁₃	—	4	2	no	—
202	C₂³×C₁₃	—	4	2	no	—
203	C₂³×C₁₃	—	4	8	no	—
204	C₂³×C₁₃	—	8	4	no	—
205	C₂³×C₁₃	—	8	4	no	—
206	C₂³×C₁₃	—	8	4	no	—
207	C₂³×C₁₃	—	8	4	no	—
208	C₂³×C₁₃	C₄×D₄	1	2	yes	—
209	C₂³×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
210	C₂³×C₁₃	#137	1	2	yes	—
211	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
212	Q₈×C₁₃	—	2	4	no	—
213	Q₈×C₁₃	—	4	2	no	—
214	D₄×C₁₃	—	2	4	no	—
215	D₄×C₁₃	—	2	4	no	—
216	D₄×C₁₃	—	4	8	no	—
217	D₄×C₁₃	—	4	2	no	—
218	D₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	2	1	no	—
222	C₂×C₄×C₁₃	—	2	1	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	2	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	1	no	—
234	C₂×C₄×C₁₃	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	4	4	no	—
237	C₂×C₄×C₁₃	—	4	4	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	2	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	2	no	—
247	C₂×C₄×C₁₃	—	4	2	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	8	4	no	—
252	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
253	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
254	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
257	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
258	C₈×C₁₃	—	2	4	no	—
259	C₈×C₁₃	—	4	2	no	—
260	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
261	C₂²×SD₁₆	C₂²×C₁₃	1	2	yes	—
262	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic, complemented
264	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
265	C₂²×C₂²⋊C₄	—	2	1	no	—
266	C₂²×C₂²⋊C₄	—	2	1	no	—
267	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
268	#450	C₄×C₁₃	1	8	yes	complemented
269	C₂×#107	C₂²×C₁₃	1	2	yes	complemented
270	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
271	C₂×#102	C₂²×C₁₃	1	2	yes	—
272	C₂×#102	C₂²×C₁₃	1	2	yes	—
273	C₂×#102	C₂²×C₁₃	1	2	yes	—
274	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#97	C₂²×C₁₃	1	2	yes	complemented
277	#391	C₂²×C₁₃	1	1	yes	characteristic, complemented
278	#390	—	2	1	no	—
279	#390	—	2	1	no	—
280	#390	C₂²×C₁₃	1	2	yes	—
281	#390	C₂²×C₁₃	1	2	yes	—
282	#389	C₂²×C₁₃	1	1	yes	characteristic, complemented
283	#387	—	2	1	no	—
284	#385	—	2	1	no	—
285	#380	C₂²×C₁₃	1	1	yes	characteristic
286	C₄×C₄⋊C₄	—	2	1	no	—
287	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic, complemented
288	C₄×C₂²⋊C₄	—	2	1	no	—
289	#340	C₂²×C₁₃	1	2	yes	complemented
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	2	no	—
295	C₂²×C₁₃	—	2	2	no	—
296	C₂²×C₁₃	—	2	2	no	—
297	C₂²×C₁₃	—	2	2	no	—
298	C₂²×C₁₃	—	4	4	no	—
299	C₂²×C₁₃	—	4	4	no	—
300	C₂²×C₁₃	—	4	4	no	—
301	C₂²×C₁₃	—	8	16	no	—
302	C₂²×C₁₃	—	8	2	no	—
303	C₂²×C₁₃	—	8	2	no	—
304	C₂²×C₁₃	—	8	2	no	—
305	C₂²×C₁₃	—	8	2	no	—
306	C₂²×C₁₃	#440	1	4	yes	—
307	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
308	C₂²×C₁₃	#534	1	1	yes	characteristic
309	C₂²×C₁₃	#535	1	1	yes	characteristic
310	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
311	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
313	C₂²×C₁₃	#575	1	1	yes	characteristic
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	2	no	—
316	C₄×C₁₃	—	4	2	no	—
317	C₄×C₁₃	—	4	1	no	—
318	C₄×C₁₃	—	4	1	no	—
319	C₄×C₁₃	—	4	1	no	—
320	C₄×C₁₃	—	4	2	no	—
321	C₄×C₁₃	—	8	1	no	—
322	C₄×C₁₃	—	8	1	no	—
323	C₄×C₁₃	—	8	2	no	—
324	C₄×C₁₃	#518	1	2	yes	—
325	C₄×C₁₃	#538	1	2	yes	—
326	C₂⁵	—	2	1	no	—
327	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	4	2	no	—
331	C₂²×D₄	—	4	2	no	—
332	C₂²×D₄	C₂×C₄×C₁₃	1	4	yes	—
333	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
334	C₂³×C₄	—	2	1	no	—
335	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
336	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
337	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
338	C₂×SD₁₆	—	4	2	no	—
339	C₂×SD₁₆	—	4	2	no	—
340	C₂×SD₁₆	C₂×C₄×C₁₃	1	8	yes	complemented
341	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
342	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	C₂×C₄×C₁₃	1	4	yes	—
345	C₄×Q₈	—	4	2	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	—	2	1	no	—
350	C₂×C₄⋊C₄	—	4	2	no	—
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	—	2	2	no	—
360	C₂×C₂²⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	4	4	no	—
362	C₂×C₂²⋊C₄	—	4	4	no	—
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	—	4	2	no	—
366	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
367	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
368	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
370	#107	—	4	2	no	—
371	#103	—	4	2	no	—
372	#102	—	4	2	no	—
373	#102	—	4	2	no	—
374	#102	C₂×C₄×C₁₃	1	8	yes	complemented
375	C₂²⋊C₈	—	2	2	no	—
376	C₂²⋊C₈	C₂×C₄×C₁₃	1	4	yes	—
377	#97	—	4	2	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	C₂×C₁₃	—	2	4	no	—
384	C₂×C₁₃	—	8	4	no	—
385	C₂×C₁₃	#2321	1	1	yes	characteristic
386	C₂×C₁₃	C₂×#440	1	1	yes	characteristic
387	C₂×C₁₃	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
388	C₂×C₁₃	#3193	1	1	yes	characteristic
389	C₂×C₁₃	#3194	1	1	yes	characteristic
390	C₂×C₁₃	#3215	1	1	yes	characteristic
391	C₂×C₁₃	#3217	1	1	yes	characteristic
392	C₂⁴	—	2	4	no	—
393	C₂⁴	—	2	2	no	—
394	C₂⁴	—	4	2	no	—
395	C₂⁴	—	4	2	no	—
396	C₂⁴	—	4	2	no	—
397	C₂⁴	—	4	2	no	—
398	C₂⁴	—	4	2	no	—
399	C₂⁴	—	4	2	no	—
400	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	2	no	—
411	C₂×D₄	—	4	8	no	—
412	C₂×D₄	—	4	2	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	8	no	—
415	C₂×D₄	C₂²×C₄×C₁₃	1	4	yes	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	4	1	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	2	no	—
430	C₂²×C₄	—	4	2	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
433	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
434	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
435	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂²×C₄	C₁₃×#41	1	2	yes	—
439	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
440	SD₁₆	—	4	8	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	C₂²×C₄×C₁₃	1	4	yes	—
447	C₄⋊C₄	—	2	4	no	—
448	C₄⋊C₄	—	2	1	no	—
449	C₄⋊C₄	—	2	2	no	—
450	C₄⋊C₄	—	2	2	no	—
451	C₄⋊C₄	—	2	2	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	4	2	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	C₂²×C₄×C₁₃	1	2	yes	—
457	C₂²⋊C₄	—	2	4	no	—
458	C₂²⋊C₄	—	4	4	no	—
459	C₂²⋊C₄	—	4	4	no	—
460	C₂²⋊C₄	—	4	4	no	—
461	C₂²⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	4	4	no	—
463	C₄²	—	2	2	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	4	1	no	—
466	C₄²	—	4	1	no	—
467	C₄²	—	4	2	no	—
468	C₄²	—	4	2	no	—
469	C₁₃	#22049	1	1	yes	characteristic, direct product factor, Sylow
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	—	2	4	no	—
475	C₂³	—	4	8	no	—
476	C₂³	—	4	8	no	—
477	C₂³	—	4	8	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	4	2	no	—
480	C₂³	—	4	2	no	—
481	C₂³	—	4	2	no	—
482	C₂³	—	4	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	8	4	no	—
485	C₂³	—	8	4	no	—
486	C₂³	—	8	4	no	—
487	C₂³	—	8	4	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	4	no	—
493	Q₈	—	4	2	no	—
494	D₄	—	2	4	no	—
495	D₄	—	2	4	no	—
496	D₄	—	4	8	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	4	no	—
504	C₂×C₄	—	2	4	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	4	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	8	4	no	—
532	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
533	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
534	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
535	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
536	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
537	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
538	C₈	—	2	4	no	—
539	C₈	—	4	2	no	—
540	C₂²	—	2	2	no	—
541	C₂²	—	2	2	no	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	2	no	—
545	C₂²	—	2	2	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	4	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	8	16	no	—
550	C₂²	—	8	2	no	—
551	C₂²	—	8	2	no	—
552	C₂²	—	8	2	no	—
553	C₂²	—	8	2	no	—
554	C₂²	C₁₃×#440	1	4	yes	—
555	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
556	C₂²	C₁₃×#534	1	1	yes	characteristic
557	C₂²	C₁₃×#535	1	1	yes	characteristic
558	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
559	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
560	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
561	C₂²	C₁₃×#575	1	1	yes	characteristic
562	C₄	—	2	2	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	2	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	2	no	—
572	C₄	C₁₃×#518	1	2	yes	—
573	C₄	C₁₃×#538	1	2	yes	—
574	C₂	—	2	4	no	—
575	C₂	—	8	4	no	—
576	C₂	C₁₃×#2321	1	1	yes	characteristic
577	C₂	C₂×C₁₃×#440	1	1	yes	characteristic
578	C₂	C₄×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
579	C₂	C₁₃×#3193	1	1	yes	characteristic
580	C₂	C₁₃×#3194	1	1	yes	characteristic
581	C₂	C₁₃×#3215	1	1	yes	characteristic
582	C₂	C₁₃×#3217	1	1	yes	characteristic

	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 ◁ C₂²×C₄²×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄×C₁₃×C₂²⋊Q₈	C₂	semidirect
4. C₁₃×#1973	C₂	semidirect
5. C₁₃×#1936	C₂	semidirect
6. C₁₃×#1925	C₂	semidirect
7. C₁₃×#1880	C₂	semidirect
8. C₁₃×#1872	C₂	semidirect
9. C₁₃×#1852	C₂	semidirect
11. C₁₃×#1749	C₂	semidirect
15. C₂×C₄×Q₈×C₁₃	C₂²	semidirect
20. C₁₃×#450	C₄	semidirect
21. C₂×C₁₃×#107	C₂²	semidirect
22. C₂×C₁₃×#103	C₂²	semidirect
28. C₂×C₁₃×#97	C₂²	semidirect
29. C₁₃×#391	C₂²	semidirect
34. C₁₃×#389	C₂²	semidirect
39. C₄×C₁₃×C₄⋊C₄	C₂²	semidirect
41. C₁₃×#340	C₂²	semidirect
42. C₁₃×#340	C₂²	semidirect
43. C₁₃×#336	C₂²	semidirect
58. C₂×C₁₃×SD₁₆	C₂×C₄	semidirect
92. C₁₃×#102	C₂×C₄	semidirect
101. #22049	C₁₃	direct (N × H)
180. C₄×C₂²⋊Q₈	C₂×C₁₃	semidirect
182. #1973	C₂×C₁₃	semidirect
183. #1936	C₂×C₁₃	semidirect
184. #1925	C₂×C₁₃	semidirect
185. #1880	C₂×C₁₃	semidirect
186. #1872	C₂×C₁₃	semidirect
187. #1852	C₂×C₁₃	semidirect
189. #1749	C₂×C₁₃	semidirect
263. C₂×C₄×Q₈	C₂²×C₁₃	semidirect
268. #450	C₄×C₁₃	semidirect
269. C₂×#107	C₂²×C₁₃	semidirect
270. C₂×#103	C₂²×C₁₃	semidirect
276. C₂×#97	C₂²×C₁₃	semidirect
277. #391	C₂²×C₁₃	semidirect
282. #389	C₂²×C₁₃	semidirect
287. C₄×C₄⋊C₄	C₂²×C₁₃	semidirect
289. #340	C₂²×C₁₃	semidirect
290. #340	C₂²×C₁₃	semidirect
291. #336	C₂²×C₁₃	semidirect
340. C₂×SD₁₆	C₂×C₄×C₁₃	semidirect
374. #102	C₂×C₄×C₁₃	semidirect
469. C₁₃	#22049	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×#450	2
C₄×C₁₃×C₂²⋊Q₈	2
C₂×C₁₃×#390	2
C₁₃×#1973	2
C₁₃×#1936	2
C₁₃×#1925	2
C₁₃×#1880	2
C₁₃×#1872	2
C₁₃×#1852	2
C₁₃×#1786	2
C₁₃×#1749	2
#22049	13

Subgroups — C13×#22049 #15708388

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#22049 #15708388