Subgroups — C₁₃×#32726 #15719065

Order 3328.

838 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2854	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#2850	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2101	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2092	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2066	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2054	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#2042	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#2036	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2034	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#2012	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#2000	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1999	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#123	—	2	1	no	—
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
38	C₁₃×#391	C₂²	1	1	yes	characteristic
39	C₁₃×#390	C₂²	1	1	yes	characteristic
40	C₁₃×#390	C₂²	1	1	yes	characteristic
41	C₁₃×#390	C₂²	1	1	yes	characteristic
42	C₁₃×#389	C₂²	1	1	yes	characteristic
43	C₁₃×#389	C₂²	1	1	yes	characteristic
44	C₁₃×#388	—	2	1	no	—
45	C₁₃×#388	—	2	1	no	—
46	C₁₃×#388	—	2	1	no	—
47	C₁₃×#388	—	2	1	no	—
48	C₁₃×#386	—	2	1	no	—
49	C₁₃×#386	—	2	1	no	—
50	C₁₃×#386	—	2	1	no	—
51	C₁₃×#382	C₂²	1	1	yes	characteristic
52	C₁₃×#380	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	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	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂×C₁₃×SD₁₆	—	4	1	no	—
68	C₂×C₁₃×SD₁₆	—	4	1	no	—
69	C₂×C₁₃×SD₁₆	—	4	1	no	—
70	C₂×C₁₃×D₈	—	4	1	no	—
71	C₂×C₁₃×D₈	—	4	1	no	—
72	C₂×C₁₃×D₈	—	4	1	no	—
73	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#124	—	4	1	no	—
78	C₁₃×#124	—	4	1	no	—
79	C₁₃×#123	—	4	4	no	—
80	C₁₃×C₂²⋊Q₈	—	4	1	no	—
81	C₁₃×C₂²⋊Q₈	—	4	1	no	—
82	C₁₃×#121	—	4	1	no	—
83	C₁₃×#121	—	4	1	no	—
84	C₁₃×#121	—	4	1	no	—
85	C₁₃×#121	—	4	1	no	—
86	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
89	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
90	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
91	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
96	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
98	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
106	C₂×C₄²×C₁₃	—	4	1	no	—
107	C₂×C₄²×C₁₃	—	4	1	no	—
108	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₁₃×#107	—	4	1	no	—
113	C₁₃×#106	—	4	1	no	—
114	C₁₃×C₄⋊C₈	—	4	1	no	—
115	C₁₃×C₄⋊C₈	—	4	1	no	—
116	C₁₃×#103	—	4	1	no	—
117	C₁₃×#103	—	4	1	no	—
118	C₁₃×#103	—	4	1	no	—
119	C₁₃×#102	—	4	1	no	—
120	C₁₃×#102	—	4	1	no	—
121	C₁₃×#102	—	4	1	no	—
122	C₁₃×#102	—	4	1	no	—
123	C₁₃×#102	—	4	1	no	—
124	C₁₃×C₂²⋊C₈	—	4	1	no	—
125	C₁₃×C₂²⋊C₈	—	4	1	no	—
126	C₁₃×#95	—	2	1	no	—
127	C₁₃×#95	—	2	1	no	—
128	C₁₃×#95	—	2	1	no	—
129	C₁₃×#95	—	2	1	no	—
130	C₁₃×#95	—	2	1	no	—
131	C₁₃×#95	—	2	1	no	—
132	C₁₃×#95	—	2	1	no	—
133	#32726	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
134	C₂⁴×C₁₃	—	2	1	no	—
135	C₂⁴×C₁₃	—	2	1	no	—
136	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
137	C₂×Q₈×C₁₃	—	2	1	no	—
138	C₂×Q₈×C₁₃	—	2	1	no	—
139	C₂×Q₈×C₁₃	—	2	1	no	—
140	C₂×Q₈×C₁₃	—	2	1	no	—
141	C₂×Q₈×C₁₃	—	2	1	no	—
142	C₂×Q₈×C₁₃	—	2	1	no	—
143	C₂×D₄×C₁₃	—	2	1	no	—
144	C₂×D₄×C₁₃	—	2	1	no	—
145	C₂×D₄×C₁₃	—	2	1	no	—
146	C₂×D₄×C₁₃	—	2	1	no	—
147	C₂×D₄×C₁₃	—	2	1	no	—
148	C₂×D₄×C₁₃	—	2	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	4	2	no	—
156	C₂×D₄×C₁₃	—	4	2	no	—
157	C₂×D₄×C₁₃	—	4	2	no	—
158	C₂×D₄×C₁₃	—	4	2	no	—
159	C₂×D₄×C₁₃	—	4	2	no	—
160	C₂×D₄×C₁₃	—	4	2	no	—
161	C₂²×C₄×C₁₃	—	2	2	no	—
162	C₂²×C₄×C₁₃	—	2	2	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	1	no	—
166	C₂²×C₄×C₁₃	—	2	1	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	2	1	no	—
171	C₂²×C₄×C₁₃	—	2	1	no	—
172	C₂²×C₄×C₁₃	—	2	1	no	—
173	C₂²×C₄×C₁₃	—	2	1	no	—
174	C₂²×C₄×C₁₃	—	2	1	no	—
175	C₂²×C₄×C₁₃	—	4	1	no	—
176	C₂²×C₄×C₁₃	—	4	1	no	—
177	C₂²×C₄×C₁₃	—	4	1	no	—
178	C₂²×C₄×C₁₃	—	4	1	no	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
185	C₁₃×SD₁₆	—	4	4	no	—
186	C₁₃×D₈	—	4	4	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	—	2	1	no	—
199	C₁₃×C₄⋊C₄	—	2	1	no	—
200	C₁₃×C₄⋊C₄	—	2	1	no	—
201	C₁₃×C₄⋊C₄	—	2	1	no	—
202	C₁₃×C₄⋊C₄	—	2	1	no	—
203	C₁₃×C₄⋊C₄	—	2	1	no	—
204	C₁₃×C₄⋊C₄	—	2	1	no	—
205	C₁₃×C₄⋊C₄	—	2	1	no	—
206	C₁₃×C₄⋊C₄	—	2	1	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	4	2	no	—
210	C₁₃×C₄⋊C₄	—	4	2	no	—
211	C₁₃×C₄⋊C₄	—	4	2	no	—
212	C₁₃×C₂²⋊C₄	—	4	2	no	—
213	C₁₃×C₂²⋊C₄	—	4	2	no	—
214	C₁₃×C₂²⋊C₄	—	4	2	no	—
215	C₁₃×C₂²⋊C₄	—	4	2	no	—
216	C₁₃×C₂²⋊C₄	—	4	2	no	—
217	C₁₃×C₂²⋊C₄	—	4	2	no	—
218	C₁₃×C₂²⋊C₄	—	4	2	no	—
219	C₁₃×C₂²⋊C₄	—	4	2	no	—
220	C₁₃×C₂²⋊C₄	—	4	2	no	—
221	C₁₃×C₂²⋊C₄	—	4	2	no	—
222	C₁₃×C₂²⋊C₄	—	4	2	no	—
223	C₁₃×C₂²⋊C₄	—	4	2	no	—
224	C₄²×C₁₃	—	2	1	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	4	1	no	—
229	C₄²×C₁₃	—	4	1	no	—
230	#2854	C₂×C₁₃	1	1	yes	characteristic, complemented
231	#2850	C₂×C₁₃	1	1	yes	characteristic, complemented
232	#2101	C₂×C₁₃	1	1	yes	characteristic, complemented
233	#2092	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#2067	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2066	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2055	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2054	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2042	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2036	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2034	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2012	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2000	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1999	C₂×C₁₃	1	1	yes	characteristic
244	#1797	C₂×C₁₃	1	1	yes	characteristic, complemented
245	C₂³×C₁₃	—	2	1	no	—
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	2	1	no	—
249	C₂³×C₁₃	—	2	1	no	—
250	C₂³×C₁₃	—	2	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	4	1	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	—	4	1	no	—
256	C₂³×C₁₃	—	4	1	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	—	4	1	no	—
265	C₂³×C₁₃	#135	1	2	yes	—
266	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	Q₈×C₁₃	—	4	1	no	—
268	Q₈×C₁₃	—	4	1	no	—
269	Q₈×C₁₃	—	4	1	no	—
270	Q₈×C₁₃	—	4	1	no	—
271	D₄×C₁₃	—	4	1	no	—
272	D₄×C₁₃	—	4	1	no	—
273	D₄×C₁₃	—	4	1	no	—
274	D₄×C₁₃	—	4	1	no	—
275	D₄×C₁₃	—	4	1	no	—
276	D₄×C₁₃	—	4	1	no	—
277	D₄×C₁₃	—	4	1	no	—
278	D₄×C₁₃	—	4	1	no	—
279	D₄×C₁₃	—	8	4	no	—
280	D₄×C₁₃	—	8	4	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	1	no	—
285	C₂×C₄×C₁₃	—	2	1	no	—
286	C₂×C₄×C₁₃	—	2	1	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	2	1	no	—
294	C₂×C₄×C₁₃	—	2	1	no	—
295	C₂×C₄×C₁₃	—	4	4	no	—
296	C₂×C₄×C₁₃	—	4	4	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	4	1	no	—
310	C₂×C₄×C₁₃	—	4	1	no	—
311	C₂×C₄×C₁₃	—	4	1	no	—
312	C₂×C₄×C₁₃	—	4	1	no	—
313	C₂×C₄×C₁₃	—	4	1	no	—
314	C₂×C₄×C₁₃	—	4	1	no	—
315	C₂×C₄×C₁₃	—	4	1	no	—
316	C₂×C₄×C₁₃	—	4	1	no	—
317	C₂×C₄×C₁₃	—	4	1	no	—
318	C₂×C₄×C₁₃	—	4	1	no	—
319	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
320	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
321	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
322	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
323	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
326	C₈×C₁₃	—	4	1	no	—
327	C₈×C₁₃	—	4	1	no	—
328	C₈×C₁₃	—	4	1	no	—
329	C₈×C₁₃	—	4	1	no	—
330	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
331	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
332	C₂×#124	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#123	—	2	1	no	—
334	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
337	C₂²×C₄²	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
342	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
352	#391	C₂²×C₁₃	1	1	yes	characteristic
353	#390	C₂²×C₁₃	1	1	yes	characteristic
354	#390	C₂²×C₁₃	1	1	yes	characteristic
355	#390	C₂²×C₁₃	1	1	yes	characteristic
356	#389	C₂²×C₁₃	1	1	yes	characteristic
357	#389	C₂²×C₁₃	1	1	yes	characteristic
358	#388	—	2	1	no	—
359	#388	—	2	1	no	—
360	#388	—	2	1	no	—
361	#388	—	2	1	no	—
362	#386	—	2	1	no	—
363	#386	—	2	1	no	—
364	#386	—	2	1	no	—
365	#382	C₂²×C₁₃	1	1	yes	characteristic
366	#380	C₂²×C₁₃	1	1	yes	characteristic
367	#340	C₂²×C₁₃	1	1	yes	characteristic
368	#340	C₂²×C₁₃	1	1	yes	characteristic
369	#340	C₂²×C₁₃	1	1	yes	characteristic
370	#340	C₂²×C₁₃	1	1	yes	characteristic
371	#336	C₂²×C₁₃	1	1	yes	characteristic
372	#336	C₂²×C₁₃	1	1	yes	characteristic
373	C₂²×C₁₃	—	2	2	no	—
374	C₂²×C₁₃	—	2	2	no	—
375	C₂²×C₁₃	—	2	2	no	—
376	C₂²×C₁₃	—	4	1	no	—
377	C₂²×C₁₃	—	4	1	no	—
378	C₂²×C₁₃	—	4	1	no	—
379	C₂²×C₁₃	—	4	1	no	—
380	C₂²×C₁₃	—	8	1	no	—
381	C₂²×C₁₃	—	8	1	no	—
382	C₂²×C₁₃	—	8	1	no	—
383	C₂²×C₁₃	—	8	1	no	—
384	C₂²×C₁₃	—	8	1	no	—
385	C₂²×C₁₃	—	8	1	no	—
386	C₂²×C₁₃	—	8	1	no	—
387	C₂²×C₁₃	—	8	1	no	—
388	C₂²×C₁₃	—	8	1	no	—
389	C₂²×C₁₃	—	8	1	no	—
390	C₂²×C₁₃	—	8	1	no	—
391	C₂²×C₁₃	—	8	1	no	—
392	C₂²×C₁₃	—	8	1	no	—
393	C₂²×C₁₃	—	8	1	no	—
394	C₂²×C₁₃	#534	1	1	yes	characteristic
395	C₂²×C₁₃	#535	1	1	yes	characteristic
396	C₂²×C₁₃	#537	1	1	yes	characteristic
397	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
398	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
399	C₂²×C₁₃	#575	1	1	yes	characteristic
400	C₂²×C₁₃	#575	1	1	yes	characteristic
401	C₄×C₁₃	—	2	2	no	—
402	C₄×C₁₃	—	4	1	no	—
403	C₄×C₁₃	—	4	1	no	—
404	C₄×C₁₃	—	4	1	no	—
405	C₄×C₁₃	—	4	1	no	—
406	C₄×C₁₃	—	8	1	no	—
407	C₄×C₁₃	—	8	1	no	—
408	C₄×C₁₃	—	8	1	no	—
409	C₄×C₁₃	—	8	1	no	—
410	C₄×C₁₃	—	8	1	no	—
411	C₄×C₁₃	—	8	1	no	—
412	C₄×C₁₃	#560	1	1	yes	characteristic
413	C₄×C₁₃	#560	1	1	yes	characteristic
414	C₄×C₁₃	#562	1	1	yes	characteristic
415	C₄×C₁₃	#562	1	1	yes	characteristic
416	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
417	C₂²×D₄	—	2	1	no	—
418	C₂²×D₄	—	2	1	no	—
419	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
421	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
422	C₂³×C₄	D₄×C₁₃	1	1	yes	characteristic
423	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
424	C₂×SD₁₆	—	4	1	no	—
425	C₂×SD₁₆	—	4	1	no	—
426	C₂×SD₁₆	—	4	1	no	—
427	C₂×D₈	—	4	1	no	—
428	C₂×D₈	—	4	1	no	—
429	C₂×D₈	—	4	1	no	—
430	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
431	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
432	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
433	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
434	#124	—	4	1	no	—
435	#124	—	4	1	no	—
436	#123	—	4	4	no	—
437	C₂²⋊Q₈	—	4	1	no	—
438	C₂²⋊Q₈	—	4	1	no	—
439	#121	—	4	1	no	—
440	#121	—	4	1	no	—
441	#121	—	4	1	no	—
442	#121	—	4	1	no	—
443	C₂×C₄⋊C₄	—	2	1	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	—	2	1	no	—
452	C₂×C₂²⋊C₄	—	2	1	no	—
453	C₂×C₂²⋊C₄	—	2	1	no	—
454	C₂×C₂²⋊C₄	—	2	1	no	—
455	C₂×C₂²⋊C₄	—	2	1	no	—
456	C₂×C₂²⋊C₄	—	2	1	no	—
457	C₂×C₂²⋊C₄	—	2	1	no	—
458	C₂×C₂²⋊C₄	—	2	1	no	—
459	C₂×C₂²⋊C₄	—	2	1	no	—
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₄²	—	4	1	no	—
464	C₂×C₄²	—	4	1	no	—
465	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
466	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
468	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
469	#107	—	4	1	no	—
470	#106	—	4	1	no	—
471	C₄⋊C₈	—	4	1	no	—
472	C₄⋊C₈	—	4	1	no	—
473	#103	—	4	1	no	—
474	#103	—	4	1	no	—
475	#103	—	4	1	no	—
476	#102	—	4	1	no	—
477	#102	—	4	1	no	—
478	#102	—	4	1	no	—
479	#102	—	4	1	no	—
480	#102	—	4	1	no	—
481	C₂²⋊C₈	—	4	1	no	—
482	C₂²⋊C₈	—	4	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	#95	—	2	1	no	—
487	#95	—	2	1	no	—
488	#95	—	2	1	no	—
489	#95	—	2	1	no	—
490	C₂×C₁₃	—	4	2	no	—
491	C₂×C₁₃	—	16	1	no	—
492	C₂×C₁₃	—	16	1	no	—
493	C₂×C₁₃	#2813	1	1	yes	characteristic
494	C₂×C₁₃	#3188	1	1	yes	characteristic
495	C₂×C₁₃	#3197	1	1	yes	characteristic
496	C₂×C₁₃	#3211	1	1	yes	characteristic
497	C₂×C₁₃	#3214	1	1	yes	characteristic
498	C₂×C₁₃	#3250	1	1	yes	characteristic
499	C₂×C₁₃	#3251	1	1	yes	characteristic
500	C₂⁴	—	2	1	no	—
501	C₂⁴	—	2	1	no	—
502	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
503	C₂×Q₈	—	2	1	no	—
504	C₂×Q₈	—	2	1	no	—
505	C₂×Q₈	—	2	1	no	—
506	C₂×Q₈	—	2	1	no	—
507	C₂×Q₈	—	2	1	no	—
508	C₂×Q₈	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	—	2	1	no	—
512	C₂×D₄	—	2	1	no	—
513	C₂×D₄	—	2	1	no	—
514	C₂×D₄	—	2	1	no	—
515	C₂×D₄	—	2	1	no	—
516	C₂×D₄	—	2	1	no	—
517	C₂×D₄	—	2	1	no	—
518	C₂×D₄	—	2	1	no	—
519	C₂×D₄	—	2	1	no	—
520	C₂×D₄	—	2	1	no	—
521	C₂×D₄	—	4	2	no	—
522	C₂×D₄	—	4	2	no	—
523	C₂×D₄	—	4	2	no	—
524	C₂×D₄	—	4	2	no	—
525	C₂×D₄	—	4	2	no	—
526	C₂×D₄	—	4	2	no	—
527	C₂²×C₄	—	2	2	no	—
528	C₂²×C₄	—	2	2	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	—	2	1	no	—
531	C₂²×C₄	—	2	1	no	—
532	C₂²×C₄	—	2	1	no	—
533	C₂²×C₄	—	2	1	no	—
534	C₂²×C₄	—	2	1	no	—
535	C₂²×C₄	—	2	1	no	—
536	C₂²×C₄	—	2	1	no	—
537	C₂²×C₄	—	2	1	no	—
538	C₂²×C₄	—	2	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	4	1	no	—
542	C₂²×C₄	—	4	1	no	—
543	C₂²×C₄	—	4	1	no	—
544	C₂²×C₄	—	4	1	no	—
545	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
546	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
547	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
548	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
550	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
551	SD₁₆	—	4	4	no	—
552	D₈	—	4	4	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	4	2	no	—
576	C₄⋊C₄	—	4	2	no	—
577	C₄⋊C₄	—	4	2	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	4	2	no	—
582	C₂²⋊C₄	—	4	2	no	—
583	C₂²⋊C₄	—	4	2	no	—
584	C₂²⋊C₄	—	4	2	no	—
585	C₂²⋊C₄	—	4	2	no	—
586	C₂²⋊C₄	—	4	2	no	—
587	C₂²⋊C₄	—	4	2	no	—
588	C₂²⋊C₄	—	4	2	no	—
589	C₂²⋊C₄	—	4	2	no	—
590	C₄²	—	2	1	no	—
591	C₄²	—	2	1	no	—
592	C₄²	—	2	1	no	—
593	C₄²	—	2	1	no	—
594	C₄²	—	4	1	no	—
595	C₄²	—	4	1	no	—
596	C₁₃	#32726	1	1	yes	characteristic, direct product factor, Sylow
597	C₂³	—	2	1	no	—
598	C₂³	—	2	1	no	—
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	—	2	1	no	—
602	C₂³	—	2	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	—	4	1	no	—
605	C₂³	—	4	1	no	—
606	C₂³	—	4	1	no	—
607	C₂³	—	4	1	no	—
608	C₂³	—	4	1	no	—
609	C₂³	—	4	1	no	—
610	C₂³	—	4	1	no	—
611	C₂³	—	4	1	no	—
612	C₂³	—	4	1	no	—
613	C₂³	—	4	1	no	—
614	C₂³	—	4	1	no	—
615	C₂³	—	4	1	no	—
616	C₂³	—	4	1	no	—
617	C₂³	C₁₃×#135	1	2	yes	—
618	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
619	Q₈	—	4	1	no	—
620	Q₈	—	4	1	no	—
621	Q₈	—	4	1	no	—
622	Q₈	—	4	1	no	—
623	D₄	—	4	1	no	—
624	D₄	—	4	1	no	—
625	D₄	—	4	1	no	—
626	D₄	—	4	1	no	—
627	D₄	—	4	1	no	—
628	D₄	—	4	1	no	—
629	D₄	—	4	1	no	—
630	D₄	—	4	1	no	—
631	D₄	—	8	4	no	—
632	D₄	—	8	4	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	2	1	no	—
639	C₂×C₄	—	2	1	no	—
640	C₂×C₄	—	2	1	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	4	4	no	—
648	C₂×C₄	—	4	4	no	—
649	C₂×C₄	—	4	1	no	—
650	C₂×C₄	—	4	1	no	—
651	C₂×C₄	—	4	1	no	—
652	C₂×C₄	—	4	1	no	—
653	C₂×C₄	—	4	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	1	no	—
657	C₂×C₄	—	4	1	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	1	no	—
663	C₂×C₄	—	4	1	no	—
664	C₂×C₄	—	4	1	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	1	no	—
667	C₂×C₄	—	4	1	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	1	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
672	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
673	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
674	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
675	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
677	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
678	C₈	—	4	1	no	—
679	C₈	—	4	1	no	—
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	2	2	no	—
684	C₂²	—	2	2	no	—
685	C₂²	—	4	1	no	—
686	C₂²	—	4	1	no	—
687	C₂²	—	4	1	no	—
688	C₂²	—	4	1	no	—
689	C₂²	—	8	1	no	—
690	C₂²	—	8	1	no	—
691	C₂²	—	8	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	—	8	1	no	—
696	C₂²	—	8	1	no	—
697	C₂²	—	8	1	no	—
698	C₂²	—	8	1	no	—
699	C₂²	—	8	1	no	—
700	C₂²	—	8	1	no	—
701	C₂²	—	8	1	no	—
702	C₂²	—	8	1	no	—
703	C₂²	C₁₃×#534	1	1	yes	characteristic
704	C₂²	C₁₃×#535	1	1	yes	characteristic
705	C₂²	C₁₃×#537	1	1	yes	characteristic
706	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
707	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
708	C₂²	C₁₃×#575	1	1	yes	characteristic
709	C₂²	C₁₃×#575	1	1	yes	characteristic
710	C₄	—	2	2	no	—
711	C₄	—	4	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	8	1	no	—
716	C₄	—	8	1	no	—
717	C₄	—	8	1	no	—
718	C₄	—	8	1	no	—
719	C₄	—	8	1	no	—
720	C₄	—	8	1	no	—
721	C₄	C₁₃×#560	1	1	yes	characteristic
722	C₄	C₁₃×#560	1	1	yes	characteristic
723	C₄	C₁₃×#562	1	1	yes	characteristic
724	C₄	C₁₃×#562	1	1	yes	characteristic
725	C₂	—	4	2	no	—
726	C₂	—	16	1	no	—
727	C₂	—	16	1	no	—
728	C₂	C₁₃×#2813	1	1	yes	characteristic
729	C₂	C₁₃×#3188	1	1	yes	characteristic
730	C₂	C₁₃×#3197	1	1	yes	characteristic
731	C₂	C₁₃×#3211	1	1	yes	characteristic
732	C₂	C₁₃×#3214	1	1	yes	characteristic
733	C₂	C₁₃×#3250	1	1	yes	characteristic
734	C₂	C₁₃×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₁₃×#1999	C₂
LCS	G ▷ C₂²×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
1. C₁₃×#2854	C₂	semidirect
2. C₁₃×#2850	C₂	semidirect
3. C₁₃×#2101	C₂	semidirect
4. C₁₃×#2092	C₂	semidirect
5. C₁₃×#2067	C₂	semidirect
6. C₁₃×#2066	C₂	semidirect
7. C₁₃×#2055	C₂	semidirect
8. C₁₃×#2054	C₂	semidirect
9. C₁₃×#2042	C₂	semidirect
10. C₁₃×#2036	C₂	semidirect
11. C₁₃×#2034	C₂	semidirect
12. C₁₃×#2012	C₂	semidirect
13. C₁₃×#2000	C₂	semidirect
15. C₁₃×#1797	C₂	semidirect
133. #32726	C₁₃	direct (N × H)
230. #2854	C₂×C₁₃	semidirect
231. #2850	C₂×C₁₃	semidirect
232. #2101	C₂×C₁₃	semidirect
233. #2092	C₂×C₁₃	semidirect
234. #2067	C₂×C₁₃	semidirect
235. #2066	C₂×C₁₃	semidirect
236. #2055	C₂×C₁₃	semidirect
237. #2054	C₂×C₁₃	semidirect
238. #2042	C₂×C₁₃	semidirect
239. #2036	C₂×C₁₃	semidirect
240. #2034	C₂×C₁₃	semidirect
241. #2012	C₂×C₁₃	semidirect
242. #2000	C₂×C₁₃	semidirect
244. #1797	C₂×C₁₃	semidirect
596. C₁₃	#32726	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₃×#2854	2
C₁₃×#2850	2
C₁₃×#2101	2
C₁₃×#2092	2
C₁₃×#2067	2
C₁₃×#2066	2
C₁₃×#2055	2
C₁₃×#2054	2
C₁₃×#2042	2
C₁₃×#2036	2
C₁₃×#2034	2
C₁₃×#2012	2
C₁₃×#2000	2
C₁₃×#1999	2
C₁₃×#1797	2
#32726	13

Subgroups — C13×#32726 #15719065

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32726 #15719065