Subgroups — C₁₃×#24520 #15710859

Order 3328.

1002 conjugacy classes of subgroups.

The subgroup lattice has 592 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×#447	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2063	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2045	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1978	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1931	C₂	1	2	yes	maximal, complemented
9	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1783	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂²×C₁₃×D₈	C₂²	1	2	yes	—
14	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
17	C₁₃×#482	—	2	1	no	—
18	C₁₃×#482	—	2	1	no	—
19	C₁₃×#481	—	2	1	no	—
20	C₁₃×#480	—	2	1	no	—
21	C₁₃×#447	—	2	1	no	—
22	C₁₃×#447	—	2	1	no	—
23	C₁₃×#447	—	2	2	no	—
24	C₁₃×#433	—	2	2	no	—
25	C₁₃×#432	—	2	1	no	—
26	C₁₃×#431	—	2	1	no	—
27	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
28	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
29	C₁₃×#428	C₂²	1	1	yes	characteristic, complemented
30	C₁₃×#424	C₂²	1	2	yes	complemented
31	C₁₃×#418	—	2	1	no	—
32	C₁₃×#418	—	2	1	no	—
33	C₁₃×#418	C₂²	1	2	yes	—
34	C₁₃×#418	C₂²	1	2	yes	—
35	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
36	C₁₃×#418	C₂²	1	1	yes	characteristic, complemented
37	C₂×C₁₃×#102	—	2	1	no	—
38	C₂×C₁₃×#102	—	2	1	no	—
39	C₂×C₁₃×#102	C₂²	1	2	yes	—
40	C₂×C₁₃×#100	C₂²	1	2	yes	—
41	C₂×C₁₃×#100	C₂²	1	2	yes	—
42	C₂×C₁₃×#100	C₂²	1	2	yes	complemented
43	C₁₃×#407	C₂²	1	1	yes	characteristic
44	C₁₃×#407	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₃×#405	C₂²	1	2	yes	complemented
47	C₁₃×#343	C₂²	1	2	yes	complemented
48	C₁₃×#341	C₂²	1	2	yes	complemented
49	C₂⁵×C₁₃	—	2	1	no	—
50	C₂²×D₄×C₁₃	—	2	4	no	—
51	C₂²×D₄×C₁₃	—	2	1	no	—
52	C₂²×D₄×C₁₃	—	2	1	no	—
53	C₂²×D₄×C₁₃	—	2	1	no	—
54	C₂²×D₄×C₁₃	—	2	1	no	—
55	C₂²×D₄×C₁₃	—	2	1	no	—
56	C₂²×D₄×C₁₃	—	2	1	no	—
57	C₂²×D₄×C₁₃	—	4	2	no	—
58	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×D₈	—	2	4	no	—
62	C₂×C₁₃×D₈	—	2	2	no	—
63	C₂×C₁₃×D₈	—	2	2	no	—
64	C₂×C₁₃×D₈	—	4	2	no	—
65	C₂×C₁₃×M₁₆	—	2	1	no	—
66	C₂×C₁₃×M₁₆	—	4	2	no	—
67	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
68	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
69	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₃	—	2	1	no	—
72	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
73	C₁₃×#121	—	2	1	no	—
74	C₁₃×#121	—	2	1	no	—
75	C₁₃×#121	—	2	1	no	—
76	C₁₃×#121	—	2	1	no	—
77	C₁₃×#117	—	2	1	no	—
78	C₁₃×#117	—	2	1	no	—
79	C₁₃×#117	D₄	1	1	yes	characteristic
80	C₁₃×#117	D₄	1	1	yes	characteristic
81	C₁₃×#117	C₂³	1	1	yes	characteristic
82	C₁₃×#117	C₂³	1	1	yes	characteristic
83	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
86	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₁₃×#108	—	4	2	no	—
90	C₁₃×#107	—	2	1	no	—
91	C₁₃×#107	—	2	1	no	—
92	C₁₃×#106	—	2	1	no	—
93	C₁₃×#106	—	2	1	no	—
94	C₁₃×C₄⋊C₈	—	2	2	no	—
95	C₁₃×C₄⋊C₈	—	2	2	no	—
96	C₁₃×#102	—	2	2	no	—
97	C₁₃×#102	—	2	2	no	—
98	C₁₃×#102	—	2	2	no	—
99	C₁₃×#102	—	2	2	no	—
100	C₁₃×#102	—	2	2	no	—
101	C₁₃×#102	—	2	2	no	—
102	C₁₃×#102	—	2	1	no	—
103	C₁₃×#102	—	2	1	no	—
104	C₁₃×#102	—	2	1	no	—
105	C₁₃×#102	—	2	1	no	—
106	C₁₃×#100	—	2	4	no	—
107	C₁₃×#100	—	4	2	no	—
108	C₁₃×#100	—	4	2	no	—
109	C₁₃×C₂²⋊C₈	—	2	1	no	—
110	C₁₃×C₂²⋊C₈	—	2	1	no	—
111	C₁₃×C₂²⋊C₈	—	2	1	no	—
112	C₁₃×C₂²⋊C₈	—	2	1	no	—
113	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
114	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
115	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
116	C₁₃×#97	—	2	2	no	—
117	C₄×C₈×C₁₃	—	2	2	no	—
118	#24520	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	2	no	—
120	C₂⁴×C₁₃	—	2	1	no	—
121	C₂⁴×C₁₃	—	4	4	no	—
122	C₂⁴×C₁₃	—	4	1	no	—
123	C₂⁴×C₁₃	—	4	1	no	—
124	C₂⁴×C₁₃	—	8	2	no	—
125	C₂⁴×C₁₃	—	8	2	no	—
126	C₂⁴×C₁₃	#41	1	1	yes	characteristic
127	C₂×D₄×C₁₃	—	2	4	no	—
128	C₂×D₄×C₁₃	—	2	4	no	—
129	C₂×D₄×C₁₃	—	2	2	no	—
130	C₂×D₄×C₁₃	—	2	2	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	2	no	—
134	C₂×D₄×C₁₃	—	2	2	no	—
135	C₂×D₄×C₁₃	—	2	2	no	—
136	C₂×D₄×C₁₃	—	2	2	no	—
137	C₂×D₄×C₁₃	—	2	2	no	—
138	C₂×D₄×C₁₃	—	4	4	no	—
139	C₂×D₄×C₁₃	—	4	4	no	—
140	C₂×D₄×C₁₃	—	4	4	no	—
141	C₂×D₄×C₁₃	—	4	2	no	—
142	C₂×D₄×C₁₃	—	4	2	no	—
143	C₂×D₄×C₁₃	—	4	1	no	—
144	C₂×D₄×C₁₃	—	4	1	no	—
145	C₂×D₄×C₁₃	—	4	1	no	—
146	C₂×D₄×C₁₃	—	4	1	no	—
147	C₂×D₄×C₁₃	—	8	2	no	—
148	C₂×D₄×C₁₃	#41	1	4	yes	—
149	C₂²×C₄×C₁₃	—	2	2	no	—
150	C₂²×C₄×C₁₃	—	2	2	no	—
151	C₂²×C₄×C₁₃	—	2	1	no	—
152	C₂²×C₄×C₁₃	—	2	1	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
159	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₁₃×D₈	—	4	4	no	—
161	C₁₃×D₈	—	4	4	no	—
162	C₁₃×M₁₆	—	2	2	no	—
163	C₁₃×M₁₆	—	2	2	no	—
164	C₁₃×M₁₆	—	2	2	no	—
165	C₁₃×M₁₆	—	2	2	no	—
166	C₁₃×M₁₆	—	2	2	no	—
167	C₁₃×M₁₆	—	2	2	no	—
168	C₁₃×M₁₆	—	4	2	no	—
169	C₂×C₈×C₁₃	—	2	2	no	—
170	C₂×C₈×C₁₃	—	2	2	no	—
171	C₂×C₈×C₁₃	—	2	2	no	—
172	C₂×C₈×C₁₃	—	2	1	no	—
173	C₂×C₈×C₁₃	—	2	1	no	—
174	C₂×C₈×C₁₃	—	2	2	no	—
175	C₂×C₈×C₁₃	—	4	2	no	—
176	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
178	C₁₃×C₄⋊C₄	—	2	1	no	—
179	C₁₃×C₄⋊C₄	—	2	1	no	—
180	C₁₃×C₄⋊C₄	—	2	1	no	—
181	C₁₃×C₄⋊C₄	—	2	1	no	—
182	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
183	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
184	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
185	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
186	C₁₃×C₂²⋊C₄	—	2	1	no	—
187	C₁₃×C₂²⋊C₄	—	2	1	no	—
188	C₁₃×C₂²⋊C₄	—	2	1	no	—
189	C₁₃×C₂²⋊C₄	—	2	1	no	—
190	C₁₃×C₂²⋊C₄	—	4	1	no	—
191	C₁₃×C₂²⋊C₄	—	4	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	#3094	C₂×C₁₃	1	1	yes	characteristic, complemented
197	C₂×#447	C₂×C₁₃	1	1	yes	characteristic
198	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
199	C₂×#418	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2063	C₂×C₁₃	1	2	yes	complemented
201	#2045	C₂×C₁₃	1	2	yes	complemented
202	#1978	C₂×C₁₃	1	2	yes	complemented
203	#1931	C₂×C₁₃	1	2	yes	complemented
204	#1900	C₂×C₁₃	1	1	yes	characteristic, complemented
205	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1783	C₂×C₁₃	1	1	yes	characteristic, complemented
207	C₂³×C₁₃	—	2	2	no	—
208	C₂³×C₁₃	—	2	2	no	—
209	C₂³×C₁₃	—	2	4	no	—
210	C₂³×C₁₃	—	4	1	no	—
211	C₂³×C₁₃	—	4	4	no	—
212	C₂³×C₁₃	—	4	4	no	—
213	C₂³×C₁₃	—	4	2	no	—
214	C₂³×C₁₃	—	4	2	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	—	4	2	no	—
217	C₂³×C₁₃	—	8	2	no	—
218	C₂³×C₁₃	—	8	2	no	—
219	C₂³×C₁₃	—	8	2	no	—
220	C₂³×C₁₃	—	8	2	no	—
221	C₂³×C₁₃	—	8	2	no	—
222	C₂³×C₁₃	—	8	1	no	—
223	C₂³×C₁₃	—	8	1	no	—
224	C₂³×C₁₃	—	8	16	no	—
225	C₂³×C₁₃	—	8	2	no	—
226	C₂³×C₁₃	#121	1	1	yes	characteristic
227	C₂³×C₁₃	#121	1	1	yes	characteristic
228	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
229	D₄×C₁₃	—	2	4	no	—
230	D₄×C₁₃	—	2	4	no	—
231	D₄×C₁₃	—	4	4	no	—
232	D₄×C₁₃	—	4	4	no	—
233	D₄×C₁₃	—	4	1	no	—
234	D₄×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	4	1	no	—
236	D₄×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	8	2	no	—
239	D₄×C₁₃	—	8	2	no	—
240	C₂×C₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	1	no	—
248	C₂×C₄×C₁₃	—	2	1	no	—
249	C₂×C₄×C₁₃	—	2	1	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	1	no	—
253	C₂×C₄×C₁₃	—	8	1	no	—
254	C₂×C₄×C₁₃	—	8	1	no	—
255	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
256	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
260	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
261	C₈×C₁₃	—	2	2	no	—
262	C₈×C₁₃	—	2	2	no	—
263	C₈×C₁₃	—	4	1	no	—
264	C₈×C₁₃	—	4	2	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	—	4	2	no	—
267	C₂³×D₄	C₂²×C₁₃	1	1	yes	characteristic
268	C₂²×D₈	C₂²×C₁₃	1	2	yes	—
269	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
272	#482	—	2	1	no	—
273	#482	—	2	1	no	—
274	#481	—	2	1	no	—
275	#480	—	2	1	no	—
276	#447	—	2	1	no	—
277	#447	—	2	1	no	—
278	#447	—	2	2	no	—
279	#433	—	2	2	no	—
280	#432	—	2	1	no	—
281	#431	—	2	1	no	—
282	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
283	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
284	#428	C₂²×C₁₃	1	1	yes	characteristic, complemented
285	#424	C₂²×C₁₃	1	2	yes	complemented
286	#418	—	2	1	no	—
287	#418	—	2	1	no	—
288	#418	C₂²×C₁₃	1	2	yes	—
289	#418	C₂²×C₁₃	1	2	yes	—
290	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
291	#418	C₂²×C₁₃	1	1	yes	characteristic, complemented
292	C₂×#102	—	2	1	no	—
293	C₂×#102	—	2	1	no	—
294	C₂×#102	C₂²×C₁₃	1	2	yes	—
295	C₂×#100	C₂²×C₁₃	1	2	yes	—
296	C₂×#100	C₂²×C₁₃	1	2	yes	—
297	C₂×#100	C₂²×C₁₃	1	2	yes	complemented
298	#407	C₂²×C₁₃	1	1	yes	characteristic
299	#407	C₂²×C₁₃	1	1	yes	characteristic
300	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
301	#405	C₂²×C₁₃	1	2	yes	complemented
302	#343	C₂²×C₁₃	1	2	yes	complemented
303	#341	C₂²×C₁₃	1	2	yes	complemented
304	C₂²×C₁₃	—	2	1	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	—	2	1	no	—
307	C₂²×C₁₃	—	2	1	no	—
308	C₂²×C₁₃	—	2	1	no	—
309	C₂²×C₁₃	—	2	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	4	4	no	—
312	C₂²×C₁₃	—	4	4	no	—
313	C₂²×C₁₃	—	8	4	no	—
314	C₂²×C₁₃	—	8	4	no	—
315	C₂²×C₁₃	—	8	8	no	—
316	C₂²×C₁₃	—	8	8	no	—
317	C₂²×C₁₃	—	8	2	no	—
318	C₂²×C₁₃	—	8	2	no	—
319	C₂²×C₁₃	—	8	1	no	—
320	C₂²×C₁₃	—	8	1	no	—
321	C₂²×C₁₃	—	8	1	no	—
322	C₂²×C₁₃	—	16	2	no	—
323	C₂²×C₁₃	#472	1	2	yes	—
324	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
325	C₂²×C₁₃	#551	1	2	yes	—
326	C₄×C₁₃	—	2	1	no	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	4	1	no	—
329	C₄×C₁₃	—	4	1	no	—
330	C₄×C₁₃	—	4	1	no	—
331	C₄×C₁₃	—	4	1	no	—
332	C₄×C₁₃	—	8	1	no	—
333	C₄×C₁₃	#525	1	1	yes	characteristic
334	C₄×C₁₃	#535	1	1	yes	characteristic
335	C₄×C₁₃	#546	1	2	yes	—
336	C₂⁵	—	2	1	no	—
337	C₂²×D₄	—	2	4	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	—	2	1	no	—
340	C₂²×D₄	—	2	1	no	—
341	C₂²×D₄	—	2	1	no	—
342	C₂²×D₄	—	2	1	no	—
343	C₂²×D₄	—	2	1	no	—
344	C₂²×D₄	—	4	2	no	—
345	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×D₄	C₂³×C₁₃	1	2	yes	—
347	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
348	C₂×D₈	—	2	4	no	—
349	C₂×D₈	—	2	2	no	—
350	C₂×D₈	—	2	2	no	—
351	C₂×D₈	—	4	2	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	4	2	no	—
354	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
355	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
357	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
360	#121	—	2	1	no	—
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	#121	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	D₄×C₁₃	1	1	yes	characteristic
367	#117	D₄×C₁₃	1	1	yes	characteristic
368	#117	C₂³×C₁₃	1	1	yes	characteristic
369	#117	C₂³×C₁₃	1	1	yes	characteristic
370	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₂²⋊C₄	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	#108	—	4	2	no	—
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#106	—	2	1	no	—
380	#106	—	2	1	no	—
381	C₄⋊C₈	—	2	2	no	—
382	C₄⋊C₈	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	2	2	no	—
389	#102	—	2	1	no	—
390	#102	—	2	1	no	—
391	#102	—	2	1	no	—
392	#102	—	2	1	no	—
393	#100	—	2	4	no	—
394	#100	—	4	2	no	—
395	#100	—	4	2	no	—
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	C₂²⋊C₈	—	2	1	no	—
400	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
401	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
402	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
403	#97	—	2	2	no	—
404	C₄×C₈	—	2	2	no	—
405	C₂×C₁₃	—	2	2	no	—
406	C₂×C₁₃	—	2	2	no	—
407	C₂×C₁₃	—	4	1	no	—
408	C₂×C₁₃	—	8	4	no	—
409	C₂×C₁₃	—	16	1	no	—
410	C₂×C₁₃	#2411	1	1	yes	characteristic
411	C₂×C₁₃	C₂×#472	1	1	yes	characteristic
412	C₂×C₁₃	#3068	1	1	yes	characteristic
413	C₂⁴	—	2	2	no	—
414	C₂⁴	—	2	1	no	—
415	C₂⁴	—	4	4	no	—
416	C₂⁴	—	4	1	no	—
417	C₂⁴	—	4	1	no	—
418	C₂⁴	—	8	2	no	—
419	C₂⁴	—	8	2	no	—
420	C₂⁴	C₁₃×#41	1	1	yes	characteristic
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	4	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	4	4	no	—
433	C₂×D₄	—	4	4	no	—
434	C₂×D₄	—	4	4	no	—
435	C₂×D₄	—	4	2	no	—
436	C₂×D₄	—	4	2	no	—
437	C₂×D₄	—	4	1	no	—
438	C₂×D₄	—	4	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	8	2	no	—
442	C₂×D₄	C₁₃×#41	1	4	yes	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
451	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
452	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
453	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
454	D₈	—	4	4	no	—
455	D₈	—	4	4	no	—
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	4	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	4	2	no	—
470	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
471	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
477	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₁₃	#24520	1	1	yes	characteristic, direct product factor, Sylow
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	4	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	2	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	8	2	no	—
502	C₂³	—	8	2	no	—
503	C₂³	—	8	2	no	—
504	C₂³	—	8	2	no	—
505	C₂³	—	8	2	no	—
506	C₂³	—	8	1	no	—
507	C₂³	—	8	1	no	—
508	C₂³	—	8	16	no	—
509	C₂³	—	8	2	no	—
510	C₂³	C₁₃×#121	1	1	yes	characteristic
511	C₂³	C₁₃×#121	1	1	yes	characteristic
512	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
513	D₄	—	2	4	no	—
514	D₄	—	2	4	no	—
515	D₄	—	4	4	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	2	no	—
521	D₄	—	4	2	no	—
522	D₄	—	8	2	no	—
523	D₄	—	8	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	8	1	no	—
538	C₂×C₄	—	8	1	no	—
539	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
540	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
542	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
543	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
544	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
545	C₈	—	2	2	no	—
546	C₈	—	2	2	no	—
547	C₈	—	4	1	no	—
548	C₈	—	4	2	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	2	no	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	8	4	no	—
561	C₂²	—	8	4	no	—
562	C₂²	—	8	8	no	—
563	C₂²	—	8	8	no	—
564	C₂²	—	8	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	16	2	no	—
570	C₂²	C₁₃×#472	1	2	yes	—
571	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
572	C₂²	C₁₃×#551	1	2	yes	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	—	4	1	no	—
578	C₄	—	4	1	no	—
579	C₄	—	8	1	no	—
580	C₄	C₁₃×#525	1	1	yes	characteristic
581	C₄	C₁₃×#535	1	1	yes	characteristic
582	C₄	C₁₃×#546	1	2	yes	—
583	C₂	—	2	2	no	—
584	C₂	—	2	2	no	—
585	C₂	—	4	1	no	—
586	C₂	—	8	4	no	—
587	C₂	—	16	1	no	—
588	C₂	C₁₃×#2411	1	1	yes	characteristic
589	C₂	C₂×C₁₃×#472	1	1	yes	characteristic
590	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×#447	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. C₂×C₁₃×#418	C₂	semidirect
5. C₁₃×#2063	C₂	semidirect
6. C₁₃×#2045	C₂	semidirect
7. C₁₃×#1978	C₂	semidirect
8. C₁₃×#1931	C₂	semidirect
9. C₁₃×#1900	C₂	semidirect
10. C₁₃×#1855	C₂	semidirect
11. C₁₃×#1783	C₂	semidirect
27. C₂×C₁₃×#108	C₂²	semidirect
28. C₁₃×#428	C₂²	semidirect
29. C₁₃×#428	C₂²	semidirect
30. C₁₃×#424	C₂²	semidirect
35. C₁₃×#418	C₂²	semidirect
36. C₁₃×#418	C₂²	semidirect
42. C₂×C₁₃×#100	C₂²	semidirect
46. C₁₃×#405	C₂²	semidirect
47. C₁₃×#343	C₂²	semidirect
48. C₁₃×#341	C₂²	semidirect
118. #24520	C₁₃	direct (N × H)
196. #3094	C₂×C₁₃	semidirect
198. #2924	C₂×C₁₃	semidirect
199. C₂×#418	C₂×C₁₃	semidirect
200. #2063	C₂×C₁₃	semidirect
201. #2045	C₂×C₁₃	semidirect
202. #1978	C₂×C₁₃	semidirect
203. #1931	C₂×C₁₃	semidirect
204. #1900	C₂×C₁₃	semidirect
205. #1855	C₂×C₁₃	semidirect
206. #1783	C₂×C₁₃	semidirect
282. C₂×#108	C₂²×C₁₃	semidirect
283. #428	C₂²×C₁₃	semidirect
284. #428	C₂²×C₁₃	semidirect
285. #424	C₂²×C₁₃	semidirect
290. #418	C₂²×C₁₃	semidirect
291. #418	C₂²×C₁₃	semidirect
297. C₂×#100	C₂²×C₁₃	semidirect
301. #405	C₂²×C₁₃	semidirect
302. #343	C₂²×C₁₃	semidirect
303. #341	C₂²×C₁₃	semidirect
490. C₁₃	#24520	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×#447	2
C₁₃×#2924	2
C₂×C₁₃×#418	2
C₁₃×#2063	2
C₁₃×#2045	2
C₁₃×#1978	2
C₁₃×#1931	2
C₁₃×#1900	2
C₁₃×#1855	2
C₁₃×#1783	2
#24520	13

Subgroups — C13×#24520 #15710859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24520 #15710859