Subgroups — C₁₃×#27135 #15713474

Order 3328.

670 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2512	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2370	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1921	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#107	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×#126	—	2	1	no	—
17	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
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×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
28	C₁₃×#397	—	2	1	no	—
29	C₁₃×#396	—	2	1	no	—
30	C₁₃×#390	C₂²	1	1	yes	characteristic
31	C₁₃×#390	C₂²	1	1	yes	characteristic
32	C₁₃×#390	C₂²	1	1	yes	characteristic
33	C₁₃×#389	—	2	1	no	—
34	C₁₃×#389	C₂²	1	1	yes	characteristic
35	C₁₃×#389	C₂²	1	1	yes	characteristic
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#388	—	2	1	no	—
38	C₁₃×#387	—	2	1	no	—
39	C₁₃×#387	—	2	1	no	—
40	C₁₃×#384	C₂²	1	1	yes	characteristic
41	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
42	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₁₃×C₄⋊C₄	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×C₄⋊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×#336	C₂²	1	1	yes	characteristic
56	C₁₃×#336	C₂²	1	1	yes	characteristic
57	C₁₃×#336	C₂²	1	1	yes	characteristic
58	C₁₃×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₁₃×#126	—	4	4	no	—
65	C₁₃×#125	—	2	2	no	—
66	C₁₃×#125	—	2	2	no	—
67	C₂×C₁₃×C₄⋊C₄	—	2	1	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	D₄	1	1	yes	characteristic
75	C₂×C₁₃×C₄⋊C₄	D₄	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×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₁₃	—	2	1	no	—
90	C₂×C₄²×C₁₃	—	2	1	no	—
91	C₂×C₄²×C₁₃	—	2	1	no	—
92	C₂×C₄²×C₁₃	—	2	1	no	—
93	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₁₃×#107	—	2	2	no	—
97	C₁₃×#107	—	2	2	no	—
98	C₁₃×#107	—	2	2	no	—
99	C₁₃×#106	—	2	2	no	—
100	C₁₃×C₄⋊C₈	—	2	2	no	—
101	C₁₃×#102	—	2	2	no	—
102	C₁₃×#102	—	2	2	no	—
103	C₁₃×#102	—	2	2	no	—
104	C₁₃×#102	—	2	2	no	—
105	C₄×C₈×C₁₃	—	2	2	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	#27135	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	1	no	—
117	C₂×D₄×C₁₃	—	2	1	no	—
118	C₂×D₄×C₁₃	—	2	1	no	—
119	C₂×D₄×C₁₃	—	2	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×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	C₂×D₄	1	1	yes	characteristic
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	C₂×C₈×C₁₃	—	2	1	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	C₁₃×C₄⋊C₄	—	2	4	no	—
150	C₁₃×C₄⋊C₄	—	2	4	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	2	2	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	—	4	2	no	—
165	C₁₃×C₄⋊C₄	—	4	2	no	—
166	C₁₃×C₄⋊C₄	—	4	2	no	—
167	C₁₃×C₄⋊C₄	—	8	1	no	—
168	C₁₃×C₄⋊C₄	—	8	1	no	—
169	C₁₃×C₄⋊C₄	#41	1	2	yes	—
170	C₁₃×C₄⋊C₄	#41	1	2	yes	—
171	C₁₃×C₄⋊C₄	#41	1	2	yes	—
172	C₁₃×C₂²⋊C₄	—	4	2	no	—
173	C₁₃×C₂²⋊C₄	—	4	2	no	—
174	C₁₃×C₂²⋊C₄	—	4	2	no	—
175	C₁₃×C₂²⋊C₄	—	4	2	no	—
176	C₁₃×C₂²⋊C₄	—	8	1	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	—	2	1	no	—
183	C₄²×C₁₃	—	2	1	no	—
184	C₄²×C₁₃	—	4	2	no	—
185	C₄²×C₁₃	—	4	2	no	—
186	C₄²×C₁₃	—	8	1	no	—
187	C₄²×C₁₃	—	8	1	no	—
188	#2512	C₂×C₁₃	1	1	yes	characteristic
189	#2370	C₂×C₁₃	1	1	yes	characteristic, complemented
190	#2100	C₂×C₁₃	1	1	yes	characteristic, complemented
191	#2067	C₂×C₁₃	1	1	yes	characteristic
192	#2059	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#2025	C₂×C₁₃	1	1	yes	characteristic
194	#1947	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#1934	C₂×C₁₃	1	1	yes	characteristic
196	#1926	C₂×C₁₃	1	1	yes	characteristic
197	#1925	C₂×C₁₃	1	1	yes	characteristic
198	#1925	C₂×C₁₃	1	1	yes	characteristic
199	#1921	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#1920	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#1916	C₂×C₁₃	1	1	yes	characteristic, complemented
202	C₄×#107	C₂×C₁₃	1	1	yes	characteristic, complemented
203	C₂³×C₁₃	—	4	1	no	—
204	C₂³×C₁₃	—	4	1	no	—
205	C₂³×C₁₃	—	4	1	no	—
206	C₂³×C₁₃	—	4	1	no	—
207	C₂³×C₁₃	—	4	1	no	—
208	C₂³×C₁₃	—	4	1	no	—
209	C₂³×C₁₃	—	4	1	no	—
210	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
211	D₄×C₁₃	—	4	1	no	—
212	D₄×C₁₃	—	4	1	no	—
213	D₄×C₁₃	—	4	1	no	—
214	D₄×C₁₃	—	4	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	—	2	2	no	—
222	C₂×C₄×C₁₃	—	2	2	no	—
223	C₂×C₄×C₁₃	—	2	1	no	—
224	C₂×C₄×C₁₃	—	2	1	no	—
225	C₂×C₄×C₁₃	—	2	2	no	—
226	C₂×C₄×C₁₃	—	2	1	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	1	no	—
230	C₂×C₄×C₁₃	—	2	1	no	—
231	C₂×C₄×C₁₃	—	2	1	no	—
232	C₂×C₄×C₁₃	—	2	1	no	—
233	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
250	C₂×C₄×C₁₃	—	4	1	no	—
251	C₂×C₄×C₁₃	—	4	1	no	—
252	C₂×C₄×C₁₃	#135	1	2	yes	—
253	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
254	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
259	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
260	C₈×C₁₃	—	2	2	no	—
261	C₈×C₁₃	—	4	1	no	—
262	C₈×C₁₃	—	4	1	no	—
263	C₈×C₁₃	—	4	1	no	—
264	C₂×#126	—	2	1	no	—
265	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
269	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
276	#397	—	2	1	no	—
277	#396	—	2	1	no	—
278	#390	C₂²×C₁₃	1	1	yes	characteristic
279	#390	C₂²×C₁₃	1	1	yes	characteristic
280	#390	C₂²×C₁₃	1	1	yes	characteristic
281	#389	—	2	1	no	—
282	#389	C₂²×C₁₃	1	1	yes	characteristic
283	#389	C₂²×C₁₃	1	1	yes	characteristic
284	#389	C₂²×C₁₃	1	1	yes	characteristic
285	#388	—	2	1	no	—
286	#387	—	2	1	no	—
287	#387	—	2	1	no	—
288	#384	C₂²×C₁₃	1	1	yes	characteristic
289	C₄×C₄⋊C₄	—	2	1	no	—
290	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
291	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
292	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
293	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
294	C₄×C₄⋊C₄	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	#340	C₂²×C₁₃	1	1	yes	characteristic
302	#340	C₂²×C₁₃	1	1	yes	characteristic
303	#336	C₂²×C₁₃	1	1	yes	characteristic
304	#336	C₂²×C₁₃	1	1	yes	characteristic
305	#336	C₂²×C₁₃	1	1	yes	characteristic
306	#336	C₂²×C₁₃	1	1	yes	characteristic
307	C₂²×C₁₃	—	8	1	no	—
308	C₂²×C₁₃	—	8	1	no	—
309	C₂²×C₁₃	—	8	1	no	—
310	C₂²×C₁₃	—	8	1	no	—
311	C₂²×C₁₃	—	8	1	no	—
312	C₂²×C₁₃	—	8	1	no	—
313	C₂²×C₁₃	—	8	1	no	—
314	C₂²×C₁₃	#525	1	1	yes	characteristic
315	C₂²×C₁₃	#547	1	1	yes	characteristic
316	C₂²×C₁₃	#548	1	1	yes	characteristic
317	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
318	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂²×C₁₃	#576	1	1	yes	characteristic
320	C₂²×C₁₃	#578	1	1	yes	characteristic
321	C₄×C₁₃	—	2	2	no	—
322	C₄×C₁₃	—	2	2	no	—
323	C₄×C₁₃	—	4	1	no	—
324	C₄×C₁₃	—	4	1	no	—
325	C₄×C₁₃	—	4	1	no	—
326	C₄×C₁₃	—	4	2	no	—
327	C₄×C₁₃	—	4	2	no	—
328	C₄×C₁₃	—	4	1	no	—
329	C₄×C₁₃	—	4	2	no	—
330	C₄×C₁₃	—	8	1	no	—
331	C₄×C₁₃	—	8	1	no	—
332	C₄×C₁₃	—	8	1	no	—
333	C₄×C₁₃	—	8	1	no	—
334	C₄×C₁₃	#529	1	1	yes	characteristic
335	C₄×C₁₃	#541	1	1	yes	characteristic
336	C₄×C₁₃	#556	1	1	yes	characteristic
337	C₄×C₁₃	#556	1	1	yes	characteristic
338	C₂²×D₄	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	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
343	#126	—	4	4	no	—
344	#125	—	2	2	no	—
345	#125	—	2	2	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	—	2	1	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
354	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
358	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
360	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
361	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
362	C₂×C₂²⋊C₄	—	2	1	no	—
363	C₂×C₂²⋊C₄	—	2	1	no	—
364	C₂×C₂²⋊C₄	—	2	1	no	—
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₄²	—	2	1	no	—
369	C₂×C₄²	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
375	#107	—	2	2	no	—
376	#107	—	2	2	no	—
377	#107	—	2	2	no	—
378	#106	—	2	2	no	—
379	C₄⋊C₈	—	2	2	no	—
380	#102	—	2	2	no	—
381	#102	—	2	2	no	—
382	#102	—	2	2	no	—
383	#102	—	2	2	no	—
384	C₄×C₈	—	2	2	no	—
385	#95	—	2	1	no	—
386	#95	—	2	1	no	—
387	#95	—	2	1	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	D₄×C₁₃	1	1	yes	characteristic
393	#95	D₄×C₁₃	1	1	yes	characteristic
394	C₂×C₁₃	—	16	1	no	—
395	C₂×C₁₃	#2469	1	1	yes	characteristic
396	C₂×C₁₃	#3106	1	1	yes	characteristic
397	C₂×C₁₃	#3124	1	1	yes	characteristic
398	C₂×C₁₃	#3339	1	1	yes	characteristic
399	C₂×C₁₃	#3343	1	1	yes	characteristic
400	C₂×C₁₃	#3364	1	1	yes	characteristic
401	C₂×C₁₃	#3366	1	1	yes	characteristic
402	C₂⁴	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	1	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	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	—	2	1	no	—
414	C₂²×C₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
417	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
418	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
419	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
420	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
421	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
422	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	1	no	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	C₁₃×#41	1	2	yes	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	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	—	2	1	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	4	2	no	—
451	C₄⋊C₄	—	4	2	no	—
452	C₄⋊C₄	—	4	2	no	—
453	C₄⋊C₄	—	8	1	no	—
454	C₄⋊C₄	—	8	1	no	—
455	C₄⋊C₄	C₁₃×#41	1	2	yes	—
456	C₄⋊C₄	C₁₃×#41	1	2	yes	—
457	C₄⋊C₄	C₁₃×#41	1	2	yes	—
458	C₂²⋊C₄	—	4	2	no	—
459	C₂²⋊C₄	—	4	2	no	—
460	C₂²⋊C₄	—	4	2	no	—
461	C₂²⋊C₄	—	4	2	no	—
462	C₂²⋊C₄	—	8	1	no	—
463	C₂²⋊C₄	—	8	1	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	2	1	no	—
466	C₄²	—	2	1	no	—
467	C₄²	—	2	1	no	—
468	C₄²	—	2	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	4	2	no	—
471	C₄²	—	4	2	no	—
472	C₄²	—	8	1	no	—
473	C₄²	—	8	1	no	—
474	C₁₃	#27135	1	1	yes	characteristic, direct product factor, Sylow
475	C₂³	—	4	1	no	—
476	C₂³	—	4	1	no	—
477	C₂³	—	4	1	no	—
478	C₂³	—	4	1	no	—
479	C₂³	—	4	1	no	—
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	1	no	—
486	D₄	—	4	1	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	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	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	C₁₃×#135	1	2	yes	—
525	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
526	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
527	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
528	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
529	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
530	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
531	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
532	C₈	—	2	2	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	4	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	8	1	no	—
538	C₂²	—	8	1	no	—
539	C₂²	—	8	1	no	—
540	C₂²	—	8	1	no	—
541	C₂²	—	8	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	C₁₃×#525	1	1	yes	characteristic
544	C₂²	C₁₃×#547	1	1	yes	characteristic
545	C₂²	C₁₃×#548	1	1	yes	characteristic
546	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
547	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
548	C₂²	C₁₃×#576	1	1	yes	characteristic
549	C₂²	C₁₃×#578	1	1	yes	characteristic
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	4	1	no	—
553	C₄	—	4	1	no	—
554	C₄	—	4	1	no	—
555	C₄	—	4	2	no	—
556	C₄	—	4	2	no	—
557	C₄	—	4	1	no	—
558	C₄	—	4	2	no	—
559	C₄	—	8	1	no	—
560	C₄	—	8	1	no	—
561	C₄	—	8	1	no	—
562	C₄	—	8	1	no	—
563	C₄	C₁₃×#529	1	1	yes	characteristic
564	C₄	C₁₃×#541	1	1	yes	characteristic
565	C₄	C₁₃×#556	1	1	yes	characteristic
566	C₄	C₁₃×#556	1	1	yes	characteristic
567	C₂	—	16	1	no	—
568	C₂	C₁₃×#2469	1	1	yes	characteristic
569	C₂	C₁₃×#3106	1	1	yes	characteristic
570	C₂	C₁₃×#3124	1	1	yes	characteristic
571	C₂	C₁₃×#3339	1	1	yes	characteristic
572	C₂	C₁₃×#3343	1	1	yes	characteristic
573	C₂	C₁₃×#3364	1	1	yes	characteristic
574	C₂	C₁₃×#3366	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2370	C₂	semidirect
3. C₁₃×#2100	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
7. C₁₃×#1947	C₂	semidirect
12. C₁₃×#1921	C₂	semidirect
13. C₁₃×#1920	C₂	semidirect
14. C₁₃×#1916	C₂	semidirect
15. C₄×C₁₃×#107	C₂	semidirect
115. #27135	C₁₃	direct (N × H)
189. #2370	C₂×C₁₃	semidirect
190. #2100	C₂×C₁₃	semidirect
192. #2059	C₂×C₁₃	semidirect
194. #1947	C₂×C₁₃	semidirect
199. #1921	C₂×C₁₃	semidirect
200. #1920	C₂×C₁₃	semidirect
201. #1916	C₂×C₁₃	semidirect
202. C₄×#107	C₂×C₁₃	semidirect
474. C₁₃	#27135	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×#2512	2
C₁₃×#2370	2
C₁₃×#2100	2
C₁₃×#2067	2
C₁₃×#2059	2
C₁₃×#2025	2
C₁₃×#1947	2
C₁₃×#1934	2
C₁₃×#1926	2
C₁₃×#1925	2
C₁₃×#1921	2
C₁₃×#1920	2
C₁₃×#1916	2
C₄×C₁₃×#107	2
#27135	13

Subgroups — C13×#27135 #15713474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#27135 #15713474