Subgroups — C₁₃×#24779 #15711118

Order 3328.

966 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₄×C₁₃	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2415	C₂	1	2	yes	maximal
6	C₁₃×#2066	C₂	1	2	yes	maximal, complemented
7	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
8	C₁₃×#1969	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1942	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1873	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
15	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
16	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#117	C₂²	1	2	yes	—
19	C₁₃×#467	—	2	4	no	—
20	C₁₃×#467	—	2	4	no	—
21	C₈×D₄×C₁₃	—	2	4	no	—
22	C₁₃×#427	—	2	4	no	—
23	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₃×#106	C₂²	1	2	yes	—
27	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#103	C₂²	1	2	yes	—
29	C₂×C₁₃×#103	C₂²	1	2	yes	—
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#397	—	2	2	no	—
35	C₁₃×#394	—	2	2	no	—
36	C₁₃×#391	C₂²	1	2	yes	—
37	C₁₃×#389	—	2	2	no	—
38	C₁₃×#389	C₂²	1	2	yes	—
39	C₁₃×#388	—	2	2	no	—
40	C₁₃×#380	C₂²	1	2	yes	—
41	C₁₃×#340	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
44	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
47	C₂×C₁₃×Q₁₆	—	2	2	no	—
48	C₂×C₁₃×Q₁₆	—	2	2	no	—
49	C₂×C₁₃×Q₁₆	—	2	2	no	—
50	C₂²×C₈×C₁₃	—	2	2	no	—
51	C₂²×C₈×C₁₃	—	2	2	no	—
52	C₂²×C₈×C₁₃	—	2	2	no	—
53	C₂²×C₈×C₁₃	—	2	2	no	—
54	C₂²×C₈×C₁₃	—	2	2	no	—
55	C₂²×C₈×C₁₃	D₄	1	4	yes	—
56	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
60	C₁₃×C₂²⋊Q₈	—	2	4	no	—
61	C₁₃×C₂²⋊Q₈	—	2	4	no	—
62	C₁₃×C₂²⋊Q₈	—	2	4	no	—
63	C₁₃×C₂²⋊Q₈	—	4	2	no	—
64	C₄×D₄×C₁₃	—	2	2	no	—
65	C₄×D₄×C₁₃	—	2	2	no	—
66	C₁₃×#117	—	2	4	no	—
67	C₁₃×#117	—	4	2	no	—
68	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
69	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
70	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
71	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
73	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
74	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
76	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
77	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
78	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
79	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
80	C₂×C₁₃×C₂²⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	—	2	2	no	—
82	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
83	C₁₃×#107	—	2	2	no	—
84	C₁₃×#107	—	2	2	no	—
85	C₁₃×#107	D₄	1	4	yes	complemented
86	C₁₃×#106	—	2	4	no	—
87	C₁₃×C₄⋊C₈	—	2	2	no	—
88	C₁₃×#103	—	2	4	no	—
89	C₁₃×#103	—	2	4	no	—
90	C₁₃×#103	—	4	2	no	—
91	C₁₃×C₂²⋊C₈	—	2	2	no	—
92	C₁₃×C₂²⋊C₈	—	2	2	no	—
93	C₄×C₈×C₁₃	—	2	2	no	—
94	C₁₃×#95	—	2	2	no	—
95	C₁₃×#95	—	2	2	no	—
96	C₁₃×#95	—	2	2	no	—
97	C₁₃×#95	—	2	2	no	—
98	#24779	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
99	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₁₃	—	2	2	no	—
102	C₂×Q₈×C₁₃	—	2	2	no	—
103	C₂×Q₈×C₁₃	—	2	2	no	—
104	C₂×Q₈×C₁₃	—	2	2	no	—
105	C₂×Q₈×C₁₃	—	2	2	no	—
106	C₂×Q₈×C₁₃	—	2	2	no	—
107	C₂×D₄×C₁₃	—	2	2	no	—
108	C₂×D₄×C₁₃	—	2	2	no	—
109	C₂×D₄×C₁₃	—	2	2	no	—
110	C₂²×C₄×C₁₃	—	2	1	no	—
111	C₂²×C₄×C₁₃	—	2	1	no	—
112	C₂²×C₄×C₁₃	—	2	1	no	—
113	C₂²×C₄×C₁₃	—	2	1	no	—
114	C₂²×C₄×C₁₃	—	2	2	no	—
115	C₂²×C₄×C₁₃	—	2	1	no	—
116	C₂²×C₄×C₁₃	—	2	1	no	—
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	2	no	—
122	C₂²×C₄×C₁₃	—	2	2	no	—
123	C₂²×C₄×C₁₃	—	2	2	no	—
124	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	#41	1	2	yes	—
130	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
131	C₁₃×Q₁₆	—	4	4	no	—
132	C₂×C₈×C₁₃	—	2	1	no	—
133	C₂×C₈×C₁₃	—	2	1	no	—
134	C₂×C₈×C₁₃	—	2	8	no	—
135	C₂×C₈×C₁₃	—	2	1	no	—
136	C₂×C₈×C₁₃	—	2	1	no	—
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	—	4	4	no	—
142	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₁₃	#41	1	2	yes	—
146	C₁₃×C₄⋊C₄	—	2	2	no	—
147	C₁₃×C₄⋊C₄	—	2	2	no	—
148	C₁₃×C₄⋊C₄	—	2	2	no	—
149	C₁₃×C₄⋊C₄	—	2	2	no	—
150	C₁₃×C₄⋊C₄	—	2	2	no	—
151	C₁₃×C₄⋊C₄	—	2	2	no	—
152	C₁₃×C₄⋊C₄	—	4	4	no	—
153	C₁₃×C₄⋊C₄	—	4	4	no	—
154	C₁₃×C₄⋊C₄	—	4	4	no	—
155	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
156	C₁₃×C₂²⋊C₄	—	2	2	no	—
157	C₁₃×C₂²⋊C₄	—	2	2	no	—
158	C₁₃×C₂²⋊C₄	—	4	4	no	—
159	C₁₃×C₂²⋊C₄	—	4	4	no	—
160	C₁₃×C₂²⋊C₄	—	4	4	no	—
161	C₁₃×C₂²⋊C₄	—	4	4	no	—
162	C₄²×C₁₃	—	2	1	no	—
163	C₄²×C₁₃	—	2	1	no	—
164	C₄²×C₁₃	—	4	4	no	—
165	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
166	C₂×#467	C₂×C₁₃	1	1	yes	characteristic, complemented
167	C₂×C₈×D₄	C₂×C₁₃	1	1	yes	characteristic
168	C₂×#427	C₂×C₁₃	1	1	yes	characteristic, complemented
169	#2415	C₂×C₁₃	1	2	yes	—
170	#2066	C₂×C₁₃	1	2	yes	complemented
171	#2035	C₂×C₁₃	1	2	yes	complemented
172	#1969	C₂×C₁₃	1	1	yes	characteristic, complemented
173	#1942	C₂×C₁₃	1	1	yes	characteristic, complemented
174	#1873	C₂×C₁₃	1	2	yes	complemented
175	#1808	C₂×C₁₃	1	1	yes	characteristic, complemented
176	C₂³×C₁₃	—	2	1	no	—
177	C₂³×C₁₃	—	2	1	no	—
178	C₂³×C₁₃	—	2	1	no	—
179	C₂³×C₁₃	—	2	1	no	—
180	C₂³×C₁₃	—	2	1	no	—
181	C₂³×C₁₃	—	2	1	no	—
182	C₂³×C₁₃	—	2	1	no	—
183	C₂³×C₁₃	—	2	1	no	—
184	C₂³×C₁₃	—	2	1	no	—
185	C₂³×C₁₃	—	2	1	no	—
186	C₂³×C₁₃	—	2	1	no	—
187	C₂³×C₁₃	—	2	1	no	—
188	C₂³×C₁₃	#121	1	2	yes	—
189	C₂³×C₁₃	#135	1	2	yes	—
190	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
191	Q₈×C₁₃	—	4	2	no	—
192	Q₈×C₁₃	—	4	2	no	—
193	Q₈×C₁₃	—	4	2	no	—
194	Q₈×C₁₃	—	4	2	no	—
195	D₄×C₁₃	—	2	8	no	—
196	C₂×C₄×C₁₃	—	2	1	no	—
197	C₂×C₄×C₁₃	—	2	1	no	—
198	C₂×C₄×C₁₃	—	2	1	no	—
199	C₂×C₄×C₁₃	—	2	1	no	—
200	C₂×C₄×C₁₃	—	2	2	no	—
201	C₂×C₄×C₁₃	—	2	2	no	—
202	C₂×C₄×C₁₃	—	2	2	no	—
203	C₂×C₄×C₁₃	—	2	2	no	—
204	C₂×C₄×C₁₃	—	2	1	no	—
205	C₂×C₄×C₁₃	—	2	1	no	—
206	C₂×C₄×C₁₃	—	2	4	no	—
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	—	4	2	no	—
212	C₂×C₄×C₁₃	—	4	2	no	—
213	C₂×C₄×C₁₃	—	4	1	no	—
214	C₂×C₄×C₁₃	—	4	1	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	2	no	—
218	C₂×C₄×C₁₃	—	4	2	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	2	no	—
222	C₂×C₄×C₁₃	—	4	2	no	—
223	C₂×C₄×C₁₃	—	4	2	no	—
224	C₂×C₄×C₁₃	—	4	2	no	—
225	C₂×C₄×C₁₃	—	4	2	no	—
226	C₂×C₄×C₁₃	#121	1	2	yes	—
227	C₂×C₄×C₁₃	#135	1	2	yes	—
228	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
233	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
234	C₈×C₁₃	—	2	2	no	—
235	C₈×C₁₃	—	4	1	no	—
236	C₈×C₁₃	—	4	1	no	—
237	C₈×C₁₃	#121	1	4	yes	—
238	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
240	C₂³×C₈	C₂²×C₁₃	1	1	yes	characteristic
241	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
242	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
243	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
244	C₂×#117	C₂²×C₁₃	1	2	yes	—
245	#467	—	2	4	no	—
246	#467	—	2	4	no	—
247	C₈×D₄	—	2	4	no	—
248	#427	—	2	4	no	—
249	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
251	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
252	C₂×#106	C₂²×C₁₃	1	2	yes	—
253	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
254	C₂×#103	C₂²×C₁₃	1	2	yes	—
255	C₂×#103	C₂²×C₁₃	1	2	yes	—
256	C₂×#103	C₂²×C₁₃	1	2	yes	—
257	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×C₂²⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
260	#397	—	2	2	no	—
261	#394	—	2	2	no	—
262	#391	C₂²×C₁₃	1	2	yes	—
263	#389	—	2	2	no	—
264	#389	C₂²×C₁₃	1	2	yes	—
265	#388	—	2	2	no	—
266	#380	C₂²×C₁₃	1	2	yes	—
267	#340	C₂²×C₁₃	1	2	yes	—
268	#340	C₂²×C₁₃	1	2	yes	—
269	C₂²×C₁₃	—	2	2	no	—
270	C₂²×C₁₃	—	2	2	no	—
271	C₂²×C₁₃	—	2	2	no	—
272	C₂²×C₁₃	—	2	2	no	—
273	C₂²×C₁₃	—	2	2	no	—
274	C₂²×C₁₃	—	2	2	no	—
275	C₂²×C₁₃	—	4	1	no	—
276	C₂²×C₁₃	—	4	1	no	—
277	C₂²×C₁₃	—	4	1	no	—
278	C₂²×C₁₃	—	4	1	no	—
279	C₂²×C₁₃	—	4	1	no	—
280	C₂²×C₁₃	—	4	1	no	—
281	C₂²×C₁₃	—	4	1	no	—
282	C₂²×C₁₃	—	4	1	no	—
283	C₂²×C₁₃	C₂×#121	1	1	yes	characteristic
284	C₂²×C₁₃	D₄²	1	1	yes	characteristic
285	C₂²×C₁₃	#547	1	1	yes	characteristic
286	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
287	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
288	C₂²×C₁₃	#578	1	1	yes	characteristic
289	C₂²×C₁₃	#578	1	1	yes	characteristic
290	C₄×C₁₃	—	2	2	no	—
291	C₄×C₁₃	—	2	2	no	—
292	C₄×C₁₃	—	4	1	no	—
293	C₄×C₁₃	—	4	4	no	—
294	C₄×C₁₃	—	4	1	no	—
295	C₄×C₁₃	—	8	2	no	—
296	C₄×C₁₃	—	8	2	no	—
297	C₄×C₁₃	—	8	2	no	—
298	C₄×C₁₃	C₂×#121	1	1	yes	characteristic
299	C₄×C₁₃	#537	1	1	yes	characteristic
300	C₄×C₁₃	#548	1	1	yes	characteristic
301	C₄×C₁₃	#553	1	1	yes	characteristic
302	C₂²×Q₈	C₂³×C₁₃	1	2	yes	—
303	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₁₃	1	1	yes	characteristic
306	C₂×Q₁₆	—	2	2	no	—
307	C₂×Q₁₆	—	2	2	no	—
308	C₂×Q₁₆	—	2	2	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	2	2	no	—
314	C₂²×C₈	D₄×C₁₃	1	4	yes	—
315	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
318	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	4	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	4	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	#117	—	2	4	no	—
326	#117	—	4	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
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	2	yes	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
339	C₂×C₂²⋊C₄	D₄×C₁₃	1	1	yes	characteristic
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
342	#107	—	2	2	no	—
343	#107	—	2	2	no	—
344	#107	D₄×C₁₃	1	4	yes	complemented
345	#106	—	2	4	no	—
346	C₄⋊C₈	—	2	2	no	—
347	#103	—	2	4	no	—
348	#103	—	2	4	no	—
349	#103	—	4	2	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	C₄×C₈	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	2	no	—
355	#95	—	2	2	no	—
356	#95	—	2	2	no	—
357	C₂×C₁₃	—	4	2	no	—
358	C₂×C₁₃	—	4	2	no	—
359	C₂×C₁₃	#2416	1	1	yes	characteristic
360	C₂×C₁₃	#3050	1	1	yes	characteristic
361	C₂×C₁₃	#3059	1	1	yes	characteristic
362	C₂×C₁₃	#3283	1	1	yes	characteristic
363	C₂×C₁₃	#3285	1	1	yes	characteristic
364	C₂×C₁₃	#3336	1	1	yes	characteristic
365	C₂×C₁₃	#3342	1	1	yes	characteristic
366	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
367	C₂⁴	C₂×D₄×C₁₃	1	1	yes	characteristic
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	2	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
394	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
395	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
396	C₂²×C₄	C₁₃×#41	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
398	Q₁₆	—	4	4	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	8	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	1	no	—
405	C₂×C₈	—	2	1	no	—
406	C₂×C₈	—	2	1	no	—
407	C₂×C₈	—	2	1	no	—
408	C₂×C₈	—	4	4	no	—
409	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
410	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
411	C₂×C₈	C₂×D₄×C₁₃	1	2	yes	—
412	C₂×C₈	C₁₃×#41	1	2	yes	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	4	4	no	—
420	C₄⋊C₄	—	4	4	no	—
421	C₄⋊C₄	—	4	4	no	—
422	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	4	4	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	4	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	4	4	no	—
432	C₁₃	#24779	1	1	yes	characteristic, direct product factor, Sylow
433	C₂³	—	2	1	no	—
434	C₂³	—	2	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	1	no	—
445	C₂³	C₁₃×#121	1	2	yes	—
446	C₂³	C₁₃×#135	1	2	yes	—
447	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
448	Q₈	—	4	2	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	2	no	—
452	D₄	—	2	8	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	C₁₃×#121	1	2	yes	—
484	C₂×C₄	C₁₃×#135	1	2	yes	—
485	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
487	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
488	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
489	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
490	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	4	1	no	—
493	C₈	—	4	1	no	—
494	C₈	C₁₃×#121	1	4	yes	—
495	C₂²	—	2	2	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	2	2	no	—
498	C₂²	—	2	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	4	1	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	4	1	no	—
509	C₂²	C₂×C₁₃×#121	1	1	yes	characteristic
510	C₂²	D₄²×C₁₃	1	1	yes	characteristic
511	C₂²	C₁₃×#547	1	1	yes	characteristic
512	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
513	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
514	C₂²	C₁₃×#578	1	1	yes	characteristic
515	C₂²	C₁₃×#578	1	1	yes	characteristic
516	C₄	—	2	2	no	—
517	C₄	—	2	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	4	1	no	—
520	C₄	—	4	1	no	—
521	C₄	—	8	2	no	—
522	C₄	—	8	2	no	—
523	C₄	—	8	2	no	—
524	C₄	C₂×C₁₃×#121	1	1	yes	characteristic
525	C₄	C₁₃×#537	1	1	yes	characteristic
526	C₄	C₁₃×#548	1	1	yes	characteristic
527	C₄	C₁₃×#553	1	1	yes	characteristic
528	C₂	—	4	2	no	—
529	C₂	—	4	2	no	—
530	C₂	C₁₃×#2416	1	1	yes	characteristic
531	C₂	C₁₃×#3050	1	1	yes	characteristic
532	C₂	C₁₃×#3059	1	1	yes	characteristic
533	C₂	C₁₃×#3283	1	1	yes	characteristic
534	C₂	C₁₃×#3285	1	1	yes	characteristic
535	C₂	C₁₃×#3336	1	1	yes	characteristic
536	C₂	C₁₃×#3342	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	D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×D₄×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#467	C₂	semidirect
2. C₂×C₁₃×#467	C₂	semidirect
4. C₂×C₁₃×#427	C₂	semidirect
6. C₁₃×#2066	C₂	semidirect
7. C₁₃×#2035	C₂	semidirect
8. C₁₃×#1969	C₂	semidirect
9. C₁₃×#1942	C₂	semidirect
10. C₁₃×#1873	C₂	semidirect
11. C₁₃×#1808	C₂	semidirect
85. C₁₃×#107	D₄	semidirect
98. #24779	C₁₃	direct (N × H)
165. C₂×#467	C₂×C₁₃	semidirect
166. C₂×#467	C₂×C₁₃	semidirect
168. C₂×#427	C₂×C₁₃	semidirect
170. #2066	C₂×C₁₃	semidirect
171. #2035	C₂×C₁₃	semidirect
172. #1969	C₂×C₁₃	semidirect
173. #1942	C₂×C₁₃	semidirect
174. #1873	C₂×C₁₃	semidirect
175. #1808	C₂×C₁₃	semidirect
344. #107	D₄×C₁₃	semidirect
432. C₁₃	#24779	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×#467	2
C₂×C₈×D₄×C₁₃	2
C₂×C₁₃×#427	2
C₁₃×#2415	2
C₁₃×#2066	2
C₁₃×#2035	2
C₁₃×#1969	2
C₁₃×#1942	2
C₁₃×#1873	2
C₁₃×#1808	2
#24779	13

Subgroups — C13×#24779 #15711118

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24779 #15711118