Subgroups — C₁₃×#32419 #15718758

Order 3328.

624 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2496	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2495	C₂	1	1	yes	maximal, characteristic
3	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2087	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2085	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2084	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2077	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#2076	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1949	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#1918	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1851	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic
15	C₁₃×#1809	C₂	1	1	yes	maximal, characteristic
16	C₂²×C₁₃×M₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#126	—	2	1	no	—
18	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₃×#400	—	2	1	no	—
28	C₁₃×#400	—	2	1	no	—
29	C₁₃×#397	—	2	1	no	—
30	C₁₃×#397	—	2	1	no	—
31	C₁₃×#389	C₂²	1	1	yes	characteristic
32	C₁₃×#389	C₂²	1	1	yes	characteristic
33	C₁₃×#389	C₂²	1	1	yes	characteristic
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#388	—	2	1	no	—
36	C₁₃×#387	—	2	1	no	—
37	C₁₃×#384	C₂²	1	1	yes	characteristic
38	C₁₃×#383	—	2	1	no	—
39	C₁₃×#382	C₂²	1	1	yes	characteristic
40	C₁₃×#380	C₂²	1	1	yes	characteristic
41	C₁₃×#380	C₂²	1	1	yes	characteristic
42	C₁₃×#380	C₂²	1	1	yes	characteristic
43	C₁₃×#380	C₂²	1	1	yes	characteristic
44	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
47	C₁₃×#340	C₂²	1	1	yes	characteristic
48	C₁₃×#340	C₂²	1	1	yes	characteristic
49	C₁₃×#340	C₂²	1	1	yes	characteristic
50	C₁₃×#340	C₂²	1	1	yes	characteristic
51	C₁₃×#340	C₂²	1	1	yes	characteristic
52	C₁₃×#340	C₂²	1	1	yes	characteristic
53	C₁₃×#340	C₂²	1	1	yes	characteristic
54	C₁₃×#340	C₂²	1	1	yes	characteristic
55	C₁₃×#340	C₂²	1	1	yes	characteristic
56	C₁₃×#340	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂×C₁₃×M₁₆	—	2	2	no	—
61	C₂×C₁₃×M₁₆	—	2	2	no	—
62	C₂×C₁₃×M₁₆	—	4	1	no	—
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
67	C₁₃×#126	—	4	4	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
80	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
84	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
85	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
87	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₃	—	2	1	no	—
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
92	C₁₃×#107	—	2	2	no	—
93	C₁₃×#107	—	4	1	no	—
94	C₁₃×#107	—	4	1	no	—
95	C₁₃×#106	—	2	2	no	—
96	C₁₃×#106	—	4	1	no	—
97	C₁₃×#106	—	4	1	no	—
98	C₁₃×C₄⋊C₈	—	2	2	no	—
99	C₁₃×C₄⋊C₈	—	2	2	no	—
100	C₁₃×C₂²⋊C₈	—	4	1	no	—
101	C₁₃×#95	—	2	1	no	—
102	C₁₃×#95	—	2	1	no	—
103	C₁₃×#95	—	2	1	no	—
104	C₁₃×#95	—	2	1	no	—
105	C₁₃×#95	—	2	1	no	—
106	C₁₃×#95	—	2	1	no	—
107	C₁₃×#95	—	2	1	no	—
108	C₁₃×#95	—	2	1	no	—
109	C₁₃×#95	—	2	1	no	—
110	C₁₃×#95	—	2	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	D₄	1	1	yes	characteristic
114	C₁₃×#95	D₄	1	1	yes	characteristic
115	#32419	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₁₃	—	2	1	no	—
118	C₂²×C₄×C₁₃	—	2	1	no	—
119	C₂²×C₄×C₁₃	—	2	1	no	—
120	C₂²×C₄×C₁₃	—	2	1	no	—
121	C₂²×C₄×C₁₃	—	2	1	no	—
122	C₂²×C₄×C₁₃	—	2	1	no	—
123	C₂²×C₄×C₁₃	—	2	1	no	—
124	C₂²×C₄×C₁₃	—	2	1	no	—
125	C₂²×C₄×C₁₃	—	2	1	no	—
126	C₂²×C₄×C₁₃	—	2	1	no	—
127	C₂²×C₄×C₁₃	—	2	1	no	—
128	C₂²×C₄×C₁₃	—	2	1	no	—
129	C₂²×C₄×C₁₃	—	2	1	no	—
130	C₂²×C₄×C₁₃	—	2	1	no	—
131	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
137	C₁₃×M₁₆	—	4	4	no	—
138	C₂×C₈×C₁₃	—	2	1	no	—
139	C₂×C₈×C₁₃	—	2	1	no	—
140	C₂×C₈×C₁₃	—	2	1	no	—
141	C₂×C₈×C₁₃	—	2	1	no	—
142	C₂×C₈×C₁₃	—	2	1	no	—
143	C₂×C₈×C₁₃	—	2	1	no	—
144	C₂×C₈×C₁₃	—	2	1	no	—
145	C₂×C₈×C₁₃	—	2	1	no	—
146	C₂×C₈×C₁₃	—	2	1	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	#41	1	2	yes	—
149	C₂×C₈×C₁₃	#41	1	2	yes	—
150	C₁₃×C₄⋊C₄	—	2	1	no	—
151	C₁₃×C₄⋊C₄	—	2	1	no	—
152	C₁₃×C₄⋊C₄	—	2	1	no	—
153	C₁₃×C₄⋊C₄	—	2	1	no	—
154	C₁₃×C₄⋊C₄	—	2	1	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	1	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	1	no	—
160	C₁₃×C₄⋊C₄	—	2	1	no	—
161	C₁₃×C₄⋊C₄	—	2	1	no	—
162	C₁₃×C₄⋊C₄	—	2	1	no	—
163	C₁₃×C₄⋊C₄	—	2	1	no	—
164	C₁₃×C₄⋊C₄	—	2	1	no	—
165	C₁₃×C₄⋊C₄	—	2	1	no	—
166	C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₁₃×C₄⋊C₄	—	4	2	no	—
168	C₁₃×C₄⋊C₄	—	4	2	no	—
169	C₁₃×C₄⋊C₄	—	4	2	no	—
170	C₁₃×C₄⋊C₄	—	8	1	no	—
171	C₁₃×C₄⋊C₄	—	8	1	no	—
172	C₁₃×C₂²⋊C₄	—	2	2	no	—
173	C₁₃×C₂²⋊C₄	—	4	1	no	—
174	C₁₃×C₂²⋊C₄	—	4	2	no	—
175	C₁₃×C₂²⋊C₄	—	4	2	no	—
176	C₁₃×C₂²⋊C₄	—	4	2	no	—
177	C₁₃×C₂²⋊C₄	—	8	1	no	—
178	C₄²×C₁₃	—	2	1	no	—
179	C₄²×C₁₃	—	2	1	no	—
180	C₄²×C₁₃	—	2	1	no	—
181	C₄²×C₁₃	—	2	1	no	—
182	C₄²×C₁₃	—	4	2	no	—
183	C₄²×C₁₃	—	4	2	no	—
184	#2496	C₂×C₁₃	1	1	yes	characteristic
185	#2495	C₂×C₁₃	1	1	yes	characteristic
186	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
187	#2087	C₂×C₁₃	1	1	yes	characteristic, complemented
188	#2085	C₂×C₁₃	1	1	yes	characteristic, complemented
189	#2084	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#2077	C₂×C₁₃	1	1	yes	characteristic
191	#2076	C₂×C₁₃	1	1	yes	characteristic
192	#1949	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
194	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#1918	C₂×C₁₃	1	1	yes	characteristic, complemented
196	#1851	C₂×C₁₃	1	1	yes	characteristic
197	#1809	C₂×C₁₃	1	1	yes	characteristic
198	#1809	C₂×C₁₃	1	1	yes	characteristic
199	C₂³×C₁₃	—	2	1	no	—
200	C₂³×C₁₃	—	2	1	no	—
201	C₂³×C₁₃	—	2	1	no	—
202	C₂³×C₁₃	—	2	1	no	—
203	C₂³×C₁₃	—	2	1	no	—
204	C₂³×C₁₃	—	2	1	no	—
205	C₂³×C₁₃	—	2	1	no	—
206	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	1	no	—
209	C₂×C₄×C₁₃	—	2	1	no	—
210	C₂×C₄×C₁₃	—	2	1	no	—
211	C₂×C₄×C₁₃	—	2	1	no	—
212	C₂×C₄×C₁₃	—	2	1	no	—
213	C₂×C₄×C₁₃	—	2	1	no	—
214	C₂×C₄×C₁₃	—	2	1	no	—
215	C₂×C₄×C₁₃	—	2	1	no	—
216	C₂×C₄×C₁₃	—	2	1	no	—
217	C₂×C₄×C₁₃	—	2	1	no	—
218	C₂×C₄×C₁₃	—	2	1	no	—
219	C₂×C₄×C₁₃	—	2	1	no	—
220	C₂×C₄×C₁₃	—	2	1	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	no	—
223	C₂×C₄×C₁₃	—	4	1	no	—
224	C₂×C₄×C₁₃	—	4	1	no	—
225	C₂×C₄×C₁₃	—	4	1	no	—
226	C₂×C₄×C₁₃	—	4	1	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	4	1	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	1	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	—	4	1	no	—
235	C₂×C₄×C₁₃	—	4	1	no	—
236	C₂×C₄×C₁₃	—	4	1	no	—
237	C₂×C₄×C₁₃	—	4	1	no	—
238	C₂×C₄×C₁₃	—	4	1	no	—
239	C₂×C₄×C₁₃	—	4	1	no	—
240	C₂×C₄×C₁₃	—	4	1	no	—
241	C₂×C₄×C₁₃	—	4	1	no	—
242	C₂×C₄×C₁₃	—	4	1	no	—
243	C₂×C₄×C₁₃	—	4	1	no	—
244	C₂×C₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	4	1	no	—
246	C₂×C₄×C₁₃	—	4	1	no	—
247	C₂×C₄×C₁₃	—	4	1	no	—
248	C₂×C₄×C₁₃	—	4	1	no	—
249	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
250	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
256	C₈×C₁₃	—	2	2	no	—
257	C₈×C₁₃	—	2	2	no	—
258	C₈×C₁₃	—	4	1	no	—
259	C₈×C₁₃	—	4	1	no	—
260	C₂²×M₁₆	C₂²×C₁₃	1	1	yes	characteristic
261	C₂×#126	—	2	1	no	—
262	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
263	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
265	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
271	#400	—	2	1	no	—
272	#400	—	2	1	no	—
273	#397	—	2	1	no	—
274	#397	—	2	1	no	—
275	#389	C₂²×C₁₃	1	1	yes	characteristic
276	#389	C₂²×C₁₃	1	1	yes	characteristic
277	#389	C₂²×C₁₃	1	1	yes	characteristic
278	#389	C₂²×C₁₃	1	1	yes	characteristic
279	#388	—	2	1	no	—
280	#387	—	2	1	no	—
281	#384	C₂²×C₁₃	1	1	yes	characteristic
282	#383	—	2	1	no	—
283	#382	C₂²×C₁₃	1	1	yes	characteristic
284	#380	C₂²×C₁₃	1	1	yes	characteristic
285	#380	C₂²×C₁₃	1	1	yes	characteristic
286	#380	C₂²×C₁₃	1	1	yes	characteristic
287	#380	C₂²×C₁₃	1	1	yes	characteristic
288	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
289	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
290	C₄×C₂²⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
291	#340	C₂²×C₁₃	1	1	yes	characteristic
292	#340	C₂²×C₁₃	1	1	yes	characteristic
293	#340	C₂²×C₁₃	1	1	yes	characteristic
294	#340	C₂²×C₁₃	1	1	yes	characteristic
295	#340	C₂²×C₁₃	1	1	yes	characteristic
296	#340	C₂²×C₁₃	1	1	yes	characteristic
297	#340	C₂²×C₁₃	1	1	yes	characteristic
298	#340	C₂²×C₁₃	1	1	yes	characteristic
299	#340	C₂²×C₁₃	1	1	yes	characteristic
300	#340	C₂²×C₁₃	1	1	yes	characteristic
301	#336	C₂²×C₁₃	1	1	yes	characteristic
302	#336	C₂²×C₁₃	1	1	yes	characteristic
303	C₂²×C₁₃	—	4	1	no	—
304	C₂²×C₁₃	—	4	1	no	—
305	C₂²×C₁₃	—	4	1	no	—
306	C₂²×C₁₃	—	4	1	no	—
307	C₂²×C₁₃	—	4	1	no	—
308	C₂²×C₁₃	—	4	1	no	—
309	C₂²×C₁₃	—	4	1	no	—
310	C₂²×C₁₃	#537	1	1	yes	characteristic
311	C₂²×C₁₃	#547	1	1	yes	characteristic
312	C₂²×C₁₃	#547	1	1	yes	characteristic
313	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
314	C₂²×C₁₃	#575	1	1	yes	characteristic
315	C₂²×C₁₃	#577	1	1	yes	characteristic
316	C₂²×C₁₃	#578	1	1	yes	characteristic
317	C₄×C₁₃	—	2	2	no	—
318	C₄×C₁₃	—	4	1	no	—
319	C₄×C₁₃	—	4	1	no	—
320	C₄×C₁₃	—	4	1	no	—
321	C₄×C₁₃	—	4	1	no	—
322	C₄×C₁₃	—	8	1	no	—
323	C₄×C₁₃	—	8	1	no	—
324	C₄×C₁₃	—	8	1	no	—
325	C₄×C₁₃	—	8	1	no	—
326	C₄×C₁₃	—	8	1	no	—
327	C₄×C₁₃	—	8	1	no	—
328	C₄×C₁₃	—	8	1	no	—
329	C₄×C₁₃	—	8	1	no	—
330	C₄×C₁₃	#541	1	1	yes	characteristic
331	C₄×C₁₃	#541	1	1	yes	characteristic
332	C₄×C₁₃	#551	1	1	yes	characteristic
333	C₄×C₁₃	#563	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	4	1	no	—
338	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
341	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
342	#126	—	4	4	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
350	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
352	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
353	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
355	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₂²⋊C₄	—	2	1	no	—
361	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	—	2	1	no	—
365	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
366	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
367	#107	—	2	2	no	—
368	#107	—	4	1	no	—
369	#107	—	4	1	no	—
370	#106	—	2	2	no	—
371	#106	—	4	1	no	—
372	#106	—	4	1	no	—
373	C₄⋊C₈	—	2	2	no	—
374	C₄⋊C₈	—	2	2	no	—
375	C₂²⋊C₈	—	4	1	no	—
376	#95	—	2	1	no	—
377	#95	—	2	1	no	—
378	#95	—	2	1	no	—
379	#95	—	2	1	no	—
380	#95	—	2	1	no	—
381	#95	—	2	1	no	—
382	#95	—	2	1	no	—
383	#95	—	2	1	no	—
384	#95	—	2	1	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	D₄×C₁₃	1	1	yes	characteristic
389	#95	D₄×C₁₃	1	1	yes	characteristic
390	C₂×C₁₃	—	8	1	no	—
391	C₂×C₁₃	#2722	1	1	yes	characteristic
392	C₂×C₁₃	#3251	1	1	yes	characteristic
393	C₂×C₁₃	#3258	1	1	yes	characteristic
394	C₂×C₁₃	#3343	1	1	yes	characteristic
395	C₂×C₁₃	#3349	1	1	yes	characteristic
396	C₂×C₁₃	#3351	1	1	yes	characteristic
397	C₂×C₁₃	#3354	1	1	yes	characteristic
398	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	—	2	1	no	—
412	C₂²×C₄	—	2	1	no	—
413	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
416	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
419	M₁₆	—	4	4	no	—
420	C₂×C₈	—	2	1	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	C₁₃×#41	1	2	yes	—
431	C₂×C₈	C₁₃×#41	1	2	yes	—
432	C₄⋊C₄	—	2	1	no	—
433	C₄⋊C₄	—	2	1	no	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	1	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	4	2	no	—
449	C₄⋊C₄	—	4	2	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	8	1	no	—
453	C₄⋊C₄	—	8	1	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₂²⋊C₄	—	4	1	no	—
456	C₂²⋊C₄	—	4	2	no	—
457	C₂²⋊C₄	—	4	2	no	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂²⋊C₄	—	8	1	no	—
460	C₄²	—	2	1	no	—
461	C₄²	—	2	1	no	—
462	C₄²	—	2	1	no	—
463	C₄²	—	2	1	no	—
464	C₄²	—	4	2	no	—
465	C₄²	—	4	2	no	—
466	C₁₃	#32419	1	1	yes	characteristic, direct product factor, Sylow
467	C₂³	—	2	1	no	—
468	C₂³	—	2	1	no	—
469	C₂³	—	2	1	no	—
470	C₂³	—	2	1	no	—
471	C₂³	—	2	1	no	—
472	C₂³	—	2	1	no	—
473	C₂³	—	2	1	no	—
474	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	1	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	4	1	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	1	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	1	no	—
504	C₂×C₄	—	4	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	1	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
518	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
519	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
520	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
521	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
522	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
523	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
524	C₈	—	2	2	no	—
525	C₈	—	2	2	no	—
526	C₈	—	4	1	no	—
527	C₈	—	4	1	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	—	4	1	no	—
534	C₂²	—	4	1	no	—
535	C₂²	C₁₃×#537	1	1	yes	characteristic
536	C₂²	C₁₃×#547	1	1	yes	characteristic
537	C₂²	C₁₃×#547	1	1	yes	characteristic
538	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
539	C₂²	C₁₃×#575	1	1	yes	characteristic
540	C₂²	C₁₃×#577	1	1	yes	characteristic
541	C₂²	C₁₃×#578	1	1	yes	characteristic
542	C₄	—	2	2	no	—
543	C₄	—	4	1	no	—
544	C₄	—	4	1	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	8	1	no	—
549	C₄	—	8	1	no	—
550	C₄	—	8	1	no	—
551	C₄	—	8	1	no	—
552	C₄	—	8	1	no	—
553	C₄	—	8	1	no	—
554	C₄	—	8	1	no	—
555	C₄	C₁₃×#541	1	1	yes	characteristic
556	C₄	C₁₃×#541	1	1	yes	characteristic
557	C₄	C₁₃×#551	1	1	yes	characteristic
558	C₄	C₁₃×#563	1	1	yes	characteristic
559	C₂	—	8	1	no	—
560	C₂	C₁₃×#2722	1	1	yes	characteristic
561	C₂	C₁₃×#3251	1	1	yes	characteristic
562	C₂	C₁₃×#3258	1	1	yes	characteristic
563	C₂	C₁₃×#3343	1	1	yes	characteristic
564	C₂	C₁₃×#3349	1	1	yes	characteristic
565	C₂	C₁₃×#3351	1	1	yes	characteristic
566	C₂	C₁₃×#3354	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₄×C₁₃×C₂²⋊C₄ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₃×#2088	C₂	semidirect
4. C₁₃×#2087	C₂	semidirect
5. C₁₃×#2085	C₂	semidirect
6. C₁₃×#2084	C₂	semidirect
9. C₁₃×#1949	C₂	semidirect
10. C₁₃×#1947	C₂	semidirect
11. C₁₃×#1919	C₂	semidirect
12. C₁₃×#1918	C₂	semidirect
115. #32419	C₁₃	direct (N × H)
186. #2088	C₂×C₁₃	semidirect
187. #2087	C₂×C₁₃	semidirect
188. #2085	C₂×C₁₃	semidirect
189. #2084	C₂×C₁₃	semidirect
192. #1949	C₂×C₁₃	semidirect
193. #1947	C₂×C₁₃	semidirect
194. #1919	C₂×C₁₃	semidirect
195. #1918	C₂×C₁₃	semidirect
466. C₁₃	#32419	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×#2496	2
C₁₃×#2495	2
C₁₃×#2088	2
C₁₃×#2087	2
C₁₃×#2085	2
C₁₃×#2084	2
C₁₃×#2077	2
C₁₃×#2076	2
C₁₃×#1949	2
C₁₃×#1947	2
C₁₃×#1919	2
C₁₃×#1918	2
C₁₃×#1851	2
C₁₃×#1809	2
#32419	13

Subgroups — C13×#32419 #15718758

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#32419 #15718758