Subgroups — C₁₃×#29435 #15715774

Order 3328.

724 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#2860	C₂	1	1	yes	maximal, characteristic
2	C₁₃×#2295	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×#2088	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2068	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2067	C₂	1	1	yes	maximal, characteristic
6	C₁₃×#2055	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#1968	C₂	1	1	yes	maximal, characteristic
8	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1934	C₂	1	1	yes	maximal, characteristic
10	C₁₃×#1933	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1925	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₃×#1880	C₂	1	1	yes	maximal, characteristic
14	C₁₃×#1863	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×SD₁₆	C₂²	1	1	yes	characteristic
17	C₂×C₁₃×#126	—	2	1	no	—
18	C₂×C₄×Q₈×C₁₃	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×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
27	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₁₃×#391	C₂²	1	1	yes	characteristic
33	C₁₃×#391	C₂²	1	1	yes	characteristic
34	C₁₃×#390	C₂²	1	1	yes	characteristic
35	C₁₃×#390	C₂²	1	1	yes	characteristic
36	C₁₃×#390	C₂²	1	1	yes	characteristic
37	C₁₃×#389	C₂²	1	1	yes	characteristic
38	C₁₃×#389	C₂²	1	1	yes	characteristic
39	C₁₃×#389	C₂²	1	1	yes	characteristic
40	C₁₃×#389	C₂²	1	1	yes	characteristic
41	C₁₃×#389	C₂²	1	1	yes	characteristic
42	C₁₃×#388	—	2	1	no	—
43	C₁₃×#388	—	2	1	no	—
44	C₁₃×#388	—	2	1	no	—
45	C₁₃×#387	—	2	1	no	—
46	C₁₃×#387	—	2	1	no	—
47	C₄×C₁₃×C₄⋊C₄	—	2	1	no	—
48	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₁₃×#376	—	2	1	no	—
50	C₄³×C₁₃	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	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×C₁₃×SD₁₆	—	2	2	no	—
62	C₂×C₁₃×SD₁₆	—	2	2	no	—
63	C₂×C₁₃×SD₁₆	—	4	1	no	—
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	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
68	C₁₃×#126	—	4	4	no	—
69	C₄×Q₈×C₁₃	—	2	2	no	—
70	C₄×Q₈×C₁₃	—	2	2	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	—	2	1	no	—
75	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
76	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
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	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
98	C₁₃×#107	—	2	2	no	—
99	C₁₃×#107	—	4	1	no	—
100	C₁₃×#106	—	2	2	no	—
101	C₁₃×C₄⋊C₈	—	2	2	no	—
102	C₁₃×C₄⋊C₈	—	2	2	no	—
103	C₁₃×#103	—	2	2	no	—
104	C₁₃×#103	—	2	2	no	—
105	C₁₃×#103	—	4	1	no	—
106	C₁₃×#102	—	2	2	no	—
107	C₁₃×#102	—	2	2	no	—
108	C₁₃×#102	—	4	1	no	—
109	C₄×C₈×C₁₃	—	4	1	no	—
110	C₄×C₈×C₁₃	—	4	1	no	—
111	C₁₃×#95	—	2	1	no	—
112	C₁₃×#95	—	2	1	no	—
113	C₁₃×#95	—	2	1	no	—
114	C₁₃×#95	—	2	1	no	—
115	C₁₃×#95	—	2	1	no	—
116	C₁₃×#95	—	2	1	no	—
117	C₁₃×#95	—	2	1	no	—
118	C₁₃×#95	—	2	1	no	—
119	C₁₃×#95	—	2	1	no	—
120	C₁₃×#95	—	2	1	no	—
121	#29435	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
122	C₂⁴×C₁₃	—	2	1	no	—
123	C₂×Q₈×C₁₃	—	2	1	no	—
124	C₂×Q₈×C₁₃	—	2	1	no	—
125	C₂×Q₈×C₁₃	—	2	1	no	—
126	C₂×Q₈×C₁₃	—	2	1	no	—
127	C₂×Q₈×C₁₃	—	2	1	no	—
128	C₂×Q₈×C₁₃	#41	1	2	yes	—
129	C₂×D₄×C₁₃	—	2	1	no	—
130	C₂×D₄×C₁₃	—	2	1	no	—
131	C₂×D₄×C₁₃	—	2	1	no	—
132	C₂×D₄×C₁₃	—	2	1	no	—
133	C₂×D₄×C₁₃	—	2	1	no	—
134	C₂×D₄×C₁₃	—	2	1	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	1	no	—
137	C₂²×C₄×C₁₃	—	2	1	no	—
138	C₂²×C₄×C₁₃	—	2	1	no	—
139	C₂²×C₄×C₁₃	—	2	1	no	—
140	C₂²×C₄×C₁₃	—	2	1	no	—
141	C₂²×C₄×C₁₃	—	2	1	no	—
142	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
149	C₁₃×SD₁₆	—	4	4	no	—
150	C₂×C₈×C₁₃	—	2	1	no	—
151	C₂×C₈×C₁₃	—	2	1	no	—
152	C₂×C₈×C₁₃	—	2	1	no	—
153	C₂×C₈×C₁₃	—	2	1	no	—
154	C₂×C₈×C₁₃	—	2	1	no	—
155	C₂×C₈×C₁₃	—	2	1	no	—
156	C₂×C₈×C₁₃	—	2	1	no	—
157	C₂×C₈×C₁₃	—	2	1	no	—
158	C₂×C₈×C₁₃	—	2	1	no	—
159	C₂×C₈×C₁₃	—	2	1	no	—
160	C₂×C₈×C₁₃	#41	1	2	yes	—
161	C₂×C₈×C₁₃	#41	1	2	yes	—
162	C₁₃×C₄⋊C₄	—	2	4	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	—	2	1	no	—
167	C₁₃×C₄⋊C₄	—	2	1	no	—
168	C₁₃×C₄⋊C₄	—	2	1	no	—
169	C₁₃×C₄⋊C₄	—	2	1	no	—
170	C₁₃×C₄⋊C₄	—	2	1	no	—
171	C₁₃×C₄⋊C₄	—	2	1	no	—
172	C₁₃×C₄⋊C₄	—	2	1	no	—
173	C₁₃×C₄⋊C₄	—	2	1	no	—
174	C₁₃×C₄⋊C₄	—	4	2	no	—
175	C₁₃×C₄⋊C₄	—	4	2	no	—
176	C₁₃×C₄⋊C₄	—	4	2	no	—
177	C₁₃×C₄⋊C₄	—	4	2	no	—
178	C₁₃×C₄⋊C₄	—	4	2	no	—
179	C₁₃×C₄⋊C₄	#41	1	2	yes	—
180	C₁₃×C₂²⋊C₄	—	4	2	no	—
181	C₁₃×C₂²⋊C₄	—	4	2	no	—
182	C₁₃×C₂²⋊C₄	—	4	2	no	—
183	C₁₃×C₂²⋊C₄	—	4	2	no	—
184	C₁₃×C₂²⋊C₄	—	4	2	no	—
185	C₁₃×C₂²⋊C₄	—	4	2	no	—
186	C₄²×C₁₃	—	2	4	no	—
187	C₄²×C₁₃	—	2	2	no	—
188	C₄²×C₁₃	—	2	2	no	—
189	C₄²×C₁₃	—	2	2	no	—
190	C₄²×C₁₃	—	2	2	no	—
191	C₄²×C₁₃	—	2	1	no	—
192	C₄²×C₁₃	—	2	1	no	—
193	C₄²×C₁₃	—	2	1	no	—
194	C₄²×C₁₃	—	2	1	no	—
195	C₄²×C₁₃	—	2	1	no	—
196	C₄²×C₁₃	—	2	1	no	—
197	C₄²×C₁₃	—	4	2	no	—
198	#2860	C₂×C₁₃	1	1	yes	characteristic
199	#2295	C₂×C₁₃	1	1	yes	characteristic, complemented
200	#2088	C₂×C₁₃	1	1	yes	characteristic, complemented
201	#2068	C₂×C₁₃	1	1	yes	characteristic, complemented
202	#2067	C₂×C₁₃	1	1	yes	characteristic
203	#2055	C₂×C₁₃	1	1	yes	characteristic
204	#1968	C₂×C₁₃	1	1	yes	characteristic
205	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
206	#1934	C₂×C₁₃	1	1	yes	characteristic
207	#1933	C₂×C₁₃	1	1	yes	characteristic, complemented
208	#1925	C₂×C₁₃	1	1	yes	characteristic
209	#1920	C₂×C₁₃	1	1	yes	characteristic, complemented
210	#1880	C₂×C₁₃	1	1	yes	characteristic
211	#1863	C₂×C₁₃	1	1	yes	characteristic, complemented
212	C₄×C₄⋊C₈	C₂×C₁₃	1	1	yes	characteristic, complemented
213	C₂³×C₁₃	—	4	1	no	—
214	C₂³×C₁₃	—	4	1	no	—
215	C₂³×C₁₃	—	4	1	no	—
216	C₂³×C₁₃	—	4	1	no	—
217	C₂³×C₁₃	—	4	1	no	—
218	C₂³×C₁₃	—	4	1	no	—
219	C₂³×C₁₃	—	4	1	no	—
220	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
221	Q₈×C₁₃	—	2	2	no	—
222	Q₈×C₁₃	—	2	2	no	—
223	Q₈×C₁₃	—	4	1	no	—
224	Q₈×C₁₃	—	4	1	no	—
225	D₄×C₁₃	—	4	1	no	—
226	D₄×C₁₃	—	4	1	no	—
227	D₄×C₁₃	—	4	1	no	—
228	D₄×C₁₃	—	4	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	—	2	1	no	—
235	C₂×C₄×C₁₃	—	2	1	no	—
236	C₂×C₄×C₁₃	—	2	1	no	—
237	C₂×C₄×C₁₃	—	2	1	no	—
238	C₂×C₄×C₁₃	—	2	2	no	—
239	C₂×C₄×C₁₃	—	2	2	no	—
240	C₂×C₄×C₁₃	—	2	1	no	—
241	C₂×C₄×C₁₃	—	2	1	no	—
242	C₂×C₄×C₁₃	—	2	1	no	—
243	C₂×C₄×C₁₃	—	2	1	no	—
244	C₂×C₄×C₁₃	—	2	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	—	4	1	no	—
255	C₂×C₄×C₁₃	—	4	1	no	—
256	C₂×C₄×C₁₃	—	4	1	no	—
257	C₂×C₄×C₁₃	—	4	1	no	—
258	C₂×C₄×C₁₃	—	4	1	no	—
259	C₂×C₄×C₁₃	—	4	1	no	—
260	C₂×C₄×C₁₃	—	4	1	no	—
261	C₂×C₄×C₁₃	—	4	1	no	—
262	C₂×C₄×C₁₃	—	4	1	no	—
263	C₂×C₄×C₁₃	—	4	1	no	—
264	C₂×C₄×C₁₃	#135	1	2	yes	—
265	C₂×C₄×C₁₃	#135	1	2	yes	—
266	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
267	C₂×C₄×C₁₃	#137	1	2	yes	—
268	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
270	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
273	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
274	C₈×C₁₃	—	2	2	no	—
275	C₈×C₁₃	—	2	2	no	—
276	C₈×C₁₃	—	4	1	no	—
277	C₈×C₁₃	—	4	1	no	—
278	C₂²×SD₁₆	C₂²×C₁₃	1	1	yes	characteristic
279	C₂×#126	—	2	1	no	—
280	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
281	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
282	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
283	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
284	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
285	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
286	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
287	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
288	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
289	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
290	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
291	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
292	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
294	#391	C₂²×C₁₃	1	1	yes	characteristic
295	#391	C₂²×C₁₃	1	1	yes	characteristic
296	#390	C₂²×C₁₃	1	1	yes	characteristic
297	#390	C₂²×C₁₃	1	1	yes	characteristic
298	#390	C₂²×C₁₃	1	1	yes	characteristic
299	#389	C₂²×C₁₃	1	1	yes	characteristic
300	#389	C₂²×C₁₃	1	1	yes	characteristic
301	#389	C₂²×C₁₃	1	1	yes	characteristic
302	#389	C₂²×C₁₃	1	1	yes	characteristic
303	#389	C₂²×C₁₃	1	1	yes	characteristic
304	#388	—	2	1	no	—
305	#388	—	2	1	no	—
306	#388	—	2	1	no	—
307	#387	—	2	1	no	—
308	#387	—	2	1	no	—
309	C₄×C₄⋊C₄	—	2	1	no	—
310	C₄×C₄⋊C₄	C₂²×C₁₃	1	1	yes	characteristic
311	#376	—	2	1	no	—
312	C₄³	C₂²×C₁₃	1	1	yes	characteristic
313	#340	C₂²×C₁₃	1	1	yes	characteristic
314	#340	C₂²×C₁₃	1	1	yes	characteristic
315	#340	C₂²×C₁₃	1	1	yes	characteristic
316	#340	C₂²×C₁₃	1	1	yes	characteristic
317	#340	C₂²×C₁₃	1	1	yes	characteristic
318	#340	C₂²×C₁₃	1	1	yes	characteristic
319	#336	C₂²×C₁₃	1	1	yes	characteristic
320	#336	C₂²×C₁₃	1	1	yes	characteristic
321	C₂²×C₁₃	—	8	1	no	—
322	C₂²×C₁₃	—	8	1	no	—
323	C₂²×C₁₃	—	8	1	no	—
324	C₂²×C₁₃	—	8	1	no	—
325	C₂²×C₁₃	—	8	1	no	—
326	C₂²×C₁₃	—	8	1	no	—
327	C₂²×C₁₃	—	8	1	no	—
328	C₂²×C₁₃	#525	1	1	yes	characteristic
329	C₂²×C₁₃	#532	1	1	yes	characteristic
330	C₂²×C₁₃	#537	1	1	yes	characteristic
331	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
332	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
333	C₂²×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
334	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
335	C₄×C₁₃	—	2	2	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	4	1	no	—
340	C₄×C₁₃	—	4	2	no	—
341	C₄×C₁₃	—	4	2	no	—
342	C₄×C₁₃	—	4	1	no	—
343	C₄×C₁₃	—	8	1	no	—
344	C₄×C₁₃	—	8	1	no	—
345	C₄×C₁₃	—	8	1	no	—
346	C₄×C₁₃	—	8	1	no	—
347	C₄×C₁₃	—	8	1	no	—
348	C₄×C₁₃	#551	1	1	yes	characteristic
349	C₄×C₁₃	#552	1	1	yes	characteristic
350	C₄×C₁₃	#553	1	1	yes	characteristic
351	C₄×C₁₃	#556	1	1	yes	characteristic
352	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
353	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
354	C₂×SD₁₆	—	2	2	no	—
355	C₂×SD₁₆	—	2	2	no	—
356	C₂×SD₁₆	—	4	1	no	—
357	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
361	#126	—	4	4	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	1	no	—
366	C₂×C₄⋊C₄	—	2	1	no	—
367	C₂×C₄⋊C₄	—	2	1	no	—
368	C₂×C₄⋊C₄	—	2	1	no	—
369	C₂×C₄⋊C₄	—	2	1	no	—
370	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
373	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
375	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₂²⋊C₄	—	2	1	no	—
379	C₂×C₂²⋊C₄	—	2	1	no	—
380	C₂×C₂²⋊C₄	—	2	1	no	—
381	C₂×C₂²⋊C₄	—	2	1	no	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
385	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
386	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
387	C₂×C₄²	D₄×C₁₃	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
391	#107	—	2	2	no	—
392	#107	—	4	1	no	—
393	#106	—	2	2	no	—
394	C₄⋊C₈	—	2	2	no	—
395	C₄⋊C₈	—	2	2	no	—
396	#103	—	2	2	no	—
397	#103	—	2	2	no	—
398	#103	—	4	1	no	—
399	#102	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	4	1	no	—
402	C₄×C₈	—	4	1	no	—
403	C₄×C₈	—	4	1	no	—
404	#95	—	2	1	no	—
405	#95	—	2	1	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	1	no	—
409	#95	—	2	1	no	—
410	#95	—	2	1	no	—
411	#95	—	2	1	no	—
412	#95	—	2	1	no	—
413	#95	—	2	1	no	—
414	C₂×C₁₃	—	16	1	no	—
415	C₂×C₁₃	#2601	1	1	yes	characteristic
416	C₂×C₁₃	#3106	1	1	yes	characteristic
417	C₂×C₁₃	#3108	1	1	yes	characteristic
418	C₂×C₁₃	#3168	1	1	yes	characteristic
419	C₂×C₁₃	#3182	1	1	yes	characteristic
420	C₂×C₁₃	#3247	1	1	yes	characteristic
421	C₂×C₁₃	#3248	1	1	yes	characteristic
422	C₂⁴	—	2	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	C₁₃×#41	1	2	yes	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
443	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
444	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
445	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
446	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
449	SD₁₆	—	4	4	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	C₁₃×#41	1	2	yes	—
461	C₂×C₈	C₁₃×#41	1	2	yes	—
462	C₄⋊C₄	—	2	4	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	4	2	no	—
475	C₄⋊C₄	—	4	2	no	—
476	C₄⋊C₄	—	4	2	no	—
477	C₄⋊C₄	—	4	2	no	—
478	C₄⋊C₄	—	4	2	no	—
479	C₄⋊C₄	C₁₃×#41	1	2	yes	—
480	C₂²⋊C₄	—	4	2	no	—
481	C₂²⋊C₄	—	4	2	no	—
482	C₂²⋊C₄	—	4	2	no	—
483	C₂²⋊C₄	—	4	2	no	—
484	C₂²⋊C₄	—	4	2	no	—
485	C₂²⋊C₄	—	4	2	no	—
486	C₄²	—	2	4	no	—
487	C₄²	—	2	2	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	4	2	no	—
498	C₁₃	#29435	1	1	yes	characteristic, direct product factor, Sylow
499	C₂³	—	4	1	no	—
500	C₂³	—	4	1	no	—
501	C₂³	—	4	1	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	1	no	—
505	C₂³	—	4	1	no	—
506	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
507	Q₈	—	2	2	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	C₁₃×#135	1	2	yes	—
551	C₂×C₄	C₁₃×#135	1	2	yes	—
552	C₂×C₄	C₁₃×AGL(1,ℤ/8)	1	2	yes	—
553	C₂×C₄	C₁₃×#137	1	2	yes	—
554	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
555	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
556	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
557	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
558	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
559	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
560	C₈	—	2	2	no	—
561	C₈	—	2	2	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	1	no	—
570	C₂²	—	8	1	no	—
571	C₂²	C₁₃×#525	1	1	yes	characteristic
572	C₂²	C₁₃×#532	1	1	yes	characteristic
573	C₂²	C₁₃×#537	1	1	yes	characteristic
574	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
575	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
576	C₂²	C₂×C₁₃×AGL(1,ℤ/8)	1	1	yes	characteristic
577	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	2	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	2	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	—	8	1	no	—
590	C₄	—	8	1	no	—
591	C₄	C₁₃×#551	1	1	yes	characteristic
592	C₄	C₁₃×#552	1	1	yes	characteristic
593	C₄	C₁₃×#553	1	1	yes	characteristic
594	C₄	C₁₃×#556	1	1	yes	characteristic
595	C₂	—	16	1	no	—
596	C₂	C₁₃×#2601	1	1	yes	characteristic
597	C₂	C₁₃×#3106	1	1	yes	characteristic
598	C₂	C₁₃×#3108	1	1	yes	characteristic
599	C₂	C₁₃×#3168	1	1	yes	characteristic
600	C₂	C₁₃×#3182	1	1	yes	characteristic
601	C₂	C₁₃×#3247	1	1	yes	characteristic
602	C₂	C₁₃×#3248	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 ◁ C₄³×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₃×#2295	C₂	semidirect
3. C₁₃×#2088	C₂	semidirect
4. C₁₃×#2068	C₂	semidirect
8. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1933	C₂	semidirect
12. C₁₃×#1920	C₂	semidirect
14. C₁₃×#1863	C₂	semidirect
15. C₄×C₁₃×C₄⋊C₈	C₂	semidirect
121. #29435	C₁₃	direct (N × H)
199. #2295	C₂×C₁₃	semidirect
200. #2088	C₂×C₁₃	semidirect
201. #2068	C₂×C₁₃	semidirect
205. #1942	C₂×C₁₃	semidirect
207. #1933	C₂×C₁₃	semidirect
209. #1920	C₂×C₁₃	semidirect
211. #1863	C₂×C₁₃	semidirect
212. C₄×C₄⋊C₈	C₂×C₁₃	semidirect
498. C₁₃	#29435	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×#2860	2
C₁₃×#2295	2
C₁₃×#2088	2
C₁₃×#2068	2
C₁₃×#2067	2
C₁₃×#2055	2
C₁₃×#1968	2
C₁₃×#1942	2
C₁₃×#1934	2
C₁₃×#1933	2
C₁₃×#1925	2
C₁₃×#1920	2
C₁₃×#1880	2
C₁₃×#1863	2
C₄×C₁₃×C₄⋊C₈	2
#29435	13

Subgroups — C13×#29435 #15715774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#29435 #15715774