Subgroups — C₁₃×#24524 #15710863

Order 3328.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#3094	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#449	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2064	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2046	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2045	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1978	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1977	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1930	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1785	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
19	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
22	C₁₃×#482	—	2	1	no	—
23	C₁₃×#482	—	2	1	no	—
24	C₁₃×#481	—	2	1	no	—
25	C₁₃×#480	—	2	1	no	—
26	C₁₃×#449	—	2	1	no	—
27	C₁₃×#449	—	2	1	no	—
28	C₁₃×#449	—	2	1	no	—
29	C₁₃×#449	—	2	1	no	—
30	C₁₃×#433	—	2	1	no	—
31	C₁₃×#433	—	2	1	no	—
32	C₁₃×#432	—	2	1	no	—
33	C₁₃×#431	—	2	1	no	—
34	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#424	C₂²	1	1	yes	characteristic
39	C₁₃×#424	C₂²	1	1	yes	characteristic
40	C₁₃×#419	C₂²	1	1	yes	characteristic
41	C₁₃×#419	C₂²	1	1	yes	characteristic
42	C₁₃×#418	C₂²	1	1	yes	characteristic
43	C₁₃×#418	C₂²	1	1	yes	characteristic
44	C₁₃×#418	C₂²	1	1	yes	characteristic
45	C₁₃×#418	C₂²	1	1	yes	characteristic
46	C₁₃×#417	—	2	1	no	—
47	C₁₃×#417	—	2	1	no	—
48	C₁₃×#416	—	2	1	no	—
49	C₁₃×#416	—	2	1	no	—
50	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#101	C₂²	1	1	yes	characteristic
54	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
55	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
57	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
58	C₁₃×#407	C₂²	1	1	yes	characteristic
59	C₁₃×#407	C₂²	1	1	yes	characteristic
60	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₃×#405	C₂²	1	1	yes	characteristic
62	C₁₃×#405	C₂²	1	1	yes	characteristic
63	C₁₃×#343	C₂²	1	1	yes	characteristic
64	C₁₃×#343	C₂²	1	1	yes	characteristic
65	C₁₃×#341	C₂²	1	1	yes	characteristic
66	C₁₃×#341	C₂²	1	1	yes	characteristic
67	C₂×C₁₃×#41	—	2	2	no	—
68	C₂×C₁₃×#41	—	2	2	no	—
69	C₂×C₁₃×#41	—	2	1	no	—
70	C₂×C₁₃×#41	—	2	1	no	—
71	C₂×C₁₃×#41	—	2	1	no	—
72	C₂×C₁₃×#41	—	2	1	no	—
73	C₂×C₁₃×#41	—	4	1	no	—
74	C₂×C₁₃×#41	—	4	1	no	—
75	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₁₃	—	2	1	no	—
77	C₂²×D₄×C₁₃	—	2	1	no	—
78	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₁₃	—	2	1	no	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×SD₁₆	—	2	2	no	—
83	C₂×C₁₃×SD₁₆	—	2	1	no	—
84	C₂×C₁₃×SD₁₆	—	2	1	no	—
85	C₂×C₁₃×SD₁₆	—	4	1	no	—
86	C₂×C₁₃×D₈	—	2	2	no	—
87	C₂×C₁₃×D₈	—	2	1	no	—
88	C₂×C₁₃×D₈	—	2	1	no	—
89	C₂×C₁₃×D₈	—	4	1	no	—
90	C₂×C₁₃×M₁₆	—	2	1	no	—
91	C₂×C₁₃×M₁₆	—	4	1	no	—
92	C₂×C₁₃×M₁₆	—	4	1	no	—
93	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
97	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
98	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₁₃	—	2	1	no	—
100	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
102	C₁₃×#121	—	2	1	no	—
103	C₁₃×#121	—	2	1	no	—
104	C₁₃×#121	—	2	1	no	—
105	C₁₃×#121	—	2	1	no	—
106	C₁₃×#117	—	2	1	no	—
107	C₁₃×#117	—	2	1	no	—
108	C₁₃×#117	D₄	1	1	yes	characteristic
109	C₁₃×#117	D₄	1	1	yes	characteristic
110	C₁₃×#117	C₂³	1	1	yes	characteristic
111	C₁₃×#117	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
114	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₄²×C₁₃	—	2	1	no	—
118	C₁₃×#108	—	4	1	no	—
119	C₁₃×#108	—	4	1	no	—
120	C₁₃×#107	—	2	1	no	—
121	C₁₃×#107	—	2	1	no	—
122	C₁₃×#106	—	2	1	no	—
123	C₁₃×#106	—	2	1	no	—
124	C₁₃×C₄⋊C₈	—	2	1	no	—
125	C₁₃×C₄⋊C₈	—	2	1	no	—
126	C₁₃×C₄⋊C₈	—	2	1	no	—
127	C₁₃×C₄⋊C₈	—	2	1	no	—
128	C₁₃×#103	—	2	1	no	—
129	C₁₃×#103	—	2	1	no	—
130	C₁₃×#103	—	2	1	no	—
131	C₁₃×#103	—	2	1	no	—
132	C₁₃×#103	—	2	1	no	—
133	C₁₃×#103	—	2	1	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#102	—	2	1	no	—
137	C₁₃×#102	—	2	1	no	—
138	C₁₃×#102	—	2	1	no	—
139	C₁₃×#102	—	2	1	no	—
140	C₁₃×#102	—	2	1	no	—
141	C₁₃×#102	—	2	1	no	—
142	C₁₃×#102	—	2	1	no	—
143	C₁₃×#102	—	2	1	no	—
144	C₁₃×#101	—	2	2	no	—
145	C₁₃×#101	—	4	1	no	—
146	C₁₃×#100	—	2	2	no	—
147	C₁₃×#100	—	4	1	no	—
148	C₁₃×#100	—	4	1	no	—
149	C₁₃×#100	—	4	1	no	—
150	C₁₃×C₂²⋊C₈	—	2	1	no	—
151	C₁₃×C₂²⋊C₈	—	2	1	no	—
152	C₁₃×C₂²⋊C₈	—	2	1	no	—
153	C₁₃×C₂²⋊C₈	—	2	1	no	—
154	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
155	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
156	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
157	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
158	C₁₃×#97	—	2	1	no	—
159	C₁₃×#97	—	2	1	no	—
160	C₄×C₈×C₁₃	—	2	1	no	—
161	C₄×C₈×C₁₃	—	2	1	no	—
162	#24524	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
163	C₂⁴×C₁₃	—	2	1	no	—
164	C₂⁴×C₁₃	—	2	1	no	—
165	C₂⁴×C₁₃	#41	1	1	yes	characteristic
166	C₁₃×#41	—	2	4	no	—
167	C₁₃×#41	—	2	4	no	—
168	C₁₃×#41	—	4	2	no	—
169	C₁₃×#41	—	4	2	no	—
170	C₁₃×#41	—	4	2	no	—
171	C₁₃×#41	—	4	2	no	—
172	C₁₃×#41	—	4	2	no	—
173	C₁₃×#41	—	4	2	no	—
174	C₂×Q₈×C₁₃	—	2	1	no	—
175	C₂×Q₈×C₁₃	—	2	1	no	—
176	C₂×Q₈×C₁₃	—	2	1	no	—
177	C₂×Q₈×C₁₃	—	2	1	no	—
178	C₂×Q₈×C₁₃	—	2	1	no	—
179	C₂×Q₈×C₁₃	#41	1	2	yes	—
180	C₂×D₄×C₁₃	—	2	1	no	—
181	C₂×D₄×C₁₃	—	2	1	no	—
182	C₂×D₄×C₁₃	—	2	1	no	—
183	C₂×D₄×C₁₃	—	2	1	no	—
184	C₂×D₄×C₁₃	—	2	1	no	—
185	C₂×D₄×C₁₃	—	2	1	no	—
186	C₂×D₄×C₁₃	—	2	1	no	—
187	C₂×D₄×C₁₃	—	2	1	no	—
188	C₂×D₄×C₁₃	—	2	1	no	—
189	C₂×D₄×C₁₃	—	2	1	no	—
190	C₂×D₄×C₁₃	—	2	1	no	—
191	C₂×D₄×C₁₃	—	4	2	no	—
192	C₂×D₄×C₁₃	—	4	2	no	—
193	C₂×D₄×C₁₃	—	4	1	no	—
194	C₂×D₄×C₁₃	—	4	1	no	—
195	C₂×D₄×C₁₃	—	4	1	no	—
196	C₂×D₄×C₁₃	—	4	1	no	—
197	C₂×D₄×C₁₃	—	8	2	no	—
198	C₂×D₄×C₁₃	#41	1	2	yes	—
199	C₂²×C₄×C₁₃	—	2	1	no	—
200	C₂²×C₄×C₁₃	—	2	1	no	—
201	C₂²×C₄×C₁₃	—	2	1	no	—
202	C₂²×C₄×C₁₃	—	2	1	no	—
203	C₂²×C₄×C₁₃	—	2	1	no	—
204	C₂²×C₄×C₁₃	—	2	1	no	—
205	C₂²×C₄×C₁₃	—	2	1	no	—
206	C₂²×C₄×C₁₃	—	2	1	no	—
207	C₂²×C₄×C₁₃	—	4	2	no	—
208	C₂²×C₄×C₁₃	—	4	2	no	—
209	C₂²×C₄×C₁₃	—	4	1	no	—
210	C₂²×C₄×C₁₃	—	4	1	no	—
211	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
212	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
213	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
214	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
216	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
217	C₁₃×SD₁₆	—	4	2	no	—
218	C₁₃×SD₁₆	—	4	2	no	—
219	C₁₃×D₈	—	4	2	no	—
220	C₁₃×D₈	—	4	2	no	—
221	C₁₃×M₁₆	—	2	1	no	—
222	C₁₃×M₁₆	—	2	1	no	—
223	C₁₃×M₁₆	—	2	1	no	—
224	C₁₃×M₁₆	—	2	1	no	—
225	C₁₃×M₁₆	—	2	1	no	—
226	C₁₃×M₁₆	—	2	1	no	—
227	C₁₃×M₁₆	—	2	1	no	—
228	C₁₃×M₁₆	—	2	1	no	—
229	C₁₃×M₁₆	—	2	1	no	—
230	C₁₃×M₁₆	—	2	1	no	—
231	C₁₃×M₁₆	—	2	1	no	—
232	C₁₃×M₁₆	—	2	1	no	—
233	C₁₃×M₁₆	—	4	2	no	—
234	C₂×C₈×C₁₃	—	2	1	no	—
235	C₂×C₈×C₁₃	—	2	1	no	—
236	C₂×C₈×C₁₃	—	2	1	no	—
237	C₂×C₈×C₁₃	—	2	1	no	—
238	C₂×C₈×C₁₃	—	2	1	no	—
239	C₂×C₈×C₁₃	—	2	1	no	—
240	C₂×C₈×C₁₃	—	2	1	no	—
241	C₂×C₈×C₁₃	—	2	1	no	—
242	C₂×C₈×C₁₃	—	2	1	no	—
243	C₂×C₈×C₁₃	—	2	1	no	—
244	C₂×C₈×C₁₃	—	4	2	no	—
245	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
246	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
247	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
248	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
249	C₁₃×C₄⋊C₄	—	2	1	no	—
250	C₁₃×C₄⋊C₄	—	2	1	no	—
251	C₁₃×C₄⋊C₄	—	2	1	no	—
252	C₁₃×C₄⋊C₄	—	2	1	no	—
253	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
254	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
255	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
256	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
257	C₁₃×C₂²⋊C₄	—	2	1	no	—
258	C₁₃×C₂²⋊C₄	—	2	1	no	—
259	C₁₃×C₂²⋊C₄	—	2	1	no	—
260	C₁₃×C₂²⋊C₄	—	2	1	no	—
261	C₁₃×C₂²⋊C₄	—	4	1	no	—
262	C₁₃×C₂²⋊C₄	—	4	1	no	—
263	C₄²×C₁₃	—	2	1	no	—
264	C₄²×C₁₃	—	2	1	no	—
265	C₄²×C₁₃	—	2	1	no	—
266	C₄²×C₁₃	—	2	1	no	—
267	#3094	C₂×C₁₃	1	1	yes	characteristic, complemented
268	C₂×#449	C₂×C₁₃	1	1	yes	characteristic
269	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
270	#2896	C₂×C₁₃	1	1	yes	characteristic, complemented
271	#2064	C₂×C₁₃	1	1	yes	characteristic, complemented
272	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
273	#2046	C₂×C₁₃	1	1	yes	characteristic, complemented
274	#2045	C₂×C₁₃	1	1	yes	characteristic, complemented
275	#1978	C₂×C₁₃	1	1	yes	characteristic, complemented
276	#1977	C₂×C₁₃	1	1	yes	characteristic, complemented
277	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
278	#1930	C₂×C₁₃	1	1	yes	characteristic, complemented
279	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
280	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
281	#1785	C₂×C₁₃	1	1	yes	characteristic, complemented
282	C₂³×C₁₃	—	2	1	no	—
283	C₂³×C₁₃	—	2	1	no	—
284	C₂³×C₁₃	—	2	2	no	—
285	C₂³×C₁₃	—	4	1	no	—
286	C₂³×C₁₃	—	4	1	no	—
287	C₂³×C₁₃	—	4	1	no	—
288	C₂³×C₁₃	—	4	1	no	—
289	C₂³×C₁₃	—	4	1	no	—
290	C₂³×C₁₃	—	4	1	no	—
291	C₂³×C₁₃	—	4	1	no	—
292	C₂³×C₁₃	—	8	1	no	—
293	C₂³×C₁₃	—	8	1	no	—
294	C₂³×C₁₃	—	8	1	no	—
295	C₂³×C₁₃	—	8	1	no	—
296	C₂³×C₁₃	#121	1	1	yes	characteristic
297	C₂³×C₁₃	#121	1	1	yes	characteristic
298	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
299	Q₈×C₁₃	—	2	2	no	—
300	Q₈×C₁₃	—	2	2	no	—
301	Q₈×C₁₃	—	4	1	no	—
302	Q₈×C₁₃	—	4	1	no	—
303	D₄×C₁₃	—	2	2	no	—
304	D₄×C₁₃	—	2	2	no	—
305	D₄×C₁₃	—	4	4	no	—
306	D₄×C₁₃	—	4	4	no	—
307	D₄×C₁₃	—	4	1	no	—
308	D₄×C₁₃	—	4	1	no	—
309	D₄×C₁₃	—	4	1	no	—
310	D₄×C₁₃	—	4	1	no	—
311	D₄×C₁₃	—	4	1	no	—
312	D₄×C₁₃	—	4	1	no	—
313	D₄×C₁₃	—	8	2	no	—
314	D₄×C₁₃	—	8	2	no	—
315	C₂×C₄×C₁₃	—	2	1	no	—
316	C₂×C₄×C₁₃	—	2	1	no	—
317	C₂×C₄×C₁₃	—	2	1	no	—
318	C₂×C₄×C₁₃	—	2	1	no	—
319	C₂×C₄×C₁₃	—	2	1	no	—
320	C₂×C₄×C₁₃	—	2	1	no	—
321	C₂×C₄×C₁₃	—	2	1	no	—
322	C₂×C₄×C₁₃	—	2	1	no	—
323	C₂×C₄×C₁₃	—	2	1	no	—
324	C₂×C₄×C₁₃	—	2	1	no	—
325	C₂×C₄×C₁₃	—	2	1	no	—
326	C₂×C₄×C₁₃	—	2	1	no	—
327	C₂×C₄×C₁₃	—	2	1	no	—
328	C₂×C₄×C₁₃	—	2	1	no	—
329	C₂×C₄×C₁₃	—	2	2	no	—
330	C₂×C₄×C₁₃	—	4	4	no	—
331	C₂×C₄×C₁₃	—	4	4	no	—
332	C₂×C₄×C₁₃	—	4	2	no	—
333	C₂×C₄×C₁₃	—	4	1	no	—
334	C₂×C₄×C₁₃	—	4	1	no	—
335	C₂×C₄×C₁₃	—	4	1	no	—
336	C₂×C₄×C₁₃	—	8	1	no	—
337	C₂×C₄×C₁₃	—	8	1	no	—
338	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
339	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
340	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
342	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
343	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
344	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
345	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
346	C₈×C₁₃	—	2	1	no	—
347	C₈×C₁₃	—	2	1	no	—
348	C₈×C₁₃	—	2	1	no	—
349	C₈×C₁₃	—	2	1	no	—
350	C₈×C₁₃	—	4	1	no	—
351	C₈×C₁₃	—	4	1	no	—
352	C₈×C₁₃	—	4	1	no	—
353	C₈×C₁₃	—	4	1	no	—
354	C₈×C₁₃	—	4	1	no	—
355	C₈×C₁₃	—	4	1	no	—
356	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
357	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
358	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
359	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
360	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
361	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
362	#482	—	2	1	no	—
363	#482	—	2	1	no	—
364	#481	—	2	1	no	—
365	#480	—	2	1	no	—
366	#449	—	2	1	no	—
367	#449	—	2	1	no	—
368	#449	—	2	1	no	—
369	#449	—	2	1	no	—
370	#433	—	2	1	no	—
371	#433	—	2	1	no	—
372	#432	—	2	1	no	—
373	#431	—	2	1	no	—
374	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
375	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
376	#428	C₂²×C₁₃	1	1	yes	characteristic
377	#428	C₂²×C₁₃	1	1	yes	characteristic
378	#424	C₂²×C₁₃	1	1	yes	characteristic
379	#424	C₂²×C₁₃	1	1	yes	characteristic
380	#419	C₂²×C₁₃	1	1	yes	characteristic
381	#419	C₂²×C₁₃	1	1	yes	characteristic
382	#418	C₂²×C₁₃	1	1	yes	characteristic
383	#418	C₂²×C₁₃	1	1	yes	characteristic
384	#418	C₂²×C₁₃	1	1	yes	characteristic
385	#418	C₂²×C₁₃	1	1	yes	characteristic
386	#417	—	2	1	no	—
387	#417	—	2	1	no	—
388	#416	—	2	1	no	—
389	#416	—	2	1	no	—
390	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
391	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
392	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
393	C₂×#101	C₂²×C₁₃	1	1	yes	characteristic
394	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
395	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
396	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
397	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
398	#407	C₂²×C₁₃	1	1	yes	characteristic
399	#407	C₂²×C₁₃	1	1	yes	characteristic
400	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
401	#405	C₂²×C₁₃	1	1	yes	characteristic
402	#405	C₂²×C₁₃	1	1	yes	characteristic
403	#343	C₂²×C₁₃	1	1	yes	characteristic
404	#343	C₂²×C₁₃	1	1	yes	characteristic
405	#341	C₂²×C₁₃	1	1	yes	characteristic
406	#341	C₂²×C₁₃	1	1	yes	characteristic
407	C₂²×C₁₃	—	2	1	no	—
408	C₂²×C₁₃	—	2	1	no	—
409	C₂²×C₁₃	—	2	1	no	—
410	C₂²×C₁₃	—	2	1	no	—
411	C₂²×C₁₃	—	2	1	no	—
412	C₂²×C₁₃	—	2	1	no	—
413	C₂²×C₁₃	—	2	1	no	—
414	C₂²×C₁₃	—	2	1	no	—
415	C₂²×C₁₃	—	4	2	no	—
416	C₂²×C₁₃	—	8	1	no	—
417	C₂²×C₁₃	—	8	1	no	—
418	C₂²×C₁₃	—	8	2	no	—
419	C₂²×C₁₃	—	8	2	no	—
420	C₂²×C₁₃	—	8	1	no	—
421	C₂²×C₁₃	—	8	1	no	—
422	C₂²×C₁₃	—	8	1	no	—
423	C₂²×C₁₃	—	8	1	no	—
424	C₂²×C₁₃	—	8	1	no	—
425	C₂²×C₁₃	—	16	1	no	—
426	C₂²×C₁₃	—	16	1	no	—
427	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
428	C₂²×C₁₃	#551	1	1	yes	characteristic
429	C₂²×C₁₃	#551	1	1	yes	characteristic
430	C₄×C₁₃	—	2	1	no	—
431	C₄×C₁₃	—	2	1	no	—
432	C₄×C₁₃	—	4	2	no	—
433	C₄×C₁₃	—	4	1	no	—
434	C₄×C₁₃	—	4	1	no	—
435	C₄×C₁₃	—	4	1	no	—
436	C₄×C₁₃	—	4	1	no	—
437	C₄×C₁₃	—	8	1	no	—
438	C₄×C₁₃	#525	1	1	yes	characteristic
439	C₄×C₁₃	#535	1	1	yes	characteristic
440	C₄×C₁₃	#546	1	1	yes	characteristic
441	C₄×C₁₃	#546	1	1	yes	characteristic
442	C₂×#41	—	2	2	no	—
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	1	no	—
445	C₂×#41	—	2	1	no	—
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	1	no	—
448	C₂×#41	—	4	1	no	—
449	C₂×#41	—	4	1	no	—
450	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
451	C₂²×D₄	—	2	1	no	—
452	C₂²×D₄	—	2	1	no	—
453	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
454	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂³×C₄	—	2	1	no	—
456	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×SD₁₆	—	2	2	no	—
458	C₂×SD₁₆	—	2	1	no	—
459	C₂×SD₁₆	—	2	1	no	—
460	C₂×SD₁₆	—	4	1	no	—
461	C₂×D₈	—	2	2	no	—
462	C₂×D₈	—	2	1	no	—
463	C₂×D₈	—	2	1	no	—
464	C₂×D₈	—	4	1	no	—
465	C₂×M₁₆	—	2	1	no	—
466	C₂×M₁₆	—	4	1	no	—
467	C₂×M₁₆	—	4	1	no	—
468	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
471	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
472	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
473	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
474	C₂²×C₈	—	2	1	no	—
475	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
476	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
477	#121	—	2	1	no	—
478	#121	—	2	1	no	—
479	#121	—	2	1	no	—
480	#121	—	2	1	no	—
481	#117	—	2	1	no	—
482	#117	—	2	1	no	—
483	#117	D₄×C₁₃	1	1	yes	characteristic
484	#117	D₄×C₁₃	1	1	yes	characteristic
485	#117	C₂³×C₁₃	1	1	yes	characteristic
486	#117	C₂³×C₁₃	1	1	yes	characteristic
487	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
488	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
489	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
490	C₂×C₂²⋊C₄	—	2	1	no	—
491	C₂×C₂²⋊C₄	—	2	1	no	—
492	C₂×C₄²	—	2	1	no	—
493	#108	—	4	1	no	—
494	#108	—	4	1	no	—
495	#107	—	2	1	no	—
496	#107	—	2	1	no	—
497	#106	—	2	1	no	—
498	#106	—	2	1	no	—
499	C₄⋊C₈	—	2	1	no	—
500	C₄⋊C₈	—	2	1	no	—
501	C₄⋊C₈	—	2	1	no	—
502	C₄⋊C₈	—	2	1	no	—
503	#103	—	2	1	no	—
504	#103	—	2	1	no	—
505	#103	—	2	1	no	—
506	#103	—	2	1	no	—
507	#103	—	2	1	no	—
508	#103	—	2	1	no	—
509	#102	—	2	1	no	—
510	#102	—	2	1	no	—
511	#102	—	2	1	no	—
512	#102	—	2	1	no	—
513	#102	—	2	1	no	—
514	#102	—	2	1	no	—
515	#102	—	2	1	no	—
516	#102	—	2	1	no	—
517	#102	—	2	1	no	—
518	#102	—	2	1	no	—
519	#101	—	2	2	no	—
520	#101	—	4	1	no	—
521	#100	—	2	2	no	—
522	#100	—	4	1	no	—
523	#100	—	4	1	no	—
524	#100	—	4	1	no	—
525	C₂²⋊C₈	—	2	1	no	—
526	C₂²⋊C₈	—	2	1	no	—
527	C₂²⋊C₈	—	2	1	no	—
528	C₂²⋊C₈	—	2	1	no	—
529	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
530	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
531	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
532	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
533	#97	—	2	1	no	—
534	#97	—	2	1	no	—
535	C₄×C₈	—	2	1	no	—
536	C₄×C₈	—	2	1	no	—
537	C₂×C₁₃	—	2	1	no	—
538	C₂×C₁₃	—	2	1	no	—
539	C₂×C₁₃	—	4	1	no	—
540	C₂×C₁₃	—	4	1	no	—
541	C₂×C₁₃	—	8	2	no	—
542	C₂×C₁₃	—	16	1	no	—
543	C₂×C₁₃	#2411	1	1	yes	characteristic
544	C₂×C₁₃	#3067	1	1	yes	characteristic
545	C₂×C₁₃	#3068	1	1	yes	characteristic
546	C₂⁴	—	2	1	no	—
547	C₂⁴	—	2	1	no	—
548	C₂⁴	C₁₃×#41	1	1	yes	characteristic
549	#41	—	2	4	no	—
550	#41	—	2	4	no	—
551	#41	—	4	2	no	—
552	#41	—	4	2	no	—
553	#41	—	4	2	no	—
554	#41	—	4	2	no	—
555	#41	—	4	2	no	—
556	#41	—	4	2	no	—
557	C₂×Q₈	—	2	1	no	—
558	C₂×Q₈	—	2	1	no	—
559	C₂×Q₈	—	2	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	1	no	—
562	C₂×Q₈	C₁₃×#41	1	2	yes	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	1	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	1	no	—
572	C₂×D₄	—	2	1	no	—
573	C₂×D₄	—	2	1	no	—
574	C₂×D₄	—	4	2	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	1	no	—
577	C₂×D₄	—	4	1	no	—
578	C₂×D₄	—	4	1	no	—
579	C₂×D₄	—	4	1	no	—
580	C₂×D₄	—	8	2	no	—
581	C₂×D₄	C₁₃×#41	1	2	yes	—
582	C₂²×C₄	—	2	1	no	—
583	C₂²×C₄	—	2	1	no	—
584	C₂²×C₄	—	2	1	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	4	2	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	1	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
598	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
599	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
600	SD₁₆	—	4	2	no	—
601	SD₁₆	—	4	2	no	—
602	D₈	—	4	2	no	—
603	D₈	—	4	2	no	—
604	M₁₆	—	2	1	no	—
605	M₁₆	—	2	1	no	—
606	M₁₆	—	2	1	no	—
607	M₁₆	—	2	1	no	—
608	M₁₆	—	2	1	no	—
609	M₁₆	—	2	1	no	—
610	M₁₆	—	2	1	no	—
611	M₁₆	—	2	1	no	—
612	M₁₆	—	2	1	no	—
613	M₁₆	—	2	1	no	—
614	M₁₆	—	2	1	no	—
615	M₁₆	—	2	1	no	—
616	M₁₆	—	4	2	no	—
617	C₂×C₈	—	2	1	no	—
618	C₂×C₈	—	2	1	no	—
619	C₂×C₈	—	2	1	no	—
620	C₂×C₈	—	2	1	no	—
621	C₂×C₈	—	2	1	no	—
622	C₂×C₈	—	2	1	no	—
623	C₂×C₈	—	2	1	no	—
624	C₂×C₈	—	2	1	no	—
625	C₂×C₈	—	2	1	no	—
626	C₂×C₈	—	2	1	no	—
627	C₂×C₈	—	4	2	no	—
628	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
629	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
630	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
631	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
632	C₄⋊C₄	—	2	1	no	—
633	C₄⋊C₄	—	2	1	no	—
634	C₄⋊C₄	—	2	1	no	—
635	C₄⋊C₄	—	2	1	no	—
636	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
637	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
638	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
639	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
640	C₂²⋊C₄	—	2	1	no	—
641	C₂²⋊C₄	—	2	1	no	—
642	C₂²⋊C₄	—	2	1	no	—
643	C₂²⋊C₄	—	2	1	no	—
644	C₂²⋊C₄	—	4	1	no	—
645	C₂²⋊C₄	—	4	1	no	—
646	C₄²	—	2	1	no	—
647	C₄²	—	2	1	no	—
648	C₄²	—	2	1	no	—
649	C₄²	—	2	1	no	—
650	C₁₃	#24524	1	1	yes	characteristic, direct product factor, Sylow
651	C₂³	—	2	1	no	—
652	C₂³	—	2	1	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	4	1	no	—
655	C₂³	—	4	1	no	—
656	C₂³	—	4	1	no	—
657	C₂³	—	4	1	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	1	no	—
660	C₂³	—	4	1	no	—
661	C₂³	—	8	1	no	—
662	C₂³	—	8	1	no	—
663	C₂³	—	8	1	no	—
664	C₂³	—	8	1	no	—
665	C₂³	C₁₃×#121	1	1	yes	characteristic
666	C₂³	C₁₃×#121	1	1	yes	characteristic
667	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
668	Q₈	—	2	2	no	—
669	Q₈	—	2	2	no	—
670	Q₈	—	4	1	no	—
671	Q₈	—	4	1	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	4	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	1	no	—
698	C₂×C₄	—	2	2	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	4	1	no	—
704	C₂×C₄	—	4	1	no	—
705	C₂×C₄	—	8	1	no	—
706	C₂×C₄	—	8	1	no	—
707	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
708	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
711	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
712	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
713	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
714	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
715	C₈	—	2	1	no	—
716	C₈	—	2	1	no	—
717	C₈	—	2	1	no	—
718	C₈	—	2	1	no	—
719	C₈	—	4	1	no	—
720	C₈	—	4	1	no	—
721	C₈	—	4	1	no	—
722	C₈	—	4	1	no	—
723	C₈	—	4	1	no	—
724	C₈	—	4	1	no	—
725	C₂²	—	2	1	no	—
726	C₂²	—	2	1	no	—
727	C₂²	—	2	1	no	—
728	C₂²	—	2	1	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	2	1	no	—
731	C₂²	—	2	1	no	—
732	C₂²	—	2	1	no	—
733	C₂²	—	4	2	no	—
734	C₂²	—	8	1	no	—
735	C₂²	—	8	1	no	—
736	C₂²	—	8	2	no	—
737	C₂²	—	8	2	no	—
738	C₂²	—	8	1	no	—
739	C₂²	—	8	1	no	—
740	C₂²	—	8	1	no	—
741	C₂²	—	8	1	no	—
742	C₂²	—	8	1	no	—
743	C₂²	—	16	1	no	—
744	C₂²	—	16	1	no	—
745	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
746	C₂²	C₁₃×#551	1	1	yes	characteristic
747	C₂²	C₁₃×#551	1	1	yes	characteristic
748	C₄	—	2	1	no	—
749	C₄	—	2	1	no	—
750	C₄	—	4	1	no	—
751	C₄	—	4	1	no	—
752	C₄	—	4	1	no	—
753	C₄	—	4	1	no	—
754	C₄	—	4	2	no	—
755	C₄	—	8	1	no	—
756	C₄	C₁₃×#525	1	1	yes	characteristic
757	C₄	C₁₃×#535	1	1	yes	characteristic
758	C₄	C₁₃×#546	1	1	yes	characteristic
759	C₄	C₁₃×#546	1	1	yes	characteristic
760	C₂	—	2	1	no	—
761	C₂	—	2	1	no	—
762	C₂	—	4	1	no	—
763	C₂	—	4	1	no	—
764	C₂	—	8	2	no	—
765	C₂	—	16	1	no	—
766	C₂	C₁₃×#2411	1	1	yes	characteristic
767	C₂	C₁₃×#3067	1	1	yes	characteristic
768	C₂	C₁₃×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂×C₁₃×#449	C₂
LCS	G ▷ C₂²×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
1. C₁₃×#3094	C₂	semidirect
3. C₁₃×#2924	C₂	semidirect
4. C₁₃×#2896	C₂	semidirect
5. C₁₃×#2064	C₂	semidirect
6. C₁₃×#2063	C₂	semidirect
7. C₁₃×#2046	C₂	semidirect
8. C₁₃×#2045	C₂	semidirect
9. C₁₃×#1978	C₂	semidirect
10. C₁₃×#1977	C₂	semidirect
11. C₁₃×#1931	C₂	semidirect
12. C₁₃×#1930	C₂	semidirect
13. C₁₃×#1900	C₂	semidirect
14. C₁₃×#1855	C₂	semidirect
15. C₁₃×#1785	C₂	semidirect
162. #24524	C₁₃	direct (N × H)
267. #3094	C₂×C₁₃	semidirect
269. #2924	C₂×C₁₃	semidirect
270. #2896	C₂×C₁₃	semidirect
271. #2064	C₂×C₁₃	semidirect
272. #2063	C₂×C₁₃	semidirect
273. #2046	C₂×C₁₃	semidirect
274. #2045	C₂×C₁₃	semidirect
275. #1978	C₂×C₁₃	semidirect
276. #1977	C₂×C₁₃	semidirect
277. #1931	C₂×C₁₃	semidirect
278. #1930	C₂×C₁₃	semidirect
279. #1900	C₂×C₁₃	semidirect
280. #1855	C₂×C₁₃	semidirect
281. #1785	C₂×C₁₃	semidirect
650. C₁₃	#24524	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×#3094	2
C₂×C₁₃×#449	2
C₁₃×#2924	2
C₁₃×#2896	2
C₁₃×#2064	2
C₁₃×#2063	2
C₁₃×#2046	2
C₁₃×#2045	2
C₁₃×#1978	2
C₁₃×#1977	2
C₁₃×#1931	2
C₁₃×#1930	2
C₁₃×#1900	2
C₁₃×#1855	2
C₁₃×#1785	2
#24524	13

Subgroups — C13×#24524 #15710863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24524 #15710863