Subgroups — C₁₃×#27130 #15713469

Order 3328.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 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×#2369	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2065	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1948	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×#1926	C₂	1	1	yes	maximal, characteristic
11	C₁₃×#1926	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1919	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1916	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×#106	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#126	—	2	1	no	—
18	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
19	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#106	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×#391	—	2	1	no	—
31	C₁₃×#391	—	2	1	no	—
32	C₁₃×#390	C₂²	1	1	yes	characteristic
33	C₁₃×#390	C₂²	1	1	yes	characteristic
34	C₁₃×#390	C₂²	1	1	yes	characteristic
35	C₁₃×#389	—	2	1	no	—
36	C₁₃×#389	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#388	—	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×Q₈×C₁₃	—	2	1	no	—
60	C₂²×D₄×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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
65	C₁₃×C₄⋊Q₈	—	2	2	no	—
66	C₁₃×C₄⋊Q₈	—	2	2	no	—
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	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×#106	—	2	2	no	—
97	C₁₃×#106	—	2	2	no	—
98	C₁₃×#106	—	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	#27130	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂⁴×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	4	no	—
118	C₂×Q₈×C₁₃	—	8	1	no	—
119	C₂×Q₈×C₁₃	—	8	1	no	—
120	C₂×D₄×C₁₃	—	2	1	no	—
121	C₂×D₄×C₁₃	—	2	1	no	—
122	C₂×D₄×C₁₃	—	2	1	no	—
123	C₂×D₄×C₁₃	—	2	1	no	—
124	C₂×D₄×C₁₃	—	2	1	no	—
125	C₂×D₄×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	—	2	1	no	—
132	C₂²×C₄×C₁₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	#41	1	2	yes	—
152	C₁₃×C₄⋊C₄	—	2	4	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	1	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	—	8	1	no	—
170	C₁₃×C₄⋊C₄	SD₁₆	1	4	yes	—
171	C₁₃×C₄⋊C₄	#41	1	2	yes	—
172	C₁₃×C₄⋊C₄	#41	1	2	yes	—
173	C₁₃×C₄⋊C₄	#41	1	2	yes	—
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	—	4	2	no	—
178	C₁₃×C₂²⋊C₄	—	8	1	no	—
179	C₁₃×C₂²⋊C₄	—	8	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	—	2	1	no	—
185	C₄²×C₁₃	—	2	1	no	—
186	C₄²×C₁₃	—	4	2	no	—
187	C₄²×C₁₃	—	4	2	no	—
188	C₄²×C₁₃	—	8	1	no	—
189	C₄²×C₁₃	—	8	1	no	—
190	#2512	C₂×C₁₃	1	1	yes	characteristic
191	#2369	C₂×C₁₃	1	1	yes	characteristic, complemented
192	#2099	C₂×C₁₃	1	1	yes	characteristic, complemented
193	#2065	C₂×C₁₃	1	1	yes	characteristic
194	#2058	C₂×C₁₃	1	1	yes	characteristic, complemented
195	#2023	C₂×C₁₃	1	1	yes	characteristic
196	#1948	C₂×C₁₃	1	1	yes	characteristic, complemented
197	#1934	C₂×C₁₃	1	1	yes	characteristic
198	#1926	C₂×C₁₃	1	1	yes	characteristic
199	#1926	C₂×C₁₃	1	1	yes	characteristic
200	#1926	C₂×C₁₃	1	1	yes	characteristic
201	#1920	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#1919	C₂×C₁₃	1	1	yes	characteristic, complemented
203	#1916	C₂×C₁₃	1	1	yes	characteristic, complemented
204	C₄×#106	C₂×C₁₃	1	1	yes	characteristic, complemented
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	—	4	1	no	—
211	C₂³×C₁₃	—	4	1	no	—
212	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₃	—	8	4	no	—
214	D₄×C₁₃	—	4	1	no	—
215	D₄×C₁₃	—	4	1	no	—
216	D₄×C₁₃	—	4	1	no	—
217	D₄×C₁₃	—	4	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	1	no	—
222	C₂×C₄×C₁₃	—	2	1	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	2	no	—
227	C₂×C₄×C₁₃	—	2	1	no	—
228	C₂×C₄×C₁₃	—	2	1	no	—
229	C₂×C₄×C₁₃	—	2	2	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	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
253	C₂×C₄×C₁₃	—	4	1	no	—
254	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
255	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
256	C₂×C₄×C₁₃	C₂×SD₁₆	1	2	yes	—
257	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
259	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
260	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
262	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
263	C₈×C₁₃	—	2	2	no	—
264	C₈×C₁₃	—	4	1	no	—
265	C₈×C₁₃	—	4	1	no	—
266	C₈×C₁₃	—	4	1	no	—
267	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
268	C₂×#126	—	2	1	no	—
269	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
270	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
271	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
272	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
273	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
274	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
275	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
276	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
277	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
278	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
279	#397	—	2	1	no	—
280	#396	—	2	1	no	—
281	#391	—	2	1	no	—
282	#391	—	2	1	no	—
283	#390	C₂²×C₁₃	1	1	yes	characteristic
284	#390	C₂²×C₁₃	1	1	yes	characteristic
285	#390	C₂²×C₁₃	1	1	yes	characteristic
286	#389	—	2	1	no	—
287	#389	C₂²×C₁₃	1	1	yes	characteristic
288	#389	C₂²×C₁₃	1	1	yes	characteristic
289	#389	C₂²×C₁₃	1	1	yes	characteristic
290	#388	—	2	1	no	—
291	#384	C₂²×C₁₃	1	1	yes	characteristic
292	C₄×C₄⋊C₄	—	2	1	no	—
293	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
294	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
295	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
296	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
297	C₄×C₄⋊C₄	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	#340	C₂²×C₁₃	1	1	yes	characteristic
304	#340	C₂²×C₁₃	1	1	yes	characteristic
305	#340	C₂²×C₁₃	1	1	yes	characteristic
306	#336	C₂²×C₁₃	1	1	yes	characteristic
307	#336	C₂²×C₁₃	1	1	yes	characteristic
308	#336	C₂²×C₁₃	1	1	yes	characteristic
309	#336	C₂²×C₁₃	1	1	yes	characteristic
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	—	8	1	no	—
315	C₂²×C₁₃	—	8	1	no	—
316	C₂²×C₁₃	—	8	1	no	—
317	C₂²×C₁₃	#525	1	1	yes	characteristic
318	C₂²×C₁₃	#547	1	1	yes	characteristic
319	C₂²×C₁₃	#548	1	1	yes	characteristic
320	C₂²×C₁₃	C₂²×SD₁₆	1	1	yes	characteristic
321	C₂²×C₁₃	#575	1	1	yes	characteristic
322	C₂²×C₁₃	#576	1	1	yes	characteristic
323	C₂²×C₁₃	#577	1	1	yes	characteristic
324	C₄×C₁₃	—	2	2	no	—
325	C₄×C₁₃	—	2	2	no	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	4	1	no	—
328	C₄×C₁₃	—	4	1	no	—
329	C₄×C₁₃	—	4	1	no	—
330	C₄×C₁₃	—	4	2	no	—
331	C₄×C₁₃	—	4	2	no	—
332	C₄×C₁₃	—	4	2	no	—
333	C₄×C₁₃	—	8	1	no	—
334	C₄×C₁₃	—	8	1	no	—
335	C₄×C₁₃	—	8	1	no	—
336	C₄×C₁₃	—	8	1	no	—
337	C₄×C₁₃	#529	1	1	yes	characteristic
338	C₄×C₁₃	#541	1	1	yes	characteristic
339	C₄×C₁₃	#556	1	1	yes	characteristic
340	C₄×C₁₃	#556	1	1	yes	characteristic
341	C₂²×Q₈	—	2	1	no	—
342	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
346	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
347	C₄⋊Q₈	—	2	2	no	—
348	C₄⋊Q₈	—	2	2	no	—
349	#126	—	4	4	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	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
357	C₂×C₄⋊C₄	D₄×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×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
363	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
365	C₂×C₂²⋊C₄	—	2	1	no	—
366	C₂×C₂²⋊C₄	—	2	1	no	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
378	#106	—	2	2	no	—
379	#106	—	2	2	no	—
380	#106	—	2	2	no	—
381	#106	—	2	2	no	—
382	C₄⋊C₈	—	2	2	no	—
383	#102	—	2	2	no	—
384	#102	—	2	2	no	—
385	#102	—	2	2	no	—
386	#102	—	2	2	no	—
387	C₄×C₈	—	2	2	no	—
388	#95	—	2	1	no	—
389	#95	—	2	1	no	—
390	#95	—	2	1	no	—
391	#95	—	2	1	no	—
392	#95	—	2	1	no	—
393	#95	—	2	1	no	—
394	#95	—	2	1	no	—
395	#95	D₄×C₁₃	1	1	yes	characteristic
396	#95	D₄×C₁₃	1	1	yes	characteristic
397	C₂×C₁₃	—	16	1	no	—
398	C₂×C₁₃	#2469	1	1	yes	characteristic
399	C₂×C₁₃	#3103	1	1	yes	characteristic
400	C₂×C₁₃	#3118	1	1	yes	characteristic
401	C₂×C₁₃	#3335	1	1	yes	characteristic
402	C₂×C₁₃	#3347	1	1	yes	characteristic
403	C₂×C₁₃	#3362	1	1	yes	characteristic
404	C₂×C₁₃	#3376	1	1	yes	characteristic
405	C₂⁴	—	2	1	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	8	1	no	—
408	C₂×Q₈	—	8	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂²×C₄	—	2	1	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	1	no	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
423	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
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	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	C₁₃×#41	1	2	yes	—
441	C₄⋊C₄	—	2	4	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	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	4	1	no	—
454	C₄⋊C₄	—	4	2	no	—
455	C₄⋊C₄	—	4	2	no	—
456	C₄⋊C₄	—	8	1	no	—
457	C₄⋊C₄	—	8	1	no	—
458	C₄⋊C₄	—	8	1	no	—
459	C₄⋊C₄	C₁₃×SD₁₆	1	4	yes	—
460	C₄⋊C₄	C₁₃×#41	1	2	yes	—
461	C₄⋊C₄	C₁₃×#41	1	2	yes	—
462	C₄⋊C₄	C₁₃×#41	1	2	yes	—
463	C₂²⋊C₄	—	4	2	no	—
464	C₂²⋊C₄	—	4	2	no	—
465	C₂²⋊C₄	—	4	2	no	—
466	C₂²⋊C₄	—	4	2	no	—
467	C₂²⋊C₄	—	8	1	no	—
468	C₂²⋊C₄	—	8	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	1	no	—
475	C₄²	—	4	2	no	—
476	C₄²	—	4	2	no	—
477	C₄²	—	8	1	no	—
478	C₄²	—	8	1	no	—
479	C₁₃	#27130	1	1	yes	characteristic, direct product factor, Sylow
480	C₂³	—	4	1	no	—
481	C₂³	—	4	1	no	—
482	C₂³	—	4	1	no	—
483	C₂³	—	4	1	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	1	no	—
486	C₂³	—	4	1	no	—
487	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
488	Q₈	—	8	4	no	—
489	D₄	—	4	1	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	4	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	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	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
530	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
531	C₂×C₄	C₂×C₁₃×SD₁₆	1	2	yes	—
532	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
533	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
534	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
535	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
536	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
537	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
538	C₈	—	2	2	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₂²	—	8	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	—	8	1	no	—
548	C₂²	—	8	1	no	—
549	C₂²	C₁₃×#525	1	1	yes	characteristic
550	C₂²	C₁₃×#547	1	1	yes	characteristic
551	C₂²	C₁₃×#548	1	1	yes	characteristic
552	C₂²	C₂²×C₁₃×SD₁₆	1	1	yes	characteristic
553	C₂²	C₁₃×#575	1	1	yes	characteristic
554	C₂²	C₁₃×#576	1	1	yes	characteristic
555	C₂²	C₁₃×#577	1	1	yes	characteristic
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	—	8	1	no	—
568	C₄	—	8	1	no	—
569	C₄	C₁₃×#529	1	1	yes	characteristic
570	C₄	C₁₃×#541	1	1	yes	characteristic
571	C₄	C₁₃×#556	1	1	yes	characteristic
572	C₄	C₁₃×#556	1	1	yes	characteristic
573	C₂	—	16	1	no	—
574	C₂	C₁₃×#2469	1	1	yes	characteristic
575	C₂	C₁₃×#3103	1	1	yes	characteristic
576	C₂	C₁₃×#3118	1	1	yes	characteristic
577	C₂	C₁₃×#3335	1	1	yes	characteristic
578	C₂	C₁₃×#3347	1	1	yes	characteristic
579	C₂	C₁₃×#3362	1	1	yes	characteristic
580	C₂	C₁₃×#3376	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×#2369	C₂	semidirect
3. C₁₃×#2099	C₂	semidirect
5. C₁₃×#2058	C₂	semidirect
7. C₁₃×#1948	C₂	semidirect
12. C₁₃×#1920	C₂	semidirect
13. C₁₃×#1919	C₂	semidirect
14. C₁₃×#1916	C₂	semidirect
15. C₄×C₁₃×#106	C₂	semidirect
115. #27130	C₁₃	direct (N × H)
191. #2369	C₂×C₁₃	semidirect
192. #2099	C₂×C₁₃	semidirect
194. #2058	C₂×C₁₃	semidirect
196. #1948	C₂×C₁₃	semidirect
201. #1920	C₂×C₁₃	semidirect
202. #1919	C₂×C₁₃	semidirect
203. #1916	C₂×C₁₃	semidirect
204. C₄×#106	C₂×C₁₃	semidirect
479. C₁₃	#27130	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×#2369	2
C₁₃×#2099	2
C₁₃×#2065	2
C₁₃×#2058	2
C₁₃×#2023	2
C₁₃×#1948	2
C₁₃×#1934	2
C₁₃×#1926	2
C₁₃×#1920	2
C₁₃×#1919	2
C₁₃×#1916	2
C₄×C₁₃×#106	2
#27130	13

Subgroups — C13×#27130 #15713469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#27130 #15713469