Subgroups — C₁₃×#24625 #15710964

Order 3328.

696 conjugacy classes of subgroups.

The subgroup lattice has 656 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
2	C₂×C₁₃×#482	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2924	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2911	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2063	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1952	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1951	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1931	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1900	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1822	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#121	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic
20	C₁₃×#482	—	2	1	no	—
21	C₁₃×#482	—	2	1	no	—
22	C₁₃×#482	—	2	1	no	—
23	C₁₃×#482	—	2	1	no	—
24	C₁₃×#482	—	2	1	no	—
25	C₁₃×#482	—	2	1	no	—
26	C₁₃×#481	—	2	1	no	—
27	C₁₃×#480	—	2	1	no	—
28	C₁₃×#433	—	2	1	no	—
29	C₁₃×#433	—	2	1	no	—
30	C₁₃×#432	—	2	1	no	—
31	C₁₃×#431	—	2	1	no	—
32	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#108	C₂²	1	1	yes	characteristic
34	C₁₃×#428	—	2	1	no	—
35	C₁₃×#428	—	2	1	no	—
36	C₁₃×#428	C₂²	1	1	yes	characteristic
37	C₁₃×#428	C₂²	1	1	yes	characteristic
38	C₁₃×#428	C₂²	1	1	yes	characteristic
39	C₁₃×#428	C₂²	1	1	yes	characteristic
40	C₁₃×#428	C₂²	1	1	yes	characteristic
41	C₁₃×#428	C₂²	1	1	yes	characteristic
42	C₁₃×#427	—	2	1	no	—
43	C₁₃×#427	—	2	1	no	—
44	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
45	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
46	C₁₃×#424	C₂²	1	1	yes	characteristic
47	C₁₃×#424	C₂²	1	1	yes	characteristic
48	C₁₃×#418	C₂²	1	1	yes	characteristic
49	C₁₃×#418	C₂²	1	1	yes	characteristic
50	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
51	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
53	C₂×C₁₃×#100	C₂²	1	1	yes	characteristic
54	C₁₃×#407	C₂²	1	1	yes	characteristic
55	C₁₃×#407	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₃×#405	C₂²	1	1	yes	characteristic
58	C₁₃×#405	C₂²	1	1	yes	characteristic
59	C₁₃×#343	C₂²	1	1	yes	characteristic
60	C₁₃×#343	C₂²	1	1	yes	characteristic
61	C₁₃×#343	C₂²	1	1	yes	characteristic
62	C₁₃×#343	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	C₂²×D₄×C₁₃	—	2	1	no	—
68	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
70	C₂×C₁₃×M₁₆	—	2	1	no	—
71	C₂×C₁₃×M₁₆	—	2	2	no	—
72	C₂×C₁₃×M₁₆	—	2	2	no	—
73	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
74	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₁₃×#121	—	2	1	no	—
83	C₁₃×#121	—	2	1	no	—
84	C₁₃×#121	—	2	1	no	—
85	C₁₃×#121	—	2	1	no	—
86	C₁₃×#117	—	2	1	no	—
87	C₁₃×#117	—	2	1	no	—
88	C₁₃×#117	—	2	1	no	—
89	C₁₃×#117	—	2	1	no	—
90	C₁₃×#117	—	2	1	no	—
91	C₁₃×#117	—	2	1	no	—
92	C₁₃×#117	D₄	1	1	yes	characteristic
93	C₁₃×#117	D₄	1	1	yes	characteristic
94	C₁₃×#117	C₂³	1	1	yes	characteristic
95	C₁₃×#117	C₂³	1	1	yes	characteristic
96	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
97	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
99	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄²×C₁₃	—	2	1	no	—
105	C₂×C₄²×C₁₃	—	2	1	no	—
106	C₁₃×#108	—	2	2	no	—
107	C₁₃×#108	—	2	2	no	—
108	C₁₃×#107	—	2	1	no	—
109	C₁₃×#107	—	2	1	no	—
110	C₁₃×#107	—	2	1	no	—
111	C₁₃×#107	—	2	1	no	—
112	C₁₃×#107	—	2	1	no	—
113	C₁₃×#107	—	2	1	no	—
114	C₁₃×#107	—	2	1	no	—
115	C₁₃×#107	—	2	1	no	—
116	C₁₃×#106	—	2	1	no	—
117	C₁₃×#106	—	2	1	no	—
118	C₁₃×#106	—	2	1	no	—
119	C₁₃×#106	—	2	1	no	—
120	C₁₃×#106	—	2	1	no	—
121	C₁₃×#106	—	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×#102	—	2	1	no	—
129	C₁₃×#102	—	2	1	no	—
130	C₁₃×#102	—	2	1	no	—
131	C₁₃×#102	—	2	1	no	—
132	C₁₃×#102	—	2	1	no	—
133	C₁₃×#102	—	2	1	no	—
134	C₁₃×#102	—	2	1	no	—
135	C₁₃×#102	—	2	1	no	—
136	C₁₃×#100	—	2	2	no	—
137	C₁₃×#100	—	2	2	no	—
138	C₁₃×C₂²⋊C₈	—	2	1	no	—
139	C₁₃×C₂²⋊C₈	—	2	1	no	—
140	C₁₃×C₂²⋊C₈	—	2	1	no	—
141	C₁₃×C₂²⋊C₈	—	2	1	no	—
142	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
143	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
144	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
145	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
146	C₁₃×#97	—	2	1	no	—
147	C₁₃×#97	—	2	1	no	—
148	C₄×C₈×C₁₃	—	2	1	no	—
149	C₄×C₈×C₁₃	—	2	1	no	—
150	#24625	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂⁴×C₁₃	—	2	1	no	—
152	C₂⁴×C₁₃	#41	1	1	yes	characteristic
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	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	—	4	1	no	—
160	C₂×D₄×C₁₃	—	4	1	no	—
161	C₂×D₄×C₁₃	—	8	2	no	—
162	C₂²×C₄×C₁₃	—	2	1	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	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
176	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₁₃×M₁₆	—	2	4	no	—
178	C₁₃×M₁₆	—	2	1	no	—
179	C₁₃×M₁₆	—	2	1	no	—
180	C₁₃×M₁₆	—	2	1	no	—
181	C₁₃×M₁₆	—	2	1	no	—
182	C₁₃×M₁₆	—	2	1	no	—
183	C₁₃×M₁₆	—	2	1	no	—
184	C₁₃×M₁₆	—	2	1	no	—
185	C₁₃×M₁₆	—	2	1	no	—
186	C₁₃×M₁₆	—	2	1	no	—
187	C₁₃×M₁₆	—	2	1	no	—
188	C₁₃×M₁₆	#41	1	2	yes	—
189	C₁₃×M₁₆	#41	1	2	yes	—
190	C₂×C₈×C₁₃	—	2	4	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	C₂×C₈×C₁₃	—	2	1	no	—
200	C₂×C₈×C₁₃	—	2	1	no	—
201	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
203	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
204	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
214	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
215	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
216	C₁₃×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
217	C₁₃×C₂²⋊C₄	—	2	1	no	—
218	C₁₃×C₂²⋊C₄	—	2	1	no	—
219	C₁₃×C₂²⋊C₄	—	2	1	no	—
220	C₁₃×C₂²⋊C₄	—	2	1	no	—
221	C₁₃×C₂²⋊C₄	—	4	1	no	—
222	C₁₃×C₂²⋊C₄	—	4	1	no	—
223	C₁₃×C₂²⋊C₄	—	4	1	no	—
224	C₁₃×C₂²⋊C₄	—	4	1	no	—
225	C₄²×C₁₃	—	2	1	no	—
226	C₄²×C₁₃	—	2	1	no	—
227	C₄²×C₁₃	—	2	1	no	—
228	C₄²×C₁₃	—	2	1	no	—
229	C₄²×C₁₃	—	4	1	no	—
230	C₄²×C₁₃	—	4	1	no	—
231	#3094	C₂×C₁₃	1	1	yes	characteristic
232	C₂×#482	C₂×C₁₃	1	1	yes	characteristic
233	#2924	C₂×C₁₃	1	1	yes	characteristic, complemented
234	#2911	C₂×C₁₃	1	1	yes	characteristic, complemented
235	#2090	C₂×C₁₃	1	1	yes	characteristic, complemented
236	#2089	C₂×C₁₃	1	1	yes	characteristic, complemented
237	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
238	#2063	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#1952	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#1951	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#1931	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1900	C₂×C₁₃	1	1	yes	characteristic
244	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1822	C₂×C₁₃	1	1	yes	characteristic, complemented
246	C₂³×C₁₃	—	2	1	no	—
247	C₂³×C₁₃	—	2	1	no	—
248	C₂³×C₁₃	—	4	1	no	—
249	C₂³×C₁₃	—	4	1	no	—
250	C₂³×C₁₃	—	4	1	no	—
251	C₂³×C₁₃	—	4	1	no	—
252	C₂³×C₁₃	—	4	1	no	—
253	C₂³×C₁₃	—	8	1	no	—
254	C₂³×C₁₃	—	8	1	no	—
255	C₂³×C₁₃	#121	1	1	yes	characteristic
256	C₂³×C₁₃	#121	1	1	yes	characteristic
257	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
258	D₄×C₁₃	—	4	1	no	—
259	D₄×C₁₃	—	4	1	no	—
260	D₄×C₁₃	—	4	1	no	—
261	D₄×C₁₃	—	4	1	no	—
262	D₄×C₁₃	—	8	2	no	—
263	D₄×C₁₃	—	8	2	no	—
264	C₂×C₄×C₁₃	—	2	1	no	—
265	C₂×C₄×C₁₃	—	2	1	no	—
266	C₂×C₄×C₁₃	—	2	1	no	—
267	C₂×C₄×C₁₃	—	2	1	no	—
268	C₂×C₄×C₁₃	—	2	1	no	—
269	C₂×C₄×C₁₃	—	2	1	no	—
270	C₂×C₄×C₁₃	—	2	1	no	—
271	C₂×C₄×C₁₃	—	2	1	no	—
272	C₂×C₄×C₁₃	—	2	1	no	—
273	C₂×C₄×C₁₃	—	2	1	no	—
274	C₂×C₄×C₁₃	—	2	1	no	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	4	2	no	—
279	C₂×C₄×C₁₃	—	4	1	no	—
280	C₂×C₄×C₁₃	—	4	1	no	—
281	C₂×C₄×C₁₃	—	4	1	no	—
282	C₂×C₄×C₁₃	—	8	1	no	—
283	C₂×C₄×C₁₃	—	8	1	no	—
284	C₂×C₄×C₁₃	—	8	1	no	—
285	C₂×C₄×C₁₃	—	8	1	no	—
286	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
287	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
288	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
290	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
291	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
292	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
293	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
294	C₈×C₁₃	—	2	2	no	—
295	C₈×C₁₃	—	2	2	no	—
296	C₈×C₁₃	—	2	1	no	—
297	C₈×C₁₃	—	2	1	no	—
298	C₈×C₁₃	—	2	1	no	—
299	C₈×C₁₃	—	2	1	no	—
300	C₈×C₁₃	—	4	1	no	—
301	C₈×C₁₃	—	4	1	no	—
302	C₈×C₁₃	—	4	1	no	—
303	C₈×C₁₃	—	4	1	no	—
304	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
305	C₂×#121	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
307	C₂×#117	C₂²×C₁₃	1	1	yes	characteristic
308	#482	—	2	1	no	—
309	#482	—	2	1	no	—
310	#482	—	2	1	no	—
311	#482	—	2	1	no	—
312	#482	—	2	1	no	—
313	#482	—	2	1	no	—
314	#481	—	2	1	no	—
315	#480	—	2	1	no	—
316	#433	—	2	1	no	—
317	#433	—	2	1	no	—
318	#432	—	2	1	no	—
319	#431	—	2	1	no	—
320	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
321	C₂×#108	C₂²×C₁₃	1	1	yes	characteristic
322	#428	—	2	1	no	—
323	#428	—	2	1	no	—
324	#428	C₂²×C₁₃	1	1	yes	characteristic
325	#428	C₂²×C₁₃	1	1	yes	characteristic
326	#428	C₂²×C₁₃	1	1	yes	characteristic
327	#428	C₂²×C₁₃	1	1	yes	characteristic
328	#428	C₂²×C₁₃	1	1	yes	characteristic
329	#428	C₂²×C₁₃	1	1	yes	characteristic
330	#427	—	2	1	no	—
331	#427	—	2	1	no	—
332	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
333	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
334	#424	C₂²×C₁₃	1	1	yes	characteristic
335	#424	C₂²×C₁₃	1	1	yes	characteristic
336	#418	C₂²×C₁₃	1	1	yes	characteristic
337	#418	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
339	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
340	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
341	C₂×#100	C₂²×C₁₃	1	1	yes	characteristic
342	#407	C₂²×C₁₃	1	1	yes	characteristic
343	#407	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
345	#405	C₂²×C₁₃	1	1	yes	characteristic
346	#405	C₂²×C₁₃	1	1	yes	characteristic
347	#343	C₂²×C₁₃	1	1	yes	characteristic
348	#343	C₂²×C₁₃	1	1	yes	characteristic
349	#343	C₂²×C₁₃	1	1	yes	characteristic
350	#343	C₂²×C₁₃	1	1	yes	characteristic
351	#343	C₂²×C₁₃	1	1	yes	characteristic
352	#343	C₂²×C₁₃	1	1	yes	characteristic
353	#341	C₂²×C₁₃	1	1	yes	characteristic
354	#341	C₂²×C₁₃	1	1	yes	characteristic
355	C₂²×C₁₃	—	2	1	no	—
356	C₂²×C₁₃	—	2	1	no	—
357	C₂²×C₁₃	—	2	1	no	—
358	C₂²×C₁₃	—	2	1	no	—
359	C₂²×C₁₃	—	2	1	no	—
360	C₂²×C₁₃	—	2	1	no	—
361	C₂²×C₁₃	—	2	1	no	—
362	C₂²×C₁₃	—	2	1	no	—
363	C₂²×C₁₃	—	8	1	no	—
364	C₂²×C₁₃	—	8	1	no	—
365	C₂²×C₁₃	—	8	1	no	—
366	C₂²×C₁₃	—	8	1	no	—
367	C₂²×C₁₃	—	8	1	no	—
368	C₂²×C₁₃	—	16	1	no	—
369	C₂²×C₁₃	—	16	1	no	—
370	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
371	C₂²×C₁₃	#552	1	1	yes	characteristic
372	C₂²×C₁₃	#552	1	1	yes	characteristic
373	C₄×C₁₃	—	2	1	no	—
374	C₄×C₁₃	—	2	1	no	—
375	C₄×C₁₃	—	4	1	no	—
376	C₄×C₁₃	—	4	1	no	—
377	C₄×C₁₃	—	4	1	no	—
378	C₄×C₁₃	—	4	1	no	—
379	C₄×C₁₃	—	8	1	no	—
380	C₄×C₁₃	—	8	1	no	—
381	C₄×C₁₃	—	8	1	no	—
382	C₄×C₁₃	#525	1	1	yes	characteristic
383	C₄×C₁₃	#536	1	1	yes	characteristic
384	C₄×C₁₃	#547	1	1	yes	characteristic
385	C₄×C₁₃	#547	1	1	yes	characteristic
386	C₂²×D₄	—	2	1	no	—
387	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×M₁₆	—	2	1	no	—
390	C₂×M₁₆	—	2	2	no	—
391	C₂×M₁₆	—	2	2	no	—
392	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
393	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
394	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
395	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
396	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
397	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
398	C₂²×C₈	—	2	1	no	—
399	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
401	#121	—	2	1	no	—
402	#121	—	2	1	no	—
403	#121	—	2	1	no	—
404	#121	—	2	1	no	—
405	#117	—	2	1	no	—
406	#117	—	2	1	no	—
407	#117	—	2	1	no	—
408	#117	—	2	1	no	—
409	#117	—	2	1	no	—
410	#117	—	2	1	no	—
411	#117	D₄×C₁₃	1	1	yes	characteristic
412	#117	D₄×C₁₃	1	1	yes	characteristic
413	#117	C₂³×C₁₃	1	1	yes	characteristic
414	#117	C₂³×C₁₃	1	1	yes	characteristic
415	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
416	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
420	C₂×C₂²⋊C₄	—	2	1	no	—
421	C₂×C₂²⋊C₄	—	2	1	no	—
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₄²	—	2	1	no	—
424	C₂×C₄²	—	2	1	no	—
425	#108	—	2	2	no	—
426	#108	—	2	2	no	—
427	#107	—	2	1	no	—
428	#107	—	2	1	no	—
429	#107	—	2	1	no	—
430	#107	—	2	1	no	—
431	#107	—	2	1	no	—
432	#107	—	2	1	no	—
433	#107	—	2	1	no	—
434	#107	—	2	1	no	—
435	#106	—	2	1	no	—
436	#106	—	2	1	no	—
437	#106	—	2	1	no	—
438	#106	—	2	1	no	—
439	#106	—	2	1	no	—
440	#106	—	2	1	no	—
441	#106	—	2	1	no	—
442	#106	—	2	1	no	—
443	C₄⋊C₈	—	2	1	no	—
444	C₄⋊C₈	—	2	1	no	—
445	C₄⋊C₈	—	2	1	no	—
446	C₄⋊C₈	—	2	1	no	—
447	#102	—	2	1	no	—
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#100	—	2	2	no	—
456	#100	—	2	2	no	—
457	C₂²⋊C₈	—	2	1	no	—
458	C₂²⋊C₈	—	2	1	no	—
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	2	1	no	—
461	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
462	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
463	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
464	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
465	#97	—	2	1	no	—
466	#97	—	2	1	no	—
467	C₄×C₈	—	2	1	no	—
468	C₄×C₈	—	2	1	no	—
469	C₂×C₁₃	—	2	1	no	—
470	C₂×C₁₃	—	2	1	no	—
471	C₂×C₁₃	—	4	1	no	—
472	C₂×C₁₃	—	4	1	no	—
473	C₂×C₁₃	—	16	1	no	—
474	C₂×C₁₃	#2413	1	1	yes	characteristic
475	C₂×C₁₃	#3067	1	1	yes	characteristic
476	C₂×C₁₃	#3068	1	1	yes	characteristic
477	C₂⁴	—	2	1	no	—
478	C₂⁴	C₁₃×#41	1	1	yes	characteristic
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	—	8	2	no	—
488	C₂²×C₄	—	2	1	no	—
489	C₂²×C₄	—	2	1	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	1	no	—
492	C₂²×C₄	—	2	1	no	—
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
501	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
502	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
503	M₁₆	—	2	4	no	—
504	M₁₆	—	2	1	no	—
505	M₁₆	—	2	1	no	—
506	M₁₆	—	2	1	no	—
507	M₁₆	—	2	1	no	—
508	M₁₆	—	2	1	no	—
509	M₁₆	—	2	1	no	—
510	M₁₆	—	2	1	no	—
511	M₁₆	—	2	1	no	—
512	M₁₆	—	2	1	no	—
513	M₁₆	—	2	1	no	—
514	M₁₆	C₁₃×#41	1	2	yes	—
515	M₁₆	C₁₃×#41	1	2	yes	—
516	C₂×C₈	—	2	4	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
528	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
529	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
530	C₂×C₈	C₂×D₄×C₁₃	1	1	yes	characteristic
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
540	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
541	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
542	C₄⋊C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₂²⋊C₄	—	2	1	no	—
547	C₂²⋊C₄	—	4	1	no	—
548	C₂²⋊C₄	—	4	1	no	—
549	C₂²⋊C₄	—	4	1	no	—
550	C₂²⋊C₄	—	4	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	1	no	—
555	C₄²	—	4	1	no	—
556	C₄²	—	4	1	no	—
557	C₁₃	#24625	1	1	yes	characteristic, direct product factor, Sylow
558	C₂³	—	2	1	no	—
559	C₂³	—	2	1	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	1	no	—
562	C₂³	—	4	1	no	—
563	C₂³	—	4	1	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	8	1	no	—
566	C₂³	—	8	1	no	—
567	C₂³	C₁₃×#121	1	1	yes	characteristic
568	C₂³	C₁₃×#121	1	1	yes	characteristic
569	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	4	1	no	—
573	D₄	—	4	1	no	—
574	D₄	—	8	2	no	—
575	D₄	—	8	2	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	1	no	—
590	C₂×C₄	—	4	2	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	8	1	no	—
595	C₂×C₄	—	8	1	no	—
596	C₂×C₄	—	8	1	no	—
597	C₂×C₄	—	8	1	no	—
598	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
599	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
600	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
601	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
602	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
603	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
604	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
605	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
606	C₈	—	2	2	no	—
607	C₈	—	2	2	no	—
608	C₈	—	2	1	no	—
609	C₈	—	2	1	no	—
610	C₈	—	2	1	no	—
611	C₈	—	2	1	no	—
612	C₈	—	4	1	no	—
613	C₈	—	4	1	no	—
614	C₈	—	4	1	no	—
615	C₈	—	4	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	1	no	—
622	C₂²	—	2	1	no	—
623	C₂²	—	2	1	no	—
624	C₂²	—	8	1	no	—
625	C₂²	—	8	1	no	—
626	C₂²	—	8	1	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	16	1	no	—
630	C₂²	—	16	1	no	—
631	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
632	C₂²	C₁₃×#552	1	1	yes	characteristic
633	C₂²	C₁₃×#552	1	1	yes	characteristic
634	C₄	—	2	1	no	—
635	C₄	—	2	1	no	—
636	C₄	—	4	1	no	—
637	C₄	—	4	1	no	—
638	C₄	—	4	1	no	—
639	C₄	—	4	1	no	—
640	C₄	—	8	1	no	—
641	C₄	—	8	1	no	—
642	C₄	—	8	1	no	—
643	C₄	C₁₃×#525	1	1	yes	characteristic
644	C₄	C₁₃×#536	1	1	yes	characteristic
645	C₄	C₁₃×#547	1	1	yes	characteristic
646	C₄	C₁₃×#547	1	1	yes	characteristic
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	4	1	no	—
650	C₂	—	4	1	no	—
651	C₂	—	16	1	no	—
652	C₂	C₁₃×#2413	1	1	yes	characteristic
653	C₂	C₁₃×#3067	1	1	yes	characteristic
654	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×#121	C₂²
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
3. C₁₃×#2924	C₂	semidirect
4. C₁₃×#2911	C₂	semidirect
5. C₁₃×#2090	C₂	semidirect
6. C₁₃×#2089	C₂	semidirect
7. C₁₃×#2063	C₂	semidirect
8. C₁₃×#2063	C₂	semidirect
9. C₁₃×#1952	C₂	semidirect
10. C₁₃×#1951	C₂	semidirect
11. C₁₃×#1931	C₂	semidirect
12. C₁₃×#1931	C₂	semidirect
14. C₁₃×#1855	C₂	semidirect
15. C₁₃×#1822	C₂	semidirect
150. #24625	C₁₃	direct (N × H)
233. #2924	C₂×C₁₃	semidirect
234. #2911	C₂×C₁₃	semidirect
235. #2090	C₂×C₁₃	semidirect
236. #2089	C₂×C₁₃	semidirect
237. #2063	C₂×C₁₃	semidirect
238. #2063	C₂×C₁₃	semidirect
239. #1952	C₂×C₁₃	semidirect
240. #1951	C₂×C₁₃	semidirect
241. #1931	C₂×C₁₃	semidirect
242. #1931	C₂×C₁₃	semidirect
244. #1855	C₂×C₁₃	semidirect
245. #1822	C₂×C₁₃	semidirect
557. C₁₃	#24625	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×#482	2
C₁₃×#2924	2
C₁₃×#2911	2
C₁₃×#2090	2
C₁₃×#2089	2
C₁₃×#2063	2
C₁₃×#1952	2
C₁₃×#1951	2
C₁₃×#1931	2
C₁₃×#1900	2
C₁₃×#1855	2
C₁₃×#1822	2
#24625	13

Subgroups — C13×#24625 #15710964

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24625 #15710964