Subgroups — C₁₃×#24571 #15710910

Order 3328.

910 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×#3007	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₃×#417	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2880	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2079	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2052	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1908	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1901	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1855	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1821	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1815	C₂	1	2	yes	maximal, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
14	C₂×C₁₃×#137	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×#131	C₂²	1	2	yes	—
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₁₃×#483	—	2	1	no	—
20	C₁₃×#483	—	2	1	no	—
21	C₁₃×#483	—	2	2	no	—
22	C₁₃×#452	—	2	1	no	—
23	C₁₃×#452	—	2	1	no	—
24	C₁₃×#451	—	2	1	no	—
25	C₁₃×#450	—	2	1	no	—
26	C₂×C₁₃×#108	C₂²	1	2	yes	complemented
27	C₂×C₁₃×#106	C₂²	1	2	yes	complemented
28	C₁₃×#417	—	2	1	no	—
29	C₁₃×#417	—	2	1	no	—
30	C₁₃×#417	C₂²	1	1	yes	characteristic
31	C₁₃×#417	C₂²	1	1	yes	characteristic
32	C₁₃×#417	C₂²	1	2	yes	—
33	C₁₃×#417	C₂²	1	2	yes	—
34	C₂×C₁₃×#103	—	2	1	no	—
35	C₂×C₁₃×#103	C₂²	1	2	yes	complemented
36	C₂×C₁₃×#102	—	2	1	no	—
37	C₂×C₁₃×#101	C₂²	1	2	yes	complemented
38	C₁₃×#408	—	2	2	no	—
39	C₁₃×#408	C₂²	1	2	yes	—
40	C₁₃×#407	—	2	1	no	—
41	C₁₃×#407	C₂²	1	1	yes	characteristic
42	C₁₃×#407	C₂²	1	1	yes	characteristic
43	C₂×C₁₃×C₂²⋊C₈	—	2	1	no	—
44	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
45	C₁₃×#343	C₂²	1	2	yes	complemented
46	C₁₃×#343	C₂²	1	2	yes	complemented
47	C₁₃×#343	C₂²	1	2	yes	complemented
48	C₁₃×#341	C₂²	1	2	yes	complemented
49	C₂×C₁₃×#41	—	2	1	no	—
50	C₂×C₁₃×#41	—	2	1	no	—
51	C₂×C₁₃×#41	—	2	4	no	—
52	C₂×C₁₃×#41	—	4	2	no	—
53	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
54	C₂×C₁₃×#41	D₄	1	1	yes	characteristic
55	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
56	C₂×C₁₃×#41	C₂³	1	1	yes	characteristic
57	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	—	2	1	no	—
60	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₃	—	2	1	no	—
62	C₂³×C₄×C₁₃	—	2	1	no	—
63	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#137	—	2	4	no	—
65	C₁₃×#137	—	4	2	no	—
66	C₂×C₁₃×Q₁₆	—	2	1	no	—
67	C₂×C₁₃×Q₁₆	—	2	1	no	—
68	C₂×C₁₃×SD₁₆	—	2	1	no	—
69	C₂×C₁₃×SD₁₆	—	2	1	no	—
70	C₁₃×#131	—	2	4	no	—
71	C₁₃×#131	—	4	2	no	—
72	C₂×C₁₃×M₁₆	—	2	1	no	—
73	C₂×C₁₃×M₁₆	—	2	2	no	—
74	C₂×C₁₃×M₁₆	—	4	2	no	—
75	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
76	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×M₁₆	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×M₁₆	C₂³	1	2	yes	—
79	C₂²×C₈×C₁₃	—	2	1	no	—
80	C₂²×C₈×C₁₃	—	2	2	no	—
81	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
82	C₁₃×C₂²⋊Q₈	—	2	1	no	—
83	C₁₃×C₂²⋊Q₈	—	2	1	no	—
84	C₁₃×C₂²⋊Q₈	—	2	1	no	—
85	C₁₃×C₂²⋊Q₈	—	2	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	—	2	1	no	—
90	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
91	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
92	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
93	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
94	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
95	C₁₃×#108	—	4	2	no	—
96	C₁₃×#106	—	2	2	no	—
97	C₁₃×#106	—	2	2	no	—
98	C₁₃×#103	—	2	2	no	—
99	C₁₃×#103	—	2	2	no	—
100	C₁₃×#103	—	2	1	no	—
101	C₁₃×#103	—	2	1	no	—
102	C₁₃×#103	—	2	2	no	—
103	C₁₃×#103	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	C₁₃×#102	—	2	2	no	—
106	C₁₃×#102	—	2	1	no	—
107	C₁₃×#102	—	2	1	no	—
108	C₁₃×#101	—	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	—	2	2	no	—
114	C₁₃×C₂²⋊C₈	—	2	2	no	—
115	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
116	C₁₃×C₂²⋊C₈	D₄	1	1	yes	characteristic
117	C₁₃×C₂²⋊C₈	D₄	1	2	yes	—
118	#24571	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
119	C₂⁴×C₁₃	—	2	1	no	—
120	C₂⁴×C₁₃	#41	1	1	yes	characteristic
121	C₁₃×#41	—	2	2	no	—
122	C₁₃×#41	—	2	2	no	—
123	C₁₃×#41	—	2	2	no	—
124	C₁₃×#41	—	2	2	no	—
125	C₁₃×#41	—	2	2	no	—
126	C₁₃×#41	—	4	4	no	—
127	C₁₃×#41	—	4	1	no	—
128	C₁₃×#41	—	4	1	no	—
129	C₁₃×#41	—	4	4	no	—
130	C₁₃×#41	#41	1	4	yes	—
131	C₂×Q₈×C₁₃	—	2	1	no	—
132	C₂×Q₈×C₁₃	—	2	2	no	—
133	C₂×Q₈×C₁₃	—	2	1	no	—
134	C₂×Q₈×C₁₃	—	2	1	no	—
135	C₂×Q₈×C₁₃	—	2	2	no	—
136	C₂×Q₈×C₁₃	—	2	2	no	—
137	C₂×Q₈×C₁₃	—	4	1	no	—
138	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Q₈×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×D₄×C₁₃	—	2	1	no	—
141	C₂×D₄×C₁₃	—	2	2	no	—
142	C₂×D₄×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	—	4	1	no	—
147	C₂×D₄×C₁₃	—	4	4	no	—
148	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
149	C₂×D₄×C₁₃	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₃	—	2	1	no	—
151	C₂²×C₄×C₁₃	—	2	2	no	—
152	C₂²×C₄×C₁₃	—	2	2	no	—
153	C₂²×C₄×C₁₃	—	2	1	no	—
154	C₂²×C₄×C₁₃	—	2	1	no	—
155	C₂²×C₄×C₁₃	—	2	1	no	—
156	C₂²×C₄×C₁₃	—	2	1	no	—
157	C₂²×C₄×C₁₃	—	2	1	no	—
158	C₂²×C₄×C₁₃	—	2	1	no	—
159	C₂²×C₄×C₁₃	—	2	2	no	—
160	C₂²×C₄×C₁₃	—	4	4	no	—
161	C₂²×C₄×C₁₃	—	4	1	no	—
162	C₂²×C₄×C₁₃	—	4	1	no	—
163	C₂²×C₄×C₁₃	—	8	2	no	—
164	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
169	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₁₃×Q₁₆	—	4	2	no	—
171	C₁₃×Q₁₆	—	4	2	no	—
172	C₁₃×SD₁₆	—	4	2	no	—
173	C₁₃×SD₁₆	—	4	2	no	—
174	C₁₃×M₁₆	—	2	2	no	—
175	C₁₃×M₁₆	—	2	2	no	—
176	C₁₃×M₁₆	—	2	2	no	—
177	C₁₃×M₁₆	—	2	2	no	—
178	C₁₃×M₁₆	—	2	2	no	—
179	C₁₃×M₁₆	—	2	2	no	—
180	C₁₃×M₁₆	—	4	4	no	—
181	C₁₃×M₁₆	—	4	2	no	—
182	C₂×C₈×C₁₃	—	2	2	no	—
183	C₂×C₈×C₁₃	—	2	2	no	—
184	C₂×C₈×C₁₃	—	2	2	no	—
185	C₂×C₈×C₁₃	—	2	1	no	—
186	C₂×C₈×C₁₃	—	2	1	no	—
187	C₂×C₈×C₁₃	—	2	2	no	—
188	C₂×C₈×C₁₃	—	4	4	no	—
189	C₂×C₈×C₁₃	—	4	2	no	—
190	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
191	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
192	C₁₃×C₄⋊C₄	—	2	2	no	—
193	C₁₃×C₄⋊C₄	—	2	1	no	—
194	C₁₃×C₄⋊C₄	—	2	2	no	—
195	C₁₃×C₄⋊C₄	—	2	1	no	—
196	C₁₃×C₄⋊C₄	—	4	1	no	—
197	C₁₃×C₄⋊C₄	—	4	1	no	—
198	C₁₃×C₄⋊C₄	—	4	1	no	—
199	C₁₃×C₄⋊C₄	—	4	1	no	—
200	C₁₃×C₂²⋊C₄	—	4	1	no	—
201	C₁₃×C₂²⋊C₄	—	4	1	no	—
202	C₂×#483	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#3007	C₂×C₁₃	1	1	yes	characteristic
204	C₂×#417	C₂×C₁₃	1	1	yes	characteristic
205	#2880	C₂×C₁₃	1	1	yes	characteristic
206	#2079	C₂×C₁₃	1	2	yes	complemented
207	#2052	C₂×C₁₃	1	2	yes	complemented
208	#1908	C₂×C₁₃	1	2	yes	complemented
209	#1901	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1855	C₂×C₁₃	1	1	yes	characteristic, complemented
211	#1821	C₂×C₁₃	1	1	yes	characteristic, complemented
212	#1815	C₂×C₁₃	1	2	yes	complemented
213	C₂³×C₁₃	—	2	1	no	—
214	C₂³×C₁₃	—	2	2	no	—
215	C₂³×C₁₃	—	2	2	no	—
216	C₂³×C₁₃	—	2	1	no	—
217	C₂³×C₁₃	—	4	1	no	—
218	C₂³×C₁₃	—	4	2	no	—
219	C₂³×C₁₃	—	4	2	no	—
220	C₂³×C₁₃	—	8	1	no	—
221	C₂³×C₁₃	#121	1	1	yes	characteristic
222	C₂³×C₁₃	#121	1	1	yes	characteristic
223	C₂³×C₁₃	C₂×#41	1	1	yes	characteristic
224	Q₈×C₁₃	—	2	1	no	—
225	Q₈×C₁₃	—	2	1	no	—
226	Q₈×C₁₃	—	2	1	no	—
227	Q₈×C₁₃	—	4	2	no	—
228	Q₈×C₁₃	—	4	1	no	—
229	Q₈×C₁₃	—	4	1	no	—
230	Q₈×C₁₃	—	4	2	no	—
231	Q₈×C₁₃	#123	1	2	yes	—
232	D₄×C₁₃	—	2	4	no	—
233	D₄×C₁₃	—	2	1	no	—
234	D₄×C₁₃	—	2	1	no	—
235	D₄×C₁₃	—	2	1	no	—
236	D₄×C₁₃	—	4	2	no	—
237	D₄×C₁₃	—	4	2	no	—
238	D₄×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	4	2	no	—
240	D₄×C₁₃	#123	1	2	yes	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	2	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	1	no	—
245	C₂×C₄×C₁₃	—	2	1	no	—
246	C₂×C₄×C₁₃	—	2	1	no	—
247	C₂×C₄×C₁₃	—	2	4	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	1	no	—
251	C₂×C₄×C₁₃	—	4	2	no	—
252	C₂×C₄×C₁₃	—	4	2	no	—
253	C₂×C₄×C₁₃	—	4	2	no	—
254	C₂×C₄×C₁₃	—	4	2	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	2	no	—
258	C₂×C₄×C₁₃	—	4	2	no	—
259	C₂×C₄×C₁₃	—	8	2	no	—
260	C₂×C₄×C₁₃	—	8	2	no	—
261	C₂×C₄×C₁₃	—	8	1	no	—
262	C₂×C₄×C₁₃	—	8	2	no	—
263	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
264	C₂×C₄×C₁₃	#121	1	1	yes	characteristic
265	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₁₃	C₂×#41	1	2	yes	—
268	C₂×C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
269	C₈×C₁₃	—	2	2	no	—
270	C₈×C₁₃	—	2	2	no	—
271	C₈×C₁₃	—	4	1	no	—
272	C₈×C₁₃	—	4	2	no	—
273	C₈×C₁₃	—	4	1	no	—
274	C₈×C₁₃	—	4	2	no	—
275	C₂²×#41	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#137	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×#131	C₂²×C₁₃	1	2	yes	—
279	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
280	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
282	#483	—	2	1	no	—
283	#483	—	2	1	no	—
284	#483	—	2	2	no	—
285	#452	—	2	1	no	—
286	#452	—	2	1	no	—
287	#451	—	2	1	no	—
288	#450	—	2	1	no	—
289	C₂×#108	C₂²×C₁₃	1	2	yes	complemented
290	C₂×#106	C₂²×C₁₃	1	2	yes	complemented
291	#417	—	2	1	no	—
292	#417	—	2	1	no	—
293	#417	C₂²×C₁₃	1	2	yes	—
294	#417	C₂²×C₁₃	1	1	yes	characteristic
295	#417	C₂²×C₁₃	1	2	yes	—
296	#417	C₂²×C₁₃	1	1	yes	characteristic
297	C₂×#103	—	2	1	no	—
298	C₂×#103	C₂²×C₁₃	1	2	yes	complemented
299	C₂×#102	—	2	1	no	—
300	C₂×#101	C₂²×C₁₃	1	2	yes	complemented
301	#408	—	2	2	no	—
302	#408	C₂²×C₁₃	1	2	yes	—
303	#407	—	2	1	no	—
304	#407	C₂²×C₁₃	1	1	yes	characteristic
305	#407	C₂²×C₁₃	1	1	yes	characteristic
306	C₂×C₂²⋊C₈	—	2	1	no	—
307	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
308	#343	C₂²×C₁₃	1	2	yes	complemented
309	#343	C₂²×C₁₃	1	2	yes	complemented
310	#343	C₂²×C₁₃	1	2	yes	complemented
311	#341	C₂²×C₁₃	1	2	yes	complemented
312	C₂²×C₁₃	—	2	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	4	4	no	—
321	C₂²×C₁₃	—	4	1	no	—
322	C₂²×C₁₃	—	4	1	no	—
323	C₂²×C₁₃	—	4	1	no	—
324	C₂²×C₁₃	—	4	1	no	—
325	C₂²×C₁₃	—	4	1	no	—
326	C₂²×C₁₃	—	8	4	no	—
327	C₂²×C₁₃	#471	1	2	yes	—
328	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
329	C₂²×C₁₃	#551	1	2	yes	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	1	no	—
332	C₄×C₁₃	—	2	2	no	—
333	C₄×C₁₃	—	4	1	no	—
334	C₄×C₁₃	—	8	1	no	—
335	C₄×C₁₃	—	8	2	no	—
336	C₄×C₁₃	—	8	1	no	—
337	C₄×C₁₃	C₂×#123	1	1	yes	characteristic
338	C₄×C₁₃	#534	1	1	yes	characteristic
339	C₄×C₁₃	#546	1	2	yes	—
340	C₂×#41	—	2	1	no	—
341	C₂×#41	—	2	1	no	—
342	C₂×#41	—	2	4	no	—
343	C₂×#41	—	4	2	no	—
344	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
345	C₂×#41	D₄×C₁₃	1	1	yes	characteristic
346	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
347	C₂×#41	C₂³×C₁₃	1	1	yes	characteristic
348	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
349	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
352	C₂³×C₄	—	2	1	no	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
355	#137	—	2	4	no	—
356	#137	—	4	2	no	—
357	C₂×Q₁₆	—	2	1	no	—
358	C₂×Q₁₆	—	2	1	no	—
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	1	no	—
361	#131	—	2	4	no	—
362	#131	—	4	2	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	4	2	no	—
366	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
367	C₂×M₁₆	C₂³×C₁₃	1	2	yes	—
368	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
369	C₂×M₁₆	C₂³×C₁₃	1	1	yes	characteristic
370	C₂²×C₈	—	2	1	no	—
371	C₂²×C₈	—	2	2	no	—
372	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
373	C₂²⋊Q₈	—	2	1	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	1	no	—
380	C₂×C₄⋊C₄	—	2	1	no	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
384	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
385	C₂×C₂²⋊C₄	—	2	1	no	—
386	#108	—	4	2	no	—
387	#106	—	2	2	no	—
388	#106	—	2	2	no	—
389	#103	—	2	2	no	—
390	#103	—	2	2	no	—
391	#103	—	2	1	no	—
392	#103	—	2	1	no	—
393	#103	—	2	2	no	—
394	#103	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	#102	—	2	1	no	—
398	#102	—	2	1	no	—
399	#101	—	4	2	no	—
400	C₂²⋊C₈	—	2	1	no	—
401	C₂²⋊C₈	—	2	1	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	C₂²⋊C₈	—	2	2	no	—
405	C₂²⋊C₈	—	2	2	no	—
406	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
407	C₂²⋊C₈	D₄×C₁₃	1	1	yes	characteristic
408	C₂²⋊C₈	D₄×C₁₃	1	2	yes	—
409	C₂×C₁₃	—	2	2	no	—
410	C₂×C₁₃	—	2	2	no	—
411	C₂×C₁₃	—	4	1	no	—
412	C₂×C₁₃	—	4	2	no	—
413	C₂×C₁₃	—	8	1	no	—
414	C₂×C₁₃	#2412	1	1	yes	characteristic
415	C₂×C₁₃	C₂×#471	1	1	yes	characteristic
416	C₂×C₁₃	#3069	1	1	yes	characteristic
417	C₂⁴	—	2	1	no	—
418	C₂⁴	C₁₃×#41	1	1	yes	characteristic
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	4	4	no	—
425	#41	—	4	1	no	—
426	#41	—	4	1	no	—
427	#41	—	4	4	no	—
428	#41	C₁₃×#41	1	4	yes	—
429	C₂×Q₈	—	2	1	no	—
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	4	1	no	—
436	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
437	C₂×Q₈	C₂×D₄×C₁₃	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	4	4	no	—
446	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂×D₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	4	4	no	—
459	C₂²×C₄	—	4	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	8	2	no	—
462	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
463	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
465	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
466	C₂²×C₄	C₁₃×#41	1	1	yes	characteristic
467	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
468	Q₁₆	—	4	2	no	—
469	Q₁₆	—	4	2	no	—
470	SD₁₆	—	4	2	no	—
471	SD₁₆	—	4	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	4	4	no	—
479	M₁₆	—	4	2	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	2	2	no	—
482	C₂×C₈	—	2	2	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	4	4	no	—
487	C₂×C₈	—	4	2	no	—
488	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
489	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	4	1	no	—
495	C₄⋊C₄	—	4	1	no	—
496	C₄⋊C₄	—	4	1	no	—
497	C₄⋊C₄	—	4	1	no	—
498	C₂²⋊C₄	—	4	1	no	—
499	C₂²⋊C₄	—	4	1	no	—
500	C₁₃	#24571	1	1	yes	characteristic, direct product factor, Sylow
501	C₂³	—	2	2	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	2	no	—
504	C₂³	—	2	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	—	8	1	no	—
509	C₂³	C₁₃×#121	1	1	yes	characteristic
510	C₂³	C₁₃×#121	1	1	yes	characteristic
511	C₂³	C₂×C₁₃×#41	1	1	yes	characteristic
512	Q₈	—	2	1	no	—
513	Q₈	—	2	1	no	—
514	Q₈	—	2	1	no	—
515	Q₈	—	4	2	no	—
516	Q₈	—	4	1	no	—
517	Q₈	—	4	1	no	—
518	Q₈	—	4	2	no	—
519	Q₈	C₁₃×#123	1	2	yes	—
520	D₄	—	2	4	no	—
521	D₄	—	2	1	no	—
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	2	no	—
528	D₄	C₁₃×#123	1	2	yes	—
529	C₂×C₄	—	2	1	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	—	2	4	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	8	2	no	—
548	C₂×C₄	—	8	2	no	—
549	C₂×C₄	—	8	2	no	—
550	C₂×C₄	—	8	1	no	—
551	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
552	C₂×C₄	C₁₃×#121	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂×C₁₃×#41	1	2	yes	—
556	C₂×C₄	C₁₃×H(5,𝔽₂)	1	2	yes	—
557	C₈	—	2	2	no	—
558	C₈	—	2	2	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	2	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	2	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	2	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	8	4	no	—
578	C₂²	C₁₃×#471	1	2	yes	—
579	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
580	C₂²	C₁₃×#551	1	2	yes	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	2	no	—
584	C₄	—	4	1	no	—
585	C₄	—	8	2	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	C₂×C₁₃×#123	1	1	yes	characteristic
589	C₄	C₁₃×#534	1	1	yes	characteristic
590	C₄	C₁₃×#546	1	2	yes	—
591	C₂	—	2	2	no	—
592	C₂	—	2	2	no	—
593	C₂	—	4	1	no	—
594	C₂	—	4	2	no	—
595	C₂	—	8	1	no	—
596	C₂	C₁₃×#2412	1	1	yes	characteristic
597	C₂	C₂×C₁₃×#471	1	1	yes	characteristic
598	C₂	C₁₃×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×#41	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
1. C₂×C₁₃×#483	C₂	semidirect
5. C₁₃×#2079	C₂	semidirect
6. C₁₃×#2052	C₂	semidirect
7. C₁₃×#1908	C₂	semidirect
8. C₁₃×#1901	C₂	semidirect
9. C₁₃×#1855	C₂	semidirect
10. C₁₃×#1821	C₂	semidirect
11. C₁₃×#1815	C₂	semidirect
26. C₂×C₁₃×#108	C₂²	semidirect
27. C₂×C₁₃×#106	C₂²	semidirect
35. C₂×C₁₃×#103	C₂²	semidirect
37. C₂×C₁₃×#101	C₂²	semidirect
45. C₁₃×#343	C₂²	semidirect
46. C₁₃×#343	C₂²	semidirect
47. C₁₃×#343	C₂²	semidirect
48. C₁₃×#341	C₂²	semidirect
118. #24571	C₁₃	direct (N × H)
202. C₂×#483	C₂×C₁₃	semidirect
206. #2079	C₂×C₁₃	semidirect
207. #2052	C₂×C₁₃	semidirect
208. #1908	C₂×C₁₃	semidirect
209. #1901	C₂×C₁₃	semidirect
210. #1855	C₂×C₁₃	semidirect
211. #1821	C₂×C₁₃	semidirect
212. #1815	C₂×C₁₃	semidirect
289. C₂×#108	C₂²×C₁₃	semidirect
290. C₂×#106	C₂²×C₁₃	semidirect
298. C₂×#103	C₂²×C₁₃	semidirect
300. C₂×#101	C₂²×C₁₃	semidirect
308. #343	C₂²×C₁₃	semidirect
309. #343	C₂²×C₁₃	semidirect
310. #343	C₂²×C₁₃	semidirect
311. #341	C₂²×C₁₃	semidirect
500. C₁₃	#24571	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×#483	2
C₁₃×#3007	2
C₂×C₁₃×#417	2
C₁₃×#2880	2
C₁₃×#2079	2
C₁₃×#2052	2
C₁₃×#1908	2
C₁₃×#1901	2
C₁₃×#1855	2
C₁₃×#1821	2
C₁₃×#1815	2
#24571	13

Subgroups — C13×#24571 #15710910

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24571 #15710910