Subgroups — C₁₃×#24335 #15710674

Order 3328.

1118 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₁₃×D₈	C₂	1	1	yes	maximal, characteristic
4	C₁₃×#2580	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₃×#2059	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₃×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#2025	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₃×#2023	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₃×#1991	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₃×#1984	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic
12	C₁₃×#1879	C₂	1	1	yes	maximal, characteristic
13	C₁₃×#1864	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₃×#1862	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₃×#1804	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₁₃×D₈	C₂²	1	1	yes	characteristic
17	C₁₃×#554	—	2	4	no	—
18	C₁₃×#554	—	2	4	no	—
19	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
21	C₂×C₁₃×#125	C₂²	1	1	yes	characteristic
22	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₁₃×C₂²⋊Q₈	—	2	1	no	—
25	C₂×C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
31	C₁₃×#478	—	2	4	no	—
32	C₄×C₁₃×D₈	—	2	4	no	—
33	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×#107	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×#106	C₂²	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
38	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
39	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
40	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
41	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
42	C₂×C₁₃×#102	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
44	C₁₃×#399	—	2	1	no	—
45	C₁₃×#393	—	2	1	no	—
46	C₁₃×#390	C₂²	1	1	yes	characteristic
47	C₁₃×#390	C₂²	1	1	yes	characteristic
48	C₁₃×#389	C₂²	1	1	yes	characteristic
49	C₁₃×#389	C₂²	1	1	yes	characteristic
50	C₁₃×#385	—	2	1	no	—
51	C₁₃×#385	—	2	1	no	—
52	C₁₃×#382	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×#340	C₂²	1	1	yes	characteristic
58	C₁₃×#340	C₂²	1	1	yes	characteristic
59	C₁₃×#336	C₂²	1	1	yes	characteristic
60	C₁₃×#336	C₂²	1	1	yes	characteristic
61	C₁₃×#336	C₂²	1	1	yes	characteristic
62	C₁₃×#336	C₂²	1	1	yes	characteristic
63	C₂²×Q₈×C₁₃	—	2	1	no	—
64	C₂²×Q₈×C₁₃	D₄	1	1	yes	characteristic
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₃	—	2	1	no	—
68	C₂³×C₄×C₁₃	—	2	1	no	—
69	C₂³×C₄×C₁₃	—	2	1	no	—
70	C₂³×C₄×C₁₃	—	2	1	no	—
71	C₂×C₁₃×D₈	—	2	2	no	—
72	C₂×C₁₃×D₈	—	2	2	no	—
73	C₂×C₁₃×D₈	Q₈	1	4	yes	complemented
74	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
78	C₁₃×C₄⋊Q₈	—	2	2	no	—
79	C₁₃×C₄⋊Q₈	—	2	2	no	—
80	C₁₃×#125	—	2	2	no	—
81	C₁₃×#125	—	2	2	no	—
82	C₁₃×#125	—	2	2	no	—
83	C₁₃×#125	D₄	1	4	yes	—
84	C₁₃×C₂²⋊Q₈	—	2	8	no	—
85	C₁₃×C₂²⋊Q₈	—	2	8	no	—
86	C₁₃×C₂²⋊Q₈	—	2	8	no	—
87	C₄×Q₈×C₁₃	—	2	2	no	—
88	C₄×Q₈×C₁₃	—	2	2	no	—
89	C₄×D₄×C₁₃	—	2	2	no	—
90	C₄×D₄×C₁₃	—	2	2	no	—
91	C₄×D₄×C₁₃	—	2	2	no	—
92	C₄×D₄×C₁₃	—	2	2	no	—
93	C₄×D₄×C₁₃	—	2	2	no	—
94	C₄×D₄×C₁₃	—	2	2	no	—
95	C₄×D₄×C₁₃	—	2	2	no	—
96	C₄×D₄×C₁₃	D₄	1	4	yes	—
97	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
98	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
99	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
100	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
101	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
102	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
104	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
105	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
106	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₁₃×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₂×C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
115	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
116	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
117	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
119	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
120	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
121	C₂×C₁₃×C₂²⋊C₄	—	2	1	no	—
122	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#107	—	2	2	no	—
126	C₁₃×#107	—	2	2	no	—
127	C₁₃×#106	—	2	2	no	—
128	C₁₃×C₄⋊C₈	—	2	2	no	—
129	C₁₃×#102	—	2	2	no	—
130	C₁₃×#102	—	2	2	no	—
131	C₁₃×#102	—	2	2	no	—
132	C₁₃×#102	—	2	2	no	—
133	C₁₃×#102	—	2	2	no	—
134	C₁₃×#102	—	2	2	no	—
135	C₄×C₈×C₁₃	—	2	2	no	—
136	C₁₃×#95	—	2	1	no	—
137	C₁₃×#95	—	2	1	no	—
138	C₁₃×#95	—	2	1	no	—
139	C₁₃×#95	—	2	1	no	—
140	#24335	C₁₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
141	C₂⁴×C₁₃	—	2	1	no	—
142	C₂⁴×C₁₃	—	2	1	no	—
143	C₂×Q₈×C₁₃	—	2	4	no	—
144	C₂×Q₈×C₁₃	—	2	2	no	—
145	C₂×Q₈×C₁₃	—	2	2	no	—
146	C₂×Q₈×C₁₃	—	4	1	no	—
147	C₂×Q₈×C₁₃	—	8	1	no	—
148	C₂×Q₈×C₁₃	—	8	1	no	—
149	C₂×D₄×C₁₃	—	2	1	no	—
150	C₂×D₄×C₁₃	—	2	1	no	—
151	C₂×D₄×C₁₃	—	2	1	no	—
152	C₂×D₄×C₁₃	—	2	1	no	—
153	C₂×D₄×C₁₃	—	2	1	no	—
154	C₂×D₄×C₁₃	—	2	1	no	—
155	C₂×D₄×C₁₃	—	2	1	no	—
156	C₂×D₄×C₁₃	—	2	1	no	—
157	C₂×D₄×C₁₃	C₂×D₄	1	2	yes	—
158	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
159	C₂×D₄×C₁₃	C₂×Q₈	1	2	yes	—
160	C₂×D₄×C₁₃	#41	1	2	yes	—
161	C₂²×C₄×C₁₃	—	2	4	no	—
162	C₂²×C₄×C₁₃	—	2	1	no	—
163	C₂²×C₄×C₁₃	—	2	1	no	—
164	C₂²×C₄×C₁₃	—	2	1	no	—
165	C₂²×C₄×C₁₃	—	2	4	no	—
166	C₂²×C₄×C₁₃	—	2	4	no	—
167	C₂²×C₄×C₁₃	—	2	1	no	—
168	C₂²×C₄×C₁₃	—	2	1	no	—
169	C₂²×C₄×C₁₃	—	2	1	no	—
170	C₂²×C₄×C₁₃	—	4	2	no	—
171	C₂²×C₄×C₁₃	—	4	2	no	—
172	C₂²×C₄×C₁₃	—	4	2	no	—
173	C₂²×C₄×C₁₃	—	8	1	no	—
174	C₂²×C₄×C₁₃	—	8	1	no	—
175	C₂²×C₄×C₁₃	—	8	1	no	—
176	C₂²×C₄×C₁₃	—	8	1	no	—
177	C₂²×C₄×C₁₃	—	8	1	no	—
178	C₂²×C₄×C₁₃	—	8	1	no	—
179	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
182	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
183	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
184	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
185	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
186	C₁₃×D₈	—	2	8	no	—
187	C₂×C₈×C₁₃	—	2	1	no	—
188	C₂×C₈×C₁₃	—	2	1	no	—
189	C₂×C₈×C₁₃	—	2	1	no	—
190	C₂×C₈×C₁₃	—	2	1	no	—
191	C₂×C₈×C₁₃	—	2	1	no	—
192	C₂×C₈×C₁₃	—	2	1	no	—
193	C₂×C₈×C₁₃	—	2	1	no	—
194	C₂×C₈×C₁₃	—	2	1	no	—
195	C₂×C₈×C₁₃	—	2	1	no	—
196	C₂×C₈×C₁₃	—	2	1	no	—
197	C₂×C₈×C₁₃	—	2	1	no	—
198	C₂×C₈×C₁₃	C₂×Q₈	1	2	yes	—
199	C₁₃×C₄⋊C₄	—	2	4	no	—
200	C₁₃×C₄⋊C₄	—	2	4	no	—
201	C₁₃×C₄⋊C₄	—	2	4	no	—
202	C₁₃×C₄⋊C₄	—	2	2	no	—
203	C₁₃×C₄⋊C₄	—	2	4	no	—
204	C₁₃×C₄⋊C₄	—	2	4	no	—
205	C₁₃×C₄⋊C₄	—	2	2	no	—
206	C₁₃×C₄⋊C₄	—	2	2	no	—
207	C₁₃×C₄⋊C₄	—	2	1	no	—
208	C₁₃×C₄⋊C₄	—	2	1	no	—
209	C₁₃×C₄⋊C₄	—	2	1	no	—
210	C₁₃×C₄⋊C₄	—	2	1	no	—
211	C₁₃×C₄⋊C₄	—	2	1	no	—
212	C₁₃×C₄⋊C₄	—	2	1	no	—
213	C₁₃×C₄⋊C₄	—	2	1	no	—
214	C₁₃×C₄⋊C₄	—	2	1	no	—
215	C₁₃×C₄⋊C₄	—	2	1	no	—
216	C₁₃×C₄⋊C₄	—	8	1	no	—
217	C₁₃×C₄⋊C₄	—	8	1	no	—
218	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
219	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
220	C₁₃×C₄⋊C₄	C₂×D₄	1	2	yes	—
221	C₁₃×C₂²⋊C₄	—	2	4	no	—
222	C₁₃×C₂²⋊C₄	—	2	4	no	—
223	C₁₃×C₂²⋊C₄	—	2	4	no	—
224	C₁₃×C₂²⋊C₄	—	4	2	no	—
225	C₁₃×C₂²⋊C₄	—	4	2	no	—
226	C₁₃×C₂²⋊C₄	—	4	2	no	—
227	C₁₃×C₂²⋊C₄	—	8	1	no	—
228	C₁₃×C₂²⋊C₄	—	8	1	no	—
229	C₄²×C₁₃	—	2	1	no	—
230	C₄²×C₁₃	—	2	1	no	—
231	C₄²×C₁₃	—	2	1	no	—
232	C₄²×C₁₃	—	2	1	no	—
233	C₄²×C₁₃	C₂×D₄	1	2	yes	—
234	C₄²×C₁₃	C₂×D₄	1	2	yes	—
235	C₂×#554	C₂×C₁₃	1	1	yes	characteristic, complemented
236	C₂×#478	C₂×C₁₃	1	1	yes	characteristic, complemented
237	C₂×C₄×D₈	C₂×C₁₃	1	1	yes	characteristic
238	#2580	C₂×C₁₃	1	1	yes	characteristic, complemented
239	#2059	C₂×C₁₃	1	1	yes	characteristic, complemented
240	#2057	C₂×C₁₃	1	1	yes	characteristic, complemented
241	#2025	C₂×C₁₃	1	1	yes	characteristic, complemented
242	#2023	C₂×C₁₃	1	1	yes	characteristic, complemented
243	#1991	C₂×C₁₃	1	1	yes	characteristic, complemented
244	#1984	C₂×C₁₃	1	1	yes	characteristic, complemented
245	#1879	C₂×C₁₃	1	1	yes	characteristic
246	#1879	C₂×C₁₃	1	1	yes	characteristic
247	#1864	C₂×C₁₃	1	1	yes	characteristic, complemented
248	#1862	C₂×C₁₃	1	1	yes	characteristic, complemented
249	#1804	C₂×C₁₃	1	1	yes	characteristic, complemented
250	C₂³×C₁₃	—	2	2	no	—
251	C₂³×C₁₃	—	2	2	no	—
252	C₂³×C₁₃	—	2	2	no	—
253	C₂³×C₁₃	—	2	2	no	—
254	C₂³×C₁₃	—	4	1	no	—
255	C₂³×C₁₃	—	4	1	no	—
256	C₂³×C₁₃	—	4	1	no	—
257	C₂³×C₁₃	—	4	1	no	—
258	C₂³×C₁₃	—	4	1	no	—
259	C₂³×C₁₃	—	4	1	no	—
260	C₂³×C₁₃	—	4	1	no	—
261	C₂³×C₁₃	—	4	1	no	—
262	C₂³×C₁₃	—	4	1	no	—
263	C₂³×C₁₃	—	4	1	no	—
264	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
265	Q₈×C₁₃	—	4	4	no	—
266	Q₈×C₁₃	—	8	4	no	—
267	D₄×C₁₃	—	2	2	no	—
268	D₄×C₁₃	—	2	2	no	—
269	D₄×C₁₃	—	2	2	no	—
270	D₄×C₁₃	—	2	2	no	—
271	D₄×C₁₃	—	2	2	no	—
272	D₄×C₁₃	—	4	1	no	—
273	D₄×C₁₃	—	4	1	no	—
274	D₄×C₁₃	C₂²⋊Q₈	1	4	yes	—
275	C₂×C₄×C₁₃	—	2	1	no	—
276	C₂×C₄×C₁₃	—	2	1	no	—
277	C₂×C₄×C₁₃	—	2	1	no	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	—	2	1	no	—
281	C₂×C₄×C₁₃	—	2	1	no	—
282	C₂×C₄×C₁₃	—	2	1	no	—
283	C₂×C₄×C₁₃	—	2	1	no	—
284	C₂×C₄×C₁₃	—	2	2	no	—
285	C₂×C₄×C₁₃	—	2	2	no	—
286	C₂×C₄×C₁₃	—	2	2	no	—
287	C₂×C₄×C₁₃	—	2	1	no	—
288	C₂×C₄×C₁₃	—	2	1	no	—
289	C₂×C₄×C₁₃	—	2	1	no	—
290	C₂×C₄×C₁₃	—	2	1	no	—
291	C₂×C₄×C₁₃	—	2	1	no	—
292	C₂×C₄×C₁₃	—	2	1	no	—
293	C₂×C₄×C₁₃	—	4	8	no	—
294	C₂×C₄×C₁₃	—	4	1	no	—
295	C₂×C₄×C₁₃	—	4	1	no	—
296	C₂×C₄×C₁₃	—	4	1	no	—
297	C₂×C₄×C₁₃	—	4	1	no	—
298	C₂×C₄×C₁₃	—	4	1	no	—
299	C₂×C₄×C₁₃	—	4	1	no	—
300	C₂×C₄×C₁₃	—	4	1	no	—
301	C₂×C₄×C₁₃	—	4	1	no	—
302	C₂×C₄×C₁₃	—	4	1	no	—
303	C₂×C₄×C₁₃	—	4	1	no	—
304	C₂×C₄×C₁₃	—	4	1	no	—
305	C₂×C₄×C₁₃	—	4	1	no	—
306	C₂×C₄×C₁₃	—	4	1	no	—
307	C₂×C₄×C₁₃	—	4	1	no	—
308	C₂×C₄×C₁₃	—	4	1	no	—
309	C₂×C₄×C₁₃	—	8	4	no	—
310	C₂×C₄×C₁₃	—	8	4	no	—
311	C₂×C₄×C₁₃	—	8	4	no	—
312	C₂×C₄×C₁₃	#120	1	2	yes	—
313	C₂×C₄×C₁₃	#120	1	2	yes	—
314	C₂×C₄×C₁₃	#135	1	2	yes	—
315	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
318	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
319	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
320	C₂×C₄×C₁₃	2₋¹⁺⁴	1	1	yes	characteristic
321	C₈×C₁₃	—	2	2	no	—
322	C₈×C₁₃	—	4	1	no	—
323	C₈×C₁₃	—	4	1	no	—
324	C₈×C₁₃	—	4	1	no	—
325	C₂²×D₈	C₂²×C₁₃	1	1	yes	characteristic
326	#554	—	2	4	no	—
327	#554	—	2	4	no	—
328	C₂×C₄⋊Q₈	C₂²×C₁₃	1	1	yes	characteristic
329	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
330	C₂×#125	C₂²×C₁₃	1	1	yes	characteristic
331	C₂×C₂²⋊Q₈	—	2	1	no	—
332	C₂×C₂²⋊Q₈	—	2	1	no	—
333	C₂×C₂²⋊Q₈	—	2	1	no	—
334	C₂×C₄×Q₈	C₂²×C₁₃	1	1	yes	characteristic
335	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
336	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
337	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
338	C₂×C₄×D₄	C₂²×C₁₃	1	1	yes	characteristic
339	C₂²×C₄⋊C₄	—	2	1	no	—
340	#478	—	2	4	no	—
341	C₄×D₈	—	2	4	no	—
342	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
343	C₂×#107	C₂²×C₁₃	1	1	yes	characteristic
344	C₂×#106	C₂²×C₁₃	1	1	yes	characteristic
345	C₂×C₄⋊C₈	C₂²×C₁₃	1	1	yes	characteristic
346	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
347	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
348	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
350	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
351	C₂×#102	C₂²×C₁₃	1	1	yes	characteristic
352	C₂×C₄×C₈	C₂²×C₁₃	1	1	yes	characteristic
353	#399	—	2	1	no	—
354	#393	—	2	1	no	—
355	#390	C₂²×C₁₃	1	1	yes	characteristic
356	#390	C₂²×C₁₃	1	1	yes	characteristic
357	#389	C₂²×C₁₃	1	1	yes	characteristic
358	#389	C₂²×C₁₃	1	1	yes	characteristic
359	#385	—	2	1	no	—
360	#385	—	2	1	no	—
361	#382	C₂²×C₁₃	1	1	yes	characteristic
362	#340	C₂²×C₁₃	1	1	yes	characteristic
363	#340	C₂²×C₁₃	1	1	yes	characteristic
364	#340	C₂²×C₁₃	1	1	yes	characteristic
365	#340	C₂²×C₁₃	1	1	yes	characteristic
366	#340	C₂²×C₁₃	1	1	yes	characteristic
367	#340	C₂²×C₁₃	1	1	yes	characteristic
368	#336	C₂²×C₁₃	1	1	yes	characteristic
369	#336	C₂²×C₁₃	1	1	yes	characteristic
370	#336	C₂²×C₁₃	1	1	yes	characteristic
371	#336	C₂²×C₁₃	1	1	yes	characteristic
372	C₂²×C₁₃	—	2	4	no	—
373	C₂²×C₁₃	—	4	2	no	—
374	C₂²×C₁₃	—	4	2	no	—
375	C₂²×C₁₃	—	4	2	no	—
376	C₂²×C₁₃	—	4	2	no	—
377	C₂²×C₁₃	—	4	2	no	—
378	C₂²×C₁₃	—	4	2	no	—
379	C₂²×C₁₃	—	4	2	no	—
380	C₂²×C₁₃	—	4	2	no	—
381	C₂²×C₁₃	—	4	2	no	—
382	C₂²×C₁₃	—	8	1	no	—
383	C₂²×C₁₃	—	8	1	no	—
384	C₂²×C₁₃	—	8	1	no	—
385	C₂²×C₁₃	—	8	1	no	—
386	C₂²×C₁₃	C₂×#120	1	1	yes	characteristic
387	C₂²×C₁₃	#548	1	1	yes	characteristic
388	C₂²×C₁₃	D₄×Q₈	1	1	yes	characteristic
389	C₂²×C₁₃	C₂×#135	1	1	yes	characteristic
390	C₂²×C₁₃	#575	1	1	yes	characteristic
391	C₂²×C₁₃	#576	1	1	yes	characteristic
392	C₂²×C₁₃	#576	1	1	yes	characteristic
393	C₄×C₁₃	—	2	2	no	—
394	C₄×C₁₃	—	2	2	no	—
395	C₄×C₁₃	—	2	2	no	—
396	C₄×C₁₃	—	4	1	no	—
397	C₄×C₁₃	—	4	2	no	—
398	C₄×C₁₃	—	4	1	no	—
399	C₄×C₁₃	—	4	1	no	—
400	C₄×C₁₃	—	4	2	no	—
401	C₄×C₁₃	—	4	2	no	—
402	C₄×C₁₃	—	8	1	no	—
403	C₄×C₁₃	—	8	1	no	—
404	C₄×C₁₃	—	8	1	no	—
405	C₄×C₁₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
406	C₄×C₁₃	#536	1	1	yes	characteristic
407	C₄×C₁₃	#548	1	1	yes	characteristic
408	C₄×C₁₃	D₄×Q₈	1	1	yes	characteristic
409	C₂²×Q₈	—	2	1	no	—
410	C₂²×Q₈	D₄×C₁₃	1	1	yes	characteristic
411	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
412	C₂²×D₄	C₂³×C₁₃	1	1	yes	characteristic
413	C₂³×C₄	—	2	1	no	—
414	C₂³×C₄	—	2	1	no	—
415	C₂³×C₄	—	2	1	no	—
416	C₂³×C₄	—	2	1	no	—
417	C₂×D₈	—	2	2	no	—
418	C₂×D₈	—	2	2	no	—
419	C₂×D₈	Q₈×C₁₃	1	4	yes	complemented
420	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
421	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
422	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
423	C₂²×C₈	C₂³×C₁₃	1	1	yes	characteristic
424	C₄⋊Q₈	—	2	2	no	—
425	C₄⋊Q₈	—	2	2	no	—
426	#125	—	2	2	no	—
427	#125	—	2	2	no	—
428	#125	—	2	2	no	—
429	#125	D₄×C₁₃	1	4	yes	—
430	C₂²⋊Q₈	—	2	8	no	—
431	C₂²⋊Q₈	—	2	8	no	—
432	C₂²⋊Q₈	—	2	8	no	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×D₄	—	2	2	no	—
436	C₄×D₄	—	2	2	no	—
437	C₄×D₄	—	2	2	no	—
438	C₄×D₄	—	2	2	no	—
439	C₄×D₄	—	2	2	no	—
440	C₄×D₄	—	2	2	no	—
441	C₄×D₄	—	2	2	no	—
442	C₄×D₄	D₄×C₁₃	1	4	yes	—
443	C₂×C₄⋊C₄	—	2	8	no	—
444	C₂×C₄⋊C₄	—	2	1	no	—
445	C₂×C₄⋊C₄	—	2	1	no	—
446	C₂×C₄⋊C₄	—	2	1	no	—
447	C₂×C₄⋊C₄	—	2	1	no	—
448	C₂×C₄⋊C₄	—	2	1	no	—
449	C₂×C₄⋊C₄	—	2	1	no	—
450	C₂×C₄⋊C₄	—	2	1	no	—
451	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
452	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
453	C₂×C₄⋊C₄	D₄×C₁₃	1	1	yes	characteristic
454	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
455	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
457	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂³×C₁₃	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	—	2	1	no	—
461	C₂×C₂²⋊C₄	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	1	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₂²⋊C₄	—	2	1	no	—
466	C₂×C₂²⋊C₄	—	2	1	no	—
467	C₂×C₂²⋊C₄	—	2	1	no	—
468	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
469	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
470	C₂×C₄²	C₂³×C₁₃	1	1	yes	characteristic
471	#107	—	2	2	no	—
472	#107	—	2	2	no	—
473	#106	—	2	2	no	—
474	C₄⋊C₈	—	2	2	no	—
475	#102	—	2	2	no	—
476	#102	—	2	2	no	—
477	#102	—	2	2	no	—
478	#102	—	2	2	no	—
479	#102	—	2	2	no	—
480	#102	—	2	2	no	—
481	C₄×C₈	—	2	2	no	—
482	#95	—	2	1	no	—
483	#95	—	2	1	no	—
484	#95	—	2	1	no	—
485	#95	—	2	1	no	—
486	C₂×C₁₃	—	4	4	no	—
487	C₂×C₁₃	—	8	2	no	—
488	C₂×C₁₃	#2409	1	1	yes	characteristic
489	C₂×C₁₃	#3002	1	1	yes	characteristic
490	C₂×C₁₃	#3008	1	1	yes	characteristic
491	C₂×C₁₃	#3361	1	1	yes	characteristic
492	C₂×C₁₃	#3370	1	1	yes	characteristic
493	C₂×C₁₃	#3380	1	1	yes	characteristic
494	C₂×C₁₃	#3389	1	1	yes	characteristic
495	C₂⁴	—	2	1	no	—
496	C₂⁴	—	2	1	no	—
497	C₂×Q₈	—	2	4	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	4	1	no	—
501	C₂×Q₈	—	8	1	no	—
502	C₂×Q₈	—	8	1	no	—
503	C₂×D₄	—	2	1	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	2	1	no	—
511	C₂×D₄	C₂×D₄×C₁₃	1	2	yes	—
512	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
513	C₂×D₄	C₂×Q₈×C₁₃	1	2	yes	—
514	C₂×D₄	C₁₃×#41	1	2	yes	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	1	no	—
517	C₂²×C₄	—	2	1	no	—
518	C₂²×C₄	—	2	1	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	2	1	no	—
522	C₂²×C₄	—	2	1	no	—
523	C₂²×C₄	—	2	1	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	2	no	—
526	C₂²×C₄	—	4	2	no	—
527	C₂²×C₄	—	8	1	no	—
528	C₂²×C₄	—	8	1	no	—
529	C₂²×C₄	—	8	1	no	—
530	C₂²×C₄	—	8	1	no	—
531	C₂²×C₄	—	8	1	no	—
532	C₂²×C₄	—	8	1	no	—
533	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
534	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
535	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
536	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
537	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
538	C₂²×C₄	C₂×D₄×C₁₃	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₁₃	1	1	yes	characteristic
540	D₈	—	2	8	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	C₂×Q₈×C₁₃	1	2	yes	—
553	C₄⋊C₄	—	2	4	no	—
554	C₄⋊C₄	—	2	4	no	—
555	C₄⋊C₄	—	2	4	no	—
556	C₄⋊C₄	—	2	2	no	—
557	C₄⋊C₄	—	2	4	no	—
558	C₄⋊C₄	—	2	4	no	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	1	no	—
562	C₄⋊C₄	—	2	1	no	—
563	C₄⋊C₄	—	2	1	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	1	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	1	no	—
570	C₄⋊C₄	—	8	1	no	—
571	C₄⋊C₄	—	8	1	no	—
572	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
573	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
574	C₄⋊C₄	C₂×D₄×C₁₃	1	2	yes	—
575	C₂²⋊C₄	—	2	4	no	—
576	C₂²⋊C₄	—	2	4	no	—
577	C₂²⋊C₄	—	2	4	no	—
578	C₂²⋊C₄	—	4	2	no	—
579	C₂²⋊C₄	—	4	2	no	—
580	C₂²⋊C₄	—	4	2	no	—
581	C₂²⋊C₄	—	8	1	no	—
582	C₂²⋊C₄	—	8	1	no	—
583	C₄²	—	2	1	no	—
584	C₄²	—	2	1	no	—
585	C₄²	—	2	1	no	—
586	C₄²	—	2	1	no	—
587	C₄²	C₂×D₄×C₁₃	1	2	yes	—
588	C₄²	C₂×D₄×C₁₃	1	2	yes	—
589	C₁₃	#24335	1	1	yes	characteristic, direct product factor, Sylow
590	C₂³	—	2	2	no	—
591	C₂³	—	2	2	no	—
592	C₂³	—	2	2	no	—
593	C₂³	—	2	2	no	—
594	C₂³	—	4	1	no	—
595	C₂³	—	4	1	no	—
596	C₂³	—	4	1	no	—
597	C₂³	—	4	1	no	—
598	C₂³	—	4	1	no	—
599	C₂³	—	4	1	no	—
600	C₂³	—	4	1	no	—
601	C₂³	—	4	1	no	—
602	C₂³	—	4	1	no	—
603	C₂³	—	4	1	no	—
604	C₂³	C₂²×D₄×C₁₃	1	1	yes	characteristic
605	Q₈	—	4	4	no	—
606	Q₈	—	8	4	no	—
607	D₄	—	2	2	no	—
608	D₄	—	2	2	no	—
609	D₄	—	2	2	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	1	no	—
613	D₄	—	4	1	no	—
614	D₄	C₁₃×C₂²⋊Q₈	1	4	yes	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	4	8	no	—
634	C₂×C₄	—	4	1	no	—
635	C₂×C₄	—	4	1	no	—
636	C₂×C₄	—	4	1	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	—	4	1	no	—
642	C₂×C₄	—	4	1	no	—
643	C₂×C₄	—	4	1	no	—
644	C₂×C₄	—	4	1	no	—
645	C₂×C₄	—	4	1	no	—
646	C₂×C₄	—	4	1	no	—
647	C₂×C₄	—	4	1	no	—
648	C₂×C₄	—	4	1	no	—
649	C₂×C₄	—	8	4	no	—
650	C₂×C₄	—	8	4	no	—
651	C₂×C₄	—	8	4	no	—
652	C₂×C₄	C₁₃×#120	1	2	yes	—
653	C₂×C₄	C₁₃×#120	1	2	yes	—
654	C₂×C₄	C₁₃×#135	1	2	yes	—
655	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
656	C₂×C₄	C₂²×D₄×C₁₃	1	1	yes	characteristic
657	C₂×C₄	C₂²×Q₈×C₁₃	1	1	yes	characteristic
658	C₂×C₄	C₂×C₁₃×#41	1	1	yes	characteristic
659	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
660	C₂×C₄	C₁₃×2₋¹⁺⁴	1	1	yes	characteristic
661	C₈	—	2	2	no	—
662	C₈	—	4	1	no	—
663	C₈	—	4	1	no	—
664	C₈	—	4	1	no	—
665	C₂²	—	2	4	no	—
666	C₂²	—	4	2	no	—
667	C₂²	—	4	2	no	—
668	C₂²	—	4	2	no	—
669	C₂²	—	4	2	no	—
670	C₂²	—	4	2	no	—
671	C₂²	—	4	2	no	—
672	C₂²	—	4	2	no	—
673	C₂²	—	4	2	no	—
674	C₂²	—	4	2	no	—
675	C₂²	—	8	1	no	—
676	C₂²	—	8	1	no	—
677	C₂²	—	8	1	no	—
678	C₂²	—	8	1	no	—
679	C₂²	C₂×C₁₃×#120	1	1	yes	characteristic
680	C₂²	C₁₃×#548	1	1	yes	characteristic
681	C₂²	D₄×Q₈×C₁₃	1	1	yes	characteristic
682	C₂²	C₂×C₁₃×#135	1	1	yes	characteristic
683	C₂²	C₁₃×#575	1	1	yes	characteristic
684	C₂²	C₁₃×#576	1	1	yes	characteristic
685	C₂²	C₁₃×#576	1	1	yes	characteristic
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	2	no	—
695	C₄	—	8	1	no	—
696	C₄	—	8	1	no	—
697	C₄	—	8	1	no	—
698	C₄	C₂×C₁₃×C₂²⋊Q₈	1	1	yes	characteristic
699	C₄	C₁₃×#536	1	1	yes	characteristic
700	C₄	C₁₃×#548	1	1	yes	characteristic
701	C₄	D₄×Q₈×C₁₃	1	1	yes	characteristic
702	C₂	—	4	4	no	—
703	C₂	—	8	2	no	—
704	C₂	C₁₃×#2409	1	1	yes	characteristic
705	C₂	C₁₃×#3002	1	1	yes	characteristic
706	C₂	C₁₃×#3008	1	1	yes	characteristic
707	C₂	C₁₃×#3361	1	1	yes	characteristic
708	C₂	C₁₃×#3370	1	1	yes	characteristic
709	C₂	C₁₃×#3380	1	1	yes	characteristic
710	C₂	C₁₃×#3389	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
prime radical	C₂²×C₁₃×D₈	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#554	C₂	semidirect
2. C₂×C₁₃×#478	C₂	semidirect
4. C₁₃×#2580	C₂	semidirect
5. C₁₃×#2059	C₂	semidirect
6. C₁₃×#2057	C₂	semidirect
7. C₁₃×#2025	C₂	semidirect
8. C₁₃×#2023	C₂	semidirect
9. C₁₃×#1991	C₂	semidirect
10. C₁₃×#1984	C₂	semidirect
13. C₁₃×#1864	C₂	semidirect
14. C₁₃×#1862	C₂	semidirect
15. C₁₃×#1804	C₂	semidirect
73. C₂×C₁₃×D₈	Q₈	semidirect
140. #24335	C₁₃	direct (N × H)
235. C₂×#554	C₂×C₁₃	semidirect
236. C₂×#478	C₂×C₁₃	semidirect
238. #2580	C₂×C₁₃	semidirect
239. #2059	C₂×C₁₃	semidirect
240. #2057	C₂×C₁₃	semidirect
241. #2025	C₂×C₁₃	semidirect
242. #2023	C₂×C₁₃	semidirect
243. #1991	C₂×C₁₃	semidirect
244. #1984	C₂×C₁₃	semidirect
247. #1864	C₂×C₁₃	semidirect
248. #1862	C₂×C₁₃	semidirect
249. #1804	C₂×C₁₃	semidirect
419. C₂×D₈	Q₈×C₁₃	semidirect
589. C₁₃	#24335	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×#554	2
C₂×C₁₃×#478	2
C₂×C₄×C₁₃×D₈	2
C₁₃×#2580	2
C₁₃×#2059	2
C₁₃×#2057	2
C₁₃×#2025	2
C₁₃×#2023	2
C₁₃×#1991	2
C₁₃×#1984	2
C₁₃×#1879	2
C₁₃×#1864	2
C₁₃×#1862	2
C₁₃×#1804	2
#24335	13

Subgroups — C13×#24335 #15710674

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×#24335 #15710674