Subgroups — C₁₃×#24123 #15710462

Order 3328.

1090 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#556	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₃×#2538	C₂	1	1	yes	maximal, characteristic
5	C₁₃×#2035	C₂	1	2	yes	maximal, complemented
6	C₁₃×#2001	C₂	1	2	yes	maximal, complemented
7	C₁₃×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#1954	C₂	1	1	yes	maximal, characteristic
9	C₁₃×#1873	C₂	1	2	yes	maximal, complemented
10	C₁₃×#1854	C₂	1	2	yes	maximal, complemented
11	C₁₃×#1803	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
13	C₁₃×#556	—	2	4	no	—
14	C₁₃×#556	—	2	4	no	—
15	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₁₃×#126	—	2	2	no	—
17	C₂×C₁₃×#124	—	2	1	no	—
18	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₁₃	—	2	1	no	—
21	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
24	C₂×C₁₃×#117	C₂²	1	2	yes	—
25	C₁₃×#475	—	2	4	no	—
26	C₄×C₁₃×Q₁₆	—	2	4	no	—
27	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
28	C₂×C₁₃×#106	C₂²	1	2	yes	—
29	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₃×#103	C₂²	1	2	yes	—
31	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
32	C₂×C₁₃×#103	C₂²	1	1	yes	characteristic
33	C₂×C₁₃×#103	C₂²	1	2	yes	—
34	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₂×C₁₃×C₂²⋊C₈	C₂²	1	2	yes	—
36	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
37	C₁₃×#396	—	2	2	no	—
38	C₁₃×#390	—	2	1	no	—
39	C₁₃×#389	—	2	1	no	—
40	C₁₃×#384	C₂²	1	1	yes	characteristic
41	C₁₃×#380	C₂²	1	2	yes	—
42	C₁₃×#340	C₂²	1	2	yes	—
43	C₁₃×#340	C₂²	1	2	yes	—
44	C₁₃×#340	C₂²	1	2	yes	—
45	C₂²×Q₈×C₁₃	—	2	1	no	—
46	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₃	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
50	C₂×C₁₃×Q₁₆	—	2	2	no	—
51	C₂×C₁₃×Q₁₆	—	2	2	no	—
52	C₂×C₁₃×Q₁₆	—	2	2	no	—
53	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₁₃	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
56	C₁₃×C₄⋊Q₈	—	2	2	no	—
57	C₁₃×C₄⋊Q₈	D₄	1	4	yes	—
58	C₁₃×#126	—	2	16	no	—
59	C₁₃×#124	—	2	8	no	—
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×Q₈×C₁₃	—	2	8	no	—
65	C₄×Q₈×C₁₃	—	2	2	no	—
66	C₄×Q₈×C₁₃	—	2	2	no	—
67	C₄×Q₈×C₁₃	—	2	2	no	—
68	C₄×Q₈×C₁₃	D₄	1	4	yes	—
69	C₄×D₄×C₁₃	—	2	2	no	—
70	C₄×D₄×C₁₃	—	2	2	no	—
71	C₁₃×#117	—	2	4	no	—
72	C₁₃×#117	—	2	4	no	—
73	C₂×C₁₃×C₄⋊C₄	—	2	2	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	—	2	2	no	—
78	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
79	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
80	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
84	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
85	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
87	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
88	C₂×C₁₃×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₁₃×C₂²⋊C₄	D₄	1	2	yes	—
90	C₂×C₄²×C₁₃	—	2	2	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	C₁₃×#107	—	2	2	no	—
95	C₁₃×#106	—	2	4	no	—
96	C₁₃×C₄⋊C₈	—	2	2	no	—
97	C₁₃×#103	—	2	2	no	—
98	C₁₃×#103	—	2	2	no	—
99	C₁₃×#103	—	2	4	no	—
100	C₁₃×#103	—	4	2	no	—
101	C₁₃×C₂²⋊C₈	—	2	4	no	—
102	C₁₃×C₂²⋊C₈	—	4	2	no	—
103	C₄×C₈×C₁₃	—	2	2	no	—
104	C₁₃×#95	—	2	2	no	—
105	#24123	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
106	C₂⁴×C₁₃	C₂×D₄	1	2	yes	—
107	C₂×Q₈×C₁₃	—	2	4	no	—
108	C₂×Q₈×C₁₃	—	2	1	no	—
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	—	2	1	no	—
111	C₂×Q₈×C₁₃	—	2	1	no	—
112	C₂×Q₈×C₁₃	—	2	1	no	—
113	C₂×Q₈×C₁₃	—	2	1	no	—
114	C₂×Q₈×C₁₃	—	2	1	no	—
115	C₂×Q₈×C₁₃	—	2	1	no	—
116	C₂×Q₈×C₁₃	—	2	1	no	—
117	C₂×Q₈×C₁₃	—	2	1	no	—
118	C₂×Q₈×C₁₃	—	4	2	no	—
119	C₂×Q₈×C₁₃	—	4	2	no	—
120	C₂×Q₈×C₁₃	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₁₃	#41	1	2	yes	—
122	C₂×D₄×C₁₃	—	2	2	no	—
123	C₂×D₄×C₁₃	—	2	2	no	—
124	C₂×D₄×C₁₃	—	2	2	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	2	no	—
129	C₂²×C₄×C₁₃	—	2	2	no	—
130	C₂²×C₄×C₁₃	—	2	2	no	—
131	C₂²×C₄×C₁₃	—	2	2	no	—
132	C₂²×C₄×C₁₃	—	2	2	no	—
133	C₂²×C₄×C₁₃	—	2	2	no	—
134	C₂²×C₄×C₁₃	—	2	2	no	—
135	C₂²×C₄×C₁₃	—	2	1	no	—
136	C₂²×C₄×C₁₃	—	2	2	no	—
137	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₁₃×Q₁₆	—	2	8	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	2	no	—
146	C₂×C₈×C₁₃	—	2	2	no	—
147	C₂×C₈×C₁₃	—	2	1	no	—
148	C₂×C₈×C₁₃	—	2	2	no	—
149	C₂×C₈×C₁₃	—	2	1	no	—
150	C₂×C₈×C₁₃	#41	1	2	yes	—
151	C₁₃×C₄⋊C₄	—	2	8	no	—
152	C₁₃×C₄⋊C₄	—	2	4	no	—
153	C₁₃×C₄⋊C₄	—	2	4	no	—
154	C₁₃×C₄⋊C₄	—	2	2	no	—
155	C₁₃×C₄⋊C₄	—	2	1	no	—
156	C₁₃×C₄⋊C₄	—	2	2	no	—
157	C₁₃×C₄⋊C₄	—	2	1	no	—
158	C₁₃×C₄⋊C₄	—	2	1	no	—
159	C₁₃×C₄⋊C₄	—	2	2	no	—
160	C₁₃×C₄⋊C₄	—	2	2	no	—
161	C₁₃×C₄⋊C₄	—	4	4	no	—
162	C₁₃×C₄⋊C₄	—	4	2	no	—
163	C₁₃×C₄⋊C₄	—	4	2	no	—
164	C₁₃×C₄⋊C₄	—	8	1	no	—
165	C₁₃×C₄⋊C₄	C₂×D₄	1	4	yes	—
166	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
167	C₁₃×C₂²⋊C₄	—	2	8	no	—
168	C₁₃×C₂²⋊C₄	—	2	8	no	—
169	C₁₃×C₂²⋊C₄	—	2	4	no	—
170	C₁₃×C₂²⋊C₄	—	4	4	no	—
171	C₁₃×C₂²⋊C₄	—	8	2	no	—
172	C₄²×C₁₃	—	2	8	no	—
173	C₄²×C₁₃	—	2	4	no	—
174	C₄²×C₁₃	—	4	2	no	—
175	C₄²×C₁₃	C₂×D₄	1	2	yes	—
176	C₄²×C₁₃	C₂×D₄	1	2	yes	—
177	C₂×#556	C₂×C₁₃	1	1	yes	characteristic
178	C₂×#475	C₂×C₁₃	1	1	yes	characteristic, complemented
179	C₂×C₄×Q₁₆	C₂×C₁₃	1	1	yes	characteristic, complemented
180	#2538	C₂×C₁₃	1	1	yes	characteristic
181	#2035	C₂×C₁₃	1	2	yes	complemented
182	#2001	C₂×C₁₃	1	2	yes	complemented
183	#1990	C₂×C₁₃	1	1	yes	characteristic, complemented
184	#1954	C₂×C₁₃	1	1	yes	characteristic
185	#1873	C₂×C₁₃	1	2	yes	complemented
186	#1854	C₂×C₁₃	1	2	yes	complemented
187	#1803	C₂×C₁₃	1	1	yes	characteristic, complemented
188	C₂³×C₁₃	—	2	2	no	—
189	C₂³×C₁₃	—	2	2	no	—
190	C₂³×C₁₃	—	2	2	no	—
191	C₂³×C₁₃	—	2	2	no	—
192	C₂³×C₁₃	—	2	2	no	—
193	C₂³×C₁₃	—	2	2	no	—
194	C₂³×C₁₃	—	2	2	no	—
195	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₁₃	—	2	2	no	—
197	Q₈×C₁₃	—	2	2	no	—
198	Q₈×C₁₃	—	2	2	no	—
199	Q₈×C₁₃	—	2	2	no	—
200	Q₈×C₁₃	—	4	1	no	—
201	Q₈×C₁₃	—	4	1	no	—
202	Q₈×C₁₃	—	4	1	no	—
203	Q₈×C₁₃	—	4	1	no	—
204	Q₈×C₁₃	—	4	8	no	—
205	D₄×C₁₃	—	4	4	no	—
206	C₂×C₄×C₁₃	—	2	1	no	—
207	C₂×C₄×C₁₃	—	2	1	no	—
208	C₂×C₄×C₁₃	—	2	2	no	—
209	C₂×C₄×C₁₃	—	2	2	no	—
210	C₂×C₄×C₁₃	—	2	2	no	—
211	C₂×C₄×C₁₃	—	2	4	no	—
212	C₂×C₄×C₁₃	—	2	2	no	—
213	C₂×C₄×C₁₃	—	2	2	no	—
214	C₂×C₄×C₁₃	—	2	2	no	—
215	C₂×C₄×C₁₃	—	4	1	no	—
216	C₂×C₄×C₁₃	—	4	1	no	—
217	C₂×C₄×C₁₃	—	4	1	no	—
218	C₂×C₄×C₁₃	—	4	1	no	—
219	C₂×C₄×C₁₃	—	4	2	no	—
220	C₂×C₄×C₁₃	—	4	2	no	—
221	C₂×C₄×C₁₃	—	4	1	no	—
222	C₂×C₄×C₁₃	—	4	1	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	—	4	2	no	—
227	C₂×C₄×C₁₃	—	4	1	no	—
228	C₂×C₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	1	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	—	4	1	no	—
233	C₂×C₄×C₁₃	#120	1	2	yes	—
234	C₂×C₄×C₁₃	#120	1	2	yes	—
235	C₂×C₄×C₁₃	#135	1	2	yes	—
236	C₂×C₄×C₁₃	#137	1	2	yes	—
237	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
241	C₂×C₄×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
242	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
243	C₈×C₁₃	—	2	2	no	—
244	C₈×C₁₃	—	4	1	no	—
245	C₈×C₁₃	—	4	2	no	—
246	C₂²×Q₁₆	C₂²×C₁₃	1	1	yes	characteristic
247	#556	—	2	4	no	—
248	#556	—	2	4	no	—
249	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
250	C₂×#126	—	2	2	no	—
251	C₂×#124	—	2	1	no	—
252	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
253	C₂×C₂²⋊Q₈	C₂²×C₁₃	1	2	yes	—
254	C₂×C₄×Q₈	—	2	1	no	—
255	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
256	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
257	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
258	C₂×#117	C₂²×C₁₃	1	2	yes	—
259	#475	—	2	4	no	—
260	C₄×Q₁₆	—	2	4	no	—
261	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
262	C₂×#106	C₂²×C₁₃	1	2	yes	—
263	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
264	C₂×#103	C₂²×C₁₃	1	2	yes	—
265	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
266	C₂×#103	C₂²×C₁₃	1	1	yes	characteristic
267	C₂×#103	C₂²×C₁₃	1	2	yes	—
268	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂²×C₁₃	1	2	yes	—
270	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
271	#396	—	2	2	no	—
272	#390	—	2	1	no	—
273	#389	—	2	1	no	—
274	#384	C₂²×C₁₃	1	1	yes	characteristic
275	#380	C₂²×C₁₃	1	2	yes	—
276	#340	C₂²×C₁₃	1	2	yes	—
277	#340	C₂²×C₁₃	1	2	yes	—
278	#340	C₂²×C₁₃	1	2	yes	—
279	C₂²×C₁₃	—	4	2	no	—
280	C₂²×C₁₃	—	4	2	no	—
281	C₂²×C₁₃	—	4	2	no	—
282	C₂²×C₁₃	—	4	2	no	—
283	C₂²×C₁₃	—	4	2	no	—
284	C₂²×C₁₃	—	4	2	no	—
285	C₂²×C₁₃	—	4	2	no	—
286	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
287	C₂²×C₁₃	#546	1	1	yes	characteristic
288	C₂²×C₁₃	#547	1	1	yes	characteristic
289	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
290	C₂²×C₁₃	C₂×#137	1	1	yes	characteristic
291	C₂²×C₁₃	#577	1	1	yes	characteristic
292	C₂²×C₁₃	#578	1	1	yes	characteristic
293	C₄×C₁₃	—	2	2	no	—
294	C₄×C₁₃	—	4	2	no	—
295	C₄×C₁₃	—	4	2	no	—
296	C₄×C₁₃	—	4	2	no	—
297	C₄×C₁₃	—	4	4	no	—
298	C₄×C₁₃	—	4	2	no	—
299	C₄×C₁₃	—	8	1	no	—
300	C₄×C₁₃	—	8	2	no	—
301	C₄×C₁₃	#452	1	4	yes	—
302	C₄×C₁₃	#525	1	1	yes	characteristic
303	C₄×C₁₃	#537	1	1	yes	characteristic
304	C₄×C₁₃	#548	1	1	yes	characteristic
305	C₄×C₁₃	#550	1	1	yes	characteristic
306	C₂²×Q₈	—	2	1	no	—
307	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
308	C₂²×Q₈	C₂³×C₁₃	1	1	yes	characteristic
309	C₂²×D₄	D₄×C₁₃	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₁₃	1	2	yes	—
311	C₂×Q₁₆	—	2	2	no	—
312	C₂×Q₁₆	—	2	2	no	—
313	C₂×Q₁₆	—	2	2	no	—
314	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₁₃	1	2	yes	—
316	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
317	C₄⋊Q₈	—	2	2	no	—
318	C₄⋊Q₈	D₄×C₁₃	1	4	yes	—
319	#126	—	2	16	no	—
320	#124	—	2	8	no	—
321	C₂²⋊Q₈	—	2	4	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	—	2	4	no	—
324	C₂²⋊Q₈	—	4	2	no	—
325	C₄×Q₈	—	2	8	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	D₄×C₁₃	1	4	yes	—
330	C₄×D₄	—	2	2	no	—
331	C₄×D₄	—	2	2	no	—
332	#117	—	2	4	no	—
333	#117	—	2	4	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
344	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₁₃	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	2	no	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	D₄×C₁₃	1	2	yes	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
355	#107	—	2	2	no	—
356	#106	—	2	4	no	—
357	C₄⋊C₈	—	2	2	no	—
358	#103	—	2	2	no	—
359	#103	—	2	2	no	—
360	#103	—	2	4	no	—
361	#103	—	4	2	no	—
362	C₂²⋊C₈	—	2	4	no	—
363	C₂²⋊C₈	—	4	2	no	—
364	C₄×C₈	—	2	2	no	—
365	#95	—	2	2	no	—
366	C₂×C₁₃	—	8	2	no	—
367	C₂×C₁₃	#2407	1	1	yes	characteristic
368	C₂×C₁₃	C₂×#452	1	1	yes	characteristic
369	C₂×C₁₃	#3013	1	1	yes	characteristic
370	C₂×C₁₃	#3304	1	1	yes	characteristic
371	C₂×C₁₃	#3328	1	1	yes	characteristic
372	C₂×C₁₃	#3342	1	1	yes	characteristic
373	C₂×C₁₃	#3356	1	1	yes	characteristic
374	C₂⁴	C₂×D₄×C₁₃	1	2	yes	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	—	2	1	no	—
382	C₂×Q₈	—	2	1	no	—
383	C₂×Q₈	—	2	1	no	—
384	C₂×Q₈	—	2	1	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	4	2	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	C₂×D₄×C₁₃	1	2	yes	—
389	C₂×Q₈	C₁₃×#41	1	2	yes	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	C₂×D₄×C₁₃	1	2	yes	—
406	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
409	Q₁₆	—	2	8	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	C₁₃×#41	1	2	yes	—
419	C₄⋊C₄	—	2	8	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	4	4	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	8	1	no	—
433	C₄⋊C₄	C₂×D₄×C₁₃	1	4	yes	—
434	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
435	C₂²⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	8	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	4	4	no	—
439	C₂²⋊C₄	—	8	2	no	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	4	2	no	—
443	C₄²	C₂×D₄×C₁₃	1	2	yes	—
444	C₄²	C₂×D₄×C₁₃	1	2	yes	—
445	C₁₃	#24123	1	1	yes	characteristic, direct product factor, Sylow
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	2	no	—
453	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
454	Q₈	—	2	2	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	2	no	—
458	Q₈	—	4	8	no	—
459	Q₈	—	4	1	no	—
460	Q₈	—	4	1	no	—
461	Q₈	—	4	1	no	—
462	Q₈	—	4	1	no	—
463	D₄	—	4	4	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	C₁₃×#120	1	2	yes	—
492	C₂×C₄	C₁₃×#120	1	2	yes	—
493	C₂×C₄	C₁₃×#135	1	2	yes	—
494	C₂×C₄	C₁₃×#137	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
497	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
498	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
499	C₂×C₄	C₁₃×H(5,𝔽₂)	1	1	yes	characteristic
500	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
501	C₈	—	2	2	no	—
502	C₈	—	4	1	no	—
503	C₈	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
512	C₂²	C₁₃×#546	1	1	yes	characteristic
513	C₂²	C₁₃×#547	1	1	yes	characteristic
514	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
515	C₂²	C₂×C₁₃×#137	1	1	yes	characteristic
516	C₂²	C₁₃×#577	1	1	yes	characteristic
517	C₂²	C₁₃×#578	1	1	yes	characteristic
518	C₄	—	2	2	no	—
519	C₄	—	4	2	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	4	2	no	—
523	C₄	—	4	4	no	—
524	C₄	—	8	1	no	—
525	C₄	—	8	2	no	—
526	C₄	C₁₃×#452	1	4	yes	—
527	C₄	C₁₃×#525	1	1	yes	characteristic
528	C₄	C₁₃×#537	1	1	yes	characteristic
529	C₄	C₁₃×#548	1	1	yes	characteristic
530	C₄	C₁₃×#550	1	1	yes	characteristic
531	C₂	—	8	2	no	—
532	C₂	C₁₃×#2407	1	1	yes	characteristic
533	C₂	C₂×C₁₃×#452	1	1	yes	characteristic
534	C₂	C₁₃×#3013	1	1	yes	characteristic
535	C₂	C₁₃×#3304	1	1	yes	characteristic
536	C₂	C₁₃×#3328	1	1	yes	characteristic
537	C₂	C₁₃×#3342	1	1	yes	characteristic
538	C₂	C₁₃×#3356	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
2. C₂×C₁₃×#475	C₂	semidirect
3. C₂×C₄×C₁₃×Q₁₆	C₂	semidirect
5. C₁₃×#2035	C₂	semidirect
6. C₁₃×#2001	C₂	semidirect
7. C₁₃×#1990	C₂	semidirect
9. C₁₃×#1873	C₂	semidirect
10. C₁₃×#1854	C₂	semidirect
11. C₁₃×#1803	C₂	semidirect
105. #24123	C₁₃	direct (N × H)
178. C₂×#475	C₂×C₁₃	semidirect
179. C₂×C₄×Q₁₆	C₂×C₁₃	semidirect
181. #2035	C₂×C₁₃	semidirect
182. #2001	C₂×C₁₃	semidirect
183. #1990	C₂×C₁₃	semidirect
185. #1873	C₂×C₁₃	semidirect
186. #1854	C₂×C₁₃	semidirect
187. #1803	C₂×C₁₃	semidirect
445. C₁₃	#24123	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×#556	2
C₂×C₁₃×#475	2
C₂×C₄×C₁₃×Q₁₆	2
C₁₃×#2538	2
C₁₃×#2035	2
C₁₃×#2001	2
C₁₃×#1990	2
C₁₃×#1954	2
C₁₃×#1873	2
C₁₃×#1854	2
C₁₃×#1803	2
#24123	13

Subgroups — C13×#24123 #15710462

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24123 #15710462