Subgroups — C₁₃×#21004 #15707343

Order 3328.

1686 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#575	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#568	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₁₃×#413	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#1908	C₂	1	4	yes	maximal, complemented
7	C₁₃×#1907	C₂	1	4	yes	maximal, complemented
8	C₂×C₁₃×#343	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1738	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
12	C₁₃×#575	—	2	4	no	—
13	C₁₃×#575	C₄	1	8	yes	complemented
14	C₂×C₁₃×#137	—	2	1	no	—
15	C₂×C₁₃×#137	C₂²	1	2	yes	—
16	C₂×C₁₃×AGL(1,ℤ/8)	—	2	1	no	—
17	C₂×C₁₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂×C₁₃×#135	—	2	2	no	—
19	C₁₃×#568	—	2	4	no	—
20	C₁₃×#568	—	2	4	no	—
21	C₂×C₁₃×#131	—	2	2	no	—
22	C₂×C₁₃×#131	C₂²	1	4	yes	—
23	C₂²×C₁₃×M₁₆	—	2	2	no	—
24	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
27	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
28	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₁₃×#417	—	2	2	no	—
30	C₁₃×#417	—	2	2	no	—
31	C₁₃×#417	—	2	2	no	—
32	C₁₃×#417	C₂²	1	4	yes	—
33	C₂×C₁₃×#103	—	2	1	no	—
34	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
35	C₂×C₁₃×#102	—	2	1	no	—
36	C₂×C₁₃×#102	C₂²	1	2	yes	complemented
37	C₁₃×#413	—	2	4	no	—
38	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
39	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
40	C₁₃×#343	C₂²	1	4	yes	complemented
41	C₁₃×#341	C₂²	1	4	yes	complemented
42	C₂×C₁₃×#41	—	2	1	no	—
43	C₂×C₁₃×#41	—	2	2	no	—
44	C₂×C₁₃×#41	—	2	2	no	—
45	C₂×C₁₃×#41	—	2	2	no	—
46	C₂×C₁₃×#41	—	2	1	no	—
47	C₂×C₁₃×#41	—	2	1	no	—
48	C₂×C₁₃×#41	—	2	1	no	—
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×#41	—	2	2	no	—
52	C₂×C₁₃×#41	—	2	2	no	—
53	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
54	C₂×C₁₃×#41	C₂×C₄	1	4	yes	—
55	C₂×C₁₃×#41	D₄	1	4	yes	—
56	C₂×C₁₃×#41	D₄	1	2	yes	—
57	C₂×C₁₃×#41	C₂³	1	2	yes	—
58	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
59	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	—	2	1	no	—
61	C₂²×D₄×C₁₃	—	2	1	no	—
62	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	—	2	1	no	—
65	C₂³×C₄×C₁₃	—	2	1	no	—
66	C₂³×C₄×C₁₃	—	2	1	no	—
67	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#137	—	2	4	no	—
69	C₁₃×#137	—	2	8	no	—
70	C₁₃×#137	C₂×C₄	1	8	yes	complemented
71	C₁₃×AGL(1,ℤ/8)	—	2	4	no	—
72	C₁₃×AGL(1,ℤ/8)	—	2	8	no	—
73	C₁₃×AGL(1,ℤ/8)	C₂×C₄	1	8	yes	complemented
74	C₁₃×#135	—	2	16	no	—
75	C₂×C₁₃×Q₁₆	—	2	2	no	—
76	C₂×C₁₃×SD₁₆	—	2	2	no	—
77	C₂×C₁₃×SD₁₆	—	2	2	no	—
78	C₂×C₁₃×D₈	—	2	2	no	—
79	C₁₃×#131	—	2	16	no	—
80	C₁₃×#131	—	2	8	no	—
81	C₁₃×#131	—	2	8	no	—
82	C₂×C₁₃×M₁₆	—	2	16	no	—
83	C₂×C₁₃×M₁₆	—	2	1	no	—
84	C₂×C₁₃×M₁₆	—	2	2	no	—
85	C₂×C₁₃×M₁₆	—	2	2	no	—
86	C₂×C₁₃×M₁₆	—	2	2	no	—
87	C₂×C₁₃×M₁₆	—	2	1	no	—
88	C₂×C₁₃×M₁₆	—	2	2	no	—
89	C₂×C₁₃×M₁₆	—	2	1	no	—
90	C₂×C₁₃×M₁₆	—	2	4	no	—
91	C₂×C₁₃×M₁₆	—	2	2	no	—
92	C₂×C₁₃×M₁₆	—	2	2	no	—
93	C₂×C₁₃×M₁₆	C₂×C₄	1	4	yes	—
94	C₂×C₁₃×M₁₆	D₄	1	4	yes	—
95	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
96	C₂×C₁₃×M₁₆	D₄	1	2	yes	—
97	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
98	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
99	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
100	C₂²×C₈×C₁₃	—	2	1	no	—
101	C₂²×C₈×C₁₃	—	2	1	no	—
102	C₂²×C₈×C₁₃	—	2	4	no	—
103	C₂²×C₈×C₁₃	—	2	1	no	—
104	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
105	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
106	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
107	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
108	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
109	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
111	C₁₃×#103	—	2	4	no	—
112	C₁₃×#103	—	2	4	no	—
113	C₁₃×#102	—	2	4	no	—
114	C₁₃×#102	—	2	4	no	—
115	C₁₃×#101	—	2	4	no	—
116	C₁₃×#100	—	2	4	no	—
117	#21004	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂⁴×C₁₃	—	2	1	no	—
119	C₂⁴×C₁₃	—	2	1	no	—
120	C₂⁴×C₁₃	#41	1	1	yes	characteristic
121	C₁₃×#41	—	2	4	no	—
122	C₁₃×#41	—	2	4	no	—
123	C₁₃×#41	—	2	4	no	—
124	C₁₃×#41	—	2	4	no	—
125	C₁₃×#41	—	2	4	no	—
126	C₁₃×#41	—	2	2	no	—
127	C₁₃×#41	—	2	2	no	—
128	C₁₃×#41	—	2	4	no	—
129	C₁₃×#41	—	2	4	no	—
130	C₁₃×#41	—	2	4	no	—
131	C₁₃×#41	—	2	4	no	—
132	C₁₃×#41	—	4	2	no	—
133	C₁₃×#41	—	4	2	no	—
134	C₁₃×#41	—	4	2	no	—
135	C₁₃×#41	—	4	2	no	—
136	C₁₃×#41	C₂²⋊C₄	1	8	yes	—
137	C₁₃×#41	C₂²×C₄	1	4	yes	—
138	C₁₃×#41	C₂×D₄	1	4	yes	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	2	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	1	no	—
144	C₂×Q₈×C₁₃	—	2	1	no	—
145	C₂×Q₈×C₁₃	—	2	1	no	—
146	C₂×Q₈×C₁₃	C₂²⋊C₄	1	4	yes	—
147	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
148	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
149	C₂×D₄×C₁₃	—	2	4	no	—
150	C₂×D₄×C₁₃	—	2	2	no	—
151	C₂×D₄×C₁₃	—	2	4	no	—
152	C₂×D₄×C₁₃	—	2	2	no	—
153	C₂×D₄×C₁₃	—	2	4	no	—
154	C₂×D₄×C₁₃	—	2	2	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	—	2	1	no	—
158	C₂×D₄×C₁₃	—	2	1	no	—
159	C₂×D₄×C₁₃	—	2	1	no	—
160	C₂×D₄×C₁₃	—	2	1	no	—
161	C₂×D₄×C₁₃	—	4	1	no	—
162	C₂×D₄×C₁₃	—	4	1	no	—
163	C₂×D₄×C₁₃	—	4	2	no	—
164	C₂×D₄×C₁₃	C₂²⋊C₄	1	4	yes	—
165	C₂×D₄×C₁₃	C₂²×C₄	1	2	yes	—
166	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	4	no	—
169	C₂²×C₄×C₁₃	—	2	4	no	—
170	C₂²×C₄×C₁₃	—	2	2	no	—
171	C₂²×C₄×C₁₃	—	2	2	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	4	no	—
174	C₂²×C₄×C₁₃	—	2	2	no	—
175	C₂²×C₄×C₁₃	—	4	1	no	—
176	C₂²×C₄×C₁₃	—	4	1	no	—
177	C₂²×C₄×C₁₃	—	4	2	no	—
178	C₂²×C₄×C₁₃	—	4	1	no	—
179	C₂²×C₄×C₁₃	—	4	1	no	—
180	C₂²×C₄×C₁₃	—	8	2	no	—
181	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
182	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
186	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
189	C₂²×C₄×C₁₃	#41	1	2	yes	—
190	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
191	C₁₃×Q₁₆	—	2	8	no	—
192	C₁₃×SD₁₆	—	2	8	no	—
193	C₁₃×SD₁₆	—	2	8	no	—
194	C₁₃×D₈	—	2	8	no	—
195	C₁₃×M₁₆	—	2	16	no	—
196	C₁₃×M₁₆	—	2	4	no	—
197	C₁₃×M₁₆	—	2	4	no	—
198	C₁₃×M₁₆	—	2	4	no	—
199	C₁₃×M₁₆	—	2	4	no	—
200	C₁₃×M₁₆	—	2	2	no	—
201	C₁₃×M₁₆	—	2	2	no	—
202	C₁₃×M₁₆	—	2	2	no	—
203	C₁₃×M₁₆	—	2	2	no	—
204	C₁₃×M₁₆	—	4	2	no	—
205	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
206	C₁₃×M₁₆	C₂×D₄	1	4	yes	—
207	C₂×C₈×C₁₃	—	2	16	no	—
208	C₂×C₈×C₁₃	—	2	4	no	—
209	C₂×C₈×C₁₃	—	2	4	no	—
210	C₂×C₈×C₁₃	—	2	2	no	—
211	C₂×C₈×C₁₃	—	2	2	no	—
212	C₂×C₈×C₁₃	—	2	2	no	—
213	C₂×C₈×C₁₃	—	2	2	no	—
214	C₂×C₈×C₁₃	—	2	2	no	—
215	C₂×C₈×C₁₃	—	4	2	no	—
216	C₂×C₈×C₁₃	C₂×D₄	1	4	yes	—
217	C₁₃×C₄⋊C₄	—	2	2	no	—
218	C₁₃×C₄⋊C₄	—	2	2	no	—
219	C₁₃×C₄⋊C₄	—	4	1	no	—
220	C₁₃×C₄⋊C₄	—	4	1	no	—
221	C₂×#575	C₂×C₁₃	1	1	yes	characteristic
222	C₂×#568	C₂×C₁₃	1	1	yes	characteristic, complemented
223	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
224	C₂×#417	C₂×C₁₃	1	1	yes	characteristic, complemented
225	C₂×#413	C₂×C₁₃	1	1	yes	characteristic, complemented
226	#1908	C₂×C₁₃	1	4	yes	complemented
227	#1907	C₂×C₁₃	1	4	yes	complemented
228	C₂×#343	C₂×C₁₃	1	1	yes	characteristic, complemented
229	#1738	C₂×C₁₃	1	1	yes	characteristic, complemented
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	2	2	no	—
233	C₂³×C₁₃	—	4	1	no	—
234	C₂³×C₁₃	—	4	1	no	—
235	C₂³×C₁₃	—	4	1	no	—
236	C₂³×C₁₃	—	4	1	no	—
237	C₂³×C₁₃	—	8	1	no	—
238	C₂³×C₁₃	—	8	1	no	—
239	C₂³×C₁₃	—	8	1	no	—
240	C₂³×C₁₃	—	8	1	no	—
241	C₂³×C₁₃	C₄×D₄	1	2	yes	—
242	C₂³×C₁₃	#121	1	1	yes	characteristic
243	C₂³×C₁₃	#121	1	1	yes	characteristic
244	C₂³×C₁₃	#123	1	2	yes	—
245	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
246	Q₈×C₁₃	—	2	2	no	—
247	Q₈×C₁₃	—	2	4	no	—
248	Q₈×C₁₃	—	2	2	no	—
249	Q₈×C₁₃	—	2	2	no	—
250	Q₈×C₁₃	—	4	1	no	—
251	Q₈×C₁₃	—	4	1	no	—
252	Q₈×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
253	D₄×C₁₃	—	2	4	no	—
254	D₄×C₁₃	—	2	4	no	—
255	D₄×C₁₃	—	2	8	no	—
256	D₄×C₁₃	—	2	2	no	—
257	D₄×C₁₃	—	2	2	no	—
258	D₄×C₁₃	—	2	2	no	—
259	D₄×C₁₃	—	2	4	no	—
260	D₄×C₁₃	—	4	4	no	—
261	D₄×C₁₃	—	4	4	no	—
262	D₄×C₁₃	—	4	1	no	—
263	D₄×C₁₃	—	4	1	no	—
264	D₄×C₁₃	C₂×C₂²⋊C₄	1	4	yes	—
265	C₂×C₄×C₁₃	—	2	2	no	—
266	C₂×C₄×C₁₃	—	2	4	no	—
267	C₂×C₄×C₁₃	—	2	4	no	—
268	C₂×C₄×C₁₃	—	2	4	no	—
269	C₂×C₄×C₁₃	—	2	8	no	—
270	C₂×C₄×C₁₃	—	2	2	no	—
271	C₂×C₄×C₁₃	—	4	1	no	—
272	C₂×C₄×C₁₃	—	4	1	no	—
273	C₂×C₄×C₁₃	—	4	4	no	—
274	C₂×C₄×C₁₃	—	4	4	no	—
275	C₂×C₄×C₁₃	—	4	2	no	—
276	C₂×C₄×C₁₃	—	8	2	no	—
277	C₂×C₄×C₁₃	—	8	2	no	—
278	C₂×C₄×C₁₃	—	8	2	no	—
279	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
280	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	2	yes	—
281	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
282	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
283	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
284	C₂×C₄×C₁₃	#120	1	2	yes	—
285	C₂×C₄×C₁₃	#120	1	2	yes	—
286	C₂×C₄×C₁₃	#121	1	2	yes	—
287	C₂×C₄×C₁₃	#121	1	2	yes	—
288	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
289	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
290	C₂×C₄×C₁₃	#123	1	2	yes	—
291	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
292	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
296	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
297	C₈×C₁₃	—	2	4	no	—
298	C₈×C₁₃	—	2	4	no	—
299	C₈×C₁₃	—	2	4	no	—
300	C₈×C₁₃	—	4	2	no	—
301	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
302	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
303	#575	—	2	4	no	—
304	#575	C₄×C₁₃	1	8	yes	complemented
305	C₂×#137	—	2	1	no	—
306	C₂×#137	C₂²×C₁₃	1	2	yes	—
307	C₂×AGL(1,ℤ/8)	—	2	1	no	—
308	C₂×AGL(1,ℤ/8)	C₂²×C₁₃	1	2	yes	—
309	C₂×#135	—	2	2	no	—
310	#568	—	2	4	no	—
311	#568	—	2	4	no	—
312	C₂×#131	—	2	2	no	—
313	C₂×#131	C₂²×C₁₃	1	4	yes	—
314	C₂²×M₁₆	—	2	2	no	—
315	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
316	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
317	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
318	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
319	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
320	#417	—	2	2	no	—
321	#417	—	2	2	no	—
322	#417	—	2	2	no	—
323	#417	C₂²×C₁₃	1	4	yes	—
324	C₂×#103	—	2	1	no	—
325	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
326	C₂×#102	—	2	1	no	—
327	C₂×#102	C₂²×C₁₃	1	2	yes	complemented
328	#413	—	2	4	no	—
329	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
330	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
331	#343	C₂²×C₁₃	1	4	yes	complemented
332	#341	C₂²×C₁₃	1	4	yes	complemented
333	C₂²×C₁₃	—	2	1	no	—
334	C₂²×C₁₃	—	2	1	no	—
335	C₂²×C₁₃	—	2	1	no	—
336	C₂²×C₁₃	—	2	1	no	—
337	C₂²×C₁₃	—	2	1	no	—
338	C₂²×C₁₃	—	2	1	no	—
339	C₂²×C₁₃	—	2	4	no	—
340	C₂²×C₁₃	—	4	2	no	—
341	C₂²×C₁₃	—	4	2	no	—
342	C₂²×C₁₃	—	4	2	no	—
343	C₂²×C₁₃	—	4	2	no	—
344	C₂²×C₁₃	—	4	2	no	—
345	C₂²×C₁₃	—	8	4	no	—
346	C₂²×C₁₃	—	8	2	no	—
347	C₂²×C₁₃	—	8	2	no	—
348	C₂²×C₁₃	—	8	1	no	—
349	C₂²×C₁₃	—	8	1	no	—
350	C₂²×C₁₃	#386	1	2	yes	—
351	C₂²×C₁₃	#386	1	2	yes	—
352	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
353	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
354	C₂²×C₁₃	C₂×#123	1	1	yes	characteristic
355	C₄×C₁₃	—	2	4	no	—
356	C₄×C₁₃	—	4	2	no	—
357	C₄×C₁₃	—	8	2	no	—
358	C₄×C₁₃	#386	1	2	yes	—
359	C₄×C₁₃	#386	1	2	yes	—
360	C₄×C₁₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
361	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
362	C₄×C₁₃	C₂×#120	1	1	yes	characteristic
363	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
364	C₂×#41	—	2	1	no	—
365	C₂×#41	—	2	2	no	—
366	C₂×#41	—	2	2	no	—
367	C₂×#41	—	2	2	no	—
368	C₂×#41	—	2	1	no	—
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	—	2	2	no	—
372	C₂×#41	—	2	1	no	—
373	C₂×#41	—	2	1	no	—
374	C₂×#41	—	2	2	no	—
375	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
376	C₂×#41	C₂×C₄×C₁₃	1	4	yes	—
377	C₂×#41	D₄×C₁₃	1	4	yes	—
378	C₂×#41	D₄×C₁₃	1	2	yes	—
379	C₂×#41	C₂³×C₁₃	1	2	yes	—
380	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
381	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
382	C₂²×D₄	—	2	1	no	—
383	C₂²×D₄	—	2	1	no	—
384	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
385	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
386	C₂³×C₄	—	2	1	no	—
387	C₂³×C₄	—	2	1	no	—
388	C₂³×C₄	—	2	1	no	—
389	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
390	#137	—	2	4	no	—
391	#137	—	2	8	no	—
392	#137	C₂×C₄×C₁₃	1	8	yes	complemented
393	AGL(1,ℤ/8)	—	2	4	no	—
394	AGL(1,ℤ/8)	—	2	8	no	—
395	AGL(1,ℤ/8)	C₂×C₄×C₁₃	1	8	yes	complemented
396	#135	—	2	16	no	—
397	C₂×Q₁₆	—	2	2	no	—
398	C₂×SD₁₆	—	2	2	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×D₈	—	2	2	no	—
401	#131	—	2	16	no	—
402	#131	—	2	8	no	—
403	#131	—	2	8	no	—
404	C₂×M₁₆	—	2	16	no	—
405	C₂×M₁₆	—	2	1	no	—
406	C₂×M₁₆	—	2	2	no	—
407	C₂×M₁₆	—	2	2	no	—
408	C₂×M₁₆	—	2	2	no	—
409	C₂×M₁₆	—	2	1	no	—
410	C₂×M₁₆	—	2	2	no	—
411	C₂×M₁₆	—	2	1	no	—
412	C₂×M₁₆	—	2	4	no	—
413	C₂×M₁₆	—	2	2	no	—
414	C₂×M₁₆	—	2	2	no	—
415	C₂×M₁₆	C₂×C₄×C₁₃	1	4	yes	—
416	C₂×M₁₆	D₄×C₁₃	1	4	yes	—
417	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
418	C₂×M₁₆	D₄×C₁₃	1	2	yes	—
419	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
420	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
421	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
422	C₂²×C₈	—	2	1	no	—
423	C₂²×C₈	—	2	1	no	—
424	C₂²×C₈	—	2	4	no	—
425	C₂²×C₈	—	2	1	no	—
426	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
427	C₂×C₄⋊C₄	—	2	1	no	—
428	C₂×C₄⋊C₄	—	2	1	no	—
429	C₂×C₄⋊C₄	—	2	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
433	#103	—	2	4	no	—
434	#103	—	2	4	no	—
435	#102	—	2	4	no	—
436	#102	—	2	4	no	—
437	#101	—	2	4	no	—
438	#100	—	2	4	no	—
439	C₂×C₁₃	—	2	1	no	—
440	C₂×C₁₃	—	2	1	no	—
441	C₂×C₁₃	—	2	2	no	—
442	C₂×C₁₃	—	2	2	no	—
443	C₂×C₁₃	—	4	4	no	—
444	C₂×C₁₃	—	8	2	no	—
445	C₂×C₁₃	C₂×#386	1	1	yes	characteristic
446	C₂×C₁₃	#3068	1	1	yes	characteristic
447	C₂×C₁₃	#3069	1	1	yes	characteristic
448	C₂⁴	—	2	1	no	—
449	C₂⁴	—	2	1	no	—
450	C₂⁴	C₁₃×#41	1	1	yes	characteristic
451	#41	—	2	4	no	—
452	#41	—	2	4	no	—
453	#41	—	2	4	no	—
454	#41	—	2	4	no	—
455	#41	—	2	4	no	—
456	#41	—	2	2	no	—
457	#41	—	2	2	no	—
458	#41	—	2	4	no	—
459	#41	—	2	4	no	—
460	#41	—	2	4	no	—
461	#41	—	2	4	no	—
462	#41	—	4	2	no	—
463	#41	—	4	2	no	—
464	#41	—	4	2	no	—
465	#41	—	4	2	no	—
466	#41	C₁₃×C₂²⋊C₄	1	8	yes	—
467	#41	C₂²×C₄×C₁₃	1	4	yes	—
468	#41	C₂×D₄×C₁₃	1	4	yes	—
469	C₂×Q₈	—	2	2	no	—
470	C₂×Q₈	—	2	1	no	—
471	C₂×Q₈	—	2	1	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	1	no	—
476	C₂×Q₈	C₁₃×C₂²⋊C₄	1	4	yes	—
477	C₂×Q₈	C₂²×C₄×C₁₃	1	2	yes	—
478	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	2	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	4	1	no	—
492	C₂×D₄	—	4	1	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	C₁₃×C₂²⋊C₄	1	4	yes	—
495	C₂×D₄	C₂²×C₄×C₁₃	1	2	yes	—
496	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	—	2	4	no	—
499	C₂²×C₄	—	2	4	no	—
500	C₂²×C₄	—	2	2	no	—
501	C₂²×C₄	—	2	2	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	4	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	4	1	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	1	no	—
509	C₂²×C₄	—	4	1	no	—
510	C₂²×C₄	—	8	2	no	—
511	C₂²×C₄	C₂²×C₄×C₁₃	1	2	yes	—
512	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
513	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
516	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
517	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
518	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
519	C₂²×C₄	C₁₃×#41	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
521	Q₁₆	—	2	8	no	—
522	SD₁₆	—	2	8	no	—
523	SD₁₆	—	2	8	no	—
524	D₈	—	2	8	no	—
525	M₁₆	—	2	16	no	—
526	M₁₆	—	2	4	no	—
527	M₁₆	—	2	4	no	—
528	M₁₆	—	2	4	no	—
529	M₁₆	—	2	4	no	—
530	M₁₆	—	2	2	no	—
531	M₁₆	—	2	2	no	—
532	M₁₆	—	2	2	no	—
533	M₁₆	—	2	2	no	—
534	M₁₆	—	4	2	no	—
535	M₁₆	C₂²×C₄×C₁₃	1	4	yes	—
536	M₁₆	C₂×D₄×C₁₃	1	4	yes	—
537	C₂×C₈	—	2	16	no	—
538	C₂×C₈	—	2	4	no	—
539	C₂×C₈	—	2	4	no	—
540	C₂×C₈	—	2	2	no	—
541	C₂×C₈	—	2	2	no	—
542	C₂×C₈	—	2	2	no	—
543	C₂×C₈	—	2	2	no	—
544	C₂×C₈	—	2	2	no	—
545	C₂×C₈	—	4	2	no	—
546	C₂×C₈	C₂×D₄×C₁₃	1	4	yes	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	4	1	no	—
550	C₄⋊C₄	—	4	1	no	—
551	C₁₃	#21004	1	1	yes	characteristic, direct product factor, Sylow
552	C₂³	—	2	2	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	2	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	1	no	—
559	C₂³	—	8	1	no	—
560	C₂³	—	8	1	no	—
561	C₂³	—	8	1	no	—
562	C₂³	—	8	1	no	—
563	C₂³	C₄×D₄×C₁₃	1	2	yes	—
564	C₂³	C₁₃×#121	1	1	yes	characteristic
565	C₂³	C₁₃×#121	1	1	yes	characteristic
566	C₂³	C₁₃×#123	1	2	yes	—
567	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
568	Q₈	—	2	4	no	—
569	Q₈	—	2	2	no	—
570	Q₈	—	2	2	no	—
571	Q₈	—	2	2	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	1	no	—
574	Q₈	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
575	D₄	—	2	8	no	—
576	D₄	—	2	4	no	—
577	D₄	—	2	4	no	—
578	D₄	—	2	4	no	—
579	D₄	—	2	2	no	—
580	D₄	—	2	2	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	4	no	—
583	D₄	—	4	4	no	—
584	D₄	—	4	1	no	—
585	D₄	—	4	1	no	—
586	D₄	C₂×C₁₃×C₂²⋊C₄	1	4	yes	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	4	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	2	no	—
598	C₂×C₄	—	8	2	no	—
599	C₂×C₄	—	8	2	no	—
600	C₂×C₄	—	8	2	no	—
601	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
602	C₂×C₄	C₂×C₁₃×C₂²⋊C₄	1	2	yes	—
603	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
604	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
605	C₂×C₄	C₄×D₄×C₁₃	1	2	yes	—
606	C₂×C₄	C₁₃×#120	1	2	yes	—
607	C₂×C₄	C₁₃×#120	1	2	yes	—
608	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
609	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
610	C₂×C₄	C₁₃×#121	1	2	yes	—
611	C₂×C₄	C₁₃×#121	1	2	yes	—
612	C₂×C₄	C₁₃×#123	1	2	yes	—
613	C₂×C₄	C₂³×C₄×C₁₃	1	1	yes	characteristic
614	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
615	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
616	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
617	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
618	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
619	C₈	—	2	4	no	—
620	C₈	—	2	4	no	—
621	C₈	—	2	4	no	—
622	C₈	—	4	2	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	2	1	no	—
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	4	2	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	2	no	—
635	C₂²	—	8	4	no	—
636	C₂²	—	8	2	no	—
637	C₂²	—	8	2	no	—
638	C₂²	—	8	1	no	—
639	C₂²	—	8	1	no	—
640	C₂²	C₁₃×#386	1	2	yes	—
641	C₂²	C₁₃×#386	1	2	yes	—
642	C₂²	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
643	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
644	C₂²	C₂×C₁₃×#123	1	1	yes	characteristic
645	C₄	—	2	4	no	—
646	C₄	—	4	2	no	—
647	C₄	—	8	2	no	—
648	C₄	C₁₃×#386	1	2	yes	—
649	C₄	C₁₃×#386	1	2	yes	—
650	C₄	C₂²×C₁₃×C₂²⋊C₄	1	1	yes	characteristic
651	C₄	C₂×C₄×D₄×C₁₃	1	1	yes	characteristic
652	C₄	C₂×C₁₃×#120	1	1	yes	characteristic
653	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
654	C₂	—	2	2	no	—
655	C₂	—	2	1	no	—
656	C₂	—	2	1	no	—
657	C₂	—	2	2	no	—
658	C₂	—	4	4	no	—
659	C₂	—	8	2	no	—
660	C₂	C₂×C₁₃×#386	1	1	yes	characteristic
661	C₂	C₁₃×#3068	1	1	yes	characteristic
662	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator	C₂×C₄	C₂³×C₄×C₁₃
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#575	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₃×#568	C₂	semidirect
3. C₂×C₁₃×#417	C₂	semidirect
4. C₂×C₁₃×#417	C₂	semidirect
5. C₂×C₁₃×#413	C₂	semidirect
6. C₁₃×#1908	C₂	semidirect
7. C₁₃×#1907	C₂	semidirect
8. C₂×C₁₃×#343	C₂	semidirect
9. C₁₃×#1738	C₂	semidirect
13. C₁₃×#575	C₄	semidirect
34. C₂×C₁₃×#103	C₂²	semidirect
36. C₂×C₁₃×#102	C₂²	semidirect
38. C₂×C₁₃×#101	C₂²	semidirect
39. C₂×C₁₃×#100	C₂²	semidirect
40. C₁₃×#343	C₂²	semidirect
41. C₁₃×#341	C₂²	semidirect
70. C₁₃×#137	C₂×C₄	semidirect
73. C₁₃×AGL(1,ℤ/8)	C₂×C₄	semidirect
117. #21004	C₁₃	direct (N × H)
222. C₂×#568	C₂×C₁₃	semidirect
223. C₂×#417	C₂×C₁₃	semidirect
224. C₂×#417	C₂×C₁₃	semidirect
225. C₂×#413	C₂×C₁₃	semidirect
226. #1908	C₂×C₁₃	semidirect
227. #1907	C₂×C₁₃	semidirect
228. C₂×#343	C₂×C₁₃	semidirect
229. #1738	C₂×C₁₃	semidirect
304. #575	C₄×C₁₃	semidirect
325. C₂×#103	C₂²×C₁₃	semidirect
327. C₂×#102	C₂²×C₁₃	semidirect
329. C₂×#101	C₂²×C₁₃	semidirect
330. C₂×#100	C₂²×C₁₃	semidirect
331. #343	C₂²×C₁₃	semidirect
332. #341	C₂²×C₁₃	semidirect
392. #137	C₂×C₄×C₁₃	semidirect
395. AGL(1,ℤ/8)	C₂×C₄×C₁₃	semidirect
551. C₁₃	#21004	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×#575	2
C₂×C₁₃×#568	2
C₂×C₁₃×#417	2
C₂×C₁₃×#413	2
C₁₃×#1908	2
C₁₃×#1907	2
C₂×C₁₃×#343	2
C₁₃×#1738	2
#21004	13

Subgroups — C13×#21004 #15707343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#21004 #15707343