Subgroups — C₁₃×#36728 #15723067

Order 3328.

1854 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2848	C₂	1	2	yes	maximal
2	C₁₃×#2747	C₂	1	4	yes	maximal, complemented
3	C₁₃×#2722	C₂	1	4	yes	maximal, complemented
4	C₁₃×#2704	C₂	1	4	yes	maximal, complemented
5	C₁₃×#2690	C₂	1	4	yes	maximal, complemented
6	C₁₃×#2659	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2480	C₂	1	4	yes	maximal
9	C₁₃×#2473	C₂	1	4	yes	maximal, complemented
10	C₁₃×#2329	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#380	C₂	1	1	yes	maximal, characteristic
12	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₁₃×#126	C₂²	1	4	yes	—
14	C₂×C₁₃×#125	C₂²	1	4	yes	complemented
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₂²×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂²×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₁₃×#400	C₂²	1	4	yes	complemented
21	C₁₃×#400	C₂²	1	4	yes	complemented
22	C₁₃×#398	C₂²	1	4	yes	complemented
23	C₁₃×#398	C₂²	1	4	yes	complemented
24	C₁₃×#398	C₂²	1	4	yes	complemented
25	C₁₃×#398	C₂²	1	4	yes	complemented
26	C₁₃×#398	C₂²	1	4	yes	complemented
27	C₁₃×#397	C₂²	1	4	yes	—
28	C₁₃×#397	C₂²	1	4	yes	—
29	C₁₃×#397	C₂²	1	4	yes	—
30	C₁₃×#396	C₂²	1	4	yes	—
31	C₁₃×#395	C₂²	1	4	yes	complemented
32	C₁₃×#391	C₂²	1	4	yes	complemented
33	C₁₃×#389	C₂²	1	4	yes	complemented
34	C₁₃×#389	C₂²	1	4	yes	complemented
35	C₁₃×#388	C₂²	1	4	yes	—
36	C₁₃×#388	C₂²	1	4	yes	—
37	C₁₃×#388	C₂²	1	4	yes	—
38	C₁₃×#387	C₂²	1	4	yes	complemented
39	C₁₃×#387	C₂²	1	4	yes	complemented
40	C₁₃×#387	C₂²	1	4	yes	complemented
41	C₁₃×#387	C₂²	1	4	yes	complemented
42	C₁₃×#385	C₂²	1	4	yes	—
43	C₁₃×#385	C₂²	1	4	yes	—
44	C₁₃×#385	C₂²	1	4	yes	—
45	C₁₃×#385	C₂²	1	4	yes	—
46	C₁₃×#385	C₂²	1	4	yes	—
47	C₁₃×#380	C₂²	1	4	yes	—
48	C₁₃×#380	C₂²	1	4	yes	—
49	C₁₃×#380	C₂²	1	2	yes	—
50	C₁₃×#380	C₂²	1	2	yes	—
51	C₁₃×#380	C₂²	1	2	yes	—
52	C₁₃×#380	C₂²	1	4	yes	—
53	C₁₃×#379	C₂²	1	4	yes	—
54	C₄×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
55	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
56	C₂×C₁₃×#95	C₂²	1	1	yes	characteristic
57	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₂³×C₄×C₁₃	—	2	4	no	—
60	C₂³×C₄×C₁₃	—	4	4	no	—
61	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
63	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
64	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
65	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
66	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#126	—	4	8	no	—
68	C₁₃×#125	—	4	8	no	—
69	C₁₃×C₂²⋊Q₈	—	2	8	no	—
70	C₁₃×C₂²⋊Q₈	—	4	4	no	—
71	C₁₃×C₂²⋊Q₈	—	4	4	no	—
72	C₂×C₁₃×C₄⋊C₄	—	4	4	no	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
85	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
86	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
87	C₂×C₁₃×C₂²⋊C₄	—	4	4	no	—
88	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
89	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
90	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
91	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
92	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
93	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
94	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
95	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
96	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
97	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
98	C₁₃×#95	C₂³	1	4	yes	—
99	C₁₃×#95	C₂³	1	4	yes	—
100	C₁₃×#95	C₂³	1	4	yes	—
101	C₁₃×#95	C₂³	1	4	yes	—
102	C₁₃×#95	C₂³	1	4	yes	—
103	C₁₃×#95	C₂³	1	4	yes	—
104	C₁₃×#95	C₂³	1	4	yes	—
105	C₁₃×#95	C₂³	1	4	yes	—
106	C₁₃×#95	C₂³	1	4	yes	—
107	C₁₃×#95	C₂³	1	4	yes	—
108	C₁₃×#95	C₂³	1	4	yes	—
109	C₁₃×#95	C₂³	1	4	yes	—
110	C₁₃×#95	C₂³	1	4	yes	—
111	#36728	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
112	C₂⁴×C₁₃	—	2	2	no	—
113	C₂⁴×C₁₃	—	2	2	no	—
114	C₂⁴×C₁₃	—	2	2	no	—
115	C₂⁴×C₁₃	—	2	4	no	—
116	C₂⁴×C₁₃	—	4	2	no	—
117	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
118	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
119	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
120	C₂×Q₈×C₁₃	—	2	4	no	—
121	C₂×Q₈×C₁₃	—	4	2	no	—
122	C₂×Q₈×C₁₃	—	4	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	—	2	4	no	—
125	C₂²×C₄×C₁₃	—	2	4	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	—	2	4	no	—
128	C₂²×C₄×C₁₃	—	2	4	no	—
129	C₂²×C₄×C₁₃	—	2	4	no	—
130	C₂²×C₄×C₁₃	—	2	4	no	—
131	C₂²×C₄×C₁₃	—	4	2	no	—
132	C₂²×C₄×C₁₃	—	4	2	no	—
133	C₂²×C₄×C₁₃	—	4	2	no	—
134	C₂²×C₄×C₁₃	—	4	2	no	—
135	C₂²×C₄×C₁₃	—	4	2	no	—
136	C₂²×C₄×C₁₃	—	4	2	no	—
137	C₂²×C₄×C₁₃	—	4	2	no	—
138	C₂²×C₄×C₁₃	—	4	16	no	—
139	C₂²×C₄×C₁₃	#41	1	4	yes	—
140	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
144	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
148	C₁₃×C₄⋊C₄	—	2	4	no	—
149	C₁₃×C₄⋊C₄	—	2	8	no	—
150	C₁₃×C₄⋊C₄	—	2	8	no	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	8	no	—
153	C₁₃×C₄⋊C₄	—	4	4	no	—
154	C₁₃×C₄⋊C₄	—	4	2	no	—
155	C₁₃×C₄⋊C₄	—	4	2	no	—
156	C₁₃×C₄⋊C₄	—	4	4	no	—
157	C₁₃×C₄⋊C₄	—	4	4	no	—
158	C₁₃×C₄⋊C₄	—	4	4	no	—
159	C₁₃×C₄⋊C₄	—	4	4	no	—
160	C₁₃×C₄⋊C₄	—	4	4	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₂²⋊C₄	—	2	8	no	—
163	C₁₃×C₂²⋊C₄	—	2	8	no	—
164	C₁₃×C₂²⋊C₄	—	2	8	no	—
165	C₁₃×C₂²⋊C₄	—	2	8	no	—
166	C₁₃×C₂²⋊C₄	—	2	8	no	—
167	C₁₃×C₂²⋊C₄	—	4	4	no	—
168	C₁₃×C₂²⋊C₄	—	4	4	no	—
169	C₁₃×C₂²⋊C₄	—	4	4	no	—
170	C₄²×C₁₃	—	4	4	no	—
171	C₄²×C₁₃	—	4	4	no	—
172	#2848	C₂×C₁₃	1	2	yes	—
173	#2747	C₂×C₁₃	1	4	yes	complemented
174	#2722	C₂×C₁₃	1	4	yes	complemented
175	#2704	C₂×C₁₃	1	4	yes	complemented
176	#2690	C₂×C₁₃	1	4	yes	complemented
177	#2659	C₂×C₁₃	1	1	yes	characteristic, complemented
178	#2646	C₂×C₁₃	1	1	yes	characteristic, complemented
179	#2480	C₂×C₁₃	1	4	yes	—
180	#2473	C₂×C₁₃	1	4	yes	complemented
181	#2329	C₂×C₁₃	1	2	yes	complemented
182	C₂×#380	C₂×C₁₃	1	1	yes	characteristic
183	C₂³×C₁₃	—	2	2	no	—
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	8	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	—	2	1	no	—
189	C₂³×C₁₃	—	2	1	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	1	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	—	4	8	no	—
196	C₂³×C₁₃	—	4	8	no	—
197	C₂³×C₁₃	—	4	4	no	—
198	C₂³×C₁₃	—	4	4	no	—
199	C₂³×C₁₃	C₂×#41	1	2	yes	—
200	C₂³×C₁₃	H(5,𝔽₂)	1	2	yes	—
201	C₂³×C₁₃	2₋¹⁺⁴	1	2	yes	—
202	C₂³×C₁₃	2₋¹⁺⁴	1	4	yes	—
203	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
204	Q₈×C₁₃	—	8	4	no	—
205	C₂×C₄×C₁₃	—	2	8	no	—
206	C₂×C₄×C₁₃	—	2	2	no	—
207	C₂×C₄×C₁₃	—	2	2	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	4	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	4	no	—
213	C₂×C₄×C₁₃	—	2	4	no	—
214	C₂×C₄×C₁₃	—	2	4	no	—
215	C₂×C₄×C₁₃	—	2	4	no	—
216	C₂×C₄×C₁₃	—	2	4	no	—
217	C₂×C₄×C₁₃	—	2	4	no	—
218	C₂×C₄×C₁₃	—	2	4	no	—
219	C₂×C₄×C₁₃	—	2	4	no	—
220	C₂×C₄×C₁₃	—	2	4	no	—
221	C₂×C₄×C₁₃	—	2	4	no	—
222	C₂×C₄×C₁₃	—	2	4	no	—
223	C₂×C₄×C₁₃	—	2	4	no	—
224	C₂×C₄×C₁₃	—	2	4	no	—
225	C₂×C₄×C₁₃	—	2	4	no	—
226	C₂×C₄×C₁₃	—	2	4	no	—
227	C₂×C₄×C₁₃	—	2	4	no	—
228	C₂×C₄×C₁₃	—	4	4	no	—
229	C₂×C₄×C₁₃	—	4	8	no	—
230	C₂×C₄×C₁₃	—	4	8	no	—
231	C₂×C₄×C₁₃	—	8	4	no	—
232	C₂×C₄×C₁₃	—	8	4	no	—
233	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
234	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
235	C₂⁴×C₄	C₂²×C₁₃	1	1	yes	characteristic
236	C₂×#126	C₂²×C₁₃	1	4	yes	—
237	C₂×#125	C₂²×C₁₃	1	4	yes	complemented
238	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
239	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
240	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
241	C₂²×C₄⋊C₄	C₂²×C₁₃	1	2	yes	—
242	C₂²×C₂²⋊C₄	C₂²×C₁₃	1	2	yes	—
243	#400	C₂²×C₁₃	1	4	yes	complemented
244	#400	C₂²×C₁₃	1	4	yes	complemented
245	#398	C₂²×C₁₃	1	4	yes	complemented
246	#398	C₂²×C₁₃	1	4	yes	complemented
247	#398	C₂²×C₁₃	1	4	yes	complemented
248	#398	C₂²×C₁₃	1	4	yes	complemented
249	#398	C₂²×C₁₃	1	4	yes	complemented
250	#397	C₂²×C₁₃	1	4	yes	—
251	#397	C₂²×C₁₃	1	4	yes	—
252	#397	C₂²×C₁₃	1	4	yes	—
253	#396	C₂²×C₁₃	1	4	yes	—
254	#395	C₂²×C₁₃	1	4	yes	complemented
255	#391	C₂²×C₁₃	1	4	yes	complemented
256	#389	C₂²×C₁₃	1	4	yes	complemented
257	#389	C₂²×C₁₃	1	4	yes	complemented
258	#388	C₂²×C₁₃	1	4	yes	—
259	#388	C₂²×C₁₃	1	4	yes	—
260	#388	C₂²×C₁₃	1	4	yes	—
261	#387	C₂²×C₁₃	1	4	yes	complemented
262	#387	C₂²×C₁₃	1	4	yes	complemented
263	#387	C₂²×C₁₃	1	4	yes	complemented
264	#387	C₂²×C₁₃	1	4	yes	complemented
265	#385	C₂²×C₁₃	1	4	yes	—
266	#385	C₂²×C₁₃	1	4	yes	—
267	#385	C₂²×C₁₃	1	4	yes	—
268	#385	C₂²×C₁₃	1	4	yes	—
269	#385	C₂²×C₁₃	1	4	yes	—
270	#380	C₂²×C₁₃	1	2	yes	—
271	#380	C₂²×C₁₃	1	2	yes	—
272	#380	C₂²×C₁₃	1	2	yes	—
273	#380	C₂²×C₁₃	1	4	yes	—
274	#380	C₂²×C₁₃	1	4	yes	—
275	#380	C₂²×C₁₃	1	4	yes	—
276	#379	C₂²×C₁₃	1	4	yes	—
277	C₄×C₂²⋊C₄	C₂²×C₁₃	1	4	yes	—
278	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#95	C₂²×C₁₃	1	1	yes	characteristic
280	C₂²×C₁₃	—	2	2	no	—
281	C₂²×C₁₃	—	2	2	no	—
282	C₂²×C₁₃	—	2	4	no	—
283	C₂²×C₁₃	—	2	4	no	—
284	C₂²×C₁₃	—	2	2	no	—
285	C₂²×C₁₃	—	2	2	no	—
286	C₂²×C₁₃	—	2	4	no	—
287	C₂²×C₁₃	—	2	4	no	—
288	C₂²×C₁₃	—	4	16	no	—
289	C₂²×C₁₃	—	4	1	no	—
290	C₂²×C₁₃	—	4	1	no	—
291	C₂²×C₁₃	—	4	1	no	—
292	C₂²×C₁₃	—	4	1	no	—
293	C₂²×C₁₃	—	4	2	no	—
294	C₂²×C₁₃	—	4	2	no	—
295	C₂²×C₁₃	#541	1	4	yes	—
296	C₂²×C₁₃	C₂²×#41	1	1	yes	characteristic
297	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
298	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
299	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	2	yes	—
300	C₂²×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
301	C₄×C₁₃	—	2	4	no	—
302	C₄×C₁₃	—	2	4	no	—
303	C₄×C₁₃	—	4	4	no	—
304	C₄×C₁₃	—	4	4	no	—
305	C₄×C₁₃	—	4	4	no	—
306	C₄×C₁₃	—	4	4	no	—
307	C₄×C₁₃	—	4	4	no	—
308	C₄×C₁₃	—	4	4	no	—
309	C₂⁵	C₂³×C₁₃	1	1	yes	characteristic
310	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
311	C₂³×C₄	—	2	4	no	—
312	C₂³×C₄	—	4	4	no	—
313	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
314	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
315	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
316	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
317	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
318	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
319	#126	—	4	8	no	—
320	#125	—	4	8	no	—
321	C₂²⋊Q₈	—	2	8	no	—
322	C₂²⋊Q₈	—	4	4	no	—
323	C₂²⋊Q₈	—	4	4	no	—
324	C₂×C₄⋊C₄	—	4	4	no	—
325	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
330	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
334	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
335	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₃	1	4	yes	—
339	C₂×C₂²⋊C₄	—	4	4	no	—
340	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₁₃	1	4	yes	—
348	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
349	C₂×C₄²	C₂³×C₁₃	1	4	yes	—
350	#95	C₂³×C₁₃	1	4	yes	—
351	#95	C₂³×C₁₃	1	4	yes	—
352	#95	C₂³×C₁₃	1	4	yes	—
353	#95	C₂³×C₁₃	1	4	yes	—
354	#95	C₂³×C₁₃	1	4	yes	—
355	#95	C₂³×C₁₃	1	4	yes	—
356	#95	C₂³×C₁₃	1	4	yes	—
357	#95	C₂³×C₁₃	1	4	yes	—
358	#95	C₂³×C₁₃	1	4	yes	—
359	#95	C₂³×C₁₃	1	4	yes	—
360	#95	C₂³×C₁₃	1	4	yes	—
361	#95	C₂³×C₁₃	1	4	yes	—
362	#95	C₂³×C₁₃	1	4	yes	—
363	C₂×C₁₃	—	2	4	no	—
364	C₂×C₁₃	—	4	2	no	—
365	C₂×C₁₃	—	4	2	no	—
366	C₂×C₁₃	C₂×#541	1	1	yes	characteristic
367	C₂×C₁₃	#3490	1	1	yes	characteristic
368	C₂×C₁₃	#3492	1	1	yes	characteristic
369	C₂×C₁₃	#3536	1	2	yes	—
370	C₂×C₁₃	#3538	1	2	yes	—
371	C₂⁴	—	2	2	no	—
372	C₂⁴	—	2	2	no	—
373	C₂⁴	—	2	2	no	—
374	C₂⁴	—	2	4	no	—
375	C₂⁴	—	4	2	no	—
376	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
377	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
378	C₂⁴	C₂⁴×C₁₃	1	1	yes	characteristic
379	C₂×Q₈	—	2	4	no	—
380	C₂×Q₈	—	4	2	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	4	no	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	—	4	2	no	—
392	C₂²×C₄	—	4	2	no	—
393	C₂²×C₄	—	4	2	no	—
394	C₂²×C₄	—	4	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	16	no	—
398	C₂²×C₄	C₁₃×#41	1	4	yes	—
399	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
401	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₁₃	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
406	C₂²×C₄	C₂⁴×C₁₃	1	2	yes	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	8	no	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	8	no	—
412	C₄⋊C₄	—	4	4	no	—
413	C₄⋊C₄	—	4	2	no	—
414	C₄⋊C₄	—	4	2	no	—
415	C₄⋊C₄	—	4	4	no	—
416	C₄⋊C₄	—	4	4	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	—	4	4	no	—
419	C₄⋊C₄	—	4	4	no	—
420	C₄⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₄²	—	4	4	no	—
430	C₄²	—	4	4	no	—
431	C₁₃	#36728	1	1	yes	characteristic, direct product factor, Sylow
432	C₂³	—	2	2	no	—
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	4	8	no	—
445	C₂³	—	4	8	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	4	no	—
448	C₂³	C₂×C₁₃×#41	1	2	yes	—
449	C₂³	C₁₃×H(5,𝔽₂)	1	2	yes	—
450	C₂³	C₁₃×2₋¹⁺⁴	1	2	yes	—
451	C₂³	C₁₃×2₋¹⁺⁴	1	4	yes	—
452	C₂³	C₂⁵×C₁₃	1	1	yes	characteristic
453	Q₈	—	8	4	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	2	4	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	8	no	—
479	C₂×C₄	—	4	8	no	—
480	C₂×C₄	—	8	4	no	—
481	C₂×C₄	—	8	4	no	—
482	C₂×C₄	C₂×C₁₃×#41	1	4	yes	—
483	C₂×C₄	C₁₃×H(5,𝔽₂)	1	4	yes	—
484	C₂²	—	2	4	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	2	4	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	16	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	C₁₃×#541	1	4	yes	—
500	C₂²	C₂²×C₁₃×#41	1	1	yes	characteristic
501	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
502	C₂²	C₂×C₁₃×H(5,𝔽₂)	1	2	yes	—
503	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	2	yes	—
504	C₂²	C₂×C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
505	C₄	—	2	4	no	—
506	C₄	—	2	4	no	—
507	C₄	—	4	4	no	—
508	C₄	—	4	4	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	4	no	—
513	C₂	—	2	4	no	—
514	C₂	—	4	2	no	—
515	C₂	—	4	2	no	—
516	C₂	C₂×C₁₃×#541	1	1	yes	characteristic
517	C₂	C₁₃×#3490	1	1	yes	characteristic
518	C₂	C₁₃×#3492	1	1	yes	characteristic
519	C₂	C₁₃×#3536	1	2	yes	—
520	C₂	C₁₃×#3538	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₃×#2747	C₂	semidirect
3. C₁₃×#2722	C₂	semidirect
4. C₁₃×#2704	C₂	semidirect
5. C₁₃×#2690	C₂	semidirect
6. C₁₃×#2659	C₂	semidirect
7. C₁₃×#2646	C₂	semidirect
9. C₁₃×#2473	C₂	semidirect
10. C₁₃×#2329	C₂	semidirect
14. C₂×C₁₃×#125	C₂²	semidirect
20. C₁₃×#400	C₂²	semidirect
21. C₁₃×#400	C₂²	semidirect
22. C₁₃×#398	C₂²	semidirect
23. C₁₃×#398	C₂²	semidirect
24. C₁₃×#398	C₂²	semidirect
25. C₁₃×#398	C₂²	semidirect
26. C₁₃×#398	C₂²	semidirect
31. C₁₃×#395	C₂²	semidirect
32. C₁₃×#391	C₂²	semidirect
33. C₁₃×#389	C₂²	semidirect
34. C₁₃×#389	C₂²	semidirect
38. C₁₃×#387	C₂²	semidirect
39. C₁₃×#387	C₂²	semidirect
40. C₁₃×#387	C₂²	semidirect
41. C₁₃×#387	C₂²	semidirect
111. #36728	C₁₃	direct (N × H)
173. #2747	C₂×C₁₃	semidirect
174. #2722	C₂×C₁₃	semidirect
175. #2704	C₂×C₁₃	semidirect
176. #2690	C₂×C₁₃	semidirect
177. #2659	C₂×C₁₃	semidirect
178. #2646	C₂×C₁₃	semidirect
180. #2473	C₂×C₁₃	semidirect
181. #2329	C₂×C₁₃	semidirect
237. C₂×#125	C₂²×C₁₃	semidirect
243. #400	C₂²×C₁₃	semidirect
244. #400	C₂²×C₁₃	semidirect
245. #398	C₂²×C₁₃	semidirect
246. #398	C₂²×C₁₃	semidirect
247. #398	C₂²×C₁₃	semidirect
248. #398	C₂²×C₁₃	semidirect
249. #398	C₂²×C₁₃	semidirect
254. #395	C₂²×C₁₃	semidirect
255. #391	C₂²×C₁₃	semidirect
256. #389	C₂²×C₁₃	semidirect
257. #389	C₂²×C₁₃	semidirect
261. #387	C₂²×C₁₃	semidirect
262. #387	C₂²×C₁₃	semidirect
263. #387	C₂²×C₁₃	semidirect
264. #387	C₂²×C₁₃	semidirect
431. C₁₃	#36728	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×#2848	2
C₁₃×#2747	2
C₁₃×#2722	2
C₁₃×#2704	2
C₁₃×#2690	2
C₁₃×#2659	2
C₁₃×#2646	2
C₁₃×#2480	2
C₁₃×#2473	2
C₁₃×#2329	2
C₂×C₁₃×#380	2
#36728	13

Subgroups — C13×#36728 #15723067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#36728 #15723067